LMFDB - Embedded newform 64.2.i.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	64.13
Dual form			64.2.i.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36881 + 0.355465i) q^{2} +(-2.00147 + 1.33734i) q^{3} +(1.74729 + 0.973128i) q^{4} +(0.756852 - 0.150547i) q^{5} +(-3.21501 + 1.11911i) q^{6} +(-1.69148 - 4.08359i) q^{7} +(2.04580 + 1.95313i) q^{8} +(1.06935 - 2.58163i) q^{9} +O(q^{10})$	\(q+(1.36881 + 0.355465i) q^{2} +(-2.00147 + 1.33734i) q^{3} +(1.74729 + 0.973128i) q^{4} +(0.756852 - 0.150547i) q^{5} +(-3.21501 + 1.11911i) q^{6} +(-1.69148 - 4.08359i) q^{7} +(2.04580 + 1.95313i) q^{8} +(1.06935 - 2.58163i) q^{9} +(1.08950 + 0.0629634i) q^{10} +(0.290161 - 0.434257i) q^{11} +(-4.79854 + 0.389032i) q^{12} +(-1.79553 - 0.357153i) q^{13} +(-0.863742 - 6.19092i) q^{14} +(-1.31348 + 1.31348i) q^{15} +(2.10604 + 3.40067i) q^{16} +(-3.04259 - 3.04259i) q^{17} +(2.38142 - 3.15366i) q^{18} +(-1.26776 + 6.37347i) q^{19} +(1.46894 + 0.473464i) q^{20} +(8.84657 + 5.91109i) q^{21} +(0.551539 - 0.491274i) q^{22} +(7.32197 + 3.03286i) q^{23} +(-6.70659 - 1.17320i) q^{24} +(-4.06924 + 1.68553i) q^{25} +(-2.33079 - 1.12712i) q^{26} +(-0.0965796 - 0.485538i) q^{27} +(1.01835 - 8.78123i) q^{28} +(-0.690042 - 1.03272i) q^{29} +(-2.26481 + 1.33101i) q^{30} -1.55847i q^{31} +(1.67396 + 5.40351i) q^{32} +1.25719i q^{33} +(-3.08320 - 5.24627i) q^{34} +(-1.89497 - 2.83602i) q^{35} +(4.38072 - 3.47025i) q^{36} +(0.371584 + 1.86808i) q^{37} +(-4.00087 + 8.27344i) q^{38} +(4.07133 - 1.68640i) q^{39} +(1.84240 + 1.17024i) q^{40} +(6.15380 + 2.54899i) q^{41} +(10.0081 + 11.2358i) q^{42} +(-7.03859 - 4.70304i) q^{43} +(0.929583 - 0.476409i) q^{44} +(0.420680 - 2.11490i) q^{45} +(8.94433 + 6.75412i) q^{46} +(1.12515 + 1.12515i) q^{47} +(-8.76302 - 3.98985i) q^{48} +(-8.86483 + 8.86483i) q^{49} +(-6.16917 + 0.860707i) q^{50} +(10.1586 + 2.02068i) q^{51} +(-2.78976 - 2.37133i) q^{52} +(3.92962 - 5.88109i) q^{53} +(0.0403925 - 0.698941i) q^{54} +(0.154233 - 0.372351i) q^{55} +(4.51535 - 11.6579i) q^{56} +(-5.98610 - 14.4517i) q^{57} +(-0.577441 - 1.65888i) q^{58} +(0.738882 - 0.146973i) q^{59} +(-3.57322 + 1.01685i) q^{60} +(-3.34952 + 2.23808i) q^{61} +(0.553981 - 2.13325i) q^{62} -12.3511 q^{63} +(0.370575 + 7.99141i) q^{64} -1.41272 q^{65} +(-0.446888 + 1.72086i) q^{66} +(3.05271 - 2.03976i) q^{67} +(-2.35546 - 8.27713i) q^{68} +(-18.7106 + 3.72178i) q^{69} +(-1.58575 - 4.55557i) q^{70} +(-0.317495 - 0.766500i) q^{71} +(7.22993 - 3.19293i) q^{72} +(0.292843 - 0.706986i) q^{73} +(-0.155407 + 2.68913i) q^{74} +(5.89032 - 8.81548i) q^{75} +(-8.41735 + 9.90261i) q^{76} +(-2.26413 - 0.450363i) q^{77} +(6.17234 - 0.861150i) q^{78} +(6.17863 - 6.17863i) q^{79} +(2.10592 + 2.25675i) q^{80} +(6.77032 + 6.77032i) q^{81} +(7.51732 + 5.67654i) q^{82} +(-0.663054 + 3.33340i) q^{83} +(9.70527 + 18.9372i) q^{84} +(-2.76085 - 1.84474i) q^{85} +(-7.96274 - 8.93954i) q^{86} +(2.76219 + 1.14414i) q^{87} +(1.44177 - 0.321679i) q^{88} +(12.3740 - 5.12547i) q^{89} +(1.32761 - 2.74537i) q^{90} +(1.57863 + 7.93632i) q^{91} +(9.84225 + 12.4245i) q^{92} +(2.08420 + 3.11923i) q^{93} +(1.14017 + 1.94007i) q^{94} +5.01463i q^{95} +(-10.5767 - 8.57629i) q^{96} +3.44120i q^{97} +(-15.2854 + 8.98315i) q^{98} +(-0.810809 - 1.21346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	1.36881	+	0.355465i	0.967896	+	0.251351i
$2$	1.36881	+	0.355465i	0.967896	+	0.251351i
$3$	−2.00147	+	1.33734i	−1.15555	+	0.772112i	−0.977297	−	0.211873i	$-0.932044\pi$
$3$	−2.00147	+	1.33734i	−1.15555	+	0.772112i	−0.178250	+	0.983985i	$0.557044\pi$
$4$	1.74729	+	0.973128i	0.873645	+	0.486564i
$5$	0.756852	−	0.150547i	0.338474	−	0.0673268i	−0.0229268	−	0.999737i	$-0.507298\pi$
$5$	0.756852	−	0.150547i	0.338474	−	0.0673268i	0.361401	+	0.932410i	$0.382298\pi$
$6$	−3.21501	+	1.11911i	−1.31252	+	0.456876i
$7$	−1.69148	−	4.08359i	−0.639318	−	1.54345i	−0.827590	−	0.561333i	$-0.810289\pi$
$7$	−1.69148	−	4.08359i	−0.639318	−	1.54345i	0.188272	−	0.982117i	$-0.439711\pi$
$8$	2.04580	+	1.95313i	0.723299	+	0.690535i
$9$	1.06935	−	2.58163i	0.356449	−	0.860545i
$10$	1.08950	+	0.0629634i	0.344531	+	0.0199108i
$11$	0.290161	−	0.434257i	0.0874869	−	0.130933i	−0.785145	−	0.619312i	$-0.787412\pi$
$11$	0.290161	−	0.434257i	0.0874869	−	0.130933i	0.872632	+	0.488379i	$0.162412\pi$
$12$	−4.79854	+	0.389032i	−1.38522	+	0.112304i
$13$	−1.79553	−	0.357153i	−0.497991	−	0.0990565i	−0.0602967	−	0.998180i	$-0.519205\pi$
$13$	−1.79553	−	0.357153i	−0.497991	−	0.0990565i	−0.437694	+	0.899124i	$0.644205\pi$
$14$	−0.863742	−	6.19092i	−0.230845	−	1.65459i
$15$	−1.31348	+	1.31348i	−0.339140	+	0.339140i
$16$	2.10604	+	3.40067i	0.526511	+	0.850169i
$17$	−3.04259	−	3.04259i	−0.737937	−	0.737937i	0.234241	−	0.972179i	$-0.424739\pi$
$17$	−3.04259	−	3.04259i	−0.737937	−	0.737937i	−0.972179	+	0.234241i	$0.924739\pi$
$18$	2.38142	−	3.15366i	0.561305	−	0.743324i
$19$	−1.26776	+	6.37347i	−0.290845	+	1.46217i	0.508375	+	0.861136i	$0.330246\pi$
$19$	−1.26776	+	6.37347i	−0.290845	+	1.46217i	−0.799220	+	0.601039i	$0.794754\pi$
$20$	1.46894	+	0.473464i	0.328465	+	0.105870i
$21$	8.84657	+	5.91109i	1.93048	+	1.28990i
$22$	0.551539	−	0.491274i	0.117589	−	0.104740i
$23$	7.32197	+	3.03286i	1.52674	+	0.632395i	0.978928	−	0.204208i	$-0.0654618\pi$
$23$	7.32197	+	3.03286i	1.52674	+	0.632395i	0.547810	+	0.836603i	$0.315462\pi$
$24$	−6.70659	−	1.17320i	−1.36898	−	0.239479i
$25$	−4.06924	+	1.68553i	−0.813847	+	0.337107i
$26$	−2.33079	−	1.12712i	−0.457105	−	0.221047i
$27$	−0.0965796	−	0.485538i	−0.0185867	−	0.0934419i
$28$	1.01835	−	8.78123i	0.192451	−	1.65950i
$29$	−0.690042	−	1.03272i	−0.128138	−	0.191771i	0.761854	−	0.647749i	$-0.224290\pi$
$29$	−0.690042	−	1.03272i	−0.128138	−	0.191771i	−0.889991	+	0.455978i	$0.849290\pi$
$30$	−2.26481	+	1.33101i	−0.413495	+	0.243009i
$31$		−	1.55847i		−	0.279910i	−0.990158	−	0.139955i	$-0.955304\pi$
$31$		−	1.55847i		−	0.279910i	0.990158	−	0.139955i	$-0.0446957\pi$
$32$	1.67396	+	5.40351i	0.295916	+	0.955214i
$33$			1.25719i			0.218849i
$34$	−3.08320	−	5.24627i	−0.528765	−	0.899728i
$35$	−1.89497	−	2.83602i	−0.320308	−	0.479375i
$36$	4.38072	−	3.47025i	0.730120	−	0.578375i
$37$	0.371584	+	1.86808i	0.0610880	+	0.307110i	0.999234	−	0.0391295i	$-0.0124585\pi$
$37$	0.371584	+	1.86808i	0.0610880	+	0.307110i	−0.938146	+	0.346239i	$0.887458\pi$
$38$	−4.00087	+	8.27344i	−0.649027	+	1.34213i
$39$	4.07133	−	1.68640i	0.651935	−	0.270040i
$40$	1.84240	+	1.17024i	0.291310	+	0.185031i
$41$	6.15380	+	2.54899i	0.961062	+	0.398085i	0.807378	−	0.590035i	$-0.200886\pi$
$41$	6.15380	+	2.54899i	0.961062	+	0.398085i	0.153685	+	0.988120i	$0.450886\pi$
$42$	10.0081	+	11.2358i	1.54428	+	1.73372i
$43$	−7.03859	−	4.70304i	−1.07338	−	0.717206i	−0.112350	−	0.993669i	$-0.535838\pi$
$43$	−7.03859	−	4.70304i	−1.07338	−	0.717206i	−0.961025	+	0.276462i	$0.910838\pi$
$44$	0.929583	−	0.476409i	0.140140	−	0.0718213i
$45$	0.420680	−	2.11490i	0.0627113	−	0.315271i
$46$	8.94433	+	6.75412i	1.31877	+	0.995840i
$47$	1.12515	+	1.12515i	0.164120	+	0.164120i	0.784389	−	0.620269i	$-0.212977\pi$
$47$	1.12515	+	1.12515i	0.164120	+	0.164120i	−0.620269	+	0.784389i	$0.712977\pi$
$48$	−8.76302	−	3.98985i	−1.26483	−	0.575885i
$49$	−8.86483	+	8.86483i	−1.26640	+	1.26640i
$50$	−6.16917	+	0.860707i	−0.872452	+	0.121722i
$51$	10.1586	+	2.02068i	1.42249	+	0.282951i
$52$	−2.78976	−	2.37133i	−0.386870	−	0.328845i
$53$	3.92962	−	5.88109i	0.539775	−	0.807830i	−0.456882	−	0.889527i	$-0.651034\pi$
$53$	3.92962	−	5.88109i	0.539775	−	0.807830i	0.996657	+	0.0816971i	$0.0260340\pi$
$54$	0.0403925	−	0.698941i	0.00549672	−	0.0951138i
$55$	0.154233	−	0.372351i	0.0207968	−	0.0502078i
$56$	4.51535	−	11.6579i	0.603389	−	1.55785i
$57$	−5.98610	−	14.4517i	−0.792878	−	1.91418i
$58$	−0.577441	−	1.65888i	−0.0758218	−	0.217822i
$59$	0.738882	−	0.146973i	0.0961942	−	0.0191342i	−0.146758	−	0.989172i	$-0.546884\pi$
$59$	0.738882	−	0.146973i	0.0961942	−	0.0191342i	0.242953	+	0.970038i	$0.421884\pi$
$60$	−3.57322	+	1.01685i	−0.461301	+	0.131274i
$61$	−3.34952	+	2.23808i	−0.428862	+	0.286556i	−0.751208	−	0.660065i	$-0.770529\pi$
$61$	−3.34952	+	2.23808i	−0.428862	+	0.286556i	0.322346	+	0.946622i	$0.395529\pi$
$62$	0.553981	−	2.13325i	0.0703557	−	0.270923i
$63$	−12.3511			−1.55609
$64$	0.370575	+	7.99141i	0.0463219	+	0.998927i
$65$	−1.41272			−0.175226
$66$	−0.446888	+	1.72086i	−0.0550081	+	0.211823i
$67$	3.05271	−	2.03976i	0.372948	−	0.249196i	−0.354944	−	0.934888i	$-0.615500\pi$
$67$	3.05271	−	2.03976i	0.372948	−	0.249196i	0.727892	+	0.685692i	$0.240500\pi$
$68$	−2.35546	−	8.27713i	−0.285641	−	1.00375i
$69$	−18.7106	+	3.72178i	−2.25250	+	0.448050i
$70$	−1.58575	−	4.55557i	−0.189533	−	0.544495i
$71$	−0.317495	−	0.766500i	−0.0376797	−	0.0909668i	0.903919	−	0.427703i	$-0.140677\pi$
$71$	−0.317495	−	0.766500i	−0.0376797	−	0.0909668i	−0.941599	+	0.336736i	$0.890677\pi$
$72$	7.22993	−	3.19293i	0.852056	−	0.376290i
$73$	0.292843	−	0.706986i	0.0342747	−	0.0827464i	−0.905815	−	0.423673i	$-0.860741\pi$
$73$	0.292843	−	0.706986i	0.0342747	−	0.0827464i	0.940090	+	0.340926i	$0.110741\pi$
$74$	−0.155407	+	2.68913i	−0.0180658	+	0.312605i
$75$	5.89032	−	8.81548i	0.680155	−	1.01792i
$76$	−8.41735	+	9.90261i	−0.965537	+	1.13591i
