LMFDB - Embedded newform 115.2.j.a.9.10

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			9.10
Character	$\chi$	$=$	115.9
Dual form			115.2.j.a.64.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.743795 + 2.53313i) q^{2} +(1.34601 - 1.16633i) q^{3} +(-4.18102 + 2.68698i) q^{4} +(2.14584 - 0.628789i) q^{5} +(3.95561 + 2.54212i) q^{6} +(-1.87277 - 0.855264i) q^{7} +(-5.92582 - 5.13475i) q^{8} +(0.0244873 - 0.170313i) q^{9} +O(q^{10})$	\(q+(0.743795 + 2.53313i) q^{2} +(1.34601 - 1.16633i) q^{3} +(-4.18102 + 2.68698i) q^{4} +(2.14584 - 0.628789i) q^{5} +(3.95561 + 2.54212i) q^{6} +(-1.87277 - 0.855264i) q^{7} +(-5.92582 - 5.13475i) q^{8} +(0.0244873 - 0.170313i) q^{9} +(3.18887 + 4.96800i) q^{10} +(-5.55748 - 1.63182i) q^{11} +(-2.49381 + 8.49314i) q^{12} +(2.87256 - 1.31185i) q^{13} +(0.773542 - 5.38010i) q^{14} +(2.15495 - 3.34911i) q^{15} +(4.47020 - 9.78837i) q^{16} +(1.10511 - 1.71958i) q^{17} +(0.449639 - 0.0646484i) q^{18} +(-1.77165 + 1.13857i) q^{19} +(-7.28225 + 8.39480i) q^{20} +(-3.51828 + 1.03306i) q^{21} -15.2916i q^{22} +(1.21456 + 4.63949i) q^{23} -13.9650 q^{24} +(4.20925 - 2.69856i) q^{25} +(5.45969 + 6.30081i) q^{26} +(2.72301 + 4.23709i) q^{27} +(10.1281 - 1.45621i) q^{28} +(1.74171 + 1.11933i) q^{29} +(10.0866 + 2.96773i) q^{30} +(-1.04153 + 1.20200i) q^{31} +(12.5978 + 1.81129i) q^{32} +(-9.38367 + 4.28538i) q^{33} +(5.17791 + 1.52037i) q^{34} +(-4.55643 - 0.657682i) q^{35} +(0.355246 + 0.777880i) q^{36} +(-0.620561 - 0.0892232i) q^{37} +(-4.20189 - 3.64095i) q^{38} +(2.33645 - 5.11610i) q^{39} +(-15.9445 - 7.29226i) q^{40} +(0.289709 + 2.01497i) q^{41} +(-5.23376 - 8.14389i) q^{42} +(3.14193 - 2.72250i) q^{43} +(27.6206 - 8.11014i) q^{44} +(-0.0545453 - 0.380862i) q^{45} +(-10.8491 + 6.52746i) q^{46} -0.403164i q^{47} +(-5.39949 - 18.3890i) q^{48} +(-1.80825 - 2.08683i) q^{49} +(9.96663 + 8.65540i) q^{50} +(-0.518105 - 3.60350i) q^{51} +(-8.48529 + 13.2034i) q^{52} +(-7.50209 - 3.42609i) q^{53} +(-8.70774 + 10.0493i) q^{54} +(-12.9515 - 0.00714551i) q^{55} +(6.70611 + 14.6843i) q^{56} +(-1.05672 + 3.59885i) q^{57} +(-1.53994 + 5.24454i) q^{58} +(3.73431 + 8.17700i) q^{59} +(-0.0109200 + 19.7930i) q^{60} +(0.892000 - 1.02942i) q^{61} +(-3.81950 - 1.74431i) q^{62} +(-0.191522 + 0.298014i) q^{63} +(1.71909 + 11.9565i) q^{64} +(5.33916 - 4.62126i) q^{65} +(-17.8350 - 20.5826i) q^{66} +(1.89660 + 6.45923i) q^{67} +10.1590i q^{68} +(7.04596 + 4.82824i) q^{69} +(-1.72306 - 12.0312i) q^{70} +(-13.3319 + 3.91459i) q^{71} +(-1.01962 + 0.883509i) q^{72} +(-5.58084 - 8.68396i) q^{73} +(-0.235556 - 1.63833i) q^{74} +(2.51830 - 8.54165i) q^{75} +(4.34798 - 9.52075i) q^{76} +(9.01222 + 7.80913i) q^{77} +(14.6976 + 2.11320i) q^{78} +(-3.54206 - 7.75603i) q^{79} +(3.43750 - 23.8151i) q^{80} +(9.10231 + 2.67268i) q^{81} +(-4.88870 + 2.23259i) q^{82} +(8.15053 + 1.17187i) q^{83} +(11.9342 - 13.7728i) q^{84} +(1.29013 - 4.38483i) q^{85} +(9.23341 + 5.93395i) q^{86} +(3.64987 - 0.524772i) q^{87} +(24.5536 + 38.2062i) q^{88} +(2.09382 + 2.41639i) q^{89} +(0.924203 - 0.421453i) q^{90} -6.50160 q^{91} +(-17.5443 - 16.1343i) q^{92} +2.83267i q^{93} +(1.02127 - 0.299871i) q^{94} +(-3.08575 + 3.55718i) q^{95} +(19.0693 - 12.2551i) q^{96} +(9.91281 - 1.42525i) q^{97} +(3.94125 - 6.13270i) q^{98} +(-0.414009 + 0.906553i) 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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	0.743795	+	2.53313i	0.525942	+	1.79119i	0.607256	+	0.794506i	$0.292270\pi$
$2$	0.743795	+	2.53313i	0.525942	+	1.79119i	−0.0813139	+	0.996689i	$0.525912\pi$
$3$	1.34601	−	1.16633i	0.777120	−	0.673379i	−0.173118	−	0.984901i	$-0.555384\pi$
$3$	1.34601	−	1.16633i	0.777120	−	0.673379i	0.950239	+	0.311522i	$0.100839\pi$
$4$	−4.18102	+	2.68698i	−2.09051	+	1.34349i
$5$	2.14584	−	0.628789i	0.959648	−	0.281203i
$5$	2.14584	−	0.628789i	0.959648	−	0.281203i
$6$	3.95561	+	2.54212i	1.61487	+	1.03782i
$7$	−1.87277	−	0.855264i	−0.707839	−	0.323259i	0.0287625	−	0.999586i	$-0.490843\pi$
$7$	−1.87277	−	0.855264i	−0.707839	−	0.323259i	−0.736601	+	0.676327i	$0.763571\pi$
$8$	−5.92582	−	5.13475i	−2.09509	−	1.81541i
$9$	0.0244873	−	0.170313i	0.00816245	−	0.0567711i
$10$	3.18887	+	4.96800i	1.00841	+	1.57102i
$11$	−5.55748	−	1.63182i	−1.67564	−	0.492013i	−0.700511	−	0.713641i	$-0.747045\pi$
$11$	−5.55748	−	1.63182i	−1.67564	−	0.492013i	−0.975131	+	0.221628i	$0.928863\pi$
$12$	−2.49381	+	8.49314i	−0.719901	+	2.45176i
$13$	2.87256	−	1.31185i	0.796703	−	0.363842i	0.0248891	−	0.999690i	$-0.492077\pi$
$13$	2.87256	−	1.31185i	0.796703	−	0.363842i	0.771814	+	0.635848i	$0.219349\pi$
$14$	0.773542	−	5.38010i	0.206738	−	1.43789i
$15$	2.15495	−	3.34911i	0.556406	−	0.864735i
$16$	4.47020	−	9.78837i	1.11755	−	2.44709i
$17$	1.10511	−	1.71958i	0.268029	−	0.417060i	−0.680984	−	0.732298i	$-0.738448\pi$
$17$	1.10511	−	1.71958i	0.268029	−	0.417060i	0.949013	+	0.315238i	$0.102084\pi$
$18$	0.449639	−	0.0646484i	0.105981	−	0.0152378i
$19$	−1.77165	+	1.13857i	−0.406444	+	0.261206i	−0.727851	−	0.685736i	$-0.759481\pi$
$19$	−1.77165	+	1.13857i	−0.406444	+	0.261206i	0.321407	+	0.946941i	$0.395844\pi$
$20$	−7.28225	+	8.39480i	−1.62836	+	1.87713i
$21$	−3.51828	+	1.03306i	−0.767752	+	0.225432i
$22$		−	15.2916i		−	3.26017i
$23$	1.21456	+	4.63949i	0.253253	+	0.967400i
$23$	1.21456	+	4.63949i	0.253253	+	0.967400i
$24$	−13.9650			−2.85060
$25$	4.20925	−	2.69856i	0.841850	−	0.539712i
$26$	5.45969	+	6.30081i	1.07073	+	1.23569i
$27$	2.72301	+	4.23709i	0.524044	+	0.815428i
$28$	10.1281	−	1.45621i	1.91404	−	0.275197i
$29$	1.74171	+	1.11933i	0.323428	+	0.207855i	0.692272	−	0.721637i	$-0.256610\pi$
$29$	1.74171	+	1.11933i	0.323428	+	0.207855i	−0.368844	+	0.929491i	$0.620246\pi$
$30$	10.0866	+	2.96773i	1.84155	+	0.541831i
$31$	−1.04153	+	1.20200i	−0.187065	+	0.215885i	−0.841534	−	0.540204i	$-0.818347\pi$
$31$	−1.04153	+	1.20200i	−0.187065	+	0.215885i	0.654469	+	0.756089i	$0.272892\pi$
$32$	12.5978	+	1.81129i	2.22699	+	0.320193i
$33$	−9.38367	+	4.28538i	−1.63349	+	0.745989i
$34$	5.17791	+	1.52037i	0.888004	+	0.260742i
$35$	−4.55643	−	0.657682i	−0.770178	−	0.111169i
$36$	0.355246	+	0.777880i	0.0592076	+	0.129647i
$37$	−0.620561	−	0.0892232i	−0.102020	−	0.0146682i	0.0911159	−	0.995840i	$-0.470957\pi$
$37$	−0.620561	−	0.0892232i	−0.102020	−	0.0146682i	−0.193136	+	0.981172i	$0.561866\pi$
$38$	−4.20189	−	3.64095i	−0.681636	−	0.590641i
$39$	2.33645	−	5.11610i	0.374131	−	0.819232i
$40$	−15.9445	−	7.29226i	−2.52105	−	1.15301i
$41$	0.289709	+	2.01497i	0.0452449	+	0.314685i	0.999858	+	0.0168374i	$0.00535976\pi$
$41$	0.289709	+	2.01497i	0.0452449	+	0.314685i	−0.954613	+	0.297848i	$0.903731\pi$
$42$	−5.23376	−	8.14389i	−0.807586	−	1.25663i
$43$	3.14193	−	2.72250i	0.479141	−	0.415178i	−0.381517	−	0.924362i	$-0.624598\pi$
$43$	3.14193	−	2.72250i	0.479141	−	0.415178i	0.860658	+	0.509184i	$0.170053\pi$
$44$	27.6206	−	8.11014i	4.16396	−	1.22265i
$45$	−0.0545453	−	0.380862i	−0.00813113	−	0.0567756i
$46$	−10.8491	+	6.52746i	−1.59961	+	0.962421i
$47$		−	0.403164i		−	0.0588075i	−0.999568	−	0.0294037i	$-0.990639\pi$
$47$		−	0.403164i		−	0.0588075i	0.999568	−	0.0294037i	$-0.00936085\pi$
$48$	−5.39949	−	18.3890i	−0.779349	−	2.65422i
$49$	−1.80825	−	2.08683i	−0.258321	−	0.298119i
$50$	9.96663	+	8.65540i	1.40949	+	1.22406i
$51$	−0.518105	−	3.60350i	−0.0725492	−	0.504591i
$52$	−8.48529	+	13.2034i	−1.17670	+	1.83098i
$53$	−7.50209	−	3.42609i	−1.03049	−	0.470610i	−0.172899	−	0.984940i	$-0.555313\pi$
$53$	−7.50209	−	3.42609i	−1.03049	−	0.470610i	−0.857593	+	0.514330i	$0.828041\pi$
$54$	−8.70774	+	10.0493i	−1.18497	+	1.36753i
$55$	−12.9515	−	0.00714551i	−1.74638	−	0.000963500i
$56$	6.70611	+	14.6843i	0.896141	+	1.96228i
$57$	−1.05672	+	3.59885i	−0.139965	+	0.476679i
$58$	−1.53994	+	5.24454i	−0.202203	+	0.688642i
$59$	3.73431	+	8.17700i	0.486166	+	1.06455i	0.980722	+	0.195409i	$0.0626033\pi$
$59$	3.73431	+	8.17700i	0.486166	+	1.06455i	−0.494556	+	0.869146i	$0.664669\pi$
$60$	−0.0109200	+	19.7930i	−0.00140977	+	2.55526i
$61$	0.892000	−	1.02942i	0.114209	−	0.131804i	−0.695766	−	0.718268i	$-0.744935\pi$
$61$	0.892000	−	1.02942i	0.114209	−	0.131804i	0.809975	+	0.586464i	$0.199481\pi$
$62$	−3.81950	−	1.74431i	−0.485077	−	0.221527i
$63$	−0.191522	+	0.298014i	−0.0241295	+	0.0375462i
$64$	1.71909	+	11.9565i	0.214886	+	1.49457i
$65$	5.33916	−	4.62126i	0.662242	−	0.573196i
$66$	−17.8350	−	20.5826i	−2.19533	−	2.53355i
$67$	1.89660	+	6.45923i	0.231707	+	0.789121i	0.990467	+	0.137751i	$0.0439873\pi$
$67$	1.89660	+	6.45923i	0.231707	+	0.789121i	−0.758760	+	0.651370i	$0.774195\pi$
$68$			10.1590i			1.23196i
$69$	7.04596	+	4.82824i	0.848234	+	0.581251i
$70$	−1.72306	−	12.0312i	−0.205944	−	1.43801i
$71$	−13.3319	+	3.91459i	−1.58220	+	0.464577i	−0.950524	−	0.310653i	$-0.899452\pi$
$71$	−13.3319	+	3.91459i	−1.58220	+	0.464577i	−0.631680	+	0.775229i	$0.717634\pi$
$72$	−1.01962	+	0.883509i	−0.120164	+	0.104123i
$73$	−5.58084	−	8.68396i	−0.653188	−	1.01638i	−0.997005	−	0.0773434i	$-0.975356\pi$
$73$	−5.58084	−	8.68396i	−0.653188	−	1.01638i	0.343817	−	0.939037i	$-0.388280\pi$
$74$	−0.235556	−	1.63833i	−0.0273828	−	0.190452i
$75$	2.51830	−	8.54165i	0.290788	−	0.986305i
