LMFDB - Embedded newform 841.2.d.f.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			$0.881748 - 1.10568i$ of defining polynomial
Character	$\chi$	$=$	841.574
Dual form			841.2.d.f.778.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50524 - 1.88751i) q^{2} +(0.537213 - 2.35368i) q^{3} +(-0.851905 - 3.73244i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-3.63396 - 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-3.97707 - 1.91526i) q^{8} +(-2.54832 - 1.22721i) q^{9} +O(q^{10})$	\(q+(1.50524 - 1.88751i) q^{2} +(0.537213 - 2.35368i) q^{3} +(-0.851905 - 3.73244i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-3.63396 - 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-3.97707 - 1.91526i) q^{8} +(-2.54832 - 1.22721i) q^{9} +(0.537213 + 2.35368i) q^{10} +(-0.373194 + 0.179721i) q^{11} -9.24264 q^{12} +(3.44929 - 1.66109i) q^{13} +(-4.25745 - 5.33868i) q^{14} +(1.50524 + 1.88751i) q^{15} +(-2.70291 + 1.30165i) q^{16} -0.828427 q^{17} +(-6.15220 + 2.96274i) q^{18} +(1.33513 + 5.84957i) q^{19} +(3.44929 + 1.66109i) q^{20} +(-6.15220 - 2.96274i) q^{21} +(-0.222521 + 0.974928i) q^{22} +(2.28001 + 2.85904i) q^{23} +(-6.64444 + 8.33186i) q^{24} +(0.890084 + 3.89971i) q^{25} +(2.05668 - 9.01091i) q^{26} +(0.258258 - 0.323845i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-6.27921 + 7.87388i) q^{31} +(0.352871 - 1.54603i) q^{32} +(0.222521 + 0.974928i) q^{33} +(-1.24698 + 1.56366i) q^{34} +(1.76350 + 2.21135i) q^{35} +(-2.40955 + 10.5569i) q^{36} +(-3.60388 - 1.73553i) q^{37} +(13.0508 + 6.28493i) q^{38} +(-2.05668 - 9.01091i) q^{39} +(3.97707 - 1.91526i) q^{40} +4.48528 q^{41} +(-14.8527 + 7.15270i) q^{42} +(-2.23570 - 2.80348i) q^{43} +(0.988722 + 1.23982i) q^{44} +(2.54832 - 1.22721i) q^{45} +8.82843 q^{46} +(-2.92152 + 1.40693i) q^{47} +(1.61164 + 7.06105i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(8.70053 + 4.18995i) q^{50} +(-0.445042 + 1.94986i) q^{51} +(-9.13840 - 11.4592i) q^{52} +(5.91398 - 7.41589i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(0.0921712 - 0.403828i) q^{55} +(-7.78445 + 9.76139i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(5.76269 - 7.22619i) q^{60} +(-1.07443 + 4.70737i) q^{61} +(5.41031 + 23.7041i) q^{62} +(-4.98792 + 6.25465i) q^{63} +(-6.12792 - 7.68417i) q^{64} +(-0.851905 + 3.73244i) q^{65} +(2.17513 + 1.04749i) q^{66} +(-5.09665 - 2.45442i) q^{67} +(0.705741 + 3.09205i) q^{68} +(7.95414 - 3.83051i) q^{69} +6.82843 q^{70} +(7.95414 - 3.83051i) q^{71} +(7.78445 + 9.76139i) q^{72} +(-2.49396 - 3.12733i) q^{73} +(-8.70053 + 4.18995i) q^{74} +9.65685 q^{75} +(20.6958 - 9.96655i) q^{76} +(0.260699 + 1.14220i) q^{77} +(-20.1040 - 9.68156i) q^{78} +(-2.17513 - 1.04749i) q^{79} +(0.667563 - 2.92478i) q^{80} +(-5.91398 - 7.41589i) q^{81} +(6.75141 - 8.46601i) q^{82} +(-1.70381 - 7.46488i) q^{83} +(-5.81717 + 25.4867i) q^{84} +(0.516516 - 0.647690i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(7.78445 - 9.76139i) q^{89} +(1.51947 - 6.65722i) q^{90} +(-2.40955 - 10.5569i) q^{91} +(8.72886 - 10.9456i) q^{92} +(15.1593 + 19.0092i) q^{93} +(-1.74199 + 7.63215i) q^{94} +(-5.40581 - 2.60330i) q^{95} +(-3.44929 - 1.66109i) q^{96} +(0.998069 + 4.37283i) q^{97} +(-2.17513 + 1.04749i) q^{98} +1.17157 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 $

$2$	1.50524	−	1.88751i	1.06436	−	1.33467i	0.124843	−	0.992176i	$-0.460157\pi$
$2$	1.50524	−	1.88751i	1.06436	−	1.33467i	0.939520	−	0.342493i	$-0.111271\pi$
$3$	0.537213	−	2.35368i	0.310160	−	1.35890i	−0.544085	−	0.839030i	$-0.683123\pi$
$3$	0.537213	−	2.35368i	0.310160	−	1.35890i	0.854245	−	0.519870i	$-0.174020\pi$
$4$	−0.851905	−	3.73244i	−0.425953	−	1.86622i
$5$	−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	$0.286069\pi$
$6$	−3.63396	−	4.55685i	−1.48356	−	1.86033i
$7$	0.629384	−	2.75751i	0.237885	−	1.04224i	−0.705022	−	0.709185i	$-0.749063\pi$
$7$	0.629384	−	2.75751i	0.237885	−	1.04224i	0.942907	−	0.333056i	$-0.108080\pi$
$8$	−3.97707	−	1.91526i	−1.40611	−	0.677145i
$9$	−2.54832	−	1.22721i	−0.849442	−	0.409070i
$10$	0.537213	+	2.35368i	0.169882	+	0.744300i
$11$	−0.373194	+	0.179721i	−0.112522	+	0.0541878i	−0.489298	−	0.872117i	$-0.662747\pi$
$11$	−0.373194	+	0.179721i	−0.112522	+	0.0541878i	0.376776	+	0.926304i	$0.377033\pi$
$12$	−9.24264			−2.66812
$13$	3.44929	−	1.66109i	0.956662	−	0.460704i	0.110645	−	0.993860i	$-0.464708\pi$
$13$	3.44929	−	1.66109i	0.956662	−	0.460704i	0.846017	+	0.533156i	$0.178994\pi$
$14$	−4.25745	−	5.33868i	−1.13785	−	1.42682i
$15$	1.50524	+	1.88751i	0.388651	+	0.487353i
$16$	−2.70291	+	1.30165i	−0.675727	+	0.325413i
$17$	−0.828427			−0.200923			−0.100462	−	0.994941i	$-0.532032\pi$
$17$	−0.828427			−0.200923			−0.100462	+	0.994941i	$0.532032\pi$
$18$	−6.15220	+	2.96274i	−1.45009	+	0.698325i
$19$	1.33513	+	5.84957i	0.306299	+	1.34198i	0.860436	+	0.509558i	$0.170191\pi$
$19$	1.33513	+	5.84957i	0.306299	+	1.34198i	−0.554138	+	0.832425i	$0.686952\pi$
$20$	3.44929	+	1.66109i	0.771286	+	0.371432i
$21$	−6.15220	−	2.96274i	−1.34252	−	0.646524i
$22$	−0.222521	+	0.974928i	−0.0474416	+	0.207855i
$23$	2.28001	+	2.85904i	0.475415	+	0.596152i	0.960488	−	0.278322i	$-0.0897783\pi$
$23$	2.28001	+	2.85904i	0.475415	+	0.596152i	−0.485073	+	0.874474i	$0.661207\pi$
$24$	−6.64444	+	8.33186i	−1.35629	+	1.70073i
$25$	0.890084	+	3.89971i	0.178017	+	0.779942i
$26$	2.05668	−	9.01091i	0.403348	−	1.76718i
$27$	0.258258	−	0.323845i	0.0497018	−	0.0623240i
$28$	−10.8284			−2.04638
$29$		0			0
$29$		0			0
$30$	5.82843			1.06412
$31$	−6.27921	+	7.87388i	−1.12778	+	1.41419i	−0.230307	+	0.973118i	$0.573973\pi$
$31$	−6.27921	+	7.87388i	−1.12778	+	1.41419i	−0.897472	+	0.441072i	$0.854598\pi$
$32$	0.352871	−	1.54603i	0.0623793	−	0.273302i
$33$	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
$36$	−2.40955	+	10.5569i	−0.401592	+	1.75949i
$37$	−3.60388	−	1.73553i	−0.592473	−	0.285320i	0.113523	−	0.993535i	$-0.463786\pi$
$37$	−3.60388	−	1.73553i	−0.592473	−	0.285320i	−0.705997	+	0.708215i	$0.749501\pi$
$38$	13.0508	+	6.28493i	2.11712	+	1.01955i
$39$	−2.05668	−	9.01091i	−0.329333	−	1.44290i
$40$	3.97707	−	1.91526i	0.628830	−	0.302828i
$41$	4.48528			0.700483			0.350242	−	0.936659i	$-0.386099\pi$
$41$	4.48528			0.700483			0.350242	+	0.936659i	$0.386099\pi$
$42$	−14.8527	+	7.15270i	−2.29183	+	1.10368i
$43$	−2.23570	−	2.80348i	−0.340941	−	0.427527i	0.581570	−	0.813496i	$-0.302438\pi$
$43$	−2.23570	−	2.80348i	−0.340941	−	0.427527i	−0.922512	+	0.385969i	$0.873867\pi$
$44$	0.988722	+	1.23982i	0.149055	+	0.186910i
$45$	2.54832	−	1.22721i	0.379882	−	0.182941i
$46$	8.82843			1.30168
$47$	−2.92152	+	1.40693i	−0.426147	+	0.205222i	−0.634649	−	0.772800i	$-0.718855\pi$
$47$	−2.92152	+	1.40693i	−0.426147	+	0.205222i	0.208502	+	0.978022i	$0.433141\pi$
$48$	1.61164	+	7.06105i	0.232620	+	1.01918i
$49$	−0.900969	−	0.433884i	−0.128710	−	0.0619834i
$50$	8.70053	+	4.18995i	1.23044	+	0.592549i
$51$	−0.445042	+	1.94986i	−0.0623183	+	0.273034i
$52$	−9.13840	−	11.4592i	−1.26727	−	1.58910i
$53$	5.91398	−	7.41589i	0.812347	−	1.01865i	−0.186994	−	0.982361i	$-0.559875\pi$
$53$	5.91398	−	7.41589i	0.812347	−	1.01865i	0.999341	−	0.0362900i	$-0.0115540\pi$
$54$	−0.222521	−	0.974928i	−0.0302813	−	0.132671i
$55$	0.0921712	−	0.403828i	0.0124284	−	0.0544522i
$56$	−7.78445	+	9.76139i	−1.04024	+	1.30442i
$57$	14.4853			1.91862
$58$		0			0
$59$	−3.65685			−0.476082			−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685			−0.476082			−0.238041	+	0.971255i	$0.576505\pi$
$60$	5.76269	−	7.22619i	0.743960	−	0.932897i
$61$	−1.07443	+	4.70737i	−0.137566	+	0.602717i	0.858400	+	0.512982i	$0.171459\pi$
$61$	−1.07443	+	4.70737i	−0.137566	+	0.602717i	−0.995966	+	0.0897350i	$0.971398\pi$
$62$	5.41031	+	23.7041i	0.687110	+	3.01043i
$63$	−4.98792	+	6.25465i	−0.628419	+	0.788012i
$64$	−6.12792	−	7.68417i	−0.765991	−	0.960522i
$65$	−0.851905	+	3.73244i	−0.105666	+	0.462952i
$66$	2.17513	+	1.04749i	0.267740	+	0.128937i
$67$	−5.09665	−	2.45442i	−0.622655	−	0.299855i	0.0958296	−	0.995398i	$-0.469450\pi$
$67$	−5.09665	−	2.45442i	−0.622655	−	0.299855i	−0.718484	+	0.695543i	$0.755164\pi$
$68$	0.705741	+	3.09205i	0.0855837	+	0.374967i
$69$	7.95414	−	3.83051i	0.957566	−	0.461139i
$70$	6.82843			0.816153
$71$	7.95414	−	3.83051i	0.943983	−	0.454598i	0.102410	−	0.994742i	$-0.467345\pi$
$71$	7.95414	−	3.83051i	0.943983	−	0.454598i	0.841572	+	0.540144i	$0.181630\pi$
$72$	7.78445	+	9.76139i	0.917406	+	1.15039i
$73$	−2.49396	−	3.12733i	−0.291896	−	0.366026i	0.614162	−	0.789180i	$-0.289494\pi$
$73$	−2.49396	−	3.12733i	−0.291896	−	0.366026i	−0.906058	+	0.423154i	$0.860923\pi$
$74$	−8.70053	+	4.18995i	−1.01142	+	0.487072i
$75$	9.65685			1.11508
$76$	20.6958	−	9.96655i	2.37397	−	1.14324i
$77$	0.260699	+	1.14220i	0.0297095	+	0.130166i
$78$	−20.1040	−	9.68156i	−2.27632	−	1.09622i
$79$	−2.17513	−	1.04749i	−0.244721	−	0.117852i	0.307503	−	0.951547i	$-0.400507\pi$
$79$	−2.17513	−	1.04749i	−0.244721	−	0.117852i	−0.552224	+	0.833695i	$0.686221\pi$
