LMFDB - Embedded newform 64.2.i.a.13.1

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			13.1
Character	$\chi$	$=$	64.13
Dual form			64.2.i.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33595 - 0.463928i) q^{2} +(-1.31138 + 0.876237i) q^{3} +(1.56954 + 1.23957i) q^{4} +(3.52249 - 0.700667i) q^{5} +(2.15846 - 0.562226i) q^{6} +(1.02503 + 2.47464i) q^{7} +(-1.52176 - 2.38416i) q^{8} +(-0.196120 + 0.473476i) q^{9} +O(q^{10})$	\(q+(-1.33595 - 0.463928i) q^{2} +(-1.31138 + 0.876237i) q^{3} +(1.56954 + 1.23957i) q^{4} +(3.52249 - 0.700667i) q^{5} +(2.15846 - 0.562226i) q^{6} +(1.02503 + 2.47464i) q^{7} +(-1.52176 - 2.38416i) q^{8} +(-0.196120 + 0.473476i) q^{9} +(-5.03094 - 0.698122i) q^{10} +(1.67900 - 2.51280i) q^{11} +(-3.14443 - 0.250260i) q^{12} +(-4.41643 - 0.878483i) q^{13} +(-0.221337 - 3.78154i) q^{14} +(-4.00538 + 4.00538i) q^{15} +(0.926926 + 3.89112i) q^{16} +(1.12567 + 1.12567i) q^{17} +(0.481666 - 0.541556i) q^{18} +(0.432994 - 2.17681i) q^{19} +(6.39722 + 3.26665i) q^{20} +(-3.51257 - 2.34703i) q^{21} +(-3.40882 + 2.57804i) q^{22} +(-4.52287 - 1.87343i) q^{23} +(4.08471 + 1.79312i) q^{24} +(7.29760 - 3.02276i) q^{25} +(5.49259 + 3.22252i) q^{26} +(-1.08077 - 5.43340i) q^{27} +(-1.45867 + 5.15465i) q^{28} +(-3.43450 - 5.14009i) q^{29} +(7.20920 - 3.49279i) q^{30} +2.88548i q^{31} +(0.566869 - 5.62838i) q^{32} +4.76643i q^{33} +(-0.981609 - 2.02606i) q^{34} +(5.34455 + 7.99868i) q^{35} +(-0.894726 + 0.500036i) q^{36} +(1.20408 + 6.05333i) q^{37} +(-1.58834 + 2.70724i) q^{38} +(6.56139 - 2.71782i) q^{39} +(-7.03090 - 7.33194i) q^{40} +(-3.20440 - 1.32731i) q^{41} +(3.60378 + 4.76510i) q^{42} +(-2.16349 - 1.44560i) q^{43} +(5.75005 - 1.86270i) q^{44} +(-0.359082 + 1.80523i) q^{45} +(5.17320 + 4.60110i) q^{46} +(-2.37708 - 2.37708i) q^{47} +(-4.62510 - 4.29054i) q^{48} +(-0.123405 + 0.123405i) q^{49} +(-11.1516 + 0.652714i) q^{50} +(-2.46253 - 0.489827i) q^{51} +(-5.84283 - 6.85330i) q^{52} +(-3.20051 + 4.78991i) q^{53} +(-1.07684 + 7.76016i) q^{54} +(4.15361 - 10.0277i) q^{55} +(4.34009 - 6.20965i) q^{56} +(1.33958 + 3.23403i) q^{57} +(2.20370 + 8.46029i) q^{58} +(1.01300 - 0.201498i) q^{59} +(-11.2516 + 1.32166i) q^{60} +(-2.23513 + 1.49347i) q^{61} +(1.33866 - 3.85487i) q^{62} -1.37271 q^{63} +(-3.36847 + 7.25627i) q^{64} -16.1724 q^{65} +(2.21128 - 6.36773i) q^{66} +(12.1226 - 8.10007i) q^{67} +(0.371437 + 3.16212i) q^{68} +(7.57278 - 1.50632i) q^{69} +(-3.42926 - 13.1654i) q^{70} +(4.63617 + 11.1927i) q^{71} +(1.42729 - 0.252936i) q^{72} +(3.99984 - 9.65646i) q^{73} +(1.19971 - 8.64558i) q^{74} +(-6.92128 + 10.3584i) q^{75} +(3.37791 - 2.87987i) q^{76} +(7.93928 + 1.57922i) q^{77} +(-10.0266 + 0.586865i) q^{78} +(1.05698 - 1.05698i) q^{79} +(5.99146 + 13.0570i) q^{80} +(5.09110 + 5.09110i) q^{81} +(3.66516 + 3.25983i) q^{82} +(-1.67409 + 8.41620i) q^{83} +(-2.60383 - 8.03785i) q^{84} +(4.75386 + 3.17643i) q^{85} +(2.21967 + 2.93496i) q^{86} +(9.00788 + 3.73119i) q^{87} +(-8.54595 - 0.179121i) q^{88} +(-5.40505 + 2.23885i) q^{89} +(1.31721 - 2.24511i) q^{90} +(-2.35304 - 11.8295i) q^{91} +(-4.77658 - 8.54685i) q^{92} +(-2.52837 - 3.78397i) q^{93} +(2.07288 + 4.27847i) q^{94} -7.97117i q^{95} +(4.18841 + 7.87767i) q^{96} +11.0691i q^{97} +(0.222115 - 0.107613i) q^{98} +(0.860463 + 1.28777i) 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 $

$2$	−1.33595	−	0.463928i	−0.944662	−	0.328046i
$2$	−1.33595	−	0.463928i	−0.944662	−	0.328046i
$3$	−1.31138	+	0.876237i	−0.757127	+	0.505896i	−0.873210	−	0.487344i	$-0.837966\pi$
$3$	−1.31138	+	0.876237i	−0.757127	+	0.505896i	0.116084	+	0.993239i	$0.462966\pi$
$4$	1.56954	+	1.23957i	0.784771	+	0.619786i
$5$	3.52249	−	0.700667i	1.57531	−	0.313348i	0.671405	−	0.741091i	$-0.265691\pi$
$5$	3.52249	−	0.700667i	1.57531	−	0.313348i	0.903900	+	0.427743i	$0.140691\pi$
$6$	2.15846	−	0.562226i	0.881186	−	0.229528i
$7$	1.02503	+	2.47464i	0.387425	+	0.935326i	0.990484	+	0.137629i	$0.0439482\pi$
$7$	1.02503	+	2.47464i	0.387425	+	0.935326i	−0.603059	+	0.797696i	$0.706052\pi$
$8$	−1.52176	−	2.38416i	−0.538025	−	0.842929i
$9$	−0.196120	+	0.473476i	−0.0653734	+	0.157825i
$10$	−5.03094	−	0.698122i	−1.59092	−	0.220766i
$11$	1.67900	−	2.51280i	0.506237	−	0.757636i	−0.487043	−	0.873378i	$-0.661924\pi$
$11$	1.67900	−	2.51280i	0.506237	−	0.757636i	0.993279	+	0.115742i	$0.0369244\pi$
$12$	−3.14443	−	0.250260i	−0.907718	−	0.0722438i
$13$	−4.41643	−	0.878483i	−1.22490	−	0.243647i	−0.460070	−	0.887882i	$-0.652176\pi$
$13$	−4.41643	−	0.878483i	−1.22490	−	0.243647i	−0.764827	+	0.644235i	$0.777176\pi$
$14$	−0.221337	−	3.78154i	−0.0591549	−	1.01066i
$15$	−4.00538	+	4.00538i	−1.03418	+	1.03418i
$16$	0.926926	+	3.89112i	0.231731	+	0.972780i
$17$	1.12567	+	1.12567i	0.273014	+	0.273014i	0.830312	−	0.557298i	$-0.188162\pi$
$17$	1.12567	+	1.12567i	0.273014	+	0.273014i	−0.557298	+	0.830312i	$0.688162\pi$
$18$	0.481666	−	0.541556i	0.113530	−	0.127646i
$19$	0.432994	−	2.17681i	0.0993357	−	0.499394i	−0.898800	−	0.438359i	$-0.855560\pi$
$19$	0.432994	−	2.17681i	0.0993357	−	0.499394i	0.998136	−	0.0610352i	$-0.0194402\pi$
$20$	6.39722	+	3.26665i	1.43046	+	0.730445i
$21$	−3.51257	−	2.34703i	−0.766507	−	0.512163i
$22$	−3.40882	+	2.57804i	−0.726762	+	0.549641i
$23$	−4.52287	−	1.87343i	−0.943084	−	0.390638i	−0.142457	−	0.989801i	$-0.545500\pi$
$23$	−4.52287	−	1.87343i	−0.943084	−	0.390638i	−0.800627	+	0.599163i	$0.795500\pi$
$24$	4.08471	+	1.79312i	0.833787	+	0.366020i
$25$	7.29760	−	3.02276i	1.45952	−	0.604553i
$26$	5.49259	+	3.22252i	1.07719	+	0.631988i
$27$	−1.08077	−	5.43340i	−0.207994	−	1.04566i
$28$	−1.45867	+	5.15465i	−0.275662	+	0.974137i
$29$	−3.43450	−	5.14009i	−0.637771	−	0.954492i	−0.999751	−	0.0223059i	$-0.992899\pi$
$29$	−3.43450	−	5.14009i	−0.637771	−	0.954492i	0.361980	−	0.932186i	$-0.382101\pi$
$30$	7.20920	−	3.49279i	1.31621	−	0.637694i
$31$			2.88548i			0.518248i	0.965844	+	0.259124i	$0.0834339\pi$
$31$			2.88548i			0.518248i	−0.965844	+	0.259124i	$0.916566\pi$
$32$	0.566869	−	5.62838i	0.100209	−	0.994966i
$33$			4.76643i			0.829730i
$34$	−0.981609	−	2.02606i	−0.168345	−	0.347467i
$35$	5.34455	+	7.99868i	0.903394	+	1.35202i
$36$	−0.894726	+	0.500036i	−0.149121	+	0.0833393i
$37$	1.20408	+	6.05333i	0.197950	+	0.995162i	0.944169	+	0.329461i	$0.106867\pi$
$37$	1.20408	+	6.05333i	0.197950	+	0.995162i	−0.746219	+	0.665700i	$0.768133\pi$
$38$	−1.58834	+	2.70724i	−0.257663	+	0.439172i
$39$	6.56139	−	2.71782i	1.05066	−	0.435199i
$40$	−7.03090	−	7.33194i	−1.11168	−	1.15928i
$41$	−3.20440	−	1.32731i	−0.500443	−	0.207290i	0.118159	−	0.992995i	$-0.462301\pi$
$41$	−3.20440	−	1.32731i	−0.500443	−	0.207290i	−0.618602	+	0.785704i	$0.712301\pi$
$42$	3.60378	+	4.76510i	0.556076	+	0.735271i
$43$	−2.16349	−	1.44560i	−0.329929	−	0.220452i	0.379561	−	0.925167i	$-0.376075\pi$
$43$	−2.16349	−	1.44560i	−0.329929	−	0.220452i	−0.709491	+	0.704715i	$0.751075\pi$
$44$	5.75005	−	1.86270i	0.866852	−	0.280813i
$45$	−0.359082	+	1.80523i	−0.0535288	+	0.269108i
$46$	5.17320	+	4.60110i	0.762747	+	0.678396i
$47$	−2.37708	−	2.37708i	−0.346733	−	0.346733i	0.512158	−	0.858891i	$-0.328846\pi$
$47$	−2.37708	−	2.37708i	−0.346733	−	0.346733i	−0.858891	+	0.512158i	$0.828846\pi$
$48$	−4.62510	−	4.29054i	−0.667575	−	0.619285i
$49$	−0.123405	+	0.123405i	−0.0176293	+	0.0176293i
$50$	−11.1516	+	0.652714i	−1.57707	+	0.0923077i
$51$	−2.46253	−	0.489827i	−0.344823	−	0.0685895i
$52$	−5.84283	−	6.85330i	−0.810255	−	0.950382i
$53$	−3.20051	+	4.78991i	−0.439624	+	0.657944i	−0.983434	−	0.181264i	$-0.941981\pi$
$53$	−3.20051	+	4.78991i	−0.439624	+	0.657944i	0.543810	+	0.839208i	$0.316981\pi$
$54$	−1.07684	+	7.76016i	−0.146540	+	1.05602i
$55$	4.15361	−	10.0277i	0.560073	−	1.35214i
$56$	4.34009	−	6.20965i	0.579969	−	0.829800i
$57$	1.33958	+	3.23403i	0.177432	+	0.428358i
$58$	2.20370	+	8.46029i	0.289360	+	1.11089i
$59$	1.01300	−	0.201498i	0.131881	−	0.0262329i	−0.128708	−	0.991683i	$-0.541083\pi$
$59$	1.01300	−	0.201498i	0.131881	−	0.0262329i	0.260590	+	0.965450i	$0.416083\pi$
$60$	−11.2516	+	1.32166i	−1.45257	+	0.170625i
$61$	−2.23513	+	1.49347i	−0.286179	+	0.191219i	−0.690371	−	0.723455i	$-0.742553\pi$
$61$	−2.23513	+	1.49347i	−0.286179	+	0.191219i	0.404192	+	0.914674i	$0.367553\pi$
$62$	1.33866	−	3.85487i	0.170010	−	0.489569i
$63$	−1.37271			−0.172945
$64$	−3.36847	+	7.25627i	−0.421059	+	0.907033i
$65$	−16.1724			−2.00593
$66$	2.21128	−	6.36773i	0.272190	−	0.783814i
$67$	12.1226	−	8.10007i	1.48101	−	0.989581i	0.487840	−	0.872933i	$-0.337785\pi$
$67$	12.1226	−	8.10007i	1.48101	−	0.989581i	0.993173	−	0.116648i	$-0.0372149\pi$
$68$	0.371437	+	3.16212i	0.0450433	+	0.383464i
$69$	7.57278	−	1.50632i	0.911656	−	0.181340i
$70$	−3.42926	−	13.1654i	−0.409875	−	1.57356i
$71$	4.63617	+	11.1927i	0.550212	+	1.32833i	0.917320	+	0.398151i	$0.130348\pi$
$71$	4.63617	+	11.1927i	0.550212	+	1.32833i	−0.367108	+	0.930178i	$0.619652\pi$
$72$	1.42729	−	0.252936i	0.168208	−	0.0298088i
$73$	3.99984	−	9.65646i	0.468146	−	1.13020i	−0.496826	−	0.867850i	$-0.665501\pi$
$73$	3.99984	−	9.65646i	0.468146	−	1.13020i	0.964972	−	0.262353i	$-0.0844986\pi$
$74$	1.19971	−	8.64558i	0.139463	−	1.00503i
$75$	−6.92128	+	10.3584i	−0.799200	+	1.19609i
$76$	3.37791	−	2.87987i	0.387473	−	0.330343i
