LMFDB - Embedded newform 87.2.g.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.1
Root			$-1.61697 + 0.778692i$ of defining polynomial
Character	$\chi$	$=$	87.7
Dual form			87.2.g.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.399359 - 1.74971i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-1.10004 + 0.529753i) q^{4} +(-0.299361 - 1.31158i) q^{5} +(0.399359 - 1.74971i) q^{6} +(1.00367 + 0.483344i) q^{7} +(-0.871733 - 1.09312i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.399359 - 1.74971i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-1.10004 + 0.529753i) q^{4} +(-0.299361 - 1.31158i) q^{5} +(0.399359 - 1.74971i) q^{6} +(1.00367 + 0.483344i) q^{7} +(-0.871733 - 1.09312i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-2.17533 + 1.04759i) q^{10} +(-1.53957 + 1.93056i) q^{11} -1.22096 q^{12} +(-1.75674 + 2.20289i) q^{13} +(0.444884 - 1.94916i) q^{14} +(0.299361 - 1.31158i) q^{15} +(-3.08701 + 3.87099i) q^{16} +5.50816 q^{17} +(1.11898 - 1.40315i) q^{18} +(0.318651 - 0.153454i) q^{19} +(1.02413 + 1.28421i) q^{20} +(0.694564 + 0.870956i) q^{21} +(3.99275 + 1.92281i) q^{22} +(-1.18272 + 5.18183i) q^{23} +(-0.311118 - 1.36310i) q^{24} +(2.87421 - 1.38414i) q^{25} +(4.55597 + 2.19404i) q^{26} +(0.222521 + 0.974928i) q^{27} -1.36014 q^{28} +(-5.29503 - 0.981140i) q^{29} -2.41444 q^{30} +(0.990316 + 4.33886i) q^{31} +(5.48653 + 2.64217i) q^{32} +(-2.22474 + 1.07138i) q^{33} +(-2.19973 - 9.63766i) q^{34} +(0.333486 - 1.46110i) q^{35} +(-1.10004 - 0.529753i) q^{36} +(-6.00176 - 7.52597i) q^{37} +(-0.395756 - 0.496262i) q^{38} +(-2.53857 + 1.22251i) q^{39} +(-1.17275 + 1.47059i) q^{40} -9.05582 q^{41} +(1.24654 - 1.56311i) q^{42} +(2.01367 - 8.82247i) q^{43} +(0.670874 - 2.93929i) q^{44} +(0.838790 - 1.05181i) q^{45} +9.53901 q^{46} +(2.24139 - 2.81061i) q^{47} +(-4.46086 + 2.14824i) q^{48} +(-3.59069 - 4.50258i) q^{49} +(-3.56969 - 4.47624i) q^{50} +(4.96268 + 2.38990i) q^{51} +(0.765509 - 3.35391i) q^{52} +(1.46472 + 6.41735i) q^{53} +(1.61697 - 0.778692i) q^{54} +(2.99298 + 1.44134i) q^{55} +(-0.346583 - 1.51848i) q^{56} +0.353676 q^{57} +(0.397912 + 9.65657i) q^{58} -6.26677 q^{59} +(0.365506 + 1.60139i) q^{60} +(-0.106516 - 0.0512953i) q^{61} +(7.19623 - 3.46552i) q^{62} +(0.247887 + 1.08606i) q^{63} +(0.228450 - 1.00091i) q^{64} +(3.41517 + 1.64466i) q^{65} +(2.76307 + 3.46478i) q^{66} +(8.91797 + 11.1828i) q^{67} +(-6.05922 + 2.91797i) q^{68} +(-3.31391 + 4.15551i) q^{69} -2.68967 q^{70} +(4.68005 - 5.86860i) q^{71} +(0.311118 - 1.36310i) q^{72} +(3.54339 - 15.5246i) q^{73} +(-10.7714 + 13.5069i) q^{74} +3.19013 q^{75} +(-0.269237 + 0.337613i) q^{76} +(-2.47835 + 1.19351i) q^{77} +(3.15283 + 3.95353i) q^{78} +(0.160241 + 0.200936i) q^{79} +(6.00126 + 2.89005i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(3.61652 + 15.8450i) q^{82} +(5.52291 - 2.65969i) q^{83} +(-1.22544 - 0.590142i) q^{84} +(-1.64893 - 7.22442i) q^{85} -16.2409 q^{86} +(-4.34496 - 3.18140i) q^{87} +3.45242 q^{88} +(-1.66948 - 7.31446i) q^{89} +(-2.17533 - 1.04759i) q^{90} +(-2.82795 + 1.36187i) q^{91} +(-1.44405 - 6.32679i) q^{92} +(-0.990316 + 4.33886i) q^{93} +(-5.81286 - 2.79933i) q^{94} +(-0.296660 - 0.372000i) q^{95} +(3.79680 + 4.76103i) q^{96} +(-6.37706 + 3.07103i) q^{97} +(-6.44422 + 8.08079i) q^{98} -2.46928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.399359	−	1.74971i	−0.282389	−	1.23723i	−0.894720	−	0.446627i	$-0.852625\pi$
$2$	−0.399359	−	1.74971i	−0.282389	−	1.23723i	0.612331	−	0.790602i	$-0.290232\pi$
$3$	0.900969	+	0.433884i	0.520175	+	0.250503i
$3$	0.900969	+	0.433884i	0.520175	+	0.250503i
$4$	−1.10004	+	0.529753i	−0.550022	+	0.264877i
$5$	−0.299361	−	1.31158i	−0.133878	−	0.586559i	−0.996709	−	0.0810654i	$-0.974168\pi$
$5$	−0.299361	−	1.31158i	−0.133878	−	0.586559i	0.862831	−	0.505493i	$-0.168689\pi$
$6$	0.399359	−	1.74971i	0.163038	−	0.714314i
$7$	1.00367	+	0.483344i	0.379353	+	0.182687i	0.613836	−	0.789433i	$-0.289625\pi$
$7$	1.00367	+	0.483344i	0.379353	+	0.182687i	−0.234483	+	0.972120i	$0.575340\pi$
$8$	−0.871733	−	1.09312i	−0.308204	−	0.386476i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	−2.17533	+	1.04759i	−0.687901	+	0.331276i
$11$	−1.53957	+	1.93056i	−0.464198	+	0.582085i	−0.957740	−	0.287637i	$-0.907130\pi$
$11$	−1.53957	+	1.93056i	−0.464198	+	0.582085i	0.493542	+	0.869722i	$0.335702\pi$
$12$	−1.22096			−0.352460
$13$	−1.75674	+	2.20289i	−0.487233	+	0.610971i	−0.963296	−	0.268440i	$-0.913492\pi$
$13$	−1.75674	+	2.20289i	−0.487233	+	0.610971i	0.476063	+	0.879411i	$0.342063\pi$
$14$	0.444884	−	1.94916i	0.118900	−	0.520936i
$15$	0.299361	−	1.31158i	0.0772946	−	0.338650i
$16$	−3.08701	+	3.87099i	−0.771752	+	0.967747i
$17$	5.50816			1.33593			0.667963	−	0.744195i	$-0.267167\pi$
$17$	5.50816			1.33593			0.667963	+	0.744195i	$0.267167\pi$
$18$	1.11898	−	1.40315i	0.263746	−	0.330727i
$19$	0.318651	−	0.153454i	0.0731035	−	0.0352048i	−0.396975	−	0.917830i	$-0.629940\pi$
$19$	0.318651	−	0.153454i	0.0731035	−	0.0352048i	0.470078	+	0.882625i	$0.344226\pi$
$20$	1.02413	+	1.28421i	0.229002	+	0.287159i
$21$	0.694564	+	0.870956i	0.151566	+	0.190058i
$22$	3.99275	+	1.92281i	0.851257	+	0.409944i
$23$	−1.18272	+	5.18183i	−0.246614	+	1.08049i	0.688248	+	0.725475i	$0.258380\pi$
$23$	−1.18272	+	5.18183i	−0.246614	+	1.08049i	−0.934862	+	0.355011i	$0.884477\pi$
$24$	−0.311118	−	1.36310i	−0.0635066	−	0.278241i
$25$	2.87421	−	1.38414i	0.574841	−	0.276829i
$26$	4.55597	+	2.19404i	0.893500	+	0.430287i
$27$	0.222521	+	0.974928i	0.0428242	+	0.187625i
$28$	−1.36014			−0.257042
$29$	−5.29503	−	0.981140i	−0.983263	−	0.182193i
$29$	−5.29503	−	0.981140i	−0.983263	−	0.182193i
$30$	−2.41444			−0.440814
$31$	0.990316	+	4.33886i	0.177866	+	0.779282i	0.982613	+	0.185664i	$0.0594436\pi$
$31$	0.990316	+	4.33886i	0.177866	+	0.779282i	−0.804747	+	0.593618i	$0.797699\pi$
$32$	5.48653	+	2.64217i	0.969891	+	0.467075i
$33$	−2.22474	+	1.07138i	−0.387278	+	0.186503i
$34$	−2.19973	−	9.63766i	−0.377251	−	1.65285i
$35$	0.333486	−	1.46110i	0.0563694	−	0.246971i
$36$	−1.10004	−	0.529753i	−0.183341	−	0.0882922i
$37$	−6.00176	−	7.52597i	−0.986684	−	1.23726i	−0.971417	−	0.237379i	$-0.923712\pi$
$37$	−6.00176	−	7.52597i	−0.986684	−	1.23726i	−0.0152665	−	0.999883i	$-0.504860\pi$
$38$	−0.395756	−	0.496262i	−0.0642001	−	0.0805043i
$39$	−2.53857	+	1.22251i	−0.406496	+	0.195758i
$40$	−1.17275	+	1.47059i	−0.185429	+	0.232520i
$41$	−9.05582			−1.41428			−0.707141	−	0.707073i	$-0.750015\pi$
$41$	−9.05582			−1.41428			−0.707141	+	0.707073i	$0.750015\pi$
$42$	1.24654	−	1.56311i	0.192345	−	0.241193i
$43$	2.01367	−	8.82247i	0.307082	−	1.34541i	−0.552114	−	0.833769i	$-0.686179\pi$
$43$	2.01367	−	8.82247i	0.307082	−	1.34541i	0.859196	−	0.511646i	$-0.170964\pi$
$44$	0.670874	−	2.93929i	0.101138	−	0.443115i
$45$	0.838790	−	1.05181i	0.125039	−	0.156794i
$46$	9.53901			1.40645
$47$	2.24139	−	2.81061i	0.326940	−	0.409970i	−0.591011	−	0.806664i	$-0.701271\pi$
$47$	2.24139	−	2.81061i	0.326940	−	0.409970i	0.917951	+	0.396694i	$0.129842\pi$
$48$	−4.46086	+	2.14824i	−0.643869	+	0.310071i
$49$	−3.59069	−	4.50258i	−0.512955	−	0.643226i
