LMFDB - Embedded newform 25.2.e.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,2,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.199626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Root			$-0.983224 + 0.644389i$ of defining polynomial
Character	$\chi$	$=$	25.19
Dual form			25.2.e.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98322 + 0.644389i) q^{2} +(1.29224 + 1.77862i) q^{3} +(1.89991 - 1.38036i) q^{4} +(-1.22570 - 1.87020i) q^{5} +(-3.70892 - 2.69469i) q^{6} -0.992398i q^{7} +(-0.427051 + 0.587785i) q^{8} +(-0.566541 + 1.74363i) q^{9} +O(q^{10})$	\(q+(-1.98322 + 0.644389i) q^{2} +(1.29224 + 1.77862i) q^{3} +(1.89991 - 1.38036i) q^{4} +(-1.22570 - 1.87020i) q^{5} +(-3.70892 - 2.69469i) q^{6} -0.992398i q^{7} +(-0.427051 + 0.587785i) q^{8} +(-0.566541 + 1.74363i) q^{9} +(3.63597 + 2.91920i) q^{10} +(0.618034 + 1.90211i) q^{11} +(4.91027 + 1.59545i) q^{12} +(-3.20892 - 1.04264i) q^{13} +(0.639490 + 1.96815i) q^{14} +(1.74248 - 4.59680i) q^{15} +(-0.983224 + 3.02605i) q^{16} +(-1.70135 + 2.34171i) q^{17} -3.82309i q^{18} +(-2.09089 - 1.51912i) q^{19} +(-4.91027 - 1.86130i) q^{20} +(1.76510 - 1.28242i) q^{21} +(-2.45140 - 3.37406i) q^{22} +(4.32696 - 1.40591i) q^{23} -1.59730 q^{24} +(-1.99532 + 4.58462i) q^{25} +7.03588 q^{26} +(2.43930 - 0.792578i) q^{27} +(-1.36987 - 1.88546i) q^{28} +(-4.35599 + 3.16481i) q^{29} +(-0.493592 + 10.2393i) q^{30} +(-0.110461 - 0.0802548i) q^{31} -8.08800i q^{32} +(-2.58448 + 3.55723i) q^{33} +(1.86519 - 5.74046i) q^{34} +(-1.85599 + 1.21638i) q^{35} +(1.33047 + 4.09478i) q^{36} +(2.04392 + 0.664110i) q^{37} +(5.12561 + 1.66541i) q^{38} +(-2.29224 - 7.05479i) q^{39} +(1.62271 + 0.0782238i) q^{40} +(2.66780 - 8.21064i) q^{41} +(-2.67421 + 3.68073i) q^{42} +4.64398i q^{43} +(3.79981 + 2.76073i) q^{44} +(3.95536 - 1.07763i) q^{45} +(-7.67537 + 5.57648i) q^{46} +(5.83453 + 8.03054i) q^{47} +(-6.65275 + 2.16161i) q^{48} +6.01515 q^{49} +(1.00289 - 10.3781i) q^{50} -6.36356 q^{51} +(-7.53588 + 2.44856i) q^{52} +(-4.44672 - 6.12038i) q^{53} +(-4.32696 + 3.14372i) q^{54} +(2.79981 - 3.48727i) q^{55} +(0.583317 + 0.423805i) q^{56} -5.68196i q^{57} +(6.59953 - 9.08347i) q^{58} +(-1.51967 + 4.67706i) q^{59} +(-3.03472 - 11.1387i) q^{60} +(-0.855890 - 2.63416i) q^{61} +(0.270785 + 0.0879833i) q^{62} +(1.73038 + 0.562235i) q^{63} +(3.24537 + 9.98822i) q^{64} +(1.98322 + 7.27931i) q^{65} +(2.83337 - 8.72020i) q^{66} +(-1.28477 + 1.76833i) q^{67} +6.79751i q^{68} +(8.09205 + 5.87922i) q^{69} +(2.89701 - 3.60834i) q^{70} +(-7.80098 + 5.66774i) q^{71} +(-0.782941 - 1.07763i) q^{72} +(-0.737953 + 0.239775i) q^{73} -4.48150 q^{74} +(-10.7327 + 2.37552i) q^{75} -6.06943 q^{76} +(1.88765 - 0.613336i) q^{77} +(9.09205 + 12.5141i) q^{78} +(12.8236 - 9.31689i) q^{79} +(6.86447 - 1.87020i) q^{80} +(9.01153 + 6.54726i) q^{81} +18.0026i q^{82} +(-1.04103 + 1.43285i) q^{83} +(1.58332 - 4.87295i) q^{84} +(6.46482 + 0.311640i) q^{85} +(-2.99252 - 9.21004i) q^{86} +(-11.2580 - 3.65794i) q^{87} +(-1.38197 - 0.449028i) q^{88} +(-4.48322 - 13.7979i) q^{89} +(-7.14996 + 4.68596i) q^{90} +(-1.03472 + 3.18453i) q^{91} +(6.28015 - 8.64388i) q^{92} -0.300177i q^{93} +(-16.7460 - 12.1667i) q^{94} +(-0.278260 + 5.77237i) q^{95} +(14.3855 - 10.4516i) q^{96} +(-10.0095 - 13.7768i) q^{97} +(-11.9294 + 3.87609i) q^{98} -3.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9} - 5 q^{10} - 4 q^{11} + 15 q^{12} - 5 q^{13} + 13 q^{14} + 15 q^{15} + 3 q^{16} - 10 q^{17} - 5 q^{19} - 15 q^{20} - 4 q^{21} + 5 q^{23} - 20 q^{24} - 10 q^{25} + 6 q^{26} - 5 q^{27} - 15 q^{28} - 5 q^{29} + 15 q^{30} - 9 q^{31} + 10 q^{33} + 13 q^{34} + 15 q^{35} + 23 q^{36} + 30 q^{37} + 15 q^{38} - 3 q^{39} + 10 q^{40} - 4 q^{41} - 15 q^{42} - 2 q^{44} - 15 q^{45} - 19 q^{46} - 30 q^{48} + 14 q^{49} - 15 q^{50} - 4 q^{51} - 10 q^{52} - 10 q^{53} - 5 q^{54} - 10 q^{55} + 10 q^{56} + 20 q^{58} - 10 q^{60} - 9 q^{61} - 30 q^{62} + 10 q^{63} + 4 q^{64} + 5 q^{65} + 12 q^{66} + 20 q^{67} + 17 q^{69} + 30 q^{70} + 6 q^{71} + 5 q^{72} + 15 q^{73} - 12 q^{74} - 10 q^{75} - 20 q^{76} + 10 q^{77} + 25 q^{78} + 15 q^{79} + 20 q^{80} + 28 q^{81} - 45 q^{83} + 18 q^{84} - 15 q^{85} - 9 q^{86} - 20 q^{87} - 20 q^{88} - 25 q^{89} - 25 q^{90} + 6 q^{91} + 30 q^{92} - 27 q^{94} + 15 q^{95} + 16 q^{96} - 60 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.98322	+	0.644389i	−1.40235	+	0.455652i	−0.909950	−	0.414717i	$-0.863881\pi$
$2$	−1.98322	+	0.644389i	−1.40235	+	0.455652i	−0.492401	+	0.870369i	$0.663881\pi$
$3$	1.29224	+	1.77862i	0.746076	+	1.02689i	0.998246	+	0.0592022i	$0.0188557\pi$
$3$	1.29224	+	1.77862i	0.746076	+	1.02689i	−0.252170	+	0.967683i	$0.581144\pi$
$4$	1.89991	−	1.38036i	0.949953	−	0.690182i
$5$	−1.22570	−	1.87020i	−0.548150	−	0.836380i
$5$	−1.22570	−	1.87020i	−0.548150	−	0.836380i
$6$	−3.70892	−	2.69469i	−1.51416	−	1.10010i
$7$		−	0.992398i		−	0.375091i	−0.982256	−	0.187546i	$-0.939947\pi$
$7$		−	0.992398i		−	0.375091i	0.982256	−	0.187546i	$-0.0600533\pi$
$8$	−0.427051	+	0.587785i	−0.150985	+	0.207813i
$9$	−0.566541	+	1.74363i	−0.188847	+	0.581211i
$10$	3.63597	+	2.91920i	1.14980	+	0.923134i
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	0.999969	−	0.00788181i	$-0.00250889\pi$
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	−0.813625	+	0.581390i	$0.802509\pi$
$12$	4.91027	+	1.59545i	1.41747	+	0.460565i
$13$	−3.20892	−	1.04264i	−0.889995	−	0.289177i	−0.171894	−	0.985115i	$-0.554989\pi$
$13$	−3.20892	−	1.04264i	−0.889995	−	0.289177i	−0.718101	+	0.695938i	$0.754989\pi$
$14$	0.639490	+	1.96815i	0.170911	+	0.526010i
$15$	1.74248	−	4.59680i	0.449905	−	1.18689i
$16$	−0.983224	+	3.02605i	−0.245806	+	0.756513i
$17$	−1.70135	+	2.34171i	−0.412638	+	0.567948i	−0.963859	−	0.266411i	$-0.914162\pi$
$17$	−1.70135	+	2.34171i	−0.412638	+	0.567948i	0.551221	+	0.834359i	$0.314162\pi$
$18$		−	3.82309i		−	0.901111i
$19$	−2.09089	−	1.51912i	−0.479683	−	0.348510i	0.321520	−	0.946903i	$-0.395806\pi$
$19$	−2.09089	−	1.51912i	−0.479683	−	0.348510i	−0.801203	+	0.598393i	$0.795806\pi$
$20$	−4.91027	−	1.86130i	−1.09797	−	0.416200i
$21$	1.76510	−	1.28242i	0.385176	−	0.279847i
$22$	−2.45140	−	3.37406i	−0.522640	−	0.719352i
$23$	4.32696	−	1.40591i	0.902233	−	0.293153i	0.179075	−	0.983835i	$-0.442690\pi$
$23$	4.32696	−	1.40591i	0.902233	−	0.293153i	0.723158	+	0.690682i	$0.242690\pi$
$24$	−1.59730			−0.326047
$25$	−1.99532	+	4.58462i	−0.399064	+	0.916923i
$26$	7.03588			1.37985
$27$	2.43930	−	0.792578i	0.469444	−	0.152532i
$28$	−1.36987	−	1.88546i	−0.258881	−	0.356319i
$29$	−4.35599	+	3.16481i	−0.808886	+	0.587690i	−0.913508	−	0.406822i	$-0.866637\pi$
$29$	−4.35599	+	3.16481i	−0.808886	+	0.587690i	0.104621	+	0.994512i	$0.466637\pi$
$30$	−0.493592	+	10.2393i	−0.0901172	+	1.86944i
$31$	−0.110461	−	0.0802548i	−0.0198394	−	0.0144142i	0.577821	−	0.816163i	$-0.303903\pi$
$31$	−0.110461	−	0.0802548i	−0.0198394	−	0.0144142i	−0.597661	+	0.801749i	$0.703903\pi$
$32$		−	8.08800i		−	1.42977i
$33$	−2.58448	+	3.55723i	−0.449901	+	0.619235i
$34$	1.86519	−	5.74046i	0.319877	−	0.984482i
$35$	−1.85599	+	1.21638i	−0.313719	+	0.205606i
$36$	1.33047	+	4.09478i	0.221746	+	0.682463i
$37$	2.04392	+	0.664110i	0.336018	+	0.109179i	0.472166	−	0.881510i	$-0.343472\pi$
$37$	2.04392	+	0.664110i	0.336018	+	0.109179i	−0.136148	+	0.990689i	$0.543472\pi$