$77$	7.93928	+	1.57922i	0.904765	+	0.179969i
$78$	−10.0266	+	0.586865i	−1.13529	+	0.0664494i
$79$	1.05698	−	1.05698i	0.118919	−	0.118919i	−0.645143	−	0.764062i	$-0.723202\pi$
$79$	1.05698	−	1.05698i	0.118919	−	0.118919i	0.764062	+	0.645143i	$0.223202\pi$
$80$	5.99146	+	13.0570i	0.669866	+	1.45981i
$81$	5.09110	+	5.09110i	0.565677	+	0.565677i
$82$	3.66516	+	3.25983i	0.404749	+	0.359988i
$83$	−1.67409	+	8.41620i	−0.183755	+	0.923798i	0.773333	+	0.634000i	$0.218588\pi$
$83$	−1.67409	+	8.41620i	−0.183755	+	0.923798i	−0.957088	+	0.289798i	$0.906412\pi$
$84$	−2.60383	−	8.03785i	−0.284101	−	0.877001i
$85$	4.75386	+	3.17643i	0.515629	+	0.344532i
$86$	2.21967	+	2.93496i	0.239353	+	0.316484i
$87$	9.00788	+	3.73119i	0.965747	+	0.400025i
$88$	−8.54595	−	0.179121i	−0.911002	−	0.0190944i
$89$	−5.40505	+	2.23885i	−0.572935	+	0.237317i	−0.650290	−	0.759686i	$-0.725352\pi$
$89$	−5.40505	+	2.23885i	−0.572935	+	0.237317i	0.0773551	+	0.997004i	$0.475352\pi$
$90$	1.31721	−	2.24511i	0.138846	−	0.236656i
$91$	−2.35304	−	11.8295i	−0.246666	−	1.24007i
$92$	−4.77658	−	8.54685i	−0.497993	−	0.891071i
$93$	−2.52837	−	3.78397i	−0.262180	−	0.392380i
$94$	2.07288	+	4.27847i	0.213801	+	0.441290i
$95$		−	7.97117i		−	0.817825i
$96$	4.18841	+	7.87767i	0.427478	+	0.804011i
$97$			11.0691i			1.12389i	0.827173	+	0.561947i	$0.189948\pi$
$97$			11.0691i			1.12389i	−0.827173	+	0.561947i	$0.810052\pi$
$98$	0.222115	−	0.107613i	0.0224370	−	0.0108705i
$99$	0.860463	+	1.28777i	0.0864798	+	0.129426i
$100$	15.2008	+	4.30154i	1.52008	+	0.430154i
$101$	−2.42413	−	12.1869i	−0.241210	−	1.21264i	−0.891522	−	0.452977i	$-0.850362\pi$
$101$	−2.42413	−	12.1869i	−0.241210	−	1.21264i	0.650313	−	0.759667i	$-0.274638\pi$
$102$	3.06258	+	1.79682i	0.303240	+	0.177912i
$103$	−7.43691	+	3.08047i	−0.732781	+	0.303528i	−0.717694	−	0.696358i	$-0.754802\pi$
$103$	−7.43691	+	3.08047i	−0.732781	+	0.303528i	−0.0150867	+	0.999886i	$0.504802\pi$
$104$	4.62632	+	11.8663i	0.453648	+	1.16359i
$105$	−14.0175	−	5.80623i	−1.36797	−	0.566630i
$106$	6.49790	−	4.91428i	0.631132	−	0.477317i
$107$	5.45543	+	3.64520i	0.527396	+	0.352395i	0.790588	−	0.612349i	$-0.209775\pi$
$107$	5.45543	+	3.64520i	0.527396	+	0.352395i	−0.263192	+	0.964744i	$0.584775\pi$
$108$	5.03877	−	9.86763i	0.484856	−	0.949514i
$109$	−2.09534	+	10.5340i	−0.200697	+	1.00897i	0.740743	+	0.671789i	$0.234474\pi$
$109$	−2.09534	+	10.5340i	−0.200697	+	1.00897i	−0.941439	+	0.337182i	$0.890526\pi$
$110$	−10.2012	+	11.4696i	−0.972643	+	1.09358i
$111$	−6.88317	−	6.88317i	−0.653321	−	0.653321i
$112$	−8.67899	+	6.28232i	−0.820087	+	0.593623i
$113$	10.9546	−	10.9546i	1.03052	−	1.03052i	0.0310050	−	0.999519i	$-0.490129\pi$
$113$	10.9546	−	10.9546i	1.03052	−	1.03052i	0.999519	−	0.0310050i	$-0.00987077\pi$
$114$	−0.289259	−	4.94199i	−0.0270916	−	0.462859i
$115$	−17.2444	−	3.43013i	−1.60805	−	0.319861i
$116$	0.980919	−	12.3249i	0.0910761	−	1.14434i
$117$	1.28209	−	1.91879i	0.118529	−	0.177392i
$118$	−1.44680	−	0.200767i	−0.133189	−	0.0184821i
$119$	−1.63178	+	3.93945i	−0.149585	+	0.361129i
$120$	15.6447	+	3.45424i	1.42816	+	0.315327i
$121$	0.714404	+	1.72472i	0.0649458	+	0.156793i
$122$	3.67889	−	0.958262i	0.333071	−	0.0867570i
$123$	5.36523	−	1.06721i	0.483766	−	0.0962271i
$124$	−3.57676	+	4.52889i	−0.321203	+	0.406706i
$125$	8.65665	−	5.78419i	0.774274	−	0.517353i
$126$	1.83388	+	0.636839i	0.163375	+	0.0567341i
$127$	13.2036			1.17163			0.585815	−	0.810445i	$-0.300775\pi$
$127$	13.2036			1.17163			0.585815	+	0.810445i	$0.300775\pi$
$128$	7.86650	−	8.13131i	0.695307	−	0.718713i
$129$	4.10385			0.361324
$130$	21.6055	+	7.50280i	1.89493	+	0.658039i
$131$	−17.0393	+	11.3853i	−1.48873	+	0.994739i	−0.496814	+	0.867857i	$0.665497\pi$
$131$	−17.0393	+	11.3853i	−1.48873	+	0.994739i	−0.991918	+	0.126881i	$0.959503\pi$
$132$	−5.90833	+	7.48112i	−0.514255	+	0.651148i
$133$	5.83065	−	1.15979i	0.505581	−	0.100566i
$134$	−19.9531	+	5.19730i	−1.72368	+	0.448978i
$135$	−7.61400	−	18.3818i	−0.655309	−	1.58205i
$136$	0.970774	−	4.39677i	0.0832432	−	0.377020i
$137$	2.61344	−	6.30941i	0.223281	−	0.539049i	−0.772050	−	0.635561i	$-0.780769\pi$
$137$	2.61344	−	6.30941i	0.223281	−	0.539049i	0.995332	+	0.0965122i	$0.0307687\pi$
$138$	−10.8157	−	1.50085i	−0.920694	−	0.127761i
$139$	−9.07641	+	13.5838i	−0.769851	+	1.15216i	0.214634	+	0.976695i	$0.431144\pi$
$139$	−9.07641	+	13.5838i	−0.769851	+	1.15216i	−0.984485	+	0.175469i	$0.943856\pi$
$140$	−1.52644	+	19.1792i	−0.129008	+	1.62094i
$141$	5.20015	+	1.03437i	0.437932	+	0.0871100i
$142$	−1.00110	−	17.1038i	−0.0840105	−	1.43532i
$143$	−9.62262	+	9.62262i	−0.804684	+	0.804684i
$144$	−2.02414	−	0.324250i	−0.168678	−	0.0270208i
$145$	−15.6995	−	15.6995i	−1.30377	−	1.30377i
$146$	−9.82350	+	11.0449i	−0.812998	+	0.914086i
$147$	0.0536992	−	0.269964i	0.00442903	−	0.0222663i
$148$	−5.61368	+	10.9935i	−0.461442	+	0.903661i
$149$	−1.58289	−	1.05765i	−0.129675	−	0.0866461i	0.489041	−	0.872261i	$-0.337347\pi$
$149$	−1.58289	−	1.05765i	−0.129675	−	0.0866461i	−0.618716	+	0.785615i	$0.712347\pi$
$150$	14.0521	−	10.6274i	1.14735	−	0.867723i
$151$	−12.8207	−	5.31052i	−1.04334	−	0.432164i	−0.205828	−	0.978588i	$-0.565989\pi$
$151$	−12.8207	−	5.31052i	−1.04334	−	0.432164i	−0.837509	+	0.546424i	$0.815989\pi$
$152$	−5.84878	+	2.28026i	−0.474399	+	0.184953i
$153$	−0.753741	+	0.312210i	−0.0609364	+	0.0252407i
$154$	−9.87387	−	5.79302i	−0.795659	−	0.466815i
$155$	2.02176	+	10.1641i	0.162392	+	0.816399i
$156$	13.6673	+	3.86758i	1.09426	+	0.309654i
$157$	1.92287	+	2.87778i	0.153462	+	0.229672i	0.900232	−	0.435410i	$-0.143397\pi$
$157$	1.92287	+	2.87778i	0.153462	+	0.229672i	−0.746770	+	0.665082i	$0.768397\pi$
$158$	−1.90243	+	0.921710i	−0.151349	+	0.0733273i
$159$		−	9.08580i		−	0.720551i
$160$	−1.94683	−	20.2231i	−0.153910	−	1.59878i
$161$		−	13.1128i		−	1.03343i
$162$	−4.43957	−	9.16337i	−0.348805	−	0.719942i
$163$	1.50597	+	2.25384i	0.117956	+	0.176534i	0.885749	−	0.464164i	$-0.153645\pi$
$163$	1.50597	+	2.25384i	0.117956	+	0.176534i	−0.767793	+	0.640698i	$0.778645\pi$
$164$	−3.38415	−	6.05535i	−0.264258	−	0.472843i
$165$	3.33968	+	16.7897i	0.259994	+	1.30708i
$166$	6.14101	−	10.4670i	0.476635	−	0.812396i
$167$	1.45504	−	0.602695i	0.112594	−	0.0466380i	−0.325675	−	0.945482i	$-0.605592\pi$
$167$	1.45504	−	0.602695i	0.112594	−	0.0466380i	0.438269	+	0.898844i	$0.355592\pi$
$168$	−0.250389	+	11.9462i	−0.0193179	+	0.921667i
$169$	6.72270	+	2.78464i	0.517131	+	0.214203i
$170$	−4.87730	−	6.44901i	−0.374072	−	0.494616i
$171$	0.945748	+	0.631929i	0.0723232	+	0.0483248i
$172$	−1.60377	−	4.95073i	−0.122286	−	0.377490i
$173$	−1.03690	+	5.21283i	−0.0788338	+	0.396324i	0.921141	+	0.389229i	$0.127258\pi$
$173$	−1.03690	+	5.21283i	−0.0788338	+	0.396324i	−0.999975	+	0.00709516i	$0.997742\pi$
$174$	−10.3031	−	9.16370i	−0.781077	−	0.694698i
$175$	14.9605	+	14.9605i	1.13091	+	1.13091i
$176$	11.3339	+	4.20400i	0.854324	+	0.316889i
$177$	−1.15187	+	1.15187i	−0.0865799	+	0.0865799i
$178$	8.25956	−	0.483440i	0.619080	−	0.0362354i
$179$	11.4548	+	2.27850i	0.856171	+	0.170303i	0.603612	−	0.797279i	$-0.293728\pi$
$179$	11.4548	+	2.27850i	0.856171	+	0.170303i	0.252559	+	0.967581i	$0.418728\pi$
$180$	−2.80131	+	2.38827i	−0.208797	+	0.178011i
$181$	−2.32452	+	3.47889i	−0.172780	+	0.258584i	−0.907746	−	0.419520i	$-0.862198\pi$
$181$	−2.32452	+	3.47889i	−0.172780	+	0.258584i	0.734966	+	0.678104i	$0.237198\pi$
$182$	−2.34450	+	16.8954i	−0.173786	+	1.25237i
$183$	1.62248	−	3.91701i	0.119937	−	0.289554i
$184$	2.41617	+	13.6342i	0.178122	+	1.00513i
$185$	8.48274	+	20.4791i	0.623663	+	1.50566i
$186$	1.62229	+	6.22819i	0.118952	+	0.456673i
$187$	4.71856	−	0.938579i	0.345055	−	0.0686357i
$188$	−0.784368	−	6.67750i	−0.0572059	−	0.487007i
$189$	12.3379	−	8.24390i	0.897448	−	0.599656i
$190$	−3.69805	+	10.6491i	−0.268285	+	0.772568i
$191$	17.8728			1.29323			0.646617	−	0.762815i	$-0.276183\pi$
$191$	17.8728			1.29323			0.646617	+	0.762815i	$0.276183\pi$
$192$	−1.94086	−	12.4673i	−0.140069	−	0.899751i
$193$	20.0233			1.44131			0.720654	−	0.693295i	$-0.243842\pi$
$193$	20.0233			1.44131			0.720654	+	0.693295i	$0.243842\pi$
$194$	5.13525	−	14.7878i	0.368689	−	1.06170i
$195$	21.2081	−	14.1708i	1.51875	−	1.01479i
$196$	−0.346660	+	0.0407202i	−0.0247614	+	0.00290859i
$197$	−16.3511	+	3.25244i	−1.16497	+	0.231727i	−0.739444	−	0.673219i	$-0.764911\pi$
$197$	−16.3511	+	3.25244i	−1.16497	+	0.231727i	−0.425527	+	0.904946i	$0.639911\pi$
$198$	−0.552105	−	2.11960i	−0.0392364	−	0.150633i
$199$	5.64872	+	13.6372i	0.400427	+	0.966716i	0.987562	+	0.157227i	$0.0502555\pi$
$199$	5.64872	+	13.6372i	0.400427	+	0.966716i	−0.587136	+	0.809489i	$0.699744\pi$
$200$	−18.3120	−	12.7987i	−1.29485	−	0.905007i
$201$	−8.79979	+	21.2446i	−0.620689	+	1.49848i
$202$	−2.41533	+	17.4058i	−0.169942	+	1.22467i
$203$	9.19941	−	13.7679i	0.645672	−	0.966317i
$204$	−3.25786	−	3.82128i	−0.228096	−	0.267543i
$205$	−12.2175	−	2.43021i	−0.853305	−	0.169733i
$206$	11.3645	−	0.665175i	0.791801	−	0.0463449i
$207$	1.77405	−	1.77405i	0.123305	−	0.123305i
$208$	−0.675422	−	17.9992i	−0.0468321	−	1.24802i
$209$	−4.74288	−	4.74288i	−0.328072	−	0.328072i
$210$	16.0330	+	14.2600i	1.10638	+	0.984031i
$211$	2.18718	−	10.9957i	0.150572	−	0.756975i	−0.829527	−	0.558466i	$-0.811390\pi$