$50$	−3.56969	−	4.47624i	−0.504830	−	0.633037i
$51$	4.96268	+	2.38990i	0.694915	+	0.334653i
$52$	0.765509	−	3.35391i	0.106157	−	0.465104i
$53$	1.46472	+	6.41735i	0.201194	+	0.881490i	0.970211	+	0.242261i	$0.0778892\pi$
$53$	1.46472	+	6.41735i	0.201194	+	0.881490i	−0.769017	+	0.639229i	$0.779254\pi$
$54$	1.61697	−	0.778692i	0.220042	−	0.105967i
$55$	2.99298	+	1.44134i	0.403573	+	0.194351i
$56$	−0.346583	−	1.51848i	−0.0463142	−	0.202916i
$57$	0.353676			0.0468455
$58$	0.397912	+	9.65657i	0.0522484	+	1.26797i
$59$	−6.26677			−0.815864			−0.407932	−	0.913012i	$-0.633750\pi$
$59$	−6.26677			−0.815864			−0.407932	+	0.913012i	$0.633750\pi$
$60$	0.365506	+	1.60139i	0.0471867	+	0.206738i
$61$	−0.106516	−	0.0512953i	−0.0136379	−	0.00656769i	0.427052	−	0.904227i	$-0.359552\pi$
$61$	−0.106516	−	0.0512953i	−0.0136379	−	0.00656769i	−0.440690	+	0.897659i	$0.645266\pi$
$62$	7.19623	−	3.46552i	0.913922	−	0.440122i
$63$	0.247887	+	1.08606i	0.0312308	+	0.136831i
$64$	0.228450	−	1.00091i	0.0285563	−	0.125113i
$65$	3.41517	+	1.64466i	0.423600	+	0.203995i
$66$	2.76307	+	3.46478i	0.340110	+	0.426485i
$67$	8.91797	+	11.1828i	1.08950	+	1.36619i	0.925066	+	0.379807i	$0.124010\pi$
$67$	8.91797	+	11.1828i	1.08950	+	1.36619i	0.164438	+	0.986387i	$0.447419\pi$
$68$	−6.05922	+	2.91797i	−0.734789	+	0.353856i
$69$	−3.31391	+	4.15551i	−0.398947	+	0.500264i
$70$	−2.68967			−0.321477
$71$	4.68005	−	5.86860i	0.555420	−	0.696475i	−0.422284	−	0.906464i	$-0.638771\pi$
$71$	4.68005	−	5.86860i	0.555420	−	0.696475i	0.977704	+	0.209989i	$0.0673428\pi$
$72$	0.311118	−	1.36310i	0.0366656	−	0.160642i
$73$	3.54339	−	15.5246i	0.414723	−	1.81702i	−0.146326	−	0.989236i	$-0.546745\pi$
$73$	3.54339	−	15.5246i	0.414723	−	1.81702i	0.561049	−	0.827783i	$-0.310398\pi$
$74$	−10.7714	+	13.5069i	−1.25215	+	1.57014i
$75$	3.19013			0.368364
$76$	−0.269237	+	0.337613i	−0.0308836	+	0.0387268i
$77$	−2.47835	+	1.19351i	−0.282434	+	0.136013i
$78$	3.15283	+	3.95353i	0.356988	+	0.447649i
$79$	0.160241	+	0.200936i	0.0180285	+	0.0226070i	0.790764	−	0.612121i	$-0.209684\pi$
$79$	0.160241	+	0.200936i	0.0180285	+	0.0226070i	−0.772736	+	0.634728i	$0.781112\pi$
$80$	6.00126	+	2.89005i	0.670961	+	0.323118i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	3.61652	+	15.8450i	0.399378	+	1.74979i
$83$	5.52291	−	2.65969i	0.606218	−	0.291939i	−0.105483	−	0.994421i	$-0.533639\pi$
$83$	5.52291	−	2.65969i	0.606218	−	0.291939i	0.711702	+	0.702482i	$0.247925\pi$
$84$	−1.22544	−	0.590142i	−0.133707	−	0.0643898i
$85$	−1.64893	−	7.22442i	−0.178851	−	0.783599i
$86$	−16.2409			−1.75130
$87$	−4.34496	−	3.18140i	−0.465828	−	0.341082i
$88$	3.45242			0.368029
$89$	−1.66948	−	7.31446i	−0.176964	−	0.775331i	−0.983021	−	0.183493i	$-0.941260\pi$
$89$	−1.66948	−	7.31446i	−0.176964	−	0.775331i	0.806057	−	0.591838i	$-0.201598\pi$
$90$	−2.17533	−	1.04759i	−0.229300	−	0.110425i
$91$	−2.82795	+	1.36187i	−0.296450	+	0.142763i
$92$	−1.44405	−	6.32679i	−0.150553	−	0.659614i
$93$	−0.990316	+	4.33886i	−0.102691	+	0.449918i
$94$	−5.81286	−	2.79933i	−0.599551	−	0.288729i
$95$	−0.296660	−	0.372000i	−0.0304367	−	0.0381664i
$96$	3.79680	+	4.76103i	0.387509	+	0.485921i
$97$	−6.37706	+	3.07103i	−0.647492	+	0.311816i	−0.728651	−	0.684885i	$-0.759852\pi$
$97$	−6.37706	+	3.07103i	−0.647492	+	0.311816i	0.0811586	+	0.996701i	$0.474138\pi$
$98$	−6.44422	+	8.08079i	−0.650964	+	0.816283i
$99$	−2.46928			−0.248172
$100$	−2.42850	+	3.04524i	−0.242850	+	0.304524i
$101$	0.578078	−	2.53272i	0.0575209	−	0.252015i	−0.937990	−	0.346662i	$-0.887315\pi$
$101$	0.578078	−	2.53272i	0.0575209	−	0.252015i	0.995511	+	0.0946468i	$0.0301722\pi$
$102$	2.19973	−	9.63766i	0.217806	−	0.954271i
$103$	−4.34138	+	5.44392i	−0.427769	+	0.536405i	−0.948274	−	0.317453i	$-0.897172\pi$
$103$	−4.34138	+	5.44392i	−0.427769	+	0.536405i	0.520505	+	0.853859i	$0.325744\pi$
$104$	3.93942			0.386292
$105$	0.934407	−	1.17171i	0.0911888	−	0.114347i
$106$	10.6435	−	5.12565i	1.03379	−	0.497847i
$107$	9.44518	+	11.8439i	0.913100	+	1.14499i	0.989006	+	0.147877i	$0.0472438\pi$
$107$	9.44518	+	11.8439i	0.913100	+	1.14499i	−0.0759056	+	0.997115i	$0.524185\pi$
$108$	−0.761254	−	0.954583i	−0.0732517	−	0.0918547i
$109$	−14.5579	−	7.01072i	−1.39439	−	0.671505i	−0.422378	−	0.906420i	$-0.638805\pi$
$109$	−14.5579	−	7.01072i	−1.39439	−	0.671505i	−0.972016	+	0.234915i	$0.924519\pi$
$110$	1.32665	−	5.81244i	0.126491	−	0.554195i
$111$	−2.14200	−	9.38473i	−0.203310	−	0.890760i
$112$	−4.96937	+	2.39312i	−0.469561	+	0.226129i
$113$	13.5689	+	6.53446i	1.27646	+	0.614710i	0.944477	−	0.328576i	$-0.106569\pi$
$113$	13.5689	+	6.53446i	1.27646	+	0.614710i	0.331981	+	0.943286i	$0.392283\pi$
$114$	−0.141244	−	0.618829i	−0.0132287	−	0.0579586i
$115$	7.15047			0.666785
$116$	6.34453	−	1.72576i	0.589075	−	0.160233i
$117$	−2.81760			−0.260487
$118$	2.50269	+	10.9650i	0.230391	+	1.00941i
$119$	5.52840	+	2.66234i	0.506788	+	0.244056i
$120$	−1.69468	+	0.816115i	−0.154702	+	0.0745007i
$121$	1.09095	+	4.77975i	0.0991769	+	0.434523i
$122$	−0.0472136	+	0.206856i	−0.00427452	+	0.0187279i
$123$	−8.15901	−	3.92917i	−0.735673	−	0.354282i
$124$	−3.38791	−	4.24831i	−0.304244	−	0.381510i
$125$	−6.86980	−	8.61445i	−0.614453	−	0.770500i
$126$	1.80130	−	0.867459i	0.160472	−	0.0772794i
$127$	0.407770	−	0.511327i	0.0361837	−	0.0453729i	−0.763410	−	0.645914i	$-0.776477\pi$
$127$	0.407770	−	0.511327i	0.0361837	−	0.0453729i	0.799594	+	0.600541i	$0.205048\pi$
$128$	10.3367			0.913640
$129$	5.64218	−	7.07508i	0.496767	−	0.622926i
$130$	1.51379	−	6.63235i	0.132768	−	0.581696i
$131$	0.0119320	−	0.0522777i	0.00104251	−	0.00456752i	−0.974404	−	0.224804i	$-0.927826\pi$
$131$	0.0119320	−	0.0522777i	0.00104251	−	0.00456752i	0.975446	+	0.220237i	$0.0706829\pi$
$132$	1.87975	−	2.35713i	0.163611	−	0.205162i
$133$	0.393993			0.0341635
$134$	16.0051	−	20.0698i	1.38263	−	1.73376i
$135$	1.21209	−	0.583710i	0.104320	−	0.0502378i
$136$	−4.80164	−	6.02107i	−0.411738	−	0.516303i
$137$	7.34575	+	9.21128i	0.627590	+	0.786973i	0.989390	−	0.145283i	$-0.0464091\pi$
$137$	7.34575	+	9.21128i	0.627590	+	0.786973i	−0.361800	+	0.932256i	$0.617838\pi$
$138$	8.59435	+	4.13882i	0.731600	+	0.352320i
$139$	1.57827	−	6.91483i	0.133867	−	0.586508i	−0.862844	−	0.505470i	$-0.831319\pi$
$139$	1.57827	−	6.91483i	0.133867	−	0.586508i	0.996711	−	0.0810385i	$-0.0258237\pi$
$140$	0.407172	+	1.78394i	0.0344123	+	0.150770i
$141$	3.23890	−	1.55977i	0.272765	−	0.131357i
$142$	−12.1373	−	5.84504i	−1.01854	−	0.490505i
$143$	−1.54817	−	6.78299i	−0.129465	−	0.567222i
$144$	−4.95118			−0.412598
$145$	0.298276	+	7.23860i	0.0247705	+	0.601133i
$146$	−28.5786			−2.36518
$147$	−1.28150	−	5.61463i	−0.105696	−	0.463087i
$148$	10.5891	+	5.09945i	0.870420	+	0.419172i
$149$	3.53906	−	1.70432i	0.289931	−	0.139624i	−0.283265	−	0.959042i	$-0.591418\pi$
$149$	3.53906	−	1.70432i	0.289931	−	0.139624i	0.573196	+	0.819418i	$0.305703\pi$
$150$	−1.27401	−	5.58179i	−0.104022	−	0.455751i
$151$	−4.86221	+	21.3028i	−0.395681	+	1.73359i	0.248419	+	0.968653i	$0.420089\pi$
$151$	−4.86221	+	21.3028i	−0.395681	+	1.73359i	−0.644101	+	0.764941i	$0.722768\pi$
$152$	−0.445522	−	0.214552i	−0.0361366	−	0.0174025i
