LMFDB - Embedded newform 63.2.h.b.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(25,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("63.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.h (of order $3$, degree $2$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.5
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	63.25
Dual form			63.2.h.b.58.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.05365 q^{2} +(-1.70867 - 0.283604i) q^{3} +2.21746 q^{4} +(0.0731228 - 0.126652i) q^{5} +(-3.50901 - 0.582422i) q^{6} +(-2.33035 + 1.25278i) q^{7} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +O(q^{10})$	\(q+2.05365 q^{2} +(-1.70867 - 0.283604i) q^{3} +2.21746 q^{4} +(0.0731228 - 0.126652i) q^{5} +(-3.50901 - 0.582422i) q^{6} +(-2.33035 + 1.25278i) q^{7} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +(0.150168 - 0.260099i) q^{10} +(-0.832020 - 1.44110i) q^{11} +(-3.78891 - 0.628880i) q^{12} +(0.0999454 + 0.173111i) q^{13} +(-4.78572 + 2.57276i) q^{14} +(-0.160862 + 0.195670i) q^{15} -3.51780 q^{16} +(3.13555 - 5.43093i) q^{17} +(5.83058 + 1.99034i) q^{18} +(3.45879 + 5.99080i) q^{19} +(0.162147 - 0.280847i) q^{20} +(4.33711 - 1.47969i) q^{21} +(-1.70867 - 2.95951i) q^{22} +(3.09092 - 5.35363i) q^{23} +(-0.763064 - 0.126652i) q^{24} +(2.48931 + 4.31160i) q^{25} +(0.205252 + 0.355508i) q^{26} +(-4.57630 - 2.46119i) q^{27} +(-5.16746 + 2.77798i) q^{28} +(-2.46757 + 4.27396i) q^{29} +(-0.330354 + 0.401837i) q^{30} -2.51780 q^{31} -8.11747 q^{32} +(1.01295 + 2.69834i) q^{33} +(6.43931 - 11.1532i) q^{34} +(-0.0117348 + 0.386752i) q^{35} +(6.29567 + 2.14910i) q^{36} +(-3.50023 - 6.06257i) q^{37} +(7.10312 + 12.3030i) q^{38} +(-0.121679 - 0.324134i) q^{39} +(0.0326554 - 0.0565608i) q^{40} +(1.15895 + 2.00736i) q^{41} +(8.90688 - 3.03876i) q^{42} +(-0.940993 + 1.62985i) q^{43} +(-1.84497 - 3.19558i) q^{44} +(0.330354 - 0.288715i) q^{45} +(6.34765 - 10.9944i) q^{46} -1.81177 q^{47} +(6.01077 + 0.997660i) q^{48} +(3.86110 - 5.83883i) q^{49} +(5.11215 + 8.85451i) q^{50} +(-6.89787 + 8.39045i) q^{51} +(0.221625 + 0.383865i) q^{52} +(-2.67307 + 4.62989i) q^{53} +(-9.39810 - 5.05442i) q^{54} -0.243359 q^{55} +(-1.04069 + 0.559468i) q^{56} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 + 8.77720i) q^{58} -4.57099 q^{59} +(-0.356705 + 0.433890i) q^{60} -0.678276 q^{61} -5.17066 q^{62} +(-7.83035 + 1.29829i) q^{63} -9.63481 q^{64} +0.0292332 q^{65} +(2.08024 + 5.54143i) q^{66} -6.18684 q^{67} +(6.95296 - 12.0429i) q^{68} +(-6.79968 + 8.27101i) q^{69} +(-0.0240991 + 0.794251i) q^{70} +1.27749 q^{71} +(1.26791 + 0.432816i) q^{72} +(-0.778603 + 1.34858i) q^{73} +(-7.18823 - 12.4504i) q^{74} +(-3.03063 - 8.07311i) q^{75} +(7.66972 + 13.2843i) q^{76} +(3.74428 + 2.31594i) q^{77} +(-0.249886 - 0.665657i) q^{78} +12.7957 q^{79} +(-0.257231 + 0.445537i) q^{80} +(7.12141 + 5.50323i) q^{81} +(2.38008 + 4.12241i) q^{82} +(3.75687 - 6.50709i) q^{83} +(9.61736 - 3.28115i) q^{84} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 + 3.34713i) q^{86} +(5.42839 - 6.60299i) q^{87} +(-0.371566 - 0.643571i) q^{88} +(4.53394 + 7.85301i) q^{89} +(0.678430 - 0.592918i) q^{90} +(-0.449777 - 0.278199i) q^{91} +(6.85398 - 11.8714i) q^{92} +(4.30209 + 0.714056i) q^{93} -3.72074 q^{94} +1.01167 q^{95} +(13.8701 + 2.30214i) q^{96} +(-3.98514 + 6.90246i) q^{97} +(7.92933 - 11.9909i) q^{98} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - q^3 + 8 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 + 11 * q^9	\( 10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9} - 7 q^{10} + 4 q^{11} - 20 q^{12} - 8 q^{13} - 20 q^{14} - 19 q^{15} - 4 q^{16} + 12 q^{17} + 4 q^{18} + q^{19} + 5 q^{20} + 13 q^{21} - q^{22} + 3 q^{23} + 6 q^{24} - q^{25} + 11 q^{26} - 7 q^{27} - 2 q^{28} + 7 q^{29} + 16 q^{30} + 6 q^{31} + 4 q^{32} + 14 q^{33} + 3 q^{34} + 5 q^{35} + 34 q^{36} + 20 q^{38} + 2 q^{39} - 3 q^{40} + 5 q^{41} - 4 q^{42} - 7 q^{43} - 10 q^{44} - 16 q^{45} + 3 q^{46} - 54 q^{47} - 5 q^{48} - 8 q^{49} + 19 q^{50} - 9 q^{51} - 10 q^{52} - 21 q^{53} + q^{54} + 4 q^{55} + 18 q^{56} - 4 q^{57} - 10 q^{58} - 60 q^{59} + 10 q^{60} + 28 q^{61} - 12 q^{62} - 59 q^{63} - 50 q^{64} + 22 q^{65} + 19 q^{66} + 4 q^{67} + 27 q^{68} + 15 q^{69} + 40 q^{70} - 6 q^{71} - 36 q^{72} + 15 q^{73} - 36 q^{74} - 14 q^{75} + 5 q^{76} + 11 q^{77} - 20 q^{78} + 8 q^{79} + 20 q^{80} + 23 q^{81} - 5 q^{82} + 9 q^{83} + 35 q^{84} - 6 q^{85} - 8 q^{86} + 2 q^{87} - 18 q^{88} + 28 q^{89} + 28 q^{90} - 4 q^{91} + 27 q^{92} - 6 q^{93} + 6 q^{94} + 28 q^{95} + 59 q^{96} - 12 q^{97} + 59 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - q^3 + 8 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 + 11 * q^9 - 7 * q^10 + 4 * q^11 - 20 * q^12 - 8 * q^13 - 20 * q^14 - 19 * q^15 - 4 * q^16 + 12 * q^17 + 4 * q^18 + q^19 + 5 * q^20 + 13 * q^21 - q^22 + 3 * q^23 + 6 * q^24 - q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 + 16 * q^30 + 6 * q^31 + 4 * q^32 + 14 * q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 + 20 * q^38 + 2 * q^39 - 3 * q^40 + 5 * q^41 - 4 * q^42 - 7 * q^43 - 10 * q^44 - 16 * q^45 + 3 * q^46 - 54 * q^47 - 5 * q^48 - 8 * q^49 + 19 * q^50 - 9 * q^51 - 10 * q^52 - 21 * q^53 + q^54 + 4 * q^55 + 18 * q^56 - 4 * q^57 - 10 * q^58 - 60 * q^59 + 10 * q^60 + 28 * q^61 - 12 * q^62 - 59 * q^63 - 50 * q^64 + 22 * q^65 + 19 * q^66 + 4 * q^67 + 27 * q^68 + 15 * q^69 + 40 * q^70 - 6 * q^71 - 36 * q^72 + 15 * q^73 - 36 * q^74 - 14 * q^75 + 5 * q^76 + 11 * q^77 - 20 * q^78 + 8 * q^79 + 20 * q^80 + 23 * q^81 - 5 * q^82 + 9 * q^83 + 35 * q^84 - 6 * q^85 - 8 * q^86 + 2 * q^87 - 18 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 6 * q^93 + 6 * q^94 + 28 * q^95 + 59 * q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.05365			1.45215			0.726073	−	0.687617i	$-0.241343\pi$
$2$	2.05365			1.45215			0.726073	+	0.687617i	$0.241343\pi$
$3$	−1.70867	−	0.283604i	−0.986504	−	0.163739i
$3$	−1.70867	−	0.283604i	−0.986504	−	0.163739i
$4$	2.21746			1.10873
$5$	0.0731228	−	0.126652i	0.0327015	−	0.0566407i	−0.849211	−	0.528053i	$-0.822922\pi$
$5$	0.0731228	−	0.126652i	0.0327015	−	0.0566407i	0.881913	+	0.471412i	$0.156256\pi$
$6$	−3.50901	−	0.582422i	−1.43255	−	0.237773i
$7$	−2.33035	+	1.25278i	−0.880791	+	0.473505i
$7$	−2.33035	+	1.25278i	−0.880791	+	0.473505i
$8$	0.446582			0.157891
$9$	2.83914	+	0.969173i	0.946379	+	0.323058i
$10$	0.150168	−	0.260099i	0.0474874	−	0.0822506i
$11$	−0.832020	−	1.44110i	−0.250864	−	0.434508i	0.712900	−	0.701265i	$-0.247381\pi$
$11$	−0.832020	−	1.44110i	−0.250864	−	0.434508i	−0.963764	+	0.266757i	$0.914048\pi$
$12$	−3.78891	−	0.628880i	−1.09377	−	0.181542i
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$	−4.78572	+	2.57276i	−1.27904	+	0.687599i
$15$	−0.160862	+	0.195670i	−0.0415345	+	0.0505218i
$16$	−3.51780			−0.879449
$17$	3.13555	−	5.43093i	0.760483	−	1.31720i	−0.182119	−	0.983277i	$-0.558296\pi$
$17$	3.13555	−	5.43093i	0.760483	−	1.31720i	0.942602	−	0.333919i	$-0.108371\pi$
$18$	5.83058	+	1.99034i	1.37428	+	0.469127i
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	0.923787	+	0.382907i	$0.125077\pi$
$19$	3.45879	+	5.99080i	0.793500	+	1.37438i	−0.130287	+	0.991476i	$0.541590\pi$
$20$	0.162147	−	0.280847i	0.0362571	−	0.0627992i
$21$	4.33711	−	1.47969i	0.946435	−	0.322895i
$22$	−1.70867	−	2.95951i	−0.364291	−	0.630970i
$23$	3.09092	−	5.35363i	0.644501	−	1.11631i	−0.339916	−	0.940456i	$-0.610399\pi$
$23$	3.09092	−	5.35363i	0.644501	−	1.11631i	0.984417	−	0.175852i	$-0.0562682\pi$
$24$	−0.763064	−	0.126652i	−0.155760	−	0.0258528i
$25$	2.48931	+	4.31160i	0.497861	+	0.862321i
$26$	0.205252	+	0.355508i	0.0402533	+	0.0697208i
$27$	−4.57630	−	2.46119i	−0.880710	−	0.473657i
$28$	−5.16746	+	2.77798i	−0.976559	+	0.524989i
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	−0.998867	−	0.0475930i	$-0.984845\pi$
$29$	−2.46757	+	4.27396i	−0.458217	+	0.793655i	0.540650	+	0.841248i	$0.318178\pi$
$30$	−0.330354	+	0.401837i	−0.0603141	+	0.0733650i
$31$	−2.51780			−0.452209			−0.226105	−	0.974103i	$-0.572599\pi$
$31$	−2.51780			−0.452209			−0.226105	+	0.974103i	$0.572599\pi$
$32$	−8.11747			−1.43498
$33$	1.01295	+	2.69834i	0.176332	+	0.469720i
$34$	6.43931	−	11.1532i	1.10433	−	1.91276i
$35$	−0.0117348	+	0.386752i	−0.00198354	+	0.0653730i
$36$	6.29567	+	2.14910i	1.04928	+	0.358184i
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	−0.995994	−	0.0894162i	$-0.971500\pi$
$37$	−3.50023	−	6.06257i	−0.575434	−	0.996681i	0.420560	−	0.907264i	$-0.361833\pi$
$38$	7.10312	+	12.3030i	1.15228	+	1.99581i
$39$	−0.121679	−	0.324134i	−0.0194843	−	0.0519030i
$40$	0.0326554	−	0.0565608i	0.00516327	−	0.00894304i
$41$	1.15895	+	2.00736i	0.180998	+	0.313498i	0.942221	−	0.334993i	$-0.108734\pi$
$41$	1.15895	+	2.00736i	0.180998	+	0.313498i	−0.761223	+	0.648491i	$0.775401\pi$
$42$	8.90688	−	3.03876i	1.37436	−	0.468891i
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	−0.928812	−	0.370550i	$-0.879169\pi$
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	0.785312	+	0.619100i	$0.212502\pi$
$44$	−1.84497	−	3.19558i	−0.278140	−	0.481752i
$45$	0.330354	−	0.288715i	0.0492463	−	0.0430391i
$46$	6.34765	−	10.9944i	0.935910	−	1.62104i
$47$	−1.81177			−0.264275			−0.132137	−	0.991231i	$-0.542184\pi$
$47$	−1.81177			−0.264275			−0.132137	+	0.991231i	$0.542184\pi$
$48$	6.01077	+	0.997660i	0.867579	+	0.144000i
$49$	3.86110	−	5.83883i	0.551586	−	0.834118i
$50$	5.11215	+	8.85451i	0.722967	+	1.25222i
$51$	−6.89787	+	8.39045i	−0.965895	+	1.17490i
$52$	0.221625	+	0.383865i	0.0307338	+	0.0532325i
$53$	−2.67307	+	4.62989i	−0.367174	+	0.635964i	−0.989123	−	0.147094i	$-0.953008\pi$