$211$	2.18718	−	10.9957i	0.150572	−	0.756975i	0.980099	−	0.198509i	$-0.0636099\pi$
$212$	−10.9608	+	3.55070i	−0.752789	+	0.243863i
$213$	−15.8872	−	10.6155i	−1.08858	−	0.727363i
$214$	−5.59709	−	7.40074i	−0.382609	−	0.505904i
$215$	−8.63376	−	3.57622i	−0.588817	−	0.243896i
$216$	−11.3094	+	10.8451i	−0.769509	+	0.737914i
$217$	−7.14053	+	2.95771i	−0.484731	+	0.200782i
$218$	7.68627	−	13.1008i	0.520580	−	0.887298i
$219$	3.21604	+	16.1681i	0.217320	+	1.09254i
$220$	18.9493	−	10.5902i	1.27756	−	0.713992i
$221$	−3.98255	−	5.96030i	−0.267895	−	0.400933i
$222$	6.00230	+	12.3889i	0.402848	+	0.831487i
$223$			7.50358i			0.502477i	0.967925	+	0.251239i	$0.0808379\pi$
$223$			7.50358i			0.502477i	−0.967925	+	0.251239i	$0.919162\pi$
$224$	14.5093	−	4.36646i	0.969441	−	0.291746i
$225$			4.04806i			0.269871i
$226$	−19.7170	+	9.55271i	−1.31156	+	0.635437i
$227$	−14.7739	−	22.1107i	−0.980580	−	1.46754i	−0.881343	−	0.472478i	$-0.843360\pi$
$227$	−14.7739	−	22.1107i	−0.980580	−	1.46754i	−0.0992374	−	0.995064i	$-0.531640\pi$
$228$	−1.90629	+	6.73646i	−0.126247	+	0.446133i
$229$	−2.93523	−	14.7564i	−0.193966	−	0.975131i	−0.947994	−	0.318289i	$-0.896892\pi$
$229$	−2.93523	−	14.7564i	−0.193966	−	0.975131i	0.754028	−	0.656842i	$-0.228108\pi$
$230$	21.4464	+	12.5826i	1.41413	+	0.829675i
$231$	−11.7952	+	4.88573i	−0.776067	+	0.321458i
$232$	−7.02833	+	16.0104i	−0.461432	+	1.05114i
$233$	17.7995	+	7.37280i	1.16609	+	0.483008i	0.879897	−	0.475165i	$-0.157612\pi$
$233$	17.7995	+	7.37280i	1.16609	+	0.483008i	0.286189	+	0.958173i	$0.407612\pi$
$234$	−2.60299	+	1.96861i	−0.170163	+	0.128692i
$235$	−10.0388	−	6.70771i	−0.654859	−	0.437563i
$236$	1.83972	+	0.939427i	0.119756	+	0.0611515i
$237$	−0.459937	+	2.31226i	−0.0298761	+	0.150198i
$238$	4.00760	−	4.50590i	0.259774	−	0.292074i
$239$	−6.71028	−	6.71028i	−0.434052	−	0.434052i	0.455952	−	0.890004i	$-0.349299\pi$
$239$	−6.71028	−	6.71028i	−0.434052	−	0.434052i	−0.890004	+	0.455952i	$0.849299\pi$
$240$	−19.2981	−	11.8727i	−1.24569	−	0.766380i
$241$	2.62074	−	2.62074i	0.168816	−	0.168816i	−0.617643	−	0.786459i	$-0.711912\pi$
$241$	2.62074	−	2.62074i	0.168816	−	0.168816i	0.786459	+	0.617643i	$0.211912\pi$
$242$	−0.154263	−	2.63558i	−0.00991641	−	0.169422i
$243$	5.16281	+	1.02695i	0.331194	+	0.0658787i
$244$	−5.35939	−	0.426545i	−0.343100	−	0.0273067i
$245$	−0.348228	+	0.521160i	−0.0222475	+	0.0332957i
$246$	−7.66280	−	1.06333i	−0.488562	−	0.0677957i
$247$	−3.82458	+	9.23335i	−0.243352	+	0.587504i
$248$	6.87947	−	4.39103i	0.436847	−	0.278830i
$249$	−5.17922	−	12.5037i	−0.328220	−	0.792393i
$250$	−14.2483	+	3.71135i	−0.901143	+	0.234726i
$251$	3.80701	−	0.757262i	0.240296	−	0.0477979i	−0.0734728	−	0.997297i	$-0.523408\pi$
$251$	3.80701	−	0.757262i	0.240296	−	0.0477979i	0.313769	+	0.949499i	$0.398408\pi$
$252$	−2.15453	−	1.70157i	−0.135722	−	0.107189i
$253$	−12.3014	+	8.21956i	−0.773385	+	0.516759i
$254$	−17.6394	−	6.12551i	−1.10679	−	0.384349i
$255$	−9.01743			−0.564693
$256$	−14.2816	+	7.21356i	−0.892601	+	0.450847i
$257$	−4.79248			−0.298947			−0.149473	−	0.988766i	$-0.547758\pi$
$257$	−4.79248			−0.298947			−0.149473	+	0.988766i	$0.547758\pi$
$258$	−5.48255	−	1.90389i	−0.341329	−	0.118531i
$259$	−13.7456	+	9.18451i	−0.854110	+	0.570698i
$260$	−25.3832	−	20.0468i	−1.57420	−	1.24325i
$261$	3.10729	−	0.618078i	0.192336	−	0.0382581i
$262$	28.0457	−	7.30522i	1.73267	−	0.451318i
$263$	5.53072	+	13.3523i	0.341039	+	0.823340i	0.997611	+	0.0690772i	$0.0220055\pi$
$263$	5.53072	+	13.3523i	0.341039	+	0.823340i	−0.656573	+	0.754263i	$0.727995\pi$
$264$	11.3640	−	7.25338i	0.699403	−	0.446415i
$265$	−7.91764	+	19.1149i	−0.486377	+	1.17422i
$266$	−8.32753	−	1.15558i	−0.510594	−	0.0708529i
$267$	5.12633	−	7.67209i	0.313726	−	0.469524i
$268$	29.0676	+	2.31344i	1.77558	+	0.141316i
$269$	12.3558	+	2.45771i	0.753344	+	0.149849i	0.556801	−	0.830646i	$-0.312029\pi$
$269$	12.3558	+	2.45771i	0.753344	+	0.149849i	0.196543	+	0.980495i	$0.437029\pi$
$270$	1.64411	+	28.0896i	0.100057	+	1.70948i
$271$	1.16587	−	1.16587i	0.0708213	−	0.0708213i	−0.670809	−	0.741630i	$-0.734053\pi$
$271$	1.16587	−	1.16587i	0.0708213	−	0.0708213i	0.741630	+	0.670809i	$0.234053\pi$
$272$	−3.33669	+	5.42351i	−0.202317	+	0.328848i
$273$	13.4512	+	13.4512i	0.814105	+	0.814105i
$274$	−6.41855	+	7.21663i	−0.387759	+	0.435972i
$275$	4.65705	−	23.4126i	0.280831	−	1.41183i
$276$	13.7530	+	7.02277i	0.827833	+	0.422721i
$277$	−8.28458	−	5.53558i	−0.497772	−	0.332601i	0.281211	−	0.959646i	$-0.409264\pi$
$277$	−8.28458	−	5.53558i	−0.497772	−	0.332601i	−0.778983	+	0.627045i	$0.784264\pi$
$278$	18.4276	−	13.9365i	1.10521	−	0.835858i
$279$	−1.36621	−	0.565902i	−0.0817927	−	0.0338797i
$280$	10.9370	−	24.9144i	0.653613	−	1.48892i
$281$	−1.78965	+	0.741299i	−0.106762	+	0.0442222i	−0.435425	−	0.900225i	$-0.643402\pi$
$281$	−1.78965	+	0.741299i	−0.106762	+	0.0442222i	0.328663	+	0.944447i	$0.393402\pi$
$282$	−6.46728	−	3.79437i	−0.385121	−	0.225951i
$283$	−2.18457	−	10.9826i	−0.129859	−	0.652845i	−0.989801	−	0.142454i	$-0.954501\pi$
$283$	−2.18457	−	10.9826i	−0.129859	−	0.652845i	0.859943	−	0.510391i	$-0.170499\pi$
$284$	−6.59749	+	23.3143i	−0.391489	+	1.38345i
$285$	6.98464	+	10.4532i	0.413734	+	0.619197i
$286$	17.3196	−	8.39117i	1.02413	−	0.496180i
$287$		−	9.29026i		−	0.548387i
$288$	2.55373	+	1.37224i	0.150480	+	0.0808599i
$289$		−	14.4658i		−	0.850927i
$290$	13.6904	+	28.2572i	0.803925	+	1.65932i
$291$	−9.69913	−	14.5158i	−0.568573	−	0.850930i
$292$	18.2478	−	10.1981i	1.06787	−	0.596801i
$293$	−0.0277262	−	0.139389i	−0.00161978	−	0.00814318i	0.979967	−	0.199160i	$-0.0638214\pi$
$293$	−0.0277262	−	0.139389i	−0.00161978	−	0.00814318i	−0.981587	+	0.191017i	$0.938821\pi$
$294$	−0.196983	+	0.335747i	−0.0114883	+	0.0195812i
$295$	3.42710	−	1.41955i	0.199534	−	0.0826495i
$296$	12.5998	−	12.0825i	0.732349	−	0.702279i
$297$	−15.4676	−	6.40690i	−0.897523	−	0.371766i
$298$	1.62399	+	2.14732i	0.0940751	+	0.124391i
$299$	18.3292	+	12.2472i	1.06000	+	0.708271i
$300$	−23.7032	+	7.67857i	−1.36851	+	0.443322i
$301$	1.35969	−	6.83564i	0.0783714	−	0.394000i
$302$	14.6642	+	13.0425i	0.843830	+	0.750512i
$303$	13.8576	+	13.8576i	0.796097	+	0.796097i
$304$	8.87158	−	0.332908i	0.508820	−	0.0190936i
$305$	−6.82680	+	6.82680i	−0.390901	+	0.390901i
$306$	1.15181	−	0.0674163i	0.0658444	−	0.00385394i
$307$	1.97782	+	0.393412i	0.112880	+	0.0224532i	0.251207	−	0.967933i	$-0.419172\pi$
$307$	1.97782	+	0.393412i	0.112880	+	0.0224532i	−0.138327	+	0.990387i	$0.544172\pi$
$308$	10.5035	+	12.3200i	0.598491	+	0.701995i
$309$	7.05341	−	10.5562i	0.401254	−	0.600520i
$310$	2.01442	−	14.5167i	0.114411	−	0.824493i
$311$	−5.97814	+	14.4325i	−0.338989	+	0.818392i	0.658824	+	0.752297i	$0.271054\pi$
$311$	−5.97814	+	14.4325i	−0.338989	+	0.818392i	−0.997813	+	0.0660951i	$0.978946\pi$
$312$	−16.4646	−	11.5075i	−0.932124	−	0.651487i
$313$	−12.3839	−	29.8974i	−0.699981	−	1.68990i	−0.723635	−	0.690183i	$-0.757530\pi$
$313$	−12.3839	−	29.8974i	−0.699981	−	1.68990i	0.0236544	−	0.999720i	$-0.492470\pi$
$314$	−1.23379	−	4.73666i	−0.0696266	−	0.267305i
$315$	−4.83536	+	0.961813i	−0.272442	+	0.0541920i
$316$	2.96917	−	0.348771i	0.167029	−	0.0196199i
$317$	−2.23554	+	1.49374i	−0.125560	+	0.0838968i	−0.616765	−	0.787148i	$-0.711557\pi$
$317$	−2.23554	+	1.49374i	−0.125560	+	0.0838968i	0.491204	+	0.871045i	$0.336557\pi$
$318$	−4.21515	+	12.1382i	−0.236374	+	0.680677i
$319$	−18.6825			−1.04602
$320$	−6.78118	+	27.9203i	−0.379079	+	1.56079i
$321$	−10.3482			−0.577581
$322$	−6.08339	+	17.5181i	−0.339014	+	0.976244i
$323$	2.93777	−	1.96295i	0.163462	−	0.109222i
$324$	1.67991	+	14.3015i	0.0933285	+	0.794526i
$325$	−34.8848	+	6.93902i	−1.93506	+	0.384907i
$326$	−0.966284	−	3.70968i	−0.0535175	−	0.205460i
$327$	−6.48247	−	15.6501i	−0.358481	−	0.865450i
$328$	1.71183	+	9.65966i	0.0945197	+	0.533366i
$329$	3.44584	−	8.31900i	0.189975	−	0.458641i
$330$	3.32755	−	23.9796i	0.183176	−	1.32004i
$331$	0.656286	−	0.982201i	0.0360727	−	0.0539866i	−0.812995	−	0.582271i	$-0.802164\pi$
$331$	0.656286	−	0.982201i	0.0360727	−	0.0539866i	0.849068	+	0.528284i	$0.177164\pi$
$332$	−13.0600	+	11.1344i	−0.716762	+	0.611081i
$333$	−3.10225	−	0.617076i	−0.170002	−	0.0338156i
$334$	−2.22347	+	0.130142i	−0.121663	+	0.00712104i
$335$	37.0263	−	37.0263i	2.02296	−	2.02296i
$336$	5.87667	−	15.8434i	0.320599	−	0.864326i
$337$	23.1614	+	23.1614i	1.26168	+	1.26168i	0.950278	+	0.311402i	$0.100798\pi$
$337$	23.1614	+	23.1614i	1.26168	+	1.26168i	0.311402	+	0.950278i	$0.399202\pi$
$338$	−7.68935	−	6.83899i	−0.418245	−	0.371992i
$339$	−4.76684	+	23.9645i	−0.258899	+	1.30158i
$340$	3.52398	+	10.8783i	0.191114	+	0.589958i
$341$	7.25063	+	4.84472i	0.392644	+	0.262356i
$342$	−0.970306	−	1.28299i	−0.0524681	−	0.0693759i
$343$	16.8906	+	6.99631i	0.912006	+	0.377765i
$344$	−0.154221	+	7.35798i	−0.00831506	+	0.396716i
$345$	25.6196	−	10.6120i	1.37931	−	0.571330i
$346$	3.80362	−	6.48305i	0.204484	−	0.348531i
$347$	2.47211	+	12.4281i	0.132710	+	0.667176i	0.988666	+	0.150129i	$0.0479688\pi$
$347$	2.47211	+	12.4281i	0.132710	+	0.667176i	−0.855957	+	0.517047i	$0.827031\pi$
$348$	9.51318	+	17.0222i	0.509960	+	0.912484i