$153$	3.43428	+	4.30645i	0.277645	+	0.348156i
$154$	3.07804	+	3.85974i	0.248036	+	0.311027i
$155$	5.39432	−	2.59777i	0.433282	−	0.208658i
$156$	2.14491	−	2.68963i	0.171730	−	0.215343i
$157$	−10.3803			−0.828438			−0.414219	−	0.910177i	$-0.635945\pi$
$157$	−10.3803			−0.828438			−0.414219	+	0.910177i	$0.635945\pi$
$158$	0.287584	−	0.360620i	0.0228790	−	0.0286893i
$159$	−1.46472	+	6.41735i	−0.116160	+	0.508929i
$160$	1.82298	−	7.98701i	0.144120	−	0.631429i
$161$	−3.69167	+	4.62921i	−0.290945	+	0.364833i
$162$	1.79470			0.141005
$163$	−5.56602	+	6.97957i	−0.435965	+	0.546682i	−0.950475	−	0.310802i	$-0.899402\pi$
$163$	−5.56602	+	6.97957i	−0.435965	+	0.546682i	0.514510	+	0.857484i	$0.327974\pi$
$164$	9.96180	−	4.79735i	0.777886	−	0.374610i
$165$	2.07121	+	2.59721i	0.161243	+	0.202192i
$166$	−6.85931	−	8.60130i	−0.532385	−	0.667590i
$167$	−18.0257	−	8.68071i	−1.39487	−	0.671733i	−0.422755	−	0.906244i	$-0.638937\pi$
$167$	−18.0257	−	8.68071i	−1.39487	−	0.671733i	−0.972114	+	0.234510i	$0.924651\pi$
$168$	0.346583	−	1.51848i	0.0267395	−	0.117153i
$169$	1.12621	+	4.93425i	0.0866316	+	0.379558i
$170$	−11.9821	+	5.77027i	−0.918985	+	0.442560i
$171$	0.318651	+	0.153454i	0.0243678	+	0.0117349i
$172$	2.45861	+	10.7719i	0.187467	+	0.821347i
$173$	−3.99833			−0.303987			−0.151994	−	0.988381i	$-0.548569\pi$
$173$	−3.99833			−0.303987			−0.151994	+	0.988381i	$0.548569\pi$
$174$	−3.83132	+	8.87292i	−0.290452	+	0.672654i
$175$	3.55379			0.268641
$176$	−2.72050	−	11.9193i	−0.205066	−	0.898451i
$177$	−5.64617	−	2.71905i	−0.424392	−	0.204376i
$178$	−12.1314	+	5.84219i	−0.909289	+	0.437890i
$179$	2.30444	+	10.0964i	0.172242	+	0.754642i	0.985072	+	0.172141i	$0.0550686\pi$
$179$	2.30444	+	10.0964i	0.172242	+	0.754642i	−0.812830	+	0.582501i	$0.802074\pi$
$180$	−0.365506	+	1.60139i	−0.0272432	+	0.119360i
$181$	8.73683	+	4.20743i	0.649403	+	0.312736i	0.729429	−	0.684057i	$-0.239786\pi$
$181$	8.73683	+	4.20743i	0.649403	+	0.312736i	−0.0800256	+	0.996793i	$0.525500\pi$
$182$	3.51224	+	4.40420i	0.260344	+	0.326461i
$183$	−0.0737112	−	0.0924309i	−0.00544889	−	0.00683269i
$184$	6.69537	−	3.22432i	0.493589	−	0.237700i
$185$	−8.07426	+	10.1248i	−0.593631	+	0.744390i
$186$	7.98721			0.585651
$187$	−8.48020	+	10.6338i	−0.620133	+	0.777623i
$188$	−0.976695	+	4.27918i	−0.0712328	+	0.312091i
$189$	−0.247887	+	1.08606i	−0.0180311	+	0.0789996i
$190$	−0.532416	+	0.667629i	−0.0386255	+	0.0484349i
$191$	1.15201			0.0833568			0.0416784	−	0.999131i	$-0.486730\pi$
$191$	1.15201			0.0833568			0.0416784	+	0.999131i	$0.486730\pi$
$192$	0.640104	−	0.802665i	0.0461955	−	0.0579273i
$193$	24.9283	−	12.0048i	1.79438	−	0.864128i	0.857494	−	0.514494i	$-0.172020\pi$
$193$	24.9283	−	12.0048i	1.79438	−	0.864128i	0.936886	−	0.349634i	$-0.113694\pi$
$194$	7.92013	+	9.93153i	0.568632	+	0.713042i
$195$	2.36337	+	2.96358i	0.169245	+	0.212226i
$196$	6.33517	+	3.05086i	0.452512	+	0.217918i
$197$	3.31415	−	14.5202i	0.236123	−	1.03452i	−0.708331	−	0.705880i	$-0.750552\pi$
$197$	3.31415	−	14.5202i	0.236123	−	1.03452i	0.944454	−	0.328643i	$-0.106591\pi$
$198$	0.986128	+	4.32051i	0.0700811	+	0.307045i
$199$	8.26420	−	3.97983i	0.585834	−	0.282123i	−0.117396	−	0.993085i	$-0.537455\pi$
$199$	8.26420	−	3.97983i	0.585834	−	0.282123i	0.703230	+	0.710962i	$0.251740\pi$
$200$	−4.01857	−	1.93524i	−0.284156	−	0.136842i
$201$	3.18279	+	13.9447i	0.224497	+	0.983584i
$202$	−4.66238			−0.328044
$203$	−4.84026	−	3.54407i	−0.339720	−	0.248745i
$204$	−6.72523			−0.470860
$205$	2.71096	+	11.8775i	0.189341	+	0.829559i
$206$	11.2590	+	5.42206i	0.784453	+	0.377773i
$207$	−4.78873	+	2.30613i	−0.332840	+	0.160287i
$208$	−3.10426	−	13.6007i	−0.215242	−	0.943036i
$209$	−0.194333	+	0.851428i	−0.0134423	+	0.0588945i
$210$	−2.42331	−	1.16701i	−0.167224	−	0.0805310i
$211$	−0.158153	−	0.198317i	−0.0108877	−	0.0136527i	0.776358	−	0.630292i	$-0.217065\pi$
$211$	−0.158153	−	0.198317i	−0.0108877	−	0.0136527i	−0.787246	+	0.616640i	$0.788494\pi$
$212$	−5.01086	−	6.28343i	−0.344148	−	0.431547i
$213$	6.76287	−	3.25683i	0.463384	−	0.223154i
$214$	16.9513	−	21.2562i	1.15877	−	1.45305i
$215$	−12.1742			−0.830276
$216$	0.871733	−	1.09312i	0.0593139	−	0.0743773i
$217$	−1.10321	+	4.83346i	−0.0748905	+	0.328117i
$218$	−6.45286	+	28.2718i	−0.437043	+	1.91481i
$219$	9.92836	−	12.4498i	0.670897	−	0.841278i
$220$	−4.05596			−0.273453
$221$	−9.67643	+	12.1339i	−0.650907	+	0.816211i
$222$	−15.5651	+	7.49575i	−1.04466	+	0.503082i
$223$	13.7933	+	17.2963i	0.923669	+	1.15824i	0.987075	+	0.160256i	$0.0512320\pi$
$223$	13.7933	+	17.2963i	0.923669	+	1.15824i	−0.0634067	+	0.997988i	$0.520197\pi$
$224$	4.22961	+	5.30376i	0.282603	+	0.354373i
$225$	2.87421	+	1.38414i	0.191614	+	0.0922763i
$226$	6.01450	−	26.3512i	0.400079	−	1.75286i
$227$	−4.31417	−	18.9016i	−0.286342	−	1.25454i	−0.889505	−	0.456926i	$-0.848950\pi$
$227$	−4.31417	−	18.9016i	−0.286342	−	1.25454i	0.603163	−	0.797618i	$-0.293907\pi$
$228$	−0.389059	+	0.187361i	−0.0257661	+	0.0124083i
$229$	−18.6550	−	8.98377i	−1.23276	−	0.593664i	−0.299920	−	0.953964i	$-0.596960\pi$
$229$	−18.6550	−	8.98377i	−1.23276	−	0.593664i	−0.932836	+	0.360300i	$0.882674\pi$
$230$	−2.85560	−	12.5112i	−0.188293	−	0.824965i
$231$	−2.75076			−0.180987
$232$	3.54335	+	6.64339i	0.232632	+	0.436160i
$233$	21.9063			1.43513			0.717566	−	0.696491i	$-0.245256\pi$
$233$	21.9063			1.43513			0.717566	+	0.696491i	$0.245256\pi$
$234$	1.12523	+	4.92997i	0.0735587	+	0.322282i
$235$	−4.35734	−	2.09838i	−0.284242	−	0.136884i
$236$	6.89373	−	3.31984i	0.448743	−	0.216103i
$237$	0.0571893	+	0.250563i	0.00371484	+	0.0162758i
$238$	2.45049	−	10.7363i	0.158842	−	0.695931i
$239$	−0.420848	−	0.202670i	−0.0272224	−	0.0131096i	0.420223	−	0.907421i	$-0.361952\pi$
$239$	−0.420848	−	0.202670i	−0.0272224	−	0.0131096i	−0.447445	+	0.894311i	$0.647666\pi$
$240$	4.15300	+	5.20770i	0.268075	+	0.336155i
$241$	5.46633	+	6.85456i	0.352117	+	0.441541i	0.926072	−	0.377346i	$-0.123163\pi$
$241$	5.46633	+	6.85456i	0.352117	+	0.441541i	−0.573955	+	0.818887i	$0.694592\pi$
$242$	7.92747	−	3.81767i	0.509597	−	0.245409i
$243$	−0.623490	+	0.781831i	−0.0399969	+	0.0501545i
$244$	0.144346			0.00924080
$245$	−4.83061	+	6.05739i	−0.308616	+	0.386992i
$246$	−3.61652	+	15.8450i	−0.230581	+	1.01024i
$247$	−0.221746	+	0.971531i	−0.0141093	+	0.0618171i
$248$	3.87959	−	4.86485i	0.246354	−	0.308919i
$249$	6.12997			0.388471
$250$	−12.3292	+	15.4604i	−0.779770	+	0.977800i
$251$	4.39668	−	2.11733i	0.277516	−	0.133645i	−0.289949	−	0.957042i	$-0.593638\pi$
$251$	4.39668	−	2.11733i	0.277516	−	0.133645i	0.567465	+	0.823397i	$0.307924\pi$
$252$	−0.848033	−	1.06340i	−0.0534211	−	0.0669879i
$253$	−8.18295	−	10.2611i	−0.514458	−	0.645110i
$254$	−1.05752	−	0.509274i	−0.0663546	−	0.0319547i
$255$	1.64893	−	7.22442i	0.103260	−	0.452411i
$256$	−4.58494	−	20.0879i	−0.286558	−	1.25549i
$257$	2.86362	−	1.37905i	0.178628	−	0.0860226i	−0.342433	−	0.939542i	$-0.611251\pi$
$257$	2.86362	−	1.37905i	0.178628	−	0.0860226i	0.521060	+	0.853520i	$0.325537\pi$
$258$	−14.6326	−	7.04667i	−0.910983	−	0.438706i
$259$	−2.38618	−	10.4545i	−0.148270	−	0.649614i
$260$	−4.62810			−0.287023
