LMFDB - Embedded newform 403.2.bt.a.82.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(82,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("403.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bt (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$35$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			82.16
Character	$\chi$	$=$	403.82
Dual form			403.2.bt.a.231.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0617274 + 0.290405i) q^{2} +(-0.640694 + 0.136184i) q^{3} +(1.74657 + 0.777621i) q^{4} +(-2.50432 + 1.44587i) q^{5} -0.194467i q^{6} +(-1.38419 - 1.90518i) q^{7} +(-0.682654 + 0.939592i) q^{8} +(-2.34869 + 1.04571i) q^{9} +O(q^{10})$	\(q+(-0.0617274 + 0.290405i) q^{2} +(-0.640694 + 0.136184i) q^{3} +(1.74657 + 0.777621i) q^{4} +(-2.50432 + 1.44587i) q^{5} -0.194467i q^{6} +(-1.38419 - 1.90518i) q^{7} +(-0.682654 + 0.939592i) q^{8} +(-2.34869 + 1.04571i) q^{9} +(-0.265302 - 0.816516i) q^{10} +(-3.24496 - 4.46631i) q^{11} +(-1.22491 - 0.260364i) q^{12} +(-3.07060 + 1.88983i) q^{13} +(0.638715 - 0.284374i) q^{14} +(1.40760 - 1.26741i) q^{15} +(2.32784 + 2.58533i) q^{16} +(-1.95358 - 1.41936i) q^{17} +(-0.158699 - 0.746620i) q^{18} +(6.97203 - 2.26535i) q^{19} +(-5.49830 + 0.577895i) q^{20} +(1.14630 + 1.03213i) q^{21} +(1.49734 - 0.666658i) q^{22} +(-1.11767 + 0.497619i) q^{23} +(0.309415 - 0.694957i) q^{24} +(1.68108 - 2.91172i) q^{25} +(-0.359274 - 1.00837i) q^{26} +(2.95212 - 2.14484i) q^{27} +(-0.936078 - 4.40390i) q^{28} +(-4.37487 - 0.929907i) q^{29} +(0.281174 + 0.487007i) q^{30} +(-4.51644 + 3.25603i) q^{31} +(-2.90608 + 1.67783i) q^{32} +(2.68727 + 2.41963i) q^{33} +(0.532777 - 0.479715i) q^{34} +(6.22111 + 2.76981i) q^{35} -4.91531 q^{36} +(-9.60910 + 5.54782i) q^{37} +(0.227503 + 2.16454i) q^{38} +(1.70995 - 1.62897i) q^{39} +(0.351055 - 3.34007i) q^{40} +(1.99532 - 0.648318i) q^{41} +(-0.370494 + 0.269180i) q^{42} +(2.47077 + 7.60425i) q^{43} +(-2.19445 - 10.3241i) q^{44} +(4.36993 - 6.01469i) q^{45} +(-0.0755199 - 0.355293i) q^{46} +(1.40205 + 0.455555i) q^{47} +(-1.84351 - 1.33939i) q^{48} +(0.449404 - 1.38312i) q^{49} +(0.741807 + 0.667926i) q^{50} +(1.44494 + 0.643328i) q^{51} +(-6.83257 + 0.912947i) q^{52} +(-1.09519 + 10.4200i) q^{53} +(0.440645 + 0.989705i) q^{54} +(14.5841 + 6.49327i) q^{55} +2.73502 q^{56} +(-4.15843 + 2.40087i) q^{57} +(0.540098 - 1.21308i) q^{58} +(-9.53278 - 3.09739i) q^{59} +(3.44403 - 1.11903i) q^{60} +(0.651677 + 1.12874i) q^{61} +(-0.666777 - 1.51258i) q^{62} +(5.24330 + 3.02722i) q^{63} +(1.84221 + 5.66975i) q^{64} +(4.95731 - 9.17241i) q^{65} +(-0.868548 + 0.631037i) q^{66} -5.61716i q^{67} +(-2.30833 - 3.99815i) q^{68} +(0.648317 - 0.471030i) q^{69} +(-1.18838 + 1.63566i) q^{70} +(-0.0103874 - 0.0233304i) q^{71} +(0.620807 - 2.92067i) q^{72} +(-0.972117 + 2.18341i) q^{73} +(-1.01797 - 3.13298i) q^{74} +(-0.680530 + 2.09445i) q^{75} +(13.9387 + 1.46502i) q^{76} +(-4.01746 + 12.3645i) q^{77} +(0.367508 + 0.597129i) q^{78} +(-2.65788 + 1.18337i) q^{79} +(-9.56770 - 3.10873i) q^{80} +(3.56162 - 3.95558i) q^{81} +(0.0651087 + 0.619468i) q^{82} +(-0.125083 - 0.112625i) q^{83} +(1.19948 + 2.69407i) q^{84} +(6.94459 + 0.729906i) q^{85} +(-2.36082 + 0.248132i) q^{86} +2.92959 q^{87} +6.41169 q^{88} +(3.88297 - 0.408117i) q^{89} +(1.47695 + 1.64032i) q^{90} +(7.85076 + 3.23415i) q^{91} -2.33905 q^{92} +(2.45024 - 2.70119i) q^{93} +(-0.218840 + 0.379043i) q^{94} +(-14.1848 + 15.7538i) q^{95} +(1.63342 - 1.47074i) q^{96} +(6.38211 - 14.3345i) q^{97} +(0.373924 + 0.215885i) q^{98} +(12.2919 + 7.09671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) $ 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9 + 3 * q^10 - 8 * q^12 - 6 * q^13 + 4 * q^14 - 45 * q^15 + 23 * q^16 + 27 * q^17 + 45 * q^18 - 15 * q^19 - 12 * q^20 - 76 * q^21 + 41 * q^22 - 10 * q^23 - 33 * q^24 + 96 * q^25 + 9 * q^26 - 24 * q^27 - 32 * q^28 + 13 * q^29 + 36 * q^30 + 2 * q^31 - 141 * q^32 - 93 * q^33 - 9 * q^34 - 43 * q^35 - 194 * q^36 + 3 * q^37 - 49 * q^38 + 50 * q^39 - 75 * q^40 - 15 * q^41 + 17 * q^42 + 33 * q^43 + 18 * q^44 - 15 * q^45 - 9 * q^46 - 59 * q^48 + 3 * q^49 + 36 * q^50 + 47 * q^51 - 56 * q^52 + 12 * q^53 - 33 * q^54 - 5 * q^55 - 50 * q^56 - 105 * q^57 - 3 * q^58 - 15 * q^59 + 90 * q^60 - 57 * q^61 - 72 * q^62 + 201 * q^63 + 13 * q^64 - 43 * q^65 + 22 * q^66 - 71 * q^68 - 7 * q^69 - 42 * q^71 + 90 * q^72 + 9 * q^73 - 113 * q^74 + 45 * q^75 + 14 * q^76 - 24 * q^77 + 61 * q^78 + 54 * q^79 + 30 * q^80 + 106 * q^81 + 16 * q^82 + 54 * q^83 + 60 * q^84 + 18 * q^85 + 84 * q^86 + 42 * q^87 - 98 * q^88 - 99 * q^89 + 11 * q^90 + 60 * q^91 + 266 * q^92 - 104 * q^93 + 33 * q^94 - 120 * q^95 + 204 * q^96 - 50 * q^97 - 15 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{15}\right)$

Coefficient data

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

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

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

$2$	−0.0617274	+	0.290405i	−0.0436479	+	0.205347i	−0.994568	−	0.104090i	$-0.966807\pi$
$2$	−0.0617274	+	0.290405i	−0.0436479	+	0.205347i	0.950920	+	0.309437i	$0.100140\pi$
$3$	−0.640694	+	0.136184i	−0.369905	+	0.0786257i	−0.389114	−	0.921190i	$-0.627219\pi$
$3$	−0.640694	+	0.136184i	−0.369905	+	0.0786257i	0.0192087	+	0.999815i	$0.493885\pi$
$4$	1.74657	+	0.777621i	0.873283	+	0.388811i
$5$	−2.50432	+	1.44587i	−1.11997	+	0.646613i	−0.941392	−	0.337314i	$-0.890482\pi$
$5$	−2.50432	+	1.44587i	−1.11997	+	0.646613i	−0.178574	+	0.983927i	$0.557148\pi$
$6$		−	0.194467i		−	0.0793907i
$7$	−1.38419	−	1.90518i	−0.523176	−	0.720090i	0.462895	−	0.886413i	$-0.346811\pi$
$7$	−1.38419	−	1.90518i	−0.523176	−	0.720090i	−0.986071	+	0.166323i	$0.946811\pi$
$8$	−0.682654	+	0.939592i	−0.241354	+	0.332196i
$9$	−2.34869	+	1.04571i	−0.782898	+	0.348569i
$10$	−0.265302	−	0.816516i	−0.0838959	−	0.258205i
$11$	−3.24496	−	4.46631i	−0.978393	−	1.34664i	−0.937691	−	0.347471i	$-0.887040\pi$
$11$	−3.24496	−	4.46631i	−0.978393	−	1.34664i	−0.0407023	−	0.999171i	$-0.512960\pi$
$12$	−1.22491	−	0.260364i	−0.353602	−	0.0751605i
$13$	−3.07060	+	1.88983i	−0.851630	+	0.524144i
$13$	−3.07060	+	1.88983i	−0.851630	+	0.524144i
$14$	0.638715	−	0.284374i	0.170704	−	0.0760022i
$15$	1.40760	−	1.26741i	0.363441	−	0.327243i
$16$	2.32784	+	2.58533i	0.581959	+	0.646331i
$17$	−1.95358	−	1.41936i	−0.473812	−	0.344245i	0.325113	−	0.945675i	$-0.394598\pi$
$17$	−1.95358	−	1.41936i	−0.473812	−	0.344245i	−0.798925	+	0.601431i	$0.794598\pi$
$18$	−0.158699	−	0.746620i	−0.0374057	−	0.175980i
$19$	6.97203	−	2.26535i	1.59949	−	0.519707i	0.632511	−	0.774552i	$-0.282024\pi$
$19$	6.97203	−	2.26535i	1.59949	−	0.519707i	0.966982	+	0.254845i	$0.0820244\pi$
$20$	−5.49830	+	0.577895i	−1.22946	+	0.129221i
$21$	1.14630	+	1.03213i	0.250143	+	0.225230i
$22$	1.49734	−	0.666658i	0.319234	−	0.142132i
$23$	−1.11767	+	0.497619i	−0.233050	+	0.103761i	−0.519940	−	0.854203i	$-0.674046\pi$
$23$	−1.11767	+	0.497619i	−0.233050	+	0.103761i	0.286889	+	0.957964i	$0.407379\pi$
$24$	0.309415	−	0.694957i	0.0631591	−	0.141858i
$25$	1.68108	−	2.91172i	0.336216	−	0.582343i
$26$	−0.359274	−	1.00837i	−0.0704595	−	0.197757i
$27$	2.95212	−	2.14484i	0.568136	−	0.412775i
$28$	−0.936078	−	4.40390i	−0.176902	−	0.832259i
$29$	−4.37487	−	0.929907i	−0.812392	−	0.172679i	−0.217059	−	0.976158i	$-0.569647\pi$
$29$	−4.37487	−	0.929907i	−0.812392	−	0.172679i	−0.595333	+	0.803479i	$0.702980\pi$
$30$	0.281174	+	0.487007i	0.0513350	+	0.0889149i
$31$	−4.51644	+	3.25603i	−0.811177	+	0.584800i
$31$	−4.51644	+	3.25603i	−0.811177	+	0.584800i
$32$	−2.90608	+	1.67783i	−0.513728	+	0.296601i
$33$	2.68727	+	2.41963i	0.467793	+	0.421203i
$34$	0.532777	−	0.479715i	0.0913705	−	0.0822704i
$35$	6.22111	+	2.76981i	1.05156	+	0.468184i
$36$	−4.91531			−0.819219
$37$	−9.60910	+	5.54782i	−1.57973	+	0.912056i	−0.584830	+	0.811156i	$0.698839\pi$
$37$	−9.60910	+	5.54782i	−1.57973	+	0.912056i	−0.994897	+	0.100900i	$0.967828\pi$
$38$	0.227503	+	2.16454i	0.0369058	+	0.351135i
$39$	1.70995	−	1.62897i	0.273811	−	0.260843i
$40$	0.351055	−	3.34007i	0.0555067	−	0.528111i
$41$	1.99532	−	0.648318i	0.311616	−	0.101250i	−0.149034	−	0.988832i	$-0.547616\pi$
$41$	1.99532	−	0.648318i	0.311616	−	0.101250i	0.460650	+	0.887582i	$0.347616\pi$
$42$	−0.370494	+	0.269180i	−0.0571685	+	0.0415353i
$43$	2.47077	+	7.60425i	0.376789	+	1.15964i	0.942264	+	0.334872i	$0.108693\pi$
$43$	2.47077	+	7.60425i	0.376789	+	1.15964i	−0.565475	+	0.824766i	$0.691307\pi$
$44$	−2.19445	−	10.3241i	−0.330825	−	1.55641i
$45$	4.36993	−	6.01469i	0.651430	−	0.896617i
$46$	−0.0755199	−	0.355293i	−0.0111348	−	0.0523851i
$47$	1.40205	+	0.455555i	0.204511	+	0.0664495i	0.409481	−	0.912319i	$-0.365710\pi$
$47$	1.40205	+	0.455555i	0.204511	+	0.0664495i	−0.204970	+	0.978768i	$0.565710\pi$
$48$	−1.84351	−	1.33939i	−0.266088	−	0.193324i
$49$	0.449404	−	1.38312i	0.0642005	−	0.197589i
$50$	0.741807	+	0.667926i	0.104907	+	0.0944590i
$51$	1.44494	+	0.643328i	0.202332	+	0.0900840i
$52$	−6.83257	+	0.912947i	−0.947507	+	0.126603i
$53$	−1.09519	+	10.4200i	−0.150435	+	1.43130i	0.615376	+	0.788233i	$0.289004\pi$
$53$	−1.09519	+	10.4200i	−0.150435	+	1.43130i	−0.765812	+	0.643065i	$0.777663\pi$
$54$	0.440645	+	0.989705i	0.0599642	+	0.134682i
$55$	14.5841	+	6.49327i	1.96652	+	0.875552i
$56$	2.73502			0.365482
$57$	−4.15843	+	2.40087i	−0.550798	+	0.318003i
$58$	0.540098	−	1.21308i	0.0709184	−	0.159285i
$59$	−9.53278	−	3.09739i	−1.24106	−	0.403246i	−0.386353	−	0.922351i	$-0.626265\pi$
$59$	−9.53278	−	3.09739i	−1.24106	−	0.403246i	−0.854710	+	0.519105i	$0.826265\pi$
$60$	3.44403	−	1.11903i	0.444622	−	0.144467i
$61$	0.651677	+	1.12874i	0.0834387	+	0.144520i	0.904725	−	0.425996i	$-0.140076\pi$
