LMFDB - Embedded newform 418.2.n.d.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (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:	$3.33774680449$
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			49.4
Character	$\chi$	$=$	418.49
Dual form			418.2.n.d.273.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(-0.876283 + 0.390146i) q^{3} +(0.913545 + 0.406737i) q^{4} +(2.35086 + 2.61090i) q^{5} +(-0.938250 + 0.199431i) q^{6} +(-1.45336 + 1.05593i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.39173 + 1.54568i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(-0.876283 + 0.390146i) q^{3} +(0.913545 + 0.406737i) q^{4} +(2.35086 + 2.61090i) q^{5} +(-0.938250 + 0.199431i) q^{6} +(-1.45336 + 1.05593i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.39173 + 1.54568i) q^{9} +(1.75666 + 3.04262i) q^{10} +(1.20137 - 3.09139i) q^{11} -0.959211 q^{12} +(-2.47526 + 2.74906i) q^{13} +(-1.64114 + 0.730683i) q^{14} +(-3.07866 - 1.37071i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-3.67942 - 4.08641i) q^{17} +(-1.68269 + 1.22254i) q^{18} +(4.32462 + 0.545589i) q^{19} +(1.08567 + 3.34136i) q^{20} +(0.861588 - 1.49231i) q^{21} +(1.81786 - 2.77406i) q^{22} +(1.50288 + 2.60306i) q^{23} +(-0.938250 - 0.199431i) q^{24} +(-0.767590 + 7.30314i) q^{25} +(-2.99273 + 2.17435i) q^{26} +(1.50575 - 4.63422i) q^{27} +(-1.75720 + 0.373503i) q^{28} +(7.16665 + 3.19080i) q^{29} +(-2.72639 - 1.98084i) q^{30} +(0.745357 + 2.29397i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.153354 + 3.17764i) q^{33} +(-2.74940 - 4.76211i) q^{34} +(-6.17358 - 1.31223i) q^{35} +(-1.90010 + 0.845977i) q^{36} +(2.53403 - 1.84108i) q^{37} +(4.11668 + 1.43281i) q^{38} +(1.09650 - 3.37467i) q^{39} +(0.367241 + 3.49407i) q^{40} +(0.533810 - 0.237667i) q^{41} +(1.15303 - 1.28057i) q^{42} +(4.51190 - 7.81484i) q^{43} +(2.35489 - 2.33549i) q^{44} -7.30739 q^{45} +(0.928829 + 2.85864i) q^{46} +(0.921608 - 8.76852i) q^{47} +(-0.876283 - 0.390146i) q^{48} +(-1.16585 + 3.58811i) q^{49} +(-2.26922 + 6.98395i) q^{50} +(4.81851 + 2.14534i) q^{51} +(-3.37941 + 1.50461i) q^{52} +(-6.92465 + 7.69060i) q^{53} +(2.43635 - 4.21989i) q^{54} +(10.8956 - 4.13079i) q^{55} -1.79645 q^{56} +(-4.00245 + 1.20914i) q^{57} +(6.34664 + 4.61110i) q^{58} +(-0.492520 - 4.68601i) q^{59} +(-2.25498 - 2.50440i) q^{60} +(9.06903 - 1.92768i) q^{61} +(0.252125 + 2.39881i) q^{62} +(0.390567 - 3.71600i) q^{63} +(0.309017 + 0.951057i) q^{64} -12.9965 q^{65} +(-0.510666 + 3.14009i) q^{66} +(-0.461262 - 0.798929i) q^{67} +(-1.69922 - 5.22968i) q^{68} +(-2.33252 - 1.69467i) q^{69} +(-5.76584 - 2.56712i) q^{70} +(7.35570 + 8.16934i) q^{71} +(-2.03446 + 0.432439i) q^{72} +(-1.61533 - 15.3688i) q^{73} +(2.86144 - 1.27400i) q^{74} +(-2.17666 - 6.69908i) q^{75} +(3.72883 + 2.25740i) q^{76} +(1.51826 + 5.76147i) q^{77} +(1.77417 - 3.07295i) q^{78} +(-7.71998 - 1.64093i) q^{79} +(-0.367241 + 3.49407i) q^{80} +(-0.163669 - 1.55721i) q^{81} +(0.571559 - 0.121489i) q^{82} +(4.40881 - 13.5689i) q^{83} +(1.39408 - 1.01286i) q^{84} +(2.01939 - 19.2132i) q^{85} +(6.03810 - 6.70599i) q^{86} -7.52489 q^{87} +(2.78900 - 1.79484i) q^{88} +(-2.87863 - 4.98593i) q^{89} +(-7.14770 - 1.51929i) q^{90} +(0.694641 - 6.60907i) q^{91} +(0.314187 + 2.98929i) q^{92} +(-1.54813 - 1.71937i) q^{93} +(2.72455 - 8.38529i) q^{94} +(8.74212 + 12.5738i) q^{95} +(-0.776018 - 0.563810i) q^{96} +(-4.45384 - 0.946692i) q^{97} +(-1.88638 + 3.26731i) q^{98} +(3.10631 + 6.15933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	−0.876283	+	0.390146i	−0.505922	+	0.225251i	−0.643794	−	0.765199i	$-0.722641\pi$
$3$	−0.876283	+	0.390146i	−0.505922	+	0.225251i	0.137872	+	0.990450i	$0.455974\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	2.35086	+	2.61090i	1.05134	+	1.16763i	0.985478	+	0.169801i	$0.0543125\pi$
$5$	2.35086	+	2.61090i	1.05134	+	1.16763i	0.0658603	+	0.997829i	$0.479021\pi$
$6$	−0.938250	+	0.199431i	−0.383039	+	0.0814174i
$7$	−1.45336	+	1.05593i	−0.549319	+	0.399103i	−0.827534	−	0.561415i	$-0.810257\pi$
$7$	−1.45336	+	1.05593i	−0.549319	+	0.399103i	0.278216	+	0.960519i	$0.410257\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−1.39173	+	1.54568i	−0.463911	+	0.515226i
$10$	1.75666	+	3.04262i	0.555503	+	0.962160i
$11$	1.20137	−	3.09139i	0.362227	−	0.932090i
$11$	1.20137	−	3.09139i	0.362227	−	0.932090i
$12$	−0.959211			−0.276900
$13$	−2.47526	+	2.74906i	−0.686514	+	0.762451i	−0.981169	−	0.193153i	$-0.938129\pi$
$13$	−2.47526	+	2.74906i	−0.686514	+	0.762451i	0.294655	+	0.955604i	$0.404795\pi$
$14$	−1.64114	+	0.730683i	−0.438613	+	0.195283i
$15$	−3.07866	−	1.37071i	−0.794905	−	0.353915i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−3.67942	−	4.08641i	−0.892390	−	0.991100i	0.107605	−	0.994194i	$-0.465682\pi$
$17$	−3.67942	−	4.08641i	−0.892390	−	0.991100i	−0.999995	+	0.00309375i	$0.999015\pi$
$18$	−1.68269	+	1.22254i	−0.396613	+	0.288156i
$19$	4.32462	+	0.545589i	0.992136	+	0.125167i
$19$	4.32462	+	0.545589i	0.992136	+	0.125167i
$20$	1.08567	+	3.34136i	0.242764	+	0.747150i
$21$	0.861588	−	1.49231i	0.188014	−	0.325650i
$22$	1.81786	−	2.77406i	0.387568	−	0.591431i
$23$	1.50288	+	2.60306i	0.313371	+	0.542775i	0.979090	−	0.203428i	$-0.0652082\pi$
$23$	1.50288	+	2.60306i	0.313371	+	0.542775i	−0.665719	+	0.746203i	$0.731875\pi$
$24$	−0.938250	−	0.199431i	−0.191519	−	0.0407087i
$25$	−0.767590	+	7.30314i	−0.153518	+	1.46063i
$26$	−2.99273	+	2.17435i	−0.586923	+	0.426425i
$27$	1.50575	−	4.63422i	0.289782	−	0.891856i
$28$	−1.75720	+	0.373503i	−0.332079	+	0.0705855i
$29$	7.16665	+	3.19080i	1.33081	+	0.592516i	0.944092	−	0.329681i	$-0.106941\pi$
$29$	7.16665	+	3.19080i	1.33081	+	0.592516i	0.386721	+	0.922197i	$0.373608\pi$
$30$	−2.72639	−	1.98084i	−0.497769	−	0.361650i
$31$	0.745357	+	2.29397i	0.133870	+	0.412009i	0.995413	−	0.0956759i	$-0.0305012\pi$
$31$	0.745357	+	2.29397i	0.133870	+	0.412009i	−0.861543	+	0.507685i	$0.830501\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.153354	+	3.17764i	0.0266955	+	0.553157i
$34$	−2.74940	−	4.76211i	−0.471519	−	0.816695i
$35$	−6.17358	−	1.31223i	−1.04352	−	0.221808i
$36$	−1.90010	+	0.845977i	−0.316683	+	0.140996i
$37$	2.53403	−	1.84108i	0.416592	−	0.302672i	−0.359673	−	0.933078i	$-0.617112\pi$
$37$	2.53403	−	1.84108i	0.416592	−	0.302672i	0.776265	+	0.630406i	$0.217112\pi$
$38$	4.11668	+	1.43281i	0.667814	+	0.232432i
$39$	1.09650	−	3.37467i	0.175580	−	0.540379i
$40$	0.367241	+	3.49407i	0.0580659	+	0.552460i
$41$	0.533810	−	0.237667i	0.0833671	−	0.0371174i	−0.364629	−	0.931153i	$-0.618804\pi$
$41$	0.533810	−	0.237667i	0.0833671	−	0.0371174i	0.447997	+	0.894035i	$0.352138\pi$
$42$	1.15303	−	1.28057i	0.177916	−	0.197596i
$43$	4.51190	−	7.81484i	0.688059	−	1.19175i	−0.284406	−	0.958704i	$-0.591797\pi$
$43$	4.51190	−	7.81484i	0.688059	−	1.19175i	0.972465	−	0.233049i	$-0.0748701\pi$
$44$	2.35489	−	2.33549i	0.355013	−	0.352088i
$45$	−7.30739			−1.08932
$46$	0.928829	+	2.85864i	0.136948	+	0.421484i
$47$	0.921608	−	8.76852i	0.134430	−	1.27902i	−0.694428	−	0.719562i	$-0.744343\pi$
$47$	0.921608	−	8.76852i	0.134430	−	1.27902i	0.828859	−	0.559458i	$-0.188991\pi$
$48$	−0.876283	−	0.390146i	−0.126481	−	0.0563128i
$49$	−1.16585	+	3.58811i	−0.166550	+	0.512587i
$50$	−2.26922	+	6.98395i	−0.320917	+	0.987680i
$51$	4.81851	+	2.14534i	0.674726	+	0.300408i
$52$	−3.37941	+	1.50461i	−0.468639	+	0.208652i
$53$	−6.92465	+	7.69060i	−0.951174	+	1.05639i	0.0471720	+	0.998887i	$0.484979\pi$
$53$	−6.92465	+	7.69060i	−0.951174	+	1.05639i	−0.998346	+	0.0574985i	$0.981688\pi$
$54$	2.43635	−	4.21989i	0.331546	−	0.574254i
$55$	10.8956	−	4.13079i	1.46916	−	0.556995i
$56$	−1.79645			−0.240061
$57$	−4.00245	+	1.20914i	−0.530137	+	0.160155i
$58$	6.34664	+	4.61110i	0.833354	+	0.605467i
$59$	−0.492520	−	4.68601i	−0.0641206	−	0.610067i	−0.978648	−	0.205543i	$-0.934104\pi$
$59$	−0.492520	−	4.68601i	−0.0641206	−	0.610067i	0.914528	−	0.404524i	$-0.132563\pi$
$60$	−2.25498	−	2.50440i	−0.291116	−	0.323317i
$61$	9.06903	−	1.92768i	1.16117	−	0.246814i	0.413259	−	0.910613i	$-0.364390\pi$
$61$	9.06903	−	1.92768i	1.16117	−	0.246814i	0.747911	+	0.663799i	$0.231057\pi$
$62$	0.252125	+	2.39881i	0.0320199	+	0.304649i
$63$	0.390567	−	3.71600i	0.0492068	−	0.468172i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−12.9965			−1.61202
$66$	−0.510666	+	3.14009i	−0.0628587	+	0.386518i
$67$	−0.461262	−	0.798929i	−0.0563521	−	0.0976048i	0.836473	−	0.548008i	$-0.184614\pi$
$67$	−0.461262	−	0.798929i	−0.0563521	−	0.0976048i	−0.892825	+	0.450403i	$0.851280\pi$
$68$	−1.69922	−	5.22968i	−0.206061	−	0.634191i
$69$	−2.33252	−	1.69467i	−0.280802	−	0.204015i
$70$	−5.76584	−	2.56712i	−0.689150	−	0.306829i
$71$	7.35570	+	8.16934i	0.872962	+	0.969522i	0.999749	−	0.0224079i	$-0.00713326\pi$
$71$	7.35570	+	8.16934i	0.872962	+	0.969522i	−0.126787	+	0.991930i	$0.540467\pi$
$72$	−2.03446	+	0.432439i	−0.239764	+	0.0509634i
$73$	−1.61533	−	15.3688i	−0.189059	−	1.79878i	−0.518995	−	0.854777i	$-0.673694\pi$
$73$	−1.61533	−	15.3688i	−0.189059	−	1.79878i	0.329935	−	0.944004i	$-0.392973\pi$
$74$	2.86144	−	1.27400i	0.332636	−	0.148099i
$75$	−2.17666	−	6.69908i	−0.251340	−	0.773544i
$76$	3.72883	+	2.25740i	0.427726	+	0.258942i
$77$	1.51826	+	5.76147i	0.173022	+	0.656580i