$261$	−2.53431	−	4.75155i	−0.156870	−	0.294114i
$262$	−0.0962357			−0.00594546
$263$	−5.40607	−	23.6855i	−0.333352	−	1.46051i	−0.812594	−	0.582830i	$-0.801946\pi$
$263$	−5.40607	−	23.6855i	−0.333352	−	1.46051i	0.479242	−	0.877683i	$-0.340912\pi$
$264$	3.11052	+	1.49795i	0.191440	+	0.0921924i
$265$	7.97841	−	3.84220i	0.490110	−	0.236025i
$266$	−0.157345	−	0.689372i	−0.00964741	−	0.0422681i
$267$	1.66948	−	7.31446i	0.102170	−	0.447638i
$268$	−15.7343	−	7.57723i	−0.961124	−	0.462853i
$269$	5.39535	+	6.76556i	0.328960	+	0.412503i	0.918616	−	0.395152i	$-0.129308\pi$
$269$	5.39535	+	6.76556i	0.328960	+	0.412503i	−0.589656	+	0.807655i	$0.700737\pi$
$270$	−1.50538	−	1.88768i	−0.0916144	−	0.114881i
$271$	12.8508	−	6.18861i	0.780630	−	0.375931i	−0.000740231	−	1.00000i	$-0.500236\pi$
$271$	12.8508	−	6.18861i	0.780630	−	0.375931i	0.781370	+	0.624068i	$0.214521\pi$
$272$	−17.0037	+	21.3220i	−1.03100	+	1.29284i
$273$	−3.13879			−0.189968
$274$	13.1834	−	16.5315i	0.796441	−	0.998705i
$275$	−1.75287	+	7.67981i	−0.105702	+	0.463110i
$276$	1.44405	−	6.32679i	0.0869215	−	0.380828i
$277$	4.73601	−	5.93876i	0.284559	−	0.356826i	−0.618923	−	0.785452i	$-0.712431\pi$
$277$	4.73601	−	5.93876i	0.284559	−	0.356826i	0.903482	+	0.428626i	$0.141002\pi$
$278$	−12.7292			−0.763447
$279$	−2.77480	+	3.47949i	−0.166123	+	0.208312i
$280$	−1.88786	+	0.909147i	−0.112821	+	0.0543319i
$281$	0.816328	+	1.02364i	0.0486980	+	0.0610654i	0.805584	−	0.592481i	$-0.201852\pi$
$281$	0.816328	+	1.02364i	0.0486980	+	0.0610654i	−0.756886	+	0.653547i	$0.773280\pi$
$282$	−4.02263	−	5.04421i	−0.239544	−	0.300379i
$283$	−21.1963	−	10.2076i	−1.25999	−	0.606780i	−0.319819	−	0.947479i	$-0.603622\pi$
$283$	−21.1963	−	10.2076i	−1.25999	−	0.606780i	−0.940172	+	0.340699i	$0.889336\pi$
$284$	−2.03935	+	8.93500i	−0.121013	+	0.530194i
$285$	−0.105877	−	0.463876i	−0.00627159	−	0.0274776i
$286$	−11.2500	+	5.41770i	−0.665224	+	0.320355i
$287$	−9.08909	−	4.37708i	−0.536512	−	0.258371i
$288$	1.35506	+	5.93691i	0.0798478	+	0.349836i
$289$	13.3399			0.784697
$290$	12.5463	−	3.41269i	0.736744	−	0.200400i
$291$	−7.07800			−0.414920
$292$	4.32633	+	18.9549i	0.253179	+	1.10925i
$293$	14.2589	+	6.86673i	0.833014	+	0.401158i	0.801245	−	0.598337i	$-0.204172\pi$
$293$	14.2589	+	6.86673i	0.833014	+	0.401158i	0.0317693	+	0.999495i	$0.489886\pi$
$294$	−9.31216	+	4.48450i	−0.543096	+	0.261541i
$295$	1.87603	+	8.21940i	0.109226	+	0.478552i
$296$	−2.99484	+	13.1213i	−0.174072	+	0.762658i
$297$	−2.22474	−	1.07138i	−0.129093	−	0.0621677i
$298$	−4.39542	−	5.51168i	−0.254620	−	0.319283i
$299$	−9.33725	−	11.7085i	−0.539987	−	0.677122i
$300$	−3.50928	+	1.68998i	−0.202608	+	0.0975711i
$301$	6.28536	−	7.88159i	0.362282	−	0.454288i
$302$	39.2153			2.25659
$303$	1.61974	−	2.03109i	0.0930515	−	0.116683i
$304$	−0.389659	+	1.70721i	−0.0223485	+	0.0979151i
$305$	−0.0353915	+	0.155060i	−0.00202651	+	0.00887872i
$306$	6.16352	−	7.72880i	0.352345	−	0.441826i
$307$	−7.55550			−0.431215			−0.215608	−	0.976480i	$-0.569173\pi$
$307$	−7.55550			−0.431215			−0.215608	+	0.976480i	$0.569173\pi$
$308$	2.09403	−	2.62583i	0.119318	−	0.149620i
$309$	−6.27348	+	3.02115i	−0.356886	+	0.171867i
$310$	−6.69959	−	8.40103i	−0.380511	−	0.477146i
$311$	8.83323	+	11.0765i	0.500886	+	0.628092i	0.966429	−	0.256934i	$-0.0827123\pi$
$311$	8.83323	+	11.0765i	0.500886	+	0.628092i	−0.465543	+	0.885025i	$0.654141\pi$
$312$	3.54930	+	1.70925i	0.200940	+	0.0967674i
$313$	−3.77415	+	16.5356i	−0.213327	+	0.934648i	0.748960	+	0.662615i	$0.230553\pi$
$313$	−3.77415	+	16.5356i	−0.213327	+	0.934648i	−0.962288	+	0.272034i	$0.912304\pi$
$314$	4.14546	+	18.1625i	0.233942	+	1.02497i
$315$	1.35026	−	0.650250i	0.0760784	−	0.0366374i
$316$	−0.282718	−	0.136150i	−0.0159041	−	0.00765903i
$317$	1.05268	+	4.61207i	0.0591241	+	0.259040i	0.995848	−	0.0910287i	$-0.0290155\pi$
$317$	1.05268	+	4.61207i	0.0591241	+	0.259040i	−0.936724	+	0.350068i	$0.886158\pi$
$318$	11.8134			0.662463
$319$	10.0462	−	8.71184i	0.562480	−	0.487769i
$320$	−1.38116			−0.0772093
$321$	3.37095	+	14.7691i	0.188148	+	0.824330i
$322$	9.57406	+	4.61062i	0.533541	+	0.256940i
$323$	1.75518	−	0.845251i	0.0976609	−	0.0470310i
$324$	−0.271688	−	1.19034i	−0.0150938	−	0.0661303i
$325$	−2.00013	+	8.76314i	−0.110947	+	0.486091i
$326$	14.4350	+	6.95155i	0.799483	+	0.385011i
$327$	−10.0744	−	12.6329i	−0.557115	−	0.698600i
$328$	7.89425	+	9.89908i	0.435887	+	0.546585i
$329$	3.60812	−	1.73758i	0.198922	−	0.0957958i
$330$	3.71720	−	4.66122i	0.204625	−	0.256592i
$331$	−1.77434			−0.0975263			−0.0487631	−	0.998810i	$-0.515528\pi$
$331$	−1.77434			−0.0975263			−0.0487631	+	0.998810i	$0.515528\pi$
$332$	−4.66647	+	5.85156i	−0.256106	+	0.321146i
$333$	2.14200	−	9.38473i	0.117381	−	0.514280i
$334$	−7.98997	+	35.0063i	−0.437192	+	1.91546i
$335$	11.9975	−	15.0444i	0.655492	−	0.821961i
$336$	−5.51558			−0.300900
$337$	0.778021	−	0.975608i	0.0423815	−	0.0531447i	−0.760189	−	0.649702i	$-0.774894\pi$
$337$	0.778021	−	0.975608i	0.0423815	−	0.0531447i	0.802571	+	0.596557i	$0.203465\pi$
$338$	8.18373	−	3.94108i	0.445136	−	0.214366i
$339$	9.39000	+	11.7747i	0.509995	+	0.639513i
$340$	5.64105	+	7.07366i	0.305929	+	0.383623i
$341$	−9.90108	−	4.76811i	−0.536173	−	0.258208i
$342$	0.141244	−	0.618829i	0.00763758	−	0.0334624i
$343$	−3.16280	−	13.8571i	−0.170775	−	0.748214i
$344$	−11.3994	+	5.48966i	−0.614614	+	0.295982i
$345$	6.44235	+	3.10247i	0.346845	+	0.167032i
$346$	1.59677	+	6.99590i	0.0858428	+	0.376102i
$347$	−26.1773			−1.40527			−0.702636	−	0.711550i	$-0.747994\pi$
$347$	−26.1773			−1.40527			−0.702636	+	0.711550i	$0.747994\pi$
$348$	6.46501	+	1.19793i	0.346561	+	0.0642158i
$349$	23.8884			1.27872			0.639359	−	0.768908i	$-0.279200\pi$
$349$	23.8884			1.27872			0.639359	+	0.768908i	$0.279200\pi$
$350$	−1.41924	−	6.21808i	−0.0758613	−	0.332370i
$351$	−2.53857	−	1.22251i	−0.135499	−	0.0652527i
$352$	−13.5478	+	6.52426i	−0.722098	+	0.347744i
$353$	0.473289	+	2.07361i	0.0251906	+	0.110367i	0.985960	−	0.166981i	$-0.0534017\pi$
$353$	0.473289	+	2.07361i	0.0251906	+	0.110367i	−0.960770	+	0.277348i	$0.910545\pi$
$354$	−2.50269	+	10.9650i	−0.133017	+	0.582784i
$355$	−9.09819	−	4.38146i	−0.482882	−	0.232544i
$356$	5.71136	+	7.16182i	0.302701	+	0.379575i
$357$	3.82577	+	4.79737i	0.202481	+	0.253904i
$358$	16.7455	−	8.06420i	0.885026	−	0.426206i
$359$	−17.0899	+	21.4300i	−0.901970	+	1.13103i	0.0888767	+	0.996043i	$0.471672\pi$
$359$	−17.0899	+	21.4300i	−0.901970	+	1.13103i	−0.990847	+	0.134992i	$0.956899\pi$
$360$	−1.88095			−0.0991349
$361$	−11.7683	+	14.7570i	−0.619385	+	0.776684i
$362$	3.87264	−	16.9672i	0.203542	−	0.891774i
$363$	−1.09095	+	4.77975i	−0.0572598	+	0.250872i
$364$	2.38942	−	2.99623i	0.125239	−	0.157045i
$365$	−21.4226			−1.12131
$366$	−0.132290	+	0.165886i	−0.00691489	+	0.00867100i
$367$	−24.5657	+	11.8302i	−1.28232	+	0.617533i	−0.945985	−	0.324210i	$-0.894902\pi$
$367$	−24.5657	+	11.8302i	−1.28232	+	0.617533i	−0.336335	+	0.941742i	$0.609187\pi$
$368$	−16.4077	−	20.5747i	−0.855312	−	1.07253i
$369$	−5.64621	−	7.08013i	−0.293930	−	0.368577i
$370$	20.9399	+	10.0841i	1.08862	+	0.524250i
$371$	−1.63169	+	7.14889i	−0.0847130	+	0.371152i