$80$	0.667563	−	2.92478i	0.0746358	−	0.327001i
$81$	−5.91398	−	7.41589i	−0.657108	−	0.823988i
$82$	6.75141	−	8.46601i	0.745569	−	0.934914i
$83$	−1.70381	−	7.46488i	−0.187017	−	0.819377i	−0.978178	−	0.207769i	$-0.933380\pi$
$83$	−1.70381	−	7.46488i	−0.187017	−	0.819377i	0.791161	−	0.611609i	$-0.209477\pi$
$84$	−5.81717	+	25.4867i	−0.634706	+	2.78083i
$85$	0.516516	−	0.647690i	0.0560240	−	0.0702519i
$86$	−8.65685			−0.933493
$87$		0			0
$88$	1.82843			0.194911
$89$	7.78445	−	9.76139i	0.825150	−	1.03470i	−0.173605	−	0.984815i	$-0.555542\pi$
$89$	7.78445	−	9.76139i	0.825150	−	1.03470i	0.998755	−	0.0498895i	$-0.0158869\pi$
$90$	1.51947	−	6.65722i	0.160166	−	0.701733i
$91$	−2.40955	−	10.5569i	−0.252590	−	1.10667i
$92$	8.72886	−	10.9456i	0.910046	−	1.14116i
$93$	15.1593	+	19.0092i	1.57195	+	1.97116i
$94$	−1.74199	+	7.63215i	−0.179672	+	0.787196i
$95$	−5.40581	−	2.60330i	−0.554625	−	0.267093i
$96$	−3.44929	−	1.66109i	−0.352042	−	0.169535i
$97$	0.998069	+	4.37283i	0.101339	+	0.443993i	0.999986	+	0.00532129i	$0.00169383\pi$
$97$	0.998069	+	4.37283i	0.101339	+	0.443993i	−0.898647	+	0.438672i	$0.855449\pi$
$98$	−2.17513	+	1.04749i	−0.219721	+	0.105812i
$99$	1.17157			0.117748
$100$	13.7972	−	6.64437i	1.37972	−	0.664437i
$101$	1.46093	+	1.83195i	0.145368	+	0.182285i	0.849185	−	0.528096i	$-0.177094\pi$
$101$	1.46093	+	1.83195i	0.145368	+	0.182285i	−0.703817	+	0.710381i	$0.748522\pi$
$102$	3.01048	+	3.77502i	0.298081	+	0.373782i
$103$	4.35026	−	2.09498i	0.428644	−	0.206424i	−0.207107	−	0.978318i	$-0.566405\pi$
$103$	4.35026	−	2.09498i	0.428644	−	0.206424i	0.635751	+	0.771894i	$0.280691\pi$
$104$	−16.8995			−1.65713
$105$	6.15220	−	2.96274i	0.600393	−	0.289134i
$106$	−5.09562	−	22.3254i	−0.494930	−	2.16843i
$107$	13.3600	+	6.43381i	1.29156	+	0.621980i	0.948334	−	0.317274i	$-0.102768\pi$
$107$	13.3600	+	6.43381i	1.29156	+	0.621980i	0.343221	+	0.939255i	$0.388482\pi$
$108$	−1.42874	−	0.688047i	−0.137481	−	0.0662073i
$109$	−2.81642	+	12.3395i	−0.269764	+	1.18191i	0.640525	+	0.767937i	$0.278717\pi$
$109$	−2.81642	+	12.3395i	−0.269764	+	1.18191i	−0.910289	+	0.413974i	$0.864140\pi$
$110$	−0.623490	−	0.781831i	−0.0594474	−	0.0745447i
$111$	−6.02095	+	7.55003i	−0.571483	+	0.716617i
$112$	1.88815	+	8.27254i	0.178414	+	0.781681i
$113$	−2.96258	+	12.9799i	−0.278696	+	1.22105i	0.620748	+	0.784010i	$0.286829\pi$
$113$	−2.96258	+	12.9799i	−0.278696	+	1.22105i	−0.899444	+	0.437037i	$0.856028\pi$
$114$	21.8038	−	27.3411i	2.04211	−	2.56073i
$115$	−3.65685			−0.341003
$116$		0			0
$117$	−10.8284			−1.00109
$118$	−5.50443	+	6.90234i	−0.506724	+	0.635412i
$119$	−0.521399	+	2.28440i	−0.0477966	+	0.209410i
$120$	−2.37137	−	10.3897i	−0.216476	−	0.948442i
$121$	−6.75141	+	8.46601i	−0.613765	+	0.769637i
$122$	7.26793	+	9.11370i	0.658007	+	0.825115i
$123$	2.40955	−	10.5569i	0.217262	−	0.951887i
$124$	34.7381	+	16.7290i	3.11957	+	1.50231i
$125$	−8.10872	−	3.90495i	−0.725266	−	0.349270i
$126$	4.29770	+	18.8295i	0.382870	+	1.67746i
$127$	−3.91304	+	1.88442i	−0.347226	+	0.167215i	−0.599365	−	0.800476i	$-0.704580\pi$
$127$	−3.91304	+	1.88442i	−0.347226	+	0.167215i	0.252139	+	0.967691i	$0.418866\pi$
$128$	−20.5563			−1.81694
$129$	−7.79956	+	3.75607i	−0.686713	+	0.330703i
$130$	5.76269	+	7.22619i	0.505422	+	0.633779i
$131$	−13.2889	−	16.6637i	−1.16105	−	1.45592i	−0.865724	−	0.500522i	$-0.833142\pi$
$131$	−13.2889	−	16.6637i	−1.16105	−	1.45592i	−0.295331	−	0.955395i	$-0.595430\pi$
$132$	3.44929	−	1.66109i	0.300222	−	0.144580i
$133$	16.9706			1.47153
$134$	−12.3044	+	5.92549i	−1.06294	+	0.511884i
$135$	0.0921712	+	0.403828i	0.00793283	+	0.0347560i
$136$	3.29471	+	1.58665i	0.282519	+	0.136054i
$137$	10.8116	+	5.20660i	0.923700	+	0.444830i	0.834391	−	0.551174i	$-0.185820\pi$
$137$	10.8116	+	5.20660i	0.923700	+	0.444830i	0.0893090	+	0.996004i	$0.471534\pi$
$138$	4.74275	−	20.7793i	0.403729	−	1.76885i
$139$	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	$0.583368\pi$
$140$	6.75141	−	8.46601i	0.570599	−	0.715508i
$141$	1.74199	+	7.63215i	0.146702	+	0.642743i
$142$	4.74275	−	20.7793i	0.398002	−	1.74376i
$143$	−0.988722	+	1.23982i	−0.0826811	+	0.103679i
$144$	8.48528			0.707107
$145$		0			0
$146$	−9.65685			−0.799207
$147$	−1.50524	+	1.88751i	−0.124150	+	0.155679i
$148$	−3.40762	+	14.9298i	−0.280105	+	1.22722i
$149$	1.74199	+	7.63215i	0.142709	+	0.625250i	0.994799	+	0.101855i	$0.0324778\pi$
$149$	1.74199	+	7.63215i	0.142709	+	0.625250i	−0.852090	+	0.523395i	$0.824665\pi$
$150$	14.5359	−	18.2274i	1.18685	−	1.48826i
$151$	−8.81748	−	11.0568i	−0.717556	−	0.899787i	0.280641	−	0.959813i	$-0.409453\pi$
$151$	−8.81748	−	11.0568i	−0.717556	−	0.899787i	−0.998197	+	0.0600260i	$0.980882\pi$
$152$	5.89353	−	25.8212i	0.478028	−	2.09438i
$153$	2.11110	+	1.01665i	0.170672	+	0.0821915i
$154$	2.54832	+	1.22721i	0.205350	+	0.0988913i
$155$	−2.24102	−	9.81857i	−0.180003	−	0.788646i
$156$	−31.8806	+	15.3529i	−2.55249	+	1.22921i
$157$	−8.48528			−0.677199			−0.338600	−	0.940931i	$-0.609953\pi$
$157$	−8.48528			−0.677199			−0.338600	+	0.940931i	$0.609953\pi$
$158$	−5.25123	+	2.52886i	−0.417766	+	0.201185i
$159$	−14.2776	−	17.9035i	−1.13229	−	1.41984i
$160$	0.988722	+	1.23982i	0.0781653	+	0.0980162i
$161$	9.31885	−	4.48772i	0.734428	−	0.353682i
$162$	−22.8995			−1.79915
$163$	3.53985	−	1.70470i	0.277262	−	0.133522i	−0.290086	−	0.957001i	$-0.593684\pi$
$163$	3.53985	−	1.70470i	0.277262	−	0.133522i	0.567348	+	0.823478i	$0.307970\pi$
$164$	−3.82103	−	16.7410i	−0.298373	−	1.30726i
$165$	−0.900969	−	0.433884i	−0.0701403	−	0.0337778i
$166$	−16.6547	−	8.02046i	−1.29265	−	0.622509i
$167$	0.705741	−	3.09205i	0.0546119	−	0.239270i	−0.940254	−	0.340474i	$-0.889412\pi$
$167$	0.705741	−	3.09205i	0.0546119	−	0.239270i	0.994866	+	0.101204i	$0.0322695\pi$
$168$	18.7933	+	23.5661i	1.44994	+	1.81816i
$169$	1.03303	−	1.29538i	0.0794640	−	0.0996447i
$170$	−0.445042	−	1.94986i	−0.0341332	−	0.149547i
$171$	3.77631	−	16.5451i	0.288781	−	1.26523i
$172$	−8.55922	+	10.7329i	−0.652634	+	0.818378i
$173$	12.3431			0.938432			0.469216	−	0.883083i	$-0.344537\pi$
$173$	12.3431			0.938432			0.469216	+	0.883083i	$0.344537\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$	0.774774	−	0.971536i	0.0584008	−	0.0732323i
$177$	−1.96451	+	8.60708i	−0.147662	+	0.646948i
$178$	−6.70726	−	29.3864i	−0.502730	−	2.20260i
$179$	−4.04351	+	5.07040i	−0.302226	+	0.378979i	−0.909634	−	0.415411i	$-0.863638\pi$
$179$	−4.04351	+	5.07040i	−0.302226	+	0.378979i	0.607408	+	0.794390i	$0.292209\pi$
$180$	−6.75141	−	8.46601i	−0.503221	−	0.631019i
$181$	−1.84997	+	8.10527i	−0.137507	+	0.602460i	0.858471	+	0.512863i	$0.171415\pi$
$181$	−1.84997	+	8.10527i	−0.137507	+	0.602460i	−0.995978	+	0.0895969i	$0.971442\pi$
$182$	−23.5533	−	11.3426i	−1.74588	−	0.840773i
$183$	10.5025	+	5.05772i	0.776364	+	0.373877i
$184$	−3.59196	−	15.7374i	−0.264803	−	1.16018i
$185$	3.60388	−	1.73553i	0.264962	−	0.127599i
$186$	58.6985			4.30398
$187$	0.309164	−	0.148885i	0.0226083	−	0.0108876i
$188$	7.74014	+	9.70582i	0.564507	+	0.707870i
$189$	−0.730464	−	0.915973i	−0.0531334	−	0.0666272i
$190$	−13.0508	+	6.28493i	−0.946804	+	0.455957i
$191$	−25.3137			−1.83164			−0.915818	−	0.401594i	$-0.868456\pi$
$191$	−25.3137			−1.83164			−0.915818	+	0.401594i	$0.868456\pi$
$192$	−21.3781	+	10.2952i	−1.54283	+	0.742989i
$193$	−1.15078	−	5.04191i	−0.0828352	−	0.362925i	0.916474	−	0.400095i	$-0.131023\pi$
$193$	−1.15078	−	5.04191i	−0.0828352	−	0.362925i	−0.999309	+	0.0371701i	$0.988166\pi$
$194$	9.75608	+	4.69828i	0.700445	+	0.337317i
$195$	8.32733	+	4.01023i	0.596333	+	0.287179i
$196$	−0.851905	+	3.73244i	−0.0608504	+	0.266603i
$197$	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
$199$	0.107985	+	0.473114i	0.00765487	+	0.0335382i	0.978611	−	0.205719i	$-0.0659533\pi$
$199$	0.107985	+	0.473114i	0.00765487	+	0.0335382i	−0.970956	+	0.239257i	$0.923096\pi$
$200$	3.92902	−	17.2142i	0.277824	−	1.21722i
$201$	−8.51491	+	10.6774i	−0.600595	+	0.753123i
$202$	5.65685			0.398015
$203$		0			0
$204$	7.65685			0.536087
$205$	−2.79653	+	3.50673i	−0.195318	+	0.244921i
$206$	2.59389	−	11.3646i	0.180725	−	0.791809i
$207$	−2.30157	−	10.0838i	−0.159970	−	0.700874i
$208$	−7.16096	+	8.97955i	−0.496523	+	0.622620i
$209$	−1.54955	−	1.94307i	−0.107184	−	0.134405i
$210$	3.66832	−	16.0720i	0.253138	−	1.10907i
$211$	−17.4651	−	8.41074i	−1.20235	−	0.579019i	−0.278002	−	0.960580i	$-0.589672\pi$
$211$	−17.4651	−	8.41074i	−1.20235	−	0.579019i	−0.924344	+	0.381561i	$0.875387\pi$
$212$	−32.7175	−	15.7559i	−2.24705	−	1.08212i
$213$	−4.74275	−	20.7793i	−0.324968	−	1.42378i
$214$	32.2538	−	15.5326i	2.20482	−	1.06179i
$215$	3.58579			0.244549
$216$	−1.64736	+	0.793325i	−0.112088	+	0.0539789i
$217$	17.7603	+	22.2707i	1.20565	+	1.51183i
$218$	19.0516	+	23.8899i	1.29034	+	1.61803i
$219$	−8.70053	+	4.18995i	−0.587927	+	0.283131i
$220$	−1.58579			−0.106914
$221$	−2.85749	+	1.37609i	−0.192215	+	0.0925661i
$222$	5.18779	+	22.7292i	0.348182	+	1.52548i