$349$	14.6597	+	21.9398i	0.784716	+	1.17441i	0.981027	+	0.193869i	$0.0621036\pi$
$349$	14.6597	+	21.9398i	0.784716	+	1.17441i	−0.196312	+	0.980542i	$0.562896\pi$
$350$	−13.0459	−	26.9271i	−0.697335	−	1.43931i
$351$			24.9457i			1.33150i
$352$	−13.1912	−	10.8745i	−0.703093	−	0.579610i
$353$			7.76818i			0.413458i	0.978398	+	0.206729i	$0.0662819\pi$
$353$			7.76818i			0.413458i	−0.978398	+	0.206729i	$0.933718\pi$
$354$	2.07323	−	1.00446i	0.110191	−	0.0533865i
$355$	24.1732	+	36.1778i	1.28298	+	1.92012i
$356$	−11.2587	−	3.18599i	−0.596708	−	0.168857i
$357$	−1.31202	−	6.59595i	−0.0694393	−	0.349095i
$358$	−14.2460	−	8.35816i	−0.752924	−	0.441742i
$359$	−5.48329	+	2.27125i	−0.289397	+	0.119872i	−0.522659	−	0.852542i	$-0.675060\pi$
$359$	−5.48329	+	2.27125i	−0.289397	+	0.119872i	0.233262	+	0.972414i	$0.425060\pi$
$360$	4.85040	−	1.89102i	0.255638	−	0.0996655i
$361$	13.0027	+	5.38589i	0.684352	+	0.283468i
$362$	4.71940	−	3.56922i	0.248046	−	0.187594i
$363$	−2.44812	−	1.63578i	−0.128493	−	0.0858564i
$364$	10.9704	−	21.4837i	0.575003	−	1.12605i
$365$	7.32342	−	36.8173i	0.383326	−	1.92711i
$366$	−3.98476	+	4.48023i	−0.208287	+	0.234185i
$367$	−24.0480	−	24.0480i	−1.25530	−	1.25530i	−0.953313	−	0.301985i	$-0.902351\pi$
$367$	−24.0480	−	24.0480i	−1.25530	−	1.25530i	−0.301985	−	0.953313i	$-0.597649\pi$
$368$	3.09739	−	19.3356i	0.161463	−	1.00794i
$369$	1.25690	−	1.25690i	0.0654314	−	0.0654314i
$370$	−1.83170	−	31.2945i	−0.0952256	−	1.62693i
$371$	−15.1339	−	3.01032i	−0.785713	−	0.156288i
$372$	0.722121	−	9.07320i	0.0374402	−	0.470423i
$373$	0.521412	−	0.780348i	0.0269977	−	0.0404049i	−0.817725	−	0.575609i	$-0.804765\pi$
$373$	0.521412	−	0.780348i	0.0269977	−	0.0404049i	0.844723	+	0.535204i	$0.179765\pi$
$374$	−6.73920	−	0.935171i	−0.348476	−	0.0483565i
$375$	−6.28385	+	15.1706i	−0.324497	+	0.783404i
$376$	−2.05000	+	9.28471i	−0.105720	+	0.478823i
$377$	10.6528	+	25.7180i	0.548645	+	1.32455i
$378$	−20.3074	+	5.28959i	−1.04450	+	0.272067i
$379$	−25.2135	+	5.01528i	−1.29513	+	0.257618i	−0.794087	−	0.607804i	$-0.792050\pi$
$379$	−25.2135	+	5.01528i	−1.29513	+	0.257618i	−0.501044	+	0.865422i	$0.667050\pi$
$380$	9.88084	−	12.5111i	0.506876	−	0.641805i
$381$	−17.3149	+	11.5695i	−0.887072	+	0.592722i
$382$	−23.8773	−	8.29170i	−1.22167	−	0.424240i
$383$	−36.1379			−1.84656			−0.923279	−	0.384130i	$-0.874501\pi$
$383$	−36.1379			−1.84656			−0.923279	+	0.384130i	$0.874501\pi$
$384$	−3.19104	+	17.5562i	−0.162842	+	0.895909i
$385$	29.0725			1.48167
$386$	−26.7502	−	9.28936i	−1.36155	−	0.472816i
$387$	1.10876	−	0.740850i	0.0563615	−	0.0376595i
$388$	−13.7209	+	17.3734i	−0.696574	+	0.882000i
$389$	17.2404	−	3.42934i	0.874125	−	0.173874i	0.262414	−	0.964955i	$-0.415482\pi$
$389$	17.2404	−	3.42934i	0.874125	−	0.173874i	0.611711	+	0.791081i	$0.290482\pi$
$390$	−34.9073	+	9.09251i	−1.76760	+	0.460417i
$391$	−2.98238	−	7.20010i	−0.150825	−	0.364125i
$392$	0.482013	+	0.106425i	0.0243453	+	0.00537527i
$393$	12.3688	−	29.8610i	0.623924	−	1.50629i
$394$	23.3533	+	3.24063i	1.17652	+	0.163261i
$395$	2.98260	−	4.46378i	0.150071	−	0.224597i
$396$	−0.245755	+	3.08782i	−0.0123496	+	0.155169i
$397$	6.70636	+	1.33398i	0.336583	+	0.0669505i	0.360488	−	0.932764i	$-0.382610\pi$
$397$	6.70636	+	1.33398i	0.336583	+	0.0669505i	−0.0239055	+	0.999714i	$0.507610\pi$
$398$	−1.21974	−	20.8393i	−0.0611402	−	1.04458i
$399$	−6.62996	+	6.62996i	−0.331913	+	0.331913i
$400$	18.5263	+	25.5939i	0.926313	+	1.27970i
$401$	−14.0108	−	14.0108i	−0.699666	−	0.699666i	0.264672	−	0.964338i	$-0.414736\pi$
$401$	−14.0108	−	14.0108i	−0.699666	−	0.699666i	−0.964338	+	0.264672i	$0.914736\pi$
$402$	21.6120	−	24.2993i	1.07791	−	1.21194i
$403$	2.53485	−	12.7435i	0.126270	−	0.634801i
$404$	11.3018	−	22.1328i	0.562284	−	1.10115i
$405$	21.5005	+	14.3662i	1.06837	+	0.713861i
$406$	−18.6773	+	14.1254i	−0.926939	+	0.701032i
$407$	17.2324	+	7.13791i	0.854180	+	0.353813i
$408$	2.57956	+	6.61647i	0.127707	+	0.327564i
$409$	−20.5325	+	8.50486i	−1.01527	+	0.420538i	−0.827374	−	0.561651i	$-0.810166\pi$
$409$	−20.5325	+	8.50486i	−1.01527	+	0.420538i	−0.187895	+	0.982189i	$0.560166\pi$
$410$	15.1945	+	8.91466i	0.750404	+	0.440264i
$411$	2.10132	+	10.5640i	0.103650	+	0.521086i
$412$	−15.4910	−	4.38366i	−0.763187	−	0.215967i
$413$	1.53699	+	2.30027i	0.0756304	+	0.113189i
$414$	−3.19308	+	1.54702i	−0.156931	+	0.0760318i
$415$			30.8189i			1.51284i
$416$	−7.44797	+	24.3594i	−0.365167	+	1.19432i
$417$		−	25.7667i		−	1.26180i
$418$	4.13591	+	8.53662i	0.202294	+	0.417540i
$419$	−12.2124	−	18.2772i	−0.596615	−	0.892898i	0.403137	−	0.915140i	$-0.367920\pi$
$419$	−12.2124	−	18.2772i	−0.596615	−	0.892898i	−0.999753	+	0.0222415i	$0.992920\pi$
$420$	−14.8038	−	26.4888i	−0.722351	−	1.29252i
$421$	−2.62271	−	13.1853i	−0.127823	−	0.642610i	−0.990574	−	0.136980i	$-0.956260\pi$
$421$	−2.62271	−	13.1853i	−0.127823	−	0.642610i	0.862751	−	0.505630i	$-0.168740\pi$
$422$	−8.02318	+	13.6750i	−0.390562	+	0.665691i
$423$	1.59169	−	0.659298i	0.0773904	−	0.0320562i
$424$	16.2903	+	0.341442i	0.791129	+	0.0165819i
$425$	11.6173	+	4.81203i	0.563521	+	0.233418i
$426$	16.2998	+	21.5524i	0.789727	+	1.04422i
$427$	−5.98686	−	4.00029i	−0.289725	−	0.193588i
$428$	4.04404	+	12.4837i	0.195476	+	0.603422i
$429$	4.18723	−	21.0506i	0.202161	−	1.01633i
$430$	9.87519	+	8.78310i	0.476224	+	0.423559i
$431$	11.2500	+	11.2500i	0.541893	+	0.541893i	0.924084	−	0.382190i	$-0.124830\pi$
$431$	11.2500	+	11.2500i	0.541893	+	0.541893i	−0.382190	+	0.924084i	$0.624830\pi$
$432$	20.1402	−	9.24176i	0.968996	−	0.444644i
$433$	−17.8833	+	17.8833i	−0.859418	+	0.859418i	−0.991269	−	0.131851i	$-0.957908\pi$
$433$	−17.8833	+	17.8833i	−0.859418	+	0.859418i	0.131851	+	0.991269i	$0.457908\pi$
$434$	10.9116	−	0.638666i	0.523773	−	0.0306569i
$435$	34.3445	+	6.83154i	1.64669	+	0.327547i
$436$	−16.3463	+	13.9362i	−0.782847	+	0.667422i
$437$	−6.03648	+	9.03424i	−0.288764	+	0.432166i
$438$	3.20436	−	23.0919i	0.153110	−	1.10337i
$439$	7.70310	−	18.5969i	0.367649	−	0.887583i	−0.626485	−	0.779433i	$-0.715507\pi$
$439$	7.70310	−	18.5969i	0.367649	−	0.887583i	0.994135	−	0.108150i	$-0.0344928\pi$
$440$	−30.2285	+	5.35691i	−1.44109	+	0.255381i
$441$	−0.0342272	−	0.0826318i	−0.00162987	−	0.00393485i
$442$	2.55535	+	9.81030i	0.121545	+	0.466628i
$443$	−23.1776	+	4.61031i	−1.10120	+	0.219043i	−0.712048	−	0.702130i	$-0.752232\pi$
$443$	−23.1776	+	4.61031i	−1.10120	+	0.219043i	−0.389153	+	0.921173i	$0.627232\pi$
$444$	−2.27124	−	19.3356i	−0.107788	−	0.917627i
$445$	−17.4706	+	11.6735i	−0.828184	+	0.553375i
$446$	3.48112	−	10.0244i	0.164836	−	0.474671i
$447$	3.00252			0.142014
$448$	−21.4094	−	0.897867i	−1.01150	−	0.0424202i
$449$	−25.3135			−1.19462			−0.597310	−	0.802010i	$-0.703764\pi$
$449$	−25.3135			−1.19462			−0.597310	+	0.802010i	$0.703764\pi$
$450$	1.87801	−	5.40802i	0.0885302	−	0.254937i
$451$	−8.71543	+	5.82346i	−0.410394	+	0.274216i
$452$	30.7728	−	3.61471i	1.44743	−	0.170021i
$453$	21.4661	−	4.26988i	1.00857	−	0.200617i
$454$	9.47949	+	36.3930i	0.444894	+	1.70801i
$455$	−16.5771	−	40.0207i	−0.777148	−	1.87620i
$456$	5.67194	−	8.11521i	0.265613	−	0.380030i
$457$	−1.63458	+	3.94622i	−0.0764624	+	0.184596i	−0.957489	−	0.288471i	$-0.906853\pi$
$457$	−1.63458	+	3.94622i	−0.0764624	+	0.184596i	0.881026	+	0.473067i	$0.156853\pi$
$458$	−2.92457	+	21.0756i	−0.136656	+	0.984798i
$459$	4.89960	−	7.33277i	0.228694	−	0.342264i
$460$	−22.8139	−	26.7594i	−1.06371	−	1.24766i
$461$	−5.97319	−	1.18814i	−0.278199	−	0.0553372i	0.0540188	−	0.998540i	$-0.482797\pi$
$461$	−5.97319	−	1.18814i	−0.278199	−	0.0553372i	−0.332218	+	0.943203i	$0.607797\pi$
$462$	18.0245	−	1.05499i	0.838574	−	0.0490826i
$463$	−4.21551	+	4.21551i	−0.195912	+	0.195912i	−0.798245	−	0.602333i	$-0.794238\pi$
$463$	−4.21551	+	4.21551i	−0.195912	+	0.195912i	0.602333	+	0.798245i	$0.294238\pi$
$464$	16.8172	−	18.1285i	0.780719	−	0.841596i
$465$	−11.5575	−	11.5575i	−0.535964	−	0.535964i
$466$	−20.3589	−	18.1074i	−0.943107	−	0.838810i
$467$	−6.66305	+	33.4974i	−0.308329	+	1.55007i	0.446882	+	0.894593i	$0.352534\pi$
$467$	−6.66305	+	33.4974i	−0.308329	+	1.55007i	−0.755211	+	0.655482i	$0.772466\pi$
$468$	4.39077	−	1.42237i	0.202963	−	0.0657491i
$469$	32.4708	+	21.6963i	1.49936	+	1.00184i
$470$	10.2995	+	13.6185i	0.475079	+	0.628173i
$471$	−5.04324	−	2.08898i	−0.232380	−	0.0962551i
$472$	−2.02195	−	2.10853i	−0.0930679	−	0.0970528i
$473$	−7.26499	+	3.00926i	−0.334045	+	0.138366i
$474$	1.68718	−	2.87570i	0.0774946	−	0.132085i
$475$	−3.42016	−	17.1943i	−0.156928	−	0.788929i
$476$	−7.44438	+	4.16044i	−0.341212	+	0.190693i
$477$	−1.64022	−	2.45476i	−0.0751005	−	0.112396i
$478$	5.85153	+	12.0777i	0.267643	+	0.552421i
$479$		−	19.6175i		−	0.896347i	−0.893947	−	0.448174i	$-0.852075\pi$
$479$		−	19.6175i		−	0.896347i	0.893947	−	0.448174i	$-0.147925\pi$
$480$	20.2733	+	24.8143i	0.925344	+	1.13261i
$481$		−	27.7919i		−	1.26720i
$482$	−4.71701	+	2.28535i	−0.214854	+	0.104095i
$483$	11.4899	+	17.1959i	0.522809	+	0.782439i
$484$	−1.01663	+	3.59258i	−0.0462105	+	0.163299i
$485$	7.75573	+	38.9907i	0.352170	+	1.77048i
$486$	−6.42084	−	3.76712i	−0.291255	−	0.170880i
$487$	39.3985	−	16.3194i	1.78532	−	0.739502i	0.794013	−	0.607901i	$-0.207988\pi$
$487$	39.3985	−	16.3194i	1.78532	−	0.739502i	0.991303	−	0.131601i	$-0.0420119\pi$
