LMFDB - Embedded newform 925.2.e.b.676.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(26,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 13 x^{12} - 16 x^{11} + 98 x^{10} - 116 x^{9} + 378 x^{8} - 264 x^{7} + 795 x^{6} + \cdots + 9 $ x^14 - 2x^13 + 13x^12 - 16x^11 + 98x^10 - 116x^9 + 378x^8 - 264x^7 + 795x^6 - 520x^5 + 927x^4 - 71x^3 + 94x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.5
Root			$-0.155125 - 0.268684i$ of defining polynomial
Character	$\chi$	$=$	925.676
Dual form			925.2.e.b.26.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.155125 - 0.268684i) q^{2} +(1.03095 + 1.78566i) q^{3} +(0.951873 + 1.64869i) q^{4} +0.639704 q^{6} +(-1.06035 - 1.83659i) q^{7} +1.21113 q^{8} +(-0.625722 + 1.08378i) q^{9} +5.48703 q^{11} +(-1.96267 + 3.39944i) q^{12} +(0.826151 + 1.43093i) q^{13} -0.657948 q^{14} +(-1.71587 + 2.97197i) q^{16} +(-1.42247 + 2.46379i) q^{17} +(0.194130 + 0.336243i) q^{18} +(1.19568 + 2.07098i) q^{19} +(2.18635 - 3.78686i) q^{21} +(0.851174 - 1.47428i) q^{22} -1.29182 q^{23} +(1.24862 + 2.16267i) q^{24} +0.512625 q^{26} +3.60535 q^{27} +(2.01864 - 3.49639i) q^{28} -0.459480 q^{29} -7.00913 q^{31} +(1.74348 + 3.01980i) q^{32} +(5.65686 + 9.79798i) q^{33} +(0.441320 + 0.764389i) q^{34} -2.38243 q^{36} +(2.41356 - 5.58343i) q^{37} +0.741917 q^{38} +(-1.70344 + 2.95045i) q^{39} +(-3.63843 - 6.30194i) q^{41} +(-0.678313 - 1.17487i) q^{42} +4.39190 q^{43} +(5.22296 + 9.04642i) q^{44} +(-0.200394 + 0.347092i) q^{46} +0.310249 q^{47} -7.07591 q^{48} +(1.25130 - 2.16731i) q^{49} -5.86599 q^{51} +(-1.57278 + 2.72414i) q^{52} +(-6.00746 + 10.4052i) q^{53} +(0.559279 - 0.968700i) q^{54} +(-1.28423 - 2.22435i) q^{56} +(-2.46537 + 4.27015i) q^{57} +(-0.0712767 + 0.123455i) q^{58} +(-4.14947 + 7.18709i) q^{59} +(-5.10365 - 8.83978i) q^{61} +(-1.08729 + 1.88324i) q^{62} +2.65395 q^{63} -5.78165 q^{64} +3.51008 q^{66} +(0.664518 + 1.15098i) q^{67} -5.41604 q^{68} +(-1.33181 - 2.30676i) q^{69} +(-0.293650 - 0.508617i) q^{71} +(-0.757834 + 1.31261i) q^{72} -10.8030 q^{73} +(-1.12578 - 1.51461i) q^{74} +(-2.27627 + 3.94261i) q^{76} +(-5.81820 - 10.0774i) q^{77} +(0.528492 + 0.915375i) q^{78} +(1.41967 + 2.45893i) q^{79} +(5.59411 + 9.68928i) q^{81} -2.25764 q^{82} +(5.91099 - 10.2381i) q^{83} +8.32450 q^{84} +(0.681292 - 1.18003i) q^{86} +(-0.473702 - 0.820476i) q^{87} +6.64553 q^{88} +(8.40980 - 14.5662i) q^{89} +(1.75202 - 3.03459i) q^{91} +(-1.22965 - 2.12982i) q^{92} +(-7.22607 - 12.5159i) q^{93} +(0.0481273 - 0.0833590i) q^{94} +(-3.59489 + 6.22653i) q^{96} +18.5979 q^{97} +(-0.388215 - 0.672407i) q^{98} +(-3.43336 + 5.94675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 2 q^{3} - 8 q^{4} + 4 q^{6} - 2 q^{7} + 6 q^{8} - 5 q^{9} - 10 q^{11} + 8 q^{12} - 6 q^{13} - 36 q^{14} - 14 q^{16} + q^{17} + 4 q^{18} + 6 q^{19} + 13 q^{21} + q^{22} - 12 q^{23} - 21 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 2 * q^3 - 8 * q^4 + 4 * q^6 - 2 * q^7 + 6 * q^8 - 5 * q^9 - 10 * q^11 + 8 * q^12 - 6 * q^13 - 36 * q^14 - 14 * q^16 + q^17 + 4 * q^18 + 6 * q^19 + 13 * q^21 + q^22 - 12 * q^23 - 21 * q^24 + 2 * q^26 - 22 * q^27 - 13 * q^28 - 12 * q^29 - 8 * q^31 - 18 * q^32 - q^33 - 11 * q^34 - 8 * q^36 - 12 * q^37 - 16 * q^38 + 23 * q^39 - 3 * q^41 - 29 * q^42 + 38 * q^43 + 25 * q^44 + 10 * q^46 - 4 * q^47 + 20 * q^48 - 7 * q^49 - 14 * q^51 - 46 * q^52 + 2 * q^53 + 23 * q^54 + 19 * q^56 - 22 * q^57 + 12 * q^58 - 18 * q^59 - 20 * q^61 + 21 * q^62 - 46 * q^63 + 50 * q^64 - 42 * q^66 + 20 * q^67 - 110 * q^68 + 17 * q^69 - 11 * q^71 + 29 * q^72 + 36 * q^73 - 66 * q^74 + 40 * q^76 + q^77 - 6 * q^78 + 23 * q^79 + 29 * q^81 + 24 * q^82 + 9 * q^83 + 8 * q^84 - 3 * q^86 + 43 * q^87 + 116 * q^88 - 16 * q^89 + 12 * q^91 + 33 * q^92 - 25 * q^93 + 22 * q^94 - 67 * q^96 + 62 * q^97 + 24 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.155125	−	0.268684i	0.109690	−	0.189988i	−0.805955	−	0.591977i	$-0.798348\pi$
$2$	0.155125	−	0.268684i	0.109690	−	0.189988i	0.915645	+	0.401989i	$0.131681\pi$
$3$	1.03095	+	1.78566i	0.595220	+	1.03095i	0.993516	+	0.113694i	$0.0362685\pi$
$3$	1.03095	+	1.78566i	0.595220	+	1.03095i	−0.398296	+	0.917257i	$0.630398\pi$
$4$	0.951873	+	1.64869i	0.475936	+	0.824346i
$5$		0			0
$5$		0			0
$6$	0.639704			0.261158
$7$	−1.06035	−	1.83659i	−0.400776	−	0.694165i	0.593044	−	0.805170i	$-0.297926\pi$
$7$	−1.06035	−	1.83659i	−0.400776	−	0.694165i	−0.993820	+	0.111006i	$0.964593\pi$
$8$	1.21113			0.428201
$9$	−0.625722	+	1.08378i	−0.208574	+	0.361261i
$10$		0			0
$11$	5.48703			1.65440			0.827201	−	0.561906i	$-0.189932\pi$
$11$	5.48703			1.65440			0.827201	+	0.561906i	$0.189932\pi$
$12$	−1.96267	+	3.39944i	−0.566574	+	0.981335i
$13$	0.826151	+	1.43093i	0.229133	+	0.396870i	0.957551	−	0.288263i	$-0.0930776\pi$
$13$	0.826151	+	1.43093i	0.229133	+	0.396870i	−0.728418	+	0.685133i	$0.759744\pi$
$14$	−0.657948			−0.175844
$15$		0			0
$16$	−1.71587	+	2.97197i	−0.428967	+	0.742993i
$17$	−1.42247	+	2.46379i	−0.345000	+	0.597557i	−0.985354	−	0.170523i	$-0.945454\pi$
$17$	−1.42247	+	2.46379i	−0.345000	+	0.597557i	0.640354	+	0.768080i	$0.278788\pi$
$18$	0.194130	+	0.336243i	0.0457568	+	0.0792532i
$19$	1.19568	+	2.07098i	0.274308	+	0.475115i	0.969960	−	0.243264i	$-0.0782180\pi$
$19$	1.19568	+	2.07098i	0.274308	+	0.475115i	−0.695653	+	0.718378i	$0.744885\pi$
$20$		0			0
$21$	2.18635	−	3.78686i	0.477100	−	0.826362i
$22$	0.851174	−	1.47428i	0.181471	−	0.314317i
$23$	−1.29182			−0.269364			−0.134682	−	0.990889i	$-0.543001\pi$
$23$	−1.29182			−0.269364			−0.134682	+	0.990889i	$0.543001\pi$
$24$	1.24862	+	2.16267i	0.254874	+	0.441454i
$25$		0			0
$26$	0.512625			0.100534
$27$	3.60535			0.693850
$28$	2.01864	−	3.49639i	0.381488	−	0.660756i
$29$	−0.459480			−0.0853234			−0.0426617	−	0.999090i	$-0.513584\pi$
$29$	−0.459480			−0.0853234			−0.0426617	+	0.999090i	$0.513584\pi$
$30$		0			0
$31$	−7.00913			−1.25888			−0.629438	−	0.777051i	$-0.716715\pi$
$31$	−7.00913			−1.25888			−0.629438	+	0.777051i	$0.716715\pi$
$32$	1.74348	+	3.01980i	0.308207	+	0.533830i
$33$	5.65686	+	9.79798i	0.984734	+	1.70561i
$34$	0.441320	+	0.764389i	0.0756858	+	0.131092i
$35$		0			0
$36$	−2.38243			−0.397072
$37$	2.41356	−	5.58343i	0.396786	−	0.917911i
$37$	2.41356	−	5.58343i	0.396786	−	0.917911i
$38$	0.741917			0.120355
$39$	−1.70344	+	2.95045i	−0.272769	+	0.472450i
$40$		0			0
$41$	−3.63843	−	6.30194i	−0.568227	−	0.984198i	−0.996741	−	0.0806634i	$-0.974296\pi$
$41$	−3.63843	−	6.30194i	−0.568227	−	0.984198i	0.428514	−	0.903535i	$-0.359037\pi$
$42$	−0.678313	−	1.17487i	−0.104666	−	0.181287i
$43$	4.39190			0.669758			0.334879	−	0.942261i	$-0.391304\pi$
$43$	4.39190			0.669758			0.334879	+	0.942261i	$0.391304\pi$
$44$	5.22296	+	9.04642i	0.787390	+	1.36380i
$45$		0			0
$46$	−0.200394	+	0.347092i	−0.0295464	+	0.0511759i
$47$	0.310249			0.0452545			0.0226273	−	0.999744i	$-0.492797\pi$
$47$	0.310249			0.0452545			0.0226273	+	0.999744i	$0.492797\pi$
$48$	−7.07591			−1.02132
$49$	1.25130	−	2.16731i	0.178757	−	0.309616i
$50$		0			0
$51$	−5.86599			−0.821403
$52$	−1.57278	+	2.72414i	−0.218105	+	0.377770i
$53$	−6.00746	+	10.4052i	−0.825188	+	1.42927i	0.0765878	+	0.997063i	$0.475597\pi$
$53$	−6.00746	+	10.4052i	−0.825188	+	1.42927i	−0.901776	+	0.432204i	$0.857736\pi$
$54$	0.559279	−	0.968700i	0.0761082	−	0.131823i
$55$		0			0
$56$	−1.28423	−	2.22435i	−0.171613	−	0.297242i
$57$	−2.46537	+	4.27015i	−0.326547	+	0.565596i
$58$	−0.0712767	+	0.123455i	−0.00935910	+	0.0162104i
$59$	−4.14947	+	7.18709i	−0.540215	+	0.935680i	0.458676	+	0.888603i	$0.348324\pi$
$59$	−4.14947	+	7.18709i	−0.540215	+	0.935680i	−0.998891	+	0.0470765i	$0.985010\pi$
$60$		0			0
$61$	−5.10365	−	8.83978i	−0.653456	−	1.13182i	−0.982279	−	0.187427i	$-0.939985\pi$
$61$	−5.10365	−	8.83978i	−0.653456	−	1.13182i	0.328823	−	0.944392i	$-0.393348\pi$