$61$	0.651677	+	1.12874i	0.0834387	+	0.144520i	−0.821286	+	0.570517i	$0.806743\pi$
$62$	−0.666777	−	1.51258i	−0.0846808	−	0.192098i
$63$	5.24330	+	3.02722i	0.660594	+	0.381394i
$64$	1.84221	+	5.66975i	0.230277	+	0.708719i
$65$	4.95731	−	9.17241i	0.614879	−	1.13770i
$66$	−0.868548	+	0.631037i	−0.106911	+	0.0776753i
$67$		−	5.61716i		−	0.686246i	−0.939291	−	0.343123i	$-0.888515\pi$
$67$		−	5.61716i		−	0.686246i	0.939291	−	0.343123i	$-0.111485\pi$
$68$	−2.30833	−	3.99815i	−0.279926	−	0.484846i
$69$	0.648317	−	0.471030i	0.0780483	−	0.0567054i
$70$	−1.18838	+	1.63566i	−0.142038	+	0.195499i
$71$	−0.0103874	−	0.0233304i	−0.00123275	−	0.00276881i	0.912928	−	0.408121i	$-0.133816\pi$
$71$	−0.0103874	−	0.0233304i	−0.00123275	−	0.00276881i	−0.914161	+	0.405352i	$0.867149\pi$
$72$	0.620807	−	2.92067i	0.0731628	−	0.344204i
$73$	−0.972117	+	2.18341i	−0.113778	+	0.255549i	−0.961454	−	0.274964i	$-0.911334\pi$
$73$	−0.972117	+	2.18341i	−0.113778	+	0.255549i	0.847677	+	0.530513i	$0.178001\pi$
$74$	−1.01797	−	3.13298i	−0.118336	−	0.364201i
$75$	−0.680530	+	2.09445i	−0.0785808	+	0.241847i
$76$	13.9387	+	1.46502i	1.59888	+	0.168049i
$77$	−4.01746	+	12.3645i	−0.457832	+	1.40906i
$78$	0.367508	+	0.597129i	0.0416121	+	0.0676115i
$79$	−2.65788	+	1.18337i	−0.299035	+	0.133139i	−0.550770	−	0.834657i	$-0.685666\pi$
$79$	−2.65788	+	1.18337i	−0.299035	+	0.133139i	0.251734	+	0.967796i	$0.418999\pi$
$80$	−9.56770	−	3.10873i	−1.06970	−	0.347567i
$81$	3.56162	−	3.95558i	0.395735	−	0.439509i
$82$	0.0651087	+	0.619468i	0.00719005	+	0.0684088i
$83$	−0.125083	−	0.112625i	−0.0137297	−	0.0123622i	0.662237	−	0.749294i	$-0.269607\pi$
$83$	−0.125083	−	0.112625i	−0.0137297	−	0.0123622i	−0.675967	+	0.736932i	$0.736274\pi$
$84$	1.19948	+	2.69407i	0.130874	+	0.293948i
$85$	6.94459	+	0.729906i	0.753247	+	0.0791694i
$86$	−2.36082	+	0.248132i	−0.254574	+	0.0267568i
$87$	2.92959			0.314085
$88$	6.41169			0.683489
$89$	3.88297	−	0.408117i	0.411594	−	0.0432603i	0.103531	−	0.994626i	$-0.466986\pi$
$89$	3.88297	−	0.408117i	0.411594	−	0.0432603i	0.308063	+	0.951366i	$0.400319\pi$
$90$	1.47695	+	1.64032i	0.155684	+	0.172905i
$91$	7.85076	+	3.23415i	0.822983	+	0.339031i
$92$	−2.33905			−0.243862
$93$	2.45024	−	2.70119i	0.254078	−	0.280100i
$94$	−0.218840	+	0.379043i	−0.0225717	+	0.0390953i
$95$	−14.1848	+	15.7538i	−1.45533	+	1.61631i
$96$	1.63342	−	1.47074i	0.166710	−	0.150106i
$97$	6.38211	−	14.3345i	0.648005	−	1.45544i	−0.228253	−	0.973602i	$-0.573301\pi$
$97$	6.38211	−	14.3345i	0.648005	−	1.45544i	0.876258	−	0.481841i	$-0.160032\pi$
$98$	0.373924	+	0.215885i	0.0377721	+	0.0218077i
$99$	12.2919	+	7.09671i	1.23538	+	0.713246i
$100$	5.20033	−	3.77826i	0.520033	−	0.377826i
$101$	14.7679	−	6.57509i	1.46946	−	0.654246i	0.493017	−	0.870020i	$-0.335894\pi$
$101$	14.7679	−	6.57509i	1.46946	−	0.654246i	0.976443	+	0.215774i	$0.0692276\pi$
$102$	−0.276018	+	0.379906i	−0.0273298	+	0.0376163i
$103$	−4.49488	+	4.99208i	−0.442894	+	0.491884i	−0.922715	−	0.385483i	$-0.874035\pi$
$103$	−4.49488	+	4.99208i	−0.442894	+	0.491884i	0.479821	+	0.877366i	$0.340702\pi$
$104$	0.320487	−	4.17520i	0.0314263	−	0.409412i
$105$	−4.36303	−	0.927390i	−0.425788	−	0.0905040i
$106$	−2.95841	−	0.961247i	−0.287347	−	0.0933646i
$107$	−0.889401	+	8.46209i	−0.0859816	+	0.818061i	0.863523	+	0.504309i	$0.168253\pi$
$107$	−0.889401	+	8.46209i	−0.0859816	+	0.818061i	−0.949505	+	0.313752i	$0.898414\pi$
$108$	6.82395	−	1.45048i	0.656635	−	0.139572i
$109$	8.80089	+	2.85958i	0.842973	+	0.273898i	0.698500	−	0.715610i	$-0.253851\pi$
$109$	8.80089	+	2.85958i	0.842973	+	0.273898i	0.144473	+	0.989509i	$0.453851\pi$
$110$	−2.78592	+	3.83448i	−0.265627	+	0.365604i
$111$	5.40097	−	4.86306i	0.512638	−	0.461581i
$112$	1.70333	−	8.01354i	0.160950	−	0.757208i
$113$	0.303629	+	2.88883i	0.0285630	+	0.271759i	0.999477	+	0.0323311i	$0.0102931\pi$
$113$	0.303629	+	2.88883i	0.0285630	+	0.271759i	−0.970914	+	0.239428i	$0.923040\pi$
$114$	−0.440535	−	1.35583i	−0.0412599	−	0.126985i
$115$	2.07951	−	2.86220i	0.193916	−	0.266902i
$116$	−6.91788	−	5.02613i	−0.642309	−	0.466665i
$117$	5.23568	−	7.64956i	0.484039	−	0.707202i
$118$	1.48793	−	2.57717i	0.136975	−	0.237248i
$119$			5.68658i			0.521288i
$120$	0.229944	+	2.18777i	0.0209909	+	0.199715i
$121$	−6.01894	+	18.5244i	−0.547176	+	1.68403i
$122$	−0.368017	+	0.119576i	−0.0333187	+	0.0108259i
$123$	−1.19010	+	0.687103i	−0.107307	+	0.0619540i
$124$	−10.4202	+	2.17479i	−0.935764	+	0.195302i
$125$		−	4.73621i		−	0.423619i
$126$	−1.20277	+	1.33582i	−0.107152	+	0.119004i
$127$	1.22180	−	0.259702i	0.108417	−	0.0230448i	−0.153383	−	0.988167i	$-0.549017\pi$
$127$	1.22180	−	0.259702i	0.108417	−	0.0230448i	0.261801	+	0.965122i	$0.415684\pi$
$128$	−8.43479	+	0.886532i	−0.745537	+	0.0783591i
$129$	−2.61858	−	4.53552i	−0.230553	−	0.399330i
$130$	2.35771	+	2.00581i	0.206785	+	0.175922i
$131$	0.679951	+	6.46930i	0.0594076	+	0.565225i	0.983226	+	0.182393i	$0.0583844\pi$
$131$	0.679951	+	6.46930i	0.0594076	+	0.565225i	−0.923818	+	0.382832i	$0.874949\pi$
$132$	2.81194	+	6.31571i	0.244748	+	0.549712i
$133$	−13.9665	−	10.1473i	−1.21105	−	0.879881i
$134$	1.63125	+	0.346733i	0.140918	+	0.0299531i
$135$	−4.29190	+	9.63976i	−0.369388	+	0.829658i
$136$	2.66723	−	0.866637i	0.228713	−	0.0743135i
$137$	−11.6797	+	10.5164i	−0.997864	+	0.898480i	−0.994834	−	0.101515i	$-0.967631\pi$
$137$	−11.6797	+	10.5164i	−0.997864	+	0.898480i	−0.00302957	+	0.999995i	$0.500964\pi$
$138$	0.0967704	+	0.217350i	0.00823764	+	0.0185020i
$139$	−7.08887	+	1.50679i	−0.601270	+	0.127804i	−0.498483	−	0.866900i	$-0.666109\pi$
$139$	−7.08887	+	1.50679i	−0.601270	+	0.127804i	−0.102787	+	0.994703i	$0.532776\pi$
$140$	8.71171	+	9.67533i	0.736274	+	0.817715i
$141$	−0.960327	−	0.100934i	−0.0808741	−	0.00850022i
$142$	0.00741644	−	0.00157641i	0.000622374	−	0.000132290i
$143$	18.4045	+	7.58181i	1.53906	+	0.634023i
$144$	−8.17087	−	3.63790i	−0.680906	−	0.303159i
$145$	12.3006	−	3.99670i	1.02151	−	0.331908i
$146$	−0.574066	−	0.417083i	−0.0475100	−	0.0345181i
$147$	−0.0995715	+	0.947360i	−0.00821252	+	0.0781369i
$148$	−21.0970	+	2.21739i	−1.73417	+	0.182268i
$149$			12.2914i			1.00695i	0.864009	+	0.503476i	$0.167946\pi$
$149$			12.2914i			1.00695i	−0.864009	+	0.503476i	$0.832054\pi$
$150$	−0.566232	−	0.326914i	−0.0462326	−	0.0266924i
$151$	−13.3273	−	18.3435i	−1.08456	−	1.49277i	−0.854400	−	0.519616i	$-0.826075\pi$
$151$	−13.3273	−	18.3435i	−1.08456	−	1.49277i	−0.230161	−	0.973153i	$-0.573925\pi$
$152$	−2.63098	+	8.09731i	−0.213400	+	0.656779i
$153$	6.07258	+	1.29077i	0.490939	+	0.104352i
$154$	−3.34271	−	1.92991i	−0.269363	−	0.155517i
$155$	6.60283	−	14.6843i	0.530352	−	1.17947i
$156$	4.25326	−	1.51540i	0.340533	−	0.121329i
$157$	−4.18519	−	12.8807i	−0.334015	−	1.02799i	−0.967205	−	0.253996i	$-0.918255\pi$
$157$	−4.18519	−	12.8807i	−0.334015	−	1.02799i	0.633191	−	0.773996i	$-0.281745\pi$
$158$	−0.179591	−	0.844907i	−0.0142875	−	0.0672172i
$159$	−0.717356	−	6.82518i	−0.0568900	−	0.541272i
$160$	4.85184	−	8.40364i	0.383572	−	0.664366i
$161$	2.49513	+	1.44056i	0.196643	+	0.113532i
$162$	0.928868	+	1.27848i	0.0729788	+	0.100447i
$163$	−11.8890	−	1.24958i	−0.931216	−	0.0978747i	−0.373243	−	0.927734i	$-0.621754\pi$
$163$	−11.8890	−	1.24958i	−0.931216	−	0.0978747i	−0.557973	+	0.829859i	$0.688421\pi$
$164$	3.98910	+	0.419271i	0.311496	+	0.0327396i
$165$	−10.2282	−	2.17408i	−0.796268	−	0.169252i
$166$	0.0404280	−	0.0293726i	0.00313782	−	0.00227976i
$167$	−6.88989	−	6.20369i	−0.533156	−	0.480056i	0.358020	−	0.933714i	$-0.383452\pi$
$167$	−6.88989	−	6.20369i	−0.533156	−	0.480056i	−0.891176	+	0.453658i	$0.850119\pi$
$168$	−1.75231	+	0.372465i	−0.135194	+	0.0287363i
$169$	5.85711	−	11.6058i	0.450547	−	0.892753i
$170$	−0.640639	+	1.97168i	−0.0491348	+	0.151221i
$171$	−14.0063	+	12.6113i	−1.07109	+	0.964410i
$172$	−1.59786	+	15.2027i	−0.121836	+	1.15919i
$173$	−13.2010	−	14.6612i	−1.00365	−	1.11467i	−0.993398	−	0.114720i	$-0.963403\pi$
$173$	−13.2010	−	14.6612i	−1.00365	−	1.11467i	−0.0102537	−	0.999947i	$-0.503264\pi$
$174$	−0.180836	+	0.850766i	−0.0137091	+	0.0644964i
$175$	−7.87428	+	0.827620i	−0.595240	+	0.0625622i
$176$	3.99311	−	18.7861i	0.300992	−	1.41606i
$177$	6.52941	+	0.686269i	0.490781	+	0.0515831i
$178$	−0.121167	+	1.15282i	−0.00908183	+	0.0864078i
$179$	0.565887	+	0.251949i	0.0422964	+	0.0188316i	0.427776	−	0.903885i	$-0.359297\pi$
$179$	0.565887	+	0.251949i	0.0422964	+	0.0188316i	−0.385479	+	0.922716i	$0.625964\pi$
$180$	12.3095	−	7.10690i	0.917497	−	0.529717i
$181$	2.40424	+	4.16426i	0.178706	+	0.309527i	0.941437	−	0.337188i	$-0.109476\pi$
$181$	2.40424	+	4.16426i	0.178706	+	0.309527i	−0.762732	+	0.646715i	$0.776142\pi$
$182$	−1.42382	+	2.08026i	−0.105540	+	0.154199i
$183$	−0.571242	−	0.634428i	−0.0422274	−	0.0468983i
$184$	0.295423	−	1.38986i	0.0217789	−	0.102462i
$185$	16.0428	−	27.7870i	1.17949	−	2.04294i
$186$	0.633189	+	0.878298i	0.0464277	+	0.0643999i
$187$			13.3310i			0.974862i
$188$	2.09453	+	1.88592i	0.152759	+	0.137545i
$189$	−8.17262	−	2.65544i	−0.594471	−	0.193155i
$190$	−3.69939	−	5.09177i	−0.268382	−	0.369396i
$191$	2.70445	−	4.68425i	0.195687	−	0.338941i	−0.751438	−	0.659803i	$-0.770640\pi$
$191$	2.70445	−	4.68425i	0.195687	−	0.338941i	0.947126	+	0.320863i	$0.103973\pi$
$192$	−1.95242	−	3.38170i	−0.140904	−	0.244053i
$193$	4.59733	−	10.3258i	0.330923	−	0.743265i	−0.669077	−	0.743193i	$-0.733310\pi$
$193$	4.59733	−	10.3258i	0.330923	−	0.743265i	1.00000		7.19851e-5i	$-2.29136e-5\pi$
$194$	3.76884	+	2.73822i	0.270587	+	0.196593i
$195$	−1.92699	+	6.55182i	−0.137994	+	0.469185i
$196$	1.86046	−	2.06625i	0.132890	−	0.147589i
