LMFDB - Embedded newform 136.2.c.a.69.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(69,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("136.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.c (of order $2$, degree $1$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.6
Root			$-0.578647 - 1.29041i$ of defining polynomial
Character	$\chi$	$=$	136.69
Dual form			136.2.c.a.69.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578647 + 1.29041i) q^{2} -2.34593i q^{3} +(-1.33034 + 1.49339i) q^{4} -3.12087i q^{5} +(3.02722 - 1.35746i) q^{6} +2.86993 q^{7} +(-2.69688 - 0.852541i) q^{8} -2.50338 q^{9} +O(q^{10})$	\(q+(0.578647 + 1.29041i) q^{2} -2.34593i q^{3} +(-1.33034 + 1.49339i) q^{4} -3.12087i q^{5} +(3.02722 - 1.35746i) q^{6} +2.86993 q^{7} +(-2.69688 - 0.852541i) q^{8} -2.50338 q^{9} +(4.02722 - 1.80588i) q^{10} +5.06085i q^{11} +(3.50338 + 3.12087i) q^{12} -2.04078i q^{13} +(1.66067 + 3.70339i) q^{14} -7.32134 q^{15} +(-0.460411 - 3.97341i) q^{16} -1.00000 q^{17} +(-1.44857 - 3.23040i) q^{18} +6.32669i q^{19} +(4.66067 + 4.15181i) q^{20} -6.73264i q^{21} +(-6.53060 + 2.92845i) q^{22} -3.18451 q^{23} +(-2.00000 + 6.32669i) q^{24} -4.73985 q^{25} +(2.63345 - 1.18089i) q^{26} -1.16504i q^{27} +(-3.81797 + 4.28591i) q^{28} +5.45095i q^{29} +(-4.23647 - 9.44757i) q^{30} +6.19127 q^{31} +(4.86093 - 2.89332i) q^{32} +11.8724 q^{33} +(-0.578647 - 1.29041i) q^{34} -8.95667i q^{35} +(3.33034 - 3.73851i) q^{36} -1.57098i q^{37} +(-8.16405 + 3.66092i) q^{38} -4.78753 q^{39} +(-2.66067 + 8.41663i) q^{40} -0.733092 q^{41} +(8.68789 - 3.89582i) q^{42} +5.97355i q^{43} +(-7.55782 - 6.73264i) q^{44} +7.81273i q^{45} +(-1.84271 - 4.10934i) q^{46} -10.0544 q^{47} +(-9.32134 + 1.08009i) q^{48} +1.23647 q^{49} +(-2.74270 - 6.11637i) q^{50} +2.34593i q^{51} +(3.04768 + 2.71493i) q^{52} -10.1217i q^{53} +(1.50338 - 0.674144i) q^{54} +15.7943 q^{55} +(-7.73985 - 2.44673i) q^{56} +14.8420 q^{57} +(-7.03398 + 3.15417i) q^{58} +0.268198i q^{59} +(9.73985 - 10.9336i) q^{60} +2.58448i q^{61} +(3.58256 + 7.98930i) q^{62} -7.18451 q^{63} +(6.54635 + 4.59841i) q^{64} -6.36902 q^{65} +(6.86993 + 15.3203i) q^{66} +0.116656i q^{67} +(1.33034 - 1.49339i) q^{68} +7.47064i q^{69} +(11.5578 - 5.18275i) q^{70} +4.49234 q^{71} +(6.75132 + 2.13423i) q^{72} +15.6494 q^{73} +(2.02722 - 0.909044i) q^{74} +11.1193i q^{75} +(-9.44820 - 8.41663i) q^{76} +14.5243i q^{77} +(-2.77029 - 6.17789i) q^{78} -0.815488 q^{79} +(-12.4005 + 1.43688i) q^{80} -10.2432 q^{81} +(-0.424201 - 0.945992i) q^{82} -3.81337i q^{83} +(10.0544 + 8.95667i) q^{84} +3.12087i q^{85} +(-7.70835 + 3.45657i) q^{86} +12.7875 q^{87} +(4.31459 - 13.6485i) q^{88} -9.87240 q^{89} +(-10.0817 + 4.52081i) q^{90} -5.85689i q^{91} +(4.23647 - 4.75571i) q^{92} -14.5243i q^{93} +(-5.81797 - 12.9744i) q^{94} +19.7448 q^{95} +(-6.78753 - 11.4034i) q^{96} -11.3758 q^{97} +(0.715480 + 1.59556i) q^{98} -12.6692i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9	$ 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9} + 6 q^{10} + 16 q^{12} - 10 q^{14} - 12 q^{15} - 7 q^{16} - 8 q^{17} + 9 q^{18} + 14 q^{20} - 14 q^{22} + 12 q^{23} - 16 q^{24} - 8 q^{25} + 24 q^{26} + 4 q^{28} - 16 q^{30} - 12 q^{31} - 11 q^{32} + 8 q^{33} + q^{34} + 15 q^{36} - 30 q^{38} + 20 q^{39} + 2 q^{40} + 20 q^{42} + 4 q^{44} - 26 q^{46} - 28 q^{47} - 28 q^{48} - 8 q^{49} + 19 q^{50} - 4 q^{52} + 44 q^{55} - 32 q^{56} + 8 q^{57} - 6 q^{58} + 48 q^{60} + 10 q^{62} - 20 q^{63} + 25 q^{64} + 24 q^{65} + 40 q^{66} - q^{68} + 28 q^{70} - 13 q^{72} + 8 q^{73} - 10 q^{74} + 6 q^{76} - 16 q^{78} - 44 q^{79} - 46 q^{80} - 40 q^{81} + 2 q^{82} + 28 q^{84} - 10 q^{86} + 44 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{90} + 16 q^{92} - 12 q^{94} - 16 q^{95} + 4 q^{96} + 8 q^{97} - 9 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9 + 6 * q^10 + 16 * q^12 - 10 * q^14 - 12 * q^15 - 7 * q^16 - 8 * q^17 + 9 * q^18 + 14 * q^20 - 14 * q^22 + 12 * q^23 - 16 * q^24 - 8 * q^25 + 24 * q^26 + 4 * q^28 - 16 * q^30 - 12 * q^31 - 11 * q^32 + 8 * q^33 + q^34 + 15 * q^36 - 30 * q^38 + 20 * q^39 + 2 * q^40 + 20 * q^42 + 4 * q^44 - 26 * q^46 - 28 * q^47 - 28 * q^48 - 8 * q^49 + 19 * q^50 - 4 * q^52 + 44 * q^55 - 32 * q^56 + 8 * q^57 - 6 * q^58 + 48 * q^60 + 10 * q^62 - 20 * q^63 + 25 * q^64 + 24 * q^65 + 40 * q^66 - q^68 + 28 * q^70 - 13 * q^72 + 8 * q^73 - 10 * q^74 + 6 * q^76 - 16 * q^78 - 44 * q^79 - 46 * q^80 - 40 * q^81 + 2 * q^82 + 28 * q^84 - 10 * q^86 + 44 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 + 16 * q^92 - 12 * q^94 - 16 * q^95 + 4 * q^96 + 8 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.578647	+	1.29041i	0.409165	+	0.912460i
$2$	0.578647	+	1.29041i	0.409165	+	0.912460i
$3$		−	2.34593i		−	1.35442i	−0.735789	−	0.677211i	$-0.763188\pi$
$3$		−	2.34593i		−	1.35442i	0.735789	−	0.677211i	$-0.236812\pi$
$4$	−1.33034	+	1.49339i	−0.665168	+	0.746694i
$5$		−	3.12087i		−	1.39570i	−0.716245	−	0.697849i	$-0.754141\pi$
$5$		−	3.12087i		−	1.39570i	0.716245	−	0.697849i	$-0.245859\pi$
$6$	3.02722	−	1.35746i	1.23586	−	0.554182i
$7$	2.86993			1.08473			0.542365	−	0.840143i	$-0.317529\pi$
$7$	2.86993			1.08473			0.542365	+	0.840143i	$0.317529\pi$
$8$	−2.69688	−	0.852541i	−0.953492	−	0.301419i
$9$	−2.50338			−0.834460
$10$	4.02722	−	1.80588i	1.27352	−	0.571070i
$11$			5.06085i			1.52591i	0.646454	+	0.762953i	$0.276251\pi$
$11$			5.06085i			1.52591i	−0.646454	+	0.762953i	$0.723749\pi$
$12$	3.50338	+	3.12087i	1.01134	+	0.900919i
$13$		−	2.04078i		−	0.566011i	−0.959118	−	0.283006i	$-0.908668\pi$
$13$		−	2.04078i		−	0.566011i	0.959118	−	0.283006i	$-0.0913315\pi$
$14$	1.66067	+	3.70339i	0.443833	+	0.989773i
$15$	−7.32134			−1.89036
$16$	−0.460411	−	3.97341i	−0.115103	−	0.993354i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−1.44857	−	3.23040i	−0.341432	−	0.761412i
$19$			6.32669i			1.45144i	0.687989	+	0.725721i	$0.258494\pi$
$19$			6.32669i			1.45144i	−0.687989	+	0.725721i	$0.741506\pi$
$20$	4.66067	+	4.15181i	1.04216	+	0.928373i
$21$		−	6.73264i		−	1.46918i
$22$	−6.53060	+	2.92845i	−1.39233	+	0.624347i
$23$	−3.18451			−0.664017			−0.332008	−	0.943276i	$-0.607726\pi$
$23$	−3.18451			−0.664017			−0.332008	+	0.943276i	$0.607726\pi$
$24$	−2.00000	+	6.32669i	−0.408248	+	1.29143i
$25$	−4.73985			−0.947970
$26$	2.63345	−	1.18089i	0.516463	−	0.231592i
$27$		−	1.16504i		−	0.224211i
$28$	−3.81797	+	4.28591i	−0.721528	+	0.809961i
$29$			5.45095i			1.01222i	0.862470	+	0.506108i	$0.168916\pi$
$29$			5.45095i			1.01222i	−0.862470	+	0.506108i	$0.831084\pi$
$30$	−4.23647	−	9.44757i	−0.773470	−	1.72488i
$31$	6.19127			1.11198			0.555992	−	0.831187i	$-0.312338\pi$
$31$	6.19127			1.11198			0.555992	+	0.831187i	$0.312338\pi$
$32$	4.86093	−	2.89332i	0.859300	−	0.511472i
$33$	11.8724			2.06672
$34$	−0.578647	−	1.29041i	−0.0992371	−	0.221304i
$35$		−	8.95667i		−	1.51395i
$36$	3.33034	−	3.73851i	0.555056	−	0.623086i
$37$		−	1.57098i		−	0.258268i	−0.991627	−	0.129134i	$-0.958780\pi$
$37$		−	1.57098i		−	0.258268i	0.991627	−	0.129134i	$-0.0412197\pi$
$38$	−8.16405	+	3.66092i	−1.32438	+	0.593879i
$39$	−4.78753			−0.766618
$40$	−2.66067	+	8.41663i	−0.420689	+	1.33079i
$41$	−0.733092			−0.114490			−0.0572449	−	0.998360i	$-0.518232\pi$
$41$	−0.733092			−0.114490			−0.0572449	+	0.998360i	$0.518232\pi$
$42$	8.68789	−	3.89582i	1.34057	−	0.601138i
$43$			5.97355i			0.910958i	0.890247	+	0.455479i	$0.150532\pi$
$43$			5.97355i			0.910958i	−0.890247	+	0.455479i	$0.849468\pi$
$44$	−7.55782	−	6.73264i	−1.13938	−	1.01498i
$45$			7.81273i			1.16465i
$46$	−1.84271	−	4.10934i	−0.271692	−	0.605889i
$47$	−10.0544			−1.46659			−0.733295	−	0.679910i	$-0.762019\pi$
$47$	−10.0544			−1.46659			−0.733295	+	0.679910i	$0.762019\pi$
$48$	−9.32134	+	1.08009i	−1.34542	+	0.155898i
$49$	1.23647			0.176639
$50$	−2.74270	−	6.11637i	−0.387876	−	0.864985i
$51$			2.34593i			0.328496i
$52$	3.04768	+	2.71493i	0.422637	+	0.376493i
$53$		−	10.1217i		−	1.39032i	−0.718853	−	0.695162i	$-0.755333\pi$
$53$		−	10.1217i		−	1.39032i	0.718853	−	0.695162i	$-0.244667\pi$
$54$	1.50338	−	0.674144i	0.204584	−	0.0917394i