$77$	−2.26413	−	0.450363i	−0.258021	−	0.0513236i
$78$	6.17234	−	0.861150i	0.698880	−	0.0975060i
$79$	6.17863	−	6.17863i	0.695150	−	0.695150i	−0.268210	−	0.963360i	$-0.586432\pi$
$79$	6.17863	−	6.17863i	0.695150	−	0.695150i	0.963360	+	0.268210i	$0.0864321\pi$
$80$	2.10592	+	2.25675i	0.235450	+	0.252312i
$81$	6.77032	+	6.77032i	0.752258	+	0.752258i
$82$	7.51732	+	5.67654i	0.830149	+	0.626869i
$83$	−0.663054	+	3.33340i	−0.0727796	+	0.365888i	−0.999962	−	0.00872251i	$-0.997224\pi$
$83$	−0.663054	+	3.33340i	−0.0727796	+	0.365888i	0.927182	+	0.374610i	$0.122224\pi$
$84$	9.70527	+	18.9372i	1.05893	+	2.06622i
$85$	−2.76085	−	1.84474i	−0.299456	−	0.200090i
$86$	−7.96274	−	8.93954i	−0.858645	−	0.963976i
$87$	2.76219	+	1.14414i	0.296138	+	0.122664i
$88$	1.44177	−	0.321679i	0.153693	−	0.0342911i
$89$	12.3740	−	5.12547i	1.31164	−	0.543299i	0.386277	−	0.922383i	$-0.373761\pi$
$89$	12.3740	−	5.12547i	1.31164	−	0.543299i	0.925362	+	0.379084i	$0.123761\pi$
$90$	1.32761	−	2.74537i	0.139942	−	0.289387i
$91$	1.57863	+	7.93632i	0.165486	+	0.831953i
$92$	9.84225	+	12.4245i	1.02613	+	1.29534i
$93$	2.08420	+	3.11923i	0.216122	+	0.323449i
$94$	1.14017	+	1.94007i	0.117599	+	0.200103i
$95$			5.01463i			0.514490i
$96$	−10.5767	−	8.57629i	−1.07948	−	0.875314i
$97$			3.44120i			0.349401i	0.984622	+	0.174700i	$0.0558956\pi$
$97$			3.44120i			0.349401i	−0.984622	+	0.174700i	$0.944104\pi$
$98$	−15.2854	+	8.98315i	−1.54406	+	0.907435i
$99$	−0.810809	−	1.21346i	−0.0814894	−	0.121958i
$100$	−8.75038	−	1.01477i	−0.875038	−	0.101477i
$101$	−0.978121	−	4.91735i	−0.0973267	−	0.489294i	−0.998446	−	0.0557237i	$-0.982253\pi$
$101$	−0.978121	−	4.91735i	−0.0973267	−	0.489294i	0.901120	−	0.433571i	$-0.142747\pi$
$102$	13.1870	+	6.37696i	1.30570	+	0.631413i
$103$	−1.88632	+	0.781338i	−0.185864	+	0.0769875i	−0.473675	−	0.880700i	$-0.657073\pi$
$103$	−1.88632	+	0.781338i	−0.185864	+	0.0769875i	0.287810	+	0.957687i	$0.407073\pi$
$104$	−2.97573	−	4.23757i	−0.291794	−	0.415528i
$105$	7.58544	+	3.14199i	0.740263	+	0.306627i
$106$	7.46943	−	6.65326i	0.725495	−	0.646222i
$107$	3.54710	+	2.37010i	0.342911	+	0.229126i	0.715086	−	0.699037i	$-0.246388\pi$
$107$	3.54710	+	2.37010i	0.342911	+	0.229126i	−0.372174	+	0.928163i	$0.621388\pi$
$108$	0.303738	−	0.942360i	0.0292272	−	0.0906787i
$109$	2.58869	−	13.0142i	0.247952	−	1.24654i	−0.633306	−	0.773901i	$-0.718303\pi$
$109$	2.58869	−	13.0142i	0.247952	−	1.24654i	0.881258	−	0.472636i	$-0.156697\pi$
$110$	0.343473	−	0.454854i	0.0327489	−	0.0433686i
$111$	−3.24196	−	3.24196i	−0.307713	−	0.307713i
$112$	10.3246	−	14.3524i	0.975585	−	1.35617i
$113$	−0.380557	+	0.380557i	−0.0357998	+	0.0357998i	−0.724780	−	0.688980i	$-0.758059\pi$
$113$	−0.380557	+	0.380557i	−0.0357998	+	0.0357998i	0.688980	+	0.724780i	$0.258059\pi$
$114$	−3.05676	−	21.9095i	−0.286292	−	2.05201i
$115$	5.99824	+	1.19312i	0.559339	+	0.111259i
$116$	−0.200733	−	2.47596i	−0.0186376	−	0.229887i
$117$	−2.84209	+	4.25348i	−0.262751	+	0.393235i
$118$	1.06363	+	0.0614684i	0.0979154	+	0.00565863i
$119$	−7.27821	+	17.5712i	−0.667193	+	1.61075i
$120$	−5.25252	+	0.121718i	−0.479487	+	0.0111113i
$121$	4.10513	+	9.91067i	0.373194	+	0.900970i
$122$	−5.38042	+	1.87287i	−0.487120	+	0.169562i
$123$	−15.7255	+	3.12799i	−1.41792	+	0.282042i
$124$	1.51659	−	2.72310i	0.136194	−	0.244542i
$125$	−6.03420	+	4.03192i	−0.539715	+	0.360626i
$126$	−16.9063	−	4.39038i	−1.50614	−	0.391126i
$127$	−10.5330			−0.934651			−0.467325	−	0.884085i	$-0.654782\pi$
$127$	−10.5330			−0.934651			−0.467325	+	0.884085i	$0.654782\pi$
$128$	−2.33342	+	11.0705i	−0.206247	+	0.978500i
$129$	20.3771			1.79410
$130$	−1.93375	−	0.502172i	−0.169601	−	0.0440434i
$131$	−13.0608	+	8.72693i	−1.14112	+	0.762475i	−0.974686	−	0.223577i	$-0.928227\pi$
$131$	−13.0608	+	8.72693i	−1.14112	+	0.762475i	−0.166438	+	0.986052i	$0.553227\pi$
$132$	−1.22341	+	2.19668i	−0.106484	+	0.191197i
$133$	28.1710	−	5.60356i	2.44274	−	0.485890i
$134$	4.90365	−	1.70691i	0.423611	−	0.147455i
$135$	−0.146193	−	0.352941i	−0.0125823	−	0.0303763i
$136$	−0.281953	−	12.1671i	−0.0241773	−	1.04332i
$137$	−5.91955	+	14.2911i	−0.505742	+	1.22097i	0.440572	+	0.897717i	$0.354776\pi$
$137$	−5.91955	+	14.2911i	−0.505742	+	1.22097i	−0.946313	+	0.323251i	$0.895224\pi$
$138$	−26.9343	−	1.55656i	−2.29280	−	0.132503i
$139$	7.35516	−	11.0078i	0.623856	−	0.933667i	−0.376119	−	0.926572i	$-0.622741\pi$
$139$	7.35516	−	11.0078i	0.623856	−	0.933667i	0.999975	−	0.00709534i	$-0.00225854\pi$
$140$	−0.551247	−	6.79940i	−0.0465889	−	0.574654i
$141$	−3.75665	−	0.747245i	−0.316367	−	0.0629294i
$142$	−0.162127	−	1.16205i	−0.0136054	−	0.0975173i
$143$	−0.676090	+	0.676090i	−0.0565375	+	0.0565375i
$144$	11.0314	−	1.80053i	0.919283	−	0.150044i
$145$	−0.677733	−	0.677733i	−0.0562826	−	0.0562826i
$146$	0.652155	−	0.863635i	0.0539728	−	0.0714749i
$147$	5.88739	−	29.5979i	0.485584	−	2.44120i
$148$	−1.16861	+	3.62567i	−0.0960595	+	0.298028i
$149$	−4.87958	−	3.26043i	−0.399751	−	0.267105i	0.339404	−	0.940641i	$-0.389775\pi$
$149$	−4.87958	−	3.26043i	−0.399751	−	0.267105i	−0.739155	+	0.673536i	$0.764775\pi$
$150$	11.1963	−	9.97293i	0.914176	−	0.814287i
$151$	−10.8095	−	4.47745i	−0.879666	−	0.364369i	−0.103298	−	0.994650i	$-0.532940\pi$
$151$	−10.8095	−	4.47745i	−0.879666	−	0.364369i	−0.776367	+	0.630281i	$0.782940\pi$
$152$	−15.0418	+	10.5627i	−1.22005	+	0.856750i
$153$	−11.1085	+	4.60127i	−0.898065	+	0.371991i
$154$	−2.93907	−	1.42128i	−0.236837	−	0.114530i
$155$	−0.234623	−	1.17953i	−0.0188454	−	0.0947423i
$156$	8.75488	+	1.01530i	0.700951	+	0.0812888i
$157$	8.18769	+	12.2537i	0.653449	+	0.977955i	0.999214	+	0.0396342i	$0.0126193\pi$
$157$	8.18769	+	12.2537i	0.653449	+	0.977955i	−0.345766	+	0.938321i	$0.612381\pi$
$158$	10.6537	−	6.26110i	0.847560	−	0.498106i
$159$			17.0260i			1.35025i
$160$	2.08042	+	3.83764i	0.164472	+	0.303392i
$161$		−	35.0299i		−	2.76074i
$162$	6.86068	+	11.6739i	0.539026	+	0.917189i
$163$	−2.55092	−	3.81772i	−0.199803	−	0.299027i	0.718015	−	0.696028i	$-0.245051\pi$
$163$	−2.55092	−	3.81772i	−0.199803	−	0.299027i	−0.917818	+	0.397001i	$0.870051\pi$
$164$	8.27198	+	10.4423i	0.645933	+	0.815404i
$165$	0.189267	+	0.951510i	0.0147344	+	0.0740749i
$166$	−2.09250	+	4.32710i	−0.162410	+	0.335848i
$167$	−6.64505	+	2.75247i	−0.514209	+	0.212992i	−0.624671	−	0.780888i	$-0.714767\pi$
$167$	−6.64505	+	2.75247i	−0.514209	+	0.212992i	0.110462	+	0.993880i	$0.464767\pi$
$168$	6.55317	+	29.3714i	0.505588	+	2.26605i
$169$	−8.91406	−	3.69232i	−0.685697	−	0.284025i
$170$	−3.12334	−	3.50648i	−0.239549	−	0.268935i
$171$	15.0983	+	10.0884i	1.15460	+	0.771476i
$172$	−7.72180	−	15.0670i	−0.588782	−	1.14885i
$173$	3.19519	−	16.0633i	0.242926	−	1.22127i	−0.646042	−	0.763302i	$-0.723577\pi$
$173$	3.19519	−	16.0633i	0.242926	−	1.22127i	0.888968	−	0.457970i	$-0.151423\pi$
$174$	3.37422	+	2.54797i	0.255799	+	0.193161i
$175$	13.7660	+	13.7660i	1.04061	+	1.04061i
$176$	2.08786	+	0.0721800i	0.157378	+	0.00544077i
$177$	−1.28230	+	1.28230i	−0.0963832	+	0.0963832i
$178$	18.7596	−	2.61729i	1.40609	−	0.196174i
$179$	−9.80775	−	1.95088i	−0.733066	−	0.145816i	−0.185578	−	0.982630i	$-0.559416\pi$
$179$	−9.80775	−	1.95088i	−0.733066	−	0.145816i	−0.547488	+	0.836814i	$0.684416\pi$
$180$	2.79312	−	3.28597i	0.208187	−	0.244922i
$181$	2.78837	−	4.17310i	0.207258	−	0.310184i	−0.713248	−	0.700912i	$-0.752777\pi$
$181$	2.78837	−	4.17310i	0.207258	−	0.310184i	0.920506	+	0.390728i	$0.127777\pi$
$182$	−0.660232	+	11.4245i	−0.0489396	+	0.846839i
$183$	3.71089	−	8.95888i	0.274317	−	0.662259i
$184$	9.05571	+	20.5054i	0.667596	+	1.51168i
$185$	0.562468	+	1.35792i	0.0413534	+	0.0998360i
$186$	1.74410	+	5.01049i	0.127884	+	0.367387i
$187$	−2.20411	+	0.438425i	−0.161180	+	0.0320608i
$188$	0.871047	+	3.06088i	0.0635276	+	0.223237i
$189$	−1.81937	+	1.21567i	−0.132340	+	0.0884268i
$190$	−1.78252	+	6.86409i	−0.129318	+	0.497973i
$191$	20.5971			1.49035			0.745176	−	0.666868i	$-0.232366\pi$
$191$	20.5971			1.49035			0.745176	+	0.666868i	$0.232366\pi$
$192$	−11.4289	−	15.4990i	−0.824810	−	1.11854i
$193$	−15.8384			−1.14008			−0.570038	−	0.821618i	$-0.693072\pi$
$193$	−15.8384			−1.14008			−0.570038	+	0.821618i	$0.693072\pi$
$194$	−1.22322	+	4.71035i	−0.0878223	+	0.338183i
$195$	2.82751	−	1.88928i	0.202482	−	0.135294i
$196$	−24.1160	+	6.86281i	−1.72257	+	0.490201i
$197$	−25.5976	+	5.09169i	−1.82376	+	0.362768i	−0.983712	−	0.179750i	$-0.942471\pi$
$197$	−25.5976	+	5.09169i	−1.82376	+	0.362768i	−0.840044	+	0.542518i	$0.817471\pi$
$198$	−0.678502	−	1.94921i	−0.0482191	−	0.138525i
$199$	−5.61103	−	13.5462i	−0.397756	−	0.960267i	−0.988197	−	0.153187i	$-0.951046\pi$
$199$	−5.61103	−	13.5462i	−0.397756	−	0.960267i	0.590442	−	0.807080i	$-0.298954\pi$
$200$	−11.6169	−	4.49949i	−0.821439	−	0.318162i
$201$	−3.38206	+	8.16501i	−0.238552	+	0.575916i
$202$	0.409080	−	7.07861i	0.0287828	−	0.498049i
$203$	−3.05001	+	4.56467i	−0.214069	+	0.320377i
$204$	15.7837	+	13.4164i	1.10508	+	0.939332i
$205$	5.04126	+	1.00277i	0.352097	+	0.0700364i
$206$	−2.85975	+	0.398985i	−0.199248	+	0.0277986i
$207$	15.6595	−	15.6595i	1.08841	−	1.08841i
$208$	−2.56690	−	6.85820i	−0.177983	−	0.475530i
$209$	2.39987	+	2.39987i	0.166002	+	0.166002i
$210$	9.26617	+	6.99715i	0.639426	+	0.482849i