$53$	−2.67307	+	4.62989i	−0.367174	+	0.635964i	0.621948	+	0.783058i	$0.286341\pi$
$54$	−9.39810	−	5.05442i	−1.27892	−	0.687819i
$55$	−0.243359			−0.0328145
$56$	−1.04069	+	0.559468i	−0.139069	+	0.0747621i
$57$	−4.21093	−	11.2172i	−0.557751	−	1.48576i
$58$	−5.06752	+	8.77720i	−0.665398	+	1.15250i
$59$	−4.57099			−0.595092			−0.297546	−	0.954708i	$-0.596168\pi$
$59$	−4.57099			−0.595092			−0.297546	+	0.954708i	$0.596168\pi$
$60$	−0.356705	+	0.433890i	−0.0460505	+	0.0560149i
$61$	−0.678276			−0.0868443			−0.0434221	−	0.999057i	$-0.513826\pi$
$61$	−0.678276			−0.0868443			−0.0434221	+	0.999057i	$0.513826\pi$
$62$	−5.17066			−0.656674
$63$	−7.83035	+	1.29829i	−0.986532	+	0.163569i
$64$	−9.63481			−1.20435
$65$	0.0292332			0.00362593
$66$	2.08024	+	5.54143i	0.256060	+	0.682103i
$67$	−6.18684			−0.755842			−0.377921	−	0.925838i	$-0.623361\pi$
$67$	−6.18684			−0.755842			−0.377921	+	0.925838i	$0.623361\pi$
$68$	6.95296	−	12.0429i	0.843170	−	1.46041i
$69$	−6.79968	+	8.27101i	−0.818586	+	0.995713i
$70$	−0.0240991	+	0.794251i	−0.00288039	+	0.0949311i
$71$	1.27749			0.151611			0.0758053	−	0.997123i	$-0.475847\pi$
$71$	1.27749			0.151611			0.0758053	+	0.997123i	$0.475847\pi$
$72$	1.26791	+	0.432816i	0.149424	+	0.0510078i
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	−0.907986	−	0.419000i	$-0.862381\pi$
$73$	−0.778603	+	1.34858i	−0.0911286	+	0.157839i	0.816858	+	0.576839i	$0.195714\pi$
$74$	−7.18823	−	12.4504i	−0.835614	−	1.44733i
$75$	−3.03063	−	8.07311i	−0.349947	−	0.932202i
$76$	7.66972	+	13.2843i	0.879777	+	1.52382i
$77$	3.74428	+	2.31594i	0.426700	+	0.263926i
$78$	−0.249886	−	0.665657i	−0.0282940	−	0.0753708i
$79$	12.7957			1.43963			0.719817	−	0.694164i	$-0.244226\pi$
$79$	12.7957			1.43963			0.719817	+	0.694164i	$0.244226\pi$
$80$	−0.257231	+	0.445537i	−0.0287593	+	0.0498126i
$81$	7.12141	+	5.50323i	0.791267	+	0.611470i
$82$	2.38008	+	4.12241i	0.262835	+	0.455244i
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	−0.582778	−	0.812631i	$-0.698034\pi$
$83$	3.75687	−	6.50709i	0.412370	−	0.714246i	0.995148	+	0.0983854i	$0.0313678\pi$
$84$	9.61736	−	3.28115i	1.04934	−	0.358003i
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$	−1.93247	+	3.34713i	−0.208383	+	0.360930i
$87$	5.42839	−	6.60299i	0.581984	−	0.707915i
$88$	−0.371566	−	0.643571i	−0.0396090	−	0.0686048i
$89$	4.53394	+	7.85301i	0.480597	+	0.832418i	0.999752	−	0.0222619i	$-0.00708678\pi$
$89$	4.53394	+	7.85301i	0.480597	+	0.832418i	−0.519155	+	0.854680i	$0.673753\pi$
$90$	0.678430	−	0.592918i	0.0715128	−	0.0624991i
$91$	−0.449777	−	0.278199i	−0.0471494	−	0.0291632i
$92$	6.85398	−	11.8714i	0.714577	−	1.23768i
$93$	4.30209	+	0.714056i	0.446106	+	0.0740442i
$94$	−3.72074			−0.383765
$95$	1.01167			0.103795
$96$	13.8701	+	2.30214i	1.41561	+	0.234962i
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	−0.994278	−	0.106821i	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$	7.92933	−	11.9909i	0.800983	−	1.21126i
$99$	−0.965543	−	4.89786i	−0.0970408	−	0.492253i
$100$	5.51993	+	9.56080i	0.551993	+	0.956080i
$101$	−7.42150	−	12.8544i	−0.738467	−	1.27906i	−0.953186	−	0.302386i	$-0.902217\pi$
$101$	−7.42150	−	12.8544i	−0.738467	−	1.27906i	0.214719	−	0.976676i	$-0.431117\pi$
$102$	−14.1658	+	17.2310i	−1.40262	+	1.70612i
$103$	0.101974	−	0.176624i	0.0100478	−	0.0174033i	−0.860958	−	0.508676i	$-0.830135\pi$
$103$	0.101974	−	0.176624i	0.0100478	−	0.0174033i	0.871006	+	0.491273i	$0.163468\pi$
$104$	0.0446339	+	0.0773081i	0.00437671	+	0.00758068i
$105$	0.129735	−	0.657505i	0.0126609	−	0.0641659i
$106$	−5.48953	+	9.50815i	−0.533191	+	0.923513i
$107$	3.48444	+	6.03524i	0.336854	+	0.583448i	0.983839	−	0.179054i	$-0.0573038\pi$
$107$	3.48444	+	6.03524i	0.336854	+	0.583448i	−0.646985	+	0.762503i	$0.723970\pi$
$108$	−10.1478	−	5.45759i	−0.976468	−	0.525157i
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	−0.661270	−	0.750148i	$-0.729982\pi$
$109$	3.33058	−	5.76874i	0.319012	−	0.552545i	0.980282	+	0.197603i	$0.0633157\pi$
$110$	−0.499772			−0.0476514
$111$	4.26138	+	11.3516i	0.404472	+	1.07745i
$112$	8.19771	−	4.40701i	0.774611	−	0.416424i
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	0.865115	−	0.501573i	$-0.167245\pi$
$113$	−0.0193234	−	0.0334691i	−0.00181779	−	0.00314851i	−0.866933	+	0.498425i	$0.833912\pi$
$114$	−8.64776	−	23.0362i	−0.809937	−	2.15754i
$115$	−0.452033	−	0.782945i	−0.0421523	−	0.0730100i
$116$	−5.47174	+	9.47733i	−0.508038	+	0.879948i
$117$	0.115985	+	0.588349i	0.0107228	+	0.0543929i
$118$	−9.38718			−0.864160
$119$	−0.503195	+	16.5841i	−0.0461278	+	1.52027i
$120$	−0.0718382	+	0.0873827i	−0.00655790	+	0.00797692i
$121$	4.11548	−	7.12823i	0.374135	−	0.648021i
$122$	−1.39294			−0.126111
$123$	−1.41098	−	3.75862i	−0.127223	−	0.338903i
$124$	−5.58311			−0.501378
$125$	1.45933			0.130526
$126$	−16.0808	+	2.66623i	−1.43259	+	0.237526i
$127$	13.4788			1.19605			0.598027	−	0.801476i	$-0.295952\pi$
$127$	13.4788			1.19605			0.598027	+	0.801476i	$0.295952\pi$
$128$	−3.55154			−0.313915
$129$	2.07008	−	2.51801i	0.182261	−	0.221698i
$130$	0.0600345			0.00526538
$131$	9.91665	−	17.1761i	0.866422	−	1.50069i	0.000793988	−	1.00000i	$-0.499747\pi$
$131$	9.91665	−	17.1761i	0.866422	−	1.50069i	0.865628	−	0.500687i	$-0.166919\pi$
$132$	2.24617	+	5.98345i	0.195504	+	0.520793i
$133$	−15.5653	−	9.62759i	−1.34969	−	0.834818i
$134$	−12.7056			−1.09759
$135$	−0.646348	+	0.399630i	−0.0556288	+	0.0343947i
$136$	1.40028	−	2.42536i	0.120073	−	0.207973i
$137$	3.22255	+	5.58162i	0.275321	+	0.476870i	0.970216	−	0.242241i	$-0.0778826\pi$
$137$	3.22255	+	5.58162i	0.275321	+	0.476870i	−0.694895	+	0.719111i	$0.744549\pi$
$138$	−13.9641	+	16.9857i	−1.18871	+	1.44592i
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	0.999328	+	0.0366611i	$0.0116722\pi$
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	−0.467914	+	0.883774i	$0.654994\pi$
$140$	−0.0260214	+	0.857606i	−0.00219921	+	0.0724809i
$141$	3.09573	+	0.513826i	0.260708	+	0.0432720i
$142$	2.62352			0.220161
$143$	0.166313	−	0.288063i	0.0139078	−	0.0240890i
$144$	−9.98750	−	3.40935i	−0.832292	−	0.284113i
$145$	0.360872	+	0.625048i	0.0299688	+	0.0519074i
$146$	−1.59897	+	2.76950i	−0.132332	+	0.229206i
$147$	−8.25328	+	8.88163i	−0.680719	+	0.732545i
$148$	−7.76161	−	13.4435i	−0.638000	−	1.10505i
$149$	−8.88364	+	15.3869i	−0.727776	+	1.26054i	0.230045	+	0.973180i	$0.426113\pi$
$149$	−8.88364	+	15.3869i	−0.727776	+	1.26054i	−0.957821	+	0.287365i	$0.907221\pi$
$150$	−6.22383	−	16.5793i	−0.508174	−	1.35369i
$151$	−4.23300	−	7.33177i	−0.344476	−	0.596651i	0.640782	−	0.767723i	$-0.278610\pi$
$151$	−4.23300	−	7.33177i	−0.344476	−	0.596651i	−0.985259	+	0.171072i	$0.945277\pi$
$152$	1.54463	+	2.67538i	0.125286	+	0.217002i
$153$	14.1658	−	12.3803i	1.14524	−	1.00089i
$154$	7.68942	+	4.75612i	0.619631	+	0.383259i
$155$	−0.184108	+	0.318885i	−0.0147879	+	0.0256135i
$156$	−0.269819	−	0.718755i	−0.0216028	−	0.0575464i
$157$	5.69935			0.454858			0.227429	−	0.973795i	$-0.426968\pi$
$157$	5.69935			0.454858			0.227429	+	0.973795i	$0.426968\pi$
$158$	26.2779			2.09056
$159$	5.88046	−	7.15288i	0.466351	−	0.567261i
$160$	−0.593572	+	1.02810i	−0.0469260	+	0.0812782i
$161$	−0.496032	+	16.3481i	−0.0390928	+	1.28841i
$162$	14.6248	+	11.3017i	1.14904	+	0.887944i
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	0.821403	−	0.570349i	$-0.193192\pi$
$163$	−1.06267	−	1.84060i	−0.0832349	−	0.144167i	−0.904638	+	0.426181i	$0.859859\pi$
$164$	2.56993	+	4.45125i	0.200678	+	0.347584i
$165$	0.415821	+	0.0690175i	0.0323716	+	0.00537300i
$166$	7.71528	−	13.3632i	0.598821	−	1.03719i
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	0.550415	−	0.834891i	$-0.314470\pi$
$167$	−5.78723	−	10.0238i	−0.447829	−	0.775663i	−0.998244	+	0.0592278i	$0.981136\pi$
$168$	1.93688	−	0.660804i	0.149433	−	0.0509821i
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$	−0.941721	−	1.63111i	−0.0722267	−	0.125100i
$171$	4.01386	+	20.3609i	0.306947	+	1.55703i
$172$	−2.08661	+	3.61412i	−0.159103	+	0.275574i
$173$	−15.9109			−1.20968			−0.604842	−	0.796345i	$-0.706764\pi$
$173$	−15.9109			−1.20968			−0.604842	+	0.796345i	$0.706764\pi$
$174$	11.1480	−	13.5602i	0.845127	−	1.02800i
$175$	−11.2024	−	6.92902i	−0.846825	−	0.523785i
$176$	2.92688	+	5.06950i	0.220622	+	0.382128i
$177$	7.81033	+	1.29635i	0.587060	+	0.0974395i
$178$	9.31110	+	16.1273i	0.697897	+	1.20879i
$179$	3.87665	−	6.71456i	0.289755	−	0.501870i	−0.683996	−	0.729485i	$-0.739760\pi$
$179$	3.87665	−	6.71456i	0.289755	−	0.501870i	0.973751	+	0.227615i	$0.0730929\pi$
$180$	0.732546	−	0.640214i	0.0546008	−	0.0477187i
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$	−0.923682	−	0.571323i	−0.0684679	−	0.0423493i
$183$	1.15895	+	0.192362i	0.0856722	+	0.0142198i
$184$	1.38035	−	2.39084i	0.101761	−	0.176255i
$185$	−1.02379			−0.0752703
$186$	8.83497	+	1.46642i	0.647812	+	0.107523i
$187$	−10.4354			−0.763110
$188$	−4.01754			−0.293009
$189$	13.7477	+	0.00236321i	1.00000	+	0.000171898i
$190$	2.07760			0.150725
$191$	−4.96765			−0.359447			−0.179723	−	0.983717i	$-0.557520\pi$
$191$	−4.96765			−0.359447			−0.179723	+	0.983717i	$0.557520\pi$
$192$	16.4628	+	2.73247i	1.18810	+	0.197199i
$193$	−14.9044			−1.07284			−0.536422	−	0.843950i	$-0.680224\pi$
$193$	−14.9044			−1.07284			−0.536422	+	0.843950i	$0.680224\pi$
$194$	−8.18406	+	14.1752i	−0.587581	+	1.01772i
$195$	−0.0499500	−	0.00829064i	−0.00357699	−	0.000593705i
$196$	8.56183	−	12.9474i	0.611559	−	0.924811i
$197$	−21.2608			−1.51477			−0.757386	−	0.652968i	$-0.773524\pi$