$55$	15.7943			2.12970
$56$	−7.73985	−	2.44673i	−1.03428	−	0.326958i
$57$	14.8420			1.96587
$58$	−7.03398	+	3.15417i	−0.923606	+	0.414163i
$59$			0.268198i			0.0349164i	0.999848	+	0.0174582i	$0.00555740\pi$
$59$			0.268198i			0.0349164i	−0.999848	+	0.0174582i	$0.994443\pi$
$60$	9.73985	−	10.9336i	1.25741	−	1.41152i
$61$			2.58448i			0.330908i	0.986217	+	0.165454i	$0.0529090\pi$
$61$			2.58448i			0.330908i	−0.986217	+	0.165454i	$0.947091\pi$
$62$	3.58256	+	7.98930i	0.454985	+	1.01464i
$63$	−7.18451			−0.905163
$64$	6.54635	+	4.59841i	0.818293	+	0.574801i
$65$	−6.36902			−0.789980
$66$	6.86993	+	15.3203i	0.845629	+	1.88580i
$67$			0.116656i			0.0142518i	0.999975	+	0.00712590i	$0.00226826\pi$
$67$			0.116656i			0.0142518i	−0.999975	+	0.00712590i	$0.997732\pi$
$68$	1.33034	−	1.49339i	0.161327	−	0.181100i
$69$			7.47064i			0.899359i
$70$	11.5578	−	5.18275i	1.38142	−	0.619457i
$71$	4.49234			0.533143			0.266571	−	0.963815i	$-0.414109\pi$
$71$	4.49234			0.533143			0.266571	+	0.963815i	$0.414109\pi$
$72$	6.75132	+	2.13423i	0.795651	+	0.251522i
$73$	15.6494			1.83163			0.915815	−	0.401601i	$-0.131546\pi$
$73$	15.6494			1.83163			0.915815	+	0.401601i	$0.131546\pi$
$74$	2.02722	−	0.909044i	0.235659	−	0.105674i
$75$			11.1193i			1.28395i
$76$	−9.44820	−	8.41663i	−1.08378	−	0.965453i
$77$			14.5243i			1.65519i
$78$	−2.77029	−	6.17789i	−0.313673	−	0.699509i
$79$	−0.815488			−0.0917496			−0.0458748	−	0.998947i	$-0.514608\pi$
$79$	−0.815488			−0.0917496			−0.0458748	+	0.998947i	$0.514608\pi$
$80$	−12.4005	+	1.43688i	−1.38642	+	0.160649i
$81$	−10.2432			−1.13814
$82$	−0.424201	−	0.945992i	−0.0468452	−	0.104467i
$83$		−	3.81337i		−	0.418571i	−0.977855	−	0.209286i	$-0.932886\pi$
$83$		−	3.81337i		−	0.418571i	0.977855	−	0.209286i	$-0.0671139\pi$
$84$	10.0544	+	8.95667i	1.09703	+	0.977253i
$85$			3.12087i			0.338506i
$86$	−7.70835	+	3.45657i	−0.831213	+	0.372732i
$87$	12.7875			1.37097
$88$	4.31459	−	13.6485i	0.459936	−	1.45494i
$89$	−9.87240			−1.04647			−0.523236	−	0.852188i	$-0.675275\pi$
$89$	−9.87240			−1.04647			−0.523236	+	0.852188i	$0.675275\pi$
$90$	−10.0817	+	4.52081i	−1.06270	+	0.476535i
$91$		−	5.85689i		−	0.613969i
$92$	4.23647	−	4.75571i	0.441683	−	0.495817i
$93$		−	14.5243i		−	1.50610i
$94$	−5.81797	−	12.9744i	−0.600077	−	1.33821i
$95$	19.7448			2.02577
$96$	−6.78753	−	11.4034i	−0.692749	−	1.16385i
$97$	−11.3758			−1.15504			−0.577518	−	0.816378i	$-0.695979\pi$
$97$	−11.3758			−1.15504			−0.577518	+	0.816378i	$0.695979\pi$
$98$	0.715480	+	1.59556i	0.0722744	+	0.161176i
$99$		−	12.6692i		−	1.27331i
$100$	6.30560	−	7.07843i	0.630560	−	0.707843i
$101$		−	0.289291i		−	0.0287855i	−0.999896	−	0.0143927i	$-0.995418\pi$
$101$		−	0.289291i		−	0.0287855i	0.999896	−	0.0143927i	$-0.00458151\pi$
$102$	−3.02722	+	1.35746i	−0.299739	+	0.134409i
$103$	−0.472943			−0.0466004			−0.0233002	−	0.999729i	$-0.507417\pi$
$103$	−0.472943			−0.0466004			−0.0233002	+	0.999729i	$0.507417\pi$
$104$	−1.73985	+	5.50375i	−0.170606	+	0.539687i
$105$	−21.0117			−2.05053
$106$	13.0612	−	5.85689i	1.26862	−	0.568872i
$107$		−	9.52727i		−	0.921036i	−0.887650	−	0.460518i	$-0.847664\pi$
$107$		−	9.52727i		−	0.921036i	0.887650	−	0.460518i	$-0.152336\pi$
$108$	1.73985	+	1.54989i	0.167417	+	0.149138i
$109$		−	11.0824i		−	1.06150i	−0.847528	−	0.530751i	$-0.821910\pi$
$109$		−	11.0824i		−	1.06150i	0.847528	−	0.530751i	$-0.178090\pi$
$110$	9.13931	+	20.3812i	0.871399	+	1.94327i
$111$	−3.68541			−0.349804
$112$	−1.32134	−	11.4034i	−0.124855	−	1.07752i
$113$	−12.3690			−1.16358			−0.581790	−	0.813339i	$-0.697647\pi$
$113$	−12.3690			−1.16358			−0.581790	+	0.813339i	$0.697647\pi$
$114$	8.58825	+	19.1523i	0.804364	+	1.79378i
$115$			9.93846i			0.926766i
$116$	−8.14037	−	7.25159i	−0.755815	−	0.673293i
$117$			5.10885i			0.472314i
$118$	−0.346086	+	0.155192i	−0.0318598	+	0.0142866i
$119$	−2.86993			−0.263086
$120$	19.7448	+	6.24175i	1.80245	+	0.569791i
$121$	−14.6123			−1.32839
$122$	−3.33505	+	1.49550i	−0.301941	+	0.135396i
$123$			1.71978i			0.155067i
$124$	−8.23647	+	9.24596i	−0.739657	+	0.830312i
$125$		−	0.811893i		−	0.0726179i
$126$	−4.15729	−	9.27099i	−0.370361	−	0.825926i
$127$	−17.3758			−1.54185			−0.770926	−	0.636925i	$-0.780206\pi$
$127$	−17.3758			−1.54185			−0.770926	+	0.636925i	$0.780206\pi$
$128$	−2.14582	+	11.1083i	−0.189666	+	0.981849i
$129$	14.0135			1.23382
$130$	−3.68541	−	8.21868i	−0.323232	−	0.720826i
$131$		−	9.60117i		−	0.838858i	−0.907788	−	0.419429i	$-0.862230\pi$
$131$		−	9.60117i		−	0.838858i	0.907788	−	0.419429i	$-0.137770\pi$
$132$	−15.7943	+	17.7301i	−1.37472	+	1.54321i
$133$			18.1571i			1.57442i
$134$	−0.150535	+	0.0675026i	−0.0130042	+	0.00583134i
$135$	−3.63593			−0.312931
$136$	2.69688	+	0.852541i	0.231256	+	0.0731048i
$137$	15.4560			1.32050			0.660249	−	0.751047i	$-0.270451\pi$
$137$	15.4560			1.32050			0.660249	+	0.751047i	$0.270451\pi$
$138$	−9.64021	+	4.32286i	−0.820629	+	0.367986i
$139$		−	11.7058i		−	0.992873i	−0.868073	−	0.496437i	$-0.834641\pi$
$139$		−	11.7058i		−	0.992873i	0.868073	−	0.496437i	$-0.165359\pi$
$140$	13.3758	+	11.9154i	1.13046	+	1.00703i
$141$			23.5870i			1.98638i
$142$	2.59948	+	5.79698i	0.218143	+	0.486472i
$143$	10.3281			0.863679
$144$	1.15258	+	9.94696i	0.0960486	+	0.828914i
$145$	17.0117			1.41275
$146$	9.05550	+	20.1943i	0.749439	+	1.67129i
$147$		−	2.90067i		−	0.239243i
$148$	2.34609	+	2.08994i	0.192847	+	0.171792i
$149$			2.86647i			0.234830i	0.993083	+	0.117415i	$0.0374608\pi$
$149$			2.86647i			0.234830i	−0.993083	+	0.117415i	$0.962539\pi$
$150$	−14.3486	+	6.43417i	−1.17156	+	0.525348i
$151$	−0.746609			−0.0607582			−0.0303791	−	0.999538i	$-0.509671\pi$
$151$	−0.746609			−0.0607582			−0.0303791	+	0.999538i	$0.509671\pi$
$152$	5.39376	−	17.0623i	0.437492	−	1.38394i
$153$	2.50338			0.202386
$154$	−18.7423	+	8.40442i	−1.51030	+	0.677248i
$155$		−	19.3222i		−	1.55199i
$156$	6.36902	−	7.14963i	0.509930	−	0.572429i
$157$		−	10.9336i		−	0.872597i	−0.899802	−	0.436298i	$-0.856289\pi$
$157$		−	10.9336i		−	0.872597i	0.899802	−	0.436298i	$-0.143711\pi$
$158$	−0.471880	−	1.05232i	−0.0375407	−	0.0837179i
$159$	−23.7448			−1.88309
$160$	−9.02970	−	15.1704i	−0.713860	−	1.19932i
$161$	−9.13931			−0.720279
$162$	−5.92721	−	13.2180i	−0.465686	−	1.03850i
$163$			16.1961i			1.26857i	0.773098	+	0.634287i	$0.218706\pi$
$163$			16.1961i			1.26857i	−0.773098	+	0.634287i	$0.781294\pi$
$164$	0.975259	−	1.09479i	0.0761549	−	0.0854888i
$165$		−	37.0523i		−	2.88451i
$166$	4.92082	−	2.20659i	0.381930	−	0.171265i
$167$	2.75249			0.212994			0.106497	−	0.994313i	$-0.466037\pi$
$167$	2.75249			0.212994			0.106497	+	0.994313i	$0.466037\pi$
$168$	−5.73985	+	18.1571i	−0.442839	+	1.40085i
$169$	8.83521			0.679631
$170$	−4.02722	+	1.80588i	−0.308874	+	0.138505i
$171$		−	15.8381i		−	1.21117i
$172$	−8.92082	−	7.94683i	−0.680206	−	0.605940i
$173$			17.3241i			1.31713i	0.752524	+	0.658565i	$0.228836\pi$
$173$			17.3241i			1.31713i	−0.752524	+	0.658565i	$0.771164\pi$
$174$	7.39946	+	16.5012i	0.560952	+	1.25095i
$175$	−13.6030			−1.02829
$176$	20.1089	−	2.33007i	1.51576	−	0.175636i
$177$	0.629173			0.0472915
$178$	−5.71263	−	12.7395i	−0.428180	−	0.954865i
$179$		−	1.43323i		−	0.107125i	−0.998565	−	0.0535625i	$-0.982942\pi$
$179$		−	1.43323i		−	0.107125i	0.998565	−	0.0535625i	$-0.0170576\pi$
$180$	−11.6674	−	10.3936i	−0.869639	−	0.774690i
$181$		−	8.34913i		−	0.620586i	−0.950641	−	0.310293i	$-0.899573\pi$
$181$		−	8.34913i		−	0.620586i	0.950641	−	0.310293i	$-0.100427\pi$
$182$	7.55782	−	3.38907i	0.560223	−	0.251215i
$183$	6.06300			0.448190
$184$	8.58825	+	2.71493i	0.633134	+	0.200147i
$185$	−4.90284			−0.360464
$186$	18.7423	−	8.40442i	1.37425	−	0.616242i
$187$		−	5.06085i		−	0.370086i
$188$	13.3758	−	15.0152i	0.975529	−	1.09509i
$189$		−	3.34357i		−	0.243209i
$190$	11.4253	+	25.4790i	0.828876	+	1.84844i
$191$	−15.5950			−1.12842			−0.564208	−	0.825633i	$-0.690818\pi$
$191$	−15.5950			−1.12842			−0.564208	+	0.825633i	$0.690818\pi$
$192$	10.7875	−	15.3573i	0.778523	−	1.10831i
$193$	18.2651			1.31475			0.657375	−	0.753563i	$-0.271667\pi$
