LMFDB - Embedded newform 136.2.h.a.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(101,136)]

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, 1]))

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

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

chi := DirichletCharacter("136.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.h (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 20x^{12} + 36x^{10} + 240x^{8} - 156x^{6} + 268x^{4} + 136x^{2} + 64 $ x^16 + 8x^14 + 20x^12 + 36x^10 + 240x^8 - 156x^6 + 268x^4 + 136*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.11
Root			$-0.476789 - 2.28924i$ of defining polynomial
Character	$\chi$	$=$	136.101
Dual form			136.2.h.a.101.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.288356 + 1.38450i) q^{2} -1.14379 q^{3} +(-1.83370 + 0.798461i) q^{4} -3.30694 q^{5} +(-0.329818 - 1.58358i) q^{6} +1.93801i q^{7} +(-1.63423 - 2.30853i) q^{8} -1.69175 q^{9} +O(q^{10})$	\(q+(0.288356 + 1.38450i) q^{2} -1.14379 q^{3} +(-1.83370 + 0.798461i) q^{4} -3.30694 q^{5} +(-0.329818 - 1.58358i) q^{6} +1.93801i q^{7} +(-1.63423 - 2.30853i) q^{8} -1.69175 q^{9} +(-0.953577 - 4.57847i) q^{10} +3.71058 q^{11} +(2.09737 - 0.913270i) q^{12} +5.23680i q^{13} +(-2.68318 + 0.558837i) q^{14} +3.78244 q^{15} +(2.72492 - 2.92828i) q^{16} +(-2.09069 + 3.55373i) q^{17} +(-0.487827 - 2.34223i) q^{18} -2.14926i q^{19} +(6.06394 - 2.64046i) q^{20} -2.21667i q^{21} +(1.06997 + 5.13731i) q^{22} -3.05569i q^{23} +(1.86921 + 2.64046i) q^{24} +5.93586 q^{25} +(-7.25037 + 1.51006i) q^{26} +5.36637 q^{27} +(-1.54743 - 3.55373i) q^{28} -4.62622 q^{29} +(1.09069 + 5.23680i) q^{30} +10.3861i q^{31} +(4.83996 + 2.92828i) q^{32} -4.24412 q^{33} +(-5.52302 - 1.86983i) q^{34} -6.40889i q^{35} +(3.10216 - 1.35080i) q^{36} -2.79494 q^{37} +(2.97565 - 0.619751i) q^{38} -5.98979i q^{39} +(5.40431 + 7.63416i) q^{40} -7.33041i q^{41} +(3.06899 - 0.639191i) q^{42} +6.21397i q^{43} +(-6.80409 + 2.96275i) q^{44} +5.59452 q^{45} +(4.23061 - 0.881126i) q^{46} -1.60106 q^{47} +(-3.11673 + 3.34933i) q^{48} +3.24412 q^{49} +(1.71164 + 8.21823i) q^{50} +(2.39131 - 4.06472i) q^{51} +(-4.18138 - 9.60273i) q^{52} -0.675957i q^{53} +(1.54743 + 7.42975i) q^{54} -12.2707 q^{55} +(4.47395 - 3.16716i) q^{56} +2.45829i q^{57} +(-1.33400 - 6.40501i) q^{58} +2.51789i q^{59} +(-6.93586 + 3.02013i) q^{60} +0.507368 q^{61} +(-14.3796 + 2.99490i) q^{62} -3.27863i q^{63} +(-2.65858 + 7.54533i) q^{64} -17.3178i q^{65} +(-1.22382 - 5.87599i) q^{66} -6.58260i q^{67} +(0.996186 - 8.18582i) q^{68} +3.49506i q^{69} +(8.87313 - 1.84804i) q^{70} -9.04548i q^{71} +(2.76471 + 3.90545i) q^{72} +4.87212i q^{73} +(-0.805939 - 3.86961i) q^{74} -6.78937 q^{75} +(1.71610 + 3.94109i) q^{76} +7.19114i q^{77} +(8.29289 - 1.72719i) q^{78} -3.27863i q^{79} +(-9.01116 + 9.68364i) q^{80} -1.06273 q^{81} +(10.1490 - 2.11377i) q^{82} +12.9915i q^{83} +(1.76993 + 4.06472i) q^{84} +(6.91379 - 11.7520i) q^{85} +(-8.60327 + 1.79184i) q^{86} +5.29141 q^{87} +(-6.06394 - 8.56597i) q^{88} -13.8090 q^{89} +(1.61321 + 7.74563i) q^{90} -10.1490 q^{91} +(2.43984 + 5.60321i) q^{92} -11.8795i q^{93} +(-0.461675 - 2.21667i) q^{94} +7.10746i q^{95} +(-5.53589 - 3.34933i) q^{96} +10.2103i q^{97} +(0.935461 + 4.49149i) q^{98} -6.27737 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9 - 8 * q^15 - 14 * q^16 - 2 * q^18 - 16 * q^30 - 2 * q^32 - 8 * q^33 + 18 * q^34 - 22 * q^36 + 36 * q^38 - 24 * q^47 - 8 * q^49 + 34 * q^50 - 8 * q^55 - 16 * q^60 - 30 * q^64 - 32 * q^66 + 38 * q^68 + 40 * q^70 + 70 * q^72 + 4 * q^76 - 24 * q^81 + 72 * q^84 + 4 * q^86 - 40 * q^87 - 24 * q^89 - 16 * q^94 + 34 * 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 $

$2$	0.288356	+	1.38450i	0.203899	+	0.978992i
$2$	0.288356	+	1.38450i	0.203899	+	0.978992i
$3$	−1.14379			−0.660366			−0.330183	−	0.943917i	$-0.607110\pi$
$3$	−1.14379			−0.660366			−0.330183	+	0.943917i	$0.607110\pi$
$4$	−1.83370	+	0.798461i	−0.916851	+	0.399230i
$5$	−3.30694			−1.47891			−0.739455	−	0.673206i	$-0.764917\pi$
$5$	−3.30694			−1.47891			−0.739455	+	0.673206i	$0.764917\pi$
$6$	−0.329818	−	1.58358i	−0.134648	−	0.646493i
$7$			1.93801i			0.732499i	0.930517	+	0.366250i	$0.119358\pi$
$7$			1.93801i			0.732499i	−0.930517	+	0.366250i	$0.880642\pi$
$8$	−1.63423	−	2.30853i	−0.577788	−	0.816187i
$9$	−1.69175			−0.563917
$10$	−0.953577	−	4.57847i	−0.301548	−	1.44784i
$11$	3.71058			1.11878			0.559391	−	0.828904i	$-0.311035\pi$
$11$	3.71058			1.11878			0.559391	+	0.828904i	$0.311035\pi$
$12$	2.09737	−	0.913270i	0.605457	−	0.263638i
$13$			5.23680i			1.45243i	0.687469	+	0.726214i	$0.258722\pi$
$13$			5.23680i			1.45243i	−0.687469	+	0.726214i	$0.741278\pi$
$14$	−2.68318	+	0.558837i	−0.717111	+	0.149356i
$15$	3.78244			0.976622
$16$	2.72492	−	2.92828i	0.681230	−	0.732069i
$17$	−2.09069	+	3.55373i	−0.507067	+	0.861907i
$17$	−2.09069	+	3.55373i	−0.507067	+	0.861907i
$18$	−0.487827	−	2.34223i	−0.114982	−	0.552070i
$19$		−	2.14926i		−	0.493073i	−0.969133	−	0.246537i	$-0.920707\pi$
$19$		−	2.14926i		−	0.493073i	0.969133	−	0.246537i	$-0.0792926\pi$
$20$	6.06394	−	2.64046i	1.35594	−	0.590425i
$21$		−	2.21667i		−	0.483718i
$22$	1.06997	+	5.13731i	0.228118	+	1.09528i
$23$		−	3.05569i		−	0.637154i	−0.947897	−	0.318577i	$-0.896795\pi$
$23$		−	3.05569i		−	0.637154i	0.947897	−	0.318577i	$-0.103205\pi$
$24$	1.86921	+	2.64046i	0.381552	+	0.538982i
$25$	5.93586			1.18717
$26$	−7.25037	+	1.51006i	−1.42191	+	0.296148i
$27$	5.36637			1.03276
$28$	−1.54743	−	3.55373i	−0.292436	−	0.671592i
$29$	−4.62622			−0.859067			−0.429533	−	0.903051i	$-0.641322\pi$
$29$	−4.62622			−0.859067			−0.429533	+	0.903051i	$0.641322\pi$
$30$	1.09069	+	5.23680i	0.199132	+	0.956105i
$31$			10.3861i			1.86540i	0.360656	+	0.932699i	$0.382553\pi$
$31$			10.3861i			1.86540i	−0.360656	+	0.932699i	$0.617447\pi$
$32$	4.83996	+	2.92828i	0.855592	+	0.517651i
$33$	−4.24412			−0.738806
$34$	−5.52302	−	1.86983i	−0.947190	−	0.320673i
$35$		−	6.40889i		−	1.08330i
$36$	3.10216	−	1.35080i	0.517027	−	0.225133i
$37$	−2.79494			−0.459486			−0.229743	−	0.973251i	$-0.573789\pi$
$37$	−2.79494			−0.459486			−0.229743	+	0.973251i	$0.573789\pi$
$38$	2.97565	−	0.619751i	0.482715	−	0.100537i
$39$		−	5.98979i		−	0.959134i
$40$	5.40431	+	7.63416i	0.854496	+	1.20707i
$41$		−	7.33041i		−	1.14482i	−0.819968	−	0.572409i	$-0.806009\pi$
$41$		−	7.33041i		−	1.14482i	0.819968	−	0.572409i	$-0.193991\pi$
$42$	3.06899	−	0.639191i	0.473556	−	0.0986294i
$43$			6.21397i			0.947622i	0.880627	+	0.473811i	$0.157122\pi$
$43$			6.21397i			0.947622i	−0.880627	+	0.473811i	$0.842878\pi$
$44$	−6.80409	+	2.96275i	−1.02576	+	0.446652i
$45$	5.59452			0.833981
$46$	4.23061	−	0.881126i	0.623769	−	0.129915i
$47$	−1.60106			−0.233539			−0.116769	−	0.993159i	$-0.537254\pi$
$47$	−1.60106			−0.233539			−0.116769	+	0.993159i	$0.537254\pi$
$48$	−3.11673	+	3.34933i	−0.449861	+	0.483434i
$49$	3.24412			0.463445
$50$	1.71164	+	8.21823i	0.242063	+	1.16223i
$51$	2.39131	−	4.06472i	0.334850	−	0.569174i
$52$	−4.18138	−	9.60273i	−0.579853	−	1.33166i
$53$		−	0.675957i		−	0.0928498i	−0.998922	−	0.0464249i	$-0.985217\pi$
$53$		−	0.675957i		−	0.0928498i	0.998922	−	0.0464249i	$-0.0147828\pi$
$54$	1.54743	+	7.42975i	0.210578	+	1.01106i
$55$	−12.2707			−1.65458
$56$	4.47395	−	3.16716i	0.597856	−	0.423229i
$57$			2.45829i			0.325609i
$58$	−1.33400	−	6.40501i	−0.175163	−	0.841019i
$59$			2.51789i			0.327801i	0.986477	+	0.163900i	$0.0524076\pi$
$59$			2.51789i			0.327801i	−0.986477	+	0.163900i	$0.947592\pi$
$60$	−6.93586	+	3.02013i	−0.895416	+	0.389897i
$61$	0.507368			0.0649618			0.0324809	−	0.999472i	$-0.489659\pi$
$61$	0.507368			0.0649618			0.0324809	+	0.999472i	$0.489659\pi$
$62$	−14.3796	+	2.99490i	−1.82621	+	0.380352i
$63$		−	3.27863i		−	0.413068i
$64$	−2.65858	+	7.54533i	−0.332322	+	0.943166i
$65$		−	17.3178i		−	2.14801i
$66$	−1.22382	−	5.87599i	−0.150641	−	0.723285i
$67$		−	6.58260i		−	0.804193i	−0.915597	−	0.402096i	$-0.868282\pi$