$211$	−3.71581	+	18.6806i	−0.255807	+	1.28603i	0.612686	+	0.790326i	$0.290089\pi$
$211$	−3.71581	+	18.6806i	−0.255807	+	1.28603i	−0.868493	+	0.495701i	$0.834911\pi$
$212$	12.5892	−	6.45195i	0.864633	−	0.443122i
$213$	1.66052	+	1.10953i	0.113777	+	0.0760235i
$214$	4.01283	+	4.50508i	0.274311	+	0.307961i
$215$	−6.03520	−	2.49986i	−0.411597	−	0.170489i
$216$	0.750736	−	1.18195i	0.0510811	−	0.0804212i
$217$	−6.36415	+	2.63612i	−0.432027	+	0.178951i
$218$	8.16953	−	16.8938i	0.553310	−	1.14419i
$219$	0.359363	+	1.80664i	0.0242835	+	0.122081i
$220$	0.631835	−	0.500517i	0.0425983	−	0.0337448i
$221$	4.37640	+	6.54974i	0.294388	+	0.440583i
$222$	−3.28523	−	5.59004i	−0.220490	−	0.375179i
$223$		−	9.71045i		−	0.650260i	−0.945669	−	0.325130i	$-0.894592\pi$
$223$		−	9.71045i		−	0.650260i	0.945669	−	0.325130i	$-0.105408\pi$
$224$	19.2342	−	15.9756i	1.28514	−	1.06742i
$225$			12.3077i			0.820514i
$226$	−0.656186	+	0.385637i	−0.0436488	+	0.0256522i
$227$	2.12248	+	3.17651i	0.140874	+	0.210833i	0.895197	−	0.445671i	$-0.147035\pi$
$227$	2.12248	+	3.17651i	0.140874	+	0.210833i	−0.754323	+	0.656503i	$0.772035\pi$
$228$	3.60393	−	31.0766i	0.238676	−	2.05810i
$229$	−1.76419	−	8.86919i	−0.116581	−	0.586093i	−0.994273	−	0.106868i	$-0.965918\pi$
$229$	−1.76419	−	8.86919i	−0.116581	−	0.586093i	0.877692	−	0.479225i	$-0.159082\pi$
$230$	7.78635	+	3.76532i	0.513416	+	0.248278i
$231$	5.13386	−	2.12651i	0.337783	−	0.139914i
$232$	0.605350	−	3.46048i	0.0397432	−	0.227191i
$233$	−2.54691	−	1.05496i	−0.166854	−	0.0691130i	0.297693	−	0.954662i	$-0.403783\pi$
$233$	−2.54691	−	1.05496i	−0.166854	−	0.0691130i	−0.464547	+	0.885549i	$0.653783\pi$
$234$	−5.40225	+	4.81196i	−0.353156	+	0.314567i
$235$	1.02096	+	0.682183i	0.0666000	+	0.0445007i
$236$	1.43406	+	0.462223i	0.0933496	+	0.0300881i
$237$	−4.10341	+	20.6292i	−0.266545	+	1.34001i
$238$	−16.2084	+	21.4645i	−1.05064	+	1.39133i
$239$	−8.73109	−	8.73109i	−0.564767	−	0.564767i	0.365891	−	0.930658i	$-0.380764\pi$
$239$	−8.73109	−	8.73109i	−0.564767	−	0.564767i	−0.930658	+	0.365891i	$0.880764\pi$
$240$	−7.23297	−	1.70047i	−0.466886	−	0.109765i
$241$	16.1373	−	16.1373i	1.03949	−	1.03949i	0.0403070	−	0.999187i	$-0.487166\pi$
$241$	16.1373	−	16.1373i	1.03949	−	1.03949i	0.999187	−	0.0403070i	$-0.0128336\pi$
$242$	2.09626	+	15.0251i	0.134753	+	0.965848i
$243$	−21.1482	−	4.20663i	−1.35666	−	0.269856i
$244$	−8.03052	+	0.651058i	−0.514101	+	0.0416797i
$245$	−5.37479	+	8.04394i	−0.343383	+	0.513908i
$246$	−22.6371	−	1.30822i	−1.44329	−	0.0834092i
$247$	4.55261	−	10.9910i	0.289676	−	0.699339i
$248$	3.04389	−	3.18832i	0.193287	−	0.202458i
$249$	−3.13080	−	7.55841i	−0.198406	−	0.478995i
$250$	−9.69289	+	3.37400i	−0.613032	+	0.213390i
$251$	23.2770	−	4.63008i	1.46923	−	0.292248i	0.605355	−	0.795956i	$-0.293031\pi$
$251$	23.2770	−	4.63008i	1.46923	−	0.292248i	0.863874	+	0.503708i	$0.168031\pi$
$252$	−21.5810	−	12.0192i	−1.35947	−	0.757139i
$253$	3.44159	−	2.29960i	0.216371	−	0.144575i
$254$	−14.4177	−	3.74410i	−0.904645	−	0.234926i
$255$	7.99278			0.500527
$256$	−7.12917	+	14.3239i	−0.445573	+	0.895246i
$257$	0.938259			0.0585270			0.0292635	−	0.999572i	$-0.490684\pi$
$257$	0.938259			0.0585270			0.0292635	+	0.999572i	$0.490684\pi$
$258$	27.8923	+	7.24332i	1.73650	+	0.450950i
$259$	6.99993	−	4.67720i	0.434954	−	0.290627i
$260$	−2.46843	−	1.37476i	−0.153086	−	0.0852589i
$261$	−3.40400	+	0.677098i	−0.210702	+	0.0419113i
$262$	−20.9798	+	7.30288i	−1.29614	+	0.451173i
$263$	4.19405	+	10.1253i	0.258616	+	0.624354i	0.998847	−	0.0479979i	$-0.0152841\pi$
$263$	4.19405	+	10.1253i	0.258616	+	0.624354i	−0.740231	+	0.672352i	$0.765284\pi$
$264$	−2.45546	+	2.57196i	−0.151123	+	0.158293i
$265$	2.08876	−	5.04271i	0.128311	−	0.309771i
$266$	40.5527	+	2.34358i	2.48644	+	0.143694i
$267$	−17.9116	+	26.8066i	−1.09617	+	1.64054i
$268$	7.31892	−	0.593366i	0.447074	−	0.0362456i
$269$	23.0601	+	4.58694i	1.40600	+	0.279671i	0.839038	−	0.544073i	$-0.183118\pi$
$269$	23.0601	+	4.58694i	1.40600	+	0.279671i	0.566963	+	0.823744i	$0.308118\pi$
$270$	−0.0746525	−	0.535076i	−0.00454321	−	0.0325637i
$271$	−2.19673	+	2.19673i	−0.133442	+	0.133442i	−0.770673	−	0.637231i	$-0.780080\pi$
$271$	−2.19673	+	2.19673i	−0.133442	+	0.133442i	0.637231	+	0.770673i	$0.280080\pi$
$272$	3.93904	−	16.7547i	0.238839	−	1.01590i
$273$	−13.7731	−	13.7731i	−0.833587	−	0.833587i
$274$	−13.1827	+	17.4576i	−0.796398	+	1.05465i
$275$	−0.448780	+	2.25617i	−0.0270625	+	0.136052i
$276$	−36.3147	−	11.7048i	−2.18589	−	0.704548i
$277$	−7.16558	−	4.78789i	−0.430538	−	0.287676i	0.321358	−	0.946958i	$-0.395861\pi$
$277$	−7.16558	−	4.78789i	−0.430538	−	0.287676i	−0.751896	+	0.659281i	$0.770861\pi$
$278$	13.9807	−	12.4531i	0.838506	−	0.746885i
$279$	−4.02340	−	1.66655i	−0.240875	−	0.0997736i
$280$	1.66239	−	9.50305i	0.0993470	−	0.567916i
$281$	2.11464	−	0.875914i	0.126149	−	0.0522527i	−0.318716	−	0.947850i	$-0.603252\pi$
$281$	2.11464	−	0.875914i	0.126149	−	0.0522527i	0.444865	+	0.895598i	$0.353252\pi$
$282$	−4.87653	−	2.35819i	−0.290393	−	0.140428i
$283$	4.65354	+	23.3949i	0.276624	+	1.39068i	0.830005	+	0.557755i	$0.188337\pi$
$283$	4.65354	+	23.3949i	0.276624	+	1.39068i	−0.553381	+	0.832928i	$0.686663\pi$
$284$	0.191148	−	1.64826i	0.0113425	−	0.0978063i
$285$	−6.70626	−	10.0366i	−0.397244	−	0.594518i
$286$	−1.16577	+	0.685113i	−0.0689332	+	0.0405116i
$287$		−	29.4411i		−	1.73785i
$288$	15.7399	+	1.45669i	0.927484	+	0.0858360i
$289$			1.51475i			0.0891029i
$290$	−0.686778	−	1.16860i	−0.0403290	−	0.0686224i
$291$	−4.60204	−	6.88744i	−0.269776	−	0.403749i
$292$	1.19967	−	0.950335i	0.0702053	−	0.0556141i
$293$	5.30837	+	26.6870i	0.310118	+	1.55907i	0.750260	+	0.661143i	$0.229928\pi$
$293$	5.30837	+	26.6870i	0.310118	+	1.55907i	−0.440142	+	0.897928i	$0.645072\pi$
$294$	18.5798	−	38.4212i	1.08359	−	2.24077i
$295$	0.537098	−	0.222473i	0.0312710	−	0.0129529i
$296$	−2.88841	+	4.54746i	−0.167885	+	0.264316i
$297$	−0.238872	−	0.0989440i	−0.0138608	−	0.00574131i
$298$	−5.52026	−	6.19743i	−0.319780	−	0.359008i
$299$	−12.0636	−	8.06067i	−0.697658	−	0.466160i
$300$	18.8707	−	9.67117i	1.08950	−	0.558365i
$301$	−7.29964	+	36.6978i	−0.420744	+	2.11522i
$302$	−13.2046	−	9.97118i	−0.759840	−	0.573777i
$303$	8.53383	+	8.53383i	0.490256	+	0.490256i
$304$	−24.3441	+	9.11156i	−1.39623	+	0.522584i
$305$	−2.19815	+	2.19815i	−0.125866	+	0.125866i
$306$	−16.8410	+	2.34961i	−0.962734	+	0.134318i
$307$	32.1099	+	6.38706i	1.83261	+	0.364529i	0.985874	−	0.167486i	$-0.0535648\pi$
$307$	32.1099	+	6.38706i	1.83261	+	0.364529i	0.846735	+	0.532015i	$0.178565\pi$
$308$	−3.51782	−	2.99020i	−0.200447	−	0.170382i
$309$	2.73049	−	4.08646i	0.155332	−	0.232471i
$310$	0.0981266	−	1.69796i	0.00557322	−	0.0964375i
$311$	−4.28733	+	10.3505i	−0.243112	+	0.586924i	−0.997589	−	0.0694024i	$-0.977891\pi$
$311$	−4.28733	+	10.3505i	−0.243112	+	0.586924i	0.754477	+	0.656327i	$0.227891\pi$
$312$	11.6229	+	4.50180i	0.658016	+	0.254864i
$313$	3.78250	+	9.13175i	0.213799	+	0.516157i	0.994001	−	0.109371i	$-0.0348836\pi$
$313$	3.78250	+	9.13175i	0.213799	+	0.516157i	−0.780202	+	0.625528i	$0.784884\pi$
$314$	6.85163	+	19.6835i	0.386660	+	1.11080i
$315$	−9.34796	+	1.85942i	−0.526698	+	0.104767i
$316$	16.8085	−	4.78326i	0.945550	−	0.269079i
$317$	14.8080	−	9.89442i	0.831703	−	0.555726i	−0.0652416	−	0.997869i	$-0.520782\pi$
$317$	14.8080	−	9.89442i	0.831703	−	0.555726i	0.896944	+	0.442143i	$0.145782\pi$
$318$	−6.05215	+	23.3054i	−0.339388	+	1.30690i
$319$	−0.648689			−0.0363196
$320$	1.48356	+	5.99253i	0.0829333	+	0.334992i
$321$	−10.2690			−0.573161
$322$	12.4519	−	47.9494i	0.693917	−	2.67211i
$323$	23.2492	−	15.5346i	1.29362	−	0.864368i
$324$	5.24132	+	18.4181i	0.291185	+	1.02323i
$325$	7.90844	−	1.57309i	0.438681	−	0.0872591i
$326$	−2.13466	−	6.13250i	−0.118228	−	0.339647i
$327$	12.2232	+	29.5095i	0.675946	+	1.63188i
$328$	7.61093	+	17.2339i	0.420243	+	0.951582i
$329$	2.69148	−	6.49781i	0.148386	−	0.358236i
$330$	−0.0791572	+	1.36972i	−0.00435746	+	0.0754004i
$331$	−9.69258	+	14.5060i	−0.532752	+	0.797320i	−0.996042	−	0.0888869i	$-0.971669\pi$
$331$	−9.69258	+	14.5060i	−0.532752	+	0.797320i	0.463289	+	0.886207i	$0.346669\pi$
$332$	−4.40237	+	5.17917i	−0.241611	+	0.284244i
$333$	5.22004	+	1.03833i	0.286057	+	0.0569002i
$334$	−10.0742	+	1.40553i	−0.551237	+	0.0769073i
$335$	2.00337	−	2.00337i	0.109456	−	0.109456i
$336$	−1.47043	+	42.5333i	−0.0802186	+	2.32038i
$337$	8.62689	+	8.62689i	0.469937	+	0.469937i	0.901894	−	0.431957i	$-0.142177\pi$
$337$	8.62689	+	8.62689i	0.469937	+	0.469937i	−0.431957	+	0.901894i	$0.642177\pi$
$338$	−10.8892	−	8.22273i	−0.592293	−	0.447258i
$339$	0.252739	−	1.27061i	0.0137269	−	0.0690099i
$340$	−3.02883	−	5.90995i	−0.164261	−	0.320512i
$341$	−0.676777	−	0.452208i	−0.0366495	−	0.0244884i
$342$	17.0807	+	19.1760i	0.923617	+	1.03692i
$343$	22.6098	+	9.36530i	1.22082	+	0.505679i
$344$	−5.21390	−	23.3687i	−0.281114	−	1.25996i
$345$	−13.6009	+	5.63367i	−0.732247	+	0.303307i
$346$	10.0836	−	20.8519i	0.542096	−	1.12100i
$347$	−2.46321	−	12.3834i	−0.132232	−	0.664776i	−0.988861	−	0.148843i	$-0.952445\pi$
$347$	−2.46321	−	12.3834i	−0.132232	−	0.664776i	0.856629	−	0.515933i	$-0.172555\pi$
$348$	3.71296	+	4.68711i	0.199035	+	0.251255i