$76$	4.34798	−	9.52075i	0.498748	−	1.09211i
$77$	9.01222	+	7.80913i	1.02704	+	0.889933i
$78$	14.6976	+	2.11320i	1.66418	+	0.239272i
$79$	−3.54206	−	7.75603i	−0.398513	−	0.872621i	−0.997419	−	0.0718020i	$-0.977125\pi$
$79$	−3.54206	−	7.75603i	−0.398513	−	0.872621i	0.598906	−	0.800819i	$-0.295602\pi$
$80$	3.43750	−	23.8151i	0.384324	−	2.66261i
$81$	9.10231	+	2.67268i	1.01137	+	0.296965i
$82$	−4.88870	+	2.23259i	−0.539867	+	0.246549i
$83$	8.15053	+	1.17187i	0.894637	+	0.128629i	0.574272	−	0.818665i	$-0.305285\pi$
$83$	8.15053	+	1.17187i	0.894637	+	0.128629i	0.320365	+	0.947294i	$0.396194\pi$
$84$	11.9342	−	13.7728i	1.30213	−	1.50273i
$85$	1.29013	−	4.38483i	0.139934	−	0.475602i
$86$	9.23341	+	5.93395i	0.995664	+	0.639875i
$87$	3.64987	−	0.524772i	0.391307	−	0.0562615i
$88$	24.5536	+	38.2062i	2.61742	+	4.07279i
$89$	2.09382	+	2.41639i	0.221944	+	0.256137i	0.855791	−	0.517321i	$-0.173071\pi$
$89$	2.09382	+	2.41639i	0.221944	+	0.256137i	−0.633847	+	0.773458i	$0.718525\pi$
$90$	0.924203	−	0.421453i	0.0974196	−	0.0444251i
$91$	−6.50160			−0.681553
$92$	−17.5443	−	16.1343i	−1.82912	−	1.68212i
$93$			2.83267i			0.293734i
$94$	1.02127	−	0.299871i	0.105336	−	0.0309293i
$95$	−3.08575	+	3.55718i	−0.316591	+	0.364959i
$96$	19.0693	−	12.2551i	1.94625	−	1.25078i
$97$	9.91281	−	1.42525i	1.00649	−	0.144712i	0.380698	−	0.924699i	$-0.375684\pi$
$97$	9.91281	−	1.42525i	1.00649	−	0.144712i	0.625795	+	0.779987i	$0.284775\pi$
$98$	3.94125	−	6.13270i	0.398126	−	0.619497i
$99$	−0.414009	+	0.906553i	−0.0416095	+	0.0911120i
$100$	−10.3480	+	22.5929i	−1.03480	+	2.25929i
$101$	−2.66635	+	18.5449i	−0.265312	+	1.84529i	0.225780	+	0.974178i	$0.427507\pi$
$101$	−2.66635	+	18.5449i	−0.265312	+	1.84529i	−0.491092	+	0.871108i	$0.663402\pi$
$102$	8.74278	−	3.99269i	0.865664	−	0.395335i
$103$	3.68489	−	12.5496i	0.363083	−	1.23655i	−0.552192	−	0.833717i	$-0.686208\pi$
$103$	3.68489	−	12.5496i	0.363083	−	1.23655i	0.915275	−	0.402830i	$-0.131973\pi$
$104$	−23.7583	−	6.97606i	−2.32969	−	0.684059i
$105$	−6.90009	+	4.42904i	−0.673380	+	0.432230i
$106$	3.09872	−	21.5521i	0.300975	−	2.09332i
$107$	−1.70218	−	1.47495i	−0.164556	−	0.142588i	0.568690	−	0.822552i	$-0.307450\pi$
$107$	−1.70218	−	1.47495i	−0.164556	−	0.142588i	−0.733246	+	0.679963i	$0.761996\pi$
$108$	−22.7699	−	10.3987i	−2.19104	−	1.00061i
$109$	5.07750	+	3.26311i	0.486336	+	0.312549i	0.760730	−	0.649068i	$-0.224841\pi$
$109$	5.07750	+	3.26311i	0.486336	+	0.312549i	−0.274394	+	0.961617i	$0.588477\pi$
$110$	−9.61517	−	32.8132i	−0.916771	−	3.12862i
$111$	−0.939346	+	0.603681i	−0.0891588	+	0.0572989i
$112$	−16.7433	+	14.5081i	−1.58209	+	1.37089i
$113$	1.49930	+	5.10615i	0.141042	+	0.480346i	0.999469	−	0.0325904i	$-0.0103757\pi$
$113$	1.49930	+	5.10615i	0.141042	+	0.480346i	−0.858426	+	0.512937i	$0.828557\pi$
$114$	−9.90233			−0.927438
$115$	5.52350	+	9.19189i	0.515069	+	0.857148i
$116$	−10.2898			−0.955379
$117$	−0.153084	−	0.521358i	−0.0141527	−	0.0481996i
$118$	−17.9358	+	15.5415i	−1.65113	+	1.43071i
$119$	−3.54031	+	2.27522i	−0.324540	+	0.208569i
$120$	−29.9667	+	8.78106i	−2.73557	+	0.801597i
$121$	18.9689	+	12.1906i	1.72445	+	1.10824i
$122$	3.27113	+	1.49387i	0.296154	+	0.135249i
$123$	2.74006	+	2.37428i	0.247063	+	0.214081i
$124$	1.12494	−	7.82415i	0.101023	−	0.702629i
$125$	7.33554	−	8.43741i	0.656111	−	0.754665i
$126$	−0.897361	−	0.263489i	−0.0799433	−	0.0234735i
$127$	2.44357	−	8.32204i	0.216832	−	0.738461i	−0.777189	−	0.629268i	$-0.783355\pi$
$127$	2.44357	−	8.32204i	0.216832	−	0.738461i	0.994020	−	0.109194i	$-0.0348269\pi$
$128$	−5.85445	+	2.67364i	−0.517465	+	0.236318i
$129$	1.05376	−	7.32904i	0.0927781	−	0.645286i
$130$	15.6775	+	10.0875i	1.37501	+	0.884735i
$131$	6.45185	−	14.1276i	0.563701	−	1.23433i	−0.386383	−	0.922338i	$-0.626276\pi$
$131$	6.45185	−	14.1276i	0.563701	−	1.23433i	0.950084	−	0.311994i	$-0.100997\pi$
$132$	27.7186	−	43.1310i	2.41259	−	3.75407i
$133$	4.29166	−	0.617047i	0.372134	−	0.0535048i
$134$	−14.9514	+	9.60869i	−1.29160	+	0.830064i
$135$	8.50738	+	7.37991i	0.732198	+	0.635161i
$136$	−15.3783	+	4.51548i	−1.31868	+	0.387199i
$137$			10.4860i			0.895881i	0.894063	+	0.447940i	$0.147842\pi$
$137$			10.4860i			0.895881i	−0.894063	+	0.447940i	$0.852158\pi$
$138$	−6.98981	+	21.4396i	−0.595012	+	1.82506i
$139$	13.5504			1.14933			0.574664	−	0.818389i	$-0.305133\pi$
$139$	13.5504			1.14933			0.574664	+	0.818389i	$0.305133\pi$
$140$	20.8177	−	9.49326i	1.75942	−	0.802327i
$141$	−0.470220	−	0.542663i	−0.0395997	−	0.0457005i
$142$	−19.8324	−	30.8598i	−1.66430	−	2.58969i
$143$	−18.1049	+	2.60309i	−1.51401	+	0.217681i
$144$	−1.55762	−	1.00102i	−0.129802	−	0.0834187i
$145$	4.44126	+	1.30673i	0.368826	+	0.108518i
$146$	17.8466	−	20.5961i	1.47700	−	1.70454i
$147$	−4.86785	−	0.699891i	−0.401493	−	0.0577260i
$148$	2.83432	−	1.29439i	0.232980	−	0.106398i
$149$	−17.5725	−	5.15974i	−1.43959	−	0.422702i	−0.533506	−	0.845796i	$-0.679126\pi$
$149$	−17.5725	−	5.15974i	−1.43959	−	0.422702i	−0.906086	+	0.423094i	$0.860944\pi$
$150$	23.5102	+	0.0259417i	1.91960	+	0.00211813i
$151$	−7.26401	−	15.9060i	−0.591137	−	1.29441i	−0.934753	−	0.355299i	$-0.884379\pi$
$151$	−7.26401	−	15.9060i	−0.591137	−	1.29441i	0.343615	−	0.939110i	$-0.388348\pi$
$152$	16.3447	+	2.35002i	1.32573	+	0.190612i
$153$	−0.265807	−	0.230323i	−0.0214892	−	0.0186205i
$154$	−13.0783	+	28.6375i	−1.05388	+	2.30768i
$155$	−1.47916	+	3.23419i	−0.118809	+	0.259777i
$156$	3.97813	+	27.6685i	0.318505	+	2.21525i
$157$	−0.612997	−	0.953842i	−0.0489225	−	0.0761249i	0.815931	−	0.578150i	$-0.196225\pi$
$157$	−0.612997	−	0.953842i	−0.0489225	−	0.0761249i	−0.864853	+	0.502025i	$0.832589\pi$
$158$	17.0125	−	14.7414i	1.35344	−	1.17276i
$159$	−14.0938	+	4.13833i	−1.11771	+	0.328191i
$160$	28.1717	−	4.03462i	2.22717	−	0.318965i
$161$	1.69340	−	9.72744i	0.133459	−	0.766630i
$162$			25.0453i			1.96774i
$163$	2.18334	+	7.43577i	0.171012	+	0.582415i	0.999741	+	0.0227638i	$0.00724658\pi$
$163$	2.18334	+	7.43577i	0.171012	+	0.582415i	−0.828728	+	0.559651i	$0.810935\pi$
$164$	−6.62546	−	7.64619i	−0.517361	−	0.597067i
$165$	−17.4412	+	15.0961i	−1.35780	+	1.17523i
$166$	3.09382	+	21.5180i	0.240127	+	1.67012i
$167$	5.15274	−	8.01781i	0.398731	−	0.620437i	−0.582601	−	0.812758i	$-0.697965\pi$
$167$	5.15274	−	8.01781i	0.398731	−	0.620437i	0.981332	+	0.192321i	$0.0616015\pi$
$168$	26.1532	+	11.9438i	2.01776	+	0.921482i
$169$	−1.98257	+	2.28801i	−0.152506	+	0.176001i
$170$	12.0670	+	0.00665748i	0.925493	+	0.000510605i
$171$	0.150530	+	0.329615i	0.0115113	+	0.0252063i
$172$	−5.82119	+	19.8251i	−0.443861	+	1.51165i
$173$	3.16279	−	10.7715i	0.240463	−	0.818941i	−0.747502	−	0.664260i	$-0.768747\pi$
$173$	3.16279	−	10.7715i	0.240463	−	0.818941i	0.987964	−	0.154681i	$-0.0494350\pi$
$174$	4.04407	+	8.85528i	0.306580	+	0.671317i
$175$	−10.1909	+	1.45376i	−0.770361	+	0.109894i
$176$	−40.8159	+	47.1041i	−3.07661	+	3.55060i
$177$	14.5635	+	6.65091i	1.09466	+	0.499913i
$178$	−4.56367	+	7.10121i	−0.342062	+	0.532259i
$179$	−0.703686	−	4.89425i	−0.0525960	−	0.365813i	−0.999073	−	0.0430426i	$-0.986295\pi$
$179$	−0.703686	−	4.89425i	−0.0525960	−	0.365813i	0.946477	−	0.322771i	$-0.104614\pi$
$180$	1.25142	+	1.44583i	0.0932755	+	0.107766i
$181$	−5.18515	−	5.98398i	−0.385409	−	0.444786i	0.529583	−	0.848258i	$-0.322349\pi$
$181$	−5.18515	−	5.98398i	−0.385409	−	0.444786i	−0.914992	+	0.403472i	$0.867803\pi$
$182$	−4.83586	−	16.4694i	−0.358458	−	1.22079i
$183$		−	2.42598i		−	0.179333i
$184$	16.6254	−	33.7292i	1.22564	−	2.48655i
$185$	−1.38773	+	0.198744i	−0.102028	+	0.0146119i
$186$	−7.17552	+	2.10692i	−0.526135	+	0.154487i
$187$	−8.94768	+	7.75321i	−0.654319	+	0.566971i
$188$	1.08329	+	1.68563i	0.0790072	+	0.122938i
$189$	−1.47574	−	10.2640i	−0.107344	−	0.746594i
$190$	−11.3060	−	5.17080i	−0.820221	−	0.375129i
$191$	−5.60445	+	12.2720i	−0.405524	+	0.887973i	0.591157	+	0.806557i	$0.298672\pi$
$191$	−5.60445	+	12.2720i	−0.405524	+	0.887973i	−0.996680	+	0.0814161i	$0.974056\pi$
$192$	16.2591	+	14.0886i	1.17340	+	1.01676i
$193$	5.46991	+	0.786454i	0.393733	+	0.0566102i	0.336338	−	0.941741i	$-0.390812\pi$
$193$	5.46991	+	0.786454i	0.393733	+	0.0566102i	0.0573948	+	0.998352i	$0.481721\pi$
$194$	10.9834	+	24.0504i	0.788565	+	1.72672i
$195$	1.79669	−	12.4475i	0.128663	−	0.891382i
$196$	13.1676	+	3.86635i	0.940542	+	0.276168i
$197$	−17.6868	+	8.07729i	−1.26013	+	0.575483i	−0.929690	−	0.368344i	$-0.879925\pi$
$197$	−17.6868	+	8.07729i	−1.26013	+	0.575483i	−0.330442	+	0.943826i	$0.607198\pi$
$198$	−2.60436	−	0.374450i	−0.185084	−	0.0266110i
$199$	7.00184	−	8.08056i	0.496347	−	0.572815i	−0.451203	−	0.892421i	$-0.649005\pi$
$199$	7.00184	−	8.08056i	0.496347	−	0.572815i	0.947551	+	0.319606i	$0.103550\pi$
$200$	−38.7997	−	5.62226i	−2.74355	−	0.397554i
$201$	10.0864	+	6.48215i	0.711441	+	0.457216i
$202$	−48.9599	+	7.03937i	−3.44481	+	0.495288i
$203$	−2.30450	−	3.58587i	−0.161744	−	0.251679i
$204$	11.8487	+	13.6742i	0.829577	+	0.957383i
$205$	1.88866	+	4.14163i	0.131910	+	0.289264i
$206$	34.5306			2.40586
$207$	0.819907	−	0.0932464i	0.0569875	−	0.00648107i
$208$		−	33.9819i		−	2.35622i
$209$	11.7038	−	3.43656i	0.809571	−	0.237712i
$210$	−16.3516	−	14.1845i	−1.12837	−	0.978826i