$78$	1.77417	−	3.07295i	0.200885	−	0.347943i
$79$	−7.71998	−	1.64093i	−0.868566	−	0.184619i	−0.247987	−	0.968763i	$-0.579769\pi$
$79$	−7.71998	−	1.64093i	−0.868566	−	0.184619i	−0.620579	+	0.784144i	$0.713102\pi$
$80$	−0.367241	+	3.49407i	−0.0410588	+	0.390648i
$81$	−0.163669	−	1.55721i	−0.0181855	−	0.173023i
$82$	0.571559	−	0.121489i	0.0631181	−	0.0134162i
$83$	4.40881	−	13.5689i	0.483930	−	1.48938i	−0.349595	−	0.936901i	$-0.613681\pi$
$83$	4.40881	−	13.5689i	0.483930	−	1.48938i	0.833525	−	0.552482i	$-0.186319\pi$
$84$	1.39408	−	1.01286i	0.152107	−	0.110512i
$85$	2.01939	−	19.2132i	0.219033	−	2.08396i
$86$	6.03810	−	6.70599i	0.651105	−	0.723126i
$87$	−7.52489			−0.806753
$88$	2.78900	−	1.79484i	0.297309	−	0.191331i
$89$	−2.87863	−	4.98593i	−0.305134	−	0.528508i	0.672157	−	0.740409i	$-0.265368\pi$
$89$	−2.87863	−	4.98593i	−0.305134	−	0.528508i	−0.977291	+	0.211901i	$0.932035\pi$
$90$	−7.14770	−	1.51929i	−0.753434	−	0.160147i
$91$	0.694641	−	6.60907i	0.0728182	−	0.692819i
$92$	0.314187	+	2.98929i	0.0327562	+	0.311655i
$93$	−1.54813	−	1.71937i	−0.160533	−	0.178290i
$94$	2.72455	−	8.38529i	0.281015	−	0.864877i
$95$	8.74212	+	12.5738i	0.896922	+	1.29004i
$96$	−0.776018	−	0.563810i	−0.0792020	−	0.0575436i
$97$	−4.45384	−	0.946692i	−0.452218	−	0.0961220i	−0.0238287	−	0.999716i	$-0.507586\pi$
$97$	−4.45384	−	0.946692i	−0.452218	−	0.0961220i	−0.428390	+	0.903594i	$0.640919\pi$
$98$	−1.88638	+	3.26731i	−0.190553	+	0.330048i
$99$	3.10631	+	6.15933i	0.312196	+	0.619036i
$100$	−3.67168	+	6.35954i	−0.367168	+	0.635954i
$101$	−1.09186	+	1.21264i	−0.108644	+	0.120662i	−0.795014	−	0.606591i	$-0.792537\pi$
$101$	−1.09186	+	1.21264i	−0.108644	+	0.120662i	0.686370	+	0.727253i	$0.259203\pi$
$102$	4.26717	+	3.10028i	0.422513	+	0.306974i
$103$	−4.97952	+	3.61783i	−0.490647	+	0.356476i	−0.805433	−	0.592687i	$-0.798067\pi$
$103$	−4.97952	+	3.61783i	−0.490647	+	0.356476i	0.314786	+	0.949163i	$0.398067\pi$
$104$	−3.61838	+	0.769111i	−0.354812	+	0.0754176i
$105$	5.92176	−	1.25871i	0.577905	−	0.122837i
$106$	−8.37229	+	6.08283i	−0.813189	+	0.590816i
$107$	−9.82009	−	7.13472i	−0.949344	−	0.689739i	0.00130739	−	0.999999i	$-0.499584\pi$
$107$	−9.82009	−	7.13472i	−0.949344	−	0.689739i	−0.950652	+	0.310260i	$0.899584\pi$
$108$	3.26048	−	3.62113i	0.313740	−	0.348443i
$109$	−2.23864	+	3.87743i	−0.214422	+	0.371391i	−0.953094	−	0.302675i	$-0.902120\pi$
$109$	−2.23864	+	3.87743i	−0.214422	+	0.371391i	0.738671	+	0.674066i	$0.235454\pi$
$110$	11.5163	−	1.77520i	1.09804	−	0.169259i
$111$	−1.50224	+	2.60195i	−0.142586	+	0.246966i
$112$	−1.75720	−	0.373503i	−0.166039	−	0.0352928i
$113$	16.6012	+	12.0614i	1.56171	+	1.13465i	0.934595	+	0.355715i	$0.115763\pi$
$113$	16.6012	+	12.0614i	1.56171	+	1.13465i	0.627110	+	0.778930i	$0.284237\pi$
$114$	−4.16638	+	0.350565i	−0.390217	+	0.0328334i
$115$	−3.26327	+	10.0433i	−0.304301	+	0.936543i
$116$	5.24924	+	5.82988i	0.487380	+	0.541290i
$117$	−0.804249	−	7.65191i	−0.0743528	−	0.707420i
$118$	0.492520	−	4.68601i	0.0453401	−	0.431382i
$119$	9.66248	+	2.05382i	0.885758	+	0.188274i
$120$	−1.68500	−	2.91851i	−0.153819	−	0.266422i
$121$	−8.11341	−	7.42782i	−0.737583	−	0.675256i
$122$	9.27164			0.839415
$123$	−0.375043	+	0.416528i	−0.0338165	+	0.0375570i
$124$	−0.252125	+	2.39881i	−0.0226415	+	0.215420i
$125$	−6.66061	+	4.83922i	−0.595743	+	0.432833i
$126$	1.15463	−	3.55359i	0.102863	−	0.316579i
$127$	3.42058	−	0.727067i	0.303527	−	0.0645167i	−0.0536303	−	0.998561i	$-0.517079\pi$
$127$	3.42058	−	0.727067i	0.303527	−	0.0645167i	0.357158	+	0.934044i	$0.383746\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.904770	+	8.60831i	−0.0796606	+	0.757920i
$130$	−12.7125	−	2.70213i	−1.11496	−	0.236992i
$131$	−6.18487	+	10.7125i	−0.540375	+	0.935957i	0.458508	+	0.888690i	$0.348384\pi$
$131$	−6.18487	+	10.7125i	−0.540375	+	0.935957i	−0.998882	+	0.0472660i	$0.984949\pi$
$132$	−1.15237	+	2.96530i	−0.100301	+	0.258096i
$133$	−6.86133	+	3.77355i	−0.594953	+	0.327208i
$134$	−0.285076	−	0.877373i	−0.0246268	−	0.0757935i
$135$	15.6393	−	6.96307i	1.34602	−	0.599285i
$136$	−0.574782	−	5.46868i	−0.0492871	−	0.468936i
$137$	6.94224	−	1.47562i	0.593116	−	0.126071i	0.0984320	−	0.995144i	$-0.468617\pi$
$137$	6.94224	−	1.47562i	0.593116	−	0.126071i	0.494684	+	0.869073i	$0.335284\pi$
$138$	−1.92921	−	2.14260i	−0.164225	−	0.182390i
$139$	9.39173	+	4.18147i	0.796596	+	0.354667i	0.764341	−	0.644812i	$-0.223064\pi$
$139$	9.39173	+	4.18147i	0.796596	+	0.354667i	0.0322550	+	0.999480i	$0.489731\pi$
$140$	−5.10611	−	3.70981i	−0.431545	−	0.313536i
$141$	2.61341	+	8.04326i	0.220089	+	0.677365i
$142$	5.49646	+	9.52015i	0.461253	+	0.798914i
$143$	5.52471	+	10.9546i	0.461999	+	0.916073i
$144$	−2.07991			−0.173326
$145$	8.51697	+	26.2125i	0.707296	+	2.17683i
$146$	1.61533	−	15.3688i	0.133685	−	1.27193i
$147$	−0.378275	−	3.59905i	−0.0311996	−	0.296844i
$148$	3.06379	−	0.651229i	0.251842	−	0.0535307i
$149$	−0.119654	−	0.132889i	−0.00980245	−	0.0108867i	0.738224	−	0.674556i	$-0.235665\pi$
$149$	−0.119654	−	0.132889i	−0.00980245	−	0.0108867i	−0.748026	+	0.663669i	$0.768998\pi$
$150$	−0.736281	−	7.00525i	−0.0601171	−	0.571976i
$151$	−4.54583	−	3.30274i	−0.369934	−	0.268773i	0.387250	−	0.921975i	$-0.373425\pi$
$151$	−4.54583	−	3.30274i	−0.369934	−	0.268773i	−0.757184	+	0.653202i	$0.773425\pi$
$152$	3.17800	+	2.98334i	0.257770	+	0.241981i
$153$	11.4370			0.924631
$154$	0.287208	+	5.95123i	0.0231439	+	0.479564i
$155$	−4.23710	+	7.33887i	−0.340332	+	0.589472i
$156$	2.37430	−	2.63693i	0.190096	−	0.211123i
$157$	−18.6228	+	8.29141i	−1.48626	+	0.661726i	−0.979698	−	0.200477i	$-0.935751\pi$
$157$	−18.6228	+	8.29141i	−1.48626	+	0.661726i	−0.506563	+	0.862203i	$0.669084\pi$
$158$	−7.21012	−	3.21015i	−0.573606	−	0.255386i
$159$	3.06749	−	9.44077i	0.243268	−	0.748701i
$160$	−1.08567	+	3.34136i	−0.0858300	+	0.264158i
$161$	−4.93286	−	2.19625i	−0.388764	−	0.173089i
$162$	0.163669	−	1.55721i	0.0128591	−	0.122346i
$163$	−1.71322	−	5.27275i	−0.134190	−	0.412994i	0.861273	−	0.508142i	$-0.169668\pi$
$163$	−1.71322	−	5.27275i	−0.134190	−	0.412994i	−0.995463	+	0.0951482i	$0.969668\pi$
$164$	0.584328			0.0456283
$165$	−7.93600	+	7.87060i	−0.617817	+	0.612726i
$166$	7.13360	−	12.3558i	0.553675	−	0.958993i
$167$	−9.49318	+	10.5432i	−0.734604	+	0.815860i	−0.988476	−	0.151377i	$-0.951629\pi$
$167$	−9.49318	+	10.5432i	−0.734604	+	0.815860i	0.253872	+	0.967238i	$0.418296\pi$
$168$	1.57420	−	0.700879i	0.121452	−	0.0540740i
$169$	−0.0715221	−	0.680487i	−0.00550170	−	0.0523452i
$170$	5.96991	−	18.3735i	0.457871	−	1.40918i
$171$	−6.86203	+	5.92515i	−0.524752	+	0.453108i
$172$	7.30041	−	5.30406i	0.556651	−	0.404431i
$173$	17.6406	−	7.85409i	1.34119	−	0.597135i	0.394383	−	0.918946i	$-0.370958\pi$
$173$	17.6406	−	7.85409i	1.34119	−	0.597135i	0.946804	+	0.321811i	$0.104292\pi$
$174$	−7.36045	−	1.56451i	−0.557994	−	0.118605i
$175$	−6.59600	−	11.4246i	−0.498611	−	0.863619i
$176$	3.10123	−	1.17575i	0.233764	−	0.0886257i
$177$	2.25982	+	3.91412i	0.169858	+	0.294203i
$178$	−1.77909	−	5.47548i	−0.133349	−	0.410405i
$179$	1.46998	+	1.06800i	0.109872	+	0.0798264i	0.641364	−	0.767236i	$-0.278369\pi$
$179$	1.46998	+	1.06800i	0.109872	+	0.0798264i	−0.531493	+	0.847063i	$0.678369\pi$
$180$	−6.67563	−	2.97218i	−0.497572	−	0.221533i
$181$	−20.0146	+	4.25424i	−1.48767	+	0.316215i	−0.878853	−	0.477092i	$-0.841691\pi$
$181$	−20.0146	+	4.25424i	−1.48767	+	0.316215i	−0.608822	+	0.793307i	$0.708357\pi$
$182$	2.05356	−	6.32022i	0.152220	−	0.468486i
$183$	−7.19496	+	5.22744i	−0.531867	+	0.386424i
$184$	−0.314187	+	2.98929i	−0.0231622	+	0.220373i
$185$	10.7641	+	2.28797i	0.791389	+	0.168215i
$186$	−1.15682	−	2.00367i	−0.0848222	−	0.146916i
$187$	−17.0530	+	6.46524i	−1.24704	+	0.472785i
$188$	4.40841	−	7.63559i	0.321516	−	0.556882i
$189$	2.70501	+	8.32516i	0.196760	+	0.605566i
$190$	5.93685	+	14.1166i	0.430704	+	1.02412i
$191$	−6.00109	+	4.36005i	−0.434224	+	0.315482i	−0.783335	−	0.621599i	$-0.786483\pi$
$191$	−6.00109	+	4.36005i	−0.434224	+	0.315482i	0.349112	+	0.937081i	$0.386483\pi$
$192$	−0.641837	−	0.712833i	−0.0463206	−	0.0514443i
$193$	−4.03248	−	4.47853i	−0.290265	−	0.322371i	0.580322	−	0.814387i	$-0.302927\pi$
$193$	−4.03248	−	4.47853i	−0.290265	−	0.322371i	−0.870586	+	0.492016i	$0.836260\pi$
$194$	−4.15968	−	1.85201i	−0.298648	−	0.132966i
$195$	11.3886	−	5.07054i	0.815556	−	0.363109i
$196$	−2.52447	+	2.80371i	−0.180319	+	0.200265i
$197$	−1.15068			−0.0819824			−0.0409912	−	0.999160i	$-0.513052\pi$
$197$	−1.15068			−0.0819824			−0.0409912	+	0.999160i	$0.513052\pi$
$198$	1.75783	+	6.67057i	0.124923	+	0.474057i
$199$	−7.57036	−	13.1122i	−0.536649	−	0.929503i	−0.999082	−	0.0428485i	$-0.986357\pi$
$199$	−7.57036	−	13.1122i	−0.536649	−	0.929503i	0.462433	−	0.886654i	$-0.346977\pi$
$200$	−4.91367	+	5.45718i	−0.347449	+	0.385881i
$201$	0.715895	+	0.520128i	0.0504954	+	0.0366870i
$202$	−1.32012	+	0.959126i	−0.0928836	+	0.0674839i
$203$	−13.7850	+	2.93009i	−0.967516	+	0.205652i
$204$	3.52934	+	3.91973i	0.247103	+	0.274436i
$205$	1.87544	+	0.835000i	0.130986	+	0.0583189i
$206$	−5.62289	+	2.50347i	−0.391766	+	0.174425i
$207$	−6.11509	−	1.29980i	−0.425028	−	0.0903426i
$208$	−3.69922			−0.256495
$209$	6.88210	−	12.7136i	0.476045	−	0.879421i
