LMFDB - Embedded newform 115.2.j.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(4,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 4]))

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

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

chi := DirichletCharacter("115.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.j (of order $22$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	115.4
Dual form			115.2.j.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.175347 - 0.0800783i) q^{2} +(-0.167074 - 0.569000i) q^{3} +(-1.28539 + 1.48342i) q^{4} +(2.18641 - 0.468631i) q^{5} +(-0.0748604 - 0.0863935i) q^{6} +(3.28793 - 0.472733i) q^{7} +(-0.215217 + 0.732961i) q^{8} +(2.22791 - 1.43179i) q^{9} +O(q^{10})$	\(q+(0.175347 - 0.0800783i) q^{2} +(-0.167074 - 0.569000i) q^{3} +(-1.28539 + 1.48342i) q^{4} +(2.18641 - 0.468631i) q^{5} +(-0.0748604 - 0.0863935i) q^{6} +(3.28793 - 0.472733i) q^{7} +(-0.215217 + 0.732961i) q^{8} +(2.22791 - 1.43179i) q^{9} +(0.345853 - 0.257257i) q^{10} +(-0.928361 + 2.03283i) q^{11} +(1.05882 + 0.483546i) q^{12} +(-6.70483 - 0.964009i) q^{13} +(0.538673 - 0.346184i) q^{14} +(-0.631942 - 1.16577i) q^{15} +(-0.537726 - 3.73997i) q^{16} +(-1.46759 + 1.27168i) q^{17} +(0.276002 - 0.429468i) q^{18} +(-1.11465 + 1.28637i) q^{19} +(-2.11521 + 3.84573i) q^{20} +(-0.818312 - 1.79185i) q^{21} +0.430792i q^{22} +(-1.75636 + 4.46264i) q^{23} +0.453012 q^{24} +(4.56077 - 2.04924i) q^{25} +(-1.25287 + 0.367875i) q^{26} +(-2.53144 - 2.19351i) q^{27} +(-3.52501 + 5.48502i) q^{28} +(-4.03098 - 4.65200i) q^{29} +(-0.204162 - 0.153810i) q^{30} +(5.15374 + 1.51327i) q^{31} +(-1.21977 - 1.89801i) q^{32} +(1.31178 + 0.188606i) q^{33} +(-0.155504 + 0.340507i) q^{34} +(6.96723 - 2.57442i) q^{35} +(-0.739787 + 5.14533i) q^{36} +(-1.72562 - 2.68512i) q^{37} +(-0.0924398 + 0.314821i) q^{38} +(0.571678 + 3.97611i) q^{39} +(-0.127064 + 1.70341i) q^{40} +(-5.62116 - 3.61250i) q^{41} +(-0.286977 - 0.248667i) q^{42} +(-2.05844 - 7.01041i) q^{43} +(-1.82223 - 3.99012i) q^{44} +(4.20015 - 4.17455i) q^{45} +(0.0493883 + 0.923158i) q^{46} +9.63634i q^{47} +(-2.03820 + 0.930816i) q^{48} +(3.87057 - 1.13650i) q^{49} +(0.635618 - 0.724546i) q^{50} +(0.968780 + 0.622597i) q^{51} +(10.0483 - 8.70693i) q^{52} +(-1.44130 + 0.207228i) q^{53} +(-0.619533 - 0.181911i) q^{54} +(-1.07713 + 4.87965i) q^{55} +(-0.361123 + 2.51167i) q^{56} +(0.918175 + 0.419317i) q^{57} +(-1.07935 - 0.492921i) q^{58} +(-1.33162 + 9.26159i) q^{59} +(2.54162 + 0.561035i) q^{60} +(10.2194 + 3.00068i) q^{61} +(1.02487 - 0.147355i) q^{62} +(6.64837 - 5.76085i) q^{63} +(5.99136 + 3.85041i) q^{64} +(-15.1113 + 1.03437i) q^{65} +(0.245121 - 0.0719739i) q^{66} +(4.44321 - 2.02915i) q^{67} -3.81165i q^{68} +(2.83269 + 0.253780i) q^{69} +(1.01553 - 1.00934i) q^{70} +(-0.0212260 - 0.0464785i) q^{71} +(0.569964 + 1.94112i) q^{72} +(4.98167 + 4.31664i) q^{73} +(-0.517603 - 0.332643i) q^{74} +(-1.92800 - 2.25271i) q^{75} +(-0.475472 - 3.30698i) q^{76} +(-2.09140 + 7.12267i) q^{77} +(0.418642 + 0.651420i) q^{78} +(1.74906 - 12.1650i) q^{79} +(-2.92835 - 7.92510i) q^{80} +(2.47529 - 5.42013i) q^{81} +(-1.27494 - 0.183308i) q^{82} +(3.94928 + 6.14520i) q^{83} +(3.70991 + 1.08933i) q^{84} +(-2.61281 + 3.46816i) q^{85} +(-0.922323 - 1.06442i) q^{86} +(-1.97352 + 3.07086i) q^{87} +(-1.29018 - 1.11795i) q^{88} +(-4.61729 + 1.35576i) q^{89} +(0.402192 - 1.06834i) q^{90} -22.5007 q^{91} +(-4.36235 - 8.34164i) q^{92} -3.18531i q^{93} +(0.771662 + 1.68970i) q^{94} +(-1.83424 + 3.33490i) q^{95} +(-0.876174 + 1.01116i) q^{96} +(-1.58420 + 2.46507i) q^{97} +(0.587684 - 0.509231i) q^{98} +(0.842280 + 5.85818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$

Coefficient data

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

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

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

$2$	0.175347	−	0.0800783i	0.123989	−	0.0566239i	−0.352455	−	0.935829i	$-0.614653\pi$
$2$	0.175347	−	0.0800783i	0.123989	−	0.0566239i	0.476444	+	0.879205i	$0.341926\pi$
$3$	−0.167074	−	0.569000i	−0.0964600	−	0.328512i	0.897099	−	0.441830i	$-0.145670\pi$
$3$	−0.167074	−	0.569000i	−0.0964600	−	0.328512i	−0.993559	+	0.113317i	$0.963852\pi$
$4$	−1.28539	+	1.48342i	−0.642694	+	0.741708i
$5$	2.18641	−	0.468631i	0.977792	−	0.209578i
$5$	2.18641	−	0.468631i	0.977792	−	0.209578i
$6$	−0.0748604	−	0.0863935i	−0.0305616	−	0.0352700i
$7$	3.28793	−	0.472733i	1.24272	−	0.178676i	0.510581	−	0.859830i	$-0.329430\pi$
$7$	3.28793	−	0.472733i	1.24272	−	0.178676i	0.732141	+	0.681153i	$0.238521\pi$
$8$	−0.215217	+	0.732961i	−0.0760906	+	0.259141i
$9$	2.22791	−	1.43179i	0.742638	−	0.477264i
$10$	0.345853	−	0.257257i	0.109368	−	0.0813518i
$11$	−0.928361	+	2.03283i	−0.279911	+	0.612921i	−0.996409	−	0.0846689i	$-0.973017\pi$
$11$	−0.928361	+	2.03283i	−0.279911	+	0.612921i	0.716498	+	0.697589i	$0.245744\pi$
$12$	1.05882	+	0.483546i	0.305655	+	0.139588i
$13$	−6.70483	−	0.964009i	−1.85959	−	0.267368i	−0.880986	−	0.473143i	$-0.843119\pi$
$13$	−6.70483	−	0.964009i	−1.85959	−	0.267368i	−0.978599	+	0.205775i	$0.934029\pi$
$14$	0.538673	−	0.346184i	0.143966	−	0.0925216i
$15$	−0.631942	−	1.16577i	−0.163167	−	0.301001i
$16$	−0.537726	−	3.73997i	−0.134432	−	0.934992i
$17$	−1.46759	+	1.27168i	−0.355944	+	0.308427i	−0.814416	−	0.580282i	$-0.802942\pi$
$17$	−1.46759	+	1.27168i	−0.355944	+	0.308427i	0.458472	+	0.888709i	$0.348397\pi$
$18$	0.276002	−	0.429468i	0.0650544	−	0.101227i
$19$	−1.11465	+	1.28637i	−0.255718	+	0.295114i	−0.869064	−	0.494700i	$-0.835278\pi$
$19$	−1.11465	+	1.28637i	−0.255718	+	0.295114i	0.613346	+	0.789815i	$0.289823\pi$
$20$	−2.11521	+	3.84573i	−0.472975	+	0.859931i
$21$	−0.818312	−	1.79185i	−0.178570	−	0.391014i
$22$			0.430792i			0.0918451i
$23$	−1.75636	+	4.46264i	−0.366227	+	0.930526i
$23$	−1.75636	+	4.46264i	−0.366227	+	0.930526i
$24$	0.453012			0.0924707
$25$	4.56077	−	2.04924i	0.912154	−	0.409848i
$26$	−1.25287	+	0.367875i	−0.245708	+	0.0721463i
$27$	−2.53144	−	2.19351i	−0.487177	−	0.422141i
$28$	−3.52501	+	5.48502i	−0.666164	+	1.03657i
$29$	−4.03098	−	4.65200i	−0.748535	−	0.863856i	0.245890	−	0.969298i	$-0.420920\pi$
$29$	−4.03098	−	4.65200i	−0.748535	−	0.863856i	−0.994425	+	0.105442i	$0.966374\pi$
$30$	−0.204162	−	0.153810i	−0.0372747	−	0.0280817i
$31$	5.15374	+	1.51327i	0.925639	+	0.271792i	0.709610	−	0.704595i	$-0.248871\pi$
$31$	5.15374	+	1.51327i	0.925639	+	0.271792i	0.216029	+	0.976387i	$0.430689\pi$
$32$	−1.21977	−	1.89801i	−0.215628	−	0.335523i
$33$	1.31178	+	0.188606i	0.228352	+	0.0328321i
$34$	−0.155504	+	0.340507i	−0.0266688	+	0.0583965i
$35$	6.96723	−	2.57442i	1.17768	−	0.435156i
$36$	−0.739787	+	5.14533i	−0.123298	+	0.857555i
$37$	−1.72562	−	2.68512i	−0.283691	−	0.441432i	0.669938	−	0.742417i	$-0.266321\pi$
$37$	−1.72562	−	2.68512i	−0.283691	−	0.441432i	−0.953629	+	0.300986i	$0.902684\pi$
$38$	−0.0924398	+	0.314821i	−0.0149957	+	0.0510707i
$39$	0.571678	+	3.97611i	0.0915418	+	0.636687i
$40$	−0.127064	+	1.70341i	−0.0200905	+	0.269333i
$41$	−5.62116	−	3.61250i	−0.877878	−	0.564178i	0.0222748	−	0.999752i	$-0.492909\pi$
$41$	−5.62116	−	3.61250i	−0.877878	−	0.564178i	−0.900153	+	0.435574i	$0.856545\pi$
$42$	−0.286977	−	0.248667i	−0.0442815	−	0.0383701i
$43$	−2.05844	−	7.01041i	−0.313909	−	1.06908i	−0.953758	−	0.300576i	$-0.902821\pi$
$43$	−2.05844	−	7.01041i	−0.313909	−	1.06908i	0.639848	−	0.768501i	$-0.278997\pi$
$44$	−1.82223	−	3.99012i	−0.274711	−	0.601533i
$45$	4.20015	−	4.17455i	0.626121	−	0.622306i
$46$	0.0493883	+	0.923158i	0.00728190	+	0.136112i
$47$			9.63634i			1.40560i	0.711385	+	0.702802i	$0.248068\pi$
$47$			9.63634i			1.40560i	−0.711385	+	0.702802i	$0.751932\pi$
$48$	−2.03820	+	0.930816i	−0.294189	+	0.134352i
$49$	3.87057	−	1.13650i	0.552939	−	0.162357i
$50$	0.635618	−	0.724546i	0.0898899	−	0.102466i
$51$	0.968780	+	0.622597i	0.135656	+	0.0871811i
$52$	10.0483	−	8.70693i	1.39345	−	1.20743i
$53$	−1.44130	+	0.207228i	−0.197978	+	0.0284649i	−0.240590	−	0.970627i	$-0.577341\pi$
$53$	−1.44130	+	0.207228i	−0.197978	+	0.0284649i	0.0426124	+	0.999092i	$0.486432\pi$
$54$	−0.619533	−	0.181911i	−0.0843078	−	0.0247550i
$55$	−1.07713	+	4.87965i	−0.145240	+	0.657972i
$56$	−0.361123	+	2.51167i	−0.0482571	+	0.335636i
$57$	0.918175	+	0.419317i	0.121615	+	0.0555399i
$58$	−1.07935	−	0.492921i	−0.141725	−	0.0647236i
$59$	−1.33162	+	9.26159i	−0.173362	+	1.20576i	0.698357	+	0.715749i	$0.253915\pi$
$59$	−1.33162	+	9.26159i	−0.173362	+	1.20576i	−0.871719	+	0.490007i	$0.836994\pi$
$60$	2.54162	+	0.561035i	0.328121	+	0.0724292i
$61$	10.2194	+	3.00068i	1.30846	+	0.384198i	0.860315	−	0.509764i	$-0.170267\pi$
$61$	10.2194	+	3.00068i	1.30846	+	0.384198i	0.448144	+	0.893962i	$0.352085\pi$
$62$	1.02487	−	0.147355i	0.130159	−	0.0187140i
$63$	6.64837	−	5.76085i	0.837616	−	0.725798i
$64$	5.99136	+	3.85041i	0.748919	+	0.481301i
$65$	−15.1113	+	1.03437i	−1.87432	+	0.128298i
$66$	0.245121	−	0.0719739i	0.0301723	−	0.00885937i
$67$	4.44321	−	2.02915i	0.542824	−	0.247900i	−0.125080	−	0.992147i	$-0.539919\pi$
$67$	4.44321	−	2.02915i	0.542824	−	0.247900i	0.667904	+	0.744247i	$0.267192\pi$
$68$		−	3.81165i		−	0.462230i
$69$	2.83269	+	0.253780i	0.341015	+	0.0305515i
$70$	1.01553	−	1.00934i	0.121379	−	0.120639i
$71$	−0.0212260	−	0.0464785i	−0.00251907	−	0.00551599i	0.908368	−	0.418171i	$-0.137329\pi$