$211$	10.5813	−	6.80021i	0.728449	−	0.468146i	−0.123118	−	0.992392i	$-0.539289\pi$
$211$	10.5813	−	6.80021i	0.728449	−	0.468146i	0.851567	+	0.524246i	$0.175653\pi$
$212$	40.5722	−	5.83341i	2.78651	−	0.400640i
$213$	−13.3792	+	20.8184i	−0.916726	+	1.42645i
$214$	2.47016	−	5.40890i	0.168857	−	0.369745i
$215$	5.03021	−	7.81767i	0.343057	−	0.533160i
$216$	5.62032	−	39.0902i	0.382414	−	2.65975i
$217$	2.97857	−	1.36027i	0.202199	−	0.0923411i
$218$	−4.48927	+	15.2891i	−0.304052	+	1.03551i
$219$	−17.6402	−	5.17963i	−1.19201	−	0.350007i
$220$	54.1698	−	34.7706i	3.65213	−	2.34423i
$221$	0.918649	−	6.38934i	0.0617950	−	0.429794i
$222$	−2.22788	−	1.93047i	−0.149526	−	0.129565i
$223$	−4.55894	−	2.08200i	−0.305289	−	0.139421i	0.256880	−	0.966443i	$-0.417306\pi$
$223$	−4.55894	−	2.08200i	−0.305289	−	0.139421i	−0.562169	+	0.827022i	$0.690033\pi$
$224$	−22.0436	−	14.1665i	−1.47285	−	0.946542i
$225$	−0.356527	−	0.782971i	−0.0237685	−	0.0521981i
$226$	−11.8194	+	7.59586i	−0.786214	+	0.505269i
$227$	−10.5661	+	9.15555i	−0.701294	+	0.607675i	−0.930755	−	0.365643i	$-0.880849\pi$
$227$	−10.5661	+	9.15555i	−0.701294	+	0.607675i	0.229461	+	0.973318i	$0.426304\pi$
$228$	−5.25187	−	17.8862i	−0.347813	−	1.18454i
$229$	−11.7736			−0.778020			−0.389010	−	0.921234i	$-0.627183\pi$
$229$	−11.7736			−0.778020			−0.389010	+	0.921234i	$0.627183\pi$
$230$	−19.1759	+	20.8286i	−1.26442	+	1.37340i
$231$	21.2385			1.39739
$232$	−4.57359	−	15.5762i	−0.300271	−	1.02263i
$233$	3.75185	−	3.25100i	0.245792	−	0.212980i	−0.523248	−	0.852180i	$-0.675280\pi$
$233$	3.75185	−	3.25100i	0.245792	−	0.212980i	0.769040	+	0.639200i	$0.220735\pi$
$234$	1.20680	−	0.775566i	0.0788913	−	0.0507004i
$235$	−0.253505	−	0.865124i	−0.0165368	−	0.0564345i
$236$	−37.5846	−	24.1542i	−2.44655	−	1.57230i
$237$	−13.8137	−	6.30851i	−0.897297	−	0.409782i
$238$	−8.39669	−	7.27578i	−0.544277	−	0.471619i
$239$	−2.02431	+	14.0794i	−0.130942	+	0.910719i	0.813389	+	0.581721i	$0.197620\pi$
$239$	−2.02431	+	14.0794i	−0.130942	+	0.910719i	−0.944330	+	0.328999i	$0.893289\pi$
$240$	−23.1492	−	36.0646i	−1.49428	−	2.32796i
$241$	3.60661	+	1.05900i	0.232322	+	0.0682160i	0.395822	−	0.918327i	$-0.370460\pi$
$241$	3.60661	+	1.05900i	0.232322	+	0.0682160i	−0.163499	+	0.986543i	$0.552278\pi$
$242$	−16.7714	+	57.1181i	−1.07811	+	3.67169i
$243$	1.62459	−	0.741924i	0.104217	−	0.0475945i
$244$	−0.963432	+	6.70082i	−0.0616774	+	0.428976i
$245$	−5.19239	−	3.34099i	−0.331729	−	0.213448i
$246$	−3.97632	+	8.70692i	−0.253521	+	0.555133i
$247$	−3.59552	+	5.59474i	−0.228778	+	0.355985i
$248$	12.3439	−	1.77478i	0.783838	−	0.112699i
$249$	12.3375	−	7.92883i	0.781857	−	0.502469i
$250$	26.8292	+	12.3062i	1.69683	+	0.778312i
$251$	−16.9265	+	4.97006i	−1.06839	+	0.313708i	−0.768225	−	0.640180i	$-0.778860\pi$
$251$	−16.9265	+	4.97006i	−1.06839	+	0.313708i	−0.300165	+	0.953887i	$0.597042\pi$
$252$		−	1.76062i		−	0.110908i
$253$	0.820947	−	27.7658i	0.0516125	−	1.74562i
$254$	22.8983			1.43677
$255$	−3.37761	−	7.40675i	−0.211514	−	0.463829i
$256$	4.69358	+	5.41668i	0.293349	+	0.338542i
$257$	−3.33079	−	5.18281i	−0.207769	−	0.323295i	0.721693	−	0.692214i	$-0.243364\pi$
$257$	−3.33079	−	5.18281i	−0.207769	−	0.323295i	−0.929462	+	0.368919i	$0.879728\pi$
$258$	19.3492	−	2.78200i	1.20463	−	0.173199i
$259$	1.08586	+	0.697838i	0.0674718	+	0.0433615i
$260$	−9.90593	+	33.6678i	−0.614340	+	2.08799i
$261$	0.233287	−	0.269227i	0.0144401	−	0.0166647i
$262$	40.5859	+	5.83537i	2.50740	+	0.360510i
$263$	18.6921	−	8.53638i	1.15260	−	0.526376i	0.254895	−	0.966969i	$-0.417959\pi$
$263$	18.6921	−	8.53638i	1.15260	−	0.526376i	0.897707	+	0.440593i	$0.145232\pi$
$264$	77.6103	+	22.7884i	4.77658	+	1.40253i
$265$	−18.2526	−	2.63460i	−1.12125	−	0.161842i
$266$	4.75517	+	10.4124i	0.291558	+	0.638424i
$267$	5.63661	+	0.810422i	0.344955	+	0.0495970i
$268$	−25.2855	−	21.9100i	−1.54456	−	1.33837i
$269$	−6.21519	+	13.6094i	−0.378947	+	0.829777i	0.620031	+	0.784577i	$0.287120\pi$
$269$	−6.21519	+	13.6094i	−0.378947	+	0.829777i	−0.998978	+	0.0452002i	$0.985607\pi$
$270$	−12.3665	+	27.0394i	−0.752603	+	1.64557i
$271$	−2.11531	−	14.7123i	−0.128496	−	0.893710i	−0.947462	−	0.319868i	$-0.896361\pi$
$271$	−2.11531	−	14.7123i	−0.128496	−	0.893710i	0.818966	−	0.573842i	$-0.194548\pi$
$272$	−11.8919	−	18.5041i	−0.721050	−	1.12198i
$273$	−8.75124	+	7.58299i	−0.529649	+	0.458943i
$274$	−26.5625	+	7.79944i	−1.60470	+	0.471181i
$275$	−27.7964	+	8.12845i	−1.67618	+	0.490164i
$276$	−42.4327	−	1.25460i	−2.55415	−	0.0755181i
$277$		−	9.98105i		−	0.599703i	−0.953986	−	0.299852i	$-0.903063\pi$
$277$		−	9.98105i		−	0.599703i	0.953986	−	0.299852i	$-0.0969372\pi$
$278$	10.0787	+	34.3249i	0.604481	+	2.05867i
$279$	0.179211	+	0.206821i	0.0107291	+	0.0123820i
$280$	23.6236	+	27.2935i	1.41178	+	1.63110i
$281$	−3.63986	−	25.3158i	−0.217136	−	1.51021i	−0.748538	−	0.663092i	$-0.769244\pi$
$281$	−3.63986	−	25.3158i	−0.217136	−	1.51021i	0.531402	−	0.847120i	$-0.321665\pi$
$282$	1.02489	−	1.59476i	0.0610313	−	0.0949666i
$283$	6.36619	+	2.90734i	0.378431	+	0.172824i	0.595544	−	0.803323i	$-0.296937\pi$
$283$	6.36619	+	2.90734i	0.378431	+	0.172824i	−0.217113	+	0.976147i	$0.569664\pi$
$284$	45.2224	−	52.1895i	2.68346	−	3.09688i
$285$	−0.00462720	+	8.38699i	−0.000274092	+	0.496803i
$286$	−20.0603	−	43.9259i	−1.18619	−	2.59739i
$287$	1.18077	−	4.02134i	0.0696988	−	0.237372i
$288$	0.616972	−	2.10121i	0.0363554	−	0.123815i
$289$	5.32635	+	11.6631i	0.313315	+	0.686064i
$290$	−0.00674315	+	12.2222i	−0.000395971	+	0.717714i
$291$	11.6805	−	13.4800i	0.684721	−	0.790210i
$292$	46.6672	+	21.3122i	2.73099	+	1.24720i
$293$	−5.62093	+	8.74634i	−0.328378	+	0.510966i	−0.965710	−	0.259623i	$-0.916402\pi$
$293$	−5.62093	+	8.74634i	−0.328378	+	0.510966i	0.637332	+	0.770589i	$0.280038\pi$
$294$	−1.84776	−	12.8515i	−0.107764	−	0.749513i
$295$	13.1548	+	15.1984i	0.765904	+	0.884886i
$296$	3.21919	+	3.71515i	0.187112	+	0.215939i
$297$	−8.21890	−	27.9910i	−0.476909	−	1.62420i
$298$		−	48.3512i		−	2.80091i
$299$	9.57520	+	11.7339i	0.553748	+	0.678587i
$300$	12.4222	+	42.4794i	0.717195	+	2.45255i
$301$	−8.21257	+	2.41143i	−0.473364	+	0.138992i
$302$	34.8890	−	30.2315i	2.00764	−	1.73963i
$303$	18.0405	+	28.0715i	1.03640	+	1.61267i
$304$	3.22511	+	22.4312i	0.184973	+	1.28652i
$305$	1.26680	−	2.76985i	0.0725366	−	0.158601i
$306$	0.385733	−	0.844637i	0.0220509	−	0.0482847i
$307$	1.97633	+	1.71250i	0.112795	+	0.0977376i	0.709432	−	0.704773i	$-0.248951\pi$
$307$	1.97633	+	1.71250i	0.112795	+	0.0977376i	−0.596637	+	0.802511i	$0.703497\pi$
$308$	−58.6632	−	8.43450i	−3.34265	−	0.480600i
$309$	−9.67700	−	21.1897i	−0.550505	−	1.20544i
$310$	−9.29283	−	1.34134i	−0.527797	−	0.0761831i
$311$	25.6899	+	7.54323i	1.45674	+	0.427737i	0.911764	−	0.410715i	$-0.134721\pi$
$311$	25.6899	+	7.54323i	1.45674	+	0.427737i	0.544975	+	0.838452i	$0.316539\pi$
$312$	−40.1153	+	18.3200i	−2.27108	+	1.03717i
$313$	−16.4725	−	2.36838i	−0.931079	−	0.133869i	−0.339948	−	0.940444i	$-0.610409\pi$
$313$	−16.4725	−	2.36838i	−0.931079	−	0.133869i	−0.591131	+	0.806575i	$0.701318\pi$
$314$	1.96026	−	2.26227i	0.110624	−	0.127667i
$315$	−0.223587	+	0.759916i	−0.0125977	+	0.0428164i
$316$	35.6497	+	22.9107i	2.00545	+	1.28883i
$317$	25.9491	−	3.73091i	1.45744	−	0.209549i	0.632411	−	0.774633i	$-0.282065\pi$
$317$	25.9491	−	3.73091i	1.45744	−	0.209549i	0.825033	+	0.565084i	$0.191156\pi$
$318$	−20.9659	−	32.6235i	−1.17571	−	1.82944i
$319$	−7.85298	−	9.06282i	−0.439682	−	0.507421i
$320$	11.2070	+	24.5758i	0.626492	+	1.37383i
$321$	−4.01142			−0.223896
$322$	25.9004	−	2.94560i	1.44337	−	0.164152i
$323$			4.30474i			0.239522i
$324$	−45.2384	+	13.2832i	−2.51324	+	0.737955i
$325$	8.55118	−	13.2737i	0.474334	−	0.736291i
$326$	−17.2118	+	11.0614i	−0.953275	+	0.612633i
$327$	10.6402	−	1.52983i	0.588406	−	0.0846000i
$328$	8.62961	−	13.4279i	0.476490	−	0.741433i
$329$	−0.344811	+	0.755031i	−0.0190101	+	0.0416262i
$330$	−51.2131	−	32.9526i	−2.81919	−	1.81398i
$331$	−1.00431	+	6.98511i	−0.0552017	+	0.383936i	0.943427	+	0.331581i	$0.107582\pi$
$331$	−1.00431	+	6.98511i	−0.0552017	+	0.383936i	−0.998629	+	0.0523554i	$0.983327\pi$
$332$	−37.2263	+	17.0007i	−2.04306	+	0.933034i
$333$	−0.0303918	+	0.103505i	−0.00166546	+	0.00567204i
$334$	24.1428	+	7.08895i	1.32103	+	0.387890i
$335$	8.13130	+	12.6679i	0.444260	+	0.692122i
$336$	−5.61544	+	39.0562i	−0.306347	+	2.13069i
$337$	12.3520	+	10.7031i	0.672857	+	0.583034i	0.922825	−	0.385220i	$-0.125874\pi$
$337$	12.3520	+	10.7031i	0.672857	+	0.583034i	−0.249967	+	0.968254i	$0.580420\pi$
$338$	−7.27046	−	3.32031i	−0.395461	−	0.180601i
$339$	7.97352	+	5.12427i	0.433062	+	0.278312i
$340$	6.38788	+	21.7996i	0.346432	+	1.18225i
$341$	7.74975	−	4.98046i	0.419672	−	0.269707i
$342$	−0.722996	+	0.626479i	−0.0390951	+	0.0338761i
$343$	5.66189	+	19.2826i	0.305713	+	1.04116i
$344$	−32.5979			−1.75756
$345$	18.1554	+	5.93019i	0.977456	+	0.319271i
$346$	29.6381			1.59335
$347$	−5.89187	−	20.0659i	−0.316292	−	1.07719i	−0.952212	−	0.305437i	$-0.901197\pi$
$347$	−5.89187	−	20.0659i	−0.316292	−	1.07719i	0.635920	−	0.771755i	$-0.280621\pi$
$348$	−13.8501	+	12.0012i	−0.742445	+	0.643332i
$349$	−20.8831	+	13.4207i	−1.11785	+	0.718396i	−0.962989	−	0.269541i	$-0.913128\pi$
