LMFDB - Embedded newform 639.2.j.c.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(37,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("639.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.j (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:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 71)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	639.91
Dual form			639.2.j.c.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0919395 - 0.402813i) q^{2} +(1.64813 - 0.793699i) q^{4} +2.73724 q^{5} +(0.0252603 - 0.110672i) q^{7} +(-0.986458 - 1.23698i) q^{8} +O(q^{10})$	\(q+(-0.0919395 - 0.402813i) q^{2} +(1.64813 - 0.793699i) q^{4} +2.73724 q^{5} +(0.0252603 - 0.110672i) q^{7} +(-0.986458 - 1.23698i) q^{8} +(-0.251661 - 1.10260i) q^{10} +(0.721709 - 0.904995i) q^{11} +(-0.294972 - 0.369884i) q^{13} -0.0469027 q^{14} +(1.87351 - 2.34931i) q^{16} +3.18709 q^{17} +(-2.70157 - 1.30101i) q^{19} +(4.51134 - 2.17255i) q^{20} +(-0.430897 - 0.207509i) q^{22} +(-0.765590 + 3.35427i) q^{23} +2.49250 q^{25} +(-0.121874 + 0.152826i) q^{26} +(-0.0462083 - 0.202452i) q^{28} +(-8.81520 + 4.24518i) q^{29} +(5.34724 + 6.70523i) q^{31} +(-3.96953 - 1.91162i) q^{32} +(-0.293020 - 1.28380i) q^{34} +(0.0691435 - 0.302937i) q^{35} +(-1.76001 - 7.71113i) q^{37} +(-0.275682 + 1.20784i) q^{38} +(-2.70018 - 3.38591i) q^{40} +(-3.04436 - 3.81751i) q^{41} +(1.13032 + 4.95224i) q^{43} +(0.471179 - 2.06437i) q^{44} +1.42153 q^{46} +(9.84988 + 4.74345i) q^{47} +(6.29517 + 3.03159i) q^{49} +(-0.229159 - 1.00401i) q^{50} +(-0.779730 - 0.375498i) q^{52} +(-4.08850 - 1.96892i) q^{53} +(1.97549 - 2.47719i) q^{55} +(-0.161818 + 0.0779273i) q^{56} +(2.52048 + 3.16058i) q^{58} +(1.50319 - 1.88494i) q^{59} +(-3.45910 - 15.1553i) q^{61} +(2.20933 - 2.77042i) q^{62} +(0.932224 - 4.08434i) q^{64} +(-0.807411 - 1.01246i) q^{65} +(-9.47831 + 4.56452i) q^{67} +(5.25275 - 2.52959i) q^{68} -0.128384 q^{70} +(6.42831 - 5.44765i) q^{71} +(-0.642582 - 2.81533i) q^{73} +(-2.94433 + 1.41791i) q^{74} -5.48515 q^{76} +(-0.0819274 - 0.102734i) q^{77} +(7.84217 + 9.83378i) q^{79} +(5.12825 - 6.43062i) q^{80} +(-1.25785 + 1.57729i) q^{82} +(-5.92971 + 7.43562i) q^{83} +8.72385 q^{85} +(1.89091 - 0.910612i) q^{86} -1.83140 q^{88} +(-1.33846 - 0.644566i) q^{89} +(-0.0483870 + 0.0233020i) q^{91} +(1.40049 + 6.13593i) q^{92} +(1.00513 - 4.40377i) q^{94} +(-7.39485 - 3.56117i) q^{95} +(-7.57856 + 9.50321i) q^{97} +(0.642392 - 2.81450i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 7 q^{4} + 10 q^{5} - 3 q^{7} - 17 q^{8}+O(q^{10}) $ 30 * q + 3 * q^2 - 7 * q^4 + 10 * q^5 - 3 * q^7 - 17 * q^8	$ 30 q + 3 q^{2} - 7 q^{4} + 10 q^{5} - 3 q^{7} - 17 q^{8} - 22 q^{10} - 7 q^{11} + q^{13} + 2 q^{14} - 15 q^{16} + 24 q^{17} + q^{19} - 8 q^{20} + 19 q^{22} - 21 q^{23} + 12 q^{25} + 32 q^{26} + 13 q^{28} + 11 q^{29} - 30 q^{31} + 5 q^{32} + 15 q^{34} + 44 q^{35} + 37 q^{37} - 24 q^{38} + 10 q^{40} - 16 q^{41} - 43 q^{43} - 33 q^{44} - 54 q^{46} + 16 q^{47} - 8 q^{49} - 20 q^{50} - 53 q^{52} - 65 q^{53} + 13 q^{55} + 21 q^{56} - 