$67$		−	6.58260i		−	0.804193i	0.915597	−	0.402096i	$-0.131718\pi$
$68$	0.996186	−	8.18582i	0.120805	−	0.992676i
$69$			3.49506i			0.420755i
$70$	8.87313	−	1.84804i	1.06054	−	0.220883i
$71$		−	9.04548i		−	1.07350i	−0.843741	−	0.536750i	$-0.819652\pi$
$71$		−	9.04548i		−	1.07350i	0.843741	−	0.536750i	$-0.180348\pi$
$72$	2.76471	+	3.90545i	0.325824	+	0.460261i
$73$			4.87212i			0.570238i	0.958492	+	0.285119i	$0.0920331\pi$
$73$			4.87212i			0.570238i	−0.958492	+	0.285119i	$0.907967\pi$
$74$	−0.805939	−	3.86961i	−0.0936885	−	0.449833i
$75$	−6.78937			−0.783969
$76$	1.71610	+	3.94109i	0.196850	+	0.452074i
$77$			7.19114i			0.819507i
$78$	8.29289	−	1.72719i	0.938985	−	0.195566i
$79$		−	3.27863i		−	0.368875i	−0.982844	−	0.184437i	$-0.940954\pi$
$79$		−	3.27863i		−	0.368875i	0.982844	−	0.184437i	$-0.0590463\pi$
$80$	−9.01116	+	9.68364i	−1.00748	+	1.08266i
$81$	−1.06273			−0.118082
$82$	10.1490	−	2.11377i	1.12077	−	0.233427i
$83$			12.9915i			1.42600i	0.701163	+	0.713001i	$0.252664\pi$
$83$			12.9915i			1.42600i	−0.701163	+	0.713001i	$0.747336\pi$
$84$	1.76993	+	4.06472i	0.193115	+	0.443497i
$85$	6.91379	−	11.7520i	0.749906	−	1.27468i
$86$	−8.60327	+	1.79184i	−0.927714	+	0.193219i
$87$	5.29141			0.567299
$88$	−6.06394	−	8.56597i	−0.646419	−	0.913135i
$89$	−13.8090			−1.46375			−0.731875	−	0.681439i	$-0.761355\pi$
$89$	−13.8090			−1.46375			−0.731875	+	0.681439i	$0.761355\pi$
$90$	1.61321	+	7.74563i	0.170048	+	0.816461i
$91$	−10.1490			−1.06390
$92$	2.43984	+	5.60321i	0.254371	+	0.584175i
$93$		−	11.8795i		−	1.23185i
$94$	−0.461675	−	2.21667i	−0.0476182	−	0.228632i
$95$			7.10746i			0.729211i
$96$	−5.53589	−	3.34933i	−0.565004	−	0.341839i
$97$			10.2103i			1.03670i	0.855168	+	0.518351i	$0.173454\pi$
$97$			10.2103i			1.03670i	−0.855168	+	0.518351i	$0.826546\pi$
$98$	0.935461	+	4.49149i	0.0944958	+	0.453709i
$99$	−6.27737			−0.630900
$100$	−10.8846	+	4.73955i	−1.08846	+	0.473955i
$101$			7.58097i			0.754335i	0.926145	+	0.377168i	$0.123102\pi$
$101$			7.58097i			0.754335i	−0.926145	+	0.377168i	$0.876898\pi$
$102$	6.31716	+	2.13869i	0.625492	+	0.211761i
$103$	14.7951			1.45780			0.728901	−	0.684619i	$-0.240031\pi$
$103$	14.7951			1.45780			0.728901	+	0.684619i	$0.240031\pi$
$104$	12.0893	−	8.55814i	1.18545	−	0.839195i
$105$			7.33041i			0.715375i
$106$	0.935865	−	0.194916i	0.0908992	−	0.0189320i
$107$	4.15082			0.401275			0.200638	−	0.979666i	$-0.435699\pi$
$107$	4.15082			0.401275			0.200638	+	0.979666i	$0.435699\pi$
$108$	−9.84031	+	4.28483i	−0.946884	+	0.412308i
$109$	10.7281			1.02757			0.513783	−	0.857920i	$-0.328244\pi$
$109$	10.7281			1.02757			0.513783	+	0.857920i	$0.328244\pi$
$110$	−3.53832	−	16.9888i	−0.337366	−	1.61982i
$111$	3.19682			0.303429
$112$	5.67503	+	5.28093i	0.536240	+	0.499001i
$113$			17.3178i			1.62912i	0.580078	+	0.814561i	$0.303022\pi$
$113$			17.3178i			1.62912i	−0.580078	+	0.814561i	$0.696978\pi$
$114$	−3.40352	+	0.708864i	−0.318768	+	0.0663912i
$115$			10.1050i			0.942294i
$116$	8.48310	−	3.69385i	0.787636	−	0.342965i
$117$		−	8.85936i		−	0.819048i
$118$	−3.48602	+	0.726048i	−0.320914	+	0.0668381i
$119$	−6.88717	−	4.05178i	−0.631346	−	0.371426i
$120$	−6.18138	−	8.73186i	−0.564280	−	0.797106i
$121$	2.76840			0.251673
$122$	0.146303	+	0.702452i	0.0132456	+	0.0635971i
$123$			8.38443i			0.755999i
$124$	−8.29289	−	19.0450i	−0.744723	−	1.71029i
$125$	−3.09485			−0.276812
$126$	4.53927	−	0.945413i	0.404391	−	0.0842241i
$127$	17.7463			1.57473			0.787363	−	0.616490i	$-0.211446\pi$
$127$	17.7463			1.57473			0.787363	+	0.616490i	$0.211446\pi$
$128$	−11.2132	−	1.50507i	−0.991112	−	0.133031i
$129$		−	7.10746i		−	0.625777i
$130$	23.9766	−	4.99370i	2.10288	−	0.437976i
$131$	3.78233			0.330464			0.165232	−	0.986255i	$-0.447163\pi$
$131$	3.78233			0.330464			0.165232	+	0.986255i	$0.447163\pi$
$132$	7.78244	−	3.38876i	0.677374	−	0.294954i
$133$	4.16528			0.361176
$134$	9.11364	−	1.89813i	0.787298	−	0.163974i
$135$	−17.7463			−1.52735
$136$	11.6206	−	0.981209i	0.996454	−	0.0841380i
$137$	13.0545			1.11532			0.557661	−	0.830069i	$-0.311699\pi$
$137$	13.0545			1.11532			0.557661	+	0.830069i	$0.311699\pi$
$138$	−4.83892	+	1.00782i	−0.411916	+	0.0857914i
$139$	−4.22258			−0.358154			−0.179077	−	0.983835i	$-0.557311\pi$
$139$	−4.22258			−0.358154			−0.179077	+	0.983835i	$0.557311\pi$
$140$	5.11725	+	11.7520i	0.432486	+	0.993224i
$141$	1.83127			0.154221
$142$	12.5235	−	2.60832i	1.05095	−	0.218885i
$143$			19.4316i			1.62495i
$144$	−4.60988	+	4.95391i	−0.384157	+	0.412826i
$145$	15.2986			1.27048
$146$	−6.74546	+	1.40490i	−0.558258	+	0.116271i
$147$	−3.71058			−0.306043
$148$	5.12509	−	2.23165i	0.421280	−	0.183441i
$149$			4.29851i			0.352148i	0.984377	+	0.176074i	$0.0563398\pi$
$149$			4.29851i			0.352148i	−0.984377	+	0.176074i	$0.943660\pi$
$150$	−1.95776	−	9.39991i	−0.159850	−	0.767499i
$151$	−11.2552			−0.915938			−0.457969	−	0.888968i	$-0.651423\pi$
$151$	−11.2552			−0.915938			−0.457969	+	0.888968i	$0.651423\pi$
$152$	−4.96161	+	3.51238i	−0.402440	+	0.284892i
$153$	3.53692	−	6.01203i	0.285943	−	0.486043i
$154$	−9.95616	+	2.07361i	−0.802290	+	0.167096i
$155$		−	34.3462i		−	2.75875i
$156$	4.78261	+	10.9835i	0.382915	+	0.879383i
$157$		−	10.0102i		−	0.798904i	−0.916754	−	0.399452i	$-0.869200\pi$
$157$		−	10.0102i		−	0.798904i	0.916754	−	0.399452i	$-0.130800\pi$
$158$	4.53927	−	0.945413i	0.361125	−	0.0752130i
$159$			0.773151i			0.0613149i
$160$	−16.0055	−	9.68364i	−1.26534	−	0.765559i
$161$	5.92195			0.466715
$162$	−0.306446	−	1.47136i	−0.0240767	−	0.115601i
$163$	−17.4503			−1.36682			−0.683408	−	0.730036i	$-0.739503\pi$
$163$	−17.4503			−1.36682			−0.683408	+	0.730036i	$0.739503\pi$
$164$	5.85304	+	13.4418i	0.457046	+	1.04963i
$165$	14.0350			1.09263
$166$	−17.9868	+	3.74618i	−1.39604	+	0.290760i
$167$			1.16486i			0.0901395i	0.998984	+	0.0450698i	$0.0143510\pi$
$167$			1.16486i			0.0901395i	−0.998984	+	0.0450698i	$0.985649\pi$
$168$	−5.11725	+	3.62256i	−0.394804	+	0.279486i
$169$	−14.4241			−1.10955
$170$	18.2643	+	6.18341i	1.40081	+	0.474246i
$171$			3.63600i			0.278052i
$172$	−4.96161	−	11.3946i	−0.378319	−	0.868828i
$173$	5.88979			0.447793			0.223896	−	0.974613i	$-0.428122\pi$
$173$	5.88979			0.447793			0.223896	+	0.974613i	$0.428122\pi$
$174$	1.52581	+	7.32598i	0.115671	+	0.555381i
$175$			11.5038i			0.869603i
$176$	10.1110	−	10.8656i	0.762148	−	0.819026i
$177$		−	2.87993i		−	0.216469i
$178$	−3.98191	−	19.1186i	−0.298457	−	1.43300i
$179$			8.53694i			0.638081i	0.947741	+	0.319040i	$0.103361\pi$
$179$			8.53694i			0.638081i	−0.947741	+	0.319040i	$0.896639\pi$
$180$	−10.2587	+	4.46700i	−0.764636	+	0.332951i
$181$	−19.4221			−1.44363			−0.721817	−	0.692084i	$-0.756693\pi$
$181$	−19.4221			−1.44363			−0.721817	+	0.692084i	$0.756693\pi$
$182$	−2.92652	−	14.0513i	−0.216928	−	1.04155i
$183$	−0.580321			−0.0428986
$184$	−7.05413	+	4.99370i	−0.520037	+	0.368140i
$185$	9.24271			0.679538
$186$	16.4472	−	3.42552i	1.20597	−	0.251172i
$187$	−7.75767	+	13.1864i	−0.567297	+	0.964286i
$188$	2.93586	−	1.27838i	0.214120	−	0.0932357i
$189$			10.4001i			0.756494i
$190$	−9.84031	+	2.04948i	−0.713891	+	0.148685i
$191$	−2.52441			−0.182660			−0.0913300	−	0.995821i	$-0.529112\pi$
$191$	−2.52441			−0.182660			−0.0913300	+	0.995821i	$0.529112\pi$
$192$	3.04085	−	8.63025i	0.219454	−	0.622835i
$193$			0.644577i			0.0463977i	0.999731	+	0.0231988i	$0.00738508\pi$
$193$			0.644577i			0.0463977i	−0.999731	+	0.0231988i	$0.992615\pi$
$194$	−14.1362	+	2.94421i	−1.01492	+	0.211382i
$195$			19.8079i			1.41847i
$196$	−5.94874	+	2.59030i	−0.424910	+	0.185021i
$197$	−4.67265			−0.332912			−0.166456	−	0.986049i	$-0.553232\pi$
$197$	−4.67265			−0.332912			−0.166456	+	0.986049i	$0.553232\pi$
$198$	−1.81012	−	8.69104i	−0.128640	−	0.617646i
$199$		−	16.4975i		−	1.16947i	−0.811223	−	0.584737i	$-0.801198\pi$
$199$		−	16.4975i		−	1.16947i	0.811223	−	0.584737i	$-0.198802\pi$
$200$	−9.70057	−	13.7031i	−0.685934	−	0.968955i
$201$			7.52910i			0.531062i
$202$	−10.4959	+	2.18602i	−0.738488	+	0.153808i
$203$		−	8.96565i		−	0.629266i