$71$	−0.0212260	−	0.0464785i	−0.00251907	−	0.00551599i	−0.910887	+	0.412655i	$0.864601\pi$
$72$	0.569964	+	1.94112i	0.0671709	+	0.228763i
$73$	4.98167	+	4.31664i	0.583061	+	0.505225i	0.895707	−	0.444645i	$-0.146670\pi$
$73$	4.98167	+	4.31664i	0.583061	+	0.505225i	−0.312646	+	0.949870i	$0.601216\pi$
$74$	−0.517603	−	0.332643i	−0.0601701	−	0.0386690i
$75$	−1.92800	−	2.25271i	−0.222626	−	0.260120i
$76$	−0.475472	−	3.30698i	−0.0545403	−	0.379336i
$77$	−2.09140	+	7.12267i	−0.238338	+	0.811703i
$78$	0.418642	+	0.651420i	0.0474019	+	0.0737588i
$79$	1.74906	−	12.1650i	0.196784	−	1.36867i	−0.616754	−	0.787156i	$-0.711553\pi$
$79$	1.74906	−	12.1650i	0.196784	−	1.36867i	0.813539	−	0.581510i	$-0.197538\pi$
$80$	−2.92835	−	7.92510i	−0.327400	−	0.886054i
$81$	2.47529	−	5.42013i	0.275033	−	0.602237i
$82$	−1.27494	−	0.183308i	−0.140793	−	0.0202430i
$83$	3.94928	+	6.14520i	0.433490	+	0.674523i	0.987434	−	0.158030i	$-0.0505144\pi$
$83$	3.94928	+	6.14520i	0.433490	+	0.674523i	−0.553944	+	0.832554i	$0.686878\pi$
$84$	3.70991	+	1.08933i	0.404785	+	0.118855i
$85$	−2.61281	+	3.46816i	−0.283399	+	0.376175i
$86$	−0.922323	−	1.06442i	−0.0994566	−	0.114779i
$87$	−1.97352	+	3.07086i	−0.211584	+	0.329231i
$88$	−1.29018	−	1.11795i	−0.137534	−	0.119174i
$89$	−4.61729	+	1.35576i	−0.489432	+	0.143710i	−0.517131	−	0.855906i	$-0.673000\pi$
$89$	−4.61729	+	1.35576i	−0.489432	+	0.143710i	0.0276993	+	0.999616i	$0.491182\pi$
$90$	0.402192	−	1.06834i	0.0423947	−	0.112612i
$91$	−22.5007			−2.35872
$92$	−4.36235	−	8.34164i	−0.454807	−	0.869676i
$93$		−	3.18531i		−	0.330301i
$94$	0.771662	+	1.68970i	0.0795908	+	0.174280i
$95$	−1.83424	+	3.33490i	−0.188190	+	0.342153i
$96$	−0.876174	+	1.01116i	−0.0894242	+	0.103201i
$97$	−1.58420	+	2.46507i	−0.160851	+	0.250290i	−0.912319	−	0.409480i	$-0.865710\pi$
$97$	−1.58420	+	2.46507i	−0.160851	+	0.250290i	0.751467	+	0.659770i	$0.229346\pi$
$98$	0.587684	−	0.509231i	0.0593650	−	0.0514401i
$99$	0.842280	+	5.85818i	0.0846523	+	0.588770i
$100$	−2.82248	+	9.39959i	−0.282248	+	0.939959i
$101$	3.89335	−	2.50211i	0.387403	−	0.248969i	−0.332413	−	0.943134i	$-0.607863\pi$
$101$	3.89335	−	2.50211i	0.387403	−	0.248969i	0.719816	+	0.694165i	$0.244226\pi$
$102$	0.219729	+	0.0315923i	0.0217564	+	0.00312810i
$103$	−0.478979	−	0.218742i	−0.0471952	−	0.0215533i	0.391678	−	0.920103i	$-0.371895\pi$
$103$	−0.478979	−	0.218742i	−0.0471952	−	0.0215533i	−0.438873	+	0.898549i	$0.644622\pi$
$104$	2.14957	−	4.70691i	0.210783	−	0.461550i
$105$	−2.62888	−	3.53424i	−0.256553	−	0.344906i
$106$	−0.236133	+	0.151754i	−0.0229353	+	0.0147396i
$107$	−4.27457	+	14.5578i	−0.413238	+	1.40736i	0.445655	+	0.895205i	$0.352971\pi$
$107$	−4.27457	+	14.5578i	−0.413238	+	1.40736i	−0.858893	+	0.512155i	$0.828847\pi$
$108$	6.50777	−	0.935676i	0.626211	−	0.0900355i
$109$	−9.38558	−	10.8315i	−0.898975	−	1.03747i	−0.999097	−	0.0424977i	$-0.986468\pi$
$109$	−9.38558	−	10.8315i	−0.898975	−	1.03747i	0.100121	−	0.994975i	$-0.468077\pi$
$110$	0.201882	+	0.941887i	0.0192487	+	0.0898054i
$111$	−1.23953	+	1.43049i	−0.117651	+	0.135776i
$112$	−3.53601	−	12.0426i	−0.334122	−	1.13791i
$113$	11.0905	−	5.06485i	1.04330	−	0.476461i	0.181335	−	0.983421i	$-0.441958\pi$
$113$	11.0905	−	5.06485i	1.04330	−	0.476461i	0.861970	+	0.506960i	$0.169231\pi$
$114$	0.194577			0.0182238
$115$	−1.74879	+	10.5803i	−0.163076	+	0.986614i
$116$	12.0822			1.12181
$117$	−16.3180	+	7.45220i	−1.50860	+	0.688956i
$118$	0.508157	+	1.73062i	0.0467797	+	0.159317i
$119$	−4.22418	+	4.87497i	−0.387230	+	0.446887i
$120$	0.990470	−	0.212296i	0.0904171	−	0.0193798i
$121$	3.93294	+	4.53885i	0.357540	+	0.412623i
$122$	2.03223	−	0.292190i	0.183989	−	0.0264537i
$123$	−1.11637	+	3.80200i	−0.100659	+	0.342815i
$124$	−8.86937	+	5.70000i	−0.796493	+	0.511875i
$125$	9.01137	−	6.61779i	0.806002	−	0.591913i
$126$	0.704453	−	1.54254i	0.0627577	−	0.137420i
$127$	3.54439	+	1.61867i	0.314513	+	0.143633i	0.566417	−	0.824119i	$-0.308329\pi$
$127$	3.54439	+	1.61867i	0.314513	+	0.143633i	−0.251903	+	0.967752i	$0.581057\pi$
$128$	5.82530	+	0.837552i	0.514889	+	0.0740298i
$129$	−3.64501	+	2.34251i	−0.320926	+	0.206246i
$130$	−2.56688	+	1.39146i	−0.225131	+	0.122039i
$131$	−1.76246	−	12.2582i	−0.153987	−	1.07100i	−0.909450	−	0.415813i	$-0.863497\pi$
$131$	−1.76246	−	12.2582i	−0.153987	−	1.07100i	0.755463	−	0.655192i	$-0.227412\pi$
$132$	−1.96593	+	1.70349i	−0.171112	+	0.148270i
$133$	−3.05678	+	4.75644i	−0.265056	+	0.412436i
$134$	0.616613	−	0.711609i	0.0532672	−	0.0614737i
$135$	−6.56272	−	3.60959i	−0.564829	−	0.310664i
$136$	−0.616239	−	1.34937i	−0.0528420	−	0.115708i
$137$		−	13.7044i		−	1.17084i	−0.810729	−	0.585421i	$-0.800929\pi$
$137$		−	13.7044i		−	1.17084i	0.810729	−	0.585421i	$-0.199071\pi$
$138$	0.517025	−	0.182337i	0.0440121	−	0.0155216i
$139$	−1.30658			−0.110823			−0.0554113	−	0.998464i	$-0.517647\pi$
$139$	−1.30658			−0.110823			−0.0554113	+	0.998464i	$0.517647\pi$
$140$	−5.13666	+	13.6444i	−0.434127	+	1.15316i
$141$	5.48308	−	1.60998i	0.461759	−	0.135585i
$142$	−0.00744384	−	0.00645013i	−0.000624674	−	0.000541283i
$143$	8.18417	−	12.7348i	0.684394	−	1.06494i
$144$	−6.55286	−	7.56241i	−0.546072	−	0.630201i
$145$	−10.9935	−	8.28214i	−0.912957	−	0.687794i
$146$	1.21919	+	0.357987i	0.100901	+	0.0296272i
$147$	−1.29334	−	2.01248i	−0.106673	−	0.165986i
$148$	6.20125	+	0.891605i	0.509740	+	0.0732895i
$149$	−0.0899971	+	0.197066i	−0.00737285	+	0.0161443i	−0.913283	−	0.407327i	$-0.866461\pi$
$149$	−0.0899971	+	0.197066i	−0.00737285	+	0.0161443i	0.905910	+	0.423471i	$0.139188\pi$
$150$	−0.518462	−	0.240614i	−0.0423322	−	0.0196461i
$151$	−0.838874	+	5.83450i	−0.0682666	+	0.474805i	0.926797	+	0.375563i	$0.122551\pi$
$151$	−0.838874	+	5.83450i	−0.0682666	+	0.474805i	−0.995063	+	0.0992415i	$0.968358\pi$
$152$	−0.702971	−	1.09384i	−0.0570185	−	0.0887225i
$153$	−1.44889	+	4.93447i	−0.117136	+	0.398929i
$154$	0.203650	+	1.41641i	0.0164106	+	0.114138i
$155$	11.9774	+	0.893435i	0.962044	+	0.0717624i
$156$	−6.63305	−	4.26280i	−0.531069	−	0.341298i
$157$	−3.28885	−	2.84980i	−0.262479	−	0.227439i	0.513672	−	0.857987i	$-0.328285\pi$
$157$	−3.28885	−	2.84980i	−0.262479	−	0.227439i	−0.776151	+	0.630548i	$0.782830\pi$
$158$	−0.667458	−	2.27315i	−0.0531001	−	0.180842i
$159$	0.358716	+	0.785479i	0.0284480	+	0.0622925i
$160$	−3.55639	−	3.57820i	−0.281157	−	0.282881i
$161$	−3.66516	+	15.5032i	−0.288855	+	1.22182i
$162$		−	1.14862i		−	0.0902442i
$163$	11.8778	−	5.42443i	0.930344	−	0.424874i	0.108184	−	0.994131i	$-0.465496\pi$
$163$	11.8778	−	5.42443i	0.930344	−	0.424874i	0.822160	+	0.569257i	$0.192769\pi$
$164$	12.5842	−	3.69506i	0.982662	−	0.288536i
$165$	2.95648	−	0.202373i	0.230162	−	0.0157547i
$166$	1.18459	+	0.761291i	0.0919421	+	0.0590876i
$167$	−1.17039	+	1.01415i	−0.0905676	+	0.0784773i	−0.698968	−	0.715153i	$-0.746357\pi$
$167$	−1.17039	+	1.01415i	−0.0905676	+	0.0784773i	0.608400	+	0.793630i	$0.291812\pi$
$168$	1.48947	−	0.214154i	0.114915	−	0.0165223i
$169$	31.5520	+	9.26451i	2.42708	+	0.712654i
$170$	−0.180424	+	0.817362i	−0.0138379	+	0.0626888i
$171$	−0.641521	+	4.46188i	−0.0490583	+	0.341208i
$172$	13.0452	+	5.95757i	0.994691	+	0.454260i
$173$	17.4774	+	7.98166i	1.32878	+	0.606834i	0.948130	−	0.317884i	$-0.102972\pi$
$173$	17.4774	+	7.98166i	1.32878	+	0.606834i	0.380652	+	0.924718i	$0.375699\pi$
$174$	−0.100142	+	0.696502i	−0.00759173	+	0.0528017i
$175$	14.0268	−	8.89378i	1.06032	−	0.672307i
$176$	8.10191	+	2.37894i	0.610705	+	0.179319i
$177$	5.49232	−	0.789677i	0.412828	−	0.0593558i
$178$	−0.701061	+	0.607473i	−0.0525468	+	0.0455320i
$179$	13.7518	+	8.83775i	1.02786	+	0.660565i	0.941955	−	0.335739i	$-0.108986\pi$
$179$	13.7518	+	8.83775i	1.02786	+	0.660565i	0.0859035	+	0.996303i	$0.472622\pi$
$180$	0.793785	+	11.5965i	0.0591652	+	0.864351i
$181$	−7.47229	+	2.19406i	−0.555411	+	0.163083i	−0.547380	−	0.836884i	$-0.684375\pi$
$181$	−7.47229	+	2.19406i	−0.555411	+	0.163083i	−0.00803105	+	0.999968i	$0.502556\pi$
$182$	−3.94544	+	1.80182i	−0.292455	+	0.133560i
$183$		−	6.31617i		−	0.466905i
$184$	−2.89295	−	2.24778i	−0.213271	−	0.165709i
$185$	−5.03125	−	5.06210i	−0.369905	−	0.372173i
$186$	−0.255074	−	0.558534i	−0.0187029	−	0.0409537i
$187$	−1.22264	−	4.16394i	−0.0894085	−	0.304497i
$188$	−14.2947	−	12.3864i	−1.04255	−	0.903373i
$189$	−9.36016	−	6.01541i	−0.680851	−	0.437557i
$190$	−0.0545763	+	0.731648i	−0.00395938	+	0.0530793i
$191$	0.984236	+	6.84551i	0.0712168	+	0.495324i	0.993946	+	0.109874i	$0.0350447\pi$
$191$	0.984236	+	6.84551i	0.0712168	+	0.495324i	−0.922729	+	0.385450i	$0.874046\pi$
$192$	1.18989	−	4.05238i	0.0858727	−	0.292456i
$193$	−3.14087	−	4.88729i	−0.226085	−	0.351795i	0.709617	−	0.704588i	$-0.248868\pi$
$193$	−3.14087	−	4.88729i	−0.226085	−	0.351795i	−0.935701	+	0.352793i	$0.885232\pi$
$194$	−0.0803868	+	0.559102i	−0.00577143	+	0.0401412i
$195$	3.11325	+	8.42550i	0.222945	+	0.603362i
$196$	−3.28928	+	7.20251i	−0.234948	+	0.514465i
$197$	−9.58401	−	1.37797i	−0.682833	−	0.0981765i	−0.207835	−	0.978164i	$-0.566642\pi$
$197$	−9.58401	−	1.37797i	−0.682833	−	0.0981765i	−0.474997	+	0.879987i	$0.657551\pi$
$198$	0.616804	+	0.959766i	0.0438344	+	0.0682076i
$199$	−15.4886	−	4.54788i	−1.09796	−	0.322390i	−0.317919	−	0.948118i	$-0.602984\pi$
$199$	−15.4886	−	4.54788i	−1.09796	−	0.322390i	−0.780042	+	0.625727i	$0.784802\pi$
$200$	0.520458	+	3.78390i	0.0368019	+	0.267562i
$201$	−1.89693	−	2.18917i	−0.133799	−	0.154412i