12 q^{58} - 30 q^{59} - 18 q^{61} - 8 q^{62} + 17 q^{64} - 14 q^{65} + 29 q^{67} + 13 q^{68} + 64 q^{70} + 5 q^{71} - 61 q^{73} + 35 q^{74} - 58 q^{76} + 82 q^{77} + 55 q^{79} + 22 q^{80} + 18 q^{82} - 45 q^{83} - 22 q^{85} + 89 q^{86} + 112 q^{88} + 8 q^{89} + 35 q^{91} - 17 q^{92} + q^{94} - 50 q^{95} - 26 q^{97} - 7 q^{98}+O(q^{100}) $ 30 * q + 3 * q^2 - 7 * q^4 + 10 * q^5 - 3 * q^7 - 17 * q^8 - 22 * q^10 - 7 * q^11 + q^13 + 2 * q^14 - 15 * q^16 + 24 * q^17 + q^19 - 8 * q^20 + 19 * q^22 - 21 * q^23 + 12 * q^25 + 32 * q^26 + 13 * q^28 + 11 * q^29 - 30 * q^31 + 5 * q^32 + 15 * q^34 + 44 * q^35 + 37 * q^37 - 24 * q^38 + 10 * q^40 - 16 * q^41 - 43 * q^43 - 33 * q^44 - 54 * q^46 + 16 * q^47 - 8 * q^49 - 20 * q^50 - 53 * q^52 - 65 * q^53 + 13 * q^55 + 21 * q^56 - 12 * q^58 - 30 * q^59 - 18 * q^61 - 8 * q^62 + 17 * q^64 - 14 * q^65 + 29 * q^67 + 13 * q^68 + 64 * q^70 + 5 * q^71 - 61 * q^73 + 35 * q^74 - 58 * q^76 + 82 * q^77 + 55 * q^79 + 22 * q^80 + 18 * q^82 - 45 * q^83 - 22 * q^85 + 89 * q^86 + 112 * q^88 + 8 * q^89 + 35 * q^91 - 17 * q^92 + q^94 - 50 * q^95 - 26 * q^97 - 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	−0.0919395	−	0.402813i	−0.0650110	−	0.284832i	0.931964	−	0.362550i	$-0.118094\pi$
$2$	−0.0919395	−	0.402813i	−0.0650110	−	0.284832i	−0.996975	+	0.0777180i	$0.975237\pi$
$3$		0			0
$3$		0			0
$4$	1.64813	−	0.793699i	0.824066	−	0.396849i
$5$	2.73724			1.22413			0.612066	−	0.790806i	$-0.290339\pi$
$5$	2.73724			1.22413			0.612066	+	0.790806i	$0.290339\pi$
$6$		0			0
$7$	0.0252603	−	0.110672i	0.00954748	−	0.0418302i	−0.969930	−	0.243385i	$-0.921742\pi$
$7$	0.0252603	−	0.110672i	0.00954748	−	0.0418302i	0.979477	+	0.201555i	$0.0645993\pi$
$8$	−0.986458	−	1.23698i	−0.348766	−	0.437338i
$9$		0			0
$10$	−0.251661	−	1.10260i	−0.0795821	−	0.348672i
$11$	0.721709	−	0.904995i	0.217604	−	0.272866i	−0.661034	−	0.750356i	$-0.729882\pi$
$11$	0.721709	−	0.904995i	0.217604	−	0.272866i	0.878637	+	0.477490i	$0.158453\pi$
$12$		0			0
$13$	−0.294972	−	0.369884i	−0.0818106	−	0.102587i	0.739242	−	0.673440i	$-0.235184\pi$
$13$	−0.294972	−	0.369884i	−0.0818106	−	0.102587i	−0.821052	+	0.570853i	$0.806613\pi$
$14$	−0.0469027			−0.0125353
$15$		0			0
$16$	1.87351	−	2.34931i	0.468377	−	0.587326i
$17$	3.18709			0.772983			0.386492	−	0.922293i	$-0.373687\pi$
$17$	3.18709			0.772983			0.386492	+	0.922293i	$0.373687\pi$
$18$		0			0
$19$	−2.70157	−	1.30101i	−0.619782	−	0.298471i	0.0975202	−	0.995234i	$-0.468909\pi$
$19$	−2.70157	−	1.30101i	−0.619782	−	0.298471i	−0.717302	+	0.696762i	$0.754623\pi$
$20$	4.51134	−	2.17255i	1.00877	−	0.485796i
$21$		0			0
$22$	−0.430897	−	0.207509i	−0.0918677	−	0.0442411i
$23$	−0.765590	+	3.35427i	−0.159637	+	0.699414i	0.830231	+	0.557420i	$0.188209\pi$
$23$	−0.765590	+	3.35427i	−0.159637	+	0.699414i	−0.989868	+	0.141994i	$0.954649\pi$
$24$		0			0
$25$	2.49250			0.498500
$26$	−0.121874	+	0.152826i	−0.0239015	+	0.0299716i
$27$		0			0
$28$	−0.0462083	−	0.202452i	−0.00873255	−	0.0382598i
$29$	−8.81520	+	4.24518i	−1.63694	+	0.788310i	−0.637096	+	0.770785i	$0.719864\pi$