$349$	−20.8831	+	13.4207i	−1.11785	+	0.718396i	−0.154857	+	0.987937i	$0.549492\pi$
$350$	−11.2625	−	24.7336i	−0.602006	−	1.32207i
$351$	13.3804	+	8.59908i	0.714194	+	0.458985i
$352$	−67.0562	−	30.6235i	−3.57411	−	1.63224i
$353$	−9.33634	−	8.08999i	−0.496923	−	0.430587i	0.369997	−	0.929033i	$-0.379359\pi$
$353$	−9.33634	−	8.08999i	−0.496923	−	0.430587i	−0.866921	+	0.498446i	$0.833904\pi$
$354$	−6.01541	+	41.8381i	−0.319715	+	2.22367i
$355$	−26.1466	+	16.7830i	−1.38772	+	0.890751i
$356$	−15.2471	−	4.47695i	−0.808094	−	0.237278i
$357$	−2.11165	+	7.19163i	−0.111760	+	0.380621i
$358$	11.8744	−	5.42284i	0.627580	−	0.286606i
$359$	−1.64830	+	11.4642i	−0.0869940	+	0.605057i	0.898959	+	0.438033i	$0.144325\pi$
$359$	−1.64830	+	11.4642i	−0.0869940	+	0.605057i	−0.985953	+	0.167024i	$0.946584\pi$
$360$	−1.63241	+	2.53700i	−0.0860354	+	0.133711i
$361$	−6.05049	+	13.2487i	−0.318447	+	0.697301i
$362$	11.3015	−	17.5855i	0.593995	−	0.924275i
$363$	39.7506	−	5.71527i	2.08637	−	0.299974i
$364$	27.1833	−	17.4697i	1.42479	−	0.915659i
$365$	−17.4360	−	15.1252i	−0.912640	−	0.791689i
$366$	6.14532	−	1.80443i	0.321221	−	0.0943190i
$367$			8.34483i			0.435596i	0.975994	+	0.217798i	$0.0698875\pi$
$367$			8.34483i			0.435596i	−0.975994	+	0.217798i	$0.930113\pi$
$368$	50.8423	+	8.85089i	2.65034	+	0.461385i
$369$	0.350270			0.0182343
$370$	−1.53563	−	3.36747i	−0.0798335	−	0.175066i
$371$	11.1195	+	12.8325i	0.577293	+	0.666232i
$372$	−7.61132	−	11.8434i	−0.394629	−	0.614054i
$373$	−27.1960	+	3.91020i	−1.40816	+	0.202462i	−0.804107	−	0.594485i	$-0.797356\pi$
$373$	−27.1960	+	3.91020i	−1.40816	+	0.202462i	−0.604049	+	0.796947i	$0.706447\pi$
$374$	−26.2951	−	16.8989i	−1.35969	−	0.873819i
$375$	0.0329579	−	19.9125i	0.00170194	−	1.02828i
$376$	−2.07015	+	2.38908i	−0.106760	+	0.123207i
$377$	6.47156	+	0.930470i	0.333302	+	0.0479217i
$378$	24.9023	−	11.3725i	1.28084	−	0.584939i
$379$	9.48787	+	2.78589i	0.487359	+	0.143102i	0.516175	−	0.856483i	$-0.327355\pi$
$379$	9.48787	+	2.78589i	0.487359	+	0.143102i	−0.0288157	+	0.999585i	$0.509174\pi$
$380$	3.34352	−	23.1640i	0.171519	−	1.18829i
$381$	−6.41713	−	14.0516i	−0.328760	−	0.719883i
$382$	−35.2552	−	5.06894i	−1.80381	−	0.259349i
$383$	8.50071	+	7.36591i	0.434366	+	0.376380i	0.844421	−	0.535681i	$-0.179945\pi$
$383$	8.50071	+	7.36591i	0.434366	+	0.376380i	−0.410055	+	0.912061i	$0.634490\pi$
$384$	−4.76182	+	10.4269i	−0.243001	+	0.532097i
$385$	24.2491	+	11.0903i	1.23585	+	0.565217i
$386$	2.07630	+	14.4410i	0.105681	+	0.735026i
$387$	−0.386740	−	0.601780i	−0.0196591	−	0.0305902i
$388$	−37.6161	+	32.5945i	−1.90967	+	1.65473i
$389$	7.81767	−	2.29548i	0.396372	−	0.116385i	−0.0774712	−	0.996995i	$-0.524685\pi$
$389$	7.81767	−	2.29548i	0.396372	−	0.116385i	0.473843	+	0.880609i	$0.342866\pi$
$390$	32.8674	−	4.70712i	1.66431	−	0.238354i
$391$	9.32021	+	3.03861i	0.471343	+	0.153669i
$392$			21.6511i			1.09355i
$393$	−7.79310	−	26.5409i	−0.393110	−	1.33881i
$394$	−33.6162	−	38.7951i	−1.69356	−	1.95447i
$395$	−12.4776	−	14.4160i	−0.627816	−	0.725346i
$396$	−0.704909	−	4.90275i	−0.0354230	−	0.246372i
$397$	−7.26030	+	11.2972i	−0.364384	+	0.566992i	−0.974238	−	0.225521i	$-0.927592\pi$
$397$	−7.26030	+	11.2972i	−0.364384	+	0.566992i	0.609854	+	0.792514i	$0.291228\pi$
$398$	25.6770	+	11.7263i	1.28707	+	0.587787i
$399$	5.05694	−	5.83602i	0.253164	−	0.292167i
$400$	−7.59834	−	53.2648i	−0.379917	−	2.66324i
$401$	−5.88901	−	12.8951i	−0.294083	−	0.643952i	0.703701	−	0.710497i	$-0.251530\pi$
$401$	−5.88901	−	12.8951i	−0.294083	−	0.643952i	−0.997783	+	0.0665450i	$0.978802\pi$
$402$	−8.91791	+	30.3716i	−0.444785	+	1.51480i
$403$	−1.41503	+	4.81914i	−0.0704875	+	0.240058i
$404$	−38.6817	−	84.7010i	−1.92448	−	4.21403i
$405$	21.2127	+	0.0117033i	1.05407	+	0.000581540i
$406$	7.36940	−	8.50474i	0.365737	−	0.422083i
$407$	3.30316	+	1.50850i	0.163731	+	0.0747737i
$408$	−15.4329	+	24.0140i	−0.764041	+	1.18887i
$409$	−2.61692	−	18.2011i	−0.129398	−	0.899985i	−0.946319	−	0.323235i	$-0.895230\pi$
$409$	−2.61692	−	18.2011i	−0.129398	−	0.899985i	0.816921	−	0.576750i	$-0.195679\pi$
$410$	−9.08653	+	7.86475i	−0.448752	+	0.388412i
$411$	12.2301	+	14.1143i	0.603267	+	0.696207i
$412$	18.3139	+	62.3713i	0.902259	+	3.07281i
$413$		−	18.5074i		−	0.910690i
$414$	0.846048	+	2.00758i	0.0415810	+	0.0986671i
$415$	18.2266	−	2.61032i	0.894708	−	0.128136i
$416$	38.5640	−	11.3234i	1.89075	−	0.555175i
$417$	18.2390	−	15.8042i	0.893167	−	0.773933i
$418$	17.4105	+	27.0913i	0.851575	+	1.32508i
$419$	4.24524	+	29.5263i	0.207394	+	1.44245i	0.781619	+	0.623757i	$0.214394\pi$
$419$	4.24524	+	29.5263i	0.207394	+	1.44245i	−0.574225	+	0.818698i	$0.694697\pi$
$420$	16.9487	−	37.0583i	0.827010	−	1.80826i
$421$	−14.0057	+	30.6682i	−0.682595	+	1.49468i	0.177274	+	0.984162i	$0.443272\pi$
$421$	−14.0057	+	30.6682i	−0.682595	+	1.49468i	−0.859869	+	0.510514i	$0.829455\pi$
$422$	25.0962	+	21.7460i	1.22166	+	1.05858i
$423$	−0.0686641	−	0.00987241i	−0.00333856	−	0.000480013i
$424$	26.8639	+	58.8238i	1.30463	+	2.85674i
$425$	0.0112774	−	10.2204i	0.000547034	−	0.495760i
$426$	−62.6871	−	18.4066i	−3.03720	−	0.891803i
$427$	−2.55093	+	1.16497i	−0.123448	+	0.0563770i
$428$	11.0800	+	1.59306i	0.535572	+	0.0770036i
$429$	−21.3333	+	24.6200i	−1.02998	+	1.18866i
$430$	23.5446	+	6.92744i	1.13542	+	0.334071i
$431$	−17.0992	−	10.9890i	−0.823639	−	0.529321i	0.0596115	−	0.998222i	$-0.481014\pi$
$431$	−17.0992	−	10.9890i	−0.823639	−	0.529321i	−0.883251	+	0.468901i	$0.844650\pi$
$432$	53.6465	−	7.71321i	2.58107	−	0.371102i
$433$	19.5882	+	30.4798i	0.941346	+	1.46476i	0.884587	+	0.466376i	$0.154441\pi$
$433$	19.5882	+	30.4798i	0.941346	+	1.46476i	0.0567597	+	0.998388i	$0.481923\pi$
$434$	5.66119	+	6.53336i	0.271746	+	0.313611i
$435$	7.50206	−	3.42108i	0.359696	−	0.164028i
$436$	−29.9970			−1.43660
$437$	−7.43414	−	6.83668i	−0.355623	−	0.327043i
$438$		−	48.5375i		−	2.31921i
$439$	2.29415	−	0.673622i	0.109494	−	0.0321502i	−0.226527	−	0.974005i	$-0.572737\pi$
$439$	2.29415	−	0.673622i	0.109494	−	0.0321502i	0.336020	+	0.941855i	$0.390919\pi$
$440$	76.7117	+	66.5452i	3.65709	+	3.17242i
$441$	−0.399694	+	0.256868i	−0.0190330	+	0.0122318i
$442$	16.8683	−	2.42530i	0.802345	−	0.115360i
$443$	−5.56770	+	8.66351i	−0.264529	+	0.411616i	−0.947955	−	0.318405i	$-0.896853\pi$
$443$	−5.56770	+	8.66351i	−0.264529	+	0.411616i	0.683426	+	0.730020i	$0.260489\pi$
$444$	2.30535	−	5.04800i	0.109407	−	0.239568i
$445$	6.01240	+	3.86862i	0.285015	+	0.183390i
$446$	1.88306	−	13.0970i	0.0891656	−	0.620160i
$447$	−29.6707	+	13.5501i	−1.40338	+	0.640900i
$448$	7.00653	−	23.8621i	0.331027	−	1.12738i
$449$	30.8344	+	9.05378i	1.45516	+	0.427275i	0.911245	−	0.411864i	$-0.135122\pi$
$449$	30.8344	+	9.05378i	1.45516	+	0.427275i	0.543918	+	0.839138i	$0.316940\pi$
$450$	1.71819	−	1.48550i	0.0809961	−	0.0700272i
$451$	1.67802	−	11.6709i	0.0790150	−	0.549561i
$452$	−19.9887	−	17.3203i	−0.940191	−	0.814680i
$453$	−28.3290	−	12.9374i	−1.33101	−	0.607853i
$454$	−31.0512	−	19.9554i	−1.45730	−	0.936553i
$455$	−13.9514	+	4.08814i	−0.654051	+	0.191655i
$456$	24.7411	−	15.9001i	1.15861	−	0.744592i
$457$	−10.1182	+	8.76749i	−0.473310	+	0.410126i	−0.858581	−	0.512678i	$-0.828654\pi$
$457$	−10.1182	+	8.76749i	−0.473310	+	0.410126i	0.385271	+	0.922804i	$0.374108\pi$
$458$	−8.75712	−	29.8240i	−0.409194	−	1.39359i
$459$	10.2953			0.480541
$460$	−47.7923	−	23.5899i	−2.22833	−	1.09989i
$461$	−30.5197			−1.42144			−0.710721	−	0.703474i	$-0.751631\pi$
$461$	−30.5197			−1.42144			−0.710721	+	0.703474i	$0.751631\pi$
$462$	15.7971	+	53.8000i	0.734948	+	2.50300i
$463$	15.8135	−	13.7024i	0.734914	−	0.636807i	−0.204786	−	0.978807i	$-0.565650\pi$
$463$	15.8135	−	13.7024i	0.734914	−	0.636807i	0.939700	+	0.342000i	$0.111104\pi$
$464$	18.7422	−	12.0449i	0.870086	−	0.559170i
$465$	1.78115	+	6.07845i	0.0825990	+	0.281881i
$466$	11.0258	+	7.08586i	0.510761	+	0.328246i
$467$	−29.8259	−	13.6210i	−1.38018	−	0.630307i	−0.419446	−	0.907780i	$-0.637776\pi$
$467$	−29.8259	−	13.6210i	−1.38018	−	0.630307i	−0.960733	+	0.277474i	$0.910503\pi$
$468$	2.04093	+	1.76847i	0.0943419	+	0.0817477i
$469$	1.97246	−	13.7187i	0.0910795	−	0.633472i
$470$	2.00292	−	1.28564i	0.0923877	−	0.0593020i
$471$	−1.93759	−	0.568929i	−0.0892796	−	0.0262148i
$472$	19.8580	−	67.6302i	0.914039	−	3.11293i
$473$	−21.9039	+	10.0032i	−1.00714	+	0.459946i
$474$	5.70572	−	39.6842i	0.262073	−	1.82275i
$475$	−4.38481	+	9.57342i	−0.201189	+	0.439258i
$476$	8.68864	−	19.0255i	0.398243	−	0.872031i
$477$	−0.767215	+	1.19381i	−0.0351284	+	0.0546608i
$478$	−37.1706	+	5.34433i	−1.70014	+	0.244444i
$479$	−27.9627	+	17.9705i	−1.27765	+	0.821093i	−0.990596	−	0.136822i	$-0.956311\pi$
$479$	−27.9627	+	17.9705i	−1.27765	+	0.821093i	−0.287051	+	0.957915i	$0.592675\pi$
$480$	33.2138	−	38.2881i	1.51600	−	1.74760i
$481$	−1.89964	+	0.557786i	−0.0866163	+	0.0254328i
$482$			9.92371i			0.452012i
$483$	−9.06603	−	15.0683i	−0.412519	−	0.685632i
$484$	−112.065			−5.09388
$485$	20.3751	−	9.29142i	0.925186	−	0.421902i
$486$	3.08775	+	3.56345i	0.140063	+	0.161642i
$487$	−11.4573	−	17.8279i	−0.519180	−	0.807860i	0.478345	−	0.878172i	$-0.341237\pi$
$487$	−11.4573	−	17.8279i	−0.519180	−	0.807860i	−0.997525	+	0.0703122i	$0.977600\pi$