$62$	−1.08729	+	1.88324i	−0.138086	+	0.239172i
$63$	2.65395			0.334366
$64$	−5.78165			−0.722706
$65$		0			0
$66$	3.51008			0.432061
$67$	0.664518	+	1.15098i	0.0811838	+	0.140614i	0.903759	−	0.428042i	$-0.140797\pi$
$67$	0.664518	+	1.15098i	0.0811838	+	0.140614i	−0.822575	+	0.568657i	$0.807463\pi$
$68$	−5.41604			−0.656792
$69$	−1.33181	−	2.30676i	−0.160331	−	0.277701i
$70$		0			0
$71$	−0.293650	−	0.508617i	−0.0348498	−	0.0603617i	0.848074	−	0.529877i	$-0.177762\pi$
$71$	−0.293650	−	0.508617i	−0.0348498	−	0.0603617i	−0.882924	+	0.469515i	$0.844429\pi$
$72$	−0.757834	+	1.31261i	−0.0893115	+	0.154692i
$73$	−10.8030			−1.26439			−0.632197	−	0.774808i	$-0.717847\pi$
$73$	−10.8030			−1.26439			−0.632197	+	0.774808i	$0.717847\pi$
$74$	−1.12578	−	1.51461i	−0.130869	−	0.176070i
$75$		0			0
$76$	−2.27627	+	3.94261i	−0.261106	+	0.452249i
$77$	−5.81820	−	10.0774i	−0.663045	−	1.14843i
$78$	0.528492	+	0.915375i	0.0598399	+	0.103646i
$79$	1.41967	+	2.45893i	0.159725	+	0.276652i	0.934769	−	0.355255i	$-0.115606\pi$
$79$	1.41967	+	2.45893i	0.159725	+	0.276652i	−0.775045	+	0.631907i	$0.782273\pi$
$80$		0			0
$81$	5.59411	+	9.68928i	0.621568	+	1.07659i
$82$	−2.25764			−0.249315
$83$	5.91099	−	10.2381i	0.648815	−	1.12378i	−0.334591	−	0.942363i	$-0.608598\pi$
$83$	5.91099	−	10.2381i	0.648815	−	1.12378i	0.983406	−	0.181417i	$-0.0580684\pi$
$84$	8.32450			0.908277
$85$		0			0
$86$	0.681292	−	1.18003i	0.0734656	−	0.127246i
$87$	−0.473702	−	0.820476i	−0.0507862	−	0.0879643i
$88$	6.64553			0.708416
$89$	8.40980	−	14.5662i	0.891437	−	1.54401i	0.0532843	−	0.998579i	$-0.483031\pi$
$89$	8.40980	−	14.5662i	0.891437	−	1.54401i	0.838153	−	0.545435i	$-0.183636\pi$
$90$		0			0
$91$	1.75202	−	3.03459i	0.183662	−	0.318112i
$92$	−1.22965	−	2.12982i	−0.128200	−	0.222049i
$93$	−7.22607	−	12.5159i	−0.749308	−	1.29784i
$94$	0.0481273	−	0.0833590i	0.00496395	−	0.00859782i
$95$		0			0
$96$	−3.59489	+	6.22653i	−0.366902	+	0.635493i
$97$	18.5979			1.88833			0.944165	−	0.329472i	$-0.106871\pi$
$97$	18.5979			1.88833			0.944165	+	0.329472i	$0.106871\pi$
$98$	−0.388215	−	0.672407i	−0.0392156	−	0.0679234i
$99$	−3.43336	+	5.94675i	−0.345065	+	0.597671i
$100$		0			0
$101$	−8.79352			−0.874988			−0.437494	−	0.899221i	$-0.644134\pi$
$101$	−8.79352			−0.874988			−0.437494	+	0.899221i	$0.644134\pi$
$102$	−0.909960	+	1.57610i	−0.0900994	+	0.156057i
$103$	−5.36532			−0.528660			−0.264330	−	0.964432i	$-0.585151\pi$
$103$	−5.36532			−0.528660			−0.264330	+	0.964432i	$0.585151\pi$
$104$	1.00058	+	1.73305i	0.0981149	+	0.169940i
$105$		0			0
$106$	1.86381	+	3.22821i	0.181029	+	0.313552i
$107$	−1.42697	−	2.47158i	−0.137950	−	0.238937i	0.788770	−	0.614688i	$-0.210718\pi$
$107$	−1.42697	−	2.47158i	−0.137950	−	0.238937i	−0.926721	+	0.375751i	$0.877385\pi$
$108$	3.43184	+	5.94412i	0.330229	+	0.571973i
$109$	−4.37956	+	7.58562i	−0.419486	+	0.726571i	−0.995888	−	0.0905956i	$-0.971123\pi$
$109$	−4.37956	+	7.58562i	−0.419486	+	0.726571i	0.576402	+	0.817166i	$0.304456\pi$
$110$		0			0
$111$	12.4584	−	1.44646i	1.18250	−	0.137292i
$112$	7.27771			0.687679
$113$	−7.88239	+	13.6527i	−0.741513	+	1.28434i	0.210294	+	0.977638i	$0.432558\pi$
$113$	−7.88239	+	13.6527i	−0.741513	+	1.28434i	−0.951806	+	0.306699i	$0.900775\pi$
$114$	0.764881	+	1.32481i	0.0716376	+	0.124080i
$115$		0			0
$116$	−0.437367	−	0.757542i	−0.0406085	−	0.0703360i
$117$	−2.06776			−0.191165
$118$	1.28737	+	2.22979i	0.118512	+	0.205269i
$119$	6.03329			0.553071
$120$		0			0
$121$	19.1075			1.73705
$122$	−3.16681			−0.286709
$123$	7.50209	−	12.9940i	0.676441	−	1.17163i
$124$	−6.67180	−	11.5559i	−0.599145	−	1.03775i
$125$		0			0
$126$	0.411693	−	0.713073i	0.0366765	−	0.0635256i
$127$	2.00325	−	3.46973i	0.177760	−	0.307889i	−0.763353	−	0.645981i	$-0.776448\pi$
$127$	2.00325	−	3.46973i	0.177760	−	0.307889i	0.941113	+	0.338093i	$0.109782\pi$
$128$	−4.38384	+	7.59303i	−0.387480	+	0.671135i
$129$	4.52784	+	7.84244i	0.398654	+	0.690489i
$130$		0			0
$131$	10.2080	−	17.6807i	0.891873	−	1.54477i	0.0542464	−	0.998528i	$-0.482724\pi$
$131$	10.2080	−	17.6807i	0.891873	−	1.54477i	0.837627	−	0.546243i	$-0.183942\pi$
$132$	−10.7692	+	18.6529i	−0.937341	+	1.62352i
$133$	2.53569	−	4.39194i	0.219872	−	0.380829i
$134$	0.412332			0.0356201
$135$		0			0
$136$	−1.72280	+	2.98398i	−0.147729	+	0.255874i
$137$	5.52931			0.472401			0.236200	−	0.971704i	$-0.424098\pi$
$137$	5.52931			0.472401			0.236200	+	0.971704i	$0.424098\pi$
$138$	−0.826385			−0.0703465
$139$	10.4632	−	18.1228i	0.887477	−	1.53716i	0.0446295	−	0.999004i	$-0.485789\pi$
$139$	10.4632	−	18.1228i	0.887477	−	1.53716i	0.842848	−	0.538152i	$-0.180877\pi$
$140$		0			0
$141$	0.319852	+	0.554000i	0.0269364	+	0.0466552i
$142$	−0.182209			−0.0152907
$143$	4.53311	+	7.85158i	0.379078	+	0.656582i
$144$	−2.14731	−	3.71926i	−0.178943	−	0.309938i
$145$		0			0
$146$	−1.67581	+	2.90259i	−0.138691	+	0.240220i
$147$	5.16011			0.425599
$148$	11.5028	−	1.33551i	0.945521	−	0.109778i
$149$	−4.87785			−0.399609			−0.199804	−	0.979836i	$-0.564031\pi$
$149$	−4.87785			−0.399609			−0.199804	+	0.979836i	$0.564031\pi$
$150$		0			0
$151$	11.8485	+	20.5222i	0.964216	+	1.67007i	0.711708	+	0.702475i	$0.247922\pi$
$151$	11.8485	+	20.5222i	0.964216	+	1.67007i	0.252507	+	0.967595i	$0.418745\pi$
$152$	1.44813	+	2.50823i	0.117459	+	0.203444i
$153$	−1.78014	−	3.08330i	−0.143916	−	0.249270i
$154$	−3.61018			−0.290917
$155$		0			0
$156$	−6.48584			−0.519283
$157$	10.5385	−	18.2533i	0.841067	−	1.45677i	−0.0479266	−	0.998851i	$-0.515261\pi$
$157$	10.5385	−	18.2533i	0.841067	−	1.45677i	0.888994	−	0.457920i	$-0.151405\pi$
$158$	0.880901			0.0700807
$159$	−24.7736			−1.96467
$160$		0			0
$161$	1.36979	+	2.37255i	0.107955	+	0.186983i
$162$	3.47114			0.272718
$163$	2.60566	−	4.51313i	0.204091	−	0.353496i	−0.745752	−	0.666224i	$-0.767910\pi$
$163$	2.60566	−	4.51313i	0.204091	−	0.353496i	0.949843	+	0.312728i	$0.101243\pi$
$164$	6.92664	−	11.9973i	0.540880	−	0.936832i
$165$		0			0
$166$	−1.83388	−	3.17637i	−0.142337	−	0.246534i
$167$	−5.28579	−	9.15526i	−0.409027	−	0.708455i	0.585754	−	0.810489i	$-0.300798\pi$
$167$	−5.28579	−	9.15526i	−0.409027	−	0.708455i	−0.994781	+	0.102034i	$0.967465\pi$
$168$	2.64796	−	4.58640i	0.204295	−	0.353849i
$169$	5.13495	−	8.89400i	0.394996	−	0.684153i
$170$		0			0
$171$	−2.99265			−0.228854
$172$	4.18053	+	7.24089i	0.318762	+	0.552113i
$173$	6.76942	−	11.7250i	0.514670	−	0.891434i	−0.485185	−	0.874411i	$-0.661248\pi$
$173$	6.76942	−	11.7250i	0.514670	−	0.891434i	0.999855	−	0.0170229i	$-0.00541882\pi$
$174$	−0.293931			−0.0222829
$175$		0			0
$176$	−9.41503	+	16.3073i	−0.709684	+	1.22921i
$177$	−17.1116			−1.28619
$178$	−2.60914	−	4.51915i	−0.195563	−	0.338725i
$179$	−14.8133			−1.10720			−0.553599	−	0.832783i	$-0.686746\pi$
$179$	−14.8133			−1.10720			−0.553599	+	0.832783i	$0.686746\pi$
$180$		0			0
$181$	−2.30881	−	3.99897i	−0.171612	−	0.297241i	0.767371	−	0.641203i	$-0.221564\pi$
$181$	−2.30881	−	3.99897i	−0.171612	−	0.297241i	−0.938984	+	0.343962i	$0.888231\pi$
$182$	−0.543564	−	0.941481i	−0.0402917	−	0.0697872i
$183$	10.5232	−	18.2268i	0.777900	−	1.34736i
$184$	−1.56457			−0.115342
$185$		0			0
$186$	−4.48377			−0.328766
$187$	−7.80514	+	13.5189i	−0.570768	+	0.988600i
$188$	0.295318	+	0.511505i	0.0215383	+	0.0373054i
$189$	−3.82295	−	6.62154i	−0.278079	−	0.481646i
$190$		0			0
$191$	−11.6768			−0.844902			−0.422451	−	0.906386i	$-0.638830\pi$
$191$	−11.6768			−0.844902			−0.422451	+	0.906386i	$0.638830\pi$
$192$	−5.96060	−	10.3241i	−0.430169	−	0.745075i
$193$	15.2222			1.09572			0.547859	−	0.836570i	$-0.315443\pi$
$193$	15.2222			1.09572			0.547859	+	0.836570i	$0.315443\pi$
$194$	2.88499	−	4.99695i	0.207130	−	0.358760i
$195$		0			0
$196$	4.76431			0.340308
$197$	5.34376	−	9.25567i	0.380727	−	0.659439i	−0.610439	−	0.792063i	$-0.709007\pi$