$29$	−8.81520	+	4.24518i	−1.63694	+	0.788310i	−0.999846	+	0.0175249i	$0.994421\pi$
$30$		0			0
$31$	5.34724	+	6.70523i	0.960393	+	1.20429i	0.978874	+	0.204466i	$0.0655457\pi$
$31$	5.34724	+	6.70523i	0.960393	+	1.20429i	−0.0184806	+	0.999829i	$0.505883\pi$
$32$	−3.96953	−	1.91162i	−0.701720	−	0.337931i
$33$		0			0
$34$	−0.293020	−	1.28380i	−0.0502525	−	0.220170i
$35$	0.0691435	−	0.302937i	0.0116874	−	0.0512058i
$36$		0			0
$37$	−1.76001	−	7.71113i	−0.289345	−	1.26770i	−0.885427	−	0.464778i	$-0.846134\pi$
$37$	−1.76001	−	7.71113i	−0.289345	−	1.26770i	0.596083	−	0.802923i	$-0.296723\pi$
$38$	−0.275682	+	1.20784i	−0.0447215	+	0.195938i
$39$		0			0
$40$	−2.70018	−	3.38591i	−0.426935	−	0.535360i
$41$	−3.04436	−	3.81751i	−0.475449	−	0.596195i	0.485047	−	0.874488i	$-0.338803\pi$
$41$	−3.04436	−	3.81751i	−0.475449	−	0.596195i	−0.960496	+	0.278294i	$0.910231\pi$
$42$		0			0
$43$	1.13032	+	4.95224i	0.172372	+	0.755209i	0.985018	+	0.172452i	$0.0551689\pi$
$43$	1.13032	+	4.95224i	0.172372	+	0.755209i	−0.812646	+	0.582757i	$0.801974\pi$
$44$	0.471179	−	2.06437i	0.0710329	−	0.311216i
$45$		0			0
$46$	1.42153			0.209594
$47$	9.84988	+	4.74345i	1.43675	+	0.691903i	0.980240	−	0.197813i	$-0.0633840\pi$
$47$	9.84988	+	4.74345i	1.43675	+	0.691903i	0.456513	+	0.889717i	$0.349098\pi$
$48$		0			0
$49$	6.29517	+	3.03159i	0.899310	+	0.433085i
$50$	−0.229159	−	1.00401i	−0.0324080	−	0.141989i
$51$		0			0
$52$	−0.779730	−	0.375498i	−0.108129	−	0.0520722i
$53$	−4.08850	−	1.96892i	−0.561599	−	0.270452i	0.131474	−	0.991320i	$-0.458029\pi$
$53$	−4.08850	−	1.96892i	−0.561599	−	0.270452i	−0.693072	+	0.720868i	$0.743743\pi$
$54$		0			0
$55$	1.97549	−	2.47719i	0.266376	−	0.334024i
$56$	−0.161818	+	0.0779273i	−0.0216238	+	0.0104135i
$57$		0			0
$58$	2.52048	+	3.16058i	0.330955	+	0.415005i
$59$	1.50319	−	1.88494i	0.195698	−	0.245398i	−0.674294	−	0.738463i	$-0.735552\pi$
$59$	1.50319	−	1.88494i	0.195698	−	0.245398i	0.869993	+	0.493065i	$0.164123\pi$
$60$		0			0
$61$	−3.45910	−	15.1553i	−0.442892	−	1.94044i	−0.317158	−	0.948373i	$-0.602729\pi$
$61$	−3.45910	−	15.1553i	−0.442892	−	1.94044i	−0.125734	−	0.992064i	$-0.540128\pi$
$62$	2.20933	−	2.77042i	0.280586	−	0.351843i
$63$		0			0
$64$	0.932224	−	4.08434i	0.116528	−	0.510542i
$65$	−0.807411	−	1.01246i	−0.100147	−	0.125580i
$66$		0			0
$67$	−9.47831	+	4.56452i	−1.15796	+	0.557644i	−0.911416	−	0.411487i	$-0.865010\pi$
$67$	−9.47831	+	4.56452i	−1.15796	+	0.557644i	−0.246545	+	0.969131i	$0.579295\pi$
$68$	5.25275	−	2.52959i	0.636989	−	0.306758i
$69$		0			0
$70$	−0.128384			−0.0153448
$71$	6.42831	−	5.44765i	0.762900	−	0.646517i
$71$	6.42831	−	5.44765i	0.762900	−	0.646517i
$72$		0			0
$73$	−0.642582	−	2.81533i	−0.0752085	−	0.329510i	0.923302	−	0.384075i	$-0.125480\pi$
$73$	−0.642582	−	2.81533i	−0.0752085	−	0.329510i	−0.998510	+	0.0545655i	$0.982623\pi$
$74$	−2.94433	+	1.41791i	−0.342271	+	0.164829i
$75$		0			0
$76$	−5.48515			−0.629189
$77$	−0.0819274	−	0.102734i	−0.00933649	−	0.0117076i
$78$		0			0
$79$	7.84217	+	9.83378i	0.882314	+	1.10639i	0.993640	+	0.112602i	$0.0359186\pi$