$488$	−10.5717	+	1.51998i	−0.478557	+	0.0688060i
$489$	11.6113	+	7.46215i	0.525083	+	0.337450i
$490$	4.60111	−	15.6380i	0.207857	−	0.706453i
$491$	−10.2856	+	11.8702i	−0.464182	+	0.535695i	−0.938784	−	0.344506i	$-0.888047\pi$
$491$	−10.2856	+	11.8702i	−0.464182	+	0.535695i	0.474602	+	0.880200i	$0.342592\pi$
$492$	−17.8359	−	2.56441i	−0.804104	−	0.115613i
$493$	3.84957	−	1.75804i	0.173376	−	0.0791781i
$494$	−16.8465	−	4.94659i	−0.757962	−	0.222558i
$495$	−0.318365	+	2.20564i	−0.0143095	+	0.0991362i
$496$	7.10970	+	15.5681i	0.319235	+	0.699027i
$497$	28.3155	+	4.07116i	1.27012	+	0.182616i
$498$	29.2613	+	25.3551i	1.31123	+	1.13619i
$499$	17.0012	−	37.2275i	0.761080	−	1.66653i	0.0157140	−	0.999877i	$-0.494998\pi$
$499$	17.0012	−	37.2275i	0.761080	−	1.66653i	0.745366	−	0.666656i	$-0.232275\pi$
$500$	−7.99891	+	54.9874i	−0.357722	+	2.45911i
$501$	−2.41574	−	16.8018i	−0.107927	−	0.750651i
$502$	−25.1797	−	39.1803i	−1.12382	−	1.74870i
$503$	19.8964	−	17.2403i	0.887135	−	0.768707i	−0.0866353	−	0.996240i	$-0.527611\pi$
$503$	19.8964	−	17.2403i	0.887135	−	0.768707i	0.973770	+	0.227533i	$0.0730660\pi$
$504$	2.66515	−	0.782559i	0.118715	−	0.0348579i
$505$	5.93927	+	41.4709i	0.264294	+	1.84543i
$506$	70.9450	−	18.5725i	3.15389	−	0.825648i
$507$			5.39201i			0.239468i
$508$	12.1445	+	41.3604i	0.538826	+	1.83507i
$509$	4.83472	+	5.57956i	0.214295	+	0.247310i	0.852712	−	0.522381i	$-0.174956\pi$
$509$	4.83472	+	5.57956i	0.214295	+	0.247310i	−0.638417	+	0.769690i	$0.720411\pi$
$510$	16.2500	−	14.0650i	0.719563	−	0.622810i
$511$	3.02454	+	21.0361i	0.133798	+	0.930583i
$512$	−17.1893	+	26.7471i	−0.759667	+	1.18206i
$513$	−9.64843	−	4.40629i	−0.425989	−	0.194542i
$514$	10.6513	−	12.2923i	0.469809	−	0.542189i
$515$	0.0161356	−	29.2464i	0.000711019	−	1.28875i
$516$	15.2872	+	33.4743i	0.672981	+	1.47362i
$517$	−0.657892	+	2.24057i	−0.0289340	+	0.0985403i
$518$	−0.960060	+	3.26967i	−0.0421826	+	0.143661i
$519$	−8.30590	−	18.1874i	−0.364589	−	0.798338i
$520$	−55.3679	−	0.0305471i	−2.42804	−	0.00133958i
$521$	19.9029	−	22.9691i	0.871960	−	1.00630i	−0.127935	−	0.991783i	$-0.540835\pi$
$521$	19.9029	−	22.9691i	0.871960	−	1.00630i	0.999895	−	0.0145129i	$-0.00461977\pi$
$522$	0.855506	+	0.390696i	0.0374445	+	0.0171003i
$523$	3.16834	−	4.93004i	0.138542	−	0.215576i	−0.765049	−	0.643972i	$-0.777285\pi$
$523$	3.16834	−	4.93004i	0.138542	−	0.215576i	0.903591	+	0.428397i	$0.140921\pi$
$524$	10.9852	+	76.4037i	0.479890	+	3.33771i
$525$	−12.0215	+	13.8427i	−0.524663	+	0.604145i
$526$	35.5268	+	41.0001i	1.54904	+	1.78769i
$527$	0.915922	+	3.11934i	0.0398982	+	0.135881i
$528$			111.007i			4.83097i
$529$	−20.0497	+	11.2698i	−0.871726	+	0.489993i
$530$	−6.90237	−	48.1958i	−0.299820	−	2.09349i
$531$	1.48409	−	0.435769i	0.0644042	−	0.0189108i
$532$	−16.2855	+	14.1115i	−0.706066	+	0.611810i
$533$	3.47555	+	5.40806i	0.150543	+	0.234249i
$534$	2.13957	+	14.8811i	0.0925883	+	0.643966i
$535$	−4.58003	−	2.09469i	−0.198012	−	0.0905611i
$536$	21.9276	−	48.0148i	0.947130	−	2.07392i
$537$	−6.65546	−	5.76699i	−0.287204	−	0.248864i
$538$	−39.0971	−	5.62132i	−1.68560	−	0.242352i
$539$	6.64396	+	14.5483i	0.286176	+	0.626638i
$540$	−55.3991	−	7.99639i	−2.38400	−	0.344110i
$541$	−4.01909	−	1.18011i	−0.172794	−	0.0507369i	0.194191	−	0.980964i	$-0.437792\pi$
$541$	−4.01909	−	1.18011i	−0.172794	−	0.0507369i	−0.366985	+	0.930227i	$0.619610\pi$
$542$	35.6949	−	16.3013i	1.53323	−	0.700201i
$543$	−13.9586	−	2.00694i	−0.599019	−	0.0861259i
$544$	17.0366	−	19.6613i	0.730438	−	0.842970i
$545$	12.9473	+	3.80943i	0.554602	+	0.163178i
$546$	−25.7178	−	16.5278i	−1.10062	−	0.707327i
$547$	−19.7158	+	2.83470i	−0.842986	+	0.121203i	−0.550260	−	0.834993i	$-0.685471\pi$
$547$	−19.7158	+	2.83470i	−0.842986	+	0.121203i	−0.292726	+	0.956196i	$0.594562\pi$
$548$	−28.1757	−	43.8422i	−1.20361	−	1.87285i
$549$	−0.153482	−	0.177127i	−0.00655043	−	0.00755960i
$550$	−41.2652	−	64.3660i	−1.75956	−	2.74457i
$551$	−4.36014			−0.185748
$552$	−16.9613	−	64.7905i	−0.721922	−	2.75767i
$553$			17.5546i			0.746498i
$554$	25.2833	−	7.42385i	1.07419	−	0.315409i
$555$	−1.63610	+	1.88605i	−0.0694485	+	0.0800585i
$556$	−56.6544	+	36.4096i	−2.40268	+	1.54411i
$557$	−44.6156	+	6.41476i	−1.89042	+	0.271802i	−0.987455	−	0.157903i	$-0.949527\pi$
$557$	−44.6156	+	6.41476i	−1.89042	+	0.271802i	−0.902969	+	0.429705i	$0.858617\pi$
$558$	−0.390608	+	0.607798i	−0.0165358	+	0.0257301i
$559$	5.45386	−	11.9423i	0.230674	−	0.505105i
$560$	−26.8058	+	41.6601i	−1.13275	+	1.76046i
$561$	−3.00092	+	20.8718i	−0.126699	+	0.881209i
$562$	61.4209	−	28.0500i	2.59088	−	1.18322i
$563$	−5.30049	+	18.0518i	−0.223389	+	0.760794i	0.769172	+	0.639042i	$0.220669\pi$
$563$	−5.30049	+	18.0518i	−0.223389	+	0.760794i	−0.992561	+	0.121751i	$0.961149\pi$
$564$	3.42412	+	1.00541i	0.144182	+	0.0423355i
$565$	6.42795	+	10.0142i	0.270426	+	0.421302i
$566$	−2.62954	+	18.2889i	−0.110528	+	0.768739i
$567$	−14.7607	−	12.7902i	−0.619889	−	0.537137i
$568$	99.1028	+	45.2587i	4.15826	+	1.89901i
$569$	9.05830	+	5.82142i	0.379744	+	0.244047i	0.716562	−	0.697523i	$-0.245715\pi$
$569$	9.05830	+	5.82142i	0.379744	+	0.244047i	−0.336818	+	0.941570i	$0.609351\pi$
$570$	−21.2488	+	6.22648i	−0.890014	+	0.260799i
$571$	−12.9103	+	8.29697i	−0.540281	+	0.347217i	−0.782149	−	0.623092i	$-0.785876\pi$
$571$	−12.9103	+	8.29697i	−0.540281	+	0.347217i	0.241868	+	0.970309i	$0.422240\pi$
$572$	68.7024	−	59.5310i	2.87259	−	2.48911i
$573$	6.76953	+	23.0549i	0.282801	+	0.963133i
$574$	11.0648			0.461838
$575$	17.6323	+	16.2512i	0.735318	+	0.677722i
$576$	2.07845			0.0866021
$577$	−4.37078	−	14.8855i	−0.181958	−	0.619692i	−0.999066	−	0.0432076i	$-0.986242\pi$
$577$	−4.37078	−	14.8855i	−0.181958	−	0.619692i	0.817108	−	0.576484i	$-0.195576\pi$
$578$	−25.5824	+	22.1673i	−1.06409	+	0.922038i
$579$	8.27983	−	5.32112i	0.344098	−	0.221138i
$580$	−22.0801	+	6.47009i	−0.916828	+	0.268656i
$581$	−14.2618	−	9.16549i	−0.591678	−	0.380249i
$582$	42.8344	+	19.5618i	1.77554	+	0.810864i
$583$	36.1019	+	31.2825i	1.49519	+	1.29559i
$584$	−11.5189	+	80.1158i	−0.476656	+	3.31522i
$585$	−0.656319	−	1.02249i	−0.0271354	−	0.0422748i
$586$	−26.3364	−	7.73308i	−1.08795	−	0.319450i
$587$	12.5744	−	42.8243i	0.518999	−	1.76755i	−0.114091	−	0.993470i	$-0.536396\pi$
$587$	12.5744	−	42.8243i	0.518999	−	1.76755i	0.633090	−	0.774078i	$-0.281786\pi$
$588$	22.2332	−	10.1535i	0.916880	−	0.418725i
$589$	0.476678	−	3.31537i	0.0196412	−	0.136607i
$590$	−28.7151	+	44.6274i	−1.18218	+	1.83728i
$591$	−14.3859	+	31.5007i	−0.591756	+	1.29576i
$592$	−3.64738	+	5.67543i	−0.149906	+	0.233259i
$593$	−8.66953	+	1.24649i	−0.356015	+	0.0511872i	−0.318002	−	0.948090i	$-0.603012\pi$
$593$	−8.66953	+	1.24649i	−0.356015	+	0.0511872i	−0.0380129	+	0.999277i	$0.512103\pi$
$594$	64.7917	−	41.6391i	2.65844	−	1.70847i
$595$	−6.16630	+	7.10836i	−0.252794	+	0.291414i
$596$	87.3349	−	25.6438i	3.57738	−	1.05041i
$597$		−	19.0430i		−	0.779376i
$598$	−22.6014	+	32.9828i	−0.924242	+	1.34877i
$599$	26.2217			1.07139			0.535694	−	0.844412i	$-0.320050\pi$
$599$	26.2217			1.07139			0.535694	+	0.844412i	$0.320050\pi$
$600$	−58.7822	+	37.6855i	−2.39977	+	1.53850i
$601$	−12.2537	−	14.1415i	−0.499838	−	0.576843i	0.448630	−	0.893718i	$-0.351912\pi$
$601$	−12.2537	−	14.1415i	−0.499838	−	0.576843i	−0.948468	+	0.316874i	$0.897367\pi$
$602$	−12.2169	−	19.0099i	−0.497925	−	0.774786i
$603$	1.14654	−	0.164847i	0.0466905	−	0.00671309i
$604$	73.1100	+	46.9849i	2.97480	+	1.91179i
$605$	48.3696	+	14.2316i	1.96650	+	0.578596i
$606$	−57.6904	+	66.5783i	−2.34351	+	2.70456i
$607$	3.44867	+	0.495843i	0.139977	+	0.0201257i	0.211947	−	0.977281i	$-0.432020\pi$
$607$	3.44867	+	0.495843i	0.139977	+	0.0201257i	−0.0719701	+	0.997407i	$0.522929\pi$
$608$	−24.3811	+	11.1345i	−0.988784	+	0.451563i
$609$	−7.28417	−	2.13883i	−0.295170	−	0.0866696i
$610$	7.95864	+	1.14876i	0.322236	+	0.0465120i
$611$	−0.528891	−	1.15811i	−0.0213966	−	0.0468521i
$612$	1.73022	+	0.248767i	0.0699398	+	0.0100558i
$613$	12.2285	+	10.5961i	0.493905	+	0.427971i	0.865865	−	0.500278i	$-0.166769\pi$
$613$	12.2285	+	10.5961i	0.493905	+	0.427971i	−0.371960	+	0.928249i	$0.621314\pi$
$614$	−2.86801	+	6.28006i	−0.115743	+	0.253443i
$615$	7.37265	+	3.37190i	0.297294	+	0.135968i
$616$	−13.3068	−	92.5510i	−0.536147	−	3.72899i
$617$	18.1414	+	28.2285i	0.730344	+	1.13644i	0.985523	+	0.169544i	$0.0542295\pi$
$617$	18.1414	+	28.2285i	0.730344	+	1.13644i	−0.255178	+	0.966894i	$0.582134\pi$
$618$	46.4785	−	40.2739i	1.86964	−	1.62005i
$619$	7.07680	−	2.07794i	0.284441	−	0.0835193i	−0.136400	−	0.990654i	$-0.543553\pi$
$619$	7.07680	−	2.07794i	0.284441	−	0.0835193i	0.420841	+	0.907135i	$0.361735\pi$
$620$	−2.50579	−	17.4967i	−0.100635	−	0.702685i
$621$	−16.3507	+	17.7796i	−0.656130	+	0.713469i
$622$			70.6865i			2.83427i
$623$	−1.85458	−	6.31611i	−0.0743020	−	0.253049i
$624$	−39.6339	−	45.7400i	−1.58663	−	1.83106i
$625$	10.4355	−	22.7178i	0.417421	−	0.908713i
$626$	−6.25270	−	43.4885i	−0.249908	−	1.73815i
$627$	11.7454	−	18.2761i	0.469064	−	0.729878i
$628$	5.12591	+	2.34092i	0.204546	+	0.0934130i
$629$	−0.839215	+	0.968506i	−0.0334617	+	0.0386169i
$630$	−2.09127	−	0.00115378i	−0.0833182	−	4.59677e-5i