$372$	−1.20913	−	5.29756i	−0.0626906	−	0.274666i
$373$	−5.81683	+	2.80124i	−0.301184	+	0.145043i	−0.578372	−	0.815773i	$-0.696312\pi$
$373$	−5.81683	+	2.80124i	−0.301184	+	0.145043i	0.277188	+	0.960816i	$0.410597\pi$
$374$	21.9927	+	10.5911i	1.13722	+	0.547655i
$375$	−2.45180	−	10.7420i	−0.126611	−	0.554717i
$376$	−5.02622			−0.259208
$377$	11.4634	−	9.94074i	0.590393	−	0.511974i
$378$	1.99929			0.102832
$379$	4.26365	+	18.6803i	0.219009	+	0.959540i	0.958212	+	0.286058i	$0.0923451\pi$
$379$	4.26365	+	18.6803i	0.219009	+	0.959540i	−0.739203	+	0.673482i	$0.764798\pi$
$380$	0.523407	+	0.252059i	0.0268502	+	0.0129304i
$381$	0.589244	−	0.283765i	0.0301879	−	0.0145377i
$382$	−0.460067	−	2.01569i	−0.0235391	−	0.103131i
$383$	5.84823	−	25.6228i	0.298831	−	1.30926i	−0.573041	−	0.819527i	$-0.694236\pi$
$383$	5.84823	−	25.6228i	0.298831	−	1.30926i	0.871871	−	0.489735i	$-0.162907\pi$
$384$	9.31300	+	4.48491i	0.475252	+	0.228869i
$385$	2.30731	+	2.89328i	0.117591	+	0.147455i
$386$	−30.9603	−	38.8230i	−1.57584	−	1.97604i
$387$	8.15319	−	3.92637i	0.414450	−	0.199589i
$388$	5.38816	−	6.75654i	0.273542	−	0.343011i
$389$	−15.8638			−0.804324			−0.402162	−	0.915568i	$-0.631741\pi$
$389$	−15.8638			−0.804324			−0.402162	+	0.915568i	$0.631741\pi$
$390$	4.24155	−	5.31874i	0.214779	−	0.269325i
$391$	−6.51461	+	28.5424i	−0.329458	+	1.44345i
$392$	−1.79173	+	7.85009i	−0.0904961	+	0.396490i
$393$	0.0334328	−	0.0419234i	0.00168646	−	0.00211476i
$394$	−26.7296			−1.34662
$395$	0.215574	−	0.270322i	0.0108467	−	0.0136014i
$396$	2.71631	−	1.30811i	0.136500	−	0.0657349i
$397$	−2.39219	−	2.99971i	−0.120060	−	0.150551i	0.718169	−	0.695869i	$-0.244980\pi$
$397$	−2.39219	−	2.99971i	−0.120060	−	0.150551i	−0.838229	+	0.545318i	$0.816409\pi$
$398$	−10.2639	−	12.8705i	−0.514484	−	0.645142i
$399$	0.354975	+	0.170947i	0.0177710	+	0.00855806i
$400$	−3.51469	+	15.3989i	−0.175735	+	0.769944i
$401$	−5.52331	−	24.1992i	−0.275821	−	1.20845i	−0.903023	−	0.429593i	$-0.858657\pi$
$401$	−5.52331	−	24.1992i	−0.275821	−	1.20845i	0.627202	−	0.778857i	$-0.284200\pi$
$402$	23.1281	−	11.1379i	1.15352	−	0.555507i
$403$	−11.2977	−	5.44070i	−0.562780	−	0.271021i
$404$	0.705808	+	3.09235i	0.0351152	+	0.153850i
$405$	1.34531			0.0668492
$406$	−4.26807	+	9.88438i	−0.211821	+	0.490554i
$407$	23.7695			1.17821
$408$	−1.71369	−	7.50815i	−0.0848402	−	0.371709i
$409$	−21.8961	−	10.5446i	−1.08269	−	0.521398i	−0.194517	−	0.980899i	$-0.562314\pi$
$409$	−21.8961	−	10.5446i	−1.08269	−	0.521398i	−0.888177	+	0.459501i	$0.848028\pi$
$410$	19.6994	−	9.48675i	0.972886	−	0.468517i
$411$	2.62167	+	11.4863i	0.129317	+	0.566577i
$412$	1.89178	−	8.28841i	0.0932011	−	0.408341i
$413$	−6.28980	−	3.02901i	−0.309501	−	0.149048i
$414$	5.94747	+	7.45790i	0.292302	+	0.366536i
$415$	−5.14176	−	6.44756i	−0.252399	−	0.316498i
$416$	−15.4588	+	7.44458i	−0.757932	+	0.365001i
$417$	4.42220	−	5.54526i	0.216556	−	0.271553i
$418$	1.56736			0.0766619
$419$	1.15814	−	1.45226i	0.0565789	−	0.0709477i	−0.752737	−	0.658322i	$-0.771267\pi$
$419$	1.15814	−	1.45226i	0.0565789	−	0.0709477i	0.809316	+	0.587374i	$0.199838\pi$
$420$	−0.407172	+	1.78394i	−0.0198680	+	0.0870473i
$421$	3.90351	−	17.1024i	0.190245	−	0.833520i	−0.786237	−	0.617925i	$-0.787974\pi$
$421$	3.90351	−	17.1024i	0.190245	−	0.833520i	0.976483	−	0.215595i	$-0.0691692\pi$
$422$	−0.283837	+	0.355920i	−0.0138170	+	0.0173259i
$423$	3.59491			0.174790
$424$	5.73808	−	7.19532i	0.278666	−	0.349436i
$425$	15.8316	−	7.62409i	0.767945	−	0.369823i
$426$	−8.39930	−	10.5324i	−0.406948	−	0.510296i
$427$	−0.0821139	−	0.102968i	−0.00397377	−	0.00498295i
$428$	−16.6645	−	8.02518i	−0.805507	−	0.387912i
$429$	1.54817	−	6.78299i	0.0747465	−	0.327486i
$430$	4.86189	+	21.3013i	0.234461	+	1.02724i
$431$	3.75976	−	1.81061i	0.181101	−	0.0872138i	−0.341136	−	0.940014i	$-0.610812\pi$
$431$	3.75976	−	1.81061i	0.181101	−	0.0872138i	0.522237	+	0.852800i	$0.325097\pi$
$432$	−4.46086	−	2.14824i	−0.214623	−	0.103357i
$433$	−4.40642	−	19.3058i	−0.211759	−	0.927777i	−0.963371	−	0.268172i	$-0.913581\pi$
$433$	−4.40642	−	19.3058i	−0.211759	−	0.927777i	0.751612	−	0.659605i	$-0.229277\pi$
$434$	8.89771			0.427104
$435$	−2.87197	+	6.65117i	−0.137701	+	0.318899i
$436$	19.7283			0.944814
$437$	0.418299	+	1.83269i	0.0200100	+	0.0876694i
$438$	−25.7484	−	12.3998i	−1.23031	−	0.592485i
$439$	24.4235	−	11.7617i	1.16567	−	0.561356i	0.251964	−	0.967737i	$-0.418924\pi$
$439$	24.4235	−	11.7617i	1.16567	−	0.561356i	0.913704	+	0.406381i	$0.133209\pi$
$440$	−1.03352	−	4.52814i	−0.0492711	−	0.215871i
$441$	1.28150	−	5.61463i	0.0610239	−	0.267363i
$442$	25.0950	+	12.0851i	1.19365	+	0.574831i
$443$	8.46977	+	10.6208i	0.402411	+	0.504608i	0.941208	−	0.337828i	$-0.109692\pi$
$443$	8.46977	+	10.6208i	0.402411	+	0.504608i	−0.538797	+	0.842436i	$0.681121\pi$
$444$	7.32789	+	9.18889i	0.347766	+	0.436085i
$445$	−9.09376	+	4.37932i	−0.431085	+	0.207600i
$446$	24.7549	−	31.0417i	1.17218	−	1.46987i
$447$	3.92807			0.185791
$448$	0.713072	−	0.894164i	0.0336895	−	0.0422453i
$449$	−3.06068	+	13.4097i	−0.144443	+	0.632844i	0.849929	+	0.526897i	$0.176645\pi$
$449$	−3.06068	+	13.4097i	−0.144443	+	0.632844i	−0.994372	+	0.105947i	$0.966213\pi$
$450$	1.27401	−	5.58179i	0.0600572	−	0.263128i
$451$	13.9421	−	17.4828i	0.656506	−	0.823233i
$452$	−18.3881			−0.864903
$453$	−13.6236	+	17.0835i	−0.640094	+	0.802652i
$454$	−31.3494	+	15.0971i	−1.47130	+	0.708540i
$455$	2.63278	+	3.30141i	0.123427	+	0.154772i
$456$	−0.308311	−	0.386610i	−0.0144380	−	0.0181046i
$457$	−2.21591	−	1.06713i	−0.103656	−	0.0499181i	0.381337	−	0.924436i	$-0.375464\pi$
$457$	−2.21591	−	1.06713i	−0.103656	−	0.0499181i	−0.484993	+	0.874518i	$0.661178\pi$
$458$	−8.26891	+	36.2285i	−0.386381	+	1.69285i
$459$	1.22568	+	5.37006i	0.0572099	+	0.250653i
$460$	−7.86583	+	3.78799i	−0.366746	+	0.176616i
$461$	32.4663	+	15.6349i	1.51211	+	0.728192i	0.992039	−	0.125933i	$-0.0401925\pi$
$461$	32.4663	+	15.6349i	1.51211	+	0.728192i	0.520068	+	0.854125i	$0.325907\pi$
$462$	1.09854	+	4.81302i	0.0511088	+	0.223922i
$463$	25.8918			1.20329			0.601646	−	0.798763i	$-0.294512\pi$
$463$	25.8918			1.20329			0.601646	+	0.798763i	$0.294512\pi$
$464$	20.1438	−	17.4682i	0.935152	−	0.810941i
$465$	5.98724			0.277652
$466$	−8.74849	−	38.3296i	−0.405266	−	1.77559i
$467$	−13.0899	−	6.30376i	−0.605728	−	0.291703i	0.105771	−	0.994391i	$-0.466269\pi$
$467$	−13.0899	−	6.30376i	−0.605728	−	0.291703i	−0.711499	+	0.702687i	$0.751983\pi$
$468$	3.09948	−	1.49263i	0.143274	−	0.0689969i
$469$	3.54561	+	15.5343i	0.163721	+	0.717308i
$470$	−1.93141	+	8.46207i	−0.0890894	+	0.390326i
$471$	−9.35232	−	4.50384i	−0.430932	−	0.207526i
$472$	5.46295	+	6.85032i	0.251453	+	0.315312i
$473$	13.9321	+	17.4703i	0.640600	+	0.803286i
$474$	0.415572	−	0.200129i	0.0190878	−	0.00919222i
$475$	0.703466	−	0.882118i	0.0322772	−	0.0404744i
$476$	−7.49187			−0.343389
$477$	−4.10405	+	5.14631i	−0.187911	+	0.235633i
$478$	−0.186543	+	0.817297i	−0.00853227	+	0.0373823i
$479$	−0.486560	+	2.13176i	−0.0222315	+	0.0974025i	−0.984826	−	0.173542i	$-0.944479\pi$
$479$	−0.486560	+	2.13176i	−0.0222315	+	0.0974025i	0.962595	+	0.270944i	$0.0873359\pi$
