LMFDB - Embedded newform 841.2.d.j.574.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.74049191673856.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2x^{10} + 4x^{8} + 8x^{6} + 16x^{4} + 32x^{2} + 64 $ x^12 + 2x^10 + 4x^8 + 8x^6 + 16x^4 + 32*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			574.2
Root			$-1.27416 + 0.613604i$ of defining polynomial
Character	$\chi$	$=$	841.574
Dual form			841.2.d.j.778.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258258 - 0.323845i) q^{2} +(0.0921712 - 0.403828i) q^{3} +(0.406863 + 1.78258i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-0.106974 - 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(1.42874 + 0.688047i) q^{8} +(2.54832 + 1.22721i) q^{9} +O(q^{10})$	\(q+(0.258258 - 0.323845i) q^{2} +(0.0921712 - 0.403828i) q^{3} +(0.406863 + 1.78258i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-0.106974 - 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(1.42874 + 0.688047i) q^{8} +(2.54832 + 1.22721i) q^{9} +(0.0921712 + 0.403828i) q^{10} +(-2.17513 + 1.04749i) q^{11} +0.757359 q^{12} +(-1.64736 + 0.793325i) q^{13} +(0.730464 + 0.915973i) q^{14} +(0.258258 + 0.323845i) q^{15} +(-2.70291 + 1.30165i) q^{16} -4.82843 q^{17} +(1.05555 - 0.508326i) q^{18} +(-1.33513 - 5.84957i) q^{19} +(-1.64736 - 0.793325i) q^{20} +(1.05555 + 0.508326i) q^{21} +(-0.222521 + 0.974928i) q^{22} +(-4.77397 - 5.98637i) q^{23} +(0.409542 - 0.513549i) q^{24} +(0.890084 + 3.89971i) q^{25} +(-0.168528 + 0.738371i) q^{26} +(1.50524 - 1.88751i) q^{27} -5.17157 q^{28} +0.171573 q^{30} +(-2.53827 + 3.18289i) q^{31} +(-0.982255 + 4.30354i) q^{32} +(0.222521 + 0.974928i) q^{33} +(-1.24698 + 1.56366i) q^{34} +(-1.76350 - 2.21135i) q^{35} +(-1.15078 + 5.04191i) q^{36} +(3.60388 + 1.73553i) q^{37} +(-2.23916 - 1.07832i) q^{38} +(0.168528 + 0.738371i) q^{39} +(-1.42874 + 0.688047i) q^{40} +12.4853 q^{41} +(0.437223 - 0.210556i) q^{42} +(3.99920 + 5.01483i) q^{43} +(-2.75222 - 3.45117i) q^{44} +(-2.54832 + 1.22721i) q^{45} -3.17157 q^{46} +(-4.72346 + 2.27470i) q^{47} +(0.276514 + 1.21149i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(1.49277 + 0.718882i) q^{50} +(-0.445042 + 1.94986i) q^{51} +(-2.08442 - 2.61378i) q^{52} +(-4.66700 + 5.85223i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(0.537213 - 2.35368i) q^{55} +(-2.79653 + 3.50673i) q^{56} -2.48528 q^{57} +7.65685 q^{59} +(-0.472206 + 0.592127i) q^{60} +(-0.184342 + 0.807657i) q^{61} +(0.375235 + 1.64401i) q^{62} +(-4.98792 + 6.25465i) q^{63} +(-2.60093 - 3.26147i) q^{64} +(0.406863 - 1.78258i) q^{65} +(0.373194 + 0.179721i) q^{66} +(5.09665 + 2.45442i) q^{67} +(-1.96451 - 8.60708i) q^{68} +(-2.85749 + 1.37609i) q^{69} -1.17157 q^{70} +(2.85749 - 1.37609i) q^{71} +(2.79653 + 3.50673i) q^{72} +(2.49396 + 3.12733i) q^{73} +(1.49277 - 0.718882i) q^{74} +1.65685 q^{75} +(9.88414 - 4.75995i) q^{76} +(-1.51947 - 6.65722i) q^{77} +(0.282642 + 0.136113i) q^{78} +(-0.373194 - 0.179721i) q^{79} +(0.667563 - 2.92478i) q^{80} +(4.66700 + 5.85223i) q^{81} +(3.22442 - 4.04330i) q^{82} +(0.813727 + 3.56517i) q^{83} +(-0.476670 + 2.08843i) q^{84} +(3.01048 - 3.77502i) q^{85} +2.65685 q^{86} -3.82843 q^{88} +(2.79653 - 3.50673i) q^{89} +(-0.260699 + 1.14220i) q^{90} +(-1.15078 - 5.04191i) q^{91} +(8.72886 - 10.9456i) q^{92} +(1.05139 + 1.31840i) q^{93} +(-0.483220 + 2.11713i) q^{94} +(5.40581 + 2.60330i) q^{95} +(1.64736 + 0.793325i) q^{96} +(2.77824 + 12.1722i) q^{97} +(-0.373194 + 0.179721i) q^{98} -6.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22} + 4 q^{23} + 10 q^{24} + 8 q^{25} - 10 q^{26} - 2 q^{27} - 96 q^{28} + 36 q^{30} - 6 q^{31} - 6 q^{32} + 2 q^{33} + 4 q^{34} - 16 q^{36} + 8 q^{37} + 12 q^{38} + 10 q^{39} - 6 q^{40} + 48 q^{41} - 16 q^{42} - 10 q^{43} + 6 q^{44} - 72 q^{46} - 2 q^{47} - 6 q^{48} - 2 q^{49} - 8 q^{50} - 4 q^{51} + 18 q^{52} - 2 q^{53} - 2 q^{54} + 2 q^{55} - 8 q^{56} + 72 q^{57} + 24 q^{59} + 10 q^{60} + 4 q^{61} + 26 q^{62} + 16 q^{63} + 14 q^{64} - 2 q^{65} - 2 q^{66} - 12 q^{68} - 12 q^{69} - 48 q^{70} + 12 q^{71} + 8 q^{72} - 8 q^{73} - 8 q^{74} - 48 q^{75} - 12 q^{76} - 8 q^{77} - 22 q^{78} + 2 q^{79} + 6 q^{80} + 2 q^{81} - 16 q^{82} - 4 q^{83} + 24 q^{84} - 4 q^{85} - 36 q^{86} - 12 q^{88} + 8 q^{89} - 8 q^{90} - 16 q^{91} - 28 q^{92} - 26 q^{93} - 10 q^{94} + 12 q^{95} - 2 q^{96} + 8 q^{97} + 2 q^{98} - 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8 - 2 * q^10 - 2 * q^11 + 60 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 6 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 10 * q^26 - 2 * q^27 - 96 * q^28 + 36 * q^30 - 6 * q^31 - 6 * q^32 + 2 * q^33 + 4 * q^34 - 16 * q^36 + 8 * q^37 + 12 * q^38 + 10 * q^39 - 6 * q^40 + 48 * q^41 - 16 * q^42 - 10 * q^43 + 6 * q^44 - 72 * q^46 - 2 * q^47 - 6 * q^48 - 2 * q^49 - 8 * q^50 - 4 * q^51 + 18 * q^52 - 2 * q^53 - 2 * q^54 + 2 * q^55 - 8 * q^56 + 72 * q^57 + 24 * q^59 + 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 + 14 * q^64 - 2 * q^65 - 2 * q^66 - 12 * q^68 - 12 * q^69 - 48 * q^70 + 12 * q^71 + 8 * q^72 - 8 * q^73 - 8 * q^74 - 48 * q^75 - 12 * q^76 - 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 + 2 * q^81 - 16 * q^82 - 4 * q^83 + 24 * q^84 - 4 * q^85 - 36 * q^86 - 12 * q^88 + 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 - 26 * q^93 - 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	0.258258	−	0.323845i	0.182616	−	0.228993i	−0.682094	−	0.731264i	$-0.738931\pi$
$2$	0.258258	−	0.323845i	0.182616	−	0.228993i	0.864710	+	0.502271i	$0.167502\pi$
$3$	0.0921712	−	0.403828i	0.0532151	−	0.233150i	−0.941326	−	0.337500i	$-0.890419\pi$
$3$	0.0921712	−	0.403828i	0.0532151	−	0.233150i	0.994541	+	0.104349i	$0.0332760\pi$
$4$	0.406863	+	1.78258i	0.203432	+	0.891292i
$5$	−0.623490	+	0.781831i	−0.278833	+	0.349646i	−0.901452	−	0.432880i	$-0.857497\pi$
$5$	−0.623490	+	0.781831i	−0.278833	+	0.349646i	0.622619	+	0.782526i	$0.286069\pi$
$6$	−0.106974	−	0.134141i	−0.0436719	−	0.0547629i
$7$	−0.629384	+	2.75751i	−0.237885	+	1.04224i	0.705022	+	0.709185i	$0.250937\pi$
$7$	−0.629384	+	2.75751i	−0.237885	+	1.04224i	−0.942907	+	0.333056i	$0.891920\pi$
$8$	1.42874	+	0.688047i	0.505137	+	0.243261i
$9$	2.54832	+	1.22721i	0.849442	+	0.409070i
$10$	0.0921712	+	0.403828i	0.0291471	+	0.127702i
$11$	−2.17513	+	1.04749i	−0.655827	+	0.315830i	−0.732040	−	0.681262i	$-0.761431\pi$
$11$	−2.17513	+	1.04749i	−0.655827	+	0.315830i	0.0762129	+	0.997092i	$0.475717\pi$
$12$	0.757359			0.218631
$13$	−1.64736	+	0.793325i	−0.456894	+	0.220029i	−0.648152	−	0.761511i	$-0.724458\pi$
$13$	−1.64736	+	0.793325i	−0.456894	+	0.220029i	0.191257	+	0.981540i	$0.438743\pi$
$14$	0.730464	+	0.915973i	0.195225	+	0.244804i
$15$	0.258258	+	0.323845i	0.0666819	+	0.0836165i
$16$	−2.70291	+	1.30165i	−0.675727	+	0.325413i
$17$	−4.82843			−1.17107			−0.585533	−	0.810649i	$-0.699115\pi$
$17$	−4.82843			−1.17107			−0.585533	+	0.810649i	$0.699115\pi$
$18$	1.05555	−	0.508326i	0.248796	−	0.119814i
$19$	−1.33513	−	5.84957i	−0.306299	−	1.34198i	−0.860436	−	0.509558i	$-0.829809\pi$
$19$	−1.33513	−	5.84957i	−0.306299	−	1.34198i	0.554138	−	0.832425i	$-0.313048\pi$
$20$	−1.64736	−	0.793325i	−0.368360	−	0.177393i
$21$	1.05555	+	0.508326i	0.230340	+	0.110926i
$22$	−0.222521	+	0.974928i	−0.0474416	+	0.207855i
$23$	−4.77397	−	5.98637i	−0.995442	−	1.24824i	−0.968605	−	0.248605i	$-0.920028\pi$
$23$	−4.77397	−	5.98637i	−0.995442	−	1.24824i	−0.0268366	−	0.999640i	$-0.508543\pi$
$24$	0.409542	−	0.513549i	0.0835974	−	0.104828i
$25$	0.890084	+	3.89971i	0.178017	+	0.779942i
$26$	−0.168528	+	0.738371i	−0.0330511	+	0.144806i
$27$	1.50524	−	1.88751i	0.289683	−	0.363251i
$28$	−5.17157			−0.977335
$29$		0			0
$29$		0			0
$30$	0.171573			0.0313248
$31$	−2.53827	+	3.18289i	−0.455887	+	0.571664i	−0.955652	−	0.294497i	$-0.904848\pi$
$31$	−2.53827	+	3.18289i	−0.455887	+	0.571664i	0.499766	+	0.866161i	$0.333419\pi$
$32$	−0.982255	+	4.30354i	−0.173640	+	0.760766i
$33$	0.222521	+	0.974928i	0.0387359	+	0.169713i
$34$	−1.24698	+	1.56366i	−0.213855	+	0.268166i
$35$	−1.76350	−	2.21135i	−0.298085	−	0.373787i
$36$	−1.15078	+	5.04191i	−0.191797	+	0.840318i
$37$	3.60388	+	1.73553i	0.592473	+	0.285320i	0.705997	−	0.708215i	$-0.250499\pi$
$37$	3.60388	+	1.73553i	0.592473	+	0.285320i	−0.113523	+	0.993535i	$0.536214\pi$
$38$	−2.23916	−	1.07832i	−0.363240	−	0.174927i
$39$	0.168528	+	0.738371i	0.0269861	+	0.118234i
$40$	−1.42874	+	0.688047i	−0.225904	+	0.108790i
$41$	12.4853			1.94987			0.974937	−	0.222483i	$-0.0714160\pi$
$41$	12.4853			1.94987			0.974937	+	0.222483i	$0.0714160\pi$
$42$	0.437223	−	0.210556i	0.0674650	−	0.0324894i
$43$	3.99920	+	5.01483i	0.609872	+	0.764755i	0.986880	−	0.161455i	$-0.0516186\pi$
$43$	3.99920	+	5.01483i	0.609872	+	0.764755i	−0.377008	+	0.926210i	$0.623047\pi$
$44$	−2.75222	−	3.45117i	−0.414912	−	0.520284i
$45$	−2.54832	+	1.22721i	−0.379882	+	0.182941i
$46$	−3.17157			−0.467623
$47$	−4.72346	+	2.27470i	−0.688987	+	0.331799i	−0.745408	−	0.666608i	$-0.767745\pi$
$47$	−4.72346	+	2.27470i	−0.688987	+	0.331799i	0.0564212	+	0.998407i	$0.482031\pi$
$48$	0.276514	+	1.21149i	0.0399113	+	0.174863i
$49$	−0.900969	−	0.433884i	−0.128710	−	0.0619834i
$50$	1.49277	+	0.718882i	0.211110	+	0.101665i
$51$	−0.445042	+	1.94986i	−0.0623183	+	0.273034i
$52$	−2.08442	−	2.61378i	−0.289057	−	0.362466i
$53$	−4.66700	+	5.85223i	−0.641061	+	0.803865i	−0.991135	−	0.132857i	$-0.957585\pi$
$53$	−4.66700	+	5.85223i	−0.641061	+	0.803865i	0.350074	+	0.936722i	$0.386156\pi$
$54$	−0.222521	−	0.974928i	−0.0302813	−	0.132671i
$55$	0.537213	−	2.35368i	0.0724378	−	0.317371i
$56$	−2.79653	+	3.50673i	−0.373702	+	0.468607i
$57$	−2.48528			−0.329184
$58$		0			0