$349$	−9.48101	−	14.1893i	−0.507507	−	0.759538i	0.485920	−	0.874003i	$-0.338485\pi$
$349$	−9.48101	−	14.1893i	−0.507507	−	0.759538i	−0.993427	+	0.114465i	$0.963485\pi$
$350$	13.9498	+	23.7365i	0.745647	+	1.26877i
$351$			0.906293i			0.0483743i
$352$	2.83223	+	0.840961i	0.150958	+	0.0448234i
$353$			23.9464i			1.27454i	0.770641	+	0.637270i	$0.219936\pi$
$353$			23.9464i			1.27454i	−0.770641	+	0.637270i	$0.780064\pi$
$354$	−2.21103	+	1.29941i	−0.117515	+	0.0690629i
$355$	−0.355691	−	0.532329i	−0.0188781	−	0.0282531i
$356$	26.6087	+	3.08579i	1.41026	+	0.163546i
$357$	−8.93147	−	44.9015i	−0.472704	−	2.37644i
$358$	−12.7315	−	6.15670i	−0.672880	−	0.325392i
$359$	−23.0491	+	9.54726i	−1.21649	+	0.503885i	−0.896291	−	0.443467i	$-0.853748\pi$
$359$	−23.0491	+	9.54726i	−1.21649	+	0.503885i	−0.320195	+	0.947352i	$0.603748\pi$
$360$	4.99130	−	3.50502i	0.263065	−	0.184731i
$361$	−21.4602	−	8.88911i	−1.12948	−	0.467848i
$362$	5.30015	−	4.72101i	0.278570	−	0.248131i
$363$	−21.4702	−	14.3459i	−1.12689	−	0.752966i
$364$	−4.96473	+	15.4033i	−0.260223	+	0.807351i
$365$	0.115204	−	0.579170i	0.00603006	−	0.0303152i
$366$	8.26407	−	10.9439i	0.431970	−	0.572048i
$367$	−23.6652	−	23.6652i	−1.23532	−	1.23532i	−0.961894	−	0.273421i	$-0.911845\pi$
$367$	−23.6652	−	23.6652i	−1.23532	−	1.23532i	−0.273421	−	0.961894i	$-0.588155\pi$
$368$	5.10662	+	31.2870i	0.266201	+	1.63095i
$369$	13.1611	−	13.1611i	0.685140	−	0.685140i
$370$	0.287221	+	2.05867i	0.0149319	+	0.107025i
$371$	−30.6628	−	6.09921i	−1.59193	−	0.316655i
$372$	0.606295	+	7.47839i	0.0314349	+	0.387736i
$373$	10.0109	−	14.9823i	0.518343	−	0.775755i	−0.476283	−	0.879292i	$-0.658016\pi$
$373$	10.0109	−	14.9823i	0.518343	−	0.775755i	0.994626	+	0.103537i	$0.0330160\pi$
$374$	−3.17286	−	0.183362i	−0.164064	−	0.00948145i
$375$	6.68521	−	16.1395i	0.345223	−	0.833441i
$376$	0.104266	+	4.49939i	0.00537711	+	0.232038i
$377$	0.870152	+	2.10073i	0.0448151	+	0.108193i
$378$	−2.92251	+	1.01730i	−0.150318	+	0.0523241i
$379$	−0.376618	+	0.0749139i	−0.0193455	+	0.00384807i	−0.204754	−	0.978814i	$-0.565639\pi$
$379$	−0.376618	+	0.0749139i	−0.0193455	+	0.00384807i	0.185408	+	0.982662i	$0.440639\pi$
$380$	−4.87988	+	8.76202i	−0.250333	+	0.449482i
$381$	21.0814	−	14.0861i	1.08003	−	0.721655i
$382$	28.1935	+	7.32153i	1.44250	+	0.374602i
$383$	17.7262			0.905768			0.452884	−	0.891569i	$-0.350395\pi$
$383$	17.7262			0.905768			0.452884	+	0.891569i	$0.350395\pi$
$384$	−10.1347	−	25.2777i	−0.517184	−	1.28995i
$385$	−1.78141			−0.0907890
$386$	−21.6798	−	5.63001i	−1.10348	−	0.286560i
$387$	−19.6682	+	13.1419i	−0.999792	+	0.668040i
$388$	−3.34873	+	6.01277i	−0.170006	+	0.305252i
$389$	7.58645	−	1.50904i	0.384648	−	0.0765113i	0.00102139	−	0.999999i	$-0.499675\pi$
$389$	7.58645	−	1.50904i	0.384648	−	0.0765113i	0.383627	+	0.923488i	$0.374675\pi$
$390$	4.54190	−	1.58099i	0.229988	−	0.0800566i
$391$	−13.0500	−	31.5056i	−0.659968	−	1.59330i
$392$	−35.4498	+	0.821491i	−1.79049	+	0.0414916i
$393$	14.4699	−	34.9333i	0.729907	−	1.76215i
$394$	−36.8483	−	2.12950i	−1.85639	−	0.107283i
$395$	3.74613	−	5.60649i	0.188488	−	0.282093i
$396$	−0.235865	−	2.90929i	−0.0118526	−	0.146197i
$397$	−8.20788	−	1.63265i	−0.411942	−	0.0819403i	−0.0152310	−	0.999884i	$-0.504848\pi$
$397$	−8.20788	−	1.63265i	−0.411942	−	0.0819403i	−0.396711	+	0.917944i	$0.629848\pi$
$398$	−2.86524	−	20.5368i	−0.143622	−	1.02942i
$399$	−48.8895	+	48.8895i	−2.44754	+	2.44754i
$400$	−14.3019	−	10.2883i	−0.715097	−	0.514417i
$401$	−18.5993	−	18.5993i	−0.928802	−	0.928802i	0.0688263	−	0.997629i	$-0.478075\pi$
$401$	−18.5993	−	18.5993i	−0.928802	−	0.928802i	−0.997629	+	0.0688263i	$0.978075\pi$
$402$	−7.53177	+	9.97416i	−0.375651	+	0.497466i
$403$	−0.556613	+	2.79828i	−0.0277269	+	0.139392i
$404$	3.07615	−	9.54387i	0.153044	−	0.474825i
$405$	6.14338	+	4.10488i	0.305267	+	0.203973i
$406$	−5.79747	+	5.16400i	−0.287724	+	0.256285i
$407$	0.919044	+	0.380681i	0.0455553	+	0.0188696i
$408$	16.8358	+	23.9750i	0.833499	+	1.18694i
$409$	23.4672	−	9.72045i	1.16038	−	0.480645i	0.282378	−	0.959303i	$-0.408877\pi$
$409$	23.4672	−	9.72045i	1.16038	−	0.480645i	0.878001	+	0.478658i	$0.158877\pi$
$410$	6.54409	+	3.16459i	0.323189	+	0.156288i
$411$	−7.26419	−	36.5195i	−0.358316	−	1.80138i
$412$	−4.05628	−	0.470404i	−0.199839	−	0.0231752i
$413$	−1.84998	−	2.76869i	−0.0910314	−	0.136238i
$414$	27.0013	−	15.8685i	1.32704	−	0.779893i
$415$			2.62271i			0.128744i
$416$	−1.07576	−	10.3000i	−0.0527435	−	0.505000i
$417$			31.8680i			1.56058i
$418$	2.43190	+	4.13804i	0.118948	+	0.202398i
$419$	−7.06866	−	10.5790i	−0.345326	−	0.516818i	0.617632	−	0.786467i	$-0.288092\pi$
$419$	−7.06866	−	10.5790i	−0.345326	−	0.516818i	−0.962959	+	0.269650i	$0.913092\pi$
$420$	10.1964	+	12.8716i	0.497533	+	0.628068i
$421$	5.87200	+	29.5205i	0.286184	+	1.43874i	0.809758	+	0.586763i	$0.199598\pi$
$421$	5.87200	+	29.5205i	0.286184	+	1.43874i	−0.523575	+	0.851980i	$0.675402\pi$
$422$	−11.7265	+	24.2494i	−0.570839	+	1.18044i
$423$	4.10790	−	1.70155i	0.199733	−	0.0827321i
$424$	19.5257	−	4.35647i	0.948254	−	0.211569i
$425$	17.5094	+	7.25264i	0.849332	+	0.351805i
$426$	1.87855	+	2.10899i	0.0910159	+	0.102181i
$427$	14.8050	+	9.89240i	0.716465	+	0.478727i
$428$	3.89140	+	7.59303i	0.188098	+	0.367023i
$429$	0.449011	−	2.25733i	0.0216785	−	0.108985i
$430$	−7.37244	−	5.56714i	−0.355531	−	0.268471i
$431$	6.82858	+	6.82858i	0.328921	+	0.328921i	0.852176	−	0.523255i	$-0.175282\pi$
$431$	6.82858	+	6.82858i	0.328921	+	0.328921i	−0.523255	+	0.852176i	$0.675282\pi$
$432$	1.44776	−	1.35100i	0.0696552	−	0.0650000i
$433$	−4.84377	+	4.84377i	−0.232777	+	0.232777i	−0.813851	−	0.581074i	$-0.802633\pi$
$433$	−4.84377	+	4.84377i	−0.232777	+	0.232777i	0.581074	+	0.813851i	$0.302633\pi$
$434$	−9.64837	+	1.34612i	−0.463136	+	0.0646157i
$435$	2.26282	+	0.450102i	0.108494	+	0.0215807i
$436$	17.1877	−	20.2205i	0.823142	−	0.968386i
$437$	−28.6124	+	42.8214i	−1.36872	+	2.04843i
$438$	−0.150296	+	2.60069i	−0.00718144	+	0.124266i
$439$	−11.2574	+	27.1777i	−0.537286	+	1.29712i	0.389325	+	0.921101i	$0.372708\pi$
$439$	−11.2574	+	27.1777i	−0.537286	+	1.29712i	−0.926611	+	0.376022i	$0.877292\pi$
$440$	1.04278	−	0.460518i	0.0497125	−	0.0219543i
$441$	13.4062	+	32.3653i	0.638389	+	1.54121i
$442$	3.66226	+	10.5210i	0.174196	+	0.500434i
$443$	31.0716	−	6.18053i	1.47626	−	0.293646i	0.609663	−	0.792661i	$-0.291305\pi$
$443$	31.0716	−	6.18053i	1.47626	−	0.293646i	0.866593	+	0.499015i	$0.166305\pi$
$444$	−2.50980	−	8.81949i	−0.119110	−	0.418554i
$445$	8.59364	−	5.74209i	0.407378	−	0.272201i
$446$	3.45172	−	13.2918i	0.163444	−	0.629384i
$447$	14.1266			0.668166
$448$	32.0068	−	15.0306i	1.51218	−	0.710127i
$449$	15.3871			0.726163			0.363082	−	0.931757i	$-0.381725\pi$
$449$	15.3871			0.726163			0.363082	+	0.931757i	$0.381725\pi$
$450$	−4.37495	+	16.8469i	−0.206237	+	0.794172i
$451$	2.89251	−	1.93271i	0.136203	−	0.0910079i
$452$	−1.03528	+	0.294613i	−0.0486953	+	0.0138574i
$453$	27.6227	−	5.49450i	1.29783	−	0.258154i
$454$	1.77613	+	5.10251i	0.0833581	+	0.239473i
$455$	2.38958	+	5.76896i	0.112025	+	0.270453i
$456$	15.9797	−	41.2569i	0.748319	−	1.93203i
$457$	3.24557	−	7.83549i	0.151821	−	0.366529i	−0.829610	−	0.558343i	$-0.811437\pi$
$457$	3.24557	−	7.83549i	0.151821	−	0.366529i	0.981431	+	0.191814i	$0.0614372\pi$
$458$	0.737838	−	12.7674i	0.0344769	−	0.596579i
$459$	−1.18344	+	1.77115i	−0.0552384	+	0.0826701i
$460$	9.31960	+	7.92179i	0.434529	+	0.369355i
$461$	−24.4880	−	4.87097i	−1.14052	−	0.226864i	−0.411536	−	0.911394i	$-0.635007\pi$
$461$	−24.4880	−	4.87097i	−1.14052	−	0.226864i	−0.728985	+	0.684530i	$0.760007\pi$
$462$	7.78319	−	1.08589i	0.362107	−	0.0505202i
$463$	−19.0846	+	19.0846i	−0.886939	+	0.886939i	−0.994228	−	0.107289i	$-0.965783\pi$
$463$	−19.0846	+	19.0846i	−0.886939	+	0.886939i	0.107289	+	0.994228i	$0.465783\pi$
$464$	2.05869	−	4.52156i	0.0955722	−	0.209908i
$465$	2.04702	+	2.04702i	0.0949284	+	0.0949284i
$466$	−3.11124	−	2.34938i	−0.144125	−	0.108833i
$467$	0.264167	−	1.32806i	0.0122242	−	0.0614552i	−0.974192	−	0.225722i	$-0.927526\pi$
$467$	0.264167	−	1.32806i	0.0122242	−	0.0614552i	0.986416	+	0.164267i	$0.0525259\pi$
$468$	−9.10514	+	4.66635i	−0.420885	+	0.215702i
$469$	−13.4931	−	9.01581i	−0.623054	−	0.416311i
$470$	1.15501	+	1.29670i	0.0532766	+	0.0598121i
$471$	−32.7748	−	13.5758i	−1.51018	−	0.625538i
$472$	1.79866	+	1.14245i	0.0827900	+	0.0525858i
$473$	−4.08465	+	1.69192i	−0.187813	+	0.0777945i
$474$	−12.9498	+	26.7789i	−0.594802	+	1.23000i
$475$	−5.58387	−	28.0720i	−0.256206	−	1.28803i
$476$	−29.8161	+	23.6193i	−1.36662	+	1.08259i
$477$	−10.9807	−	16.4338i	−0.502772	−	0.752451i
$478$	−8.84762	−	15.0548i	−0.404681	−	0.688591i
$479$		−	3.51984i		−	0.160826i	−0.996762	−	0.0804128i	$-0.974376\pi$
$479$		−	3.51984i		−	0.160826i	0.996762	−	0.0804128i	$-0.0256239\pi$
$480$	−9.29612	−	4.89870i	−0.424308	−	0.223594i
$481$		−	3.48690i		−	0.158989i
$482$	27.8251	−	16.3527i	1.26740	−	0.744844i
$483$	46.8468	+	70.1112i	2.13160	+	3.19017i
$484$	−2.47149	+	21.3116i	−0.112341	+	0.968710i
$485$	0.518062	+	2.60448i	0.0235240	+	0.118263i
$486$	−27.4525	−	13.2755i	−1.24527	−	0.602189i
$487$	25.4932	−	10.5596i	1.15521	−	0.478503i	0.278932	−	0.960311i	$-0.410020\pi$
$487$	25.4932	−	10.5596i	1.15521	−	0.478503i	0.876277	+	0.481808i	$0.160020\pi$