$197$	−21.2608			−1.51477			−0.757386	+	0.652968i	$0.773524\pi$
$198$	−1.98288	−	10.0585i	−0.140917	−	0.714824i
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	0.259098	+	0.965851i	$0.416575\pi$
$199$	−9.97208	+	17.2722i	−0.706902	+	1.22439i	−0.966001	+	0.258540i	$0.916759\pi$
$200$	1.11168	+	1.92549i	0.0786077	+	0.136152i
$201$	10.5713	+	1.75461i	0.745641	+	0.123761i
$202$	−15.2411	−	26.3984i	−1.07236	−	1.85739i
$203$	0.395997	−	13.0512i	0.0277935	−	0.916012i
$204$	−15.2957	+	18.6055i	−1.07092	+	1.30264i
$205$	0.338983			0.0236756
$206$	0.209419	−	0.362724i	0.0145909	−	0.0252722i
$207$	13.9641	−	12.2040i	0.970574	−	0.848240i
$208$	−0.351587	−	0.608967i	−0.0243782	−	0.0422243i
$209$	5.75556	−	9.96893i	0.398121	−	0.689565i
$210$	0.266430	−	1.35028i	0.0183854	−	0.0931783i
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	0.913293	+	0.407303i	$0.133531\pi$
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	−0.103912	+	0.994587i	$0.533136\pi$
$212$	−5.92742	+	10.2666i	−0.407097	+	0.705112i
$213$	−2.18282	−	0.362302i	−0.149564	−	0.0248245i
$214$	7.15581	+	12.3942i	0.489161	+	0.847252i
$215$	0.137616	+	0.238358i	0.00938535	+	0.0162559i
$216$	−2.04370	−	1.09912i	−0.139056	−	0.0747860i
$217$	5.86735	−	3.15424i	0.398302	−	0.214123i
$218$	6.83983	−	11.8469i	0.463252	−	0.802376i
$219$	1.71284	−	2.08347i	0.115743	−	0.140788i
$220$	−0.539638			−0.0363824
$221$	1.25354			0.0843220
$222$	8.75137	+	23.3122i	0.587353	+	1.56462i
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	−0.789995	−	0.613113i	$-0.789917\pi$
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	0.925969	+	0.377600i	$0.123250\pi$
$224$	18.9166	−	10.1694i	1.26392	−	0.679470i
$225$	2.88879	+	14.6538i	0.192586	+	0.976921i
$226$	−0.0396834	−	0.0687336i	−0.00263970	−	0.00457209i
$227$	1.92643	+	3.33667i	0.127861	+	0.221462i	0.922848	−	0.385165i	$-0.125855\pi$
$227$	1.92643	+	3.33667i	0.127861	+	0.221462i	−0.794986	+	0.606627i	$0.792522\pi$
$228$	−9.33756	−	24.8738i	−0.618395	−	1.64731i
$229$	−6.55812	+	11.3590i	−0.433373	+	0.750624i	−0.997161	−	0.0752952i	$-0.976010\pi$
$229$	−6.55812	+	11.3590i	−0.433373	+	0.750624i	0.563788	+	0.825919i	$0.309343\pi$
$230$	−0.928316	−	1.60789i	−0.0612113	−	0.106021i
$231$	−5.74095	−	5.01908i	−0.377727	−	0.330231i
$232$	−1.10197	+	1.90868i	−0.0723481	+	0.125311i
$233$	−8.75115	−	15.1574i	−0.573307	−	0.992997i	−0.996223	−	0.0868284i	$-0.972327\pi$
$233$	−8.75115	−	15.1574i	−0.573307	−	0.992997i	0.422916	−	0.906169i	$-0.361007\pi$
$234$	0.238191	+	1.20826i	0.0155711	+	0.0789864i
$235$	−0.132482	+	0.229466i	−0.00864218	+	0.0149687i
$236$	−10.1360			−0.659795
$237$	−21.8638	−	3.62892i	−1.42020	−	0.235724i
$238$	−1.03338	+	34.0580i	−0.0669843	+	2.20765i
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	0.959752	−	0.280849i	$-0.0906161\pi$
$239$	3.65857	+	6.33683i	0.236653	+	0.409895i	−0.723099	+	0.690745i	$0.757283\pi$
$240$	0.565880	−	0.688327i	0.0365274	−	0.0444313i
$241$	−3.11553	−	5.39626i	−0.200689	−	0.347604i	0.748062	−	0.663629i	$-0.230985\pi$
$241$	−3.11553	−	5.39626i	−0.200689	−	0.347604i	−0.948751	+	0.316026i	$0.897651\pi$
$242$	8.45174	−	14.6389i	0.543299	−	0.941021i
$243$	−10.6074	−	11.4229i	−0.680467	−	0.732779i
$244$	−1.50405			−0.0962868
$245$	−0.457167	−	0.915969i	−0.0292074	−	0.0585191i
$246$	−2.89764	−	7.71886i	−0.184747	−	0.492137i
$247$	−0.691380	+	1.19751i	−0.0439915	+	0.0761954i
$248$	−1.12440			−0.0713997
$249$	−8.26470	+	10.0530i	−0.523754	+	0.637085i
$250$	2.99694			0.189543
$251$	5.65283			0.356803			0.178402	−	0.983958i	$-0.442907\pi$
$251$	5.65283			0.356803			0.178402	+	0.983958i	$0.442907\pi$
$252$	−17.3635	+	2.87890i	−1.09380	+	0.181354i
$253$	−10.2868			−0.646727
$254$	27.6808			1.73684
$255$	0.558279	+	1.48717i	0.0349608	+	0.0931299i
$256$	11.9760			0.748501
$257$	−5.90082	+	10.2205i	−0.368083	+	0.637539i	−0.989266	−	0.146127i	$-0.953319\pi$
$257$	−5.90082	+	10.2205i	−0.368083	+	0.637539i	0.621183	+	0.783666i	$0.286653\pi$
$258$	4.25121	−	5.17110i	0.264669	−	0.321939i
$259$	15.7518	+	9.74293i	0.978770	+	0.605396i
$260$	0.0648233			0.00402017
$261$	−11.1480	+	9.74286i	−0.690043	+	0.603068i
$262$	20.3653	−	35.2737i	1.25817	−	2.17922i
$263$	11.1200	+	19.2605i	0.685691	+	1.18765i	0.973219	+	0.229879i	$0.0738331\pi$
$263$	11.1200	+	19.2605i	0.685691	+	1.18765i	−0.287528	+	0.957772i	$0.592834\pi$
$264$	0.452366	+	1.20503i	0.0278412	+	0.0741645i
$265$	0.390925	+	0.677101i	0.0240143	+	0.0415940i
$266$	−31.9657	−	19.7716i	−1.95994	−	1.21228i
$267$	−5.51988	−	14.7041i	−0.337811	−	0.899876i
$268$	−13.7191			−0.838024
$269$	−1.19442	+	2.06880i	−0.0728251	+	0.126137i	−0.900138	−	0.435604i	$-0.856535\pi$
$269$	−1.19442	+	2.06880i	−0.0728251	+	0.126137i	0.827313	+	0.561741i	$0.189868\pi$
$270$	−1.32737	+	0.820699i	−0.0807811	+	0.0499462i
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	−0.966534	−	0.256537i	$-0.917419\pi$
$271$	−11.6129	−	20.1142i	−0.705435	−	1.22185i	0.261100	−	0.965312i	$-0.415915\pi$
$272$	−11.0302	+	19.1049i	−0.668806	+	1.15841i
$273$	0.689624	+	0.602911i	0.0417380	+	0.0364898i
$274$	6.61797	+	11.4627i	0.399806	+	0.692484i
$275$	4.14231	−	7.17469i	0.249790	−	0.432650i
$276$	−15.0780	+	18.3406i	−0.907590	+	1.10398i
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	0.927018	−	0.375017i	$-0.122363\pi$
$277$	2.30900	+	3.99931i	0.138734	+	0.240295i	−0.788283	+	0.615312i	$0.789030\pi$
$278$	12.8666	+	22.2857i	0.771690	+	1.33661i
$279$	−7.14837	−	2.44018i	−0.427962	−	0.146090i
$280$	−0.00524055	+	0.172716i	−0.000313183	+	0.0103218i
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	−0.634215	−	0.773157i	$-0.718676\pi$
$281$	5.90841	−	10.2337i	0.352466	−	0.610489i	0.986681	+	0.162668i	$0.0520098\pi$
$282$	6.35754	+	1.05522i	0.378586	+	0.0628372i
$283$	15.8497			0.942165			0.471082	−	0.882089i	$-0.343863\pi$
$283$	15.8497			0.942165			0.471082	+	0.882089i	$0.343863\pi$
$284$	2.83279			0.168095
$285$	−1.72861	−	0.286912i	−0.102394	−	0.0169952i
$286$	0.341548	−	0.591579i	0.0201962	−	0.0349808i
$287$	−5.21555	−	3.22596i	−0.307864	−	0.190422i
$288$	−23.0466	−	7.86723i	−1.35803	−	0.463581i
$289$	−11.1634	−	19.3355i	−0.656669	−	1.13738i
$290$	0.741102	+	1.28363i	0.0435190	+	0.0753772i
$291$	8.76687	−	10.6639i	0.513923	−	0.625127i
$292$	−1.72652	+	2.99042i	−0.101037	+	0.175001i
$293$	7.04804	+	12.2076i	0.411751	+	0.713173i	0.995081	−	0.0990615i	$-0.0315841\pi$
$293$	7.04804	+	12.2076i	0.411751	+	0.713173i	−0.583330	+	0.812235i	$0.698251\pi$
$294$	−16.9493	+	18.2397i	−0.988503	+	1.06376i
$295$	−0.334243	+	0.578927i	−0.0194604	+	0.0337064i
$296$	−1.56314	−	2.70744i	−0.0908557	−	0.157367i
$297$	0.260748	+	8.64268i	0.0151302	+	0.501499i
$298$	−18.2438	+	31.5993i	−1.05684	+	1.83050i
$299$	1.23569			0.0714619
$300$	−6.72029	−	17.9018i	−0.387996	−	1.03356i
$301$	0.151011	−	4.97698i	0.00870413	−	0.286868i
$302$	−8.69307	−	15.0568i	−0.500230	−	0.866424i
$303$	9.03537	+	24.0688i	0.519068	+	1.38272i
$304$	−12.1673	−	21.0744i	−0.697843	−	1.20870i
$305$	−0.0495974	+	0.0859053i	−0.00283994	+	0.00491892i
$306$	29.0915	−	25.4247i	1.66305	−	1.45343i
$307$	27.3916			1.56332			0.781660	−	0.623704i	$-0.214373\pi$
$307$	27.3916			1.56332			0.781660	+	0.623704i	$0.214373\pi$
$308$	8.30279	+	5.13550i	0.473095	+	0.292622i
$309$	−0.224332	+	0.272873i	−0.0127618	+	0.0155232i
$310$	−0.378093	+	0.654877i	−0.0214742	+	0.0371945i
$311$	−14.0557			−0.797026			−0.398513	−	0.917163i	$-0.630474\pi$
$311$	−14.0557			−0.797026			−0.398513	+	0.917163i	$0.630474\pi$
$312$	−0.0543399	−	0.144753i	−0.00307639	−	0.00819501i
$313$	21.7446			1.22908			0.614540	−	0.788886i	$-0.289342\pi$
$313$	21.7446			1.22908			0.614540	+	0.788886i	$0.289342\pi$
$314$	11.7045			0.660520
$315$	−0.408146	+	1.08667i	−0.0229964	+	0.0612268i
$316$	28.3740			1.59616
$317$	8.56297			0.480944			0.240472	−	0.970656i	$-0.422698\pi$
$317$	8.56297			0.480944			0.240472	+	0.970656i	$0.422698\pi$
$318$	12.0764	−	14.6895i	0.677209	−	0.823745i
$319$	8.21228			0.459799
$320$	−0.704524	+	1.22027i	−0.0393841	+	0.0682153i
$321$	−4.24217	−	11.3005i	−0.236775	−	0.630730i
$322$	−1.01867	+	33.5731i	−0.0567684	+	1.87096i
$323$	43.3808			2.41377
$324$	15.7914	+	12.2032i	0.877301	+	0.677955i
$325$	−0.497589	+	0.861850i	−0.0276013	+	0.0478068i
$326$	−2.18235	−	3.77995i	−0.120869	−	0.209352i
$327$	−7.32692	+	8.91233i	−0.405179	+	0.492853i
$328$	0.517568	+	0.896453i	0.0285779	+	0.0494984i
$329$	4.22208	−	2.26975i	0.232771	−	0.125135i
$330$	0.853949	+	0.141737i	0.0470083	+	0.00780239i
$331$	10.8472			0.596216			0.298108	−	0.954532i	$-0.403644\pi$
$331$	10.8472			0.596216			0.298108	+	0.954532i	$0.403644\pi$
$332$	8.33070	−	14.4292i	0.457207	−	0.791905i
$333$	−4.06195	−	20.6048i	−0.222593	−	1.12914i
$334$	−11.8849	−	20.5853i	−0.650314	−	1.12638i
$335$	−0.452399	+	0.783578i	−0.0247172	+	0.0428114i
$336$	−15.2571	+	5.20525i	−0.832341	+	0.283970i
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$	13.3077	−	23.0496i	0.723842	−	1.25373i
$339$	0.0235254	+	0.0626679i	0.00127772	+	0.00340365i
$340$	−1.01684	−	1.76122i	−0.0551459	−	0.0955154i
$341$	2.09486	+	3.62840i	0.113443	+	0.196489i
$342$	8.24304	+	41.8140i	0.445732	+	2.26104i
$343$	−1.68298	+	18.4436i	−0.0908723	+	0.995863i
$344$	−0.420231	+	0.727861i	−0.0226573	+	0.0392437i
$345$	0.550332	+	1.46600i	0.0296289	+	0.0789266i
$346$	−32.6754			−1.75664
$347$	−11.5330			−0.619126			−0.309563	−	0.950879i	$-0.600183\pi$
$347$	−11.5330			−0.619126			−0.309563	+	0.950879i	$0.600183\pi$
$348$	12.0372	−	14.6419i	0.645263	−	0.784886i
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	−0.960186	−	0.279362i	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$	−23.0058	−	14.2297i	−1.22971	−	0.760612i