$38$	5.12561	+	1.66541i	0.831483	+	0.270165i
$39$	−2.29224	−	7.05479i	−0.367052	−	1.12967i
$40$	1.62271	+	0.0782238i	0.256574	+	0.0123683i
$41$	2.66780	−	8.21064i	0.416640	−	1.28229i	−0.494135	−	0.869385i	$-0.664515\pi$
$41$	2.66780	−	8.21064i	0.416640	−	1.28229i	0.910776	−	0.412902i	$-0.135485\pi$
$42$	−2.67421	+	3.68073i	−0.412639	+	0.567949i
$43$			4.64398i			0.708200i	0.935208	+	0.354100i	$0.115213\pi$
$43$			4.64398i			0.708200i	−0.935208	+	0.354100i	$0.884787\pi$
$44$	3.79981	+	2.76073i	0.572843	+	0.416195i
$45$	3.95536	−	1.07763i	0.589630	−	0.160643i
$46$	−7.67537	+	5.57648i	−1.13167	+	0.822208i
$47$	5.83453	+	8.03054i	0.851054	+	1.17137i	0.983630	+	0.180202i	$0.0576752\pi$
$47$	5.83453	+	8.03054i	0.851054	+	1.17137i	−0.132576	+	0.991173i	$0.542325\pi$
$48$	−6.65275	+	2.16161i	−0.960242	+	0.312001i
$49$	6.01515			0.859306
$50$	1.00289	−	10.3781i	0.141830	−	1.46768i
$51$	−6.36356			−0.891077
$52$	−7.53588	+	2.44856i	−1.04504	+	0.339554i
$53$	−4.44672	−	6.12038i	−0.610804	−	0.840699i	0.385839	−	0.922566i	$-0.373912\pi$
$53$	−4.44672	−	6.12038i	−0.610804	−	0.840699i	−0.996643	+	0.0818665i	$0.973912\pi$
$54$	−4.32696	+	3.14372i	−0.588824	+	0.427806i
$55$	2.79981	−	3.48727i	0.377527	−	0.470223i
$56$	0.583317	+	0.423805i	0.0779490	+	0.0566333i
$57$		−	5.68196i		−	0.752594i
$58$	6.59953	−	9.08347i	0.866561	−	1.19272i
$59$	−1.51967	+	4.67706i	−0.197844	+	0.608901i	0.802088	+	0.597206i	$0.203723\pi$
$59$	−1.51967	+	4.67706i	−0.197844	+	0.608901i	−0.999932	+	0.0116948i	$0.996277\pi$
$60$	−3.03472	−	11.1387i	−0.391780	−	1.43801i
$61$	−0.855890	−	2.63416i	−0.109585	−	0.337269i	0.881194	−	0.472755i	$-0.156740\pi$
$61$	−0.855890	−	2.63416i	−0.109585	−	0.337269i	−0.990779	+	0.135486i	$0.956740\pi$
$62$	0.270785	+	0.0879833i	0.0343897	+	0.0111739i
$63$	1.73038	+	0.562235i	0.218007	+	0.0708349i
$64$	3.24537	+	9.98822i	0.405671	+	1.24853i
$65$	1.98322	+	7.27931i	0.245989	+	0.902887i
$66$	2.83337	−	8.72020i	0.348763	−	1.07338i
$67$	−1.28477	+	1.76833i	−0.156959	+	0.216036i	−0.880253	−	0.474505i	$-0.842627\pi$
$67$	−1.28477	+	1.76833i	−0.156959	+	0.216036i	0.723294	+	0.690540i	$0.242627\pi$
$68$			6.79751i			0.824319i
$69$	8.09205	+	5.87922i	0.974169	+	0.707775i
$70$	2.89701	−	3.60834i	0.346259	−	0.431279i
$71$	−7.80098	+	5.66774i	−0.925806	+	0.672637i	−0.944962	−	0.327179i	$-0.893902\pi$
$71$	−7.80098	+	5.66774i	−0.925806	+	0.672637i	0.0191565	+	0.999816i	$0.493902\pi$
$72$	−0.782941	−	1.07763i	−0.0922704	−	0.126999i
$73$	−0.737953	+	0.239775i	−0.0863708	+	0.0280636i	−0.351884	−	0.936044i	$-0.614459\pi$
$73$	−0.737953	+	0.239775i	−0.0863708	+	0.0280636i	0.265513	+	0.964107i	$0.414459\pi$
$74$	−4.48150			−0.520963
$75$	−10.7327	+	2.37552i	−1.23931	+	0.274301i
$76$	−6.06943			−0.696212
$77$	1.88765	−	0.613336i	0.215118	−	0.0698961i
$78$	9.09205	+	12.5141i	1.02947	+	1.41695i
$79$	12.8236	−	9.31689i	1.44277	−	1.04823i	0.455313	−	0.890332i	$-0.349527\pi$
$79$	12.8236	−	9.31689i	1.44277	−	1.04823i	0.987455	−	0.157900i	$-0.0504725\pi$
$80$	6.86447	−	1.87020i	0.767471	−	0.209095i
$81$	9.01153	+	6.54726i	1.00128	+	0.727474i
$82$			18.0026i			1.98806i
$83$	−1.04103	+	1.43285i	−0.114268	+	0.157276i	−0.862320	−	0.506364i	$-0.830989\pi$
$83$	−1.04103	+	1.43285i	−0.114268	+	0.157276i	0.748052	+	0.663640i	$0.230989\pi$
$84$	1.58332	−	4.87295i	0.172754	−	0.531682i
$85$	6.46482	+	0.311640i	0.701208	+	0.0338021i
$86$	−2.99252	−	9.21004i	−0.322692	−	0.993144i
$87$	−11.2580	−	3.65794i	−1.20698	−	0.392172i
$88$	−1.38197	−	0.449028i	−0.147318	−	0.0478665i
$89$	−4.48322	−	13.7979i	−0.475221	−	1.46258i	−0.845660	−	0.533722i	$-0.820793\pi$
$89$	−4.48322	−	13.7979i	−0.475221	−	1.46258i	0.370439	−	0.928857i	$-0.379207\pi$
$90$	−7.14996	+	4.68596i	−0.753671	+	0.493944i
$91$	−1.03472	+	3.18453i	−0.108468	+	0.333830i
$92$	6.28015	−	8.64388i	0.654750	−	0.901187i
$93$		−	0.300177i		−	0.0311269i
$94$	−16.7460	−	12.1667i	−1.72721	−	1.25490i
$95$	−0.278260	+	5.77237i	−0.0285489	+	0.592233i
$96$	14.3855	−	10.4516i	1.46821	−	1.06672i
$97$	−10.0095	−	13.7768i	−1.01631	−	1.39883i	−0.914761	−	0.403995i	$-0.867621\pi$
$97$	−10.0095	−	13.7768i	−1.01631	−	1.39883i	−0.101545	−	0.994831i	$-0.532379\pi$
$98$	−11.9294	+	3.87609i	−1.20505	+	0.391544i
$99$	−3.66673			−0.368520
$100$	2.53751	+	11.4646i	0.253751	+	1.14646i
$101$	−2.54716			−0.253452			−0.126726	−	0.991938i	$-0.540447\pi$
$101$	−2.54716			−0.253452			−0.126726	+	0.991938i	$0.540447\pi$
$102$	12.6204	−	4.10060i	1.24960	−	0.406020i
$103$	−5.97509	−	8.22400i	−0.588743	−	0.810335i	0.405877	−	0.913928i	$-0.366966\pi$
$103$	−5.97509	−	8.22400i	−0.588743	−	0.810335i	−0.994620	+	0.103593i	$0.966966\pi$
$104$	1.98322	−	1.44090i	0.194471	−	0.141292i
$105$	−4.56186	−	1.72923i	−0.445192	−	0.168756i
$106$	12.7627	+	9.27268i	1.23963	+	0.900642i
$107$			4.81720i			0.465697i	0.972513	+	0.232848i	$0.0748046\pi$
$107$			4.81720i			0.465697i	−0.972513	+	0.232848i	$0.925195\pi$
$108$	3.54040	−	4.87295i	0.340676	−	0.468900i
$109$	−5.02903	+	15.4778i	−0.481694	+	1.48250i	0.355019	+	0.934859i	$0.384474\pi$
$109$	−5.02903	+	15.4778i	−0.481694	+	1.48250i	−0.836713	+	0.547642i	$0.815526\pi$
$110$	−3.30550	+	8.72020i	−0.315167	+	0.831439i
$111$	1.46004	+	4.49354i	0.138581	+	0.426508i
$112$	3.00305	+	0.975750i	0.283762	+	0.0921997i
$113$	6.42633	+	2.08804i	0.604538	+	0.196426i	0.595264	−	0.803531i	$-0.297048\pi$
$113$	6.42633	+	2.08804i	0.604538	+	0.196426i	0.00927487	+	0.999957i	$0.497048\pi$
$114$	3.66139	+	11.2686i	0.342921	+	1.05540i
$115$	−7.93290	−	6.36906i	−0.739746	−	0.593918i
$116$	−3.90738	+	12.0257i	−0.362791	+	1.11656i
$117$	3.63597	−	5.00449i	0.336146	−	0.462665i
$118$		−	10.2549i		−	0.944041i
$119$	2.32391	+	1.68842i	0.213032	+	0.154777i
$120$	1.95781	+	2.98727i	0.178723	+	0.272699i
$121$	5.66312	−	4.11450i	0.514829	−	0.374045i
$122$	3.39484	+	4.67260i	0.307355	+	0.423037i
$123$	18.0510	−	5.86513i	1.62761	−	0.528841i
$124$	−0.320647			−0.0287950
$125$	11.0198	−	1.88771i	0.985643	−	0.168842i
$126$	−3.79403			−0.337999
$127$	−1.41785	+	0.460687i	−0.125814	+	0.0408793i	−0.371247	−	0.928534i	$-0.621070\pi$
$127$	−1.41785	+	0.460687i	−0.125814	+	0.0408793i	0.245433	+	0.969413i	$0.421070\pi$
$128$	−3.36457	−	4.63093i	−0.297389	−	0.409320i
$129$	−8.25985	+	6.00114i	−0.727240	+	0.528370i
$130$	−8.62388	−	13.1585i	−0.756364	−	1.15408i
$131$	−11.4190	−	8.29640i	−0.997684	−	0.724860i	−0.0360934	−	0.999348i	$-0.511491\pi$
$131$	−11.4190	−	8.29640i	−0.997684	−	0.724860i	−0.961590	+	0.274489i	$0.911491\pi$
$132$			10.3259i			0.898757i
$133$	−1.50757	+	2.07500i	−0.130723	+	0.179925i
$134$	1.40849	−	4.33488i	0.121675	−	0.374476i
$135$	−4.47214	−	3.59053i	−0.384900	−	0.309024i
$136$	−0.649858	−	2.00006i	−0.0557249	−	0.171504i
$137$	0.655703	+	0.213051i	0.0560205	+	0.0182022i	0.336893	−	0.941543i	$-0.390624\pi$
$137$	0.655703	+	0.213051i	0.0560205	+	0.0182022i	−0.280873	+	0.959745i	$0.590624\pi$
$138$	−19.8369	−	6.44539i	−1.68863	−	0.548668i
$139$	5.12099	+	15.7608i	0.434356	+	1.33681i	0.893745	+	0.448576i	$0.148069\pi$
$139$	5.12099	+	15.7608i	0.434356	+	1.33681i	−0.459388	+	0.888236i	$0.651931\pi$
$140$	−1.84715	+	4.87295i	−0.156113	+	0.411839i
$141$	−6.74364	+	20.7548i	−0.567917	+	1.74787i
$142$	11.8189	−	16.2673i	0.991817	−	1.36512i
$143$		−	6.74812i		−	0.564307i