$223$	2.85749	+	1.37609i	0.191352	+	0.0921501i	0.527106	−	0.849799i	$-0.323277\pi$
$223$	2.85749	+	1.37609i	0.191352	+	0.0921501i	−0.335755	+	0.941949i	$0.608991\pi$
$224$	−4.04110	−	1.94609i	−0.270007	−	0.130029i
$225$	2.51754	−	11.0301i	0.167836	−	0.735337i
$226$	20.0403	+	25.1297i	1.33306	+	1.67161i
$227$	−5.07654	+	6.36578i	−0.336942	+	0.422512i	−0.921220	−	0.389042i	$-0.872806\pi$
$227$	−5.07654	+	6.36578i	−0.336942	+	0.422512i	0.584278	+	0.811553i	$0.301378\pi$
$228$	−12.3401	−	54.0655i	−0.817242	−	3.58057i
$229$	−0.782098	+	3.42660i	−0.0516825	+	0.226436i	−0.994173	−	0.107797i	$-0.965620\pi$
$229$	−0.782098	+	3.42660i	−0.0516825	+	0.226436i	0.942490	+	0.334233i	$0.108477\pi$
$230$	−5.50443	+	6.90234i	−0.362952	+	0.455127i
$231$	2.82843			0.186097
$232$		0			0
$233$	18.3137			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$234$	−16.2994	+	20.4387i	−1.06552	+	1.33612i
$235$	0.721555	−	3.16134i	0.0470691	−	0.206223i
$236$	3.11529	+	13.6490i	0.202788	+	0.888474i
$237$	−3.63396	+	4.55685i	−0.236051	+	0.295999i
$238$	3.52699	+	4.42271i	0.228621	+	0.286681i
$239$	4.37406	−	19.1640i	0.282935	−	1.23962i	−0.611076	−	0.791572i	$-0.709263\pi$
$239$	4.37406	−	19.1640i	0.282935	−	1.23962i	0.894011	−	0.448045i	$-0.147880\pi$
$240$	−6.52539	−	3.14246i	−0.421212	−	0.202845i
$241$	16.5001	+	7.94602i	1.06286	+	0.511848i	0.881800	−	0.471623i	$-0.156332\pi$
$241$	16.5001	+	7.94602i	1.06286	+	0.511848i	0.181064	+	0.983471i	$0.442046\pi$
$242$	5.81717	+	25.4867i	0.373942	+	1.63835i
$243$	−19.5122	+	9.39656i	−1.25171	+	0.602789i
$244$	18.4853			1.18340
$245$	0.900969	−	0.433884i	0.0575608	−	0.0277198i
$246$	−16.2994	−	20.4387i	−1.03921	−	1.30313i
$247$	14.3219	+	17.9591i	0.911281	+	1.14271i
$248$	40.0533	−	19.2887i	2.54339	−	1.22483i
$249$	−18.4853			−1.17146
$250$	−19.5762	+	9.42739i	−1.23811	+	0.596241i
$251$	4.46623	+	19.5678i	0.281906	+	1.23511i	0.895346	+	0.445370i	$0.146928\pi$
$251$	4.46623	+	19.5678i	0.281906	+	1.23511i	−0.613440	+	0.789741i	$0.710215\pi$
$252$	27.5943	+	13.2887i	1.73828	+	0.837112i
$253$	−1.36471	−	0.657212i	−0.0857989	−	0.0413186i
$254$	−2.33319	+	10.2224i	−0.146398	+	0.641410i
$255$	−1.24698	−	1.56366i	−0.0780889	−	0.0979204i
$256$	−18.6863	+	23.4319i	−1.16790	+	1.46450i
$257$	4.04356	+	17.7160i	0.252230	+	1.10509i	0.929344	+	0.369214i	$0.120373\pi$
$257$	4.04356	+	17.7160i	0.252230	+	1.10509i	−0.677114	+	0.735878i	$0.736770\pi$
$258$	−4.65058	+	20.3755i	−0.289532	+	1.26852i
$259$	−7.05398	+	8.84541i	−0.438313	+	0.549627i
$260$	14.6569			0.908980
$261$		0			0
$262$	−51.4558			−3.17895
$263$	−1.71919	+	2.15579i	−0.106010	+	0.132932i	−0.832006	−	0.554767i	$-0.812807\pi$
$263$	−1.71919	+	2.15579i	−0.106010	+	0.132932i	0.725996	+	0.687699i	$0.241379\pi$
$264$	0.982255	−	4.30354i	0.0604536	−	0.264865i
$265$	2.11067	+	9.24747i	0.129658	+	0.568067i
$266$	25.5447	−	32.0321i	1.56625	−	1.96401i
$267$	−18.7933	−	23.5661i	−1.15013	−	1.44222i
$268$	−4.81910	+	21.1139i	−0.294374	+	1.28973i
$269$	28.3407	+	13.6482i	1.72797	+	0.832144i	0.987024	+	0.160575i	$0.0513347\pi$
$269$	28.3407	+	13.6482i	1.72797	+	0.832144i	0.740941	+	0.671570i	$0.234380\pi$
$270$	0.900969	+	0.433884i	0.0548312	+	0.0264053i
$271$	3.68413	+	16.1412i	0.223795	+	0.980511i	0.954592	+	0.297916i	$0.0962915\pi$
$271$	3.68413	+	16.1412i	0.223795	+	0.980511i	−0.730797	+	0.682595i	$0.760851\pi$
$272$	2.23916	−	1.07832i	0.135769	−	0.0653829i
$273$	−26.1421			−1.58219
$274$	26.1016	−	12.5699i	1.57685	−	0.759373i
$275$	−1.03303	−	1.29538i	−0.0622942	−	0.0781144i
$276$	−21.0733	−	26.4251i	−1.26847	−	1.59060i
$277$	15.5991	−	7.51214i	0.937260	−	0.451361i	0.0980580	−	0.995181i	$-0.468737\pi$
$277$	15.5991	−	7.51214i	0.937260	−	0.451361i	0.839202	+	0.543820i	$0.183023\pi$
$278$	33.7990			2.02713
$279$	25.6644	−	12.3593i	1.53648	−	0.739932i
$280$	−2.77824	−	12.1722i	−0.166031	−	0.727431i
$281$	−28.8045	−	13.8715i	−1.71833	−	0.827505i	−0.989795	−	0.142497i	$-0.954487\pi$
$281$	−28.8045	−	13.8715i	−1.71833	−	0.827505i	−0.728536	−	0.685007i	$-0.759799\pi$
$282$	17.0279	+	8.20018i	1.01399	+	0.488314i
$283$	−2.59389	+	11.3646i	−0.154191	+	0.675555i	0.837449	+	0.546516i	$0.184046\pi$
$283$	−2.59389	+	11.3646i	−0.154191	+	0.675555i	−0.991640	+	0.129039i	$0.958811\pi$
$284$	−21.0733	−	26.4251i	−1.25047	−	1.56804i
$285$	−9.03143	+	11.3250i	−0.534975	+	0.670838i
$286$	0.851905	+	3.73244i	0.0503742	+	0.220704i
$287$	2.82297	−	12.3682i	0.166634	−	0.730073i
$288$	−2.79653	+	3.50673i	−0.164787	+	0.206636i
$289$	−16.3137			−0.959630
$290$		0			0
$291$	10.8284			0.634774
$292$	−9.54794	+	11.9727i	−0.558751	+	0.700652i
$293$	1.70381	−	7.46488i	0.0995377	−	0.436103i	−0.900462	−	0.434935i	$-0.856771\pi$
$293$	1.70381	−	7.46488i	0.0995377	−	0.436103i	0.999999	−	0.00116759i	$-0.000371656\pi$
$294$	1.29695	+	5.68230i	0.0756395	+	0.331398i
$295$	2.28001	−	2.85904i	0.132747	−	0.166460i
$296$	11.0089	+	13.8047i	0.639877	+	0.802381i
$297$	−0.0381786	+	0.167271i	−0.00221534	+	0.00970606i
$298$	17.0279	+	8.20018i	0.986397	+	0.475024i
$299$	12.6136	+	6.07437i	0.729461	+	0.351290i
$300$	−8.22672	−	36.0436i	−0.474970	−	2.08098i
$301$	−9.13775	+	4.40051i	−0.526691	+	0.253641i
$302$	−34.1421			−1.96466
$303$	5.09665	−	2.45442i	0.292795	−	0.141003i
$304$	−11.2228	−	14.0730i	−0.643673	−	0.807140i
$305$	−3.01048	−	3.77502i	−0.172379	−	0.216157i
$306$	5.09665	−	2.45442i	0.291356	−	0.140310i
$307$	−2.89949			−0.165483			−0.0827415	−	0.996571i	$-0.526368\pi$
$307$	−2.89949			−0.165483			−0.0827415	+	0.996571i	$0.526368\pi$
$308$	4.04110	−	1.94609i	0.230263	−	0.110889i
$309$	−2.59389	−	11.3646i	−0.147561	−	0.646509i
$310$	−21.9059	−	10.5493i	−1.24417	−	0.599161i
$311$	2.42027	+	1.16554i	0.137241	+	0.0660916i	0.501244	−	0.865306i	$-0.332876\pi$
$311$	2.42027	+	1.16554i	0.137241	+	0.0660916i	−0.364003	+	0.931398i	$0.618590\pi$
$312$	−9.07863	+	39.7761i	−0.513976	+	2.25188i
$313$	6.12792	+	7.68417i	0.346371	+	0.434335i	0.924250	−	0.381787i	$-0.124691\pi$
$313$	6.12792	+	7.68417i	0.346371	+	0.434335i	−0.577880	+	0.816122i	$0.696120\pi$
$314$	−12.7724	+	16.0160i	−0.720786	+	0.903837i
$315$	−1.78017	−	7.79942i	−0.100301	−	0.439448i
$316$	−2.05668	+	9.01091i	−0.115697	+	0.506903i
$317$	19.6124	−	24.5932i	1.10154	−	1.38129i	0.184342	−	0.982862i	$-0.440984\pi$
$317$	19.6124	−	24.5932i	1.10154	−	1.38129i	0.917200	−	0.398428i	$-0.130444\pi$
$318$	−55.2843			−3.10019
$319$		0			0
$320$	9.82843			0.549426
$321$	22.3203	−	27.9888i	1.24580	−	1.56218i
$322$	5.55647	−	24.3445i	0.309650	−	1.35667i
$323$	−1.10605	−	4.84594i	−0.0615425	−	0.269635i
$324$	−22.6412	+	28.3912i	−1.25785	+	1.57729i
$325$	9.54794	+	11.9727i	0.529624	+	0.664128i
$326$	2.11067	−	9.24747i	0.116899	−	0.512170i
$327$	27.5303	+	13.2579i	1.52243	+	0.733164i
$328$	−17.8383	−	8.59046i	−0.984954	−	0.474329i
$329$	2.04087	+	8.94162i	0.112517	+	0.492968i
$330$	−2.17513	+	1.04749i	−0.119737	+	0.0576623i
$331$	2.41421			0.132697			0.0663486	−	0.997797i	$-0.478865\pi$
$331$	2.41421			0.132697			0.0663486	+	0.997797i	$0.478865\pi$
$332$	−26.4107	+	12.7187i	−1.44948	+	0.698032i
$333$	7.05398	+	8.84541i	0.386556	+	0.484726i
$334$	−4.77397	−	5.98637i	−0.261220	−	0.327560i
$335$	5.09665	−	2.45442i	0.278460	−	0.134099i
$336$	20.4853			1.11756
$337$	19.6402	−	9.45823i	1.06987	−	0.515222i	0.185806	−	0.982587i	$-0.440511\pi$
$337$	19.6402	−	9.45823i	1.06987	−	0.515222i	0.884065	+	0.467364i	$0.154796\pi$
$338$	−0.890084	−	3.89971i	−0.0484142	−	0.212116i
$339$	28.9591	+	13.9459i	1.57284	+	0.757440i
$340$	−2.85749	−	1.37609i	−0.154969	−	0.0746292i
$341$	0.928262	−	4.06698i	0.0502682	−	0.220239i
$342$	−25.5447	−	32.0321i	−1.38130	−	1.73210i
$343$	10.5810	−	13.2681i	0.571319	−	0.716411i
$344$	3.52216	+	15.4316i	0.189902	+	0.832015i
$345$	−1.96451	+	8.60708i	−0.105766	+	0.463390i
$346$	18.5794	−	23.2978i	0.998833	−	1.25250i
$347$	2.48528			0.133417			0.0667084	−	0.997773i	$-0.478750\pi$
$347$	2.48528			0.133417			0.0667084	+	0.997773i	$0.478750\pi$
$348$		0			0
$349$	−5.14214			−0.275252			−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214			−0.275252			−0.137626	+	0.990484i	$0.543947\pi$
$350$	17.0298	−	21.3547i	0.910282	−	1.14146i
$351$	0.352871	−	1.54603i	0.0188348	−	0.0825208i
$352$	0.146164	+	0.640386i	0.00779056	+	0.0341327i
$353$	16.8159	−	21.0864i	0.895018	−	1.12232i	−0.0968814	−	0.995296i	$-0.530887\pi$
$353$	16.8159	−	21.0864i	0.895018	−	1.12232i	0.991900	−	0.127022i	$-0.0405418\pi$
$354$	13.2889	+	16.6637i	0.706296	+	0.885667i
$355$	−1.96451	+	8.60708i	−0.104265	+	0.456816i
$356$	−43.0654	−	20.7392i	−2.28246	−	1.09918i
$357$	5.09665	+	2.45442i	0.269743	+	0.129902i
$358$	3.48398	+	15.2643i	0.184134	+	0.806744i
$359$	3.53985	−	1.70470i	0.186826	−	0.0899706i	−0.338132	−	0.941099i	$-0.609795\pi$
$359$	3.53985	−	1.70470i	0.186826	−	0.0899706i	0.524958	+	0.851128i	$0.324081\pi$
$360$	−12.4853			−0.658032
$361$	−15.3165	+	7.37602i	−0.806130	+	0.388212i
$362$	12.5141	+	15.6922i	0.657727	+	0.824763i