$202$	0.482323	−	0.750510i	0.0339361	−	0.0528057i
$203$	−15.4528	−	13.3899i	−1.08457	−	0.939786i
$204$	−2.16883	+	0.636826i	−0.151848	+	0.0445867i
$205$	−13.9831	−	5.26416i	−0.976622	−	0.367665i
$206$	−0.101504			−0.00707211
$207$	2.47656	+	12.4571i	0.172133	+	0.865830i
$208$			25.5942i			1.77464i
$209$	−1.58018	−	3.46011i	−0.109303	−	0.239341i
$210$	−0.743982	−	0.409201i	−0.0513397	−	0.0282376i
$211$	8.81677	−	10.1751i	0.606972	−	0.700483i	−0.366207	−	0.930533i	$-0.619344\pi$
$211$	8.81677	−	10.1751i	0.606972	−	0.700483i	0.973179	+	0.230051i	$0.0738893\pi$
$212$	1.54523	−	2.40442i	0.106127	−	0.165136i
$213$	−0.0229000	+	0.0198430i	−0.00156908	+	0.00135962i
$214$	0.416234	+	2.89497i	0.0284532	+	0.197896i
$215$	−7.78589	−	14.3630i	−0.530993	−	0.979547i
$216$	2.15257	−	1.38337i	0.146464	−	0.0941264i
$217$	17.6605	+	2.53920i	1.19887	+	0.172372i
$218$	−2.51310	−	1.14770i	−0.170209	−	0.0777318i
$219$	1.62387	−	3.55577i	0.109731	−	0.240277i
$220$	−5.85402	−	7.87008i	−0.394678	−	0.530600i
$221$	11.0659	−	7.11160i	0.744371	−	0.478378i
$222$	−0.102796	+	0.350092i	−0.00689924	+	0.0234966i
$223$	−11.8262	+	1.70035i	−0.791941	+	0.113864i	−0.526402	−	0.850236i	$-0.676459\pi$
$223$	−11.8262	+	1.70035i	−0.791941	+	0.113864i	−0.265539	+	0.964100i	$0.585550\pi$
$224$	−4.90779	−	5.66389i	−0.327915	−	0.378435i
$225$	7.22691	−	11.0956i	0.481794	−	0.739707i
$226$	1.53910	−	1.77621i	0.102379	−	0.118152i
$227$	2.52632	+	8.60387i	0.167678	+	0.571059i	0.999863	+	0.0165605i	$0.00527161\pi$
$227$	2.52632	+	8.60387i	0.167678	+	0.571059i	−0.832185	+	0.554498i	$0.812910\pi$
$228$	−1.80223	+	0.823052i	−0.119356	+	0.0545079i
$229$	−3.05115			−0.201626			−0.100813	−	0.994905i	$-0.532144\pi$
$229$	−3.05115			−0.201626			−0.100813	+	0.994905i	$0.532144\pi$
$230$	0.540603	+	1.99526i	0.0356463	+	0.131563i
$231$	4.40222			0.289645
$232$	4.27727	−	1.95337i	0.280817	−	0.128245i
$233$	3.93207	+	13.3914i	0.257598	+	0.877300i	0.982153	+	0.188083i	$0.0602272\pi$
$233$	3.93207	+	13.3914i	0.257598	+	0.877300i	−0.724555	+	0.689217i	$0.757955\pi$
$234$	−2.26456	+	2.61344i	−0.148039	+	0.170846i
$235$	4.51589	+	21.0690i	0.294584	+	1.37439i
$236$	−12.0271	−	13.8801i	−0.782901	−	0.903516i
$237$	−7.21409	+	1.03723i	−0.468606	+	0.0673753i
$238$	−0.350319	+	1.19308i	−0.0227078	+	0.0773356i
$239$	0.753569	−	0.484289i	0.0487443	−	0.0313261i	−0.516042	−	0.856563i	$-0.672595\pi$
$239$	0.753569	−	0.484289i	0.0487443	−	0.0313261i	0.564786	+	0.825237i	$0.308959\pi$
$240$	−4.02014	+	2.99031i	−0.259499	+	0.193024i
$241$	0.270835	−	0.593047i	0.0174460	−	0.0382015i	−0.900708	−	0.434424i	$-0.856952\pi$
$241$	0.270835	−	0.593047i	0.0174460	−	0.0382015i	0.918154	+	0.396223i	$0.129679\pi$
$242$	1.05309	+	0.480931i	0.0676953	+	0.0309154i
$243$	−13.4441	−	1.93297i	−0.862438	−	0.124000i
$244$	−17.5871	+	11.3026i	−1.12590	+	0.723572i
$245$	7.93005	−	4.29873i	0.506632	−	0.274636i
$246$	0.108706	+	0.756065i	0.00693083	+	0.0482050i
$247$	8.71361	−	7.55039i	0.554434	−	0.480419i
$248$	−2.21834	+	3.45181i	−0.140865	+	0.219190i
$249$	2.83680	−	3.27384i	0.179775	−	0.207471i
$250$	1.05018	−	1.88203i	0.0664189	−	0.119030i
$251$	2.77052	+	6.06660i	0.174874	+	0.382920i	0.976691	−	0.214649i	$-0.0688607\pi$
$251$	2.77052	+	6.06660i	0.174874	+	0.382920i	−0.801818	+	0.597569i	$0.796133\pi$
$252$			17.2672i			1.08773i
$253$	−7.44125	−	7.71333i	−0.467827	−	0.484933i
$254$	0.751117			0.0471293
$255$	2.40992	+	0.907252i	0.150915	+	0.0568143i
$256$	−12.5784	+	3.69335i	−0.786149	+	0.230834i
$257$	3.18618	+	2.76084i	0.198748	+	0.172217i	0.748549	−	0.663079i	$-0.230751\pi$
$257$	3.18618	+	2.76084i	0.198748	+	0.172217i	−0.549801	+	0.835296i	$0.685296\pi$
$258$	−0.451558	+	0.702638i	−0.0281128	+	0.0437443i
$259$	−6.94308	−	8.01274i	−0.431422	−	0.497888i
$260$	17.8894	−	23.7459i	1.10945	−	1.47266i
$261$	−15.6414	−	4.59273i	−0.968178	−	0.284283i
$262$	−1.29066	−	2.00830i	−0.0797372	−	0.124073i
$263$	−21.3499	−	3.06965i	−1.31649	−	0.189283i	−0.551960	−	0.833870i	$-0.686120\pi$
$263$	−21.3499	−	3.06965i	−1.31649	−	0.189283i	−0.764530	+	0.644588i	$0.777029\pi$
$264$	−0.420559	+	0.920896i	−0.0258836	+	0.0566772i
$265$	−3.05416	+	1.12852i	−0.187616	+	0.0693246i
$266$	−0.155109	+	1.07881i	−0.00951036	+	0.0661460i
$267$	1.54285	+	2.40073i	0.0944212	+	0.146922i
$268$	−2.70118	+	9.19937i	−0.165001	+	0.561941i
$269$	0.990380	+	6.88824i	0.0603845	+	0.419983i	0.997482	+	0.0709164i	$0.0225924\pi$
$269$	0.990380	+	6.88824i	0.0603845	+	0.419983i	−0.937098	+	0.349067i	$0.886499\pi$
$270$	−1.43980	−	0.107400i	−0.0876236	−	0.00653617i
$271$	−3.65615	−	2.34966i	−0.222095	−	0.142732i	0.424862	−	0.905258i	$-0.360323\pi$
$271$	−3.65615	−	2.34966i	−0.222095	−	0.142732i	−0.646957	+	0.762526i	$0.723959\pi$
$272$	5.54519	+	4.80494i	0.336227	+	0.291342i
$273$	3.75928	+	12.8029i	0.227522	+	0.774868i
$274$	−1.09742	−	2.40302i	−0.0662977	−	0.145172i
$275$	−0.0682934	+	11.1737i	−0.00411825	+	0.673799i
$276$	−4.01756	+	3.87585i	−0.241829	+	0.233299i
$277$		−	19.1889i		−	1.15295i	−0.817116	−	0.576473i	$-0.804428\pi$
$277$		−	19.1889i		−	1.15295i	0.817116	−	0.576473i	$-0.195572\pi$
$278$	−0.229105	+	0.104629i	−0.0137408	+	0.00627521i
$279$	13.6488	−	4.00764i	0.817131	−	0.239931i
$280$	0.387482	+	5.66076i	0.0231565	+	0.338295i
$281$	5.60582	+	3.60264i	0.334415	+	0.214916i	0.697062	−	0.717011i	$-0.254490\pi$
$281$	5.60582	+	3.60264i	0.334415	+	0.214916i	−0.362646	+	0.931927i	$0.618127\pi$
$282$	0.832517	−	0.721380i	0.0495757	−	0.0429576i
$283$	5.94385	−	0.854596i	0.353325	−	0.0508005i	0.0366328	−	0.999329i	$-0.488337\pi$
$283$	5.94385	−	0.854596i	0.353325	−	0.0508005i	0.316692	+	0.948528i	$0.397428\pi$
$284$	0.0962307	+	0.0282559i	0.00571024	+	0.00167668i
$285$	2.20401	+	0.486512i	0.130554	+	0.0288185i
$286$	0.415287	−	2.88838i	0.0245564	−	0.170794i
$287$	−20.1898	−	9.22035i	−1.19176	−	0.544260i
$288$	−5.43510	−	2.48213i	−0.320267	−	0.146261i
$289$	−1.88268	+	13.0944i	−0.110746	+	0.770256i
$290$	−2.59089	−	0.571911i	−0.152142	−	0.0335838i
$291$	1.66730	+	0.489564i	0.0977390	+	0.0286988i
$292$	−12.8068	+	1.84133i	−0.749459	+	0.107756i
$293$	−12.0927	+	10.4784i	−0.706464	+	0.612155i	−0.932161	−	0.362043i	$-0.882079\pi$
$293$	−12.0927	+	10.4784i	−0.706464	+	0.612155i	0.225697	+	0.974197i	$0.427534\pi$
$294$	−0.387939	−	0.249313i	−0.0226250	−	0.0145402i
$295$	1.42881	+	20.8737i	0.0831887	+	1.21531i
$296$	2.33948	−	0.686932i	0.135979	−	0.0399271i
$297$	6.80912	−	3.10962i	0.395105	−	0.180438i
$298$			0.0417618i			0.00241919i
$299$	16.0781	−	28.2281i	0.929822	−	1.63247i
$300$	5.81993	+	0.0355713i	0.336014	+	0.00205371i
$301$	−10.0821	−	22.0767i	−0.581121	−	1.27248i
$302$	0.320123	+	1.09024i	0.0184210	+	0.0627361i
$303$	−2.07417	−	1.79728i	−0.119158	−	0.103251i
$304$	5.41037	+	3.47704i	0.310306	+	0.199422i
$305$	23.7500	+	1.77160i	1.35992	+	0.101441i
$306$	0.141085	+	0.981270i	0.00806531	+	0.0560955i
$307$	−1.05789	+	3.60285i	−0.0603770	+	0.205625i	−0.984157	−	0.177298i	$-0.943264\pi$
$307$	−1.05789	+	3.60285i	−0.0603770	+	0.205625i	0.923780	+	0.382923i	$0.125083\pi$
$308$	−7.87761	−	12.2578i	−0.448869	−	0.698453i
$309$	−0.0444397	+	0.309085i	−0.00252809	+	0.0175832i
$310$	2.17174	−	0.802465i	0.123346	−	0.0455769i
$311$	4.31409	−	9.44654i	0.244630	−	0.535664i	−0.746993	−	0.664832i	$-0.768503\pi$
$311$	4.31409	−	9.44654i	0.244630	−	0.535664i	0.991623	+	0.129168i	$0.0412305\pi$
$312$	−3.03737	−	0.436708i	−0.171957	−	0.0247237i
$313$	6.16831	+	9.59809i	0.348654	+	0.542516i	0.970648	−	0.240506i	$-0.0773135\pi$
$313$	6.16831	+	9.59809i	0.348654	+	0.542516i	−0.621994	+	0.783022i	$0.713677\pi$
$314$	−0.804897	−	0.236339i	−0.0454230	−	0.0133374i
$315$	11.8363	−	15.7112i	0.666903	−	0.885226i
$316$	15.7975	+	18.2313i	0.888679	+	1.02559i
$317$	8.68395	−	13.5125i	0.487739	−	0.758937i	−0.506937	−	0.861983i	$-0.669222\pi$
$317$	8.68395	−	13.5125i	0.487739	−	0.758937i	0.994677	+	0.103046i	$0.0328589\pi$
$318$	0.125800	+	0.109006i	0.00705449	+	0.00611275i
$319$	13.1989	−	3.87556i	0.738998	−	0.216989i
$320$	14.9040	+	5.61084i	0.833158	+	0.313655i
$321$	8.99758			0.502196
$322$	0.598793	+	3.01193i	0.0333694	+	0.167848i
$323$		−	3.30535i		−	0.183914i
$324$	4.85861	+	10.6389i	0.269923	+	0.591048i
$325$	−32.5547	+	9.34317i	−1.80581	+	0.518266i
$326$	1.64836	−	1.90231i	0.0912944	−	0.105359i
$327$	−4.59506	+	7.15006i	−0.254108	+	0.395399i
$328$	3.85759	−	3.34262i	0.213000	−	0.184565i
$329$	4.55542	+	31.6836i	0.251148	+	1.74678i
$330$	0.502205	−	0.272236i	0.0276455	−	0.0149861i
$331$	4.84987	−	3.11682i	0.266573	−	0.171316i	−0.400525	−	0.916286i	$-0.631172\pi$
$331$	4.84987	−	3.11682i	0.266573	−	0.171316i	0.667099	+	0.744969i	$0.267536\pi$
$332$	−14.1922	−	2.04054i	−0.778901	−	0.111989i
$333$	−7.68908	−	3.51149i	−0.421359	−	0.192428i
$334$	−0.124013	+	0.271551i	−0.00678570	+	0.0148586i
$335$	8.76375	−	6.51877i	0.478815	−	0.356158i
$336$	−6.26144	+	4.02399i	−0.341590	+	0.219526i
$337$	9.08835	−	30.9521i	0.495074	−	1.68607i	−0.210634	−	0.977565i	$-0.567553\pi$
$337$	9.08835	−	30.9521i	0.495074	−	1.68607i	0.705708	−	0.708503i	$-0.250629\pi$
$338$	6.27444	−	0.902128i	0.341284	−	0.0490693i
$339$	−4.73483	−	5.46428i	−0.257161	−	0.296779i
$340$	−1.78626	−	8.33382i	−0.0968734	−	0.451965i
$341$	−7.86076	+	9.07180i	−0.425684	+	0.491266i
$342$	0.244811	+	0.833748i	0.0132378	+	0.0450839i
$343$	−8.96204	+	4.09282i	−0.483904	+	0.220992i
$344$	5.58137			0.300927
$345$	6.31234	−	0.772618i	0.339845	−	0.0415964i