$204$	−1.13943	+	9.36284i	−0.0797757	+	0.655530i
$205$			24.2412i			1.69308i
$206$	4.26625	+	20.4838i	0.297244	+	1.42718i
$207$			5.16945i			0.359302i
$208$	15.3348	+	14.2699i	1.06328	+	0.989438i
$209$		−	7.97499i		−	0.551641i
$210$	−10.1490	+	2.11377i	−0.700346	+	0.145864i
$211$	22.3047			1.53552			0.767760	−	0.640738i	$-0.221371\pi$
$211$	22.3047			1.53552			0.767760	+	0.640738i	$0.221371\pi$
$212$	0.539725	+	1.23950i	0.0370685	+	0.0851294i
$213$			10.3461i			0.708903i
$214$	1.19692	+	5.74683i	0.0818195	+	0.392845i
$215$		−	20.5492i		−	1.40145i
$216$	−8.76988	−	12.3884i	−0.596715	−	0.842923i
$217$	−20.1284			−1.36640
$218$	3.09351	+	14.8531i	0.209519	+	1.00598i
$219$		−	5.57267i		−	0.376566i
$220$	22.5007	−	9.79765i	1.51700	−	0.660557i
$221$	−18.6102	−	10.9485i	−1.25186	−	0.736478i
$222$	0.921824	+	4.42601i	0.0618687	+	0.297054i
$223$	−8.24259			−0.551965			−0.275982	−	0.961163i	$-0.589003\pi$
$223$	−8.24259			−0.551965			−0.275982	+	0.961163i	$0.589003\pi$
$224$	−5.67503	+	9.37989i	−0.379179	+	0.626720i
$225$	−10.0420			−0.669466
$226$	−23.9766	+	4.99370i	−1.59490	+	0.332176i
$227$	24.8715			1.65078			0.825390	−	0.564563i	$-0.190955\pi$
$227$	24.8715			1.65078			0.825390	+	0.564563i	$0.190955\pi$
$228$	−1.96285	−	4.50777i	−0.129993	−	0.298535i
$229$		−	14.3585i		−	0.948836i	−0.880300	−	0.474418i	$-0.842659\pi$
$229$		−	14.3585i		−	0.948836i	0.880300	−	0.474418i	$-0.157341\pi$
$230$	−13.9904	+	2.91383i	−0.922498	+	0.192132i
$231$		−	8.22514i		−	0.541174i
$232$	7.56030	+	10.6797i	0.496358	+	0.701159i
$233$		−	5.29375i		−	0.346805i	−0.984851	−	0.173403i	$-0.944524\pi$
$233$		−	5.29375i		−	0.346805i	0.984851	−	0.173403i	$-0.0554762\pi$
$234$	12.2658	−	2.55465i	0.801841	−	0.167003i
$235$	5.29461			0.345382
$236$	−2.01043	−	4.61705i	−0.130868	−	0.300544i
$237$			3.75006i			0.243592i
$238$	3.62375	−	10.7037i	0.234893	−	0.693816i
$239$	20.3238			1.31464			0.657318	−	0.753613i	$-0.271691\pi$
$239$	20.3238			1.31464			0.657318	+	0.753613i	$0.271691\pi$
$240$	10.3069	−	11.0760i	0.665304	−	0.714955i
$241$		−	0.222943i		−	0.0143610i	−0.999974	−	0.00718051i	$-0.997714\pi$
$241$		−	0.222943i		−	0.0143610i	0.999974	−	0.00718051i	$-0.00228565\pi$
$242$	0.798285	+	3.83286i	0.0513157	+	0.246385i
$243$	−14.8836			−0.954780
$244$	−0.930361	+	0.405113i	−0.0595602	+	0.0259347i
$245$	−10.7281			−0.685393
$246$	−11.6083	+	2.41770i	−0.740117	+	0.154147i
$247$	11.2552			0.716153
$248$	23.9766	−	16.9733i	1.52251	−	1.07780i
$249$		−	14.8595i		−	0.941683i
$250$	−0.892419	−	4.28483i	−0.0564416	−	0.270997i
$251$		−	25.4406i		−	1.60580i	−0.596115	−	0.802899i	$-0.703290\pi$
$251$		−	25.4406i		−	1.60580i	0.596115	−	0.802899i	$-0.296710\pi$
$252$	2.61786	+	6.01203i	0.164909	+	0.378722i
$253$		−	11.3384i		−	0.712837i
$254$	5.11725	+	24.5698i	0.321085	+	1.54164i
$255$	−7.90791	+	13.4418i	−0.495212	+	0.841757i
$256$	−1.14961	−	15.9586i	−0.0718506	−	0.997415i
$257$	−29.7213			−1.85397			−0.926983	−	0.375105i	$-0.877607\pi$
$257$	−29.7213			−1.85397			−0.926983	+	0.375105i	$0.877607\pi$
$258$	9.84031	−	2.04948i	0.612631	−	0.127595i
$259$		−	5.41663i		−	0.336573i
$260$	13.8276	+	31.7557i	0.857550	+	1.96940i
$261$	7.82640			0.484442
$262$	1.09066	+	5.23666i	0.0673812	+	0.323522i
$263$	−14.7951			−0.912304			−0.456152	−	0.889902i	$-0.650773\pi$
$263$	−14.7951			−0.912304			−0.456152	+	0.889902i	$0.650773\pi$
$264$	6.93586	+	9.79765i	0.426873	+	0.603004i
$265$			2.23535i			0.137316i
$266$	1.20108	+	5.76685i	0.0736432	+	0.353588i
$267$	15.7946			0.966611
$268$	5.25595	+	12.0705i	0.321058	+	0.737325i
$269$	−7.67968			−0.468239			−0.234119	−	0.972208i	$-0.575221\pi$
$269$	−7.67968			−0.468239			−0.234119	+	0.972208i	$0.575221\pi$
$270$	−5.11725	−	24.5698i	−0.311426	−	1.49527i
$271$	12.3681			0.751306			0.375653	−	0.926760i	$-0.377418\pi$
$271$	12.3681			0.751306			0.375653	+	0.926760i	$0.377418\pi$
$272$	4.70935	+	15.8058i	0.285546	+	0.958365i
$273$	11.6083			0.702565
$274$	3.76435	+	18.0740i	0.227413	+	1.09189i
$275$	22.0255			1.32819
$276$	−2.79066	−	6.40889i	−0.167978	−	0.385770i
$277$	15.3033			0.919483			0.459742	−	0.888053i	$-0.347942\pi$
$277$	15.3033			0.919483			0.459742	+	0.888053i	$0.347942\pi$
$278$	−1.21761	−	5.84618i	−0.0730272	−	0.350630i
$279$		−	17.5707i		−	1.05193i
$280$	−14.7951	+	10.4736i	−0.884175	+	0.625918i
$281$	4.47572			0.266999			0.133499	−	0.991049i	$-0.457379\pi$
$281$	4.47572			0.266999			0.133499	+	0.991049i	$0.457379\pi$
$282$	0.528059	+	2.53540i	0.0314454	+	0.150981i
$283$	−8.49319			−0.504868			−0.252434	−	0.967614i	$-0.581231\pi$
$283$	−8.49319			−0.504868			−0.252434	+	0.967614i	$0.581231\pi$
$284$	7.22246	+	16.5867i	0.428574	+	0.984240i
$285$		−	8.12943i		−	0.481546i
$286$	−26.9031	+	5.60321i	−1.59081	+	0.331325i
$287$	14.2064			0.838578
$288$	−8.18800	−	4.95391i	−0.482482	−	0.291912i
$289$	−8.25803	−	14.8595i	−0.485766	−	0.874089i
$290$	4.41145	+	21.1810i	0.259050	+	1.24379i
$291$		−	11.6785i		−	0.684603i
$292$	−3.89019	−	8.93400i	−0.227656	−	0.522823i
$293$			1.74175i			0.101754i	0.998705	+	0.0508770i	$0.0162016\pi$
$293$			1.74175i			0.101754i	−0.998705	+	0.0508770i	$0.983798\pi$
$294$	−1.06997	−	5.13731i	−0.0624018	−	0.299614i
$295$		−	8.32650i		−	0.484788i
$296$	4.56758	+	6.45220i	0.265485	+	0.375026i
$297$	19.9123			1.15543
$298$	−5.95131	+	1.23950i	−0.344750	+	0.0718025i
$299$	16.0020			0.925421
$300$	12.4497	−	5.42104i	0.718782	−	0.312984i
$301$	−12.0427			−0.694132
$302$	−3.24552	−	15.5829i	−0.186758	−	0.896695i
$303$		−	8.67103i		−	0.498137i
$304$	−6.29362	−	5.85655i	−0.360964	−	0.335896i
$305$	−1.67784			−0.0960726
$306$	9.34357	+	3.16328i	0.534136	+	0.180833i
$307$		−	32.4520i		−	1.85213i	−0.377363	−	0.926065i	$-0.623169\pi$
$307$		−	32.4520i		−	1.85213i	0.377363	−	0.926065i	$-0.376831\pi$
$308$	−5.74184	−	13.1864i	−0.327172	−	0.751365i
$309$	−16.9224			−0.962684
$310$	47.5525	−	9.90394i	2.70080	−	0.562506i
$311$			10.9091i			0.618598i	0.950965	+	0.309299i	$0.100094\pi$
$311$			10.9091i			0.618598i	−0.950965	+	0.309299i	$0.899906\pi$
$312$	−13.8276	+	9.78870i	−0.782833	+	0.554176i
$313$			22.4129i			1.26685i	0.773804	+	0.633425i	$0.218351\pi$
$313$			22.4129i			1.26685i	−0.773804	+	0.633425i	$0.781649\pi$
$314$	13.8592	−	2.88652i	0.782121	−	0.162895i
$315$			10.8422i			0.610891i
$316$	2.61786	+	6.01203i	0.147266	+	0.338203i
$317$	7.16263			0.402294			0.201147	−	0.979561i	$-0.435533\pi$
$317$	7.16263			0.402294			0.201147	+	0.979561i	$0.435533\pi$
$318$	−1.07043	+	0.222943i	−0.0600268	+	0.0125020i
$319$	−17.1659			−0.961108
$320$	8.79176	−	24.9520i	0.491474	−	1.39486i
$321$	−4.74766			−0.264989
$322$	1.70763	+	8.19896i	0.0951626	+	0.456910i
$323$	7.63788	+	4.49343i	0.424983	+	0.250021i
$324$	1.94874	−	0.848552i	0.108263	−	0.0471418i
$325$			31.0849i			1.72428i
$326$	−5.03192	−	24.1601i	−0.278692	−	1.33810i
$327$	−12.2707			−0.678570
$328$	−16.9224	+	11.9796i	−0.934385	+	0.661462i
$329$		−	3.10287i		−	0.171067i
$330$	4.04709	+	19.4316i	0.222785	+	1.06967i
$331$			26.0219i			1.43029i	0.698976	+	0.715145i	$0.253640\pi$
$331$			26.0219i			1.43029i	−0.698976	+	0.715145i	$0.746360\pi$
$332$	−10.3732	−	23.8225i	−0.569303	−	1.30743i
$333$	4.72834			0.259112
$334$	−1.61275	+	0.335895i	−0.0882459	+	0.0183793i
$335$			21.7683i			1.18933i
$336$	−6.49103	−	6.04026i	−0.354115	−	0.329523i
$337$			13.7933i			0.751369i	0.926748	+	0.375684i	$0.122592\pi$
$337$			13.7933i			0.751369i	−0.926748	+	0.375684i	$0.877408\pi$
$338$	−4.15928	−	19.9702i	−0.226235	−	1.08624i
$339$		−	19.8079i		−	1.07582i
$340$	−3.29433	+	27.0700i	−0.178660	+	1.46808i
$341$			38.5384i			2.08697i
$342$	−5.03406	+	1.04846i	−0.272211	+	0.0566945i
$343$			19.8532i			1.07197i
$344$	14.3451	−	10.1551i	0.773437	−	0.547524i
$345$		−	11.5579i		−	0.622259i
$346$	1.69836	+	8.15444i	0.0913043	+	0.438385i
$347$	−18.8750			−1.01326			−0.506630	−	0.862163i	$-0.669109\pi$
$347$	−18.8750			−1.01326			−0.506630	+	0.862163i	$0.669109\pi$
$348$	−9.70286	+	4.22498i	−0.520128	+	0.226483i