$79$	7.84217	+	9.83378i	0.882314	+	1.10639i	−0.111327	+	0.993784i	$0.535510\pi$
$80$	5.12825	−	6.43062i	0.573356	−	0.718965i
$81$		0			0
$82$	−1.25785	+	1.57729i	−0.138906	+	0.174182i
$83$	−5.92971	+	7.43562i	−0.650870	+	0.816165i	−0.992315	−	0.123737i	$-0.960512\pi$
$83$	−5.92971	+	7.43562i	−0.650870	+	0.816165i	0.341445	+	0.939902i	$0.389084\pi$
$84$		0			0
$85$	8.72385			0.946234
$86$	1.89091	−	0.910612i	0.203902	−	0.0981938i
$87$		0			0
$88$	−1.83140			−0.195227
$89$	−1.33846	−	0.644566i	−0.141876	−	0.0683239i	0.361599	−	0.932334i	$-0.382231\pi$
$89$	−1.33846	−	0.644566i	−0.141876	−	0.0683239i	−0.503475	+	0.864010i	$0.667945\pi$
$90$		0			0
$91$	−0.0483870	+	0.0233020i	−0.00507234	+	0.00244271i
$92$	1.40049	+	6.13593i	0.146011	+	0.639715i
$93$		0			0
$94$	1.00513	−	4.40377i	0.103671	−	0.454214i
$95$	−7.39485	−	3.56117i	−0.758695	−	0.365368i
$96$		0			0
$97$	−7.57856	+	9.50321i	−0.769486	+	0.964905i	−0.999967	−	0.00817201i	$-0.997399\pi$
$97$	−7.57856	+	9.50321i	−0.769486	+	0.964905i	0.230481	+	0.973077i	$0.425970\pi$
$98$	0.642392	−	2.81450i	0.0648914	−	0.284308i
$99$		0			0
$100$	4.10797	−	1.97830i	0.410797	−	0.197830i
$101$	3.15842	+	3.96053i	0.314275	+	0.394088i	0.913731	−	0.406319i	$-0.133188\pi$
$101$	3.15842	+	3.96053i	0.314275	+	0.394088i	−0.599456	+	0.800407i	$0.704617\pi$
$102$		0			0
$103$	−4.68893	−	2.25807i	−0.462014	−	0.222494i	0.188372	−	0.982098i	$-0.439679\pi$
$103$	−4.68893	−	2.25807i	−0.462014	−	0.222494i	−0.650387	+	0.759603i	$0.725393\pi$
$104$	−0.166561	+	0.729750i	−0.0163326	+	0.0715578i
$105$		0			0
$106$	−0.417212	+	1.82792i	−0.0405232	+	0.177544i
$107$	−1.33368	+	5.84325i	−0.128932	+	0.564888i	0.868652	+	0.495422i	$0.164987\pi$
$107$	−1.33368	+	5.84325i	−0.128932	+	0.564888i	−0.997584	+	0.0694658i	$0.977871\pi$
$108$		0			0
$109$	0.212311	−	0.930196i	0.0203357	−	0.0890966i	−0.963742	−	0.266837i	$-0.914022\pi$
$109$	0.212311	−	0.930196i	0.0203357	−	0.0890966i	0.984077	+	0.177740i	$0.0568787\pi$
$110$	−1.17947	−	0.568003i	−0.112458	−	0.0541570i
$111$		0			0
$112$	−0.212678	−	0.266690i	−0.0200962	−	0.0251998i
$113$	−4.92961	+	2.37398i	−0.463739	+	0.223325i	−0.651138	−	0.758959i	$-0.725708\pi$
$113$	−4.92961	+	2.37398i	−0.463739	+	0.223325i	0.187400	+	0.982284i	$0.439994\pi$
$114$		0			0
$115$	−2.09561	+	9.18146i	−0.195416	+	0.856175i
$116$	−11.1592	+	13.9932i	−1.03611	+	1.29924i
$117$		0			0
$118$	−0.897481	−	0.432204i	−0.0826198	−	0.0397876i
$119$	0.0805068	−	0.352723i	0.00738004	−	0.0323341i
$120$		0			0
$121$	2.14958	+	9.41792i	0.195416	+	0.856175i
$122$	−5.78673	+	2.78674i	−0.523906	+	0.252300i
$123$		0			0
$124$	14.1349	+	6.80701i	1.26935	+	0.611287i
$125$	−6.86363			−0.613902
$126$		0			0
$127$	−13.7028	+	6.59892i	−1.21593	+	0.585560i	−0.928175	−	0.372145i	$-0.878622\pi$
$127$	−13.7028	+	6.59892i	−1.21593	+	0.585560i	−0.287753	+	0.957705i	$0.592908\pi$
$128$	−10.5426			−0.931845
$129$		0			0
$130$	−0.333600	+	0.418321i	−0.0292587	+	0.0366892i
$131$	3.04855	−	3.82276i	0.266353	−	0.333996i	−0.630612	−	0.776099i	$-0.717196\pi$