$488$	−11.2237	−	1.96339i	−0.508073	−	0.0888785i
$489$	10.2112	+	4.22960i	0.461764	+	0.191269i
$490$	−10.2164	+	9.10009i	−0.461530	+	0.411100i
$491$	18.5780	+	12.4134i	0.838412	+	0.560209i	0.898997	−	0.437954i	$-0.144297\pi$
$491$	18.5780	+	12.4134i	0.838412	+	0.560209i	−0.0605855	+	0.998163i	$0.519297\pi$
$492$	−30.5209	−	9.83741i	−1.37599	−	0.443505i
$493$	−1.04263	+	5.24166i	−0.0469578	+	0.236073i
$494$	10.1386	−	13.4263i	0.456156	−	0.604077i
$495$	−0.796346	−	0.796346i	−0.0357931	−	0.0357931i
$496$	5.29985	−	3.28221i	0.237970	−	0.147375i
$497$	−2.59303	+	2.59303i	−0.116313	+	0.116313i
$498$	−1.59872	−	11.4589i	−0.0716404	−	0.513487i
$499$	−7.61559	−	1.51483i	−0.340921	−	0.0678133i	0.0216610	−	0.999765i	$-0.493105\pi$
$499$	−7.61559	−	1.51483i	−0.340921	−	0.0678133i	−0.362582	+	0.931952i	$0.618105\pi$
$500$	−14.4671	+	1.17289i	−0.646987	+	0.0524531i
$501$	9.61886	−	14.3956i	0.429739	−	0.643150i
$502$	33.5076	+	1.93644i	1.49552	+	0.0864274i
$503$	16.2329	−	39.1897i	0.723789	−	1.74738i	0.0615295	−	0.998105i	$-0.480402\pi$
$503$	16.2329	−	39.1897i	0.723789	−	1.74738i	0.662259	−	0.749275i	$-0.269598\pi$
$504$	−25.2679	−	24.1233i	−1.12552	−	1.07454i
$505$	−1.48059	−	3.57445i	−0.0658852	−	0.159061i
$506$	5.52832	−	1.92435i	0.245764	−	0.0855479i
$507$	22.7791	−	4.53104i	1.01165	−	0.201231i
$508$	−18.4042	−	10.2499i	−0.816553	−	0.454768i
$509$	−27.0838	+	18.0968i	−1.20047	+	0.802126i	−0.984690	−	0.174316i	$-0.944229\pi$
$509$	−27.0838	+	18.0968i	−1.20047	+	0.802126i	−0.215777	+	0.976443i	$0.569229\pi$
$510$	10.9406	+	2.84115i	0.484458	+	0.125808i
$511$	−3.38237			−0.149627
$512$	−14.8501	+	17.0726i	−0.656290	+	0.754509i
$513$	3.21700			0.142034
$514$	1.28430	+	0.333518i	0.0566481	+	0.0147109i
$515$	−1.31003	+	0.875337i	−0.0577270	+	0.0385719i
$516$	35.6046	+	19.8295i	1.56741	+	0.872945i
$517$	0.815078	−	0.162129i	0.0358471	−	0.00713043i
$518$	11.2442	−	3.91398i	0.494040	−	0.171970i
$519$	15.0870	+	36.4233i	0.662246	+	1.59880i
$520$	−2.89014	−	2.75922i	−0.126741	−	0.121000i
$521$	−9.90054	+	23.9020i	−0.433750	+	1.04717i	0.544318	+	0.838879i	$0.316789\pi$
$521$	−9.90054	+	23.9020i	−0.433750	+	1.04717i	−0.978068	+	0.208287i	$0.933211\pi$
$522$	−4.90012	−	0.283183i	−0.214472	−	0.0123946i
$523$	11.2609	−	16.8531i	0.492404	−	0.736935i	−0.499166	−	0.866507i	$-0.666360\pi$
$523$	11.2609	−	16.8531i	0.492404	−	0.736935i	0.991570	+	0.129571i	$0.0413601\pi$
$524$	−31.3134	+	2.53867i	−1.36793	+	0.110902i
$525$	−45.9621	−	9.14243i	−2.00595	−	0.399008i
$526$	2.14166	+	15.3505i	0.0933810	+	0.669313i
$527$	−4.74179	+	4.74179i	−0.206556	+	0.206556i
$528$	−4.27531	+	2.64770i	−0.186059	+	0.115227i
$529$	28.1496	+	28.1496i	1.22390	+	1.22390i
$530$	4.65162	−	6.16004i	0.202054	−	0.267575i
$531$	0.410692	−	2.06469i	0.0178225	−	0.0895998i
$532$	54.6759	+	17.6230i	2.37050	+	0.764052i
$533$	−10.1390	−	6.77464i	−0.439167	−	0.293442i
$534$	−34.0464	+	30.3263i	−1.47333	+	1.31235i
$535$	3.04144	+	1.25981i	0.131493	+	0.0544662i
$536$	10.2291	+	1.78941i	0.441831	+	0.0772908i
$537$	22.2389	−	9.21165i	0.959678	−	0.397512i
$538$	29.9345	+	14.4757i	1.29057	+	0.624093i
$539$	1.27738	+	6.42184i	0.0550208	+	0.276608i
$540$	0.0880154	−	0.758954i	0.00378758	−	0.0326602i
$541$	−22.9671	−	34.3728i	−0.987435	−	1.47780i	−0.874989	−	0.484142i	$-0.839132\pi$
$541$	−22.9671	−	34.3728i	−0.987435	−	1.47780i	−0.112445	−	0.993658i	$-0.535868\pi$
$542$	−3.78776	+	2.22605i	−0.162698	+	0.0956168i
$543$			12.0813i			0.518459i
$544$	11.3475	−	21.5338i	0.486520	−	0.923256i
$545$		−	10.2396i		−	0.438615i
$546$	−13.9569	−	23.7487i	−0.597302	−	1.01635i
$547$	−7.05928	−	10.5650i	−0.301833	−	0.451725i	0.649288	−	0.760542i	$-0.275067\pi$
$547$	−7.05928	−	10.5650i	−0.301833	−	0.451725i	−0.951121	+	0.308817i	$0.900067\pi$
$548$	−24.2502	+	19.2102i	−1.03592	+	0.820617i
$549$	2.19610	+	11.0405i	0.0937271	+	0.471198i
$550$	−1.41628	+	2.92875i	−0.0603906	+	0.124882i
$551$	7.45682	−	3.08872i	0.317671	−	0.131584i
$552$	−45.5473	−	28.9303i	−1.93862	−	1.23136i
$553$	−35.6820	−	14.7800i	−1.51735	−	0.628508i
$554$	−8.10640	−	9.10083i	−0.344408	−	0.386657i
$555$	−2.94175	−	1.96562i	−0.124870	−	0.0834358i
$556$	23.5636	−	12.0763i	0.999318	−	0.512147i
$557$	3.09194	−	15.5442i	0.131010	−	0.658630i	−0.858341	−	0.513079i	$-0.828505\pi$
$557$	3.09194	−	15.5442i	0.131010	−	0.658630i	0.989351	−	0.145551i	$-0.0464954\pi$
$558$	−4.91488	−	3.71137i	−0.208063	−	0.157115i
$559$	10.9583	+	10.9583i	0.463487	+	0.463487i
$560$	5.65350	−	12.4170i	0.238904	−	0.524712i
$561$	3.82513	−	3.82513i	0.161497	−	0.161497i
$562$	3.20591	−	0.447280i	0.135233	−	0.0188674i
$563$	−4.98076	−	0.990736i	−0.209914	−	0.0417545i	0.0890130	−	0.996030i	$-0.471629\pi$
$563$	−4.98076	−	0.990736i	−0.209914	−	0.0417545i	−0.298927	+	0.954276i	$0.596629\pi$
$564$	−5.83680	−	4.96136i	−0.245773	−	0.208911i
$565$	−0.230734	+	0.345317i	−0.00970704	+	0.0145276i
$566$	−1.94625	+	33.6774i	−0.0818070	+	1.41557i
$567$	16.1953	−	39.0990i	0.680141	−	1.64200i
$568$	0.847544	−	2.18821i	0.0355621	−	0.0918153i
$569$	10.4799	+	25.3007i	0.439340	+	1.06066i	0.976177	+	0.216975i	$0.0696189\pi$
$569$	10.4799	+	25.3007i	0.439340	+	1.06066i	−0.536837	+	0.843686i	$0.680381\pi$
$570$	−5.61194	−	16.1221i	−0.235058	−	0.675280i
$571$	−26.9468	+	5.36006i	−1.12769	+	0.224311i	−0.723474	−	0.690352i	$-0.757456\pi$
$571$	−26.9468	+	5.36006i	−1.12769	+	0.224311i	−0.404216	+	0.914664i	$0.632456\pi$
$572$	−1.83925	+	0.523403i	−0.0769028	+	0.0218846i
$573$	−41.2243	+	27.5452i	−1.72217	+	1.15072i
$574$	10.4653	−	40.2994i	0.436812	−	1.68206i
$575$	−34.9068			−1.45572
$576$	21.0272	+	7.58891i	0.876133	+	0.316205i
$577$	−42.3036			−1.76112			−0.880560	−	0.473935i	$-0.842833\pi$
$577$	−42.3036			−1.76112			−0.880560	+	0.473935i	$0.842833\pi$
$578$	−0.538440	+	2.07341i	−0.0223962	+	0.0862424i
$579$	31.7001	−	21.1813i	1.31741	−	0.880267i
$580$	−0.524674	−	1.84372i	−0.0217859	−	0.0765561i
$581$	14.7337	−	2.93073i	0.611259	−	0.121587i
$582$	−3.85108	−	11.0635i	−0.159633	−	0.458596i
$583$	−1.41368	−	3.41293i	−0.0585487	−	0.141349i
$584$	1.97993	−	0.874389i	0.0819302	−	0.0361825i
$585$	−1.51069	+	3.64713i	−0.0624593	+	0.150790i
$586$	−2.22012	+	38.4164i	−0.0917124	+	1.58697i
$587$	−0.763948	+	1.14333i	−0.0315315	+	0.0471902i	−0.846901	−	0.531751i	$-0.821534\pi$
$587$	−0.763948	+	1.14333i	−0.0315315	+	0.0471902i	0.815369	+	0.578942i	$0.196534\pi$
$588$	39.0896	−	45.9870i	1.61203	−	1.89647i
$589$	9.93287	+	1.97577i	0.409277	+	0.0814102i
$590$	0.814267	−	0.113605i	0.0335228	−	0.00467703i
$591$	44.4235	−	44.4235i	1.82734	−	1.82734i
$592$	−5.57015	+	5.19788i	−0.228932	+	0.213632i
$593$	5.66121	+	5.66121i	0.232478	+	0.232478i	0.813726	−	0.581248i	$-0.197436\pi$
$593$	5.66121	+	5.66121i	0.232478	+	0.232478i	−0.581248	+	0.813726i	$0.697436\pi$
$594$	−0.291800	−	0.220346i	−0.0119727	−	0.00904092i
$595$	−2.86324	+	14.3945i	−0.117381	+	0.590116i
$596$	−5.35322	−	10.4454i	−0.219277	−	0.427859i
$597$	29.3462	+	19.6085i	1.20106	+	0.802522i
$598$	−13.6476	−	15.3217i	−0.558090	−	0.626552i
$599$	12.4047	+	5.13818i	0.506841	+	0.209941i	0.621426	−	0.783473i	$-0.286554\pi$
$599$	12.4047	+	5.13818i	0.506841	+	0.209941i	−0.114585	+	0.993413i	$0.536554\pi$
$600$	29.2682	−	6.53014i	1.19487	−	0.266592i
$601$	−6.28652	+	2.60396i	−0.256433	+	0.106218i	−0.507197	−	0.861830i	$-0.669318\pi$
$601$	−6.28652	+	2.60396i	−0.256433	+	0.106218i	0.250764	+	0.968048i	$0.419318\pi$
$602$	−23.0366	+	47.6376i	−0.938901	+	1.94156i
$603$	−2.00150	−	10.0622i	−0.0815072	−	0.409764i
$604$	−14.5302	−	18.3424i	−0.591226	−	0.746343i
$605$	4.59900	+	6.88289i	0.186976	+	0.279829i
$606$	8.64773	+	14.7147i	0.351290	+	0.597743i
$607$			31.2974i			1.27032i	0.772379	+	0.635161i	$0.219066\pi$
$607$			31.2974i			1.27032i	−0.772379	+	0.635161i	$0.780934\pi$
$608$	−36.5613	+	3.81855i	−1.48276	+	0.154863i
$609$		−	13.2149i		−	0.535496i
$610$	−3.79023	+	2.22749i	−0.153462	+	0.0901885i
$611$	−1.61839	−	2.42209i	−0.0654730	−	0.0979873i
$612$	−23.8873	−	2.77020i	−0.965588	−	0.111979i
$613$	4.01591	+	20.1894i	0.162201	+	0.815441i	0.973123	+	0.230286i	$0.0739662\pi$
$613$	4.01591	+	20.1894i	0.162201	+	0.815441i	−0.810922	+	0.585155i	$0.801034\pi$
$614$	41.6820	+	20.1566i	1.68215	+	0.813455i
$615$	−11.4310	+	4.73486i	−0.460941	+	0.190928i
$616$	−3.75233	−	5.34348i	−0.151186	−	0.215295i
$617$	0.720564	+	0.298468i	0.0290088	+	0.0120159i	0.397141	−	0.917758i	$-0.370002\pi$
$617$	0.720564	+	0.298468i	0.0290088	+	0.0120159i	−0.368132	+	0.929774i	$0.620002\pi$
$618$	5.19012	−	4.62301i	0.208777	−	0.185965i
$619$	−12.1862	−	8.14255i	−0.489804	−	0.327277i	0.286022	−	0.958223i	$-0.407667\pi$
$619$	−12.1862	−	8.14255i	−0.489804	−	0.327277i	−0.775826	+	0.630946i	$0.782667\pi$
$620$	0.737880	−	2.28930i	0.0296340	−	0.0919406i
$621$	0.765417	−	3.84801i	0.0307151	−	0.154415i
$622$	−9.54779	+	12.6439i	−0.382831	+	0.506975i
$623$	−41.8606	−	41.8606i	−1.67711	−	1.67711i
$624$	14.3093	+	10.2936i	0.572830	+	0.412075i
$625$	11.6123	−	11.6123i	0.464492	−	0.464492i
$626$	1.93151	+	13.8442i	0.0771986	+	0.553325i
$627$	−8.01269	−	1.59382i	−0.319996	−	0.0636512i
$628$	2.38180	+	29.3785i	0.0950442	+	1.17233i
$629$	4.55322	−	6.81438i	0.181549	−	0.271707i
$630$	−13.4565	−	0.777667i	−0.536122	−	0.0309830i