$349$		−	6.71622i		−	0.359511i	−0.983711	−	0.179755i	$-0.942469\pi$
$349$		−	6.71622i		−	0.359511i	0.983711	−	0.179755i	$-0.0575306\pi$
$350$	−15.9270	+	3.31718i	−0.851335	+	0.177311i
$351$			28.1026i			1.50001i
$352$	17.9590	+	10.8656i	0.957221	+	0.579139i
$353$	19.7029			1.04868			0.524339	−	0.851510i	$-0.324313\pi$
$353$	19.7029			1.04868			0.524339	+	0.851510i	$0.324313\pi$
$354$	3.98727	−	0.830445i	0.211921	−	0.0441377i
$355$			29.9129i			1.58761i
$356$	25.3216	−	11.0259i	1.34204	−	0.584374i
$357$	7.87746	+	4.63438i	0.416919	+	0.245277i
$358$	−11.8194	+	2.46168i	−0.624676	+	0.130104i
$359$	−12.4549			−0.657342			−0.328671	−	0.944444i	$-0.606601\pi$
$359$	−12.4549			−0.657342			−0.328671	+	0.944444i	$0.606601\pi$
$360$	−9.14273	−	12.9151i	−0.481864	−	0.680685i
$361$	14.3807			0.756879
$362$	−5.60048	−	26.8900i	−0.294355	−	1.41331i
$363$	−3.16646			−0.166196
$364$	18.6102	−	8.10356i	0.975439	−	0.424742i
$365$		−	16.1118i		−	0.843330i
$366$	−0.167339	−	0.803457i	−0.00874696	−	0.0419973i
$367$		−	11.5038i		−	0.600492i	−0.953862	−	0.300246i	$-0.902931\pi$
$367$		−	11.5038i		−	0.600492i	0.953862	−	0.300246i	$-0.0970687\pi$
$368$	−8.94789	−	8.32650i	−0.466441	−	0.434049i
$369$			12.4012i			0.645581i
$370$	2.66519	+	12.7966i	0.138557	+	0.665262i
$371$	1.31001			0.0680124
$372$	9.48530	+	21.7834i	0.491790	+	1.12942i
$373$		−	8.93289i		−	0.462527i	−0.972891	−	0.231264i	$-0.925714\pi$
$373$		−	8.93289i		−	0.462527i	0.972891	−	0.231264i	$-0.0742860\pi$
$374$	−20.4936	−	6.93814i	−1.05970	−	0.358763i
$375$	3.53985			0.182797
$376$	2.61650	+	3.69609i	0.134936	+	0.190611i
$377$		−	24.2266i		−	1.24773i
$378$	−14.3989	+	2.99893i	−0.740602	+	0.154248i
$379$	26.8799			1.38073			0.690363	−	0.723463i	$-0.257451\pi$
$379$	26.8799			1.38073			0.690363	+	0.723463i	$0.257451\pi$
$380$	−5.67503	−	13.0330i	−0.291123	−	0.668577i
$381$	−20.2980			−1.03990
$382$	−0.727930	−	3.49506i	−0.0372441	−	0.178823i
$383$	21.2861			1.08767			0.543835	−	0.839192i	$-0.316972\pi$
$383$	21.2861			1.08767			0.543835	+	0.839192i	$0.316972\pi$
$384$	12.8255	+	1.72148i	0.654497	+	0.0878489i
$385$		−	23.7807i		−	1.21198i
$386$	−0.892419	+	0.185868i	−0.0454230	+	0.00946042i
$387$		−	10.5125i		−	0.534380i
$388$	−8.15255	−	18.7227i	−0.413883	−	0.950501i
$389$		−	20.6113i		−	1.04504i	−0.852628	−	0.522518i	$-0.824993\pi$
$389$		−	20.6113i		−	1.04504i	0.852628	−	0.522518i	$-0.175007\pi$
$390$	−27.4241	+	5.71173i	−1.38867	+	0.289225i
$391$	10.8591	+	6.38849i	0.549168	+	0.323080i
$392$	−5.30163	−	7.48912i	−0.267773	−	0.378258i
$393$	−4.32619			−0.218227
$394$	−1.34739	−	6.46930i	−0.0678804	−	0.325919i
$395$			10.8422i			0.545532i
$396$	11.5108	−	5.01223i	0.578441	−	0.251874i
$397$	−26.1970			−1.31479			−0.657395	−	0.753546i	$-0.728342\pi$
$397$	−26.1970			−1.31479			−0.657395	+	0.753546i	$0.728342\pi$
$398$	22.8408	−	4.75715i	1.14491	−	0.238454i
$399$	−4.76420			−0.238508
$400$	16.1748	−	17.3819i	0.808738	−	0.869093i
$401$			36.4048i			1.81797i	0.416828	+	0.908986i	$0.363142\pi$
$401$			36.4048i			1.81797i	−0.416828	+	0.908986i	$0.636858\pi$
$402$	−10.4241	+	2.17106i	−0.519905	+	0.108283i
$403$	−54.3899			−2.70935
$404$	−6.05311	−	13.9012i	−0.301153	−	0.691613i
$405$	3.51440			0.174632
$406$	12.4130	−	2.58530i	0.616046	−	0.128306i
$407$	−10.3709			−0.514064
$408$	−13.2914	+	1.12229i	−0.658025	+	0.0555619i
$409$	−1.23020			−0.0608295			−0.0304148	−	0.999537i	$-0.509683\pi$
$409$	−1.23020			−0.0608295			−0.0304148	+	0.999537i	$0.509683\pi$
$410$	−33.5621	+	6.99011i	−1.65751	+	0.345217i
$411$	−14.9316			−0.736521
$412$	−27.1298	+	11.8133i	−1.33659	+	0.581999i
$413$	−4.87969			−0.240114
$414$	−7.15713	+	1.49064i	−0.351754	+	0.0732612i
$415$		−	42.9621i		−	2.10893i
$416$	−15.3348	+	25.3459i	−0.751851	+	1.24269i
$417$	4.82973			0.236513
$418$	11.0414	−	2.29964i	0.540052	−	0.112479i
$419$	13.6985			0.669217			0.334608	−	0.942357i	$-0.391396\pi$
$419$	13.6985			0.669217			0.334608	+	0.942357i	$0.391396\pi$
$420$	−5.85304	−	13.4418i	−0.285599	−	0.655892i
$421$			12.0143i			0.585542i	0.956183	+	0.292771i	$0.0945774\pi$
$421$			12.0143i			0.585542i	−0.956183	+	0.292771i	$0.905423\pi$
$422$	6.43170	+	30.8810i	0.313090	+	1.50326i
$423$	2.70859			0.131696
$424$	−1.56046	+	1.10467i	−0.0757828	+	0.0536475i
$425$	−12.4101	+	21.0945i	−0.601976	+	1.02323i
$426$	−14.3242	+	2.98336i	−0.694011	+	0.144544i
$427$			0.983284i			0.0475844i
$428$	−7.61137	+	3.31427i	−0.367909	+	0.160201i
$429$		−	22.2256i		−	1.07306i
$430$	28.4505	−	5.92550i	1.37201	−	0.285753i
$431$			9.39000i			0.452300i	0.974092	+	0.226150i	$0.0726140\pi$
$431$			9.39000i			0.452300i	−0.974092	+	0.226150i	$0.927386\pi$
$432$	14.6229	−	15.7142i	0.703546	−	0.756050i
$433$	−3.13938			−0.150869			−0.0754346	−	0.997151i	$-0.524034\pi$
$433$	−3.13938			−0.150869			−0.0754346	+	0.997151i	$0.524034\pi$
$434$	−5.80414	−	27.8678i	−0.278608	−	1.33770i
$435$	−17.4984			−0.838983
$436$	−19.6721	+	8.56597i	−0.942124	+	0.410235i
$437$	−6.56745			−0.314164
$438$	7.71538	−	1.60691i	0.368655	−	0.0767813i
$439$		−	16.0244i		−	0.764801i	−0.923997	−	0.382401i	$-0.875097\pi$
$439$		−	16.0244i		−	0.764801i	0.923997	−	0.382401i	$-0.124903\pi$
$440$	20.0531	+	28.3272i	0.955994	+	1.35044i
$441$	−5.48823			−0.261344
$442$	9.79192	−	28.9230i	0.465754	−	1.37572i
$443$			7.58709i			0.360473i	0.983623	+	0.180237i	$0.0576864\pi$
$443$			7.58709i			0.360473i	−0.983623	+	0.180237i	$0.942314\pi$
$444$	−5.86202	+	2.55254i	−0.278199	+	0.121138i
$445$	45.6655			2.16475
$446$	−2.37680	−	11.4119i	−0.112545	−	0.540369i
$447$		−	4.91659i		−	0.232547i
$448$	−14.6229	−	5.15235i	−0.690868	−	0.243426i
$449$		−	19.0870i		−	0.900773i	−0.892834	−	0.450387i	$-0.851286\pi$
$449$		−	19.0870i		−	0.900773i	0.892834	−	0.450387i	$-0.148714\pi$
$450$	−2.89567	−	13.9032i	−0.136503	−	0.655402i
$451$		−	27.2001i		−	1.28080i
$452$	−13.8276	−	31.7557i	−0.650395	−	1.49366i
$453$	12.8736			0.604854
$454$	7.17185	+	34.4347i	0.336592	+	1.61610i
$455$	33.5621			1.57341
$456$	5.67503	−	4.01742i	0.265758	−	0.188133i
$457$	−8.52288			−0.398684			−0.199342	−	0.979930i	$-0.563880\pi$
$457$	−8.52288			−0.398684			−0.199342	+	0.979930i	$0.563880\pi$
$458$	19.8794	−	4.14036i	0.928903	−	0.193466i
$459$	−11.2194	+	19.0706i	−0.523677	+	0.890141i
$460$	−8.06842	−	18.5295i	−0.376192	−	0.863943i
$461$			20.7388i			0.965904i	0.875647	+	0.482952i	$0.160435\pi$
$461$			20.7388i			0.965904i	−0.875647	+	0.482952i	$0.839565\pi$
$462$	11.3877	−	2.37177i	0.529805	−	0.110345i
$463$	−13.7743			−0.640148			−0.320074	−	0.947393i	$-0.603708\pi$
$463$	−13.7743			−0.640148			−0.320074	+	0.947393i	$0.603708\pi$
$464$	−12.6061	+	13.5468i	−0.585222	+	0.628896i
$465$			39.2848i			1.82179i
$466$	7.32922	−	1.52649i	0.339519	−	0.0707131i
$467$			26.0431i			1.20513i	0.798070	+	0.602565i	$0.205854\pi$
$467$			26.0431i			1.20513i	−0.798070	+	0.602565i	$0.794146\pi$
$468$	7.07385	+	16.2454i	0.326989	+	0.750945i
$469$	12.7572			0.589071
$470$	1.52673	+	7.33041i	0.0704230	+	0.338127i
$471$			11.4496i			0.527569i
$472$	5.81260	−	4.11481i	0.267547	−	0.189399i
$473$			23.0574i			1.06018i
$474$	−5.19197	+	1.08135i	−0.238475	+	0.0496681i
$475$		−	12.7577i		−	0.585363i
$476$	15.8642	+	1.93062i	0.727134	+	0.0884898i
$477$			1.14355i			0.0523595i
$478$	5.86049	+	28.1383i	0.268053	+	1.28702i
$479$			17.9152i			0.818566i	0.912407	+	0.409283i	$0.134221\pi$
$479$			17.9152i			0.818566i	−0.912407	+	0.409283i	$0.865779\pi$
$480$	18.3069	+	11.0760i	0.835590	+	0.505549i
$481$		−	14.6366i		−	0.667370i
$482$	0.308665	−	0.0642870i	0.0140593	−	0.00292819i
$483$	−6.77345			−0.308203
$484$	−5.07642	+	2.21046i	−0.230746	+	0.100475i
$485$		−	33.7650i		−	1.53319i
$486$	−4.29177	−	20.6063i	−0.194678	−	0.934722i
$487$			32.0530i			1.45246i	0.687451	+	0.726230i	$0.258729\pi$
$487$			32.0530i			1.45246i	−0.687451	+	0.726230i	$0.741271\pi$
$488$	−0.829156	−	1.17127i	−0.0375341	−	0.0530210i
$489$	19.9595			0.902599
$490$	−3.09351	−	14.8531i	−0.139751	−	0.670994i
$491$			21.8794i			0.987403i	0.869631	+	0.493701i	$0.164356\pi$