$363$	16.2994	+	20.4387i	0.855494	+	1.07276i
$364$	−37.3504	+	17.9870i	−1.95769	+	0.942776i
$365$	4.00000			0.209370
$366$	25.3552	−	12.2104i	1.32534	−	0.638249i
$367$	4.00538	+	17.5487i	0.209079	+	0.916035i	0.965181	+	0.261582i	$0.0842440\pi$
$367$	4.00538	+	17.5487i	0.209079	+	0.916035i	−0.756102	+	0.654453i	$0.772899\pi$
$368$	−9.88414	−	4.75995i	−0.515246	−	0.248129i
$369$	−11.4300	−	5.50438i	−0.595020	−	0.286546i
$370$	2.14885	−	9.41474i	0.111714	−	0.489449i
$371$	−16.7273	−	20.9753i	−0.868436	−	1.08898i
$372$	58.0365	−	72.7754i	3.00905	−	3.77323i
$373$	5.85535	+	25.6540i	0.303179	+	1.32831i	0.865299	+	0.501257i	$0.167129\pi$
$373$	5.85535	+	25.6540i	0.303179	+	1.32831i	−0.562120	+	0.827056i	$0.690014\pi$
$374$	0.184342	−	0.807657i	0.00953212	−	0.0417629i
$375$	−13.5471	+	16.9876i	−0.699571	+	0.877235i
$376$	14.3137			0.738173
$377$		0			0
$378$	−2.82843			−0.145479
$379$	4.34607	−	5.44981i	0.223243	−	0.279938i	−0.657579	−	0.753386i	$-0.728419\pi$
$379$	4.34607	−	5.44981i	0.223243	−	0.279938i	0.880822	+	0.473448i	$0.156991\pi$
$380$	−5.11143	+	22.3946i	−0.262211	+	1.14882i
$381$	2.33319	+	10.2224i	0.119533	+	0.523709i
$382$	−38.1031	+	47.7798i	−1.94953	+	2.44463i
$383$	−2.19139	−	2.74792i	−0.111975	−	0.140412i	0.722686	−	0.691177i	$-0.242907\pi$
$383$	−2.19139	−	2.74792i	−0.111975	−	0.140412i	−0.834660	+	0.550765i	$0.814336\pi$
$384$	−11.0431	+	48.3832i	−0.563543	+	2.46904i
$385$	−1.05555	−	0.508326i	−0.0537958	−	0.0259067i
$386$	−11.2488	−	5.41716i	−0.572551	−	0.275726i
$387$	2.25684	+	9.88785i	0.114721	+	0.502628i
$388$	15.4711	−	7.45047i	0.785424	−	0.378240i
$389$	−3.02944			−0.153599			−0.0767993	−	0.997047i	$-0.524470\pi$
$389$	−3.02944			−0.153599			−0.0767993	+	0.997047i	$0.524470\pi$
$390$	20.1040	−	9.68156i	1.01800	−	0.490245i
$391$	−1.88882	−	2.36851i	−0.0955219	−	0.119781i
$392$	2.75222	+	3.45117i	0.139008	+	0.174310i
$393$	−46.3601	+	22.3259i	−2.33856	+	1.12619i
$394$	4.82843			0.243253
$395$	2.17513	−	1.04749i	0.109443	−	0.0527048i
$396$	−0.998069	−	4.37283i	−0.0501549	−	0.219743i
$397$	−17.4276	−	8.39268i	−0.874665	−	0.421216i	−0.0579918	−	0.998317i	$-0.518470\pi$
$397$	−17.4276	−	8.39268i	−0.874665	−	0.421216i	−0.816673	+	0.577101i	$0.804184\pi$
$398$	1.05555	+	0.508326i	0.0529100	+	0.0254801i
$399$	9.11681	−	39.9433i	0.456411	−	1.99967i
$400$	−7.48188	−	9.38198i	−0.374094	−	0.469099i
$401$	−11.6324	+	14.5865i	−0.580892	+	0.728416i	−0.982265	−	0.187499i	$-0.939962\pi$
$401$	−11.6324	+	14.5865i	−0.580892	+	0.728416i	0.401373	+	0.915915i	$0.368533\pi$
$402$	7.33664	+	32.1439i	0.365918	+	1.60319i
$403$	−8.57959	+	37.5897i	−0.427380	+	1.87247i
$404$	5.59305	−	7.01347i	0.278265	−	0.348933i
$405$	9.48528			0.471327
$406$		0			0
$407$	1.65685			0.0821272
$408$	5.50443	−	6.90234i	0.272510	−	0.341717i
$409$	−4.22135	+	18.4949i	−0.208732	+	0.914515i	0.756680	+	0.653786i	$0.226820\pi$
$409$	−4.22135	+	18.4949i	−0.208732	+	0.914515i	−0.965412	+	0.260730i	$0.916037\pi$
$410$	2.40955	+	10.5569i	0.118999	+	0.521370i
$411$	18.0629	−	22.6501i	0.890975	−	1.11725i
$412$	−11.5254	−	14.4524i	−0.567815	−	0.712017i
$413$	−2.30157	+	10.0838i	−0.113253	+	0.496192i
$414$	−22.4977	−	10.8343i	−1.10570	−	0.532478i
$415$	6.89859	+	3.32218i	0.338638	+	0.163080i
$416$	−1.35094	−	5.91885i	−0.0662353	−	0.290196i
$417$	30.4518	−	14.6648i	1.49123	−	0.718140i
$418$	−6.00000			−0.293470
$419$	8.57247	−	4.12828i	0.418792	−	0.201680i	−0.212607	−	0.977138i	$-0.568195\pi$
$419$	8.57247	−	4.12828i	0.418792	−	0.201680i	0.631399	+	0.775458i	$0.282481\pi$
$420$	−16.2994	−	20.4387i	−0.795327	−	0.997309i
$421$	−23.1394	−	29.0159i	−1.12774	−	1.41415i	−0.897500	−	0.441015i	$-0.854619\pi$
$421$	−23.1394	−	29.0159i	−1.12774	−	1.41415i	−0.230245	−	0.973133i	$-0.573953\pi$
$422$	−42.1644	+	20.3053i	−2.05253	+	0.988448i
$423$	9.17157			0.445937
$424$	−37.7236	+	18.1667i	−1.83202	+	0.882255i
$425$	−0.737370	−	3.23063i	−0.0357677	−	0.156708i
$426$	−46.3601	−	22.3259i	−2.24615	−	1.08169i
$427$	12.3044	+	5.92549i	0.595452	+	0.286754i
$428$	12.6324	−	55.3462i	0.610611	−	2.67526i
$429$	2.38699	+	2.99318i	0.115245	+	0.144512i
$430$	5.39746	−	6.76820i	0.260289	−	0.326392i
$431$	−4.37406	−	19.1640i	−0.210691	−	0.923098i	−0.964099	−	0.265544i	$-0.914448\pi$
$431$	−4.37406	−	19.1640i	−0.210691	−	0.923098i	0.753408	−	0.657554i	$-0.228409\pi$
$432$	−0.276514	+	1.21149i	−0.0133038	+	0.0582876i
$433$	−19.0959	+	23.9455i	−0.917690	+	1.15075i	0.0705003	+	0.997512i	$0.477540\pi$
$433$	−19.0959	+	23.9455i	−0.917690	+	1.15075i	−0.988190	+	0.153235i	$0.951031\pi$
$434$	68.7696			3.30104
$435$		0			0
$436$	48.4558			2.32061
$437$	−13.6801	+	17.1543i	−0.654406	+	0.820600i
$438$	−5.18779	+	22.7292i	−0.247882	+	1.08604i
$439$	0.0763571	+	0.334542i	0.00364433	+	0.0159668i	0.976717	−	0.214530i	$-0.0688220\pi$
$439$	0.0763571	+	0.334542i	0.00364433	+	0.0159668i	−0.973073	+	0.230497i	$0.925965\pi$
$440$	−1.14001	+	1.42952i	−0.0543476	+	0.0681498i
$441$	1.76350	+	2.21135i	0.0839760	+	0.105303i
$442$	−1.70381	+	7.46488i	−0.0810420	+	0.355068i
$443$	−21.9324	−	10.5621i	−1.04204	−	0.501820i	−0.167044	−	0.985949i	$-0.553422\pi$
$443$	−21.9324	−	10.5621i	−1.04204	−	0.501820i	−0.874997	+	0.484129i	$0.839136\pi$
$444$	33.3093	+	16.0409i	1.58079	+	0.761269i
$445$	2.77824	+	12.1722i	0.131701	+	0.577020i
$446$	6.89859	−	3.32218i	0.326658	−	0.157310i
$447$	18.8995			0.893915
$448$	−25.0460	+	12.0615i	−1.18331	+	0.569854i
$449$	21.8038	+	27.3411i	1.02898	+	1.29031i	0.956124	+	0.292964i	$0.0946415\pi$
$449$	21.8038	+	27.3411i	1.02898	+	1.29031i	0.0728608	+	0.997342i	$0.476787\pi$
$450$	−17.0298	−	21.3547i	−0.802793	−	1.00667i
$451$	−1.67388	+	0.806097i	−0.0788198	+	0.0379576i
$452$	50.9706			2.39745
$453$	−30.7610	+	14.8137i	−1.44528	+	0.696009i
$454$	4.37406	+	19.1640i	0.205285	+	0.899412i
$455$	9.75608	+	4.69828i	0.457372	+	0.220259i
$456$	−57.6090	−	27.7430i	−2.69779	−	1.29919i
$457$	−0.229071	+	1.00363i	−0.0107155	+	0.0469477i	−0.980003	−	0.198983i	$-0.936236\pi$
$457$	−0.229071	+	1.00363i	−0.0107155	+	0.0469477i	0.969288	+	0.245930i	$0.0790934\pi$
$458$	5.29049	+	6.63406i	0.247208	+	0.309989i
$459$	−0.213948	+	0.268282i	−0.00998623	+	0.0125223i
$460$	3.11529	+	13.6490i	0.145251	+	0.636387i
$461$	3.11529	−	13.6490i	0.145094	−	0.635697i	−0.849113	−	0.528211i	$-0.822863\pi$
$461$	3.11529	−	13.6490i	0.145094	−	0.635697i	0.994207	−	0.107486i	$-0.0342800\pi$
$462$	4.25745	−	5.33868i	0.198075	−	0.248378i
$463$	−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
$465$	−24.3137			−1.12752
$466$	27.5665	−	34.5673i	1.27699	−	1.60130i
$467$	−8.53487	+	37.3937i	−0.394946	+	1.73037i	0.251900	+	0.967753i	$0.418945\pi$
$467$	−8.53487	+	37.3937i	−0.394946	+	1.73037i	−0.646846	+	0.762620i	$0.723913\pi$
$468$	9.22479	+	40.4165i	0.426416	+	1.86825i
$469$	−9.97584	+	12.5093i	−0.460641	+	0.577626i
$470$	−4.88094	−	6.12051i	−0.225141	−	0.282318i
$471$	−4.55840	+	19.9717i	−0.210040	+	0.920246i
$472$	14.5436	+	7.00381i	0.669422	+	0.322376i
$473$	1.33819	+	0.644439i	0.0615301	+	0.0296314i
$474$	3.13111	+	13.7183i	0.143817	+	0.630101i
$475$	−21.6233	+	10.4132i	−0.992143	+	0.477791i
$476$	8.97056			0.411165
$477$	−24.1716	+	11.6404i	−1.10674	+	0.532978i
$478$	−29.5882	−	37.1025i	−1.35333	−	1.69703i
$479$	−4.30176	−	5.39424i	−0.196553	−	0.246469i	0.673782	−	0.738930i	$-0.264669\pi$
$479$	−4.30176	−	5.39424i	−0.196553	−	0.246469i	−0.870334	+	0.492461i	$0.836097\pi$
$480$	3.44929	−	1.66109i	0.157438	−	0.0758181i
$481$	−15.3137			−0.698245
$482$	39.8347	−	19.1834i	1.81442	−	0.873779i
$483$	−5.55647	−	24.3445i	−0.252828	−	1.10771i
$484$	37.3504	+	17.9870i	1.69775	+	0.817592i
$485$	−4.04110	−	1.94609i	−0.183497	−	0.0883674i
$486$	−11.6343	+	50.9734i	−0.527745	+	2.31220i
$487$	−7.17931	−	9.00257i	−0.325326	−	0.407945i	0.592093	−	0.805870i	$-0.298302\pi$
$487$	−7.17931	−	9.00257i	−0.325326	−	0.407945i	−0.917418	+	0.397925i	$0.869731\pi$
$488$	13.2889	−	16.6637i	0.601559	−	0.754332i
$489$	−2.11067	−	9.24747i	−0.0954480	−	0.418185i
$490$	0.537213	−	2.35368i	0.0242688	−	0.106329i
$491$	13.2446	−	16.6082i	0.597719	−	0.749516i	−0.387301	−	0.921953i	$-0.626593\pi$
$491$	13.2446	−	16.6082i	0.597719	−	0.749516i	0.985021	+	0.172437i	$0.0551642\pi$
$492$	−41.4558			−1.86897
$493$		0			0
$494$	55.4558			2.49508
$495$	−0.730464	+	0.915973i	−0.0328319	+	0.0411699i
$496$	6.72307	−	29.4557i	0.301875	−	1.32260i
$497$	−5.55647	−	24.3445i	−0.249242	−	1.09200i
$498$	−27.8247	+	34.8911i	−1.24686	+	1.56351i
$499$	11.8280	+	14.8318i	0.529492	+	0.663962i	0.972594	−	0.232509i	$-0.0746936\pi$
$499$	11.8280	+	14.8318i	0.529492	+	0.663962i	−0.443102	+	0.896471i	$0.646122\pi$
$500$	−7.66715	+	33.5920i	−0.342885	+	1.50228i
$501$	−6.89859	−	3.32218i	−0.308206	−	0.148424i
$502$	43.6572	+	21.0242i	1.94852	+	0.938356i
$503$	0.0605430	+	0.265256i	0.00269948	+	0.0118272i	0.976260	−	0.216603i	$-0.0694978\pi$
$503$	0.0605430	+	0.265256i	0.00269948	+	0.0118272i	−0.973560	+	0.228430i	$0.926641\pi$
$504$	31.8166	−	15.3220i	1.41722	−	0.682498i