$197$	−1.11423	−	1.53360i	−0.0793853	−	0.109264i	0.767478	−	0.641076i	$-0.221512\pi$
$197$	−1.11423	−	1.53360i	−0.0793853	−	0.109264i	−0.846863	+	0.531811i	$0.821512\pi$
$198$	−2.81966	+	3.13155i	−0.200385	+	0.222550i
$199$	−4.90767	−	5.45052i	−0.347896	−	0.386377i	0.543647	−	0.839314i	$-0.317043\pi$
$199$	−4.90767	−	5.45052i	−0.347896	−	0.386377i	−0.891543	+	0.452937i	$0.850376\pi$
$200$	1.58823	+	3.56722i	0.112305	+	0.252241i
$201$	0.764966	+	3.59888i	0.0539565	+	0.253846i
$202$	0.997852	+	4.69452i	0.0702086	+	0.330306i
$203$	4.28402	+	9.62208i	0.300680	+	0.675337i
$204$	2.02342	+	2.24723i	0.141667	+	0.157338i
$205$	−4.05953	+	4.50856i	−0.283530	+	0.314892i
$206$	−1.17226	−	1.61348i	−0.0816755	−	0.112417i
$207$	2.10470	−	2.33751i	0.146287	−	0.162468i
$208$	−12.0337	−	3.53928i	−0.834385	−	0.245405i
$209$	−32.7417	−	23.7882i	−2.26479	−	1.64547i
$210$	0.538637	−	1.20980i	0.0371695	−	0.0834840i
$211$	−4.43074	−	7.67426i	−0.305024	−	0.528318i	0.672242	−	0.740331i	$-0.265331\pi$
$211$	−4.43074	−	7.67426i	−0.305024	−	0.528318i	−0.977267	+	0.212013i	$0.931998\pi$
$212$	−10.0156	+	17.3476i	−0.687877	+	1.19144i
$213$	0.00983235	+	0.0135331i	0.000673702	+	0.000927271i
$214$	−2.40253	−	0.780629i	−0.164233	−	0.0533627i
$215$	−17.1824	−	15.4711i	−1.17183	−	1.05512i
$216$			4.23798i			0.288358i
$217$	12.4550	+	4.09766i	0.845497	+	0.278167i
$218$	−1.37369	+	2.37930i	−0.0930382	+	0.161147i
$219$	0.325485	−	1.53128i	0.0219942	−	0.103475i
$220$	20.4228	+	22.6819i	1.37691	+	1.52921i
$221$	8.68098	+	0.666349i	0.583946	+	0.0448235i
$222$	1.07887	+	1.86865i	0.0724088	+	0.125416i
$223$	25.3059	−	14.6104i	1.69461	−	0.978384i	0.743907	−	0.668284i	$-0.232971\pi$
$223$	25.3059	−	14.6104i	1.69461	−	0.978384i	0.950704	−	0.310100i	$-0.100363\pi$
$224$	7.21915	+	3.21417i	0.482350	+	0.214756i
$225$	−0.903544	+	8.59664i	−0.0602362	+	0.573109i
$226$	−0.857673	−	0.0901450i	−0.0570515	−	0.00599636i
$227$	−4.67615	+	21.9995i	−0.310367	+	1.46016i	0.495782	+	0.868447i	$0.334882\pi$
$227$	−4.67615	+	21.9995i	−0.310367	+	1.46016i	−0.806148	+	0.591714i	$0.798452\pi$
$228$	−9.12995	+	0.959596i	−0.604646	+	0.0635508i
$229$	−4.75467	+	22.3690i	−0.314197	+	1.47818i	0.483617	+	0.875280i	$0.339323\pi$
$229$	−4.75467	+	22.3690i	−0.314197	+	1.47818i	−0.797814	+	0.602903i	$0.794011\pi$
$230$	0.702834	+	0.780576i	0.0463435	+	0.0514697i
$231$	0.890123	−	8.46896i	0.0585658	−	0.557216i
$232$	3.86025	−	3.47579i	0.253438	−	0.228197i
$233$	−0.0977874	+	0.300959i	−0.00640627	+	0.0197165i	−0.954209	−	0.299142i	$-0.903300\pi$
$233$	−0.0977874	+	0.300959i	−0.00640627	+	0.0197165i	0.947802	+	0.318859i	$0.103300\pi$
$234$	1.89828	+	1.99265i	0.124095	+	0.130264i
$235$	−4.16987	+	0.886333i	−0.272012	+	0.0578180i
$236$	−14.2410	−	12.8227i	−0.927013	−	0.834686i
$237$	1.54174	−	1.12014i	0.100146	−	0.0727607i
$238$	−1.65141	−	0.351018i	−0.107045	−	0.0227531i
$239$	22.4022	+	2.35457i	1.44908	+	0.152304i	0.796142	−	0.605110i	$-0.206871\pi$
$239$	22.4022	+	2.35457i	1.44908	+	0.152304i	0.652935	+	0.757414i	$0.273537\pi$
$240$	6.55333	+	0.688782i	0.423015	+	0.0444607i
$241$	−0.176678	−	0.243177i	−0.0113808	−	0.0156644i	0.803289	−	0.595590i	$-0.203082\pi$
$241$	−0.176678	−	0.243177i	−0.0113808	−	0.0156644i	−0.814670	+	0.579926i	$0.803082\pi$
$242$	−5.00803	−	2.89139i	−0.321928	−	0.185865i
$243$	−7.21676	+	12.4998i	−0.462955	+	0.801862i
$244$	0.260467	+	2.47817i	0.0166747	+	0.158649i
$245$	0.874364	+	4.11356i	0.0558611	+	0.262806i
$246$	−0.126076	−	0.388023i	−0.00803832	−	0.0247394i
$247$	−17.1272	+	20.1319i	−1.08977	+	1.28096i
$248$	0.0238274	−	6.46636i	0.00151304	−	0.410614i
$249$	0.0954778	+	0.0551241i	0.00605066	+	0.00349335i
$250$	1.37542	+	0.292354i	0.0869890	+	0.0184901i
$251$	0.864125	−	2.65950i	0.0545431	−	0.167866i	−0.920074	−	0.391744i	$-0.871872\pi$
$251$	0.864125	−	2.65950i	0.0545431	−	0.167866i	0.974617	+	0.223878i	$0.0718717\pi$
$252$	6.80374	+	9.36455i	0.428596	+	0.589911i
$253$	5.84932	+	3.37711i	0.367744	+	0.212317i
$254$			0.370848i			0.0232691i
$255$	−4.54876	+	0.478094i	−0.284854	+	0.0299394i
$256$	−0.983095	+	9.35352i	−0.0614434	+	0.584595i
$257$	−3.10379	−	2.25503i	−0.193609	−	0.140665i	0.486758	−	0.873537i	$-0.338179\pi$
$257$	−3.10379	−	2.25503i	−0.193609	−	0.140665i	−0.680367	+	0.732872i	$0.738179\pi$
$258$	1.47877	−	0.480483i	0.0920644	−	0.0299135i
$259$	23.8704	+	10.6278i	1.48324	+	0.660380i
$260$	15.7909	−	12.1653i	0.979312	−	0.754461i
$261$	11.2476	−	2.39076i	0.696211	−	0.147984i
$262$	−1.92068	−	0.201872i	−0.118660	−	0.0124717i
$263$	1.66314	+	1.84710i	0.102554	+	0.113897i	0.792236	−	0.610214i	$-0.208917\pi$
$263$	1.66314	+	1.84710i	0.102554	+	0.113897i	−0.689683	+	0.724112i	$0.742250\pi$
$264$	−4.10793	+	0.873168i	−0.252826	+	0.0537398i
$265$	−12.3233	−	27.6785i	−0.757013	−	1.70028i
$266$	3.80893	−	3.42958i	0.233541	−	0.210281i
$267$	−2.43222	+	0.790275i	−0.148849	+	0.0483641i
$268$	4.36803	−	9.81075i	0.266820	−	0.599287i
$269$	−23.9414	−	5.08890i	−1.45973	−	0.310276i	−0.591448	−	0.806343i	$-0.701444\pi$
$269$	−23.9414	−	5.08890i	−1.45973	−	0.310276i	−0.868284	+	0.496067i	$0.834777\pi$
$270$	−2.53450	−	1.84142i	−0.154245	−	0.112065i
$271$	−9.17231	−	20.6013i	−0.557178	−	1.25144i	−0.944200	−	0.329372i	$-0.893163\pi$
$271$	−9.17231	−	20.6013i	−0.557178	−	1.25144i	0.387022	−	0.922070i	$-0.373504\pi$
$272$	−0.878111	−	8.35467i	−0.0532433	−	0.506576i
$273$	−5.47037	−	1.00295i	−0.331082	−	0.0607015i
$274$	−2.33307	−	4.04099i	−0.140946	−	0.244125i
$275$	−18.4597	+	1.94019i	−1.11316	+	0.116998i
$276$	1.49861	−	0.318540i	0.0902059	−	0.0191739i
$277$	−13.0547	+	14.4987i	−0.784379	+	0.871141i	−0.994305	−	0.106576i	$-0.966011\pi$
$277$	−13.0547	+	14.4987i	−0.784379	+	0.871141i	0.209926	+	0.977717i	$0.432678\pi$
$278$		−	2.15165i		−	0.129047i
$279$	7.20289	−	12.3703i	0.431226	−	0.740590i
$280$	−6.84936	+	3.95448i	−0.409327	+	0.236325i
$281$	0.883754	−	0.287149i	0.0527203	−	0.0171299i	−0.282538	−	0.959256i	$-0.591176\pi$
$281$	0.883754	−	0.287149i	0.0527203	−	0.0171299i	0.335258	+	0.942126i	$0.391176\pi$
$282$	0.0885903	−	0.272653i	0.00527548	−	0.0162362i
$283$	1.13200	+	10.7703i	0.0672905	+	0.640226i	0.975240	+	0.221147i	$0.0709802\pi$
$283$	1.13200	+	10.7703i	0.0672905	+	0.640226i	−0.907950	+	0.419079i	$0.862353\pi$
$284$		−	0.0488256i		−	0.00289726i
$285$	6.94270	−	12.0251i	0.411250	−	0.712306i
$286$	−3.33785	+	4.87675i	−0.197371	+	0.288368i
$287$	−3.99706	−	2.90404i	−0.235939	−	0.171420i
$288$	5.07099	−	6.97962i	0.298811	−	0.411278i
$289$	−3.45140	−	10.6223i	−0.203023	−	0.624842i
$290$	0.401378	+	3.81885i	0.0235697	+	0.224251i
$291$	−2.13686	+	10.0531i	−0.125265	+	0.589325i
$292$	−3.39573	+	3.05753i	−0.198720	+	0.178929i
$293$	−8.99221	+	12.3767i	−0.525330	+	0.723055i	−0.986410	−	0.164304i	$-0.947462\pi$
$293$	−8.99221	+	12.3767i	−0.525330	+	0.723055i	0.461079	+	0.887359i	$0.347462\pi$
$294$	−0.268971	−	0.0873941i	−0.0156867	−	0.00509693i
$295$	28.3516	−	6.02631i	1.65069	−	0.350865i
$296$	1.34700	−	12.8159i	0.0782930	−	0.744908i
$297$	−19.1591	−	6.22515i	−1.11172	−	0.361220i
$298$	−3.56948	−	0.758716i	−0.206774	−	0.0439513i
$299$	2.49150	−	3.64019i	0.144087	−	0.210518i
$300$	−2.81728	+	3.12891i	−0.162656	+	0.180648i
$301$	11.0674	−	15.2330i	0.637916	−	0.878016i
$302$	6.14968	−	2.73801i	0.353874	−	0.157555i
$303$	−8.56628	+	6.22377i	−0.492120	+	0.357546i
$304$	22.0864	+	12.7516i	1.26674	+	0.731354i
$305$	−3.26402	−	1.88448i	−0.186897	−	0.107905i
$306$	−0.749690	+	1.68383i	−0.0428569	+	0.0962582i
$307$	9.30467	−	8.37797i	0.531046	−	0.478156i	−0.359439	−	0.933169i	$-0.617032\pi$
$307$	9.30467	−	8.37797i	0.531046	−	0.478156i	0.890485	+	0.455013i	$0.150365\pi$
$308$	−16.6316	+	18.4713i	−0.947675	+	1.05250i
$309$	2.20001	−	3.81052i	0.125154	−	0.216773i
$310$	3.85682	+	2.82392i	0.219053	+	0.160388i
$311$	21.4792			1.21797			0.608986	−	0.793181i	$-0.291577\pi$
$311$	21.4792			1.21797			0.608986	+	0.793181i	$0.291577\pi$
$312$	0.363261	+	2.71867i	0.0205656	+	0.153915i
$313$	−10.2439	−	11.3771i	−0.579022	−	0.643069i	0.380474	−	0.924792i	$-0.375761\pi$
$313$	−10.2439	−	11.3771i	−0.579022	−	0.643069i	−0.959496	+	0.281722i	$0.909094\pi$
$314$	3.99895	−	0.420307i	0.225674	−	0.0237193i
$315$	−17.5079			−0.986457
$316$	−5.56238			−0.312908
$317$	−19.7571	+	2.07656i	−1.10967	+	0.116631i	−0.641585	−	0.767052i	$-0.721723\pi$
$317$	−19.7571	+	2.07656i	−1.10967	+	0.116631i	−0.468086	+	0.883683i	$0.655056\pi$
$318$	2.02634	+	0.212977i	0.113632	+	0.0119432i
$319$	10.0430	+	22.5570i	0.562302	+	1.26295i
$320$	−12.8112	−	11.5353i	−0.716169	−	0.644841i
$321$	−0.582564	−	5.54273i	−0.0325156	−	0.309365i
$322$	−0.572363	+	0.635674i	−0.0318966	+	0.0354247i
$323$	−16.8357	−	5.47026i	−0.936765	−	0.304374i
$324$	9.29655	−	4.13909i	0.516475	−	0.229949i
$325$	0.340722	+	12.1177i	0.0188999	+	0.672166i
$326$	1.09676	−	3.37548i	0.0607438	−	0.186950i
$327$	−6.02811	−	0.633580i	−0.333355	−	0.0350370i
$328$	−0.752956	+	2.31736i	−0.0415750	+	0.127955i
$329$	−1.07280	−	3.30174i	−0.0591454	−	0.182031i
$330$	1.26273	−	2.83613i	0.0695107	−	0.156124i
$331$	−3.55404	+	16.7205i	−0.195348	+	0.919040i	0.765816	+	0.643060i	$0.222336\pi$
$331$	−3.55404	+	16.7205i	−0.195348	+	0.919040i	−0.961163	+	0.275980i	$0.910998\pi$
$332$	−0.130886	−	0.293975i	−0.00718331	−	0.0161340i
$333$	16.7675	−	23.0784i	0.918851	−	1.26469i
$334$	2.22687	−	1.61792i	0.121849	−	0.0885286i
$335$	8.12169	+	14.0672i	0.443735	+	0.768572i
$336$			5.36619i			0.292750i
$337$	−28.5602	+	20.7502i	−1.55577	+	1.13034i	−0.616404	+	0.787430i	$0.711411\pi$
$337$	−28.5602	+	20.7502i	−1.55577	+	1.13034i	−0.939370	+	0.342906i	$0.888589\pi$
$338$	3.00883	+	2.41733i	0.163659	+	0.131485i