$210$	6.05406			0.417770
$211$	−1.18338	−	0.251535i	−0.0814671	−	0.0173164i	0.166998	−	0.985957i	$-0.446593\pi$
$211$	−1.18338	−	0.251535i	−0.0814671	−	0.0173164i	−0.248465	+	0.968641i	$0.579926\pi$
$212$	−9.45403	+	4.20921i	−0.649305	+	0.289089i
$213$	−9.63291	−	4.28885i	−0.660036	−	0.293867i
$214$	−8.12211	−	9.02052i	−0.555216	−	0.616630i
$215$	31.0106	−	6.59152i	2.11491	−	0.449538i
$216$	3.94210	−	2.86411i	0.268226	−	0.194878i
$217$	−3.50554	−	2.54692i	−0.237972	−	0.172897i
$218$	−2.99588	+	3.32726i	−0.202907	+	0.225351i
$219$	7.41156	+	12.8372i	0.500827	+	0.867457i
$220$	11.6337	+	0.657970i	0.784347	+	0.0443603i
$221$	20.3413			1.36830
$222$	−2.01039	+	2.23276i	−0.134928	+	0.149853i
$223$	15.9355	−	7.09494i	1.06712	−	0.475113i	0.203406	−	0.979094i	$-0.434799\pi$
$223$	15.9355	−	7.09494i	1.06712	−	0.475113i	0.863714	+	0.503982i	$0.168132\pi$
$224$	−1.64114	−	0.730683i	−0.109653	−	0.0488208i
$225$	−10.2200	−	11.3505i	−0.681334	−	0.756698i
$226$	13.7307	+	15.2494i	0.913350	+	1.01438i
$227$	−13.3835	+	9.72369i	−0.888294	+	0.645384i	−0.935433	−	0.353505i	$-0.884990\pi$
$227$	−13.3835	+	9.72369i	−0.888294	+	0.645384i	0.0471383	+	0.998888i	$0.484990\pi$
$228$	−4.14822	−	0.523335i	−0.274723	−	0.0346587i
$229$	5.24777	+	16.1510i	0.346782	+	1.06729i	0.960623	+	0.277856i	$0.0896239\pi$
$229$	5.24777	+	16.1510i	0.346782	+	1.06729i	−0.613840	+	0.789430i	$0.710376\pi$
$230$	−5.28008	+	9.14536i	−0.348158	+	0.603027i
$231$	−3.57824	−	4.45633i	−0.235431	−	0.293205i
$232$	3.92244	+	6.79386i	0.257521	+	0.446039i
$233$	15.7130	+	3.33991i	1.02940	+	0.218805i	0.691498	−	0.722378i	$-0.256951\pi$
$233$	15.7130	+	3.33991i	1.02940	+	0.218805i	0.337898	+	0.941183i	$0.390284\pi$
$234$	0.804249	−	7.65191i	0.0525754	−	0.500221i
$235$	25.0603	−	18.2074i	1.63475	−	1.18772i
$236$	1.45603	−	4.48121i	0.0947797	−	0.291702i
$237$	7.40509	−	1.57400i	0.481013	−	0.102242i
$238$	9.02432	+	4.01788i	0.584960	+	0.260441i
$239$	3.67118	+	2.66727i	0.237469	+	0.172531i	0.700155	−	0.713991i	$-0.253114\pi$
$239$	3.67118	+	2.66727i	0.237469	+	0.172531i	−0.462686	+	0.886522i	$0.653114\pi$
$240$	−1.04139	−	3.20507i	−0.0672214	−	0.206886i
$241$	−4.26952	−	7.39503i	−0.275024	−	0.476356i	0.695117	−	0.718897i	$-0.255353\pi$
$241$	−4.26952	−	7.39503i	−0.275024	−	0.476356i	−0.970141	+	0.242541i	$0.922019\pi$
$242$	−6.39179	−	8.95238i	−0.410880	−	0.575481i
$243$	8.06002	+	13.9604i	0.517051	+	0.895558i
$244$	9.06903	+	1.92768i	0.580585	+	0.123407i
$245$	−12.1089	+	5.39125i	−0.773612	+	0.344434i
$246$	−0.453449	+	0.329450i	−0.0289108	+	0.0210049i
$247$	−12.2044	+	10.5381i	−0.776549	+	0.670526i
$248$	−0.745357	+	2.29397i	−0.0473302	+	0.145667i
$249$	1.43050	+	13.6103i	0.0906542	+	0.862517i
$250$	−7.52119	+	3.34865i	−0.475682	+	0.211787i
$251$	12.1152	−	13.4553i	0.764707	−	0.849294i	−0.227515	−	0.973775i	$-0.573060\pi$
$251$	12.1152	−	13.4553i	0.764707	−	0.849294i	0.992222	+	0.124481i	$0.0397266\pi$
$252$	1.86823	−	3.23588i	0.117688	−	0.203841i
$253$	9.85259	−	1.51874i	0.619427	−	0.0954825i
$254$	3.49700			0.219421
$255$	5.72640	+	17.6240i	0.358601	+	1.10366i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−19.2924	−	8.58952i	−1.20343	−	0.535800i	−0.295667	−	0.955291i	$-0.595542\pi$
$257$	−19.2924	−	8.58952i	−1.20343	−	0.535800i	−0.907759	+	0.419491i	$0.862208\pi$
$258$	−2.67477	+	8.23209i	−0.166524	+	0.512508i
$259$	−1.73881	+	5.35151i	−0.108045	+	0.332527i
$260$	−11.8729	−	5.28616i	−0.736327	−	0.327834i
$261$	−14.9060	+	6.63658i	−0.922659	+	0.410794i
$262$	−8.27697	+	9.19251i	−0.511353	+	0.567915i
$263$	−13.8918	+	24.0612i	−0.856602	+	1.48368i	0.0185487	+	0.999828i	$0.494095\pi$
$263$	−13.8918	+	24.0612i	−0.856602	+	1.48368i	−0.875151	+	0.483850i	$0.839238\pi$
$264$	−1.74371	+	2.66091i	−0.107318	+	0.163768i
$265$	−36.3583			−2.23347
$266$	−7.49596	+	2.26454i	−0.459607	+	0.138848i
$267$	4.46774	+	3.24600i	0.273421	+	0.198652i
$268$	−0.0964300	−	0.917471i	−0.00589040	−	0.0560434i
$269$	1.85773	+	2.06322i	0.113268	+	0.125797i	0.797112	−	0.603831i	$-0.206360\pi$
$269$	1.85773	+	2.06322i	0.113268	+	0.125797i	−0.683844	+	0.729628i	$0.739693\pi$
$270$	16.7453	−	3.55931i	1.01908	−	0.216613i
$271$	−1.95418	−	18.5928i	−0.118708	−	1.12943i	−0.877993	−	0.478673i	$-0.841118\pi$
$271$	−1.95418	−	18.5928i	−0.118708	−	1.12943i	0.759286	−	0.650758i	$-0.225549\pi$
$272$	0.574782	−	5.46868i	0.0348513	−	0.331588i
$273$	1.96980	+	6.06243i	0.119218	+	0.366915i
$274$	7.09733			0.428766
$275$	21.6547	+	11.1467i	1.30583	+	0.672171i
$276$	−1.44158	−	2.49688i	−0.0867727	−	0.150295i
$277$	−2.93093	−	9.02048i	−0.176103	−	0.541988i	0.823579	−	0.567201i	$-0.191974\pi$
$277$	−2.93093	−	9.02048i	−0.176103	−	0.541988i	−0.999682	+	0.0252127i	$0.991974\pi$
$278$	8.31712	+	6.04274i	0.498828	+	0.362420i
$279$	−4.58308	−	2.04052i	−0.274382	−	0.122163i
$280$	−4.22322	−	4.69036i	−0.252385	−	0.280302i
$281$	19.2704	−	4.09604i	1.14957	−	0.244349i	0.406559	−	0.913625i	$-0.366729\pi$
$281$	19.2704	−	4.09604i	1.14957	−	0.244349i	0.743014	+	0.669275i	$0.233395\pi$
$282$	0.884017	+	8.41086i	0.0526424	+	0.500859i
$283$	−16.9542	+	7.54849i	−1.00782	+	0.448711i	−0.843174	−	0.537641i	$-0.819315\pi$
$283$	−16.9542	+	7.54849i	−1.00782	+	0.448711i	−0.164648	+	0.986352i	$0.552649\pi$
$284$	3.39700	+	10.4549i	0.201575	+	0.620384i
$285$	−12.5662	−	7.60746i	−0.744356	−	0.450627i
$286$	3.12638	+	11.8639i	0.184867	+	0.701528i
$287$	−0.524858	+	0.909081i	−0.0309814	+	0.0536614i
$288$	−2.03446	−	0.432439i	−0.119882	−	0.0254817i
$289$	−1.38363	+	13.1644i	−0.0813900	+	0.774374i
$290$	2.88096	+	27.4105i	0.169176	+	1.60960i
$291$	4.27217	−	0.908077i	0.250439	−	0.0532324i
$292$	4.77538	−	14.6971i	0.279458	−	0.860083i
$293$	−20.9168	+	15.1969i	−1.22197	+	0.887815i	−0.996262	−	0.0863799i	$-0.972470\pi$
$293$	−20.9168	+	15.1969i	−1.22197	+	0.887815i	−0.225710	+	0.974195i	$0.572470\pi$
$294$	0.378275	−	3.59905i	0.0220615	−	0.209901i
$295$	11.0769	−	12.3021i	0.644920	−	0.716256i
$296$	3.13224			0.182058
$297$	−12.5172	−	10.2223i	−0.726324	−	0.593157i
$298$	−0.0894101	−	0.154863i	−0.00517939	−	0.00897097i
$299$	−10.8760	−	2.31176i	−0.628974	−	0.133692i
$300$	0.736281	−	7.00525i	0.0425092	−	0.404448i
$301$	1.69449	+	16.1220i	0.0976690	+	0.929258i
$302$	−3.75981	−	4.17569i	−0.216353	−	0.240284i
$303$	0.483675	−	1.48860i	0.0277864	−	0.0855177i
$304$	2.48828	+	3.57889i	0.142713	+	0.205263i
$305$	26.3531	+	19.1466i	1.50897	+	1.09633i
$306$	11.1871	+	2.37790i	0.639525	+	0.135935i
$307$	11.2522	−	19.4893i	0.642195	−	1.11231i	−0.342747	−	0.939428i	$-0.611357\pi$
$307$	11.2522	−	19.4893i	0.642195	−	1.11231i	0.984942	−	0.172887i	$-0.0553094\pi$
$308$	−0.956399	+	5.88090i	−0.0544959	+	0.335095i
$309$	2.95198	−	5.11298i	0.167932	−	0.290868i
$310$	−5.67034	+	6.29755i	−0.322054	+	0.357677i
$311$	13.0755	+	9.49990i	0.741443	+	0.538690i	0.893163	−	0.449734i	$-0.148481\pi$
$311$	13.0755	+	9.49990i	0.741443	+	0.538690i	−0.151720	+	0.988424i	$0.548481\pi$
$312$	2.87066	−	2.08566i	0.162519	−	0.118077i
$313$	20.8345	−	4.42851i	1.17764	−	0.250314i	0.422797	−	0.906224i	$-0.361048\pi$
$313$	20.8345	−	4.42851i	1.17764	−	0.250314i	0.754839	+	0.655910i	$0.227715\pi$
$314$	−19.9397	+	4.23832i	−1.12526	+	0.239182i
$315$	10.6203	−	7.71608i	0.598384	−	0.434752i
$316$	−6.38513	−	4.63907i	−0.359192	−	0.260968i
$317$	−14.2281	+	15.8019i	−0.799130	+	0.887524i	−0.995669	−	0.0929723i	$-0.970363\pi$
$317$	−14.2281	+	15.8019i	−0.799130	+	0.887524i	0.196539	+	0.980496i	$0.437030\pi$
$318$	4.96330	−	8.59670i	0.278328	−	0.482079i
$319$	18.4738	−	18.3216i	1.03433	−	1.02581i
$320$	−1.75666	+	3.04262i	−0.0982001	+	0.170088i
$321$	11.3888	+	2.42076i	0.635659	+	0.135113i
$322$	−4.36844	−	3.17386i	−0.243444	−	0.176872i
$323$	−13.6826	−	19.6796i	−0.761320	−	1.09500i
$324$	0.483855	−	1.48915i	0.0268808	−	0.0827307i
$325$	−18.1767	−	20.1873i	−1.00826	−	1.11979i
$326$	−0.579516	−	5.51373i	−0.0320964	−	0.305377i
$327$	0.448913	−	4.27112i	0.0248249	−	0.236194i
$328$	0.571559	+	0.121489i	0.0315590	+	0.00670808i
$329$	7.91950	+	13.7170i	0.436616	+	0.756241i
$330$	−9.39897	+	6.04863i	−0.517396	+	0.332966i
$331$	−26.4598			−1.45436			−0.727180	−	0.686447i	$-0.759170\pi$
$331$	−26.4598			−1.45436			−0.727180	+	0.686447i	$0.759170\pi$
$332$	9.54662	−	10.6026i	0.523939	−	0.581893i
$333$	−0.680980	+	6.47910i	−0.0373175	+	0.355052i
$334$	−11.4778	+	8.33910i	−0.628037	+	0.456295i
$335$	1.00156	−	3.08248i	0.0547211	−	0.168414i
$336$	1.68552	−	0.358269i	0.0919527	−	0.0195452i
$337$	−0.181894	−	1.73061i	−0.00990841	−	0.0942722i	0.988450	−	0.151547i	$-0.0484255\pi$
$337$	−0.181894	−	1.73061i	−0.00990841	−	0.0942722i	−0.998358	+	0.0572749i	$0.981759\pi$
$338$	0.0715221	−	0.680487i	0.00389029	−	0.0370136i
$339$	−19.2530	−	4.09236i	−1.04568	−	0.222266i
$340$	9.65951	−	16.7308i	0.523861	−	0.907353i
$341$	7.98702	+	0.451722i	0.432521	+	0.0244621i
$342$	−7.94398	+	4.36898i	−0.429561	+	0.236247i
$343$	−5.98033	−	18.4056i	−0.322907	−	0.993807i
$344$	8.24366	−	3.67031i	0.444468	−	0.197890i
$345$	−1.05881	−	10.0739i	−0.0570045	−	0.542362i
$346$	18.8880	−	4.01478i	1.01543	−	0.215836i
$347$	−5.40544	−	6.00335i	−0.290179	−	0.322277i	0.580375	−	0.814350i	$-0.302906\pi$
$347$	−5.40544	−	6.00335i	−0.290179	−	0.322277i	−0.870554	+	0.492073i	$0.836239\pi$