$505$	−2.34315			−0.104269
$506$	−3.29471	+	1.58665i	−0.146468	+	0.0705352i
$507$	−2.49396	−	3.12733i	−0.110761	−	0.138889i
$508$	10.3670	+	12.9998i	0.459962	+	0.576775i
$509$	9.47343	−	4.56217i	0.419903	−	0.202214i	−0.211988	−	0.977272i	$-0.567994\pi$
$509$	9.47343	−	4.56217i	0.419903	−	0.202214i	0.631890	+	0.775058i	$0.282279\pi$
$510$	−4.82843			−0.213806
$511$	−10.1933	+	4.90883i	−0.450925	+	0.217154i
$512$	6.95214	+	30.4593i	0.307244	+	1.34612i
$513$	2.23916	+	1.07832i	0.0988614	+	0.0476091i
$514$	39.5256	+	19.0345i	1.74340	+	0.839576i
$515$	−1.07443	+	4.70737i	−0.0473449	+	0.207431i
$516$	20.6638	+	25.9116i	0.909672	+	1.14069i
$517$	0.837438	−	1.05011i	0.0368305	−	0.0461839i
$518$	6.07787	+	26.6289i	0.267046	+	1.17001i
$519$	6.63090	−	29.0519i	0.291064	−	1.27524i
$520$	10.5367	−	13.2126i	0.462063	−	0.579409i
$521$	−29.1421			−1.27674			−0.638370	−	0.769730i	$-0.720391\pi$
$521$	−29.1421			−1.27674			−0.638370	+	0.769730i	$0.720391\pi$
$522$		0			0
$523$	4.68629			0.204917			0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629			0.204917			0.102459	+	0.994737i	$0.467329\pi$
$524$	−50.8755	+	63.7959i	−2.22251	+	2.78694i
$525$	6.07787	−	26.6289i	0.265260	−	1.16218i
$526$	1.48129	+	6.48995i	0.0645873	+	0.282975i
$527$	5.20187	−	6.52293i	0.226597	−	0.284143i
$528$	−1.87047	−	2.34549i	−0.0814017	−	0.102075i
$529$	2.14230	−	9.38604i	0.0931436	−	0.408089i
$530$	20.6317	+	9.93572i	0.896185	+	0.431580i
$531$	9.31885	+	4.48772i	0.404404	+	0.194751i
$532$	−14.4573	−	63.3416i	−0.626804	−	2.74621i
$533$	15.4711	−	7.45047i	0.670126	−	0.322716i
$534$	−72.7696			−3.14905
$535$	−13.3600	+	6.43381i	−0.577601	+	0.278158i
$536$	15.5689	+	19.5228i	0.672474	+	0.843255i
$537$	9.76189	+	12.2410i	0.421257	+	0.528239i
$538$	68.4206	−	32.9496i	2.94982	−	1.42056i
$539$	0.414214			0.0178414
$540$	1.42874	−	0.688047i	0.0614834	−	0.0296088i
$541$	−2.30157	−	10.0838i	−0.0989521	−	0.433537i	0.901048	−	0.433720i	$-0.142799\pi$
$541$	−2.30157	−	10.0838i	−0.0989521	−	0.433537i	−1.00000		0.000182215i	$0.999942\pi$
$542$	36.0122	+	17.3426i	1.54686	+	0.744927i
$543$	18.0834	+	8.70851i	0.776033	+	0.373718i
$544$	−0.292328	+	1.28077i	−0.0125334	+	0.0549126i
$545$	−7.89142	−	9.89553i	−0.338031	−	0.423878i
$546$	−39.3501	+	49.3435i	−1.68403	+	2.11171i
$547$	−7.96602	−	34.9014i	−0.340603	−	1.49228i	−0.797805	−	0.602915i	$-0.794006\pi$
$547$	−7.96602	−	34.9014i	−0.340603	−	1.49228i	0.457203	−	0.889362i	$-0.348851\pi$
$548$	10.2229	−	44.7893i	0.436699	−	1.91330i
$549$	8.51491	−	10.6774i	0.363407	−	0.455699i
$550$	−4.00000			−0.170561
$551$		0			0
$552$	−38.9706			−1.65870
$553$	−4.25745	+	5.33868i	−0.181045	+	0.227024i
$554$	9.30115	−	40.7510i	0.395168	−	1.73134i
$555$	−2.14885	−	9.41474i	−0.0912137	−	0.399633i
$556$	33.4178	−	41.9046i	1.41723	−	1.77715i
$557$	−10.7949	−	13.5364i	−0.457395	−	0.573556i	0.498639	−	0.866810i	$-0.333833\pi$
$557$	−10.7949	−	13.5364i	−0.457395	−	0.573556i	−0.956035	+	0.293254i	$0.905262\pi$
$558$	15.3027	−	67.0454i	0.647813	−	2.83826i
$559$	−12.3684	−	5.95632i	−0.523129	−	0.251926i
$560$	−7.64497	−	3.68163i	−0.323059	−	0.155577i
$561$	−0.184342	−	0.807657i	−0.00778294	−	0.0340993i
$562$	−69.5402	+	33.4888i	−2.93338	+	1.41264i
$563$	0.757359			0.0319189			0.0159594	−	0.999873i	$-0.494920\pi$
$563$	0.757359			0.0319189			0.0159594	+	0.999873i	$0.494920\pi$
$564$	27.0025	−	13.0037i	1.13701	−	0.547556i
$565$	−8.30096	−	10.4091i	−0.349224	−	0.437913i
$566$	17.5463	+	22.0024i	0.737527	+	0.924830i
$567$	−24.1716	+	11.6404i	−1.01511	+	0.488852i
$568$	−38.9706			−1.63517
$569$	−35.7296	+	17.2065i	−1.49786	+	0.721333i	−0.990126	−	0.140180i	$-0.955232\pi$
$569$	−35.7296	+	17.2065i	−1.49786	+	0.721333i	−0.507736	+	0.861513i	$0.669518\pi$
$570$	7.78168	+	34.0938i	0.325939	+	1.42803i
$571$	−13.1788	−	6.34660i	−0.551518	−	0.265597i	0.137303	−	0.990529i	$-0.456157\pi$
$571$	−13.1788	−	6.34660i	−0.551518	−	0.265597i	−0.688820	+	0.724932i	$0.741871\pi$
$572$	5.46984	+	2.63414i	0.228706	+	0.110139i
$573$	−13.5989	+	59.5805i	−0.568100	+	2.48901i
$574$	−19.0959	−	23.9455i	−0.797047	−	0.999465i
$575$	−9.12005	+	11.4362i	−0.380332	+	0.476921i
$576$	6.18586	+	27.1020i	0.257744	+	1.12925i
$577$	−6.63090	+	29.0519i	−0.276048	+	1.20945i	0.626695	+	0.779265i	$0.284407\pi$
$577$	−6.63090	+	29.0519i	−0.276048	+	1.20945i	−0.902743	+	0.430180i	$0.858450\pi$
$578$	−24.5560	+	30.7923i	−1.02140	+	1.28079i
$579$	−12.4853			−0.518871
$580$		0			0
$581$	−21.6569			−0.898478
$582$	16.2994	−	20.4387i	0.675630	−	0.847213i
$583$	−0.874270	+	3.83043i	−0.0362085	+	0.158640i
$584$	3.92902	+	17.2142i	0.162584	+	0.712327i
$585$	6.75141	−	8.46601i	0.279137	−	0.350026i
$586$	−11.5254	−	14.4524i	−0.476109	−	0.597022i
$587$	−1.70381	+	7.46488i	−0.0703238	+	0.308109i	−0.997841	−	0.0656710i	$-0.979081\pi$
$587$	−1.70381	+	7.46488i	−0.0703238	+	0.308109i	0.927518	+	0.373780i	$0.121938\pi$
$588$	8.32733	+	4.01023i	0.343413	+	0.165379i
$589$	−54.4423	−	26.2180i	−2.24326	−	1.08030i
$590$	−1.96451	−	8.60708i	−0.0808776	−	0.354348i
$591$	4.35026	−	2.09498i	0.178946	−	0.0861758i
$592$	12.0000			0.493197
$593$	17.5556	−	8.45435i	0.720923	−	0.347178i	−0.0371837	−	0.999308i	$-0.511839\pi$
$593$	17.5556	−	8.45435i	0.720923	−	0.347178i	0.758107	+	0.652130i	$0.226124\pi$
$594$	0.258258	+	0.323845i	0.0105965	+	0.0132875i
$595$	−1.46093	−	1.83195i	−0.0598922	−	0.0751024i
$596$	27.0025	−	13.0037i	1.10607	−	0.532654i
$597$	1.17157			0.0479493
$598$	30.4518	−	14.6648i	1.24527	−	0.599690i
$599$	2.19629	+	9.62259i	0.0897382	+	0.393169i	0.999772	−	0.0213660i	$-0.00680153\pi$
$599$	2.19629	+	9.62259i	0.0897382	+	0.393169i	−0.910034	+	0.414535i	$0.863944\pi$
$600$	−38.4060	−	18.4953i	−1.56792	−	0.755069i
$601$	−15.4711	−	7.45047i	−0.631077	−	0.303911i	0.0908658	−	0.995863i	$-0.471037\pi$
$601$	−15.4711	−	7.45047i	−0.631077	−	0.303911i	−0.721943	+	0.691952i	$0.756751\pi$
$602$	−5.44849	+	23.8714i	−0.222064	+	0.972925i
$603$	9.97584	+	12.5093i	0.406247	+	0.509418i
$604$	−33.7571	+	42.3300i	−1.37356	+	1.72238i
$605$	−2.40955	−	10.5569i	−0.0979622	−	0.429200i
$606$	3.03894	−	13.3144i	0.123448	−	0.540862i
$607$	4.81828	−	6.04193i	0.195568	−	0.245234i	−0.674372	−	0.738391i	$-0.735586\pi$
$607$	4.81828	−	6.04193i	0.195568	−	0.245234i	0.869940	+	0.493157i	$0.164157\pi$
$608$	9.51472			0.385873
$609$		0			0
$610$	−11.6569			−0.471972
$611$	−7.74014	+	9.70582i	−0.313132	+	0.392656i
$612$	1.99614	−	8.74565i	0.0806891	−	0.353522i
$613$	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
$615$	6.75141	+	8.46601i	0.272243	+	0.341382i
$616$	1.15078	−	5.04191i	0.0463664	−	0.203144i
$617$	0.618327	+	0.297771i	0.0248929	+	0.0119878i	0.446289	−	0.894889i	$-0.352745\pi$
$617$	0.618327	+	0.297771i	0.0248929	+	0.0119878i	−0.421396	+	0.906877i	$0.638460\pi$
$618$	−25.3552	−	12.2104i	−1.01994	−	0.491175i
$619$	7.47354	+	32.7437i	0.300387	+	1.31608i	0.869545	+	0.493853i	$0.164412\pi$
$619$	7.47354	+	32.7437i	0.300387	+	1.31608i	−0.569158	+	0.822228i	$0.692731\pi$
$620$	−34.7381	+	16.7290i	−1.39511	+	0.671852i
$621$	1.51472			0.0607836
$622$	5.84304	−	2.81386i	0.234284	−	0.112825i
$623$	−22.0177	−	27.6094i	−0.882122	−	1.10615i
$624$	17.2881	+	21.6786i	0.692077	+	0.867837i
$625$	−9.91066	+	4.77272i	−0.396426	+	0.190909i
$626$	23.7279			0.948358
$627$	−5.40581	+	2.60330i	−0.215887	+	0.103966i
$628$	7.22866	+	31.6708i	0.288455	+	1.26380i
$629$	2.98555	+	1.43776i	0.119042	+	0.0573274i
$630$	−17.4011	−	8.37990i	−0.693274	−	0.333863i
$631$	8.19510	−	35.9051i	0.326242	−	1.42936i	−0.499992	−	0.866030i	$-0.666664\pi$
$631$	8.19510	−	35.9051i	0.326242	−	1.42936i	0.826233	−	0.563328i	$-0.190479\pi$
$632$	6.64444	+	8.33186i	0.264302	+	0.331424i
$633$	−29.1787	+	36.5889i	−1.15975	+	1.45428i
$634$	−16.8985	−	74.0371i	−0.671125	−	2.94039i
$635$	0.966441	−	4.23425i	0.0383520	−	0.168031i
$636$	−54.6608	+	68.5424i	−2.16744	+	2.71788i
$637$	−3.82843			−0.151688
$638$		0			0
$639$	−24.9706			−0.987820
$640$	12.8167	−	16.0716i	0.506624	−	0.635286i
$641$	3.96065	−	17.3527i	0.156436	−	0.685392i	−0.834494	−	0.551017i	$-0.814240\pi$
$641$	3.96065	−	17.3527i	0.156436	−	0.685392i	0.990931	−	0.134375i	$-0.0429027\pi$
$642$	−19.2317	−	84.2595i	−0.759014	−	3.32546i
$643$	20.2542	−	25.3980i	0.798749	−	1.00160i	−0.201008	−	0.979590i	$-0.564422\pi$
$643$	20.2542	−	25.3980i	0.798749	−	1.00160i	0.999758	−	0.0220105i	$-0.00700671\pi$
$644$	−24.6889	−	30.9589i	−0.972880	−	1.21995i
$645$	1.92633	−	8.43981i	0.0758492	−	0.332317i
$646$	−10.8116	−	5.20660i	−0.425378	−	0.204851i
$647$	−35.7296	−	17.2065i	−1.40468	−	0.676456i	−0.430571	−	0.902557i	$-0.641688\pi$
$647$	−35.7296	−	17.2065i	−1.40468	−	0.676456i	−0.974104	+	0.226101i	$0.927402\pi$
$648$	9.31696	+	40.8203i	0.366005	+	1.60357i
$649$	1.36471	−	0.657212i	0.0535697	−	0.0257978i
$650$	36.9706			1.45010
$651$	61.9592	−	29.8380i	2.42837	−	1.16944i
$652$	−9.37830	−	11.7600i	−0.367283	−	0.460558i
$653$	18.7933	+	23.5661i	0.735439	+	0.922212i	0.999101	−	0.0424037i	$-0.0135016\pi$