$631$	−14.7859	+	35.6964i	−0.588619	+	1.42105i	0.296204	+	0.955125i	$0.404279\pi$
$631$	−14.7859	+	35.6964i	−0.588619	+	1.42105i	−0.884823	+	0.465927i	$0.845721\pi$
$632$	24.7079	−	0.572565i	0.982827	−	0.0227754i
$633$	−17.5452	−	42.3580i	−0.697361	−	1.68358i
$634$	23.7865	−	8.27986i	0.944684	−	0.328835i
$635$	−7.97191	+	1.58571i	−0.316355	+	0.0629270i
$636$	−16.5685	+	29.7494i	−0.656984	+	1.17964i
$637$	19.0832	−	12.7510i	0.756103	−	0.505212i
$638$	−0.887933	−	0.230586i	−0.0351536	−	0.00912899i
$639$	−2.31834			−0.0917119
$640$	−0.0994244	+	8.72999i	−0.00393010	+	0.345083i
$641$	−39.2736			−1.55121			−0.775607	−	0.631216i	$-0.782556\pi$
$641$	−39.2736			−1.55121			−0.775607	+	0.631216i	$0.782556\pi$
$642$	−14.0564	−	3.65027i	−0.554760	−	0.144065i
$643$	−20.6027	+	13.7663i	−0.812489	+	0.542888i	−0.890988	−	0.454026i	$-0.849987\pi$
$643$	−20.6027	+	13.7663i	−0.812489	+	0.542888i	0.0784990	+	0.996914i	$0.474987\pi$
$644$	34.0886	−	61.2074i	1.34328	−	2.41191i
$645$	15.4224	−	3.06771i	0.607257	−	0.120791i
$646$	37.3457	−	12.9997i	1.46935	−	0.511465i
$647$	15.7086	+	37.9240i	0.617570	+	1.49095i	0.854517	+	0.519423i	$0.173853\pi$
$647$	15.7086	+	37.9240i	0.617570	+	1.49095i	−0.236948	+	0.971522i	$0.576147\pi$
$648$	0.627396	+	27.0740i	0.0246464	+	1.06357i
$649$	0.150571	−	0.363510i	0.00591042	−	0.0142690i
$650$	11.3843	+	0.657912i	0.446530	+	0.0258054i
$651$	9.21225	−	13.7871i	0.361057	−	0.540360i
$652$	−0.742063	−	9.15303i	−0.0290614	−	0.358460i
$653$	45.4088	+	9.03238i	1.77698	+	0.353464i	0.971112	−	0.238624i	$-0.0766965\pi$
$653$	45.4088	+	9.03238i	1.77698	+	0.353464i	0.805873	+	0.592089i	$0.201696\pi$
$654$	6.24172	+	44.7379i	0.244071	+	1.74939i
$655$	−8.57125	+	8.57125i	−0.334907	+	0.334907i
$656$	4.29189	+	26.2954i	0.167570	+	1.02666i
$657$	−1.51203	−	1.51203i	−0.0589898	−	0.0589898i
$658$	5.99387	−	7.93755i	0.233665	−	0.309438i
$659$	7.92659	−	39.8497i	0.308776	−	1.55232i	−0.445206	−	0.895428i	$-0.646870\pi$
$659$	7.92659	−	39.8497i	0.308776	−	1.55232i	0.753983	−	0.656894i	$-0.228130\pi$
$660$	−0.595237	+	1.84674i	−0.0231696	+	0.0718844i
$661$	−29.3540	−	19.6137i	−1.14174	−	0.762886i	−0.166940	−	0.985967i	$-0.553389\pi$
$661$	−29.3540	−	19.6137i	−1.14174	−	0.762886i	−0.974800	+	0.223081i	$0.928389\pi$
$662$	−18.4237	+	16.4106i	−0.716056	+	0.637815i
$663$	−17.5184	−	7.25637i	−0.680360	−	0.281814i
$664$	−7.86703	+	5.52442i	−0.305300	+	0.214389i
$665$	20.4777	−	8.48213i	0.794090	−	0.328923i
$666$	6.77617	+	3.27682i	0.262571	+	0.126974i
$667$	−1.92037	−	9.65435i	−0.0743570	−	0.373818i
$668$	−14.2893	−	1.65712i	−0.552871	−	0.0641160i
$669$	12.9861	+	19.4351i	0.502073	+	0.751406i
$670$	3.45437	−	2.03011i	0.133454	−	0.0784300i
$671$			2.10396i			0.0812223i
$672$	−17.1318	+	57.6974i	−0.660874	+	2.22572i
$673$			24.2851i			0.936122i	0.883696	+	0.468061i	$0.155047\pi$
$673$			24.2851i			0.936122i	−0.883696	+	0.468061i	$0.844953\pi$
$674$	8.74203	+	14.8751i	0.336731	+	0.572969i
$675$	1.21140	+	1.81298i	0.0466266	+	0.0697817i
$676$	−11.9823	−	15.1261i	−0.460859	−	0.581772i
$677$	−4.33107	−	21.7738i	−0.166456	−	0.836833i	−0.970284	−	0.241970i	$-0.922206\pi$
$677$	−4.33107	−	21.7738i	−0.166456	−	0.836833i	0.803827	−	0.594863i	$-0.202794\pi$
$678$	0.797608	−	1.64938i	0.0306320	−	0.0633441i
$679$	14.0524	−	5.82070i	0.539282	−	0.223378i
$680$	−2.04512	−	9.16625i	−0.0784268	−	0.351510i
$681$	−8.49614	−	3.51922i	−0.325573	−	0.134857i
$682$	−0.765636	−	0.859557i	−0.0293177	−	0.0329142i
$683$	−12.0613	−	8.05912i	−0.461514	−	0.308374i	0.302989	−	0.952994i	$-0.402015\pi$
$683$	−12.0613	−	8.05912i	−0.461514	−	0.308374i	−0.764503	+	0.644620i	$0.777015\pi$
$684$	16.5638	+	32.3199i	0.633334	+	1.23578i
$685$	−2.32875	+	11.7074i	−0.0889768	+	0.447317i
$686$	27.6196	+	20.8563i	1.05452	+	0.796298i
$687$	15.3921	+	15.3921i	0.587244	+	0.587244i
$688$	1.16992	−	33.8408i	0.0446028	−	1.29017i
$689$	−9.15621	+	9.15621i	−0.348824	+	0.348824i
$690$	−20.6196	+	2.87680i	−0.784976	+	0.109518i
$691$	3.89100	+	0.773968i	0.148021	+	0.0294431i	0.268544	−	0.963267i	$-0.413457\pi$
$691$	3.89100	+	0.773968i	0.148021	+	0.0294431i	−0.120524	+	0.992710i	$0.538457\pi$
$692$	21.2146	−	24.9579i	0.806458	−	0.948759i
$693$	−3.58381	+	5.36355i	−0.136138	+	0.203744i
$694$	1.03019	−	17.8261i	0.0391055	−	0.676671i
$695$	3.90958	−	9.43855i	0.148299	−	0.358025i
$696$	3.41624	+	7.73559i	0.129492	+	0.293217i
$697$	−10.9680	−	26.4791i	−0.415442	−	1.00297i
$698$	−7.93391	−	22.7927i	−0.300303	−	0.862716i
$699$	6.50840	−	1.29460i	0.246170	−	0.0489663i
$700$	10.6571	+	37.4494i	0.402802	+	1.41545i
$701$	32.0550	−	21.4185i	1.21070	−	0.808965i	0.224494	−	0.974476i	$-0.427927\pi$
$701$	32.0550	−	21.4185i	1.21070	−	0.808965i	0.986208	+	0.165511i	$0.0529272\pi$
$702$	−0.322155	+	1.24054i	−0.0121590	+	0.0468213i
$703$	−12.3772			−0.466815
$704$	3.57785	+	2.15787i	0.134845	+	0.0813279i
$705$	−2.95573			−0.111319
$706$	−8.51211	+	32.7781i	−0.320357	+	1.23362i
$707$	−18.4259	+	12.3118i	−0.692979	+	0.463034i
$708$	−3.48838	+	0.992704i	−0.131101	+	0.0373081i
$709$	14.3830	−	2.86095i	0.540164	−	0.107445i	0.0825345	−	0.996588i	$-0.473699\pi$
$709$	14.3830	−	2.86095i	0.540164	−	0.107445i	0.457630	+	0.889143i	$0.348699\pi$
$710$	−0.297650	−	0.855094i	−0.0111706	−	0.0320911i
$711$	−9.34386	−	22.5581i	−0.350422	−	0.845994i
$712$	35.3253	+	13.6823i	1.32387	+	0.512766i
$713$	4.72663	−	11.4111i	0.177014	−	0.427348i
$714$	3.73541	−	64.6366i	0.139794	−	2.41896i
$715$	−0.409916	+	0.613483i	−0.0153300	+	0.0229430i
$716$	−15.2385	−	12.9530i	−0.569490	−	0.484075i
$717$	29.1514	+	5.79857i	1.08868	+	0.216552i
$718$	−34.9436	+	4.87525i	−1.30408	+	0.181943i
$719$	16.4835	−	16.4835i	0.614730	−	0.614730i	−0.329445	−	0.944175i	$-0.606862\pi$
$719$	16.4835	−	16.4835i	0.614730	−	0.614730i	0.944175	+	0.329445i	$0.106862\pi$
$720$	8.07806	−	3.02348i	0.301052	−	0.112678i
$721$	6.38132	+	6.38132i	0.237653	+	0.237653i
$722$	−26.2152	−	19.7959i	−0.975629	−	0.736725i
$723$	−10.7173	+	53.8793i	−0.398579	+	2.00379i
$724$	8.93306	−	4.57816i	0.331994	−	0.170146i
$725$	4.54863	+	3.03930i	0.168932	+	0.112877i
$726$	−24.2892	−	27.2688i	−0.901456	−	1.01204i
$727$	−1.94412	−	0.805280i	−0.0721034	−	0.0298662i	0.346340	−	0.938109i	$-0.387424\pi$
$727$	−1.94412	−	0.805280i	−0.0721034	−	0.0298662i	−0.418444	+	0.908243i	$0.637424\pi$
$728$	−12.2711	+	19.3194i	−0.454797	+	0.716024i
$729$	21.4155	−	8.87058i	0.793166	−	0.328540i
$730$	0.363567	−	0.751824i	0.0134562	−	0.0278262i
$731$	7.10614	+	35.7250i	0.262830	+	1.32134i
$732$	15.2021	−	12.0426i	0.561887	−	0.445107i
$733$	0.341596	+	0.511235i	0.0126171	+	0.0188829i	0.837725	−	0.546093i	$-0.183885\pi$
$733$	0.341596	+	0.511235i	0.0126171	+	0.0188829i	−0.825107	+	0.564976i	$0.808885\pi$
$734$	−23.9811	−	40.8054i	−0.885159	−	1.50616i
$735$		−	23.2876i		−	0.858975i
$736$	−4.13142	+	44.6412i	−0.152286	+	1.64550i
$737$		−	1.91752i		−	0.0706327i
$738$	22.6934	−	13.3368i	0.835355	−	0.490933i
$739$	5.04853	+	7.55566i	0.185713	+	0.277939i	0.912630	−	0.408786i	$-0.134048\pi$
$739$	5.04853	+	7.55566i	0.185713	+	0.277939i	−0.726917	+	0.686725i	$0.759048\pi$
$740$	−0.338633	+	2.92003i	−0.0124484	+	0.107342i
$741$	5.58675	+	28.0865i	0.205234	+	1.03178i
$742$	−39.8035	−	19.2482i	−1.46123	−	0.706624i
$743$	38.3032	−	15.8657i	1.40521	−	0.582056i	0.454109	−	0.890946i	$-0.349958\pi$
$743$	38.3032	−	15.8657i	1.40521	−	0.582056i	0.951098	+	0.308890i	$0.0999576\pi$
$744$	−1.82840	+	10.4520i	−0.0670324	+	0.383190i
$745$	−4.18397	−	1.73306i	−0.153289	−	0.0634943i
$746$	19.0287	−	16.9495i	0.696689	−	0.620564i
$747$	7.89658	+	5.27632i	0.288921	+	0.193051i
$748$	−4.27786	−	1.37883i	−0.156414	−	0.0504149i
$749$	3.67865	−	18.4938i	0.134415	−	0.675750i
$750$	14.8878	−	19.7156i	0.543626	−	0.719912i
$751$	24.7263	+	24.7263i	0.902275	+	0.902275i	0.995633	−	0.0933574i	$-0.0297599\pi$
$751$	24.7263	+	24.7263i	0.902275	+	0.902275i	−0.0933574	+	0.995633i	$0.529760\pi$
$752$	−1.45665	+	6.19588i	−0.0531187	+	0.225940i
$753$	−40.3961	+	40.3961i	−1.47212	+	1.47212i
$754$	0.444338	+	3.18482i	0.0161818	+	0.115984i
$755$	−8.85527	−	1.76142i	−0.322276	−	0.0641047i
$756$	−4.36197	+	0.353638i	−0.158643	+	0.0128617i
$757$	−15.3171	+	22.9237i	−0.556710	+	0.833175i	−0.997936	−	0.0642212i	$-0.979544\pi$
$757$	−15.3171	+	22.9237i	−0.556710	+	0.833175i	0.441226	+	0.897396i	$0.354544\pi$
$758$	−0.542148	−	0.0313312i	−0.0196917	−	0.00113800i
$759$	−3.81290	+	9.20514i	−0.138399	+	0.334126i
$760$	−9.79422	+	10.2589i	−0.355274	+	0.372130i
$761$	2.39831	+	5.79004i	0.0869388	+	0.209889i	0.961369	−	0.275262i	$-0.0887646\pi$
$761$	2.39831	+	5.79004i	0.0869388	+	0.209889i	−0.874430	+	0.485151i	$0.838765\pi$
$762$	33.8636	−	11.7876i	1.22675	−	0.427019i
$763$	−57.5234	+	11.4421i	−2.08249	+	0.414232i
$764$	35.9890	+	20.0436i	1.30204	+	0.725152i
$765$	−7.71475	+	5.15483i	−0.278927	+	0.186373i
$766$	24.2639	+	6.30105i	0.876690	+	0.227666i
$767$	−1.37918			−0.0497992
$768$	−4.88713	−	38.2030i	−0.176349	−	1.37853i
$769$	13.9845			0.504295			0.252147	−	0.967689i	$-0.418863\pi$
$769$	13.9845			0.504295			0.252147	+	0.967689i	$0.418863\pi$
$770$	−2.43841	−	0.633228i	−0.0878743	−	0.0228200i
$771$	−1.87790	+	1.25477i	−0.0676307	+	0.0451894i
$772$	−27.6744	−	15.4128i	−0.996022	−	0.554720i