$346$	3.70377			0.199116
$347$	23.0792	−	10.5399i	1.23895	−	0.565812i	0.315284	−	0.948998i	$-0.397900\pi$
$347$	23.0792	−	10.5399i	1.23895	−	0.565812i	0.923671	+	0.383186i	$0.125173\pi$
$348$	−2.01862	−	6.87480i	−0.108210	−	0.368528i
$349$	−9.34118	+	10.7803i	−0.500022	+	0.577056i	−0.948516	−	0.316730i	$-0.897415\pi$
$349$	−9.34118	+	10.7803i	−0.500022	+	0.577056i	0.448494	+	0.893786i	$0.351961\pi$
$350$	1.74735	−	2.68274i	0.0933998	−	0.143398i
$351$	14.8583	+	17.1474i	0.793079	+	0.915262i
$352$	4.99071	−	0.717556i	0.266006	−	0.0382459i
$353$	−2.37791	+	8.09840i	−0.126563	+	0.431035i	−0.998257	−	0.0590163i	$-0.981204\pi$
$353$	−2.37791	+	8.09840i	−0.126563	+	0.431035i	0.871694	+	0.490051i	$0.163022\pi$
$354$	0.899826	−	0.578283i	0.0478252	−	0.0307354i
$355$	−0.0681901	−	0.0916739i	−0.00361915	−	0.00486555i
$356$	3.92385	−	8.59204i	0.207964	−	0.455377i
$357$	3.47961	+	1.58908i	0.184160	+	0.0841032i
$358$	3.11905	+	0.448452i	0.164847	+	0.0237014i
$359$	−17.5251	+	11.2627i	−0.924937	+	0.594421i	−0.914086	−	0.405520i	$-0.867090\pi$
$359$	−17.5251	+	11.2627i	−0.924937	+	0.594421i	−0.0108509	+	0.999941i	$0.503454\pi$
$360$	2.15584	+	3.97698i	0.113623	+	0.209605i
$361$	2.29167	+	15.9389i	0.120614	+	0.838889i
$362$	−1.13455	+	0.983090i	−0.0596304	+	0.0516700i
$363$	1.92552	−	2.99616i	0.101063	−	0.157258i
$364$	28.9222	−	33.3780i	1.51593	−	1.74948i
$365$	12.9149	+	7.10338i	0.675996	+	0.371808i
$366$	−0.505788	−	1.10752i	−0.0264380	−	0.0578910i
$367$		−	8.95879i		−	0.467645i	−0.972279	−	0.233823i	$-0.924877\pi$
$367$		−	8.95879i		−	0.467645i	0.972279	−	0.233823i	$-0.0751235\pi$
$368$	17.6346	+	4.16905i	0.919266	+	0.217327i
$369$	−17.6958			−0.921207
$370$	−1.28758	−	0.484729i	−0.0669381	−	0.0251999i
$371$	−4.64094	+	1.36270i	−0.240945	+	0.0707480i
$372$	4.72514	+	4.09436i	0.244987	+	0.212282i
$373$	−4.99668	+	7.77499i	−0.258718	+	0.402574i	−0.946177	−	0.323650i	$-0.895090\pi$
$373$	−4.99668	+	7.77499i	−0.258718	+	0.402574i	0.687459	+	0.726224i	$0.258726\pi$
$374$	−0.547828	−	0.632227i	−0.0283275	−	0.0326917i
$375$	−5.27109	−	4.02181i	−0.272198	−	0.207686i
$376$	−7.06306	−	2.07390i	−0.364250	−	0.106953i
$377$	22.5425	+	35.0768i	1.16100	+	1.80655i
$378$	−2.12298	−	0.305238i	−0.109194	−	0.0156998i
$379$	−4.43910	+	9.72027i	−0.228021	+	0.499297i	−0.988714	−	0.149815i	$-0.952132\pi$
$379$	−4.43910	+	9.72027i	−0.228021	+	0.499297i	0.760693	+	0.649112i	$0.224859\pi$
$380$	−2.58933	−	7.00759i	−0.132830	−	0.359482i
$381$	0.328849	−	2.28719i	0.0168474	−	0.117176i
$382$	0.720760	+	1.12152i	0.0368773	+	0.0573822i
$383$	8.12875	−	27.6840i	0.415360	−	1.41458i	−0.440675	−	0.897667i	$-0.645261\pi$
$383$	8.12875	−	27.6840i	0.415360	−	1.41458i	0.856035	−	0.516918i	$-0.172921\pi$
$384$	−0.496687	−	3.45453i	−0.0253464	−	0.176288i
$385$	−1.23476	+	16.5532i	−0.0629292	+	0.843627i
$386$	−0.942108	−	0.605456i	−0.0479520	−	0.0308169i
$387$	−14.6235	−	12.6713i	−0.743353	−	0.644119i
$388$	−1.62041	−	5.51860i	−0.0822637	−	0.280164i
$389$	−5.78463	−	12.6666i	−0.293292	−	0.642221i	0.704423	−	0.709781i	$-0.251206\pi$
$389$	−5.78463	−	12.6666i	−0.293292	−	0.642221i	−0.997715	+	0.0675598i	$0.978479\pi$
$390$	1.22060	+	1.22808i	0.0618074	+	0.0621863i
$391$	−3.09742	−	8.78287i	−0.156643	−	0.444169i
$392$			3.08157i			0.155643i
$393$	−6.68046	+	3.05087i	−0.336985	+	0.153896i
$394$	−1.79087	+	0.525848i	−0.0902229	+	0.0264918i
$395$	−1.87673	−	27.4173i	−0.0944283	−	1.37951i
$396$	−9.77278	−	6.28058i	−0.491101	−	0.315611i
$397$	−23.4830	+	20.3481i	−1.17858	+	1.02124i	−0.179280	+	0.983798i	$0.557377\pi$
$397$	−23.4830	+	20.3481i	−1.17858	+	1.02124i	−0.999299	+	0.0374461i	$0.988078\pi$
$398$	−3.08007	+	0.442848i	−0.154390	+	0.0221979i
$399$	3.21712	+	0.944633i	0.161058	+	0.0472908i
$400$	−10.1165	−	15.9552i	−0.505827	−	0.797760i
$401$	−3.07410	+	21.3809i	−0.153513	+	1.06771i	0.756757	+	0.653696i	$0.226782\pi$
$401$	−3.07410	+	21.3809i	−0.153513	+	1.06771i	−0.910271	+	0.414013i	$0.864127\pi$
$402$	−0.507925	−	0.231962i	−0.0253330	−	0.0115692i
$403$	−33.0961	−	15.1145i	−1.64864	−	0.752907i
$404$	−1.29280	+	8.99164i	−0.0643193	+	0.447351i
$405$	2.87196	−	13.0106i	0.142709	−	0.646503i
$406$	−3.78183	−	1.11045i	−0.187689	−	0.0551106i
$407$	7.06040	−	1.01513i	0.349971	−	0.0503182i
$408$	−0.664837	+	0.576085i	−0.0329144	+	0.0285205i
$409$	13.2182	+	8.49479i	0.653596	+	0.420040i	0.824979	−	0.565164i	$-0.191187\pi$
$409$	13.2182	+	8.49479i	0.653596	+	0.420040i	−0.171383	+	0.985205i	$0.554824\pi$
$410$	−2.87344	+	0.196688i	−0.141909	+	0.00971374i
$411$	−7.79778	+	2.28964i	−0.384636	+	0.112939i
$412$	0.940159	−	0.429356i	0.0463183	−	0.0211529i
$413$			31.0810i			1.52939i
$414$	1.43180	+	1.98600i	0.0703693	+	0.0976066i
$415$	11.5146	+	11.5852i	0.565228	+	0.568693i
$416$	6.34869	+	13.9017i	0.311270	+	0.681586i
$417$	0.218295	+	0.743444i	0.0106899	+	0.0364066i
$418$	−0.554159	−	0.480182i	−0.0271048	−	0.0234865i
$419$	−29.6705	−	19.0681i	−1.44950	−	0.931537i	−0.999253	−	0.0386328i	$-0.987700\pi$
$419$	−29.6705	−	19.0681i	−1.44950	−	0.931537i	−0.450247	−	0.892904i	$-0.648664\pi$
$420$	8.62188	+	0.643138i	0.420705	+	0.0313819i
$421$	−3.71916	−	25.8673i	−0.181261	−	1.26070i	−0.853787	−	0.520622i	$-0.825700\pi$
$421$	−3.71916	−	25.8673i	−0.181261	−	1.26070i	0.672526	−	0.740073i	$-0.265209\pi$
$422$	0.731190	−	2.49020i	0.0355938	−	0.121221i
$423$	13.7972	+	21.4689i	0.670845	+	1.04386i
$424$	0.158302	−	1.10102i	0.00768784	−	0.0534701i
$425$	−4.08739	+	8.80727i	−0.198267	+	0.427215i
$426$	−0.00242645	+	0.00531319i	−0.000117562	+	0.000257425i
$427$	35.0192	+	5.03500i	1.69470	+	0.243661i
$428$	−16.1009	−	25.0534i	−0.778265	−	1.21100i
$429$	−8.61347	−	2.52914i	−0.415862	−	0.122108i
$430$	−2.51539	−	1.89502i	−0.121303	−	0.0913861i
$431$	−0.618262	−	0.713512i	−0.0297806	−	0.0343687i	0.740664	−	0.671876i	$-0.234511\pi$
$431$	−0.618262	−	0.713512i	−0.0297806	−	0.0343687i	−0.770444	+	0.637507i	$0.779966\pi$
$432$	−6.84243	+	10.6470i	−0.329206	+	0.512255i
$433$	28.3777	+	24.5894i	1.36374	+	1.18169i	0.964262	+	0.264951i	$0.0853557\pi$
$433$	28.3777	+	24.5894i	1.36374	+	1.18169i	0.399483	+	0.916741i	$0.369190\pi$
$434$	3.30005	−	0.968983i	0.158408	−	0.0465127i
$435$	−2.87582	+	7.63901i	−0.137885	+	0.366262i
$436$	28.1318			1.34727
$437$	−3.78290	−	7.23362i	−0.180961	−	0.346031i
$438$		−	0.753530i		−	0.0360050i
$439$	−13.0134	−	28.4954i	−0.621097	−	1.36001i	−0.914719	−	0.404091i	$-0.867588\pi$
$439$	−13.0134	−	28.4954i	−0.621097	−	1.36001i	0.293622	−	0.955922i	$-0.405139\pi$
$440$	−3.34478	−	1.83968i	−0.159456	−	0.0877032i
$441$	6.99606	−	8.07388i	0.333146	−	0.384470i
$442$	1.37088	−	2.13313i	0.0652062	−	0.101463i
$443$	−11.4266	+	9.90118i	−0.542893	+	0.470419i	−0.882608	−	0.470109i	$-0.844215\pi$
$443$	−11.4266	+	9.90118i	−0.542893	+	0.470419i	0.339716	+	0.940528i	$0.389669\pi$
$444$	−0.528741	−	3.67748i	−0.0250930	−	0.174525i
$445$	−9.45994	+	5.12805i	−0.448444	+	0.243093i
$446$	−1.93753	+	1.24517i	−0.0917446	+	0.0589607i
$447$	0.127167	+	0.0182838i	0.00601479	+	0.000864796i
$448$	21.5194	+	9.82758i	1.01670	+	0.464309i
$449$	−12.1138	+	26.5254i	−0.571684	+	1.25181i	0.374212	+	0.927343i	$0.377913\pi$
$449$	−12.1138	+	26.5254i	−0.571684	+	1.25181i	−0.945896	+	0.324470i	$0.894814\pi$
$450$	0.378701	−	2.52430i	0.0178521	−	0.118997i
$451$	12.5621	−	8.07315i	0.591524	−	0.380150i
$452$	−6.74228	+	22.9621i	−0.317130	+	1.08005i
$453$	3.45999	−	0.497471i	0.162564	−	0.0233732i
$454$	1.13197	+	1.30636i	0.0531258	+	0.0613104i
$455$	−49.1958	+	10.5445i	−2.30634	+	0.494336i
$456$	−0.504950	+	0.582743i	−0.0236464	+	0.0272894i
$457$	−0.882742	−	3.00634i	−0.0412929	−	0.140631i	0.936267	−	0.351290i	$-0.114257\pi$
$457$	−0.882742	−	3.00634i	−0.0412929	−	0.140631i	−0.977559	+	0.210660i	$0.932439\pi$
$458$	−0.535010	+	0.244331i	−0.0249994	+	0.0114168i
$459$	6.50456			0.303607
$460$	−13.4470	−	16.1939i	−0.626972	−	0.755045i
$461$	−35.6709			−1.66136			−0.830679	−	0.556751i	$-0.812048\pi$
$461$	−35.6709			−1.66136			−0.830679	+	0.556751i	$0.812048\pi$
$462$	0.771915	−	0.352522i	0.0359128	−	0.0164008i
$463$	−8.14417	−	27.7365i	−0.378491	−	1.28902i	−0.900042	−	0.435803i	$-0.856464\pi$
$463$	−8.14417	−	27.7365i	−0.378491	−	1.28902i	0.521550	−	0.853220i	$-0.325354\pi$
$464$	−15.2308	+	17.5773i	−0.707071	+	0.816004i
$465$	−1.49273	−	6.96439i	−0.0692239	−	0.322966i
$466$	1.76184	+	2.03327i	0.0816155	+	0.0941893i
$467$	−39.4110	+	5.66644i	−1.82372	+	0.262212i	−0.967221	−	0.253934i	$-0.918275\pi$
$467$	−39.4110	+	5.66644i	−1.82372	+	0.262212i	−0.856501	+	0.516146i	$0.827366\pi$
$468$	9.92029	−	33.7854i	0.458566	−	1.56173i
$469$	13.6497	−	8.77214i	0.630286	−	0.405060i
$470$	2.47902	+	3.33276i	0.114348	+	0.153729i
$471$	−1.07206	+	2.34748i	−0.0493979	+	0.108166i
$472$	−6.50180	−	2.96927i	−0.299270	−	0.136672i
$473$	16.1619	+	2.32373i	0.743126	+	0.106845i
$474$	−1.18191	+	0.759567i	−0.0542869	+	0.0348881i
$475$	−2.44757	+	8.15104i	−0.112302	+	0.373995i
$476$	−1.80189	−	12.5324i	−0.0825896	−	0.574423i
$477$	−2.91439	+	2.52533i	−0.133441	+	0.115627i
$478$	0.0933550	−	0.145263i	0.00426996	−	0.00664418i
$479$	21.5479	−	24.8676i	0.984547	−	1.13623i	−0.00612775	−	0.999981i	$-0.501951\pi$
$479$	21.5479	−	24.8676i	0.984547	−	1.13623i	0.990675	−	0.136247i	$-0.0435040\pi$
$480$	−1.44181	+	2.62141i	−0.0658095	+	0.119650i
$481$	8.98153	+	19.6668i	0.409523	+	0.896730i
$482$		−	0.125677i		−	0.00572443i