$631$	7.29135	+	15.9658i	0.290264	+	0.635590i	0.997445	−	0.0714433i	$-0.0227605\pi$
$631$	7.29135	+	15.9658i	0.290264	+	0.635590i	−0.707181	+	0.707033i	$0.750033\pi$
$632$	−18.8357	+	64.1484i	−0.749243	+	2.55169i
$633$	6.31134	−	21.4944i	0.250853	−	0.854328i
$634$	28.7517	+	62.9574i	1.14187	+	2.50036i
$635$	0.0107000	−	19.3942i	0.000424618	−	0.769637i
$636$	47.8070	−	55.1723i	1.89567	−	2.18772i
$637$	−7.93191	−	3.62238i	−0.314274	−	0.143524i
$638$	17.1163	−	26.6335i	0.677642	−	1.05443i
$639$	0.340245	+	2.36645i	0.0134599	+	0.0936155i
$640$	−10.8815	+	9.41840i	−0.430131	+	0.372295i
$641$	−21.4742	−	24.7826i	−0.848181	−	0.978853i	0.151773	−	0.988415i	$-0.451502\pi$
$641$	−21.4742	−	24.7826i	−0.848181	−	0.978853i	−0.999954	+	0.00956193i	$0.996956\pi$
$642$	−2.98367	−	10.1615i	−0.117756	−	0.401041i
$643$		−	17.2988i		−	0.682198i	−0.940027	−	0.341099i	$-0.889201\pi$
$643$		−	17.2988i		−	0.682198i	0.940027	−	0.341099i	$-0.110799\pi$
$644$	19.0573	+	45.2208i	0.750962	+	1.78195i
$645$	−2.34723	−	16.3895i	−0.0924221	−	0.645337i
$646$	−10.9045	+	3.20184i	−0.429031	+	0.125975i
$647$	−27.7286	+	24.0270i	−1.09012	+	0.944599i	−0.998688	−	0.0512122i	$-0.983692\pi$
$647$	−27.7286	+	24.0270i	−1.09012	+	0.944599i	−0.0914371	+	0.995811i	$0.529146\pi$
$648$	−40.2151	−	62.5760i	−1.57980	−	2.45822i
$649$	−7.40993	−	51.5372i	−0.290865	−	2.02301i
$650$	39.9843	+	11.7884i	1.56831	+	0.462379i
$651$	2.42268	−	5.30493i	0.0949523	−	0.207916i
$652$	−29.1083	−	25.2225i	−1.13997	−	0.987790i
$653$	31.5106	+	4.53054i	1.23311	+	0.177294i	0.727887	−	0.685697i	$-0.240503\pi$
$653$	31.5106	+	4.53054i	1.23311	+	0.177294i	0.505219	+	0.862991i	$0.331412\pi$
$654$	11.7894	+	25.8152i	0.461003	+	1.00945i
$655$	4.96136	−	34.3724i	0.193856	−	1.34304i
$656$	21.0183	+	6.17153i	0.820627	+	0.240958i
$657$	−1.61565	+	0.737844i	−0.0630326	+	0.0287860i
$658$	−2.16906	−	0.311864i	−0.0845588	−	0.0121577i
$659$	20.1626	−	23.2689i	0.785424	−	0.906428i	−0.212064	−	0.977256i	$-0.568019\pi$
$659$	20.1626	−	23.2689i	0.785424	−	0.906428i	0.997489	+	0.0708277i	$0.0225640\pi$
$660$	32.3593	−	109.981i	1.25959	−	4.28101i
$661$	−28.3663	−	18.2299i	−1.10332	−	0.709061i	−0.143493	−	0.989651i	$-0.545834\pi$
$661$	−28.3663	−	18.2299i	−1.10332	−	0.709061i	−0.959828	+	0.280590i	$0.909470\pi$
$662$	−18.4412	+	2.65144i	−0.716737	+	0.103051i
$663$	−6.21554	−	9.67157i	−0.241392	−	0.375613i
$664$	−42.2813	−	48.7952i	−1.64083	−	1.89362i
$665$	8.82121	−	4.02263i	0.342072	−	0.155991i
$666$	−0.284797			−0.0110357
$667$	−3.07771	+	9.44015i	−0.119169	+	0.365524i
$668$			47.3679i			1.83272i
$669$	−8.56468	+	2.51482i	−0.331130	+	0.0972285i
$670$	−26.0415	+	30.0200i	−1.00607	+	1.15977i
$671$	−6.63710	+	4.26541i	−0.256223	+	0.164664i
$672$	−46.1937	+	6.64165i	−1.78196	+	0.256207i
$673$	1.52933	−	2.37968i	0.0589511	−	0.0917298i	−0.810527	−	0.585702i	$-0.800819\pi$
$673$	1.52933	−	2.37968i	0.0589511	−	0.0917298i	0.869478	+	0.493972i	$0.164455\pi$
$674$	−17.9250	+	39.2502i	−0.690444	+	1.51186i
$675$	22.8959	+	10.4867i	0.881262	+	0.403635i
$676$	2.14134	−	14.8933i	0.0823592	−	0.572821i
$677$	1.60190	−	0.731565i	0.0615662	−	0.0281163i	−0.384394	−	0.923169i	$-0.625590\pi$
$677$	1.60190	−	0.731565i	0.0615662	−	0.0281163i	0.445960	+	0.895053i	$0.352862\pi$
$678$	−7.04979	+	24.0094i	−0.270745	+	0.922074i
$679$	−19.7833	−	5.80891i	−0.759215	−	0.222926i
$680$	−30.1601	+	19.3592i	−1.15659	+	0.742392i
$681$	−3.54370	+	24.6470i	−0.135795	+	0.944473i
$682$	18.3804	+	15.9267i	0.703821	+	0.609865i
$683$	−11.7951	−	5.38662i	−0.451326	−	0.206113i	0.176766	−	0.984253i	$-0.443436\pi$
$683$	−11.7951	−	5.38662i	−0.451326	−	0.206113i	−0.628092	+	0.778139i	$0.716164\pi$
$684$	−1.51504	−	0.973657i	−0.0579290	−	0.0372287i
$685$	6.59349	+	22.5013i	0.251924	+	0.859730i
$686$	−44.6341	+	28.6846i	−1.70414	+	1.09518i
$687$	−15.8474	+	13.7318i	−0.604615	+	0.523902i
$688$	−12.6038	−	42.9245i	−0.480515	−	1.63648i
$689$	−26.0447			−0.992224
$690$	−1.51803	+	50.4010i	−0.0577904	+	1.91873i
$691$	−9.31109			−0.354210			−0.177105	−	0.984192i	$-0.556673\pi$
$691$	−9.31109			−0.354210			−0.177105	+	0.984192i	$0.556673\pi$
$692$	15.7190	+	53.5341i	0.597548	+	2.03506i
$693$	1.55068	−	1.34367i	0.0589056	−	0.0510420i
$694$	46.4471	−	29.8498i	1.76311	−	1.13308i
$695$	29.0769	−	8.52034i	1.10295	−	0.323195i
$696$	−24.3231	−	15.6315i	−0.921963	−	0.592510i
$697$	3.78507	+	1.72858i	0.143370	+	0.0654748i
$698$	−49.5292	−	42.9173i	−1.87471	−	1.62444i
$699$	1.25831	−	8.75176i	0.0475938	−	0.331022i
$700$	38.7022	−	33.4610i	1.46281	−	1.26471i
$701$	24.1132	+	7.08026i	0.910742	+	0.267418i	0.703353	−	0.710841i	$-0.251685\pi$
$701$	24.1132	+	7.08026i	0.910742	+	0.267418i	0.207389	+	0.978259i	$0.433504\pi$
$702$	−11.8303	+	40.2903i	−0.446506	+	1.52066i
$703$	1.20100	−	0.548479i	0.0452967	−	0.0206863i
$704$	9.95713	−	69.2534i	0.375274	−	2.61009i
$705$	−1.35024	−	0.868798i	−0.0508529	−	0.0327208i
$706$	13.5487	−	29.6675i	0.509911	−	1.11655i
$707$	20.8542	−	32.4498i	0.784304	−	1.22040i
$708$	−78.7610	+	11.3241i	−2.96002	+	0.425586i
$709$	24.3663	−	15.6593i	0.915095	−	0.588096i	0.00386426	−	0.999993i	$-0.498770\pi$
$709$	24.3663	−	15.6593i	0.915095	−	0.588096i	0.911230	+	0.411897i	$0.135134\pi$
$710$	−61.9613	−	53.7497i	−2.32537	−	2.01719i
$711$	−1.40769	+	0.413335i	−0.0527925	+	0.0155013i
$712$		−	25.0703i		−	0.939551i
$713$	−6.84165	−	3.37230i	−0.256222	−	0.126293i
$714$	−19.7880			−0.740546
$715$	−37.2133	+	16.9700i	−1.39170	+	0.634640i
$716$	16.0929	+	18.5721i	0.601418	+	0.694074i
$717$	13.6964	+	21.3120i	0.511502	+	0.795912i
$718$	−30.2663	+	4.35164i	−1.12953	+	0.162402i
$719$	−24.1127	−	15.4963i	−0.899253	−	0.577915i	0.00731583	−	0.999973i	$-0.497671\pi$
$719$	−24.1127	−	15.4963i	−0.899253	−	0.577915i	−0.906569	+	0.422059i	$0.861308\pi$
$720$	−3.97185	−	1.16862i	−0.148022	−	0.0435519i
$721$	−17.6341	+	20.3509i	−0.656730	+	0.757907i
$722$	−38.0611	−	5.47236i	−1.41649	−	0.203660i
$723$	6.08968	−	2.78107i	0.226478	−	0.103429i
$724$	37.7580	+	11.0868i	1.40327	+	0.412036i
$725$	10.3519	+	0.0114225i	0.384459	+	0.000424222i
$726$	44.0438	+	96.4425i	1.63462	+	3.57932i
$727$	26.1416	+	3.75859i	0.969538	+	0.139398i	0.608848	−	0.793287i	$-0.291632\pi$
$727$	26.1416	+	3.75859i	0.969538	+	0.139398i	0.360690	+	0.932686i	$0.382541\pi$
$728$	38.5273	+	33.3841i	1.42792	+	1.23730i
$729$	−10.5012	+	22.9945i	−0.388934	+	0.851647i
$730$	25.3453	−	55.4176i	0.938073	−	2.05110i
$731$	−1.20939	−	8.41149i	−0.0447309	−	0.311110i
$732$	6.51855	+	10.1431i	0.240932	+	0.374898i
$733$	40.2210	−	34.8517i	1.48560	−	1.28728i	0.622080	−	0.782954i	$-0.286288\pi$
$733$	40.2210	−	34.8517i	1.48560	−	1.28728i	0.863516	−	0.504322i	$-0.168257\pi$
$734$	−21.1385	+	6.20684i	−0.780238	+	0.229099i
$735$	−10.8857	+	1.55900i	−0.401525	+	0.0575045i
$736$	6.89728	+	60.6472i	0.254237	+	2.23548i
$737$		−	38.9920i		−	1.43629i
$738$	0.260529	+	0.887281i	0.00959021	+	0.0326612i
$739$	16.3546	+	18.8742i	0.601614	+	0.694300i	0.972108	−	0.234535i	$-0.0753569\pi$
$739$	16.3546	+	18.8742i	0.601614	+	0.694300i	−0.370493	+	0.928835i	$0.620811\pi$
$740$	5.26809	−	4.55974i	0.193659	−	0.167619i
$741$	1.68568	+	11.7241i	0.0619249	+	0.430697i
$742$	−24.2359	+	37.7118i	−0.889728	+	1.38444i
$743$	−28.6938	−	13.1040i	−1.05267	−	0.480741i	−0.187528	−	0.982259i	$-0.560048\pi$
$743$	−28.6938	−	13.1040i	−1.05267	−	0.480741i	−0.865147	+	0.501519i	$0.832775\pi$
$744$	14.5451	−	16.7859i	0.533248	−	0.615400i
$745$	−40.9521	−	0.0225937i	−1.50037	−	0.000827771i
$746$	−30.1333	−	65.9827i	−1.10326	−	2.41580i
$747$	0.399170	−	1.35945i	0.0146049	−	0.0497396i
$748$	16.5777	−	56.4585i	0.606142	−	2.06433i
$749$	1.92631	+	4.21804i	0.0703860	+	0.154124i
$750$	50.4655	−	14.7273i	1.84274	−	0.537765i
$751$	−0.178172	+	0.205622i	−0.00650159	+	0.00750324i	−0.758991	−	0.651101i	$-0.774307\pi$
$751$	−0.178172	+	0.205622i	−0.00650159	+	0.00750324i	0.752489	+	0.658604i	$0.228853\pi$
$752$	−3.94631	−	1.80222i	−0.143907	−	0.0657202i
$753$	−16.9865	+	26.4316i	−0.619024	+	0.963220i
$754$	2.45651	+	17.0854i	0.0894608	+	0.622213i
$755$	−25.5889	−	29.5641i	−0.931276	−	1.07595i
$756$	33.7491	+	38.9486i	1.22744	+	1.41655i
$757$	0.581408	+	1.98009i	0.0211316	+	0.0719678i	0.969384	−	0.245550i	$-0.0789687\pi$
$757$	0.581408	+	1.98009i	0.0211316	+	0.0719678i	−0.948252	+	0.317518i	$0.897151\pi$
$758$			26.1062i			0.948219i
$759$	−31.2790	−	38.3306i	−1.13535	−	1.39131i
$760$	36.5508	−	5.23463i	1.32584	−	0.189880i
$761$	39.8954	−	11.7143i	1.44621	−	0.424644i	0.537921	−	0.842996i	$-0.319210\pi$
$761$	39.8954	−	11.7143i	1.44621	−	0.424644i	0.908285	+	0.418351i	$0.137392\pi$
$762$	30.8214	−	26.7069i	1.11654	−	0.967489i
$763$	−6.71815	−	10.4536i	−0.243213	−	0.378447i
$764$	−9.54237	−	66.3686i	−0.345231	−	2.40113i
$765$	−0.715203	−	0.327099i	−0.0258582	−	0.0118263i
$766$	−12.3360	+	27.0122i	−0.445719	+	0.975989i
$767$	21.4540	+	18.5900i	0.774660	+	0.671246i
$768$	12.6352	+	1.81667i	0.455934	+	0.0655535i
$769$	18.8182	+	41.2062i	0.678602	+	1.48593i	0.864117	+	0.503290i	$0.167877\pi$
$769$	18.8182	+	41.2062i	0.678602	+	1.48593i	−0.185515	+	0.982641i	$0.559395\pi$
$770$	−10.0570	+	69.6750i	−0.362429	+	2.51091i
$771$	−10.5281	−	3.09134i	−0.379161	−	0.111332i