$491$			21.8794i			0.987403i	−0.869631	+	0.493701i	$0.835644\pi$
$492$	−6.69464	−	15.3745i	−0.301818	−	0.693138i
$493$	9.67198	−	16.4403i	0.435604	−	0.740435i
$494$	3.24552	+	15.5829i	0.146023	+	0.701108i
$495$	20.7589			0.933043
$496$	30.4134	+	28.3013i	1.36560	+	1.27077i
$497$	17.5302			0.786338
$498$	20.5730	−	4.28483i	0.921900	−	0.192008i
$499$	10.1185			0.452964			0.226482	−	0.974015i	$-0.427277\pi$
$499$	10.1185			0.452964			0.226482	+	0.974015i	$0.427277\pi$
$500$	5.67503	−	2.47112i	0.253795	−	0.110512i
$501$		−	1.33235i		−	0.0595251i
$502$	35.2227	−	7.33597i	1.57206	−	0.327420i
$503$		−	18.0166i		−	0.803318i	−0.915789	−	0.401659i	$-0.868434\pi$
$503$		−	18.0166i		−	0.803318i	0.915789	−	0.401659i	$-0.131566\pi$
$504$	−7.56880	+	5.35804i	−0.337141	+	0.238666i
$505$		−	25.0698i		−	1.11559i
$506$	15.6980	−	3.26949i	0.697862	−	0.145346i
$507$	16.4981			0.732707
$508$	−32.5413	+	14.1697i	−1.44379	+	0.628678i
$509$			40.8899i			1.81241i	0.422834	+	0.906207i	$0.361035\pi$
$509$			40.8899i			1.81241i	−0.422834	+	0.906207i	$0.638965\pi$
$510$	−20.8905	−	7.07251i	−0.925046	−	0.313176i
$511$	−9.44221			−0.417699
$512$	21.7633	−	6.19341i	0.961811	−	0.273713i
$513$		−	11.5337i		−	0.509225i
$514$	−8.57033	−	41.1493i	−0.378021	−	1.81502i
$515$	−48.9265			−2.15596
$516$	5.67503	+	13.0330i	0.249829	+	0.573744i
$517$	−5.94086			−0.261279
$518$	7.49934	−	1.56192i	0.329502	−	0.0686268i
$519$	−6.73667			−0.295707
$520$	−39.9786	+	28.3013i	−1.75318	+	1.24109i
$521$			13.7933i			0.604295i	0.953261	+	0.302148i	$0.0977036\pi$
$521$			13.7933i			0.604295i	−0.953261	+	0.302148i	$0.902296\pi$
$522$	2.25679	+	10.8357i	0.0987770	+	0.474265i
$523$		−	4.23843i		−	0.185334i	−0.995697	−	0.0926668i	$-0.970461\pi$
$523$		−	4.23843i		−	0.185334i	0.995697	−	0.0926668i	$-0.0295391\pi$
$524$	−6.93567	+	3.02005i	−0.302986	+	0.131931i
$525$		−	13.1579i		−	0.574257i
$526$	−4.26625	−	20.4838i	−0.186018	−	0.893138i
$527$	−36.9094	−	21.7141i	−1.60780	−	0.945881i
$528$	−11.5649	+	12.4279i	−0.503297	+	0.540857i
$529$	13.6628			0.594034
$530$	−3.09485	+	0.644577i	−0.134432	+	0.0279986i
$531$		−	4.25963i		−	0.184852i
$532$	−7.63788	+	3.32581i	−0.331144	+	0.144192i
$533$	38.3879			1.66276
$534$	4.55446	+	21.8676i	0.197091	+	0.946305i
$535$	−13.7265			−0.593450
$536$	−15.1961	+	10.7575i	−0.656372	+	0.464653i
$537$		−	9.76445i		−	0.421367i
$538$	−2.21448	−	10.6326i	−0.0954732	−	0.458402i
$539$	12.0375			0.518494
$540$	32.5413	−	14.1697i	1.40036	−	0.609766i
$541$	22.8390			0.981925			0.490963	−	0.871181i	$-0.336645\pi$
$541$	22.8390			0.981925			0.490963	+	0.871181i	$0.336645\pi$
$542$	3.56641	+	17.1236i	0.153190	+	0.735523i
$543$	22.2148			0.953327
$544$	−20.5252	+	11.0778i	−0.880009	+	0.474957i
$545$	−35.4772			−1.51968
$546$	3.34732	+	16.0717i	0.143252	+	0.687805i
$547$	−7.09391			−0.303314			−0.151657	−	0.988433i	$-0.548461\pi$
$547$	−7.09391			−0.303314			−0.151657	+	0.988433i	$0.548461\pi$
$548$	−23.9381	+	10.4235i	−1.02258	+	0.445270i
$549$	−0.858339			−0.0366330
$550$	6.35119	+	30.4944i	0.270816	+	1.30028i
$551$			9.94292i			0.423583i
$552$	8.06842	−	5.71173i	0.343415	−	0.243107i
$553$	6.35402			0.270200
$554$	4.41279	+	21.1874i	0.187481	+	0.900167i
$555$	−10.5717			−0.448744
$556$	7.74295	−	3.37156i	0.328374	−	0.142986i
$557$		−	2.41037i		−	0.102131i	−0.998695	−	0.0510653i	$-0.983738\pi$
$557$		−	2.41037i		−	0.102131i	0.998695	−	0.0510653i	$-0.0162617\pi$
$558$	24.3267	−	5.06661i	1.02983	−	0.214487i
$559$	−32.5413			−1.37635
$560$	−18.7670	−	17.4637i	−0.793050	−	0.737977i
$561$	8.87313	−	15.0825i	0.374624	−	0.636782i
$562$	1.29060	+	6.19665i	0.0544407	+	0.261390i
$563$		−	7.55366i		−	0.318349i	−0.987250	−	0.159174i	$-0.949117\pi$
$563$		−	7.55366i		−	0.318349i	0.987250	−	0.159174i	$-0.0508832\pi$
$564$	−3.35801	+	1.46220i	−0.141398	+	0.0615697i
$565$		−	57.2690i		−	2.40932i
$566$	−2.44906	−	11.7589i	−0.102942	−	0.494262i
$567$		−	2.05959i		−	0.0864947i
$568$	−20.8817	+	14.7824i	−0.876177	+	0.620256i
$569$	−23.4800			−0.984333			−0.492167	−	0.870501i	$-0.663795\pi$
$569$	−23.4800			−0.984333			−0.492167	+	0.870501i	$0.663795\pi$
$570$	11.2552	−	2.34417i	0.471430	−	0.0981866i
$571$	42.0442			1.75950			0.879748	−	0.475440i	$-0.157711\pi$
$571$	42.0442			1.75950			0.879748	+	0.475440i	$0.157711\pi$
$572$	−15.5153	−	35.6317i	−0.648729	−	1.48984i
$573$	2.88739			0.120622
$574$	4.09651	+	19.6688i	0.170985	+	0.820961i
$575$		−	18.1381i		−	0.756413i
$576$	4.49765	−	12.7648i	0.187402	−	0.531867i
$577$	−3.67101			−0.152826			−0.0764131	−	0.997076i	$-0.524347\pi$
$577$	−3.67101			−0.152826			−0.0764131	+	0.997076i	$0.524347\pi$
$578$	18.1918	−	15.7181i	0.756679	−	0.653787i
$579$		−	0.737259i		−	0.0306395i
$580$	−28.0531	+	12.2154i	−1.16484	+	0.507215i
$581$	−25.1776			−1.04454
$582$	16.1689	−	3.36756i	0.670221	−	0.139590i
$583$		−	2.50819i		−	0.103879i
$584$	11.2474	−	7.96216i	0.465421	−	0.329477i
$585$			29.2974i			1.21130i
$586$	−2.41145	+	0.502243i	−0.0996163	+	0.0207475i
$587$		−	10.0661i		−	0.415472i	−0.978185	−	0.207736i	$-0.933390\pi$
$587$		−	10.0661i		−	0.415472i	0.978185	−	0.207736i	$-0.0666095\pi$
$588$	6.80409	−	2.96275i	0.280596	−	0.122182i
$589$	22.3224			0.919777
$590$	11.5281	−	2.40100i	0.474603	−	0.0988476i
$591$	5.34452			0.219844
$592$	−7.61600	+	8.18437i	−0.313016	+	0.336375i
$593$	23.6586			0.971542			0.485771	−	0.874086i	$-0.338539\pi$
$593$	23.6586			0.971542			0.485771	+	0.874086i	$0.338539\pi$
$594$	5.74184	+	27.5687i	0.235591	+	1.13116i
$595$	22.7755	+	13.3990i	0.933703	+	0.549305i
$596$	−3.43219	−	7.88219i	−0.140588	−	0.322867i
$597$			18.8696i			0.772281i
$598$	4.61428	+	22.1549i	0.188692	+	0.905979i
$599$	32.5413			1.32960			0.664802	−	0.747020i	$-0.268516\pi$
$599$	32.5413			1.32960			0.664802	+	0.747020i	$0.268516\pi$
$600$	11.0954	+	15.6734i	0.452968	+	0.639865i
$601$		−	44.8459i		−	1.82930i	−0.404242	−	0.914652i	$-0.632465\pi$
$601$		−	44.8459i		−	1.82930i	0.404242	−	0.914652i	$-0.367535\pi$
$602$	−3.47260	−	16.6732i	−0.141533	−	0.679550i
$603$			11.1361i			0.453498i
$604$	20.6387	−	8.98686i	0.839778	−	0.365670i
$605$	−9.15493			−0.372201
$606$	12.0051	−	2.50034i	0.487673	−	0.101570i
$607$		−	19.2628i		−	0.781853i	−0.920422	−	0.390927i	$-0.872155\pi$
$607$		−	19.2628i		−	0.781853i	0.920422	−	0.390927i	$-0.127845\pi$
$608$	6.29362	−	10.4023i	0.255240	−	0.421869i
$609$			10.2548i			0.415546i
$610$	−0.483814	−	2.32297i	−0.0195891	−	0.0940543i
$611$		−	8.38443i		−	0.339198i
$612$	−1.68530	+	13.8484i	−0.0681241	+	0.559787i
$613$		−	11.2231i		−	0.453296i	−0.973977	−	0.226648i	$-0.927223\pi$
$613$		−	11.2231i		−	0.453296i	0.973977	−	0.226648i	$-0.0727768\pi$
$614$	44.9298	−	9.35772i	1.81322	−	0.377647i
$615$		−	27.7268i		−	1.11805i
$616$	16.6009	−	11.7520i	0.668871	−	0.473501i
$617$			20.1977i			0.813130i	0.913622	+	0.406565i	$0.133274\pi$
$617$			20.1977i			0.813130i	−0.913622	+	0.406565i	$0.866726\pi$
$618$	−4.87969	−	23.4292i	−0.196290	−	0.942459i
$619$	−10.7486			−0.432025			−0.216012	−	0.976391i	$-0.569305\pi$
$619$	−10.7486			−0.432025			−0.216012	+	0.976391i	$0.569305\pi$
$620$	27.4241	+	62.9807i	1.10138	+	2.52937i
$621$		−	16.3979i		−	0.658026i
$622$	−15.1037	+	3.14570i	−0.605602	+	0.126131i
$623$		−	26.7620i		−	1.07220i
$624$	−17.5398	−	16.3217i	−0.702152	−	0.653391i
$625$	−19.4448			−0.777793
$626$	−31.0307	+	6.46289i	−1.24024	+	0.258309i
$627$			9.12169i			0.364285i
$628$	7.99278	+	18.3558i	0.318947	+	0.732476i
$629$	5.84336	−	9.93248i	0.232990	−	0.396034i
$630$	−15.0111	+	3.12643i	−0.598057	+	0.124560i
$631$	4.94308			0.196781			0.0983905	−	0.995148i	$-0.468631\pi$
$631$	4.94308			0.196781			0.0983905	+	0.995148i	$0.468631\pi$
$632$	−7.56880	+	5.35804i	−0.301071	+	0.213131i
$633$	−25.5119			−1.01401
$634$	2.06539	+	9.91669i	0.0820271	+	0.393842i
$635$	−58.6858			−2.32888
$636$	−0.617331	−	1.41773i	−0.0244788	−	0.0562166i
$637$			16.9888i			0.673120i
$638$	−4.94991	−	23.7663i	−0.195969	−	0.940917i
$639$			15.3027i			0.605365i
$640$	37.0812	+	4.97717i	1.46576	+	0.196740i