$483$	9.43365	−	0.504694i	0.429246	−	0.0229644i
$484$	−11.7883			−0.535834
$485$	−2.30851	+	6.13205i	−0.104824	+	0.278442i
$486$	−2.51217	+	0.737638i	−0.113954	+	0.0334600i
$487$	13.3388	+	11.5581i	0.604437	+	0.523748i	0.902439	−	0.430818i	$-0.141775\pi$
$487$	13.3388	+	11.5581i	0.604437	+	0.523748i	−0.298002	+	0.954565i	$0.596320\pi$
$488$	−4.39877	+	6.84462i	−0.199123	+	0.309841i
$489$	−5.07097	−	5.85221i	−0.229317	−	0.264646i
$490$	1.04628	−	1.38879i	0.0472659	−	0.0627393i
$491$	−18.5782	−	5.45504i	−0.838421	−	0.246183i	−0.165791	−	0.986161i	$-0.553018\pi$
$491$	−18.5782	−	5.45504i	−0.838421	−	0.246183i	−0.672631	+	0.739978i	$0.734836\pi$
$492$	−4.20498	−	6.54308i	−0.189575	−	0.294985i
$493$	11.8317	+	1.70114i	0.532873	+	0.0766155i
$494$	0.923283	−	2.02171i	0.0415405	−	0.0909609i
$495$	4.58689	+	12.4137i	0.206166	+	0.557953i
$496$	2.88830	−	20.0886i	0.129688	−	0.902003i
$497$	−0.0917617	−	0.142784i	−0.00411608	−	0.00640474i
$498$	0.235261	−	0.801224i	0.0105423	−	0.0359037i
$499$	4.09970	+	28.5140i	0.183528	+	1.27646i	0.848340	+	0.529452i	$0.177602\pi$
$499$	4.09970	+	28.5140i	0.183528	+	1.27646i	−0.664812	+	0.747011i	$0.731488\pi$
$500$	−1.76616	+	21.8740i	−0.0789853	+	0.978237i
$501$	0.772593	+	0.496515i	0.0345169	+	0.0221827i
$502$	0.971605	+	0.841901i	0.0433649	+	0.0375759i
$503$	−2.81375	−	9.58275i	−0.125459	−	0.427274i	0.872677	−	0.488297i	$-0.162382\pi$
$503$	−2.81375	−	9.58275i	−0.125459	−	0.427274i	−0.998136	+	0.0610233i	$0.980564\pi$
$504$	2.79164	+	6.11283i	0.124349	+	0.272287i
$505$	7.33990	−	7.29517i	0.326621	−	0.324631i
$506$	−1.92247	−	0.756626i	−0.0854642	−	0.0336361i
$507$		−	19.5010i		−	0.866068i
$508$	−6.95707	+	3.17719i	−0.308670	+	0.140965i
$509$	30.6279	−	8.99315i	1.35756	−	0.398615i	0.479656	−	0.877457i	$-0.340762\pi$
$509$	30.6279	−	8.99315i	1.35756	−	0.398615i	0.877901	+	0.478842i	$0.158943\pi$
$510$	0.495223	−	0.0338983i	0.0219288	−	0.00150104i
$511$	18.4200	+	11.8378i	0.814854	+	0.523675i
$512$	−10.8053	+	9.36285i	−0.477532	+	0.413783i
$513$	5.64334	−	0.811390i	0.249160	−	0.0358238i
$514$	0.779770	+	0.228961i	0.0343942	+	0.0100990i
$515$	−1.14975	−	0.253796i	−0.0506642	−	0.0111836i
$516$	1.21034	−	8.41810i	0.0532823	−	0.370586i
$517$	−19.5890	−	8.94601i	−0.861524	−	0.393445i
$518$	−1.85910	−	0.849020i	−0.0816840	−	0.0373038i
$519$	1.62156	−	11.2782i	0.0711784	−	0.495057i
$520$	2.49404	−	11.2986i	0.109371	−	0.495476i
$521$	−28.5753	−	8.39048i	−1.25191	−	0.367594i	−0.412432	−	0.910989i	$-0.635320\pi$
$521$	−28.5753	−	8.39048i	−1.25191	−	0.367594i	−0.839477	+	0.543395i	$0.817139\pi$
$522$	−3.11045	+	0.447215i	−0.136141	+	0.0195741i
$523$	16.4176	−	14.2259i	0.717890	−	0.622055i	−0.217340	−	0.976096i	$-0.569738\pi$
$523$	16.4176	−	14.2259i	0.717890	−	0.622055i	0.935230	+	0.354041i	$0.115193\pi$
$524$	20.4495	+	13.1421i	0.893339	+	0.574114i
$525$	−7.40407	−	6.49531i	−0.323140	−	0.283479i
$526$	−3.98945	+	1.17141i	−0.173948	+	0.0510758i
$527$	−9.48799	+	4.33302i	−0.413303	+	0.188749i
$528$		−	5.00745i		−	0.217921i
$529$	−16.8304	−	15.6760i	−0.731756	−	0.681567i
$530$	−0.445168	+	0.442455i	−0.0193368	+	0.0192190i
$531$	10.2940	+	22.5406i	0.446719	+	0.978179i
$532$	−3.12664	−	10.6483i	−0.135557	−	0.461664i
$533$	34.2065	+	29.6401i	1.48165	+	1.28385i
$534$	0.462781	+	0.297411i	0.0200265	+	0.0128702i
$535$	−2.52370	+	33.8326i	−0.109109	+	1.46271i
$536$	0.531032	+	3.69341i	0.0229371	+	0.159531i
$537$	2.73112	−	9.30134i	0.117857	−	0.401382i
$538$	0.725259	+	1.12852i	0.0312681	+	0.0486541i
$539$	−1.28297	+	8.92328i	−0.0552616	+	0.384353i
$540$	13.7902	−	5.09552i	0.593434	−	0.219276i
$541$	−2.16838	+	4.74808i	−0.0932257	+	0.204136i	−0.950500	−	0.310724i	$-0.899429\pi$
$541$	−2.16838	+	4.74808i	−0.0932257	+	0.204136i	0.857275	+	0.514860i	$0.172156\pi$
$542$	−0.829252	−	0.119228i	−0.0356194	−	0.00512130i
$543$	2.49684	+	3.88516i	0.107150	+	0.166728i
$544$	4.20378	+	1.23434i	0.180236	+	0.0529220i
$545$	−25.5967	−	19.2838i	−1.09644	−	0.826027i
$546$	1.68441	+	1.94392i	0.0720863	+	0.0831920i
$547$	−5.49555	+	8.55124i	−0.234973	+	0.365625i	−0.938636	−	0.344909i	$-0.887910\pi$
$547$	−5.49555	+	8.55124i	−0.234973	+	0.365625i	0.703663	+	0.710533i	$0.251546\pi$
$548$	20.3293	+	17.6154i	0.868423	+	0.752493i
$549$	27.0643	−	7.94678i	1.15507	−	0.339160i
$550$	0.882795	+	1.96474i	0.0376425	+	0.0837769i
$551$	10.4774			0.446350
$552$	−0.795653	+	2.02163i	−0.0338652	+	0.0860464i
$553$		−	40.8244i		−	1.73603i
$554$	−1.53661	−	3.36471i	−0.0652843	−	0.142953i
$555$	−2.03975	+	3.70853i	−0.0865824	+	0.157418i
$556$	1.67946	−	1.93820i	0.0712250	−	0.0821981i
$557$	19.0010	−	29.5661i	0.805096	−	1.25275i	−0.159020	−	0.987275i	$-0.550833\pi$
$557$	19.0010	−	29.5661i	0.805096	−	1.25275i	0.964117	−	0.265479i	$-0.0855302\pi$
$558$	2.07235	−	1.79570i	0.0877295	−	0.0760180i
$559$	7.04340	+	48.9879i	0.297904	+	2.07197i
$560$	−13.3747	−	24.6729i	−0.565184	−	1.04262i
$561$	−2.16501	+	1.39137i	−0.0914068	+	0.0587436i
$562$	1.27146	+	0.182808i	0.0536332	+	0.00771129i
$563$	28.3121	+	12.9297i	1.19321	+	0.544921i	0.910189	−	0.414192i	$-0.135936\pi$
$563$	28.3121	+	12.9297i	1.19321	+	0.544921i	0.283022	+	0.959113i	$0.408663\pi$
$564$	−4.65962	+	10.2031i	−0.196205	+	0.429630i
$565$	21.8748	−	16.2712i	0.920279	−	0.684534i
$566$	0.973801	−	0.625824i	0.0409319	−	0.0263053i
$567$	5.57632	−	18.9912i	0.234183	−	0.797555i
$568$	0.0386352	−	0.00555490i	0.00162110	−	0.000233078i
$569$	−29.1395	−	33.6288i	−1.22159	−	1.40979i	−0.883337	−	0.468739i	$-0.844708\pi$
$569$	−29.1395	−	33.6288i	−1.22159	−	1.40979i	−0.338256	−	0.941054i	$-0.609837\pi$
$570$	0.425426	−	0.0911850i	0.0178191	−	0.00381932i
$571$	−10.7055	+	12.3548i	−0.448013	+	0.517034i	−0.934166	−	0.356840i	$-0.883854\pi$
$571$	−10.7055	+	12.3548i	−0.448013	+	0.517034i	0.486153	+	0.873874i	$0.338400\pi$
$572$	8.37120	+	28.5097i	0.350018	+	1.19205i
$573$	3.73066	−	1.70373i	0.155850	−	0.0711745i
$574$	−4.27856			−0.178584
$575$	1.13466	+	23.9523i	0.0473188	+	0.998880i
$576$	18.8612			0.785884
$577$	18.4367	−	8.41977i	0.767531	−	0.350520i	0.00713075	−	0.999975i	$-0.497730\pi$
$577$	18.4367	−	8.41977i	0.767531	−	0.350520i	0.760400	+	0.649455i	$0.225003\pi$
$578$	0.718451	+	2.44682i	0.0298836	+	0.101774i
$579$	−2.25611	+	2.60369i	−0.0937608	+	0.108206i
$580$	26.4167	−	5.66211i	1.09689	−	0.235106i
$581$	15.8900	+	18.3380i	0.659229	+	0.760790i
$582$	0.331560	−	0.0476711i	0.0137436	−	0.00197603i
$583$	0.916790	−	3.12230i	0.0379696	−	0.129312i
$584$	−4.23607	+	2.72236i	−0.175290	+	0.112652i
$585$	−32.1856	+	23.9407i	−1.33071	+	0.989826i
$586$	−1.28133	+	2.80572i	−0.0529312	+	0.115903i
$587$	−22.3982	−	10.2289i	−0.924474	−	0.422193i	−0.104455	−	0.994530i	$-0.533310\pi$
$587$	−22.3982	−	10.2289i	−0.924474	−	0.422193i	−0.820019	+	0.572337i	$0.806037\pi$
$588$	4.64778	+	0.668250i	0.191671	+	0.0275582i
$589$	−7.69125	+	4.94287i	−0.316912	+	0.203667i
$590$	1.92206	+	3.54572i	0.0791301	+	0.145975i
$591$	0.817168	+	5.68353i	0.0336138	+	0.233789i
$592$	−9.11436	+	7.89764i	−0.374598	+	0.324591i
$593$	14.1304	−	21.9873i	0.580266	−	0.902912i	−0.419723	−	0.907652i	$-0.637873\pi$
$593$	14.1304	−	21.9873i	0.580266	−	0.902912i	0.999989	+	0.00474074i	$0.00150903\pi$
$594$	0.944945	−	1.09052i	0.0387716	−	0.0447448i
$595$	−6.95123	+	12.6383i	−0.284973	+	0.518118i
$596$	−0.176650	−	0.386810i	−0.00723587	−	0.0158443i
$597$			9.57287i			0.391792i
$598$	0.558792	−	6.23722i	0.0228507	−	0.255059i
$599$	7.94091			0.324457			0.162228	−	0.986753i	$-0.448132\pi$
$599$	7.94091			0.324457			0.162228	+	0.986753i	$0.448132\pi$
$600$	2.06608	−	0.928330i	0.0843475	−	0.0378989i
$601$	−5.24492	+	1.54005i	−0.213945	+	0.0628198i	−0.386948	−	0.922101i	$-0.626471\pi$
$601$	−5.24492	+	1.54005i	−0.213945	+	0.0628198i	0.173004	+	0.984921i	$0.444653\pi$
$602$	−3.53572	−	3.06372i	−0.144105	−	0.124868i
$603$	6.99377	−	10.8825i	0.284808	−	0.443170i
$604$	−7.57671	−	8.74399i	−0.308292	−	0.355788i
$605$	10.7261	+	8.08069i	0.436076	+	0.328527i
$606$	−0.507624	−	0.149052i	−0.0206208	−	0.00605481i
$607$	−10.7420	−	16.7149i	−0.436005	−	0.678437i	0.551827	−	0.833958i	$-0.313931\pi$
$607$	−10.7420	−	16.7149i	−0.436005	−	0.678437i	−0.987833	+	0.155521i	$0.950294\pi$
$608$	3.80117	+	0.546525i	0.154158	+	0.0221645i
$609$	−5.03711	+	11.0297i	−0.204114	+	0.446947i
$610$	4.30635	−	1.59121i	0.174359	−	0.0644263i
$611$	9.28952	−	64.6100i	0.375814	−	2.61384i
$612$	−5.45749	−	8.49202i	−0.220606	−	0.343270i
$613$	−5.11722	+	17.4277i	−0.206683	+	0.703897i	0.789272	+	0.614043i	$0.210458\pi$
$613$	−5.11722	+	17.4277i	−0.206683	+	0.703897i	−0.995955	+	0.0898532i	$0.971360\pi$
$614$	0.103012	+	0.716462i	0.00415721	+	0.0289141i
$615$	−0.659101	+	8.83589i	−0.0265775	+	0.356297i
$616$	−4.77053	−	3.06584i	−0.192210	−	0.123526i
$617$	9.83715	+	8.52394i	0.396029	+	0.343161i	0.829998	−	0.557767i	$-0.188342\pi$
$617$	9.83715	+	8.52394i	0.396029	+	0.343161i	−0.433969	+	0.900928i	$0.642887\pi$
$618$	0.0169586	+	0.0577558i	0.000682176	+	0.00232328i
$619$	15.6451	+	34.2580i	0.628830	+	1.37695i	0.908919	+	0.416972i	$0.136909\pi$
$619$	15.6451	+	34.2580i	0.628830	+	1.37695i	−0.280089	+	0.959974i	$0.590364\pi$
$620$	−16.7209	+	16.6190i	−0.671527	+	0.667435i
$621$	14.2350	−	7.44434i	0.571230	−	0.298731i
$622$		−	2.00189i		−	0.0802683i
$623$	−14.5404	+	6.64039i	−0.582550	+	0.266042i
$624$	14.5631	−	4.27612i	0.582991	−	0.171182i
$625$	16.6012	−	18.6922i	0.664050	−	0.747688i