$144$	−4.71929	−	3.42877i	−0.393274	−	0.285731i
$145$	11.2580	+	4.26747i	0.934923	+	0.354394i
$146$	1.30902	−	0.951057i	0.108335	−	0.0787100i
$147$	7.77302	+	10.6986i	0.641108	+	0.882409i
$148$	4.79997	−	1.55961i	0.394555	−	0.128199i
$149$	−3.21156			−0.263101			−0.131551	−	0.991309i	$-0.541996\pi$
$149$	−3.21156			−0.263101			−0.131551	+	0.991309i	$0.541996\pi$
$150$	19.7546	−	11.6272i	1.61296	−	0.949358i
$151$	17.6863			1.43929			0.719647	−	0.694340i	$-0.244304\pi$
$151$	17.6863			1.43929			0.719647	+	0.694340i	$0.244304\pi$
$152$	1.78583	−	0.580252i	0.144850	−	0.0470647i
$153$	−3.11920	−	4.29321i	−0.252172	−	0.347085i
$154$	−3.34841	+	2.43277i	−0.269823	+	0.196038i
$155$	−0.0147004	+	0.304953i	−0.00118077	+	0.0244944i
$156$	−14.0932	−	10.2393i	−1.12836	−	0.819802i
$157$		−	1.65512i		−	0.132093i	−0.997817	−	0.0660465i	$-0.978961\pi$
$157$		−	1.65512i		−	0.132093i	0.997817	−	0.0660465i	$-0.0210386\pi$
$158$	−19.4284	+	26.7409i	−1.54564	+	2.12739i
$159$	5.13959	−	15.8180i	0.407596	−	1.25445i
$160$	−15.1262	+	9.91346i	−1.19583	+	0.783728i
$161$	−1.39523	−	4.29407i	−0.109959	−	0.338420i
$162$	−22.0909	−	7.17776i	−1.73562	−	0.563938i
$163$	0.849231	+	0.275932i	0.0665169	+	0.0216127i	0.342086	−	0.939668i	$-0.388866\pi$
$163$	0.849231	+	0.275932i	0.0665169	+	0.0216127i	−0.275570	+	0.961281i	$0.588866\pi$
$164$	−6.26510	−	19.2820i	−0.489222	−	1.50567i
$165$	9.82055	+	0.473405i	0.764529	+	0.0368545i
$166$	1.14128	−	3.51249i	0.0885803	−	0.272622i
$167$	−3.05388	+	4.20331i	−0.236317	+	0.325262i	−0.910660	−	0.413156i	$-0.864427\pi$
$167$	−3.05388	+	4.20331i	−0.236317	+	0.325262i	0.674344	+	0.738417i	$0.264427\pi$
$168$			1.58516i			0.122297i
$169$	−1.30713	−	0.949687i	−0.100549	−	0.0730529i
$170$	−13.0220	+	3.54780i	−0.998742	+	0.272104i
$171$	3.83337	−	2.78510i	0.293145	−	0.212982i
$172$	6.41037	+	8.82312i	0.488786	+	0.672757i
$173$	5.48250	−	1.78137i	0.416827	−	0.135435i	−0.0930924	−	0.995657i	$-0.529675\pi$
$173$	5.48250	−	1.78137i	0.416827	−	0.135435i	0.509919	+	0.860222i	$0.329675\pi$
$174$	24.6842			1.87130
$175$	4.54977	+	1.98015i	0.343930	+	0.149685i
$176$	−6.36356			−0.479671
$177$	−10.2825	+	3.34098i	−0.772878	+	0.251123i
$178$	17.7825	+	24.4755i	1.33285	+	1.83451i
$179$	7.01326	−	5.09543i	0.524196	−	0.380850i	−0.293986	−	0.955810i	$-0.594982\pi$
$179$	7.01326	−	5.09543i	0.524196	−	0.380850i	0.818182	+	0.574959i	$0.194982\pi$
$180$	6.02730	−	7.50722i	0.449249	−	0.559555i
$181$	−11.5616	−	8.39996i	−0.859363	−	0.624364i	0.0683483	−	0.997662i	$-0.478227\pi$
$181$	−11.5616	−	8.39996i	−0.859363	−	0.624364i	−0.927712	+	0.373297i	$0.878227\pi$
$182$		−	6.98240i		−	0.517570i
$183$	3.57914	−	4.92627i	0.264578	−	0.364160i
$184$	−1.02146	+	3.14372i	−0.0753027	+	0.231758i
$185$	−1.26321	−	4.63655i	−0.0928732	−	0.340886i
$186$	0.193431	+	0.595318i	0.0141830	+	0.0436508i
$187$	−5.50569	−	1.78891i	−0.402616	−	0.130818i
$188$	22.1701	+	7.20351i	1.61692	+	0.525370i
$189$	−0.786553	−	2.42076i	−0.0572133	−	0.176084i
$190$	−3.16780	−	11.6272i	−0.229816	−	0.843527i
$191$	−0.391326	+	1.20438i	−0.0283154	+	0.0871458i	−0.964216	−	0.265120i	$-0.914589\pi$
$191$	−0.391326	+	1.20438i	−0.0283154	+	0.0871458i	0.935900	+	0.352265i	$0.114589\pi$
$192$	−13.5714	+	18.6795i	−0.979433	+	1.34807i
$193$			21.1730i			1.52406i	0.647540	+	0.762031i	$0.275798\pi$
$193$			21.1730i			1.52406i	−0.647540	+	0.762031i	$0.724202\pi$
$194$	28.7286	+	20.8726i	2.06260	+	1.49856i
$195$	−10.3843	+	12.9340i	−0.743635	+	0.926224i
$196$	11.4282	−	8.30308i	0.816301	−	0.593077i
$197$	−7.17176	−	9.87108i	−0.510967	−	0.703285i	0.473115	−	0.881001i	$-0.343129\pi$
$197$	−7.17176	−	9.87108i	−0.510967	−	0.703285i	−0.984082	+	0.177715i	$0.943129\pi$
$198$	7.27195	−	2.36280i	0.516795	−	0.167917i
$199$	−10.4065			−0.737695			−0.368848	−	0.929490i	$-0.620248\pi$
$199$	−10.4065			−0.737695			−0.368848	+	0.929490i	$0.620248\pi$
$200$	−1.84267	−	3.13068i	−0.130296	−	0.221373i
$201$	−4.80540			−0.338947
$202$	5.05159	−	1.64136i	0.355429	−	0.115486i
$203$	3.14075	+	4.32287i	0.220438	+	0.303406i
$204$	−12.0902	+	8.78402i	−0.846481	+	0.615005i
$205$	−18.6255	+	5.07446i	−1.30086	+	0.354415i
$206$	17.1494	+	12.4598i	1.19485	+	0.868113i
$207$			8.34114i			0.579749i
$208$	6.31018	−	8.68522i	0.437532	−	0.602212i
$209$	1.59730	−	4.91598i	0.110487	−	0.340045i
$210$	10.1615	+	0.489840i	0.701209	+	0.0338022i
$211$	−2.67537	−	8.23395i	−0.184180	−	0.566848i	0.815753	−	0.578400i	$-0.196323\pi$
$211$	−2.67537	−	8.23395i	−0.184180	−	0.566848i	−0.999933	+	0.0115520i	$0.996323\pi$
$212$	−16.8967	−	5.49007i	−1.16047	−	0.377060i
$213$	−20.1615	−	6.55086i	−1.38144	−	0.448858i
$214$	−3.10415	−	9.55359i	−0.212195	−	0.653070i
$215$	8.68518	−	5.69212i	0.592324	−	0.388199i
$216$	−0.575842	+	1.77226i	−0.0391811	+	0.120587i
$217$	−0.0796448	+	0.109622i	−0.00540664	+	0.00744160i
$218$		−	33.9365i		−	2.29847i
$219$	−1.38008	−	1.00269i	−0.0932573	−	0.0677554i
$220$	0.505688	−	10.4902i	0.0340935	−	0.707252i
$221$	7.90107	−	5.74046i	0.531484	−	0.386145i
$222$	−5.79117	−	7.97087i	−0.388678	−	0.534970i
$223$	−26.9562	+	8.75859i	−1.80512	+	0.586518i	−0.999978	−	0.00656747i	$-0.997909\pi$
$223$	−26.9562	+	8.75859i	−1.80512	+	0.586518i	−0.805139	+	0.593086i	$0.797909\pi$
$224$	−8.02652			−0.536295
$225$	−6.86346	−	6.07648i	−0.457564	−	0.405099i
$226$	−14.0904			−0.937277
$227$	21.1529	−	6.87299i	1.40397	−	0.456176i	0.493495	−	0.869749i	$-0.335719\pi$
$227$	21.1529	−	6.87299i	1.40397	−	0.456176i	0.910471	+	0.413572i	$0.135719\pi$
$228$	−7.84317	−	10.7952i	−0.519427	−	0.714929i
$229$	2.00280	−	1.45512i	0.132348	−	0.0961568i	−0.519641	−	0.854384i	$-0.673934\pi$
$229$	2.00280	−	1.45512i	0.132348	−	0.0961568i	0.651990	+	0.758228i	$0.273934\pi$
$230$	19.8369	+	7.51941i	1.30800	+	0.495815i
$231$	3.53019	+	2.56484i	0.232270	+	0.168754i
$232$		−	3.91192i		−	0.256830i
$233$	3.50088	−	4.81854i	0.229350	−	0.315673i	−0.678796	−	0.734327i	$-0.737498\pi$
$233$	3.50088	−	4.81854i	0.229350	−	0.315673i	0.908146	+	0.418654i	$0.137498\pi$
$234$	−3.98612	+	12.2680i	−0.260581	+	0.801985i
$235$	7.86736	−	20.7548i	0.513210	−	1.35389i
$236$	3.56881	+	10.9837i	0.232310	+	0.714976i
$237$	33.1424	+	10.7686i	2.15283	+	0.699496i
$238$	−5.69683	−	1.85101i	−0.369271	−	0.119983i
$239$	2.17314	+	6.68823i	0.140569	+	0.432626i	0.996415	−	0.0846050i	$-0.0269628\pi$
$239$	2.17314	+	6.68823i	0.140569	+	0.432626i	−0.855846	+	0.517231i	$0.826963\pi$
$240$	12.1969	+	9.79251i	0.787308	+	0.632104i
$241$	0.364567	−	1.12202i	0.0234838	−	0.0722758i	−0.938628	−	0.344932i	$-0.887902\pi$
$241$	0.364567	−	1.12202i	0.0234838	−	0.0722758i	0.962112	+	0.272656i	$0.0879021\pi$
$242$	−8.57990	+	11.8092i	−0.551537	+	0.759125i
$243$			16.7942i			1.07735i
$244$	−5.26220	−	3.82322i	−0.336878	−	0.244756i
$245$	−7.37276	−	11.2495i	−0.471029	−	0.718707i
$246$	−32.0198	+	23.2637i	−2.04151	+	1.48324i
$247$	5.12561	+	7.05479i	0.326135	+	0.448886i
$248$	0.0943452	−	0.0306546i	0.00599093	−	0.00194657i
$249$	−3.89375			−0.246757
$250$	−20.6384	+	10.8448i	−1.30528	+	0.685885i
$251$	4.60867			0.290897			0.145448	−	0.989366i	$-0.453538\pi$
$251$	4.60867			0.290897			0.145448	+	0.989366i	$0.453538\pi$
$252$	4.06365	−	1.32036i	0.255986	−	0.0831748i
$253$	5.34841	+	7.36146i	0.336252	+	0.462811i
$254$	2.51505	−	1.82729i	0.157808	−	0.114654i