$641$		−	35.8047i		−	1.41420i	−0.707112	−	0.707101i	$-0.750003\pi$
$641$		−	35.8047i		−	1.41420i	0.707112	−	0.707101i	$-0.249997\pi$
$642$	−1.36902	−	6.57315i	−0.0540308	−	0.259422i
$643$	−5.10986			−0.201513			−0.100757	−	0.994911i	$-0.532126\pi$
$643$	−5.10986			−0.201513			−0.100757	+	0.994911i	$0.532126\pi$
$644$	−10.8591	+	4.72844i	−0.427908	+	0.186327i
$645$			23.5040i			0.925468i
$646$	−4.01874	+	11.8704i	−0.158115	+	0.467034i
$647$	−31.5790			−1.24150			−0.620749	−	0.784009i	$-0.713172\pi$
$647$	−31.5790			−1.24150			−0.620749	+	0.784009i	$0.713172\pi$
$648$	1.73675	+	2.45335i	0.0682262	+	0.0963767i
$649$			9.34281i			0.366738i
$650$	−43.0372	+	8.96354i	−1.68806	+	0.351579i
$651$	23.0226			0.902326
$652$	31.9987	−	13.9334i	1.25317	−	0.545675i
$653$	32.7138			1.28019			0.640095	−	0.768296i	$-0.278895\pi$
$653$	32.7138			1.28019			0.640095	+	0.768296i	$0.278895\pi$
$654$	−3.53832	−	16.9888i	−0.138359	−	0.664314i
$655$	−12.5080			−0.488726
$656$	−21.4655	−	19.9748i	−0.838086	−	0.779884i
$657$		−	8.24240i		−	0.321567i
$658$	4.29594	−	0.894732i	0.167473	−	0.0348803i
$659$			4.60706i			0.179466i	0.995966	+	0.0897328i	$0.0286013\pi$
$659$			4.60706i			0.179466i	−0.995966	+	0.0897328i	$0.971399\pi$
$660$	−25.7361	+	11.2064i	−1.00178	+	0.436210i
$661$			16.3790i			0.637070i	0.947911	+	0.318535i	$0.103191\pi$
$661$			16.3790i			0.637070i	−0.947911	+	0.318535i	$0.896809\pi$
$662$	−36.0274	+	7.50357i	−1.40024	+	0.291634i
$663$	21.2861	+	12.5228i	0.826684	+	0.486345i
$664$	29.9912	−	21.2311i	1.16388	−	0.823926i
$665$	−13.7743			−0.534146
$666$	1.36345	+	6.54641i	0.0528325	+	0.253668i
$667$			14.1363i			0.547358i
$668$	−0.930094	−	2.13600i	−0.0359864	−	0.0826445i
$669$	9.42777			0.364499
$670$	−30.1383	+	6.27702i	−1.16434	+	0.242502i
$671$	1.88263			0.0726780
$672$	6.49103	−	10.7286i	0.250397	−	0.413865i
$673$		−	24.0036i		−	0.925272i	−0.886548	−	0.462636i	$-0.846904\pi$
$673$		−	24.0036i		−	0.925272i	0.886548	−	0.462636i	$-0.153096\pi$
$674$	−19.0969	+	3.97738i	−0.735584	+	0.153203i
$675$	31.8540			1.22606
$676$	26.4495	−	11.5171i	1.01729	−	0.442964i
$677$	−34.3233			−1.31915			−0.659576	−	0.751638i	$-0.729264\pi$
$677$	−34.3233			−1.31915			−0.659576	+	0.751638i	$0.729264\pi$
$678$	27.4241	−	5.71173i	1.05322	−	0.219358i
$679$	−19.7877			−0.759384
$680$	−38.4285	+	3.24480i	−1.47367	+	0.124432i
$681$	−28.4477			−1.09012
$682$	−53.3566	+	11.1128i	−2.04313	+	0.425531i
$683$	−15.4420			−0.590871			−0.295436	−	0.955363i	$-0.595465\pi$
$683$	−15.4420			−0.590871			−0.295436	+	0.955363i	$0.595465\pi$
$684$	−2.90321	−	6.66734i	−0.111007	−	0.254932i
$685$	−43.1705			−1.64946
$686$	−27.4868	+	5.72480i	−1.04945	+	0.218574i
$687$			16.4231i			0.626579i
$688$	18.1962	+	16.9326i	0.693725	+	0.645549i
$689$	3.53985			0.134858
$690$	16.0020	−	3.33281i	0.609186	−	0.126878i
$691$	7.18318			0.273261			0.136631	−	0.990622i	$-0.456373\pi$
$691$	7.18318			0.273261			0.136631	+	0.990622i	$0.456373\pi$
$692$	−10.8001	+	4.70277i	−0.410559	+	0.178772i
$693$		−	12.1656i		−	0.462133i
$694$	−5.44271	−	26.1324i	−0.206602	−	0.991974i
$695$	13.9638			0.529678
$696$	−8.64738	−	12.2154i	−0.327778	−	0.463022i
$697$	26.0503	+	15.3256i	0.986726	+	0.580499i
$698$	9.29863	−	1.93666i	0.351958	−	0.0733038i
$699$			6.05493i			0.229018i
$700$	−9.18531	−	21.0945i	−0.347172	−	0.797296i
$701$			26.6092i			1.00502i	0.864573	+	0.502508i	$0.167589\pi$
$701$			26.6092i			1.00502i	−0.864573	+	0.502508i	$0.832411\pi$
$702$	−38.9081	+	8.10356i	−1.46849	+	0.305849i
$703$			6.00705i			0.226560i
$704$	−9.86486	+	27.9975i	−0.371796	+	1.05520i
$705$	−6.05591			−0.228079
$706$	5.68144	+	27.2787i	0.213824	+	1.02665i
$707$	−14.6920			−0.552550
$708$	2.29951	+	5.28093i	0.0864208	+	0.198469i
$709$	−5.24355			−0.196926			−0.0984628	−	0.995141i	$-0.531393\pi$
$709$	−5.24355			−0.196926			−0.0984628	+	0.995141i	$0.531393\pi$
$710$	−41.4145	+	8.62556i	−1.55426	+	0.323712i
$711$			5.54662i			0.208014i
$712$	22.5671	+	31.8784i	0.845737	+	1.19469i
$713$	31.7366			1.18855
$714$	−4.14480	+	12.2427i	−0.155115	+	0.458173i
$715$		−	64.2591i		−	2.40315i
$716$	−6.81641	−	15.6542i	−0.254741	−	0.585025i
$717$	−23.2461			−0.868141
$718$	−3.59143	−	17.2438i	−0.134031	−	0.643532i
$719$		−	5.81403i		−	0.216827i	−0.994106	−	0.108413i	$-0.965423\pi$
$719$		−	5.81403i		−	0.216827i	0.994106	−	0.108413i	$-0.0345770\pi$
$720$	15.2446	−	16.3823i	0.568133	−	0.610532i
$721$			28.6730i			1.06784i
$722$	4.14676	+	19.9101i	0.154327	+	0.740978i
$723$			0.254999i			0.00948353i
$724$	35.6143	−	15.5078i	1.32360	−	0.576342i
$725$	−27.4606			−1.01986
$726$	−0.913069	−	4.38398i	−0.0338872	−	0.162705i
$727$	25.8384			0.958291			0.479146	−	0.877735i	$-0.340947\pi$
$727$	25.8384			0.958291			0.479146	+	0.877735i	$0.340947\pi$
$728$	16.5858	+	23.4292i	0.614710	+	0.868343i
$729$	20.2118			0.748586
$730$	22.3069	−	4.64594i	0.825614	−	0.171954i
$731$	−22.0828	−	12.9915i	−0.816762	−	0.480508i
$732$	1.06414	−	0.463363i	0.0393316	−	0.0171264i
$733$			35.4643i			1.30990i	0.755670	+	0.654952i	$0.227311\pi$
$733$			35.4643i			1.30990i	−0.755670	+	0.654952i	$0.772689\pi$
$734$	15.9270	−	3.31718i	0.587877	−	0.122439i
$735$	12.2707			0.452610
$736$	8.94789	−	14.7894i	0.329824	−	0.545144i
$737$		−	24.4253i		−	0.899716i
$738$	−17.1695	+	3.57597i	−0.632019	+	0.131633i
$739$			1.54683i			0.0569011i	0.999595	+	0.0284505i	$0.00905731\pi$
$739$			1.54683i			0.0569011i	−0.999595	+	0.0284505i	$0.990943\pi$
$740$	−16.9484	+	7.37994i	−0.623035	+	0.271292i
$741$	−12.8736			−0.472923
$742$	0.377750	+	1.81372i	0.0138676	+	0.0665836i
$743$			24.8240i			0.910703i	0.890312	+	0.455352i	$0.150486\pi$
$743$			24.8240i			0.910703i	−0.890312	+	0.455352i	$0.849514\pi$
$744$	−27.4241	+	19.4138i	−1.00542	+	0.711745i
$745$		−	14.2149i		−	0.520795i
$746$	12.3676	−	2.57585i	0.452811	−	0.0943087i
$747$		−	21.9783i		−	0.804146i
$748$	3.69643	−	30.3741i	0.135155	−	1.11059i
$749$			8.04434i			0.293934i
$750$	1.02074	+	4.90094i	0.0372721	+	0.178957i
$751$		−	33.0249i		−	1.20509i	−0.798083	−	0.602547i	$-0.794153\pi$
$751$		−	33.0249i		−	1.20509i	0.798083	−	0.602547i	$-0.205847\pi$
$752$	−4.36276	+	4.68834i	−0.159094	+	0.170966i
$753$			29.0987i			1.06042i
$754$	33.5418	−	6.98588i	1.22152	−	0.254411i
$755$	37.2204			1.35459
$756$	−8.30405	−	19.0706i	−0.302015	−	0.693592i
$757$			25.0871i			0.911806i	0.890029	+	0.455903i	$0.150684\pi$
$757$			25.0871i			0.911806i	−0.890029	+	0.455903i	$0.849316\pi$
$758$	7.75098	+	37.2153i	0.281528	+	1.35172i
$759$			12.9687i			0.470733i
$760$	16.4078	−	11.6152i	0.595172	−	0.421329i
$761$	16.5944			0.601545			0.300773	−	0.953696i	$-0.402755\pi$
$761$	16.5944			0.601545			0.300773	+	0.953696i	$0.402755\pi$
$762$	−5.85304	−	28.1026i	−0.212033	−	1.01805i
$763$			20.7912i			0.752691i
$764$	4.62901	−	2.01564i	0.167472	−	0.0729234i
$765$	−11.6964	+	19.8814i	−0.422884	+	0.718814i
$766$	6.13798	+	29.4707i	0.221774	+	1.06482i
$767$	−13.1857			−0.476107
$768$	1.31491	+	18.2533i	0.0474477	+	0.658659i
$769$	4.63304			0.167072			0.0835358	−	0.996505i	$-0.473379\pi$
$769$	4.63304			0.167072			0.0835358	+	0.996505i	$0.473379\pi$
$770$	32.9245	−	6.85731i	1.18651	−	0.247120i
$771$	33.9949			1.22430
$772$	−0.514669	−	1.18196i	−0.0185234	−	0.0425397i
$773$		−	51.9898i		−	1.86994i	−0.354725	−	0.934971i	$-0.615426\pi$
$773$		−	51.9898i		−	1.86994i	0.354725	−	0.934971i	$-0.384574\pi$
$774$	14.5546	−	3.03134i	0.523153	−	0.108959i
$775$			61.6504i			2.21455i
$776$	23.5708	−	16.6860i	0.846143	−	0.598994i
$777$			6.19547i			0.222261i
$778$	28.5365	−	5.94341i	1.02308	−	0.213082i
$779$	−15.7549			−0.564479
$780$	−15.8158	−	36.3218i	−0.566297	−	1.30053i
$781$		−	33.5640i		−	1.20101i
$782$	−5.71360	+	16.8766i	−0.204318	+	0.603506i
$783$	−24.8260			−0.887208
$784$	8.83996	−	9.49967i	0.315713	−	0.339274i
$785$			33.1033i			1.18151i
$786$	−1.24748	−	5.98962i	−0.0444963	−	0.213643i
$787$	24.0375			0.856843			0.428421	−	0.903579i	$-0.359070\pi$
$787$	24.0375			0.856843			0.428421	+	0.903579i	$0.359070\pi$