$626$	1.85019	+	1.18905i	0.0739486	+	0.0475239i
$627$	−1.70480	+	1.47721i	−0.0680830	+	0.0589943i
$628$	8.45489	−	1.21563i	0.337387	−	0.0485089i
$629$	5.94712	+	1.74623i	0.237127	+	0.0696269i
$630$	0.817342	−	3.70275i	0.0325637	−	0.147521i
$631$	3.45896	−	24.0576i	0.137699	−	0.957717i	−0.797431	−	0.603411i	$-0.793808\pi$
$631$	3.45896	−	24.0576i	0.137699	−	0.957717i	0.935130	−	0.354306i	$-0.115283\pi$
$632$	8.54002	+	3.90010i	0.339704	+	0.155138i
$633$	−7.26268	−	3.31676i	−0.288666	−	0.131829i
$634$	0.440647	−	3.06477i	0.0175003	−	0.121718i
$635$	8.50804	+	1.87806i	0.337631	+	0.0745285i
$636$	−1.62628	−	0.477519i	−0.0644862	−	0.0189349i
$637$	−27.0471	+	3.88879i	−1.07165	+	0.154079i
$638$	2.00405	−	1.73651i	0.0793409	−	0.0687493i
$639$	−0.113837	−	0.0731589i	−0.00450334	−	0.00289412i
$640$	13.1290	−	0.898686i	0.518969	−	0.0355237i
$641$	31.3889	−	9.21661i	1.23979	−	0.364034i	0.404852	−	0.914382i	$-0.367323\pi$
$641$	31.3889	−	9.21661i	1.23979	−	0.364034i	0.834935	+	0.550348i	$0.185505\pi$
$642$	1.57770	−	0.720511i	0.0622668	−	0.0284363i
$643$		−	8.09996i		−	0.319431i	−0.987163	−	0.159716i	$-0.948942\pi$
$643$		−	8.09996i		−	0.319431i	0.987163	−	0.159716i	$-0.0510577\pi$
$644$	−18.2865	−	25.3645i	−0.720589	−	0.999502i
$645$	−6.87172	+	6.82985i	−0.270574	+	0.268925i
$646$	−0.264686	−	0.579582i	−0.0104139	−	0.0228034i
$647$	3.82802	+	13.0370i	0.150495	+	0.512539i	0.999884	−	0.0152284i	$-0.00484753\pi$
$647$	3.82802	+	13.0370i	0.150495	+	0.512539i	−0.849389	+	0.527767i	$0.823029\pi$
$648$	3.44002	+	2.98080i	0.135137	+	0.117097i
$649$	−17.5910	−	11.3050i	−0.690507	−	0.443762i
$650$	−4.96018	+	4.24522i	−0.194554	+	0.166511i
$651$	−1.50580	−	10.4731i	−0.0590170	−	0.410472i
$652$	−7.22094	+	24.5923i	−0.282794	+	0.963107i
$653$	−14.8207	−	23.0614i	−0.579978	−	0.902463i	0.420010	−	0.907520i	$-0.362027\pi$
$653$	−14.8207	−	23.0614i	−0.579978	−	0.902463i	−0.999987	+	0.00505700i	$0.998390\pi$
$654$	−0.233166	+	1.62171i	−0.00911752	+	0.0634137i
$655$	−9.59805	−	25.9755i	−0.375027	−	1.01495i
$656$	−10.4880	+	22.9655i	−0.409487	+	0.896652i
$657$	17.2793	+	2.48438i	0.674128	+	0.0969250i
$658$	3.33595	+	5.19084i	0.130049	+	0.202360i
$659$	−18.9335	−	5.55939i	−0.737546	−	0.216563i	−0.108680	−	0.994077i	$-0.534662\pi$
$659$	−18.9335	−	5.55939i	−0.737546	−	0.216563i	−0.628866	+	0.777514i	$0.716481\pi$
$660$	−3.50002	+	4.64582i	−0.136238	+	0.180838i
$661$	13.2575	+	15.3000i	0.515658	+	0.595101i	0.952538	−	0.304419i	$-0.0984622\pi$
$661$	13.2575	+	15.3000i	0.515658	+	0.595101i	−0.436880	+	0.899520i	$0.643917\pi$
$662$	0.600821	−	0.934895i	0.0233516	−	0.0363357i
$663$	−5.89532	−	5.10832i	−0.228955	−	0.198391i
$664$	−5.35415	+	1.57212i	−0.207781	+	0.0610100i
$665$	−4.45435	+	11.8320i	−0.172732	+	0.458826i
$666$	−1.62945			−0.0631399
$667$	27.8401	−	9.81825i	1.07797	−	0.380164i
$668$		−	3.03975i		−	0.117612i
$669$	2.94335	+	6.44503i	0.113796	+	0.249179i
$670$	1.01469	−	1.84483i	0.0392007	−	0.0712721i
$671$	−15.5872	+	17.9885i	−0.601735	+	0.694440i
$672$	−2.40279	+	3.73882i	−0.0926897	+	0.144228i
$673$	−12.4252	+	10.7665i	−0.478957	+	0.415019i	−0.860592	−	0.509294i	$-0.829906\pi$
$673$	−12.4252	+	10.7665i	−0.478957	+	0.415019i	0.381635	+	0.924313i	$0.375361\pi$
$674$	−0.884975	−	6.15513i	−0.0340880	−	0.237087i
$675$	−16.0404	−	4.81656i	−0.617393	−	0.185389i
$676$	−54.2997	+	34.8963i	−2.08845	+	1.34216i
$677$	−25.0565	−	3.60259i	−0.963001	−	0.138459i	−0.357159	−	0.934044i	$-0.616255\pi$
$677$	−25.0565	−	3.60259i	−0.963001	−	0.138459i	−0.605842	+	0.795585i	$0.707164\pi$
$678$	−1.26781	−	0.578989i	−0.0486899	−	0.0222359i
$679$	−4.04343	+	8.85388i	−0.155173	+	0.339781i
$680$	−1.97971	−	2.66150i	−0.0759184	−	0.102064i
$681$	4.47352	−	2.87496i	0.171426	−	0.110169i
$682$	−0.651906	+	2.22019i	−0.0249628	+	0.0850154i
$683$	−3.47427	+	0.499524i	−0.132939	+	0.0191138i	−0.208463	−	0.978030i	$-0.566846\pi$
$683$	−3.47427	+	0.499524i	−0.132939	+	0.0191138i	0.0755240	+	0.997144i	$0.475937\pi$
$684$	−5.79422	−	6.68688i	−0.221547	−	0.255679i
$685$	−6.42229	−	29.9633i	−0.245383	−	1.14484i
$686$	−1.24372	+	1.43533i	−0.0474854	+	0.0548011i
$687$	0.509767	+	1.73611i	0.0194488	+	0.0662366i
$688$	−25.1118	+	11.4682i	−0.957379	+	0.437220i
$689$	9.86345			0.375767
$690$	1.04498	−	0.640958i	0.0397817	−	0.0244008i
$691$	−23.1533			−0.880793			−0.440397	−	0.897803i	$-0.645162\pi$
$691$	−23.1533			−0.880793			−0.440397	+	0.897803i	$0.645162\pi$
$692$	−34.3054	+	15.6667i	−1.30409	+	0.595560i
$693$	5.53872	+	18.8631i	0.210398	+	0.716551i
$694$	3.20285	−	3.69628i	0.121578	−	0.140309i
$695$	−2.85672	+	0.612304i	−0.108361	+	0.0232260i
$696$	−1.82609	−	2.10741i	−0.0692176	−	0.0798813i
$697$	12.8435	−	1.84662i	0.486483	−	0.0699457i
$698$	−0.774680	+	2.63832i	−0.0293221	+	0.0998618i
$699$	6.96276	−	4.47470i	0.263356	−	0.169249i
$700$	−4.83663	+	32.2395i	−0.182808	+	1.21854i
$701$	0.707265	−	1.54869i	0.0267130	−	0.0584934i	−0.895805	−	0.444447i	$-0.853400\pi$
$701$	0.707265	−	1.54869i	0.0267130	−	0.0584934i	0.922518	+	0.385954i	$0.126128\pi$
$702$	3.97850	+	1.81692i	0.150159	+	0.0685752i
$703$	5.37754	+	0.773173i	0.202818	+	0.0291608i
$704$	−13.3894	+	8.60482i	−0.504631	+	0.324306i
$705$	11.2338	−	6.08961i	0.423088	−	0.229348i
$706$	0.231548	+	1.61045i	0.00871441	+	0.0606101i
$707$	11.6182	−	10.0673i	0.436949	−	0.378619i
$708$	−5.88834	+	9.16244i	−0.221298	+	0.344346i
$709$	32.3210	−	37.3005i	1.21384	−	1.40085i	0.323084	−	0.946370i	$-0.395281\pi$
$709$	32.3210	−	37.3005i	1.21384	−	1.40085i	0.890758	−	0.454478i	$-0.150174\pi$
$710$	−0.0192980	−	0.0106142i	−0.000724242	−	0.000398344i
$711$	−13.5210	−	29.6068i	−0.507076	−	1.11034i
$712$		−	3.67608i		−	0.137767i
$713$	−15.8050	+	20.3415i	−0.591903	+	0.761794i
$714$	0.737389			0.0275961
$715$	11.9260	−	31.6789i	0.446007	−	1.18472i
$716$	−30.7865	+	9.03972i	−1.15054	+	0.337830i
$717$	−0.401462	−	0.347869i	−0.0149929	−	0.0129914i
$718$	−2.17107	+	3.37825i	−0.0810236	+	0.126075i
$719$	13.2519	+	15.2935i	0.494211	+	0.570350i	0.946986	−	0.321275i	$-0.104111\pi$
$719$	13.2519	+	15.2935i	0.494211	+	0.570350i	−0.452775	+	0.891625i	$0.649566\pi$
$720$	−17.8712	−	13.4636i	−0.666021	−	0.501760i
$721$	−1.67826	−	0.492780i	−0.0625015	−	0.0183521i
$722$	1.67820	+	2.61132i	0.0624560	+	0.0971834i
$723$	−0.382693	−	0.0550230i	−0.0142325	−	0.00204633i
$724$	6.35008	−	13.9047i	0.235999	−	0.516765i
$725$	−27.9175	−	12.9563i	−1.03683	−	0.481184i
$726$	0.0977060	−	0.679560i	0.00362621	−	0.0252208i
$727$	14.2732	+	22.2096i	0.529364	+	0.823707i	0.998224	−	0.0595657i	$-0.0189716\pi$
$727$	14.2732	+	22.2096i	0.529364	+	0.823707i	−0.468860	+	0.883272i	$0.655335\pi$
$728$	4.84254	−	16.4922i	0.179476	−	0.611241i
$729$	−1.39770	−	9.72123i	−0.0517667	−	0.360045i
$730$	2.83341	+	0.211355i	0.104869	+	0.00782259i
$731$	11.9359	+	7.67075i	0.441466	+	0.283713i
$732$	9.36951	+	8.11872i	0.346307	+	0.300077i
$733$	7.23354	+	24.6352i	0.267177	+	0.909921i	0.978359	+	0.206914i	$0.0663419\pi$
$733$	7.23354	+	24.6352i	0.267177	+	0.909921i	−0.711182	+	0.703008i	$0.751840\pi$
$734$	−0.717405	−	1.57090i	−0.0264799	−	0.0579829i
$735$	−3.77088	−	3.79400i	−0.139091	−	0.139944i
$736$	10.6125	−	2.10984i	0.391182	−	0.0777696i
$737$			10.9161i			0.402098i
$738$	−3.10291	+	1.41705i	−0.114220	+	0.0521624i
$739$	14.2986	−	4.19846i	0.525984	−	0.154443i	−0.00795122	−	0.999968i	$-0.502531\pi$
$739$	14.2986	−	4.19846i	0.525984	−	0.154443i	0.533935	+	0.845526i	$0.320713\pi$
$740$	13.9763	−	0.956685i	0.513779	−	0.0351684i
$741$	−5.75198	−	3.69658i	−0.211304	−	0.135797i
$742$	−0.704651	+	0.610584i	−0.0258686	+	0.0224152i
$743$	−23.0482	+	3.31384i	−0.845558	+	0.121573i	−0.551459	−	0.834202i	$-0.685929\pi$
$743$	−23.0482	+	3.31384i	−0.845558	+	0.121573i	−0.294099	+	0.955775i	$0.595020\pi$
$744$	2.33471	+	0.685532i	0.0855945	+	0.0251328i
$745$	−0.104419	+	0.473043i	−0.00382562	+	0.0173309i
$746$	−0.253545	+	1.76345i	−0.00928295	+	0.0645643i
$747$	17.5973	+	8.03642i	0.643852	+	0.294037i
$748$	7.74842	+	3.53859i	0.283310	+	0.129384i
$749$	−7.17251	+	49.8859i	−0.262078	+	1.82279i
$750$	−1.24633	−	0.283113i	−0.0455095	−	0.0103378i
$751$	−7.02028	−	2.06134i	−0.256173	−	0.0752193i	0.151124	−	0.988515i	$-0.451711\pi$
$751$	−7.02028	−	2.06134i	−0.256173	−	0.0752193i	−0.407298	+	0.913295i	$0.633529\pi$
$752$	36.0396	−	5.18171i	1.31423	−	0.188958i
$753$	2.98901	−	2.59000i	0.108926	−	0.0943847i
$754$	6.76165	+	4.34545i	0.246245	+	0.158252i
$755$	0.900105	+	13.1497i	0.0327582	+	0.478568i
$756$	20.9548	−	6.15288i	0.762118	−	0.223778i
$757$	−27.4138	+	12.5195i	−0.996372	+	0.455028i	−0.845759	−	0.533565i	$-0.820852\pi$
$757$	−27.4138	+	12.5195i	−0.996372	+	0.455028i	−0.150613	+	0.988593i	$0.548125\pi$
$758$			2.05990i			0.0748188i
$759$	−3.14565	+	5.52277i	−0.114180	+	0.200464i
$760$	−2.04959	−	2.06216i	−0.0743465	−	0.0748023i
$761$	9.46300	+	20.7211i	0.343034	+	0.751139i	0.999996	−	0.00278453i	$-0.000886345\pi$
$761$	9.46300	+	20.7211i	0.343034	+	0.751139i	−0.656963	+	0.753923i	$0.728159\pi$
$762$	−0.125492	−	0.427386i	−0.00454609	−	0.0154826i
$763$	−35.9796	−	31.1765i	−1.30255	−	1.12866i
$764$	−11.4199	−	7.33910i	−0.413156	−	0.265519i
$765$	−0.855423	+	11.4678i	−0.0309279	+	0.414618i
$766$	−0.791534	−	5.50524i	−0.0285993	−	0.198912i
$767$	17.8565	−	60.8137i	0.644761	−	2.19585i
$768$	4.20303	+	6.54004i	0.151664	+	0.235993i
$769$	4.58151	−	31.8651i	0.165214	−	1.14909i	−0.723400	−	0.690429i	$-0.757422\pi$