$351$	−0.0313221	−	1.03819i	−0.00167185	−	0.0554145i
$352$	6.75390	+	11.6981i	0.359984	+	0.623511i
$353$	1.32349	+	2.29236i	0.0704424	+	0.122010i	0.899095	−	0.437753i	$-0.144226\pi$
$353$	1.32349	+	2.29236i	0.0704424	+	0.122010i	−0.828653	+	0.559763i	$0.810892\pi$
$354$	16.0396	+	2.66224i	0.852497	+	0.141496i
$355$	0.0934139	−	0.161798i	0.00495790	−	0.00858733i
$356$	10.0538	+	17.4137i	0.532852	+	0.922926i
$357$	5.56312	−	28.1942i	0.294432	−	1.49220i
$358$	7.96127	−	13.7893i	0.420766	−	0.728789i
$359$	−12.9835	−	22.4882i	−0.685245	−	1.18688i	−0.973360	−	0.229284i	$-0.926362\pi$
$359$	−12.9835	−	22.4882i	−0.685245	−	1.18688i	0.288114	−	0.957596i	$-0.406972\pi$
$360$	0.147530	−	0.128935i	0.00777553	−	0.00679547i
$361$	−14.4264	+	24.9873i	−0.759286	+	1.31512i
$362$	−24.9761			−1.31271
$363$	−9.05362	+	11.0127i	−0.475192	+	0.578014i
$364$	−0.997362	−	0.616896i	−0.0522760	−	0.0323341i
$365$	0.113867	+	0.197224i	0.00596009	+	0.0103232i
$366$	2.38008	+	0.395042i	0.124409	+	0.0206492i
$367$	−8.79371	−	15.2312i	−0.459028	−	0.795060i	0.539882	−	0.841741i	$-0.318469\pi$
$367$	−8.79371	−	15.2312i	−0.459028	−	0.795060i	−0.998910	+	0.0466808i	$0.985136\pi$
$368$	−10.8732	+	18.8330i	−0.566806	+	0.981736i
$369$	1.34494	+	6.82241i	0.0700148	+	0.355160i
$370$	−2.10249			−0.109303
$371$	0.428975	−	14.1380i	0.0222713	−	0.734011i
$372$	9.53971	+	1.58339i	0.494611	+	0.0820950i
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	−0.876383	−	0.481614i	$-0.840051\pi$
$373$	−0.407538	+	0.705876i	−0.0211015	+	0.0365489i	0.855282	+	0.518163i	$0.173384\pi$
$374$	−21.4306			−1.10815
$375$	−2.49352	−	0.413871i	−0.128765	−	0.0213722i
$376$	−0.809107			−0.0417265
$377$	−0.986490			−0.0508068
$378$	28.2330	+	0.00485319i	1.45215	+	0.000249621i
$379$	−20.4312			−1.04948			−0.524741	−	0.851262i	$-0.675838\pi$
$379$	−20.4312			−1.04948			−0.524741	+	0.851262i	$0.675838\pi$
$380$	2.24333			0.115080
$381$	−23.0310	−	3.82265i	−1.17991	−	0.195840i
$382$	−10.2018			−0.521969
$383$	−8.94638	+	15.4956i	−0.457139	+	0.791788i	−0.998808	−	0.0488039i	$-0.984459\pi$
$383$	−8.94638	+	15.4956i	−0.457139	+	0.791788i	0.541670	+	0.840591i	$0.317792\pi$
$384$	6.06843	+	1.00723i	0.309678	+	0.0514000i
$385$	0.567112	−	0.304874i	0.0289027	−	0.0155378i
$386$	−30.6084			−1.55793
$387$	−4.25121	+	3.71538i	−0.216101	+	0.188863i
$388$	−8.83688	+	15.3059i	−0.448625	+	0.777041i
$389$	−7.81392	−	13.5341i	−0.396181	−	0.686206i	0.597070	−	0.802189i	$-0.296331\pi$
$389$	−7.81392	−	13.5341i	−0.396181	−	0.686206i	−0.993251	+	0.115983i	$0.962998\pi$
$390$	−0.102580	−	0.0170260i	−0.00519431	−	0.000862146i
$391$	−19.3835	−	33.5731i	−0.980264	−	1.69787i
$392$	1.72430	−	2.60752i	0.0870902	−	0.131700i
$393$	−21.8156	+	26.5360i	−1.10045	+	1.33857i
$394$	−43.6622			−2.19967
$395$	0.935661	−	1.62061i	0.0470782	−	0.0815419i
$396$	−2.14105	−	10.8608i	−0.107592	−	0.545776i
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	0.999817	−	0.0191225i	$-0.00608724\pi$
$397$	9.63064	+	16.6808i	0.483348	+	0.837183i	−0.516469	+	0.856306i	$0.672754\pi$
$398$	−20.4791	+	35.4709i	−1.02653	+	1.77799i
$399$	23.8657	+	20.8648i	1.19478	+	1.04455i
$400$	−8.75687	−	15.1673i	−0.437843	−	0.758367i
$401$	−7.15064	+	12.3853i	−0.357086	+	0.618491i	−0.987473	−	0.157790i	$-0.949563\pi$
$401$	−7.15064	+	12.3853i	−0.357086	+	0.618491i	0.630387	+	0.776281i	$0.282896\pi$
$402$	21.7097	+	3.60335i	1.08278	+	0.179719i
$403$	−0.251642	−	0.435857i	−0.0125352	−	0.0217116i
$404$	−16.4569	−	28.5041i	−0.818760	−	1.41813i
$405$	1.21774	−	0.499532i	0.0605098	−	0.0248219i
$406$	0.813237	−	26.8024i	0.0403603	−	1.33018i
$407$	−5.82452	+	10.0884i	−0.288711	+	0.500062i
$408$	−3.08047	+	3.74703i	−0.152506	+	0.185505i
$409$	31.8610			1.57542			0.787712	−	0.616044i	$-0.211266\pi$
$409$	31.8610			1.57542			0.787712	+	0.616044i	$0.211266\pi$
$410$	0.696152			0.0343805
$411$	−3.92332	−	10.4511i	−0.193523	−	0.515514i
$412$	0.226124	−	0.391657i	0.0111403	−	0.0192956i
$413$	10.6520	−	5.72643i	0.524151	−	0.281779i
$414$	28.6774	−	25.0628i	1.40942	−	1.23177i
$415$	−0.549426	−	0.951633i	−0.0269702	−	0.0467138i
$416$	−0.811304	−	1.40522i	−0.0397774	−	0.0688965i
$417$	−7.62771	−	20.3190i	−0.373530	−	0.995025i
$418$	11.8199	−	20.4726i	0.578130	−	1.00135i
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	0.995036	+	0.0995110i	$0.0317278\pi$
$419$	11.9480	+	20.6945i	0.583697	+	1.01099i	−0.411339	+	0.911482i	$0.634939\pi$
$420$	0.287682	−	1.45799i	0.0140375	−	0.0711426i
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$	24.1446	+	41.8197i	1.17534	+	2.03575i
$423$	−5.14388	−	1.75592i	−0.250104	−	0.0853759i
$424$	−1.19375	+	2.06763i	−0.0579734	+	0.100413i
$425$	31.2214			1.51446
$426$	−4.48274	−	0.744039i	−0.217189	−	0.0360488i
$427$	1.58062	−	0.849728i	0.0764917	−	0.0411212i
$428$	7.72661	+	13.3829i	0.373480	+	0.646886i
$429$	−0.365871	+	0.445039i	−0.0176644	+	0.0214867i
$430$	0.282615	+	0.489503i	0.0136289	+	0.0236059i
$431$	2.46382	−	4.26746i	0.118678	−	0.205556i	−0.800566	−	0.599244i	$-0.795468\pi$
$431$	2.46382	−	4.26746i	0.118678	−	0.205556i	0.919244	+	0.393688i	$0.128801\pi$
$432$	16.0985	+	8.65797i	0.774539	+	0.416557i
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$	12.0495	−	6.47768i	0.578393	−	0.310939i
$435$	−0.439346	−	1.17035i	−0.0210650	−	0.0561139i
$436$	7.38543	−	12.7919i	0.353698	−	0.612622i
$437$	42.7633			2.04565
$438$	3.51757	−	4.27871i	0.168076	−	0.204444i
$439$	2.44822			0.116847			0.0584235	−	0.998292i	$-0.481393\pi$
$439$	2.44822			0.116847			0.0584235	+	0.998292i	$0.481393\pi$
$440$	−0.108680			−0.00518110
$441$	16.6210	−	12.8352i	0.791478	−	0.611198i
$442$	2.57432			0.122448
$443$	−26.2950			−1.24931			−0.624657	−	0.780899i	$-0.714761\pi$
$443$	−26.2950			−1.24931			−0.624657	+	0.780899i	$0.714761\pi$
$444$	9.44944	+	25.1718i	0.448450	+	1.19460i
$445$	1.32614			0.0628650
$446$	4.16996	−	7.22259i	0.197453	−	0.341999i
$447$	19.5430	−	23.7718i	0.924354	−	1.12437i
$448$	22.4525	−	12.0703i	1.06078	−	0.570266i
$449$	−38.7077			−1.82673			−0.913365	−	0.407141i	$-0.866526\pi$
$449$	−38.7077			−1.82673			−0.913365	+	0.407141i	$0.866526\pi$
$450$	5.93255	+	30.0937i	0.279663	+	1.41863i
$451$	1.92854	−	3.34034i	0.0908116	−	0.157290i
$452$	−0.0428488	−	0.0742163i	−0.00201544	−	0.00349084i
$453$	5.15350	+	13.7281i	0.242132	+	0.645002i
$454$	3.95620	+	6.85233i	0.185673	+	0.321596i
$455$	−0.0681236	+	0.0366226i	−0.00319368	+	0.00171690i
$456$	−1.88053	−	5.00943i	−0.0880638	−	0.234588i
$457$	−9.15511			−0.428258			−0.214129	−	0.976805i	$-0.568691\pi$
$457$	−9.15511			−0.428258			−0.214129	+	0.976805i	$0.568691\pi$
$458$	−13.4681	+	23.3274i	−0.629321	+	1.09002i
$459$	−27.7158	+	17.1364i	−1.29366	+	0.799859i
$460$	−1.00237	−	1.73615i	−0.0467355	−	0.0809483i
$461$	14.6152	−	25.3143i	0.680698	−	1.17900i	−0.294070	−	0.955784i	$-0.595010\pi$
$461$	14.6152	−	25.3143i	0.680698	−	1.17900i	0.974768	−	0.223220i	$-0.0716568\pi$
$462$	−11.7899	−	10.3074i	−0.548514	−	0.479544i
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	0.609721	−	0.792616i	$-0.291282\pi$
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	−0.991286	+	0.131726i	$0.957948\pi$
$464$	8.68041	−	15.0349i	0.402978	−	0.697978i
$465$	0.405018	−	0.492657i	0.0187823	−	0.0228464i
$466$	−17.9718	−	31.1280i	−0.832526	−	1.44198i
$467$	7.68632	+	13.3131i	0.355680	+	0.616057i	0.987234	−	0.159276i	$-0.0509158\pi$
$467$	7.68632	+	13.3131i	0.355680	+	0.616057i	−0.631554	+	0.775332i	$0.717582\pi$
$468$	0.257191	+	1.30464i	0.0118887	+	0.0603070i
$469$	14.4175	−	7.75073i	0.665739	−	0.357895i
$470$	−0.272071	+	0.471241i	−0.0125497	+	0.0217367i
$471$	−9.73834	−	1.61636i	−0.448719	−	0.0744779i
$472$	−2.04132			−0.0939594
$473$	3.13170			0.143996
$474$	−44.9004	−	7.45252i	−2.06234	−	0.342305i
$475$	−17.2200	+	29.8259i	−0.790106	+	1.36850i
$476$	−1.11581	+	36.7747i	−0.0511432	+	1.68556i
$477$	−12.0764	+	10.5542i	−0.552939	+	0.483245i
$478$	7.51341	+	13.0136i	0.343655	+	0.595228i
$479$	18.9646	+	32.8476i	0.866513	+	1.50084i	0.865537	+	0.500844i	$0.166977\pi$
$479$	18.9646	+	32.8476i	0.866513	+	1.50084i	0.000975329		1.00000i	$0.499690\pi$
$480$	1.30579	−	1.58834i	0.0596011	−	0.0724977i
$481$	0.699663	−	1.21185i	0.0319019	−	0.0552557i
$482$	−6.39820	−	11.0820i	−0.291430	−	0.504772i
$483$	5.48393	−	27.7929i	0.249528	−	1.26462i
$484$	9.12591	−	15.8065i	0.414814	−	0.718479i
$485$	0.582809	+	1.00946i	0.0264640	+	0.0458370i
$486$	−21.7839	−	23.4586i	−0.988137	−	1.06410i
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	−0.809131	−	0.587628i	$-0.800062\pi$
$487$	2.30247	−	3.98800i	0.104335	−	0.180714i	0.913466	+	0.406914i	$0.133395\pi$
$488$	−0.302906			−0.0137119
$489$	1.29376	+	3.44637i	0.0585058	+	0.155850i
$490$	−0.938860	−	1.88108i	−0.0424134	−	0.0849784i
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	−0.973309	−	0.229497i	$-0.926292\pi$
$491$	−15.1876	−	26.3056i	−0.685405	−	1.18716i	0.287904	−	0.957659i	$-0.407042\pi$
$492$	−3.12878	−	8.33457i	−0.141056	−	0.375752i
$493$	15.4744	+	26.8024i	0.696932	+	1.20712i
$494$	−1.41985	+	2.45925i	−0.0638820	+	0.110647i
$495$	−0.690929	−	0.235857i	−0.0310549	−	0.0106010i
$496$	8.85709			0.397695
$497$	−2.97701	+	1.60041i	−0.133537	+	0.0717884i
$498$	−16.9728	+	20.6454i	−0.760568	+	0.925141i
$499$	−4.63436	+	8.02694i	−0.207462	+	0.359335i	−0.950914	−	0.309454i	$-0.899854\pi$
$499$	−4.63436	+	8.02694i	−0.207462	+	0.359335i	0.743452	+	0.668789i	$0.233187\pi$
$500$	3.23600			0.144718
$501$	7.04571	+	18.7687i	0.314779	+	0.838522i
$502$	11.6089			0.518131