$348$	−6.87433	−	3.06065i	−0.368503	−	0.164068i
$349$	−19.5597	−	14.2110i	−1.04701	−	0.760696i	−0.0753667	−	0.997156i	$-0.524013\pi$
$349$	−19.5597	−	14.2110i	−1.04701	−	0.760696i	−0.971641	+	0.236460i	$0.924013\pi$
$350$	−4.07655	−	12.5463i	−0.217901	−	0.670630i
$351$	9.01261	+	15.6103i	0.481058	+	0.833216i
$352$	3.27791	−	0.505278i	0.174713	−	0.0269314i
$353$	−1.60035			−0.0851782			−0.0425891	−	0.999093i	$-0.513561\pi$
$353$	−1.60035			−0.0851782			−0.0425891	+	0.999093i	$0.513561\pi$
$354$	1.39664	+	4.29843i	0.0742307	+	0.228459i
$355$	−4.03706	+	38.4100i	−0.214265	+	2.03859i
$356$	−0.601798	−	5.72572i	−0.0318952	−	0.303463i
$357$	−9.26836	+	1.97005i	−0.490533	+	0.104266i
$358$	1.21581	+	1.35029i	0.0642575	+	0.0713652i
$359$	−1.29087	−	12.2818i	−0.0681293	−	0.648207i	−0.974294	−	0.225281i	$-0.927670\pi$
$359$	−1.29087	−	12.2818i	−0.0681293	−	0.648207i	0.906164	−	0.422926i	$-0.138997\pi$
$360$	−5.91180	−	4.29518i	−0.311579	−	0.226376i
$361$	18.4047	+	4.71893i	0.968667	+	0.248365i
$362$	−20.4618			−1.07545
$363$	10.0076	+	3.34345i	0.525262	+	0.175486i
$364$	3.32274	−	5.75515i	0.174159	−	0.301652i
$365$	36.3290	−	40.3474i	1.90154	−	2.11188i
$366$	−8.12458	+	3.61730i	−0.424679	+	0.189079i
$367$	−16.6715	−	7.42263i	−0.870245	−	0.387458i	−0.0774863	−	0.996993i	$-0.524689\pi$
$367$	−16.6715	−	7.42263i	−0.870245	−	0.387458i	−0.792759	+	0.609535i	$0.791356\pi$
$368$	−0.928829	+	2.85864i	−0.0484186	+	0.149017i
$369$	−0.375564	+	1.15587i	−0.0195511	+	0.0601721i
$370$	10.0531	+	4.47594i	0.522638	+	0.232693i
$371$	1.94329	−	18.4891i	0.100890	−	0.959909i
$372$	−0.714954	−	2.20040i	−0.0370686	−	0.114086i
$373$	37.7064			1.95236			0.976181	−	0.216958i	$-0.0696135\pi$
$373$	37.7064			1.95236			0.976181	+	0.216958i	$0.0696135\pi$
$374$	−18.0246	+	2.77843i	−0.932030	+	0.143669i
$375$	3.94858	−	6.83913i	0.203904	−	0.353171i
$376$	5.89960	−	6.55217i	0.304249	−	0.337902i
$377$	−26.5110	+	11.8035i	−1.36539	+	0.607909i
$378$	0.914999	+	8.70564i	0.0470625	+	0.447770i
$379$	0.822262	−	2.53066i	0.0422368	−	0.129991i	−0.927715	−	0.373290i	$-0.878230\pi$
$379$	0.822262	−	2.53066i	0.0422368	−	0.129991i	0.969951	+	0.243299i	$0.0782296\pi$
$380$	2.87211	+	15.0424i	0.147336	+	0.771661i
$381$	−2.71373	+	1.97164i	−0.139029	+	0.101010i
$382$	−6.77646	+	3.01707i	−0.346714	+	0.154367i
$383$	−11.5966	−	2.46493i	−0.592559	−	0.125952i	−0.0981347	−	0.995173i	$-0.531288\pi$
$383$	−11.5966	−	2.46493i	−0.592559	−	0.125952i	−0.494424	+	0.869221i	$0.664621\pi$
$384$	−0.479605	−	0.830701i	−0.0244748	−	0.0423915i
$385$	−11.4734	+	17.5085i	−0.584738	+	0.892314i
$386$	−3.01323	−	5.21906i	−0.153369	−	0.265643i
$387$	5.79986	+	17.8501i	0.294823	+	0.907373i
$388$	−3.68373	−	2.67638i	−0.187013	−	0.135873i
$389$	14.5732	+	6.48843i	0.738893	+	0.328976i	0.741439	−	0.671020i	$-0.234144\pi$
$389$	14.5732	+	6.48843i	0.738893	+	0.328976i	−0.00254592	+	0.999997i	$0.500810\pi$
$390$	12.1940	−	2.59191i	0.617466	−	0.131247i
$391$	5.10745	−	15.7191i	0.258295	−	0.794950i
$392$	−3.05223	+	2.21757i	−0.154161	+	0.112004i
$393$	1.24025	−	11.8002i	0.0625624	−	0.595241i
$394$	−1.12553	−	0.239239i	−0.0567035	−	0.0120527i
$395$	−13.8643	−	24.0137i	−0.697590	−	1.20826i
$396$	0.332527	+	6.89028i	0.0167101	+	0.346249i
$397$	8.89058	−	15.3989i	0.446206	−	0.772851i	−0.551930	−	0.833891i	$-0.686108\pi$
$397$	8.89058	−	15.3989i	0.446206	−	0.772851i	0.998135	+	0.0610398i	$0.0194417\pi$
$398$	−4.67874	−	14.3997i	−0.234524	−	0.721791i
$399$	4.54023	−	5.98362i	0.227296	−	0.299556i
$400$	−5.94091	+	4.31632i	−0.297045	+	0.215816i
$401$	25.9449	+	28.8147i	1.29563	+	1.43894i	0.833898	+	0.551918i	$0.186104\pi$
$401$	25.9449	+	28.8147i	1.29563	+	1.43894i	0.461729	+	0.887021i	$0.347229\pi$
$402$	0.592111	+	0.657605i	0.0295318	+	0.0327984i
$403$	−8.15121	−	3.62915i	−0.406041	−	0.180781i
$404$	−1.49069	+	0.663698i	−0.0741646	+	0.0330202i
$405$	3.68095	−	4.08811i	0.182908	−	0.203140i
$406$	−14.0929			−0.699421
$407$	−2.64719	−	10.0455i	−0.131217	−	0.497938i
$408$	2.63726	+	4.56786i	0.130564	+	0.226143i
$409$	−5.74900	+	6.38491i	−0.284270	+	0.315714i	−0.868320	−	0.496004i	$-0.834800\pi$
$409$	−5.74900	+	6.38491i	−0.284270	+	0.315714i	0.584051	+	0.811717i	$0.301467\pi$
$410$	1.66085	+	1.20668i	0.0820236	+	0.0595936i
$411$	−5.50766	+	4.00155i	−0.271673	+	0.197382i
$412$	−6.02052	+	1.27970i	−0.296610	+	0.0630464i
$413$	5.66390	+	6.29040i	0.278702	+	0.309530i
$414$	−5.71122	−	2.54280i	−0.280691	−	0.124972i
$415$	45.7916	−	20.3877i	2.24782	−	1.00079i
$416$	−3.61838	−	0.769111i	−0.177406	−	0.0377088i
$417$	−9.86119			−0.482905
$418$	9.37503	−	11.0049i	0.458548	−	0.538270i
$419$	−39.0954			−1.90994			−0.954968	−	0.296708i	$-0.904111\pi$
$419$	−39.0954			−1.90994			−0.954968	+	0.296708i	$0.904111\pi$
$420$	5.92176	+	1.25871i	0.288952	+	0.0614187i
$421$	−21.6477	+	9.63816i	−1.05504	+	0.469735i	−0.859593	−	0.510979i	$-0.829283\pi$
$421$	−21.6477	+	9.63816i	−1.05504	+	0.469735i	−0.195449	+	0.980714i	$0.562616\pi$
$422$	−1.10522	−	0.492076i	−0.0538013	−	0.0239539i
$423$	12.2707	+	13.6280i	0.596620	+	0.662614i
$424$	−10.1226	+	2.15162i	−0.491596	+	0.104492i
$425$	32.6679	−	23.7346i	1.58463	−	1.15130i
$426$	−8.53071	−	6.19792i	−0.413314	−	0.300290i
$427$	−11.1451	+	12.3779i	−0.539348	+	0.599007i
$428$	−6.06915	−	10.5121i	−0.293364	−	0.508121i
$429$	−9.11512	−	7.44392i	−0.440082	−	0.359396i
$430$	31.7034			1.52888
$431$	3.62069	−	4.02119i	0.174403	−	0.193694i	−0.649606	−	0.760271i	$-0.725066\pi$
$431$	3.62069	−	4.02119i	0.174403	−	0.193694i	0.824009	+	0.566577i	$0.191733\pi$
$432$	4.45144	−	1.98191i	0.214170	−	0.0953547i
$433$	9.45288	+	4.20869i	0.454276	+	0.202257i	0.621102	−	0.783730i	$-0.286685\pi$
$433$	9.45288	+	4.20869i	0.454276	+	0.202257i	−0.166826	+	0.985986i	$0.553352\pi$
$434$	−2.89940	−	3.22011i	−0.139176	−	0.154570i
$435$	−17.6900	−	19.6467i	−0.848170	−	0.941989i
$436$	−3.62219	+	2.63167i	−0.173471	+	0.126034i
$437$	5.07917	+	12.0772i	0.242970	+	0.577730i
$438$	4.58059	+	14.0976i	0.218869	+	0.673610i
$439$	16.3113	−	28.2520i	0.778497	−	1.34840i	−0.154311	−	0.988022i	$-0.549316\pi$
$439$	16.3113	−	28.2520i	0.778497	−	1.34840i	0.932808	−	0.360374i	$-0.117351\pi$
$440$	11.2427	+	3.06238i	0.535976	+	0.145993i
$441$	−3.92351	−	6.79572i	−0.186834	−	0.323605i
$442$	19.8968	+	4.22919i	0.946394	+	0.201162i
$443$	2.22069	−	21.1285i	0.105508	−	1.00384i	−0.805819	−	0.592162i	$-0.798275\pi$
$443$	2.22069	−	21.1285i	0.105508	−	1.00384i	0.911327	−	0.411683i	$-0.135059\pi$
$444$	−2.43067	+	1.76599i	−0.115355	+	0.0838100i
$445$	6.25050	−	19.2371i	0.296302	−	0.911925i
$446$	17.0624	−	3.62672i	0.807928	−	0.171730i
$447$	0.156697	+	0.0697661i	0.00741152	+	0.00329982i
$448$	−1.45336	−	1.05593i	−0.0686648	−	0.0498879i
$449$	−7.26024	−	22.3447i	−0.342632	−	1.05451i	−0.962839	−	0.270075i	$-0.912951\pi$
$449$	−7.26024	−	22.3447i	−0.342632	−	1.05451i	0.620207	−	0.784438i	$-0.287049\pi$
$450$	−7.63678	−	13.2273i	−0.360001	−	0.623541i
$451$	−0.0934195	−	1.93574i	−0.00439895	−	0.0911505i
$452$	10.2601	+	17.7710i	0.482593	+	0.835876i
$453$	5.27198	+	1.12059i	0.247699	+	0.0526501i
$454$	−15.1127	+	6.72861i	−0.709275	+	0.315789i
$455$	18.8886	−	13.7234i	0.885512	−	0.643362i
$456$	−3.94877	−	1.37436i	−0.184918	−	0.0643604i
$457$	0.163985	−	0.504695i	0.00767092	−	0.0236087i	−0.947148	−	0.320798i	$-0.896049\pi$
$457$	0.163985	−	0.504695i	0.00767092	−	0.0236087i	0.954819	+	0.297189i	$0.0960491\pi$
$458$	1.77512	+	16.8891i	0.0829458	+	0.789176i
$459$	−24.4776	+	10.8981i	−1.14252	+	0.508682i
$460$	−7.06612	+	7.84772i	−0.329460	+	0.365902i
$461$	14.9179	−	25.8386i	0.694798	−	1.20342i	−0.275451	−	0.961315i	$-0.588827\pi$
$461$	14.9179	−	25.8386i	0.694798	−	1.20342i	0.970249	−	0.242110i	$-0.0778394\pi$
$462$	−2.57353	−	5.10291i	−0.119731	−	0.237409i
$463$	−20.0400			−0.931339			−0.465669	−	0.884959i	$-0.654186\pi$
$463$	−20.0400			−0.931339			−0.465669	+	0.884959i	$0.654186\pi$
$464$	2.42420	+	7.46092i	0.112541	+	0.346364i
$465$	0.849664	−	8.08401i	0.0394022	−	0.374887i
$466$	14.6753	+	6.53385i	0.679819	+	0.302675i
$467$	−5.96739	+	18.3657i	−0.276138	+	0.849865i	0.712778	+	0.701389i	$0.247437\pi$
$467$	−5.96739	+	18.3657i	−0.276138	+	0.849865i	−0.988916	+	0.148475i	$0.952563\pi$
$468$	2.37760	−	7.31749i	0.109904	−	0.338251i
$469$	1.51399	+	0.674073i	0.0699097	+	0.0311258i
$470$	28.2982	−	12.5992i	1.30530	−	0.581156i
$471$	13.0840	−	14.5312i	0.602878	−	0.669564i
$472$	2.35591	−	4.08056i	0.108440	−	0.187823i
$473$	−18.7383	−	23.3366i	−0.861587	−	1.07302i
$474$	7.57053			0.347726
$475$	−7.30405	+	31.1645i	−0.335133	+	1.42993i
$476$	7.99175	+	5.80635i	0.366301	+	0.266133i
$477$	−2.24992	−	21.4065i	−0.103017	−	0.980138i
$478$	3.03640	+	3.37226i	0.138882	+	0.154244i
$479$	3.95133	−	0.839881i	0.180541	−	0.0383751i	−0.116754	−	0.993161i	$-0.537249\pi$
$479$	3.95133	−	0.839881i	0.180541	−	0.0383751i	0.297295	+	0.954786i	$0.403916\pi$
$480$	−0.352262	−	3.35155i	−0.0160785	−	0.152976i
$481$	−1.21115	+	11.5234i	−0.0552239	+	0.525420i
$482$	−2.63871	−	8.12112i	−0.120190	−	0.369907i
$483$	5.17944			0.235673
$484$	−4.39081	−	10.0857i	−0.199582	−	0.458440i
$485$	−7.99865	−	13.8541i	−0.363200	−	0.629081i
$486$	4.98137	+	15.3311i	0.225959	+	0.695432i