$197$	5.34376	−	9.25567i	0.380727	−	0.659439i	0.991166	+	0.132624i	$0.0423403\pi$
$198$	1.06520	+	1.84497i	0.0757002	+	0.131117i
$199$	−3.95137			−0.280105			−0.140052	−	0.990144i	$-0.544727\pi$
$199$	−3.95137			−0.280105			−0.140052	+	0.990144i	$0.544727\pi$
$200$		0			0
$201$	−1.37017	+	2.37321i	−0.0966444	+	0.167393i
$202$	−1.36409	+	2.36268i	−0.0959771	+	0.166237i
$203$	0.487212	+	0.843876i	0.0341956	+	0.0592285i
$204$	−5.58368	−	9.67121i	−0.390936	−	0.677120i
$205$		0			0
$206$	−0.832293	+	1.44157i	−0.0579886	+	0.100439i
$207$	0.808323	−	1.40006i	0.0561823	−	0.0973106i
$208$	−5.67026			−0.393162
$209$	6.56073	+	11.3635i	0.453815	+	0.786031i
$210$		0			0
$211$	8.40966			0.578945			0.289472	−	0.957186i	$-0.406520\pi$
$211$	8.40966			0.578945			0.289472	+	0.957186i	$0.406520\pi$
$212$	−22.8733			−1.57095
$213$	0.605478	−	1.04872i	0.0414867	−	0.0718570i
$214$	−0.885432			−0.0605269
$215$		0			0
$216$	4.36657			0.297107
$217$	7.43216	+	12.8729i	0.504528	+	0.873867i
$218$	1.35876	+	2.35343i	0.0920265	+	0.159395i
$219$	−11.1374	−	19.2905i	−0.752593	−	1.30353i
$220$		0			0
$221$	−4.70070			−0.316203
$222$	1.54396	−	3.57175i	0.103624	−	0.239720i
$223$	−16.4686			−1.10282			−0.551411	−	0.834234i	$-0.685910\pi$
$223$	−16.4686			−1.10282			−0.551411	+	0.834234i	$0.685910\pi$
$224$	3.69741	−	6.40411i	0.247044	−	0.427893i
$225$		0			0
$226$	2.44551	+	4.23574i	0.162673	+	0.281757i
$227$	−6.79120	−	11.7627i	−0.450748	−	0.780719i	0.547685	−	0.836685i	$-0.315509\pi$
$227$	−6.79120	−	11.7627i	−0.450748	−	0.780719i	−0.998433	+	0.0559663i	$0.982176\pi$
$228$	−9.38689			−0.621662
$229$	10.9009	+	18.8809i	0.720351	+	1.24768i	0.960859	+	0.277037i	$0.0893524\pi$
$229$	10.9009	+	18.8809i	0.720351	+	1.24768i	−0.240509	+	0.970647i	$0.577314\pi$
$230$		0			0
$231$	11.9966	−	20.7786i	0.789316	−	1.36713i
$232$	−0.556493			−0.0365355
$233$	−13.2237			−0.866313			−0.433156	−	0.901319i	$-0.642600\pi$
$233$	−13.2237			−0.866313			−0.433156	+	0.901319i	$0.642600\pi$
$234$	−0.320761	+	0.555574i	−0.0209688	+	0.0363190i
$235$		0			0
$236$	−15.7991			−1.02843
$237$	−2.92721	+	5.07008i	−0.190143	+	0.329337i
$238$	0.935912	−	1.62105i	0.0606661	−	0.105077i
$239$	−6.04811	+	10.4756i	−0.391220	+	0.677613i	−0.992611	−	0.121342i	$-0.961280\pi$
$239$	−6.04811	+	10.4756i	−0.391220	+	0.677613i	0.601391	+	0.798955i	$0.294613\pi$
$240$		0			0
$241$	7.34971	+	12.7301i	0.473436	+	0.820016i	0.999538	−	0.0304061i	$-0.00968004\pi$
$241$	7.34971	+	12.7301i	0.473436	+	0.820016i	−0.526101	+	0.850422i	$0.676347\pi$
$242$	2.96405	−	5.13388i	0.190536	−	0.330018i
$243$	−6.12648	+	10.6114i	−0.393014	+	0.680720i
$244$	9.71605	−	16.8287i	0.622007	−	1.07735i
$245$		0			0
$246$	−2.32752	−	4.03138i	−0.148397	−	0.257031i
$247$	−1.97562	+	3.42188i	−0.125706	+	0.217729i
$248$	−8.48899			−0.539052
$249$	24.3758			1.54475
$250$		0			0
$251$	−27.4854			−1.73486			−0.867430	−	0.497559i	$-0.834230\pi$
$251$	−27.4854			−1.73486			−0.867430	+	0.497559i	$0.834230\pi$
$252$	2.52622	+	4.37554i	0.159137	+	0.275633i
$253$	−7.08828			−0.445636
$254$	−0.621507	−	1.07648i	−0.0389968	−	0.0675445i
$255$		0			0
$256$	−4.42156	−	7.65837i	−0.276348	−	0.478648i
$257$	−11.8389	+	20.5056i	−0.738491	+	1.27910i	0.214683	+	0.976684i	$0.431128\pi$
$257$	−11.8389	+	20.5056i	−0.738491	+	1.27910i	−0.953174	+	0.302421i	$0.902205\pi$
$258$	2.80952			0.174913
$259$	−12.8137	+	1.48771i	−0.796204	+	0.0924417i
$260$		0			0
$261$	0.287507	−	0.497977i	0.0177962	−	0.0308240i
$262$	−3.16701	−	5.48543i	−0.195659	−	0.338891i
$263$	−9.38548	−	16.2561i	−0.578733	−	1.00240i	−0.995625	−	0.0934393i	$-0.970214\pi$
$263$	−9.38548	−	16.2561i	−0.578733	−	1.00240i	0.416892	−	0.908956i	$-0.363119\pi$
$264$	6.85122	+	11.8667i	0.421664	+	0.730343i
$265$		0			0
$266$	−0.786695	−	1.36260i	−0.0482354	−	0.0835461i
$267$	34.6804			2.12241
$268$	−1.26507	+	2.19117i	−0.0772766	+	0.133847i
$269$	2.86020			0.174389			0.0871947	−	0.996191i	$-0.472210\pi$
$269$	2.86020			0.174389			0.0871947	+	0.996191i	$0.472210\pi$
$270$		0			0
$271$	11.3218	−	19.6099i	0.687750	−	1.19122i	−0.284814	−	0.958583i	$-0.591932\pi$
$271$	11.3218	−	19.6099i	0.687750	−	1.19122i	0.972564	−	0.232635i	$-0.0747349\pi$
$272$	−4.88154	−	8.45508i	−0.295987	−	0.512665i
$273$	7.22501			0.437277
$274$	0.857732	−	1.48564i	0.0518175	−	0.0897506i
$275$		0			0
$276$	2.53542	−	4.39148i	0.152615	−	0.264336i
$277$	0.0821921	+	0.142361i	0.00493844	+	0.00855364i	0.868484	−	0.495717i	$-0.165095\pi$
$277$	0.0821921	+	0.142361i	0.00493844	+	0.00855364i	−0.863546	+	0.504271i	$0.831761\pi$
$278$	−3.24620	−	5.62259i	−0.194694	−	0.337220i
$279$	4.38577	−	7.59637i	0.262569	−	0.454783i
$280$		0			0
$281$	−12.2966	+	21.2983i	−0.733554	+	1.27055i	0.221801	+	0.975092i	$0.428807\pi$
$281$	−12.2966	+	21.2983i	−0.733554	+	1.27055i	−0.955355	+	0.295461i	$0.904527\pi$
$282$	0.198468			0.0118186
$283$	−10.4090	−	18.0290i	−0.618752	−	1.07171i	−0.989714	−	0.143062i	$-0.954305\pi$
$283$	−10.4090	−	18.0290i	−0.618752	−	1.07171i	0.370962	−	0.928648i	$-0.379028\pi$
$284$	0.559035	−	0.968277i	0.0331726	−	0.0574567i
$285$		0			0
$286$	2.81279			0.166324
$287$	−7.71605	+	13.3646i	−0.455464	+	0.788887i
$288$	−4.36374			−0.257136
$289$	4.45316	+	7.71309i	0.261950	+	0.453711i
$290$		0			0
$291$	19.1735	+	33.2095i	1.12397	+	1.94678i
$292$	−10.2831	−	17.8108i	−0.601771	−	1.04230i
$293$	5.83149	+	10.1004i	0.340679	+	0.590074i	0.984559	−	0.175053i	$-0.0560096\pi$
$293$	5.83149	+	10.1004i	0.340679	+	0.590074i	−0.643880	+	0.765127i	$0.722676\pi$
$294$	0.800461	−	1.38644i	0.0466838	−	0.0808587i
$295$		0			0
$296$	2.92314	−	6.76229i	0.169904	−	0.393050i
$297$	19.7827			1.14791
$298$	−0.756674	+	1.31060i	−0.0438330	+	0.0759209i
$299$	−1.06724	−	1.84852i	−0.0617201	−	0.106902i
$300$		0			0
$301$	−4.65697	−	8.06611i	−0.268423	−	0.464923i
$302$	7.35196			0.423058
$303$	−9.06569	−	15.7022i	−0.520810	−	0.902070i
$304$	−8.20651			−0.470676
$305$		0			0
$306$	−1.10458			−0.0631444
$307$	13.5798			0.775039			0.387520	−	0.921861i	$-0.373332\pi$
$307$	13.5798			0.775039			0.387520	+	0.921861i	$0.373332\pi$
$308$	11.0764	−	19.1848i	0.631134	−	1.09316i
$309$	−5.53138	−	9.58063i	−0.314669	−	0.545023i
$310$		0			0
$311$	1.32600	−	2.29670i	0.0751907	−	0.130234i	−0.825978	−	0.563702i	$-0.809377\pi$
$311$	1.32600	−	2.29670i	0.0751907	−	0.130234i	0.901169	+	0.433468i	$0.142710\pi$
$312$	−2.06310	+	3.57339i	−0.116800	+	0.202303i
$313$	−0.296906	+	0.514255i	−0.0167821	+	0.0290674i	−0.874294	−	0.485396i	$-0.838675\pi$
$313$	−0.296906	+	0.514255i	−0.0167821	+	0.0290674i	0.857512	+	0.514463i	$0.172009\pi$
$314$	−3.26957	−	5.66307i	−0.184513	−	0.319585i
$315$		0			0
$316$	−2.70268	+	4.68118i	−0.152038	+	0.263337i
$317$	−3.38803	+	5.86825i	−0.190291	+	0.329594i	−0.945347	−	0.326067i	$-0.894276\pi$
$317$	−3.38803	+	5.86825i	−0.190291	+	0.329594i	0.755056	+	0.655661i	$0.227610\pi$
$318$	−3.84299	+	6.65626i	−0.215504	+	0.373265i
$319$	−2.52118			−0.141159
$320$		0			0
$321$	2.94227	−	5.09616i	0.164221	−	0.284440i
$322$	0.849953			0.0473660
$323$	−6.80327			−0.378544
$324$	−10.6498	+	18.4459i	−0.591653	+	1.02477i
$325$		0			0
$326$	−0.808404	−	1.40020i	−0.0447733	−	0.0775497i
$327$	−18.0605			−0.998746
$328$	−4.40663	−	7.63250i	−0.243315	−	0.421434i
$329$	−0.328974	−	0.569800i	−0.0181369	−	0.0314141i
$330$		0			0
$331$	1.40790	−	2.43855i	0.0773850	−	0.134035i	−0.824736	−	0.565518i	$-0.808676\pi$
$331$	1.40790	−	2.43855i	0.0773850	−	0.134035i	0.902121	+	0.431483i	$0.142010\pi$
$332$	22.5060			1.23518
$333$	4.54101	+	6.10945i	0.248846	+	0.334796i
$334$	−3.27983			−0.179464
$335$		0			0
$336$	7.50297	+	12.9955i	0.409321	+	0.708964i
$337$	−12.3263	−	21.3498i	−0.671457	−	1.16300i	−0.977491	−	0.210976i	$-0.932336\pi$
$337$	−12.3263	−	21.3498i	−0.671457	−	1.16300i	0.306035	−	0.952020i	$-0.400998\pi$
$338$	−1.59311	−	2.75936i	−0.0866540	−	0.150089i