$503$	−22.4230			−0.999791			−0.499896	−	0.866086i	$-0.666628\pi$
$503$	−22.4230			−0.999791			−0.499896	+	0.866086i	$0.666628\pi$
$504$	−3.49690	+	0.579793i	−0.155764	+	0.0258260i
$505$	−2.17072			−0.0965960
$506$	−21.1255			−0.939143
$507$	−14.2553	+	17.3399i	−0.633102	+	0.770094i
$508$	29.8888			1.32610
$509$	18.8207	−	32.5984i	0.834213	−	1.44490i	−0.0604572	−	0.998171i	$-0.519256\pi$
$509$	18.8207	−	32.5984i	0.834213	−	1.44490i	0.894670	−	0.446728i	$-0.147411\pi$
$510$	1.14651	+	3.05411i	0.0507682	+	0.135238i
$511$	0.124951	−	4.11808i	0.00552748	−	0.182173i
$512$	31.6976			1.40085
$513$	−1.08396	−	35.9284i	−0.0478578	−	1.58628i
$514$	−12.1182	+	20.9893i	−0.534511	+	0.925800i
$515$	−0.0149133	−	0.0258306i	−0.000657158	−	0.00113823i
$516$	4.59032	−	5.58358i	0.202078	−	0.245804i
$517$	1.50743	+	2.61095i	0.0662969	+	0.114830i
$518$	32.3486	+	20.0085i	1.42132	+	0.879124i
$519$	27.1866	+	4.51240i	1.19336	+	0.198072i
$520$	0.0130550			0.000572500
$521$	17.4641	−	30.2488i	0.765117	−	1.32522i	−0.175067	−	0.984556i	$-0.556014\pi$
$521$	17.4641	−	30.2488i	0.765117	−	1.32522i	0.940185	−	0.340666i	$-0.110652\pi$
$522$	−22.8940	+	20.0084i	−1.00204	+	0.875743i
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	−0.999751	−	0.0223069i	$-0.992899\pi$
$523$	−11.8735	−	20.5656i	−0.519194	−	0.899270i	0.480557	−	0.876963i	$-0.340434\pi$
$524$	21.9898	−	38.0874i	0.960628	−	1.66386i
$525$	17.1762	+	15.0165i	0.749632	+	0.655374i
$526$	22.8366	+	39.5542i	0.995723	+	1.72464i
$527$	−7.89468	+	13.6740i	−0.343898	+	0.595648i
$528$	−3.56335	−	9.49220i	−0.155075	−	0.413095i
$529$	−7.60755	−	13.1767i	−0.330763	−	0.572898i
$530$	0.802820	+	1.39053i	0.0348723	+	0.0604006i
$531$	−12.9777	−	4.43008i	−0.563182	−	0.192249i
$532$	−34.5155	−	21.3488i	−1.49644	−	0.925587i
$533$	−0.231664	+	0.401254i	−0.0100345	+	0.0173802i
$534$	−11.3359	−	30.1970i	−0.490552	−	1.30675i
$535$	1.01917			0.0440626
$536$	−2.76293			−0.119340
$537$	−8.52822	+	10.3736i	−0.368020	+	0.447652i
$538$	−2.45292	+	4.24857i	−0.105753	+	0.183169i
$539$	−11.6269	−	0.706212i	−0.500804	−	0.0304187i
$540$	−1.43325	+	0.886164i	−0.0616773	+	0.0381344i
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	0.989428	−	0.145028i	$-0.0463271\pi$
$541$	8.58542	+	14.8704i	0.369116	+	0.639328i	−0.620311	+	0.784356i	$0.712994\pi$
$542$	−23.8488	−	41.3074i	−1.02439	−	1.77430i
$543$	20.7806	+	3.44914i	0.891782	+	0.148017i
$544$	−25.4527	+	44.0854i	−1.09128	+	1.89015i
$545$	−0.487083	−	0.843653i	−0.0208643	−	0.0361381i
$546$	1.41624	+	1.23816i	0.0606096	+	0.0529886i
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	−0.996674	−	0.0814901i	$-0.974032\pi$
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	0.568910	+	0.822400i	$0.307365\pi$
$548$	7.14586	+	12.3770i	0.305256	+	0.528719i
$549$	−1.92572	−	0.657366i	−0.0821876	−	0.0280557i
$550$	8.50683	−	14.7343i	0.362732	−	0.628271i
$551$	−34.1392			−1.45438
$552$	−3.03662	+	3.69369i	−0.129247	+	0.157214i
$553$	−29.8186	+	16.0302i	−1.26802	+	0.681674i
$554$	4.74187	+	8.21316i	0.201463	+	0.348944i
$555$	1.74932	+	0.290350i	0.0742544	+	0.0123247i
$556$	13.8930	+	24.0633i	0.589193	+	1.02051i
$557$	−0.122740	+	0.212593i	−0.00520068	+	0.00900784i	−0.868614	−	0.495489i	$-0.834989\pi$
$557$	−0.122740	+	0.212593i	−0.00520068	+	0.00900784i	0.863413	+	0.504497i	$0.168322\pi$
$558$	−14.6802	−	5.01126i	−0.621463	−	0.212144i
$559$	−0.376192			−0.0159112
$560$	0.0412806	−	1.36051i	0.00174442	−	0.0574922i
$561$	17.8307	+	2.95951i	0.752811	+	0.124951i
$562$	12.1338	−	21.0163i	0.511833	−	0.886520i
$563$	−44.2509			−1.86495			−0.932477	−	0.361230i	$-0.882357\pi$
$563$	−44.2509			−1.86495			−0.932477	+	0.361230i	$0.882357\pi$
$564$	6.86466	+	1.13939i	0.289054	+	0.0479769i
$565$	−0.00565192			−0.000237778
$566$	32.5496			1.36816
$567$	−23.4897	−	3.90295i	−0.986476	−	0.163908i
$568$	0.570506			0.0239379
$569$	−5.53533			−0.232053			−0.116027	−	0.993246i	$-0.537016\pi$
$569$	−5.53533			−0.232053			−0.116027	+	0.993246i	$0.537016\pi$
$570$	−3.54995	−	0.589216i	−0.148691	−	0.0246795i
$571$	−4.10381			−0.171739			−0.0858696	−	0.996306i	$-0.527367\pi$
$571$	−4.10381			−0.171739			−0.0858696	+	0.996306i	$0.527367\pi$
$572$	0.368793	−	0.638768i	0.0154200	−	0.0267082i
$573$	8.48810	+	1.40884i	0.354595	+	0.0588553i
$574$	−10.7109	−	6.62498i	−0.447064	−	0.276521i
$575$	30.7770			1.28349
$576$	−27.3545	−	9.33780i	−1.13977	−	0.389075i
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	−0.918781	−	0.394767i	$-0.870825\pi$
$577$	−2.82275	+	4.88915i	−0.117513	+	0.203538i	0.801269	+	0.598305i	$0.204159\pi$
$578$	−22.9256	−	39.7083i	−0.953579	−	1.65165i
$579$	25.4668	+	4.22695i	1.05836	+	0.175666i
$580$	0.800218	+	1.38602i	0.0332272	+	0.0575513i
$581$	−0.602904	+	19.8703i	−0.0250127	+	0.824360i
$582$	18.0040	−	21.8998i	0.746292	−	0.907776i
$583$	8.89619			0.368442
$584$	−0.347710	+	0.602252i	−0.0143884	+	0.0249214i
$585$	0.0829970	+	0.0283320i	0.00343150	+	0.00117138i
$586$	14.4742	+	25.0700i	0.597923	+	1.03563i
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	−0.605394	−	0.795926i	$-0.706985\pi$
$587$	9.36644	−	16.2232i	0.386595	−	0.669601i	0.991989	+	0.126324i	$0.0403180\pi$
$588$	−18.3013	+	19.6947i	−0.754733	+	0.812194i
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$	−0.686417	+	1.18891i	−0.0282594	+	0.0489466i
$591$	36.3278	+	6.02965i	1.49433	+	0.248027i
$592$	12.3131	+	21.3269i	0.506065	+	0.876530i
$593$	−9.43516	−	16.3422i	−0.387456	−	0.671093i	0.604651	−	0.796491i	$-0.293313\pi$
$593$	−9.43516	−	16.3422i	−0.387456	−	0.671093i	−0.992107	+	0.125398i	$0.959979\pi$
$594$	0.535484	+	17.7490i	0.0219712	+	0.728250i
$595$	2.06363	+	1.27641i	0.0846005	+	0.0523277i
$596$	−19.6991	+	34.1198i	−0.806906	+	1.39760i
$597$	21.9375	−	26.6844i	0.897842	−	1.09212i
$598$	2.53767			0.103773
$599$	2.67451			0.109278			0.0546388	−	0.998506i	$-0.482599\pi$
$599$	2.67451			0.109278			0.0546388	+	0.998506i	$0.482599\pi$
$600$	−1.35342	−	3.60531i	−0.0552533	−	0.147186i
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	−0.968736	−	0.248095i	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$	0.310123	−	10.2209i	0.0126397	−	0.416575i
$603$	−17.5653	−	5.99612i	−0.715313	−	0.244181i
$604$	−9.38650	−	16.2579i	−0.381931	−	0.661524i
$605$	−0.601872	−	1.04247i	−0.0244696	−	0.0423825i
$606$	18.5554	+	49.4287i	0.753763	+	2.00790i
$607$	−12.9026	+	22.3480i	−0.523701	+	0.907076i	0.475919	+	0.879489i	$0.342116\pi$
$607$	−12.9026	+	22.3480i	−0.523701	+	0.907076i	−0.999619	+	0.0275869i	$0.991218\pi$
$608$	−28.0766	−	48.6301i	−1.13866	−	1.97221i
$609$	−4.37799	+	22.1879i	−0.177405	+	0.899098i
$610$	−0.101856	+	0.176419i	−0.00412401	+	0.00714299i
$611$	−0.181079	−	0.313637i	−0.00732565	−	0.0126884i
$612$	31.4120	−	27.4528i	1.26976	−	1.10971i
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	−0.454333	−	0.890832i	$-0.650122\pi$
$613$	13.4766	−	23.3422i	0.544316	−	0.942784i	0.998650	−	0.0519519i	$-0.0165443\pi$
$614$	56.2526			2.27017
$615$	−0.579212	−	0.0961370i	−0.0233561	−	0.00387662i
$616$	1.67213	+	1.03426i	0.0673720	+	0.0416715i
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	0.754002	−	0.656872i	$-0.228121\pi$
$617$	−4.76588	−	8.25474i	−0.191867	−	0.332323i	−0.945869	+	0.324549i	$0.894788\pi$
$618$	−0.460698	+	0.560385i	−0.0185320	+	0.0225420i
$619$	−17.3536	−	30.0573i	−0.697499	−	1.20810i	−0.969331	−	0.245759i	$-0.920963\pi$
$619$	−17.3536	−	30.0573i	−0.697499	−	1.20810i	0.271832	−	0.962345i	$-0.412370\pi$
$620$	−0.408253	+	0.707114i	−0.0163958	+	0.0283984i
$621$	−27.3213	+	16.8925i	−1.09637	+	0.677871i
$622$	−28.8654			−1.15740
$623$	−20.4038	−	12.6203i	−0.817459	−	0.505621i
$624$	0.428043	+	1.14024i	0.0171354	+	0.0456461i
$625$	−12.3398	+	21.3732i	−0.493593	+	0.854928i
$626$	44.6558			1.78480
$627$	−12.6616	+	15.4014i	−0.505656	+	0.615071i
$628$	12.6381			0.504314
$629$	−43.9006			−1.75043
$630$	−0.838187	+	2.23163i	−0.0333942	+	0.0889103i
$631$	−36.7963			−1.46484			−0.732419	−	0.680854i	$-0.761609\pi$
$631$	−36.7963			−1.46484			−0.732419	+	0.680854i	$0.761609\pi$
$632$	5.71435			0.227305
$633$	−14.3136	−	38.1291i	−0.568914	−	1.51550i
$634$	17.5853			0.698401
$635$	0.985611	−	1.70713i	0.0391128	−	0.0677453i
$636$	13.0397	−	15.8612i	0.517057	−	0.628938i
$637$	1.39666	+	0.0848329i	0.0553378	+	0.00336120i
$638$	16.8651			0.667696
$639$	3.62698	+	1.23811i	0.143481	+	0.0489790i
$640$	−0.259699	+	0.449811i	−0.0102655	+	0.0177804i
$641$	22.0922	+	38.2648i	0.872590	+	1.51137i	0.859308	+	0.511458i	$0.170894\pi$
$641$	22.0922	+	38.2648i	0.872590	+	1.51137i	0.0132813	+	0.999912i	$0.495772\pi$
$642$	−8.71191	−	23.2071i	−0.343831	−	0.915912i
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	0.972741	−	0.231895i	$-0.0744926\pi$
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	−0.687197	+	0.726471i	$0.741159\pi$
$644$	−1.09993	+	36.2512i	−0.0433433	+	1.42850i
$645$	−0.167542	−	0.446305i	−0.00659696	−	0.0175732i
$646$	89.0889			3.50515
$647$	−16.6536	+	28.8448i	−0.654719	+	1.13401i	0.327245	+	0.944940i	$0.393880\pi$
$647$	−16.6536	+	28.8448i	−0.654719	+	1.13401i	−0.981964	+	0.189068i	$0.939453\pi$
$648$	3.18029	+	2.45765i	0.124934	+	0.0965455i
$649$	3.80315	+	6.58725i	0.149287	+	0.258572i
$650$	−1.02187	+	1.76993i	−0.0400811	+	0.0694225i
$651$	−10.9200	+	3.72556i	−0.427987	+	0.146016i
$652$	−2.35643	−	4.08146i	−0.0922850	−	0.159842i
$653$	4.53322	−	7.85176i	0.177398	−	0.307263i	−0.763590	−	0.645701i	$-0.776565\pi$
$653$	4.53322	−	7.85176i	0.177398	−	0.307263i	0.940989	+	0.338438i	$0.109899\pi$
$654$	−15.0469	+	18.3028i	−0.588380	+	0.715694i
$655$	−1.45027	−	2.51194i	−0.0566666	−	0.0981495i