$488$	6.96201	+	3.05621i	0.315155	+	0.138348i
$489$	−3.94980	−	1.63606i	−0.178616	−	0.0739852i
$490$	0.706997	−	0.534693i	0.0319389	−	0.0241550i
$491$	3.04811	+	2.03668i	0.137559	+	0.0919141i	0.622446	−	0.782663i	$-0.286139\pi$
$491$	3.04811	+	2.03668i	0.137559	+	0.0919141i	−0.484887	+	0.874577i	$0.661139\pi$
$492$	9.74383	+	4.97555i	0.439286	+	0.224315i
$493$	1.91993	−	9.65213i	0.0864692	−	0.434710i
$494$	9.39307	−	10.5610i	0.422614	−	0.475162i
$495$	3.93327	+	3.93327i	0.176788	+	0.176788i
$496$	−11.2278	+	2.67463i	−0.504142	+	0.120094i
$497$	−22.9457	+	22.9457i	−1.02925	+	1.02925i
$498$	1.11836	+	19.1072i	0.0501151	+	0.856214i
$499$	0.0620242	+	0.0123374i	0.00277658	+	0.000552297i	0.196478	−	0.980508i	$-0.437049\pi$
$499$	0.0620242	+	0.0123374i	0.00277658	+	0.000552297i	−0.193702	+	0.981060i	$0.562049\pi$
$500$	20.7569	+	1.65201i	0.928276	+	0.0738800i
$501$	−1.38000	+	2.06532i	−0.0616540	+	0.0922717i
$502$	−5.43730	−	0.754512i	−0.242679	−	0.0336755i
$503$	9.58180	−	23.1325i	0.427231	−	1.03143i	−0.552930	−	0.833228i	$-0.686490\pi$
$503$	9.58180	−	23.1325i	0.427231	−	1.03143i	0.980162	−	0.198200i	$-0.0635096\pi$
$504$	2.08894	+	3.27277i	0.0930489	+	0.145781i
$505$	−17.0779	−	41.2298i	−0.759958	−	1.83470i
$506$	20.2474	−	5.27397i	0.900108	−	0.234457i
$507$	−11.2560	+	2.23896i	−0.499898	+	0.0994359i
$508$	20.7236	+	16.3668i	0.919461	+	0.726159i
$509$	28.5244	−	19.0594i	1.26432	−	0.844792i	0.271273	−	0.962503i	$-0.412555\pi$
$509$	28.5244	−	19.0594i	1.26432	−	0.844792i	0.993048	+	0.117710i	$0.0375555\pi$
$510$	12.0469	+	4.18343i	0.533444	+	0.185246i
$511$	27.9962			1.23848
$512$	22.4261	−	3.01134i	0.991105	−	0.133083i
$513$	−12.2954			−0.542857
$514$	6.40253	+	2.22336i	0.282404	+	0.0980684i
$515$	−24.0381	+	16.0617i	−1.05924	+	0.707764i
$516$	6.44117	+	5.08702i	0.283557	+	0.223943i
$517$	−9.96424	+	1.98201i	−0.438227	+	0.0871687i
$518$	22.6244	−	5.89312i	0.994060	−	0.258929i
$519$	−3.20791	−	7.74457i	−0.140812	−	0.339949i
$520$	24.6105	+	38.5575i	1.07924	+	1.69086i
$521$	−10.5629	+	25.5011i	−0.462769	+	1.11722i	0.504487	+	0.863420i	$0.331682\pi$
$521$	−10.5629	+	25.5011i	−0.462769	+	1.11722i	−0.967256	+	0.253804i	$0.918318\pi$
$522$	−4.43793	−	0.615833i	−0.194243	−	0.0269543i
$523$	8.36875	−	12.5247i	0.365940	−	0.547668i	−0.602114	−	0.798410i	$-0.705675\pi$
$523$	8.36875	−	12.5247i	0.365940	−	0.547668i	0.968054	+	0.250742i	$0.0806747\pi$
$524$	−40.8568	−	3.25173i	−1.78484	−	0.142052i
$525$	−32.7279	−	6.50998i	−1.42836	−	0.284119i
$526$	−1.19426	−	20.4039i	−0.0520723	−	0.889654i
$527$	−3.24809	+	3.24809i	−0.141489	+	0.141489i
$528$	−18.5468	+	4.41813i	−0.807144	+	0.192274i
$529$	0.683141	+	0.683141i	0.0297018	+	0.0297018i
$530$	19.4455	−	21.8634i	0.844660	−	0.949684i
$531$	−0.103265	+	0.519150i	−0.00448133	+	0.0225292i
$532$	10.5891	+	5.40717i	0.459095	+	0.234430i
$533$	12.9860	+	8.67697i	0.562486	+	0.375841i
$534$	−10.4078	+	7.87131i	−0.450391	+	0.340625i
$535$	21.7708	+	9.01774i	0.941232	+	0.389871i
$536$	−37.7596	−	16.5759i	−1.63097	−	0.715970i
$537$	−17.0181	+	7.04913i	−0.734385	+	0.304192i
$538$	−15.3665	−	9.01557i	−0.662497	−	0.388689i
$539$	0.102895	+	0.517290i	0.00443202	+	0.0222813i
$540$	10.8351	−	38.2891i	0.466268	−	1.64770i
$541$	−4.97281	−	7.44233i	−0.213798	−	0.319971i	0.709034	−	0.705174i	$-0.249131\pi$
$541$	−4.97281	−	7.44233i	−0.213798	−	0.319971i	−0.922832	+	0.385203i	$0.874131\pi$
$542$	−2.09842	+	1.01666i	−0.0901348	+	0.0436695i
$543$		−	6.59898i		−	0.283189i
$544$	6.97378	−	5.69757i	0.298998	−	0.244281i
$545$			38.5739i			1.65232i
$546$	−11.7298	−	24.2106i	−0.501990	−	1.03612i
$547$	−17.1415	−	25.6541i	−0.732920	−	1.09689i	−0.991399	−	0.130875i	$-0.958221\pi$
$547$	−17.1415	−	25.6541i	−0.732920	−	1.09689i	0.258479	−	0.966017i	$-0.416779\pi$
$548$	11.9229	−	6.66333i	0.509320	−	0.284644i
$549$	−0.268766	−	1.35118i	−0.0114707	−	0.0576669i
$550$	−17.0834	+	29.1176i	−0.728437	+	1.24158i
$551$	−12.6761	+	5.25062i	−0.540021	+	0.223684i
$552$	−15.1153	−	15.7625i	−0.643350	−	0.670896i
$553$	3.69907	+	1.53220i	0.157300	+	0.0651559i
$554$	8.49970	+	11.2387i	0.361118	+	0.477487i
$555$	−29.0687	−	19.4231i	−1.23390	−	0.824464i
$556$	−31.0839	+	10.0695i	−1.31825	+	0.427042i
$557$	−6.97599	+	35.0707i	−0.295582	+	1.48599i	0.492440	+	0.870346i	$0.336105\pi$
$557$	−6.97599	+	35.0707i	−0.295582	+	1.48599i	−0.788022	+	0.615647i	$0.788895\pi$
$558$	1.56265	+	1.38984i	0.0661523	+	0.0588366i
$559$	8.28498	+	8.28498i	0.350417	+	0.350417i
$560$	−26.1698	+	28.2105i	−1.10588	+	1.19211i
$561$	−5.36541	+	5.36541i	−0.226528	+	0.226528i
$562$	2.73480	−	0.160071i	0.115361	−	0.00675217i
$563$	21.7512	+	4.32658i	0.916704	+	0.182344i	0.630828	−	0.775923i	$-0.282715\pi$
$563$	21.7512	+	4.32658i	0.916704	+	0.182344i	0.285876	+	0.958267i	$0.407715\pi$
$564$	6.87968	+	8.06945i	0.289687	+	0.339785i
$565$	30.9120	−	46.2631i	1.30048	−	1.94630i
$566$	−2.17663	+	15.6857i	−0.0914907	+	0.659317i
$567$	−7.38010	+	17.8171i	−0.309935	+	0.748250i
$568$	19.6301	−	28.0860i	0.823660	−	1.17846i
$569$	−13.8493	−	33.4353i	−0.580594	−	1.40168i	−0.892275	−	0.451492i	$-0.850892\pi$
$569$	−13.8493	−	33.4353i	−0.580594	−	1.40168i	0.311681	−	0.950187i	$-0.399108\pi$
$570$	−4.48160	−	17.2054i	−0.187713	−	0.720656i
$571$	40.7190	−	8.09951i	1.70404	−	0.338954i	0.755386	−	0.655280i	$-0.227449\pi$
$571$	40.7190	−	8.09951i	1.70404	−	0.338954i	0.948650	+	0.316326i	$0.102449\pi$
$572$	−27.0310	+	3.17518i	−1.13022	+	0.132761i
$573$	−23.4381	+	15.6608i	−0.979141	+	0.654241i
$574$	−4.31001	+	12.4114i	−0.179896	+	0.518040i
$575$	−38.6690			−1.61261
$576$	−2.77504	−	3.01799i	−0.115627	−	0.125750i
$577$	11.4102			0.475014			0.237507	−	0.971386i	$-0.423670\pi$
$577$	11.4102			0.475014			0.237507	+	0.971386i	$0.423670\pi$
$578$	−6.71106	+	19.3256i	−0.279143	+	0.803838i
$579$	−26.2582	+	17.5451i	−1.09125	+	0.729151i
$580$	−5.18037	−	44.1016i	−0.215103	−	1.83122i
$581$	−22.5430	+	4.48409i	−0.935243	+	0.186031i
$582$	6.22332	+	23.8921i	0.257965	+	0.990359i
$583$	6.66241	+	16.0845i	0.275929	+	0.666151i
$584$	−29.1094	+	5.15859i	−1.20456	+	0.213464i
$585$	3.17173	−	7.65722i	0.131135	−	0.316587i
$586$	−0.0276255	+	0.199080i	−0.00114120	+	0.00822391i
$587$	12.5001	−	18.7077i	0.515934	−	0.772150i	−0.478435	−	0.878123i	$-0.658796\pi$
$587$	12.5001	−	18.7077i	0.515934	−	0.772150i	0.994369	+	0.105973i	$0.0337957\pi$
$588$	0.418923	−	0.357156i	0.0172761	−	0.0147289i
$589$	6.28115	+	1.24940i	0.258810	+	0.0514806i
$590$	−5.23702	+	0.306528i	−0.215605	+	0.0126195i
$591$	18.5927	−	18.5927i	0.764800	−	0.764800i
$592$	−22.4381	+	10.2962i	−0.922202	+	0.423172i
$593$	−1.24913	−	1.24913i	−0.0512956	−	0.0512956i	0.680994	−	0.732289i	$-0.261548\pi$
$593$	−1.24913	−	1.24913i	−0.0512956	−	0.0512956i	−0.732289	+	0.680994i	$0.761548\pi$
$594$	17.6917	+	15.7352i	0.725899	+	0.645622i
$595$	−2.98767	+	15.0200i	−0.122482	+	0.615761i
$596$	−1.17337	−	3.62213i	−0.0480632	−	0.148368i
$597$	−19.3570	−	12.9340i	−0.792231	−	0.529352i
$598$	−18.8051	−	24.8650i	−0.768998	−	1.01681i
$599$	2.75750	+	1.14220i	0.112669	+	0.0466689i	0.438306	−	0.898826i	$-0.355579\pi$
$599$	2.75750	+	1.14220i	0.112669	+	0.0466689i	−0.325637	+	0.945495i	$0.605579\pi$
$600$	35.2287	+	0.738386i	1.43821	+	0.0301445i
$601$	21.5982	−	8.94628i	0.881010	−	0.364926i	0.104121	−	0.994565i	$-0.466797\pi$
$601$	21.5982	−	8.94628i	0.881010	−	0.364926i	0.776888	+	0.629638i	$0.216797\pi$
$602$	−4.98773	+	8.50130i	−0.203285	+	0.346487i
$603$	1.45770	+	7.32835i	0.0593621	+	0.298434i
$604$	−13.5399	−	24.2273i	−0.550931	−	0.985795i
$605$	3.72494	+	5.57476i	0.151440	+	0.226646i
$606$	−12.0842	−	24.9420i	−0.490886	−	1.01320i
$607$		−	24.7172i		−	1.00324i	−0.865088	−	0.501620i	$-0.832738\pi$
$607$		−	24.7172i		−	1.00324i	0.865088	−	0.501620i	$-0.167262\pi$
$608$	−12.0065	−	3.67102i	−0.486926	−	0.148880i
$609$			26.1158i			1.05827i
$610$	12.2874	−	5.95314i	0.497503	−	0.241036i
$611$	8.41000	+	12.5865i	0.340232	+	0.509193i
$612$	−1.57004	−	0.444290i	−0.0634649	−	0.0179593i
$613$	−1.44115	−	7.24514i	−0.0582074	−	0.292629i	0.940707	−	0.339222i	$-0.110164\pi$
$613$	−1.44115	−	7.24514i	−0.0582074	−	0.292629i	−0.998914	+	0.0465930i	$0.985164\pi$
$614$	−2.45976	−	1.44315i	−0.0992677	−	0.0582406i
$615$	18.1512	−	7.51847i	0.731927	−	0.303174i
$616$	−8.31659	−	21.3317i	−0.335085	−	0.859481i
$617$	−3.89273	−	1.61242i	−0.156715	−	0.0649136i	0.302947	−	0.953007i	$-0.402030\pi$
$617$	−3.89273	−	1.61242i	−0.156715	−	0.0649136i	−0.459662	+	0.888094i	$0.652030\pi$
$618$	−14.3203	+	10.8303i	−0.576048	+	0.435658i
$619$	6.36631	+	4.25383i	0.255884	+	0.170976i	0.676895	−	0.736079i	$-0.263325\pi$
$619$	6.36631	+	4.25383i	0.255884	+	0.170976i	−0.421012	+	0.907055i	$0.638325\pi$
$620$	−9.42587	+	18.4591i	−0.378552	+	0.741335i
$621$	−5.29093	+	26.5993i	−0.212318	+	1.06739i
$622$	14.6821	−	16.5077i	0.588701	−	0.661899i
$623$	−11.0807	−	11.0807i	−0.443938	−	0.443938i
$624$	16.6573	+	23.0119i	0.666824	+	0.921214i
$625$	−1.48653	+	1.48653i	−0.0594614	+	0.0594614i
$626$	2.67409	+	45.6868i	0.106878	+	1.82601i
$627$	10.3756	+	2.06384i	0.414362	+	0.0824218i
$628$	−0.549187	+	6.90034i	−0.0219150	+	0.275354i
$629$	−5.45863	+	8.16942i	−0.217650	+	0.325736i