$339$	−32.5054			−1.76545
$340$		0			0
$341$	−38.4593			−2.08269
$342$	−0.464234	+	0.804077i	−0.0251029	+	0.0434795i
$343$	−20.1522			−1.08812
$344$	5.31918			0.286791
$345$		0			0
$346$	−2.10021	−	3.63767i	−0.112908	−	0.195562i
$347$	−8.80294			−0.472566			−0.236283	−	0.971684i	$-0.575929\pi$
$347$	−8.80294			−0.472566			−0.236283	+	0.971684i	$0.575929\pi$
$348$	0.901808	−	1.56198i	0.0483420	−	0.0837308i
$349$	1.42867	−	2.47454i	0.0764752	−	0.132459i	−0.825252	−	0.564765i	$-0.808967\pi$
$349$	1.42867	−	2.47454i	0.0764752	−	0.132459i	0.901727	+	0.432306i	$0.142300\pi$
$350$		0			0
$351$	2.97856	+	5.15902i	0.158984	+	0.275368i
$352$	9.56654	+	16.5697i	0.509898	+	0.883170i
$353$	−6.20795	+	10.7525i	−0.330416	+	0.572297i	−0.982593	−	0.185769i	$-0.940522\pi$
$353$	−6.20795	+	10.7525i	−0.330416	+	0.572297i	0.652177	+	0.758066i	$0.273856\pi$
$354$	−2.65443	+	4.59761i	−0.141082	+	0.244360i
$355$		0			0
$356$	32.0202			1.69707
$357$	6.22003	+	10.7734i	0.329199	+	0.570189i
$358$	−2.29791	+	3.98010i	−0.121448	+	0.210355i
$359$	21.7819			1.14961			0.574803	−	0.818292i	$-0.305079\pi$
$359$	21.7819			1.14961			0.574803	+	0.818292i	$0.305079\pi$
$360$		0			0
$361$	6.64070	−	11.5020i	0.349511	−	0.605370i
$362$	−1.43261			−0.0752964
$363$	19.6989	+	34.1195i	1.03393	+	1.79081i
$364$	6.67082			0.349646
$365$		0			0
$366$	−3.26483	−	5.65484i	−0.170655	−	0.295583i
$367$	11.6653	+	20.2050i	0.608926	+	1.05469i	0.991418	+	0.130732i	$0.0417327\pi$
$367$	11.6653	+	20.2050i	0.608926	+	1.05469i	−0.382492	+	0.923959i	$0.624934\pi$
$368$	2.21660	−	3.83926i	0.115548	−	0.200135i
$369$	9.10658			0.474070
$370$		0			0
$371$	25.4801			1.32286
$372$	13.7566	−	23.8271i	0.713246	−	1.23538i
$373$	14.4904	+	25.0981i	0.750283	+	1.29953i	0.947685	+	0.319206i	$0.103416\pi$
$373$	14.4904	+	25.0981i	0.750283	+	1.29953i	−0.197402	+	0.980323i	$0.563251\pi$
$374$	2.42154	+	4.19423i	0.125215	+	0.216878i
$375$		0			0
$376$	0.375754			0.0193780
$377$	−0.379600	−	0.657487i	−0.0195504	−	0.0338623i
$378$	−2.37214			−0.122009
$379$	8.18583	−	14.1783i	0.420478	−	0.728289i	−0.575509	−	0.817796i	$-0.695196\pi$
$379$	8.18583	−	14.1783i	0.420478	−	0.728289i	0.995986	+	0.0895072i	$0.0285292\pi$
$380$		0			0
$381$	8.26102			0.423225
$382$	−1.81136	+	3.13736i	−0.0926770	+	0.160521i
$383$	−2.00449	−	3.47188i	−0.102425	−	0.177405i	0.810258	−	0.586073i	$-0.199327\pi$
$383$	−2.00449	−	3.47188i	−0.102425	−	0.177405i	−0.912683	+	0.408668i	$0.865993\pi$
$384$	−18.0781			−0.922544
$385$		0			0
$386$	2.36134	−	4.08996i	0.120189	−	0.208174i
$387$	−2.74811	+	4.75986i	−0.139694	+	0.241958i
$388$	17.7028	+	30.6622i	0.898725	+	1.55664i
$389$	9.11602	+	15.7894i	0.462200	+	0.800555i	0.999070	−	0.0431105i	$-0.0137267\pi$
$389$	9.11602	+	15.7894i	0.462200	+	0.800555i	−0.536870	+	0.843665i	$0.680393\pi$
$390$		0			0
$391$	1.83758	−	3.18278i	0.0929305	−	0.160960i
$392$	1.51549	−	2.62491i	0.0765438	−	0.132578i
$393$	42.0956			2.12344
$394$	−1.65790	−	2.87156i	−0.0835237	−	0.144667i
$395$		0			0
$396$	−13.0725			−0.656917
$397$	−25.9749			−1.30364			−0.651822	−	0.758372i	$-0.725995\pi$
$397$	−25.9749			−1.30364			−0.651822	+	0.758372i	$0.725995\pi$
$398$	−0.612954	+	1.06167i	−0.0307246	+	0.0532166i
$399$	10.4567			0.523489
$400$		0			0
$401$	−16.7311			−0.835510			−0.417755	−	0.908560i	$-0.637183\pi$
$401$	−16.7311			−0.835510			−0.417755	+	0.908560i	$0.637183\pi$
$402$	0.425095	+	0.736286i	0.0212018	+	0.0367226i
$403$	−5.79059	−	10.0296i	−0.288450	−	0.499610i
$404$	−8.37031	−	14.4978i	−0.416439	−	0.721293i
$405$		0			0
$406$	0.302314			0.0150036
$407$	13.2433	−	30.6365i	0.656444	−	1.51859i
$408$	−7.10450			−0.351725
$409$	−0.181239	+	0.313915i	−0.00896170	+	0.0155221i	−0.870471	−	0.492219i	$-0.836186\pi$
$409$	−0.181239	+	0.313915i	−0.00896170	+	0.0155221i	0.861510	+	0.507741i	$0.169519\pi$
$410$		0			0
$411$	5.70045	+	9.87347i	0.281183	+	0.487022i
$412$	−5.10710	−	8.84575i	−0.251609	−	0.435799i
$413$	17.5996			0.866021
$414$	−0.250782	−	0.434366i	−0.0123252	−	0.0213479i
$415$		0			0
$416$	−2.88076	+	4.98962i	−0.141241	+	0.244636i
$417$	43.1482			2.11298
$418$	4.07092			0.199115
$419$	−8.20109	+	14.2047i	−0.400649	+	0.693945i	−0.993804	−	0.111143i	$-0.964549\pi$
$419$	−8.20109	+	14.2047i	−0.400649	+	0.693945i	0.593155	+	0.805088i	$0.297882\pi$
$420$		0			0
$421$	−5.36363			−0.261407			−0.130704	−	0.991421i	$-0.541724\pi$
$421$	−5.36363			−0.261407			−0.130704	+	0.991421i	$0.541724\pi$
$422$	1.30455	−	2.25954i	0.0635043	−	0.109993i
$423$	−0.194130	+	0.336243i	−0.00943892	+	0.0163487i
$424$	−7.27584	+	12.6021i	−0.353346	+	0.612013i
$425$		0			0
$426$	−0.187849	−	0.325364i	−0.00910132	−	0.0157639i
$427$	−10.8234	+	18.7466i	−0.523779	+	0.907212i
$428$	2.71658	−	4.70526i	0.131311	−	0.227437i
$429$	−9.34684	+	16.1892i	−0.451270	+	0.781622i
$430$		0			0
$431$	−20.0498	−	34.7272i	−0.965763	−	1.67275i	−0.707551	−	0.706662i	$-0.750200\pi$
$431$	−20.0498	−	34.7272i	−0.965763	−	1.67275i	−0.258212	−	0.966088i	$-0.583133\pi$
$432$	−6.18631	+	10.7150i	−0.297639	+	0.515526i
$433$	−8.94867			−0.430046			−0.215023	−	0.976609i	$-0.568983\pi$
$433$	−8.94867			−0.430046			−0.215023	+	0.976609i	$0.568983\pi$
$434$	4.61164			0.221366
$435$		0			0
$436$	−16.6751			−0.798594
$437$	−1.54461	−	2.67534i	−0.0738885	−	0.127979i
$438$	−6.91071			−0.330207
$439$	11.9458	+	20.6906i	0.570140	+	0.987511i	0.996551	+	0.0829815i	$0.0264442\pi$
$439$	11.9458	+	20.6906i	0.570140	+	0.987511i	−0.426411	+	0.904529i	$0.640222\pi$
$440$		0			0
$441$	1.56593	+	2.71227i	0.0745681	+	0.129156i
$442$	−0.729194	+	1.26300i	−0.0346842	+	0.0600748i
$443$	40.0576			1.90320			0.951598	−	0.307346i	$-0.0994408\pi$
$443$	40.0576			1.90320			0.951598	+	0.307346i	$0.0994408\pi$
$444$	14.2436	+	19.1632i	0.675969	+	0.909445i
$445$		0			0
$446$	−2.55469	+	4.42486i	−0.120968	+	0.209523i
$447$	−5.02882	−	8.71018i	−0.237855	−	0.411977i
$448$	6.13059	+	10.6185i	0.289643	+	0.501677i
$449$	3.83167	+	6.63665i	0.180828	+	0.313203i	0.942163	−	0.335156i	$-0.108789\pi$
$449$	3.83167	+	6.63665i	0.180828	+	0.313203i	−0.761335	+	0.648359i	$0.775456\pi$
$450$		0			0
$451$	−19.9642	−	34.5790i	−0.940076	−	1.62826i
$452$	−30.0121			−1.41165
$453$	−24.4304	+	42.3147i	−1.14784	+	1.98812i
$454$	−4.21393			−0.197770
$455$		0			0
$456$	−2.98590	+	5.17173i	−0.139828	+	0.242188i
$457$	16.9554	+	29.3676i	0.793141	+	1.37376i	0.924013	+	0.382361i	$0.124889\pi$
$457$	16.9554	+	29.3676i	0.793141	+	1.37376i	−0.130872	+	0.991399i	$0.541778\pi$
$458$	6.76398			0.316060
$459$	−5.12851	+	8.88283i	−0.239378	+	0.414615i
$460$		0			0
$461$	−7.29012	+	12.6269i	−0.339535	+	0.588091i	−0.984345	−	0.176251i	$-0.943603\pi$
$461$	−7.29012	+	12.6269i	−0.339535	+	0.588091i	0.644811	+	0.764342i	$0.276936\pi$
$462$	−3.72192	−	6.44656i	−0.173160	−	0.299921i
$463$	1.99424	+	3.45413i	0.0926802	+	0.160527i	0.908638	−	0.417585i	$-0.137123\pi$
$463$	1.99424	+	3.45413i	0.0926802	+	0.160527i	−0.815958	+	0.578111i	$0.803790\pi$
$464$	0.788408	−	1.36556i	0.0366009	−	0.0633947i
$465$		0			0
$466$	−2.05132	+	3.55299i	−0.0950256	+	0.164589i
$467$	−14.7664			−0.683307			−0.341653	−	0.939826i	$-0.610987\pi$
$467$	−14.7664			−0.683307			−0.341653	+	0.939826i	$0.610987\pi$
$468$	−1.96825	−	3.40910i	−0.0909822	−	0.157586i
$469$	1.40925	−	2.44089i	0.0650730	−	0.112710i
$470$		0			0
$471$	43.4589			2.00248
$472$	−5.02557	+	8.70454i	−0.231320	+	0.400659i
$473$	24.0985			1.10805
$474$	0.908166	+	1.57299i	0.0417134	+	0.0722498i
$475$		0			0
$476$	5.74292	+	9.94703i	0.263226	+	0.455922i
$477$	−7.51800	−	13.0216i	−0.344226	−	0.596216i
$478$	1.87642	+	3.25006i	0.0858256	+	0.148654i
$479$	−7.80662	+	13.5215i	−0.356693	+	0.617811i	−0.987406	−	0.158205i	$-0.949429\pi$
$479$	−7.80662	+	13.5215i	−0.356693	+	0.617811i	0.630713	+	0.776016i	$0.282763\pi$
$480$		0			0
$481$	9.98349	−	1.15911i	0.455208	−	0.0528511i