$131$	3.04855	−	3.82276i	0.266353	−	0.333996i	0.896964	+	0.442103i	$0.145767\pi$
$132$		0			0
$133$	−0.212228	+	0.266125i	−0.0184025	+	0.0230760i
$134$	2.71008	+	3.39833i	0.234115	+	0.293571i
$135$		0			0
$136$	−3.14393	−	3.94237i	−0.269590	−	0.338055i
$137$	16.0887			1.37455			0.687277	−	0.726396i	$-0.258806\pi$
$137$	16.0887			1.37455			0.687277	+	0.726396i	$0.258806\pi$
$138$		0			0
$139$	−7.84735	+	3.77909i	−0.665604	+	0.320538i	−0.736000	−	0.676981i	$-0.763288\pi$
$139$	−7.84735	+	3.77909i	−0.665604	+	0.320538i	0.0703966	+	0.997519i	$0.477574\pi$
$140$	−0.126483	−	0.554160i	−0.0106898	−	0.0468351i
$141$		0			0
$142$	−2.78540	−	2.08855i	−0.233746	−	0.175267i
$143$	−0.547627			−0.0457949
$144$		0			0
$145$	−24.1294	+	11.6201i	−2.00383	+	0.964996i
$146$	−1.07498	+	0.517681i	−0.0889656	+	0.0428436i
$147$		0			0
$148$	−9.02105	−	11.3120i	−0.741525	−	0.929843i
$149$	1.24094	−	5.43690i	0.101661	−	0.445408i	−0.898320	−	0.439341i	$-0.855212\pi$
$149$	1.24094	−	5.43690i	0.101661	−	0.445408i	0.999982	−	0.00606645i	$-0.00193102\pi$
$150$		0			0
$151$	1.26235	−	1.58294i	0.102729	−	0.128818i	−0.727810	−	0.685779i	$-0.759462\pi$
$151$	1.26235	−	1.58294i	0.102729	−	0.128818i	0.830538	+	0.556962i	$0.188033\pi$
$152$	1.05567	+	4.62517i	0.0856257	+	0.375151i
$153$		0			0
$154$	−0.0338501	+	0.0424467i	−0.00272772	+	0.00342046i
$155$	14.6367	+	18.3538i	1.17565	+	1.47422i
$156$		0			0
$157$	−13.4433	+	6.47395i	−1.07289	+	0.516678i	−0.885038	−	0.465519i	$-0.845868\pi$
$157$	−13.4433	+	6.47395i	−1.07289	+	0.516678i	−0.187854	+	0.982197i	$0.560153\pi$
$158$	3.24017	−	4.06304i	0.257774	−	0.323238i
$159$		0			0
$160$	−10.8656	−	5.23258i	−0.858998	−	0.413672i
$161$	0.351886	+	0.169459i	0.0277325	+	0.0133553i
$162$		0			0
$163$	3.91923	+	17.1713i	0.306978	+	1.34496i	0.859362	+	0.511368i	$0.170861\pi$
$163$	3.91923	+	17.1713i	0.306978	+	1.34496i	−0.552384	+	0.833590i	$0.686282\pi$
$164$	−8.04746	−	3.87545i	−0.628401	−	0.302622i
$165$		0			0
$166$	3.54034	+	1.70494i	0.274784	+	0.132329i
$167$	−12.0970			−0.936093			−0.468047	−	0.883704i	$-0.655042\pi$
$167$	−12.0970			−0.936093			−0.468047	+	0.883704i	$0.655042\pi$
$168$		0			0
$169$	2.84297	−	12.4559i	0.218690	−	0.958142i
$170$	−0.802066	−	3.51408i	−0.0615157	−	0.269518i
$171$		0			0
$172$	5.79349	+	7.26481i	0.441750	+	0.553937i
$173$	10.2809	+	12.8918i	0.781639	+	0.980144i	0.999991	+	0.00427419i	$0.00136052\pi$
$173$	10.2809	+	12.8918i	0.781639	+	0.980144i	−0.218352	+	0.975870i	$0.570068\pi$
$174$		0			0
$175$	0.0629613	−	0.275851i	0.00475942	−	0.0208524i
$176$	−0.773981	−	3.39103i	−0.0583410	−	0.255609i
$177$		0			0
$178$	−0.136583	+	0.598409i	−0.0102373	+	0.0448526i
$179$	−0.298256	−	1.30674i	−0.0222927	−	0.0976705i	0.962558	−	0.271077i	$-0.0873798\pi$
$179$	−0.298256	−	1.30674i	−0.0222927	−	0.0976705i	−0.984850	+	0.173406i	$0.944523\pi$
$180$		0			0
$181$	14.4844	+	6.97531i	1.07661	+	0.518470i	0.886233	−	0.463240i	$-0.153313\pi$
$181$	14.4844	+	6.97531i	1.07661	+	0.518470i	0.190382	+	0.981710i	$0.439027\pi$
$182$	0.0138350	+	0.0173486i	0.00102552	+	0.00128596i
$183$		0			0