$193$	18.2651			1.31475			0.657375	+	0.753563i	$0.271667\pi$
$194$	−6.58256	−	14.6795i	−0.472600	−	1.05392i
$195$			14.9413i			1.06997i
$196$	−1.64492	+	1.84653i	−0.117494	+	0.131895i
$197$			20.6994i			1.47477i	0.675471	+	0.737387i	$0.263940\pi$
$197$			20.6994i			1.47477i	−0.675471	+	0.737387i	$0.736060\pi$
$198$	16.3486	−	7.33101i	1.16184	−	0.520992i
$199$	−0.451420			−0.0320003			−0.0160001	−	0.999872i	$-0.505093\pi$
$199$	−0.451420			−0.0320003			−0.0160001	+	0.999872i	$0.505093\pi$
$200$	12.7828	+	4.04092i	0.903882	+	0.285736i
$201$	0.273667			0.0193030
$202$	0.373305	−	0.167397i	0.0262656	−	0.0117780i
$203$			15.6438i			1.09798i
$204$	−3.50338	−	3.12087i	−0.245286	−	0.218505i
$205$			2.28789i			0.159793i
$206$	−0.273667	−	0.610292i	−0.0190673	−	0.0425210i
$207$	7.97204			0.554095
$208$	−8.10887	+	0.939599i	−0.562249	+	0.0651494i
$209$	−32.0185			−2.21476
$210$	−12.1584	−	27.1138i	−0.839006	−	1.87103i
$211$			21.2728i			1.46448i	0.681048	+	0.732239i	$0.261525\pi$
$211$			21.2728i			1.46448i	−0.681048	+	0.732239i	$0.738475\pi$
$212$	15.1156	+	13.4653i	1.03815	+	0.924799i
$213$		−	10.5387i		−	0.722100i
$214$	12.2941	−	5.51292i	0.840409	−	0.376856i
$215$	18.6427			1.27142
$216$	−0.993241	+	3.14197i	−0.0675815	+	0.213784i
$217$	17.7685			1.20620
$218$	14.3009	−	6.41279i	0.968578	−	0.434329i
$219$		−	36.7125i		−	2.48080i
$220$	−21.0117	+	23.5870i	−1.41661	+	1.59023i
$221$			2.04078i			0.137278i
$222$	−2.13255	−	4.75571i	−0.143128	−	0.319182i
$223$	2.80105			0.187572			0.0937860	−	0.995592i	$-0.470103\pi$
$223$	2.80105			0.187572			0.0937860	+	0.995592i	$0.470103\pi$
$224$	13.9505	−	8.30362i	0.932108	−	0.554809i
$225$	11.8656			0.791043
$226$	−7.15729	−	15.9612i	−0.476096	−	1.06172i
$227$		−	1.71729i		−	0.113980i	−0.998375	−	0.0569902i	$-0.981850\pi$
$227$		−	1.71729i		−	0.113980i	0.998375	−	0.0569902i	$-0.0181504\pi$
$228$	−19.7448	+	22.1648i	−1.30763	+	1.46790i
$229$			14.1633i			0.935934i	0.883746	+	0.467967i	$0.155013\pi$
$229$			14.1633i			0.935934i	−0.883746	+	0.467967i	$0.844987\pi$
$230$	−12.8247	+	5.75085i	−0.845637	+	0.379200i
$231$	34.0729			2.24183
$232$	4.64716	−	14.7006i	0.305101	−	0.965139i
$233$	3.89608			0.255241			0.127620	−	0.991823i	$-0.459266\pi$
$233$	3.89608			0.255241			0.127620	+	0.991823i	$0.459266\pi$
$234$	−6.59253	+	2.95622i	−0.430967	+	0.193254i
$235$			31.3786i			2.04692i
$236$	−0.400523	−	0.356793i	−0.0260718	−	0.0232253i
$237$			1.91308i			0.124268i
$238$	−1.66067	−	3.70339i	−0.107645	−	0.240055i
$239$	−19.0747			−1.23384			−0.616920	−	0.787026i	$-0.711620\pi$
$239$	−19.0747			−1.23384			−0.616920	+	0.787026i	$0.711620\pi$
$240$	3.37083	+	29.0907i	0.217586	+	1.87780i
$241$	−5.51849			−0.355477			−0.177739	−	0.984078i	$-0.556878\pi$
$241$	−5.51849			−0.355477			−0.177739	+	0.984078i	$0.556878\pi$
$242$	−8.45533	−	18.8559i	−0.543529	−	1.21210i
$243$			20.5348i			1.31731i
$244$	−3.85963	−	3.43822i	−0.247087	−	0.220110i
$245$		−	3.85887i		−	0.246534i
$246$	−2.21923	+	0.995146i	−0.141493	+	0.0634482i
$247$	12.9114			0.821533
$248$	−16.6971	−	5.27831i	−1.06027	−	0.335173i
$249$	−8.94589			−0.566922
$250$	1.04768	−	0.469799i	0.0662610	−	0.0297127i
$251$			20.3601i			1.28512i	0.766237	+	0.642558i	$0.222127\pi$
$251$			20.3601i			1.28512i	−0.766237	+	0.642558i	$0.777873\pi$
$252$	9.55782	−	10.7293i	0.602086	−	0.675880i
$253$		−	16.1164i		−	1.01323i
$254$	−10.0544	−	22.4220i	−0.630871	−	1.40688i
$255$	7.32134			0.458480
$256$	−15.5760	+	3.65881i	−0.973503	+	0.228675i
$257$	23.6123			1.47289			0.736446	−	0.676496i	$-0.236503\pi$
$257$	23.6123			1.47289			0.736446	+	0.676496i	$0.236503\pi$
$258$	8.10887	+	18.0832i	0.504836	+	1.12581i
$259$		−	4.50860i		−	0.280151i
$260$	8.47294	−	9.51142i	0.525470	−	0.589873i
$261$		−	13.6458i		−	0.844653i
$262$	12.3895	−	5.55568i	0.765425	−	0.343231i
$263$	5.58362			0.344301			0.172150	−	0.985071i	$-0.444928\pi$
$263$	5.58362			0.344301			0.172150	+	0.985071i	$0.444928\pi$
$264$	−32.0185	−	10.1217i	−1.97060	−	0.622948i
$265$	−31.5886			−1.94047
$266$	−23.4302	+	10.5066i	−1.43660	+	0.644199i
$267$			23.1599i			1.41737i
$268$	−0.174213	−	0.155192i	−0.0106417	−	0.00947984i
$269$		−	24.7548i		−	1.50932i	−0.656113	−	0.754662i	$-0.727801\pi$
$269$		−	24.7548i		−	1.50932i	0.656113	−	0.754662i	$-0.272199\pi$
$270$	−2.10392	−	4.69186i	−0.128040	−	0.285537i
$271$	1.97260			0.119827			0.0599134	−	0.998204i	$-0.480918\pi$
$271$	1.97260			0.119827			0.0599134	+	0.998204i	$0.480918\pi$
$272$	0.460411	+	3.97341i	0.0279165	+	0.240924i
$273$	−13.7399			−0.831574
$274$	8.94358	+	19.9447i	0.540301	+	1.20490i
$275$		−	23.9877i		−	1.44651i
$276$	−11.1566	−	9.93846i	−0.671546	−	0.598225i
$277$			11.7244i			0.704451i	0.935915	+	0.352226i	$0.114575\pi$
$277$			11.7244i			0.704451i	−0.935915	+	0.352226i	$0.885425\pi$
$278$	15.1053	−	6.77352i	0.905958	−	0.406249i
$279$	−15.4991			−0.927907
$280$	−7.63593	+	24.1551i	−0.456334	+	1.44354i
$281$	29.8622			1.78143			0.890716	−	0.454560i	$-0.150204\pi$
$281$	29.8622			1.78143			0.890716	+	0.454560i	$0.150204\pi$
$282$	−30.4370	+	13.6485i	−1.81250	+	0.812758i
$283$		−	7.01944i		−	0.417262i	−0.977994	−	0.208631i	$-0.933099\pi$
$283$		−	7.01944i		−	0.417262i	0.977994	−	0.208631i	$-0.0669008\pi$
$284$	−5.97632	+	6.70880i	−0.354629	+	0.398094i
$285$		−	46.3199i		−	2.74375i
$286$	5.97632	+	13.3275i	0.353387	+	0.788073i
$287$	−2.10392			−0.124190
$288$	−12.1688	+	7.24309i	−0.717051	+	0.426803i
$289$	1.00000			0.0588235
$290$	9.84377	+	21.9522i	0.578046	+	1.28907i
$291$			26.6868i			1.56441i
$292$	−20.8190	+	23.3707i	−1.21834	+	1.36767i
$293$			13.8740i			0.810526i	0.914200	+	0.405263i	$0.132820\pi$
$293$			13.8740i			0.810526i	−0.914200	+	0.405263i	$0.867180\pi$
$294$	3.74307	−	1.67846i	0.218300	−	0.0978900i
$295$	0.837011			0.0487327
$296$	−1.33933	+	4.23676i	−0.0778468	+	0.246256i
$297$	5.89608			0.342125
$298$	−3.69893	+	1.65867i	−0.214273	+	0.0960843i
$299$			6.49890i			0.375841i
$300$	−16.6055	−	14.7925i	−0.958719	−	0.854044i
$301$			17.1436i			0.988143i
$302$	−0.432023	−	0.963435i	−0.0248601	−	0.0554395i
$303$	−0.678655			−0.0389877
$304$	25.1386	−	2.91288i	1.44180	−	0.167065i
$305$	8.06583			0.461848
$306$	1.44857	+	3.23040i	0.0828093	+	0.184669i
$307$		−	12.4169i		−	0.708670i	−0.935119	−	0.354335i	$-0.884707\pi$
$307$		−	12.4169i		−	0.708670i	0.935119	−	0.354335i	$-0.115293\pi$
$308$	−21.6904	−	19.3222i	−1.23592	−	1.10098i
$309$			1.10949i			0.0631167i
$310$	24.9336	−	11.1807i	1.41613	−	0.635022i
$311$	26.3411			1.49366			0.746832	−	0.665012i	$-0.231574\pi$
$311$	26.3411			1.49366			0.746832	+	0.665012i	$0.231574\pi$
$312$	12.9114	+	4.08156i	0.730964	+	0.231073i
$313$	11.2583			0.636359			0.318180	−	0.948030i	$-0.396928\pi$
$313$	11.2583			0.636359			0.318180	+	0.948030i	$0.396928\pi$
$314$	14.1089	−	6.32669i	0.796210	−	0.357036i
$315$			22.4220i			1.26333i
$316$	1.08487	−	1.21784i	0.0610289	−	0.0685088i
$317$			2.30898i			0.129685i	0.997896	+	0.0648426i	$0.0206545\pi$
$317$			2.30898i			0.129685i	−0.997896	+	0.0648426i	$0.979345\pi$
$318$	−13.7399	−	30.6406i	−0.770493	−	1.71824i
$319$	−27.5864			−1.54454
$320$	14.3510	−	20.4303i	0.802248	−	1.14209i
$321$	−22.3503			−1.24747
$322$	−5.28843	−	11.7935i	−0.294713	−	0.657226i
$323$		−	6.32669i		−	0.352027i
$324$	13.6269	−	15.2971i	0.757052	−	0.849839i
$325$			9.67300i			0.536562i
$326$	−20.8996	+	9.37179i	−1.15752	+	0.519056i
$327$	−25.9985			−1.43772
$328$	1.97706	+	0.624991i	0.109165	+	0.0345094i
$329$	−28.8555			−1.59085
$330$	47.8128	−	21.4402i	2.63201	−	1.18024i
$331$		−	8.26144i		−	0.454090i	−0.973884	−	0.227045i	$-0.927094\pi$
$331$		−	8.26144i		−	0.454090i	0.973884	−	0.227045i	$-0.0729064\pi$
$332$	5.69483	+	5.07306i	0.312545	+	0.278420i
$333$			3.93277i			0.215514i
$334$	1.59272	+	3.55185i	0.0871497	+	0.194349i
$335$	0.364069			0.0198912
$336$	−26.7516	+	3.09978i	−1.45942	+	0.169107i
$337$	0.212793			0.0115916			0.00579579	−	0.999983i	$-0.498155\pi$
$337$	0.212793			0.0115916			0.00579579	+	0.999983i	$0.498155\pi$
$338$	5.11246	+	11.4011i	0.278081	+	0.620137i
$339$			29.0168i			1.57598i
$340$	−4.66067	−	4.15181i	−0.252760	−	0.225164i