$480$	5.10789	−	6.40509i	0.233142	−	0.292351i
$481$	27.1224			1.23668
$482$	9.81043	−	12.3019i	0.446853	−	0.560336i
$483$	−5.33462	+	2.56902i	−0.242734	+	0.116894i
$484$	−3.73218	−	4.68000i	−0.169644	−	0.212727i
$485$	5.93696	+	7.44471i	0.269583	+	0.338047i
$486$	1.61697	+	0.778692i	0.0733473	+	0.0353222i
$487$	1.06851	−	4.68147i	0.0484190	−	0.212138i	−0.944931	−	0.327269i	$-0.893872\pi$
$487$	1.06851	−	4.68147i	0.0484190	−	0.212138i	0.993350	+	0.115131i	$0.0367289\pi$
$488$	0.0367815	+	0.161150i	0.00166502	+	0.00729492i
$489$	−8.04314	+	3.87337i	−0.363723	+	0.175160i
$490$	12.5278	+	6.03307i	0.565948	+	0.272546i
$491$	3.81468	+	16.7132i	0.172154	+	0.754256i	0.985109	+	0.171930i	$0.0550003\pi$
$491$	3.81468	+	16.7132i	0.172154	+	0.754256i	−0.812955	+	0.582326i	$0.802143\pi$
$492$	11.0568			0.498478
$493$	−29.1659	−	5.40428i	−1.31357	−	0.243396i
$494$	1.78845			0.0804662
$495$	0.739205	+	3.23867i	0.0332248	+	0.145567i
$496$	−19.8528	−	9.56059i	−0.891416	−	0.429283i
$497$	7.53380	−	3.62809i	0.337937	−	0.162742i
$498$	−2.44806	−	10.7256i	−0.109700	−	0.480628i
$499$	0.775879	−	3.39935i	0.0347331	−	0.152176i	−0.954588	−	0.297930i	$-0.903704\pi$
$499$	0.775879	−	3.39935i	0.0347331	−	0.152176i	0.989321	+	0.145754i	$0.0465609\pi$
$500$	12.1206	+	5.83698i	0.542050	+	0.261038i
$501$	−12.4742	−	15.6421i	−0.557304	−	0.698837i
$502$	−5.46055	−	6.84732i	−0.243716	−	0.305611i
$503$	−29.7212	+	14.3130i	−1.32520	+	0.638185i	−0.956601	−	0.291401i	$-0.905878\pi$
$503$	−29.7212	+	14.3130i	−1.32520	+	0.638185i	−0.368604	+	0.929586i	$0.620164\pi$
$504$	0.971105	−	1.21773i	0.0432565	−	0.0542419i
$505$	−3.49493			−0.155523
$506$	−14.6860	+	18.4156i	−0.652871	+	0.818674i
$507$	−1.12621	+	4.93425i	−0.0500168	+	0.219138i
$508$	−0.177687	+	0.778500i	−0.00788361	+	0.0345403i
$509$	−19.3443	+	24.2570i	−0.857421	+	1.07517i	0.138971	+	0.990296i	$0.455621\pi$
$509$	−19.3443	+	24.2570i	−0.857421	+	1.07517i	−0.996392	+	0.0848752i	$0.972951\pi$
$510$	−13.2991			−0.588895
$511$	11.0601	−	13.8690i	0.489272	−	0.613528i
$512$	−14.6909	+	7.07476i	−0.649252	+	0.312663i
$513$	0.220513	+	0.276515i	0.00973590	+	0.0122084i
$514$	−3.55654	−	4.45976i	−0.156872	−	0.196712i
$515$	8.43980	+	4.06439i	0.371902	+	0.179099i
$516$	−2.45861	+	10.7719i	−0.108234	+	0.474205i
$517$	1.97528	+	8.65427i	0.0868727	+	0.380614i
$518$	−17.3394	+	8.35023i	−0.761851	+	0.366888i
$519$	−3.60237	−	1.73481i	−0.158126	−	0.0761497i
$520$	−1.17931	−	5.16689i	−0.0517161	−	0.226583i
$521$	22.9227			1.00426			0.502130	−	0.864792i	$-0.332550\pi$
$521$	22.9227			1.00426			0.502130	+	0.864792i	$0.332550\pi$
$522$	−7.30172	+	6.33188i	−0.319588	+	0.277139i
$523$	−40.2928			−1.76188			−0.880940	−	0.473229i	$-0.843088\pi$
$523$	−40.2928			−1.76188			−0.880940	+	0.473229i	$0.843088\pi$
$524$	0.0145685	+	0.0638288i	0.000636428	+	0.00278837i
$525$	3.20185	+	1.54193i	0.139740	+	0.0672953i
$526$	−39.2837	+	18.9181i	−1.71285	+	0.824866i
$527$	5.45482	+	23.8991i	0.237616	+	1.04106i
$528$	2.72050	−	11.9193i	0.118395	−	0.518721i
$529$	−4.73027	−	2.27798i	−0.205664	−	0.0990425i
$530$	−9.90897	−	12.4255i	−0.430418	−	0.539727i
$531$	−3.90727	−	4.89956i	−0.169561	−	0.212623i
$532$	−0.433410	+	0.208719i	−0.0187907	+	0.00904912i
$533$	15.9087	−	19.9489i	0.689084	−	0.864085i
$534$	−13.4649			−0.582682
$535$	12.7067	−	15.9338i	0.549360	−	0.688876i
$536$	4.45002	−	19.4968i	0.192211	−	0.842133i
$537$	−2.30444	+	10.0964i	−0.0994441	+	0.435693i
$538$	9.68305	−	12.1422i	0.417466	−	0.523486i
$539$	14.2206			0.612525
$540$	−1.02413	+	1.28421i	−0.0440714	+	0.0552638i
$541$	−19.5947	+	9.43631i	−0.842442	+	0.405699i	−0.804767	−	0.593591i	$-0.797710\pi$
$541$	−19.5947	+	9.43631i	−0.842442	+	0.405699i	−0.0376755	+	0.999290i	$0.511995\pi$
$542$	−15.9603	−	20.0136i	−0.685555	−	0.859658i
$543$	6.04607	+	7.58154i	0.259462	+	0.325355i
$544$	30.2207	+	14.5535i	1.29570	+	0.623977i
$545$	−4.83709	+	21.1927i	−0.207198	+	0.907794i
$546$	1.25350	+	5.49195i	0.0536450	+	0.235034i
$547$	34.1837	−	16.4620i	1.46159	−	0.703864i	0.477026	−	0.878889i	$-0.341715\pi$
$547$	34.1837	−	16.4620i	1.46159	−	0.703864i	0.984564	+	0.175025i	$0.0560006\pi$
$548$	−12.9604	−	6.24138i	−0.553639	−	0.266619i
$549$	−0.0263072	−	0.115259i	−0.00112276	−	0.00491915i
$550$	14.1374			0.602822
$551$	−1.83783	+	0.499904i	−0.0782941	+	0.0212966i
$552$	7.43130			0.316297
$553$	0.0637085	+	0.279125i	0.00270916	+	0.0118696i
$554$	−12.2825	−	5.91492i	−0.521831	−	0.251301i
$555$	−11.6676	+	5.61884i	−0.495264	+	0.238507i
$556$	1.92699	+	8.44271i	0.0817227	+	0.358051i
$557$	1.64996	−	7.22894i	0.0699110	−	0.306300i	−0.927868	−	0.372908i	$-0.878361\pi$
$557$	1.64996	−	7.22894i	0.0699110	−	0.306300i	0.997779	+	0.0666082i	$0.0212177\pi$
$558$	7.19623	+	3.46552i	0.304641	+	0.146707i
$559$	15.8974	+	19.9347i	0.672388	+	0.843148i
$560$	4.62642	+	5.80134i	0.195502	+	0.245152i
$561$	−12.2542	+	5.90133i	−0.517374	+	0.249154i
$562$	1.46507	−	1.83713i	0.0618001	−	0.0774948i
$563$	33.6129			1.41661			0.708307	−	0.705904i	$-0.249459\pi$
$563$	33.6129			1.41661			0.708307	+	0.705904i	$0.249459\pi$
$564$	−2.73664	+	3.43164i	−0.115233	+	0.144498i
$565$	4.50849	−	19.7530i	0.189673	−	0.831014i
$566$	−9.39538	+	41.1638i	−0.394917	+	1.73024i
$567$	−0.694564	+	0.870956i	−0.0291690	+	0.0365767i
$568$	−10.4948			−0.440353
$569$	−10.8101	+	13.5555i	−0.453184	+	0.568275i	−0.954964	−	0.296720i	$-0.904107\pi$
$569$	−10.8101	+	13.5555i	−0.453184	+	0.568275i	0.501780	+	0.864995i	$0.332679\pi$
$570$	−0.769363	+	0.370506i	−0.0322251	+	0.0155188i
$571$	−10.6261	−	13.3247i	−0.444688	−	0.557621i	0.508084	−	0.861307i	$-0.330354\pi$
$571$	−10.6261	−	13.3247i	−0.444688	−	0.557621i	−0.952772	+	0.303686i	$0.901782\pi$
$572$	5.29637	+	6.64144i	0.221452	+	0.277693i
$573$	1.03793	+	0.499840i	0.0433601	+	0.0208811i
$574$	−4.02879	+	17.6513i	−0.168158	+	0.736749i
$575$	3.77303	+	16.5307i	0.157346	+	0.689378i
$576$	0.924977	−	0.445445i	0.0385407	−	0.0185602i
$577$	20.0898	+	9.67472i	0.836348	+	0.402764i	0.802492	−	0.596663i	$-0.203507\pi$
$577$	20.0898	+	9.67472i	0.836348	+	0.402764i	0.0338560	+	0.999427i	$0.489221\pi$
$578$	−5.32739	−	23.3408i	−0.221590	−	0.970850i
$579$	27.6684			1.14986
$580$	−4.16279	−	7.80477i	−0.172850	−	0.324075i
$581$	6.82875			0.283304
$582$	2.82666	+	12.3844i	0.117169	+	0.513351i
$583$	−14.6441	−	7.05223i	−0.606497	−	0.292073i
$584$	−20.0591	+	9.65997i	−0.830053	+	0.399732i
$585$	0.843478	+	3.69552i	0.0348735	+	0.152791i
$586$	6.32033	−	27.6912i	0.261090	−	1.14391i
$587$	10.8564	+	5.22817i	0.448092	+	0.215790i	0.644300	−	0.764773i	$-0.277149\pi$
$587$	10.8564	+	5.22817i	0.448092	+	0.215790i	−0.196209	+	0.980562i	$0.562863\pi$
$588$	4.38408	+	5.49746i	0.180796	+	0.226711i
$589$	0.981381	+	1.23061i	0.0404371	+	0.0507065i
$590$	13.6323	−	6.56498i	0.561234	−	0.270276i
$591$	9.28603	−	11.6443i	0.381976	−	0.478983i
$592$	47.6604			1.95883
$593$	1.38694	−	1.73917i	0.0569549	−	0.0714192i	−0.752538	−	0.658549i	$-0.771171\pi$
$593$	1.38694	−	1.73917i	0.0569549	−	0.0714192i	0.809493	+	0.587130i	$0.199742\pi$
$594$	−0.986128	+	4.32051i	−0.0404613	+	0.177273i