$339$	−0.587945	−	1.80951i	−0.0319328	−	0.0982791i
$340$	11.5616	+	6.67509i	0.627016	+	0.362008i
$341$	29.1981	+	9.60614i	1.58117	+	0.520201i
$342$	−2.79781	−	4.84595i	−0.151288	−	0.262039i
$343$	−18.9349	+	6.15231i	−1.02239	+	0.332194i
$344$	−8.83157	−	2.86955i	−0.476167	−	0.154716i
$345$	−0.942546	+	2.11699i	−0.0507450	+	0.113975i
$346$	5.07253	−	2.92863i	0.272701	−	0.157444i
$347$	12.3971			0.665513			0.332756	−	0.943013i	$-0.392021\pi$
$347$	12.3971			0.665513			0.332756	+	0.943013i	$0.392021\pi$
$348$	5.11672	+	2.27811i	0.274285	+	0.122120i
$349$	2.50807	+	5.63323i	0.134254	+	0.301540i	0.968145	−	0.250389i	$-0.0805586\pi$
$349$	2.50807	+	5.63323i	0.134254	+	0.301540i	−0.833891	+	0.551929i	$0.813892\pi$
$350$	0.245714	−	2.33781i	0.0131340	−	0.124961i
$351$	−5.01139	+	12.1649i	−0.267488	+	0.649317i
$352$	16.9238	+	7.53498i	0.902044	+	0.401616i
$353$	14.1963	+	12.7824i	0.755595	+	0.680341i	0.954009	−	0.299777i	$-0.0969124\pi$
$353$	14.1963	+	12.7824i	0.755595	+	0.680341i	−0.198414	+	0.980118i	$0.563579\pi$
$354$	−0.602339	+	1.85381i	−0.0320140	+	0.0985289i
$355$	0.0597460	+	0.0434080i	0.00317099	+	0.00230386i
$356$	7.09923	+	2.30668i	0.376258	+	0.122254i
$357$	−0.774420	−	3.64336i	−0.0409866	−	0.192827i
$358$	−0.108098	+	0.148784i	−0.00571316	+	0.00786348i
$359$	6.44504	+	30.3215i	0.340156	+	1.60031i	0.732684	+	0.680569i	$0.238267\pi$
$359$	6.44504	+	30.3215i	0.340156	+	1.60031i	−0.392528	+	0.919740i	$0.628399\pi$
$360$	2.66821	+	8.21190i	0.140627	+	0.432805i
$361$	28.1060	−	20.4202i	1.47927	−	1.07475i
$362$	−1.35773	+	0.441152i	−0.0713606	+	0.0231865i
$363$	1.33358	−	12.6881i	0.0699947	−	0.665955i
$364$	11.1969	+	11.7536i	0.586878	+	0.616054i
$365$	−0.722435	−	6.87351i	−0.0378140	−	0.359776i
$366$	0.219502	−	0.126730i	0.0114736	−	0.00662426i
$367$	10.5427			0.550326			0.275163	−	0.961398i	$-0.411268\pi$
$367$	10.5427			0.550326			0.275163	+	0.961398i	$0.411268\pi$
$368$	−3.88826	−	1.73117i	−0.202690	−	0.0902433i
$369$	−4.00844	+	3.60921i	−0.208671	+	0.187888i
$370$	7.07920	+	6.37414i	0.368030	+	0.331376i
$371$	21.3679	−	12.3368i	1.10937	−	0.640494i
$372$	6.38001	−	2.81244i	0.330788	−	0.145818i
$373$	−5.15267	−	8.92469i	−0.266795	−	0.462103i	0.701237	−	0.712928i	$-0.252631\pi$
$373$	−5.15267	−	8.92469i	−0.266795	−	0.462103i	−0.968032	+	0.250825i	$0.919298\pi$
$374$	−3.87139	−	0.822890i	−0.200185	−	0.0425506i
$375$	0.644995	+	3.03446i	0.0333074	+	0.156699i
$376$	−1.38515	+	1.00637i	−0.0714338	+	0.0518997i
$377$	15.1908	−	5.41237i	0.782366	−	0.278751i
$378$	1.27563	−	2.20945i	0.0656112	−	0.113642i
$379$	−4.82511	+	10.8374i	−0.247849	+	0.556678i	−0.994035	−	0.109059i	$-0.965216\pi$
$379$	−4.82511	+	10.8374i	−0.247849	+	0.556678i	0.746186	+	0.665737i	$0.231883\pi$
$380$	−37.0252	+	16.4847i	−1.89935	+	0.845646i
$381$	−0.747434	+	0.332779i	−0.0382922	+	0.0170488i
$382$	1.19339	+	1.07453i	0.0610591	+	0.0549779i
$383$	−0.779447	+	0.0819232i	−0.0398279	+	0.00418608i	−0.124421	−	0.992229i	$-0.539707\pi$
$383$	−0.779447	+	0.0819232i	−0.0398279	+	0.00418608i	0.0845936	+	0.996416i	$0.473041\pi$
$384$	5.28339	−	1.71668i	0.269617	−	0.0876038i
$385$	−7.81641	−	36.7733i	−0.398361	−	1.87414i
$386$	2.71487	+	1.97247i	0.138183	+	0.100396i
$387$	−13.7549	−	15.2764i	−0.699200	−	0.776541i
$388$	22.2936	−	20.0732i	1.13178	−	1.01906i
$389$	−13.0009	+	5.78837i	−0.659171	+	0.293482i	−0.708930	−	0.705279i	$-0.750822\pi$
$389$	−13.0009	+	5.78837i	−0.659171	+	0.293482i	0.0497582	+	0.998761i	$0.484155\pi$
$390$	−1.78373	−	0.964032i	−0.0903226	−	0.0488157i
$391$	2.88976	+	0.614237i	0.146141	+	0.0310633i
$392$	0.992784	+	1.36645i	0.0501432	+	0.0690161i
$393$	−1.31665	−	4.05224i	−0.0664164	−	0.204409i
$394$	0.514142	−	0.228911i	0.0259021	−	0.0115324i
$395$	4.94520	−	6.80648i	0.248820	−	0.342471i
$396$	15.9500	+	21.9533i	0.801518	+	1.10319i
$397$			8.47700i			0.425448i	0.977112	+	0.212724i	$0.0682336\pi$
$397$			8.47700i			0.425448i	−0.977112	+	0.212724i	$0.931766\pi$
$398$	1.88579	−	1.08876i	0.0945263	−	0.0545748i
$399$	10.3302	+	4.59929i	0.517155	+	0.230252i
$400$	11.4410	−	2.43186i	0.572051	−	0.121593i
$401$	4.03467	−	18.9816i	0.201482	−	0.947898i	−0.754914	−	0.655824i	$-0.772321\pi$
$401$	4.03467	−	18.9816i	0.201482	−	0.947898i	0.956396	−	0.292074i	$-0.0943454\pi$
$402$	−1.09235			−0.0544815
$403$	7.71484	−	18.5332i	0.384304	−	0.923207i
$404$	30.9060			1.53763
$405$	−3.20018	+	15.0557i	−0.159018	+	0.748122i
$406$	−3.05874	+	0.650154i	−0.151803	+	0.0322666i
$407$	55.9595	+	24.9148i	2.77381	+	1.23498i
$408$	−1.59086	+	0.918483i	−0.0787593	+	0.0454717i
$409$			4.65139i			0.229997i	0.993366	+	0.114998i	$0.0366863\pi$
$409$			4.65139i			0.229997i	−0.993366	+	0.114998i	$0.963314\pi$
$410$	−1.05872	−	1.45721i	−0.0522866	−	0.0719663i
$411$	6.05094	−	8.32841i	0.298471	−	0.410810i
$412$	−11.7326	+	5.22367i	−0.578022	+	0.257352i
$413$	7.29414	+	22.4490i	0.358921	+	1.10465i
$414$	0.548905	+	0.755504i	0.0269772	+	0.0371310i
$415$	0.476090	+	0.101196i	0.0233703	+	0.00496752i
$416$	5.75260	−	10.6439i	0.282045	−	0.521862i
$417$	4.33660	−	1.93078i	0.212364	−	0.0945505i
$418$	8.92927	−	8.03995i	0.436745	−	0.393247i
$419$	4.71333	+	5.23468i	0.230261	+	0.255731i	0.847193	−	0.531286i	$-0.178291\pi$
$419$	4.71333	+	5.23468i	0.230261	+	0.255731i	−0.616931	+	0.787017i	$0.711624\pi$
$420$	−6.89916	−	5.01253i	−0.336645	−	0.244587i
$421$	−0.597759	−	2.81224i	−0.0291330	−	0.137060i	0.961178	−	0.275931i	$-0.0889861\pi$
$421$	−0.597759	−	2.81224i	−0.0291330	−	0.137060i	−0.990311	+	0.138871i	$0.955653\pi$
$422$	2.50214	−	0.812994i	0.121802	−	0.0395759i
$423$	−3.76937	+	0.396177i	−0.183273	+	0.0192628i
$424$	−9.04292	−	8.14228i	−0.439163	−	0.395424i
$425$	−7.41688	+	3.30221i	−0.359772	+	0.160181i
$426$	−0.00453699	+	0.00202000i	−0.000219818	+	9.78692e-5i
$427$	1.24840	−	2.80395i	0.0604144	−	0.135693i
$428$	−8.13370	+	14.0880i	−0.393157	+	0.680968i
$429$	−12.8242	−	2.35122i	−0.619157	−	0.113518i
$430$	5.55349	−	4.03485i	0.267813	−	0.194578i
$431$	8.25280	+	38.8264i	0.397523	+	1.87020i	0.485747	+	0.874100i	$0.338548\pi$
$431$	8.25280	+	38.8264i	0.397523	+	1.87020i	−0.0882233	+	0.996101i	$0.528119\pi$
$432$	12.4172	+	2.63935i	0.597422	+	0.126986i
$433$	10.9990	+	19.0509i	0.528580	+	0.915528i	0.999445	+	0.0333225i	$0.0106088\pi$
$433$	10.9990	+	19.0509i	0.528580	+	0.915528i	−0.470864	+	0.882206i	$0.656058\pi$
$434$	−1.95879	+	3.36404i	−0.0940250	+	0.161479i
$435$	−7.33663	+	4.23581i	−0.351765	+	0.203091i
$436$	13.1477	+	11.8382i	0.629659	+	0.566948i
$437$	−6.66515	+	6.00133i	−0.318837	+	0.287082i
$438$	0.424601	+	0.189044i	0.0202882	+	0.00903289i
$439$	22.6064			1.07895			0.539473	−	0.842003i	$-0.318624\pi$
$439$	22.6064			1.07895			0.539473	+	0.842003i	$0.318624\pi$
$440$	−16.0569	+	9.27047i	−0.765484	+	0.441953i
$441$	0.390827	+	3.71847i	0.0186108	+	0.177070i
$442$	−0.729365	+	2.47987i	−0.0346924	+	0.117955i
$443$	−0.694503	+	6.60776i	−0.0329969	+	0.313944i	0.965557	+	0.260190i	$0.0837853\pi$
$443$	−0.694503	+	6.60776i	−0.0329969	+	0.313944i	−0.998554	+	0.0537538i	$0.982881\pi$
$444$	13.2148	−	4.29374i	0.627146	−	0.203772i
$445$	−9.13412	+	6.63632i	−0.432999	+	0.314592i
$446$	2.68085	+	8.25082i	0.126942	+	0.390688i
$447$	−1.67389	−	7.87503i	−0.0791723	−	0.372476i
$448$	8.25191	−	11.3578i	0.389866	−	0.536605i
$449$	−6.37488	−	29.9914i	−0.300849	−	1.41538i	−0.825662	−	0.564165i	$-0.809198\pi$
$449$	−6.37488	−	29.9914i	−0.300849	−	1.41538i	0.524813	−	0.851218i	$-0.324135\pi$
$450$	−2.44073	−	0.793041i	−0.115057	−	0.0373843i
$451$	−9.37031	−	6.80793i	−0.441231	−	0.320573i
$452$	−1.71611	+	5.28165i	−0.0807191	+	0.248428i
$453$	11.0368	+	9.93758i	0.518554	+	0.466908i
$454$	−6.10012	−	2.71595i	−0.286293	−	0.127466i
$455$	−24.3370	+	3.25183i	−1.14093	+	0.152448i
$456$	0.582929	−	5.54620i	0.0272981	−	0.259724i
$457$	−12.0190	−	26.9952i	−0.562226	−	1.26278i	−0.941349	−	0.337434i	$-0.890441\pi$
$457$	−12.0190	−	26.9952i	−0.562226	−	1.26278i	0.379123	−	0.925346i	$-0.376226\pi$
$458$	−6.20256	−	2.76156i	−0.289826	−	0.129039i
$459$	−8.81150			−0.411286
$460$	5.85772	−	3.38196i	0.273118	−	0.157685i
$461$	−0.409832	+	0.920497i	−0.0190878	+	0.0428718i	−0.922838	−	0.385189i	$-0.874136\pi$
$461$	−0.409832	+	0.920497i	−0.0190878	+	0.0428718i	0.903750	+	0.428061i	$0.140803\pi$
$462$	2.40448	+	0.781262i	0.111866	+	0.0363476i
$463$	−27.2813	+	8.86423i	−1.26787	+	0.411956i	−0.864292	−	0.502990i	$-0.832233\pi$
$463$	−27.2813	+	8.86423i	−1.26787	+	0.411956i	−0.403577	+	0.914946i	$0.632233\pi$
$464$	−7.77987	−	13.4751i	−0.361171	−	0.625567i
$465$	−2.23063	+	10.3074i	−0.103443	+	0.477993i
$466$	−0.0813636	−	0.0469753i	−0.00376910	−	0.00217609i
$467$	−5.27052	−	16.2210i	−0.243890	−	0.750618i	−0.995817	−	0.0913707i	$-0.970875\pi$
$467$	−5.27052	−	16.2210i	−0.243890	−	0.750618i	0.751926	−	0.659247i	$-0.229125\pi$
$468$	15.0929	−	9.28909i	0.697671	−	0.429388i
$469$	−10.7017	+	7.77524i	−0.494159	+	0.359027i
$470$		−	1.26566i		−	0.0583805i
$471$	4.43557	+	7.68263i	0.204380	+	0.353997i
$472$	9.41787	−	6.84248i	0.433493	−	0.314951i
$473$	25.9454	−	35.7107i	1.19297	−	1.64198i
$474$	0.230125	+	0.516870i	0.0105700	+	0.0237406i
$475$	5.12448	−	24.1088i	0.235127	−	1.10619i
$476$	−4.42201	+	9.93199i	−0.202682	+	0.455232i
$477$	−8.32400	−	25.6186i	−0.381130	−	1.17300i
$478$	−2.06661	+	6.36036i	−0.0945243	+	0.290916i
$479$	−39.2919	−	4.12975i	−1.79529	−	0.188693i	−0.852647	−	0.522487i	$-0.825004\pi$
$479$	−39.2919	−	4.12975i	−1.79529	−	0.188693i	−0.942646	+	0.333794i	$0.891671\pi$
$480$	−1.96411	+	6.04491i	−0.0896489	+	0.275911i
$481$	19.0213	−	35.1946i	0.867295	−	1.60474i
$482$	0.0815255	−	0.0362975i	0.00371338	−	0.00165330i
$483$	−1.79479	−	0.583164i	−0.0816659	−	0.0265349i