$482$	4.56048			0.207724
$483$	−2.82438	+	4.89196i	−0.128514	+	0.222592i
$484$	18.1879	+	31.5024i	0.826724	+	1.43193i
$485$		0			0
$486$	1.90074	+	3.29217i	0.0862192	+	0.149336i
$487$	−35.6982			−1.61764			−0.808820	−	0.588056i	$-0.799893\pi$
$487$	−35.6982			−1.61764			−0.808820	+	0.588056i	$0.799893\pi$
$488$	−6.18121	−	10.7062i	−0.279810	−	0.484645i
$489$	10.7452			0.485916
$490$		0			0
$491$	−0.411627			−0.0185765			−0.00928823	−	0.999957i	$-0.502957\pi$
$491$	−0.411627			−0.0185765			−0.00928823	+	0.999957i	$0.502957\pi$
$492$	28.5641			1.28777
$493$	0.653597	−	1.13206i	0.0294365	−	0.0509856i
$494$	0.612935	+	1.06163i	0.0275773	+	0.0477652i
$495$		0			0
$496$	12.0267	−	20.8309i	0.540017	−	0.935336i
$497$	−0.622746	+	1.07863i	−0.0279340	+	0.0483831i
$498$	3.78128	−	6.54937i	0.169443	−	0.293484i
$499$	−19.0374	−	32.9738i	−0.852232	−	1.47611i	−0.879190	−	0.476472i	$-0.841915\pi$
$499$	−19.0374	−	32.9738i	−0.852232	−	1.47611i	0.0269579	−	0.999637i	$-0.491418\pi$
$500$		0			0
$501$	10.8988	−	18.8773i	0.486922	−	0.843374i
$502$	−4.26366	+	7.38487i	−0.190296	+	0.329603i
$503$	−7.75338	+	13.4292i	−0.345706	+	0.598780i	−0.985482	−	0.169781i	$-0.945694\pi$
$503$	−7.75338	+	13.4292i	−0.345706	+	0.598780i	0.639776	+	0.768562i	$0.279027\pi$
$504$	3.21429			0.143176
$505$		0			0
$506$	−1.09957	+	1.90451i	−0.0488817	+	0.0846656i
$507$	21.1755			0.940439
$508$	7.62736			0.338409
$509$	−2.99718	+	5.19127i	−0.132848	+	0.230099i	−0.924773	−	0.380519i	$-0.875745\pi$
$509$	−2.99718	+	5.19127i	−0.132848	+	0.230099i	0.791926	+	0.610618i	$0.209079\pi$
$510$		0			0
$511$	11.4550	+	19.8406i	0.506739	+	0.877698i
$512$	−20.2789			−0.896210
$513$	4.31084	+	7.46660i	0.190328	+	0.329658i
$514$	3.67302	+	6.36185i	0.162010	+	0.280609i
$515$		0			0
$516$	−8.61985	+	14.9300i	−0.379468	+	0.657257i
$517$	1.70235			0.0748692
$518$	−1.58800	+	3.67361i	−0.0697725	+	0.161409i
$519$	27.9158			1.22537
$520$		0			0
$521$	−8.46908	−	14.6689i	−0.371037	−	0.642655i	0.618688	−	0.785637i	$-0.287664\pi$
$521$	−8.46908	−	14.6689i	−0.371037	−	0.642655i	−0.989725	+	0.142982i	$0.954331\pi$
$522$	−0.0891989	−	0.154497i	−0.00390413	−	0.00676215i
$523$	−1.72028	−	2.97961i	−0.0752226	−	0.130289i	0.825960	−	0.563728i	$-0.190633\pi$
$523$	−1.72028	−	2.97961i	−0.0752226	−	0.130289i	−0.901183	+	0.433439i	$0.857300\pi$
$524$	38.8667			1.69790
$525$		0			0
$526$	−5.82368			−0.253924
$527$	9.97027	−	17.2690i	0.434312	−	0.752250i
$528$	−38.8257			−1.68967
$529$	−21.3312			−0.927443
$530$		0			0
$531$	−5.19283	−	8.99425i	−0.225350	−	0.390317i
$532$	9.65460			0.418580
$533$	6.01178	−	10.4127i	0.260399	−	0.451025i
$534$	5.37978	−	9.31806i	0.232806	−	0.403232i
$535$		0			0
$536$	0.804820	+	1.39399i	0.0347629	+	0.0602112i
$537$	−15.2718	−	26.4515i	−0.659027	−	1.14147i
$538$	0.443687	−	0.768489i	0.0191287	−	0.0331319i
$539$	6.86592	−	11.8921i	0.295736	−	0.512230i
$540$		0			0
$541$	26.7548			1.15028			0.575140	−	0.818055i	$-0.304948\pi$
$541$	26.7548			1.15028			0.575140	+	0.818055i	$0.304948\pi$
$542$	−3.51258	−	6.08397i	−0.150878	−	0.261329i
$543$	4.76054	−	8.24549i	0.204294	−	0.353848i
$544$	−9.92020			−0.425325
$545$		0			0
$546$	1.12078	−	1.94124i	0.0479648	−	0.0830775i
$547$	−10.5797			−0.452357			−0.226178	−	0.974086i	$-0.572623\pi$
$547$	−10.5797			−0.452357			−0.226178	+	0.974086i	$0.572623\pi$
$548$	5.26320	+	9.11613i	0.224833	+	0.389422i
$549$	12.7739			0.545175
$550$		0			0
$551$	−0.549391	−	0.951573i	−0.0234048	−	0.0405384i
$552$	−1.61300	−	2.79379i	−0.0686537	−	0.118912i
$553$	3.01070	−	5.21468i	0.128028	−	0.221751i
$554$	0.0510001			0.00216679
$555$		0			0
$556$	39.8385			1.68953
$557$	−21.0151	+	36.3993i	−0.890440	+	1.54229i	−0.0510917	+	0.998694i	$0.516270\pi$
$557$	−21.0151	+	36.3993i	−0.890440	+	1.54229i	−0.839349	+	0.543594i	$0.817063\pi$
$558$	−1.36068	−	2.35677i	−0.0576022	−	0.0997699i
$559$	3.62837	+	6.28452i	0.153464	+	0.265807i
$560$		0			0
$561$	−32.1869			−1.35893
$562$	3.81501	+	6.60780i	0.160927	+	0.278733i
$563$	−15.1171			−0.637108			−0.318554	−	0.947905i	$-0.603197\pi$
$563$	−15.1171			−0.637108			−0.318554	+	0.947905i	$0.603197\pi$
$564$	−0.608917	+	1.05467i	−0.0256400	+	0.0444098i
$565$		0			0
$566$	−6.45878			−0.271483
$567$	11.8635	−	20.5481i	0.498219	−	0.862941i
$568$	−0.355650	−	0.616003i	−0.0149227	−	0.0258469i
$569$	29.9574			1.25588			0.627940	−	0.778262i	$-0.283898\pi$
$569$	29.9574			1.25588			0.627940	+	0.778262i	$0.283898\pi$
$570$		0			0
$571$	−15.6228	+	27.0594i	−0.653792	+	1.13240i	0.328403	+	0.944538i	$0.393490\pi$
$571$	−15.6228	+	27.0594i	−0.653792	+	1.13240i	−0.982195	+	0.187863i	$0.939844\pi$
$572$	−8.62990	+	14.9474i	−0.360834	+	0.624983i
$573$	−12.0382	−	20.8507i	−0.502902	−	0.871053i
$574$	2.39390	+	4.14635i	0.0999194	+	0.173065i
$575$		0			0
$576$	3.61770	−	6.26605i	0.150738	−	0.261085i
$577$	14.3757	−	24.8994i	0.598467	−	1.03658i	−0.394581	−	0.918861i	$-0.629110\pi$
$577$	14.3757	−	24.8994i	0.598467	−	1.03658i	0.993048	−	0.117714i	$-0.0375566\pi$
$578$	2.76318			0.114933
$579$	15.6934	+	27.1817i	0.652194	+	1.12963i
$580$		0			0
$581$	−25.0710			−1.04012
$582$	11.8971			0.493153
$583$	−32.9631	+	57.0938i	−1.36519	+	2.36458i
$584$	−13.0839			−0.541414
$585$		0			0
$586$	3.61843			0.149476
$587$	−7.05861	−	12.2259i	−0.291340	−	0.504616i	0.682787	−	0.730618i	$-0.260768\pi$
$587$	−7.05861	−	12.2259i	−0.291340	−	0.504616i	−0.974127	+	0.226002i	$0.927434\pi$
$588$	4.91177	+	8.50744i	0.202558	+	0.350841i
$589$	−8.38066	−	14.5157i	−0.345319	−	0.598110i
$590$		0			0
$591$	22.0366			0.906466
$592$	12.4525	+	16.7535i	0.511793	+	0.688563i
$593$	5.88296			0.241584			0.120792	−	0.992678i	$-0.461457\pi$
$593$	5.88296			0.241584			0.120792	+	0.992678i	$0.461457\pi$
$594$	3.06878	−	5.31529i	0.125914	−	0.218089i
$595$		0			0
$596$	−4.64309	−	8.04207i	−0.190188	−	0.329416i
$597$	−4.07367	−	7.05580i	−0.166724	−	0.288775i
$598$	−0.662221			−0.0270802
$599$	−7.85750	−	13.6096i	−0.321049	−	0.556073i	0.659656	−	0.751568i	$-0.270702\pi$
$599$	−7.85750	−	13.6096i	−0.321049	−	0.556073i	−0.980705	+	0.195495i	$0.937369\pi$
$600$		0			0
$601$	−7.77357	+	13.4642i	−0.317090	+	0.549217i	−0.979880	−	0.199589i	$-0.936039\pi$
$601$	−7.77357	+	13.4642i	−0.317090	+	0.549217i	0.662789	+	0.748806i	$0.269373\pi$
$602$	−2.88964			−0.117773
$603$	−1.66321			−0.0677313
$604$	−22.5565	+	39.0690i	−0.917810	+	1.58969i
$605$		0			0
$606$	−5.62525			−0.228510
$607$	10.9690	−	18.9989i	0.445219	−	0.771141i	−0.552849	−	0.833282i	$-0.686459\pi$
$607$	10.9690	−	18.9989i	0.445219	−	0.771141i	0.998067	+	0.0621402i	$0.0197926\pi$
$608$	−4.16929	+	7.22142i	−0.169087	+	0.292867i
$609$	−1.00458	+	1.73999i	−0.0407078	+	0.0705080i
$610$		0			0
$611$	0.256313	+	0.443946i	0.0103693	+	0.0179602i
$612$	3.38894	−	5.86981i	0.136990	−	0.237273i
$613$	14.2377	−	24.6605i	0.575057	−	0.996027i	−0.420979	−	0.907070i	$-0.638313\pi$
$613$	14.2377	−	24.6605i	0.575057	−	0.996027i	0.996035	−	0.0889567i	$-0.0283533\pi$
$614$	2.10656	−	3.64867i	0.0850138	−	0.147248i
$615$		0			0
$616$	−7.04662	−	12.2051i	−0.283916	−	0.491757i
$617$	−17.7869	+	30.8078i	−0.716072	+	1.24027i	0.246472	+	0.969150i	$0.420729\pi$
$617$	−17.7869	+	30.8078i	−0.716072	+	1.24027i	−0.962545	+	0.271124i	$0.912605\pi$
$618$	−3.43221			−0.138064
$619$	−9.30332			−0.373932			−0.186966	−	0.982366i	$-0.559865\pi$
$619$	−9.30332			−0.373932			−0.186966	+	0.982366i	$0.559865\pi$
$620$		0			0
$621$	−4.65748			−0.186898
$622$	−0.411391	−	0.712551i	−0.0164953	−	0.0285707i
$623$	−35.6695			−1.42907
$624$	−5.84577	−	10.1252i	−0.234018	−	0.405331i
$625$		0			0
$626$	0.0921147	+	0.159547i	0.00368164	+	0.00637680i
$627$	−13.5276	+	23.4305i	−0.540240	+	0.935723i
$628$	40.1254			1.60118
$629$	10.3232	+	13.8888i	0.411613	+	0.553782i
$630$		0			0
$631$	−11.6294	+	20.1428i	−0.462961	+	0.801872i	−0.999107	−	0.0422534i	$-0.986546\pi$