$769$	4.58151	−	31.8651i	0.165214	−	1.14909i	0.888614	−	0.458657i	$-0.151669\pi$
$770$	1.10904	+	3.00142i	0.0399669	+	0.108164i
$771$	1.03859	−	2.27420i	0.0374040	−	0.0819033i
$772$	11.2871	+	1.62284i	0.406232	+	0.0584074i
$773$	−1.79500	−	2.79308i	−0.0645617	−	0.100460i	0.807472	−	0.589906i	$-0.200835\pi$
$773$	−1.79500	−	2.79308i	−0.0645617	−	0.100460i	−0.872033	+	0.489446i	$0.837199\pi$
$774$	−3.57888	−	1.05085i	−0.128640	−	0.0377722i
$775$	26.6061	−	3.65955i	0.955719	−	0.131455i
$776$	−1.46585	−	1.69168i	−0.0526210	−	0.0607279i
$777$	−3.39925	+	5.28933i	−0.121947	+	0.189754i
$778$	−2.02863	−	1.75782i	−0.0727301	−	0.0630210i
$779$	10.9127	−	3.20424i	0.390986	−	0.114804i
$780$	−16.5003	−	6.21178i	−0.590804	−	0.222417i
$781$	0.114188			0.00408598
$782$	−1.24644	−	1.29201i	−0.0445726	−	0.0462023i
$783$			20.6183i			0.736837i
$784$	−6.33179	−	13.8647i	−0.226135	−	0.495167i
$785$	−8.52627	−	4.68958i	−0.304316	−	0.167378i
$786$	−0.927091	+	1.06992i	−0.0330682	+	0.0381628i
$787$	−20.7750	+	32.3266i	−0.740550	+	1.15232i	0.242709	+	0.970099i	$0.421964\pi$
$787$	−20.7750	+	32.3266i	−0.740550	+	1.15232i	−0.983258	+	0.182218i	$0.941672\pi$
$788$	14.3633	−	12.4458i	0.511671	−	0.443365i
$789$	1.82037	+	12.6610i	0.0648069	+	0.450742i
$790$	−2.52461	−	4.65725i	−0.0898214	−	0.165697i
$791$	34.0704	−	21.8957i	1.21141	−	0.778523i
$792$	−4.47509	−	0.643421i	−0.159016	−	0.0228630i
$793$	−65.6266	−	29.9706i	−2.33047	−	1.06429i
$794$	−2.48823	+	5.44847i	−0.0883040	+	0.193359i
$795$	1.15240	+	1.54927i	0.0408714	+	0.0549470i
$796$	26.6553	−	17.1303i	0.944772	−	0.607168i
$797$	7.70924	−	26.2553i	0.273075	−	0.930009i	−0.702746	−	0.711441i	$-0.748043\pi$
$797$	7.70924	−	26.2553i	0.273075	−	0.930009i	0.975822	−	0.218569i	$-0.0701387\pi$
$798$	0.639757	−	0.0919832i	0.0226472	−	0.00325617i
$799$	−12.2543	−	14.1422i	−0.433526	−	0.500316i
$800$	−9.45258	−	6.15676i	−0.334199	−	0.217674i
$801$	−8.34576	+	9.63152i	−0.294883	+	0.340313i
$802$	1.17311	+	3.99524i	0.0414239	+	0.141077i
$803$	−13.3998	+	6.11948i	−0.472868	+	0.215952i
$804$	5.68574			0.200520
$805$	−0.748266	+	35.6139i	−0.0263729	+	1.25522i
$806$	−7.01365			−0.247045
$807$	3.75394	−	1.71437i	0.132145	−	0.0603487i
$808$	0.996031	+	3.39217i	0.0350403	+	0.119336i
$809$	16.9392	−	19.5488i	0.595549	−	0.687300i	−0.375324	−	0.926894i	$-0.622469\pi$
$809$	16.9392	−	19.5488i	0.595549	−	0.687300i	0.970873	+	0.239593i	$0.0770141\pi$
$810$	−0.538280	−	2.51136i	−0.0189132	−	0.0882401i
$811$	18.6222	+	21.4911i	0.653912	+	0.754655i	0.981770	−	0.190072i	$-0.0608722\pi$
$811$	18.6222	+	21.4911i	0.653912	+	0.754655i	−0.327858	+	0.944727i	$0.606327\pi$
$812$	39.7256	−	5.71167i	1.39409	−	0.200440i
$813$	−0.726114	+	2.47292i	−0.0254659	+	0.0867290i
$814$	1.15673	−	0.743385i	0.0405433	−	0.0260556i
$815$	23.4278	−	17.4263i	0.820639	−	0.610418i
$816$	1.80755	−	3.95799i	0.0632771	−	0.138557i
$817$	11.3124	+	5.16622i	0.395772	+	0.180743i
$818$	2.99801	+	0.431049i	0.104823	+	0.0150713i
$819$	−50.1297	+	32.2164i	−1.75167	+	1.12573i
$820$	25.7826	−	13.9763i	0.900368	−	0.488072i
$821$	3.43766	+	23.9095i	0.119975	+	0.834446i	0.957580	+	0.288169i	$0.0930464\pi$
$821$	3.43766	+	23.9095i	0.119975	+	0.834446i	−0.837604	+	0.546277i	$0.816044\pi$
$822$	−1.18397	+	1.02591i	−0.0412956	+	0.0357829i
$823$	−1.90560	+	2.96517i	−0.0664251	+	0.103359i	−0.872877	−	0.487940i	$-0.837748\pi$
$823$	−1.90560	+	2.96517i	−0.0664251	+	0.103359i	0.806452	+	0.591299i	$0.201385\pi$
$824$	0.263414	−	0.303996i	0.00917645	−	0.0105902i
$825$	6.36924	−	1.82797i	0.221749	−	0.0636417i
$826$	2.48891	+	5.44995i	0.0866003	+	0.189628i
$827$			25.0301i			0.870383i	0.900338	+	0.435191i	$0.143319\pi$
$827$			25.0301i			0.870383i	−0.900338	+	0.435191i	$0.856681\pi$
$828$	−21.6624	−	12.3385i	−0.752822	−	0.428791i
$829$	−37.6396			−1.30728			−0.653639	−	0.756807i	$-0.726758\pi$
$829$	−37.6396			−1.30728			−0.653639	+	0.756807i	$0.726758\pi$
$830$	2.94677	+	1.10936i	0.102284	+	0.0385063i
$831$	−10.9185	+	3.20595i	−0.378757	+	0.111213i
$832$	−36.4592	−	31.5921i	−1.26399	−	1.09526i
$833$	−4.23516	+	6.59003i	−0.146740	+	0.228331i
$834$	0.0978111	+	0.112880i	0.00338692	+	0.00390872i
$835$	−2.08369	+	2.76583i	−0.0721091	+	0.0957154i
$836$	7.16392	+	2.10352i	0.247769	+	0.0727517i
$837$	−9.72702	−	15.1355i	−0.336215	−	0.523161i
$838$	−6.72958	−	0.967567i	−0.232469	−	0.0334240i
$839$	−2.73179	+	5.98180i	−0.0943120	+	0.206515i	−0.950908	−	0.309473i	$-0.899847\pi$
$839$	−2.73179	+	5.98180i	−0.0943120	+	0.206515i	0.856596	+	0.515987i	$0.172575\pi$
$840$	3.15624	−	1.16624i	0.108901	−	0.0402392i
$841$	−1.26518	+	8.79950i	−0.0436268	+	0.303431i
$842$	−2.72355	−	4.23793i	−0.0938598	−	0.146049i
$843$	1.11332	−	3.79162i	0.0383448	−	0.130590i
$844$	3.76094	+	26.1579i	0.129457	+	0.900391i
$845$	73.3272	+	5.46975i	2.52253	+	0.188165i
$846$	4.13850	+	2.65965i	0.142285	+	0.0914407i
$847$	15.0769	+	13.0642i	0.518048	+	0.448891i
$848$	1.55005	+	5.27899i	0.0532290	+	0.181281i
$849$	−1.47933	−	3.23927i	−0.0507703	−	0.111171i
$850$	−0.0114394	+	1.87164i	−0.000392369	+	0.0641967i
$851$	15.0136	−	2.98480i	0.514659	−	0.102318i
$852$		−	0.0594761i		−	0.00203762i
$853$	43.8532	−	20.0271i	1.50150	−	0.685714i	0.516191	−	0.856474i	$-0.327350\pi$
$853$	43.8532	−	20.0271i	1.50150	−	0.685714i	0.985313	+	0.170760i	$0.0546223\pi$
$854$	6.54370	−	1.92140i	0.223921	−	0.0657491i
$855$	0.688346	+	10.0561i	0.0235410	+	0.343912i
$856$	−9.75037	−	6.26619i	−0.333261	−	0.214174i
$857$	21.8606	−	18.9423i	0.746745	−	0.647058i	−0.195988	−	0.980606i	$-0.562791\pi$
$857$	21.8606	−	18.9423i	0.746745	−	0.647058i	0.942733	+	0.333548i	$0.108246\pi$
$858$	−1.71288	+	0.246274i	−0.0584766	+	0.00840767i
$859$	16.8106	+	4.93604i	0.573571	+	0.168416i	0.555639	−	0.831424i	$-0.312474\pi$
$859$	16.8106	+	4.93604i	0.573571	+	0.168416i	0.0179317	+	0.999839i	$0.494292\pi$
$860$	31.3142	+	6.91227i	1.06780	+	0.235706i
$861$	−1.87321	+	13.0285i	−0.0638388	+	0.444008i
$862$	−0.165547	−	0.0756029i	−0.00563856	−	0.00257504i
$863$	28.6828	+	13.0990i	0.976373	+	0.445894i	0.838706	−	0.544584i	$-0.183313\pi$
$863$	28.6828	+	13.0990i	0.976373	+	0.445894i	0.137667	+	0.990479i	$0.456040\pi$
$864$	−1.07550	+	7.48028i	−0.0365893	+	0.254484i
$865$	41.9532	+	9.26072i	1.42645	+	0.314874i
$866$	6.94502	+	2.03924i	0.236001	+	0.0692962i
$867$	7.76524	−	1.11647i	0.263721	−	0.0379174i
$868$	−26.4673	+	22.9341i	−0.898359	+	0.778433i
$869$	23.1055	+	14.8490i	0.783801	+	0.503719i
$870$	0.107451	+	1.56977i	0.00364294	+	0.0532201i
$871$	−31.7471	+	9.32178i	−1.07571	+	0.315856i
$872$	9.95903	−	4.54814i	0.337255	−	0.154019i
$873$			7.76020i			0.262643i
$874$	−1.24258	−	0.965465i	−0.0420308	−	0.0326573i
$875$	26.5003	−	26.0188i	0.895875	−	0.879597i
$876$	3.18739	+	6.97941i	0.107692	+	0.235812i
$877$	−4.76295	−	16.2211i	−0.160833	−	0.547748i	−0.999993	−	0.00386222i	$-0.998771\pi$
$877$	−4.76295	−	16.2211i	−0.160833	−	0.547748i	0.839159	−	0.543886i	$-0.183048\pi$
$878$	−4.56373	−	3.95449i	−0.154018	−	0.133458i
$879$	7.98259	+	5.13010i	0.269246	+	0.173034i
$880$	18.8289	+	1.40452i	0.634723	+	0.0473464i
$881$	−8.33373	−	57.9624i	−0.280771	−	1.95280i	−0.302827	−	0.953046i	$-0.597930\pi$
$881$	−8.33373	−	57.9624i	−0.280771	−	1.95280i	0.0220564	−	0.999757i	$-0.492979\pi$
$882$	0.580195	−	1.97596i	0.0195362	−	0.0665341i
$883$	12.2453	+	19.0541i	0.412088	+	0.641221i	0.983808	−	0.179228i	$-0.0573599\pi$
$883$	12.2453	+	19.0541i	0.412088	+	0.641221i	−0.571720	+	0.820449i	$0.693724\pi$
$884$	−3.67446	+	25.5565i	−0.123586	+	0.859556i
$885$	11.6384	−	4.30043i	0.391221	−	0.144557i
$886$	−1.21074	+	2.65116i	−0.0406758	+	0.0890675i
$887$	−43.4945	−	6.25357i	−1.46040	−	0.209974i	−0.634122	−	0.773233i	$-0.718638\pi$
$887$	−43.4945	−	6.25357i	−1.46040	−	0.209974i	−0.826281	+	0.563258i	$0.809548\pi$
$888$	−0.781729	−	1.21639i	−0.0262331	−	0.0408195i
$889$	12.4189	+	3.64652i	0.416516	+	0.122300i
$890$	−1.24813	+	1.65672i	−0.0418373	+	0.0555335i
$891$	8.72023	+	10.0637i	0.292139	+	0.337146i
$892$	12.6789	−	19.7288i	0.424522	−	0.660569i
$893$	−12.3959	−	10.7411i	−0.414814	−	0.359439i
$894$	0.0237625	−	0.00697729i	0.000794736	−	0.000233355i
$895$	34.2087	+	12.8784i	1.14347	+	0.430478i
$896$	19.5491			0.653091
$897$	−18.7480	−	4.43229i	−0.625979	−	0.147990i
$898$			5.62121i			0.187582i
$899$	−13.7349	−	30.0752i	−0.458084	−	1.00306i
$900$	7.17001	+	24.9827i	0.239000	+	0.832756i
$901$	1.85172	−	2.13700i	0.0616896	−	0.0711936i
$902$	1.55624	−	2.42155i	0.0518170	−	0.0806288i
$903$	−10.8772	+	9.42513i	−0.361970	+	0.313649i
$904$	1.32548	+	9.21894i	0.0440849	+	0.306617i
$905$	−15.3093	+	8.29886i	−0.508897	+	0.275863i
$906$	0.566861	−	0.364300i	0.0188327	−	0.0121030i
$907$	11.1067	+	1.59690i	0.368792	+	0.0530243i	0.324220	−	0.945982i	$-0.394898\pi$
$907$	11.1067	+	1.59690i	0.368792	+	0.0530243i	0.0445726	+	0.999006i	$0.485807\pi$
$908$	−16.0104	−	7.31171i	−0.531324	−	0.242648i
$909$	5.09155	−	11.1489i	0.168876	−	0.369787i
$910$	−7.78195	+	5.78847i	−0.257969	+	0.191886i
$911$	−33.4328	+	21.4860i	−1.10768	+	0.711862i	−0.960786	−	0.277291i	$-0.910563\pi$
$911$	−33.4328	+	21.4860i	−1.10768	+	0.711862i	−0.146892	+	0.989153i	$0.546927\pi$
$912$	1.07450	−	3.65942i	0.0355804	−	0.121176i
$913$	−16.1585	+	2.32324i	−0.534768	+	0.0768880i
$914$	−0.395529	−	0.456465i	−0.0130829	−	0.0150985i
$915$	−2.95995	−	13.8097i	−0.0978530	−	0.456535i