$630$	6.90603	+	0.958320i	0.275143	+	0.0381804i
$631$	10.3902	−	25.0842i	0.413628	−	0.998587i	−0.570527	−	0.821279i	$-0.693261\pi$
$631$	10.3902	−	25.0842i	0.413628	−	0.998587i	0.984155	−	0.177308i	$-0.0567390\pi$
$632$	−4.12847	−	0.911536i	−0.164222	−	0.0362590i
$633$	6.76661	+	16.3360i	0.268949	+	0.649300i
$634$	3.67956	−	0.958438i	0.146134	−	0.0380644i
$635$	46.5095	−	9.25132i	1.84567	−	0.367127i
$636$	11.2625	−	14.2605i	0.446587	−	0.565468i
$637$	0.653421	−	0.436602i	0.0258895	−	0.0172988i
$638$	24.9590	+	8.66734i	0.988136	+	0.343143i
$639$	−6.20872			−0.245613
$640$	22.0123	−	34.1542i	0.870114	−	1.35006i
$641$	48.6538			1.92171			0.960855	−	0.277053i	$-0.0893579\pi$
$641$	48.6538			1.92171			0.960855	+	0.277053i	$0.0893579\pi$
$642$	13.8247	+	4.80082i	0.545618	+	0.189473i
$643$	24.2613	−	16.2109i	0.956772	−	0.639295i	0.0239813	−	0.999712i	$-0.492366\pi$
$643$	24.2613	−	16.2109i	0.956772	−	0.639295i	0.932791	+	0.360418i	$0.117366\pi$
$644$	16.2542	−	20.5811i	0.640507	−	0.811008i
$645$	14.4558	−	2.87543i	0.569195	−	0.113220i
$646$	−4.83538	+	1.25950i	−0.190246	+	0.0495544i
$647$	5.55831	+	13.4190i	0.218520	+	0.527553i	0.994684	−	0.102978i	$-0.0328371\pi$
$647$	5.55831	+	13.4190i	0.218520	+	0.527553i	−0.776164	+	0.630531i	$0.782837\pi$
$648$	4.39056	−	19.8855i	0.172478	−	0.781174i
$649$	1.19450	−	2.88378i	0.0468883	−	0.113198i
$650$	49.8237	+	6.91382i	1.95424	+	0.271182i
$651$	6.77231	−	10.1355i	0.265428	−	0.397241i
$652$	−0.430116	+	5.40425i	−0.0168446	+	0.211647i
$653$	−32.4067	−	6.44610i	−1.26817	−	0.252255i	−0.485251	−	0.874375i	$-0.661272\pi$
$653$	−32.4067	−	6.44610i	−1.26817	−	0.252255i	−0.782922	+	0.622120i	$0.786272\pi$
$654$	1.39978	+	23.9151i	0.0547356	+	0.935156i
$655$	−52.0435	+	52.0435i	−2.03351	+	2.03351i
$656$	2.19447	−	13.6990i	0.0856795	−	0.534857i
$657$	3.78765	+	3.78765i	0.147770	+	0.147770i
$658$	−8.46290	+	9.51518i	−0.329918	+	0.370940i
$659$	−0.862145	+	4.33430i	−0.0335844	+	0.168840i	−0.993938	−	0.109946i	$-0.964932\pi$
$659$	−0.862145	+	4.33430i	−0.0335844	+	0.168840i	0.960353	+	0.278786i	$0.0899321\pi$
$660$	−15.5703	+	30.4919i	−0.606072	+	1.18690i
$661$	25.3472	+	16.9364i	0.985891	+	0.658751i	0.940349	−	0.340211i	$-0.110499\pi$
$661$	25.3472	+	16.9364i	0.985891	+	0.658751i	0.0455418	+	0.998962i	$0.485499\pi$
$662$	−1.33244	+	1.00771i	−0.0517866	+	0.0391656i
$663$	10.4453	+	4.32658i	0.405661	+	0.168030i
$664$	22.6132	−	8.81617i	0.877561	−	0.342134i
$665$	19.7258	−	8.17068i	0.764933	−	0.316845i
$666$	3.85819	+	2.26361i	0.149502	+	0.0877130i
$667$	5.90418	+	29.6823i	0.228611	+	1.14930i
$668$	3.03082	+	0.857664i	0.117266	+	0.0331840i
$669$	−6.57492	−	9.84006i	−0.254201	−	0.380439i
$670$	−66.6430	+	32.2879i	−2.57464	+	1.24739i
$671$			8.12395i			0.313622i
$672$	−15.2011	+	18.4396i	−0.586396	+	0.711325i
$673$			26.5263i			1.02251i	0.859428	+	0.511257i	$0.170820\pi$
$673$			26.5263i			1.02251i	−0.859428	+	0.511257i	$0.829180\pi$
$674$	−20.1973	−	41.6877i	−0.777971	−	1.60575i
$675$	−24.3109	−	36.3838i	−0.935727	−	1.40041i
$676$	7.09981	+	12.7039i	0.273070	+	0.488611i
$677$	5.43408	+	27.3189i	0.208849	+	1.04995i	0.932881	+	0.360186i	$0.117287\pi$
$677$	5.43408	+	27.3189i	0.208849	+	1.04995i	−0.724032	+	0.689766i	$0.757713\pi$
$678$	17.4861	−	29.8040i	0.671549	−	1.14462i
$679$	−27.3920	+	11.3461i	−1.05121	+	0.435424i
$680$	0.338872	−	16.1678i	0.0129952	−	0.620005i
$681$	38.7485	+	16.0502i	1.48485	+	0.615043i
$682$	−7.43891	−	9.83609i	−0.284851	−	0.376643i
$683$	−31.4771	−	21.0323i	−1.20444	−	0.804779i	−0.219151	−	0.975691i	$-0.570329\pi$
$683$	−31.4771	−	21.0323i	−1.20444	−	0.804779i	−0.985286	+	0.170912i	$0.945329\pi$
$684$	0.701071	+	2.16416i	0.0268061	+	0.0827488i
$685$	4.78503	−	24.0560i	0.182827	−	0.919132i
$686$	−19.3193	−	17.1828i	−0.737613	−	0.656041i
$687$	16.7793	+	16.7793i	0.640171	+	0.640171i
$688$	3.61960	−	9.75837i	0.137996	−	0.372034i
$689$	18.3427	−	18.3427i	0.698801	−	0.698801i
$690$	−39.1498	+	2.29148i	−1.49041	+	0.0872350i
$691$	25.4829	+	5.06887i	0.969416	+	0.192829i	0.654309	−	0.756227i	$-0.272960\pi$
$691$	25.4829	+	5.06887i	0.969416	+	0.192829i	0.315107	+	0.949056i	$0.397960\pi$
$692$	−8.08913	+	6.89645i	−0.307502	+	0.262164i
$693$	−2.30478	+	3.44934i	−0.0875512	+	0.131030i
$694$	2.46313	−	17.7503i	0.0934991	−	0.673790i
$695$	−22.4538	+	54.2084i	−0.851723	+	2.05624i
$696$	−4.81211	−	27.1543i	−0.182402	−	1.02928i
$697$	−2.11298	−	5.10119i	−0.0800348	−	0.193221i
$698$	−9.40620	−	36.1116i	−0.356030	−	1.36684i
$699$	−29.8023	+	5.92804i	−1.12723	+	0.224219i
$700$	4.93653	+	42.0257i	0.186583	+	1.58842i
$701$	30.2742	−	20.2286i	1.14344	−	0.764023i	0.168328	−	0.985731i	$-0.446163\pi$
$701$	30.2742	−	20.2286i	1.14344	−	0.764023i	0.975113	+	0.221708i	$0.0711633\pi$
$702$	11.5730	−	33.3262i	0.436794	−	1.25782i
$703$	13.6983			0.516642
$704$	12.5779	+	20.6475i	0.474046	+	0.778183i
$705$	19.0422			0.717172
$706$	3.60387	−	10.3779i	0.135634	−	0.390578i
$707$	27.6734	−	18.4908i	1.04077	−	0.695417i
$708$	−3.23573	+	0.380084i	−0.121606	+	0.0142844i
$709$	−7.11157	+	1.41458i	−0.267081	+	0.0531256i	−0.326814	−	0.945089i	$-0.605975\pi$
$709$	−7.11157	+	1.41458i	−0.267081	+	0.0531256i	0.0597332	+	0.998214i	$0.480975\pi$
$710$	−15.5104	−	59.5464i	−0.582095	−	2.23474i
$711$	0.293159	+	0.707747i	0.0109943	+	0.0265426i
$712$	13.5630	+	9.47954i	0.508295	+	0.355261i
$713$	5.40577	−	13.0507i	0.202448	−	0.488752i
$714$	−1.30725	+	9.42056i	−0.0489227	+	0.352556i
$715$	−27.1533	+	40.6378i	−1.01548	+	1.51977i
$716$	15.1544	+	17.7752i	0.566347	+	0.664291i
$717$	14.6795	+	2.91994i	0.548217	+	0.109047i
$718$	8.37912	−	0.490438i	0.312706	−	0.0183030i
$719$	24.9786	−	24.9786i	0.931543	−	0.931543i	−0.0662593	−	0.997802i	$-0.521106\pi$
$719$	24.9786	−	24.9786i	0.931543	−	0.931543i	0.997802	+	0.0662593i	$0.0211064\pi$
$720$	−7.35720	+	0.276080i	−0.274187	+	0.0102889i
$721$	−15.2461	−	15.2461i	−0.567795	−	0.567795i
$722$	−14.8723	−	13.2276i	−0.553491	−	0.492281i
$723$	−1.14040	+	5.73317i	−0.0424119	+	0.213219i
$724$	−7.96076	+	2.57886i	−0.295859	+	0.0958424i
$725$	−40.6009	−	27.1287i	−1.50788	−	1.00753i
$726$	2.51169	+	3.32108i	0.0932176	+	0.123257i
$727$	−49.4936	−	20.5009i	−1.83562	−	0.760337i	−0.961608	−	0.274425i	$-0.911512\pi$
$727$	−49.4936	−	20.5009i	−1.83562	−	0.760337i	−0.874008	−	0.485912i	$-0.838488\pi$
$728$	−24.6228	+	23.6118i	−0.912581	+	0.875112i
$729$	−27.6258	+	11.4430i	−1.02318	+	0.423814i
$730$	−26.8643	+	45.7887i	−0.994294	+	1.69472i
$731$	−0.808107	−	4.06263i	−0.0298889	−	0.150262i
$732$	7.40196	−	4.13673i	0.273584	−	0.152898i
$733$	−16.9138	−	25.3133i	−0.624725	−	0.934967i	−0.999968	−	0.00804070i	$-0.997441\pi$
$733$	−16.9138	−	25.3133i	−0.624725	−	0.934967i	0.375242	−	0.926927i	$-0.377559\pi$
$734$	20.9705	+	43.2836i	0.774036	+	1.59763i
$735$		−	0.988571i		−	0.0364640i
$736$	−13.1083	+	24.3944i	−0.483177	+	0.899191i
$737$		−	44.0616i		−	1.62303i
$738$	−2.26226	+	1.09604i	−0.0832750	+	0.0403460i
$739$	23.5325	+	35.2188i	0.865656	+	1.29555i	0.954107	+	0.299465i	$0.0968082\pi$
$739$	23.5325	+	35.2188i	0.865656	+	1.29555i	−0.0884513	+	0.996081i	$0.528192\pi$
$740$	−12.0713	+	42.6578i	−0.443751	+	1.56813i
$741$	−3.07512	−	15.4597i	−0.112967	−	0.567926i
$742$	18.8216	+	11.0427i	0.690963	+	0.405390i
$743$	14.7692	−	6.11761i	0.541830	−	0.224433i	−0.0949455	−	0.995482i	$-0.530268\pi$
$743$	14.7692	−	6.11761i	0.541830	−	0.224433i	0.636776	+	0.771049i	$0.280268\pi$
$744$	−5.17403	+	11.7864i	−0.189689	+	0.432109i
$745$	−6.31676	−	2.61649i	−0.231428	−	0.0958607i
$746$	−1.05861	+	0.800611i	−0.0387584	+	0.0293125i
$747$	−3.65655	−	2.44323i	−0.133786	−	0.0893930i
$748$	8.56941	+	4.37585i	0.313329	+	0.159997i
$749$	−3.42858	+	17.2367i	−0.125278	+	0.629814i
$750$	15.4330	−	17.3519i	0.563532	−	0.633602i
$751$	−27.8491	−	27.8491i	−1.01623	−	1.01623i	−0.999866	−	0.0163606i	$-0.994792\pi$
$751$	−27.8491	−	27.8491i	−1.01623	−	1.01623i	−0.0163606	−	0.999866i	$-0.505208\pi$
$752$	7.04614	−	11.4529i	0.256946	−	0.417644i
$753$	−4.32890	+	4.32890i	−0.157754	+	0.157754i
$754$	−2.30028	−	39.3002i	−0.0837712	−	1.43123i
$755$	−48.8818	−	9.72319i	−1.77899	−	0.353863i
$756$	29.5837	+	2.35452i	1.07595	+	0.0856331i
$757$	1.58238	−	2.36820i	0.0575127	−	0.0860738i	−0.801599	−	0.597862i	$-0.796017\pi$
$757$	1.58238	−	2.36820i	0.0575127	−	0.0860738i	0.859111	+	0.511789i	$0.171017\pi$
$758$	36.0108	+	4.99707i	1.30797	+	0.181502i
$759$	8.92960	−	21.5580i	0.324124	−	0.782504i
$760$	−19.0046	+	12.1302i	−0.689368	+	0.440010i
$761$	10.1275	+	24.4500i	0.367123	+	0.886312i	0.994219	+	0.107371i	$0.0342432\pi$
$761$	10.1275	+	24.4500i	0.367123	+	0.886312i	−0.627096	+	0.778942i	$0.715757\pi$
$762$	28.4994	−	7.42340i	1.03242	−	0.268921i
$763$	−28.2155	+	5.61242i	−1.02147	+	0.203183i
$764$	28.0522	+	22.1547i	1.01489	+	0.801527i
$765$	−2.43629	+	1.62788i	−0.0880843	+	0.0588560i
$766$	48.2785	+	16.7653i	1.74437	+	0.605757i
$767$	−4.65086			−0.167933
$768$	12.4079	−	21.9738i	0.447730	−	0.792912i
$769$	−48.9485			−1.76513			−0.882564	−	0.470193i	$-0.844184\pi$
$769$	−48.9485			−1.76513			−0.882564	+	0.470193i	$0.844184\pi$
$770$	−38.8396	−	13.4876i	−1.39968	−	0.486058i
$771$	6.28477	−	4.19935i	0.226341	−	0.151236i
$772$	31.4274	+	24.8203i	1.13110	+	0.893302i