$484$	−24.9174	+	27.6736i	−1.13261	+	1.25789i
$485$	4.74291	+	45.1258i	0.215364	+	2.04906i
$486$	−3.18452	−	2.86736i	−0.144453	−	0.130066i
$487$	−5.69525	−	12.7917i	−0.258076	−	0.579649i	0.737315	−	0.675550i	$-0.236094\pi$
$487$	−5.69525	−	12.7917i	−0.258076	−	0.579649i	−0.995391	+	0.0959007i	$0.969427\pi$
$488$	−1.50542	−	0.158226i	−0.0681473	−	0.00716257i
$489$	7.78736	−	0.818485i	0.352157	−	0.0370132i
$490$	−1.24857			−0.0564046
$491$	−13.5356			−0.610854			−0.305427	−	0.952215i	$-0.598799\pi$
$491$	−13.5356			−0.610854			−0.305427	+	0.952215i	$0.598799\pi$
$492$	−2.61289	+	0.274626i	−0.117798	+	0.0123811i
$493$	7.22677	+	8.02614i	0.325477	+	0.361479i
$494$	−4.78918	−	6.21649i	−0.215475	−	0.279693i
$495$	−41.0437			−1.84478
$496$	−18.9314	−	4.09697i	−0.850047	−	0.183959i
$497$	−0.0300705	+	0.0520836i	−0.00134885	+	0.00233627i
$498$	−0.0219019	+	0.0243245i	−0.000981447	+	0.00109001i
$499$	−5.80026	+	5.22257i	−0.259655	+	0.233795i	−0.788668	−	0.614819i	$-0.789229\pi$
$499$	−5.80026	+	5.22257i	−0.259655	+	0.233795i	0.529013	+	0.848614i	$0.322562\pi$
$500$	3.68298	−	8.27210i	0.164708	−	0.369940i
$501$	5.25915	+	3.03637i	0.234962	+	0.135655i
$502$	0.718992	+	0.415110i	0.0320902	+	0.0185273i
$503$	22.9936	−	16.7059i	1.02524	−	0.744877i	0.0578858	−	0.998323i	$-0.481564\pi$
$503$	22.9936	−	16.7059i	1.02524	−	0.744877i	0.967349	+	0.253446i	$0.0815641\pi$
$504$	−6.42371	+	2.86002i	−0.286135	+	0.127395i
$505$	−27.4768	+	37.8186i	−1.22270	+	1.68290i
$506$	−1.34179	+	1.49021i	−0.0596498	+	0.0662479i
$507$	−2.17210	+	8.23340i	−0.0964662	+	0.365658i
$508$	2.33591	+	0.496513i	0.103639	+	0.0220292i
$509$	−37.5586	−	12.2035i	−1.66475	−	0.540911i	−0.682893	−	0.730518i	$-0.739279\pi$
$509$	−37.5586	−	12.2035i	−1.66475	−	0.540911i	−0.981860	+	0.189607i	$0.939279\pi$
$510$	0.141942	−	1.35049i	0.00628531	−	0.0598008i
$511$	5.50539	−	1.17021i	0.243544	−	0.0517669i
$512$	−18.7879	−	6.10456i	−0.830316	−	0.269786i
$513$	15.7235	−	21.6415i	0.694208	−	0.955495i
$514$	0.846461	−	0.762157i	0.0373358	−	0.0336173i
$515$	4.03874	−	19.0008i	0.177968	−	0.837274i
$516$	−1.04661	−	9.95785i	−0.0460745	−	0.438370i
$517$	−2.51496	−	7.74027i	−0.110608	−	0.340417i
$518$	−4.55982	+	6.27606i	−0.200347	+	0.275754i
$519$	10.4544	+	7.59557i	0.458897	+	0.333408i
$520$	5.23420	+	10.9194i	0.229535	+	0.478849i
$521$	19.5223	−	33.8136i	0.855286	−	1.48140i	−0.0210927	−	0.999778i	$-0.506715\pi$
$521$	19.5223	−	33.8136i	0.855286	−	1.48140i	0.876379	−	0.481622i	$-0.159952\pi$
$522$			3.41394i			0.149424i
$523$	−2.24654	−	21.3744i	−0.0982342	−	0.934636i	−0.927005	−	0.375048i	$-0.877626\pi$
$523$	−2.24654	−	21.3744i	−0.0982342	−	0.934636i	0.828771	−	0.559588i	$-0.189041\pi$
$524$	−3.84309	+	11.8278i	−0.167886	+	0.516700i
$525$	4.93230	−	1.60260i	0.215263	−	0.0699432i
$526$	−0.639068	+	0.368966i	−0.0278647	+	0.0160877i
$527$	13.4447	+	0.0495414i	0.585660	+	0.00215806i
$528$			12.5800i			0.547472i
$529$	−14.3884	+	15.9800i	−0.625584	+	0.694782i
$530$	8.79865	−	1.87021i	0.382189	−	0.0812368i
$531$	25.6285	−	2.69367i	1.11218	−	0.116895i
$532$	−16.5027	−	28.5836i	−0.715484	−	1.23925i
$533$	−4.90160	+	5.76152i	−0.212312	+	0.249559i
$534$	−0.0793651	−	0.755108i	−0.00343446	−	0.0326767i
$535$	−10.0077	−	22.4777i	−0.432672	−	0.971797i
$536$	5.27784	+	3.83458i	0.227968	+	0.165628i
$537$	−0.396872	−	0.0843578i	−0.0171263	−	0.00364031i
$538$	2.95568	−	6.63856i	0.127428	−	0.286209i
$539$	−7.63575	+	2.48101i	−0.328895	+	0.106864i
$540$	−14.9922	+	13.4990i	−0.645160	+	0.580905i
$541$	17.5808	+	39.4871i	0.755858	+	1.69768i	0.715615	+	0.698495i	$0.246147\pi$
$541$	17.5808	+	39.4871i	0.755858	+	1.69768i	0.0402429	+	0.999190i	$0.487187\pi$
$542$	6.54890	−	1.39201i	0.281299	−	0.0597920i
$543$	−2.10749	−	2.34060i	−0.0904408	−	0.100445i
$544$	8.05870	+	0.847004i	0.345514	+	0.0363150i
$545$	−26.1748	+	5.56363i	−1.12121	+	0.238320i
$546$	0.628934	−	1.52671i	0.0269159	−	0.0653372i
$547$	−5.20978	−	2.31955i	−0.222754	−	0.0991766i	0.292325	−	0.956319i	$-0.405571\pi$
$547$	−5.20978	−	2.31955i	−0.222754	−	0.0991766i	−0.515080	+	0.857142i	$0.672238\pi$
$548$	−28.5772	+	9.28529i	−1.22076	+	0.396648i
$549$	−2.71092	−	1.96960i	−0.115699	−	0.0840604i
$550$	0.576027	−	5.48053i	0.0245619	−	0.233691i
$551$	−32.6083	+	3.42727i	−1.38916	+	0.146006i
$552$			0.930704i			0.0396134i
$553$	5.93355	+	3.42574i	0.252320	+	0.145677i
$554$	−3.40465	−	4.68610i	−0.144650	−	0.199093i
$555$	−6.49442	+	19.9878i	−0.275673	+	0.848433i
$556$	−13.5529	−	2.88075i	−0.574770	−	0.122171i
$557$	16.5971	+	9.58235i	0.703242	+	0.406017i	0.808554	−	0.588422i	$-0.200251\pi$
$557$	16.5971	+	9.58235i	0.703242	+	0.406017i	−0.105312	+	0.994439i	$0.533584\pi$
$558$	3.14777	+	2.85534i	0.133256	+	0.120876i
$559$	−21.9574	−	18.6802i	−0.928701	−	0.790090i
$560$	7.32085	+	22.5313i	0.309362	+	0.952120i
$561$	−1.81547	−	8.54112i	−0.0766492	−	0.360606i
$562$	0.0288376	+	0.274371i	0.00121644	+	0.0115736i
$563$	14.9835	−	25.9523i	0.631481	−	1.09376i	−0.355768	−	0.934574i	$-0.615781\pi$
$563$	14.9835	−	25.9523i	0.631481	−	1.09376i	0.987249	−	0.159183i	$-0.0508861\pi$
$564$	−1.59879	−	0.923060i	−0.0673211	−	0.0388678i
$565$	−4.93726	−	6.79556i	−0.207712	−	0.285891i
$566$	−3.19761	−	0.336082i	−0.134406	−	0.0141266i
$567$	−12.4661	−	1.31024i	−0.523525	−	0.0550247i
$568$	0.0290120	+	0.00616670i	0.00121732	+	0.000258749i
$569$	−16.8104	+	12.2135i	−0.704728	+	0.512015i	−0.881469	−	0.472243i	$-0.843445\pi$
$569$	−16.8104	+	12.2135i	−0.704728	+	0.512015i	0.176741	+	0.984257i	$0.443445\pi$
$570$	3.06359	+	2.75847i	0.128320	+	0.115540i
$571$	32.5081	−	6.90980i	1.36042	−	0.289166i	0.530801	−	0.847496i	$-0.321891\pi$
$571$	32.5081	−	6.90980i	1.36042	−	0.289166i	0.829619	+	0.558330i	$0.188558\pi$
$572$	26.2489	+	27.5539i	1.09752	+	1.15209i
$573$	−1.09481	+	3.36948i	−0.0457363	+	0.140762i
$574$	1.09007	−	0.981507i	0.0454988	−	0.0409673i
$575$	−0.429969	+	4.09088i	−0.0179309	+	0.170601i
$576$	−10.2557	−	11.3901i	−0.427320	−	0.474587i
$577$	−8.27350	+	38.9238i	−0.344430	+	1.62042i	0.375813	+	0.926696i	$0.377364\pi$
$577$	−8.27350	+	38.9238i	−0.344430	+	1.62042i	−0.720243	+	0.693722i	$0.755970\pi$
$578$	3.29781	−	0.346614i	0.137171	−	0.0144172i
$579$	−1.53928	+	7.24174i	−0.0639703	+	0.300956i
$580$	24.5917	+	2.58469i	1.02112	+	0.107324i
$581$	−0.0414322	+	0.394201i	−0.00171890	+	0.0163542i
$582$	−2.78757	−	1.24111i	−0.115549	−	0.0514456i
$583$	50.0928	−	28.9211i	2.07463	−	1.19779i
$584$	−1.38790	−	2.40391i	−0.0574315	−	0.0994743i
$585$	−2.05156	+	26.7271i	−0.0848215	+	1.10503i
$586$	−3.03919	−	3.37536i	−0.125548	−	0.139435i
$587$	0.412412	−	1.94025i	0.0170221	−	0.0800826i	−0.968817	−	0.247779i	$-0.920299\pi$
$587$	0.412412	−	1.94025i	0.0170221	−	0.0800826i	0.985839	+	0.167696i	$0.0536327\pi$
$588$	−0.910596	+	1.57720i	−0.0375523	+	0.0650425i
$589$	−24.1127	+	32.9325i	−0.993548	+	1.35696i
$590$			8.60541i			0.354279i
$591$	0.922729	+	0.830829i	0.0379560	+	0.0341757i
$592$	−36.7114	−	11.9282i	−1.50883	−	0.490248i
$593$	−0.938626	−	1.29191i	−0.0385447	−	0.0530523i	0.789310	−	0.613995i	$-0.210439\pi$
$593$	−0.938626	−	1.29191i	−0.0385447	−	0.0530523i	−0.827854	+	0.560943i	$0.810439\pi$
$594$	2.99045	−	5.17961i	0.122700	−	0.212522i
$595$	−8.22206	−	14.2410i	−0.337071	−	0.583825i
$596$	−9.55806	+	21.4678i	−0.391513	+	0.879354i
$597$	3.88659	+	2.82377i	0.159068	+	0.115569i
$598$	0.903334	+	0.948243i	0.0369401	+	0.0387765i
$599$	17.6528	−	19.6054i	0.721274	−	0.801056i	−0.265336	−	0.964156i	$-0.585483\pi$
$599$	17.6528	−	19.6054i	0.721274	−	0.801056i	0.986609	+	0.163101i	$0.0521495\pi$
$600$	−1.50337	−	2.06921i	−0.0613747	−	0.0844750i
$601$	6.51071	−	7.23088i	0.265577	−	0.294954i	−0.595576	−	0.803299i	$-0.703076\pi$
$601$	6.51071	−	7.23088i	0.265577	−	0.294954i	0.861153	+	0.508345i	$0.169743\pi$
$602$	3.74057	+	4.15433i	0.152454	+	0.169318i
$603$	5.87390	+	13.1930i	0.239204	+	0.537260i
$604$	−9.01275	−	42.4017i	−0.366724	−	1.72530i
$605$	−11.7105	−	55.0936i	−0.476100	−	2.23987i
$606$	−1.27864	−	2.87186i	−0.0519410	−	0.116661i
$607$	−18.4548	−	20.4961i	−0.749058	−	0.831913i	0.241299	−	0.970451i	$-0.422426\pi$
$607$	−18.4548	−	20.4961i	−0.749058	−	0.831913i	−0.990357	+	0.138538i	$0.955760\pi$
$608$	−16.4604	+	18.2812i	−0.667559	+	0.741399i
$609$	−4.05512	−	5.58139i	−0.164322	−	0.226169i
$610$	0.748741	−	0.831561i	0.0303156	−	0.0336689i
$611$	−5.16606	+	1.25081i	−0.208997	+	0.0506025i
$612$	9.60244	+	6.97658i	0.388156	+	0.282012i
$613$	4.10677	−	9.22396i	0.165871	−	0.372552i	−0.811417	−	0.584468i	$-0.801303\pi$
$613$	4.10677	−	9.22396i	0.165871	−	0.372552i	0.977288	+	0.211915i	$0.0679701\pi$
$614$	1.85865	+	3.21927i	0.0750088	+	0.129919i
$615$	1.98692	−	3.44145i	0.0801205	−	0.138773i
$616$	−8.87502	−	12.2154i	−0.357585	−	0.492173i
$617$	−29.0453	−	9.43737i	−1.16932	−	0.379934i	−0.340930	−	0.940089i	$-0.610742\pi$
$617$	−29.0453	−	9.43737i	−1.16932	−	0.379934i	−0.828388	+	0.560154i	$0.810742\pi$
$618$	0.970793	+	0.874106i	0.0390510	+	0.0351617i
$619$			45.0679i			1.81143i	0.423884	+	0.905717i	$0.360666\pi$
$619$			45.0679i			1.81143i	−0.423884	+	0.905717i	$0.639334\pi$
$620$	22.9511	−	20.5127i	0.921740	−	0.823808i
$621$	−2.23219	+	3.86626i	−0.0895746	+	0.155148i
$622$	−1.32585	+	6.23765i	−0.0531618	+	0.250107i
$623$	−6.15232	−	6.83284i	−0.246487	−	0.273752i
$624$	8.19189	+	0.628806i	0.327938	+	0.0251724i
$625$	15.2533	+	26.4196i	0.610134	+	1.05678i
$626$	3.93628	−	2.27261i	0.157325	−	0.0908319i
$627$	24.2170	+	10.7821i	0.967134	+	0.430596i
$628$	2.70659	−	25.7515i	0.108005	−	1.02760i
$629$	26.6465	+	2.80066i	1.06246	+	0.111669i
$630$	1.08072	−	5.08437i	0.0430567	−	0.202566i