$59$	7.65685			0.996838			0.498419	−	0.866936i	$-0.333914\pi$
$59$	7.65685			0.996838			0.498419	+	0.866936i	$0.333914\pi$
$60$	−0.472206	+	0.592127i	−0.0609615	+	0.0764433i
$61$	−0.184342	+	0.807657i	−0.0236026	+	0.103410i	−0.985357	−	0.170503i	$-0.945461\pi$
$61$	−0.184342	+	0.807657i	−0.0236026	+	0.103410i	0.961755	+	0.273913i	$0.0883179\pi$
$62$	0.375235	+	1.64401i	0.0476549	+	0.208790i
$63$	−4.98792	+	6.25465i	−0.628419	+	0.788012i
$64$	−2.60093	−	3.26147i	−0.325117	−	0.407683i
$65$	0.406863	−	1.78258i	0.0504652	−	0.221102i
$66$	0.373194	+	0.179721i	0.0459369	+	0.0221221i
$67$	5.09665	+	2.45442i	0.622655	+	0.299855i	0.718484	−	0.695543i	$-0.244836\pi$
$67$	5.09665	+	2.45442i	0.622655	+	0.299855i	−0.0958296	+	0.995398i	$0.530550\pi$
$68$	−1.96451	−	8.60708i	−0.238232	−	1.04376i
$69$	−2.85749	+	1.37609i	−0.344001	+	0.165662i
$70$	−1.17157			−0.140030
$71$	2.85749	−	1.37609i	0.339121	−	0.163312i	−0.256570	−	0.966526i	$-0.582592\pi$
$71$	2.85749	−	1.37609i	0.339121	−	0.163312i	0.595691	+	0.803213i	$0.296878\pi$
$72$	2.79653	+	3.50673i	0.329574	+	0.413273i
$73$	2.49396	+	3.12733i	0.291896	+	0.366026i	0.906058	−	0.423154i	$-0.139077\pi$
$73$	2.49396	+	3.12733i	0.291896	+	0.366026i	−0.614162	+	0.789180i	$0.710506\pi$
$74$	1.49277	−	0.718882i	0.173531	−	0.0835683i
$75$	1.65685			0.191317
$76$	9.88414	−	4.75995i	1.13379	−	0.546004i
$77$	−1.51947	−	6.65722i	−0.173159	−	0.758661i
$78$	0.282642	+	0.136113i	0.0320029	+	0.0154118i
$79$	−0.373194	−	0.179721i	−0.0419876	−	0.0202201i	0.412772	−	0.910834i	$-0.364561\pi$
$79$	−0.373194	−	0.179721i	−0.0419876	−	0.0202201i	−0.454760	+	0.890614i	$0.650275\pi$
$80$	0.667563	−	2.92478i	0.0746358	−	0.327001i
$81$	4.66700	+	5.85223i	0.518555	+	0.650248i
$82$	3.22442	−	4.04330i	0.356078	−	0.446508i
$83$	0.813727	+	3.56517i	0.0893181	+	0.391328i	0.999751	−	0.0223293i	$-0.00710824\pi$
$83$	0.813727	+	3.56517i	0.0893181	+	0.391328i	−0.910433	+	0.413658i	$0.864251\pi$
$84$	−0.476670	+	2.08843i	−0.0520090	+	0.227866i
$85$	3.01048	−	3.77502i	0.326532	−	0.409458i
$86$	2.65685			0.286496
$87$		0			0
$88$	−3.82843			−0.408112
$89$	2.79653	−	3.50673i	0.296431	−	0.371713i	−0.611204	−	0.791473i	$-0.709314\pi$
$89$	2.79653	−	3.50673i	0.296431	−	0.371713i	0.907635	+	0.419760i	$0.137886\pi$
$90$	−0.260699	+	1.14220i	−0.0274801	+	0.120398i
$91$	−1.15078	−	5.04191i	−0.120635	−	0.528536i
$92$	8.72886	−	10.9456i	0.910046	−	1.14116i
$93$	1.05139	+	1.31840i	0.109024	+	0.136711i
$94$	−0.483220	+	2.11713i	−0.0498404	+	0.218365i
$95$	5.40581	+	2.60330i	0.554625	+	0.267093i
$96$	1.64736	+	0.793325i	0.168133	+	0.0809684i
$97$	2.77824	+	12.1722i	0.282087	+	1.23590i	0.895112	+	0.445841i	$0.147095\pi$
$97$	2.77824	+	12.1722i	0.282087	+	1.23590i	−0.613025	+	0.790064i	$0.710047\pi$
$98$	−0.373194	+	0.179721i	−0.0376982	+	0.0181545i
$99$	−6.82843			−0.686283
$100$	−6.58942	+	3.17330i	−0.658942	+	0.317330i
$101$	−8.51491	−	10.6774i	−0.847265	−	1.06244i	−0.997277	−	0.0737526i	$-0.976502\pi$
$101$	−8.51491	−	10.6774i	−0.847265	−	1.06244i	0.150011	−	0.988684i	$-0.452069\pi$
$102$	0.516516	+	0.647690i	0.0511427	+	0.0641309i
$103$	−0.746387	+	0.359441i	−0.0735437	+	0.0354168i	−0.470294	−	0.882510i	$-0.655852\pi$
$103$	−0.746387	+	0.359441i	−0.0735437	+	0.0354168i	0.396750	+	0.917927i	$0.370138\pi$
$104$	−2.89949			−0.284319
$105$	−1.05555	+	0.508326i	−0.103011	+	0.0496076i
$106$	0.689927	+	3.02277i	0.0670117	+	0.293597i
$107$	8.26330	+	3.97940i	0.798844	+	0.384703i	0.788338	−	0.615242i	$-0.210942\pi$
$107$	8.26330	+	3.97940i	0.798844	+	0.384703i	0.0105053	+	0.999945i	$0.496656\pi$
$108$	3.97707	+	1.91526i	0.382694	+	0.184296i
$109$	−0.298878	+	1.30947i	−0.0286273	+	0.125425i	−0.987223	−	0.159348i	$-0.949061\pi$
$109$	−0.298878	+	1.30947i	−0.0286273	+	0.125425i	0.958595	+	0.284772i	$0.0919180\pi$
$110$	−0.623490	−	0.781831i	−0.0594474	−	0.0745447i
$111$	1.03303	−	1.29538i	0.0980510	−	0.122952i
$112$	−1.88815	−	8.27254i	−0.178414	−	0.781681i
$113$	−2.07250	+	9.08019i	−0.194964	+	0.854193i	0.778916	+	0.627128i	$0.215770\pi$
$113$	−2.07250	+	9.08019i	−0.194964	+	0.854193i	−0.973880	+	0.227064i	$0.927087\pi$
$114$	−0.641844	+	0.804846i	−0.0601142	+	0.0753808i
$115$	7.65685			0.714005
$116$		0			0
$117$	−5.17157			−0.478112
$118$	1.97744	−	2.47964i	0.182038	−	0.228269i
$119$	3.03894	−	13.3144i	0.278579	−	1.22053i
$120$	0.146164	+	0.640386i	0.0133429	+	0.0584589i
$121$	−3.22442	+	4.04330i	−0.293129	+	0.367573i
$122$	0.213948	+	0.268282i	0.0193699	+	0.0242891i
$123$	1.15078	−	5.04191i	0.103763	−	0.454614i
$124$	−6.70650	−	3.22968i	−0.602261	−	0.290034i
$125$	−8.10872	−	3.90495i	−0.725266	−	0.349270i
$126$	0.737370	+	3.23063i	0.0656901	+	0.287807i
$127$	14.1063	−	6.79325i	1.25174	−	0.602804i	0.313759	−	0.949503i	$-0.398412\pi$
$127$	14.1063	−	6.79325i	1.25174	−	0.602804i	0.937976	+	0.346699i	$0.112697\pi$
$128$	−10.5563			−0.933058
$129$	2.39374	−	1.15277i	0.210757	−	0.101495i
$130$	−0.472206	−	0.592127i	−0.0414152	−	0.0519330i
$131$	−0.819084	−	1.02710i	−0.0715637	−	0.0897380i	0.744761	−	0.667331i	$-0.232563\pi$
$131$	−0.819084	−	1.02710i	−0.0715637	−	0.0897380i	−0.816325	+	0.577593i	$0.803992\pi$
$132$	−1.64736	+	0.793325i	−0.143384	+	0.0690501i
$133$	16.9706			1.47153
$134$	2.11110	−	1.01665i	0.182371	−	0.0878254i
$135$	0.537213	+	2.35368i	0.0462359	+	0.202573i
$136$	−6.89859	−	3.32218i	−0.591549	−	0.284875i
$137$	−10.8116	−	5.20660i	−0.923700	−	0.444830i	−0.0893090	−	0.996004i	$-0.528466\pi$
$137$	−10.8116	−	5.20660i	−0.923700	−	0.444830i	−0.834391	+	0.551174i	$0.814180\pi$
$138$	−0.292328	+	1.28077i	−0.0248846	+	0.109026i
$139$	8.72886	+	10.9456i	0.740372	+	0.928397i	0.999297	−	0.0375004i	$-0.0119395\pi$
$139$	8.72886	+	10.9456i	0.740372	+	0.928397i	−0.258925	+	0.965898i	$0.583368\pi$
$140$	3.22442	−	4.04330i	0.272513	−	0.341721i
$141$	0.483220	+	2.11713i	0.0406945	+	0.178294i
$142$	0.292328	−	1.28077i	0.0245316	−	0.107480i
$143$	2.75222	−	3.45117i	0.230152	−	0.288601i
$144$	−8.48528			−0.707107
$145$		0			0
$146$	1.65685			0.137122
$147$	−0.258258	+	0.323845i	−0.0213008	+	0.0267103i
$148$	−1.62745	+	7.13034i	−0.133776	+	0.586110i
$149$	0.483220	+	2.11713i	0.0395870	+	0.173442i	0.990857	−	0.134918i	$-0.0430771\pi$
$149$	0.483220	+	2.11713i	0.0395870	+	0.173442i	−0.951270	+	0.308360i	$0.900220\pi$
$150$	0.427896	−	0.536564i	0.0349375	−	0.0438103i
$151$	8.81748	+	11.0568i	0.717556	+	0.899787i	0.998197	−	0.0600260i	$-0.0191184\pi$
$151$	8.81748	+	11.0568i	0.717556	+	0.899787i	−0.280641	+	0.959813i	$0.590547\pi$
$152$	2.11722	−	9.27616i	0.171730	−	0.752396i
$153$	−12.3044	−	5.92549i	−0.994752	−	0.479047i
$154$	−2.54832	−	1.22721i	−0.205350	−	0.0988913i
$155$	−0.905898	−	3.96900i	−0.0727635	−	0.318798i
$156$	−1.24764	+	0.600832i	−0.0998912	+	0.0481051i
$157$	−8.48528			−0.677199			−0.338600	−	0.940931i	$-0.609953\pi$
$157$	−8.48528			−0.677199			−0.338600	+	0.940931i	$0.609953\pi$
$158$	−0.154582	+	0.0744427i	−0.0122979	+	0.00592234i
$159$	1.93313	+	2.42407i	0.153307	+	0.192241i
$160$	−2.75222	−	3.45117i	−0.217582	−	0.272839i
$161$	19.5122	−	9.39656i	1.53777	−	0.740552i
$162$	3.10051			0.243599
$163$	−16.2815	+	7.84074i	−1.27526	+	0.614134i	−0.944168	−	0.329463i	$-0.893132\pi$
$163$	−16.2815	+	7.84074i	−1.27526	+	0.614134i	−0.331095	+	0.943598i	$0.607418\pi$
$164$	5.07980	+	22.2561i	0.396666	+	1.73791i
$165$	−0.900969	−	0.433884i	−0.0701403	−	0.0337778i
$166$	1.36471	+	0.657212i	0.105922	+	0.0510095i
$167$	1.96451	−	8.60708i	0.152018	−	0.666036i	−0.840279	−	0.542155i	$-0.817609\pi$
$167$	1.96451	−	8.60708i	0.152018	−	0.666036i	0.992297	−	0.123881i	$-0.0395342\pi$
$168$	1.15836	+	1.45254i	0.0893694	+	0.112066i
$169$	−6.02095	+	7.55003i	−0.463150	+	0.580772i
$170$	−0.445042	−	1.94986i	−0.0341332	−	0.149547i
$171$	3.77631	−	16.5451i	0.288781	−	1.26523i
$172$	−7.31224	+	9.16926i	−0.557553	+	0.699149i
$173$	23.6569			1.79860			0.899299	−	0.437335i	$-0.144078\pi$
$173$	23.6569			1.79860			0.899299	+	0.437335i	$0.144078\pi$
$174$		0			0
$175$	−11.3137			−0.855236
$176$	4.51571	−	5.66252i	0.340385	−	0.426829i
$177$	0.705741	−	3.09205i	0.0530468	−	0.232413i
$178$	−0.413414	−	1.81128i	−0.0309867	−	0.135761i
$179$	6.53747	−	8.19772i	0.488633	−	0.612727i	−0.474990	−	0.879991i	$-0.657548\pi$
$179$	6.53747	−	8.19772i	0.488633	−	0.612727i	0.963623	+	0.267265i	$0.0861198\pi$
$180$	−3.22442	−	4.04330i	−0.240334	−	0.301370i
$181$	3.18510	−	13.9548i	0.236747	−	1.03725i	−0.707163	−	0.707051i	$-0.750025\pi$
$181$	3.18510	−	13.9548i	0.236747	−	1.03725i	0.943910	−	0.330204i	$-0.107118\pi$
$182$	−1.93000	−	0.929438i	−0.143061	−	0.0688945i
$183$	0.309164	+	0.148885i	0.0228540	+	0.0110059i
$184$	−2.70188	−	11.8377i	−0.199185	−	0.872687i
$185$	−3.60388	+	1.73553i	−0.264962	+	0.127599i
$186$	0.698485			0.0512154
$187$	10.5025	−	5.05772i	0.768016	−	0.369857i
$188$	−5.97664	−	7.49447i	−0.435891	−	0.546590i
$189$	4.25745	+	5.33868i	0.309684	+	0.388332i
$190$	2.23916	−	1.07832i	0.162446	−	0.0782298i
$191$	2.68629			0.194373			0.0971866	−	0.995266i	$-0.469016\pi$
$191$	2.68629			0.194373			0.0971866	+	0.995266i	$0.469016\pi$
$192$	−1.55680	+	0.749717i	−0.112353	+	0.0541062i
$193$	2.40955	+	10.5569i	0.173443	+	0.759905i	0.984564	+	0.175026i	$0.0560009\pi$
$193$	2.40955	+	10.5569i	0.173443	+	0.759905i	−0.811121	+	0.584879i	$0.801142\pi$
$194$	4.65943	+	2.24386i	0.334527	+	0.161100i
$195$	−0.682357	−	0.328606i	−0.0488646	−	0.0235320i
$196$	0.406863	−	1.78258i	0.0290617	−	0.127327i
$197$	1.24698	+	1.56366i	0.0888436	+	0.111406i	0.824266	−	0.566202i	$-0.191588\pi$
$197$	1.24698	+	1.56366i	0.0888436	+	0.111406i	−0.735423	+	0.677609i	$0.763016\pi$
$198$	−1.76350	+	2.21135i	−0.125326	+	0.157154i