$773$	−30.5401	+	6.07480i	−1.09845	+	0.218495i	−0.710858	−	0.703335i	$-0.751693\pi$
$773$	−30.5401	+	6.07480i	−1.09845	+	0.218495i	−0.387593	+	0.921831i	$0.626693\pi$
$774$	−1.82495	+	0.475356i	−0.0655966	+	0.0170863i
$775$	8.72214	+	21.0571i	0.313309	+	0.756394i
$776$	26.3905	−	16.8445i	0.947363	−	0.604683i
$777$	9.97791	−	24.0888i	0.357955	−	0.864181i
$778$	−24.6234	−	3.41688i	−0.882791	−	0.122501i
$779$	−4.27678	+	6.40065i	−0.153232	+	0.229327i
$780$	50.8528	+	4.04729i	1.82082	+	0.144916i
$781$	35.9091	+	7.14276i	1.28493	+	0.255588i
$782$	0.643993	+	11.0026i	0.0230291	+	0.393452i
$783$	−24.2163	+	24.2163i	−0.865419	+	0.865419i
$784$	−0.594573	−	0.365798i	−0.0212347	−	0.0130642i
$785$	8.78967	+	8.78967i	0.313717	+	0.313717i
$786$	−30.3775	+	34.1546i	−1.08353	+	1.21825i
$787$	7.20769	−	36.2355i	0.256926	−	1.29166i	−0.609674	−	0.792652i	$-0.708700\pi$
$787$	7.20769	−	36.2355i	0.256926	−	1.29166i	0.866600	−	0.499003i	$-0.166300\pi$
$788$	−29.6954	−	15.1636i	−1.05786	−	0.540179i
$789$	−18.9527	−	12.6638i	−0.674733	−	0.450842i
$790$	−6.05548	+	4.57969i	−0.215444	+	0.162938i
$791$	38.3375	+	15.8799i	1.36313	+	0.564625i
$792$	1.76084	−	4.01117i	0.0625688	−	0.142531i
$793$	11.1833	−	4.63227i	0.397130	−	0.164497i
$794$	−8.34052	−	4.89340i	−0.295994	−	0.173660i
$795$	−6.36612	−	32.0046i	−0.225783	−	1.13509i
$796$	−8.03839	+	28.4062i	−0.284913	+	1.00683i
$797$	−7.09159	−	10.6133i	−0.251197	−	0.375943i	0.684345	−	0.729158i	$-0.260088\pi$
$797$	−7.09159	−	10.6133i	−0.251197	−	0.375943i	−0.935542	+	0.353215i	$0.885088\pi$
$798$	11.9331	−	5.78149i	0.422428	−	0.204663i
$799$		−	5.35160i		−	0.189326i
$800$	−12.8765	−	42.7872i	−0.455252	−	1.51275i
$801$		−	2.99825i		−	0.105938i
$802$	12.2178	+	25.2178i	0.431425	+	0.890471i
$803$	−17.5490	−	26.2639i	−0.619291	−	0.926834i
$804$	−40.1458	+	22.4363i	−1.41583	+	0.791267i
$805$	−9.18770	−	46.1897i	−0.323824	−	1.62797i
$806$	−9.29852	+	15.8488i	−0.327527	+	0.558250i
$807$	−18.3566	+	7.60357i	−0.646185	+	0.267658i
$808$	−25.3666	+	24.3251i	−0.892395	+	0.855755i
$809$	−18.8371	−	7.80259i	−0.662277	−	0.274324i	0.0261191	−	0.999659i	$-0.491685\pi$
$809$	−18.8371	−	7.80259i	−0.662277	−	0.274324i	−0.688397	+	0.725335i	$0.741685\pi$
$810$	−22.0588	−	29.1672i	−0.775067	−	1.02483i
$811$	30.9904	+	20.7071i	1.08822	+	0.727126i	0.964206	−	0.265154i	$-0.0854228\pi$
$811$	30.9904	+	20.7071i	1.08822	+	0.727126i	0.124015	+	0.992280i	$0.460423\pi$
$812$	31.5052	−	10.2060i	1.10561	−	0.358159i
$813$	−0.507320	+	2.55047i	−0.0177925	+	0.0894488i
$814$	−19.7103	−	17.5305i	−0.690844	−	0.614444i
$815$	6.88394	+	6.88394i	0.241134	+	0.241134i
$816$	−0.376604	−	10.0360i	−0.0131838	−	0.351331i
$817$	−4.08357	+	4.08357i	−0.142866	+	0.142866i
$818$	31.3762	−	1.83648i	1.09704	−	0.0642109i
$819$	6.06248	+	1.20590i	0.211840	+	0.0421377i
$820$	−16.1634	−	18.9587i	−0.564451	−	0.662068i
$821$	−20.3593	+	30.4698i	−0.710544	+	1.06340i	0.283974	+	0.958832i	$0.408347\pi$
$821$	−20.3593	+	30.4698i	−0.710544	+	1.06340i	−0.994517	+	0.104571i	$0.966653\pi$
$822$	2.09369	−	15.0879i	0.0730257	−	0.526252i
$823$	4.39690	−	10.6151i	0.153266	−	0.370018i	−0.828533	−	0.559941i	$-0.810824\pi$
$823$	4.39690	−	10.6151i	0.153266	−	0.370018i	0.981799	+	0.189923i	$0.0608239\pi$
$824$	18.6616	+	13.0431i	0.650107	+	0.454377i
$825$	14.4078	+	34.7835i	0.501615	+	1.21101i
$826$	−0.986189	−	3.78611i	−0.0343139	−	0.131735i
$827$	−20.2588	+	4.02973i	−0.704467	+	0.140127i	−0.534309	−	0.845289i	$-0.679428\pi$
$827$	−20.2588	+	4.02973i	−0.704467	+	0.140127i	−0.170159	+	0.985417i	$0.554428\pi$
$828$	4.98351	−	0.585385i	0.173189	−	0.0203436i
$829$	−0.0650754	+	0.0434820i	−0.00226016	+	0.00151019i	−0.556700	−	0.830714i	$-0.687933\pi$
$829$	−0.0650754	+	0.0434820i	−0.00226016	+	0.00151019i	0.554440	+	0.832224i	$0.312933\pi$
$830$	14.2978	−	41.1727i	0.496283	−	1.42912i
$831$	15.7147			0.545138
$832$	21.2511	−	29.0877i	0.736750	−	1.00843i
$833$	−0.277826			−0.00962612
$834$	−11.9539	+	34.4230i	−0.413928	+	1.19197i
$835$	4.70306	−	3.14248i	0.162756	−	0.108750i
$836$	−1.56501	−	13.3233i	−0.0541271	−	0.460796i
$837$	15.6780	−	3.11854i	0.541910	−	0.107793i
$838$	7.83593	+	30.0831i	0.270688	+	1.03920i
$839$	−8.26659	−	19.9573i	−0.285394	−	0.689003i	0.714550	−	0.699585i	$-0.246632\pi$
$839$	−8.26659	−	19.9573i	−0.285394	−	0.689003i	−0.999944	+	0.0105819i	$0.996632\pi$
$840$	7.48829	+	42.2557i	0.258371	+	1.45796i
$841$	−3.52696	+	8.51482i	−0.121619	+	0.293615i
$842$	−2.61319	+	18.8316i	−0.0900563	+	0.648981i
$843$	1.69736	−	2.54029i	0.0584604	−	0.0874921i
$844$	17.0628	−	14.5470i	0.587327	−	0.500730i
$845$	25.6318	+	5.09847i	0.881759	+	0.175393i
$846$	−2.43228	+	0.142364i	−0.0836237	+	0.00489458i
$847$	−3.53578	+	3.53578i	−0.121491	+	0.121491i
$848$	−21.6047	−	8.01369i	−0.741909	−	0.275191i
$849$	12.4881	+	12.4881i	0.428591	+	0.428591i
$850$	−13.2877	−	11.8182i	−0.455764	−	0.405362i
$851$	5.89461	−	29.6342i	0.202065	−	1.01585i
$852$	−11.7770	−	36.3549i	−0.403474	−	1.24550i
$853$	29.9713	+	20.0262i	1.02620	+	0.685683i	0.950269	−	0.311431i	$-0.100808\pi$
$853$	29.9713	+	20.0262i	1.02620	+	0.685683i	0.0759277	+	0.997113i	$0.475808\pi$
$854$	6.14232	+	8.12167i	0.210186	+	0.277918i
$855$	3.77416	+	1.56331i	0.129073	+	0.0534640i
$856$	0.388882	−	18.5538i	0.0132917	−	0.634155i
$857$	17.6508	−	7.31122i	0.602941	−	0.249747i	−0.0602657	−	0.998182i	$-0.519195\pi$
$857$	17.6508	−	7.31122i	0.602941	−	0.249747i	0.663207	+	0.748436i	$0.269195\pi$
$858$	−15.3599	+	26.1801i	−0.524379	+	0.893773i
$859$	−2.96755	−	14.9189i	−0.101252	−	0.509026i	−0.997813	−	0.0661060i	$-0.978942\pi$
$859$	−2.96755	−	14.9189i	−0.101252	−	0.509026i	0.896561	−	0.442920i	$-0.146058\pi$
$860$	−9.11807	−	16.3152i	−0.310924	−	0.556343i
$861$	8.14047	+	12.1831i	0.277427	+	0.415198i
$862$	−9.81029	−	20.2487i	−0.334140	−	0.689672i
$863$			55.1695i			1.87799i	0.343930	+	0.938995i	$0.388242\pi$
$863$			55.1695i			1.87799i	−0.343930	+	0.938995i	$0.611758\pi$
$864$	−31.1939	+	3.00296i	−1.06124	+	0.102163i
$865$			19.0887i			0.649034i
$866$	32.1879	−	15.5947i	1.09379	−	0.529930i
$867$	12.6754	+	18.9701i	0.430480	+	0.644259i
$868$	−14.8737	−	4.20896i	−0.504845	−	0.142861i
$869$	−0.881306	−	4.43063i	−0.0298963	−	0.150299i
$870$	−42.7133	−	25.0600i	−1.44812	−	0.849613i
$871$	−60.6545	+	25.1239i	−2.05520	+	0.851291i
$872$	28.3033	−	11.0346i	0.958471	−	0.373678i
$873$	−5.24094	−	2.17087i	−0.177379	−	0.0734728i
$874$	12.2557	−	9.26883i	0.414555	−	0.313523i
$875$	23.1871	+	15.4931i	0.783867	+	0.523763i
$876$	−14.9938	+	29.3630i	−0.506594	+	0.992085i
$877$	7.99284	−	40.1827i	0.269899	−	1.35687i	−0.573332	−	0.819323i	$-0.694350\pi$
$877$	7.99284	−	40.1827i	0.269899	−	1.35687i	0.843231	−	0.537551i	$-0.180650\pi$
$878$	−18.9186	+	21.2710i	−0.638473	+	0.717860i
$879$	0.158497	+	0.158497i	0.00534598	+	0.00534598i
$880$	42.8691	+	6.86727i	1.44512	+	0.231496i
$881$	41.4201	−	41.4201i	1.39548	−	1.39548i	0.583018	−	0.812459i	$-0.301872\pi$
$881$	41.4201	−	41.4201i	1.39548	−	1.39548i	0.812459	−	0.583018i	$-0.198128\pi$
$882$	0.00739078	+	0.126271i	0.000248860	+	0.00425177i
$883$	−20.2589	−	4.02975i	−0.681766	−	0.135612i	−0.157955	−	0.987446i	$-0.550490\pi$
$883$	−20.2589	−	4.02975i	−0.681766	−	0.135612i	−0.523811	+	0.851834i	$0.675490\pi$
$884$	1.13745	−	14.2916i	0.0382564	−	0.480678i
$885$	−3.25037	+	4.86453i	−0.109260	+	0.163519i
$886$	33.1031	+	4.59357i	1.11212	+	0.154324i
$887$	−18.0495	+	43.5752i	−0.606042	+	1.46311i	0.261229	+	0.965277i	$0.415872\pi$
$887$	−18.0495	+	43.5752i	−0.606042	+	1.46311i	−0.867271	+	0.497837i	$0.834128\pi$
$888$	−5.93604	+	26.8851i	−0.199201	+	0.902207i
$889$	13.5341	+	32.6741i	0.453918	+	1.09585i
$890$	28.7555	−	7.49011i	0.963886	−	0.251069i
$891$	21.3408	−	4.24495i	0.714944	−	0.142211i
$892$	−9.30123	+	11.7772i	−0.311428	+	0.394330i
$893$	−6.20372	+	4.14519i	−0.207600	+	0.138714i
$894$	−4.01123	−	1.39295i	−0.134155	−	0.0465873i
$895$	41.9458			1.40209
$896$	28.1854	+	11.1319i	0.941609	+	0.371892i
$897$	−34.7679			−1.16087
$898$	33.8177	+	11.7437i	1.12851	+	0.391891i
$899$	14.8317	−	9.91020i	0.494664	−	0.330524i
$900$	−5.01786	+	6.35361i	−0.167262	+	0.211787i
$901$	−8.99454	+	1.78912i	−0.299651	+	0.0596044i
$902$	14.3451	−	3.73655i	0.477639	−	0.124413i
$903$	4.20657	+	10.1555i	0.139986	+	0.337955i
$904$	−42.7880	−	9.44727i	−1.42311	−	0.314211i
$905$	−5.75055	+	13.8831i	−0.191155	+	0.461489i
$906$	−30.6587	−	4.25438i	−1.01857	−	0.141342i
$907$	−14.0167	+	20.9775i	−0.465418	+	0.696548i	−0.987724	−	0.156211i	$-0.950072\pi$
$907$	−14.0167	+	20.9775i	−0.465418	+	0.696548i	0.522305	+	0.852758i	$0.325072\pi$
$908$	4.21954	−	53.0171i	0.140030	−	1.75943i
$909$	6.24563	+	1.24233i	0.207155	+	0.0412056i
$910$	3.57955	+	61.1564i	0.118661	+	2.02732i
$911$	3.97097	−	3.97097i	0.131564	−	0.131564i	−0.638258	−	0.769822i	$-0.720345\pi$
$911$	3.97097	−	3.97097i	0.131564	−	0.131564i	0.769822	+	0.638258i	$0.220345\pi$
$912$	−11.3423	+	8.21017i	−0.375582	+	0.271866i
$913$	18.3374	+	18.3374i	0.606880	+	0.606880i
$914$	4.01448	−	4.51364i	0.132787	−	0.149298i
$915$	2.97064	−	14.9344i	0.0982064	−	0.493717i
$916$	13.6846	−	26.7992i	0.452153	−	0.885471i
$917$	−45.6403	−	30.4959i	−1.50718	−	1.00706i
$918$	−9.94751	+	7.52318i	−0.328317	+	0.248302i