$653$	18.7933	+	23.5661i	0.735439	+	0.922212i	−0.263661	+	0.964615i	$0.584930\pi$
$654$	66.4641	−	32.0074i	2.59895	−	1.25159i
$655$	21.3137			0.832796
$656$	−12.1233	+	5.83827i	−0.473335	+	0.227946i
$657$	2.51754	+	11.0301i	0.0982185	+	0.430323i
$658$	19.9494	+	9.60711i	0.777708	+	0.374524i
$659$	12.9868	+	6.25409i	0.505892	+	0.243625i	0.669380	−	0.742921i	$-0.266560\pi$
$659$	12.9868	+	6.25409i	0.505892	+	0.243625i	−0.163487	+	0.986545i	$0.552274\pi$
$660$	−0.851905	+	3.73244i	−0.0331604	+	0.145285i
$661$	20.7708	+	26.0457i	0.807889	+	1.01306i	0.999501	+	0.0315898i	$0.0100570\pi$
$661$	20.7708	+	26.0457i	0.807889	+	1.01306i	−0.191612	+	0.981471i	$0.561372\pi$
$662$	3.63396	−	4.55685i	0.141238	−	0.177107i
$663$	1.70381	+	7.46488i	0.0661705	+	0.289912i
$664$	−7.52098	+	32.9516i	−0.291871	+	1.27877i
$665$	−10.5810	+	13.2681i	−0.410313	+	0.514516i
$666$	27.3137			1.05838
$667$		0			0
$668$	−12.1421			−0.469793
$669$	4.77397	−	5.98637i	0.184572	−	0.231446i
$670$	3.03894	−	13.3144i	0.117404	−	0.514382i
$671$	−0.445042	−	1.94986i	−0.0171807	−	0.0752733i
$672$	−6.75141	+	8.46601i	−0.260441	+	0.326583i
$673$	−13.4845	−	16.9090i	−0.519788	−	0.651794i	0.450776	−	0.892637i	$-0.351147\pi$
$673$	−13.4845	−	16.9090i	−0.519788	−	0.651794i	−0.970564	+	0.240843i	$0.922576\pi$
$674$	11.7107	−	51.3079i	0.451079	−	1.97631i
$675$	1.49277	+	0.718882i	0.0574569	+	0.0276698i
$676$	−5.71498	−	2.75219i	−0.219807	−	0.105853i
$677$	−4.89546	−	21.4484i	−0.188148	−	0.824330i	−0.977592	−	0.210507i	$-0.932488\pi$
$677$	−4.89546	−	21.4484i	−0.188148	−	0.824330i	0.789444	−	0.613822i	$-0.210369\pi$
$678$	69.9134	−	33.6685i	2.68501	−	1.29303i
$679$	12.6863			0.486855
$680$	−3.29471	+	1.58665i	−0.126346	+	0.0608452i
$681$	12.2558	+	15.3683i	0.469645	+	0.588916i
$682$	−6.27921	−	7.87388i	−0.240443	−	0.301506i
$683$	−18.8938	+	9.09879i	−0.722952	+	0.348155i	−0.758908	−	0.651198i	$-0.774267\pi$
$683$	−18.8938	+	9.09879i	−0.722952	+	0.348155i	0.0359558	+	0.999353i	$0.488552\pi$
$684$	−64.9706			−2.48421
$685$	−10.8116	+	5.20660i	−0.413091	+	0.198934i
$686$	−9.11681	−	39.9433i	−0.348081	−	1.52504i
$687$	7.64497	+	3.68163i	0.291674	+	0.140463i
$688$	9.69205	+	4.66744i	0.369506	+	0.177945i
$689$	8.08056	−	35.4032i	0.307845	−	1.34876i
$690$	13.2889	+	16.6637i	0.505899	+	0.634377i
$691$	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	$-0.151957\pi$
$692$	−10.5152	−	46.0701i	−0.399728	−	1.75132i
$693$	0.737370	−	3.23063i	0.0280104	−	0.122721i
$694$	3.74094	−	4.69099i	0.142004	−	0.178068i
$695$	−14.0000			−0.531050
$696$		0			0
$697$	−3.71573			−0.140743
$698$	−7.74014	+	9.70582i	−0.292968	+	0.367371i
$699$	9.83836	−	43.1047i	0.372121	−	1.63037i
$700$	−9.63821	−	42.2277i	−0.364290	−	1.59606i
$701$	−25.0099	+	31.3614i	−0.944609	+	1.18450i	0.0380862	+	0.999274i	$0.487874\pi$
$701$	−25.0099	+	31.3614i	−0.944609	+	1.18450i	−0.982696	+	0.185228i	$0.940698\pi$
$702$	−2.38699	−	2.99318i	−0.0900910	−	0.112970i
$703$	5.34050	−	23.3983i	0.201421	−	0.882482i
$704$	3.66791	+	1.76637i	0.138239	+	0.0665726i
$705$	−7.05317	−	3.39663i	−0.265638	−	0.127924i
$706$	−14.4889	−	63.4802i	−0.545298	−	2.38911i
$707$	5.97110	−	2.87553i	0.224566	−	0.108145i
$708$	33.7990			1.27024
$709$	−26.2562	+	12.6443i	−0.986071	+	0.474867i	−0.856189	−	0.516663i	$-0.827174\pi$
$709$	−26.2562	+	12.6443i	−0.986071	+	0.474867i	−0.129882	+	0.991529i	$0.541460\pi$
$710$	13.2889	+	16.6637i	0.498723	+	0.625379i
$711$	4.25745	+	5.33868i	0.159667	+	0.200216i
$712$	−49.6548	+	23.9125i	−1.86089	+	0.896159i
$713$	−36.8284			−1.37924
$714$	12.3044	−	5.92549i	0.460481	−	0.221756i
$715$	−0.352871	−	1.54603i	−0.0131966	−	0.0578181i
$716$	22.3696	+	10.7727i	0.835993	+	0.402593i
$717$	−42.7562	−	20.5903i	−1.59676	−	0.768960i
$718$	2.11067	−	9.24747i	0.0787696	−	0.345112i
$719$	−12.5584	−	15.7478i	−0.468350	−	0.587292i	0.490416	−	0.871488i	$-0.336845\pi$
$719$	−12.5584	−	15.7478i	−0.468350	−	0.587292i	−0.958766	+	0.284196i	$0.908273\pi$
$720$	−5.29049	+	6.63406i	−0.197165	+	0.247237i
$721$	−3.03894	−	13.3144i	−0.113176	−	0.495856i
$722$	−9.13262	+	40.0126i	−0.339881	+	1.48912i
$723$	27.5665	−	34.5673i	1.02521	−	1.28557i
$724$	31.8284			1.18289
$725$		0			0
$726$	63.1127			2.34233
$727$	−0.819084	+	1.02710i	−0.0303781	+	0.0380930i	−0.796789	−	0.604258i	$-0.793470\pi$
$727$	−0.819084	+	1.02710i	−0.0303781	+	0.0380930i	0.766410	+	0.642351i	$0.222041\pi$
$728$	−10.6363	+	46.6006i	−0.394207	+	1.72713i
$729$	5.30232	+	23.2310i	0.196382	+	0.860407i
$730$	6.02095	−	7.55003i	0.222845	−	0.279439i
$731$	1.85212	+	2.32248i	0.0685030	+	0.0859000i
$732$	9.93053	−	43.5085i	0.367043	−	1.60812i
$733$	−37.1693	−	17.8998i	−1.37288	−	0.661144i	−0.405411	−	0.914134i	$-0.632872\pi$
$733$	−37.1693	−	17.8998i	−1.37288	−	0.661144i	−0.967469	+	0.252990i	$0.918586\pi$
$734$	39.1524	+	18.8548i	1.44514	+	0.695943i
$735$	−0.537213	−	2.35368i	−0.0198154	−	0.0868169i
$736$	5.22471	−	2.51609i	0.192585	−	0.0927442i
$737$	2.34315			0.0863109
$738$	−27.5943	+	13.2887i	−1.01576	+	0.489165i
$739$	−2.53827	−	3.18289i	−0.0933717	−	0.117084i	0.732951	−	0.680282i	$-0.238143\pi$
$739$	−2.53827	−	3.18289i	−0.0933717	−	0.117084i	−0.826323	+	0.563197i	$0.809571\pi$
$740$	−9.54794	−	11.9727i	−0.350989	−	0.440127i
$741$	49.9640	−	24.0614i	1.83547	−	0.883917i
$742$	−64.7696			−2.37777
$743$	21.3141	−	10.2643i	0.781938	−	0.376562i	6.56698e−5	−	1.00000i	$-0.499979\pi$
$743$	21.3141	−	10.2643i	0.781938	−	0.376562i	0.781872	+	0.623438i	$0.214265\pi$
$744$	−23.8823	−	104.635i	−0.875566	−	3.83611i
$745$	−7.05317	−	3.39663i	−0.258408	−	0.124443i
$746$	57.2358	+	27.5633i	2.09555	+	1.00916i
$747$	−4.81910	+	21.1139i	−0.176322	+	0.772516i
$748$	−0.819084	−	1.02710i	−0.0299487	−	0.0375544i
$749$	26.1499	−	32.7909i	0.955495	−	1.19815i
$750$	11.6725	+	51.1407i	0.426220	+	1.86739i
$751$	5.63283	−	24.6790i	0.205545	−	0.900551i	−0.761945	−	0.647642i	$-0.775755\pi$
$751$	5.63283	−	24.6790i	0.205545	−	0.900551i	0.967490	−	0.252909i	$-0.0813874\pi$
$752$	6.06526	−	7.60560i	0.221177	−	0.277348i
$753$	48.4558			1.76583
$754$		0			0
$755$	14.1421			0.514685
$756$	−2.79653	+	3.50673i	−0.101709	+	0.127539i
$757$	5.67756	−	24.8750i	0.206354	−	0.904098i	−0.760615	−	0.649204i	$-0.775102\pi$
$757$	5.67756	−	24.8750i	0.206354	−	0.904098i	0.966969	−	0.254894i	$-0.0820406\pi$
$758$	−3.74468	−	16.4065i	−0.136013	−	0.595911i
$759$	−2.28001	+	2.85904i	−0.0827592	+	0.103777i
$760$	16.5133	+	20.7070i	0.599000	+	0.751123i
$761$	−10.1465	+	44.4547i	−0.367811	+	1.61148i	0.364971	+	0.931019i	$0.381079\pi$
$761$	−10.1465	+	44.4547i	−0.367811	+	1.61148i	−0.732781	+	0.680464i	$0.761778\pi$
$762$	22.8069	+	10.9832i	0.826205	+	0.397880i
$763$	32.2538	+	15.5326i	1.16767	+	0.562318i
$764$	21.5649	+	94.4819i	0.780190	+	3.41824i
$765$	−2.11110	+	1.01665i	−0.0763270	+	0.0367572i
$766$	−8.48528			−0.306586
$767$	−12.6136	+	6.07437i	−0.455449	+	0.219333i
$768$	45.1128	+	56.5697i	1.62787	+	2.04128i
$769$	30.6213	+	38.3979i	1.10423	+	1.38466i	0.915349	+	0.402662i	$0.131915\pi$
$769$	30.6213	+	38.3979i	1.10423	+	1.38466i	0.188883	+	0.982000i	$0.439513\pi$
$770$	−2.54832	+	1.22721i	−0.0918353	+	0.0442255i
$771$	43.8701			1.57994
$772$	−17.8383	+	8.59046i	−0.642014	+	0.309177i
$773$	−4.34243	−	19.0254i	−0.156186	−	0.684298i	−0.991011	−	0.133781i	$-0.957288\pi$
$773$	−4.34243	−	19.0254i	−0.156186	−	0.684298i	0.834824	−	0.550516i	$-0.185569\pi$
$774$	22.0605	+	10.6238i	0.792947	+	0.381863i
$775$	−36.2949	−	17.4787i	−1.30375	−	0.627853i
$776$	4.40569	−	19.3026i	0.158155	−	0.692923i
$777$	17.0298	+	21.3547i	0.610941	+	0.766096i
$778$	−4.56002	+	5.71809i	−0.163485	+	0.205003i
$779$	5.98841	+	26.2370i	0.214557	+	0.940037i
$780$	7.87385	−	34.4976i	0.281929	−	1.23521i
$781$	−2.28001	+	2.85904i	−0.0815852	+	0.102305i
$782$	−7.31371			−0.261538
$783$		0			0
$784$	3.00000			0.107143
$785$	5.29049	−	6.63406i	0.188826	−	0.236780i
$786$	−27.6428	+	121.111i	−0.985984	+	4.31988i
$787$	12.0347	+	52.7273i	0.428989	+	1.87952i	0.473977	+	0.880537i	$0.342818\pi$
$787$	12.0347	+	52.7273i	0.428989	+	1.87952i	−0.0449881	+	0.998988i	$0.514325\pi$
$788$	4.77397	−	5.98637i	0.170066	−	0.213256i
$789$	4.15048	+	5.20454i	0.147761	+	0.185286i
$790$	1.29695	−	5.68230i	0.0461433	−	0.202167i
$791$	33.9277	+	16.3387i	1.20633	+	0.580937i
$792$	−4.65943	−	2.24386i	−0.165565	−	0.0797321i
$793$	4.11336	+	18.0218i	0.146070	+	0.639973i
$794$	−42.0739	+	20.2617i	−1.49315	+	0.719061i
$795$	22.8995			0.812161
$796$	1.67388	−	0.806097i	0.0593290	−	0.0285714i
$797$	−32.2594	−	40.4521i	−1.14269	−	1.43289i	−0.884346	−	0.466832i	$-0.845395\pi$
$797$	−32.2594	−	40.4521i	−1.14269	−	1.43289i	−0.258342	−	0.966054i	$-0.583176\pi$
$798$	−61.6704	−	77.3323i	−2.18311	−	2.73753i
$799$	2.42027	−	1.16554i	0.0856228	−	0.0412338i
$800$	6.34315			0.224264
$801$	−31.8166	+	15.3220i	−1.12418	+	0.541378i
$802$	10.0227	+	43.9123i	0.353914	+	1.55060i
$803$	1.49277	+	0.718882i	0.0526789	+	0.0253688i