$772$	−24.9830	+	11.4093i	−0.899157	+	0.410631i
$773$	−11.6427	−	1.67397i	−0.418759	−	0.0602085i	−0.0702852	−	0.997527i	$-0.522391\pi$
$773$	−11.6427	−	1.67397i	−0.418759	−	0.0602085i	−0.348474	+	0.937318i	$0.613300\pi$
$774$	1.23673	−	1.42727i	0.0444534	−	0.0513020i
$775$	−1.14042	+	7.87014i	−0.0409651	+	0.282704i
$776$	−66.0598	−	42.4541i	−2.37141	−	1.52401i
$777$	2.27548	−	0.327165i	0.0816325	−	0.0117370i
$778$	11.6295	+	18.0958i	0.416937	+	0.648767i
$779$	−2.80744	−	3.23996i	−0.100587	−	0.116084i
$780$	25.9341	+	56.8708i	0.928589	+	2.03630i
$781$	80.4796			2.87979
$782$	−0.764877	+	25.8694i	−0.0273520	+	0.925089i
$783$			10.4277i			0.372657i
$784$	−28.5099	+	8.37126i	−1.01821	+	0.298973i
$785$	−1.91516	−	1.66135i	−0.0683550	−	0.0592960i
$786$	61.4350	−	39.4819i	2.19132	−	1.40827i
$787$	35.1816	−	5.05835i	1.25409	−	0.180311i	0.516928	−	0.856029i	$-0.327075\pi$
$787$	35.1816	−	5.05835i	1.25409	−	0.180311i	0.737160	+	0.675718i	$0.236166\pi$
$788$	52.2453	−	81.2953i	1.86116	−	2.89602i
$789$	15.2035	−	33.2911i	0.541260	−	1.18519i
$790$	27.2368	−	42.3299i	0.969042	−	1.50603i
$791$	1.55927	−	10.8449i	0.0554411	−	0.385601i
$792$	7.10827	−	3.24624i	0.252581	−	0.115350i
$793$	1.21187	−	4.12724i	0.0430347	−	0.146563i
$794$	−34.0176	−	9.98846i	−1.20724	−	0.354477i
$795$	−27.6410	+	17.7422i	−0.980325	+	0.629252i
$796$	−7.56256	+	52.5988i	−0.268048	+	1.86431i
$797$	4.42871	+	3.83750i	0.156873	+	0.135931i	0.729761	−	0.683703i	$-0.239631\pi$
$797$	4.42871	+	3.83750i	0.156873	+	0.135931i	−0.572888	+	0.819634i	$0.694177\pi$
$798$	18.5447	+	8.46910i	0.656477	+	0.299803i
$799$	−0.693274	−	0.445540i	−0.0245263	−	0.0157621i
$800$	57.9150	−	26.3717i	2.04761	−	0.932381i
$801$	0.462816	−	0.297434i	0.0163528	−	0.0105093i
$802$	28.2848	−	24.5090i	0.998772	−	0.865441i
$803$	16.8447	+	57.3678i	0.594437	+	2.02447i
$804$	−59.5889			−2.10154
$805$	−2.48274	−	21.9383i	−0.0875051	−	0.773224i
$806$	−13.2600			−0.467064
$807$	7.50723	+	25.5673i	0.264267	+	0.900011i
$808$	111.024	−	96.2027i	3.90580	−	3.38440i
$809$	31.2095	−	20.0571i	1.09727	−	0.705171i	0.138785	−	0.990323i	$-0.455680\pi$
$809$	31.2095	−	20.0571i	1.09727	−	0.705171i	0.958482	+	0.285152i	$0.0920441\pi$
$810$	15.7482	+	53.7431i	0.553336	+	1.88834i
$811$	−8.22031	−	5.28287i	−0.288654	−	0.185507i	0.388298	−	0.921534i	$-0.373063\pi$
$811$	−8.22031	−	5.28287i	−0.288654	−	0.185507i	−0.676952	+	0.736027i	$0.736700\pi$
$812$	19.2703	+	8.80045i	0.676255	+	0.308835i
$813$	−20.0066	−	17.3358i	−0.701662	−	0.607994i
$814$	−1.36436	+	9.48935i	−0.0478209	+	0.332602i
$815$	9.36063	+	14.5831i	0.327889	+	0.510824i
$816$	−37.5884	−	11.0370i	−1.31586	−	0.386371i
$817$	−2.46665	+	8.40062i	−0.0862970	+	0.293901i
$818$	44.1593	−	20.1669i	1.54399	−	0.705118i
$819$	−0.159207	+	1.10731i	−0.00556314	+	0.0386925i
$820$	−19.0250	−	12.2415i	−0.664382	−	0.427490i
$821$	1.01096	−	2.21369i	0.0352827	−	0.0772583i	−0.891170	−	0.453669i	$-0.850115\pi$
$821$	1.01096	−	2.21369i	0.0352827	−	0.0772583i	0.926453	+	0.376411i	$0.122842\pi$
$822$	−26.6567	+	41.4786i	−0.929759	+	1.44673i
$823$	41.8903	−	6.02292i	1.46020	−	0.209946i	0.634007	−	0.773327i	$-0.281409\pi$
$823$	41.8903	−	6.02292i	1.46020	−	0.209946i	0.826197	+	0.563381i	$0.190500\pi$
$824$	−86.2750	+	55.4456i	−3.00553	+	1.93154i
$825$	−27.9338	+	43.3606i	−0.972531	+	1.50962i
$826$	46.8817	−	13.7657i	1.63122	−	0.478971i
$827$			31.4841i			1.09481i	0.836867	+	0.547406i	$0.184384\pi$
$827$			31.4841i			1.09481i	−0.836867	+	0.547406i	$0.815616\pi$
$828$	−3.17750	+	2.59294i	−0.110426	+	0.0901108i
$829$	−39.5914			−1.37507			−0.687534	−	0.726152i	$-0.741307\pi$
$829$	−39.5914			−1.37507			−0.687534	+	0.726152i	$0.741307\pi$
$830$	20.1691	+	44.2288i	0.700081	+	1.53520i
$831$	−11.6412	−	13.4346i	−0.403827	−	0.466042i
$832$	20.6234	+	32.0906i	0.714987	+	1.11254i
$833$	−5.58679	+	0.803260i	−0.193571	+	0.0278313i
$834$	53.6001	+	34.4467i	1.85602	+	1.19279i
$835$	6.01542	−	20.4449i	0.208172	−	0.707526i
$836$	−39.7000	+	45.8162i	−1.37305	+	1.58459i
$837$	−7.92907	−	1.14003i	−0.274069	−	0.0394051i
$838$	−71.6364	+	32.7153i	−2.47464	+	1.13013i
$839$	−7.51083	−	2.20538i	−0.259303	−	0.0761382i	0.149497	−	0.988762i	$-0.452234\pi$
$839$	−7.51083	−	2.20538i	−0.259303	−	0.0761382i	−0.408800	+	0.912624i	$0.634053\pi$
$840$	63.6307	+	9.18455i	2.19547	+	0.316897i
$841$	−10.2664	−	22.4802i	−0.354013	−	0.775180i
$842$	−88.1039	−	12.6674i	−3.03626	−	0.436548i
$843$	−34.4257	−	29.8301i	−1.18569	−	1.02740i
$844$	−25.9687	+	56.8636i	−0.893881	+	1.95733i
$845$	−2.81560	+	6.15632i	−0.0968597	+	0.211784i
$846$	−0.0260639	−	0.181278i	−0.000896095	−	0.00623248i
$847$	−25.0982	−	39.0536i	−0.862384	−	1.34190i
$848$	−67.0717	+	58.1179i	−2.30325	+	1.99578i
$849$	11.9599	−	3.51174i	0.410462	−	0.120523i
$850$	25.8979	−	7.57328i	0.888291	−	0.259762i
$851$	−0.339757	−	2.98745i	−0.0116467	−	0.102409i
$852$		−	122.992i		−	4.21363i
$853$	4.71569	+	16.0602i	0.161462	+	0.549890i	0.999987	+	0.00502706i	$0.00160017\pi$
$853$	4.71569	+	16.0602i	0.161462	+	0.549890i	−0.838525	+	0.544863i	$0.816582\pi$
$854$	−4.84840	−	5.59535i	−0.165909	−	0.191469i
$855$	0.530273	+	0.612650i	0.0181349	+	0.0209522i
$856$	2.51332	+	17.4805i	0.0859036	+	0.597472i
$857$	21.8585	−	34.0126i	0.746673	−	1.16185i	−0.235133	−	0.971963i	$-0.575553\pi$
$857$	21.8585	−	34.0126i	0.746673	−	1.16185i	0.981807	−	0.189883i	$-0.0608110\pi$
$858$	−78.2332	−	35.7279i	−2.67084	−	1.21973i
$859$	−23.0015	+	26.5451i	−0.784800	+	0.905708i	−0.997446	−	0.0714213i	$-0.977247\pi$
$859$	−23.0015	+	26.5451i	−0.784800	+	0.905708i	0.212646	+	0.977129i	$0.431792\pi$
$860$	−0.0254901	+	46.2019i	−0.000869206	+	1.57547i
$861$	−3.10086	−	6.78994i	−0.105677	−	0.231401i
$862$	15.1183	−	51.4881i	0.514930	−	1.75369i
$863$	−7.14758	+	24.3424i	−0.243307	+	0.828626i	0.743778	+	0.668427i	$0.233032\pi$
$863$	−7.14758	+	24.3424i	−0.243307	+	0.828626i	−0.987085	+	0.160199i	$0.948786\pi$
$864$	26.6293	+	58.3100i	0.905947	+	1.98375i
$865$	0.0138494	−	25.1026i	0.000470894	−	0.853514i
$866$	−62.6397	+	72.2900i	−2.12858	+	2.45652i
$867$	20.7723	+	9.48639i	0.705464	+	0.322175i
$868$	−8.79846	+	13.6907i	−0.298639	+	0.464692i
$869$	7.02845	+	48.8840i	0.238424	+	1.65827i
$870$	14.2460	+	16.4591i	0.482986	+	0.558017i
$871$	13.9217	+	16.0664i	0.471717	+	0.544391i
$872$	−13.3331	−	45.4083i	−0.451515	−	1.53772i
$873$		−	1.72318i		−	0.0583209i
$874$	11.7887	−	23.9167i	0.398760	−	0.808996i
$875$	−20.9540	+	9.52747i	−0.708373	+	0.322087i
$876$	87.6716	−	25.7427i	2.96215	−	0.869765i
$877$	−19.5255	+	16.9189i	−0.659329	+	0.571312i	−0.918938	−	0.394402i	$-0.870952\pi$
$877$	−19.5255	+	16.9189i	−0.659329	+	0.571312i	0.259609	+	0.965714i	$0.416406\pi$
$878$	3.41275	+	5.31034i	0.115175	+	0.179215i
$879$	2.63524	+	18.3285i	0.0888845	+	0.618205i
$880$	−57.9658	+	126.742i	−1.95403	+	4.27248i
$881$	1.31705	−	2.88393i	0.0443725	−	0.0971622i	−0.886148	−	0.463403i	$-0.846628\pi$
$881$	1.31705	−	2.88393i	0.0443725	−	0.0971622i	0.930520	+	0.366241i	$0.119355\pi$
$882$	−0.947970	−	0.821421i	−0.0319198	−	0.0276587i
$883$	−3.20194	−	0.460370i	−0.107754	−	0.0154927i	0.0882269	−	0.996100i	$-0.471880\pi$
$883$	−3.20194	−	0.460370i	−0.107754	−	0.0154927i	−0.195981	+	0.980608i	$0.562789\pi$
$884$	13.3271	+	29.1823i	0.448240	+	0.981509i
$885$	35.4329	+	5.11443i	1.19106	+	0.171920i
$886$	−26.0870	−	7.65984i	−0.876411	−	0.257337i
$887$	−23.3433	+	10.6605i	−0.783792	+	0.357946i	−0.766781	−	0.641909i	$-0.778143\pi$
$887$	−23.3433	+	10.6605i	−0.783792	+	0.357946i	−0.0170118	+	0.999855i	$0.505415\pi$
$888$	8.66615	+	1.24600i	0.290817	+	0.0418132i
$889$	−11.6938	+	13.4953i	−0.392196	+	0.452619i
$890$	−5.32774	+	18.1077i	−0.178586	+	0.606970i
$891$	−46.2246	−	29.7067i	−1.54858	−	0.995213i
$892$	24.6553	−	3.54490i	0.825521	−	0.118692i
$893$	0.459029	+	0.714264i	0.0153608	+	0.0239019i
$894$	−56.3932	−	65.0812i	−1.88607	−	2.17664i
$895$	−4.58745	−	10.0598i	−0.153341	−	0.336262i
$896$	13.2507			0.442674
$897$	26.5739	+	4.62611i	0.887275	+	0.154461i
$898$			84.8416i			2.83120i
$899$	−3.15948	+	0.927708i	−0.105375	+	0.0309408i
$900$	3.59447	+	2.31564i	0.119816	+	0.0771879i
$901$	−14.1821	+	9.11428i	−0.472474	+	0.303641i
$902$	30.8120	−	4.43010i	1.02593	−	0.147506i
$903$	−8.24170	+	12.8243i	−0.274267	+	0.426767i
$904$	17.3342	−	37.9567i	0.576528	−	1.26242i
$905$	−14.8892	−	9.58030i	−0.494933	−	0.318460i
$906$	11.7012	−	81.3839i	0.388748	−	2.70380i
$907$	13.2479	−	6.05013i	0.439890	−	0.200891i	−0.183143	−	0.983086i	$-0.558627\pi$
$907$	13.2479	−	6.05013i	0.439890	−	0.200891i	0.623034	+	0.782195i	$0.285900\pi$
$908$	19.5762	−	66.6703i	0.649658	−	2.21253i
$909$	3.09315	+	0.908231i	0.102593	+	0.0301241i
$910$	−20.7328	−	32.3000i	−0.687284	−	1.07073i
$911$	−5.66346	+	39.3902i	−0.187639	+	1.30506i	0.650461	+	0.759539i	$0.274576\pi$
$911$	−5.66346	+	39.3902i	−0.187639	+	1.30506i	−0.838100	+	0.545516i	$0.816334\pi$
$912$	30.5031	+	26.4311i	1.01006	+	0.875220i
$913$	−43.3841	−	19.8129i	−1.43580	−	0.655710i
$914$	−29.7351	−	19.1096i	−0.983549	−	0.632089i
$915$	−1.52543	−	5.20576i	−0.0504291	−	0.172097i
$916$	49.2256	−	31.6353i	1.62646	−	1.04526i
$917$	−24.1656	+	20.9396i	−0.798019	+	0.691487i