$773$	−37.5256	+	7.46432i	−1.34970	+	0.268473i	−0.816418	−	0.577462i	$-0.804043\pi$
$773$	−37.5256	+	7.46432i	−1.34970	+	0.268473i	−0.533286	+	0.845935i	$0.679043\pi$
$774$	−31.5936	+	10.9974i	−1.13561	+	0.395294i
$775$	2.62685	+	6.34179i	0.0943594	+	0.227804i
$776$	−6.72110	+	7.03999i	−0.241273	+	0.252721i
$777$	−7.75513	+	18.7225i	−0.278214	+	0.671667i
$778$	10.9208	+	0.631125i	0.391531	+	0.0226269i
$779$	−24.0475	+	35.9896i	−0.861590	+	1.28946i
$780$	6.77900	−	0.549593i	0.242727	−	0.0196786i
$781$	−0.424983	−	0.0845343i	−0.0152071	−	0.00302488i
$782$	−6.66392	−	47.7640i	−0.238301	−	1.70804i
$783$	−0.434781	+	0.434781i	−0.0155378	+	0.0155378i
$784$	−48.8161	−	11.4767i	−1.74343	−	0.409882i
$785$	8.04164	+	8.04164i	0.287018	+	0.287018i
$786$	32.2241	−	42.6736i	1.14939	−	1.52212i
$787$	9.74437	−	48.9883i	0.347349	−	1.74624i	−0.273090	−	0.961989i	$-0.588046\pi$
$787$	9.74437	−	48.9883i	0.347349	−	1.74624i	0.620439	−	0.784255i	$-0.286954\pi$
$788$	−49.6814	−	16.0131i	−1.76983	−	0.570444i
$789$	−21.9352	−	14.6566i	−0.780914	−	0.521790i
$790$	7.12066	−	6.34260i	0.253342	−	0.225660i
$791$	2.19774	+	0.910335i	0.0781427	+	0.0323678i
$792$	0.711296	−	4.06611i	0.0252748	−	0.144483i
$793$	6.81351	−	2.82225i	0.241955	−	0.100221i
$794$	−10.6547	−	5.15240i	−0.378121	−	0.182852i
$795$	2.56322	+	12.8862i	0.0909081	+	0.457026i
$796$	3.37812	−	29.1295i	0.119734	−	1.03247i
$797$	24.7495	+	37.0403i	0.876674	+	1.31203i	0.949202	+	0.314668i	$0.101893\pi$
$797$	24.7495	+	37.0403i	0.876674	+	1.31203i	−0.0725281	+	0.997366i	$0.523107\pi$
$798$	−84.2990	+	49.5420i	−2.98415	+	1.75377i
$799$		−	6.84674i		−	0.242220i
$800$	−15.9195	−	19.1666i	−0.562840	−	0.677643i
$801$		−	37.4260i		−	1.32238i
$802$	−18.8475	−	32.0702i	−0.665528	−	1.13244i
$803$	−0.222042	−	0.332309i	−0.00783568	−	0.0117269i
$804$	−13.8550	+	10.9755i	−0.488630	+	0.387075i
$805$	−5.27366	−	26.5125i	−0.185872	−	0.934442i
$806$	−1.75659	+	3.63247i	−0.0618732	+	0.127948i
$807$	−52.2884	+	21.6586i	−1.84064	+	0.762417i
$808$	7.60318	−	11.9703i	0.267479	−	0.421114i
$809$	5.38797	+	2.23177i	0.189431	+	0.0784649i	0.475383	−	0.879779i	$-0.342310\pi$
$809$	5.38797	+	2.23177i	0.189431	+	0.0784649i	−0.285952	+	0.958244i	$0.592310\pi$
$810$	6.95000	+	7.80256i	0.244198	+	0.274154i
$811$	8.53124	+	5.70039i	0.299572	+	0.200168i	0.696267	−	0.717783i	$-0.254843\pi$
$811$	8.53124	+	5.70039i	0.299572	+	0.200168i	−0.396695	+	0.917951i	$0.629843\pi$
$812$	−9.77126	+	5.00774i	−0.342904	+	0.175737i
$813$	1.45891	−	7.33444i	0.0511662	−	0.257230i
$814$	1.12268	+	0.847768i	0.0393499	+	0.0297143i
$815$	−2.50541	−	2.50541i	−0.0877608	−	0.0877608i
$816$	14.5228	+	38.8018i	0.508401	+	1.35833i
$817$	38.8979	−	38.8979i	1.36087	−	1.36087i
$818$	35.5775	−	4.96369i	1.24394	−	0.173551i
$819$	22.1768	+	4.41124i	0.774920	+	0.154141i
$820$	7.83272	+	6.65792i	0.273530	+	0.232505i
$821$	19.7190	−	29.5116i	0.688199	−	1.02996i	−0.308691	−	0.951162i	$-0.599891\pi$
$821$	19.7190	−	29.5116i	0.688199	−	1.02996i	0.996890	−	0.0788007i	$-0.0251091\pi$
$822$	3.03810	−	52.5705i	0.105966	−	1.83361i
$823$	0.550722	−	1.32956i	0.0191970	−	0.0463456i	−0.913990	−	0.405736i	$-0.867015\pi$
$823$	0.550722	−	1.32956i	0.0191970	−	0.0463456i	0.933187	+	0.359390i	$0.117015\pi$
$824$	−5.38508	−	2.08576i	−0.187598	−	0.0726609i
$825$	−2.11904	−	5.11582i	−0.0737756	−	0.178110i
$826$	−1.54810	−	4.44741i	−0.0538653	−	0.154745i
$827$	−13.6122	+	2.70763i	−0.473341	+	0.0941534i	−0.425996	−	0.904725i	$-0.640076\pi$
$827$	−13.6122	+	2.70763i	−0.473341	+	0.0941534i	−0.0473454	+	0.998879i	$0.515076\pi$
$828$	42.6003	−	12.1230i	1.48046	−	0.421302i
$829$	−8.09646	+	5.40988i	−0.281202	+	0.187893i	−0.688170	−	0.725549i	$-0.741586\pi$
$829$	−8.09646	+	5.40988i	−0.281202	+	0.187893i	0.406969	+	0.913442i	$0.366586\pi$
$830$	−0.932280	+	3.58999i	−0.0323599	+	0.124611i
$831$	20.7447			0.719625
$832$	2.18878	−	14.4812i	0.0758823	−	0.502045i
$833$	53.9441			1.86905
$834$	−11.3280	+	43.6213i	−0.392255	+	1.51048i
$835$	−4.61494	+	3.08361i	−0.159707	+	0.106713i
$836$	1.85789	+	6.52865i	0.0642563	+	0.225798i
$837$	−0.756697	+	0.150516i	−0.0261553	+	0.00520261i
$838$	−5.91520	−	16.9933i	−0.204337	−	0.587024i
$839$	−3.39992	−	8.20812i	−0.117378	−	0.283376i	0.854261	−	0.519844i	$-0.174010\pi$
$839$	−3.39992	−	8.20812i	−0.117378	−	0.283376i	−0.971639	+	0.236468i	$0.924010\pi$
$840$	9.38156	+	21.2432i	0.323694	+	0.732961i
$841$	10.5075	−	25.3673i	0.362326	−	0.874733i
$842$	−2.45585	+	42.4953i	−0.0846341	+	1.46449i
$843$	−3.06100	+	4.58111i	−0.105426	+	0.157782i
$844$	−24.6712	+	29.0245i	−0.849219	+	0.999065i
$845$	−7.30249	−	1.45256i	−0.251213	−	0.0499694i
$846$	6.22778	−	0.868885i	0.214116	−	0.0298729i
$847$	33.5273	−	33.5273i	1.15201	−	1.15201i
$848$	28.2756	+	0.977526i	0.970989	+	0.0335684i
$849$	−40.6008	−	40.6008i	−1.39342	−	1.39342i
$850$	21.3890	+	16.1515i	0.733638	+	0.553991i
$851$	−2.94489	+	14.8050i	−0.100950	+	0.507508i
$852$	1.82171	+	3.55457i	0.0624106	+	0.121778i
$853$	18.5526	+	12.3964i	0.635228	+	0.424446i	0.831053	−	0.556193i	$-0.187738\pi$
$853$	18.5526	+	12.3964i	0.635228	+	0.424446i	−0.195825	+	0.980639i	$0.562738\pi$
$854$	16.7489	+	18.8035i	0.573135	+	0.643442i
$855$	12.9459	+	5.36239i	0.442742	+	0.183390i
$856$	2.62754	+	11.7767i	0.0898076	+	0.402519i
$857$	−34.9162	+	14.4628i	−1.19272	+	0.494039i	−0.888639	−	0.458608i	$-0.848348\pi$
$857$	−34.9162	+	14.4628i	−1.19272	+	0.494039i	−0.304077	+	0.952647i	$0.598348\pi$
$858$	1.41701	−	2.93025i	0.0483760	−	0.100037i
$859$	5.27751	+	26.5318i	0.180066	+	0.905255i	0.960130	+	0.279554i	$0.0901867\pi$
$859$	5.27751	+	26.5318i	0.180066	+	0.905255i	−0.780063	+	0.625700i	$0.784813\pi$
$860$	−8.11256	−	10.2410i	−0.276636	−	0.349215i
$861$	39.3727	+	58.9254i	1.34182	+	2.00817i
$862$	6.91972	+	11.7744i	0.235687	+	0.401036i
$863$		−	21.2314i		−	0.722726i	−0.932425	−	0.361363i	$-0.882311\pi$
$863$		−	21.2314i		−	0.722726i	0.932425	−	0.361363i	$-0.117689\pi$
$864$	2.46194	−	1.33464i	0.0837568	−	0.0454053i
$865$		−	12.6386i		−	0.429725i
$866$	−8.35199	+	4.90842i	−0.283812	+	0.166795i
$867$	−2.02573	−	3.03172i	−0.0687974	−	0.102963i
$868$	−13.6853	−	1.58707i	−0.464509	−	0.0538688i
$869$	−0.890314	−	4.47591i	−0.0302019	−	0.151835i
$870$	2.93737	+	1.42046i	0.0995863	+	0.0481580i
$871$	−6.20975	+	2.57216i	−0.210409	+	0.0871544i
$872$	30.7144	−	21.5684i	1.04012	−	0.730399i
$873$	8.88391	+	3.67984i	0.300675	+	0.124544i
$874$	−54.3865	+	48.4438i	−1.83965	+	1.63864i
$875$	26.6714	+	17.8213i	0.901658	+	0.602469i
$876$	−1.13018	+	3.50643i	−0.0381852	+	0.118471i
$877$	−2.10738	+	10.5945i	−0.0711613	+	0.357752i	−0.999916	−	0.0129422i	$-0.995880\pi$
$877$	−2.10738	+	10.5945i	−0.0711613	+	0.357752i	0.928755	+	0.370694i	$0.120880\pi$
$878$	−25.0700	+	33.1996i	−0.846070	+	1.12043i
$879$	−46.3140	−	46.3140i	−1.56213	−	1.56213i
$880$	1.59107	−	0.259692i	0.0536348	−	0.00875420i
$881$	−15.1953	+	15.1953i	−0.511944	+	0.511944i	−0.915122	−	0.403178i	$-0.867906\pi$
$881$	−15.1953	+	15.1953i	−0.511944	+	0.511944i	0.403178	+	0.915122i	$0.367906\pi$
$882$	6.84577	+	49.0675i	0.230509	+	1.65219i
$883$	16.8801	+	3.35767i	0.568062	+	0.112995i	0.470761	−	0.882261i	$-0.343979\pi$
$883$	16.8801	+	3.35767i	0.568062	+	0.112995i	0.0973004	+	0.995255i	$0.468979\pi$
$884$	1.27310	+	15.7031i	0.0428189	+	0.528152i
$885$	−0.777462	+	1.16355i	−0.0261341	+	0.0391124i
$886$	44.7281	+	2.58488i	1.50267	+	0.0868408i
$887$	−7.36626	+	17.7837i	−0.247335	+	0.597119i	−0.997976	−	0.0635908i	$-0.979745\pi$
$887$	−7.36626	+	17.7837i	−0.247335	+	0.597119i	0.750641	+	0.660710i	$0.229745\pi$
$888$	−0.300428	−	12.9644i	−0.0100817	−	0.435056i
$889$	17.8163	+	43.0123i	0.597539	+	1.44259i
$890$	13.8042	−	4.80510i	0.462717	−	0.161067i
$891$	4.90454	−	0.975574i	0.164308	−	0.0326830i
$892$	9.44951	−	16.9670i	0.316393	−	0.568096i
$893$	−8.59753	+	5.74468i	−0.287705	+	0.192239i
$894$	19.3367	+	5.02151i	0.646715	+	0.167945i
$895$	−7.71672			−0.257941
$896$	49.1541	−	9.19672i	1.64212	−	0.307241i
$897$	34.9248			1.16611
$898$	21.0621	+	5.46958i	0.702851	+	0.182522i
$899$	−1.60946	+	1.07541i	−0.0536786	+	0.0358669i
$900$	−11.9770	+	21.5051i	−0.399233	+	0.716838i
$901$	−29.8500	+	5.93754i	−0.994448	+	0.197808i
$902$	4.64631	−	1.61734i	0.154705	−	0.0538514i
$903$	−34.4673	−	83.2114i	−1.14700	−	2.76910i
$904$	−1.52182	+	0.0352657i	−0.0506150	+	0.00117292i
$905$	1.48214	−	3.57820i	0.0492680	−	0.118943i
$906$	39.7634	+	2.29797i	1.32105	+	0.0763448i
$907$	2.40873	−	3.60492i	0.0799806	−	0.119699i	−0.789322	−	0.613979i	$-0.789568\pi$
$907$	2.40873	−	3.60492i	0.0799806	−	0.119699i	0.869303	+	0.494279i	$0.164568\pi$
$908$	0.617429	+	7.61573i	0.0204901	+	0.252737i
$909$	−13.7407	−	2.73320i	−0.455752	−	0.0906547i
$910$	1.22023	+	8.74603i	0.0404501	+	0.289928i
$911$	−32.8907	+	32.8907i	−1.08972	+	1.08972i	−0.0941591	+	0.995557i	$0.530016\pi$
$911$	−32.8907	+	32.8907i	−1.08972	+	1.08972i	−0.995557	+	0.0941591i	$0.969984\pi$
$912$	36.5386	−	50.7927i	1.20991	−	1.68191i
$913$	1.25516	+	1.25516i	0.0415397	+	0.0415397i
$914$	7.22781	−	9.57163i	0.239075	−	0.316601i
$915$	1.45986	−	7.33921i	0.0482615	−	0.242627i
$916$	5.54831	−	17.2138i	0.183321	−	0.568761i
$917$	57.7291	+	38.5734i	1.90638	+	1.27381i