$341$			31.3331i			1.69678i
$342$	20.4377	−	9.16467i	1.10515	−	0.495569i
$343$	−16.5409			−0.893124
$344$	5.09270	−	16.1100i	0.274580	−	0.868591i
$345$	23.3149			1.25523
$346$	−22.3553	+	10.0246i	−1.20183	+	0.538924i
$347$		−	18.9348i		−	1.01647i	−0.861217	−	0.508237i	$-0.830297\pi$
$347$		−	18.9348i		−	1.01647i	0.861217	−	0.508237i	$-0.169703\pi$
$348$	−17.0117	+	19.0967i	−0.911924	+	1.02369i
$349$		−	24.2290i		−	1.29695i	−0.761237	−	0.648474i	$-0.775407\pi$
$349$		−	24.2290i		−	1.29695i	0.761237	−	0.648474i	$-0.224593\pi$
$350$	−7.87134	−	17.5535i	−0.420741	−	0.938275i
$351$	−2.37759			−0.126906
$352$	14.6427	+	24.6005i	0.780458	+	1.31121i
$353$	18.4644			0.982760			0.491380	−	0.870945i	$-0.336493\pi$
$353$	18.4644			0.982760			0.491380	+	0.870945i	$0.336493\pi$
$354$	0.364069	+	0.811893i	0.0193500	+	0.0431516i
$355$		−	14.0200i		−	0.744106i
$356$	13.1336	−	14.7433i	0.696080	−	0.781394i
$357$			6.73264i			0.356329i
$358$	1.84947	−	0.829336i	0.0977473	−	0.0438318i
$359$	−19.9032			−1.05045			−0.525224	−	0.850964i	$-0.676019\pi$
$359$	−19.9032			−1.05045			−0.525224	+	0.850964i	$0.676019\pi$
$360$	6.66067	−	21.0700i	0.351048	−	1.11049i
$361$	−21.0270			−1.10669
$362$	10.7738	−	4.83119i	0.566260	−	0.253922i
$363$			34.2793i			1.79920i
$364$	8.74661	+	7.79164i	0.458447	+	0.408393i
$365$		−	48.8399i		−	2.55640i
$366$	3.50833	+	7.82378i	0.183384	+	0.408955i
$367$	−26.2592			−1.37072			−0.685360	−	0.728204i	$-0.740355\pi$
$367$	−26.2592			−1.37072			−0.685360	+	0.728204i	$0.740355\pi$
$368$	1.46618	+	12.6534i	0.0764301	+	0.659603i
$369$	1.83521			0.0955371
$370$	−2.83701	−	6.32669i	−0.147489	−	0.328909i
$371$		−	29.0486i		−	1.50813i
$372$	21.6904	+	19.3222i	1.12459	+	1.00181i
$373$		−	9.49763i		−	0.491768i	−0.969299	−	0.245884i	$-0.920922\pi$
$373$		−	9.49763i		−	0.491768i	0.969299	−	0.245884i	$-0.0790783\pi$
$374$	6.53060	−	2.92845i	0.337689	−	0.151426i
$375$	−1.90464			−0.0983554
$376$	27.1156	+	8.57182i	1.39838	+	0.442058i
$377$	11.1242			0.572925
$378$	4.31459	−	1.93474i	0.221918	−	0.0995125i
$379$		−	15.6096i		−	0.801812i	−0.916119	−	0.400906i	$-0.868695\pi$
$379$		−	15.6096i		−	0.801812i	0.916119	−	0.400906i	$-0.131305\pi$
$380$	−26.2672	+	29.4866i	−1.34748	+	1.51263i
$381$			40.7623i			2.08832i
$382$	−9.02400	−	20.1240i	−0.461708	−	1.02963i
$383$	−11.3623			−0.580585			−0.290292	−	0.956938i	$-0.593753\pi$
$383$	−11.3623			−0.580585			−0.290292	+	0.956938i	$0.593753\pi$
$384$	26.0594	+	5.03395i	1.32984	+	0.256888i
$385$	45.3284			2.31015
$386$	10.5690	+	23.5695i	0.537950	+	1.19966i
$387$		−	14.9541i		−	0.760158i
$388$	15.1336	−	16.9884i	0.768293	−	0.862458i
$389$			9.63082i			0.488302i	0.969737	+	0.244151i	$0.0785092\pi$
$389$			9.63082i			0.488302i	−0.969737	+	0.244151i	$0.921491\pi$
$390$	−19.2804	+	8.64572i	−0.976302	+	0.437793i
$391$	3.18451			0.161048
$392$	−3.33462	−	1.05414i	−0.168424	−	0.0532422i
$393$	−22.5237			−1.13617
$394$	−26.7108	+	11.9777i	−1.34567	+	0.603425i
$395$			2.54504i			0.128055i
$396$	18.9201	+	16.8543i	0.950770	+	0.846963i
$397$		−	34.7433i		−	1.74372i	−0.489759	−	0.871858i	$-0.662915\pi$
$397$		−	34.7433i		−	1.74372i	0.489759	−	0.871858i	$-0.337085\pi$
$398$	−0.261212	−	0.582518i	−0.0130934	−	0.0291990i
$399$	42.5953			2.13243
$400$	2.18228	+	18.8334i	0.109114	+	0.941670i
$401$	13.2331			0.660828			0.330414	−	0.943836i	$-0.392812\pi$
$401$	13.2331			0.660828			0.330414	+	0.943836i	$0.392812\pi$
$402$	0.158356	+	0.353143i	0.00789809	+	0.0176132i
$403$		−	12.6350i		−	0.629396i
$404$	0.432023	+	0.384854i	0.0214939	+	0.0191472i
$405$			31.9678i			1.58849i
$406$	−20.1870	+	9.05224i	−1.00186	+	0.449255i
$407$	7.95052			0.394093
$408$	2.00000	−	6.32669i	0.0990148	−	0.313218i
$409$	−15.3672			−0.759860			−0.379930	−	0.925015i	$-0.624052\pi$
$409$	−15.3672			−0.759860			−0.379930	+	0.925015i	$0.624052\pi$
$410$	−2.95232	+	1.32388i	−0.145805	+	0.0653817i
$411$		−	36.2587i		−	1.78851i
$412$	0.629173	−	0.706286i	0.0309971	−	0.0347962i
$413$			0.769708i			0.0378748i
$414$	4.61299	+	10.2872i	0.226716	+	0.505590i
$415$	−11.9010			−0.584199
$416$	−5.90464	−	9.92011i	−0.289499	−	0.486373i
$417$	−27.4610			−1.34477
$418$	−18.5274	−	41.3171i	−0.906204	−	2.02088i
$419$		−	3.31724i		−	0.162058i	−0.996712	−	0.0810288i	$-0.974179\pi$
$419$		−	3.31724i		−	0.162058i	0.996712	−	0.0810288i	$-0.0258206\pi$
$420$	27.9526	−	31.3786i	1.36395	−	1.53112i
$421$		−	13.7546i		−	0.670357i	−0.942155	−	0.335178i	$-0.891203\pi$
$421$		−	13.7546i		−	0.670357i	0.942155	−	0.335178i	$-0.108797\pi$
$422$	−27.4507	+	12.3094i	−1.33628	+	0.599213i
$423$	25.1701			1.22381
$424$	−8.62917	+	27.2971i	−0.419070	+	1.32566i
$425$	4.73985			0.229917
$426$	13.5993	−	6.09819i	0.658888	−	0.295458i
$427$			7.41726i			0.358946i
$428$	14.2279	+	12.6745i	0.687732	+	0.612644i
$429$		−	24.2290i		−	1.16979i
$430$	10.7875	+	24.0568i	0.520221	+	1.16012i
$431$	39.3204			1.89400			0.946999	−	0.321237i	$-0.104098\pi$
$431$	39.3204			1.89400			0.946999	+	0.321237i	$0.104098\pi$
$432$	−4.62917	+	0.536396i	−0.222721	+	0.0258073i
$433$	−0.770287			−0.0370176			−0.0185088	−	0.999829i	$-0.505892\pi$
$433$	−0.770287			−0.0370176			−0.0185088	+	0.999829i	$0.505892\pi$
$434$	10.2817	+	22.9287i	0.493536	+	1.10061i
$435$		−	39.9083i		−	1.91345i
$436$	16.5503	+	14.7433i	0.792616	+	0.706077i
$437$		−	20.1474i		−	0.963782i
$438$	47.3743	−	21.2436i	2.26363	−	1.01506i
$439$	6.95176			0.331790			0.165895	−	0.986143i	$-0.446949\pi$
$439$	6.95176			0.331790			0.165895	+	0.986143i	$0.446949\pi$
$440$	−42.5953	−	13.4653i	−2.03065	−	0.641932i
$441$	−3.09536			−0.147398
$442$	−2.63345	+	1.18089i	−0.125261	+	0.0561693i
$443$			34.7704i			1.65199i	0.563675	+	0.825997i	$0.309387\pi$
$443$			34.7704i			1.65199i	−0.563675	+	0.825997i	$0.690613\pi$
$444$	4.90284	−	5.50375i	0.232678	−	0.261196i
$445$			30.8105i			1.46056i
$446$	1.62082	+	3.61451i	0.0767479	+	0.171152i
$447$	6.72453			0.318059
$448$	18.7875	+	13.1971i	0.887627	+	0.623503i
$449$	26.1089			1.23215			0.616077	−	0.787686i	$-0.288721\pi$
$449$	26.1089			1.23215			0.616077	+	0.787686i	$0.288721\pi$
$450$	6.86601	+	15.3116i	0.323667	+	0.721795i
$451$		−	3.71007i		−	0.174700i
$452$	16.4550	−	18.4717i	0.773976	−	0.868838i
$453$			1.75149i			0.0822923i
$454$	2.21601	−	0.993702i	0.104003	−	0.0466368i
$455$	−18.2786			−0.856915
$456$	−40.0270	−	12.6534i	−1.87444	−	0.592549i
$457$	−15.0219			−0.702694			−0.351347	−	0.936245i	$-0.614276\pi$
$457$	−15.0219			−0.702694			−0.351347	+	0.936245i	$0.614276\pi$
$458$	−18.2765	+	8.19552i	−0.854003	+	0.382952i
$459$			1.16504i			0.0543792i
$460$	−14.8420	−	13.2215i	−0.692010	−	0.616455i
$461$			9.75521i			0.454345i	0.973855	+	0.227173i	$0.0729482\pi$
$461$			9.75521i			0.454345i	−0.973855	+	0.227173i	$0.927052\pi$
$462$	19.7162	+	43.9682i	0.917279	+	2.04558i
$463$	−19.4797			−0.905298			−0.452649	−	0.891689i	$-0.649521\pi$
$463$	−19.4797			−0.905298			−0.452649	+	0.891689i	$0.649521\pi$
$464$	21.6589	−	2.50968i	1.00549	−	0.116509i
$465$	−45.3284			−2.10206
$466$	2.25445	+	5.02756i	0.104436	+	0.232897i
$467$			1.30004i			0.0601588i	0.999548	+	0.0300794i	$0.00957601\pi$
$467$			1.30004i			0.0601588i	−0.999548	+	0.0300794i	$0.990424\pi$
$468$	−7.62949	−	6.79649i	−0.352674	−	0.314168i
$469$			0.334794i			0.0154594i
$470$	−40.4914	+	18.1571i	−1.86773	+	0.837526i
$471$	−25.6494			−1.18186
$472$	0.228650	−	0.723298i	0.0105245	−	0.0332925i
$473$	−30.2313			−1.39004
$474$	−2.46866	+	1.10700i	−0.113389	+	0.0508460i
$475$		−	29.9876i		−	1.37592i
$476$	3.81797	−	4.28591i	0.174996	−	0.196444i
$477$			25.3385i			1.16017i
$478$	−11.0375	−	24.6143i	−0.504844	−	1.12583i
$479$	26.7774			1.22349			0.611745	−	0.791055i	$-0.290468\pi$
$479$	26.7774			1.22349			0.611745	+	0.791055i	$0.290468\pi$
$480$	−35.5886	+	21.1830i	−1.62439	+	0.966868i
$481$	−3.20603			−0.146183
$482$	−3.19326	−	7.12114i	−0.145449	−	0.324359i
$483$			21.4402i			0.975561i
$484$	19.4392	−	21.8218i	0.883600	−	0.991898i
$485$			35.5024i			1.61208i
$486$	−26.4984	+	11.8824i	−1.20199	+	0.538996i
$487$	23.6165			1.07017			0.535084	−	0.844799i	$-0.320280\pi$