$199$	−3.66832	−	16.0720i	−0.260040	−	1.13931i	−0.921207	−	0.389072i	$-0.872796\pi$
$199$	−3.66832	−	16.0720i	−0.260040	−	1.13931i	0.661167	−	0.750239i	$-0.270062\pi$
$200$	−1.41148	+	6.18411i	−0.0998069	+	0.437283i
$201$	1.46093	−	1.83195i	0.103046	−	0.129215i
$202$	−5.65685			−0.398015
$203$		0			0
$204$	−3.65685			−0.256031
$205$	−7.78445	+	9.76139i	−0.543689	+	0.681765i
$206$	−0.0763571	+	0.334542i	−0.00532005	+	0.0233087i
$207$	−4.81910	−	21.1139i	−0.334951	−	1.46752i
$208$	3.42002	−	4.28857i	0.237136	−	0.297359i
$209$	9.03143	+	11.3250i	0.624717	+	0.783370i
$210$	−0.107985	+	0.473114i	−0.00745169	+	0.0326480i
$211$	−15.6631	−	7.54297i	−1.07830	−	0.519280i	−0.191524	−	0.981488i	$-0.561343\pi$
$211$	−15.6631	−	7.54297i	−1.07830	−	0.519280i	−0.886771	+	0.462208i	$0.847057\pi$
$212$	−12.3309	−	5.93826i	−0.846891	−	0.407841i
$213$	−0.292328	−	1.28077i	−0.0200300	−	0.0877570i
$214$	3.42277	−	1.64832i	0.233976	−	0.112677i
$215$	−6.41421			−0.437446
$216$	3.44929	−	1.66109i	0.234695	−	0.113023i
$217$	−7.17931	−	9.00257i	−0.487363	−	0.611134i
$218$	0.346878	+	0.434971i	0.0234935	+	0.0294600i
$219$	1.49277	−	0.718882i	0.100872	−	0.0485776i
$220$	4.41421			0.297606
$221$	7.95414	−	3.83051i	0.535053	−	0.257668i
$222$	−0.152714	−	0.669085i	−0.0102495	−	0.0449060i
$223$	7.95414	+	3.83051i	0.532648	+	0.256510i	0.680819	−	0.732452i	$-0.261624\pi$
$223$	7.95414	+	3.83051i	0.532648	+	0.256510i	−0.148170	+	0.988962i	$0.547338\pi$
$224$	−11.2488	−	5.41716i	−0.751595	−	0.361949i
$225$	−2.51754	+	11.0301i	−0.167836	+	0.735337i
$226$	2.40534	+	3.01620i	0.160001	+	0.200635i
$227$	12.5584	−	15.7478i	0.833531	−	1.04522i	−0.164734	−	0.986338i	$-0.552677\pi$
$227$	12.5584	−	15.7478i	0.833531	−	1.04522i	0.998265	−	0.0588772i	$-0.0187520\pi$
$228$	−1.01117	−	4.43022i	−0.0669664	−	0.293399i
$229$	4.55840	−	19.9717i	0.301228	−	1.31977i	−0.567049	−	0.823684i	$-0.691915\pi$
$229$	4.55840	−	19.9717i	0.301228	−	1.31977i	0.868276	−	0.496081i	$-0.165228\pi$
$230$	1.97744	−	2.47964i	0.130389	−	0.163502i
$231$	−2.82843			−0.186097
$232$		0			0
$233$	−4.31371			−0.282600			−0.141300	−	0.989967i	$-0.545128\pi$
$233$	−4.31371			−0.282600			−0.141300	+	0.989967i	$0.545128\pi$
$234$	−1.33560	+	1.67479i	−0.0873109	+	0.109484i
$235$	1.16660	−	5.11120i	0.0761004	−	0.333418i
$236$	3.11529	+	13.6490i	0.202788	+	0.888474i
$237$	−0.106974	+	0.134141i	−0.00694870	+	0.00871340i
$238$	−3.52699	−	4.42271i	−0.228621	−	0.286681i
$239$	1.85652	−	8.13397i	0.120089	−	0.526143i	−0.878720	−	0.477338i	$-0.841602\pi$
$239$	1.85652	−	8.13397i	0.120089	−	0.526143i	0.998808	−	0.0488045i	$-0.0155411\pi$
$240$	−1.11958	−	0.539162i	−0.0722686	−	0.0348027i
$241$	−3.88652	−	1.87165i	−0.250353	−	0.120563i	0.304499	−	0.952513i	$-0.401511\pi$
$241$	−3.88652	−	1.87165i	−0.250353	−	0.120563i	−0.554852	+	0.831949i	$0.687225\pi$
$242$	0.476670	+	2.08843i	0.0306415	+	0.134249i
$243$	9.31885	−	4.48772i	0.597805	−	0.287888i
$244$	−1.51472			−0.0969699
$245$	0.900969	−	0.433884i	0.0575608	−	0.0277198i
$246$	−1.33560	−	1.67479i	−0.0851547	−	0.106781i
$247$	6.84003	+	8.57713i	0.435221	+	0.545750i
$248$	−5.81651	+	2.80109i	−0.369349	+	0.177869i
$249$	1.51472			0.0959914
$250$	−3.35874	+	1.61748i	−0.212425	+	0.102299i
$251$	−1.31931	−	5.78028i	−0.0832742	−	0.364848i	0.916072	−	0.401015i	$-0.131342\pi$
$251$	−1.31931	−	5.78028i	−0.0832742	−	0.364848i	−0.999346	+	0.0361667i	$0.988485\pi$
$252$	−13.1788	−	6.34660i	−0.830189	−	0.399798i
$253$	16.6547	+	8.02046i	1.04707	+	0.504242i
$254$	1.44311	−	6.32268i	0.0905488	−	0.396720i
$255$	−1.24698	−	1.56366i	−0.0780889	−	0.0979204i
$256$	2.47561	−	3.10431i	0.154725	−	0.194019i
$257$	5.30232	+	23.2310i	0.330750	+	1.44911i	0.817682	+	0.575670i	$0.195259\pi$
$257$	5.30232	+	23.2310i	0.330750	+	1.44911i	−0.486932	+	0.873440i	$0.661884\pi$
$258$	0.244885	−	1.07291i	0.0152459	−	0.0667967i
$259$	−7.05398	+	8.84541i	−0.438313	+	0.549627i
$260$	3.34315			0.207333
$261$		0			0
$262$	−0.544156			−0.0336181
$263$	7.00967	−	8.78985i	0.432235	−	0.542005i	−0.517243	−	0.855838i	$-0.673042\pi$
$263$	7.00967	−	8.78985i	0.432235	−	0.542005i	0.949478	+	0.313833i	$0.101613\pi$
$264$	−0.352871	+	1.54603i	−0.0217177	+	0.0951514i
$265$	−1.66563	−	7.29761i	−0.102319	−	0.448289i
$266$	4.38278	−	5.49584i	0.268726	−	0.336971i
$267$	−1.15836	−	1.45254i	−0.0708904	−	0.0888938i
$268$	−2.30157	+	10.0838i	−0.140591	+	0.615967i
$269$	17.5291	+	8.44157i	1.06877	+	0.514692i	0.883710	−	0.468036i	$-0.155038\pi$
$269$	17.5291	+	8.44157i	1.06877	+	0.514692i	0.185059	+	0.982727i	$0.440752\pi$
$270$	0.900969	+	0.433884i	0.0548312	+	0.0264053i
$271$	3.23909	+	14.1914i	0.196761	+	0.862066i	0.972849	+	0.231441i	$0.0743441\pi$
$271$	3.23909	+	14.1914i	0.196761	+	0.862066i	−0.776088	+	0.630625i	$0.782799\pi$
$272$	13.0508	−	6.28493i	0.791320	−	0.381080i
$273$	−2.14214			−0.129648
$274$	−4.47832	+	2.15665i	−0.270545	+	0.130288i
$275$	−6.02095	−	7.55003i	−0.363077	−	0.455284i
$276$	−3.61561	−	4.53383i	−0.217634	−	0.272905i
$277$	−4.78749	+	2.30553i	−0.287652	+	0.138526i	−0.572146	−	0.820152i	$-0.693889\pi$
$277$	−4.78749	+	2.30553i	−0.287652	+	0.138526i	0.284494	+	0.958678i	$0.408175\pi$
$278$	5.79899			0.347800
$279$	−10.3744	+	4.99605i	−0.621099	+	0.299106i
$280$	−0.998069	−	4.37283i	−0.0596460	−	0.261326i
$281$	1.77542	+	0.854995i	0.105912	+	0.0510047i	0.486090	−	0.873909i	$-0.338423\pi$
$281$	1.77542	+	0.854995i	0.105912	+	0.0510047i	−0.380177	+	0.924914i	$0.624137\pi$
$282$	0.810417	+	0.390276i	0.0482596	+	0.0232406i
$283$	−0.0763571	+	0.334542i	−0.00453896	+	0.0198865i	−0.977147	−	0.212566i	$-0.931818\pi$
$283$	−0.0763571	+	0.334542i	−0.00453896	+	0.0198865i	0.972608	+	0.232453i	$0.0746751\pi$
$284$	3.61561	+	4.53383i	0.214547	+	0.269033i
$285$	1.54955	−	1.94307i	0.0917873	−	0.115098i
$286$	−0.406863	−	1.78258i	−0.0240583	−	0.105406i
$287$	−7.85804	+	34.4283i	−0.463845	+	2.03224i
$288$	−7.78445	+	9.76139i	−0.458703	+	0.575195i
$289$	6.31371			0.371395
$290$		0			0
$291$	5.17157			0.303163
$292$	−4.56002	+	5.71809i	−0.266855	+	0.334626i
$293$	0.813727	−	3.56517i	0.0475384	−	0.208279i	−0.945581	−	0.325388i	$-0.894505\pi$
$293$	0.813727	−	3.56517i	0.0475384	−	0.208279i	0.993119	+	0.117108i	$0.0373624\pi$
$294$	0.0381786	+	0.167271i	0.00222662	+	0.00975545i
$295$	−4.77397	+	5.98637i	−0.277951	+	0.348540i
$296$	3.95489	+	4.95927i	0.229873	+	0.288252i
$297$	−1.29695	+	5.68230i	−0.0752565	+	0.329720i
$298$	0.810417	+	0.390276i	0.0469462	+	0.0226081i
$299$	12.6136	+	6.07437i	0.729461	+	0.351290i
$300$	0.674113	+	2.95348i	0.0389199	+	0.170519i
$301$	−16.3455	+	7.87158i	−0.942139	+	0.453710i
$302$	5.85786			0.337082
$303$	−5.09665	+	2.45442i	−0.292795	+	0.141003i
$304$	11.2228	+	14.0730i	0.643673	+	0.807140i
$305$	−0.516516	−	0.647690i	−0.0295756	−	0.0370866i
$306$	−5.09665	+	2.45442i	−0.291356	+	0.140310i
$307$	−16.8995			−0.964505			−0.482253	−	0.876032i	$-0.660181\pi$
$307$	−16.8995			−0.964505			−0.482253	+	0.876032i	$0.660181\pi$
$308$	11.2488	−	5.41716i	0.640963	−	0.308671i
$309$	0.0763571	+	0.334542i	0.00434380	+	0.0190315i
$310$	−1.51930	−	0.731654i	−0.0862902	−	0.0415552i
$311$	−22.8069	−	10.9832i	−1.29326	−	0.622801i	−0.344495	−	0.938788i	$-0.611950\pi$
$311$	−22.8069	−	10.9832i	−1.29326	−	0.622801i	−0.948763	+	0.315988i	$0.897664\pi$
$312$	−0.267250	+	1.17090i	−0.0151300	+	0.0662891i
$313$	2.60093	+	3.26147i	0.147013	+	0.184349i	0.849886	−	0.526967i	$-0.176671\pi$
$313$	2.60093	+	3.26147i	0.147013	+	0.184349i	−0.702872	+	0.711316i	$0.748099\pi$
$314$	−2.19139	+	2.74792i	−0.123667	+	0.155074i
$315$	−1.78017	−	7.79942i	−0.100301	−	0.439448i
$316$	0.168528	−	0.738371i	0.00948046	−	0.0415366i
$317$	12.1305	−	15.2112i	0.681318	−	0.854346i	−0.314157	−	0.949371i	$-0.601722\pi$
$317$	12.1305	−	15.2112i	0.681318	−	0.854346i	0.995475	+	0.0950254i	$0.0302932\pi$
$318$	1.28427			0.0720184
$319$		0			0
$320$	4.17157			0.233198
$321$	2.36863	−	2.97017i	0.132204	−	0.165779i
$322$	1.99614	−	8.74565i	0.111240	−	0.487376i
$323$	6.44656	+	28.2442i	0.358696	+	1.57155i
$324$	−8.53326	+	10.7004i	−0.474070	+	0.594465i
$325$	−4.56002	−	5.71809i	−0.252945	−	0.317182i
$326$	−1.66563	+	7.29761i	−0.0922508	+	0.404177i
$327$	0.501253	+	0.241391i	0.0277194	+	0.0133489i
$328$	17.8383	+	8.59046i	0.984954	+	0.474329i
$329$	−3.29964	−	14.4566i	−0.181915	−	0.797021i
$330$	−0.373194	+	0.179721i	−0.0205436	+	0.00989329i
$331$	0.414214			0.0227672			0.0113836	−	0.999935i	$-0.496376\pi$
$331$	0.414214			0.0227672			0.0113836	+	0.999935i	$0.496376\pi$
$332$	−6.02414	+	2.90107i	−0.330618	+	0.159217i
$333$	7.05398	+	8.84541i	0.386556	+	0.484726i
$334$	−2.28001	−	2.85904i	−0.124757	−	0.156440i
$335$	−5.09665	+	2.45442i	−0.278460	+	0.134099i
$336$	−3.51472			−0.191744
$337$	16.0363	−	7.72269i	0.873555	−	0.420682i	0.0572886	−	0.998358i	$-0.481754\pi$
$337$	16.0363	−	7.72269i	0.873555	−	0.420682i	0.816266	+	0.577676i	$0.196040\pi$
$338$	0.890084	+	3.89971i	0.0484142	+	0.212116i
$339$	3.47582	+	1.67386i	0.188780	+	0.0909118i
$340$	7.95414	+	3.83051i	0.431374	+	0.207739i
$341$	2.18703	−	9.58201i	0.118434	−	0.518895i
$342$	−4.38278	−	5.49584i	−0.236994	−	0.297181i
$343$	−10.5810	+	13.2681i	−0.571319	+	0.716411i
$344$	2.26339	+	9.91655i	0.122034	+	0.534665i
$345$	0.705741	−	3.09205i	0.0379958	−	0.166471i
$346$	6.10957	−	7.66116i	0.328453	−	0.411866i
$347$	−14.4853			−0.777611			−0.388805	−	0.921320i	$-0.627112\pi$
$347$	−14.4853			−0.777611			−0.388805	+	0.921320i	$0.627112\pi$
$348$		0			0
$349$	23.1421			1.23877			0.619385	−	0.785087i	$-0.287382\pi$
$349$	23.1421			1.23877			0.619385	+	0.785087i	$0.287382\pi$
$350$	−2.92185	+	3.66389i	−0.156180	+	0.195843i
$351$	−0.982255	+	4.30354i	−0.0524289	+	0.229706i
$352$	−2.37137	−	10.3897i	−0.126395	−	0.553771i