$918$	7.65756	+	26.0792i	0.252737	+	0.860743i
$919$	14.0233			0.462587			0.231293	−	0.972884i	$-0.425704\pi$
$919$	14.0233			0.462587			0.231293	+	0.972884i	$0.425704\pi$
$920$	14.4668	−	82.8313i	0.476956	−	2.73087i
$921$	4.65750			0.153470
$922$	−22.7004	−	77.3103i	−0.747596	−	2.54608i
$923$	−33.1612	+	28.7343i	−1.09151	+	0.945802i
$924$	−88.7988	+	57.0675i	−2.92126	+	1.87738i
$925$	−2.85287	+	1.29906i	−0.0938018	+	0.0427128i
$926$	46.4721	+	29.8658i	1.52717	+	0.981450i
$927$	−2.04713	−	0.934892i	−0.0672365	−	0.0307059i
$928$	19.9143	+	17.2558i	0.653718	+	0.566450i
$929$	6.86381	−	47.7389i	0.225194	−	1.56626i	−0.492756	−	0.870167i	$-0.664011\pi$
$929$	6.86381	−	47.7389i	0.225194	−	1.56626i	0.717951	−	0.696094i	$-0.245080\pi$
$930$	−14.0727	+	9.03301i	−0.461462	+	0.296204i
$931$	5.57958	+	1.63831i	0.182863	+	0.0536935i
$932$	−6.95120	+	23.6736i	−0.227694	+	0.775455i
$933$	43.3767	−	19.8095i	1.42009	−	0.648534i
$934$	12.3195	−	85.6842i	0.403107	−	2.80367i
$935$	−14.3251	+	22.2633i	−0.468482	+	0.728089i
$936$	−1.76989	+	3.87552i	−0.0578507	+	0.126675i
$937$	−16.0195	+	24.9268i	−0.523335	+	0.814325i	−0.997824	−	0.0659368i	$-0.978996\pi$
$937$	−16.0195	+	24.9268i	−0.523335	+	0.814325i	0.474489	+	0.880261i	$0.342633\pi$
$938$	36.2184	−	5.20743i	1.18257	−	0.170028i
$939$	−24.9344	+	16.0244i	−0.813705	+	0.522936i
$940$	3.38448	+	2.93594i	0.110390	+	0.0957598i
$941$	15.2867	−	4.48857i	0.498331	−	0.146323i	−0.0229019	−	0.999738i	$-0.507291\pi$
$941$	15.2867	−	4.48857i	0.498331	−	0.146323i	0.521233	+	0.853415i	$0.325472\pi$
$942$		−	5.33134i		−	0.173705i
$943$	−8.99656	+	3.79140i	−0.292968	+	0.123465i
$944$	96.7325			3.14838
$945$	−9.62056	−	21.0969i	−0.312957	−	0.686282i
$946$	−41.6313	−	48.0451i	−1.35355	−	1.56208i
$947$	30.1753	+	46.9537i	0.980565	+	1.52579i	0.844823	+	0.535045i	$0.179706\pi$
$947$	30.1753	+	46.9537i	0.980565	+	1.52579i	0.135742	+	0.990744i	$0.456658\pi$
$948$	74.7062	−	10.7411i	2.42635	−	0.348856i
$949$	−27.4233	−	17.6239i	−0.890199	−	0.572096i
$950$	−27.5121	−	3.98664i	−0.892611	−	0.129344i
$951$	30.5763	−	35.2869i	0.991504	−	1.14426i
$952$	32.6619	+	4.69608i	1.05858	+	0.152201i
$953$	−39.8521	+	18.1999i	−1.29094	+	0.589551i	−0.938175	−	0.346162i	$-0.887485\pi$
$953$	−39.8521	+	18.1999i	−1.29094	+	0.589551i	−0.352763	+	0.935713i	$0.614758\pi$
$954$	−3.59473	−	1.05551i	−0.116384	−	0.0341733i
$955$	−4.30972	+	29.8578i	−0.139459	+	0.966176i
$956$	−29.3673	−	64.3054i	−0.949807	−	2.07979i
$957$	−21.1404	−	3.03953i	−0.683372	−	0.0982541i
$958$	−66.3201	−	57.4667i	−2.14271	−	1.85667i
$959$	8.96831	−	19.6379i	0.289602	−	0.634139i
$960$	43.7482	+	20.0083i	1.41197	+	0.645766i
$961$	4.05176	+	28.1806i	0.130702	+	0.909052i
$962$	−2.82589	−	4.39717i	−0.0911103	−	0.141770i
$963$	−0.292885	+	0.253786i	−0.00943808	+	0.00817814i
$964$	−17.9248	+	5.26320i	−0.577320	+	0.169516i
$965$	12.2321	−	1.75182i	0.393764	−	0.0563930i
$966$	31.4268	−	34.1732i	1.01114	−	1.09950i
$967$		−	13.4070i		−	0.431139i	−0.976488	−	0.215570i	$-0.930839\pi$
$967$		−	13.4070i		−	0.431139i	0.976488	−	0.215570i	$-0.0691608\pi$
$968$	−49.8108	−	169.640i	−1.60098	−	5.45244i
$969$	5.02073	+	5.79423i	0.161289	+	0.186138i
$970$	38.6913	+	44.7019i	1.24230	+	1.43529i
$971$	5.71226	+	39.7296i	0.183315	+	1.27498i	0.848856	+	0.528623i	$0.177292\pi$
$971$	5.71226	+	39.7296i	0.183315	+	1.27498i	−0.665541	+	0.746361i	$0.731799\pi$
$972$	−4.79890	+	7.46723i	−0.153925	+	0.239511i
$973$	−25.3767	−	11.5892i	−0.813540	−	0.371531i
$974$	36.6386	−	42.2832i	1.17398	−	1.35484i
$975$	−3.97144	−	27.8400i	−0.127188	−	0.891593i
$976$	−6.08895	−	13.3329i	−0.194903	−	0.426777i
$977$	10.4549	−	35.6061i	0.334482	−	1.13914i	−0.604910	−	0.796294i	$-0.706791\pi$
$977$	10.4549	−	35.6061i	0.334482	−	1.13914i	0.939392	−	0.342846i	$-0.111391\pi$
$978$	−10.2662	+	34.9634i	−0.328276	+	1.11800i
$979$	−7.69322	−	16.8458i	−0.245876	−	0.538394i
$980$	30.6866	+	0.0169302i	0.980249	+	0.000540815i
$981$	0.680086	−	0.784861i	0.0217135	−	0.0250587i
$982$	−37.7192	−	17.2258i	−1.20367	−	0.549696i
$983$	17.3757	−	27.0372i	0.554200	−	0.862352i	−0.445254	−	0.895404i	$-0.646887\pi$
$983$	17.3757	−	27.0372i	0.554200	−	0.862352i	0.999454	+	0.0330527i	$0.0105229\pi$
$984$	−4.04579	−	28.1391i	−0.128975	−	0.897041i
$985$	−32.8741	+	28.4538i	−1.04746	+	0.906614i
$986$	7.31663	+	8.44384i	0.233009	+	0.268907i
$987$	0.416493	+	1.41844i	0.0132571	+	0.0451495i
$988$		−	33.0528i		−	1.05155i
$989$	16.4471	+	11.2703i	0.522987	+	0.358376i
$990$	−5.82398	+	0.834082i	−0.185098	+	0.0265089i
$991$	3.91774	−	1.15035i	0.124451	−	0.0365421i	−0.218914	−	0.975744i	$-0.570251\pi$
$991$	3.91774	−	1.15035i	0.124451	−	0.0365421i	0.343365	+	0.939202i	$0.388433\pi$
$992$	−15.2982	+	13.2560i	−0.485718	+	0.420877i
$993$	6.79510	+	10.5734i	0.215636	+	0.335536i
$994$	10.7481	+	74.7550i	0.340911	+	2.37108i
$995$	9.94386	−	21.7423i	0.315241	−	0.689276i
$996$	−30.2787	+	66.3011i	−0.959418	+	2.10083i
$997$	−13.9441	−	12.0826i	−0.441613	−	0.382660i	0.405480	−	0.914104i	$-0.367104\pi$
$997$	−13.9441	−	12.0826i	−0.441613	−	0.382660i	−0.847094	+	0.531444i	$0.821650\pi$
$998$	106.948	+	15.3767i	3.38537	+	0.486742i
$999$	−1.31175	−	2.87233i	−0.0415019	−	0.0908764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.9.10	yes	100
5.2	odd	4		575.2.k.g.101.1		100
5.3	odd	4		575.2.k.g.101.10		100
5.4	even	2	inner	115.2.j.a.9.1	✓	100
23.18	even	11	inner	115.2.j.a.64.1	yes	100
115.18	odd	44		575.2.k.g.501.10		100
115.64	even	22	inner	115.2.j.a.64.10	yes	100
115.87	odd	44		575.2.k.g.501.1		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.1	✓	100	5.4	even	2	inner
115.2.j.a.9.10	yes	100	1.1	even	1	trivial
115.2.j.a.64.1	yes	100	23.18	even	11	inner
115.2.j.a.64.10	yes	100	115.64	even	22	inner
575.2.k.g.101.1		100	5.2	odd	4
575.2.k.g.101.10		100	5.3	odd	4
575.2.k.g.501.1		100	115.87	odd	44
575.2.k.g.501.10		100	115.18	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)

\(f(q)\)	\(=\)	\(q+(0.743795 + 2.53313i) q^{2} +(1.34601 - 1.16633i) q^{3} +(-4.18102 + 2.68698i) q^{4} +(2.14584 - 0.628789i) q^{5} +(3.95561 + 2.54212i) q^{6} +(-1.87277 - 0.855264i) q^{7} +(-5.92582 - 5.13475i) q^{8} +(0.0244873 - 0.170313i) q^{9} +O(q^{10})\)	\(q+(0.743795 + 2.53313i) q^{2} +(1.34601 - 1.16633i) q^{3} +(-4.18102 + 2.68698i) q^{4} +(2.14584 - 0.628789i) q^{5} +(3.95561 + 2.54212i) q^{6} +(-1.87277 - 0.855264i) q^{7} +(-5.92582 - 5.13475i) q^{8} +(0.0244873 - 0.170313i) q^{9} +(3.18887 + 4.96800i) q^{10} +(-5.55748 - 1.63182i) q^{11} +(-2.49381 + 8.49314i) q^{12} +(2.87256 - 1.31185i) q^{13} +(0.773542 - 5.38010i) q^{14} +(2.15495 - 3.34911i) q^{15} +(4.47020 - 9.78837i) q^{16} +(1.10511 - 1.71958i) q^{17} +(0.449639 - 0.0646484i) q^{18} +(-1.77165 + 1.13857i) q^{19} +(-7.28225 + 8.39480i) q^{20} +(-3.51828 + 1.03306i) q^{21} -15.2916i q^{22} +(1.21456 + 4.63949i) q^{23} -13.9650 q^{24} +(4.20925 - 2.69856i) q^{25} +(5.45969 + 6.30081i) q^{26} +(2.72301 + 4.23709i) q^{27} +(10.1281 - 1.45621i) q^{28} +(1.74171 + 1.11933i) q^{29} +(10.0866 + 2.96773i) q^{30} +(-1.04153 + 1.20200i) q^{31} +(12.5978 + 1.81129i) q^{32} +(-9.38367 + 4.28538i) q^{33} +(5.17791 + 1.52037i) q^{34} +(-4.55643 - 0.657682i) q^{35} +(0.355246 + 0.777880i) q^{36} +(-0.620561 - 0.0892232i) q^{37} +(-4.20189 - 3.64095i) q^{38} +(2.33645 - 5.11610i) q^{39} +(-15.9445 - 7.29226i) q^{40} +(0.289709 + 2.01497i) q^{41} +(-5.23376 - 8.14389i) q^{42} +(3.14193 - 2.72250i) q^{43} +(27.6206 - 8.11014i) q^{44} +(-0.0545453 - 0.380862i) q^{45} +(-10.8491 + 6.52746i) q^{46} -0.403164i q^{47} +(-5.39949 - 18.3890i) q^{48} +(-1.80825 - 2.08683i) q^{49} +(9.96663 + 8.65540i) q^{50} +(-0.518105 - 3.60350i) q^{51} +(-8.48529 + 13.2034i) q^{52} +(-7.50209 - 3.42609i) q^{53} +(-8.70774 + 10.0493i) q^{54} +(-12.9515 - 0.00714551i) q^{55} +(6.70611 + 14.6843i) q^{56} +(-1.05672 + 3.59885i) q^{57} +(-1.53994 + 5.24454i) q^{58} +(3.73431 + 8.17700i) q^{59} +(-0.0109200 + 19.7930i) q^{60} +(0.892000 - 1.02942i) q^{61} +(-3.81950 - 1.74431i) q^{62} +(-0.191522 + 0.298014i) q^{63} +(1.71909 + 11.9565i) q^{64} +(5.33916 - 4.62126i) q^{65} +(-17.8350 - 20.5826i) q^{66} +(1.89660 + 6.45923i) q^{67} +10.1590i q^{68} +(7.04596 + 4.82824i) q^{69} +(-1.72306 - 12.0312i) q^{70} +(-13.3319 + 3.91459i) q^{71} +(-1.01962 + 0.883509i) q^{72} +(-5.58084 - 8.68396i) q^{73} +(-0.235556 - 1.63833i) q^{74} +(2.51830 - 8.54165i) q^{75} +(4.34798 - 9.52075i) q^{76} +(9.01222 + 7.80913i) q^{77} +(14.6976 + 2.11320i) q^{78} +(-3.54206 - 7.75603i) q^{79} +(3.43750 - 23.8151i) q^{80} +(9.10231 + 2.67268i) q^{81} +(-4.88870 + 2.23259i) q^{82} +(8.15053 + 1.17187i) q^{83} +(11.9342 - 13.7728i) q^{84} +(1.29013 - 4.38483i) q^{85} +(9.23341 + 5.93395i) q^{86} +(3.64987 - 0.524772i) q^{87} +(24.5536 + 38.2062i) q^{88} +(2.09382 + 2.41639i) q^{89} +(0.924203 - 0.421453i) q^{90} -6.50160 q^{91} +(-17.5443 - 16.1343i) q^{92} +2.83267i q^{93} +(1.02127 - 0.299871i) q^{94} +(-3.08575 + 3.55718i) q^{95} +(19.0693 - 12.2551i) q^{96} +(9.91281 - 1.42525i) q^{97} +(3.94125 - 6.13270i) q^{98} +(-0.414009 + 0.906553i) 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

Introduction

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