$804$	47.1065	+	22.6853i	1.66132	+	0.800049i
$805$	−2.30157	+	10.0838i	−0.0811196	+	0.355408i
$806$	58.0365	+	72.7754i	2.04425	+	2.56340i
$807$	47.3485	−	59.3732i	1.66675	−	2.09003i
$808$	−2.30157	−	10.0838i	−0.0809688	−	0.354748i
$809$	8.07401	−	35.3745i	0.283867	−	1.24370i	−0.608923	−	0.793230i	$-0.708398\pi$
$809$	8.07401	−	35.3745i	0.283867	−	1.24370i	0.892790	−	0.450473i	$-0.148745\pi$
$810$	14.2776	−	17.9035i	0.501664	−	0.629066i
$811$	10.8284			0.380238			0.190119	−	0.981761i	$-0.439113\pi$
$811$	10.8284			0.380238			0.190119	+	0.981761i	$0.439113\pi$
$812$		0			0
$813$	39.9706			1.40183
$814$	2.49396	−	3.12733i	0.0874132	−	0.109613i
$815$	−0.874270	+	3.83043i	−0.0306243	+	0.134174i
$816$	−1.33513	−	5.84957i	−0.0467387	−	0.204776i
$817$	13.4142	−	16.8209i	0.469304	−	0.588488i
$818$	28.5552	+	35.8071i	0.998409	+	1.25197i
$819$	−6.81524	+	29.8595i	−0.238144	+	1.04338i
$820$	15.4711	+	7.45047i	0.540273	+	0.260182i
$821$	1.33819	+	0.644439i	0.0467032	+	0.0224911i	0.457090	−	0.889421i	$-0.348892\pi$
$821$	1.33819	+	0.644439i	0.0467032	+	0.0224911i	−0.410386	+	0.911912i	$0.634606\pi$
$822$	−15.5634	−	68.1876i	−0.542835	−	2.37831i
$823$	−48.9084	+	23.5531i	−1.70484	+	0.821008i	−0.711916	+	0.702265i	$0.752172\pi$
$823$	−48.9084	+	23.5531i	−1.70484	+	0.821008i	−0.992925	+	0.118744i	$0.962113\pi$
$824$	−21.3137			−0.742498
$825$	−3.60388	+	1.73553i	−0.125471	+	0.0604236i
$826$	15.5689	+	19.5228i	0.541711	+	0.679284i
$827$	−20.5125	−	25.7219i	−0.713289	−	0.894437i	0.284648	−	0.958632i	$-0.408123\pi$
$827$	−20.5125	−	25.7219i	−0.713289	−	0.894437i	−0.997937	+	0.0641954i	$0.979552\pi$
$828$	−35.6765	+	17.1809i	−1.23985	+	0.597078i
$829$	29.7990			1.03496			0.517481	−	0.855695i	$-0.326870\pi$
$829$	29.7990			1.03496			0.517481	+	0.855695i	$0.326870\pi$
$830$	16.6547	−	8.02046i	0.578092	−	0.278394i
$831$	−9.30115	−	40.7510i	−0.322653	−	1.41364i
$832$	−33.9011	−	16.3259i	−1.17531	−	0.566000i
$833$	0.746387	+	0.359441i	0.0258608	+	0.0124539i
$834$	18.1573	−	79.5521i	0.628734	−	2.75467i
$835$	1.97744	+	2.47964i	0.0684322	+	0.0858113i
$836$	−5.93233	+	7.43891i	−0.205174	+	0.257280i
$837$	0.928262	+	4.06698i	0.0320854	+	0.140575i
$838$	5.11143	−	22.3946i	0.176571	−	0.773610i
$839$	4.94361	−	6.19909i	0.170672	−	0.214016i	−0.689138	−	0.724630i	$-0.742010\pi$
$839$	4.94361	−	6.19909i	0.170672	−	0.214016i	0.859810	+	0.510614i	$0.170582\pi$
$840$	−30.1421			−1.04000
$841$		0			0
$842$	−89.5980			−3.08775
$843$	−48.1233	+	60.3447i	−1.65745	+	2.07838i
$844$	−16.5140	+	72.3525i	−0.568435	+	2.49048i
$845$	0.368685	+	1.61531i	0.0126831	+	0.0555685i
$846$	13.8054	−	17.3114i	0.474639	−	0.595179i
$847$	19.0959	+	23.9455i	0.656142	+	0.822776i
$848$	−6.33202	+	27.7424i	−0.217442	+	0.952678i
$849$	25.3552	+	12.2104i	0.870188	+	0.419060i
$850$	−7.20775	−	3.47107i	−0.247224	−	0.119057i
$851$	−3.25491	−	14.2607i	−0.111577	−	0.488850i
$852$	−73.5172	+	35.4040i	−2.51866	+	1.21292i
$853$	22.9706			0.786497			0.393249	−	0.919432i	$-0.371351\pi$
$853$	22.9706			0.786497			0.393249	+	0.919432i	$0.371351\pi$
$854$	29.7055	−	14.3054i	1.01650	−	0.489520i
$855$	10.5810	+	13.2681i	0.361862	+	0.453760i
$856$	−40.8111	−	51.1754i	−1.39489	−	1.74914i
$857$	5.56040	−	2.67775i	0.189939	−	0.0914700i	−0.336497	−	0.941685i	$-0.609242\pi$
$857$	5.56040	−	2.67775i	0.189939	−	0.0914700i	0.526436	+	0.850215i	$0.323528\pi$
$858$	9.24264			0.315539
$859$	17.7742	−	8.55962i	0.606449	−	0.292051i	−0.105348	−	0.994435i	$-0.533596\pi$
$859$	17.7742	−	8.55962i	0.606449	−	0.292051i	0.711797	+	0.702385i	$0.247881\pi$
$860$	−3.05475	−	13.3837i	−0.104166	−	0.456382i
$861$	−27.5943	−	13.2887i	−0.940413	−	0.452879i
$862$	−42.7562	−	20.5903i	−1.45628	−	0.701309i
$863$	−3.80793	+	16.6836i	−0.129624	+	0.567918i	0.867847	+	0.496832i	$0.165504\pi$
$863$	−3.80793	+	16.6836i	−0.129624	+	0.567918i	−0.997470	+	0.0710858i	$0.977354\pi$
$864$	−0.409542	−	0.513549i	−0.0139329	−	0.0174713i
$865$	−7.69583	+	9.65026i	−0.261666	+	0.328119i
$866$	16.4534	+	72.0873i	0.559111	+	2.44963i
$867$	−8.76394	+	38.3973i	−0.297639	+	1.30404i
$868$	67.9939	−	85.2617i	2.30786	−	2.89397i
$869$	1.00000			0.0339227
$870$		0			0
$871$	−21.6569			−0.733815
$872$	34.8344	−	43.6810i	1.17964	−	1.47922i
$873$	2.82297	−	12.3682i	0.0955429	−	0.418601i
$874$	11.7871	+	51.6425i	0.398703	+	1.74683i
$875$	−15.8715	+	19.9022i	−0.536553	+	0.672816i
$876$	23.0508	+	28.9047i	0.778813	+	0.976601i
$877$	8.26490	−	36.2109i	0.279086	−	1.22276i	−0.619866	−	0.784708i	$-0.712813\pi$
$877$	8.26490	−	36.2109i	0.279086	−	1.22276i	0.898952	−	0.438048i	$-0.144330\pi$
$878$	0.746387	+	0.359441i	0.0251893	+	0.0121305i
$879$	−16.6547	−	8.02046i	−0.561748	−	0.270524i
$880$	0.276514	+	1.21149i	0.00932127	+	0.0408392i
$881$	12.6136	−	6.07437i	0.424962	−	0.204651i	−0.209164	−	0.977881i	$-0.567074\pi$
$881$	12.6136	−	6.07437i	0.424962	−	0.204651i	0.634126	+	0.773230i	$0.281360\pi$
$882$	6.82843			0.229925
$883$	−34.6210	+	16.6726i	−1.16509	+	0.561077i	−0.913533	−	0.406765i	$-0.866657\pi$
$883$	−34.6210	+	16.6726i	−1.16509	+	0.561077i	−0.251557	+	0.967843i	$0.580942\pi$
$884$	7.57050	+	9.49310i	0.254623	+	0.319288i
$885$	−5.50443	−	6.90234i	−0.185030	−	0.232020i
$886$	−52.9495	+	25.4992i	−1.77887	+	0.856661i
$887$	−17.1005			−0.574179			−0.287089	−	0.957904i	$-0.592688\pi$
$887$	−17.1005			−0.574179			−0.287089	+	0.957904i	$0.592688\pi$
$888$	38.4060	−	18.4953i	1.28882	−	0.620663i
$889$	2.73351	+	11.9763i	0.0916789	+	0.401672i
$890$	27.1571	+	13.0782i	0.910309	+	0.438382i
$891$	3.53985	+	1.70470i	0.118589	+	0.0571096i
$892$	2.70188	−	11.8377i	0.0904656	−	0.396356i
$893$	−12.1305	−	15.2112i	−0.405932	−	0.509023i
$894$	28.4482	−	35.6730i	0.951451	−	1.19308i
$895$	−1.44311	−	6.32268i	−0.0482379	−	0.211344i
$896$	−12.9378	+	56.6844i	−0.432223	+	1.89369i
$897$	21.0733	−	26.4251i	0.703618	−	0.882309i
$898$	84.4264			2.81735
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−4.89930	+	6.14353i	−0.163219	+	0.204671i
$902$	−0.998069	+	4.37283i	−0.0332321	+	0.145599i
$903$	5.44849	+	23.8714i	0.181314	+	0.794390i
$904$	36.6422	−	45.9479i	1.21870	−	1.52820i
$905$	−5.18351	−	6.49992i	−0.172306	−	0.216065i
$906$	−18.3416	+	80.3598i	−0.609359	+	2.66978i
$907$	20.0774	+	9.66878i	0.666660	+	0.321047i	0.736427	−	0.676517i	$-0.236511\pi$
$907$	20.0774	+	9.66878i	0.666660	+	0.321047i	−0.0697671	+	0.997563i	$0.522226\pi$
$908$	28.0846	+	13.5248i	0.932021	+	0.448838i
$909$	−1.47474	−	6.46125i	−0.0489140	−	0.214306i
$910$	23.5533	−	11.3426i	0.780783	−	0.376005i
$911$	15.4437			0.511671			0.255835	−	0.966720i	$-0.417649\pi$
$911$	15.4437			0.511671			0.255835	+	0.966720i	$0.417649\pi$
$912$	−39.1524	+	18.8548i	−1.29646	+	0.624344i
$913$	1.97744	+	2.47964i	0.0654438	+	0.0820640i
$914$	1.54955	+	1.94307i	0.0512545	+	0.0642711i
$915$	−10.5025	+	5.05772i	−0.347201	+	0.167203i
$916$	13.4558			0.444594
$917$	−54.3143	+	26.1564i	−1.79361	+	0.863759i
$918$	0.184342	+	0.807657i	0.00608421	+	0.0266566i
$919$	−7.33581	−	3.53274i	−0.241986	−	0.116534i	0.308960	−	0.951075i	$-0.400019\pi$
$919$	−7.33581	−	3.53274i	−0.241986	−	0.116534i	−0.550947	+	0.834541i	$0.685733\pi$
$920$	14.5436	+	7.00381i	0.479487	+	0.230909i
$921$	−1.55765	+	6.82450i	−0.0513262	+	0.224875i
$922$	−21.0733	−	26.4251i	−0.694013	−	0.870265i
$923$	21.0733	−	26.4251i	0.693637	−	0.869793i
$924$	−2.40955	−	10.5569i	−0.0792684	−	0.347298i
$925$	3.56033	−	15.5988i	0.117063	−	0.512887i
$926$	−39.1362	+	49.0752i	−1.28609	+	1.61271i
$927$	−13.6569			−0.448550
$928$		0			0
$929$	18.6863			0.613077			0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863			0.613077			0.306539	+	0.951858i	$0.400829\pi$
$930$	−36.5979	+	45.8923i	−1.20009	+	1.50487i
$931$	1.33513	−	5.84957i	0.0437570	−	0.191712i
$932$	−15.6015	−	68.3548i	−0.511046	−	2.23904i
$933$	4.04351	−	5.07040i	0.132378	−	0.165997i
$934$	57.7339	+	72.3960i	1.88911	+	2.36887i
$935$	−0.0763571	+	0.334542i	−0.00249714	+	0.0109407i
$936$	43.0654	+	20.7392i	1.40764	+	0.677882i
$937$	14.9808	+	7.21437i	0.489401	+	0.235683i	0.662275	−	0.749261i	$-0.269591\pi$
$937$	14.9808	+	7.21437i	0.489401	+	0.235683i	−0.172874	+	0.984944i	$0.555305\pi$
$938$	8.59541	+	37.6589i	0.280650	+	1.22961i
$939$	21.3781	−	10.2952i	0.697649	−	0.335970i
$940$	−12.4142			−0.404907
$941$	50.9930	−	24.5569i	1.66232	−	0.800533i	0.663706	−	0.747994i	$-0.268983\pi$
$941$	50.9930	−	24.5569i	1.66232	−	0.800533i	0.998619	−	0.0525400i	$-0.0167317\pi$
$942$	30.8352	+	38.6661i	1.00467	+	1.25981i
$943$	10.2265	+	12.8236i	0.333020	+	0.417594i
$944$	9.88414	−	4.75995i	0.321701	−	0.154923i
$945$	1.17157			0.0381113
$946$	3.23068	−	1.55581i	0.105039	−	0.0505839i
$947$	0.581942	+	2.54965i	0.0189106	+	0.0828526i	0.983503	−	0.180894i	$-0.0578990\pi$
$947$	0.581942	+	2.54965i	0.0189106	+	0.0828526i	−0.964592	+	0.263746i	$0.915042\pi$
$948$	20.1040	+	9.68156i	0.652946	+	0.314442i
$949$	−13.7972	−	6.64437i	−0.447875	−	0.215685i
$950$	−12.8931	+	56.4884i	−0.418308	+	1.83273i