$595$	1.83690	−	8.04797i	0.0753054	−	0.329934i
$596$	−2.99026	+	3.74966i	−0.122486	+	0.153592i
$597$	9.17257			0.375408
$598$	−16.7576	+	21.0133i	−0.685269	+	0.859300i
$599$	−1.24124	+	0.597750i	−0.0507157	+	0.0244234i	−0.459070	−	0.888400i	$-0.651817\pi$
$599$	−1.24124	+	0.597750i	−0.0507157	+	0.0244234i	0.408354	+	0.912824i	$0.366103\pi$
$600$	−2.78094	−	3.48719i	−0.113531	−	0.142364i
$601$	−11.1072	−	13.9280i	−0.453073	−	0.568135i	0.501863	−	0.864947i	$-0.332648\pi$
$601$	−11.1072	−	13.9280i	−0.453073	−	0.568135i	−0.954936	+	0.296812i	$0.904077\pi$
$602$	−16.3006	−	7.84995i	−0.664362	−	0.319940i
$603$	−3.18279	+	13.9447i	−0.129613	+	0.567872i
$604$	−5.93655	−	26.0097i	−0.241555	−	1.05832i
$605$	5.94246	−	2.86174i	0.241595	−	0.116346i
$606$	−4.20066	−	2.02293i	−0.170640	−	0.0821760i
$607$	8.84235	+	38.7409i	0.358900	+	1.57244i	0.755939	+	0.654642i	$0.227180\pi$
$607$	8.84235	+	38.7409i	0.358900	+	1.57244i	−0.397039	+	0.917802i	$0.629962\pi$
$608$	2.15374			0.0873457
$609$	−2.82321	−	5.29320i	−0.114402	−	0.214491i
$610$	0.285444			0.0115573
$611$	2.25392	+	9.87505i	0.0911837	+	0.399502i
$612$	−6.05922	−	2.91797i	−0.244930	−	0.117952i
$613$	19.8105	−	9.54021i	0.800137	−	0.385326i	0.0113060	−	0.999936i	$-0.496401\pi$
$613$	19.8105	−	9.54021i	0.800137	−	0.385326i	0.788831	+	0.614611i	$0.210687\pi$
$614$	3.01736	+	13.2199i	0.121771	+	0.533512i
$615$	−2.71096	+	11.8775i	−0.109316	+	0.478946i
$616$	3.46511	+	1.66871i	0.139613	+	0.0672341i
$617$	−21.0225	−	26.3614i	−0.846335	−	1.06127i	−0.997351	−	0.0727397i	$-0.976826\pi$
$617$	−21.0225	−	26.3614i	−0.846335	−	1.06127i	0.151015	−	0.988531i	$-0.451746\pi$
$618$	7.79149	+	9.77021i	0.313420	+	0.393016i
$619$	−36.5273	+	17.5906i	−1.46815	+	0.707026i	−0.985640	−	0.168862i	$-0.945991\pi$
$619$	−36.5273	+	17.5906i	−1.46815	+	0.707026i	−0.482515	+	0.875888i	$0.660277\pi$
$620$	−4.55781	+	5.71531i	−0.183046	+	0.229533i
$621$	−5.31509			−0.213287
$622$	15.8530	−	19.8790i	0.635648	−	0.797077i
$623$	1.85979	−	8.14827i	0.0745108	−	0.326453i
$624$	3.10426	−	13.6007i	0.124270	−	0.544462i
$625$	0.703023	−	0.881563i	0.0281209	−	0.0352625i
$626$	30.4397			1.21661
$627$	−0.544509	+	0.682792i	−0.0217456	+	0.0272681i
$628$	11.4188	−	5.49900i	0.455659	−	0.219434i
$629$	−33.0587	−	41.4543i	−1.31814	−	1.65289i
$630$	−1.67698	−	2.10287i	−0.0668126	−	0.0837804i
$631$	7.47192	+	3.59829i	0.297452	+	0.143246i	0.576658	−	0.816986i	$-0.304357\pi$
$631$	7.47192	+	3.59829i	0.297452	+	0.143246i	−0.279205	+	0.960231i	$0.590071\pi$
$632$	0.0799592	−	0.350324i	0.00318061	−	0.0139351i
$633$	−0.0564440	−	0.247297i	−0.00224345	−	0.00982919i
$634$	7.64937	−	3.68374i	0.303795	−	0.146300i
$635$	−0.792719	−	0.381753i	−0.0314581	−	0.0151494i
$636$	−1.78836	−	7.83530i	−0.0709130	−	0.310690i
$637$	16.2266			0.642921
$638$	−19.2552	−	14.0988i	−0.762321	−	0.558176i
$639$	7.50622			0.296942
$640$	−3.09439	−	13.5574i	−0.122316	−	0.535903i
$641$	−11.0732	−	5.33257i	−0.437365	−	0.210624i	0.202227	−	0.979339i	$-0.435182\pi$
$641$	−11.0732	−	5.33257i	−0.437365	−	0.210624i	−0.639592	+	0.768715i	$0.720896\pi$
$642$	24.4953	−	11.7963i	0.966753	−	0.465564i
$643$	−2.51796	−	11.0319i	−0.0992985	−	0.435055i	−1.00000		0.000616161i	$-0.999804\pi$
$643$	−2.51796	−	11.0319i	−0.0992985	−	0.435055i	0.900701	−	0.434439i	$-0.143053\pi$
$644$	1.60866	−	7.04801i	0.0633902	−	0.277731i
$645$	−10.9686	−	5.28220i	−0.431889	−	0.207987i
$646$	−2.17989	−	2.73349i	−0.0857665	−	0.107548i
$647$	−18.1509	−	22.7605i	−0.713584	−	0.894806i	0.284372	−	0.958714i	$-0.408215\pi$
$647$	−18.1509	−	22.7605i	−0.713584	−	0.894806i	−0.997956	+	0.0639081i	$0.979644\pi$
$648$	1.25969	−	0.606635i	0.0494853	−	0.0238309i
$649$	9.64813	−	12.0984i	0.378722	−	0.474903i
$650$	16.1317			0.632736
$651$	−3.09112	+	3.87614i	−0.121150	+	0.151918i
$652$	2.42542	−	10.6265i	0.0949868	−	0.416164i
$653$	5.30073	−	23.2240i	0.207434	−	0.908826i	−0.758833	−	0.651285i	$-0.774230\pi$
$653$	5.30073	−	23.2240i	0.207434	−	0.908826i	0.966267	−	0.257542i	$-0.0829125\pi$
$654$	−18.0805	+	22.6723i	−0.707004	+	0.886555i
$655$	−0.0721386			−0.00281869
$656$	27.9554	−	35.0550i	1.09147	−	1.36867i
$657$	14.3469	−	6.90910i	0.559726	−	0.269550i
$658$	−4.48118	−	5.61923i	−0.174695	−	0.219060i
$659$	7.09350	+	8.89497i	0.276323	+	0.346499i	0.900556	−	0.434740i	$-0.143160\pi$
$659$	7.09350	+	8.89497i	0.276323	+	0.346499i	−0.624233	+	0.781239i	$0.714588\pi$
$660$	−3.65430	−	1.75982i	−0.142243	−	0.0685008i
$661$	−8.26838	+	36.2261i	−0.321603	+	1.40903i	0.513098	+	0.858330i	$0.328498\pi$
$661$	−8.26838	+	36.2261i	−0.321603	+	1.40903i	−0.834701	+	0.550704i	$0.814359\pi$
$662$	0.708597	+	3.10456i	0.0275404	+	0.120662i
$663$	−13.9828	+	6.73378i	−0.543049	+	0.261518i
$664$	−7.72186	−	3.71865i	−0.299666	−	0.144312i
$665$	−0.117946	−	0.516755i	−0.00457375	−	0.0200389i
$666$	−17.2759			−0.669429
$667$	11.3466	−	26.2776i	0.439344	−	1.01747i
$668$	24.4277			0.945135
$669$	4.92278	+	21.5681i	0.190326	+	0.833871i
$670$	−31.1145	−	14.9840i	−1.20206	−	0.578881i
$671$	0.263017	−	0.126662i	0.0101537	−	0.00488974i
$672$	1.50953	+	6.61369i	0.0582314	+	0.255128i
$673$	1.81059	−	7.93270i	0.0697930	−	0.305783i	−0.927968	−	0.372659i	$-0.878446\pi$
$673$	1.81059	−	7.93270i	0.0697930	−	0.305783i	0.997761	+	0.0668760i	$0.0213032\pi$
$674$	−2.01774	−	0.971690i	−0.0777203	−	0.0374281i
$675$	1.98901	+	2.49414i	0.0765571	+	0.0959996i
$676$	−3.85282	−	4.83128i	−0.148185	−	0.185819i
$677$	−21.1533	+	10.1869i	−0.812986	+	0.391513i	−0.793707	−	0.608301i	$-0.791852\pi$
$677$	−21.1533	+	10.1869i	−0.812986	+	0.391513i	−0.0192794	+	0.999814i	$0.506137\pi$
$678$	16.8523	−	21.1321i	0.647207	−	0.811572i
$679$	−7.88485			−0.302593
$680$	−6.45972	+	8.10024i	−0.247719	+	0.310630i
$681$	4.31417	−	18.9016i	0.165319	−	0.724312i
$682$	−4.38870	+	19.2282i	−0.168052	+	0.736284i
$683$	−29.3595	+	36.8157i	−1.12341	+	1.40871i	−0.222380	+	0.974960i	$0.571383\pi$
$683$	−29.3595	+	36.8157i	−1.12341	+	1.40871i	−0.901032	+	0.433754i	$0.857189\pi$
$684$	−0.431823			−0.0165112
$685$	9.88235	−	12.3921i	0.377585	−	0.473477i
$686$	−22.9828	+	11.0679i	−0.877486	+	0.422575i
$687$	−12.9097	−	16.1882i	−0.492534	−	0.617618i
$688$	27.9355	+	35.0300i	1.06503	+	1.33550i
$689$	−16.7098	−	8.04702i	−0.636593	−	0.306567i
$690$	2.85560	−	12.5112i	0.108711	−	0.476294i
$691$	−5.42868	−	23.7846i	−0.206517	−	0.904809i	−0.966864	−	0.255292i	$-0.917828\pi$
$691$	−5.42868	−	23.7846i	−0.206517	−	0.904809i	0.760347	−	0.649517i	$-0.225029\pi$
$692$	4.39834	−	2.11813i	0.167200	−	0.0805191i
$693$	−2.47835	−	1.19351i	−0.0941447	−	0.0453377i
$694$	10.4541	+	45.8026i	0.396834	+	1.73864i
$695$	−9.54186			−0.361943
$696$	0.309990	+	7.52289i	0.0117502	+	0.285154i
$697$	−49.8809			−1.88937
$698$	−9.54006	−	41.7977i	−0.361097	−	1.58207i
$699$	19.7369	+	9.50480i	0.746519	+	0.359505i
$700$	−3.90932	+	1.88263i	−0.147758	+	0.0711567i
$701$	1.50620	+	6.59911i	0.0568885	+	0.249245i	0.995374	−	0.0960730i	$-0.0306282\pi$
$701$	1.50620	+	6.59911i	0.0568885	+	0.249245i	−0.938486	+	0.345318i	$0.887771\pi$
$702$	−1.12523	+	4.92997i	−0.0424692	+	0.186070i
$703$	−3.06736	−	1.47716i	−0.115688	−	0.0557122i