$487$	−18.2517	−	13.2607i	−0.827065	−	0.600898i	0.0916627	−	0.995790i	$-0.470782\pi$
$487$	−18.2517	−	13.2607i	−0.827065	−	0.600898i	−0.918727	+	0.394893i	$0.870782\pi$
$488$	8.47006	+	3.77112i	0.383422	+	0.170710i
$489$	3.55841	+	3.95202i	0.160917	+	0.178716i
$490$	−12.9652	+	2.75584i	−0.585709	+	0.124496i
$491$	0.832331	+	7.91910i	0.0375626	+	0.357384i	0.997118	+	0.0758646i	$0.0241717\pi$
$491$	0.832331	+	7.91910i	0.0375626	+	0.357384i	−0.959556	+	0.281519i	$0.909162\pi$
$492$	−0.512036	+	0.227973i	−0.0230844	+	0.0102778i
$493$	−13.3302	−	41.0261i	−0.600362	−	1.84772i
$494$	−14.1287	+	7.77042i	−0.635682	+	0.349608i
$495$	−8.77889	+	22.5900i	−0.394582	+	1.01535i
$496$	−1.20601	+	2.08887i	−0.0541515	+	0.0937932i
$497$	−19.3167	−	4.10590i	−0.866473	−	0.184175i
$498$	−1.43050	+	13.6103i	−0.0641022	+	0.609892i
$499$	1.04548	+	9.94711i	0.0468023	+	0.445294i	0.992680	+	0.120772i	$0.0385368\pi$
$499$	1.04548	+	9.94711i	0.0468023	+	0.445294i	−0.945878	+	0.324522i	$0.894796\pi$
$500$	−8.05306	+	1.71173i	−0.360144	+	0.0765509i
$501$	4.20530	−	12.9426i	0.187879	−	0.578232i
$502$	14.6480	−	10.6424i	0.653773	−	0.474994i
$503$	−2.87866	+	27.3886i	−0.128353	+	1.22120i	0.720835	+	0.693107i	$0.243759\pi$
$503$	−2.87866	+	27.3886i	−0.128353	+	1.22120i	−0.849188	+	0.528091i	$0.822908\pi$
$504$	2.50018	−	2.77674i	0.111367	−	0.123686i
$505$	−5.73289			−0.255110
$506$	9.95305	+	0.562915i	0.442467	+	0.0250246i
$507$	0.328163	+	0.568395i	0.0145742	+	0.0252433i
$508$	3.42058	+	0.727067i	0.151764	+	0.0322584i
$509$	−2.59540	+	24.6936i	−0.115039	+	1.09452i	0.772889	+	0.634541i	$0.218811\pi$
$509$	−2.59540	+	24.6936i	−0.115039	+	1.09452i	−0.887928	+	0.459982i	$0.847856\pi$
$510$	1.93702	+	18.4295i	0.0857727	+	0.816072i
$511$	18.5760	+	20.6307i	0.821753	+	0.912650i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	9.04018	−	19.2197i	0.399134	−	0.848572i
$514$	−17.0849	−	12.4129i	−0.753584	−	0.547511i
$515$	−21.1520	−	4.49599i	−0.932067	−	0.198117i
$516$	−4.32787	+	7.49608i	−0.190524	+	0.329997i
$517$	−25.9997	−	13.3833i	−1.14347	−	0.588597i
$518$	−2.81346	+	4.87305i	−0.123616	+	0.214110i
$519$	−12.3939	+	13.7648i	−0.544031	+	0.604208i
$520$	−10.5144	−	7.63916i	−0.461087	−	0.334999i
$521$	−27.3895	+	19.8997i	−1.19996	+	0.871820i	−0.994281	−	0.106799i	$-0.965940\pi$
$521$	−27.3895	+	19.8997i	−1.19996	+	0.871820i	−0.205677	+	0.978620i	$0.565940\pi$
$522$	−15.9601	+	3.39243i	−0.698555	+	0.148482i
$523$	−22.4915	+	4.78072i	−0.983484	+	0.209046i	−0.671470	−	0.741031i	$-0.734337\pi$
$523$	−22.4915	+	4.78072i	−0.983484	+	0.209046i	−0.312014	+	0.950077i	$0.601004\pi$
$524$	−10.0073	+	7.27075i	−0.437172	+	0.317624i
$525$	10.2372	+	7.43778i	0.446789	+	0.324611i
$526$	−18.5908	+	20.6472i	−0.810597	+	0.900259i
$527$	6.63163	−	11.4863i	0.288878	−	0.500352i
$528$	−2.25884	+	2.24022i	−0.0983032	+	0.0974932i
$529$	6.98272	−	12.0944i	0.303597	−	0.525845i
$530$	−35.5638	−	7.55932i	−1.54479	−	0.328356i
$531$	7.92852	+	5.76041i	0.344068	+	0.249980i
$532$	−7.80298	+	0.656554i	−0.338302	+	0.0284652i
$533$	−0.667958	+	2.05576i	−0.0289325	+	0.0890450i
$534$	3.69522	+	4.10396i	0.159908	+	0.177596i
$535$	−4.45768	−	42.4120i	−0.192723	−	1.83363i
$536$	0.0964300	−	0.917471i	0.00416514	−	0.0396287i
$537$	−1.70480	−	0.362366i	−0.0735675	−	0.0156373i
$538$	1.38817	+	2.40437i	0.0598481	+	0.103660i
$539$	9.69163	+	7.91474i	0.417448	+	0.340912i
$540$	17.1194			0.736700
$541$	18.1639	−	20.1731i	0.780928	−	0.867308i	−0.213033	−	0.977045i	$-0.568334\pi$
$541$	18.1639	−	20.1731i	0.780928	−	0.867308i	0.993961	+	0.109737i	$0.0350009\pi$
$542$	1.95418	−	18.5928i	0.0839392	−	0.798628i
$543$	15.8787	−	11.5365i	0.681420	−	0.495080i
$544$	1.69922	−	5.22968i	0.0728537	−	0.224221i
$545$	−15.3863	+	3.27046i	−0.659077	+	0.140091i
$546$	0.666307	+	6.33949i	0.0285153	+	0.271305i
$547$	0.853647	−	8.12191i	0.0364993	−	0.347268i	−0.960998	−	0.276557i	$-0.910807\pi$
$547$	0.853647	−	8.12191i	0.0364993	−	0.347268i	0.997497	−	0.0707109i	$-0.0225268\pi$
$548$	6.94224	+	1.47562i	0.296558	+	0.0630353i
$549$	−9.64211	+	16.7006i	−0.411515	+	0.712765i
$550$	18.8640	+	15.4054i	0.804362	+	0.656888i
$551$	29.2522	+	17.7090i	1.24618	+	0.754430i
$552$	−0.890943	−	2.74204i	−0.0379210	−	0.116709i
$553$	12.9526	−	5.76688i	0.550802	−	0.245233i
$554$	−0.991421	−	9.43274i	−0.0421214	−	0.400759i
$555$	−10.3250	+	2.19465i	−0.438272	+	0.0931575i
$556$	6.87901	+	7.63992i	0.291735	+	0.324005i
$557$	9.87543	+	4.39682i	0.418435	+	0.186299i	0.605144	−	0.796116i	$-0.293115\pi$
$557$	9.87543	+	4.39682i	0.418435	+	0.186299i	−0.186709	+	0.982415i	$0.559782\pi$
$558$	−4.05868	−	2.94880i	−0.171818	−	0.124833i
$559$	10.3153	+	31.7473i	0.436291	+	1.34277i
$560$	−3.15575	−	5.46592i	−0.133355	−	0.230977i
$561$	12.4209	−	12.3186i	0.524411	−	0.520090i
$562$	19.7009			0.831031
$563$	5.83931	+	17.9715i	0.246097	+	0.757410i	0.995454	+	0.0952434i	$0.0303629\pi$
$563$	5.83931	+	17.9715i	0.246097	+	0.757410i	−0.749357	+	0.662167i	$0.769637\pi$
$564$	−0.884017	+	8.41086i	−0.0372238	+	0.354161i
$565$	7.53584	+	71.6988i	0.317035	+	3.01639i
$566$	−18.1531	+	3.85856i	−0.763032	+	0.162187i
$567$	1.88217	+	2.09036i	0.0790438	+	0.0877870i
$568$	1.14907	+	10.9327i	0.0482141	+	0.458726i
$569$	14.5634	+	10.5809i	0.610529	+	0.443575i	0.849601	−	0.527427i	$-0.176843\pi$
$569$	14.5634	+	10.5809i	0.610529	+	0.443575i	−0.239071	+	0.971002i	$0.576843\pi$
$570$	−10.7099	−	10.0539i	−0.448588	−	0.421110i
$571$	−20.1805			−0.844528			−0.422264	−	0.906473i	$-0.638764\pi$
$571$	−20.1805			−0.844528			−0.422264	+	0.906473i	$0.638764\pi$
$572$	0.591414	+	12.2547i	0.0247283	+	0.512393i
$573$	3.55760	−	6.16194i	0.148621	−	0.257419i
$574$	−0.702398	+	0.780091i	−0.0293175	+	0.0325604i
$575$	−20.1641	+	8.97763i	−0.840901	+	0.374393i
$576$	−1.90010	−	0.845977i	−0.0791707	−	0.0352491i
$577$	1.22029	−	3.75566i	0.0508013	−	0.156350i	−0.922437	−	0.386146i	$-0.873806\pi$
$577$	1.22029	−	3.75566i	0.0508013	−	0.156350i	0.973239	+	0.229796i	$0.0738059\pi$
$578$	−4.09042	+	12.5890i	−0.170139	+	0.523634i
$579$	5.28088	+	2.35120i	0.219466	+	0.0977125i
$580$	−2.88096	+	27.4105i	−0.119625	+	1.13816i
$581$	7.92022	+	24.3759i	0.328586	+	1.01128i
$582$	4.36761			0.181043
$583$	15.4556	+	30.6461i	0.640105	+	1.26923i
$584$	7.72672	−	13.3831i	0.319734	−	0.553796i
$585$	18.0877	−	20.0884i	0.747834	−	0.830554i
$586$	−23.6193	+	10.5160i	−0.975706	+	0.434412i
$587$	3.88692	+	36.9816i	0.160430	+	1.52639i	0.717871	+	0.696177i	$0.245117\pi$
$587$	3.88692	+	36.9816i	0.160430	+	1.52639i	−0.557440	+	0.830217i	$0.688216\pi$
$588$	1.11829	−	3.44175i	0.0461176	−	0.141935i
$589$	1.97182	+	10.3272i	0.0812473	+	0.425525i
$590$	13.3926	−	9.73026i	0.551363	−	0.400588i
$591$	1.00832	−	0.448933i	0.0414767	−	0.0184666i
$592$	3.06379	+	0.651229i	0.125921	+	0.0267653i
$593$	7.32242	+	12.6828i	0.300696	+	0.520821i	0.976294	−	0.216450i	$-0.0694478\pi$
$593$	7.32242	+	12.6828i	0.300696	+	0.520821i	−0.675598	+	0.737270i	$0.736114\pi$
$594$	−10.1184	−	12.6014i	−0.415162	−	0.517041i
$595$	17.3529	+	30.0560i	0.711398	+	1.23218i
$596$	−0.0552585	−	0.170068i	−0.00226348	−	0.00696626i
$597$	11.7495	+	8.53649i	0.480874	+	0.349375i
$598$	−10.1577	−	4.52248i	−0.415378	−	0.184938i
$599$	16.1272	−	3.42795i	0.658941	−	0.140062i	0.133708	−	0.991021i	$-0.457311\pi$
$599$	16.1272	−	3.42795i	0.658941	−	0.140062i	0.525233	+	0.850958i	$0.323978\pi$
$600$	2.17666	−	6.69908i	0.0888620	−	0.273489i
$601$	−6.88983	+	5.00576i	−0.281042	+	0.204189i	−0.719372	−	0.694625i	$-0.755570\pi$
$601$	−6.88983	+	5.00576i	−0.281042	+	0.204189i	0.438330	+	0.898814i	$0.355570\pi$
$602$	−1.69449	+	16.1220i	−0.0690624	+	0.657085i
$603$	1.87684	+	0.398935i	0.0764309	+	0.0162459i
$604$	−2.80947	−	4.86615i	−0.114316	−	0.198001i
$605$	0.319755	−	38.6451i	0.0129999	−	1.57115i
$606$	0.782602	−	1.35551i	0.0317910	−	0.0550637i
$607$	−9.26648	−	28.5193i	−0.376115	−	1.15756i	−0.942723	−	0.333575i	$-0.891745\pi$
$607$	−9.26648	−	28.5193i	−0.376115	−	1.15756i	0.566609	−	0.823987i	$-0.308255\pi$
$608$	1.68982	+	4.01802i	0.0685311	+	0.162952i
$609$	10.9364	−	7.94574i	0.443164	−	0.321978i
$610$	21.7964	+	24.2073i	0.882509	+	0.980126i
$611$	21.8239	+	24.2379i	0.882902	+	0.980562i
$612$	10.4483	+	4.65187i	0.422346	+	0.188041i
$613$	−24.7374	+	11.0138i	−0.999135	+	0.444844i	−0.840101	−	0.542430i	$-0.817505\pi$
$613$	−24.7374	+	11.0138i	−0.999135	+	0.444844i	−0.159034	+	0.987273i	$0.550838\pi$
$614$	15.0583	−	16.7240i	0.607705	−	0.674925i
$615$	−1.96919			−0.0794053
$616$	−2.15821	+	5.55354i	−0.0869566	+	0.223758i
$617$	−8.84555	−	15.3209i	−0.356109	−	0.616798i	0.631198	−	0.775621i	$-0.282563\pi$
$617$	−8.84555	−	15.3209i	−0.356109	−	0.616798i	−0.987307	+	0.158823i	$0.949230\pi$
$618$	3.95052	−	4.38750i	0.158913	−	0.176491i
$619$	−34.5899	−	25.1310i	−1.39029	−	1.01010i	−0.995834	−	0.0911848i	$-0.970935\pi$
$619$	−34.5899	−	25.1310i	−1.39029	−	1.01010i	−0.394452	−	0.918917i	$-0.629065\pi$
$620$	−6.85577	+	4.98101i	−0.275334	+	0.200042i
$621$	14.3261	−	3.04511i	0.574887	−	0.122196i
$622$	10.8146	+	12.0108i	0.433627	+	0.481591i
$623$	9.44847	+	4.20673i	0.378545	+	0.168539i
$624$	3.24156	−	1.44324i	0.129766	−	0.0577757i
$625$	7.62156	+	1.62001i	0.304862	+	0.0648005i
$626$	21.3000			0.851318