$656$	−4.07696	−	7.06150i	−0.159178	−	0.275705i
$657$	−3.51757	+	3.07420i	−0.137233	+	0.119936i
$658$	8.67065	−	4.66126i	0.338017	−	0.181715i
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	−0.357184	−	0.934034i	$-0.616263\pi$
$659$	16.1806	−	28.0256i	0.630305	−	1.09172i	0.987489	−	0.157686i	$-0.0504035\pi$
$660$	0.922066	+	0.153043i	0.0358914	+	0.00595720i
$661$	−8.65915			−0.336802			−0.168401	−	0.985719i	$-0.553860\pi$
$661$	−8.65915			−0.336802			−0.168401	+	0.985719i	$0.553860\pi$
$662$	22.2763			0.865794
$663$	−2.14189	−	0.355508i	−0.0831839	−	0.0138068i
$664$	1.67775	−	2.90595i	0.0651094	−	0.112773i
$665$	−2.35754	+	1.26739i	−0.0914214	+	0.0491473i
$666$	−8.34179	−	42.3150i	−0.323238	−	1.63967i
$667$	15.2541	+	26.4209i	0.590642	+	1.02302i
$668$	−12.8329	−	22.2273i	−0.496522	−	0.860001i
$669$	−4.46692	+	5.43348i	−0.172701	+	0.210070i
$670$	−0.929067	+	1.60919i	−0.0358930	+	0.0621685i
$671$	0.564339	+	0.977464i	0.0217861	+	0.0377346i
$672$	−35.2063	+	12.0113i	−1.35811	+	0.463348i
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$	3.43803	+	5.95484i	0.132428	+	0.229372i
$675$	−0.780128	−	25.8579i	−0.0300271	−	0.995270i
$676$	14.3692	−	24.8881i	0.552661	−	0.957236i
$677$	38.3315			1.47320			0.736600	−	0.676329i	$-0.236430\pi$
$677$	38.3315			1.47320			0.736600	+	0.676329i	$0.236430\pi$
$678$	0.0483128	+	0.128698i	0.00185544	+	0.00494260i
$679$	0.639537	−	21.0777i	0.0245432	−	0.808887i
$680$	−0.204785	−	0.354698i	−0.00785315	−	0.0136021i
$681$	−2.34534	−	6.24762i	−0.0898738	−	0.239409i
$682$	4.30209	+	7.45144i	0.164736	+	0.285330i
$683$	−3.31659	+	5.74450i	−0.126906	+	0.219807i	−0.922476	−	0.386054i	$-0.873838\pi$
$683$	−3.31659	+	5.74450i	−0.126906	+	0.219807i	0.795570	+	0.605861i	$0.207171\pi$
$684$	8.90056	+	45.1494i	0.340321	+	1.72633i
$685$	0.942567			0.0360136
$686$	−3.45624	+	37.8767i	−0.131960	+	1.44614i
$687$	14.4272	−	17.5489i	0.550430	−	0.669534i
$688$	3.31022	−	5.73347i	0.126201	−	0.218587i
$689$	−1.06864			−0.0407121
$690$	1.13019	+	3.01064i	0.0430255	+	0.114613i
$691$	−23.3875			−0.889704			−0.444852	−	0.895604i	$-0.646744\pi$
$691$	−23.3875			−0.889704			−0.444852	+	0.895604i	$0.646744\pi$
$692$	−35.2818			−1.34121
$693$	8.38598	+	10.2041i	0.318557	+	0.387623i
$694$	−23.6848			−0.899061
$695$	1.83254			0.0695121
$696$	2.42422	−	2.94878i	0.0918899	−	0.111773i
$697$	14.5358			0.550583
$698$	−9.13702	+	15.8258i	−0.345841	+	0.599015i
$699$	10.6542	+	28.3810i	0.402978	+	1.07347i
$700$	−24.8410	−	15.3648i	−0.938900	−	0.580735i
$701$	9.26736			0.350023			0.175012	−	0.984566i	$-0.444004\pi$
$701$	9.26736			0.350023			0.175012	+	0.984566i	$0.444004\pi$
$702$	−0.0643244	−	2.13208i	−0.00242777	−	0.0804700i
$703$	24.2131	−	41.9383i	0.913214	−	1.58173i
$704$	8.01636	+	13.8847i	0.302128	+	0.523301i
$705$	0.291446	−	0.354510i	0.0109765	−	0.0133516i
$706$	2.71799	+	4.70769i	0.102293	+	0.177176i
$707$	33.3984	+	20.6579i	1.25608	+	0.776918i
$708$	17.3191	+	2.87460i	0.650891	+	0.108034i
$709$	14.2355			0.534626			0.267313	−	0.963610i	$-0.413864\pi$
$709$	14.2355			0.534626			0.267313	+	0.963610i	$0.413864\pi$
$710$	0.191839	−	0.332275i	0.00719959	−	0.0124701i
$711$	36.3289	+	12.4013i	1.36244	+	0.465085i
$712$	2.02478	+	3.50702i	0.0758817	+	0.131431i
$713$	−7.78230	+	13.4793i	−0.291449	+	0.504805i
$714$	11.4247	−	57.9009i	0.427558	−	2.16689i
$715$	−0.0243226	−	0.0421280i	−0.000909613	−	0.00157550i
$716$	8.59632	−	14.8893i	0.321260	−	0.556438i
$717$	−4.45416	−	11.8652i	−0.166344	−	0.443113i
$718$	−26.6636	−	46.1827i	−0.995077	−	1.72352i
$719$	6.92848	+	12.0005i	0.258389	+	0.447542i	0.965810	−	0.259249i	$-0.0834752\pi$
$719$	6.92848	+	12.0005i	0.258389	+	0.447542i	−0.707422	+	0.706792i	$0.750142\pi$
$720$	−1.16212	+	1.01564i	−0.0433096	+	0.0378507i
$721$	−0.0163649	+	0.539348i	−0.000609459	+	0.0200864i
$722$	−29.6268	+	51.3151i	−1.10259	+	1.90975i
$723$	3.79303	+	10.1040i	0.141064	+	0.375773i
$724$	−26.9684			−1.00227
$725$	−24.5702			−0.912513
$726$	−18.5929	+	22.6161i	−0.690048	+	0.839362i
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	−0.412928	−	0.910764i	$-0.635494\pi$
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	0.995208	−	0.0977755i	$-0.0311727\pi$
$728$	−0.200862	−	0.124239i	−0.00744446	−	0.00460460i
$729$	14.8851	+	22.5263i	0.551299	+	0.834308i
$730$	0.233843	+	0.405028i	0.00865492	+	0.0149908i
$731$	5.90107	+	10.2209i	0.218259	+	0.378035i
$732$	2.56993	+	0.426554i	0.0949873	+	0.0157659i
$733$	13.3003	−	23.0368i	0.491257	−	0.850883i	−0.508692	−	0.860949i	$-0.669871\pi$
$733$	13.3003	−	23.0368i	0.491257	−	0.850883i	0.999949	+	0.0100658i	$0.00320409\pi$
$734$	−18.0592	−	31.2794i	−0.666576	−	1.15454i
$735$	0.521378	+	1.69475i	0.0192313	+	0.0625117i
$736$	−25.0904	+	43.4579i	−0.924845	+	1.60188i
$737$	5.14757	+	8.91586i	0.189613	+	0.328420i
$738$	2.76203	+	14.0108i	0.101672	+	0.515745i
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	−0.384693	−	0.923045i	$-0.625693\pi$
$739$	16.5019	−	28.5822i	0.607034	−	1.05141i	0.991727	−	0.128368i	$-0.0409740\pi$
$740$	−2.27020			−0.0834543
$741$	1.52096	−	1.85007i	0.0558739	−	0.0679640i
$742$	0.880963	−	29.0345i	0.0323412	−	1.06589i
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	0.965570	+	0.260144i	$0.0837701\pi$
$743$	19.3008	+	33.4299i	0.708076	+	1.22642i	−0.257493	+	0.966280i	$0.582897\pi$
$744$	1.92124	+	0.318885i	0.0704360	+	0.0116909i
$745$	1.29919	+	2.25027i	0.0475988	+	0.0824435i
$746$	−0.836938	+	1.44962i	−0.0306425	+	0.0530743i
$747$	16.9728	−	14.8335i	0.621001	−	0.542728i
$748$	−23.1400			−0.846082
$749$	−15.6808	−	9.69900i	−0.572964	−	0.354394i
$750$	−5.12080	−	0.849945i	−0.186985	−	0.0310356i
$751$	18.9498	−	32.8220i	0.691487	−	1.19769i	−0.279863	−	0.960040i	$-0.590289\pi$
$751$	18.9498	−	32.8220i	0.691487	−	1.19769i	0.971351	−	0.237651i	$-0.0763776\pi$
$752$	6.37345			0.232416
$753$	−9.65885	−	1.60316i	−0.351988	−	0.0584226i
$754$	−2.02590			−0.0737789
$755$	−1.23811			−0.0450596
$756$	30.4850	+	0.00524031i	1.10873	+	0.000190588i
$757$	22.5927			0.821147			0.410573	−	0.911828i	$-0.365329\pi$
$757$	22.5927			0.821147			0.410573	+	0.911828i	$0.365329\pi$
$758$	−41.9585			−1.52400
$759$	17.5768	+	2.91738i	0.637999	+	0.105894i
$760$	0.451792			0.0163882
$761$	−13.8735	+	24.0296i	−0.502913	+	0.871072i	0.497081	+	0.867704i	$0.334405\pi$
$761$	−13.8735	+	24.0296i	−0.502913	+	0.871072i	−0.999994	+	0.00336738i	$0.998928\pi$
$762$	−47.2974	−	7.85037i	−1.71340	−	0.284389i
$763$	−0.534493	+	17.6157i	−0.0193500	+	0.637730i
$764$	−11.0156			−0.398529
$765$	−0.532151	−	2.69941i	−0.0192400	−	0.0975974i
$766$	−18.3727	+	31.8224i	−0.663832	+	1.14979i
$767$	−0.456849	−	0.791286i	−0.0164959	−	0.0285717i
$768$	−20.4631	−	3.39644i	−0.738399	−	0.122559i
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$	1.16465	−	0.626104i	0.0419710	−	0.0225632i
$771$	12.9812	−	15.7901i	0.467505	−	0.568665i
$772$	−33.0499			−1.18949
$773$	−20.7795	+	35.9912i	−0.747388	+	1.29451i	0.201682	+	0.979451i	$0.435359\pi$
$773$	−20.7795	+	35.9912i	−0.747388	+	1.29451i	−0.949071	+	0.315063i	$0.897974\pi$
$774$	−8.73049	+	7.63007i	−0.313811	+	0.274257i
$775$	−6.26756	−	10.8557i	−0.225137	−	0.389950i
$776$	−1.77969	+	3.08252i	−0.0638873	+	0.110656i
$777$	−24.1516	−	21.1148i	−0.866434	−	0.757488i
$778$	−16.0470	−	27.7942i	−0.575313	−	0.996472i
$779$	−8.01714	+	13.8861i	−0.287244	+	0.497521i
$780$	−0.110762	−	0.0183841i	−0.00396591	−	0.000658258i
$781$	−1.06290	−	1.84100i	−0.0380336	−	0.0658761i
$782$	−39.8068	−	68.9473i	−1.42349	−	2.46555i
$783$	21.8114	−	13.4858i	0.779476	−	0.481942i
$784$	−13.5826	+	20.5398i	−0.485091	+	0.733564i
$785$	0.416753	−	0.721837i	0.0148746	−	0.0257635i
$786$	−44.8014	+	54.4956i	−1.59801	+	1.94379i
$787$	−20.8969			−0.744893			−0.372446	−	0.928054i	$-0.621481\pi$
$787$	−20.8969			−0.744893			−0.372446	+	0.928054i	$0.621481\pi$
$788$	−47.1450			−1.67947
$789$	−13.5382	−	36.0636i	−0.481972	−	1.28390i
$790$	1.92152	−	3.32816i	0.0683645	−	0.118411i
$791$	0.0869596	+	0.0537869i	0.00309193	+	0.00191244i
$792$	−0.431195	−	2.18730i	−0.0153218	−	0.0777222i
$793$	−0.0677905	−	0.117417i	−0.00240731	−	0.00416959i
$794$	19.7779	+	34.2564i	0.701892	+	1.21571i
$795$	−0.475934	−	1.26781i	−0.0168797	−	0.0449647i
$796$	−22.1127	+	38.3003i	−0.783763	+	1.35752i
$797$	−0.319383	−	0.553188i	−0.0113131	−	0.0195949i	0.860313	−	0.509765i	$-0.170268\pi$
$797$	−0.319383	−	0.553188i	−0.0113131	−	0.0195949i	−0.871627	+	0.490171i	$0.836934\pi$
$798$	49.0116	+	42.8489i	1.73499	+	1.51683i
$799$	−5.68091	+	9.83963i	−0.200976	+	0.348101i
$800$	−20.2069	−	34.9993i	−0.714420	−	1.23741i
$801$	5.26155	+	26.6900i	0.185908	+	0.943043i
$802$	−14.6849	+	25.4350i	−0.518541	+	0.898139i
$803$	2.59125			0.0914433
$804$	23.4414	+	3.89078i	0.826714	+	0.137217i
$805$	2.03425	+	1.25824i	0.0716980	+	0.0443472i
$806$	−0.516783	−	0.895095i	−0.0182029	−	0.0315284i
$807$	2.62759	−	3.19616i	0.0924957	−	0.112510i
$808$	−3.31431	−	5.74055i	−0.116597	−	0.201952i
$809$	25.2796	−	43.7856i	0.888783	−	1.53942i	0.0474686	−	0.998873i	$-0.484885\pi$
$809$	25.2796	−	43.7856i	0.888783	−	1.53942i	0.841315	−	0.540545i	$-0.181782\pi$
$810$	2.50080	−	1.02586i	0.0878690	−	0.0360451i
$811$	−0.784071			−0.0275325			−0.0137662	−	0.999905i	$-0.504382\pi$
$811$	−0.784071			−0.0275325			−0.0137662	+	0.999905i	$0.504382\pi$
$812$	0.878107	−	28.9404i	0.0308155	−	1.01561i
$813$	14.1382	+	37.6620i	0.495850	+	1.32087i
$814$	−11.9615	+	20.7179i	−0.419250	+	0.726163i
$815$	−0.310823			−0.0108876
$816$	24.2653	−	29.5159i	0.849455	−	1.03326i
$817$	−13.0188			−0.455470
$818$	65.4311			2.28775