$704$	1.58059	+	1.98200i	0.0595709	+	0.0746995i
$705$	−3.01537	−	3.78116i	−0.113566	−	0.142407i
$706$	3.43920	−	1.65623i	0.129436	−	0.0623331i
$707$	1.80438	−	2.26262i	0.0678606	−	0.0850945i
$708$	7.65146			0.287559
$709$	−1.39012	+	1.74315i	−0.0522070	+	0.0654655i	−0.807249	−	0.590210i	$-0.799045\pi$
$709$	−1.39012	+	1.74315i	−0.0522070	+	0.0654655i	0.755042	+	0.655676i	$0.227616\pi$
$710$	−4.03282	+	17.6689i	−0.151349	+	0.663103i
$711$	−0.0571893	+	0.250563i	−0.00214476	+	0.00939683i
$712$	−6.54023	+	8.20119i	−0.245105	+	0.307352i
$713$	−23.6545			−0.885868
$714$	6.86612	−	8.60985i	0.256958	−	0.322215i
$715$	−8.43301	+	4.06112i	−0.315377	+	0.151877i
$716$	−7.88361	−	9.88573i	−0.294624	−	0.369447i
$717$	−0.291236	−	0.365198i	−0.0108764	−	0.0136386i
$718$	44.3213	+	21.3440i	1.65406	+	0.796551i
$719$	6.84297	−	29.9810i	0.255200	−	1.11810i	−0.671115	−	0.741353i	$-0.734184\pi$
$719$	6.84297	−	29.9810i	0.255200	−	1.11810i	0.926315	−	0.376750i	$-0.122959\pi$
$720$	1.48219	+	6.49389i	0.0552379	+	0.242013i
$721$	−6.98862	+	3.36554i	−0.260270	+	0.125339i
$722$	30.5202	+	14.6977i	1.13584	+	0.546994i
$723$	1.95091	+	8.54749i	0.0725551	+	0.317885i
$724$	−11.8398			−0.440023
$725$	−16.5771	+	4.50909i	−0.615656	+	0.167463i
$726$	8.79883			0.326555
$727$	−4.44938	−	19.4940i	−0.165018	−	0.722992i	−0.987940	−	0.154837i	$-0.950515\pi$
$727$	−4.44938	−	19.4940i	−0.165018	−	0.722992i	0.822922	−	0.568155i	$-0.192342\pi$
$728$	3.95390	+	1.90410i	0.146541	+	0.0705706i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	8.55531	+	37.4832i	0.316646	+	1.38732i
$731$	11.0916	−	48.5956i	0.410239	−	1.79737i
$732$	0.130051	+	0.0626293i	0.00480683	+	0.00231485i
$733$	4.69062	+	5.88185i	0.173252	+	0.217251i	0.860875	−	0.508817i	$-0.169917\pi$
$733$	4.69062	+	5.88185i	0.173252	+	0.217251i	−0.687623	+	0.726068i	$0.741346\pi$
$734$	30.5099	+	38.2583i	1.12614	+	1.41214i
$735$	−6.98043	+	3.36160i	−0.257477	+	0.123994i
$736$	−20.1803	+	25.3053i	−0.743857	+	0.932767i
$737$	−35.3189			−1.30099
$738$	−10.1333	+	12.7067i	−0.373011	+	0.467741i
$739$	−3.86208	+	16.9209i	−0.142069	+	0.622444i	0.852884	+	0.522101i	$0.174851\pi$
$739$	−3.86208	+	16.9209i	−0.142069	+	0.622444i	−0.994953	+	0.100344i	$0.968006\pi$
$740$	3.51839	−	15.4151i	0.129339	−	0.566670i
$741$	−0.621318	+	0.779108i	−0.0228247	+	0.0286212i
$742$	13.1601			0.483122
$743$	−33.3942	+	41.8750i	−1.22512	+	1.53625i	−0.466793	+	0.884366i	$0.654591\pi$
$743$	−33.3942	+	41.8750i	−1.22512	+	1.53625i	−0.758322	+	0.651880i	$0.773981\pi$
$744$	5.60617	−	2.69979i	0.205532	−	0.0989791i
$745$	−3.29482	−	4.13158i	−0.120713	−	0.151369i
$746$	7.22434	+	9.05904i	0.264502	+	0.331675i
$747$	5.52291	+	2.65969i	0.202073	+	0.0973131i
$748$	3.69528	−	16.1901i	0.135113	−	0.591969i
$749$	3.75522	+	16.4527i	0.137213	+	0.601168i
$750$	−17.8163	+	8.57986i	−0.650558	+	0.313292i
$751$	36.0836	+	17.3770i	1.31671	+	0.634094i	0.954558	−	0.298024i	$-0.0963277\pi$
$751$	36.0836	+	17.3770i	1.31671	+	0.634094i	0.362153	+	0.932119i	$0.382042\pi$
$752$	3.96066	+	17.3528i	0.144430	+	0.632791i
$753$	4.87995			0.177835
$754$	−21.9714	−	16.0876i	−0.800150	−	0.585875i
$755$	29.3959			1.06983
$756$	−0.302659	−	1.32604i	−0.0110076	−	0.0482275i
$757$	2.93082	+	1.41141i	0.106522	+	0.0512985i	0.486386	−	0.873744i	$-0.338315\pi$
$757$	2.93082	+	1.41141i	0.106522	+	0.0512985i	−0.379864	+	0.925042i	$0.624029\pi$
$758$	30.9822	−	14.9203i	1.12533	−	0.541928i
$759$	−2.92046	−	12.7954i	−0.106006	−	0.464443i
$760$	−0.148031	+	0.648568i	−0.00536967	+	0.0235260i
$761$	37.8911	+	18.2474i	1.37355	+	0.661467i	0.967614	−	0.252434i	$-0.0812310\pi$
$761$	37.8911	+	18.2474i	1.37355	+	0.661467i	0.405937	+	0.913901i	$0.366945\pi$
$762$	−0.731825	−	0.917680i	−0.0265112	−	0.0332440i
$763$	−11.2228	−	14.0730i	−0.406293	−	0.509475i
$764$	−1.26727	+	0.610284i	−0.0458481	+	0.0220793i
$765$	4.62019	−	5.79354i	0.167043	−	0.209466i

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.399359 - 1.74971i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-1.10004 + 0.529753i) q^{4} +(-0.299361 - 1.31158i) q^{5} +(0.399359 - 1.74971i) q^{6} +(1.00367 + 0.483344i) q^{7} +(-0.871733 - 1.09312i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.399359 - 1.74971i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-1.10004 + 0.529753i) q^{4} +(-0.299361 - 1.31158i) q^{5} +(0.399359 - 1.74971i) q^{6} +(1.00367 + 0.483344i) q^{7} +(-0.871733 - 1.09312i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-2.17533 + 1.04759i) q^{10} +(-1.53957 + 1.93056i) q^{11} -1.22096 q^{12} +(-1.75674 + 2.20289i) q^{13} +(0.444884 - 1.94916i) q^{14} +(0.299361 - 1.31158i) q^{15} +(-3.08701 + 3.87099i) q^{16} +5.50816 q^{17} +(1.11898 - 1.40315i) q^{18} +(0.318651 - 0.153454i) q^{19} +(1.02413 + 1.28421i) q^{20} +(0.694564 + 0.870956i) q^{21} +(3.99275 + 1.92281i) q^{22} +(-1.18272 + 5.18183i) q^{23} +(-0.311118 - 1.36310i) q^{24} +(2.87421 - 1.38414i) q^{25} +(4.55597 + 2.19404i) q^{26} +(0.222521 + 0.974928i) q^{27} -1.36014 q^{28} +(-5.29503 - 0.981140i) q^{29} -2.41444 q^{30} +(0.990316 + 4.33886i) q^{31} +(5.48653 + 2.64217i) q^{32} +(-2.22474 + 1.07138i) q^{33} +(-2.19973 - 9.63766i) q^{34} +(0.333486 - 1.46110i) q^{35} +(-1.10004 - 0.529753i) q^{36} +(-6.00176 - 7.52597i) q^{37} +(-0.395756 - 0.496262i) q^{38} +(-2.53857 + 1.22251i) q^{39} +(-1.17275 + 1.47059i) q^{40} -9.05582 q^{41} +(1.24654 - 1.56311i) q^{42} +(2.01367 - 8.82247i) q^{43} +(0.670874 - 2.93929i) q^{44} +(0.838790 - 1.05181i) q^{45} +9.53901 q^{46} +(2.24139 - 2.81061i) q^{47} +(-4.46086 + 2.14824i) q^{48} +(-3.59069 - 4.50258i) q^{49} +(-3.56969 - 4.47624i) q^{50} +(4.96268 + 2.38990i) q^{51} +(0.765509 - 3.35391i) q^{52} +(1.46472 + 6.41735i) q^{53} +(1.61697 - 0.778692i) q^{54} +(2.99298 + 1.44134i) q^{55} +(-0.346583 - 1.51848i) q^{56} +0.353676 q^{57} +(0.397912 + 9.65657i) q^{58} -6.26677 q^{59} +(0.365506 + 1.60139i) q^{60} +(-0.106516 - 0.0512953i) q^{61} +(7.19623 - 3.46552i) q^{62} +(0.247887 + 1.08606i) q^{63} +(0.228450 - 1.00091i) q^{64} +(3.41517 + 1.64466i) q^{65} +(2.76307 + 3.46478i) q^{66} +(8.91797 + 11.1828i) q^{67} +(-6.05922 + 2.91797i) q^{68} +(-3.31391 + 4.15551i) q^{69} -2.68967 q^{70} +(4.68005 - 5.86860i) q^{71} +(0.311118 - 1.36310i) q^{72} +(3.54339 - 15.5246i) q^{73} +(-10.7714 + 13.5069i) q^{74} +3.19013 q^{75} +(-0.269237 + 0.337613i) q^{76} +(-2.47835 + 1.19351i) q^{77} +(3.15283 + 3.95353i) q^{78} +(0.160241 + 0.200936i) q^{79} +(6.00126 + 2.89005i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(3.61652 + 15.8450i) q^{82} +(5.52291 - 2.65969i) q^{83} +(-1.22544 - 0.590142i) q^{84} +(-1.64893 - 7.22442i) q^{85} -16.2409 q^{86} +(-4.34496 - 3.18140i) q^{87} +3.45242 q^{88} +(-1.66948 - 7.31446i) q^{89} +(-2.17533 - 1.04759i) q^{90} +(-2.82795 + 1.36187i) q^{91} +(-1.44405 - 6.32679i) q^{92} +(-0.990316 + 4.33886i) q^{93} +(-5.81286 - 2.79933i) q^{94} +(-0.296660 - 0.372000i) q^{95} +(3.79680 + 4.76103i) q^{96} +(-6.37706 + 3.07103i) q^{97} +(-6.44422 + 8.08079i) q^{98} -2.46928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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