$627$	−1.07049	+	13.8258i	−0.0427512	+	0.552148i
$628$	−20.3852			−0.813458
$629$	−16.8472	−	3.58098i	−0.671741	−	0.142783i
$630$	11.9925	−	5.33938i	0.477791	−	0.212726i
$631$	33.9567	+	15.1185i	1.35180	+	0.601858i	0.949533	−	0.313666i	$-0.101557\pi$
$631$	33.9567	+	15.1185i	1.35180	+	0.601858i	0.402262	+	0.915525i	$0.368224\pi$
$632$	−5.28108	−	5.86524i	−0.210070	−	0.233307i
$633$	1.13511	−	0.241275i	0.0451165	−	0.00958981i
$634$	−17.2026	+	12.4984i	−0.683202	+	0.496375i
$635$	9.93962	+	7.22155i	0.394442	+	0.286579i
$636$	6.64220	−	7.37691i	0.263380	−	0.292513i
$637$	−6.97813	−	12.0865i	−0.276484	−	0.478884i
$638$	21.8794	−	14.0803i	0.866213	−	0.557444i
$639$	−22.8643			−0.904500
$640$	−2.35086	+	2.61090i	−0.0929261	+	0.103205i
$641$	−6.69461	+	2.98063i	−0.264421	+	0.117728i	−0.534665	−	0.845064i	$-0.679562\pi$
$641$	−6.69461	+	2.98063i	−0.264421	+	0.117728i	0.270244	+	0.962792i	$0.412896\pi$
$642$	10.6366	+	4.73571i	0.419793	+	0.186904i
$643$	−1.54185	−	1.71240i	−0.0608048	−	0.0675305i	0.711975	−	0.702205i	$-0.247801\pi$
$643$	−1.54185	−	1.71240i	−0.0608048	−	0.0675305i	−0.772780	+	0.634674i	$0.781134\pi$
$644$	−3.61310	−	4.01275i	−0.142376	−	0.158125i
$645$	−24.6024	+	17.8747i	−0.968720	+	0.703816i
$646$	−9.29197	−	22.0943i	−0.365588	−	0.869290i
$647$	9.39648	+	28.9194i	0.369414	+	1.13694i	0.947171	+	0.320730i	$0.103928\pi$
$647$	9.39648	+	28.9194i	0.369414	+	1.13694i	−0.577757	+	0.816209i	$0.696072\pi$
$648$	0.782893	−	1.35601i	0.0307550	−	0.0532692i
$649$	−15.0780	−	4.10707i	−0.591863	−	0.161217i
$650$	−13.5824	−	23.5253i	−0.532744	−	0.922740i
$651$	4.06552	+	0.864153i	0.159340	+	0.0338688i
$652$	0.579516	−	5.51373i	0.0226956	−	0.215934i
$653$	24.3764	−	17.7105i	0.953922	−	0.693065i	0.00219092	−	0.999998i	$-0.499303\pi$
$653$	24.3764	−	17.7105i	0.953922	−	0.693065i	0.951731	+	0.306933i	$0.0993026\pi$
$654$	1.32712	−	4.08445i	0.0518945	−	0.159715i
$655$	−42.5091	+	9.03559i	−1.66097	+	0.353050i
$656$	0.533810	+	0.237667i	0.0208418	+	0.00927935i
$657$	26.0033	+	18.8925i	1.01449	+	0.737067i
$658$	4.89452	+	15.0638i	0.190808	+	0.587247i
$659$	10.9211	+	18.9159i	0.425426	+	0.736859i	0.996460	−	0.0840671i	$-0.0267910\pi$
$659$	10.9211	+	18.9159i	0.425426	+	0.736859i	−0.571034	+	0.820926i	$0.693458\pi$
$660$	−10.4512	+	3.96229i	−0.406811	+	0.154232i
$661$	0.114335	+	0.198035i	0.00444713	+	0.00770266i	0.868240	−	0.496144i	$-0.165251\pi$
$661$	0.114335	+	0.198035i	0.00444713	+	0.00770266i	−0.863793	+	0.503846i	$0.831918\pi$
$662$	−25.8816	−	5.50130i	−1.00592	−	0.213814i
$663$	−17.8247	+	7.93608i	−0.692255	+	0.308212i
$664$	11.5424	−	8.38605i	0.447932	−	0.325442i
$665$	−25.9824	−	9.04315i	−1.00756	−	0.350678i
$666$	−2.01318	+	6.19593i	−0.0780091	+	0.240087i
$667$	2.46476	+	23.4506i	0.0954357	+	0.908010i
$668$	−12.9608	+	5.77051i	−0.501467	+	0.223268i
$669$	−11.1959	+	12.4344i	−0.432860	+	0.480740i
$670$	1.62056	−	2.80689i	0.0626076	−	0.108440i
$671$	4.93605	−	30.3518i	0.190554	−	1.17172i
$672$	1.72318			0.0664730
$673$	5.31229	+	16.3496i	0.204774	+	0.630229i	0.999723	+	0.0235525i	$0.00749769\pi$
$673$	5.31229	+	16.3496i	0.204774	+	0.630229i	−0.794949	+	0.606677i	$0.792502\pi$
$674$	0.181894	−	1.73061i	0.00700631	−	0.0666605i
$675$	32.6886	+	14.5539i	1.25818	+	0.560179i
$676$	0.211440	−	0.650746i	0.00813232	−	0.0250287i
$677$	−5.62266	+	17.3048i	−0.216096	+	0.665076i	0.782978	+	0.622050i	$0.213700\pi$
$677$	−5.62266	+	17.3048i	−0.216096	+	0.665076i	−0.999074	+	0.0430262i	$0.986300\pi$
$678$	−17.9815	−	8.00586i	−0.690574	−	0.307463i
$679$	7.47267	−	3.32705i	0.286775	−	0.127680i
$680$	12.9270	−	14.3568i	0.495726	−	0.550559i
$681$	7.93408	−	13.7422i	0.304034	−	0.526603i
$682$	7.71856	+	2.10244i	0.295559	+	0.0805068i
$683$	−5.43777			−0.208071			−0.104035	−	0.994574i	$-0.533175\pi$
$683$	−5.43777			−0.208071			−0.104035	+	0.994574i	$0.533175\pi$
$684$	−8.67875	+	2.62186i	−0.331840	+	0.100249i
$685$	20.1730	+	14.6565i	0.770769	+	0.559997i
$686$	−2.02291	−	19.2467i	−0.0772352	−	0.734844i
$687$	−10.8998	−	12.1054i	−0.415852	−	0.461851i
$688$	8.82661	−	1.87615i	0.336511	−	0.0715277i
$689$	−4.00158	−	38.0725i	−0.152448	−	1.45045i
$690$	1.05881	−	10.0739i	0.0403083	−	0.383508i
$691$	2.00311	+	6.16494i	0.0762019	+	0.234525i	0.981901	−	0.189396i	$-0.0606531\pi$
$691$	2.00311	+	6.16494i	0.0762019	+	0.234525i	−0.905699	+	0.423922i	$0.860653\pi$
$692$	19.3100			0.734056
$693$	−11.0184	−	5.67169i	−0.418554	−	0.215450i
$694$	−4.03915	−	6.99602i	−0.153324	−	0.265565i
$695$	11.1613	+	34.3509i	0.423372	+	1.30300i
$696$	−6.08776	−	4.42302i	−0.230756	−	0.167654i
$697$	−2.93532	−	1.30689i	−0.111183	−	0.0495019i
$698$	−16.1777	−	17.9671i	−0.612334	−	0.680066i
$699$	−15.0721	+	3.20368i	−0.570080	+	0.121174i
$700$	−1.37894	−	13.1197i	−0.0521190	−	0.495879i
$701$	−8.79211	+	3.91450i	−0.332073	+	0.147849i	−0.565999	−	0.824406i	$-0.691509\pi$
$701$	−8.79211	+	3.91450i	−0.332073	+	0.147849i	0.233926	+	0.972254i	$0.424843\pi$
$702$	5.57010	+	17.1430i	0.210230	+	0.647021i
$703$	11.9632	−	6.57944i	0.451201	−	0.248148i
$704$	3.31133	+	0.187279i	0.124801	+	0.00705835i
$705$	−14.8564	+	25.7320i	−0.559523	+	0.969123i
$706$	−1.56538	−	0.332732i	−0.0589139	−	0.0125225i
$707$	0.306413	−	2.91533i	0.0115239	−	0.109642i
$708$	0.472430	+	4.49487i	0.0177550	+	0.168928i
$709$	33.5758	−	7.13676i	1.26097	−	0.268027i	0.471525	−	0.881853i	$-0.343704\pi$
$709$	33.5758	−	7.13676i	1.26097	−	0.268027i	0.789441	+	0.613826i	$0.210370\pi$
$710$	−11.9347	+	36.7313i	−0.447902	+	1.37850i
$711$	13.2805	−	9.64886i	0.498059	−	0.361861i
$712$	0.601798	−	5.72572i	0.0225533	−	0.214580i
$713$	−4.85116	+	5.38776i	−0.181678	+	0.201773i
$714$	−9.47542			−0.354609
$715$	−15.6136	+	40.1773i	−0.583917	+	1.50255i
$716$	0.908499	+	1.57357i	0.0339522	+	0.0588069i
$717$	−4.25761	−	0.904984i	−0.159004	−	0.0337972i
$718$	1.29087	−	12.2818i	0.0481747	−	0.458352i
$719$	−3.87554	−	36.8733i	−0.144533	−	1.37514i	−0.790820	−	0.612048i	$-0.790346\pi$
$719$	−3.87554	−	36.8733i	−0.144533	−	1.37514i	0.646287	−	0.763094i	$-0.276321\pi$
$720$	−4.88960	−	5.43045i	−0.182225	−	0.202381i
$721$	3.41686	−	10.5160i	0.127251	−	0.391637i
$722$	17.0214	+	8.44235i	0.633469	+	0.314192i
$723$	6.62645	+	4.81440i	0.246440	+	0.179049i
$724$	−20.0146	−	4.25424i	−0.743837	−	0.158108i
$725$	−28.8039	+	49.8898i	−1.06975	+	1.85286i
$726$	9.09375	+	5.35108i	0.337501	+	0.198597i
$727$	2.71850	−	4.70858i	0.100824	−	0.174632i	−0.811201	−	0.584768i	$-0.801186\pi$
$727$	2.71850	−	4.70858i	0.100824	−	0.174632i	0.912024	+	0.410136i	$0.134519\pi$
$728$	4.44669	−	4.93855i	0.164805	−	0.183035i
$729$	−8.70920	−	6.32761i	−0.322563	−	0.234356i
$730$	43.9238	−	31.9125i	1.62569	−	1.18113i
$731$	−48.5358	+	10.3166i	−1.79516	+	0.381574i
$732$	−8.69911	+	1.84905i	−0.321529	+	0.0683430i
$733$	−12.8600	+	9.34331i	−0.474994	+	0.345103i	−0.799384	−	0.600820i	$-0.794841\pi$
$733$	−12.8600	+	9.34331i	−0.474994	+	0.345103i	0.324391	+	0.945923i	$0.394841\pi$
$734$	−14.7639	−	10.7266i	−0.544947	−	0.395927i
$735$	8.50748	−	9.44851i	0.313803	−	0.348514i
$736$	−1.50288	+	2.60306i	−0.0553968	+	0.0959500i
$737$	−3.02395	+	0.466131i	−0.111389	+	0.0171702i
$738$	−0.607676	+	1.05253i	−0.0223688	+	0.0387440i
$739$	26.8694	+	5.71127i	0.988407	+	0.210092i	0.673626	−	0.739072i	$-0.264736\pi$
$739$	26.8694	+	5.71127i	0.988407	+	0.210092i	0.314781	+	0.949164i	$0.398069\pi$
$740$	8.90285	+	6.46830i	0.327275	+	0.237779i
$741$	6.58310	−	13.9959i	0.241836	−	0.514153i
$742$	5.74493	−	17.6811i	0.210903	−	0.649093i
$743$	−19.7635	−	21.9496i	−0.725053	−	0.805253i	0.262098	−	0.965041i	$-0.415586\pi$
$743$	−19.7635	−	21.9496i	−0.725053	−	0.805253i	−0.987151	+	0.159788i	$0.948919\pi$
$744$	−0.241841	−	2.30097i	−0.00886633	−	0.0843575i
$745$	0.0656702	−	0.624810i	0.00240597	−	0.0228913i
$746$	36.8824	+	7.83960i	1.35036	+	0.287028i
$747$	14.8373	+	25.6989i	0.542868	+	0.940275i
$748$	−18.2084	−	1.02981i	−0.665764	−	0.0376537i
$749$	21.8059			0.796770
$750$	5.28423	−	5.86873i	0.192953	−	0.214296i
$751$	2.38804	−	22.7207i	0.0871408	−	0.829089i	−0.860435	−	0.509559i	$-0.829808\pi$
$751$	2.38804	−	22.7207i	0.0871408	−	0.829089i	0.947576	−	0.319530i	$-0.103525\pi$
$752$	7.13295	−	5.18240i	0.260112	−	0.188983i
$753$	−5.36683	+	16.5174i	−0.195578	+	0.601928i
$754$	−28.3858	+	6.03358i	−1.03375	+	0.219730i
$755$	−2.06351	−	19.6330i	−0.0750988	−	0.714517i
$756$	−0.914999	+	8.70564i	−0.0332782	+	0.316621i
$757$	4.19170	+	0.890974i	0.152350	+	0.0323830i	0.283455	−	0.958985i	$-0.408519\pi$
$757$	4.19170	+	0.890974i	0.152350	+	0.0323830i	−0.131105	+	0.991368i	$0.541853\pi$
$758$	1.33045	−	2.30440i	0.0483241	−	0.0836997i
$759$	−8.04112	+	5.17480i	−0.291874	+	0.187833i
$760$	−0.318146	+	15.3109i	−0.0115404	+	0.555384i
$761$	−11.2156	−	34.5181i	−0.406566	−	1.25128i	−0.919581	−	0.392901i	$-0.871471\pi$
$761$	−11.2156	−	34.5181i	−0.406566	−	1.25128i	0.513015	−	0.858380i	$-0.328529\pi$
$762$	−3.06436	+	1.36434i	−0.111010	+	0.0494248i
$763$	−0.840744	−	7.99914i	−0.0304370	−	0.289588i
$764$	−7.25566	+	1.54224i	−0.262500	+	0.0557962i
$765$	26.8870	+	29.8610i	0.972100	+	1.07963i
$766$	−10.8307	−	4.82214i	−0.391329	−	0.174231i
$767$	14.1012	+	10.2451i	0.509166	+	0.369931i
$768$	−0.296412	−	0.912264i	−0.0106959	−	0.0329185i