$919$	−40.2073	−	16.6544i	−1.32632	−	0.549378i	−0.396714	−	0.917942i	$-0.629850\pi$
$919$	−40.2073	−	16.6544i	−1.32632	−	0.549378i	−0.929602	+	0.368564i	$0.879850\pi$
$920$	18.0639	+	46.3333i	0.595550	+	1.52757i
$921$	−2.93840	+	1.21712i	−0.0968235	+	0.0401056i
$922$	7.42869	+	4.35843i	0.244651	+	0.143537i
$923$	−10.6427	−	53.5046i	−0.350310	−	1.76113i
$924$	−24.5693	−	6.95263i	−0.808270	−	0.228725i
$925$	27.0847	+	40.5351i	0.890540	+	1.33279i
$926$	7.58742	−	3.67604i	0.249338	−	0.120802i
$927$		−	4.12534i		−	0.135494i
$928$	−30.8773	+	16.4169i	−1.01360	+	0.538912i
$929$		−	5.16429i		−	0.169435i	−0.996405	−	0.0847174i	$-0.973001\pi$
$929$		−	5.16429i		−	0.169435i	0.996405	−	0.0847174i	$-0.0269987\pi$
$930$	10.0784	+	20.8020i	0.330484	+	0.682126i
$931$	0.215196	+	0.322064i	0.00705277	+	0.0105552i
$932$	18.7980	+	33.6357i	0.615748	+	1.10177i
$933$	−4.80667	−	24.1648i	−0.157363	−	0.791119i
$934$	24.4419	−	41.6598i	0.799763	−	1.36315i
$935$	15.9634	−	6.61227i	0.522060	−	0.216244i
$936$	−6.52574	−	0.136778i	−0.213301	−	0.00447073i
$937$	−12.9512	−	5.36457i	−0.423097	−	0.175253i	0.160967	−	0.986960i	$-0.448539\pi$
$937$	−12.9512	−	5.36457i	−0.423097	−	0.175253i	−0.584065	+	0.811707i	$0.698539\pi$
$938$	−33.3139	−	44.0493i	−1.08774	−	1.43826i
$939$	42.4373	+	28.3557i	1.38489	+	0.925353i
$940$	−7.44163	−	22.9718i	−0.242719	−	0.749258i
$941$	3.17307	−	15.9521i	0.103439	−	0.520023i	−0.893973	−	0.448121i	$-0.852093\pi$
$941$	3.17307	−	15.9521i	0.103439	−	0.520023i	0.997412	−	0.0719017i	$-0.0229068\pi$
$942$	5.76840	+	5.13048i	0.187945	+	0.167160i
$943$	12.0065	+	12.0065i	0.390984	+	0.390984i
$944$	1.72303	+	3.75493i	0.0560799	+	0.122213i
$945$	37.6838	−	37.6838i	1.22585	−	1.22585i
$946$	11.1018	−	0.649797i	0.360949	−	0.0211267i
$947$	−43.7095	−	8.69436i	−1.42037	−	0.282529i	−0.575630	−	0.817710i	$-0.695243\pi$
$947$	−43.7095	−	8.69436i	−1.42037	−	0.282529i	−0.844737	+	0.535181i	$0.820243\pi$
$948$	−3.58810	+	3.05907i	−0.116536	+	0.0993539i
$949$	−26.1480	+	39.1333i	−0.848802	+	1.27032i
$950$	−3.40774	+	24.5575i	−0.110562	+	0.796751i
$951$	1.62278	−	3.91773i	0.0526221	−	0.127041i
$952$	11.8755	−	2.10450i	0.384887	−	0.0682072i
$953$	4.09229	+	9.87966i	0.132562	+	0.320033i	0.976198	−	0.216883i	$-0.0695890\pi$
$953$	4.09229	+	9.87966i	0.132562	+	0.320033i	−0.843635	+	0.536916i	$0.819589\pi$
$954$	1.05243	+	4.04039i	0.0340735	+	0.130813i
$955$	62.9569	−	12.5229i	2.03724	−	0.405232i
$956$	−2.21420	−	18.8499i	−0.0716122	−	0.609650i
$957$	24.4999	−	16.3703i	0.791970	−	0.529177i
$958$	−9.10111	+	26.2081i	−0.294044	+	0.846745i
$959$	18.2924			0.590691
$960$	−15.5721	−	42.5561i	−0.502587	−	1.37349i
$961$	22.6740			0.731419
$962$	−12.8934	+	37.1287i	−0.415701	+	1.19708i
$963$	−2.79583	+	1.86812i	−0.0900945	+	0.0601992i
$964$	7.36194	−	0.864766i	0.237112	−	0.0278522i
$965$	70.5318	−	14.0296i	2.27050	−	0.451630i
$966$	−7.37235	−	28.3034i	−0.237201	−	0.910646i
$967$	−8.17090	−	19.7263i	−0.262758	−	0.634355i	0.736349	−	0.676602i	$-0.236548\pi$
$967$	−8.17090	−	19.7263i	−0.262758	−	0.634355i	−0.999107	+	0.0422473i	$0.986548\pi$
$968$	3.02487	−	4.32788i	0.0972230	−	0.139103i
$969$	−2.13252	+	5.14836i	−0.0685064	+	0.165389i
$970$	7.72757	−	55.6878i	0.248117	−	1.78803i
$971$	−12.6361	+	18.9113i	−0.405513	+	0.606893i	−0.976877	−	0.213804i	$-0.931415\pi$
$971$	−12.6361	+	18.9113i	−0.405513	+	0.606893i	0.571364	+	0.820697i	$0.306415\pi$
$972$	6.83027	+	8.01151i	0.219081	+	0.256969i
$973$	−42.9186	−	8.53704i	−1.37591	−	0.273685i
$974$	−60.2056	+	3.52389i	−1.92911	+	0.112913i
$975$	39.6670	−	39.6670i	1.27036	−	1.27036i
$976$	−7.88305	−	7.31282i	−0.252330	−	0.234078i
$977$	−6.39950	−	6.39950i	−0.204738	−	0.204738i	0.597288	−	0.802027i	$-0.296245\pi$
$977$	−6.39950	−	6.39950i	−0.204738	−	0.204738i	−0.802027	+	0.597288i	$0.796245\pi$
$978$	4.51773	+	4.01812i	0.144461	+	0.128485i
$979$	−3.44930	+	17.3408i	−0.110240	+	0.554215i
$980$	−1.19257	+	0.386329i	−0.0380954	+	0.0123408i
$981$	−4.57664	−	3.05801i	−0.146121	−	0.0976349i
$982$	−3.12726	−	4.13501i	−0.0997948	−	0.131954i
$983$	0.428626	+	0.177543i	0.0136710	+	0.00566273i	0.389508	−	0.921023i	$-0.372645\pi$
$983$	0.428626	+	0.177543i	0.0136710	+	0.00566273i	−0.375837	+	0.926686i	$0.622645\pi$
$984$	−10.7090	−	11.1675i	−0.341391	−	0.356008i
$985$	−55.3178	+	22.9134i	−1.76257	+	0.730082i
$986$	−7.04282	+	12.0041i	−0.224289	+	0.382288i
$987$	2.77060	+	13.9288i	0.0881893	+	0.443357i
$988$	−17.4482	+	9.75130i	−0.555102	+	0.310230i
$989$	7.07696	+	10.5914i	0.225034	+	0.336787i
$990$	−3.42992	−	7.07942i	−0.109010	−	0.224999i
$991$		−	44.6212i		−	1.41744i	−0.705490	−	0.708720i	$-0.749273\pi$
$991$		−	44.6212i		−	1.41744i	0.705490	−	0.708720i	$-0.250727\pi$
$992$	16.2406	+	1.63569i	0.515640	+	0.0519332i
$993$			1.86310i			0.0591238i
$994$	41.2995	−	20.0092i	1.30994	−	0.634654i
$995$	29.4527	+	44.0790i	0.933713	+	1.39740i
$996$	7.37028	−	26.0452i	0.233536	−	0.825273i
$997$	11.3063	+	56.8407i	0.358075	+	1.80016i	0.568643	+	0.822584i	$0.307469\pi$
$997$	11.3063	+	56.8407i	0.358075	+	1.80016i	−0.210568	+	0.977579i	$0.567531\pi$
$998$	−0.0771377	−	0.0452569i	−0.00244175	−	0.00143258i
$999$	31.5888	−	13.0845i	0.999426	−	0.413976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.13.1	yes	56
3.2	odd	2		576.2.bd.a.397.7		56
4.3	odd	2		256.2.i.a.145.5		56
8.3	odd	2		512.2.i.a.33.3		56
8.5	even	2		512.2.i.b.33.5		56
64.5	even	16	inner	64.2.i.a.5.1	✓	56
64.27	odd	16		512.2.i.a.481.3		56
64.37	even	16		512.2.i.b.481.5		56
64.59	odd	16		256.2.i.a.113.5		56
192.5	odd	16		576.2.bd.a.325.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.1	✓	56	64.5	even	16	inner
64.2.i.a.13.1	yes	56	1.1	even	1	trivial
256.2.i.a.113.5		56	64.59	odd	16
256.2.i.a.145.5		56	4.3	odd	2
512.2.i.a.33.3		56	8.3	odd	2
512.2.i.a.481.3		56	64.27	odd	16
512.2.i.b.33.5		56	8.5	even	2
512.2.i.b.481.5		56	64.37	even	16
576.2.bd.a.325.7		56	192.5	odd	16
576.2.bd.a.397.7		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)

\(f(q)\)	\(=\)	\(q+(-1.33595 - 0.463928i) q^{2} +(-1.31138 + 0.876237i) q^{3} +(1.56954 + 1.23957i) q^{4} +(3.52249 - 0.700667i) q^{5} +(2.15846 - 0.562226i) q^{6} +(1.02503 + 2.47464i) q^{7} +(-1.52176 - 2.38416i) q^{8} +(-0.196120 + 0.473476i) q^{9} +O(q^{10})\)	\(q+(-1.33595 - 0.463928i) q^{2} +(-1.31138 + 0.876237i) q^{3} +(1.56954 + 1.23957i) q^{4} +(3.52249 - 0.700667i) q^{5} +(2.15846 - 0.562226i) q^{6} +(1.02503 + 2.47464i) q^{7} +(-1.52176 - 2.38416i) q^{8} +(-0.196120 + 0.473476i) q^{9} +(-5.03094 - 0.698122i) q^{10} +(1.67900 - 2.51280i) q^{11} +(-3.14443 - 0.250260i) q^{12} +(-4.41643 - 0.878483i) q^{13} +(-0.221337 - 3.78154i) q^{14} +(-4.00538 + 4.00538i) q^{15} +(0.926926 + 3.89112i) q^{16} +(1.12567 + 1.12567i) q^{17} +(0.481666 - 0.541556i) q^{18} +(0.432994 - 2.17681i) q^{19} +(6.39722 + 3.26665i) q^{20} +(-3.51257 - 2.34703i) q^{21} +(-3.40882 + 2.57804i) q^{22} +(-4.52287 - 1.87343i) q^{23} +(4.08471 + 1.79312i) q^{24} +(7.29760 - 3.02276i) q^{25} +(5.49259 + 3.22252i) q^{26} +(-1.08077 - 5.43340i) q^{27} +(-1.45867 + 5.15465i) q^{28} +(-3.43450 - 5.14009i) q^{29} +(7.20920 - 3.49279i) q^{30} +2.88548i q^{31} +(0.566869 - 5.62838i) q^{32} +4.76643i q^{33} +(-0.981609 - 2.02606i) q^{34} +(5.34455 + 7.99868i) q^{35} +(-0.894726 + 0.500036i) q^{36} +(1.20408 + 6.05333i) q^{37} +(-1.58834 + 2.70724i) q^{38} +(6.56139 - 2.71782i) q^{39} +(-7.03090 - 7.33194i) q^{40} +(-3.20440 - 1.32731i) q^{41} +(3.60378 + 4.76510i) q^{42} +(-2.16349 - 1.44560i) q^{43} +(5.75005 - 1.86270i) q^{44} +(-0.359082 + 1.80523i) q^{45} +(5.17320 + 4.60110i) q^{46} +(-2.37708 - 2.37708i) q^{47} +(-4.62510 - 4.29054i) q^{48} +(-0.123405 + 0.123405i) q^{49} +(-11.1516 + 0.652714i) q^{50} +(-2.46253 - 0.489827i) q^{51} +(-5.84283 - 6.85330i) q^{52} +(-3.20051 + 4.78991i) q^{53} +(-1.07684 + 7.76016i) q^{54} +(4.15361 - 10.0277i) q^{55} +(4.34009 - 6.20965i) q^{56} +(1.33958 + 3.23403i) q^{57} +(2.20370 + 8.46029i) q^{58} +(1.01300 - 0.201498i) q^{59} +(-11.2516 + 1.32166i) q^{60} +(-2.23513 + 1.49347i) q^{61} +(1.33866 - 3.85487i) q^{62} -1.37271 q^{63} +(-3.36847 + 7.25627i) q^{64} -16.1724 q^{65} +(2.21128 - 6.36773i) q^{66} +(12.1226 - 8.10007i) q^{67} +(0.371437 + 3.16212i) q^{68} +(7.57278 - 1.50632i) q^{69} +(-3.42926 - 13.1654i) q^{70} +(4.63617 + 11.1927i) q^{71} +(1.42729 - 0.252936i) q^{72} +(3.99984 - 9.65646i) q^{73} +(1.19971 - 8.64558i) q^{74} +(-6.92128 + 10.3584i) q^{75} +(3.37791 - 2.87987i) q^{76} +(7.93928 + 1.57922i) q^{77} +(-10.0266 + 0.586865i) q^{78} +(1.05698 - 1.05698i) q^{79} +(5.99146 + 13.0570i) q^{80} +(5.09110 + 5.09110i) q^{81} +(3.66516 + 3.25983i) q^{82} +(-1.67409 + 8.41620i) q^{83} +(-2.60383 - 8.03785i) q^{84} +(4.75386 + 3.17643i) q^{85} +(2.21967 + 2.93496i) q^{86} +(9.00788 + 3.73119i) q^{87} +(-8.54595 - 0.179121i) q^{88} +(-5.40505 + 2.23885i) q^{89} +(1.31721 - 2.24511i) q^{90} +(-2.35304 - 11.8295i) q^{91} +(-4.77658 - 8.54685i) q^{92} +(-2.52837 - 3.78397i) q^{93} +(2.07288 + 4.27847i) q^{94} -7.97117i q^{95} +(4.18841 + 7.87767i) q^{96} +11.0691i q^{97} +(0.222115 - 0.107613i) q^{98} +(0.860463 + 1.28777i) 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

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