$788$	8.56824	−	3.73093i	0.305231	−	0.132909i
$789$	16.9224			0.602455
$790$	−15.0111	+	3.12643i	−0.534071	+	0.111233i
$791$	−33.5621			−1.19333
$792$	10.2587	+	14.4915i	0.364526	+	0.514932i
$793$			2.65698i			0.0943523i
$794$	−7.55407	−	36.2699i	−0.268084	−	1.28717i
$795$		−	2.55677i		−	0.0906791i
$796$	13.1726	+	30.2514i	0.466890	+	1.07223i
$797$		−	14.9847i		−	0.530786i	−0.964140	−	0.265393i	$-0.914498\pi$
$797$		−	14.9847i		−	0.530786i	0.964140	−	0.265393i	$-0.0855016\pi$
$798$	−1.37379	−	6.59605i	−0.0486315	−	0.233498i
$799$	3.34732	−	5.68974i	0.118420	−	0.201288i
$800$	28.7293	+	17.3819i	1.01574	+	0.614541i
$801$	23.3614			0.825433
$802$	−50.4026	+	10.4976i	−1.77978	+	0.370682i
$803$			18.0784i			0.637972i
$804$	−6.01169	−	13.8061i	−0.212016	−	0.486904i
$805$	−19.5835			−0.690229
$806$	−15.6837	−	75.3030i	−0.552434	−	2.65244i
$807$	8.78393			0.309209
$808$	17.5009	−	12.3891i	0.615678	−	0.435846i
$809$		−	14.9040i		−	0.523996i	−0.965068	−	0.261998i	$-0.915619\pi$
$809$		−	14.9040i		−	0.523996i	0.965068	−	0.261998i	$-0.0843814\pi$
$810$	1.01340	+	4.86570i	0.0356072	+	0.170963i
$811$	36.3701			1.27713			0.638564	−	0.769569i	$-0.279529\pi$
$811$	36.3701			1.27713			0.638564	+	0.769569i	$0.279529\pi$
$812$	7.15872	+	16.4403i	0.251222	+	0.576943i
$813$	−14.1464			−0.496137
$814$	−2.99050	−	14.3585i	−0.104817	−	0.503265i
$815$	57.7073			2.02140
$816$	−5.38649	−	18.0784i	−0.188565	−	0.632872i
$817$	13.3554			0.467247
$818$	−0.354736	−	1.70322i	−0.0124031	−	0.0595516i
$819$	17.1695			0.599952
$820$	−19.3557	−	44.4512i	−0.675929	−	1.55230i
$821$	17.0881			0.596378			0.298189	−	0.954507i	$-0.403617\pi$
$821$	17.0881			0.596378			0.298189	+	0.954507i	$0.403617\pi$
$822$	−4.30562	−	20.6728i	−0.150176	−	0.721048i
$823$			18.3953i			0.641219i	0.947211	+	0.320610i	$0.103888\pi$
$823$			18.3953i			0.641219i	−0.947211	+	0.320610i	$0.896112\pi$
$824$	−24.1786	−	34.1548i	−0.842301	−	1.18984i
$825$	−25.1925			−0.877090
$826$	−1.40709	−	6.75595i	−0.0489589	−	0.235069i
$827$	0.488278			0.0169791			0.00848955	−	0.999964i	$-0.497298\pi$
$827$	0.488278			0.0169791			0.00848955	+	0.999964i	$0.497298\pi$
$828$	−4.12761	−	9.47924i	−0.143444	−	0.329426i
$829$			27.3938i			0.951424i	0.879601	+	0.475712i	$0.157810\pi$
$829$			27.3938i			0.951424i	−0.879601	+	0.475712i	$0.842190\pi$
$830$	59.4812	−	12.3884i	2.06462	−	0.430007i
$831$	−17.5037			−0.607196
$832$	−39.5134	−	13.9224i	−1.36988	−	0.482674i
$833$	−6.78244	+	11.5287i	−0.234998	+	0.399446i
$834$	1.39268	+	6.68678i	0.0482247	+	0.231544i
$835$		−	3.85212i		−	0.133308i
$836$	6.36771	+	14.6237i	0.220232	+	0.505773i
$837$			55.7356i			1.92650i
$838$	3.95006	+	18.9657i	0.136452	+	0.655158i
$839$			42.7092i			1.47449i	0.675627	+	0.737243i	$0.263873\pi$
$839$			42.7092i			1.47449i	−0.675627	+	0.737243i	$0.736127\pi$
$840$	16.9224	−	11.9796i	0.583879	−	0.413335i
$841$	−7.59813			−0.262005
$842$	−16.6339	+	3.46440i	−0.573241	+	0.119391i
$843$	−5.11927			−0.176317
$844$	−40.9002	+	17.8094i	−1.40784	+	0.613026i
$845$	47.6996			1.64092
$846$	0.781039	+	3.75006i	0.0268527	+	0.128930i
$847$			5.36519i			0.184350i
$848$	−1.97939	−	1.84193i	−0.0679725	−	0.0632521i
$849$	9.71441			0.333398
$850$	−32.7839	−	11.0990i	−1.12448	−	0.380694i
$851$			8.54047i			0.292763i
$852$	−8.26096	−	18.9717i	−0.283016	−	0.649959i
$853$	−1.72451			−0.0590462			−0.0295231	−	0.999564i	$-0.509399\pi$
$853$	−1.72451			−0.0590462			−0.0295231	+	0.999564i	$0.509399\pi$
$854$	−1.36136	+	0.283536i	−0.0465848	+	0.00970240i
$855$		−	12.0241i		−	0.411214i
$856$	−6.78340	−	9.58228i	−0.231852	−	0.327516i
$857$		−	48.6074i		−	1.66040i	−0.557469	−	0.830198i	$-0.688227\pi$
$857$		−	48.6074i		−	1.66040i	0.557469	−	0.830198i	$-0.311773\pi$
$858$	30.7714	−	6.40889i	1.05052	−	0.218796i
$859$		−	30.5330i		−	1.04177i	−0.853626	−	0.520886i	$-0.825602\pi$
$859$		−	30.5330i		−	1.04177i	0.853626	−	0.520886i	$-0.174398\pi$
$860$	16.4078	+	37.6812i	0.559500	+	1.28492i
$861$	−16.2491			−0.553768
$862$	−13.0005	+	2.70767i	−0.442798	+	0.0922234i
$863$	−25.2580			−0.859793			−0.429897	−	0.902878i	$-0.641450\pi$
$863$	−25.2580			−0.859793			−0.429897	+	0.902878i	$0.641450\pi$
$864$	25.9730	+	15.7142i	0.883619	+	0.534608i
$865$	−19.4772			−0.662245
$866$	−0.905261	−	4.34649i	−0.0307620	−	0.147700i
$867$	9.44543	+	16.9961i	0.320784	+	0.577219i
$868$	36.9094	−	16.0717i	1.25279	−	0.545509i
$869$		−	12.1656i		−	0.412690i
$870$	−5.04577	−	24.2266i	−0.171068	−	0.821358i
$871$	34.4718			1.16803
$872$	−17.5322	−	24.7661i	−0.593715	−	0.838686i
$873$		−	17.2733i		−	0.584614i
$874$	−1.89377	−	9.09266i	−0.0640576	−	0.307564i
$875$		−	5.99785i		−	0.202764i
$876$	4.44955	+	10.2186i	0.150337	+	0.345255i
$877$	−30.1870			−1.01934			−0.509670	−	0.860370i	$-0.670233\pi$
$877$	−30.1870			−1.01934			−0.509670	+	0.860370i	$0.670233\pi$
$878$	22.1858	−	4.62073i	0.748734	−	0.155942i
$879$		−	1.99219i		−	0.0671948i
$880$	−33.4366	+	35.9319i	−1.12715	+	1.21126i
$881$		−	12.8471i		−	0.432830i	−0.976301	−	0.216415i	$-0.930564\pi$
$881$		−	12.8471i		−	0.432830i	0.976301	−	0.216415i	$-0.0694364\pi$
$882$	−1.58257	−	7.59848i	−0.0532878	−	0.255854i
$883$			34.6548i			1.16623i	0.812391	+	0.583113i	$0.198165\pi$
$883$			34.6548i			1.16623i	−0.812391	+	0.583113i	$0.801835\pi$
$884$	42.8675	+	5.21683i	1.44179	+	0.175461i
$885$			9.52375i			0.320137i
$886$	−10.5044	+	2.18778i	−0.352901	+	0.0735001i
$887$			30.3609i			1.01942i	0.860347	+	0.509709i	$0.170247\pi$
$887$			30.3609i			1.01942i	−0.860347	+	0.509709i	$0.829753\pi$
$888$	−5.22435	−	7.37994i	−0.175318	−	0.247655i
$889$			34.3924i			1.15349i
$890$	13.1679	+	63.2241i	0.441391	+	2.11928i
$891$	−3.94336			−0.132108
$892$	15.1144	−	6.58138i	0.506069	−	0.220361i
$893$			3.44109i			0.115152i
$894$	6.80703	−	1.41773i	0.227661	−	0.0474159i
$895$		−	28.2312i		−	0.943664i
$896$	2.91684	−	21.7312i	0.0974448	−	0.725989i
$897$	−18.3029			−0.611117
$898$	26.4261	−	5.50387i	0.881850	−	0.183666i
$899$		−	48.0483i		−	1.60250i
$900$	18.4140	−	8.01814i	0.613801	−	0.267271i
$901$	2.40217	+	1.41322i	0.0800279	+	0.0470811i
$902$	37.6586	−	7.84331i	1.25389	−	0.261154i
$903$	13.7743			0.458381
$904$	39.9786	−	28.3013i	1.32967	−	0.941287i
$905$	64.2278			2.13500
$906$	3.71218	+	17.8235i	0.123329	+	0.592147i
$907$	−17.8653			−0.593206			−0.296603	−	0.955001i	$-0.595854\pi$
$907$	−17.8653			−0.593206			−0.296603	+	0.955001i	$0.595854\pi$
$908$	−45.6069	+	19.8589i	−1.51352	+	0.659041i
$909$		−	12.8251i		−	0.425382i
$910$	9.67784	+	46.4668i	0.320817	+	1.54036i
$911$		−	15.9542i		−	0.528588i	−0.964442	−	0.264294i	$-0.914861\pi$
$911$		−	15.9542i		−	0.528588i	0.964442	−	0.264294i	$-0.0851389\pi$
$912$	7.19856	+	6.69865i	0.238368	+	0.221815i
$913$			48.2060i			1.59538i
$914$	−2.45763	−	11.8000i	−0.0812911	−	0.390308i
$915$	1.91909			0.0634431
$916$	11.4647	+	26.3292i	0.378804	+	0.869941i
$917$			7.33020i			0.242065i
$918$	−29.6385	−	10.0342i	−0.978218	−	0.331177i
$919$	52.4743			1.73097			0.865483	−	0.500938i	$-0.167011\pi$
$919$	52.4743			1.73097			0.865483	+	0.500938i	$0.167011\pi$
$920$	23.3276	−	16.5139i	0.769088	−	0.544446i
$921$			37.1181i			1.22308i
$922$	−28.7130	+	5.98018i	−0.945613	+	0.196947i
$923$	47.3694			1.55918
$924$	6.56745	+	15.0825i	0.216053	+	0.496176i
$925$	−16.5904			−0.545489
$926$	−3.97192	−	19.0706i	−0.130525	−	0.626700i
$927$	−25.0296			−0.822079
$928$	−22.3907	−	13.5468i	−0.735010	−	0.444697i
$929$			42.6106i			1.39801i	0.715118	+	0.699004i	$0.246373\pi$
$929$			42.6106i			1.39801i	−0.715118	+	0.699004i	$0.753627\pi$
$930$	−54.3899	+	11.3280i	−1.78352	+	0.371460i
$931$		−	6.97243i		−	0.228512i
$932$	4.22685	+	9.70716i	0.138455	+	0.317968i
$933$		−	12.4777i		−	0.408501i
$934$	−36.0567	+	7.50968i	−1.17981	+	0.245724i
$935$	25.6542	−	43.6067i	0.838981	−	1.42609i
$936$	−20.4521	+	14.4782i	−0.668496	+	0.473236i
$937$	−15.8687			−0.518407			−0.259204	−	0.965823i	$-0.583460\pi$
$937$	−15.8687			−0.518407			−0.259204	+	0.965823i	$0.583460\pi$
$938$	3.67860	+	17.6623i	0.120111	+	0.576695i