$769$	2.63753	+	4.56834i	0.0951119	+	0.164739i	0.909655	−	0.415364i	$-0.136346\pi$
$769$	2.63753	+	4.56834i	0.0951119	+	0.164739i	−0.814543	+	0.580103i	$0.803012\pi$
$770$	−14.8629	+	14.7404i	−0.535621	+	0.531208i
$771$	20.2568			0.729529
$772$	−1.86228	−	5.73150i	−0.0670248	−	0.206281i
$773$	4.20809	−	40.0373i	0.151354	−	1.44004i	−0.610358	−	0.792126i	$-0.708974\pi$
$773$	4.20809	−	40.0373i	0.151354	−	1.44004i	0.761712	−	0.647916i	$-0.224359\pi$
$774$	1.96187	+	18.6659i	0.0705179	+	0.670933i
$775$	−17.3253	+	3.68261i	−0.622344	+	0.132283i
$776$	−3.04678	−	3.38379i	−0.109373	−	0.121471i
$777$	−0.564182	−	5.36783i	−0.0202399	−	0.192570i
$778$	12.9058	+	9.37659i	0.462694	+	0.336167i
$779$	2.43819	−	0.736580i	0.0873573	−	0.0263907i
$780$	12.4664			0.446369
$781$	34.0916	−	12.9250i	1.21989	−	0.462491i
$782$	8.26403	−	14.3137i	0.295521	−	0.511858i
$783$	25.5780	−	28.4073i	0.914085	−	1.01519i
$784$	−3.44659	+	1.53452i	−0.123092	+	0.0548043i
$785$	−65.4277	−	29.1303i	−2.33522	−	1.03970i
$786$	3.66655	−	11.2845i	0.130781	−	0.402504i
$787$	1.62712	−	5.00775i	0.0580004	−	0.178507i	−0.917859	−	0.396907i	$-0.870084\pi$
$787$	1.62712	−	5.00775i	0.0580004	−	0.178507i	0.975859	+	0.218400i	$0.0700837\pi$
$788$	−1.05120	−	0.468023i	−0.0374473	−	0.0166726i
$789$	2.78571	−	26.5042i	0.0991739	−	0.943576i
$790$	−8.56863	−	26.3715i	−0.304858	−	0.938257i
$791$	−36.8635			−1.31071
$792$	−1.10731	+	6.80884i	−0.0393465	+	0.241942i
$793$	−17.1489	+	29.7028i	−0.608976	+	1.05478i
$794$	11.8979	−	13.2140i	0.422242	−	0.468947i
$795$	31.8602	−	14.1851i	1.12996	−	0.503092i
$796$	−1.58264	−	15.0578i	−0.0560951	−	0.533709i
$797$	11.2017	−	34.4753i	0.396785	−	1.22118i	−0.530779	−	0.847511i	$-0.678100\pi$
$797$	11.2017	−	34.4753i	0.396785	−	1.22118i	0.927563	−	0.373667i	$-0.121900\pi$
$798$	5.68508	−	4.90890i	0.201250	−	0.173773i
$799$	−39.2227	+	28.4970i	−1.38760	+	1.00815i
$800$	−6.70850	+	2.98681i	−0.237181	+	0.105600i
$801$	11.7129	+	2.48966i	0.413856	+	0.0879678i
$802$	19.3870	+	33.5793i	0.684580	+	1.18573i
$803$	−49.4516	−	13.4700i	−1.74511	−	0.475347i
$804$	0.442448	+	0.766342i	0.0156039	+	0.0270268i
$805$	−5.86230	−	18.0423i	−0.206619	−	0.635908i
$806$	−7.21854	−	5.24458i	−0.254262	−	0.184732i
$807$	−2.43285	−	1.08318i	−0.0856404	−	0.0381296i
$808$	−1.59610	+	0.339263i	−0.0561508	+	0.0119352i
$809$	3.37533	−	10.3882i	0.118670	−	0.365230i	−0.874024	−	0.485882i	$-0.838499\pi$
$809$	3.37533	−	10.3882i	0.118670	−	0.365230i	0.992695	+	0.120652i	$0.0384985\pi$
$810$	4.45048	−	3.23346i	0.156374	−	0.113612i
$811$	−3.20354	+	30.4797i	−0.112492	+	1.07029i	0.782024	+	0.623249i	$0.214188\pi$
$811$	−3.20354	+	30.4797i	−0.112492	+	1.07029i	−0.894515	+	0.447038i	$0.852479\pi$
$812$	−13.7850	−	2.93009i	−0.483758	−	0.102826i
$813$	8.96631	+	15.5301i	0.314462	+	0.544665i
$814$	−0.500767	−	10.3764i	−0.0175519	−	0.363692i
$815$	9.73908	−	16.8686i	0.341145	−	0.590881i
$816$	1.62992	+	5.01636i	0.0570584	+	0.175608i
$817$	23.7760	−	31.3346i	0.831815	−	1.09626i
$818$	−6.95087	+	5.05010i	−0.243031	+	0.176573i
$819$	9.24873	+	10.2718i	0.323177	+	0.358924i
$820$	1.37368	+	1.52562i	0.0479708	+	0.0532770i
$821$	−41.2983	−	18.3872i	−1.44132	−	0.641717i	−0.470690	−	0.882299i	$-0.655995\pi$
$821$	−41.2983	−	18.3872i	−1.44132	−	0.641717i	−0.970629	+	0.240582i	$0.922662\pi$
$822$	−6.21927	+	2.76900i	−0.216922	+	0.0965799i
$823$	28.0781	−	31.1839i	0.978742	−	1.08700i	−0.0174523	−	0.999848i	$-0.505556\pi$
$823$	28.0781	−	31.1839i	0.978742	−	1.08700i	0.996195	−	0.0871559i	$-0.0277778\pi$
$824$	−6.15502			−0.214420
$825$	−23.3245	−	1.31916i	−0.812054	−	0.0459274i
$826$	4.23228	+	7.33053i	0.147260	+	0.255062i
$827$	−29.1467	+	32.3706i	−1.01353	+	1.12564i	−0.0214816	+	0.999769i	$0.506838\pi$
$827$	−29.1467	+	32.3706i	−1.01353	+	1.12564i	−0.992047	+	0.125868i	$0.959828\pi$
$828$	−5.05774	−	3.67466i	−0.175769	−	0.127703i
$829$	−16.5016	+	11.9891i	−0.573125	+	0.416400i	−0.836239	−	0.548365i	$-0.815250\pi$
$829$	−16.5016	+	11.9891i	−0.573125	+	0.416400i	0.263114	+	0.964765i	$0.415250\pi$
$830$	49.0298	−	10.4216i	1.70185	−	0.361739i
$831$	6.08763	+	6.76100i	0.211178	+	0.234537i
$832$	−3.37941	−	1.50461i	−0.117160	−	0.0521629i
$833$	18.9521	−	8.43803i	0.656652	−	0.292360i
$834$	−9.64570	−	2.05026i	−0.334003	−	0.0709946i
$835$	−49.8445			−1.72494
$836$	11.4582	−	8.81529i	0.396291	−	0.304883i
$837$	11.7531			0.406246
$838$	−38.2411	−	8.12840i	−1.32102	−	0.280791i
$839$	29.9900	−	13.3524i	1.03537	−	0.460976i	0.182557	−	0.983195i	$-0.441563\pi$
$839$	29.9900	−	13.3524i	1.03537	−	0.460976i	0.852811	+	0.522220i	$0.174896\pi$
$840$	5.53066	+	2.46241i	0.190826	+	0.0849611i
$841$	21.7749	+	24.1834i	0.750858	+	0.833912i
$842$	−23.1785	+	4.92674i	−0.798783	+	0.169787i
$843$	−15.2882	+	11.1075i	−0.526554	+	0.382564i
$844$	−0.978761	−	0.711112i	−0.0336903	−	0.0244775i
$845$	1.60854	−	1.78647i	0.0553356	−	0.0614564i
$846$	9.16911	+	15.8814i	0.315241	+	0.546013i
$847$	19.6350	+	2.22812i	0.674665	+	0.0765590i
$848$	−10.3487			−0.355377
$849$	11.9116	−	13.2292i	0.408807	−	0.454026i
$850$	36.8887	−	16.4239i	1.26527	−	0.563336i
$851$	8.60078	+	3.82932i	0.294831	+	0.131267i
$852$	−7.05567	−	7.83612i	−0.241723	−	0.268461i
$853$	10.6786	+	11.8597i	0.365627	+	0.406070i	0.897685	−	0.440638i	$-0.145248\pi$
$853$	10.6786	+	11.8597i	0.365627	+	0.406070i	−0.532058	+	0.846708i	$0.678581\pi$
$854$	−13.4750	+	9.79019i	−0.461106	+	0.335013i
$855$	−31.6017	−	3.98683i	−1.08075	−	0.136347i
$856$	−3.75094	−	11.5442i	−0.128205	−	0.394573i
$857$	−15.6979	+	27.1896i	−0.536231	+	0.928779i	0.462872	+	0.886425i	$0.346819\pi$
$857$	−15.6979	+	27.1896i	−0.536231	+	0.928779i	−0.999103	+	0.0423535i	$0.986514\pi$
$858$	−7.36825	−	9.17640i	−0.251548	−	0.313277i
$859$	14.0311	+	24.3026i	0.478735	+	0.829193i	0.999703	−	0.0243831i	$-0.00776217\pi$
$859$	14.0311	+	24.3026i	0.478735	+	0.829193i	−0.520968	+	0.853576i	$0.674429\pi$
$860$	31.0106	+	6.59152i	1.05745	+	0.224769i
$861$	0.105250	−	1.00138i	0.00358690	−	0.0341271i
$862$	4.37762	−	3.18053i	0.149102	−	0.108329i
$863$	−11.0395	+	33.9759i	−0.375787	+	1.15655i	0.567159	+	0.823609i	$0.308043\pi$
$863$	−11.0395	+	33.9759i	−0.375787	+	1.15655i	−0.942946	+	0.332946i	$0.891957\pi$
$864$	4.76623	−	1.01309i	0.162150	−	0.0344661i
$865$	61.9768	+	27.5939i	2.10728	+	0.938219i
$866$	8.37127	+	6.08208i	0.284467	+	0.206678i
$867$	−3.92358	−	12.0755i	−0.133252	−	0.410106i
$868$	−2.16654	−	3.75256i	−0.0735373	−	0.127370i
$869$	−14.3473	+	21.8941i	−0.486700	+	0.742708i
$870$	−13.2186	−	22.8954i	−0.448154	−	0.776225i
$871$	3.33805	+	0.709524i	0.113105	+	0.0240413i
$872$	−4.09019	+	1.82107i	−0.138511	+	0.0616692i
$873$	7.66184	−	5.56665i	0.259314	−	0.188403i
$874$	2.45719	+	12.8693i	0.0831156	+	0.435310i
$875$	4.57040	−	14.0663i	0.154508	−	0.475526i
$876$	1.54944	+	14.7419i	0.0523506	+	0.498083i
$877$	17.9007	−	7.96989i	0.604463	−	0.269124i	−0.0816016	−	0.996665i	$-0.526004\pi$
$877$	17.9007	−	7.96989i	0.604463	−	0.269124i	0.686064	+	0.727541i	$0.259337\pi$
$878$	21.8288	−	24.2434i	0.736687	−	0.818174i
$879$	12.4000	−	21.4774i	0.418242	−	0.724416i
$880$	10.3603	+	5.33296i	0.349247	+	0.179774i
$881$	−17.4800			−0.588915			−0.294457	−	0.955665i	$-0.595139\pi$
$881$	−17.4800			−0.588915			−0.294457	+	0.955665i	$0.595139\pi$
$882$	−2.42486	−	7.46296i	−0.0816493	−	0.251291i
$883$	−0.412158	+	3.92142i	−0.0138702	+	0.131966i	−0.999266	−	0.0383150i	$-0.987801\pi$
$883$	−0.412158	+	3.92142i	−0.0138702	+	0.131966i	0.985395	+	0.170281i	$0.0544676\pi$
$884$	18.5827	+	8.27355i	0.625004	+	0.278270i
$885$	−4.90684	+	15.1017i	−0.164942	+	0.507638i
$886$	6.56503	−	20.2051i	0.220556	−	0.678803i
$887$	−6.16968	−	2.74692i	−0.207158	−	0.0922325i	0.300535	−	0.953771i	$-0.402835\pi$
$887$	−6.16968	−	2.74692i	−0.207158	−	0.0922325i	−0.507693	+	0.861538i	$0.669501\pi$
$888$	−2.74473	+	1.22203i	−0.0921069	+	0.0410087i
$889$	−4.20360	+	4.66858i	−0.140984	+	0.156579i
$890$	10.1135	−	17.5171i	0.339006	−	0.587176i
$891$	−5.01057	−	1.36482i	−0.167860	−	0.0457232i
$892$	17.4436			0.584054
$893$	8.76961	−	37.4177i	0.293464	−	1.25213i
$894$	0.138768	+	0.100821i	0.00464109	+	0.00337195i
$895$	0.667277	+	6.34871i	0.0223046	+	0.212214i
$896$	−1.20206	−	1.33502i	−0.0401580	−	0.0446000i
$897$	10.4323	−	2.21746i	0.348326	−	0.0740390i
$898$	−2.45586	−	23.3659i	−0.0819531	−	0.779732i
$899$	−1.97789	+	18.8184i	−0.0659663	+	0.627628i
$900$	−4.71979	−	14.5260i	−0.157326	−	0.484201i
$901$	56.9056			1.89580
$902$	0.311085	−	1.91286i	0.0103580	−	0.0636914i
$903$	−7.77480	−	13.4664i	−0.258729	−	0.448132i
$904$	6.34108	+	19.5158i	0.210901	+	0.649087i
$905$	−58.1590	−	42.2550i	−1.93327	−	1.40460i
$906$	4.92379	+	2.19221i	0.163582	+	0.0728314i
$907$	4.46444	+	4.95826i	0.148239	+	0.164636i	0.812691	−	0.582695i	$-0.198002\pi$
$907$	4.46444	+	4.95826i	0.148239	+	0.164636i	−0.664452	+	0.747331i	$0.731335\pi$
$908$	−16.1814	+	3.43947i	−0.536999	+	0.114143i
$909$	−0.354762	−	3.37533i	−0.0117667	−	0.111953i
$910$	21.3291	−	9.49633i	0.707053	−	0.314800i
$911$	4.32351	+	13.3064i	0.143244	+	0.440861i	0.996781	−	0.0801718i	$-0.0255469\pi$
$911$	4.32351	+	13.3064i	0.143244	+	0.440861i	−0.853537	+	0.521033i	$0.825547\pi$
$912$	−3.57673	−	2.16532i	−0.118437	−	0.0717010i