$487$	23.6165			1.07017			0.535084	+	0.844799i	$0.320280\pi$
$488$	2.20337	−	6.97003i	0.0997420	−	0.315519i
$489$	37.9948			1.71818
$490$	4.97954	−	2.23292i	0.224953	−	0.100873i
$491$		−	3.95443i		−	0.178461i	−0.996011	−	0.0892305i	$-0.971559\pi$
$491$		−	3.95443i		−	0.178461i	0.996011	−	0.0892305i	$-0.0284408\pi$
$492$	−2.56830	−	2.28789i	−0.115788	−	0.103146i
$493$		−	5.45095i		−	0.245498i
$494$	7.47114	+	16.6611i	0.336142	+	0.749616i
$495$	−39.5391			−1.77715
$496$	−2.85053	−	24.6005i	−0.127993	−	1.10459i
$497$	12.8927			0.578316
$498$	−5.17651	−	11.5439i	−0.231965	−	0.517294i
$499$			18.6038i			0.832819i	0.909177	+	0.416410i	$0.136712\pi$
$499$			18.6038i			0.832819i	−0.909177	+	0.416410i	$0.863288\pi$
$500$	1.21247	+	1.08009i	0.0542234	+	0.0483031i
$501$		−	6.45714i		−	0.288484i
$502$	−26.2729	+	11.7813i	−1.17262	+	0.525825i
$503$	−23.8158			−1.06189			−0.530947	−	0.847405i	$-0.678164\pi$
$503$	−23.8158			−1.06189			−0.530947	+	0.847405i	$0.678164\pi$
$504$	19.3758	+	6.12509i	0.863066	+	0.272833i
$505$	−0.902839			−0.0401758
$506$	20.7968	−	9.32567i	0.924529	−	0.414577i
$507$		−	20.7268i		−	0.920508i
$508$	23.1156	−	25.9488i	1.02559	−	1.15129i
$509$		−	8.69952i		−	0.385600i	−0.981238	−	0.192800i	$-0.938243\pi$
$509$		−	8.69952i		−	0.385600i	0.981238	−	0.192800i	$-0.0617568\pi$
$510$	4.23647	+	9.44757i	0.187594	+	0.418345i
$511$	44.9127			1.98682
$512$	−13.7344	−	17.9824i	−0.606980	−	0.794717i
$513$	7.37083			0.325430
$514$	13.6631	+	30.4696i	0.602656	+	1.34396i
$515$			1.47599i			0.0650401i
$516$	−18.6427	+	20.9276i	−0.820699	+	0.921287i
$517$		−	50.8840i		−	2.23788i
$518$	5.81797	−	2.60889i	0.255627	−	0.114628i
$519$	40.6412			1.78395
$520$	17.1765	+	5.42985i	0.753240	+	0.238115i
$521$	6.22631			0.272780			0.136390	−	0.990655i	$-0.456450\pi$
$521$	6.22631			0.272780			0.136390	+	0.990655i	$0.456450\pi$
$522$	17.6087	−	7.89609i	0.770712	−	0.345602i
$523$			19.7815i			0.864984i	0.901638	+	0.432492i	$0.142366\pi$
$523$			19.7815i			0.864984i	−0.901638	+	0.432492i	$0.857634\pi$
$524$	14.3383	+	12.7728i	0.626370	+	0.557982i
$525$			31.9117i			1.39274i
$526$	3.23094	+	7.20518i	0.140876	+	0.314161i
$527$	−6.19127			−0.269696
$528$	−5.46618	−	47.1740i	−0.237885	−	2.05298i
$529$	−12.8589			−0.559082
$530$	−18.2786	−	40.7623i	−0.793973	−	1.77060i
$531$		−	0.671401i		−	0.0291363i
$532$	−27.1156	−	24.1551i	−1.17561	−	1.04726i
$533$			1.49608i			0.0648025i
$534$	−29.8859	+	13.4014i	−1.29329	+	0.579936i
$535$	−29.7334			−1.28549
$536$	0.0994540	−	0.314608i	0.00429576	−	0.0135890i
$537$	−3.36226			−0.145092
$538$	31.9439	−	14.3243i	1.37720	−	0.617563i
$539$			6.25760i			0.269534i
$540$	4.83701	−	5.42985i	0.208152	−	0.233664i
$541$			4.79847i			0.206302i	0.994666	+	0.103151i	$0.0328925\pi$
$541$			4.79847i			0.206302i	−0.994666	+	0.103151i	$0.967107\pi$
$542$	1.14144	+	2.54547i	0.0490289	+	0.109337i
$543$	−19.5864			−0.840535
$544$	−4.86093	+	2.89332i	−0.208411	+	0.124050i
$545$	−34.5868			−1.48153
$546$	−7.95052	−	17.7301i	−0.340251	−	0.758778i
$547$		−	20.8641i		−	0.892084i	−0.895012	−	0.446042i	$-0.852833\pi$
$547$		−	20.8641i		−	0.892084i	0.895012	−	0.446042i	$-0.147167\pi$
$548$	−20.5617	+	23.0818i	−0.878353	+	0.986007i
$549$		−	6.46993i		−	0.276130i
$550$	30.9541	−	13.8804i	1.31989	−	0.591862i
$551$	−34.4865			−1.46917
$552$	6.36902	−	20.1474i	0.271084	−	0.857531i
$553$	−2.34039			−0.0995235
$554$	−15.1293	+	6.78429i	−0.642784	+	0.288237i
$555$			11.5017i			0.488220i
$556$	17.4813	+	15.5727i	0.741372	+	0.660428i
$557$			17.7084i			0.750330i	0.926958	+	0.375165i	$0.122414\pi$
$557$			17.7084i			0.750330i	−0.926958	+	0.375165i	$0.877586\pi$
$558$	−8.96850	−	20.0003i	−0.379667	−	0.846678i
$559$	12.1907			0.515612
$560$	−35.5886	+	4.12375i	−1.50389	+	0.174260i
$561$	−11.8724			−0.501253
$562$	17.2797	+	38.5347i	0.728899	+	1.62549i
$563$		−	17.5817i		−	0.740981i	−0.928836	−	0.370491i	$-0.879190\pi$
$563$		−	17.5817i		−	0.740981i	0.928836	−	0.370491i	$-0.120810\pi$
$564$	−35.2245	−	31.3786i	−1.48322	−	1.32128i
$565$			38.6022i			1.62400i
$566$	9.05798	−	4.06177i	0.380735	−	0.170729i
$567$	−29.3973			−1.23457
$568$	−12.1153	−	3.82990i	−0.508347	−	0.160699i
$569$	2.98468			0.125124			0.0625621	−	0.998041i	$-0.480073\pi$
$569$	2.98468			0.125124			0.0625621	+	0.998041i	$0.480073\pi$
$570$	59.7718	−	26.8029i	2.50357	−	1.12265i
$571$			18.1096i			0.757862i	0.925425	+	0.378931i	$0.123708\pi$
$571$			18.1096i			0.757862i	−0.925425	+	0.378931i	$0.876292\pi$
$572$	−13.7399	+	15.4239i	−0.574492	+	0.644904i
$573$			36.5848i			1.52835i
$574$	−1.21743	−	2.71493i	−0.0508144	−	0.113319i
$575$	15.0941			0.629468
$576$	−16.3880	−	11.5116i	−0.682833	−	0.479648i
$577$	−41.2143			−1.71578			−0.857888	−	0.513837i	$-0.828224\pi$
$577$	−41.2143			−1.71578			−0.857888	+	0.513837i	$0.828224\pi$
$578$	0.578647	+	1.29041i	0.0240685	+	0.0536741i
$579$		−	42.8486i		−	1.78073i
$580$	−22.6313	+	25.4051i	−0.939714	+	1.05489i
$581$		−	10.9441i		−	0.454037i
$582$	−34.4370	+	15.4422i	−1.42746	+	0.640100i
$583$	51.2245			2.12150
$584$	−42.2047	−	13.3418i	−1.74644	−	0.552087i
$585$	15.9441			0.659207
$586$	−17.9032	+	8.02812i	−0.739573	+	0.331639i
$587$		−	30.1153i		−	1.24299i	−0.783418	−	0.621495i	$-0.786525\pi$
$587$		−	30.1153i		−	1.24299i	0.783418	−	0.621495i	$-0.213475\pi$
$588$	4.33183	+	3.85887i	0.178642	+	0.159137i
$589$			39.1703i			1.61398i
$590$	0.484334	+	1.08009i	0.0199397	+	0.0444666i
$591$	48.5594			1.99747
$592$	−6.24217	+	0.723298i	−0.256551	+	0.0297274i
$593$	−13.0972			−0.537836			−0.268918	−	0.963163i	$-0.586666\pi$
$593$	−13.0972			−0.537836			−0.268918	+	0.963163i	$0.586666\pi$
$594$	3.41175	+	7.60838i	0.139986	+	0.312176i
$595$			8.95667i			0.367188i
$596$	−4.28075	−	3.81337i	−0.175346	−	0.156202i
$597$			1.05900i			0.0433419i
$598$	−8.38627	+	3.76056i	−0.342940	+	0.153781i
$599$	20.9729			0.856930			0.428465	−	0.903558i	$-0.359054\pi$
$599$	20.9729			0.856930			0.428465	+	0.903558i	$0.359054\pi$
$600$	9.47970	−	29.9876i	0.387007	−	1.22424i
$601$	25.1242			1.02484			0.512419	−	0.858736i	$-0.328750\pi$
$601$	25.1242			1.02484			0.512419	+	0.858736i	$0.328750\pi$
$602$	−22.1224	+	9.92011i	−0.901641	+	0.404313i
$603$		−	0.292034i		−	0.0118926i
$604$	0.993241	−	1.11498i	0.0404144	−	0.0453678i
$605$			45.6030i			1.85403i
$606$	−0.392701	−	0.875746i	−0.0159524	−	0.0355747i
$607$	41.4158			1.68101			0.840507	−	0.541800i	$-0.182257\pi$
$607$	41.4158			1.68101			0.840507	+	0.541800i	$0.182257\pi$
$608$	18.3052	+	30.7536i	0.742373	+	1.24722i
$609$	36.6993			1.48713
$610$	4.66726	+	10.4083i	0.188972	+	0.421418i
$611$			20.5189i			0.830107i
$612$	−3.33034	+	3.73851i	−0.134621	+	0.151121i
$613$		−	33.6665i		−	1.35978i	−0.733315	−	0.679889i	$-0.762028\pi$
$613$		−	33.6665i		−	1.35978i	0.733315	−	0.679889i	$-0.237972\pi$
$614$	16.0229	−	7.18500i	0.646633	−	0.289963i
$615$	5.36722			0.216427
$616$	12.3825	−	39.1703i	0.498907	−	1.57821i
$617$	−24.7430			−0.996116			−0.498058	−	0.867144i	$-0.665953\pi$
$617$	−24.7430			−0.996116			−0.498058	+	0.867144i	$0.665953\pi$
$618$	−1.43170	+	0.642002i	−0.0575914	+	0.0258251i
$619$			22.4061i			0.900577i	0.892883	+	0.450289i	$0.148679\pi$
$619$			22.4061i			0.900577i	−0.892883	+	0.450289i	$0.851321\pi$
$620$	28.8555	+	25.7050i	1.15886	+	1.03234i
$621$			3.71007i			0.148880i
$622$	15.2422	+	33.9909i	0.611155	+	1.36291i
$623$	−28.3331			−1.13514
$624$	2.20423	+	19.0228i	0.0882398	+	0.761523i
$625$	−26.2331			−1.04932
$626$	6.51460	+	14.5279i	0.260376	+	0.580653i
$627$			75.1130i			2.99973i
$628$	16.3281	+	14.5454i	0.651562	+	0.580423i
$629$			1.57098i			0.0626392i
$630$	−28.9336	+	12.9744i	−1.15274	+	0.516912i
$631$	−3.43022			−0.136555			−0.0682774	−	0.997666i	$-0.521750\pi$
$631$	−3.43022			−0.136555			−0.0682774	+	0.997666i	$0.521750\pi$
$632$	2.19928	+	0.695237i	0.0874825	+	0.0276551i
$633$	49.9044			1.98352
$634$	−2.97954	+	1.33608i	−0.118333	+	0.0530627i
$635$			54.2276i			2.15196i
$636$	31.5886	−	35.4602i	1.25257	−	1.40609i
$637$		−	2.52337i		−	0.0999795i
$638$	−15.9628	−	35.5979i	−0.631973	−	1.40934i
$639$	−11.2460			−0.444886