$631$	−11.6294	+	20.1428i	−0.462961	+	0.801872i	0.536146	+	0.844125i	$0.319880\pi$
$632$	1.71941	+	2.97810i	0.0683943	+	0.118462i
$633$	8.66995	+	15.0168i	0.344600	+	0.596864i
$634$	1.05114	+	1.82062i	0.0417459	+	0.0723060i
$635$		0			0
$636$	−23.5813	−	40.8440i	−0.935060	−	1.61957i
$637$	4.13504			0.163836
$638$	−0.391098	+	0.677401i	−0.0154837	+	0.0268186i
$639$	0.734973			0.0290751
$640$		0			0
$641$	4.09344	−	7.09004i	0.161681	−	0.280040i	−0.773791	−	0.633441i	$-0.781642\pi$
$641$	4.09344	−	7.09004i	0.161681	−	0.280040i	0.935472	+	0.353402i	$0.114975\pi$
$642$	−0.912837	−	1.58108i	−0.0360268	−	0.0624003i
$643$	−11.4564			−0.451796			−0.225898	−	0.974151i	$-0.572532\pi$
$643$	−11.4564			−0.451796			−0.225898	+	0.974151i	$0.572532\pi$
$644$	−2.60773	+	4.51672i	−0.102759	+	0.177984i
$645$		0			0
$646$	−1.05535	+	1.82793i	−0.0415224	+	0.0719189i
$647$	7.96151	+	13.7897i	0.312999	+	0.542130i	0.979010	−	0.203812i	$-0.0653330\pi$
$647$	7.96151	+	13.7897i	0.312999	+	0.542130i	−0.666011	+	0.745942i	$0.732000\pi$
$648$	6.77522	+	11.7350i	0.266156	+	0.460995i
$649$	−22.7683	+	39.4358i	−0.893733	+	1.54799i
$650$		0			0
$651$	−15.3244	+	26.5426i	−0.600610	+	1.04029i
$652$	9.92102			0.388537
$653$	−10.4891	−	18.1677i	−0.410471	−	0.710957i	0.584470	−	0.811415i	$-0.301302\pi$
$653$	−10.4891	−	18.1677i	−0.410471	−	0.710957i	−0.994941	+	0.100458i	$0.967969\pi$
$654$	−2.80162	+	4.85255i	−0.109552	+	0.189750i
$655$		0			0
$656$	24.9723			0.975003
$657$	6.75967	−	11.7081i	0.263720	−	0.456776i
$658$	−0.204128			−0.00795774
$659$	0.598998	+	1.03749i	0.0233336	+	0.0404151i	0.877456	−	0.479656i	$-0.159239\pi$
$659$	0.598998	+	1.03749i	0.0233336	+	0.0404151i	−0.854123	+	0.520071i	$0.825905\pi$
$660$		0			0
$661$	16.1732	+	28.0129i	0.629066	+	1.08957i	0.987740	+	0.156111i	$0.0498958\pi$
$661$	16.1732	+	28.0129i	0.629066	+	1.08957i	−0.358674	+	0.933463i	$0.616771\pi$
$662$	−0.436799	−	0.756558i	−0.0169767	−	0.0294045i
$663$	−4.84619	−	8.39385i	−0.188210	−	0.325990i
$664$	7.15900	−	12.3997i	0.277823	−	0.481204i
$665$		0			0
$666$	2.34593	−	0.272370i	0.0909031	−	0.0105541i
$667$	0.593568			0.0229830
$668$	10.0628	−	17.4293i	0.389341	−	0.674359i
$669$	−16.9784	−	29.4074i	−0.656422	−	1.13696i
$670$		0			0
$671$	−28.0039	−	48.5042i	−1.08108	−	1.87248i
$672$	15.2474			0.588182
$673$	−18.5482	−	32.1264i	−0.714981	−	1.23838i	−0.962967	−	0.269620i	$-0.913102\pi$
$673$	−18.5482	−	32.1264i	−0.714981	−	1.23838i	0.247986	−	0.968764i	$-0.420231\pi$
$674$	−7.64845			−0.294607
$675$		0			0
$676$	19.5513			0.751972
$677$	−6.39266			−0.245690			−0.122845	−	0.992426i	$-0.539202\pi$
$677$	−6.39266			−0.245690			−0.122845	+	0.992426i	$0.539202\pi$
$678$	−5.04239	+	8.73368i	−0.193652	+	0.335415i
$679$	−19.7204	−	34.1567i	−0.756798	−	1.31081i
$680$		0			0
$681$	14.0028	−	24.2536i	0.536589	−	0.929399i
$682$	−5.96599	+	10.3334i	−0.228449	+	0.395686i
$683$	7.57751	−	13.1246i	0.289945	−	0.502200i	−0.683851	−	0.729622i	$-0.739696\pi$
$683$	7.57751	−	13.1246i	0.289945	−	0.502200i	0.973796	+	0.227421i	$0.0730295\pi$
$684$	−2.84862	−	4.93396i	−0.108920	−	0.188655i
$685$		0			0
$686$	−3.12611	+	5.41458i	−0.119355	+	0.206730i
$687$	−22.4766	+	38.9306i	−0.857534	+	1.48529i
$688$	−7.53592	+	13.0526i	−0.287304	+	0.497626i
$689$	−19.8523			−0.756311
$690$		0			0
$691$	−19.1544	+	33.1764i	−0.728668	+	1.26209i	0.228779	+	0.973478i	$0.426527\pi$
$691$	−19.1544	+	33.1764i	−0.728668	+	1.26209i	−0.957447	+	0.288611i	$0.906807\pi$
$692$	25.7745			0.979800
$693$	14.5623			0.553176
$694$	−1.36555	+	2.36521i	−0.0518357	+	0.0897820i
$695$		0			0
$696$	−0.573717	−	0.993707i	−0.0217467	−	0.0376664i
$697$	20.7022			0.784153
$698$	−0.443245	−	0.767723i	−0.0167771	−	0.0290587i
$699$	−13.6330	−	23.6130i	−0.515647	−	0.893126i
$700$		0			0
$701$	−7.37527	+	12.7743i	−0.278560	+	0.482480i	−0.971027	−	0.238969i	$-0.923191\pi$
$701$	−7.37527	+	12.7743i	−0.278560	+	0.482480i	0.692467	+	0.721450i	$0.256524\pi$
$702$	1.84819			0.0697556
$703$	14.4490	−	1.67757i	0.544954	−	0.0632709i
$704$	−31.7241			−1.19565
$705$		0			0
$706$	1.92601	+	3.33595i	0.0724865	+	0.125550i
$707$	9.32424	+	16.1501i	0.350674	+	0.607386i
$708$	−16.2881	−	28.2118i	−0.612143	−	1.06026i
$709$	−15.3282			−0.575664			−0.287832	−	0.957681i	$-0.592935\pi$
$709$	−15.3282			−0.575664			−0.287832	+	0.957681i	$0.592935\pi$
$710$		0			0
$711$	−3.55327			−0.133258
$712$	10.1854	−	17.6416i	0.381714	−	0.661148i
$713$	9.05456			0.339096
$714$	3.85952			0.144439
$715$		0			0
$716$	−14.1004	−	24.4226i	−0.526956	−	0.912715i
$717$	−24.9412			−0.931448
$718$	3.37891	−	5.85245i	0.126100	−	0.218411i
$719$	2.50682	−	4.34194i	0.0934885	−	0.161927i	−0.815488	−	0.578774i	$-0.803531\pi$
$719$	2.50682	−	4.34194i	0.0934885	−	0.161927i	0.908977	+	0.416847i	$0.136865\pi$
$720$		0			0
$721$	5.68913	+	9.85387i	0.211874	+	0.366977i
$722$	−2.06027	−	3.56850i	−0.0766755	−	0.132806i
$723$	−15.1544	+	26.2482i	−0.563598	+	0.976180i
$724$	4.39538	−	7.61302i	0.163353	−	0.282936i
$725$		0			0
$726$	12.2232			0.453644
$727$	−15.2817	−	26.4687i	−0.566767	−	0.981670i	−0.996883	−	0.0788961i	$-0.974860\pi$
$727$	−15.2817	−	26.4687i	−0.566767	−	0.981670i	0.430115	−	0.902774i	$-0.358473\pi$
$728$	2.12194	−	3.67530i	0.0786442	−	0.136216i
$729$	8.30023			0.307416
$730$		0			0
$731$	−6.24735	+	10.8207i	−0.231066	+	0.400219i
$732$	40.0671			1.48092
$733$	−0.0641308	−	0.111078i	−0.00236872	−	0.00410275i	0.864839	−	0.502050i	$-0.167421\pi$
$733$	−0.0641308	−	0.111078i	−0.00236872	−	0.00410275i	−0.867207	+	0.497947i	$0.834087\pi$
$734$	7.23833			0.267172
$735$		0			0
$736$	−2.25227	−	3.90105i	−0.0830198	−	0.143794i
$737$	3.64623	+	6.31546i	0.134311	+	0.232633i
$738$	1.41266	−	2.44679i	0.0520006	−	0.0900676i
$739$	3.03253			0.111553			0.0557767	−	0.998443i	$-0.482237\pi$
$739$	3.03253			0.111553			0.0557767	+	0.998443i	$0.482237\pi$
$740$		0			0
$741$	−8.14708			−0.299290
$742$	3.95260	−	6.84610i	0.145104	−	0.251328i
$743$	0.962952	+	1.66788i	0.0353273	+	0.0611886i	0.883148	−	0.469094i	$-0.155419\pi$
$743$	0.962952	+	1.66788i	0.0353273	+	0.0611886i	−0.847821	+	0.530282i	$0.822086\pi$
$744$	−8.75174	−	15.1585i	−0.320854	−	0.555736i
$745$		0			0
$746$	8.99126			0.329193
$747$	7.39727	+	12.8124i	0.270652	+	0.468783i
$748$	−29.7180			−1.08660
$749$	−3.02618	+	5.24150i	−0.110574	+	0.191520i
$750$		0			0
$751$	11.6540			0.425261			0.212630	−	0.977133i	$-0.431797\pi$
$751$	11.6540			0.425261			0.212630	+	0.977133i	$0.431797\pi$
$752$	−0.532347	+	0.922052i	−0.0194127	+	0.0336238i
$753$	−28.3361	−	49.0795i	−1.03262	−	1.78856i
$754$	−0.235541			−0.00857791
$755$		0			0
$756$	7.27792	−	12.6057i	0.264696	−	0.458466i
$757$	2.32020	−	4.01870i	0.0843290	−	0.146062i	−0.820776	−	0.571250i	$-0.806459\pi$
$757$	2.32020	−	4.01870i	0.0843290	−	0.146062i	0.905105	+	0.425188i	$0.139792\pi$
$758$	−2.53965	−	4.39880i	−0.0922441	−	0.159771i
$759$	−7.30767	−	12.6573i	−0.265252	−	0.459429i
$760$		0			0
$761$	−6.38323	+	11.0561i	−0.231392	+	0.400782i	−0.958218	−	0.286039i	$-0.907661\pi$
$761$	−6.38323	+	11.0561i	−0.231392	+	0.400782i	0.726826	+	0.686822i	$0.240995\pi$
$762$	1.28149	−	2.21960i	0.0464234	−	0.0804077i
$763$	18.5755			0.672480
$764$	−11.1148	−	19.2514i	−0.402119	−	0.696491i
$765$		0			0
$766$	−1.24379			−0.0449398
$767$	−13.7124			−0.495124
$768$	9.11684	−	15.7908i	0.328975	−	0.569802i
$769$	37.0113			1.33466			0.667330	−	0.744762i	$-0.267437\pi$
$769$	37.0113			1.33466			0.667330	+	0.744762i	$0.267437\pi$
$770$		0			0
$771$	−48.8214			−1.75826
$772$	14.4896	+	25.0967i	0.521492	+	0.903251i
$773$	21.9124	+	37.9535i	0.788136	+	1.36509i	0.927108	+	0.374795i	$0.122287\pi$
$773$	21.9124	+	37.9535i	0.788136	+	1.36509i	−0.138972	+	0.990296i	$0.544380\pi$
$774$	0.852599	+	1.47674i	0.0306460	+	0.0530805i
$775$		0			0
$776$	22.5246			0.808584