$631$	9.40163	−	0.988151i	0.374273	−	0.0393377i	0.0844752	−	0.996426i	$-0.473079\pi$
$631$	9.40163	−	0.988151i	0.374273	−	0.0393377i	0.289798	+	0.957088i	$0.406412\pi$
$632$	0.702532	−	3.30516i	0.0279452	−	0.131472i
$633$	3.88386	+	4.31346i	0.154369	+	0.171445i
$634$	0.616514	−	5.86574i	0.0244849	−	0.232958i
$635$	−2.68429	+	2.41694i	−0.106523	+	0.0959135i
$636$	4.05450	−	12.4785i	0.160771	−	0.494803i
$637$	1.23392	+	5.09630i	0.0488899	+	0.201923i
$638$	−7.17059	+	1.52416i	−0.283886	+	0.0603419i
$639$	0.0487935	+	0.0439339i	0.00193024	+	0.00173800i
$640$	19.8416	−	14.4158i	0.784308	−	0.569833i
$641$	20.2136	+	4.29653i	0.798389	+	0.169703i	0.589003	−	0.808131i	$-0.299520\pi$
$641$	20.2136	+	4.29653i	0.798389	+	0.169703i	0.209385	+	0.977833i	$0.432854\pi$
$642$	1.64559	+	0.172959i	0.0649464	+	0.00682614i
$643$	14.8878	+	1.56477i	0.587118	+	0.0617086i	0.393430	−	0.919355i	$-0.371288\pi$
$643$	14.8878	+	1.56477i	0.587118	+	0.0617086i	0.193688	+	0.981063i	$0.437955\pi$
$644$	3.23769	+	4.45630i	0.127583	+	0.175603i
$645$	13.1155	+	7.57226i	0.516424	+	0.298158i
$646$	2.62781	−	4.55151i	0.103390	−	0.179077i
$647$	2.58021	+	24.5491i	0.101439	+	0.965124i	0.920321	+	0.391163i	$0.127927\pi$
$647$	2.58021	+	24.5491i	0.101439	+	0.965124i	−0.818883	+	0.573961i	$0.805406\pi$
$648$	1.28528	+	6.04676i	0.0504905	+	0.237539i
$649$	17.0996	+	52.6273i	0.671219	+	2.06580i
$650$	−3.54005	−	0.649044i	−0.138852	−	0.0254576i
$651$	−8.53785	−	0.929185i	−0.334625	−	0.0364176i
$652$	−19.7932	−	11.4276i	−0.775160	−	0.447539i
$653$	28.5585	+	6.07029i	1.11758	+	0.237549i	0.729435	−	0.684050i	$-0.239783\pi$
$653$	28.5585	+	6.07029i	1.11758	+	0.237549i	0.388144	+	0.921599i	$0.373116\pi$
$654$	0.556094	−	1.71148i	0.0217450	−	0.0669242i
$655$	−11.0566	−	15.2181i	−0.432016	−	0.594619i
$656$	6.32088	+	3.64936i	0.246789	+	0.142484i
$657$		−	6.14471i		−	0.239728i
$658$	1.02506	−	0.107738i	0.0399611	−	0.00420008i
$659$	−4.59465	+	43.7152i	−0.178982	+	1.70290i	0.424421	+	0.905465i	$0.360478\pi$
$659$	−4.59465	+	43.7152i	−0.178982	+	1.70290i	−0.603403	+	0.797436i	$0.706189\pi$
$660$	−16.1737	−	11.7509i	−0.629560	−	0.457402i
$661$	−24.7488	+	8.04138i	−0.962618	+	0.312774i	−0.747832	−	0.663888i	$-0.768905\pi$
$661$	−24.7488	+	8.04138i	−0.962618	+	0.312774i	−0.214786	+	0.976661i	$0.568905\pi$
$662$	−4.63632	−	2.06422i	−0.180196	−	0.0802282i
$663$	−5.65260	+	0.755283i	−0.219529	+	0.0293328i
$664$	0.191210	−	0.0406430i	0.00742040	−	0.00157725i
$665$	49.6483	+	5.21825i	1.92528	+	0.202355i
$666$	5.66707	+	6.29391i	0.219594	+	0.243884i
$667$	5.35240	−	1.13769i	0.207246	−	0.0440515i
$668$	−7.20953	−	16.1929i	−0.278945	−	0.626521i
$669$	−14.2237	+	12.8070i	−0.549919	+	0.495149i
$670$	−4.58650	+	1.49024i	−0.177192	+	0.0575732i
$671$	2.92662	−	6.57331i	0.112981	−	0.253760i
$672$	−5.06298	−	1.07617i	−0.195309	−	0.0415142i
$673$	−11.7301	−	8.52244i	−0.452164	−	0.328516i	0.338286	−	0.941043i	$-0.390153\pi$
$673$	−11.7301	−	8.52244i	−0.452164	−	0.328516i	−0.790449	+	0.612527i	$0.790153\pi$
$674$	−4.26301	−	9.57487i	−0.164205	−	0.368810i
$675$	−1.28242	−	12.2014i	−0.0493603	−	0.469632i
$676$	19.2547	−	15.7157i	0.740567	−	0.604448i
$677$	15.0042	+	25.9880i	0.576657	+	0.998799i	0.995859	+	0.0909061i	$0.0289763\pi$
$677$	15.0042	+	25.9880i	0.576657	+	0.998799i	−0.419203	+	0.907893i	$0.637690\pi$
$678$	0.561782	−	0.0590457i	0.0215751	−	0.00226764i
$679$	−36.1438	+	7.68260i	−1.38707	+	0.294831i
$680$	−5.42656	+	6.02681i	−0.208099	+	0.231118i
$681$		−	14.7318i		−	0.564523i
$682$	−4.59199	+	7.88631i	−0.175836	+	0.301982i
$683$	3.16327	−	1.82632i	0.121039	−	0.0698820i	−0.438258	−	0.898849i	$-0.644404\pi$
$683$	3.16327	−	1.82632i	0.121039	−	0.0698820i	0.559297	+	0.828967i	$0.311071\pi$
$684$	−34.2697	+	11.1349i	−1.31033	+	0.425753i
$685$	14.0443	−	43.2239i	0.536604	−	1.65150i
$686$	−0.617859	−	5.87854i	−0.0235900	−	0.224444i
$687$		−	14.9792i		−	0.571491i
$688$	−13.9079	+	24.0892i	−0.530234	+	0.918392i
$689$	−16.3291	−	34.0653i	−0.622090	−	1.29779i
$690$	−0.556603	−	0.404396i	−0.0211895	−	0.0153951i
$691$	−22.2499	+	30.6244i	−0.846427	+	1.16501i	0.138212	+	0.990403i	$0.455865\pi$
$691$	−22.2499	+	30.6244i	−0.846427	+	1.16501i	−0.984639	+	0.174604i	$0.944135\pi$
$692$	−11.6555	−	35.8721i	−0.443077	−	1.36365i
$693$	−3.49381	−	33.2414i	−0.132719	−	1.26274i
$694$	−0.765242	+	3.60018i	−0.0290482	+	0.136661i
$695$	15.5742	−	14.0231i	0.590762	−	0.531925i
$696$	−1.99990	+	2.75262i	−0.0758058	+	0.104338i
$697$	−4.81820	−	1.56553i	−0.182502	−	0.0592986i
$698$	−1.79073	+	0.380632i	−0.0677802	+	0.0144071i
$699$	0.0216661	−	0.206140i	0.000819489	−	0.00779691i
$700$	−14.3965	−	4.67772i	−0.544138	−	0.176801i
$701$	−27.5404	−	5.85389i	−1.04019	−	0.221098i	−0.344008	−	0.938967i	$-0.611785\pi$
$701$	−27.5404	−	5.85389i	−1.04019	−	0.221098i	−0.696179	+	0.717868i	$0.745118\pi$
$702$	−3.22341	−	2.20624i	−0.121660	−	0.0832692i
$703$	−54.4272	+	60.4475i	−2.05276	+	2.27982i
$704$	19.3449	−	26.6260i	0.729090	−	1.00351i
$705$	2.55091	−	1.13574i	0.0960726	−	0.0427743i
$706$	−4.58838	+	3.33365i	−0.172686	+	0.125464i
$707$	−32.9683	−	19.0343i	−1.23990	−	0.715858i
$708$	10.8704	+	6.27603i	0.408535	+	0.235868i
$709$	−4.07509	+	9.15279i	−0.153043	+	0.343740i	−0.973754	−	0.227603i	$-0.926911\pi$
$709$	−4.07509	+	9.15279i	−0.153043	+	0.343740i	0.820711	+	0.571344i	$0.193578\pi$
$710$	−0.0162939	+	0.0146711i	−0.000611498	+	0.000550595i
$711$	5.00510	−	5.55873i	0.187706	−	0.208469i
$712$	−2.26726	+	3.92701i	−0.0849692	+	0.147171i
$713$	3.42764	−	5.88664i	0.128366	−	0.220456i
$714$	1.10585			0.0413854
$715$	−57.0531	+	7.62326i	−2.13367	+	0.285094i
$716$	0.792439	+	0.880092i	0.0296148	+	0.0328906i
$717$	−14.6736	+	1.54226i	−0.547996	+	0.0575967i
$718$	−9.20334			−0.343466
$719$	29.2734			1.09171			0.545857	−	0.837878i	$-0.316204\pi$
$719$	29.2734			1.09171			0.545857	+	0.837878i	$0.316204\pi$
$720$	25.7224	−	2.70353i	0.958618	−	0.100755i
$721$	15.7326	+	1.65356i	0.585912	+	0.0615819i
$722$	4.19521	+	9.42261i	0.156130	+	0.350673i
$723$	0.146313	+	0.131741i	0.00544145	+	0.00489951i
$724$	0.960941	+	9.14274i	0.0357131	+	0.339787i
$725$	−10.0621	+	11.1751i	−0.373698	+	0.415034i
$726$	3.60238	+	1.17048i	0.133697	+	0.0434407i
$727$	−29.9012	+	13.3129i	−1.10897	+	0.493747i	−0.877733	−	0.479150i	$-0.840945\pi$
$727$	−29.9012	+	13.3129i	−1.10897	+	0.493747i	−0.231240	+	0.972897i	$0.574278\pi$
$728$	−8.39813	+	5.16871i	−0.311255	+	0.191565i
$729$	−2.01300	+	6.19538i	−0.0745555	+	0.229458i
$730$	2.04069	+	0.214485i	0.0755294	+	0.00793846i
$731$	5.96630	−	18.3624i	0.220672	−	0.679158i
$732$	−0.504367	−	1.55228i	−0.0186419	−	0.0573739i
$733$	−17.6196	+	39.5742i	−0.650794	+	1.46171i	0.222707	+	0.974885i	$0.428511\pi$
$733$	−17.6196	+	39.5742i	−0.650794	+	1.46171i	−0.873501	+	0.486822i	$0.838156\pi$
$734$	−0.650775	+	3.06166i	−0.0240206	+	0.113008i
$735$	−1.12040	−	2.51646i	−0.0413266	−	0.0928210i
$736$	2.41313	−	3.32138i	0.0889490	−	0.122428i
$737$	−25.0880	+	18.2275i	−0.924127	+	0.671418i
$738$	−0.800701	−	1.38686i	−0.0294742	−	0.0510508i
$739$		−	25.2411i		−	0.928510i	−0.885702	−	0.464255i	$-0.846322\pi$
$739$		−	25.2411i		−	0.928510i	0.885702	−	0.464255i	$-0.153678\pi$
$740$	49.6277	−	36.0566i	1.82435	−	1.32547i
$741$	8.23163	−	15.2308i	0.302397	−	0.559518i
$742$	2.26367	+	6.96686i	0.0831019	+	0.255761i
$743$	32.0077	+	18.4797i	1.17425	+	0.677953i	0.954677	−	0.297643i	$-0.0962006\pi$
$743$	32.0077	+	18.4797i	1.17425	+	0.677953i	0.219572	+	0.975596i	$0.429534\pi$
$744$	0.865346	+	4.14620i	0.0317251	+	0.152007i
$745$	−17.7718	−	30.7816i	−0.651108	−	1.12775i
$746$	2.90983	−	0.945462i	0.106537	−	0.0346158i
$747$	0.411555	+	0.133722i	0.0150580	+	0.00489264i
$748$	−10.3665	+	23.2835i	−0.379037	+	0.851331i
$749$	17.3529	−	10.0187i	0.634061	−	0.366075i
$750$	−0.921035			−0.0336314
$751$	−24.1870	−	10.7688i	−0.882597	−	0.392958i	−0.0851656	−	0.996367i	$-0.527142\pi$
$751$	−24.1870	−	10.7688i	−0.882597	−	0.392958i	−0.797432	+	0.603409i	$0.793809\pi$
$752$	2.08600	+	4.68523i	0.0760685	+	0.170853i
$753$	−0.191459	+	1.82161i	−0.00697714	+	0.0663831i
$754$	0.634089	+	4.74557i	0.0230921	+	0.172824i
$755$	59.8981	+	26.6683i	2.17991	+	0.970560i
$756$	−12.2091	−	10.9931i	−0.444040	−	0.399816i
$757$	4.77644	−	14.7004i	0.173603	−	0.534294i	−0.825964	−	0.563722i	$-0.809369\pi$
$757$	4.77644	−	14.7004i	0.173603	−	0.534294i	0.999567	+	0.0294286i	$0.00936878\pi$
$758$	−2.84938	−	2.07019i	−0.103494	−	0.0751928i
$759$	−4.20753	−	1.36711i	−0.152724	−	0.0496229i
$760$	−5.11885	−	24.0823i	−0.185680	−	0.873557i
$761$	14.7270	−	20.2700i	0.533854	−	0.734787i	−0.453858	−	0.891074i	$-0.649953\pi$
$761$	14.7270	−	20.2700i	0.533854	−	0.734787i	0.987712	+	0.156287i	$0.0499525\pi$
$762$	−0.0505034	−	0.237600i	−0.00182955	−	0.00860734i
$763$	−6.73412	−	20.7255i	−0.243792	−	0.750313i
$764$	8.36608	−	6.07832i	0.302674	−	0.219906i
$765$	−17.0740	+	5.54767i	−0.617311	+	0.200577i
$766$	0.0243224	−	0.231412i	0.000878803	−	0.00836125i
$767$	35.1249	−	8.50448i	1.26828	−	0.307079i
$768$	−0.643934	−	6.12663i	−0.0232360	−	0.221076i
$769$	−31.2242	+	18.0273i	−1.12597	+	0.650081i	−0.942919	−	0.333022i	$-0.891932\pi$
$769$	−31.2242	+	18.0273i	−1.12597	+	0.650081i	−0.183054	+	0.983103i	$0.558598\pi$
$770$	11.1616			0.402237
$771$	2.29568	+	1.02210i	0.0826768	+	0.0368101i
$772$	16.0591	−	14.4597i	0.577979	−	0.520414i
$773$	−1.53404	−	1.38126i	−0.0551757	−	0.0496804i	0.641082	−	0.767473i	$-0.278486\pi$
$773$	−1.53404	−	1.38126i	−0.0551757	−	0.0496804i	−0.696257	+	0.717792i	$0.745153\pi$
$774$	5.28537	−	3.05151i	0.189979	−	0.109684i
$775$	1.88813	+	18.6242i	0.0678236	+	0.669003i
$776$	9.11177	+	15.7820i	0.327093	+	0.566542i