$640$	34.6678	+	6.69685i	1.37036	+	0.264716i
$641$	31.3758			1.23927			0.619634	−	0.784891i	$-0.287281\pi$
$641$	31.3758			1.23927			0.619634	+	0.784891i	$0.287281\pi$
$642$	−12.9329	−	28.8411i	−0.510422	−	1.13827i
$643$		−	20.2593i		−	0.798948i	−0.916745	−	0.399474i	$-0.869193\pi$
$643$		−	20.2593i		−	0.798948i	0.916745	−	0.399474i	$-0.130807\pi$
$644$	12.1584	−	13.6485i	0.479106	−	0.537827i
$645$		−	43.7344i		−	1.72204i
$646$	8.16405	−	3.66092i	0.321210	−	0.144037i
$647$	26.8195			1.05438			0.527192	−	0.849746i	$-0.323245\pi$
$647$	26.8195			1.05438			0.527192	+	0.849746i	$0.323245\pi$
$648$	27.6248	+	8.73277i	1.08520	+	0.343056i
$649$	−1.35731			−0.0532791
$650$	−12.4822	+	5.59725i	−0.489591	+	0.219542i
$651$		−	41.6836i		−	1.63371i
$652$	−24.1870	−	21.5462i	−0.947236	−	0.843815i
$653$		−	27.9547i		−	1.09395i	−0.837149	−	0.546975i	$-0.815779\pi$
$653$		−	27.9547i		−	1.09395i	0.837149	−	0.546975i	$-0.184221\pi$
$654$	−15.0440	−	33.5489i	−0.588265	−	1.31186i
$655$	−29.9640			−1.17079
$656$	0.337524	+	2.91288i	0.0131781	+	0.113729i
$657$	−39.1765			−1.52842
$658$	−16.6971	−	37.2355i	−0.650922	−	1.45159i
$659$		−	6.58384i		−	0.256470i	−0.991744	−	0.128235i	$-0.959069\pi$
$659$		−	6.58384i		−	0.256470i	0.991744	−	0.128235i	$-0.0409312\pi$
$660$	55.3334	+	49.2920i	2.15385	+	1.91869i
$661$			5.25448i			0.204375i	0.994765	+	0.102188i	$0.0325842\pi$
$661$			5.25448i			0.204375i	−0.994765	+	0.102188i	$0.967416\pi$
$662$	10.6607	−	4.78045i	0.414339	−	0.185798i
$663$	4.78753			0.185932
$664$	−3.25105	+	10.2842i	−0.126165	+	0.399104i
$665$	56.6661			2.19742
$666$	−5.07490	+	2.27568i	−0.196648	+	0.0881809i
$667$		−	17.3586i		−	0.672128i
$668$	−3.66174	+	4.11053i	−0.141677	+	0.159041i
$669$		−	6.57105i		−	0.254052i
$670$	0.210667	+	0.469799i	0.00813878	+	0.0181499i
$671$	−13.0797			−0.504935
$672$	−19.4797	−	32.7269i	−0.751446	−	1.26247i
$673$	9.56154			0.368570			0.184285	−	0.982873i	$-0.441003\pi$
$673$	9.56154			0.368570			0.184285	+	0.982873i	$0.441003\pi$
$674$	0.123132	+	0.274591i	0.00474287	+	0.0105769i
$675$			5.52210i			0.212546i
$676$	−11.7538	+	13.1944i	−0.452069	+	0.507476i
$677$			46.1816i			1.77490i	0.460902	+	0.887451i	$0.347526\pi$
$677$			46.1816i			1.77490i	−0.460902	+	0.887451i	$0.652474\pi$
$678$	−37.4437	+	16.7905i	−1.43802	+	0.644835i
$679$	−32.6476			−1.25290
$680$	2.66067	−	8.41663i	0.102032	−	0.322763i
$681$	−4.02863			−0.154378
$682$	−40.4327	+	18.1308i	−1.54825	+	0.694264i
$683$			15.6780i			0.599903i	0.953955	+	0.299951i	$0.0969704\pi$
$683$			15.6780i			0.599903i	−0.953955	+	0.299951i	$0.903030\pi$
$684$	23.6524	+	21.0700i	0.904373	+	0.805632i
$685$		−	48.2363i		−	1.84301i
$686$	−9.57133	−	21.3446i	−0.365435	−	0.814941i
$687$	33.2260			1.26765
$688$	23.7354	−	2.75029i	0.904903	−	0.104854i
$689$	−20.6562			−0.786939
$690$	13.4911	+	30.0859i	0.513597	+	1.14535i
$691$		−	38.5362i		−	1.46599i	−0.680235	−	0.732994i	$-0.738122\pi$
$691$		−	38.5362i		−	1.46599i	0.680235	−	0.732994i	$-0.261878\pi$
$692$	−25.8717	−	23.0469i	−0.983493	−	0.876113i
$693$		−	36.3598i		−	1.38119i
$694$	24.4338	−	10.9566i	0.927493	−	0.415906i
$695$	−36.5323			−1.38575
$696$	−34.4865	−	10.9019i	−1.30721	−	0.413235i
$697$	0.733092			0.0277678
$698$	31.2654	−	14.0200i	1.18341	−	0.530666i
$699$		−	9.13993i		−	0.345704i
$700$	18.0966	−	20.3146i	0.683987	−	0.767819i
$701$		−	2.38056i		−	0.0899127i	−0.998989	−	0.0449563i	$-0.985685\pi$
$701$		−	2.38056i		−	0.0899127i	0.998989	−	0.0449563i	$-0.0143149\pi$
$702$	−1.37578	−	3.06807i	−0.0519255	−	0.115797i
$703$	9.93913			0.374861
$704$	−23.2719	+	33.1301i	−0.877091	+	1.24864i
$705$	73.6120			2.77239
$706$	10.6844	+	23.8267i	0.402111	+	0.896729i
$707$		−	0.830242i		−	0.0312245i
$708$	−0.837011	+	0.939599i	−0.0314568	+	0.0353123i
$709$		−	9.98339i		−	0.374934i	−0.982271	−	0.187467i	$-0.939972\pi$
$709$		−	9.98339i		−	0.374934i	0.982271	−	0.187467i	$-0.0600278\pi$
$710$	18.0916	−	8.11264i	0.678967	−	0.304462i
$711$	2.04148			0.0765614
$712$	26.6247	+	8.41663i	0.997803	+	0.315426i
$713$	−19.7162			−0.738376
$714$	−8.68789	+	3.89582i	−0.325136	+	0.145797i
$715$		−	32.2327i		−	1.20543i
$716$	2.14037	+	1.90668i	0.0799895	+	0.0712561i
$717$			44.7479i			1.67114i
$718$	−11.5169	−	25.6833i	−0.429807	−	0.958493i
$719$	11.5421			0.430449			0.215225	−	0.976565i	$-0.430952\pi$
$719$	11.5421			0.430449			0.215225	+	0.976565i	$0.430952\pi$
$720$	31.0432	−	3.59707i	1.15691	−	0.134055i
$721$	−1.35731			−0.0505489
$722$	−12.1672	−	27.1336i	−0.452817	−	1.00981i
$723$			12.9460i			0.481467i
$724$	12.4685	+	11.1071i	0.463387	+	0.412794i
$725$		−	25.8367i		−	0.959550i
$726$	−44.2345	+	19.8356i	−1.64170	+	0.736168i
$727$	36.3331			1.34752			0.673759	−	0.738951i	$-0.264678\pi$
$727$	36.3331			1.34752			0.673759	+	0.738951i	$0.264678\pi$
$728$	−4.99324	+	15.7954i	−0.185062	+	0.585415i
$729$	17.4434			0.646052
$730$	63.0237	−	28.2611i	2.33261	−	1.04599i
$731$		−	5.97355i		−	0.220940i
$732$	−8.06583	+	9.05441i	−0.298122	+	0.334660i
$733$		−	34.9660i		−	1.29150i	−0.763550	−	0.645749i	$-0.776545\pi$
$733$		−	34.9660i		−	1.29150i	0.763550	−	0.645749i	$-0.223455\pi$
$734$	−15.1948	−	33.8853i	−0.560851	−	1.25073i
$735$	−9.05263			−0.333911
$736$	−15.4797	+	9.21382i	−0.570589	+	0.339626i
$737$	−0.590379			−0.0217469
$738$	1.06194	+	2.36818i	0.0390904	+	0.0871738i
$739$			28.8359i			1.06075i	0.847764	+	0.530373i	$0.177948\pi$
$739$			28.8359i			1.06075i	−0.847764	+	0.530373i	$0.822052\pi$
$740$	6.52242	−	7.32184i	0.239769	−	0.269156i
$741$		−	30.2892i		−	1.11270i
$742$	37.4847	−	16.8088i	1.37611	−	0.617072i
$743$	−26.2731			−0.963867			−0.481933	−	0.876208i	$-0.660065\pi$
$743$	−26.2731			−0.963867			−0.481933	+	0.876208i	$0.660065\pi$
$744$	−12.3825	+	39.1703i	−0.453966	+	1.43605i
$745$	8.94589			0.327752
$746$	12.2559	−	5.49577i	0.448719	−	0.201214i
$747$			9.54630i			0.349281i
$748$	7.55782	+	6.73264i	0.276341	+	0.246170i
$749$		−	27.3426i		−	0.999076i
$750$	−1.10212	−	2.45778i	−0.0402436	−	0.0897454i
$751$	−43.4788			−1.58656			−0.793282	−	0.608855i	$-0.791629\pi$
$751$	−43.4788			−1.58656			−0.793282	+	0.608855i	$0.791629\pi$
$752$	4.62917	+	39.9504i	0.168809	+	1.45684i
$753$	47.7633			1.74059
$754$	6.43698	+	14.3548i	0.234421	+	0.522772i
$755$			2.33007i			0.0848000i
$756$	4.99324	+	4.44807i	0.181602	+	0.161775i
$757$		−	26.2326i		−	0.953439i	−0.879055	−	0.476720i	$-0.841826\pi$
$757$		−	26.2326i		−	0.953439i	0.879055	−	0.476720i	$-0.158174\pi$
$758$	20.1429	−	9.03244i	0.731621	−	0.328073i
$759$	−37.8078			−1.37234
$760$	−53.2494	−	16.8333i	−1.93156	−	0.610606i
$761$	−40.1866			−1.45676			−0.728382	−	0.685171i	$-0.759727\pi$
$761$	−40.1866			−1.45676			−0.728382	+	0.685171i	$0.759727\pi$
$762$	−52.6003	+	23.5870i	−1.90551	+	0.854466i
$763$		−	31.8057i		−	1.15144i
$764$	20.7466	−	23.2894i	0.750586	−	0.842581i
$765$		−	7.81273i		−	0.282470i
$766$	−6.57474	−	14.6620i	−0.237555	−	0.529760i
$767$	0.547333			0.0197631
$768$	8.58330	+	36.5403i	0.309723	+	1.31853i
$769$	−7.87736			−0.284065			−0.142032	−	0.989862i	$-0.545364\pi$
$769$	−7.87736			−0.284065			−0.142032	+	0.989862i	$0.545364\pi$
$770$	26.2291	+	58.4924i	0.945233	+	2.10792i
$771$		−	55.3927i		−	1.99492i
$772$	−24.2987	+	27.2769i	−0.874530	+	0.981716i
$773$			45.4142i			1.63343i	0.577038	+	0.816717i	$0.304208\pi$
$773$			45.4142i			1.63343i	−0.577038	+	0.816717i	$0.695792\pi$
$774$	19.2969	−	8.65312i	0.693614	−	0.311030i
$775$	−29.3457			−1.05413
$776$	30.6791	+	9.69832i	1.10132	+	0.348149i
$777$	−10.5769			−0.379443
$778$	−12.4277	+	5.57284i	−0.445556	+	0.199796i
$779$		−	4.63805i		−	0.166175i
$780$	−22.3131	−	19.8769i	−0.798937	−	0.711708i
$781$			22.7351i			0.813525i
$782$	1.84271	+	4.10934i	0.0658951	+	0.146950i
$783$	6.35055			0.226950
$784$	−0.569285	−	4.91301i	−0.0203316	−	0.175465i
$785$	−34.1224			−1.21788
$786$	−13.0332	−	29.0648i	−0.464880	−	1.03671i
$787$			37.3846i			1.33262i	0.745677	+	0.666308i	$0.232126\pi$
$787$			37.3846i			1.33262i	−0.745677	+	0.666308i	$0.767874\pi$
$788$	−30.9123	−	27.5372i	−1.10120	−	0.980972i
$789$		−	13.0988i		−	0.466329i
$790$	−3.28415	+	1.47268i	−0.116845	+	0.0523955i