$819$	−1.00736	−	1.22576i	−0.0351999	−	0.0428315i
$820$	0.751682			0.0262499
$821$	43.4413			1.51611			0.758056	−	0.652189i	$-0.226149\pi$
$821$	43.4413			1.51611			0.758056	+	0.652189i	$0.226149\pi$
$822$	−8.05710	−	21.4628i	−0.281024	−	0.748602i
$823$	3.96546			0.138227			0.0691136	−	0.997609i	$-0.477983\pi$
$823$	3.96546			0.138227			0.0691136	+	0.997609i	$0.477983\pi$
$824$	0.0455399	−	0.0788774i	0.00158646	−	0.00274782i
$825$	−9.11262	+	11.0844i	−0.317261	+	0.385910i
$826$	21.8755	−	11.7600i	0.761144	−	0.409184i
$827$	29.3159			1.01941			0.509707	−	0.860348i	$-0.329754\pi$
$827$	29.3159			1.01941			0.509707	+	0.860348i	$0.329754\pi$
$828$	30.9649	−	27.0620i	1.07610	−	0.940469i
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	0.382940	+	0.923773i	$0.374912\pi$
$829$	−17.5213	+	30.3478i	−0.608541	+	1.05402i	−0.991481	+	0.130251i	$0.958422\pi$
$830$	−1.12833	−	1.95432i	−0.0391648	−	0.0678353i
$831$	−2.81111	−	7.48836i	−0.0975165	−	0.259768i
$832$	−0.962955	−	1.66789i	−0.0333844	−	0.0578236i
$833$	−19.6036	−	39.2773i	−0.679225	−	1.36088i
$834$	−15.6646	−	41.7280i	−0.542421	−	1.44492i
$835$	−1.69272			−0.0585788
$836$	12.7627	−	22.1057i	0.441408	−	0.764541i
$837$	11.5222	+	6.19678i	0.398265	+	0.214192i
$838$	24.5369	+	42.4992i	0.847614	+	1.46811i
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	0.334639	+	0.942347i	$0.391386\pi$
$839$	−18.7921	+	32.5489i	−0.648777	+	1.12371i	−0.983415	+	0.181368i	$0.941948\pi$
$840$	0.0579374	−	0.293630i	0.00199903	−	0.0101312i
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$	−2.51060	+	4.34848i	−0.0865208	+	0.149858i
$843$	−12.9979	+	15.8104i	−0.447670	+	0.544538i
$844$	26.0705	+	45.1555i	0.897385	+	1.55432i
$845$	−0.947675	−	1.64142i	−0.0326010	−	0.0564666i
$846$	−10.5637	−	3.60604i	−0.363188	−	0.123978i
$847$	−0.660455	+	21.7671i	−0.0226935	+	0.747926i
$848$	9.40331	−	16.2870i	0.322911	−	0.559298i
$849$	−27.0819	−	4.49503i	−0.929449	−	0.154269i
$850$	64.1177			2.19922
$851$	−43.2757			−1.48347
$852$	−4.84031	−	0.803389i	−0.165826	−	0.0275237i
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$	3.24604	−	1.74504i	0.111077	−	0.0597140i
$855$	2.87226	+	0.980479i	0.0982291	+	0.0335317i
$856$	1.55609	+	2.69523i	0.0531861	+	0.0921211i
$857$	−13.7673	−	23.8457i	−0.470283	−	0.814554i	0.529139	−	0.848535i	$-0.322515\pi$
$857$	−13.7673	−	23.8457i	−0.470283	−	0.814554i	−0.999422	+	0.0339808i	$0.989181\pi$
$858$	−0.751369	+	0.913952i	−0.0256513	+	0.0312018i
$859$	23.2550	−	40.2789i	0.793451	−	1.37430i	−0.130366	−	0.991466i	$-0.541615\pi$
$859$	23.2550	−	40.2789i	0.793451	−	1.37430i	0.923818	−	0.382832i	$-0.125051\pi$
$860$	0.305158	+	0.528549i	0.0104058	+	0.0180234i
$861$	7.99678	+	6.99127i	0.272530	+	0.238262i
$862$	5.05981	−	8.76384i	0.172338	−	0.298498i
$863$	2.44007	+	4.22633i	0.0830610	+	0.143866i	0.904563	−	0.426339i	$-0.140197\pi$
$863$	2.44007	+	4.22633i	0.0830610	+	0.143866i	−0.821502	+	0.570205i	$0.806864\pi$
$864$	37.1480	+	19.9786i	1.26380	+	0.679687i
$865$	−1.16345	+	2.01516i	−0.0395585	+	0.0685174i
$866$	63.3629			2.15316
$867$	13.5909	+	36.2041i	0.461572	+	1.22956i
$868$	13.0106	−	6.99439i	0.441609	−	0.237405i
$869$	−10.6463	−	18.4400i	−0.361152	−	0.625533i
$870$	−0.902261	−	2.40348i	−0.0305895	−	0.0814856i
$871$	−0.618346	−	1.07101i	−0.0209518	−	0.0362897i
$872$	1.48738	−	2.57622i	0.0503690	−	0.0872417i
$873$	−18.0040	+	15.7348i	−0.609345	+	0.532541i
$874$	87.8207			2.97058
$875$	−3.40075	+	1.82821i	−0.114966	+	0.0618049i
$876$	3.79815	−	4.62001i	0.128328	−	0.156096i
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	0.316378	+	0.948633i	$0.397533\pi$
$877$	−19.6446	+	34.0255i	−0.663352	+	1.14896i	−0.979729	+	0.200326i	$0.935800\pi$
$878$	5.02777			0.169679
$879$	−8.58070	−	22.8576i	−0.289420	−	0.770968i
$880$	0.856086			0.0288587
$881$	47.3713			1.59598			0.797990	−	0.602670i	$-0.205897\pi$
$881$	47.3713			1.59598			0.797990	+	0.602670i	$0.205897\pi$
$882$	34.1337	−	26.3589i	1.14934	−	0.887549i
$883$	−2.67206			−0.0899221			−0.0449610	−	0.998989i	$-0.514316\pi$
$883$	−2.67206			−0.0899221			−0.0449610	+	0.998989i	$0.514316\pi$
$884$	2.77966			0.0934902
$885$	0.735299	−	0.894404i	0.0247168	−	0.0300651i
$886$	−54.0007			−1.81419
$887$	11.4800	−	19.8840i	0.385461	−	0.667638i	−0.606372	−	0.795181i	$-0.707376\pi$
$887$	11.4800	−	19.8840i	0.385461	−	0.667638i	0.991833	+	0.127543i	$0.0407091\pi$
$888$	1.90306	+	5.06944i	0.0638624	+	0.170119i
$889$	−31.4105	+	16.8860i	−1.05347	+	0.566338i
$890$	2.72342			0.0912891
$891$	2.00556	−	14.8415i	0.0671889	−	0.497208i
$892$	4.50259	−	7.79871i	0.150758	−	0.261120i
$893$	−6.26655	−	10.8540i	−0.209702	−	0.363214i
$894$	40.1345	−	48.8188i	1.34230	−	1.63275i
$895$	−0.566944	−	0.981976i	−0.0189508	−	0.0328238i
$896$	8.27635	−	4.44929i	0.276493	−	0.148640i
$897$	−2.11140	−	0.350447i	−0.0704975	−	0.0117011i
$898$	−79.4920			−2.65268
$899$	6.21284	−	10.7610i	0.207210	−	0.358898i
$900$	6.40577	+	32.4942i	0.213526	+	1.08314i
$901$	16.7631	+	29.0345i	0.558459	+	0.967280i
$902$	3.96054	−	6.85986i	0.131872	−	0.228408i
$903$	−1.66952	+	8.46121i	−0.0555581	+	0.281571i
$904$	−0.00862948	−	0.0149467i	−0.000287012	−	0.000497120i
$905$	−0.889308	+	1.54033i	−0.0295616	+	0.0512022i
$906$	10.5835	+	28.1926i	0.351612	+	0.936638i
$907$	13.9491	+	24.1606i	0.463173	+	0.802238i	0.999117	−	0.0420148i	$-0.0133777\pi$
$907$	13.9491	+	24.1606i	0.463173	+	0.802238i	−0.535944	+	0.844253i	$0.680044\pi$
$908$	4.27177	+	7.39892i	0.141764	+	0.245542i
$909$	−8.61250	−	43.6882i	−0.285659	−	1.44905i
$910$	−0.139902	+	0.0752099i	−0.00463770	+	0.00249318i
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	0.368513	+	0.929623i	$0.379867\pi$
$911$	−18.7381	+	32.4553i	−0.620820	+	1.07529i	−0.989333	+	0.145670i	$0.953466\pi$
$912$	14.8132	+	39.4600i	0.490514	+	1.30665i
$913$	−12.5032			−0.413794
$914$	−18.8014			−0.621894
$915$	0.109109	−	0.132718i	0.00360703	−	0.00438753i
$916$	−14.5424	+	25.1881i	−0.480493	+	0.832239i
$917$	−1.59143	+	52.4499i	−0.0525536	+	1.73205i
$918$	−56.9184	+	35.1921i	−1.87859	+	1.16151i
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	0.501653	−	0.865069i	$-0.332726\pi$
$919$	−15.1073	−	26.1667i	−0.498345	−	0.863160i	−0.999998	+	0.00190951i	$0.999392\pi$
$920$	−0.201870	−	0.349649i	−0.00665546	−	0.0115276i
$921$	−46.8033	−	7.76836i	−1.54222	−	0.255976i
$922$	30.0145	−	51.9866i	0.988474	−	1.71209i
$923$	0.127680	+	0.221147i	0.00420262	+	0.00727916i
$924$	−12.7303	−	11.1296i	−0.418797	−	0.366137i
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$	−16.8611	−	29.2042i	−0.554089	−	0.959710i
$927$	0.460698	−	0.402631i	0.0151313	−	0.0132241i
$928$	20.0304	−	34.6937i	0.657531	−	1.13888i
$929$	−45.9351			−1.50708			−0.753540	−	0.657402i	$-0.771656\pi$
$929$	−45.9351			−1.50708			−0.753540	+	0.657402i	$0.771656\pi$
$930$	0.831764	−	1.01174i	0.0272746	−	0.0331763i
$931$	48.3340	+	2.93579i	1.58408	+	0.0962167i
$932$	−19.4053	−	33.6110i	−0.635642	−	1.10096i
$933$	24.0166	+	3.98625i	0.786269	+	0.130504i
$934$	15.7850	+	27.3404i	0.516500	+	0.894604i
$935$	−0.763064	+	1.32167i	−0.0249549	+	0.0432231i
$936$	0.0517967	+	0.262746i	0.00169303	+	0.00858813i
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$	29.6085	−	15.9172i	0.966751	−	0.519716i
$939$	−37.1545	−	6.16686i	−1.21249	−	0.201248i
$940$	−0.293774	+	0.508831i	−0.00958184	+	0.0165962i
$941$	49.4003			1.61040			0.805202	−	0.593000i	$-0.202057\pi$
$941$	49.4003			1.61040			0.805202	+	0.593000i	$0.202057\pi$
$942$	−19.9991	−	3.31943i	−0.651606	−	0.108153i
$943$	14.3289			0.466613
$944$	16.0798			0.523353
$945$	1.00557	−	1.74101i	0.0327113	−	0.0566351i
$946$	6.43141			0.209103
$947$	31.6505			1.02850			0.514252	−	0.857639i	$-0.328070\pi$
$947$	31.6505			1.02850			0.514252	+	0.857639i	$0.328070\pi$
$948$	−48.4820	−	8.04698i	−1.57462	−	0.261354i
$949$	−0.311271			−0.0101043
$950$	−35.3637	+	61.2517i	−1.14735	+	1.98727i
$951$	−14.6313	−	2.42849i	−0.474453	−	0.0787492i
$952$	−0.224718	+	7.40619i	−0.00728315	+	0.240036i
$953$	−19.1237			−0.619477			−0.309739	−	0.950822i	$-0.600242\pi$
$953$	−19.1237			−0.619477			−0.309739	+	0.950822i	$0.600242\pi$
$954$	−24.8006	+	21.6746i	−0.802949	+	0.701742i
$955$	−0.363249	+	0.629165i	−0.0117545	+	0.0203593i
$956$	8.11273	+	14.0517i	0.262384	+	0.454463i
$957$	−14.0321	−	2.32903i	−0.453594	−	0.0752870i
$958$	38.9465	+	67.4573i	1.25830	+	2.17945i
$959$	−14.5022	−	8.97001i	−0.468300	−	0.289657i
$960$	1.54988	−	1.88524i	0.0500221	−	0.0608459i
$961$	−24.6607			−0.795507
$962$	1.43686	−	2.48871i	0.0463262	−	0.0802394i
$963$	4.04363	+	20.5119i	0.130304	+	0.660987i
$964$	−6.90857	−	11.9660i	−0.222510	−	0.385399i
$965$	−1.08985	+	1.88768i	−0.0350836	+	0.0607666i
$966$	11.2621	−	57.0767i	0.362351	−	1.83641i
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	0.934982	−	0.354696i	$-0.115416\pi$
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	−0.774667	+	0.632370i	$0.782082\pi$
$968$	1.83790	−	3.18334i	0.0590724	−	0.102316i
$969$	−74.1237	−	12.3030i	−2.38120	−	0.395228i
$970$	1.19688	+	2.07306i	0.0384296	+	0.0665621i
$971$	0.522554	+	0.905090i	0.0167695	+	0.0290457i	0.874288	−	0.485407i	$-0.161329\pi$
$971$	0.522554	+	0.905090i	0.0167695	+	0.0290457i	−0.857519	+	0.514453i	$0.827995\pi$
$972$	−23.5215	−	25.3298i	−0.754453	−	0.812453i
$973$	−28.1951	−	17.4395i	−0.903895	−	0.559084i
$974$	4.72847	−	8.18994i	0.151510	−	0.262423i
$975$	1.09464	−	1.33150i	0.0350566	−	0.0426422i
$976$	2.38603			0.0763751
$977$	−18.8862			−0.604222			−0.302111	−	0.953273i	$-0.597691\pi$
$977$	−18.8862			−0.604222			−0.302111	+	0.953273i	$0.597691\pi$