$184$	4.90439	−	2.36183i	0.361556	−	0.174116i
$185$	−4.81759	−	21.1072i	−0.354196	−	1.55183i
$186$		0			0
$187$	2.30015	−	2.88430i	0.168204	−	0.210921i
$188$	19.9988			1.45856
$189$		0			0
$190$	−0.754608	+	3.30615i	−0.0547450	+	0.239854i
$191$	−14.0360	−	6.75939i	−1.01561	−	0.489093i	−0.149403	−	0.988776i	$-0.547735\pi$
$191$	−14.0360	−	6.75939i	−1.01561	−	0.489093i	−0.866208	+	0.499684i	$0.833450\pi$
$192$		0			0
$193$	8.91665	−	4.29403i	0.641834	−	0.309091i	−0.0845096	−	0.996423i	$-0.526932\pi$
$193$	8.91665	−	4.29403i	0.641834	−	0.309091i	0.726344	+	0.687332i	$0.241218\pi$
$194$	4.52479	+	2.17902i	0.324861	+	0.156445i
$195$		0			0
$196$	12.7814			0.912961
$197$	0.358936	−	0.450092i	0.0255732	−	0.0320677i	−0.768880	−	0.639393i	$-0.779186\pi$
$197$	0.358936	−	0.450092i	0.0255732	−	0.0320677i	0.794454	+	0.607325i	$0.207757\pi$
$198$		0			0
$199$	4.16228			0.295056			0.147528	−	0.989058i	$-0.452868\pi$
$199$	4.16228			0.295056			0.147528	+	0.989058i	$0.452868\pi$
$200$	−2.45875	−	3.08317i	−0.173860	−	0.218013i
$201$		0			0
$202$	1.30497	−	1.63638i	0.0918175	−	0.115136i
$203$	0.247150	+	1.08283i	0.0173465	+	0.0760001i
$204$		0			0
$205$	−8.33316	−	10.4494i	−0.582013	−	0.729821i
$206$	−0.478483	+	2.09637i	−0.0333375	+	0.146061i
$207$		0			0
$208$	−1.42160			−0.0985704
$209$	−3.12715	+	1.50596i	−0.216309	+	0.104169i
$210$		0			0
$211$	−4.77496	−	20.9205i	−0.328722	−	1.44022i	−0.821569	−	0.570109i	$-0.806901\pi$
$211$	−4.77496	−	20.9205i	−0.328722	−	1.44022i	0.492848	−	0.870116i	$-0.335956\pi$
$212$	−8.30112			−0.570123
$213$		0			0
$214$	2.47636			0.169280
$215$	3.09395	+	13.5555i	0.211006	+	0.924476i
$216$		0			0
$217$	0.877157	−	0.422416i	0.0595453	−	0.0286755i
$218$	−0.394215			−0.0266996
$219$		0			0
$220$	1.28973	−	5.65069i	0.0869537	−	0.380969i
$221$	−0.940104	−	1.17885i	−0.0632382	−	0.0792982i
$222$		0			0
$223$	4.78363	+	20.9584i	0.320335	+	1.40348i	0.836958	+	0.547268i	$0.184332\pi$
$223$	4.78363	+	20.9584i	0.320335	+	1.40348i	−0.516622	+	0.856213i	$0.672811\pi$
$224$	−0.311835	+	0.391029i	−0.0208354	+	0.0261267i
$225$		0			0
$226$	1.40949	+	1.76745i	0.0937582	+	0.117569i
$227$	−18.9129			−1.25529			−0.627645	−	0.778500i	$-0.715981\pi$
$227$	−18.9129			−1.25529			−0.627645	+	0.778500i	$0.715981\pi$
$228$		0			0
$229$	−1.60017	+	2.00655i	−0.105742	+	0.132597i	−0.831887	−	0.554946i	$-0.812739\pi$
$229$	−1.60017	+	2.00655i	−0.105742	+	0.132597i	0.726144	+	0.687542i	$0.241310\pi$
$230$	3.89108			0.256570
$231$		0			0
$232$	13.9470	+	6.71653i	0.915667	+	0.440962i
$233$	−18.3061	+	8.81577i	−1.19927	+	0.577540i	−0.923469	−	0.383673i	$-0.874659\pi$
$233$	−18.3061	+	8.81577i	−1.19927	+	0.577540i	−0.275806	+	0.961213i	$0.588945\pi$
$234$		0			0
$235$	26.9615	+	12.9840i	1.75878	+	0.846982i
$236$	0.981380	−	4.29971i	0.0638824	−	0.279887i
$237$		0			0
$238$	−0.149483			−0.00968956
$239$	12.1748	−	15.2667i	0.787523	−	0.987523i	−0.212423	−	0.977178i	$-0.568136\pi$
$239$	12.1748	−	15.2667i	0.787523	−	0.987523i	0.999946	−	0.0103452i	$-0.00329304\pi$
$240$		0			0