$791$	−35.4982			−1.26217
$792$	−10.8010	+	34.1674i	−0.383798	+	1.21409i
$793$	5.27436			0.187298
$794$	44.8332	−	20.1041i	1.59107	−	0.713467i
$795$			74.1045i			2.62822i
$796$	0.600540	−	0.674144i	0.0212856	−	0.0238944i
$797$			24.4728i			0.866870i	0.901185	+	0.433435i	$0.142699\pi$
$797$			24.4728i			0.866870i	−0.901185	+	0.433435i	$0.857301\pi$
$798$	24.6476	+	54.9656i	0.872517	+	1.94576i
$799$	10.0544			0.355700
$800$	−23.0401	+	13.7139i	−0.814591	+	0.484860i
$801$	24.7144			0.873239
$802$	7.65727	+	17.0761i	0.270388	+	0.602979i
$803$			79.1996i			2.79489i
$804$	−0.364069	+	0.408690i	−0.0128397	+	0.0144134i
$805$			28.5226i			1.00529i
$806$	16.3044	−	7.31122i	0.574299	−	0.257527i
$807$	−58.0729			−2.04426
$808$	−0.246632	+	0.780183i	−0.00867649	+	0.0274467i
$809$	5.08860			0.178906			0.0894528	−	0.995991i	$-0.471488\pi$
$809$	5.08860			0.178906			0.0894528	+	0.995991i	$0.471488\pi$
$810$	−41.2517	+	18.4981i	−1.44944	+	0.649956i
$811$		−	13.8343i		−	0.485787i	−0.970053	−	0.242894i	$-0.921903\pi$
$811$		−	13.8343i		−	0.485787i	0.970053	−	0.242894i	$-0.0780966\pi$
$812$	−23.3623	−	20.8115i	−0.819855	−	0.730341i
$813$		−	4.62757i		−	0.162296i
$814$	4.60054	+	10.2595i	0.161249	+	0.359594i
$815$	50.5459			1.77054
$816$	9.32134	−	1.08009i	0.326312	−	0.0378107i
$817$	−37.7928			−1.32220
$818$	−8.89219	−	19.8301i	−0.310908	−	0.693342i
$819$			14.6620i			0.512333i
$820$	−3.41670	−	3.04366i	−0.119316	−	0.106289i
$821$		−	47.4601i		−	1.65637i	−0.560456	−	0.828184i	$-0.689374\pi$
$821$		−	47.4601i		−	1.65637i	0.560456	−	0.828184i	$-0.310626\pi$
$822$	46.7888	−	20.9810i	1.63195	−	0.731796i
$823$	3.61866			0.126139			0.0630693	−	0.998009i	$-0.479911\pi$
$823$	3.61866			0.126139			0.0630693	+	0.998009i	$0.479911\pi$
$824$	1.27547	+	0.403203i	0.0444331	+	0.0140462i
$825$	−56.2734			−1.95919
$826$	−0.993241	+	0.445389i	−0.0345593	+	0.0154971i
$827$			9.03855i			0.314301i	0.987575	+	0.157151i	$0.0502308\pi$
$827$			9.03855i			0.314301i	−0.987575	+	0.157151i	$0.949769\pi$
$828$	−10.6055	+	11.9053i	−0.368566	+	0.413739i
$829$			55.3743i			1.92323i	0.274404	+	0.961615i	$0.411519\pi$
$829$			55.3743i			1.92323i	−0.274404	+	0.961615i	$0.588481\pi$
$830$	−6.88649	−	15.3573i	−0.239034	−	0.533058i
$831$	27.5046			0.954124
$832$	9.38434	−	13.3597i	0.325344	−	0.463163i
$833$	−1.23647			−0.0428412
$834$	−15.8902	−	35.4360i	−0.550233	−	1.22705i
$835$		−	8.59017i		−	0.297275i
$836$	42.5953	−	47.8160i	1.47319	−	1.65375i
$837$		−	7.21306i		−	0.249320i
$838$	4.28061	−	1.91951i	0.147871	−	0.0663083i
$839$	−0.000924806	0		−3.19279e−5	0		−1.59639e−5	−	1.00000i	$-0.500005\pi$
$839$	−0.000924806	0		−3.19279e−5	0		−1.59639e−5		1.00000i	$0.500005\pi$
$840$	56.6661	+	17.9133i	1.95517	+	0.618069i
$841$	−0.712816			−0.0245799
$842$	17.7491	−	7.95903i	0.611674	−	0.274286i
$843$		−	70.0547i		−	2.41281i
$844$	−31.7685	−	28.2999i	−1.09352	−	0.974124i
$845$		−	27.5736i		−	0.948559i
$846$	14.5646	+	32.4798i	0.500740	+	1.11668i
$847$	−41.9361			−1.44094
$848$	−40.2177	+	4.66015i	−1.38108	+	0.160030i
$849$	−16.4671			−0.565149
$850$	2.74270	+	6.11637i	0.0940738	+	0.209790i
$851$			5.00281i			0.171494i
$852$	15.7384	+	14.0200i	0.539188	+	0.480318i
$853$			31.1187i			1.06549i	0.846277	+	0.532743i	$0.178839\pi$
$853$			31.1187i			1.06549i	−0.846277	+	0.532743i	$0.821161\pi$
$854$	−9.57133	+	4.29197i	−0.327524	+	0.146868i
$855$	−49.4287			−1.69043
$856$	−8.12239	+	25.6939i	−0.277618	+	0.878201i
$857$	−45.8063			−1.56471			−0.782357	−	0.622830i	$-0.785983\pi$
$857$	−45.8063			−1.56471			−0.782357	+	0.622830i	$0.785983\pi$
$858$	31.2654	−	14.0200i	1.06738	−	0.478636i
$859$			27.6930i			0.944872i	0.881365	+	0.472436i	$0.156625\pi$
$859$			27.6930i			0.944872i	−0.881365	+	0.472436i	$0.843375\pi$
$860$	−24.8010	+	27.8408i	−0.845709	+	0.949362i
$861$			4.93564i			0.168206i
$862$	22.7526	+	50.7396i	0.774958	+	1.72820i
$863$	−40.4484			−1.37688			−0.688439	−	0.725294i	$-0.741704\pi$
$863$	−40.4484			−1.37688			−0.688439	+	0.725294i	$0.741704\pi$
$864$	−3.37083	−	5.66317i	−0.114678	−	0.192665i
$865$	54.0665			1.83832
$866$	−0.445724	−	0.993989i	−0.0151463	−	0.0337771i
$867$		−	2.34593i		−	0.0796719i
$868$	−23.6381	+	26.5352i	−0.802328	+	0.900664i
$869$		−	4.12707i		−	0.140001i
$870$	51.4982	−	23.0928i	1.74595	−	0.782918i
$871$	0.238070			0.00806668
$872$	−9.44820	+	29.8879i	−0.319956	+	1.01213i
$873$	28.4779			0.963831
$874$	25.9985	−	11.6582i	0.879413	−	0.394346i
$875$		−	2.33007i		−	0.0787708i
$876$	54.8260	+	48.8399i	1.85240	+	1.65015i
$877$		−	31.4259i		−	1.06118i	−0.847629	−	0.530589i	$-0.821971\pi$
$877$		−	31.4259i		−	1.06118i	0.847629	−	0.530589i	$-0.178029\pi$
$878$	4.02261	+	8.97065i	0.135757	+	0.302745i
$879$	32.5473			1.09779
$880$	−7.27186	−	62.7572i	−0.245134	−	2.11555i
$881$	5.90960			0.199099			0.0995497	−	0.995033i	$-0.468260\pi$
$881$	5.90960			0.199099			0.0995497	+	0.995033i	$0.468260\pi$
$882$	−1.79112	−	3.99429i	−0.0603101	−	0.134495i
$883$			50.6935i			1.70597i	0.521934	+	0.852986i	$0.325211\pi$
$883$			50.6935i			1.70597i	−0.521934	+	0.852986i	$0.674789\pi$
$884$	−3.04768	−	2.71493i	−0.102505	−	0.0913129i
$885$		−	1.96357i		−	0.0660046i
$886$	−44.8683	+	20.1198i	−1.50738	+	0.675938i
$887$	22.0966			0.741930			0.370965	−	0.928647i	$-0.379027\pi$
$887$	22.0966			0.741930			0.370965	+	0.928647i	$0.379027\pi$
$888$	9.93913	+	3.14197i	0.333535	+	0.105437i
$889$	−49.8672			−1.67249
$890$	−39.7583	+	17.8284i	−1.33270	+	0.597609i
$891$		−	51.8395i		−	1.73669i
$892$	−3.72633	+	4.18305i	−0.124767	+	0.140059i
$893$		−	63.6113i		−	2.12867i
$894$	3.89113	+	8.67743i	0.130139	+	0.290217i
$895$	−4.47294			−0.149514
$896$	−6.15836	+	31.8801i	−0.205736	+	1.06504i
$897$	15.2459			0.509047
$898$	15.1078	+	33.6913i	0.504154	+	1.12429i
$899$			33.7483i			1.12557i
$900$	−15.7853	+	17.7200i	−0.526177	+	0.590667i
$901$			10.1217i			0.337203i
$902$	4.78753	−	2.14682i	0.159407	−	0.0714813i
$903$	40.2177			1.33836
$904$	33.3578	+	10.5451i	1.10946	+	0.350725i
$905$	−26.0566			−0.866149
$906$	−2.26015	+	1.01349i	−0.0750884	+	0.0336711i
$907$		−	32.5383i		−	1.08042i	−0.841532	−	0.540208i	$-0.818346\pi$
$907$		−	32.5383i		−	1.08042i	0.841532	−	0.540208i	$-0.181654\pi$
$908$	2.56457	+	2.28457i	0.0851084	+	0.0758161i
$909$			0.724204i			0.0240203i
$910$	−10.5769	−	23.5870i	−0.350620	−	0.781901i
$911$	18.9603			0.628184			0.314092	−	0.949393i	$-0.398300\pi$
$911$	18.9603			0.628184			0.314092	+	0.949393i	$0.398300\pi$
$912$	−6.83340	−	58.9733i	−0.226277	−	1.95280i
$913$	19.2989			0.638700
$914$	−8.69236	−	19.3844i	−0.287518	−	0.641180i
$915$		−	18.9219i		−	0.625537i
$916$	−21.1512	−	18.8419i	−0.698856	−	0.622554i
$917$		−	27.5546i		−	0.909934i
$918$	−1.50338	+	0.674144i	−0.0496189	+	0.0222501i
$919$	24.2857			0.801111			0.400556	−	0.916272i	$-0.368817\pi$
$919$	24.2857			0.801111			0.400556	+	0.916272i	$0.368817\pi$
$920$	8.47294	−	26.8029i	0.279345	−	0.883664i
$921$	−29.1291			−0.959838
$922$	−12.5883	+	5.64482i	−0.414572	+	0.185902i
$923$		−	9.16789i		−	0.301765i
$924$	−45.3284	+	50.8840i	−1.49120	+	1.67396i
$925$			7.44623i			0.244830i
$926$	−11.2719	−	25.1369i	−0.370416	−	0.826049i
$927$	1.18395			0.0388862
$928$	15.7714	+	26.4967i	0.517720	+	0.869796i
$929$	13.3278			0.437270			0.218635	−	0.975807i	$-0.429840\pi$
$929$	13.3278			0.437270			0.218635	+	0.975807i	$0.429840\pi$
$930$	−26.2291	−	58.4924i	−0.860087	−	1.91804i
$931$			7.82277i			0.256381i
$932$	−5.18310	+	5.81836i	−0.169778	+	0.190587i
$933$		−	61.7942i		−	2.02305i
$934$	−1.67759	+	0.752265i	−0.0548925	+	0.0246149i
$935$	−15.7943			−0.516528
$936$	4.35551	−	13.7780i	0.142364	−	0.450347i
$937$	−12.2042			−0.398695			−0.199347	−	0.979929i	$-0.563882\pi$
$937$	−12.2042			−0.398695			−0.199347	+	0.979929i	$0.563882\pi$
$938$	−0.432023	+	0.193727i	−0.0141060	+	0.00632542i
$939$		−	26.4113i		−	0.861899i
$940$	−46.8604	−	41.7441i	−1.52842	−	1.36154i
$941$		−	15.8115i		−	0.515439i	−0.966220	−	0.257719i	$-0.917029\pi$
$941$		−	15.8115i		−	0.515439i	0.966220	−	0.257719i	$-0.0829710\pi$
$942$	−14.8420	−	33.0984i	−0.483577	−	1.07840i
$943$	2.33454			0.0760231