$255$	7.79981	+	11.9011i	0.488443	+	0.745279i
$256$	−7.33616	−	5.33003i	−0.458510	−	0.333127i
$257$			9.75542i			0.608526i	0.952588	+	0.304263i	$0.0984102\pi$
$257$			9.75542i			0.608526i	−0.952588	+	0.304263i	$0.901590\pi$
$258$	12.5141	−	17.2242i	0.779092	−	1.07233i
$259$	0.659062	−	2.02838i	0.0409521	−	0.126038i
$260$	13.8160	+	11.0924i	0.856834	+	0.687924i
$261$	−3.05043	−	9.38824i	−0.188817	−	0.581118i
$262$	27.9926	+	9.09534i	1.72939	+	0.561912i
$263$	0.947088	+	0.307728i	0.0584000	+	0.0189753i	0.338071	−	0.941121i	$-0.390225\pi$
$263$	0.947088	+	0.307728i	0.0584000	+	0.0189753i	−0.279671	+	0.960096i	$0.590225\pi$
$264$	−0.987184	−	3.03824i	−0.0607570	−	0.186991i
$265$	−5.99602	+	15.8180i	−0.368333	+	0.971693i
$266$	1.65275	−	5.08664i	0.101337	−	0.311882i
$267$	18.7479	−	25.8042i	1.14735	−	1.57919i
$268$			5.13310i			0.313554i
$269$	−2.66048	−	1.93295i	−0.162212	−	0.117854i	0.503718	−	0.863868i	$-0.331965\pi$
$269$	−2.66048	−	1.93295i	−0.162212	−	0.117854i	−0.665930	+	0.746014i	$0.731965\pi$
$270$	11.1829	+	4.23903i	0.680572	+	0.257979i
$271$	−9.82960	+	7.14162i	−0.597105	+	0.433823i	−0.844850	−	0.535003i	$-0.820311\pi$
$271$	−9.82960	+	7.14162i	−0.597105	+	0.433823i	0.247745	+	0.968825i	$0.420311\pi$
$272$	−5.41332	−	7.45080i	−0.328231	−	0.451771i
$273$	−7.00116	+	2.27482i	−0.423730	+	0.137678i
$274$	−1.43769			−0.0868543
$275$	−9.95363	−	0.961876i	−0.600227	−	0.0580033i
$276$	23.4896			1.41391
$277$	−11.2858	+	3.66697i	−0.678096	+	0.220327i	−0.627762	−	0.778406i	$-0.716029\pi$
$277$	−11.2858	+	3.66697i	−0.678096	+	0.220327i	−0.0503346	+	0.998732i	$0.516029\pi$
$278$	−20.3121	−	27.9572i	−1.21824	−	1.67676i
$279$	0.202516	−	0.147136i	0.0121243	−	0.00880883i
$280$	0.0776292	−	1.61038i	0.00463923	−	0.0962386i
$281$	19.9355	+	14.4840i	1.18925	+	0.864041i	0.993185	−	0.116549i	$-0.0371833\pi$
$281$	19.9355	+	14.4840i	1.18925	+	0.864041i	0.196066	+	0.980591i	$0.437183\pi$
$282$		−	45.5069i		−	2.70990i
$283$	−1.97697	+	2.72107i	−0.117519	+	0.161751i	−0.863724	−	0.503965i	$-0.831874\pi$
$283$	−1.97697	+	2.72107i	−0.117519	+	0.161751i	0.746205	+	0.665716i	$0.231874\pi$
$284$	−6.99759	+	21.5364i	−0.415231	+	1.27795i
$285$	−10.6264	+	6.96438i	−0.629455	+	0.412534i
$286$	4.34841	+	13.3830i	0.257127	+	0.791356i
$287$	−8.14823	−	2.64752i	−0.480975	−	0.156278i
$288$	14.1025	+	4.58219i	0.830999	+	0.270008i
$289$	2.66428	+	8.19982i	0.156723	+	0.482342i
$290$	−25.0770	−	1.20885i	−1.47257	−	0.0709861i
$291$	11.5691	−	35.6060i	0.678192	−	2.08726i
$292$	−1.07106	+	1.47419i	−0.0626793	+	0.0862707i
$293$		−	8.96340i		−	0.523647i	−0.965116	−	0.261824i	$-0.915676\pi$
$293$		−	8.96340i		−	0.523647i	0.965116	−	0.261824i	$-0.0843239\pi$
$294$	−22.3097	−	16.2090i	−1.30113	−	0.945326i
$295$	10.6097	−	2.89058i	0.617721	−	0.168296i
$296$	−1.26321	+	0.917777i	−0.0734227	+	0.0533447i
$297$	3.01515	+	4.14999i	0.174956	+	0.240807i
$298$	6.36925	−	2.06949i	0.368961	−	0.119883i
$299$	−15.3507			−0.887756
$300$	−17.1121	+	19.3283i	−0.987966	+	1.11592i
$301$	4.60867			0.265640
$302$	−35.0760	+	11.3969i	−2.01840	+	0.655817i
$303$	−3.29155	−	4.53042i	−0.189094	−	0.260266i
$304$	6.65275	−	4.83351i	0.381561	−	0.277221i
$305$	−3.87735	+	4.82937i	−0.222016	+	0.276529i
$306$	8.95256	+	6.50442i	0.511784	+	0.371833i
$307$		−	9.48133i		−	0.541128i	−0.962702	−	0.270564i	$-0.912790\pi$
$307$		−	9.48133i		−	0.541128i	0.962702	−	0.270564i	$-0.0872102\pi$
$308$	2.73974	−	3.77093i	0.156111	−	0.214869i
$309$	6.90610	−	21.2548i	0.392874	−	1.20914i
$310$	−0.167354	−	0.614264i	−0.00950508	−	0.0348878i
$311$	9.06409	+	27.8964i	0.513978	+	1.58186i	0.785135	+	0.619325i	$0.212594\pi$
$311$	9.06409	+	27.8964i	0.513978	+	1.58186i	−0.271157	+	0.962535i	$0.587406\pi$
$312$	5.12561	+	1.66541i	0.290180	+	0.0942853i
$313$	17.9655	+	5.83735i	1.01547	+	0.329947i	0.769031	−	0.639212i	$-0.220739\pi$
$313$	17.9655	+	5.83735i	1.01547	+	0.329947i	0.246440	+	0.969158i	$0.420739\pi$
$314$	1.06654	+	3.28248i	0.0601884	+	0.185241i
$315$	−1.06943	−	3.92529i	−0.0602558	−	0.221165i
$316$	11.5030	−	35.4024i	0.647092	−	1.99154i
$317$	−13.3952	+	18.4369i	−0.752351	+	1.03552i	0.245461	+	0.969406i	$0.421061\pi$
$317$	−13.3952	+	18.4369i	−0.752351	+	1.03552i	−0.997812	+	0.0661157i	$0.978939\pi$
$318$			34.6826i			1.94490i
$319$	−8.71197	−	6.32962i	−0.487777	−	0.354391i
$320$	14.7021	−	18.3121i	0.821875	−	1.02367i
$321$	−8.56796	+	6.22499i	−0.478217	+	0.347445i
$322$	5.53409	+	7.61703i	0.308403	+	0.424480i
$323$	7.11468	−	2.31170i	0.395871	−	0.128626i
$324$	26.1587			1.45326
$325$	11.1829	−	12.6313i	0.620318	−	0.700657i
$326$	−1.86202			−0.103128
$327$	−34.0277	+	11.0563i	−1.88174	+	0.611414i
$328$	3.68681	+	5.07446i	0.203570	+	0.280190i
$329$	7.96950	−	5.79018i	0.439373	−	0.319223i
$330$	−19.7814	+	5.38938i	−1.08893	+	0.296676i
$331$	−2.39711	−	1.74160i	−0.131757	−	0.0957272i	0.519955	−	0.854194i	$-0.325949\pi$
$331$	−2.39711	−	1.74160i	−0.131757	−	0.0957272i	−0.651712	+	0.758467i	$0.725949\pi$
$332$			4.15928i			0.228270i
$333$	−2.31593	+	3.18760i	−0.126912	+	0.174680i
$334$	3.34797	−	10.3040i	0.183193	−	0.563809i
$335$	4.88187	+	0.235333i	0.266725	+	0.0128576i
$336$	2.14518	+	6.60218i	0.117029	+	0.360178i
$337$	17.8916	+	5.81332i	0.974615	+	0.316672i	0.752678	−	0.658389i	$-0.228762\pi$
$337$	17.8916	+	5.81332i	0.974615	+	0.316672i	0.221937	+	0.975061i	$0.428762\pi$
$338$	3.20430	+	1.04114i	0.174291	+	0.0566306i
$339$	4.59054	+	14.1282i	0.249324	+	0.767340i
$340$	12.7127	−	8.33171i	0.689444	−	0.451850i
$341$	0.0843849	−	0.259710i	0.00456970	−	0.0140641i
$342$	−5.80773	+	7.99366i	−0.314046	+	0.432248i
$343$		−	12.9162i		−	0.697410i
$344$	−2.72966	−	1.98321i	−0.147173	−	0.106928i
$345$	1.07691	−	22.3399i	0.0579788	−	1.20274i
$346$	−9.72514	+	7.06573i	−0.522827	+	0.379856i
$347$	−13.3652	−	18.3956i	−0.717480	−	0.987526i	−0.999604	−	0.0281483i	$-0.991039\pi$
$347$	−13.3652	−	18.3956i	−0.717480	−	0.987526i	0.282124	−	0.959378i	$-0.408961\pi$
$348$	−26.4384	+	8.59035i	−1.41725	+	0.460491i
$349$	−1.93849			−0.103765			−0.0518824	−	0.998653i	$-0.516522\pi$
$349$	−1.93849			−0.103765			−0.0518824	+	0.998653i	$0.516522\pi$
$350$	−10.2992	−	0.995269i	−0.550515	−	0.0531994i
$351$	−8.65392			−0.461912
$352$	15.3843	−	4.99866i	0.819986	−	0.266430i
$353$	−3.08555	−	4.24689i	−0.164227	−	0.226039i	0.718970	−	0.695041i	$-0.244614\pi$
$353$	−3.08555	−	4.24689i	−0.164227	−	0.226039i	−0.883197	+	0.469002i	$0.844614\pi$
$354$	18.2396	−	13.2518i	0.969422	−	0.704326i
$355$	20.1615	+	7.64246i	1.07006	+	0.405620i
$356$	−27.5639	−	20.0263i	−1.46088	−	1.06139i
$357$			6.31519i			0.334235i
$358$	−10.6254	+	14.6246i	−0.561571	+	0.772937i
$359$	−6.98184	+	21.4879i	−0.368488	+	1.13409i	0.579281	+	0.815128i	$0.303334\pi$
$359$	−6.98184	+	21.4879i	−0.368488	+	1.13409i	−0.947768	+	0.318960i	$0.896666\pi$
$360$	−1.05573	+	2.78510i	−0.0556418	+	0.146788i
$361$	−3.80723	−	11.7174i	−0.200380	−	0.616708i
$362$	28.3420	+	9.20887i	1.48962	+	0.484007i
$363$	14.6362	+	4.75560i	0.768203	+	0.249604i
$364$	2.42994	+	7.47860i	0.127364	+	0.391985i
$365$	1.35294	+	1.08623i	0.0708160	+	0.0568558i
$366$	−3.92381	+	12.0762i	−0.205101	+	0.631236i
$367$	4.29008	−	5.90479i	0.223940	−	0.308228i	−0.682232	−	0.731136i	$-0.738991\pi$
$367$	4.29008	−	5.90479i	0.223940	−	0.308228i	0.906173	+	0.422908i	$0.138991\pi$