$353$	−4.34607	+	5.44981i	−0.231318	+	0.290064i	−0.883921	−	0.467636i	$-0.845106\pi$
$353$	−4.34607	+	5.44981i	−0.231318	+	0.290064i	0.652603	+	0.757700i	$0.273677\pi$
$354$	−0.819084	−	1.02710i	−0.0435338	−	0.0545897i
$355$	−0.705741	+	3.09205i	−0.0374569	+	0.164109i
$356$	7.38885	+	3.55828i	0.391609	+	0.188589i
$357$	−5.09665	−	2.45442i	−0.269743	−	0.129902i
$358$	−0.966441	−	4.23425i	−0.0510780	−	0.223787i
$359$	−16.2815	+	7.84074i	−0.859303	+	0.413819i	−0.811022	−	0.585015i	$-0.801089\pi$
$359$	−16.2815	+	7.84074i	−0.859303	+	0.413819i	−0.0482808	+	0.998834i	$0.515374\pi$
$360$	−4.48528			−0.236395
$361$	−15.3165	+	7.37602i	−0.806130	+	0.388212i
$362$	−3.69663	−	4.63543i	−0.194290	−	0.243633i
$363$	1.33560	+	1.67479i	0.0701008	+	0.0879036i
$364$	8.51942	−	4.10274i	0.446539	−	0.215042i
$365$	−4.00000			−0.209370
$366$	0.128060	−	0.0616703i	0.00669379	−	0.00322356i
$367$	−4.00538	−	17.5487i	−0.209079	−	0.916035i	−0.965181	−	0.261582i	$-0.915756\pi$
$367$	−4.00538	−	17.5487i	−0.209079	−	0.916035i	0.756102	−	0.654453i	$-0.227101\pi$
$368$	20.6958	+	9.96655i	1.07884	+	0.519543i
$369$	31.8166	+	15.3220i	1.65630	+	0.797634i
$370$	−0.368685	+	1.61531i	−0.0191670	+	0.0839761i
$371$	−13.2003	−	16.5526i	−0.685323	−	0.859368i
$372$	−1.92238	+	2.41059i	−0.0996709	+	0.124983i
$373$	0.820277	+	3.59387i	0.0424723	+	0.186083i	0.991714	−	0.128464i	$-0.0410045\pi$
$373$	0.820277	+	3.59387i	0.0424723	+	0.186083i	−0.949242	+	0.314547i	$0.898147\pi$
$374$	1.07443	−	4.70737i	0.0555573	−	0.243412i
$375$	−2.32432	+	2.91461i	−0.120027	+	0.150510i
$376$	−8.31371			−0.428747
$377$		0			0
$378$	2.82843			0.145479
$379$	16.8159	−	21.0864i	0.863773	−	1.08314i	−0.131996	−	0.991250i	$-0.542139\pi$
$379$	16.8159	−	21.0864i	0.863773	−	1.08314i	0.995769	−	0.0918872i	$-0.0292899\pi$
$380$	−2.44118	+	10.6955i	−0.125230	+	0.548668i
$381$	−1.44311	−	6.32268i	−0.0739328	−	0.323921i
$382$	0.693756	−	0.869943i	0.0354956	−	0.0445101i
$383$	−12.7724	−	16.0160i	−0.652637	−	0.818381i	0.339882	−	0.940468i	$-0.389613\pi$
$383$	−12.7724	−	16.0160i	−0.652637	−	0.818381i	−0.992519	+	0.122087i	$0.961041\pi$
$384$	−0.972991	+	4.26295i	−0.0496528	+	0.217543i
$385$	6.15220	+	2.96274i	0.313545	+	0.150995i
$386$	4.04110	+	1.94609i	0.205687	+	0.0990534i
$387$	4.03700	+	17.6873i	0.205212	+	0.899095i
$388$	−20.5677	+	9.90488i	−1.04417	+	0.502844i
$389$	36.9706			1.87448			0.937241	−	0.348682i	$-0.113371\pi$
$389$	36.9706			1.87448			0.937241	+	0.348682i	$0.113371\pi$
$390$	−0.282642	+	0.136113i	−0.0143121	+	0.00689235i
$391$	23.0508	+	28.9047i	1.16573	+	1.46178i
$392$	−0.988722	−	1.23982i	−0.0499380	−	0.0626203i
$393$	−0.490268	+	0.236100i	−0.0247307	+	0.0119097i
$394$	0.828427			0.0417356
$395$	0.373194	−	0.179721i	0.0187774	−	0.00904272i
$396$	−2.77824	−	12.1722i	−0.139612	−	0.611679i
$397$	−27.6209	−	13.3015i	−1.38625	−	0.667584i	−0.415929	−	0.909397i	$-0.636544\pi$
$397$	−27.6209	−	13.3015i	−1.38625	−	0.667584i	−0.970323	+	0.241813i	$0.922258\pi$
$398$	−6.15220	−	2.96274i	−0.308382	−	0.148509i
$399$	1.56420	−	6.85319i	0.0783078	−	0.343089i
$400$	−7.48188	−	9.38198i	−0.374094	−	0.469099i
$401$	−4.57838	+	5.74110i	−0.228633	+	0.286697i	−0.882894	−	0.469572i	$-0.844408\pi$
$401$	−4.57838	+	5.74110i	−0.228633	+	0.286697i	0.654261	+	0.756269i	$0.272980\pi$
$402$	−0.215971	−	0.946229i	−0.0107716	−	0.0471936i
$403$	1.65637	−	7.25702i	0.0825096	−	0.361498i
$404$	15.5689	−	19.5228i	0.774581	−	0.971294i
$405$	−7.48528			−0.371947
$406$		0			0
$407$	−9.65685			−0.478672
$408$	−1.97744	+	2.47964i	−0.0978980	+	0.122760i
$409$	−3.33126	+	14.5952i	−0.164720	+	0.721687i	0.823331	+	0.567562i	$0.192113\pi$
$409$	−3.33126	+	14.5952i	−0.164720	+	0.721687i	−0.988051	+	0.154125i	$0.950744\pi$
$410$	1.15078	+	5.04191i	0.0568331	+	0.249002i
$411$	−3.09910	+	3.88614i	−0.152867	+	0.191689i
$412$	−0.944412	−	1.18425i	−0.0465278	−	0.0583440i
$413$	−4.81910	+	21.1139i	−0.237133	+	1.03895i
$414$	−8.08220	−	3.89218i	−0.397218	−	0.191290i
$415$	−3.29471	−	1.58665i	−0.161731	−	0.0778856i
$416$	−1.79598	−	7.86871i	−0.0880552	−	0.385795i
$417$	5.22471	−	2.51609i	0.255855	−	0.123213i
$418$	6.00000			0.293470
$419$	23.8624	−	11.4915i	1.16576	−	0.561398i	0.252025	−	0.967721i	$-0.418903\pi$
$419$	23.8624	−	11.4915i	1.16576	−	0.561398i	0.913730	+	0.406322i	$0.133189\pi$
$420$	−1.33560	−	1.67479i	−0.0651706	−	0.0817213i
$421$	−15.6575	−	19.6339i	−0.763100	−	0.956898i	0.236792	−	0.971560i	$-0.423904\pi$
$421$	−15.6575	−	19.6339i	−0.763100	−	0.956898i	−0.999892	+	0.0146627i	$0.995333\pi$
$422$	−6.48789	+	3.12440i	−0.315825	+	0.152093i
$423$	−14.8284			−0.720983
$424$	−10.6946	+	5.15023i	−0.519373	+	0.250117i
$425$	−4.29770	−	18.8295i	−0.208469	−	0.913364i
$426$	−0.490268	−	0.236100i	−0.0237535	−	0.0114391i
$427$	−2.11110	−	1.01665i	−0.102163	−	0.0491993i
$428$	−3.73158	+	16.3491i	−0.180373	+	0.790264i
$429$	−1.14001	−	1.42952i	−0.0550400	−	0.0690180i
$430$	−1.65652	+	2.07721i	−0.0798846	+	0.100172i
$431$	−1.85652	−	8.13397i	−0.0894256	−	0.391799i	0.910331	−	0.413882i	$-0.135827\pi$
$431$	−1.85652	−	8.13397i	−0.0894256	−	0.391799i	−0.999756	+	0.0220827i	$0.992970\pi$
$432$	−1.61164	+	7.06105i	−0.0775400	+	0.339725i
$433$	−9.12005	+	11.4362i	−0.438281	+	0.549588i	−0.951089	−	0.308916i	$-0.900034\pi$
$433$	−9.12005	+	11.4362i	−0.438281	+	0.549588i	0.512808	+	0.858503i	$0.328605\pi$
$434$	−4.76955			−0.228946
$435$		0			0
$436$	−2.45584			−0.117614
$437$	−28.6438	+	35.9182i	−1.37022	+	1.71820i
$438$	0.152714	−	0.669085i	0.00729697	−	0.0319701i
$439$	2.59389	+	11.3646i	0.123800	+	0.542402i	0.998348	+	0.0574631i	$0.0183012\pi$
$439$	2.59389	+	11.3646i	0.123800	+	0.542402i	−0.874548	+	0.484939i	$0.838842\pi$
$440$	2.38699	−	2.99318i	0.113795	−	0.142694i
$441$	−1.76350	−	2.21135i	−0.0839760	−	0.105303i
$442$	0.813727	−	3.56517i	0.0387050	−	0.169578i
$443$	32.1257	+	15.4709i	1.52634	+	0.735046i	0.993781	−	0.111348i	$-0.0355168\pi$
$443$	32.1257	+	15.4709i	1.52634	+	0.735046i	0.532557	+	0.846394i	$0.321231\pi$
$444$	2.72943	+	1.31442i	0.129533	+	0.0623798i
$445$	0.998069	+	4.37283i	0.0473130	+	0.207292i
$446$	3.29471	−	1.58665i	0.156009	−	0.0751300i
$447$	0.899495			0.0425447
$448$	10.6305	−	5.11939i	0.502245	−	0.241868i
$449$	−0.641844	−	0.804846i	−0.0302905	−	0.0379831i	0.766456	−	0.642297i	$-0.222019\pi$
$449$	−0.641844	−	0.804846i	−0.0302905	−	0.0379831i	−0.796746	+	0.604314i	$0.793447\pi$
$450$	2.92185	+	3.66389i	0.137738	+	0.172717i
$451$	−27.1571	+	13.0782i	−1.27878	+	0.615828i
$452$	−17.0294			−0.800997
$453$	5.27775	−	2.54163i	0.247970	−	0.119416i
$454$	−1.85652	−	8.13397i	−0.0871310	−	0.381746i
$455$	4.65943	+	2.24386i	0.218437	+	0.105194i
$456$	−3.55083	−	1.70999i	−0.166283	−	0.0800776i
$457$	−7.78168	+	34.0938i	−0.364012	+	1.59484i	0.378892	+	0.925441i	$0.376305\pi$
$457$	−7.78168	+	34.0938i	−0.364012	+	1.59484i	−0.742903	+	0.669399i	$0.766552\pi$
$458$	−5.29049	−	6.63406i	−0.247208	−	0.309989i
$459$	−7.26793	+	9.11370i	−0.339238	+	0.425391i
$460$	3.11529	+	13.6490i	0.145251	+	0.636387i
$461$	−3.11529	+	13.6490i	−0.145094	+	0.635697i	0.849113	+	0.528211i	$0.177137\pi$
$461$	−3.11529	+	13.6490i	−0.145094	+	0.635697i	−0.994207	+	0.107486i	$0.965720\pi$
$462$	−0.730464	+	0.915973i	−0.0339842	+	0.0426149i
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$		0			0
$465$	−1.68629			−0.0781999
$466$	−1.11405	+	1.39697i	−0.0516073	+	0.0647136i
$467$	−7.19974	+	31.5441i	−0.333164	+	1.45969i	0.479802	+	0.877377i	$0.340709\pi$
$467$	−7.19974	+	31.5441i	−0.333164	+	1.45969i	−0.812966	+	0.582311i	$0.802149\pi$
$468$	−2.10412	−	9.21877i	−0.0972631	−	0.426138i
$469$	−9.97584	+	12.5093i	−0.460641	+	0.577626i
$470$	−1.35395	−	1.69780i	−0.0624532	−	0.0783139i
$471$	−0.782098	+	3.42660i	−0.0360372	+	0.157889i
$472$	10.9397	+	5.26828i	0.503540	+	0.242492i
$473$	−13.9518	−	6.71881i	−0.641502	−	0.308931i
$474$	0.0158141	+	0.0692860i	0.000726365	+	0.00318241i
$475$	21.6233	−	10.4132i	0.992143	−	0.477791i
$476$	24.9706			1.14452
$477$	−19.0749	+	9.18600i	−0.873381	+	0.420598i
$478$	−2.15468	−	2.70189i	−0.0985529	−	0.123581i
$479$	−8.04270	−	10.0852i	−0.367481	−	0.460806i	0.563371	−	0.826204i	$-0.309504\pi$
$479$	−8.04270	−	10.0852i	−0.367481	−	0.460806i	−0.930851	+	0.365398i	$0.880933\pi$
$480$	−1.64736	+	0.793325i	−0.0751912	+	0.0362102i
$481$	−7.31371			−0.333476
$482$	−1.60985	+	0.775262i	−0.0733266	+	0.0353122i
$483$	−1.99614	−	8.74565i	−0.0908274	−	0.397941i
$484$	−8.51942	−	4.10274i	−0.387246	−	0.186488i
$485$	−11.2488	−	5.41716i	−0.510784	−	0.245981i
$486$	0.953340	−	4.17686i	0.0432444	−	0.189466i
$487$	−17.7603	−	22.2707i	−0.804795	−	1.00918i	−0.999598	−	0.0283389i	$-0.990978\pi$
$487$	−17.7603	−	22.2707i	−0.804795	−	1.00918i	0.194803	−	0.980842i	$-0.437593\pi$
$488$	−0.819084	+	1.02710i	−0.0370782	+	0.0464946i
$489$	1.66563	+	7.29761i	0.0753225	+	0.330009i
$490$	0.0921712	−	0.403828i	0.00416387	−	0.0182431i
$491$	−7.95408	+	9.97411i	−0.358963	+	0.450125i	−0.928219	−	0.372035i	$-0.878660\pi$
$491$	−7.95408	+	9.97411i	−0.358963	+	0.450125i	0.569256	+	0.822160i	$0.307231\pi$
$492$	9.45584			0.426302
$493$		0			0
$494$	4.54416			0.204451
$495$	4.25745	−	5.33868i	0.191358	−	0.239956i
$496$	2.71769	−	11.9070i	0.122028	−	0.534640i
$497$	1.99614	+	8.74565i	0.0895390	+	0.392296i
$498$	0.391188	−	0.490534i	0.0175296	−	0.0219814i
$499$	−9.33399	−	11.7045i	−0.417847	−	0.523963i	0.527708	−	0.849426i	$-0.323052\pi$
$499$	−9.33399	−	11.7045i	−0.417847	−	0.523963i	−0.945555	+	0.325462i	$0.894480\pi$
$500$	3.66177	−	16.0433i	0.163759	−	0.717476i
$501$	−3.29471	−	1.58665i	−0.147197	−	0.0708863i
$502$	−2.21264	−	1.06555i	−0.0987549	−	0.0475579i