$944$	1.06566	−	0.123481i	0.0346843	−	0.00401897i
$945$	−10.4349			−0.339446
$946$	−17.4932	−	39.0108i	−0.568754	−	1.26835i
$947$		−	5.94664i		−	0.193240i	−0.995321	−	0.0966200i	$-0.969197\pi$
$947$		−	5.94664i		−	0.193240i	0.995321	−	0.0966200i	$-0.0308032\pi$
$948$	−2.85696	−	2.54504i	−0.0927899	−	0.0826589i
$949$		−	31.9371i		−	1.03672i
$950$	38.6964	−	17.3522i	1.25548	−	0.562980i
$951$	5.41670			0.175649
$952$	7.73985	+	2.44673i	0.250850	+	0.0792989i
$953$	35.1578			1.13887			0.569436	−	0.822036i	$-0.307162\pi$
$953$	35.1578			1.13887			0.569436	+	0.822036i	$0.307162\pi$
$954$	−32.6971	+	14.6620i	−1.05861	+	0.474701i
$955$			48.6701i			1.57493i
$956$	25.3758	−	28.4859i	0.820711	−	0.921301i
$957$			64.7158i			2.09197i
$958$	15.4946	+	34.5539i	0.500609	+	1.11639i
$959$	44.3576			1.43238
$960$	−47.9281	−	33.6665i	−1.54687	−	1.08658i
$961$	7.33183			0.236511
$962$	−1.85516	−	4.13711i	−0.0598128	−	0.133386i
$963$			23.8504i			0.768568i
$964$	7.34145	−	8.24125i	0.236452	−	0.265433i
$965$		−	57.0031i		−	1.83499i
$966$	−27.6667	+	12.4063i	−0.890161	+	0.399166i
$967$	48.7974			1.56922			0.784610	−	0.619990i	$-0.212863\pi$
$967$	48.7974			1.56922			0.784610	+	0.619990i	$0.212863\pi$
$968$	39.4075	+	12.4575i	1.26661	+	0.400401i
$969$	−14.8420			−0.476793
$970$	−45.8128	+	20.5433i	−1.47096	+	0.659607i
$971$			41.8369i			1.34261i	0.741181	+	0.671306i	$0.234266\pi$
$971$			41.8369i			1.34261i	−0.741181	+	0.671306i	$0.765734\pi$
$972$	−30.6664	−	27.3182i	−0.983624	−	0.876230i
$973$		−	33.5948i		−	1.07700i
$974$	13.6656	+	30.4751i	0.437875	+	0.976485i
$975$	22.6922			0.726731
$976$	10.2692	−	1.18992i	0.328709	−	0.0380885i
$977$	33.2159			1.06267			0.531336	−	0.847161i	$-0.321690\pi$
$977$	33.2159			1.06267			0.531336	+	0.847161i	$0.321690\pi$
$978$	21.9856	+	49.0290i	0.703021	+	1.56777i
$979$		−	49.9628i		−	1.59682i
$980$	5.76279	+	5.13360i	0.184086	+	0.163987i
$981$			27.7435i			0.885780i
$982$	5.10286	−	2.28822i	0.162839	−	0.0730200i
$983$	−16.7186			−0.533242			−0.266621	−	0.963801i	$-0.585907\pi$
$983$	−16.7186			−0.533242			−0.266621	+	0.963801i	$0.585907\pi$
$984$	1.46618	−	4.63805i	0.0467402	−	0.147856i
$985$	64.6003			2.05834
$986$	7.03398	−	3.15417i	0.224007	−	0.100449i
$987$			67.6929i			2.15469i
$988$	−17.1765	+	19.2817i	−0.546457	+	0.613433i
$989$		−	19.0228i		−	0.604891i
$990$	−22.8792	−	51.0218i	−0.727147	−	1.62158i
$991$	−36.5268			−1.16031			−0.580156	−	0.814505i	$-0.697009\pi$
$991$	−36.5268			−1.16031			−0.580156	+	0.814505i	$0.697009\pi$
$992$	30.0954	−	17.9133i	0.955529	−	0.568749i
$993$	−19.3807			−0.615029
$994$	7.46030	+	16.6369i	0.236626	+	0.527690i
$995$			1.40882i			0.0446627i
$996$	11.9010	−	13.3597i	0.377099	−	0.423317i
$997$			6.59215i			0.208775i	0.994537	+	0.104388i	$0.0332883\pi$
$997$			6.59215i			0.208775i	−0.994537	+	0.104388i	$0.966712\pi$
$998$	−24.0066	+	10.7650i	−0.759915	+	0.340761i
$999$	−1.83025			−0.0579066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.c.a.69.6	yes	8
3.2	odd	2		1224.2.f.d.613.3		8
4.3	odd	2		544.2.c.a.273.7		8
8.3	odd	2		544.2.c.a.273.2		8
8.5	even	2	inner	136.2.c.a.69.5	✓	8
12.11	even	2		4896.2.f.c.2449.7		8
16.3	odd	4		4352.2.a.be.1.2		8
16.5	even	4		4352.2.a.bc.1.2		8
16.11	odd	4		4352.2.a.be.1.7		8
16.13	even	4		4352.2.a.bc.1.7		8
24.5	odd	2		1224.2.f.d.613.4		8
24.11	even	2		4896.2.f.c.2449.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.c.a.69.5	✓	8	8.5	even	2	inner
136.2.c.a.69.6	yes	8	1.1	even	1	trivial
544.2.c.a.273.2		8	8.3	odd	2
544.2.c.a.273.7		8	4.3	odd	2
1224.2.f.d.613.3		8	3.2	odd	2
1224.2.f.d.613.4		8	24.5	odd	2
4352.2.a.bc.1.2		8	16.5	even	4
4352.2.a.bc.1.7		8	16.13	even	4
4352.2.a.be.1.2		8	16.3	odd	4
4352.2.a.be.1.7		8	16.11	odd	4
4896.2.f.c.2449.2		8	24.11	even	2
4896.2.f.c.2449.7		8	12.11	even	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.578647 + 1.29041i) q^{2} -2.34593i q^{3} +(-1.33034 + 1.49339i) q^{4} -3.12087i q^{5} +(3.02722 - 1.35746i) q^{6} +2.86993 q^{7} +(-2.69688 - 0.852541i) q^{8} -2.50338 q^{9} +O(q^{10})\)	\(q+(0.578647 + 1.29041i) q^{2} -2.34593i q^{3} +(-1.33034 + 1.49339i) q^{4} -3.12087i q^{5} +(3.02722 - 1.35746i) q^{6} +2.86993 q^{7} +(-2.69688 - 0.852541i) q^{8} -2.50338 q^{9} +(4.02722 - 1.80588i) q^{10} +5.06085i q^{11} +(3.50338 + 3.12087i) q^{12} -2.04078i q^{13} +(1.66067 + 3.70339i) q^{14} -7.32134 q^{15} +(-0.460411 - 3.97341i) q^{16} -1.00000 q^{17} +(-1.44857 - 3.23040i) q^{18} +6.32669i q^{19} +(4.66067 + 4.15181i) q^{20} -6.73264i q^{21} +(-6.53060 + 2.92845i) q^{22} -3.18451 q^{23} +(-2.00000 + 6.32669i) q^{24} -4.73985 q^{25} +(2.63345 - 1.18089i) q^{26} -1.16504i q^{27} +(-3.81797 + 4.28591i) q^{28} +5.45095i q^{29} +(-4.23647 - 9.44757i) q^{30} +6.19127 q^{31} +(4.86093 - 2.89332i) q^{32} +11.8724 q^{33} +(-0.578647 - 1.29041i) q^{34} -8.95667i q^{35} +(3.33034 - 3.73851i) q^{36} -1.57098i q^{37} +(-8.16405 + 3.66092i) q^{38} -4.78753 q^{39} +(-2.66067 + 8.41663i) q^{40} -0.733092 q^{41} +(8.68789 - 3.89582i) q^{42} +5.97355i q^{43} +(-7.55782 - 6.73264i) q^{44} +7.81273i q^{45} +(-1.84271 - 4.10934i) q^{46} -10.0544 q^{47} +(-9.32134 + 1.08009i) q^{48} +1.23647 q^{49} +(-2.74270 - 6.11637i) q^{50} +2.34593i q^{51} +(3.04768 + 2.71493i) q^{52} -10.1217i q^{53} +(1.50338 - 0.674144i) q^{54} +15.7943 q^{55} +(-7.73985 - 2.44673i) q^{56} +14.8420 q^{57} +(-7.03398 + 3.15417i) q^{58} +0.268198i q^{59} +(9.73985 - 10.9336i) q^{60} +2.58448i q^{61} +(3.58256 + 7.98930i) q^{62} -7.18451 q^{63} +(6.54635 + 4.59841i) q^{64} -6.36902 q^{65} +(6.86993 + 15.3203i) q^{66} +0.116656i q^{67} +(1.33034 - 1.49339i) q^{68} +7.47064i q^{69} +(11.5578 - 5.18275i) q^{70} +4.49234 q^{71} +(6.75132 + 2.13423i) q^{72} +15.6494 q^{73} +(2.02722 - 0.909044i) q^{74} +11.1193i q^{75} +(-9.44820 - 8.41663i) q^{76} +14.5243i q^{77} +(-2.77029 - 6.17789i) q^{78} -0.815488 q^{79} +(-12.4005 + 1.43688i) q^{80} -10.2432 q^{81} +(-0.424201 - 0.945992i) q^{82} -3.81337i q^{83} +(10.0544 + 8.95667i) q^{84} +3.12087i q^{85} +(-7.70835 + 3.45657i) q^{86} +12.7875 q^{87} +(4.31459 - 13.6485i) q^{88} -9.87240 q^{89} +(-10.0817 + 4.52081i) q^{90} -5.85689i q^{91} +(4.23647 - 4.75571i) q^{92} -14.5243i q^{93} +(-5.81797 - 12.9744i) q^{94} +19.7448 q^{95} +(-6.78753 - 11.4034i) q^{96} -11.3758 q^{97} +(0.715480 + 1.59556i) q^{98} -12.6692i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9	\( 8 q - q^{2} + q^{4} - 2 q^{6} + 8 q^{7} - 7 q^{8} - 8 q^{9} + 6 q^{10} + 16 q^{12} - 10 q^{14} - 12 q^{15} - 7 q^{16} - 8 q^{17} + 9 q^{18} + 14 q^{20} - 14 q^{22} + 12 q^{23} - 16 q^{24} - 8 q^{25} + 24 q^{26} + 4 q^{28} - 16 q^{30} - 12 q^{31} - 11 q^{32} + 8 q^{33} + q^{34} + 15 q^{36} - 30 q^{38} + 20 q^{39} + 2 q^{40} + 20 q^{42} + 4 q^{44} - 26 q^{46} - 28 q^{47} - 28 q^{48} - 8 q^{49} + 19 q^{50} - 4 q^{52} + 44 q^{55} - 32 q^{56} + 8 q^{57} - 6 q^{58} + 48 q^{60} + 10 q^{62} - 20 q^{63} + 25 q^{64} + 24 q^{65} + 40 q^{66} - q^{68} + 28 q^{70} - 13 q^{72} + 8 q^{73} - 10 q^{74} + 6 q^{76} - 16 q^{78} - 44 q^{79} - 46 q^{80} - 40 q^{81} + 2 q^{82} + 28 q^{84} - 10 q^{86} + 44 q^{87} + 12 q^{88} + 8 q^{89} - 2 q^{90} + 16 q^{92} - 12 q^{94} - 16 q^{95} + 4 q^{96} + 8 q^{97} - 9 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^4 - 2 * q^6 + 8 * q^7 - 7 * q^8 - 8 * q^9 + 6 * q^10 + 16 * q^12 - 10 * q^14 - 12 * q^15 - 7 * q^16 - 8 * q^17 + 9 * q^18 + 14 * q^20 - 14 * q^22 + 12 * q^23 - 16 * q^24 - 8 * q^25 + 24 * q^26 + 4 * q^28 - 16 * q^30 - 12 * q^31 - 11 * q^32 + 8 * q^33 + q^34 + 15 * q^36 - 30 * q^38 + 20 * q^39 + 2 * q^40 + 20 * q^42 + 4 * q^44 - 26 * q^46 - 28 * q^47 - 28 * q^48 - 8 * q^49 + 19 * q^50 - 4 * q^52 + 44 * q^55 - 32 * q^56 + 8 * q^57 - 6 * q^58 + 48 * q^60 + 10 * q^62 - 20 * q^63 + 25 * q^64 + 24 * q^65 + 40 * q^66 - q^68 + 28 * q^70 - 13 * q^72 + 8 * q^73 - 10 * q^74 + 6 * q^76 - 16 * q^78 - 44 * q^79 - 46 * q^80 - 40 * q^81 + 2 * q^82 + 28 * q^84 - 10 * q^86 + 44 * q^87 + 12 * q^88 + 8 * q^89 - 2 * q^90 + 16 * q^92 - 12 * q^94 - 16 * q^95 + 4 * q^96 + 8 * q^97 - 9 * q^98

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