$368$			14.4759i			0.754610i
$369$	12.8049	+	9.30333i	0.666598	+	0.484312i
$370$	5.49297	+	8.38131i	0.285566	+	0.435723i
$371$	−6.07386	+	4.41292i	−0.315339	+	0.229107i
$372$	−0.414353	−	0.570308i	−0.0214832	−	0.0295691i
$373$	21.2156	−	6.89335i	1.09850	−	0.356924i	0.296975	−	0.954885i	$-0.404022\pi$
$373$	21.2156	−	6.89335i	1.09850	−	0.356924i	0.801525	+	0.597961i	$0.204022\pi$
$374$	12.0718			0.624216
$375$	17.5978	+	17.1607i	0.908746	+	0.886173i
$376$	−7.21188			−0.371924
$377$	17.2778	−	5.61390i	0.889852	−	0.289130i
$378$	3.11982	+	4.29407i	0.160466	+	0.220863i
$379$	−26.6544	+	19.3655i	−1.36914	+	0.994740i	−0.371339	+	0.928497i	$0.621101\pi$
$379$	−26.6544	+	19.3655i	−1.36914	+	0.994740i	−0.997804	+	0.0662429i	$0.978899\pi$
$380$	7.43930	+	11.3511i	0.381628	+	0.582298i
$381$	−2.65159	−	1.92649i	−0.135845	−	0.0986971i
$382$		−	2.64072i		−	0.135111i
$383$	−12.1673	+	16.7468i	−0.621719	+	0.855722i	−0.997477	−	0.0709955i	$-0.977382\pi$
$383$	−12.1673	+	16.7468i	−0.621719	+	0.855722i	0.375758	+	0.926718i	$0.377382\pi$
$384$	3.88882	−	11.9686i	0.198450	−	0.610768i
$385$	−3.46076	−	2.77853i	−0.176377	−	0.141607i
$386$	−13.6436	−	41.9907i	−0.694441	−	2.13727i
$387$	−8.09739	−	2.63100i	−0.411614	−	0.133741i
$388$	−38.0341	−	12.3580i	−1.93089	−	0.627383i
$389$	0.353657	+	1.08844i	0.0179311	+	0.0551863i	0.959622	−	0.281294i	$-0.0907635\pi$
$389$	0.353657	+	1.08844i	0.0179311	+	0.0551863i	−0.941691	+	0.336480i	$0.890764\pi$
$390$	12.2599	−	32.3426i	0.620802	−	1.63773i
$391$	−4.06943	+	12.5244i	−0.205800	+	0.633388i
$392$	−2.56877	+	3.53561i	−0.129743	+	0.178575i
$393$		−	31.0310i		−	1.56531i
$394$	20.5840	+	14.9552i	1.03701	+	0.753430i
$395$	−33.1424	−	12.5630i	−1.66757	−	0.632114i
$396$	−6.96645	+	5.06142i	−0.350077	+	0.254346i
$397$	−2.75385	−	3.79035i	−0.138212	−	0.190232i	0.734300	−	0.678825i	$-0.237510\pi$
$397$	−2.75385	−	3.79035i	−0.138212	−	0.190232i	−0.872512	+	0.488593i	$0.837510\pi$
$398$	20.6384	−	6.70581i	1.03451	−	0.336132i
$399$	−5.63877			−0.282292
$400$	−11.9114	−	10.5456i	−0.595572	−	0.527282i
$401$	−24.0851			−1.20275			−0.601376	−	0.798966i	$-0.705381\pi$
$401$	−24.0851			−1.20275			−0.601376	+	0.798966i	$0.705381\pi$
$402$	9.53019	−	3.09655i	0.475323	−	0.154442i
$403$	0.270785	+	0.372703i	0.0134888	+	0.0185657i
$404$	−4.83937	+	3.51601i	−0.240768	+	0.174928i
$405$	1.19928	−	24.8784i	0.0595925	−	1.23622i
$406$	−9.01443	−	6.54936i	−0.447378	−	0.325039i
$407$			4.29821i			0.213054i
$408$	2.71756	−	3.74041i	0.134539	−	0.185178i
$409$	0.586930	−	1.80638i	0.0290218	−	0.0893199i	−0.935496	−	0.353336i	$-0.885047\pi$
$409$	0.586930	−	1.80638i	0.0290218	−	0.0893199i	0.964518	+	0.264016i	$0.0850472\pi$
$410$	33.6686	−	22.0658i	1.66277	−	1.08975i
$411$	0.468391	+	1.44156i	0.0231040	+	0.0711068i
$412$	−22.7042	−	7.37705i	−1.11856	−	0.363441i
$413$	4.64151	+	1.50812i	0.228394	+	0.0742096i
$414$	−5.37494	−	16.5423i	−0.264164	−	0.813012i
$415$	3.95571	+	0.190687i	0.194178	+	0.00936047i
$416$	−8.43290	+	25.9538i	−0.413457	+	1.27249i
$417$	−21.4148	+	29.4750i	−1.04869	+	1.44340i
$418$			10.7788i			0.527207i
$419$	−1.88344	−	1.36840i	−0.0920120	−	0.0668507i	0.540828	−	0.841133i	$-0.318111\pi$
$419$	−1.88344	−	1.36840i	−0.0920120	−	0.0668507i	−0.632840	+	0.774283i	$0.718111\pi$
$420$	−11.0541	+	3.01165i	−0.539384	+	0.146953i
$421$	19.3760	−	14.0775i	0.944329	−	0.686095i	−0.00513010	−	0.999987i	$-0.501633\pi$
$421$	19.3760	−	14.0775i	0.944329	−	0.686095i	0.949459	+	0.313892i	$0.101633\pi$
$422$	10.6117	+	14.6058i	0.516571	+	0.710998i
$423$	−17.3078	+	5.62366i	−0.841536	+	0.273431i
$424$	5.49645			0.266931
$425$	−7.34110	−	12.4725i	−0.356095	−	0.605005i
$426$	44.2060			2.14179
$427$	−2.61413	+	0.849384i	−0.126507	+	0.0411045i
$428$	6.64949	+	9.15224i	0.321415	+	0.442390i
$429$	12.0023	−	8.72020i	0.579478	−	0.421015i
$430$	−13.5567	+	16.8854i	−0.653763	+	0.814285i
$431$	−0.964563	−	0.700796i	−0.0464614	−	0.0337562i	0.564312	−	0.825561i	$-0.309141\pi$
$431$	−0.964563	−	0.700796i	−0.0464614	−	0.0337562i	−0.610774	+	0.791805i	$0.709141\pi$
$432$			8.16074i			0.392634i
$433$	15.0554	−	20.7220i	0.723518	−	0.995837i	−0.275882	−	0.961192i	$-0.588970\pi$
$433$	15.0554	−	20.7220i	0.723518	−	0.995837i	0.999400	−	0.0346454i	$-0.0110302\pi$
$434$	0.0873145	−	0.268726i	0.00419123	−	0.0128993i
$435$	6.95781	+	25.5382i	0.333601	+	1.22446i
$436$	11.8102	+	36.3482i	0.565608	+	1.74076i
$437$	−11.1829	−	3.63356i	−0.534953	−	0.173817i
$438$	3.38313	+	1.09925i	0.161652	+	0.0525240i
$439$	−5.98693	−	18.4259i	−0.285741	−	0.879420i	−0.986176	−	0.165703i	$-0.947011\pi$
$439$	−5.98693	−	18.4259i	−0.285741	−	0.879420i	0.700435	−	0.713716i	$-0.252989\pi$
$440$	0.854102	+	3.13493i	0.0407177	+	0.149452i
$441$	−3.40783	+	10.4882i	−0.162277	+	0.499439i
$442$	−11.9705	+	16.4760i	−0.569379	+	0.783683i
$443$		−	2.46263i		−	0.117003i	−0.998287	−	0.0585016i	$-0.981368\pi$
$443$		−	2.46263i		−	0.117003i	0.998287	−	0.0585016i	$-0.0186323\pi$
$444$	8.97666	+	6.52192i	0.426013	+	0.309517i
$445$	−20.3099	+	25.2967i	−0.962780	+	1.19918i
$446$	47.8162	−	34.7405i	2.26416	−	1.64501i
$447$	−4.15011	−	5.71214i	−0.196294	−	0.270175i
$448$	9.91229	−	3.22070i	0.468312	−	0.152164i
$449$	14.3585			0.677618			0.338809	−	0.940855i	$-0.389976\pi$
$449$	14.3585			0.677618			0.338809	+	0.940855i	$0.389976\pi$
$450$	17.5274	+	7.62829i	0.826249	+	0.359601i
$451$	17.2664			0.813041
$452$	15.0917	−	4.90359i	0.709853	−	0.230645i
$453$	22.8550	+	31.4572i	1.07382	+	1.47799i
$454$	−37.5220	+	27.2614i	−1.76100	+	1.27944i
$455$	7.22397	−	1.96815i	0.338665	−	0.0922682i
$456$	3.33977	+	2.42649i	0.156399	+	0.113631i
$457$		−	25.1964i		−	1.17864i	−0.807901	−	0.589319i	$-0.799396\pi$
$457$		−	25.1964i		−	1.17864i	0.807901	−	0.589319i	$-0.200604\pi$
$458$	−3.03433	+	4.17640i	−0.141785	+	0.195150i
$459$	−2.29413	+	7.06059i	−0.107081	+	0.329560i
$460$	−23.8634	−	1.15035i	−1.11264	−	0.0536352i
$461$	8.90758	+	27.4147i	0.414867	+	1.27683i	0.912370	+	0.409367i	$0.134251\pi$
$461$	8.90758	+	27.4147i	0.414867	+	1.27683i	−0.497502	+	0.867463i	$0.665749\pi$
$462$	−8.65392	−	2.81183i	−0.402617	−	0.130818i
$463$	−30.3193	−	9.85134i	−1.40906	−	0.457831i	−0.496949	−	0.867780i	$-0.665547\pi$
$463$	−30.3193	−	9.85134i	−1.40906	−	0.457831i	−0.912108	+	0.409949i	$0.865547\pi$
$464$	−5.29397	−	16.2932i	−0.245766	−	0.756391i
$465$	−0.561392	+	0.367927i	−0.0260339	+	0.0170622i
$466$	−3.83801	+	11.8122i	−0.177792	+	0.547189i
$467$	25.3333	−	34.8683i	1.17229	−	1.61351i	0.525706	−	0.850666i	$-0.323801\pi$
$467$	25.3333	−	34.8683i	1.17229	−	1.61351i	0.646580	−	0.762847i	$-0.276199\pi$
$468$		−	14.5270i		−	0.671512i
$469$	1.75489	+	1.27500i	0.0810331	+	0.0588740i
$470$	−2.22859	+	46.2310i	−0.102797	+	2.13248i
$471$	2.94383	−	2.13882i	0.135644	−	0.0985514i
$472$	−2.10013	−	2.89058i	−0.0966663	−	0.133050i
$473$	−8.83337	+	2.87013i	−0.406159	+	0.131969i
$474$	−72.6679			−3.33775
$475$	11.1366	−	6.55479i	0.510981	−	0.300755i
$476$	6.74584			0.309195
$477$	13.1910	−	4.28600i	0.603973	−	0.196243i
$478$	−8.61964	−	11.8639i	−0.394253	−	0.542643i
$479$	17.0107	−	12.3590i	0.777237	−	0.564696i	−0.126912	−	0.991914i	$-0.540506\pi$
$479$	17.0107	−	12.3590i	0.777237	−	0.564696i	0.904148	+	0.427218i	$0.140506\pi$
$480$	−37.1790	−	14.0931i	−1.69698	−	0.643261i