$503$	−5.72500	−	25.0829i	−0.255265	−	1.11839i	−0.926247	−	0.376916i	$-0.876984\pi$
$503$	−5.72500	−	25.0829i	−0.255265	−	1.11839i	0.670982	−	0.741474i	$-0.265873\pi$
$504$	−11.4300	+	5.50438i	−0.509131	+	0.245184i
$505$	13.6569			0.607722
$506$	6.89859	−	3.32218i	0.306680	−	0.147689i
$507$	2.49396	+	3.12733i	0.110761	+	0.138889i
$508$	17.8489	+	22.3818i	0.791917	+	0.993033i
$509$	24.7634	−	11.9254i	1.09762	−	0.528585i	0.204709	−	0.978823i	$-0.434375\pi$
$509$	24.7634	−	11.9254i	1.09762	−	0.528585i	0.892909	+	0.450238i	$0.148661\pi$
$510$	−0.828427			−0.0366834
$511$	−10.1933	+	4.90883i	−0.450925	+	0.217154i
$512$	−5.06399	−	22.1868i	−0.223799	−	0.980527i
$513$	−13.0508	−	6.28493i	−0.576206	−	0.277486i
$514$	8.89261	+	4.28246i	0.392236	+	0.188891i
$515$	0.184342	−	0.807657i	0.00812310	−	0.0355896i
$516$	3.02883	+	3.79803i	0.133337	+	0.167199i
$517$	7.89142	−	9.89553i	0.347064	−	0.435205i
$518$	1.04280	+	4.56880i	0.0458179	+	0.200741i
$519$	2.18048	−	9.55331i	0.0957125	−	0.419344i
$520$	1.80781	−	2.26692i	0.0792775	−	0.0994109i
$521$	−0.857864			−0.0375837			−0.0187919	−	0.999823i	$-0.505982\pi$
$521$	−0.857864			−0.0375837			−0.0187919	+	0.999823i	$0.505982\pi$
$522$		0			0
$523$	27.3137			1.19435			0.597173	−	0.802113i	$-0.296291\pi$
$523$	27.3137			1.19435			0.597173	+	0.802113i	$0.296291\pi$
$524$	1.49764	−	1.87798i	0.0654245	−	0.0820397i
$525$	−1.04280	+	4.56880i	−0.0455114	+	0.199399i
$526$	−1.03625	−	4.54010i	−0.0451825	−	0.197958i
$527$	12.2558	−	15.3683i	0.533873	−	0.669456i
$528$	−1.87047	−	2.34549i	−0.0814017	−	0.102075i
$529$	−7.92785	+	34.7342i	−0.344689	+	1.51018i
$530$	−2.79346	−	1.34526i	−0.121340	−	0.0584343i
$531$	19.5122	+	9.39656i	0.846755	+	0.407776i
$532$	6.90470	+	30.2515i	0.299357	+	1.31157i
$533$	−20.5677	+	9.90488i	−0.890886	+	0.429028i
$534$	−0.769553			−0.0333018
$535$	−8.26330	+	3.97940i	−0.357254	+	0.172044i
$536$	5.59305	+	7.01347i	0.241583	+	0.302936i
$537$	−2.70791	−	3.39561i	−0.116855	−	0.146531i
$538$	7.26080	−	3.49661i	0.313035	−	0.150750i
$539$	2.41421			0.103988
$540$	−3.97707	+	1.91526i	−0.171146	+	0.0824195i
$541$	4.81910	+	21.1139i	0.207189	+	0.907756i	0.966427	+	0.256942i	$0.0827150\pi$
$541$	4.81910	+	21.1139i	0.207189	+	0.907756i	−0.759237	+	0.650814i	$0.774428\pi$
$542$	5.43234	+	2.61607i	0.233339	+	0.112370i
$543$	−5.34178	−	2.57247i	−0.229238	−	0.110395i
$544$	4.74275	−	20.7793i	0.203344	−	0.890906i
$545$	−0.837438	−	1.05011i	−0.0358719	−	0.0449819i
$546$	−0.553224	+	0.693720i	−0.0236758	+	0.0296885i
$547$	0.845355	+	3.70374i	0.0361448	+	0.158361i	0.989780	−	0.142606i	$-0.0455480\pi$
$547$	0.845355	+	3.70374i	0.0361448	+	0.158361i	−0.953635	+	0.300966i	$0.902691\pi$
$548$	4.88236	−	21.3910i	0.208564	−	0.913779i
$549$	−1.46093	+	1.83195i	−0.0623509	+	0.0781855i
$550$	−4.00000			−0.170561
$551$		0			0
$552$	−5.02944			−0.214067
$553$	0.730464	−	0.915973i	0.0310625	−	0.0389511i
$554$	−0.489771	+	2.14583i	−0.0208084	+	0.0911674i
$555$	0.368685	+	1.61531i	0.0156498	+	0.0685662i
$556$	−15.9601	+	20.0133i	−0.676858	+	0.848753i
$557$	3.31304	+	4.15442i	0.140378	+	0.176029i	0.847051	−	0.531512i	$-0.178376\pi$
$557$	3.31304	+	4.15442i	0.140378	+	0.176029i	−0.706673	+	0.707541i	$0.749805\pi$
$558$	−1.06133	+	4.64997i	−0.0449295	+	0.196849i
$559$	−10.5665	−	5.08855i	−0.446915	−	0.215223i
$560$	7.64497	+	3.68163i	0.323059	+	0.155577i
$561$	−1.07443	−	4.70737i	−0.0453623	−	0.198745i
$562$	0.735401	−	0.354151i	0.0310210	−	0.0149389i
$563$	−9.24264			−0.389531			−0.194765	−	0.980850i	$-0.562395\pi$
$563$	−9.24264			−0.389531			−0.194765	+	0.980850i	$0.562395\pi$
$564$	−3.57735	+	1.72276i	−0.150634	+	0.0725414i
$565$	−5.80700	−	7.28175i	−0.244302	−	0.306346i
$566$	0.0886201	+	0.111126i	0.00372498	+	0.00467098i
$567$	−19.0749	+	9.18600i	−0.801072	+	0.385776i
$568$	5.02944			0.211030
$569$	25.5363	−	12.2976i	1.07054	−	0.515543i	0.186257	−	0.982501i	$-0.440364\pi$
$569$	25.5363	−	12.2976i	1.07054	−	0.515543i	0.884280	+	0.466958i	$0.154650\pi$
$570$	−0.229071	−	1.00363i	−0.00959474	−	0.0420373i
$571$	27.5943	+	13.2887i	1.15479	+	0.556116i	0.910468	−	0.413579i	$-0.135721\pi$
$571$	27.5943	+	13.2887i	1.15479	+	0.556116i	0.244319	+	0.969695i	$0.421436\pi$
$572$	7.27178	+	3.50191i	0.304048	+	0.146422i
$573$	0.247599	−	1.08480i	0.0103436	−	0.0453182i
$574$	9.12005	+	11.4362i	0.380663	+	0.477337i
$575$	19.0959	−	23.9455i	0.796353	−	0.998595i
$576$	−2.62552	−	11.5032i	−0.109397	−	0.479299i
$577$	−2.18048	+	9.55331i	−0.0907746	+	0.397709i	−0.999820	−	0.0189882i	$-0.993955\pi$
$577$	−2.18048	+	9.55331i	−0.0907746	+	0.397709i	0.909045	+	0.416698i	$0.136813\pi$
$578$	1.63057	−	2.04466i	0.0678226	−	0.0850468i
$579$	4.48528			0.186402
$580$		0			0
$581$	−10.3431			−0.429106
$582$	1.33560	−	1.67479i	0.0553624	−	0.0694222i
$583$	4.02119	−	17.6180i	0.166541	−	0.729663i
$584$	1.41148	+	6.18411i	0.0584076	+	0.255900i
$585$	3.22442	−	4.04330i	0.133313	−	0.167170i
$586$	−0.944412	−	1.18425i	−0.0390133	−	0.0489211i
$587$	0.813727	−	3.56517i	0.0335861	−	0.147150i	−0.955355	−	0.295462i	$-0.904527\pi$
$587$	0.813727	−	3.56517i	0.0335861	−	0.147150i	0.988941	+	0.148311i	$0.0473837\pi$
$588$	−0.682357	−	0.328606i	−0.0281399	−	0.0135515i
$589$	22.0074	+	10.5982i	0.906800	+	0.436692i
$590$	0.705741	+	3.09205i	0.0290549	+	0.127298i
$591$	0.746387	−	0.359441i	0.0307023	−	0.0147854i
$592$	−12.0000			−0.493197
$593$	2.26568	−	1.09110i	0.0930405	−	0.0448059i	−0.386785	−	0.922170i	$-0.626414\pi$
$593$	2.26568	−	1.09110i	0.0930405	−	0.0448059i	0.479825	+	0.877364i	$0.340700\pi$
$594$	1.50524	+	1.88751i	0.0617606	+	0.0774454i
$595$	8.51491	+	10.6774i	0.349077	+	0.437729i
$596$	−3.57735	+	1.72276i	−0.146534	+	0.0705671i
$597$	−6.82843			−0.279469
$598$	5.22471	−	2.51609i	0.213654	−	0.102890i
$599$	9.76201	+	42.7701i	0.398865	+	1.74754i	0.631879	+	0.775067i	$0.282284\pi$
$599$	9.76201	+	42.7701i	0.398865	+	1.74754i	−0.233014	+	0.972473i	$0.574859\pi$
$600$	2.36722	+	1.13999i	0.0966414	+	0.0465400i
$601$	20.5677	+	9.90488i	0.838974	+	0.404029i	0.803473	−	0.595341i	$-0.202983\pi$
$601$	20.5677	+	9.90488i	0.838974	+	0.404029i	0.0355009	+	0.999370i	$0.488697\pi$
$602$	−1.67218	+	7.32631i	−0.0681531	+	0.298598i
$603$	9.97584	+	12.5093i	0.406247	+	0.509418i
$604$	−16.1221	+	20.2165i	−0.656000	+	0.822597i
$605$	−1.15078	−	5.04191i	−0.0467860	−	0.204983i
$606$	−0.521399	+	2.28440i	−0.0211804	+	0.0927973i
$607$	11.0532	−	13.8602i	0.448635	−	0.562570i	−0.505161	−	0.863025i	$-0.668567\pi$
$607$	11.0532	−	13.8602i	0.448635	−	0.562570i	0.953796	+	0.300455i	$0.0971385\pi$
$608$	26.4853			1.07412
$609$		0			0
$610$	−0.343146			−0.0138936
$611$	5.97664	−	7.49447i	0.241789	−	0.303194i
$612$	5.55647	−	24.3445i	0.224607	−	0.984068i
$613$	2.00269	+	8.77435i	0.0808878	+	0.354393i	0.999134	−	0.0416183i	$-0.0132513\pi$
$613$	2.00269	+	8.77435i	0.0808878	+	0.354393i	−0.918246	+	0.396011i	$0.870394\pi$
$614$	−4.36443	+	5.47282i	−0.176134	+	0.220865i
$615$	3.22442	+	4.04330i	0.130021	+	0.163042i
$616$	2.40955	−	10.5569i	0.0970836	−	0.425351i
$617$	−21.0049	−	10.1154i	−0.845626	−	0.407232i	−0.0396741	−	0.999213i	$-0.512632\pi$
$617$	−21.0049	−	10.1154i	−0.845626	−	0.407232i	−0.805952	+	0.591980i	$0.798346\pi$
$618$	0.128060	+	0.0616703i	0.00515132	+	0.00248074i
$619$	−8.10292	−	35.5012i	−0.325684	−	1.42692i	−0.827269	−	0.561806i	$-0.810107\pi$
$619$	−8.10292	−	35.5012i	−0.325684	−	1.42692i	0.501585	−	0.865109i	$-0.332751\pi$
$620$	6.70650	−	3.22968i	0.269339	−	0.129707i
$621$	−18.4853			−0.741789
$622$	−9.44691	+	4.54939i	−0.378787	+	0.182414i
$623$	7.90977	+	9.91854i	0.316898	+	0.397378i
$624$	−1.41662	−	1.77638i	−0.0567101	−	0.0711122i
$625$	−9.91066	+	4.77272i	−0.396426	+	0.190909i
$626$	1.72792			0.0690617
$627$	5.40581	−	2.60330i	0.215887	−	0.103966i
$628$	−3.45235	−	15.1257i	−0.137764	−	0.603582i
$629$	−17.4011	−	8.37990i	−0.693825	−	0.334129i
$630$	−2.98555	−	1.43776i	−0.118947	−	0.0572819i
$631$	6.93633	−	30.3900i	0.276131	−	1.20981i	−0.626510	−	0.779413i	$-0.715517\pi$
$631$	6.93633	−	30.3900i	0.276131	−	1.20981i	0.902641	−	0.430395i	$-0.141626\pi$
$632$	−0.409542	−	0.513549i	−0.0162907	−	0.0204279i
$633$	−4.48976	+	5.62998i	−0.178452	+	0.223771i
$634$	−1.79327	−	7.85682i	−0.0712198	−	0.312034i
$635$	−3.48398	+	15.2643i	−0.138257	+	0.605745i
$636$	−3.53459	+	4.43224i	−0.140156	+	0.175750i
$637$	1.82843			0.0724449
$638$		0			0
$639$	8.97056			0.354870
$640$	6.58178	−	8.25329i	0.260168	−	0.326240i
$641$	4.85073	−	21.2524i	0.191592	−	0.839421i	−0.784163	−	0.620555i	$-0.786907\pi$
$641$	4.85073	−	21.2524i	0.191592	−	0.839421i	0.975755	−	0.218866i	$-0.0702357\pi$
$642$	−0.350157	−	1.53414i	−0.0138196	−	0.0605477i
$643$	9.67327	−	12.1299i	0.381476	−	0.478356i	−0.553610	−	0.832776i	$-0.686750\pi$
$643$	9.67327	−	12.1299i	0.381476	−	0.478356i	0.935086	+	0.354420i	$0.115322\pi$
$644$	24.6889	+	30.9589i	0.972880	+	1.21995i
$645$	−0.591206	+	2.59024i	−0.0232787	+	0.101991i
$646$	10.8116	+	5.20660i	0.425378	+	0.204851i
$647$	−25.5363	−	12.2976i	−1.00394	−	0.483470i	−0.141663	−	0.989915i	$-0.545245\pi$
$647$	−25.5363	−	12.2976i	−1.00394	−	0.483470i	−0.862272	+	0.506445i	$0.830959\pi$
$648$	2.64134	+	11.5725i	0.103761	+	0.454609i
$649$	−16.6547	+	8.02046i	−0.653753	+	0.314831i
$650$	−3.02944			−0.118824
$651$	−4.29722	+	2.06943i	−0.168421	+	0.0811074i
$652$	−20.6011	−	25.8330i	−0.806802	−	1.01170i
$653$	−1.15836	−	1.45254i	−0.0453301	−	0.0568422i	0.758650	−	0.651499i	$-0.225859\pi$
$653$	−1.15836	−	1.45254i	−0.0453301	−	0.0568422i	−0.803980	+	0.594657i	$0.797288\pi$
$654$	0.207626	−	0.0999874i	0.00811882	−	0.00390982i
$655$	1.31371			0.0513308
$656$	−33.7465	+	16.2515i	−1.31758	+	0.634514i
$657$	2.51754	+	11.0301i	0.0982185	+	0.430323i