$939$		−	25.6356i		−	0.836585i
$940$	−9.70873	+	4.22754i	−0.316664	+	0.137887i
$941$	−41.3614			−1.34834			−0.674171	−	0.738575i	$-0.735499\pi$
$941$	−41.3614			−1.34834			−0.674171	+	0.738575i	$0.735499\pi$
$942$	−15.8520	+	3.30156i	−0.516486	+	0.107571i
$943$	−22.3994			−0.729426
$944$	7.37307	+	6.86104i	0.239973	+	0.223308i
$945$		−	34.3924i		−	1.11879i
$946$	−31.9231	+	6.64876i	−1.03791	+	0.216170i
$947$	−30.7567			−0.999457			−0.499729	−	0.866182i	$-0.666567\pi$
$947$	−30.7567			−0.999457			−0.499729	+	0.866182i	$0.666567\pi$
$948$	−2.99427	−	6.87648i	−0.0972494	−	0.223338i
$949$	−25.5143			−0.828229
$950$	17.6631	−	3.67876i	0.573066	−	0.119355i
$951$	−8.19253			−0.265661
$952$	1.90159	+	22.5208i	0.0616310	+	0.729902i
$953$	−26.0213			−0.842911			−0.421456	−	0.906849i	$-0.638481\pi$
$953$	−26.0213			−0.842911			−0.421456	+	0.906849i	$0.638481\pi$
$954$	−1.58325	+	0.329750i	−0.0512596	+	0.0106760i
$955$	8.34808			0.270137
$956$	−37.2677	+	16.2277i	−1.20532	+	0.524843i
$957$	19.6342			0.634683
$958$	−24.8037	+	5.16596i	−0.801370	+	0.166905i
$959$			25.2998i			0.816972i
$960$	−10.0559	+	28.5397i	−0.324553	+	0.921116i
$961$	−76.8709			−2.47971
$962$	20.2644	−	4.22054i	0.653350	−	0.136076i
$963$	−7.02215			−0.226286
$964$	0.178011	+	0.408811i	0.00573335	+	0.0131669i
$965$		−	2.13158i		−	0.0686180i
$966$	−1.95317	−	9.37787i	−0.0628422	−	0.301728i
$967$	31.7101			1.01973			0.509864	−	0.860255i	$-0.329696\pi$
$967$	31.7101			1.01973			0.509864	+	0.860255i	$0.329696\pi$
$968$	−4.52420	−	6.39092i	−0.145413	−	0.205412i
$969$	−8.73612	−	5.13953i	−0.280644	−	0.165105i
$970$	46.7477	−	9.73634i	1.50098	−	0.312615i
$971$		−	18.1743i		−	0.583242i	−0.956534	−	0.291621i	$-0.905805\pi$
$971$		−	18.1743i		−	0.583242i	0.956534	−	0.291621i	$-0.0941946\pi$
$972$	27.2920	−	11.8839i	0.875391	−	0.381177i
$973$		−	8.18340i		−	0.262348i
$974$	−44.3775	+	9.24269i	−1.42195	+	0.296155i
$975$		−	35.5546i		−	1.13866i
$976$	1.38254	−	1.48571i	0.0442539	−	0.0475565i
$977$	8.03754			0.257144			0.128572	−	0.991700i	$-0.458961\pi$
$977$	8.03754			0.257144			0.128572	+	0.991700i	$0.458961\pi$
$978$	5.75544	+	27.6340i	0.184039	+	0.883638i
$979$	−51.2394			−1.63762
$980$	19.6721	−	8.56597i	0.628403	−	0.273630i
$981$	−18.1493			−0.579461
$982$	−30.2921	+	6.30906i	−0.966659	+	0.201330i
$983$			3.10715i			0.0991027i	0.998772	+	0.0495513i	$0.0157791\pi$
$983$			3.10715i			0.0991027i	−0.998772	+	0.0495513i	$0.984221\pi$
$984$	19.3557	−	13.7021i	0.617036	−	0.436807i
$985$	15.4522			0.492347
$986$	25.5507	+	8.65022i	0.813699	+	0.275479i
$987$			3.54902i			0.112967i
$988$	−20.6387	+	8.98686i	−0.656605	+	0.285910i
$989$	18.9879			0.603781
$990$	5.98596	+	28.7408i	0.190246	+	0.913442i
$991$		−	48.4588i		−	1.53935i	−0.638439	−	0.769673i	$-0.720419\pi$
$991$		−	48.4588i		−	1.53935i	0.638439	−	0.769673i	$-0.279581\pi$
$992$	−30.4134	+	50.2683i	−0.965625	+	1.59602i
$993$		−	29.7635i		−	0.944516i
$994$	5.05495	+	24.2707i	0.160333	+	0.769819i
$995$			54.5562i			1.72955i
$996$	11.8647	+	27.2479i	0.375948	+	0.863383i
$997$	−13.7301			−0.434836			−0.217418	−	0.976079i	$-0.569763\pi$
$997$	−13.7301			−0.434836			−0.217418	+	0.976079i	$0.569763\pi$
$998$	2.91772	+	14.0090i	0.0923588	+	0.443449i
$999$	−14.9987			−0.474537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.h.a.101.11	yes	16
3.2	odd	2		1224.2.l.b.1189.6		16
4.3	odd	2		544.2.h.a.305.11		16
8.3	odd	2		544.2.h.a.305.5		16
8.5	even	2	inner	136.2.h.a.101.10	yes	16
12.11	even	2		4896.2.l.b.3025.15		16
17.16	even	2	inner	136.2.h.a.101.12	yes	16
24.5	odd	2		1224.2.l.b.1189.7		16
24.11	even	2		4896.2.l.b.3025.1		16
51.50	odd	2		1224.2.l.b.1189.5		16
68.67	odd	2		544.2.h.a.305.6		16
136.67	odd	2		544.2.h.a.305.12		16
136.101	even	2	inner	136.2.h.a.101.9	✓	16
204.203	even	2		4896.2.l.b.3025.2		16
408.101	odd	2		1224.2.l.b.1189.8		16
408.203	even	2		4896.2.l.b.3025.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.h.a.101.9	✓	16	136.101	even	2	inner
136.2.h.a.101.10	yes	16	8.5	even	2	inner
136.2.h.a.101.11	yes	16	1.1	even	1	trivial
136.2.h.a.101.12	yes	16	17.16	even	2	inner
544.2.h.a.305.5		16	8.3	odd	2
544.2.h.a.305.6		16	68.67	odd	2
544.2.h.a.305.11		16	4.3	odd	2
544.2.h.a.305.12		16	136.67	odd	2
1224.2.l.b.1189.5		16	51.50	odd	2
1224.2.l.b.1189.6		16	3.2	odd	2
1224.2.l.b.1189.7		16	24.5	odd	2
1224.2.l.b.1189.8		16	408.101	odd	2
4896.2.l.b.3025.1		16	24.11	even	2
4896.2.l.b.3025.2		16	204.203	even	2
4896.2.l.b.3025.15		16	12.11	even	2
4896.2.l.b.3025.16		16	408.203	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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.288356 + 1.38450i) q^{2} -1.14379 q^{3} +(-1.83370 + 0.798461i) q^{4} -3.30694 q^{5} +(-0.329818 - 1.58358i) q^{6} +1.93801i q^{7} +(-1.63423 - 2.30853i) q^{8} -1.69175 q^{9} +O(q^{10})\)	\(q+(0.288356 + 1.38450i) q^{2} -1.14379 q^{3} +(-1.83370 + 0.798461i) q^{4} -3.30694 q^{5} +(-0.329818 - 1.58358i) q^{6} +1.93801i q^{7} +(-1.63423 - 2.30853i) q^{8} -1.69175 q^{9} +(-0.953577 - 4.57847i) q^{10} +3.71058 q^{11} +(2.09737 - 0.913270i) q^{12} +5.23680i q^{13} +(-2.68318 + 0.558837i) q^{14} +3.78244 q^{15} +(2.72492 - 2.92828i) q^{16} +(-2.09069 + 3.55373i) q^{17} +(-0.487827 - 2.34223i) q^{18} -2.14926i q^{19} +(6.06394 - 2.64046i) q^{20} -2.21667i q^{21} +(1.06997 + 5.13731i) q^{22} -3.05569i q^{23} +(1.86921 + 2.64046i) q^{24} +5.93586 q^{25} +(-7.25037 + 1.51006i) q^{26} +5.36637 q^{27} +(-1.54743 - 3.55373i) q^{28} -4.62622 q^{29} +(1.09069 + 5.23680i) q^{30} +10.3861i q^{31} +(4.83996 + 2.92828i) q^{32} -4.24412 q^{33} +(-5.52302 - 1.86983i) q^{34} -6.40889i q^{35} +(3.10216 - 1.35080i) q^{36} -2.79494 q^{37} +(2.97565 - 0.619751i) q^{38} -5.98979i q^{39} +(5.40431 + 7.63416i) q^{40} -7.33041i q^{41} +(3.06899 - 0.639191i) q^{42} +6.21397i q^{43} +(-6.80409 + 2.96275i) q^{44} +5.59452 q^{45} +(4.23061 - 0.881126i) q^{46} -1.60106 q^{47} +(-3.11673 + 3.34933i) q^{48} +3.24412 q^{49} +(1.71164 + 8.21823i) q^{50} +(2.39131 - 4.06472i) q^{51} +(-4.18138 - 9.60273i) q^{52} -0.675957i q^{53} +(1.54743 + 7.42975i) q^{54} -12.2707 q^{55} +(4.47395 - 3.16716i) q^{56} +2.45829i q^{57} +(-1.33400 - 6.40501i) q^{58} +2.51789i q^{59} +(-6.93586 + 3.02013i) q^{60} +0.507368 q^{61} +(-14.3796 + 2.99490i) q^{62} -3.27863i q^{63} +(-2.65858 + 7.54533i) q^{64} -17.3178i q^{65} +(-1.22382 - 5.87599i) q^{66} -6.58260i q^{67} +(0.996186 - 8.18582i) q^{68} +3.49506i q^{69} +(8.87313 - 1.84804i) q^{70} -9.04548i q^{71} +(2.76471 + 3.90545i) q^{72} +4.87212i q^{73} +(-0.805939 - 3.86961i) q^{74} -6.78937 q^{75} +(1.71610 + 3.94109i) q^{76} +7.19114i q^{77} +(8.29289 - 1.72719i) q^{78} -3.27863i q^{79} +(-9.01116 + 9.68364i) q^{80} -1.06273 q^{81} +(10.1490 - 2.11377i) q^{82} +12.9915i q^{83} +(1.76993 + 4.06472i) q^{84} +(6.91379 - 11.7520i) q^{85} +(-8.60327 + 1.79184i) q^{86} +5.29141 q^{87} +(-6.06394 - 8.56597i) q^{88} -13.8090 q^{89} +(1.61321 + 7.74563i) q^{90} -10.1490 q^{91} +(2.43984 + 5.60321i) q^{92} -11.8795i q^{93} +(-0.461675 - 2.21667i) q^{94} +7.10746i q^{95} +(-5.53589 - 3.34933i) q^{96} +10.2103i q^{97} +(0.935461 + 4.49149i) q^{98} -6.27737 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 2 q^{8} + 8 q^{9} - 8 q^{15} - 14 q^{16} - 2 q^{18} - 16 q^{30} - 2 q^{32} - 8 q^{33} + 18 q^{34} - 22 q^{36} + 36 q^{38} - 24 q^{47} - 8 q^{49} + 34 q^{50} - 8 q^{55} - 16 q^{60} - 30 q^{64} - 32 q^{66} + 38 q^{68} + 40 q^{70} + 70 q^{72} + 4 q^{76} - 24 q^{81} + 72 q^{84} + 4 q^{86} - 40 q^{87} - 24 q^{89} - 16 q^{94} + 34 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 2 * q^8 + 8 * q^9 - 8 * q^15 - 14 * q^16 - 2 * q^18 - 16 * q^30 - 2 * q^32 - 8 * q^33 + 18 * q^34 - 22 * q^36 + 36 * q^38 - 24 * q^47 - 8 * q^49 + 34 * q^50 - 8 * q^55 - 16 * q^60 - 30 * q^64 - 32 * q^66 + 38 * q^68 + 40 * q^70 + 70 * q^72 + 4 * q^76 - 24 * q^81 + 72 * q^84 + 4 * q^86 - 40 * q^87 - 24 * q^89 - 16 * q^94 + 34 * q^98

Introduction

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