$481$	−5.86635	−	4.26216i	−0.267483	−	0.194338i
$482$			2.46014i			0.112057i
$483$	5.83453	−	8.03054i	0.265480	−	0.365402i
$484$	5.07990	−	15.6343i	0.230904	−	0.710651i
$485$	−13.4969	+	35.6060i	−0.612862	+	1.61678i
$486$	−10.8220	−	33.3067i	−0.490895	−	1.51082i
$487$	−26.5525	−	8.62744i	−1.20321	−	0.390947i	−0.362269	−	0.932073i	$-0.617998\pi$
$487$	−26.5525	−	8.62744i	−1.20321	−	0.390947i	−0.840941	+	0.541127i	$0.817998\pi$
$488$	1.91383	+	0.621840i	0.0866349	+	0.0281494i
$489$	0.606634	+	1.86703i	0.0274329	+	0.0844299i
$490$	21.8709	+	17.5594i	0.988027	+	0.793255i
$491$	4.62322	−	14.2288i	0.208643	−	0.642137i	−0.790901	−	0.611944i	$-0.790388\pi$
$491$	4.62322	−	14.2288i	0.208643	−	0.642137i	0.999544	−	0.0301930i	$-0.00961220\pi$
$492$	26.1993	−	36.0602i	1.18115	−	1.62572i
$493$		−	15.5849i		−	0.701909i
$494$	−14.7113	−	10.6884i	−0.661891	−	0.480892i
$495$	4.49431	+	6.85753i	0.202004	+	0.308223i
$496$	0.351464	−	0.255353i	0.0157812	−	0.0114657i
$497$	5.62466	+	7.74168i	0.252300	+	0.347262i
$498$	7.72218	−	2.50909i	0.346039	−	0.112435i
$499$	44.3253			1.98427			0.992137	−	0.125160i	$-0.0399443\pi$
$499$	44.3253			1.98427			0.992137	+	0.125160i	$0.0399443\pi$
$500$	18.3309	−	18.7978i	0.819784	−	0.840665i
$501$	−11.4224			−0.510316
$502$	−9.14003	+	2.96978i	−0.407940	+	0.132548i
$503$	13.8842	+	19.1100i	0.619066	+	0.852071i	0.997284	−	0.0736453i	$-0.0234633\pi$
$503$	13.8842	+	19.1100i	0.619066	+	0.852071i	−0.378219	+	0.925716i	$0.623463\pi$
$504$	−1.06943	+	0.776989i	−0.0476364	+	0.0346098i
$505$	3.12205	+	4.76371i	0.138930	+	0.211982i
$506$	−15.3507	−	11.1530i	−0.682424	−	0.495810i
$507$		−	3.55211i		−	0.157755i
$508$	−2.05786	+	2.83241i	−0.0913029	+	0.125668i
$509$	8.25552	−	25.4079i	0.365920	−	1.12618i	−0.583484	−	0.812125i	$-0.698311\pi$
$509$	8.25552	−	25.4079i	0.365920	−	1.12618i	0.949403	−	0.314060i	$-0.101689\pi$
$510$	−23.1377	−	18.5765i	−1.02456	−	0.822583i
$511$	0.237953	+	0.732343i	0.0105264	+	0.0323970i
$512$	28.8718	+	9.38103i	1.27597	+	0.414587i
$513$	−6.30434	−	2.04840i	−0.278343	−	0.0904392i
$514$	−6.28628	−	19.3472i	−0.277276	−	0.853367i
$515$	−8.05689	+	21.2548i	−0.355029	+	0.936598i
$516$	−7.40921	+	22.8032i	−0.326172	+	1.00385i
$517$	−11.6691	+	16.0611i	−0.513205	+	0.706366i
$518$			4.44743i			0.195409i
$519$	10.2531	+	7.44931i	0.450061	+	0.326988i
$520$	−5.12561	−	1.94293i	−0.224773	−	0.0852029i
$521$	−26.4607	+	19.2249i	−1.15927	+	0.842256i	−0.989685	−	0.143260i	$-0.954241\pi$
$521$	−26.4607	+	19.2249i	−1.15927	+	0.842256i	−0.169581	+	0.985516i	$0.554241\pi$
$522$	12.0994	+	16.6533i	0.529574	+	0.728896i
$523$	−0.224417	+	0.0729175i	−0.00981307	+	0.00318846i	−0.313919	−	0.949450i	$-0.601642\pi$
$523$	−0.224417	+	0.0729175i	−0.00981307	+	0.00318846i	0.304106	+	0.952638i	$0.401642\pi$
$524$	−33.1471			−1.44804
$525$	2.35746	+	10.6511i	0.102888	+	0.464853i
$526$	−2.07658			−0.0905434
$527$	0.375867	−	0.122127i	0.0163730	−	0.00531992i
$528$	−8.22325	−	11.3183i	−0.357871	−	0.492567i
$529$	−1.86142	+	1.35240i	−0.0809313	+	0.0588001i
$530$	1.69850	−	35.2344i	0.0737779	−	1.53049i
$531$	−7.29413	−	5.29949i	−0.316538	−	0.229978i
$532$			6.02330i			0.261143i
$533$	−17.1215	+	23.5658i	−0.741616	+	1.02075i
$534$	−20.5533	+	63.2564i	−0.889427	+	2.73737i
$535$	9.00915	−	5.90445i	0.389499	−	0.255271i
$536$	−0.490737	−	1.51033i	−0.0211966	−	0.0652364i
$537$	18.1256	+	5.88938i	0.782179	+	0.254145i
$538$	6.52190	+	2.11909i	0.281179	+	0.0913606i
$539$	3.71756	+	11.4415i	0.160127	+	0.492820i
$540$	−13.4529	−	0.648503i	−0.578920	−	0.0279071i
$541$	−10.3698	+	31.9148i	−0.445830	+	1.37213i	0.435740	+	0.900073i	$0.356487\pi$
$541$	−10.3698	+	31.9148i	−0.445830	+	1.37213i	−0.881570	+	0.472053i	$0.843513\pi$
$542$	14.8923	−	20.4975i	0.639680	−	0.880443i
$543$		−	31.4183i		−	1.34829i
$544$	18.9397	+	13.7605i	0.812035	+	0.589978i
$545$	35.1106	−	9.56578i	1.50397	−	0.409753i
$546$	12.4190	−	9.02294i	0.531485	−	0.386146i
$547$	22.6371	+	31.1573i	0.967892	+	1.33219i	0.943105	+	0.332496i	$0.107891\pi$
$547$	22.6371	+	31.1573i	0.967892	+	1.33219i	0.0247869	+	0.999693i	$0.492109\pi$
$548$	1.53986	−	0.500332i	0.0657797	−	0.0213731i
$549$	5.07790			0.216720
$550$	20.3601	−	4.50639i	0.868158	−	0.192153i
$551$	13.9156			0.592825
$552$	−6.91144	+	2.24566i	−0.294170	+	0.0955818i
$553$	−9.24607	−	12.7261i	−0.393183	−	0.541170i
$554$	20.0193	−	14.5448i	0.850537	−	0.617951i
$555$	6.61426	−	8.23830i	0.280760	−	0.349697i
$556$	31.4850	+	22.8752i	1.33526	+	0.970124i
$557$		−	4.33445i		−	0.183657i	−0.995775	−	0.0918283i	$-0.970729\pi$
$557$		−	4.33445i		−	0.183657i	0.995775	−	0.0918283i	$-0.0292711\pi$
$558$	−0.306821	+	0.422304i	−0.0129888	+	0.0178775i
$559$	4.84201	−	14.9022i	0.204795	−	0.630294i
$560$	−1.85599	−	6.81229i	−0.0784298	−	0.287872i
$561$	−3.93290	−	12.1042i	−0.166047	−	0.511040i
$562$	−48.8698	−	15.8788i	−2.06145	−	0.669805i
$563$	−33.1936	−	10.7853i	−1.39894	−	0.454544i	−0.490094	−	0.871669i	$-0.663038\pi$
$563$	−33.1936	−	10.7853i	−1.39894	−	0.454544i	−0.908849	+	0.417125i	$0.863038\pi$
$564$	15.8369	+	48.7408i	0.666852	+	2.05236i
$565$	−3.97169	−	14.5779i	−0.167090	−	0.613295i
$566$	2.16735	−	6.67043i	0.0911007	−	0.280379i
$567$	6.49749	−	8.94303i	0.272869	−	0.375572i
$568$		−	7.00572i		−	0.293953i
$569$	−33.9501	−	24.6662i	−1.42326	−	1.03406i	−0.991223	−	0.132204i	$-0.957795\pi$
$569$	−33.9501	−	24.6662i	−1.42326	−	1.03406i	−0.432038	−	0.901855i	$-0.642205\pi$
$570$	16.5868	−	20.6595i	0.694745	−	0.865330i
$571$	11.1913	−	8.13093i	0.468340	−	0.340269i	−0.328454	−	0.944520i	$-0.606528\pi$
$571$	11.1913	−	8.13093i	0.468340	−	0.340269i	0.796794	+	0.604251i	$0.206528\pi$
$572$	−9.31486	−	12.8208i	−0.389474	−	0.536065i
$573$	−2.64782	+	0.860328i	−0.110614	+	0.0359407i
$574$	17.8658			0.745704
$575$	−2.18809	+	22.6427i	−0.0912497	+	0.944265i
$576$	−19.2544			−0.802268
$577$	12.1538	−	3.94902i	0.505970	−	0.164400i	−0.0448986	−	0.998992i	$-0.514296\pi$
$577$	12.1538	−	3.94902i	0.505970	−	0.164400i	0.550869	+	0.834592i	$0.314296\pi$
$578$	−10.5677	−	14.5453i	−0.439560	−	0.605003i
$579$	−37.6586	+	27.3606i	−1.56504	+	1.13707i
$580$	27.2798	−	7.43228i	1.13273	−	0.308609i
$581$	1.42196	+	1.03311i	0.0589928	+	0.0428608i
$582$			78.0696i			3.23609i
$583$	8.89344	−	12.2408i	0.368329	−	0.506961i
$584$	0.174207	−	0.536154i	0.00720874	−	0.0221862i
$585$	−13.8160	−	0.666009i	−0.571222	−	0.0275361i
$586$	5.77591	+	17.7764i	0.238601	+	0.734337i
$587$	−11.5905	−	3.76597i	−0.478390	−	0.155438i	0.0598889	−	0.998205i	$-0.480925\pi$
$587$	−11.5905	−	3.76597i	−0.478390	−	0.155438i	−0.538279	+	0.842767i	$0.680925\pi$
$588$	29.5360	+	9.59683i	1.21804	+	0.395767i
$589$	0.109046	+	0.335608i	0.00449315	+	0.0138285i
$590$	−19.1788	+	12.5694i	−0.789577	+	0.517476i
$591$	8.28923	−	25.5116i	0.340973	−	1.04941i
$592$	−4.01926	+	5.53204i	−0.165191	+	0.227365i
$593$			31.2580i			1.28361i	0.766866	+	0.641807i	$0.221815\pi$
$593$			31.2580i			1.28361i	−0.766866	+	0.641807i	$0.778185\pi$
$594$	−8.65392	−	6.28744i	−0.355074	−	0.257977i
$595$	0.309271	−	6.41567i	0.0126789	−	0.263017i
$596$	−6.10167	+	4.43312i	−0.249934	+	0.181588i
$597$	−13.4477	−	18.5091i	−0.550376	−	0.757528i
$598$	30.4440	−	9.89184i	1.24495	−	0.404508i
$599$	33.3707			1.36349			0.681746	−	0.731589i	$-0.261221\pi$
$599$	33.3707			1.36349			0.681746	+	0.731589i	$0.261221\pi$