$658$	−5.53387	−	2.66497i	−0.215733	−	0.103891i
$659$	−10.4384	−	5.02688i	−0.406624	−	0.195820i	0.219380	−	0.975639i	$-0.429596\pi$
$659$	−10.4384	−	5.02688i	−0.406624	−	0.195820i	−0.626004	+	0.779820i	$0.715311\pi$
$660$	0.406863	−	1.78258i	0.0158371	−	0.0693870i
$661$	6.66279	+	8.35488i	0.259153	+	0.324967i	0.894337	−	0.447393i	$-0.147647\pi$
$661$	6.66279	+	8.35488i	0.259153	+	0.324967i	−0.635185	+	0.772360i	$0.719076\pi$
$662$	0.106974	−	0.134141i	0.00415766	−	0.00521354i
$663$	−0.813727	−	3.56517i	−0.0316025	−	0.138460i
$664$	−1.29040	+	5.65360i	−0.0500771	+	0.219402i
$665$	−10.5810	+	13.2681i	−0.410313	+	0.514516i
$666$	4.68629			0.181590
$667$		0			0
$668$	16.1421			0.624558
$669$	2.28001	−	2.85904i	0.0881503	−	0.110537i
$670$	−0.521399	+	2.28440i	−0.0201434	+	0.0882540i
$671$	−0.445042	−	1.94986i	−0.0171807	−	0.0752733i
$672$	−3.22442	+	4.04330i	−0.124385	+	0.155974i
$673$	14.7315	+	18.4727i	0.567856	+	0.712069i	0.979988	−	0.199055i	$-0.0637873\pi$
$673$	14.7315	+	18.4727i	0.567856	+	0.712069i	−0.412132	+	0.911124i	$0.635216\pi$
$674$	1.64055	−	7.18774i	0.0631918	−	0.276861i
$675$	8.70053	+	4.18995i	0.334883	+	0.161271i
$676$	−15.9083	−	7.66102i	−0.611857	−	0.294655i
$677$	4.89546	+	21.4484i	0.188148	+	0.824330i	0.977592	+	0.210507i	$0.0675116\pi$
$677$	4.89546	+	21.4484i	0.188148	+	0.824330i	−0.789444	+	0.613822i	$0.789631\pi$
$678$	1.43973	−	0.693337i	0.0552925	−	0.0266275i
$679$	−35.3137			−1.35522
$680$	6.89859	−	3.32218i	0.264549	−	0.127400i
$681$	−5.20187	−	6.52293i	−0.199336	−	0.249959i
$682$	−2.53827	−	3.18289i	−0.0971954	−	0.121879i
$683$	11.6861	−	5.62772i	0.447155	−	0.215339i	−0.196735	−	0.980457i	$-0.563034\pi$
$683$	11.6861	−	5.62772i	0.447155	−	0.215339i	0.643890	+	0.765118i	$0.277319\pi$
$684$	31.0294			1.18644
$685$	10.8116	−	5.20660i	0.413091	−	0.198934i
$686$	1.56420	+	6.85319i	0.0597213	+	0.261656i
$687$	−7.64497	−	3.68163i	−0.291674	−	0.140463i
$688$	−17.3370	−	8.34907i	−0.660968	−	0.318305i
$689$	3.04549	−	13.3431i	0.116024	−	0.508333i
$690$	−0.819084	−	1.02710i	−0.0311820	−	0.0391010i
$691$	29.9275	−	37.5279i	1.13850	−	1.42763i	0.250298	−	0.968169i	$-0.419471\pi$
$691$	29.9275	−	37.5279i	1.13850	−	1.42763i	0.888198	−	0.459460i	$-0.151957\pi$
$692$	9.62511	+	42.1703i	0.365892	+	1.60308i
$693$	4.29770	−	18.8295i	0.163256	−	0.715273i
$694$	−3.74094	+	4.69099i	−0.142004	+	0.178068i
$695$	−14.0000			−0.531050
$696$		0			0
$697$	−60.2843			−2.28343
$698$	5.97664	−	7.49447i	0.226219	−	0.283670i
$699$	−0.397600	+	1.74200i	−0.0150386	+	0.0658884i
$700$	−4.60313	−	20.1676i	−0.173982	−	0.762265i
$701$	13.7870	−	17.2884i	0.520729	−	0.652974i	−0.450034	−	0.893011i	$-0.648588\pi$
$701$	13.7870	−	17.2884i	0.520729	−	0.652974i	0.970764	+	0.240037i	$0.0771597\pi$
$702$	1.14001	+	1.42952i	0.0430267	+	0.0539538i
$703$	5.34050	−	23.3983i	0.201421	−	0.882482i
$704$	9.07372	+	4.36967i	0.341979	+	0.164688i
$705$	−1.95652	−	0.942210i	−0.0736868	−	0.0354857i
$706$	0.642485	+	2.81491i	0.0241802	+	0.105941i
$707$	34.8021	−	16.7598i	1.30887	−	0.630317i
$708$	5.79899			0.217939
$709$	−0.772909	+	0.372213i	−0.0290272	+	0.0139788i	−0.448341	−	0.893863i	$-0.647985\pi$
$709$	−0.772909	+	0.372213i	−0.0290272	+	0.0139788i	0.419314	+	0.907841i	$0.362271\pi$
$710$	0.819084	+	1.02710i	0.0307397	+	0.0385463i
$711$	−0.730464	−	0.915973i	−0.0273945	−	0.0343517i
$712$	6.40832	−	3.08608i	0.240162	−	0.115656i
$713$	31.1716			1.16738
$714$	−2.11110	+	1.01665i	−0.0790060	+	0.0380473i
$715$	0.982255	+	4.30354i	0.0367343	+	0.160943i
$716$	17.2730	+	8.31823i	0.645522	+	0.310867i
$717$	−3.11361	−	1.49943i	−0.116280	−	0.0559974i
$718$	−1.66563	+	7.29761i	−0.0621608	+	0.272344i
$719$	5.07654	+	6.36578i	0.189323	+	0.237403i	0.867429	−	0.497560i	$-0.165771\pi$
$719$	5.07654	+	6.36578i	0.189323	+	0.237403i	−0.678107	+	0.734964i	$0.737199\pi$
$720$	5.29049	−	6.63406i	0.197165	−	0.247237i
$721$	−0.521399	−	2.28440i	−0.0194179	−	0.0850754i
$722$	−1.56691	+	6.86508i	−0.0583144	+	0.255492i
$723$	−1.11405	+	1.39697i	−0.0414319	+	0.0519540i
$724$	26.1716			0.972659
$725$		0			0
$726$	0.887302			0.0329309
$727$	−13.2889	+	16.6637i	−0.492857	+	0.618023i	−0.964601	−	0.263712i	$-0.915053\pi$
$727$	−13.2889	+	16.6637i	−0.492857	+	0.618023i	0.471744	+	0.881735i	$0.343625\pi$
$728$	1.82490	−	7.99539i	0.0676352	−	0.296329i
$729$	4.04356	+	17.7160i	0.149761	+	0.656147i
$730$	−1.03303	+	1.29538i	−0.0382342	+	0.0479442i
$731$	−19.3098	−	24.2138i	−0.714200	−	0.895578i
$732$	−0.139613	+	0.611686i	−0.00516026	+	0.0226086i
$733$	−44.3771	−	21.3709i	−1.63910	−	0.789351i	−0.999792	−	0.0204043i	$-0.993505\pi$
$733$	−44.3771	−	21.3709i	−1.63910	−	0.789351i	−0.639313	−	0.768947i	$-0.720781\pi$
$734$	−6.71748	−	3.23497i	−0.247947	−	0.119405i
$735$	−0.0921712	−	0.403828i	−0.00339979	−	0.0148954i
$736$	30.4518	−	14.6648i	1.12247	−	0.540553i
$737$	−13.6569			−0.503057
$738$	13.1788	−	6.34660i	0.485120	−	0.233622i
$739$	−6.27921	−	7.87388i	−0.230984	−	0.289645i	0.652809	−	0.757522i	$-0.273590\pi$
$739$	−6.27921	−	7.87388i	−0.230984	−	0.289645i	−0.883793	+	0.467877i	$0.845019\pi$
$740$	−4.56002	−	5.71809i	−0.167630	−	0.210201i
$741$	4.09414	−	1.97164i	0.150402	−	0.0724298i
$742$	−8.76955			−0.321940
$743$	−11.1208	+	5.35549i	−0.407982	+	0.196474i	−0.626607	−	0.779335i	$-0.715557\pi$
$743$	−11.1208	+	5.35549i	−0.407982	+	0.196474i	0.218625	+	0.975809i	$0.429843\pi$
$744$	0.595043	+	2.60705i	0.0218153	+	0.0955792i
$745$	−1.95652	−	0.942210i	−0.0716813	−	0.0345199i
$746$	1.37570	+	0.662502i	0.0503680	+	0.0242559i
$747$	−2.30157	+	10.0838i	−0.0842099	+	0.368948i
$748$	13.2889	+	16.6637i	0.485890	+	0.609286i
$749$	−16.1740	+	20.2816i	−0.590986	+	0.741073i
$750$	0.343607	+	1.50544i	0.0125468	+	0.0549709i
$751$	−0.597756	+	2.61894i	−0.0218124	+	0.0955665i	−0.984662	−	0.174470i	$-0.944179\pi$
$751$	−0.597756	+	2.61894i	−0.0218124	+	0.0955665i	0.962850	+	0.270037i	$0.0870359\pi$
$752$	9.80620	−	12.2966i	0.357595	−	0.448410i
$753$	−2.45584			−0.0894959
$754$		0			0
$755$	−14.1421			−0.514685
$756$	−7.78445	+	9.76139i	−0.283118	+	0.355018i
$757$	−9.45386	+	41.4201i	−0.343607	+	1.50544i	0.447792	+	0.894138i	$0.352211\pi$
$757$	−9.45386	+	41.4201i	−0.343607	+	1.50544i	−0.791398	+	0.611301i	$0.790647\pi$
$758$	−2.48591	−	10.8915i	−0.0902923	−	0.395596i
$759$	4.77397	−	5.98637i	0.173284	−	0.217291i
$760$	5.93233	+	7.43891i	0.215188	+	0.269838i
$761$	7.47625	−	32.7556i	0.271014	−	1.18739i	−0.637805	−	0.770198i	$-0.720157\pi$
$761$	7.47625	−	32.7556i	0.271014	−	1.18739i	0.908819	−	0.417192i	$-0.136986\pi$
$762$	−2.42027	−	1.16554i	−0.0876770	−	0.0422230i
$763$	−3.42277	−	1.64832i	−0.123913	−	0.0596732i
$764$	1.09295	+	4.78854i	0.0395417	+	0.173243i
$765$	12.3044	−	5.92549i	0.444867	−	0.214236i
$766$	−8.48528			−0.306586
$767$	−12.6136	+	6.07437i	−0.455449	+	0.219333i
$768$	−1.02543	−	1.28585i	−0.0370020	−	0.0463990i
$769$	8.17563	+	10.2519i	0.294821	+	0.369694i	0.907076	−	0.420966i	$-0.138309\pi$
$769$	8.17563	+	10.2519i	0.294821	+	0.369694i	−0.612255	+	0.790660i	$0.709738\pi$
$770$	2.54832	−	1.22721i	0.0918353	−	0.0442255i
$771$	9.87006			0.355461
$772$	−17.8383	+	8.59046i	−0.642014	+	0.309177i
$773$	8.11874	+	35.5705i	0.292011	+	1.27938i	0.881722	+	0.471769i	$0.156384\pi$
$773$	8.11874	+	35.5705i	0.292011	+	1.27938i	−0.589712	+	0.807614i	$0.700759\pi$
$774$	6.77053	+	3.26051i	0.243362	+	0.117197i
$775$	−14.6716	−	7.06548i	−0.527020	−	0.253800i
$776$	−4.40569	+	19.3026i	−0.158155	+	0.692923i
$777$	2.92185	+	3.66389i	0.104821	+	0.131441i
$778$	9.54794	−	11.9727i	0.342310	−	0.429244i
$779$	−16.6694	−	73.0335i	−0.597244	−	2.61670i
$780$	0.308142	−	1.35006i	0.0110332	−	0.0483398i
$781$	−4.77397	+	5.98637i	−0.170826	+	0.214209i
$782$	15.3137			0.547617
$783$		0			0
$784$	3.00000			0.107143
$785$	5.29049	−	6.63406i	0.188826	−	0.236780i
$786$	−0.0501555	+	0.219746i	−0.00178899	+	0.00783807i
$787$	−9.36441	−	41.0281i	−0.333805	−	1.46250i	−0.811698	−	0.584077i	$-0.801456\pi$
$787$	−9.36441	−	41.0281i	−0.333805	−	1.46250i	0.477893	−	0.878418i	$-0.341401\pi$
$788$	−2.28001	+	2.85904i	−0.0812220	+	0.101849i
$789$	−2.90350	−	3.64088i	−0.103367	−	0.129619i
$790$	0.0381786	−	0.167271i	0.00135833	−	0.00595124i
$791$	−23.7344	−	11.4299i	−0.843896	−	0.406399i
$792$	−9.75608	−	4.69828i	−0.346667	−	0.166946i
$793$	−0.337057	−	1.47674i	−0.0119692	−	0.0524406i
$794$	−11.4409	+	5.50967i	−0.406024	+	0.195531i
$795$	−3.10051			−0.109964
$796$	27.1571	−	13.0782i	0.962559	−	0.463544i
$797$	−34.7534	−	43.5794i	−1.23103	−	1.54366i	−0.740167	−	0.672423i	$-0.765254\pi$
$797$	−34.7534	−	43.5794i	−1.23103	−	1.54366i	−0.490861	−	0.871238i	$-0.663318\pi$
$798$	−1.81541	−	2.27645i	−0.0642647	−	0.0805854i
$799$	22.8069	−	10.9832i	0.806849	−	0.388558i
$800$	−17.6569			−0.624264
$801$	11.4300	−	5.50438i	0.403858	−	0.194488i
$802$	0.676826	+	2.96537i	0.0238996	+	0.104711i
$803$	−8.70053	−	4.18995i	−0.307035	−	0.147860i
$804$	3.86000	+	1.85888i	0.136132	+	0.0655575i
$805$	−4.81910	+	21.1139i	−0.169851	+	0.744166i
$806$	−1.92238	−	2.41059i	−0.0677130	−	0.0849094i
$807$	5.02463	−	6.30068i	0.176875	−	0.221795i
$808$	−4.81910	−	21.1139i	−0.169535	−	0.742783i
$809$	4.51367	−	19.7757i	0.158692	−	0.695277i	−0.831495	−	0.555532i	$-0.812515\pi$
$809$	4.51367	−	19.7757i	0.158692	−	0.695277i	0.990188	−	0.139745i	$-0.0446282\pi$
$810$	−1.93313	+	2.42407i	−0.0679234	+	0.0851732i
$811$	5.17157			0.181598			0.0907992	−	0.995869i	$-0.471058\pi$
$811$	5.17157			0.181598			0.0907992	+	0.995869i	$0.471058\pi$
$812$		0			0
$813$	6.02944			0.211462
$814$	−2.49396	+	3.12733i	−0.0874132	+	0.109613i
$815$	4.02119	−	17.6180i	0.140856	−	0.617131i
$816$	−1.33513	−	5.84957i	−0.0467387	−	0.204776i