$777$	−15.8668	−	21.3471i	−0.569220	−	0.765824i
$778$	5.65648			0.202794
$779$	8.70079	−	15.0702i	0.311738	−	0.539946i
$780$		0			0
$781$	−1.61127	−	2.79080i	−0.0576557	−	0.0998625i
$782$	−0.570108	−	0.987456i	−0.0203870	−	0.0353114i
$783$	−1.65659			−0.0592017
$784$	4.29413	+	7.43765i	0.153362	+	0.265630i
$785$		0			0
$786$	6.53007	−	11.3104i	0.232920	−	0.403429i
$787$	19.9883			0.712506			0.356253	−	0.934389i	$-0.384054\pi$
$787$	19.9883			0.712506			0.356253	+	0.934389i	$0.384054\pi$
$788$	20.3463			0.724808
$789$	19.3519	−	33.5186i	0.688947	−	1.19329i
$790$		0			0
$791$	33.4325			1.18872
$792$	−4.15826	+	7.20231i	−0.147757	+	0.255923i
$793$	8.43277	−	14.6060i	0.299456	−	0.518674i
$794$	−4.02935	+	6.97904i	−0.142996	+	0.247677i
$795$		0			0
$796$	−3.76120	−	6.51459i	−0.133312	−	0.230903i
$797$	20.4059	−	35.3441i	0.722814	−	1.25195i	−0.237053	−	0.971497i	$-0.576182\pi$
$797$	20.4059	−	35.3441i	0.722814	−	1.25195i	0.959867	−	0.280454i	$-0.0904851\pi$
$798$	1.62209	−	2.80954i	0.0574213	−	0.0994566i
$799$	−0.441320	+	0.764389i	−0.0156128	+	0.0270421i
$800$		0			0
$801$	10.5244	+	18.2288i	0.371861	+	0.644083i
$802$	−2.59540	+	4.49537i	−0.0916468	+	0.158737i
$803$	−59.2763			−2.09182
$804$	−5.21691			−0.183986
$805$		0			0
$806$	−3.59305			−0.126560
$807$	2.94873	+	5.10734i	0.103800	+	0.179787i
$808$	−10.6501			−0.374670
$809$	−1.45711	−	2.52378i	−0.0512292	−	0.0887315i	0.839274	−	0.543709i	$-0.182981\pi$
$809$	−1.45711	−	2.52378i	−0.0512292	−	0.0887315i	−0.890503	+	0.454978i	$0.849647\pi$
$810$		0			0
$811$	13.8960	+	24.0686i	0.487956	+	0.845164i	0.999904	−	0.0138524i	$-0.00440949\pi$
$811$	13.8960	+	24.0686i	0.487956	+	0.845164i	−0.511949	+	0.859016i	$0.671076\pi$
$812$	−0.927528	+	1.60652i	−0.0325498	+	0.0563780i
$813$	46.6889			1.63745
$814$	−6.17717	−	8.31072i	−0.216510	−	0.291291i
$815$		0			0
$816$	10.0653	−	17.4336i	0.352355	−	0.610297i
$817$	5.25130	+	9.09552i	0.183720	+	0.318212i
$818$	0.0562293	+	0.0973920i	0.00196601	+	0.00340523i
$819$	2.19256	+	3.79763i	0.0766143	+	0.132700i
$820$		0			0
$821$	20.8119	+	36.0473i	0.726342	+	1.25806i	0.958419	+	0.285364i	$0.0921144\pi$
$821$	20.8119	+	36.0473i	0.726342	+	1.25806i	−0.232077	+	0.972697i	$0.574552\pi$
$822$	3.53712			0.123371
$823$	11.8160	−	20.4659i	0.411880	−	0.713398i	−0.583215	−	0.812318i	$-0.698206\pi$
$823$	11.8160	−	20.4659i	0.411880	−	0.713398i	0.995095	+	0.0989202i	$0.0315388\pi$
$824$	−6.49812			−0.226373
$825$		0			0
$826$	2.73014	−	4.72874i	0.0949936	−	0.164534i
$827$	−6.09101	−	10.5499i	−0.211805	−	0.366857i	0.740474	−	0.672085i	$-0.234601\pi$
$827$	−6.09101	−	10.5499i	−0.211805	−	0.366857i	−0.952279	+	0.305227i	$0.901268\pi$
$828$	3.07768			0.106957
$829$	3.01060	−	5.21452i	0.104563	−	0.181108i	−0.808997	−	0.587813i	$-0.799989\pi$
$829$	3.01060	−	5.21452i	0.104563	−	0.181108i	0.913559	+	0.406705i	$0.133322\pi$
$830$		0			0
$831$	−0.169472	+	0.293534i	−0.00587892	+	0.0101826i
$832$	−4.77651	−	8.27316i	−0.165596	−	0.286820i
$833$	3.55987	+	6.16588i	0.123342	+	0.213635i
$834$	6.69335	−	11.5932i	0.231772	−	0.401441i
$835$		0			0
$836$	−12.4900	+	21.6332i	−0.431974	+	0.748201i
$837$	−25.2704			−0.873472
$838$	2.54438	+	4.40700i	0.0878942	+	0.152237i
$839$	4.03238	−	6.98429i	0.139213	−	0.241124i	−0.787986	−	0.615693i	$-0.788876\pi$
$839$	4.03238	−	6.98429i	0.139213	−	0.241124i	0.927199	+	0.374569i	$0.122209\pi$
$840$		0			0
$841$	−28.7889			−0.992720
$842$	−0.832031	+	1.44112i	−0.0286737	+	0.0496643i
$843$	−50.7088			−1.74650
$844$	8.00493	+	13.8649i	0.275541	+	0.477251i
$845$		0			0
$846$	0.0602287	+	0.104319i	0.00207070	+	0.00358656i
$847$	−20.2607	−	35.0926i	−0.696167	−	1.20580i
$848$	−20.6160	−	35.7080i	−0.707957	−	1.22622i
$849$	21.4624	−	37.1740i	0.736587	−	1.27581i
$850$		0			0
$851$	−3.11789	+	7.21281i	−0.106880	+	0.247252i
$852$	2.30535			0.0789800
$853$	21.5722	−	37.3642i	0.738619	−	1.27933i	−0.214498	−	0.976724i	$-0.568812\pi$
$853$	21.5722	−	37.3642i	0.738619	−	1.27933i	0.953117	−	0.302602i	$-0.0978552\pi$
$854$	3.35794	+	5.81612i	0.114906	+	0.199024i
$855$		0			0
$856$	−1.72825	−	2.99342i	−0.0590704	−	0.102313i
$857$	33.4524			1.14271			0.571356	−	0.820703i	$-0.306418\pi$
$857$	33.4524			1.14271			0.571356	+	0.820703i	$0.306418\pi$
$858$	2.89985	+	5.02269i	0.0989993	+	0.171472i
$859$	7.52085			0.256608			0.128304	−	0.991735i	$-0.459047\pi$
$859$	7.52085			0.256608			0.128304	+	0.991735i	$0.459047\pi$
$860$		0			0
$861$	−31.8195			−1.08441
$862$	−12.4408			−0.423737
$863$	−11.5106	+	19.9370i	−0.391827	+	0.678664i	−0.992691	−	0.120688i	$-0.961490\pi$
$863$	−11.5106	+	19.9370i	−0.391827	+	0.678664i	0.600864	+	0.799351i	$0.294823\pi$
$864$	6.28586	+	10.8874i	0.213849	+	0.370398i
$865$		0			0
$866$	−1.38816	+	2.40436i	−0.0471716	+	0.0817036i
$867$	−9.18198	+	15.9037i	−0.311836	+	0.540116i
$868$	−14.1489	+	24.5067i	−0.480246	+	0.831810i
$869$	7.78975	+	13.4922i	0.264249	+	0.457693i
$870$		0			0
$871$	−1.09798	+	1.90176i	−0.0372038	+	0.0644388i
$872$	−5.30424	+	9.18721i	−0.179624	+	0.311118i
$873$	−11.6371	+	20.1561i	−0.393857	+	0.682180i
$874$	−0.958426			−0.0324192
$875$		0			0
$876$	21.2027	−	36.7241i	0.716373	−	1.24079i
$877$	−12.6479			−0.427089			−0.213545	−	0.976933i	$-0.568501\pi$
$877$	−12.6479			−0.427089			−0.213545	+	0.976933i	$0.568501\pi$
$878$	7.41232			0.250154
$879$	−12.0240	+	20.8261i	−0.405558	+	0.702448i
$880$		0			0
$881$	−2.42275	−	4.19633i	−0.0816247	−	0.141378i	0.822323	−	0.569021i	$-0.192678\pi$
$881$	−2.42275	−	4.19633i	−0.0816247	−	0.141378i	−0.903948	+	0.427643i	$0.859344\pi$
$882$	0.971658			0.0327174
$883$	22.8338	+	39.5494i	0.768420	+	1.33094i	0.938419	+	0.345498i	$0.112290\pi$
$883$	22.8338	+	39.5494i	0.768420	+	1.33094i	−0.169999	+	0.985444i	$0.554377\pi$
$884$	−4.47447	−	7.75000i	−0.150493	−	0.260661i
$885$		0			0
$886$	6.21393	−	10.7628i	0.208761	−	0.361585i
$887$	−48.0641			−1.61383			−0.806917	−	0.590665i	$-0.798866\pi$
$887$	−48.0641			−1.61383			−0.806917	+	0.590665i	$0.798866\pi$
$888$	15.0888	−	1.75185i	0.506346	−	0.0587883i
$889$	−8.49662			−0.284967
$890$		0			0
$891$	30.6951	+	53.1654i	1.02832	+	1.78111i
$892$	−15.6761	−	27.1517i	−0.524873	−	0.909107i
$893$	0.370959	+	0.642519i	0.0124137	+	0.0215011i
$894$	−3.12038			−0.104361
$895$		0			0
$896$	18.5937			0.621171
$897$	2.20055	−	3.81146i	0.0734741	−	0.127261i
$898$	2.37755			0.0793398
$899$	3.22056			0.107412
$900$		0			0
$901$	−17.0909	−	29.6022i	−0.569379	−	0.986194i
$902$	−12.3877			−0.412467
$903$	9.60222	−	16.6315i	0.319542	−	0.553463i
$904$	−9.54663	+	16.5352i	−0.317516	+	0.549954i
$905$		0			0
$906$	7.57952	+	13.1281i	0.251813	+	0.436152i
$907$	23.2510	+	40.2719i	0.772036	+	1.33721i	0.936446	+	0.350813i	$0.114095\pi$
$907$	23.2510	+	40.2719i	0.772036	+	1.33721i	−0.164410	+	0.986392i	$0.552572\pi$
$908$	12.9287	−	22.3932i	0.429055	−	0.743145i
$909$	5.50230	−	9.53026i	0.182500	−	0.316099i
$910$		0			0
$911$	14.3173			0.474353			0.237177	−	0.971467i	$-0.423778\pi$
$911$	14.3173			0.474353			0.237177	+	0.971467i	$0.423778\pi$
$912$	−8.46052	−	14.6540i	−0.280156	−	0.485244i
$913$	32.4338	−	56.1769i	1.07340	−	1.85919i
$914$	10.5208			0.347997
$915$		0			0
$916$	−20.7525	+	35.9444i	−0.685682	+	1.18764i
$917$	−43.2962			−1.42977
$918$	1.59112	+	2.75589i	0.0525146	+	0.0909580i
$919$	−43.3839			−1.43110			−0.715552	−	0.698559i	$-0.753825\pi$
$919$	−43.3839			−1.43110			−0.715552	+	0.698559i	$0.753825\pi$
$920$		0			0
$921$	14.0001	+	24.2489i	0.461319	+	0.799028i
$922$	2.26175	+	3.91747i	0.0744869	+	0.129015i
$923$	0.485198	−	0.840388i	0.0159705	−	0.0276617i
$924$	45.6768			1.50266
$925$		0			0
$926$	1.23742			0.0406643
$927$	3.35720	−	5.81484i	0.110265	−	0.190984i
$928$	−0.801096	−	1.38754i	−0.0262973	−	0.0455482i
$929$	14.8015	+	25.6370i	0.485623	+	0.841124i	0.999863	−	0.0165222i	$-0.00525942\pi$