$978$	2.65692	+	7.07762i	0.0849590	+	0.226317i
$979$	7.54466	−	13.0677i	0.241128	−	0.417647i
$980$	−1.01375	−	2.03112i	−0.0323830	−	0.0648819i
$981$	15.0469	−	13.1503i	0.480410	−	0.419858i
$982$	−31.1899	−	54.0224i	−0.995309	−	1.72393i
$983$	−1.14446	−	1.98226i	−0.0365025	−	0.0632242i	0.847197	−	0.531279i	$-0.178288\pi$
$983$	−1.14446	−	1.98226i	−0.0365025	−	0.0632242i	−0.883700	+	0.468055i	$0.844955\pi$
$984$	−0.630117	−	1.67853i	−0.0200874	−	0.0535096i
$985$	−1.55465	+	2.69274i	−0.0495353	+	0.0857977i
$986$	31.7789	+	55.0427i	1.01205	+	1.75292i
$987$	−7.85786	+	2.68087i	−0.250119	+	0.0853329i
$988$	−1.53311	+	2.65542i	−0.0487746	+	0.0844801i
$989$	5.81707	+	10.0755i	0.184972	+	0.320381i
$990$	−1.41892	−	0.484366i	−0.0450963	−	0.0153942i
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	−0.976789	−	0.214206i	$-0.931284\pi$
$991$	−9.53491	+	16.5150i	−0.302886	+	0.524615i	0.673902	+	0.738821i	$0.264617\pi$
$992$	20.4381			0.648911
$993$	−18.5343	−	3.07631i	−0.588170	−	0.0976237i
$994$	−6.11372	+	3.28668i	−0.193916	+	0.104247i
$995$	1.45837	+	2.52598i	0.0462336	+	0.0800789i
$996$	−18.3266	+	22.2922i	−0.580702	+	0.706355i
$997$	−18.5075	−	32.0560i	−0.586139	−	1.01522i	−0.994732	−	0.102507i	$-0.967314\pi$
$997$	−18.5075	−	32.0560i	−0.586139	−	1.01522i	0.408593	−	0.912717i	$-0.366020\pi$
$998$	−9.51732	+	16.4845i	−0.301266	+	0.521807i
$999$	1.09694	+	36.3589i	0.0347057	+	1.15034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.h.b.25.5	yes	10
3.2	odd	2		189.2.h.b.46.1		10
4.3	odd	2		1008.2.q.i.529.5		10
7.2	even	3		63.2.g.b.16.1	yes	10
7.3	odd	6		441.2.f.f.295.1		10
7.4	even	3		441.2.f.e.295.1		10
7.5	odd	6		441.2.g.f.79.1		10
7.6	odd	2		441.2.h.f.214.5		10
9.2	odd	6		567.2.e.e.487.5		10
9.4	even	3		63.2.g.b.4.1	✓	10
9.5	odd	6		189.2.g.b.172.5		10
9.7	even	3		567.2.e.f.487.1		10
12.11	even	2		3024.2.q.i.2881.3		10
21.2	odd	6		189.2.g.b.100.5		10
21.5	even	6		1323.2.g.f.667.5		10
21.11	odd	6		1323.2.f.e.883.5		10
21.17	even	6		1323.2.f.f.883.5		10
21.20	even	2		1323.2.h.f.802.1		10
28.23	odd	6		1008.2.t.i.961.2		10
36.23	even	6		3024.2.t.i.1873.3		10
36.31	odd	6		1008.2.t.i.193.2		10
63.2	odd	6		567.2.e.e.163.5		10
63.4	even	3		441.2.f.e.148.1		10
63.5	even	6		1323.2.h.f.226.1		10
63.11	odd	6		3969.2.a.bc.1.1		5
63.13	odd	6		441.2.g.f.67.1		10
63.16	even	3		567.2.e.f.163.1		10
63.23	odd	6		189.2.h.b.37.1		10
63.25	even	3		3969.2.a.z.1.5		5
63.31	odd	6		441.2.f.f.148.1		10
63.32	odd	6		1323.2.f.e.442.5		10
63.38	even	6		3969.2.a.bb.1.1		5
63.40	odd	6		441.2.h.f.373.5		10
63.41	even	6		1323.2.g.f.361.5		10
63.52	odd	6		3969.2.a.ba.1.5		5
63.58	even	3	inner	63.2.h.b.58.5	yes	10
63.59	even	6		1323.2.f.f.442.5		10
84.23	even	6		3024.2.t.i.289.3		10
252.23	even	6		3024.2.q.i.2305.3		10
252.247	odd	6		1008.2.q.i.625.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	9.4	even	3
63.2.g.b.16.1	yes	10	7.2	even	3
63.2.h.b.25.5	yes	10	1.1	even	1	trivial
63.2.h.b.58.5	yes	10	63.58	even	3	inner
189.2.g.b.100.5		10	21.2	odd	6
189.2.g.b.172.5		10	9.5	odd	6
189.2.h.b.37.1		10	63.23	odd	6
189.2.h.b.46.1		10	3.2	odd	2
441.2.f.e.148.1		10	63.4	even	3
441.2.f.e.295.1		10	7.4	even	3
441.2.f.f.148.1		10	63.31	odd	6
441.2.f.f.295.1		10	7.3	odd	6
441.2.g.f.67.1		10	63.13	odd	6
441.2.g.f.79.1		10	7.5	odd	6
441.2.h.f.214.5		10	7.6	odd	2
441.2.h.f.373.5		10	63.40	odd	6
567.2.e.e.163.5		10	63.2	odd	6
567.2.e.e.487.5		10	9.2	odd	6
567.2.e.f.163.1		10	63.16	even	3
567.2.e.f.487.1		10	9.7	even	3
1008.2.q.i.529.5		10	4.3	odd	2
1008.2.q.i.625.5		10	252.247	odd	6
1008.2.t.i.193.2		10	36.31	odd	6
1008.2.t.i.961.2		10	28.23	odd	6
1323.2.f.e.442.5		10	63.32	odd	6
1323.2.f.e.883.5		10	21.11	odd	6
1323.2.f.f.442.5		10	63.59	even	6
1323.2.f.f.883.5		10	21.17	even	6
1323.2.g.f.361.5		10	63.41	even	6
1323.2.g.f.667.5		10	21.5	even	6
1323.2.h.f.226.1		10	63.5	even	6
1323.2.h.f.802.1		10	21.20	even	2
3024.2.q.i.2305.3		10	252.23	even	6
3024.2.q.i.2881.3		10	12.11	even	2
3024.2.t.i.289.3		10	84.23	even	6
3024.2.t.i.1873.3		10	36.23	even	6
3969.2.a.z.1.5		5	63.25	even	3
3969.2.a.ba.1.5		5	63.52	odd	6
3969.2.a.bb.1.1		5	63.38	even	6
3969.2.a.bc.1.1		5	63.11	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.05365 q^{2} +(-1.70867 - 0.283604i) q^{3} +2.21746 q^{4} +(0.0731228 - 0.126652i) q^{5} +(-3.50901 - 0.582422i) q^{6} +(-2.33035 + 1.25278i) q^{7} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +O(q^{10})\)	\(q+2.05365 q^{2} +(-1.70867 - 0.283604i) q^{3} +2.21746 q^{4} +(0.0731228 - 0.126652i) q^{5} +(-3.50901 - 0.582422i) q^{6} +(-2.33035 + 1.25278i) q^{7} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +(0.150168 - 0.260099i) q^{10} +(-0.832020 - 1.44110i) q^{11} +(-3.78891 - 0.628880i) q^{12} +(0.0999454 + 0.173111i) q^{13} +(-4.78572 + 2.57276i) q^{14} +(-0.160862 + 0.195670i) q^{15} -3.51780 q^{16} +(3.13555 - 5.43093i) q^{17} +(5.83058 + 1.99034i) q^{18} +(3.45879 + 5.99080i) q^{19} +(0.162147 - 0.280847i) q^{20} +(4.33711 - 1.47969i) q^{21} +(-1.70867 - 2.95951i) q^{22} +(3.09092 - 5.35363i) q^{23} +(-0.763064 - 0.126652i) q^{24} +(2.48931 + 4.31160i) q^{25} +(0.205252 + 0.355508i) q^{26} +(-4.57630 - 2.46119i) q^{27} +(-5.16746 + 2.77798i) q^{28} +(-2.46757 + 4.27396i) q^{29} +(-0.330354 + 0.401837i) q^{30} -2.51780 q^{31} -8.11747 q^{32} +(1.01295 + 2.69834i) q^{33} +(6.43931 - 11.1532i) q^{34} +(-0.0117348 + 0.386752i) q^{35} +(6.29567 + 2.14910i) q^{36} +(-3.50023 - 6.06257i) q^{37} +(7.10312 + 12.3030i) q^{38} +(-0.121679 - 0.324134i) q^{39} +(0.0326554 - 0.0565608i) q^{40} +(1.15895 + 2.00736i) q^{41} +(8.90688 - 3.03876i) q^{42} +(-0.940993 + 1.62985i) q^{43} +(-1.84497 - 3.19558i) q^{44} +(0.330354 - 0.288715i) q^{45} +(6.34765 - 10.9944i) q^{46} -1.81177 q^{47} +(6.01077 + 0.997660i) q^{48} +(3.86110 - 5.83883i) q^{49} +(5.11215 + 8.85451i) q^{50} +(-6.89787 + 8.39045i) q^{51} +(0.221625 + 0.383865i) q^{52} +(-2.67307 + 4.62989i) q^{53} +(-9.39810 - 5.05442i) q^{54} -0.243359 q^{55} +(-1.04069 + 0.559468i) q^{56} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 + 8.77720i) q^{58} -4.57099 q^{59} +(-0.356705 + 0.433890i) q^{60} -0.678276 q^{61} -5.17066 q^{62} +(-7.83035 + 1.29829i) q^{63} -9.63481 q^{64} +0.0292332 q^{65} +(2.08024 + 5.54143i) q^{66} -6.18684 q^{67} +(6.95296 - 12.0429i) q^{68} +(-6.79968 + 8.27101i) q^{69} +(-0.0240991 + 0.794251i) q^{70} +1.27749 q^{71} +(1.26791 + 0.432816i) q^{72} +(-0.778603 + 1.34858i) q^{73} +(-7.18823 - 12.4504i) q^{74} +(-3.03063 - 8.07311i) q^{75} +(7.66972 + 13.2843i) q^{76} +(3.74428 + 2.31594i) q^{77} +(-0.249886 - 0.665657i) q^{78} +12.7957 q^{79} +(-0.257231 + 0.445537i) q^{80} +(7.12141 + 5.50323i) q^{81} +(2.38008 + 4.12241i) q^{82} +(3.75687 - 6.50709i) q^{83} +(9.61736 - 3.28115i) q^{84} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 + 3.34713i) q^{86} +(5.42839 - 6.60299i) q^{87} +(-0.371566 - 0.643571i) q^{88} +(4.53394 + 7.85301i) q^{89} +(0.678430 - 0.592918i) q^{90} +(-0.449777 - 0.278199i) q^{91} +(6.85398 - 11.8714i) q^{92} +(4.30209 + 0.714056i) q^{93} -3.72074 q^{94} +1.01167 q^{95} +(13.8701 + 2.30214i) q^{96} +(-3.98514 + 6.90246i) q^{97} +(7.92933 - 11.9909i) q^{98} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - q^3 + 8 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 + 11 * q^9	\( 10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9} - 7 q^{10} + 4 q^{11} - 20 q^{12} - 8 q^{13} - 20 q^{14} - 19 q^{15} - 4 q^{16} + 12 q^{17} + 4 q^{18} + q^{19} + 5 q^{20} + 13 q^{21} - q^{22} + 3 q^{23} + 6 q^{24} - q^{25} + 11 q^{26} - 7 q^{27} - 2 q^{28} + 7 q^{29} + 16 q^{30} + 6 q^{31} + 4 q^{32} + 14 q^{33} + 3 q^{34} + 5 q^{35} + 34 q^{36} + 20 q^{38} + 2 q^{39} - 3 q^{40} + 5 q^{41} - 4 q^{42} - 7 q^{43} - 10 q^{44} - 16 q^{45} + 3 q^{46} - 54 q^{47} - 5 q^{48} - 8 q^{49} + 19 q^{50} - 9 q^{51} - 10 q^{52} - 21 q^{53} + q^{54} + 4 q^{55} + 18 q^{56} - 4 q^{57} - 10 q^{58} - 60 q^{59} + 10 q^{60} + 28 q^{61} - 12 q^{62} - 59 q^{63} - 50 q^{64} + 22 q^{65} + 19 q^{66} + 4 q^{67} + 27 q^{68} + 15 q^{69} + 40 q^{70} - 6 q^{71} - 36 q^{72} + 15 q^{73} - 36 q^{74} - 14 q^{75} + 5 q^{76} + 11 q^{77} - 20 q^{78} + 8 q^{79} + 20 q^{80} + 23 q^{81} - 5 q^{82} + 9 q^{83} + 35 q^{84} - 6 q^{85} - 8 q^{86} + 2 q^{87} - 18 q^{88} + 28 q^{89} + 28 q^{90} - 4 q^{91} + 27 q^{92} - 6 q^{93} + 6 q^{94} + 28 q^{95} + 59 q^{96} - 12 q^{97} + 59 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - q^3 + 8 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 + 11 * q^9 - 7 * q^10 + 4 * q^11 - 20 * q^12 - 8 * q^13 - 20 * q^14 - 19 * q^15 - 4 * q^16 + 12 * q^17 + 4 * q^18 + q^19 + 5 * q^20 + 13 * q^21 - q^22 + 3 * q^23 + 6 * q^24 - q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 + 16 * q^30 + 6 * q^31 + 4 * q^32 + 14 * q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 + 20 * q^38 + 2 * q^39 - 3 * q^40 + 5 * q^41 - 4 * q^42 - 7 * q^43 - 10 * q^44 - 16 * q^45 + 3 * q^46 - 54 * q^47 - 5 * q^48 - 8 * q^49 + 19 * q^50 - 9 * q^51 - 10 * q^52 - 21 * q^53 + q^54 + 4 * q^55 + 18 * q^56 - 4 * q^57 - 10 * q^58 - 60 * q^59 + 10 * q^60 + 28 * q^61 - 12 * q^62 - 59 * q^63 - 50 * q^64 + 22 * q^65 + 19 * q^66 + 4 * q^67 + 27 * q^68 + 15 * q^69 + 40 * q^70 - 6 * q^71 - 36 * q^72 + 15 * q^73 - 36 * q^74 - 14 * q^75 + 5 * q^76 + 11 * q^77 - 20 * q^78 + 8 * q^79 + 20 * q^80 + 23 * q^81 - 5 * q^82 + 9 * q^83 + 35 * q^84 - 6 * q^85 - 8 * q^86 + 2 * q^87 - 18 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 6 * q^93 + 6 * q^94 + 28 * q^95 + 59 * q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

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