$817$	23.9952	−	30.0890i	0.839485	−	1.05268i
$818$	3.86627	+	4.84814i	0.135181	+	0.169511i
$819$	3.25491	−	14.2607i	0.113736	−	0.498308i
$820$	−20.5677	−	9.90488i	−0.718255	−	0.345894i
$821$	−13.9518	−	6.71881i	−0.486920	−	0.234488i	0.174283	−	0.984696i	$-0.444239\pi$
$821$	−13.9518	−	6.71881i	−0.486920	−	0.234488i	−0.661202	+	0.750207i	$0.729954\pi$
$822$	0.458143	+	2.00725i	0.0159796	+	0.0700110i
$823$	−2.05806	+	0.991108i	−0.0717394	+	0.0345479i	−0.469409	−	0.882981i	$-0.655533\pi$
$823$	−2.05806	+	0.991108i	−0.0717394	+	0.0345479i	0.397670	+	0.917528i	$0.369819\pi$
$824$	−1.31371			−0.0457652
$825$	−3.60388	+	1.73553i	−0.125471	+	0.0604236i
$826$	5.59305	+	7.01347i	0.194607	+	0.244030i
$827$	8.16803	+	10.2424i	0.284030	+	0.356163i	0.903295	−	0.429019i	$-0.141141\pi$
$827$	8.16803	+	10.2424i	0.284030	+	0.356163i	−0.619265	+	0.785182i	$0.712569\pi$
$828$	35.6765	−	17.1809i	1.23985	−	0.597078i
$829$	9.79899			0.340333			0.170166	−	0.985415i	$-0.445569\pi$
$829$	9.79899			0.340333			0.170166	+	0.985415i	$0.445569\pi$
$830$	−1.36471	+	0.657212i	−0.0473699	+	0.0228122i
$831$	0.489771	+	2.14583i	0.0169900	+	0.0744379i
$832$	6.87207	+	3.30941i	0.238246	+	0.114733i
$833$	4.35026	+	2.09498i	0.150728	+	0.0725866i
$834$	0.534500	−	2.34180i	0.0185082	−	0.0810898i
$835$	5.50443	+	6.90234i	0.190489	+	0.238865i
$836$	−16.5133	+	20.7070i	−0.571125	+	0.716167i
$837$	2.18703	+	9.58201i	0.0755948	+	0.331203i
$838$	2.44118	−	10.6955i	0.0843292	−	0.369470i
$839$	−13.7611	+	17.2559i	−0.475085	+	0.595738i	−0.960408	−	0.278597i	$-0.910131\pi$
$839$	−13.7611	+	17.2559i	−0.475085	+	0.595738i	0.485323	+	0.874335i	$0.338702\pi$
$840$	−1.85786			−0.0641024
$841$		0			0
$842$	−10.4020			−0.358477
$843$	0.508913	−	0.638157i	0.0175279	−	0.0219793i
$844$	7.07323	−	30.9898i	0.243471	−	1.06671i
$845$	−2.14885	−	9.41474i	−0.0739228	−	0.323877i
$846$	−3.82956	+	4.80212i	−0.131663	+	0.165100i
$847$	−9.12005	−	11.4362i	−0.313368	−	0.392952i
$848$	4.99690	−	21.8928i	0.171594	−	0.751803i
$849$	0.128060	+	0.0616703i	0.00439500	+	0.00211652i
$850$	−7.20775	−	3.47107i	−0.247224	−	0.119057i
$851$	−6.81524	−	29.8595i	−0.233623	−	1.02357i
$852$	2.16415	−	1.04220i	0.0741424	−	0.0357051i
$853$	10.9706			0.375625			0.187812	−	0.982205i	$-0.439860\pi$
$853$	10.9706			0.375625			0.187812	+	0.982205i	$0.439860\pi$
$854$	−0.874447	+	0.421111i	−0.0299230	+	0.0144101i
$855$	10.5810	+	13.2681i	0.361862	+	0.453760i
$856$	9.06813	+	11.3711i	0.309942	+	0.388655i
$857$	10.6570	−	5.13216i	0.364038	−	0.175311i	−0.242918	−	0.970047i	$-0.578105\pi$
$857$	10.6570	−	5.13216i	0.364038	−	0.175311i	0.606956	+	0.794735i	$0.292390\pi$
$858$	−0.757359			−0.0258558
$859$	5.16068	−	2.48525i	0.176080	−	0.0847957i	−0.343767	−	0.939055i	$-0.611703\pi$
$859$	5.16068	−	2.48525i	0.176080	−	0.0847957i	0.519847	+	0.854259i	$0.325989\pi$
$860$	−2.60971	−	11.4339i	−0.0889903	−	0.389892i
$861$	13.1788	+	6.34660i	0.449134	+	0.216291i
$862$	−3.11361	−	1.49943i	−0.106050	−	0.0510709i
$863$	10.0385	−	43.9816i	0.341715	−	1.49715i	−0.453737	−	0.891136i	$-0.649909\pi$
$863$	10.0385	−	43.9816i	0.341715	−	1.49715i	0.795452	−	0.606016i	$-0.207233\pi$
$864$	6.64444	+	8.33186i	0.226048	+	0.283456i
$865$	−14.7498	+	18.4957i	−0.501508	+	0.628872i
$866$	1.34823	+	5.90697i	0.0458146	+	0.200727i
$867$	0.581942	−	2.54965i	0.0197638	−	0.0865908i
$868$	13.1268	−	16.4605i	0.445554	−	0.558707i
$869$	1.00000			0.0339227
$870$		0			0
$871$	−10.3431			−0.350464
$872$	−1.32800	+	1.66526i	−0.0449717	+	0.0563927i
$873$	−7.85804	+	34.4283i	−0.265954	+	1.16522i
$874$	4.23445	+	18.5523i	0.143232	+	0.627542i
$875$	15.8715	−	19.9022i	0.536553	−	0.672816i
$876$	1.88882	+	2.36851i	0.0638174	+	0.0800245i
$877$	1.97106	−	8.63578i	0.0665580	−	0.291610i	−0.930684	−	0.365823i	$-0.880788\pi$
$877$	1.97106	−	8.63578i	0.0665580	−	0.291610i	0.997242	+	0.0742136i	$0.0236447\pi$
$878$	4.35026	+	2.09498i	0.146814	+	0.0707020i
$879$	−1.36471	−	0.657212i	−0.0460307	−	0.0221672i
$880$	1.61164	+	7.06105i	0.0543283	+	0.238028i
$881$	−12.6136	+	6.07437i	−0.424962	+	0.204651i	−0.634126	−	0.773230i	$-0.718640\pi$
$881$	−12.6136	+	6.07437i	−0.424962	+	0.204651i	0.209164	+	0.977881i	$0.432926\pi$
$882$	−1.17157			−0.0394489
$883$	41.8287	−	20.1437i	1.40765	−	0.677888i	0.432952	−	0.901417i	$-0.357472\pi$
$883$	41.8287	−	20.1437i	1.40765	−	0.677888i	0.974697	+	0.223529i	$0.0717576\pi$
$884$	10.0645	+	12.6204i	0.338504	+	0.424471i
$885$	1.97744	+	2.47964i	0.0664710	+	0.0833520i
$886$	13.3069	−	6.40827i	0.447054	−	0.215290i
$887$	36.8995			1.23896			0.619482	−	0.785011i	$-0.287343\pi$
$887$	36.8995			1.23896			0.619482	+	0.785011i	$0.287343\pi$
$888$	2.36722	−	1.13999i	0.0794387	−	0.0382557i
$889$	9.85418	+	43.1740i	0.330499	+	1.44801i
$890$	1.67388	+	0.806097i	0.0561085	+	0.0270204i
$891$	−16.2815	−	7.84074i	−0.545450	−	0.262675i
$892$	−3.59196	+	15.7374i	−0.120268	+	0.526928i
$893$	19.6124	+	24.5932i	0.656304	+	0.822979i
$894$	0.232302	−	0.291297i	0.00776933	−	0.00974243i
$895$	2.33319	+	10.2224i	0.0779901	+	0.341697i
$896$	6.64400	−	29.1093i	0.221960	−	0.972472i
$897$	3.61561	−	4.53383i	0.120722	−	0.151380i
$898$	−0.426407			−0.0142294
$899$		0			0
$900$	−20.6863			−0.689543
$901$	22.5343	−	28.2571i	0.750725	−	0.941379i
$902$	−2.77824	+	12.1722i	−0.0925052	+	0.405292i
$903$	1.67218	+	7.32631i	0.0556467	+	0.243804i
$904$	−9.20867	+	11.5473i	−0.306276	+	0.384058i
$905$	8.92445	+	11.1909i	0.296659	+	0.371998i
$906$	0.539926	−	2.36557i	0.0179379	−	0.0785909i
$907$	30.8891	+	14.8754i	1.02565	+	0.493929i	0.869567	−	0.493814i	$-0.164398\pi$
$907$	30.8891	+	14.8754i	1.02565	+	0.493929i	0.156087	+	0.987743i	$0.450112\pi$
$908$	33.1813	+	15.9793i	1.10116	+	0.530290i
$909$	−8.59541	−	37.6589i	−0.285092	−	1.24907i
$910$	1.93000	−	0.929438i	0.0639788	−	0.0308106i
$911$	−46.5563			−1.54248			−0.771240	−	0.636544i	$-0.780363\pi$
$911$	−46.5563			−1.54248			−0.771240	+	0.636544i	$0.780363\pi$
$912$	6.71748	−	3.23497i	0.222438	−	0.107121i
$913$	−5.50443	−	6.90234i	−0.182170	−	0.228434i
$914$	9.03143	+	11.3250i	0.298733	+	0.374599i
$915$	−0.309164	+	0.148885i	−0.0102206	+	0.00492200i
$916$	37.4558			1.23758
$917$	3.34776	−	1.61219i	0.110553	−	0.0532393i
$918$	1.07443	+	4.70737i	0.0354613	+	0.155366i
$919$	18.1474	+	8.73935i	0.598629	+	0.288284i	0.708555	−	0.705655i	$-0.249347\pi$
$919$	18.1474	+	8.73935i	0.598629	+	0.288284i	−0.109927	+	0.993940i	$0.535062\pi$
$920$	10.9397	+	5.26828i	0.360671	+	0.173690i
$921$	−1.55765	+	6.82450i	−0.0513262	+	0.224875i
$922$	3.61561	+	4.53383i	0.119074	+	0.149314i
$923$	−3.61561	+	4.53383i	−0.119009	+	0.149233i
$924$	−1.15078	−	5.04191i	−0.0378580	−	0.165867i
$925$	−3.56033	+	15.5988i	−0.117063	+	0.512887i
$926$	−6.71471	+	8.41998i	−0.220659	+	0.276698i
$927$	−2.34315			−0.0769590
$928$		0			0
$929$	41.3137			1.35546			0.677729	−	0.735311i	$-0.262964\pi$
$929$	41.3137			1.35546			0.677729	+	0.735311i	$0.262964\pi$
$930$	−0.435498	+	0.546097i	−0.0142805	+	0.0179072i
$931$	−1.33513	+	5.84957i	−0.0437570	+	0.191712i
$932$	−1.75509	−	7.68955i	−0.0574899	−	0.251880i
$933$	−6.53747	+	8.19772i	−0.214027	+	0.268381i
$934$	8.35602	+	10.4781i	0.273417	+	0.342855i
$935$	−2.59389	+	11.3646i	−0.0848294	+	0.371662i
$936$	−7.38885	−	3.55828i	−0.241512	−	0.116306i
$937$	−25.7924	−	12.4210i	−0.842601	−	0.405775i	−0.0377754	−	0.999286i	$-0.512027\pi$
$937$	−25.7924	−	12.4210i	−0.842601	−	0.405775i	−0.804826	+	0.593511i	$0.797741\pi$
$938$	1.47474	+	6.46125i	0.0481519	+	0.210967i
$939$	1.55680	−	0.749717i	0.0508044	−	0.0244661i
$940$	9.58579			0.312654
$941$	−20.3601	+	9.80490i	−0.663720	+	0.319630i	−0.735238	−	0.677809i	$-0.762930\pi$
$941$	−20.3601	+	9.80490i	−0.663720	+	0.319630i	0.0715187	+	0.997439i	$0.477215\pi$
$942$	0.907704	+	1.13822i	0.0295746	+	0.0370854i
$943$	−59.6044	−	74.7415i	−1.94099	−	2.43392i
$944$	−20.6958	+	9.96655i	−0.673590	+	0.324384i
$945$	−6.82843			−0.222129
$946$	−5.77901	+	2.78302i	−0.187892	+	0.0904839i
$947$	−8.76394	−	38.3973i	−0.284790	−	1.24775i	−0.891573	−	0.452878i	$-0.850397\pi$
$947$	−8.76394	−	38.3973i	−0.284790	−	1.24775i	0.606783	−	0.794868i	$-0.292460\pi$
$948$	−0.282642	−	0.136113i	−0.00917977	−	0.00442075i
$949$	−6.58942	−	3.17330i	−0.213902	−	0.103010i
$950$	2.21211	−	9.69188i	0.0717703	−	0.314446i
$951$	−5.02463	−	6.30068i	−0.162935	−	0.204314i
$952$	13.5028	−	16.9320i	0.437629	−	0.548770i
$953$	−2.14230	−	9.38604i	−0.0693960	−	0.304044i	0.928305	−	0.371821i	$-0.121266\pi$
$953$	−2.14230	−	9.38604i	−0.0693960	−	0.304044i	−0.997700	+	0.0677772i	$0.978409\pi$
$954$	−1.95141	+	8.54968i	−0.0631792	+	0.276806i
$955$	−1.67488	+	2.10023i	−0.0541977	+	0.0679618i
$956$	15.2548			0.493377
$957$		0			0
$958$	−5.34315			−0.172629
$959$	21.1619	−	26.5362i	0.683355	−	0.856900i
$960$	0.384499	−	1.68460i	0.0124096	−	0.0543702i
$961$	3.21018	+	14.0647i	0.103554	+	0.453700i
$962$	−1.88882	+	2.36851i	−0.0608981	+	0.0763638i
$963$	16.1740	+	20.2816i	0.521201	+	0.653565i
$964$	1.75509	−	7.68955i	0.0565276	−	0.247664i
$965$	−9.75608	−	4.69828i	−0.314059	−	0.151243i
$966$	−3.34776	−	1.61219i	−0.107712	−	0.0518715i
$967$	5.95407	+	26.0865i	0.191470	+	0.838885i	0.975822	+	0.218569i	$0.0701387\pi$
$967$	5.95407	+	26.0865i	0.191470	+	0.838885i	−0.784352	+	0.620317i	$0.787004\pi$
$968$	−7.38885	+	3.55828i	−0.237487	+	0.114368i
$969$	12.0000			0.385496
$970$	−4.65943	+	2.24386i	−0.149605	+	0.0720460i
$971$	−2.70791	−	3.39561i	−0.0869009	−	0.108970i	0.736480	−	0.676459i	$-0.236486\pi$
$971$	−2.70791	−	3.39561i	−0.0869009	−	0.108970i	−0.823381	+	0.567489i	$0.807915\pi$
$972$	11.7912	+	14.7858i	0.378204	+	0.474253i
$973$	−35.6765	+	17.1809i	−1.14374	+	0.550795i
$974$	−11.7990			−0.378064