$929$	14.8015	+	25.6370i	0.485623	+	0.841124i	−0.514240	+	0.857646i	$0.671926\pi$
$930$		0			0
$931$	5.98461			0.196138
$932$	−12.5873	−	21.8018i	−0.412310	−	0.714141i
$933$	5.46818			0.179020
$934$	−2.29063	+	3.96749i	−0.0749517	+	0.129820i
$935$		0			0
$936$	−2.50434			−0.0818569
$937$	5.69829	−	9.86973i	0.186155	−	0.322430i	−0.757810	−	0.652475i	$-0.773731\pi$
$937$	5.69829	−	9.86973i	0.186155	−	0.322430i	0.943965	+	0.330045i	$0.107064\pi$
$938$	−0.437218	−	0.757284i	−0.0142757	−	0.0247262i
$939$	−1.22438			−0.0399562
$940$		0			0
$941$	12.7126	−	22.0189i	0.414419	−	0.717795i	−0.580948	−	0.813940i	$-0.697318\pi$
$941$	12.7126	−	22.0189i	0.414419	−	0.717795i	0.995367	+	0.0961458i	$0.0306515\pi$
$942$	6.74154	−	11.6767i	0.219651	−	0.380447i
$943$	4.70021	+	8.14100i	0.153060	+	0.265107i
$944$	−14.2399	−	24.6642i	−0.463469	−	0.802752i
$945$		0			0
$946$	3.73827	−	6.47487i	0.121542	−	0.210516i
$947$	−8.09396	+	14.0192i	−0.263018	+	0.455561i	−0.967043	−	0.254615i	$-0.918051\pi$
$947$	−8.09396	+	14.0192i	−0.263018	+	0.455561i	0.704024	+	0.710176i	$0.251385\pi$
$948$	−11.1453			−0.361984
$949$	−8.92489	−	15.4584i	−0.289714	−	0.501800i
$950$		0			0
$951$	−13.9716			−0.453060
$952$	7.30712			0.236825
$953$	−9.72346	+	16.8415i	−0.314974	+	0.545550i	−0.979432	−	0.201775i	$-0.935329\pi$
$953$	−9.72346	+	16.8415i	−0.314974	+	0.545550i	0.664458	+	0.747325i	$0.268662\pi$
$954$	−4.66491			−0.151032
$955$		0			0
$956$	−23.0281			−0.744783
$957$	−2.59922	−	4.50198i	−0.0840208	−	0.145528i
$958$	2.42200	+	4.19502i	0.0782512	+	0.135535i
$959$	−5.86303	−	10.1551i	−0.189327	−	0.327924i
$960$		0			0
$961$	18.1278			0.584769
$962$	1.23725	−	2.86221i	0.0398906	−	0.0922813i
$963$	3.57154			0.115091
$964$	−13.9920	+	24.2348i	−0.450651	+	0.780551i
$965$		0			0
$966$	0.876260	+	1.51773i	0.0281932	+	0.0488321i
$967$	0.352631	+	0.610774i	0.0113398	+	0.0196412i	0.871640	−	0.490147i	$-0.163057\pi$
$967$	0.352631	+	0.610774i	0.0113398	+	0.0196412i	−0.860300	+	0.509788i	$0.829724\pi$
$968$	23.1418			0.743805
$969$	−7.01384	−	12.1483i	−0.225317	−	0.390261i
$970$		0			0
$971$	−5.02834	+	8.70933i	−0.161367	+	0.279496i	−0.935359	−	0.353699i	$-0.884924\pi$
$971$	−5.02834	+	8.70933i	−0.161367	+	0.279496i	0.773992	+	0.633195i	$0.218257\pi$
$972$	−23.3265			−0.748199
$973$	−44.3788			−1.42272
$974$	−5.53767	+	9.59153i	−0.177438	+	0.307332i
$975$		0			0
$976$	35.0288			1.12124
$977$	−21.8771	+	37.8923i	−0.699911	+	1.21228i	0.268586	+	0.963256i	$0.413444\pi$
$977$	−21.8771	+	37.8923i	−0.699911	+	1.21228i	−0.968497	+	0.249025i	$0.919890\pi$
$978$	1.66685	−	2.88707i	0.0533000	−	0.0923183i
$979$	46.1449	−	79.9252i	1.47480	−	2.55442i
$980$		0			0
$981$	−5.48078	−	9.49298i	−0.174988	−	0.303088i
$982$	−0.0638534	+	0.110597i	−0.00203765	+	0.00352931i
$983$	6.04809	−	10.4756i	0.192904	−	0.334119i	−0.753307	−	0.657669i	$-0.771543\pi$
$983$	6.04809	−	10.4756i	0.192904	−	0.334119i	0.946211	+	0.323549i	$0.104876\pi$
$984$	9.08604	−	15.7375i	0.289652	−	0.501692i
$985$		0			0
$986$	−0.202778	−	0.351222i	−0.00645777	−	0.0111852i
$987$	0.678313	−	1.17487i	0.0215909	−	0.0373966i
$988$	−7.52216			−0.239312
$989$	−5.67356			−0.180409
$990$		0			0
$991$	−37.4383			−1.18927			−0.594633	−	0.803997i	$-0.702703\pi$
$991$	−37.4383			−1.18927			−0.594633	+	0.803997i	$0.702703\pi$
$992$	−12.2203	−	21.1661i	−0.387994	−	0.672026i
$993$	5.80589			0.184244
$994$	0.193206	+	0.334643i	0.00612814	+	0.0106142i
$995$		0			0
$996$	23.2026	+	40.1881i	0.735203	+	1.27341i
$997$	−15.4743	+	26.8024i	−0.490078	+	0.848839i	−0.999935	−	0.0114198i	$-0.996365\pi$
$997$	−15.4743	+	26.8024i	−0.490078	+	0.848839i	0.509857	+	0.860259i	$0.329698\pi$
$998$	−11.8127			−0.373924
$999$	8.70173	−	20.1302i	0.275310	−	0.636893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.e.b.676.5		14
5.2	odd	4		925.2.o.c.824.8		28
5.3	odd	4		925.2.o.c.824.7		28
5.4	even	2		185.2.e.b.121.3	yes	14
37.26	even	3	inner	925.2.e.b.26.5		14
185.63	odd	12		925.2.o.c.174.8		28
185.64	even	6		6845.2.a.m.1.3		7
185.84	even	6		6845.2.a.j.1.5		7
185.137	odd	12		925.2.o.c.174.7		28
185.174	even	6		185.2.e.b.26.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.3	✓	14	185.174	even	6
185.2.e.b.121.3	yes	14	5.4	even	2
925.2.e.b.26.5		14	37.26	even	3	inner
925.2.e.b.676.5		14	1.1	even	1	trivial
925.2.o.c.174.7		28	185.137	odd	12
925.2.o.c.174.8		28	185.63	odd	12
925.2.o.c.824.7		28	5.3	odd	4
925.2.o.c.824.8		28	5.2	odd	4
6845.2.a.j.1.5		7	185.84	even	6
6845.2.a.m.1.3		7	185.64	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.155125 - 0.268684i) q^{2} +(1.03095 + 1.78566i) q^{3} +(0.951873 + 1.64869i) q^{4} +0.639704 q^{6} +(-1.06035 - 1.83659i) q^{7} +1.21113 q^{8} +(-0.625722 + 1.08378i) q^{9} +5.48703 q^{11} +(-1.96267 + 3.39944i) q^{12} +(0.826151 + 1.43093i) q^{13} -0.657948 q^{14} +(-1.71587 + 2.97197i) q^{16} +(-1.42247 + 2.46379i) q^{17} +(0.194130 + 0.336243i) q^{18} +(1.19568 + 2.07098i) q^{19} +(2.18635 - 3.78686i) q^{21} +(0.851174 - 1.47428i) q^{22} -1.29182 q^{23} +(1.24862 + 2.16267i) q^{24} +0.512625 q^{26} +3.60535 q^{27} +(2.01864 - 3.49639i) q^{28} -0.459480 q^{29} -7.00913 q^{31} +(1.74348 + 3.01980i) q^{32} +(5.65686 + 9.79798i) q^{33} +(0.441320 + 0.764389i) q^{34} -2.38243 q^{36} +(2.41356 - 5.58343i) q^{37} +0.741917 q^{38} +(-1.70344 + 2.95045i) q^{39} +(-3.63843 - 6.30194i) q^{41} +(-0.678313 - 1.17487i) q^{42} +4.39190 q^{43} +(5.22296 + 9.04642i) q^{44} +(-0.200394 + 0.347092i) q^{46} +0.310249 q^{47} -7.07591 q^{48} +(1.25130 - 2.16731i) q^{49} -5.86599 q^{51} +(-1.57278 + 2.72414i) q^{52} +(-6.00746 + 10.4052i) q^{53} +(0.559279 - 0.968700i) q^{54} +(-1.28423 - 2.22435i) q^{56} +(-2.46537 + 4.27015i) q^{57} +(-0.0712767 + 0.123455i) q^{58} +(-4.14947 + 7.18709i) q^{59} +(-5.10365 - 8.83978i) q^{61} +(-1.08729 + 1.88324i) q^{62} +2.65395 q^{63} -5.78165 q^{64} +3.51008 q^{66} +(0.664518 + 1.15098i) q^{67} -5.41604 q^{68} +(-1.33181 - 2.30676i) q^{69} +(-0.293650 - 0.508617i) q^{71} +(-0.757834 + 1.31261i) q^{72} -10.8030 q^{73} +(-1.12578 - 1.51461i) q^{74} +(-2.27627 + 3.94261i) q^{76} +(-5.81820 - 10.0774i) q^{77} +(0.528492 + 0.915375i) q^{78} +(1.41967 + 2.45893i) q^{79} +(5.59411 + 9.68928i) q^{81} -2.25764 q^{82} +(5.91099 - 10.2381i) q^{83} +8.32450 q^{84} +(0.681292 - 1.18003i) q^{86} +(-0.473702 - 0.820476i) q^{87} +6.64553 q^{88} +(8.40980 - 14.5662i) q^{89} +(1.75202 - 3.03459i) q^{91} +(-1.22965 - 2.12982i) q^{92} +(-7.22607 - 12.5159i) q^{93} +(0.0481273 - 0.0833590i) q^{94} +(-3.59489 + 6.22653i) q^{96} +18.5979 q^{97} +(-0.388215 - 0.672407i) q^{98} +(-3.43336 + 5.94675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{3} - 8 q^{4} + 4 q^{6} - 2 q^{7} + 6 q^{8} - 5 q^{9} - 10 q^{11} + 8 q^{12} - 6 q^{13} - 36 q^{14} - 14 q^{16} + q^{17} + 4 q^{18} + 6 q^{19} + 13 q^{21} + q^{22} - 12 q^{23} - 21 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 2 * q^3 - 8 * q^4 + 4 * q^6 - 2 * q^7 + 6 * q^8 - 5 * q^9 - 10 * q^11 + 8 * q^12 - 6 * q^13 - 36 * q^14 - 14 * q^16 + q^17 + 4 * q^18 + 6 * q^19 + 13 * q^21 + q^22 - 12 * q^23 - 21 * q^24 + 2 * q^26 - 22 * q^27 - 13 * q^28 - 12 * q^29 - 8 * q^31 - 18 * q^32 - q^33 - 11 * q^34 - 8 * q^36 - 12 * q^37 - 16 * q^38 + 23 * q^39 - 3 * q^41 - 29 * q^42 + 38 * q^43 + 25 * q^44 + 10 * q^46 - 4 * q^47 + 20 * q^48 - 7 * q^49 - 14 * q^51 - 46 * q^52 + 2 * q^53 + 23 * q^54 + 19 * q^56 - 22 * q^57 + 12 * q^58 - 18 * q^59 - 20 * q^61 + 21 * q^62 - 46 * q^63 + 50 * q^64 - 42 * q^66 + 20 * q^67 - 110 * q^68 + 17 * q^69 - 11 * q^71 + 29 * q^72 + 36 * q^73 - 66 * q^74 + 40 * q^76 + q^77 - 6 * q^78 + 23 * q^79 + 29 * q^81 + 24 * q^82 + 9 * q^83 + 8 * q^84 - 3 * q^86 + 43 * q^87 + 116 * q^88 - 16 * q^89 + 12 * q^91 + 33 * q^92 - 25 * q^93 + 22 * q^94 - 67 * q^96 + 62 * q^97 + 24 * q^98 + 4 * q^99

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