$918$	−2.24949	+	2.00370i	−0.0742443	+	0.0661318i
$919$	31.3195	+	12.9730i	1.03314	+	0.427939i	0.833843	−	0.552001i	$-0.186136\pi$
$919$	31.3195	+	12.9730i	1.03314	+	0.427939i	0.199292	+	0.979940i	$0.436136\pi$
$920$	9.94086	+	14.1562i	0.327740	+	0.466717i
$921$	−72.8086	+	30.1583i	−2.39912	+	0.993750i
$922$	−31.7880	−	15.3721i	−1.04688	−	0.506252i
$923$	0.296314	+	1.48967i	0.00975328	+	0.0490331i
$924$	11.0397	+	1.28027i	0.363180	+	0.0421177i
$925$	−4.66077	−	6.97533i	−0.153245	−	0.229347i
$926$	−32.9072	+	19.3394i	−1.08140	+	0.635531i
$927$			5.70530i			0.187387i
$928$	4.42521	−	5.45737i	0.145265	−	0.179147i
$929$		−	10.7407i		−	0.352390i	−0.984355	−	0.176195i	$-0.943621\pi$
$929$		−	10.7407i		−	0.352390i	0.984355	−	0.176195i	$-0.0563789\pi$
$930$	2.07434	+	3.52963i	0.0680204	+	0.115741i
$931$	−45.2612	−	67.7382i	−1.48338	−	2.22003i
$932$	−3.42357	−	4.32180i	−0.112143	−	0.141565i
$933$	−5.26120	−	26.4498i	−0.172244	−	0.865929i
$934$	0.833672	−	1.72396i	0.0272786	−	0.0564096i
$935$	−1.60218	+	0.663645i	−0.0523969	+	0.0217035i
$936$	−14.1219	+	3.15080i	−0.461590	+	0.102987i
$937$	49.2806	+	20.4127i	1.60993	+	0.666853i	0.992775	−	0.119992i	$-0.0382869\pi$
$937$	49.2806	+	20.4127i	1.60993	+	0.666853i	0.617151	+	0.786845i	$0.288287\pi$
$938$	−15.2647	−	17.1373i	−0.498411	−	0.559552i
$939$	−19.7828	−	13.2184i	−0.645587	−	0.431367i
$940$	1.12006	+	2.18550i	0.0365323	+	0.0712830i
$941$	5.66109	−	28.4602i	0.184546	−	0.927777i	−0.771872	−	0.635778i	$-0.780679\pi$
$941$	5.66109	−	28.4602i	0.184546	−	0.927777i	0.956418	−	0.292000i	$-0.0943206\pi$
$942$	−40.0368	−	30.2329i	−1.30447	−	0.985042i
$943$	37.3273	+	37.3273i	1.21554	+	1.21554i
$944$	2.05592	+	2.20317i	0.0669146	+	0.0717069i
$945$	−1.19398	+	1.19398i	−0.0388402	+	0.0388402i
$946$	−6.19254	+	0.863968i	−0.201337	+	0.0280900i
$947$	23.1134	+	4.59754i	0.751084	+	0.149400i	0.555764	−	0.831340i	$-0.312426\pi$
$947$	23.1134	+	4.59754i	0.751084	+	0.149400i	0.195319	+	0.980740i	$0.437426\pi$
$948$	−27.2448	+	32.0521i	−0.884868	+	1.04100i
$949$	−0.778311	+	1.16482i	−0.0252651	+	0.0378118i
$950$	2.33534	−	40.4102i	0.0757686	−	1.31108i
$951$	−16.4056	+	39.6067i	−0.531989	+	1.28434i
$952$	−49.2085	+	21.7318i	−1.59486	+	0.704330i
$953$	−17.9673	−	43.3769i	−0.582018	−	1.40512i	−0.890981	−	0.454041i	$-0.849982\pi$
$953$	−17.9673	−	43.3769i	−0.582018	−	1.40512i	0.308963	−	0.951074i	$-0.400018\pi$
$954$	−9.18888	−	26.3980i	−0.297501	−	0.854667i
$955$	15.5889	−	3.10083i	0.504446	−	0.100341i
$956$	−6.75927	−	23.7522i	−0.218611	−	0.768202i
$957$	1.29833	−	0.867516i	0.0419691	−	0.0280428i
$958$	1.25118	−	4.81800i	0.0404238	−	0.155663i
$959$	68.3716			2.20783
$960$	−10.9833	−	10.0098i	−0.354485	−	0.323066i
$961$	28.5712			0.921651
$962$	1.23947	−	4.77291i	0.0399621	−	0.153885i
$963$	9.91181	−	6.62286i	0.319404	−	0.213419i
$964$	43.9002	−	12.4929i	1.41393	−	0.402368i
$965$	−11.9874	+	2.38443i	−0.385887	+	0.0767576i
$966$	39.2024	+	112.621i	1.26132	+	3.62354i
$967$	−4.97953	−	12.0217i	−0.160131	−	0.386590i	0.823367	−	0.567509i	$-0.192093\pi$
$967$	−4.97953	−	12.0217i	−0.160131	−	0.386590i	−0.983498	+	0.180919i	$0.942093\pi$
$968$	−10.9585	+	28.2931i	−0.352221	+	0.909374i
$969$	−25.7574	+	62.1840i	−0.827448	+	1.99764i
$970$	−0.216669	+	3.74919i	−0.00695683	+	0.120379i
$971$	20.1628	−	30.1758i	0.647055	−	0.968386i	−0.352415	−	0.935844i	$-0.614640\pi$
$971$	20.1628	−	30.1758i	0.647055	−	0.968386i	0.999470	−	0.0325425i	$-0.0103604\pi$
$972$	−32.8584	−	27.9301i	−1.05393	−	0.895858i
$973$	−57.3922	−	11.4160i	−1.83991	−	0.365981i
$974$	38.6490	−	5.39222i	1.23839	−	0.172778i
$975$	−13.7247	+	13.7247i	−0.439543	+	0.439543i
$976$	−14.6652	−	6.67714i	−0.469422	−	0.213730i
$977$	−40.4140	−	40.4140i	−1.29296	−	1.29296i	−0.932949	−	0.360009i	$-0.882774\pi$
$977$	−40.4140	−	40.4140i	−1.29296	−	1.29296i	−0.360009	−	0.932949i	$-0.617226\pi$
$978$	12.4737	+	9.41922i	0.398864	+	0.301194i
$979$	1.36468	−	6.86070i	0.0436153	−	0.219269i
$980$	−17.2191	+	8.82473i	−0.550044	+	0.281896i
$981$	−30.8298	−	20.5998i	−0.984319	−	0.657701i
$982$	21.0172	+	23.5954i	0.670686	+	0.752960i
$983$	−35.5045	−	14.7065i	−1.13242	−	0.469063i	−0.263816	−	0.964573i	$-0.584981\pi$
$983$	−35.5045	−	14.7065i	−1.13242	−	0.469063i	−0.868602	+	0.495510i	$0.834981\pi$
$984$	−38.2805	−	24.3147i	−1.22034	−	0.775123i
$985$	−18.6071	+	7.70731i	−0.592871	+	0.245575i
$986$	−3.29039	+	6.80423i	−0.104787	+	0.216691i
$987$	3.30285	+	16.6046i	0.105131	+	0.528529i
$988$	18.6504	−	14.7742i	0.593347	−	0.470028i
$989$	−37.2727	−	55.7826i	−1.18520	−	1.77378i
$990$	−0.806975	−	1.37312i	−0.0256473	−	0.0436406i
$991$		−	16.3018i		−	0.517845i	−0.965898	−	0.258922i	$-0.916633\pi$
$991$		−	16.3018i		−	0.517845i	0.965898	−	0.258922i	$-0.0833674\pi$
$992$	8.42120	−	2.60881i	0.267374	−	0.0828298i
$993$		−	41.9955i		−	1.33269i
$994$	−4.47111	+	2.62764i	−0.141815	+	0.0833438i
$995$	−6.28607	−	9.40777i	−0.199282	−	0.298246i
$996$	1.88489	−	16.2534i	0.0597252	−	0.515009i
$997$	3.51164	+	17.6542i	0.111215	+	0.559114i	0.995707	+	0.0925594i	$0.0295048\pi$
$997$	3.51164	+	17.6542i	0.111215	+	0.559114i	−0.884493	+	0.466554i	$0.845495\pi$
$998$	−9.88583	−	4.78060i	−0.312931	−	0.151327i
$999$	0.871135	−	0.360836i	0.0275615	−	0.0114163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.13.7	yes	56
3.2	odd	2		576.2.bd.a.397.1		56
4.3	odd	2		256.2.i.a.145.6		56
8.3	odd	2		512.2.i.a.33.2		56
8.5	even	2		512.2.i.b.33.6		56
64.5	even	16	inner	64.2.i.a.5.7	✓	56
64.27	odd	16		512.2.i.a.481.2		56
64.37	even	16		512.2.i.b.481.6		56
64.59	odd	16		256.2.i.a.113.6		56
192.5	odd	16		576.2.bd.a.325.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.7	✓	56	64.5	even	16	inner
64.2.i.a.13.7	yes	56	1.1	even	1	trivial
256.2.i.a.113.6		56	64.59	odd	16
256.2.i.a.145.6		56	4.3	odd	2
512.2.i.a.33.2		56	8.3	odd	2
512.2.i.a.481.2		56	64.27	odd	16
512.2.i.b.33.6		56	8.5	even	2
512.2.i.b.481.6		56	64.37	even	16
576.2.bd.a.325.1		56	192.5	odd	16
576.2.bd.a.397.1		56	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36881 + 0.355465i) q^{2} +(-2.00147 + 1.33734i) q^{3} +(1.74729 + 0.973128i) q^{4} +(0.756852 - 0.150547i) q^{5} +(-3.21501 + 1.11911i) q^{6} +(-1.69148 - 4.08359i) q^{7} +(2.04580 + 1.95313i) q^{8} +(1.06935 - 2.58163i) q^{9} +O(q^{10})\)	\(q+(1.36881 + 0.355465i) q^{2} +(-2.00147 + 1.33734i) q^{3} +(1.74729 + 0.973128i) q^{4} +(0.756852 - 0.150547i) q^{5} +(-3.21501 + 1.11911i) q^{6} +(-1.69148 - 4.08359i) q^{7} +(2.04580 + 1.95313i) q^{8} +(1.06935 - 2.58163i) q^{9} +(1.08950 + 0.0629634i) q^{10} +(0.290161 - 0.434257i) q^{11} +(-4.79854 + 0.389032i) q^{12} +(-1.79553 - 0.357153i) q^{13} +(-0.863742 - 6.19092i) q^{14} +(-1.31348 + 1.31348i) q^{15} +(2.10604 + 3.40067i) q^{16} +(-3.04259 - 3.04259i) q^{17} +(2.38142 - 3.15366i) q^{18} +(-1.26776 + 6.37347i) q^{19} +(1.46894 + 0.473464i) q^{20} +(8.84657 + 5.91109i) q^{21} +(0.551539 - 0.491274i) q^{22} +(7.32197 + 3.03286i) q^{23} +(-6.70659 - 1.17320i) q^{24} +(-4.06924 + 1.68553i) q^{25} +(-2.33079 - 1.12712i) q^{26} +(-0.0965796 - 0.485538i) q^{27} +(1.01835 - 8.78123i) q^{28} +(-0.690042 - 1.03272i) q^{29} +(-2.26481 + 1.33101i) q^{30} -1.55847i q^{31} +(1.67396 + 5.40351i) q^{32} +1.25719i q^{33} +(-3.08320 - 5.24627i) q^{34} +(-1.89497 - 2.83602i) q^{35} +(4.38072 - 3.47025i) q^{36} +(0.371584 + 1.86808i) q^{37} +(-4.00087 + 8.27344i) q^{38} +(4.07133 - 1.68640i) q^{39} +(1.84240 + 1.17024i) q^{40} +(6.15380 + 2.54899i) q^{41} +(10.0081 + 11.2358i) q^{42} +(-7.03859 - 4.70304i) q^{43} +(0.929583 - 0.476409i) q^{44} +(0.420680 - 2.11490i) q^{45} +(8.94433 + 6.75412i) q^{46} +(1.12515 + 1.12515i) q^{47} +(-8.76302 - 3.98985i) q^{48} +(-8.86483 + 8.86483i) q^{49} +(-6.16917 + 0.860707i) q^{50} +(10.1586 + 2.02068i) q^{51} +(-2.78976 - 2.37133i) q^{52} +(3.92962 - 5.88109i) q^{53} +(0.0403925 - 0.698941i) q^{54} +(0.154233 - 0.372351i) q^{55} +(4.51535 - 11.6579i) q^{56} +(-5.98610 - 14.4517i) q^{57} +(-0.577441 - 1.65888i) q^{58} +(0.738882 - 0.146973i) q^{59} +(-3.57322 + 1.01685i) q^{60} +(-3.34952 + 2.23808i) q^{61} +(0.553981 - 2.13325i) q^{62} -12.3511 q^{63} +(0.370575 + 7.99141i) q^{64} -1.41272 q^{65} +(-0.446888 + 1.72086i) q^{66} +(3.05271 - 2.03976i) q^{67} +(-2.35546 - 8.27713i) q^{68} +(-18.7106 + 3.72178i) q^{69} +(-1.58575 - 4.55557i) q^{70} +(-0.317495 - 0.766500i) q^{71} +(7.22993 - 3.19293i) q^{72} +(0.292843 - 0.706986i) q^{73} +(-0.155407 + 2.68913i) q^{74} +(5.89032 - 8.81548i) q^{75} +(-8.41735 + 9.90261i) q^{76} +(-2.26413 - 0.450363i) q^{77} +(6.17234 - 0.861150i) q^{78} +(6.17863 - 6.17863i) q^{79} +(2.10592 + 2.25675i) q^{80} +(6.77032 + 6.77032i) q^{81} +(7.51732 + 5.67654i) q^{82} +(-0.663054 + 3.33340i) q^{83} +(9.70527 + 18.9372i) q^{84} +(-2.76085 - 1.84474i) q^{85} +(-7.96274 - 8.93954i) q^{86} +(2.76219 + 1.14414i) q^{87} +(1.44177 - 0.321679i) q^{88} +(12.3740 - 5.12547i) q^{89} +(1.32761 - 2.74537i) q^{90} +(1.57863 + 7.93632i) q^{91} +(9.84225 + 12.4245i) q^{92} +(2.08420 + 3.11923i) q^{93} +(1.14017 + 1.94007i) q^{94} +5.01463i q^{95} +(-10.5767 - 8.57629i) q^{96} +3.44120i q^{97} +(-15.2854 + 8.98315i) q^{98} +(-0.810809 - 1.21346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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