$600$	3.18712	−	7.32300i	0.130114	−	0.298960i
$601$	−46.8052			−1.90922			−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052			−1.90922			−0.954611	+	0.297854i	$0.903729\pi$
$602$	−9.14003	+	2.96978i	−0.372520	+	0.121039i
$603$	−2.35544	−	3.24199i	−0.0959211	−	0.132024i
$604$	33.6024	−	24.4136i	1.36726	−	0.993374i
$605$	−14.6362	−	5.54805i	−0.595047	−	0.225560i
$606$	9.44722	+	6.86381i	0.383767	+	0.278823i
$607$			30.7401i			1.24770i	0.781543	+	0.623851i	$0.214433\pi$
$607$			30.7401i			1.24770i	−0.781543	+	0.623851i	$0.785567\pi$
$608$	−12.2867	+	16.9111i	−0.498289	+	0.685837i
$609$	−3.63013	+	11.1724i	−0.147100	+	0.452728i
$610$	4.57765	−	12.0762i	0.185344	−	0.488953i
$611$	−10.3496	−	31.8527i	−0.418699	−	1.28862i
$612$	−11.8524	−	3.85107i	−0.479104	−	0.155670i
$613$	36.4154	+	11.8321i	1.47081	+	0.477894i	0.931352	−	0.364121i	$-0.118631\pi$
$613$	36.4154	+	11.8321i	1.47081	+	0.477894i	0.539454	+	0.842015i	$0.318631\pi$
$614$	6.10966	+	18.8036i	0.246566	+	0.758852i
$615$	−33.0941	−	26.5702i	−1.33448	−	1.07141i
$616$	−0.445615	+	1.37146i	−0.0179543	+	0.0552577i
$617$	0.249989	−	0.344080i	0.0100642	−	0.0138521i	−0.803955	−	0.594690i	$-0.797275\pi$
$617$	0.249989	−	0.344080i	0.0100642	−	0.0138521i	0.814019	+	0.580838i	$0.197275\pi$
$618$			46.6032i			1.87466i
$619$	6.07691	+	4.41513i	0.244252	+	0.177459i	0.703175	−	0.711016i	$-0.251765\pi$
$619$	6.07691	+	4.41513i	0.244252	+	0.177459i	−0.458924	+	0.888476i	$0.651765\pi$
$620$	0.393017	+	0.599675i	0.0157839	+	0.0240835i
$621$	9.44047	−	6.85890i	0.378833	−	0.275238i
$622$	−35.9523	−	49.4840i	−1.44155	−	1.98413i
$623$	−13.6931	+	4.44914i	−0.548601	+	0.178251i
$624$	23.6020			0.944834
$625$	−17.0374	−	18.2955i	−0.681496	−	0.731822i
$626$	−39.3912			−1.57439
$627$	10.8077	−	3.51165i	0.431619	−	0.140242i
$628$	−2.28467	−	3.14458i	−0.0911682	−	0.125482i
$629$	−5.03258	+	3.65638i	−0.200662	+	0.145789i
$630$	4.65034	+	7.09560i	0.185274	+	0.282696i
$631$	9.11889	+	6.62526i	0.363017	+	0.263747i	0.754309	−	0.656519i	$-0.227972\pi$
$631$	9.11889	+	6.62526i	0.363017	+	0.263747i	−0.391292	+	0.920266i	$0.627972\pi$
$632$			11.5163i			0.458094i
$633$	11.1878	−	15.3987i	0.444676	−	0.612044i
$634$	14.6852	−	45.1963i	0.583223	−	1.79498i
$635$	2.59943	+	2.08700i	0.103155	+	0.0828201i
$636$	−12.0699	−	37.1473i	−0.478602	−	1.47298i
$637$	−19.3021	−	6.27165i	−0.764779	−	0.248492i
$638$	21.3565	+	6.93916i	0.845513	+	0.274724i
$639$	−5.46290	−	16.8131i	−0.216109	−	0.665115i
$640$	−4.53683	+	11.9686i	−0.179334	+	0.473099i
$641$	8.05994	−	24.8060i	0.318349	−	0.979776i	−0.656006	−	0.754756i	$-0.727755\pi$
$641$	8.05994	−	24.8060i	0.318349	−	0.979776i	0.974354	−	0.225020i	$-0.0722448\pi$
$642$	12.9809	−	17.8666i	0.512314	−	0.705140i
$643$			31.9492i			1.25995i	0.776614	+	0.629977i	$0.216936\pi$
$643$			31.9492i			1.25995i	−0.776614	+	0.629977i	$0.783064\pi$
$644$	−8.57817	−	6.23241i	−0.338027	−	0.245591i
$645$	21.3474	+	8.09201i	0.840555	+	0.318623i
$646$	−12.6204	+	9.16923i	−0.496542	+	0.360759i
$647$	4.34628	+	5.98214i	0.170870	+	0.235182i	0.885860	−	0.463952i	$-0.153569\pi$
$647$	4.34628	+	5.98214i	0.170870	+	0.235182i	−0.714990	+	0.699134i	$0.753569\pi$
$648$	−7.69677	+	2.50083i	−0.302358	+	0.0982419i
$649$	−9.83550			−0.386077
$650$	−14.0388	+	32.2568i	−0.550648	+	1.26522i
$651$	−0.297895			−0.0116754
$652$	1.99435	−	0.648002i	0.0781046	−	0.0253777i
$653$	10.9829	+	15.1167i	0.429796	+	0.591563i	0.967906	−	0.251311i	$-0.0808618\pi$
$653$	10.9829	+	15.1167i	0.429796	+	0.591563i	−0.538111	+	0.842874i	$0.680862\pi$
$654$	60.3601	−	43.8542i	2.36027	−	1.71483i
$655$	−1.51967	+	31.5248i	−0.0593784	+	1.23177i
$656$	22.2228	+	16.1458i	0.867654	+	0.630388i
$657$		−	1.42256i		−	0.0554994i
$658$	−12.0742	+	16.6187i	−0.470700	+	0.647863i
$659$	−3.02885	+	9.32184i	−0.117987	+	0.363128i	−0.992558	−	0.121770i	$-0.961143\pi$
$659$	−3.02885	+	9.32184i	−0.117987	+	0.363128i	0.874571	+	0.484897i	$0.161143\pi$
$660$	19.3116	−	12.6565i	0.751703	−	0.492654i
$661$	−8.70145	−	26.7803i	−0.338447	−	1.04163i	−0.964999	−	0.262253i	$-0.915534\pi$
$661$	−8.70145	−	26.7803i	−0.338447	−	1.04163i	0.626552	−	0.779380i	$-0.284466\pi$
$662$	5.87628	+	1.90932i	0.228388	+	0.0742078i
$663$	20.4202	+	6.63492i	0.793054	+	0.257679i
$664$	−0.397637	−	1.22380i	−0.0154313	−	0.0474927i
$665$	5.72850	+	0.276145i	0.222142	+	0.0107085i
$666$	2.53895	−	7.81409i	0.0983824	−	0.302790i
$667$	−14.3987	+	19.8181i	−0.557521	+	0.767361i
$668$			12.2014i			0.472085i
$669$	−50.4120	−	36.6265i	−1.94904	−	1.41606i
$670$	−9.83349	+	2.67910i	−0.379901	+	0.103503i
$671$	4.48150	−	3.25600i	0.173006	−	0.125696i
$672$	−10.3722	−	14.2761i	−0.400116	−	0.550713i
$673$	−37.1153	+	12.0595i	−1.43069	+	0.464859i	−0.918981	−	0.394301i	$-0.870987\pi$
$673$	−37.1153	+	12.0595i	−1.43069	+	0.464859i	−0.511707	+	0.859160i	$0.670987\pi$
$674$	−39.2290			−1.51104
$675$	−1.23353	+	12.7647i	−0.0474785	+	0.491314i
$676$	−3.79434			−0.145936
$677$	−4.78888	+	1.55600i	−0.184052	+	0.0598020i	−0.399593	−	0.916693i	$-0.630848\pi$
$677$	−4.78888	+	1.55600i	−0.184052	+	0.0598020i	0.215541	+	0.976495i	$0.430848\pi$
$678$	−18.2081	−	25.0614i	−0.699280	−	0.962476i
$679$	−13.6721	+	9.93337i	−0.524687	+	0.381208i
$680$	−2.94398	+	3.66684i	−0.112897	+	0.140617i
$681$	39.5590	+	28.7413i	1.51591	+	1.10137i
$682$			0.569440i			0.0218050i
$683$	17.8282	−	24.5384i	0.682178	−	0.938937i	−0.317780	−	0.948165i	$-0.602937\pi$
$683$	17.8282	−	24.5384i	0.682178	−	0.938937i	0.999957	+	0.00922734i	$0.00293719\pi$
$684$	3.43858	−	10.5829i	0.131478	−	0.404646i
$685$	−0.405247	−	1.48743i	−0.0154837	−	0.0568320i
$686$	8.32306	+	25.6157i	0.317776	+	0.978013i
$687$	5.17619	+	1.68185i	0.197484	+	0.0641664i
$688$	−14.0529	−	4.56607i	−0.535762	−	0.174080i
$689$	7.88781	+	24.2762i	0.300502	+	0.924849i
$690$	12.2599	+	44.9991i	0.466725	+	1.71309i
$691$	−6.56134	+	20.1937i	−0.249605	+	0.768205i	0.745240	+	0.666796i	$0.232335\pi$
$691$	−6.56134	+	20.1937i	−0.249605	+	0.768205i	−0.994845	+	0.101409i	$0.967665\pi$
$692$	7.95730	−	10.9523i	0.302491	−	0.416344i
$693$			3.63886i			0.138229i
$694$	38.3600	+	27.8702i	1.45613	+	1.05794i
$695$	23.1991	−	28.8953i	0.879991	−	1.09606i
$696$	6.95781	−	5.05514i	0.263735	−	0.191615i
$697$	14.6881	+	20.2164i	0.556350	+	0.765751i
$698$	3.84445	−	1.24914i	0.145515	−	0.0472806i
$699$	13.0943			0.495273
$700$	11.3775	−	2.51822i	0.430028	−	0.0951799i
$701$	32.7698			1.23770			0.618849	−	0.785510i	$-0.287599\pi$
$701$	32.7698			1.23770			0.618849	+	0.785510i	$0.287599\pi$
$702$	17.1627	−	5.57648i	0.647763	−	0.210471i
$703$	−3.26475	−	4.49354i	−0.123132	−	0.169477i
$704$	−16.9930	+	12.3461i	−0.640447	+	0.465312i
$705$	47.0814	−	12.8272i	1.77319	−	0.483099i
$706$	8.85599	+	6.43425i	0.333299	+	0.242156i
$707$			2.52780i			0.0950676i
$708$	−14.9240	+	20.5411i	−0.560878	+	0.771982i
$709$	−6.13273	+	18.8746i	−0.230320	+	0.708851i	0.767388	+	0.641183i	$0.221556\pi$
$709$	−6.13273	+	18.8746i	−0.230320	+	0.708851i	−0.997708	+	0.0676683i	$0.978444\pi$
$710$	−44.9095	−	2.16489i	−1.68542	−	0.0812467i
$711$	8.98015	+	27.6381i	0.336782	+	1.03651i
$712$	10.0248	+	3.25725i	0.375695	+	0.122071i
$713$	−0.590793	−	0.191960i	−0.0221254	−	0.00718897i
$714$	−4.06943	−	12.5244i	−0.152295	−	0.468715i
$715$	−12.6204	+	8.27117i	−0.471975	+	0.309324i