$777$	−16.7410	−	3.55841i	−0.600580	−	0.127657i
$778$	−0.878458	−	4.13282i	−0.0314942	−	0.148169i
$779$	12.4427	−	9.04017i	0.445807	−	0.323898i
$780$	−8.46044	+	9.94472i	−0.302932	+	0.356078i
$781$	−0.0704942	+	0.122100i	−0.00252248	+	0.00436906i
$782$	−0.356754	+	0.801283i	−0.0127575	+	0.0286538i
$783$	−14.9096	+	6.63820i	−0.532827	+	0.237230i
$784$	4.62196	−	2.05783i	0.165070	−	0.0734939i
$785$	29.1049	+	26.2061i	1.03880	+	0.935337i
$786$	1.25806	−	0.132228i	0.0448736	−	0.00471641i
$787$	7.84122	−	2.54777i	0.279509	−	0.0908181i	−0.165908	−	0.986141i	$-0.553055\pi$
$787$	7.84122	−	2.54777i	0.279509	−	0.0908181i	0.445417	+	0.895323i	$0.353055\pi$
$788$	−0.753509	−	3.54498i	−0.0268426	−	0.126285i
$789$	−1.31711	−	0.956935i	−0.0468903	−	0.0340678i
$790$	1.67138	+	1.85625i	0.0594650	+	0.0660426i
$791$	5.08347	−	4.57717i	0.180747	−	0.162746i
$792$	−15.0591	+	6.70474i	−0.535102	+	0.238243i
$793$	−4.13416	−	2.23434i	−0.146808	−	0.0793438i
$794$	−2.46176	−	0.523263i	−0.0873645	−	0.0185699i
$795$	11.6648	+	16.0552i	0.413708	+	0.569421i
$796$	−4.33313	−	13.3360i	−0.153584	−	0.472683i
$797$	41.4741	−	18.4655i	1.46909	−	0.654080i	0.492718	−	0.870189i	$-0.336003\pi$
$797$	41.4741	−	18.4655i	1.46909	−	0.654080i	0.976369	+	0.216109i	$0.0693366\pi$
$798$	−1.97331	+	2.71603i	−0.0698543	+	0.0961463i
$799$	−2.09243	−	2.87998i	−0.0740247	−	0.101886i
$800$			11.2823i			0.398888i
$801$	−8.69314	+	5.01898i	−0.307157	+	0.177337i
$802$	5.26331	+	2.34337i	0.185854	+	0.0827474i
$803$	12.9063	−	2.74331i	0.455452	−	0.0968093i
$804$	−1.46250	+	6.88054i	−0.0515785	+	0.242658i
$805$	−8.33146			−0.293645
$806$	4.90592	+	3.38443i	0.172804	+	0.119212i
$807$	16.0321			0.564358
$808$	−3.90345	+	18.3643i	−0.137323	+	0.646054i
$809$	16.9983	−	3.61310i	0.597628	−	0.127030i	0.100841	−	0.994903i	$-0.467847\pi$
$809$	16.9983	−	3.61310i	0.597628	−	0.127030i	0.496786	+	0.867873i	$0.334513\pi$
$810$	−4.17470	−	1.85869i	−0.146684	−	0.0653079i
$811$	19.0456	−	10.9960i	0.668783	−	0.386122i	−0.126833	−	0.991924i	$-0.540481\pi$
$811$	19.0456	−	10.9960i	0.668783	−	0.386122i	0.795615	+	0.605802i	$0.207148\pi$
$812$			20.1369i			0.706668i
$813$	8.68221	+	11.9500i	0.304498	+	0.419106i
$814$	−10.6896	+	14.7130i	−0.374670	+	0.515689i
$815$	31.5805	−	14.0605i	1.10622	−	0.492519i
$816$	1.70037	+	5.23320i	0.0595249	+	0.183199i
$817$	34.4526	+	47.4199i	1.20534	+	1.65901i
$818$	−1.35079	−	0.287118i	−0.0472291	−	0.0100389i
$819$	−21.8210	+	0.613559i	−0.762487	+	0.0214395i
$820$	−10.5962	+	4.71773i	−0.370035	+	0.164750i
$821$	−2.12328	+	1.91181i	−0.0741031	+	0.0667227i	−0.705350	−	0.708859i	$-0.749210\pi$
$821$	−2.12328	+	1.91181i	−0.0741031	+	0.0667227i	0.631247	+	0.775582i	$0.282543\pi$
$822$	2.04510	+	2.27131i	0.0713310	+	0.0792211i
$823$	−25.2530	−	18.3473i	−0.880263	−	0.639548i	0.0530582	−	0.998591i	$-0.483103\pi$
$823$	−25.2530	−	18.3473i	−0.880263	−	0.639548i	−0.933321	+	0.359043i	$0.883103\pi$
$824$	−1.62207	−	7.63122i	−0.0565073	−	0.265846i
$825$	11.5628	−	3.75697i	0.402564	−	0.130801i
$826$	−6.96955	+	0.732530i	−0.242502	+	0.0254880i
$827$	28.5984	+	25.7501i	0.994463	+	0.895418i	0.994516	−	0.104582i	$-0.0333504\pi$
$827$	28.5984	+	25.7501i	0.994463	+	0.895418i	−5.36039e−5		1.00000i	$0.500017\pi$
$828$	5.49370	−	2.44595i	0.190919	−	0.0850028i
$829$	22.3307	−	9.94226i	0.775577	−	0.345309i	0.0195151	−	0.999810i	$-0.493788\pi$
$829$	22.3307	−	9.94226i	0.775577	−	0.345309i	0.756061	+	0.654501i	$0.227121\pi$
$830$	−0.0587756	+	0.132012i	−0.00204013	+	0.00458221i
$831$	6.38956	−	11.0670i	0.221651	−	0.383912i
$832$	−16.3715	−	13.9280i	−0.567581	−	0.482868i
$833$	−2.84109	+	2.06417i	−0.0984379	+	0.0715193i
$834$	0.293020	+	1.37855i	0.0101464	+	0.0477352i
$835$	26.2242	+	5.57413i	0.907527	+	0.192901i
$836$	−38.6873	−	67.0084i	−1.33803	−	2.31753i
$837$	−6.34943	+	19.2993i	−0.219468	+	0.667080i
$838$	−1.81112	+	1.04565i	−0.0625640	+	0.0361213i
$839$	30.6335	+	27.5825i	1.05759	+	0.952254i	0.998940	−	0.0460246i	$-0.0146553\pi$
$839$	30.6335	+	27.5825i	1.05759	+	0.952254i	0.0586452	+	0.998279i	$0.481322\pi$
$840$	3.84981	−	3.46638i	0.132831	−	0.119602i
$841$	−8.21808	−	3.65893i	−0.283382	−	0.126170i
$842$	0.853584			0.0294165
$843$	−0.527111	+	0.304328i	−0.0181547	+	0.0104816i
$844$	−1.77091	−	16.8490i	−0.0609571	−	0.579968i
$845$	2.11238	+	37.5332i	0.0726679	+	1.29118i
$846$	0.117622	−	1.11910i	0.00404392	−	0.0384754i
$847$	43.6236	−	14.1742i	1.49893	−	0.487031i
$848$	−29.4885	+	21.4247i	−1.01264	+	0.735726i
$849$	−2.19200	−	6.74629i	−0.0752293	−	0.231532i
$850$	−0.501152	−	2.35773i	−0.0171894	−	0.0808696i
$851$	7.97911	−	10.9823i	0.273521	−	0.376469i
$852$	0.00664925	+	0.0312822i	0.000227799	+	0.00107171i
$853$	26.6782	+	8.66829i	0.913446	+	0.296797i	0.727775	−	0.685816i	$-0.240554\pi$
$853$	26.6782	+	8.66829i	0.913446	+	0.296797i	0.185670	+	0.982612i	$0.440554\pi$
$854$	0.737220	+	0.535622i	0.0252272	+	0.0183286i
$855$	16.8419	−	51.8340i	0.575980	−	1.77268i
$856$	−7.34376	−	6.61235i	−0.251004	−	0.226005i
$857$	−2.31684	−	1.03152i	−0.0791418	−	0.0352362i	0.366784	−	0.930306i	$-0.380459\pi$
$857$	−2.31684	−	1.03152i	−0.0791418	−	0.0352362i	−0.445926	+	0.895070i	$0.647125\pi$
$858$	1.47441	−	3.57907i	0.0503355	−	0.122187i
$859$	−2.24357	+	21.3462i	−0.0765497	+	0.728322i	0.887177	+	0.461430i	$0.152663\pi$
$859$	−2.24357	+	21.3462i	−0.0765497	+	0.728322i	−0.963726	+	0.266892i	$0.914003\pi$
$860$	−17.9795	−	40.3826i	−0.613096	−	1.37704i
$861$	2.95638	+	1.31626i	0.100753	+	0.0448582i
$862$	−11.7848			−0.401391
$863$	−25.0037	+	14.4359i	−0.851135	+	0.491403i	−0.861034	−	0.508548i	$-0.830183\pi$
$863$	−25.0037	+	14.4359i	−0.851135	+	0.491403i	0.00989841	+	0.999951i	$0.496849\pi$
$864$	−4.98044	+	11.1863i	−0.169438	+	0.380564i
$865$	54.2576	+	17.6294i	1.84481	+	0.599416i
$866$	−6.21141	+	2.01821i	−0.211072	+	0.0685816i
$867$	3.65788	+	6.33563i	0.124228	+	0.215169i
$868$	18.5670	+	16.8421i	0.630204	+	0.571657i
$869$	13.9100	+	8.03095i	0.471865	+	0.272431i
$870$	−0.777226	−	2.39206i	−0.0263504	−	0.0810983i
$871$	10.6155	+	17.2480i	0.359691	+	0.584427i
$872$	−8.69480	+	6.31714i	−0.294443	+	0.213926i
$873$			40.3410i			1.36534i
$874$	−1.33139	−	2.30604i	−0.0450350	−	0.0780028i
$875$	−9.02332	+	6.55583i	−0.305044	+	0.221627i
$876$	1.75924	−	2.42139i	0.0594392	−	0.0818111i
$877$	−4.94942	−	11.1166i	−0.167130	−	0.375380i	0.810492	−	0.585750i	$-0.199200\pi$
$877$	−4.94942	−	11.1166i	−0.167130	−	0.375380i	−0.977622	+	0.210370i	$0.932533\pi$
$878$	−1.39543	+	6.56500i	−0.0470936	+	0.221558i
$879$	4.07575	−	9.15428i	0.137472	−	0.308766i
$880$	17.1623	+	52.8200i	0.578540	+	1.78056i
$881$	12.6446	−	38.9162i	0.426009	−	1.31112i	−0.476016	−	0.879437i	$-0.657920\pi$
$881$	12.6446	−	38.9162i	0.426009	−	1.31112i	0.902025	−	0.431684i	$-0.142080\pi$
$882$	−1.10399	−	0.116034i	−0.0371732	−	0.00390706i
$883$	11.0378	−	33.9707i	0.371450	−	1.14321i	−0.574392	−	0.818580i	$-0.694762\pi$
$883$	11.0378	−	33.9707i	0.371450	−	1.14321i	0.945843	−	0.324626i	$-0.105238\pi$
$884$	14.6437	+	7.91434i	0.492523	+	0.266188i
$885$	−17.3440	+	7.72205i	−0.583012	+	0.259574i
$886$	−1.87605	−	0.609567i	−0.0630272	−	0.0204788i
$887$	−11.6987	+	12.9928i	−0.392805	+	0.436254i	−0.906814	−	0.421530i	$-0.861493\pi$
$887$	−11.6987	+	12.9928i	−0.392805	+	0.436254i	0.514009	+	0.857785i	$0.328160\pi$
$888$	0.882297	+	8.39450i	0.0296080	+	0.281701i
$889$	−2.18599	−	1.96827i	−0.0733158	−	0.0660138i
$890$	−1.36339	−	3.06223i	−0.0457011	−	0.102646i
$891$	−29.2242	−	3.07158i	−0.979046	−	0.102902i
$892$	55.5598	−	5.83957i	1.86028	−	0.195523i
$893$	10.8072			0.361648
$894$	2.39027			0.0799426
$895$	−1.78145	+	0.187238i	−0.0595473	+	0.00625867i
$896$	13.3644	+	14.8426i	0.446473	+	0.495858i
$897$	−1.10056	+	2.67155i	−0.0367465	+	0.0892005i
$898$	9.10315			0.303776
$899$	22.7866	−	10.0448i	0.759977	−	0.335014i
$900$	−8.26303	+	14.3120i	−0.275434	+	0.477066i
$901$	16.9292	−	18.8018i	0.563995	−	0.626380i
$902$	2.55546	−	2.30095i	0.0850875	−	0.0766131i
$903$	−5.01635	+	11.2669i	−0.166934	+	0.374939i
$904$	−2.92160	−	1.68679i	−0.0971709	−	0.0561017i
$905$	−12.0420	−	6.95243i	−0.400288	−	0.231107i
$906$	−3.56719	+	2.59172i	−0.118512	+	0.0861040i
$907$	−17.7731	+	7.91308i	−0.590145	+	0.262749i	−0.680008	−	0.733205i	$-0.738024\pi$
$907$	−17.7731	+	7.91308i	−0.590145	+	0.262749i	0.0898631	+	0.995954i	$0.471357\pi$
$908$	−25.2745	+	34.7874i	−0.838764	+	1.15446i
$909$	−27.8096	+	30.8857i	−0.922387	+	1.02441i
$910$	0.557911	−	7.26829i	0.0184946	−	0.240942i
$911$	55.8062	+	11.8620i	1.84894	+	0.393005i	0.992398	−	0.123070i	$-0.0392740\pi$
$911$	55.8062	+	11.8620i	1.84894	+	0.393005i	0.856544	+	0.516075i	$0.172607\pi$
$912$	−15.8872	−	5.16206i	−0.526078	−	0.170933i
$913$	−0.0971294	+	0.924125i	−0.00321452	+	0.0305841i
$914$	8.58142	−	1.82404i	0.283848	−	0.0603338i
$915$	2.34787	+	0.762870i	0.0776183	+	0.0252197i
$916$	−25.6989	+	35.3716i	−0.849117	+	1.16871i
$917$	11.3840	−	10.2502i	0.375932	−	0.338491i
$918$	0.543911	−	2.55890i	0.0179517	−	0.0844563i
$919$	−3.11866	−	29.6720i	−0.102875	−	0.978790i	−0.917212	−	0.398398i	$-0.869566\pi$
$919$	−3.11866	−	29.6720i	−0.102875	−	0.978790i	0.814337	−	0.580392i	$-0.197101\pi$
$920$	1.26972	+	3.90779i	0.0418613	+	0.128836i
$921$	−4.82051	+	6.63486i	−0.158841	+	0.218626i
$922$	−0.242019	−	0.175837i	−0.00797046	−	0.00579088i
$923$	0.0759858	+	0.0520079i	0.00250110	+	0.00171186i
$924$	8.14030	−	14.0994i	0.267796	−	0.463837i
$925$			37.3053i			1.22659i
$926$	−0.890210	−	8.46978i	−0.0292541	−	0.278334i
$927$	5.33686	−	16.4252i	0.175286	−	0.539474i
$928$	14.2740	−	4.63789i	0.468566	−	0.152246i
$929$	−36.8634	+	21.2831i	−1.20945	+	0.698276i	−0.962639	−	0.270788i	$-0.912716\pi$