$241$	−2.58136	−	11.3097i	−0.166280	−	0.728521i	−0.987462	−	0.157855i	$-0.949542\pi$
$241$	−2.58136	−	11.3097i	−0.166280	−	0.728521i	0.821182	−	0.570666i	$-0.193315\pi$
$242$	3.59603	−	1.73176i	0.231162	−	0.111322i
$243$		0			0
$244$	−17.7298	−	22.2324i	−1.13503	−	1.42329i
$245$	17.2314	+	8.29821i	1.10087	+	0.530153i
$246$		0			0
$247$	0.315667	+	1.38303i	0.0200854	+	0.0879999i
$248$	3.01940	−	13.2289i	0.191732	−	0.840033i
$249$		0			0
$250$	0.631039	+	2.76476i	0.0399104	+	0.174859i
$251$	−3.41791	+	14.9748i	−0.215737	+	0.945204i	0.744852	+	0.667230i	$0.232520\pi$
$251$	−3.41791	+	14.9748i	−0.215737	+	0.945204i	−0.960589	+	0.277974i	$0.910337\pi$
$252$		0			0
$253$	2.48306	+	3.11366i	0.156109	+	0.195754i
$254$	3.91796	+	4.91297i	0.245835	+	0.308267i
$255$		0			0
$256$	−0.895164	−	3.92197i	−0.0559478	−	0.245123i
$257$	5.58982	−	24.4906i	0.348683	−	1.52768i	−0.431490	−	0.902118i	$-0.642012\pi$
$257$	5.58982	−	24.4906i	0.348683	−	1.52768i	0.780173	−	0.625563i	$-0.215131\pi$
$258$		0			0
$259$	−0.897867			−0.0557908
$260$	−2.13431	−	1.02783i	−0.132364	−	0.0637433i
$261$		0			0
$262$	−1.82014	−	0.876533i	−0.112449	−	0.0541524i
$263$	6.77033	+	29.6627i	0.417476	+	1.82908i	0.546522	+	0.837445i	$0.315952\pi$
$263$	6.77033	+	29.6627i	0.417476	+	1.82908i	−0.129046	+	0.991639i	$0.541191\pi$
$264$		0			0
$265$	−11.1912	−	5.38941i	−0.687471	−	0.331069i
$266$	0.126711	+	0.0610207i	0.00776914	+	0.00374142i
$267$		0			0
$268$	−11.9987	+	15.0459i	−0.732935	+	0.919072i
$269$	−2.26411	+	1.09034i	−0.138045	+	0.0664791i	−0.501631	−	0.865082i	$-0.667267\pi$
$269$	−2.26411	+	1.09034i	−0.138045	+	0.0664791i	0.363586	+	0.931561i	$0.381552\pi$
$270$		0			0
$271$	−3.04027	−	3.81237i	−0.184683	−	0.231585i	0.680868	−	0.732406i	$-0.261603\pi$
$271$	−3.04027	−	3.81237i	−0.184683	−	0.231585i	−0.865551	+	0.500821i	$0.833031\pi$
$272$	5.97104	−	7.48745i	0.362048	−	0.453993i
$273$		0			0
$274$	−1.47919	−	6.48076i	−0.0893612	−	0.391517i
$275$	1.79886	−	2.25570i	0.108475	−	0.136024i
$276$		0			0
$277$	4.45215	−	19.5062i	0.267504	−	1.17201i	−0.645403	−	0.763843i	$-0.723310\pi$
$277$	4.45215	−	19.5062i	0.267504	−	1.17201i	0.912907	−	0.408169i	$-0.133832\pi$
$278$	2.24375	+	2.81357i	0.134571	+	0.168747i
$279$		0			0
$280$	−0.442934	+	0.213306i	−0.0264704	+	0.0127475i
$281$	6.94012	−	3.34219i	0.414013	−	0.199378i	−0.215270	−	0.976555i	$-0.569063\pi$
$281$	6.94012	−	3.34219i	0.414013	−	0.199378i	0.629283	+	0.777176i	$0.283349\pi$
$282$		0			0
$283$	9.53939			0.567058			0.283529	−	0.958964i	$-0.408495\pi$
$283$	9.53939			0.567058			0.283529	+	0.958964i	$0.408495\pi$
$284$	6.27091	−	14.0806i	0.372110	−	0.835529i
$285$		0			0
$286$	0.0503486	+	0.220591i	0.00297717	+	0.0130438i
$287$	−0.499394	+	0.240496i	−0.0294783	+	0.0141960i
$288$		0			0
$289$	−6.84245			−0.402497
$290$	6.89917	+	8.65128i	0.405133	+	0.508021i
$291$		0			0
$292$	−3.29359	−	4.13003i	−0.192743	−	0.241692i
$293$	−7.60585	+	9.53744i	−0.444339	+	0.557183i	−0.952681	−	0.303972i	$-0.901687\pi$
$293$	−7.60585	+	9.53744i	−0.444339	+	0.557183i	0.508342	+	0.861155i	$0.330259\pi$
$294$		0			0