$716$	6.29100	−	19.3617i	0.235106	−	0.723580i
$717$	−9.08759	+	12.5080i	−0.339382	+	0.467120i
$718$		−	47.1144i		−	1.75829i
$719$	19.5945	+	14.2362i	0.730751	+	0.530922i	0.889801	−	0.456349i	$-0.150843\pi$
$719$	19.5945	+	14.2362i	0.730751	+	0.530922i	−0.159050	+	0.987271i	$0.550843\pi$
$720$	−0.628054	+	13.0287i	−0.0234062	+	0.485550i
$721$	−8.16149	+	5.92967i	−0.303950	+	0.220832i
$722$	15.1012	+	20.7850i	0.562008	+	0.773537i
$723$	2.46676	−	0.801498i	0.0917397	−	0.0298080i
$724$	−33.5609			−1.24728
$725$	−5.81785	−	26.2853i	−0.216069	−	0.976213i
$726$	−32.0914			−1.19102
$727$	5.57804	−	1.81242i	0.206878	−	0.0672188i	−0.203745	−	0.979024i	$-0.565311\pi$
$727$	5.57804	−	1.81242i	0.206878	−	0.0672188i	0.410623	+	0.911805i	$0.365311\pi$
$728$	−1.42994	−	1.96815i	−0.0529972	−	0.0729444i
$729$	−2.83585	+	2.06037i	−0.105032	+	0.0763099i
$730$	−3.38313	−	1.28242i	−0.125215	−	0.0474644i
$731$	−10.8748	−	7.90103i	−0.402220	−	0.292230i
$732$		−	14.3000i		−	0.528542i
$733$	20.2795	−	27.9123i	0.749039	−	1.03096i	−0.249008	−	0.968501i	$-0.580105\pi$
$733$	20.2795	−	27.9123i	0.749039	−	1.03096i	0.998047	−	0.0624625i	$-0.0198954\pi$
$734$	−4.70321	+	14.4750i	−0.173599	+	0.534282i
$735$	10.4812	−	27.6504i	0.386607	−	1.01990i
$736$	−11.3710	−	34.9964i	−0.419142	−	1.28999i
$737$	−4.15759	−	1.35088i	−0.153147	−	0.0497604i
$738$	−31.3900	−	10.1992i	−1.15548	−	0.375439i
$739$	−12.2282	−	37.6345i	−0.449821	−	1.38441i	−0.877109	−	0.480291i	$-0.840531\pi$
$739$	−12.2282	−	37.6345i	−0.449821	−	1.38441i	0.427288	−	0.904116i	$-0.359469\pi$
$740$	−8.80010	−	7.06531i	−0.323498	−	0.259726i
$741$	−5.92426	+	18.2330i	−0.217633	+	0.669805i
$742$	9.20219	−	12.6657i	0.337823	−	0.464974i
$743$		−	29.7058i		−	1.08980i	−0.838501	−	0.544900i	$-0.816567\pi$
$743$		−	29.7058i		−	1.08980i	0.838501	−	0.544900i	$-0.183433\pi$
$744$	0.176440	+	0.128191i	0.00646859	+	0.00469971i
$745$	3.93641	+	6.00627i	0.144219	+	0.220053i
$746$	−37.6332	+	27.3421i	−1.37785	+	1.00107i
$747$	−1.90858	−	2.62694i	−0.0698314	−	0.0961147i
$748$	−12.9296	+	4.20109i	−0.472754	+	0.153607i
$749$	4.78058			0.174679
$750$	−45.9585	−	22.6937i	−1.67817	−	0.828655i
$751$	26.8870			0.981122			0.490561	−	0.871407i	$-0.336792\pi$
$751$	26.8870			0.981122			0.490561	+	0.871407i	$0.336792\pi$
$752$	−30.0375	+	9.75977i	−1.09535	+	0.355902i
$753$	5.95552	+	8.19707i	0.217031	+	0.298718i
$754$	−30.6482	+	22.2672i	−1.11614	+	0.810925i
$755$	−21.6781	−	33.0771i	−0.788949	−	1.20380i
$756$	−4.83591	−	3.51349i	−0.175880	−	0.127784i
$757$		−	44.6792i		−	1.62389i	−0.583731	−	0.811947i	$-0.698408\pi$
$757$		−	44.6792i		−	1.62389i	0.583731	−	0.811947i	$-0.301592\pi$
$758$	40.3826	−	55.5819i	1.46676	−	2.01883i
$759$	−6.18178	+	19.0256i	−0.224384	+	0.690584i
$760$	−3.27409	−	2.62866i	−0.118764	−	0.0953514i
$761$	6.27550	+	19.3140i	0.227487	+	0.700132i	0.998030	+	0.0627441i	$0.0199852\pi$
$761$	6.27550	+	19.3140i	0.227487	+	0.700132i	−0.770543	+	0.637388i	$0.780015\pi$
$762$	6.50010	+	2.11201i	0.235474	+	0.0765100i
$763$	15.3601	+	4.99080i	0.556073	+	0.180679i
$764$	0.918996	+	2.82838i	0.0332481	+	0.102327i
$765$	−4.20597	+	11.0957i	−0.152067	+

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98322 + 0.644389i) q^{2} +(1.29224 + 1.77862i) q^{3} +(1.89991 - 1.38036i) q^{4} +(-1.22570 - 1.87020i) q^{5} +(-3.70892 - 2.69469i) q^{6} -0.992398i q^{7} +(-0.427051 + 0.587785i) q^{8} +(-0.566541 + 1.74363i) q^{9} +O(q^{10})\)	\(q+(-1.98322 + 0.644389i) q^{2} +(1.29224 + 1.77862i) q^{3} +(1.89991 - 1.38036i) q^{4} +(-1.22570 - 1.87020i) q^{5} +(-3.70892 - 2.69469i) q^{6} -0.992398i q^{7} +(-0.427051 + 0.587785i) q^{8} +(-0.566541 + 1.74363i) q^{9} +(3.63597 + 2.91920i) q^{10} +(0.618034 + 1.90211i) q^{11} +(4.91027 + 1.59545i) q^{12} +(-3.20892 - 1.04264i) q^{13} +(0.639490 + 1.96815i) q^{14} +(1.74248 - 4.59680i) q^{15} +(-0.983224 + 3.02605i) q^{16} +(-1.70135 + 2.34171i) q^{17} -3.82309i q^{18} +(-2.09089 - 1.51912i) q^{19} +(-4.91027 - 1.86130i) q^{20} +(1.76510 - 1.28242i) q^{21} +(-2.45140 - 3.37406i) q^{22} +(4.32696 - 1.40591i) q^{23} -1.59730 q^{24} +(-1.99532 + 4.58462i) q^{25} +7.03588 q^{26} +(2.43930 - 0.792578i) q^{27} +(-1.36987 - 1.88546i) q^{28} +(-4.35599 + 3.16481i) q^{29} +(-0.493592 + 10.2393i) q^{30} +(-0.110461 - 0.0802548i) q^{31} -8.08800i q^{32} +(-2.58448 + 3.55723i) q^{33} +(1.86519 - 5.74046i) q^{34} +(-1.85599 + 1.21638i) q^{35} +(1.33047 + 4.09478i) q^{36} +(2.04392 + 0.664110i) q^{37} +(5.12561 + 1.66541i) q^{38} +(-2.29224 - 7.05479i) q^{39} +(1.62271 + 0.0782238i) q^{40} +(2.66780 - 8.21064i) q^{41} +(-2.67421 + 3.68073i) q^{42} +4.64398i q^{43} +(3.79981 + 2.76073i) q^{44} +(3.95536 - 1.07763i) q^{45} +(-7.67537 + 5.57648i) q^{46} +(5.83453 + 8.03054i) q^{47} +(-6.65275 + 2.16161i) q^{48} +6.01515 q^{49} +(1.00289 - 10.3781i) q^{50} -6.36356 q^{51} +(-7.53588 + 2.44856i) q^{52} +(-4.44672 - 6.12038i) q^{53} +(-4.32696 + 3.14372i) q^{54} +(2.79981 - 3.48727i) q^{55} +(0.583317 + 0.423805i) q^{56} -5.68196i q^{57} +(6.59953 - 9.08347i) q^{58} +(-1.51967 + 4.67706i) q^{59} +(-3.03472 - 11.1387i) q^{60} +(-0.855890 - 2.63416i) q^{61} +(0.270785 + 0.0879833i) q^{62} +(1.73038 + 0.562235i) q^{63} +(3.24537 + 9.98822i) q^{64} +(1.98322 + 7.27931i) q^{65} +(2.83337 - 8.72020i) q^{66} +(-1.28477 + 1.76833i) q^{67} +6.79751i q^{68} +(8.09205 + 5.87922i) q^{69} +(2.89701 - 3.60834i) q^{70} +(-7.80098 + 5.66774i) q^{71} +(-0.782941 - 1.07763i) q^{72} +(-0.737953 + 0.239775i) q^{73} -4.48150 q^{74} +(-10.7327 + 2.37552i) q^{75} -6.06943 q^{76} +(1.88765 - 0.613336i) q^{77} +(9.09205 + 12.5141i) q^{78} +(12.8236 - 9.31689i) q^{79} +(6.86447 - 1.87020i) q^{80} +(9.01153 + 6.54726i) q^{81} +18.0026i q^{82} +(-1.04103 + 1.43285i) q^{83} +(1.58332 - 4.87295i) q^{84} +(6.46482 + 0.311640i) q^{85} +(-2.99252 - 9.21004i) q^{86} +(-11.2580 - 3.65794i) q^{87} +(-1.38197 - 0.449028i) q^{88} +(-4.48322 - 13.7979i) q^{89} +(-7.14996 + 4.68596i) q^{90} +(-1.03472 + 3.18453i) q^{91} +(6.28015 - 8.64388i) q^{92} -0.300177i q^{93} +(-16.7460 - 12.1667i) q^{94} +(-0.278260 + 5.77237i) q^{95} +(14.3855 - 10.4516i) q^{96} +(-10.0095 - 13.7768i) q^{97} +(-11.9294 + 3.87609i) q^{98} -3.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9} - 5 q^{10} - 4 q^{11} + 15 q^{12} - 5 q^{13} + 13 q^{14} + 15 q^{15} + 3 q^{16} - 10 q^{17} - 5 q^{19} - 15 q^{20} - 4 q^{21} + 5 q^{23} - 20 q^{24} - 10 q^{25} + 6 q^{26} - 5 q^{27} - 15 q^{28} - 5 q^{29} + 15 q^{30} - 9 q^{31} + 10 q^{33} + 13 q^{34} + 15 q^{35} + 23 q^{36} + 30 q^{37} + 15 q^{38} - 3 q^{39} + 10 q^{40} - 4 q^{41} - 15 q^{42} - 2 q^{44} - 15 q^{45} - 19 q^{46} - 30 q^{48} + 14 q^{49} - 15 q^{50} - 4 q^{51} - 10 q^{52} - 10 q^{53} - 5 q^{54} - 10 q^{55} + 10 q^{56} + 20 q^{58} - 10 q^{60} - 9 q^{61} - 30 q^{62} + 10 q^{63} + 4 q^{64} + 5 q^{65} + 12 q^{66} + 20 q^{67} + 17 q^{69} + 30 q^{70} + 6 q^{71} + 5 q^{72} + 15 q^{73} - 12 q^{74} - 10 q^{75} - 20 q^{76} + 10 q^{77} + 25 q^{78} + 15 q^{79} + 20 q^{80} + 28 q^{81} - 45 q^{83} + 18 q^{84} - 15 q^{85} - 9 q^{86} - 20 q^{87} - 20 q^{88} - 25 q^{89} - 25 q^{90} + 6 q^{91} + 30 q^{92} - 27 q^{94} + 15 q^{95} + 16 q^{96} - 60 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

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