$975$	−2.72943	+	1.31442i	−0.0874117	+	0.0420952i
$976$	−0.553027	−	2.42297i	−0.0177020	−	0.0775574i
$977$	−37.6861	−	18.1487i	−1.20569	−	0.580628i	−0.280394	−	0.959885i	$-0.590465\pi$
$977$	−37.6861	−	18.1487i	−1.20569	−	0.580628i	−0.925291	+	0.379257i	$0.876179\pi$
$978$	2.79346	+	1.34526i	0.0893250	+	0.0430166i
$979$	−2.40955	+	10.5569i	−0.0770096	+	0.337401i
$980$	1.14001	+	1.42952i	0.0364161	+	0.0456644i
$981$	−2.36863	+	2.97017i	−0.0756246	+	0.0948302i
$982$	1.17586	+	5.15178i	0.0375232	+	0.164400i
$983$	−7.09176	+	31.0710i	−0.226192	+	0.991011i	0.726522	+	0.687143i	$0.241135\pi$
$983$	−7.09176	+	31.0710i	−0.226192	+	0.991011i	−0.952714	+	0.303868i	$0.901722\pi$
$984$	5.11325	−	6.41181i	0.163004	−	0.204401i
$985$	−2.00000			−0.0637253
$986$		0			0
$987$	−6.14214			−0.195506
$988$	−12.5065	+	15.6827i	−0.397885	+	0.498932i
$989$	10.9286	−	47.8813i	0.347509	−	1.52254i
$990$	−0.629384	−	2.75751i	−0.0200031	−	0.0876395i
$991$	−4.47140	+	5.60696i	−0.142039	+	0.178111i	−0.847762	−	0.530376i	$-0.822051\pi$
$991$	−4.47140	+	5.60696i	−0.142039	+	0.178111i	0.705724	+	0.708487i	$0.250622\pi$
$992$	−11.2045	−	14.0500i	−0.355742	−	0.446086i
$993$	0.0381786	−	0.167271i	0.00121156	−	0.00530819i
$994$	3.34776	+	1.61219i	0.106184	+	0.0511357i
$995$	14.8527	+	7.15270i	0.470863	+	0.226756i
$996$	0.616283	+	2.70011i	0.0195277	+	0.0855564i
$997$	25.4832	−	12.2721i	0.807063	−	0.388661i	0.0155999	−	0.999878i	$-0.495034\pi$
$997$	25.4832	−	12.2721i	0.807063	−	0.388661i	0.791463	+	0.611217i	$0.209320\pi$
$998$	−6.20101			−0.196290
$999$	8.70053	−	4.18995i	0.275272	−	0.132564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.j.574.2		12
29.2	odd	28		841.2.e.k.63.3		24
29.3	odd	28		841.2.e.k.236.3		24
29.4	even	14		841.2.d.f.571.2		12
29.5	even	14		841.2.d.f.778.1		12
29.6	even	14		841.2.d.f.190.2		12
29.7	even	7	inner	841.2.d.j.605.1		12
29.8	odd	28		841.2.e.k.196.3		24
29.9	even	14		841.2.d.f.645.2		12
29.10	odd	28		841.2.e.k.270.2		24
29.11	odd	28		841.2.b.a.840.2		4
29.12	odd	4		841.2.e.k.267.3		24
29.13	even	14		841.2.a.d.1.1		2
29.14	odd	28		841.2.e.k.651.2		24
29.15	odd	28		841.2.e.k.651.3		24
29.16	even	7		29.2.a.a.1.2	✓	2
29.17	odd	4		841.2.e.k.267.2		24
29.18	odd	28		841.2.b.a.840.3		4
29.19	odd	28		841.2.e.k.270.3		24
29.20	even	7	inner	841.2.d.j.645.1		12
29.21	odd	28		841.2.e.k.196.2		24
29.22	even	14		841.2.d.f.605.2		12
29.23	even	7	inner	841.2.d.j.190.1		12
29.24	even	7	inner	841.2.d.j.778.2		12
29.25	even	7	inner	841.2.d.j.571.1		12
29.26	odd	28		841.2.e.k.236.2		24
29.27	odd	28		841.2.e.k.63.2		24
29.28	even	2		841.2.d.f.574.1		12
87.71	odd	14		7569.2.a.c.1.2		2
87.74	odd	14		261.2.a.d.1.1		2
116.103	odd	14		464.2.a.h.1.2		2
145.74	even	14		725.2.a.b.1.1		2
145.103	odd	28		725.2.b.b.349.2		4
145.132	odd	28		725.2.b.b.349.3		4
203.132	odd	14		1421.2.a.j.1.2		2
232.45	even	14		1856.2.a.r.1.2		2
232.219	odd	14		1856.2.a.w.1.1		2
319.219	odd	14		3509.2.a.j.1.1		2
348.335	even	14		4176.2.a.bq.1.1		2
377.103	even	14		4901.2.a.g.1.1		2
435.74	odd	14		6525.2.a.o.1.2		2
493.16	even	14		8381.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.2	✓	2	29.16	even	7
261.2.a.d.1.1		2	87.74	odd	14
464.2.a.h.1.2		2	116.103	odd	14
725.2.a.b.1.1		2	145.74	even	14
725.2.b.b.349.2		4	145.103	odd	28
725.2.b.b.349.3		4	145.132	odd	28
841.2.a.d.1.1		2	29.13	even	14
841.2.b.a.840.2		4	29.11	odd	28
841.2.b.a.840.3		4	29.18	odd	28
841.2.d.f.190.2		12	29.6	even	14
841.2.d.f.571.2		12	29.4	even	14
841.2.d.f.574.1		12	29.28	even	2
841.2.d.f.605.2		12	29.22	even	14
841.2.d.f.645.2		12	29.9	even	14
841.2.d.f.778.1		12	29.5	even	14
841.2.d.j.190.1		12	29.23	even	7	inner
841.2.d.j.571.1		12	29.25	even	7	inner
841.2.d.j.574.2		12	1.1	even	1	trivial
841.2.d.j.605.1		12	29.7	even	7	inner
841.2.d.j.645.1		12	29.20	even	7	inner
841.2.d.j.778.2		12	29.24	even	7	inner
841.2.e.k.63.2		24	29.27	odd	28
841.2.e.k.63.3		24	29.2	odd	28
841.2.e.k.196.2		24	29.21	odd	28
841.2.e.k.196.3		24	29.8	odd	28
841.2.e.k.236.2		24	29.26	odd	28
841.2.e.k.236.3		24	29.3	odd	28
841.2.e.k.267.2		24	29.17	odd	4
841.2.e.k.267.3		24	29.12	odd	4
841.2.e.k.270.2		24	29.10	odd	28
841.2.e.k.270.3		24	29.19	odd	28
841.2.e.k.651.2		24	29.14	odd	28
841.2.e.k.651.3		24	29.15	odd	28
1421.2.a.j.1.2		2	203.132	odd	14
1856.2.a.r.1.2		2	232.45	even	14
1856.2.a.w.1.1		2	232.219	odd	14
3509.2.a.j.1.1		2	319.219	odd	14
4176.2.a.bq.1.1		2	348.335	even	14
4901.2.a.g.1.1		2	377.103	even	14
6525.2.a.o.1.2		2	435.74	odd	14
7569.2.a.c.1.2		2	87.71	odd	14
8381.2.a.e.1.2		2	493.16	even	14

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258258 - 0.323845i) q^{2} +(0.0921712 - 0.403828i) q^{3} +(0.406863 + 1.78258i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-0.106974 - 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(1.42874 + 0.688047i) q^{8} +(2.54832 + 1.22721i) q^{9} +O(q^{10})\)	\(q+(0.258258 - 0.323845i) q^{2} +(0.0921712 - 0.403828i) q^{3} +(0.406863 + 1.78258i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-0.106974 - 0.134141i) q^{6} +(-0.629384 + 2.75751i) q^{7} +(1.42874 + 0.688047i) q^{8} +(2.54832 + 1.22721i) q^{9} +(0.0921712 + 0.403828i) q^{10} +(-2.17513 + 1.04749i) q^{11} +0.757359 q^{12} +(-1.64736 + 0.793325i) q^{13} +(0.730464 + 0.915973i) q^{14} +(0.258258 + 0.323845i) q^{15} +(-2.70291 + 1.30165i) q^{16} -4.82843 q^{17} +(1.05555 - 0.508326i) q^{18} +(-1.33513 - 5.84957i) q^{19} +(-1.64736 - 0.793325i) q^{20} +(1.05555 + 0.508326i) q^{21} +(-0.222521 + 0.974928i) q^{22} +(-4.77397 - 5.98637i) q^{23} +(0.409542 - 0.513549i) q^{24} +(0.890084 + 3.89971i) q^{25} +(-0.168528 + 0.738371i) q^{26} +(1.50524 - 1.88751i) q^{27} -5.17157 q^{28} +0.171573 q^{30} +(-2.53827 + 3.18289i) q^{31} +(-0.982255 + 4.30354i) q^{32} +(0.222521 + 0.974928i) q^{33} +(-1.24698 + 1.56366i) q^{34} +(-1.76350 - 2.21135i) q^{35} +(-1.15078 + 5.04191i) q^{36} +(3.60388 + 1.73553i) q^{37} +(-2.23916 - 1.07832i) q^{38} +(0.168528 + 0.738371i) q^{39} +(-1.42874 + 0.688047i) q^{40} +12.4853 q^{41} +(0.437223 - 0.210556i) q^{42} +(3.99920 + 5.01483i) q^{43} +(-2.75222 - 3.45117i) q^{44} +(-2.54832 + 1.22721i) q^{45} -3.17157 q^{46} +(-4.72346 + 2.27470i) q^{47} +(0.276514 + 1.21149i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(1.49277 + 0.718882i) q^{50} +(-0.445042 + 1.94986i) q^{51} +(-2.08442 - 2.61378i) q^{52} +(-4.66700 + 5.85223i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(0.537213 - 2.35368i) q^{55} +(-2.79653 + 3.50673i) q^{56} -2.48528 q^{57} +7.65685 q^{59} +(-0.472206 + 0.592127i) q^{60} +(-0.184342 + 0.807657i) q^{61} +(0.375235 + 1.64401i) q^{62} +(-4.98792 + 6.25465i) q^{63} +(-2.60093 - 3.26147i) q^{64} +(0.406863 - 1.78258i) q^{65} +(0.373194 + 0.179721i) q^{66} +(5.09665 + 2.45442i) q^{67} +(-1.96451 - 8.60708i) q^{68} +(-2.85749 + 1.37609i) q^{69} -1.17157 q^{70} +(2.85749 - 1.37609i) q^{71} +(2.79653 + 3.50673i) q^{72} +(2.49396 + 3.12733i) q^{73} +(1.49277 - 0.718882i) q^{74} +1.65685 q^{75} +(9.88414 - 4.75995i) q^{76} +(-1.51947 - 6.65722i) q^{77} +(0.282642 + 0.136113i) q^{78} +(-0.373194 - 0.179721i) q^{79} +(0.667563 - 2.92478i) q^{80} +(4.66700 + 5.85223i) q^{81} +(3.22442 - 4.04330i) q^{82} +(0.813727 + 3.56517i) q^{83} +(-0.476670 + 2.08843i) q^{84} +(3.01048 - 3.77502i) q^{85} +2.65685 q^{86} -3.82843 q^{88} +(2.79653 - 3.50673i) q^{89} +(-0.260699 + 1.14220i) q^{90} +(-1.15078 - 5.04191i) q^{91} +(8.72886 - 10.9456i) q^{92} +(1.05139 + 1.31840i) q^{93} +(-0.483220 + 2.11713i) q^{94} +(5.40581 + 2.60330i) q^{95} +(1.64736 + 0.793325i) q^{96} +(2.77824 + 12.1722i) q^{97} +(-0.373194 + 0.179721i) q^{98} -6.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8	\( 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22} + 4 q^{23} + 10 q^{24} + 8 q^{25} - 10 q^{26} - 2 q^{27} - 96 q^{28} + 36 q^{30} - 6 q^{31} - 6 q^{32} + 2 q^{33} + 4 q^{34} - 16 q^{36} + 8 q^{37} + 12 q^{38} + 10 q^{39} - 6 q^{40} + 48 q^{41} - 16 q^{42} - 10 q^{43} + 6 q^{44} - 72 q^{46} - 2 q^{47} - 6 q^{48} - 2 q^{49} - 8 q^{50} - 4 q^{51} + 18 q^{52} - 2 q^{53} - 2 q^{54} + 2 q^{55} - 8 q^{56} + 72 q^{57} + 24 q^{59} + 10 q^{60} + 4 q^{61} + 26 q^{62} + 16 q^{63} + 14 q^{64} - 2 q^{65} - 2 q^{66} - 12 q^{68} - 12 q^{69} - 48 q^{70} + 12 q^{71} + 8 q^{72} - 8 q^{73} - 8 q^{74} - 48 q^{75} - 12 q^{76} - 8 q^{77} - 22 q^{78} + 2 q^{79} + 6 q^{80} + 2 q^{81} - 16 q^{82} - 4 q^{83} + 24 q^{84} - 4 q^{85} - 36 q^{86} - 12 q^{88} + 8 q^{89} - 8 q^{90} - 16 q^{91} - 28 q^{92} - 26 q^{93} - 10 q^{94} + 12 q^{95} - 2 q^{96} + 8 q^{97} + 2 q^{98} - 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 6 * q^6 + 6 * q^8 - 2 * q^10 - 2 * q^11 + 60 * q^12 + 2 * q^13 - 8 * q^14 + 2 * q^15 - 6 * q^16 - 24 * q^17 + 8 * q^18 - 12 * q^19 + 2 * q^20 + 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 + 8 * q^25 - 10 * q^26 - 2 * q^27 - 96 * q^28 + 36 * q^30 - 6 * q^31 - 6 * q^32 + 2 * q^33 + 4 * q^34 - 16 * q^36 + 8 * q^37 + 12 * q^38 + 10 * q^39 - 6 * q^40 + 48 * q^41 - 16 * q^42 - 10 * q^43 + 6 * q^44 - 72 * q^46 - 2 * q^47 - 6 * q^48 - 2 * q^49 - 8 * q^50 - 4 * q^51 + 18 * q^52 - 2 * q^53 - 2 * q^54 + 2 * q^55 - 8 * q^56 + 72 * q^57 + 24 * q^59 + 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 + 14 * q^64 - 2 * q^65 - 2 * q^66 - 12 * q^68 - 12 * q^69 - 48 * q^70 + 12 * q^71 + 8 * q^72 - 8 * q^73 - 8 * q^74 - 48 * q^75 - 12 * q^76 - 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 + 2 * q^81 - 16 * q^82 - 4 * q^83 + 24 * q^84 - 4 * q^85 - 36 * q^86 - 12 * q^88 + 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 - 26 * q^93 - 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 48 * q^99

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