$951$	−47.3485	−	59.3732i	−1.53538	−	1.92531i
$952$	6.44885	−	8.08660i	0.209008	−	0.262088i
$953$	7.92785	+	34.7342i	0.256808	+	1.12515i	0.924641	+	0.380839i	$0.124365\pi$
$953$	7.92785	+	34.7342i	0.256808	+	1.12515i	−0.667833	+	0.744311i	$0.732778\pi$
$954$	−14.4126	+	63.1456i	−0.466625	+	2.04442i
$955$	15.7828	−	19.7911i	0.510721	−	0.640423i
$956$	−75.2548			−2.43392
$957$		0			0
$958$	−16.6569			−0.538159
$959$	21.1619	−	26.5362i	0.683355	−	0.856900i
$960$	5.27996	−	23.1330i	0.170410	−	0.746615i
$961$	−15.6713	−	68.6607i	−0.505527	−	2.21486i
$962$	−23.0508	+	28.9047i	−0.743187	+	0.931927i
$963$	−26.1499	−	32.7909i	−0.842668	−	1.05667i
$964$	15.6015	−	68.3548i	0.502492	−	2.20156i
$965$	4.65943	+	2.24386i	0.149992	+	0.0722325i
$966$	−54.3143	−	26.1564i	−1.74753	−	0.841567i
$967$	−7.84223	−	34.3590i	−0.252189	−	1.10491i	−0.929386	−	0.369110i	$-0.879663\pi$
$967$	−7.84223	−	34.3590i	−0.252189	−	1.10491i	0.677197	−	0.735802i	$-0.263195\pi$
$968$	43.0654	−	20.7392i	1.38417	−	0.666583i
$969$	−12.0000			−0.385496
$970$	−9.75608	+	4.69828i	−0.313249	+	0.150853i
$971$	9.76189	+	12.2410i	0.313274	+	0.392833i	0.913394	−	0.407077i	$-0.133452\pi$
$971$	9.76189	+	12.2410i	0.313274	+	0.392833i	−0.600120	+	0.799910i	$0.704880\pi$
$972$	51.6946	+	64.8230i	1.65810	+	2.07920i
$973$	35.6765	−	17.1809i	1.14374	−	0.550795i
$974$	−27.7990			−0.890737
$975$	33.3093	−	16.0409i	1.06675	−	0.513721i
$976$	−3.22328	−	14.1221i	−0.103175	−	0.452038i
$977$	−32.5895	−	15.6943i	−1.04263	−	0.502104i	−0.167439	−	0.985882i	$-0.553550\pi$
$977$	−32.5895	−	15.6943i	−1.04263	−	0.502104i	−0.875190	+	0.483779i	$0.839264\pi$
$978$	−20.6317	−	9.93572i	−0.659730	−	0.317709i
$979$	−1.15078	+	5.04191i	−0.0367792	+	0.161140i
$980$	−2.38699	−	2.99318i	−0.0762494	−	0.0956138i
$981$	22.3203	−	27.9888i	0.712632	−	0.893613i
$982$	−11.4118	−	49.9985i	−0.364166	−	1.59552i
$983$	−4.86655	+	21.3217i	−0.155219	+	0.680058i	0.836100	+	0.548577i	$0.184830\pi$
$983$	−4.86655	+	21.3217i	−0.155219	+	0.680058i	−0.991319	+	0.131481i	$0.958027\pi$
$984$	−29.8022	+	37.3708i	−0.950059	+	1.19134i
$985$	−2.00000			−0.0637253
$986$		0			0
$987$	22.1421			0.704792
$988$	54.8304	−	68.7551i	1.74439	−	2.18739i
$989$	2.91785	−	12.7839i	0.0927822	−	0.406506i
$990$	0.629384	+	2.75751i	0.0200031	+	0.0876395i
$991$	−7.99839	+	10.0297i	−0.254077	+	0.318603i	−0.892469	−	0.451109i	$-0.851029\pi$
$991$	−7.99839	+	10.0297i	−0.254077	+	0.318603i	0.638392	+	0.769712i	$0.279600\pi$
$992$	9.95748	+	12.4863i	0.316150	+	0.396440i
$993$	1.29695	−	5.68230i	0.0411574	−	0.180322i
$994$	−54.3143	−	26.1564i	−1.72274	−	0.829630i
$995$	−0.437223	−	0.210556i	−0.0138609	−	0.00667506i
$996$	15.7477	+	68.9952i	0.498985	+	2.18620i
$997$	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	$0.209320\pi$
$998$	45.7990			1.44974
$999$	−1.49277	+	0.718882i	−0.0472293	+	0.0227444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.f.574.2		12
29.2	odd	28		841.2.e.k.63.4		24
29.3	odd	28		841.2.e.k.236.4		24
29.4	even	14		841.2.d.j.571.2		12
29.5	even	14		841.2.d.j.778.1		12
29.6	even	14		841.2.d.j.190.2		12
29.7	even	7	inner	841.2.d.f.605.1		12
29.8	odd	28		841.2.e.k.196.4		24
29.9	even	14		841.2.d.j.645.2		12
29.10	odd	28		841.2.e.k.270.1		24
29.11	odd	28		841.2.b.a.840.1		4
29.12	odd	4		841.2.e.k.267.4		24
29.13	even	14		29.2.a.a.1.1	✓	2
29.14	odd	28		841.2.e.k.651.1		24
29.15	odd	28		841.2.e.k.651.4		24
29.16	even	7		841.2.a.d.1.2		2
29.17	odd	4		841.2.e.k.267.1		24
29.18	odd	28		841.2.b.a.840.4		4
29.19	odd	28		841.2.e.k.270.4		24
29.20	even	7	inner	841.2.d.f.645.1		12
29.21	odd	28		841.2.e.k.196.1		24
29.22	even	14		841.2.d.j.605.2		12
29.23	even	7	inner	841.2.d.f.190.1		12
29.24	even	7	inner	841.2.d.f.778.2		12
29.25	even	7	inner	841.2.d.f.571.1		12
29.26	odd	28		841.2.e.k.236.1		24
29.27	odd	28		841.2.e.k.63.1		24
29.28	even	2		841.2.d.j.574.1		12
87.71	odd	14		261.2.a.d.1.2		2
87.74	odd	14		7569.2.a.c.1.1		2
116.71	odd	14		464.2.a.h.1.1		2
145.13	odd	28		725.2.b.b.349.4		4
145.42	odd	28		725.2.b.b.349.1		4
145.129	even	14		725.2.a.b.1.2		2
203.13	odd	14		1421.2.a.j.1.1		2
232.13	even	14		1856.2.a.r.1.1		2
232.187	odd	14		1856.2.a.w.1.2		2
319.274	odd	14		3509.2.a.j.1.2		2
348.71	even	14		4176.2.a.bq.1.2		2
377.129	even	14		4901.2.a.g.1.2		2
435.419	odd	14		6525.2.a.o.1.1		2
493.390	even	14		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.13	even	14
261.2.a.d.1.2		2	87.71	odd	14
464.2.a.h.1.1		2	116.71	odd	14
725.2.a.b.1.2		2	145.129	even	14
725.2.b.b.349.1		4	145.42	odd	28
725.2.b.b.349.4		4	145.13	odd	28
841.2.a.d.1.2		2	29.16	even	7
841.2.b.a.840.1		4	29.11	odd	28
841.2.b.a.840.4		4	29.18	odd	28
841.2.d.f.190.1		12	29.23	even	7	inner
841.2.d.f.571.1		12	29.25	even	7	inner
841.2.d.f.574.2		12	1.1	even	1	trivial
841.2.d.f.605.1		12	29.7	even	7	inner
841.2.d.f.645.1		12	29.20	even	7	inner
841.2.d.f.778.2		12	29.24	even	7	inner
841.2.d.j.190.2		12	29.6	even	14
841.2.d.j.571.2		12	29.4	even	14
841.2.d.j.574.1		12	29.28	even	2
841.2.d.j.605.2		12	29.22	even	14
841.2.d.j.645.2		12	29.9	even	14
841.2.d.j.778.1		12	29.5	even	14
841.2.e.k.63.1		24	29.27	odd	28
841.2.e.k.63.4		24	29.2	odd	28
841.2.e.k.196.1		24	29.21	odd	28
841.2.e.k.196.4		24	29.8	odd	28
841.2.e.k.236.1		24	29.26	odd	28
841.2.e.k.236.4		24	29.3	odd	28
841.2.e.k.267.1		24	29.17	odd	4
841.2.e.k.267.4		24	29.12	odd	4
841.2.e.k.270.1		24	29.10	odd	28
841.2.e.k.270.4		24	29.19	odd	28
841.2.e.k.651.1		24	29.14	odd	28
841.2.e.k.651.4		24	29.15	odd	28
1421.2.a.j.1.1		2	203.13	odd	14
1856.2.a.r.1.1		2	232.13	even	14
1856.2.a.w.1.2		2	232.187	odd	14
3509.2.a.j.1.2		2	319.274	odd	14
4176.2.a.bq.1.2		2	348.71	even	14
4901.2.a.g.1.2		2	377.129	even	14
6525.2.a.o.1.1		2	435.419	odd	14
7569.2.a.c.1.1		2	87.74	odd	14
8381.2.a.e.1.1		2	493.390	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)

\(f(q)\)	\(=\)	\(q+(1.50524 - 1.88751i) q^{2} +(0.537213 - 2.35368i) q^{3} +(-0.851905 - 3.73244i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-3.63396 - 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-3.97707 - 1.91526i) q^{8} +(-2.54832 - 1.22721i) q^{9} +O(q^{10})\)	\(q+(1.50524 - 1.88751i) q^{2} +(0.537213 - 2.35368i) q^{3} +(-0.851905 - 3.73244i) q^{4} +(-0.623490 + 0.781831i) q^{5} +(-3.63396 - 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-3.97707 - 1.91526i) q^{8} +(-2.54832 - 1.22721i) q^{9} +(0.537213 + 2.35368i) q^{10} +(-0.373194 + 0.179721i) q^{11} -9.24264 q^{12} +(3.44929 - 1.66109i) q^{13} +(-4.25745 - 5.33868i) q^{14} +(1.50524 + 1.88751i) q^{15} +(-2.70291 + 1.30165i) q^{16} -0.828427 q^{17} +(-6.15220 + 2.96274i) q^{18} +(1.33513 + 5.84957i) q^{19} +(3.44929 + 1.66109i) q^{20} +(-6.15220 - 2.96274i) q^{21} +(-0.222521 + 0.974928i) q^{22} +(2.28001 + 2.85904i) q^{23} +(-6.64444 + 8.33186i) q^{24} +(0.890084 + 3.89971i) q^{25} +(2.05668 - 9.01091i) q^{26} +(0.258258 - 0.323845i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-6.27921 + 7.87388i) q^{31} +(0.352871 - 1.54603i) q^{32} +(0.222521 + 0.974928i) q^{33} +(-1.24698 + 1.56366i) q^{34} +(1.76350 + 2.21135i) q^{35} +(-2.40955 + 10.5569i) q^{36} +(-3.60388 - 1.73553i) q^{37} +(13.0508 + 6.28493i) q^{38} +(-2.05668 - 9.01091i) q^{39} +(3.97707 - 1.91526i) q^{40} +4.48528 q^{41} +(-14.8527 + 7.15270i) q^{42} +(-2.23570 - 2.80348i) q^{43} +(0.988722 + 1.23982i) q^{44} +(2.54832 - 1.22721i) q^{45} +8.82843 q^{46} +(-2.92152 + 1.40693i) q^{47} +(1.61164 + 7.06105i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(8.70053 + 4.18995i) q^{50} +(-0.445042 + 1.94986i) q^{51} +(-9.13840 - 11.4592i) q^{52} +(5.91398 - 7.41589i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(0.0921712 - 0.403828i) q^{55} +(-7.78445 + 9.76139i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(5.76269 - 7.22619i) q^{60} +(-1.07443 + 4.70737i) q^{61} +(5.41031 + 23.7041i) q^{62} +(-4.98792 + 6.25465i) q^{63} +(-6.12792 - 7.68417i) q^{64} +(-0.851905 + 3.73244i) q^{65} +(2.17513 + 1.04749i) q^{66} +(-5.09665 - 2.45442i) q^{67} +(0.705741 + 3.09205i) q^{68} +(7.95414 - 3.83051i) q^{69} +6.82843 q^{70} +(7.95414 - 3.83051i) q^{71} +(7.78445 + 9.76139i) q^{72} +(-2.49396 - 3.12733i) q^{73} +(-8.70053 + 4.18995i) q^{74} +9.65685 q^{75} +(20.6958 - 9.96655i) q^{76} +(0.260699 + 1.14220i) q^{77} +(-20.1040 - 9.68156i) q^{78} +(-2.17513 - 1.04749i) q^{79} +(0.667563 - 2.92478i) q^{80} +(-5.91398 - 7.41589i) q^{81} +(6.75141 - 8.46601i) q^{82} +(-1.70381 - 7.46488i) q^{83} +(-5.81717 + 25.4867i) q^{84} +(0.516516 - 0.647690i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(7.78445 - 9.76139i) q^{89} +(1.51947 - 6.65722i) q^{90} +(-2.40955 - 10.5569i) q^{91} +(8.72886 - 10.9456i) q^{92} +(15.1593 + 19.0092i) q^{93} +(-1.74199 + 7.63215i) q^{94} +(-5.40581 - 2.60330i) q^{95} +(-3.44929 - 1.66109i) q^{96} +(0.998069 + 4.37283i) q^{97} +(-2.17513 + 1.04749i) q^{98} +1.17157 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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