$916$	3.92191	−	4.52613i	0.129584	−	0.149547i
$917$	−11.5897	−	39.4710i	−0.382726	−	1.30345i
$918$	1.14056	−	0.520874i	0.0376439	−	0.0171914i
$919$	11.3416			0.374126			0.187063	−	0.982348i	$-0.440103\pi$
$919$	11.3416			0.374126			0.187063	+	0.982348i	$0.440103\pi$
$920$	−7.37855	−	3.55884i	−0.243263	−	0.117332i
$921$	2.22677			0.0733744
$922$	−6.25478	+	2.85646i	−0.205990	+	0.0940726i
$923$	0.0975112	+	0.332093i	0.00320962	+	0.0109310i
$924$	−5.65855	+	6.53032i	−0.186153	+	0.214832i
$925$	−13.3726	−	8.71002i	−0.439690	−	0.286384i
$926$	−3.64914	−	4.21134i	−0.119918	−	0.138393i
$927$	−1.38032	+	0.198459i	−0.0453355	+	0.00651826i
$928$	−3.91264	+	13.3252i	−0.128439	+	0.437422i
$929$	−18.1945	+	11.6929i	−0.596943	+	0.383632i	−0.803941	−	0.594709i	$-0.797267\pi$
$929$	−18.1945	+	11.6929i	−0.596943	+	0.383632i	0.206998	+	0.978341i	$0.433631\pi$
$930$	−0.819443	−	1.10165i	−0.0268706	−	0.0361245i
$931$	−2.85236	+	6.24580i	−0.0934824	+	0.204698i
$932$	−24.9193	−	11.3802i	−0.816257	−	0.372772i
$933$	−6.09585	−	0.876451i	−0.199569	−	0.0286937i
$934$	−6.45684	+	4.14956i	−0.211274	+	0.135778i
$935$	−4.62455	−	8.53110i	−0.151239	−	0.278997i
$936$	−1.95026	−	13.5643i	−0.0637461	−	0.443364i
$937$	−33.4645	+	28.9971i	−1.09324	+	0.947294i	−0.998836	−	0.0482400i	$-0.984639\pi$
$937$	−33.4645	+	28.9971i	−1.09324	+	0.947294i	−0.0944002	+	0.995534i	$0.530093\pi$
$938$	1.69098	−	2.63122i	0.0552124	−	0.0859122i
$939$	4.43075	−	5.11336i	0.144592	−	0.166868i
$940$	−37.0587	−	20.3829i	−1.20872	−	0.664816i
$941$	−5.38047	−	11.7816i	−0.175398	−	0.384069i	0.801431	−	0.598087i	$-0.204072\pi$
$941$	−5.38047	−	11.7816i	−0.175398	−	0.384069i	−0.976830	+	0.214018i	$0.931345\pi$
$942$			0.497473i			0.0162085i
$943$	25.9941	−	18.7404i	0.846485	−	0.610271i
$944$	35.3541			1.15068
$945$	−23.2841	−	8.76568i	−0.757433	−	0.285148i
$946$	3.02003	−	0.886760i	0.0981895	−	0.0288310i
$947$	24.2066	+	20.9751i	0.786607	+	0.681599i	0.952498	−	0.304545i	$-0.0985044\pi$
$947$	24.2066	+	20.9751i	0.786607	+	0.681599i	−0.165891	+	0.986144i	$0.553050\pi$
$948$	7.73426	−	12.0347i	0.251197	−	0.390870i
$949$	−29.2400	−	33.7447i	−0.949170	−	1.09540i
$950$	0.223547	+	1.62526i	0.00725281	+	0.0527303i
$951$	−9.13947	−	2.68359i	−0.296368	−	0.0870214i
$952$	−2.66405	−	4.14534i	−0.0863422	−	0.134351i
$953$	−27.7779	−	3.99387i	−0.899816	−	0.129374i	−0.323144	−	0.946350i	$-0.604740\pi$
$953$	−27.7779	−	3.99387i	−0.899816	−	0.129374i	−0.576672	+	0.816976i	$0.695649\pi$
$954$	−0.308805	+	0.676188i	−0.00999792	+	0.0218924i
$955$	5.35996	+	14.5058i	0.173444	+	0.469398i
$956$	−0.250225	+	1.74036i	−0.00809287	+	0.0562871i
$957$	−4.41039	−	6.86269i	−0.142568	−	0.221839i
$958$	1.78700	−	6.08597i	0.0577354	−	0.196629i
$959$	−6.47851	−	45.0590i	−0.209202	−	1.45503i
$960$	0.702508	−	9.41779i	0.0226733	−	0.303958i
$961$	−1.80781	−	1.16181i	−0.0583165	−	0.0374777i
$962$	3.14977	+	2.72929i	0.101553	+	0.0879959i
$963$	11.3204	+	38.5539i	0.364796	+	1.24238i
$964$	0.531607	+	1.16406i	0.0171219	+	0.0374917i
$965$	−9.15756	−	9.21370i	−0.294792	−	0.296600i
$966$	1.61375	−	0.843927i	0.0519215	−	0.0271529i
$967$			43.7547i			1.40706i	0.710667	+	0.703528i	$0.248393\pi$
$967$			43.7547i			1.40706i	−0.710667	+	0.703528i	$0.751607\pi$
$968$	−4.17323	+	1.90585i	−0.134133	+	0.0612564i
$969$	−1.88074	+	0.552236i	−0.0604182	+	0.0177404i
$970$	0.0862543	+	1.26010i	0.00276946	+	0.0404593i
$971$	43.0776	+	27.6843i	1.38243	+	0.888432i	0.999377	−	0.0352951i	$-0.0112371\pi$
$971$	43.0776	+	27.6843i	1.38243	+	0.888432i	0.383051	+	0.923727i	$0.374873\pi$
$972$	20.1482	−	17.4585i	0.646255	−	0.559983i
$973$	−4.29595	+	0.617664i	−0.137722	+	0.0198014i
$974$	3.26446	+	0.958533i	0.104600	+	0.0307134i
$975$	10.7553	+	16.9626i	0.344445	+	0.543239i
$976$	5.72722	−	39.8337i	0.183324	−	1.27505i
$977$	47.8740	+	21.8633i	1.53163	+	0.699470i	0.989989	−	0.141143i	$-0.0450779\pi$
$977$	47.8740	+	21.8633i	1.53163	+	0.699470i	0.541636	+	0.840613i	$0.317805\pi$
$978$	−1.35781	−	0.620093i	−0.0434181	−	0.0198284i
$979$	1.53049	−	10.6448i	0.0489147	−	0.340209i
$980$	−3.81638	+	17.2891i	−0.121910	+	0.552280i
$981$	−36.4188	−	10.6935i	−1.16276	−	0.341418i
$982$	−3.69446	+	0.531183i	−0.117895	+	0.0169507i
$983$	−39.9661	+	34.6308i	−1.27472	+	1.10455i	−0.285459	+	0.958391i	$0.592146\pi$
$983$	−39.9661	+	34.6308i	−1.27472	+	1.10455i	−0.989261	+	0.146160i	$0.953309\pi$
$984$	−2.54646	−	1.63651i	−0.0811780	−	0.0521700i
$985$	−21.6003	+	1.47855i	−0.688244	+	0.0471106i
$986$	2.21088	−	0.649172i	0.0704086	−	0.0206738i
$987$	17.2669	−	7.88553i	0.549612	−	0.250999i
$988$			22.6311i			0.719991i
$989$	34.9003	+	3.12672i	1.10977	+	0.0994238i
$990$	1.79836	+	1.80939i	0.0571557	+	0.0575061i
$991$	−0.597968	−	1.30937i	−0.0189951	−	0.0415934i	0.899897	−	0.436103i	$-0.143642\pi$
$991$	−0.597968	−	1.30937i	−0.0189951	−	0.0415934i	−0.918892	+	0.394510i	$0.870914\pi$
$992$	−3.41420	−	11.6277i	−0.108401	−	0.369180i
$993$	−2.58376	−	2.23884i	−0.0819931	−	0.0710475i
$994$	−0.0275240	−	0.0176886i	−0.000873010	−	0.000561049i
$995$	−35.9958	−	2.68506i	−1.14114	−	0.0851221i
$996$	1.21008	+	8.41631i	0.0383429	+	0.266681i
$997$	−12.5519	+	42.7479i	−0.397523	+	1.35384i	0.481244	+	0.876587i	$0.340185\pi$
$997$	−12.5519	+	42.7479i	−0.397523	+	1.35384i	−0.878767	+	0.477252i	$0.841633\pi$
$998$	3.00222	+	4.67155i	0.0950337	+	0.147875i
$999$	−1.52152	+	10.5824i	−0.0481388	+	0.334813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.4.6	yes	100
5.2	odd	4		575.2.k.g.326.6		100
5.3	odd	4		575.2.k.g.326.5		100
5.4	even	2	inner	115.2.j.a.4.5	✓	100
23.6	even	11	inner	115.2.j.a.29.5	yes	100
115.29	even	22	inner	115.2.j.a.29.6	yes	100
115.52	odd	44		575.2.k.g.351.6		100
115.98	odd	44		575.2.k.g.351.5		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.4.5	✓	100	5.4	even	2	inner
115.2.j.a.4.6	yes	100	1.1	even	1	trivial
115.2.j.a.29.5	yes	100	23.6	even	11	inner
115.2.j.a.29.6	yes	100	115.29	even	22	inner
575.2.k.g.326.5		100	5.3	odd	4
575.2.k.g.326.6		100	5.2	odd	4
575.2.k.g.351.5		100	115.98	odd	44
575.2.k.g.351.6		100	115.52	odd	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.175347 - 0.0800783i) q^{2} +(-0.167074 - 0.569000i) q^{3} +(-1.28539 + 1.48342i) q^{4} +(2.18641 - 0.468631i) q^{5} +(-0.0748604 - 0.0863935i) q^{6} +(3.28793 - 0.472733i) q^{7} +(-0.215217 + 0.732961i) q^{8} +(2.22791 - 1.43179i) q^{9} +O(q^{10})\)	\(q+(0.175347 - 0.0800783i) q^{2} +(-0.167074 - 0.569000i) q^{3} +(-1.28539 + 1.48342i) q^{4} +(2.18641 - 0.468631i) q^{5} +(-0.0748604 - 0.0863935i) q^{6} +(3.28793 - 0.472733i) q^{7} +(-0.215217 + 0.732961i) q^{8} +(2.22791 - 1.43179i) q^{9} +(0.345853 - 0.257257i) q^{10} +(-0.928361 + 2.03283i) q^{11} +(1.05882 + 0.483546i) q^{12} +(-6.70483 - 0.964009i) q^{13} +(0.538673 - 0.346184i) q^{14} +(-0.631942 - 1.16577i) q^{15} +(-0.537726 - 3.73997i) q^{16} +(-1.46759 + 1.27168i) q^{17} +(0.276002 - 0.429468i) q^{18} +(-1.11465 + 1.28637i) q^{19} +(-2.11521 + 3.84573i) q^{20} +(-0.818312 - 1.79185i) q^{21} +0.430792i q^{22} +(-1.75636 + 4.46264i) q^{23} +0.453012 q^{24} +(4.56077 - 2.04924i) q^{25} +(-1.25287 + 0.367875i) q^{26} +(-2.53144 - 2.19351i) q^{27} +(-3.52501 + 5.48502i) q^{28} +(-4.03098 - 4.65200i) q^{29} +(-0.204162 - 0.153810i) q^{30} +(5.15374 + 1.51327i) q^{31} +(-1.21977 - 1.89801i) q^{32} +(1.31178 + 0.188606i) q^{33} +(-0.155504 + 0.340507i) q^{34} +(6.96723 - 2.57442i) q^{35} +(-0.739787 + 5.14533i) q^{36} +(-1.72562 - 2.68512i) q^{37} +(-0.0924398 + 0.314821i) q^{38} +(0.571678 + 3.97611i) q^{39} +(-0.127064 + 1.70341i) q^{40} +(-5.62116 - 3.61250i) q^{41} +(-0.286977 - 0.248667i) q^{42} +(-2.05844 - 7.01041i) q^{43} +(-1.82223 - 3.99012i) q^{44} +(4.20015 - 4.17455i) q^{45} +(0.0493883 + 0.923158i) q^{46} +9.63634i q^{47} +(-2.03820 + 0.930816i) q^{48} +(3.87057 - 1.13650i) q^{49} +(0.635618 - 0.724546i) q^{50} +(0.968780 + 0.622597i) q^{51} +(10.0483 - 8.70693i) q^{52} +(-1.44130 + 0.207228i) q^{53} +(-0.619533 - 0.181911i) q^{54} +(-1.07713 + 4.87965i) q^{55} +(-0.361123 + 2.51167i) q^{56} +(0.918175 + 0.419317i) q^{57} +(-1.07935 - 0.492921i) q^{58} +(-1.33162 + 9.26159i) q^{59} +(2.54162 + 0.561035i) q^{60} +(10.2194 + 3.00068i) q^{61} +(1.02487 - 0.147355i) q^{62} +(6.64837 - 5.76085i) q^{63} +(5.99136 + 3.85041i) q^{64} +(-15.1113 + 1.03437i) q^{65} +(0.245121 - 0.0719739i) q^{66} +(4.44321 - 2.02915i) q^{67} -3.81165i q^{68} +(2.83269 + 0.253780i) q^{69} +(1.01553 - 1.00934i) q^{70} +(-0.0212260 - 0.0464785i) q^{71} +(0.569964 + 1.94112i) q^{72} +(4.98167 + 4.31664i) q^{73} +(-0.517603 - 0.332643i) q^{74} +(-1.92800 - 2.25271i) q^{75} +(-0.475472 - 3.30698i) q^{76} +(-2.09140 + 7.12267i) q^{77} +(0.418642 + 0.651420i) q^{78} +(1.74906 - 12.1650i) q^{79} +(-2.92835 - 7.92510i) q^{80} +(2.47529 - 5.42013i) q^{81} +(-1.27494 - 0.183308i) q^{82} +(3.94928 + 6.14520i) q^{83} +(3.70991 + 1.08933i) q^{84} +(-2.61281 + 3.46816i) q^{85} +(-0.922323 - 1.06442i) q^{86} +(-1.97352 + 3.07086i) q^{87} +(-1.29018 - 1.11795i) q^{88} +(-4.61729 + 1.35576i) q^{89} +(0.402192 - 1.06834i) q^{90} -22.5007 q^{91} +(-4.36235 - 8.34164i) q^{92} -3.18531i q^{93} +(0.771662 + 1.68970i) q^{94} +(-1.83424 + 3.33490i) q^{95} +(-0.876174 + 1.01116i) q^{96} +(-1.58420 + 2.46507i) q^{97} +(0.587684 - 0.509231i) q^{98} +(0.842280 + 5.85818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

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