$929$	−36.8634	+	21.2831i	−1.20945	+	0.698276i	−0.246810	+	0.969064i	$0.579382\pi$
$930$	−2.85561	−	1.28403i	−0.0936393	−	0.0421050i
$931$		−	10.6612i		−	0.349407i
$932$	−0.404824	+	0.449603i	−0.0132605	+	0.0147272i
$933$	−13.7616	+	2.92511i	−0.450534	+	0.0957639i
$934$	5.03598	−	0.529303i	0.164782	−	0.0173193i
$935$	−19.2749	−	33.3852i	−0.630358	−	1.09181i
$936$	3.61331	+	10.1414i	0.118105	+	0.331482i
$937$	−4.09764	−	38.9864i	−0.133864	−	1.27363i	−0.830830	−	0.556527i	$-0.812134\pi$
$937$	−4.09764	−	38.9864i	−0.133864	−	1.27363i	0.696966	−	0.717104i	$-0.254533\pi$
$938$	−1.59738	−	3.58777i	−0.0521562	−	0.117145i
$939$	8.11261	+	5.89416i	0.264745	+	0.192348i
$940$	−7.97218	−	1.69454i	−0.260024	−	0.0552698i
$941$	2.17712	−	4.88989i	0.0709720	−	0.159406i	−0.874576	−	0.484889i	$-0.838860\pi$
$941$	2.17712	−	4.88989i	0.0709720	−	0.159406i	0.945548	+	0.325483i	$0.105527\pi$
$942$	−2.50487	+	0.813881i	−0.0816130	+	0.0265177i
$943$	−1.90749	+	1.71751i	−0.0621165	+	0.0559299i
$944$	−14.1830	−	31.8556i	−0.461618	−	1.03681i
$945$	24.3063	−	5.16646i	0.790683	−	0.168065i
$946$	8.76902	+	9.73898i	0.285105	+	0.316642i
$947$	11.3662	+	1.19464i	0.369352	+	0.0388205i	0.287387	−	0.957815i	$-0.407214\pi$
$947$	11.3662	+	1.19464i	0.369352	+	0.0388205i	0.0819658	+	0.996635i	$0.473880\pi$
$948$	3.56378	−	0.757506i	0.115746	−	0.0246026i
$949$	−1.14129	−	8.54150i	−0.0370478	−	0.277269i
$950$	6.68498	+	2.97635i	0.216889	+	0.0965654i
$951$	12.3755	−	4.02104i	0.401303	−	0.130391i
$952$	−5.34307	−	3.88196i	−0.173170	−	0.125815i
$953$	0.945003	−	8.99110i	0.0306116	−	0.291250i	−0.968497	−	0.249027i	$-0.919889\pi$
$953$	0.945003	−	8.99110i	0.0306116	−	0.291250i	0.999108	−	0.0422234i	$-0.0134441\pi$
$954$	7.95359	−	0.835956i	0.257507	−	0.0270651i
$955$			15.6412i			0.506136i
$956$	37.2960	+	21.5328i	1.20624	+	0.696422i
$957$	−9.50641	−	13.0845i	−0.307299	−	0.422960i
$958$	3.62468	−	11.1556i	0.117108	−	0.360422i
$959$	36.2027	+	7.69511i	1.16905	+	0.248488i
$960$	9.77899	+	5.64590i	0.315615	+	0.182221i
$961$	9.79654	−	29.4114i	0.316017	−	0.948753i
$962$	9.04655	+	7.69633i	0.291673	+	0.248140i
$963$	−6.75992	−	20.8049i	−0.217835	−	0.670428i
$964$	−0.119481	−	0.562113i	−0.00384822	−	0.0181044i
$965$	3.41654	+	32.5062i	0.109982	+	1.04641i
$966$	0.280141	−	0.485219i	0.00901340	−	0.0156117i
$967$	−6.81256	−	3.93323i	−0.219077	−	0.126484i	0.386446	−	0.922312i	$-0.373703\pi$
$967$	−6.81256	−	3.93323i	−0.219077	−	0.126484i	−0.605523	+	0.795828i	$0.707036\pi$
$968$	−13.2965	−	18.3011i	−0.427366	−	0.588219i
$969$	11.5315	+	1.21201i	0.370446	+	0.0389354i
$970$	−13.3975	−	1.40813i	−0.430168	−	0.0452124i
$971$	−50.7834	−	10.7943i	−1.62972	−	0.346407i	−0.699846	−	0.714294i	$-0.746748\pi$
$971$	−50.7834	−	10.7943i	−1.62972	−	0.346407i	−0.929870	+	0.367887i	$0.880081\pi$
$972$	−22.3247	+	16.2198i	−0.716064	+	0.520251i
$973$	12.6831	+	11.4199i	0.406600	+	0.366104i
$974$	4.06633	−	0.864325i	0.130294	−	0.0276948i
$975$	−1.86853	−	7.71731i	−0.0598407	−	0.247152i
$976$	−1.40116	+	4.31232i	−0.0448499	+	0.138034i
$977$	0.0101280	−	0.00911930i	0.000324024	−	0.000291752i	−0.668969	−	0.743291i	$-0.733264\pi$
$977$	0.0101280	−	0.00911930i	0.000324024	−	0.000291752i	0.669293	+	0.742999i	$0.266597\pi$
$978$	−0.243002	+	2.31201i	−0.00777034	+	0.0739299i
$979$	−14.4229	−	16.0182i	−0.460957	−	0.511944i
$980$	−1.67166	+	7.86453i	−0.0533991	+	0.251223i
$981$	−23.6609	+	2.48686i	−0.755434	+	0.0793993i
$982$	0.835518	−	3.93081i	0.0266625	−	0.125437i
$983$	−34.7677	−	3.65423i	−1.10892	−	0.116552i	−0.467682	−	0.883897i	$-0.654911\pi$
$983$	−34.7677	−	3.65423i	−1.10892	−	0.116552i	−0.641235	+	0.767345i	$0.721577\pi$
$984$	0.166828	−	1.58726i	0.00531827	−	0.0506000i
$985$	5.00776	+	2.22960i	0.159561	+	0.0710409i
$986$	−2.77692	+	1.60325i	−0.0884351	+	0.0510580i
$987$	1.13698	+	1.96931i	0.0361905	+	0.0626838i
$988$	−45.5687	+	21.8432i	−1.44973	+	0.694926i
$989$	−6.54553	−	7.26955i	−0.208136	−	0.231158i
$990$	2.53352	−	11.9193i	0.0805205	−	0.378819i
$991$	7.15791	−	12.3979i	0.227378	−	0.393831i	−0.729652	−	0.683819i	$-0.760318\pi$
$991$	7.15791	−	12.3979i	0.227378	−	0.393831i	0.957030	+	0.289988i	$0.0936512\pi$
$992$	7.66211	−	17.0401i	0.243272	−	0.541024i
$993$		−	11.1967i		−	0.355317i
$994$	−0.0132691	−	0.0119476i	−0.000420872	−	0.000378955i
$995$	20.1711	+	6.55400i	0.639468	+	0.207776i
$996$	0.123893	+	0.170523i	0.00392569	+	0.00540324i
$997$	−13.7116	+	23.7492i	−0.434250	+	0.752144i	−0.997234	−	0.0743244i	$-0.976320\pi$
$997$	−13.7116	+	23.7492i	−0.434250	+	0.752144i	0.562984	+	0.826468i	$0.309653\pi$
$998$	−1.15862	−	2.00680i	−0.0366756	−	0.0635240i
$999$	−16.4681	+	36.9879i	−0.521026	+	1.17024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bt.a.82.16	yes	280
13.10	even	6		403.2.bp.a.361.20	yes	280
31.14	even	15		403.2.bp.a.355.20	✓	280
403.231	even	30	inner	403.2.bt.a.231.16	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bp.a.355.20	✓	280	31.14	even	15
403.2.bp.a.361.20	yes	280	13.10	even	6
403.2.bt.a.82.16	yes	280	1.1	even	1	trivial
403.2.bt.a.231.16	yes	280	403.231	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bt (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0617274 + 0.290405i) q^{2} +(-0.640694 + 0.136184i) q^{3} +(1.74657 + 0.777621i) q^{4} +(-2.50432 + 1.44587i) q^{5} -0.194467i q^{6} +(-1.38419 - 1.90518i) q^{7} +(-0.682654 + 0.939592i) q^{8} +(-2.34869 + 1.04571i) q^{9} +O(q^{10})\)	\(q+(-0.0617274 + 0.290405i) q^{2} +(-0.640694 + 0.136184i) q^{3} +(1.74657 + 0.777621i) q^{4} +(-2.50432 + 1.44587i) q^{5} -0.194467i q^{6} +(-1.38419 - 1.90518i) q^{7} +(-0.682654 + 0.939592i) q^{8} +(-2.34869 + 1.04571i) q^{9} +(-0.265302 - 0.816516i) q^{10} +(-3.24496 - 4.46631i) q^{11} +(-1.22491 - 0.260364i) q^{12} +(-3.07060 + 1.88983i) q^{13} +(0.638715 - 0.284374i) q^{14} +(1.40760 - 1.26741i) q^{15} +(2.32784 + 2.58533i) q^{16} +(-1.95358 - 1.41936i) q^{17} +(-0.158699 - 0.746620i) q^{18} +(6.97203 - 2.26535i) q^{19} +(-5.49830 + 0.577895i) q^{20} +(1.14630 + 1.03213i) q^{21} +(1.49734 - 0.666658i) q^{22} +(-1.11767 + 0.497619i) q^{23} +(0.309415 - 0.694957i) q^{24} +(1.68108 - 2.91172i) q^{25} +(-0.359274 - 1.00837i) q^{26} +(2.95212 - 2.14484i) q^{27} +(-0.936078 - 4.40390i) q^{28} +(-4.37487 - 0.929907i) q^{29} +(0.281174 + 0.487007i) q^{30} +(-4.51644 + 3.25603i) q^{31} +(-2.90608 + 1.67783i) q^{32} +(2.68727 + 2.41963i) q^{33} +(0.532777 - 0.479715i) q^{34} +(6.22111 + 2.76981i) q^{35} -4.91531 q^{36} +(-9.60910 + 5.54782i) q^{37} +(0.227503 + 2.16454i) q^{38} +(1.70995 - 1.62897i) q^{39} +(0.351055 - 3.34007i) q^{40} +(1.99532 - 0.648318i) q^{41} +(-0.370494 + 0.269180i) q^{42} +(2.47077 + 7.60425i) q^{43} +(-2.19445 - 10.3241i) q^{44} +(4.36993 - 6.01469i) q^{45} +(-0.0755199 - 0.355293i) q^{46} +(1.40205 + 0.455555i) q^{47} +(-1.84351 - 1.33939i) q^{48} +(0.449404 - 1.38312i) q^{49} +(0.741807 + 0.667926i) q^{50} +(1.44494 + 0.643328i) q^{51} +(-6.83257 + 0.912947i) q^{52} +(-1.09519 + 10.4200i) q^{53} +(0.440645 + 0.989705i) q^{54} +(14.5841 + 6.49327i) q^{55} +2.73502 q^{56} +(-4.15843 + 2.40087i) q^{57} +(0.540098 - 1.21308i) q^{58} +(-9.53278 - 3.09739i) q^{59} +(3.44403 - 1.11903i) q^{60} +(0.651677 + 1.12874i) q^{61} +(-0.666777 - 1.51258i) q^{62} +(5.24330 + 3.02722i) q^{63} +(1.84221 + 5.66975i) q^{64} +(4.95731 - 9.17241i) q^{65} +(-0.868548 + 0.631037i) q^{66} -5.61716i q^{67} +(-2.30833 - 3.99815i) q^{68} +(0.648317 - 0.471030i) q^{69} +(-1.18838 + 1.63566i) q^{70} +(-0.0103874 - 0.0233304i) q^{71} +(0.620807 - 2.92067i) q^{72} +(-0.972117 + 2.18341i) q^{73} +(-1.01797 - 3.13298i) q^{74} +(-0.680530 + 2.09445i) q^{75} +(13.9387 + 1.46502i) q^{76} +(-4.01746 + 12.3645i) q^{77} +(0.367508 + 0.597129i) q^{78} +(-2.65788 + 1.18337i) q^{79} +(-9.56770 - 3.10873i) q^{80} +(3.56162 - 3.95558i) q^{81} +(0.0651087 + 0.619468i) q^{82} +(-0.125083 - 0.112625i) q^{83} +(1.19948 + 2.69407i) q^{84} +(6.94459 + 0.729906i) q^{85} +(-2.36082 + 0.248132i) q^{86} +2.92959 q^{87} +6.41169 q^{88} +(3.88297 - 0.408117i) q^{89} +(1.47695 + 1.64032i) q^{90} +(7.85076 + 3.23415i) q^{91} -2.33905 q^{92} +(2.45024 - 2.70119i) q^{93} +(-0.218840 + 0.379043i) q^{94} +(-14.1848 + 15.7538i) q^{95} +(1.63342 - 1.47074i) q^{96} +(6.38211 - 14.3345i) q^{97} +(0.373924 + 0.215885i) q^{98} +(12.2919 + 7.09671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9	\( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) 280 * q - 9 * q^2 - 3 * q^3 - 35 * q^4 - 15 * q^7 + 45 * q^8 + 24 * q^9 + 3 * q^10 - 8 * q^12 - 6 * q^13 + 4 * q^14 - 45 * q^15 + 23 * q^16 + 27 * q^17 + 45 * q^18 - 15 * q^19 - 12 * q^20 - 76 * q^21 + 41 * q^22 - 10 * q^23 - 33 * q^24 + 96 * q^25 + 9 * q^26 - 24 * q^27 - 32 * q^28 + 13 * q^29 + 36 * q^30 + 2 * q^31 - 141 * q^32 - 93 * q^33 - 9 * q^34 - 43 * q^35 - 194 * q^36 + 3 * q^37 - 49 * q^38 + 50 * q^39 - 75 * q^40 - 15 * q^41 + 17 * q^42 + 33 * q^43 + 18 * q^44 - 15 * q^45 - 9 * q^46 - 59 * q^48 + 3 * q^49 + 36 * q^50 + 47 * q^51 - 56 * q^52 + 12 * q^53 - 33 * q^54 - 5 * q^55 - 50 * q^56 - 105 * q^57 - 3 * q^58 - 15 * q^59 + 90 * q^60 - 57 * q^61 - 72 * q^62 + 201 * q^63 + 13 * q^64 - 43 * q^65 + 22 * q^66 - 71 * q^68 - 7 * q^69 - 42 * q^71 + 90 * q^72 + 9 * q^73 - 113 * q^74 + 45 * q^75 + 14 * q^76 - 24 * q^77 + 61 * q^78 + 54 * q^79 + 30 * q^80 + 106 * q^81 + 16 * q^82 + 54 * q^83 + 60 * q^84 + 18 * q^85 + 84 * q^86 + 42 * q^87 - 98 * q^88 - 99 * q^89 + 11 * q^90 + 60 * q^91 + 266 * q^92 - 104 * q^93 + 33 * q^94 - 120 * q^95 + 204 * q^96 - 50 * q^97 - 15 * q^98 - 168 * q^99

Introduction

L-functions

Modular forms

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