$913$	−36.6502	−	29.9307i	−1.21295	−	0.990561i
$914$	0.265334	−	0.459572i	0.00877647	−	0.0152013i
$915$	−30.5627	−	6.49630i	−1.01037	−	0.214761i
$916$	−1.77512	+	16.8891i	−0.0586515	+	0.558032i
$917$	−2.32280	−	22.0999i	−0.0767055	−	0.729804i
$918$	−26.2086	+	5.57080i	−0.865012	+	0.183864i
$919$	−2.40212	+	7.39298i	−0.0792388	+	0.243872i	−0.982827	−	0.184531i	$-0.940923\pi$
$919$	−2.40212	+	7.39298i	−0.0792388	+	0.243872i	0.903588	+	0.428403i	$0.140923\pi$
$920$	−8.54334	+	6.20710i	−0.281666	+	0.204642i
$921$	−2.25639	+	21.4681i	−0.0743507	+	0.707400i
$922$	19.9641	−	22.1724i	0.657482	−	0.730208i
$923$	−40.6653			−1.33851
$924$	−1.45633	−	5.52646i	−0.0479099	−	0.181807i
$925$	11.5006	+	19.9196i	0.378137	+	0.654952i
$926$	−19.6021	−	4.16656i	−0.644165	−	0.136922i
$927$	1.33817	−	12.7318i	0.0439511	−	0.418167i
$928$	0.820012	+	7.80190i	0.0269182	+	0.256110i
$929$	−13.8855	−	15.4214i	−0.455568	−	0.505959i	0.470976	−	0.882146i	$-0.343902\pi$
$929$	−13.8855	−	15.4214i	−0.455568	−	0.505959i	−0.926544	+	0.376187i	$0.877235\pi$
$930$	2.51186	−	7.73070i	0.0823670	−	0.253500i
$931$	−6.99947	+	14.8811i	−0.229399	+	0.487709i
$932$	12.9961	+	9.44223i	0.425702	+	0.309291i
$933$	−15.1642	−	3.22324i	−0.496453	−	0.105524i
$934$	−9.65543	+	16.7237i	−0.315935	+	0.547216i
$935$	−56.9695	−	29.3249i	−1.86310	−	0.959027i
$936$	3.84703	−	6.66325i	0.125744	−	0.217795i
$937$	27.6217	−	30.6770i	0.902362	−	1.00217i	−0.0976141	−	0.995224i	$-0.531121\pi$
$937$	27.6217	−	30.6770i	0.902362	−	1.00217i	0.999976	−	0.00694990i	$-0.00221224\pi$
$938$	1.34076	+	0.974119i	0.0437774	+	0.0318061i
$939$	−16.5292	+	12.0091i	−0.539409	+	0.391903i
$940$	30.2993	−	6.44032i	0.988255	−	0.210060i
$941$	11.0649	−	2.35191i	0.360704	−	0.0766700i	−0.0239950	−	0.999712i	$-0.507639\pi$
$941$	11.0649	−	2.35191i	0.360704	−	0.0766700i	0.384699	+	0.923042i	$0.374305\pi$
$942$	15.8193	−	11.4934i	0.515420	−	0.374474i
$943$	1.42091	+	1.03235i	0.0462713	+	0.0336181i
$944$	3.15282	−	3.50157i	0.102616	−	0.113966i
$945$	−15.3770	+	26.6338i	−0.500215	+	0.866399i
$946$	−13.4769	−	26.7225i	−0.438170	−	0.868825i
$947$	12.2765	−	21.2635i	0.398933	−	0.690972i	−0.594662	−	0.803976i	$-0.702714\pi$
$947$	12.2765	−	21.2635i	0.398933	−	0.690972i	0.993594	+	0.113004i	$0.0360474\pi$
$948$	7.40509	+	1.57400i	0.240506	+	0.0511212i
$949$	46.2480	+	33.6012i	1.50127	+	1.09074i
$950$	−13.6239	+	28.9649i	−0.442018	+	0.939745i
$951$	6.30279	−	19.3980i	0.204382	−	0.629023i
$952$	6.60990	+	7.34104i	0.214228	+	0.237924i
$953$	4.92444	+	46.8529i	0.159518	+	1.51772i	0.722572	+	0.691296i	$0.242960\pi$
$953$	4.92444	+	46.8529i	0.159518	+	1.51772i	−0.563054	+	0.826420i	$0.690374\pi$
$954$	2.24992	−	21.4065i	0.0728438	−	0.693063i
$955$	−25.4914	−	5.41836i	−0.824882	−	0.175334i
$956$	2.26891	+	3.92987i	0.0733819	+	0.127101i
$957$	−9.04018	+	23.2624i	−0.292228	+	0.751966i
$958$	4.03960			0.130514
$959$	−8.53143	+	9.47511i	−0.275494	+	0.305967i
$960$	0.352262	−	3.35155i	0.0113692	−	0.108171i
$961$	20.3728	−	14.8017i	0.657186	−	0.477474i
$962$	−3.58053	+	11.0197i	−0.115441	+	0.355291i
$963$	24.6949	−	5.24907i	0.795783	−	0.169149i
$964$	−0.892574	−	8.49227i	−0.0287479	−	0.273518i
$965$	2.21316	−	21.0568i	0.0712442	−	0.677843i
$966$	5.06626	+	1.07687i	0.163004	+	0.0346476i
$967$	0.0438364	−	0.0759269i	0.00140968	−	0.00244164i	−0.865320	−	0.501220i	$-0.832885\pi$
$967$	0.0438364	−	0.0759269i	0.00140968	−	0.00244164i	0.866729	+	0.498779i	$0.166218\pi$
$968$	−2.19793	−	10.7782i	−0.0706440	−	0.346424i
$969$	19.6677	+	11.9067i	0.631819	+	0.382498i
$970$	−4.94344	−	15.2143i	−0.158724	−	0.488503i
$971$	42.1240	−	18.7548i	1.35182	−	0.601870i	0.402283	−	0.915516i	$-0.368217\pi$
$971$	42.1240	−	18.7548i	1.35182	−	0.601870i	0.949540	+	0.313645i	$0.101550\pi$
$972$	1.68500	+	16.0317i	0.0540465	+	0.514218i
$973$	−18.0649	+	3.83981i	−0.579134	+	0.123099i
$974$	−15.0958	−	16.7656i	−0.483702	−	0.537205i
$975$	23.8040	+	10.5982i	0.762337	+	0.339415i
$976$	7.50091	+	5.44973i	0.240098	+	0.174442i
$977$	1.81516	+	5.58648i	0.0580721	+	0.178727i	0.975885	−	0.218286i	$-0.0700466\pi$
$977$	1.81516	+	5.58648i	0.0580721	+	0.178727i	−0.917813	+	0.397014i	$0.870047\pi$
$978$	2.65898	+	4.60549i	0.0850248	+	0.147267i
$979$	−18.8718	+	2.90902i	−0.603145	+	0.0929726i
$980$	−13.2549			−0.423412
$981$	−2.87767	−	8.85656i	−0.0918770	−	0.282768i
$982$	−0.832331	+	7.91910i	−0.0265607	+	0.252709i
$983$	1.63059	+	15.5141i	0.0520078	+	0.494821i	0.989260	+	0.146168i	$0.0466942\pi$
$983$	1.63059	+	15.5141i	0.0520078	+	0.494821i	−0.937252	+	0.348653i	$0.886639\pi$
$984$	−0.548245	+	0.116533i	−0.0174774	+	0.00371494i
$985$	−2.70509	−	3.00430i	−0.0861913	−	0.0957251i
$986$	−4.50909	−	42.9011i	−0.143599	−	1.36625i
$987$	−12.2913	−	8.93018i	−0.391238	−	0.284251i
$988$	−15.4355	+	4.66309i	−0.491070	+	0.148353i
$989$	27.1233			0.862472
$990$	−13.2838	+	20.2711i	−0.422186	+	0.644259i
$991$	15.4614	−	26.7800i	0.491149	−	0.850695i	−0.508799	−	0.860885i	$-0.669910\pi$
$991$	15.4614	−	26.7800i	0.491149	−	0.850695i	0.999948	+	0.0101903i	$0.00324372\pi$
$992$	−1.61396	+	1.79248i	−0.0512433	+	0.0569114i
$993$	23.1862	−	10.3232i	0.735793	−	0.327596i
$994$	−18.0409	−	8.03235i	−0.572224	−	0.254771i
$995$	16.4379	−	50.5906i	0.521116	−	1.60383i
$996$	−4.22898	+	13.0155i	−0.134000	+	0.412410i
$997$	−0.610800	−	0.271946i	−0.0193442	−	0.00861261i	0.397042	−	0.917801i	$-0.370037\pi$
$997$	−0.610800	−	0.271946i	−0.0193442	−	0.00861261i	−0.416386	+	0.909188i	$0.636703\pi$
$998$	−1.04548	+	9.94711i	−0.0330942	+	0.314870i
$999$	−4.71637	−	14.5155i	−0.149219	−	0.459249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.49.4	✓	64
11.9	even	5	inner	418.2.n.d.163.5	yes	64
19.7	even	3	inner	418.2.n.d.159.5	yes	64
209.64	even	15	inner	418.2.n.d.273.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.4	✓	64	1.1	even	1	trivial
418.2.n.d.159.5	yes	64	19.7	even	3	inner
418.2.n.d.163.5	yes	64	11.9	even	5	inner
418.2.n.d.273.4	yes	64	209.64	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(-0.876283 + 0.390146i) q^{3} +(0.913545 + 0.406737i) q^{4} +(2.35086 + 2.61090i) q^{5} +(-0.938250 + 0.199431i) q^{6} +(-1.45336 + 1.05593i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.39173 + 1.54568i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(-0.876283 + 0.390146i) q^{3} +(0.913545 + 0.406737i) q^{4} +(2.35086 + 2.61090i) q^{5} +(-0.938250 + 0.199431i) q^{6} +(-1.45336 + 1.05593i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.39173 + 1.54568i) q^{9} +(1.75666 + 3.04262i) q^{10} +(1.20137 - 3.09139i) q^{11} -0.959211 q^{12} +(-2.47526 + 2.74906i) q^{13} +(-1.64114 + 0.730683i) q^{14} +(-3.07866 - 1.37071i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-3.67942 - 4.08641i) q^{17} +(-1.68269 + 1.22254i) q^{18} +(4.32462 + 0.545589i) q^{19} +(1.08567 + 3.34136i) q^{20} +(0.861588 - 1.49231i) q^{21} +(1.81786 - 2.77406i) q^{22} +(1.50288 + 2.60306i) q^{23} +(-0.938250 - 0.199431i) q^{24} +(-0.767590 + 7.30314i) q^{25} +(-2.99273 + 2.17435i) q^{26} +(1.50575 - 4.63422i) q^{27} +(-1.75720 + 0.373503i) q^{28} +(7.16665 + 3.19080i) q^{29} +(-2.72639 - 1.98084i) q^{30} +(0.745357 + 2.29397i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.153354 + 3.17764i) q^{33} +(-2.74940 - 4.76211i) q^{34} +(-6.17358 - 1.31223i) q^{35} +(-1.90010 + 0.845977i) q^{36} +(2.53403 - 1.84108i) q^{37} +(4.11668 + 1.43281i) q^{38} +(1.09650 - 3.37467i) q^{39} +(0.367241 + 3.49407i) q^{40} +(0.533810 - 0.237667i) q^{41} +(1.15303 - 1.28057i) q^{42} +(4.51190 - 7.81484i) q^{43} +(2.35489 - 2.33549i) q^{44} -7.30739 q^{45} +(0.928829 + 2.85864i) q^{46} +(0.921608 - 8.76852i) q^{47} +(-0.876283 - 0.390146i) q^{48} +(-1.16585 + 3.58811i) q^{49} +(-2.26922 + 6.98395i) q^{50} +(4.81851 + 2.14534i) q^{51} +(-3.37941 + 1.50461i) q^{52} +(-6.92465 + 7.69060i) q^{53} +(2.43635 - 4.21989i) q^{54} +(10.8956 - 4.13079i) q^{55} -1.79645 q^{56} +(-4.00245 + 1.20914i) q^{57} +(6.34664 + 4.61110i) q^{58} +(-0.492520 - 4.68601i) q^{59} +(-2.25498 - 2.50440i) q^{60} +(9.06903 - 1.92768i) q^{61} +(0.252125 + 2.39881i) q^{62} +(0.390567 - 3.71600i) q^{63} +(0.309017 + 0.951057i) q^{64} -12.9965 q^{65} +(-0.510666 + 3.14009i) q^{66} +(-0.461262 - 0.798929i) q^{67} +(-1.69922 - 5.22968i) q^{68} +(-2.33252 - 1.69467i) q^{69} +(-5.76584 - 2.56712i) q^{70} +(7.35570 + 8.16934i) q^{71} +(-2.03446 + 0.432439i) q^{72} +(-1.61533 - 15.3688i) q^{73} +(2.86144 - 1.27400i) q^{74} +(-2.17666 - 6.69908i) q^{75} +(3.72883 + 2.25740i) q^{76} +(1.51826 + 5.76147i) q^{77} +(1.77417 - 3.07295i) q^{78} +(-7.71998 - 1.64093i) q^{79} +(-0.367241 + 3.49407i) q^{80} +(-0.163669 - 1.55721i) q^{81} +(0.571559 - 0.121489i) q^{82} +(4.40881 - 13.5689i) q^{83} +(1.39408 - 1.01286i) q^{84} +(2.01939 - 19.2132i) q^{85} +(6.03810 - 6.70599i) q^{86} -7.52489 q^{87} +(2.78900 - 1.79484i) q^{88} +(-2.87863 - 4.98593i) q^{89} +(-7.14770 - 1.51929i) q^{90} +(0.694641 - 6.60907i) q^{91} +(0.314187 + 2.98929i) q^{92} +(-1.54813 - 1.71937i) q^{93} +(2.72455 - 8.38529i) q^{94} +(8.74212 + 12.5738i) q^{95} +(-0.776018 - 0.563810i) q^{96} +(-4.45384 - 0.946692i) q^{97} +(-1.88638 + 3.26731i) q^{98} +(3.10631 + 6.15933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more