$295$	4.11459	−	5.15954i	0.239561	−	0.300400i
$296$	−7.80232	+	9.78381i	−0.453501	+	0.568672i
$297$		0			0
$298$	−2.30414			−0.133476
$299$	1.46652	−	0.706238i	0.0848109	−	0.0408428i
$300$		0			0
$301$	0.576628			0.0332363
$302$	−0.753688	−	0.362957i	−0.0433699	−	0.0208858i
$303$		0			0
$304$	−8.11787	+	3.90936i	−0.465592	+	0.224217i
$305$	−9.46839	−	41.4837i	−0.542159	−	2.37535i
$306$		0			0
$307$	4.06083	−	17.7917i	0.231764	−	1.01542i	−0.716412	−	0.697678i	$-0.754217\pi$
$307$	4.06083	−	17.7917i	0.231764	−	1.01542i	0.948176	−	0.317746i	$-0.102926\pi$
$308$	−0.216567	−	0.104293i	−0.0123400	−	0.00594265i
$309$		0			0
$310$	6.04748	−	7.58330i	0.343474	−	0.430703i
$311$	1.98905	−	8.71461i	0.112789	−	0.494160i	−0.886705	−	0.462336i	$-0.847011\pi$
$311$	1.98905	−	8.71461i	0.112789	−	0.494160i	0.999493	−	0.0318240i	$-0.0101316\pi$
$312$		0			0
$313$	−9.44600	+	4.54895i	−0.533919	+	0.257122i	−0.681359	−	0.731949i	$-0.738611\pi$
$313$	−9.44600	+	4.54895i	−0.533919	+	0.257122i	0.147440	+	0.989071i	$0.452897\pi$
$314$	3.84376	+	4.81993i	0.216916	+	0.272004i
$315$		0			0
$316$	20.7300	+	9.98304i	1.16615	+	0.561590i
$317$	−0.773802	+	3.39025i	−0.0434610	+	0.190415i	−0.991998	−	0.126250i	$-0.959706\pi$
$317$	−0.773802	+	3.39025i	−0.0434610	+	0.190415i	0.948537	+	0.316665i	$0.102563\pi$
$318$		0			0
$319$	−2.52015	+	11.0415i	−0.141101	+	0.618205i
$320$	2.55172	−	11.1798i	0.142646	−	0.624972i
$321$		0			0
$322$	0.0359083	−	0.157324i	0.00200109	−	0.00876735i
$323$	−8.61014	−	4.14643i	−0.479081	−	0.230713i
$324$		0			0
$325$	−0.735219	−	0.921936i	−0.0407826	−	0.0511398i
$326$	6.55648	−	3.15744i	0.363130	−	0.174874i
$327$		0			0
$328$	−1.71904	+	7.53162i	−0.0949183	+	0.415864i
$329$	0.773780	−	0.970289i	0.0426599	−	0.0534938i
$330$		0			0
$331$	0.863422	+	0.415802i	0.0474579	+	0.0228545i	0.457462	−	0.889229i	$-0.348759\pi$
$331$	0.863422	+	0.415802i	0.0474579	+	0.0228545i	−0.410004	+	0.912084i	$0.634473\pi$
$332$	−3.87130	+	16.9613i	−0.212465	+	0.930871i
$333$		0			0
$334$	1.11219	+	4.87283i	0.0608564	+	0.266629i
$335$	−25.9445	+	12.4942i	−1.41750	+	0.682631i
$336$		0			0
$337$	24.8751	+	11.9792i	1.35503	+	0.652550i	0.963523	−	0.267624i	$-0.0862386\pi$
$337$	24.8751	+	11.9792i	1.35503	+	0.652550i	0.391510	+	0.920174i	$0.371953\pi$
$338$	−5.27876			−0.287127
$339$		0			0
$340$	14.3781	−	6.92410i	0.779759	−	0.375512i
$341$	9.92735			0.537596
$342$		0			0
$343$	0.989975	−	1.24139i	0.0534536	−	0.0670287i
$344$	5.01081	−	6.28335i	0.270165	−	0.338776i
$345$		0			0
$346$	4.24777	−	5.32653i	0.228361	−	0.286356i
$347$	−2.94974	−	3.69885i	−0.158350	−	0.198565i	0.696327	−	0.717725i	$-0.254816\pi$
$347$	−2.94974	−	3.69885i	−0.158350	−	0.198565i	−0.854677	+	0.519160i	$0.826245\pi$
$348$		0			0
$349$	−13.7901	−	17.2922i	−0.738167	−	0.925632i	0.261045	−	0.965327i	$-0.415933\pi$
$349$	−13.7901	−	17.2922i	−0.738167	−	0.925632i	−0.999212	+	0.0396950i	$0.987361\pi$
$350$	−0.116905			−0.00624884
$351$		0			0
$352$	−4.59485	+	2.21277i	−0.244907	+	0.117941i
$353$	−1.74848	−	7.66060i	−0.0930624	−	0.407733i	0.906843	−	0.421468i	$-0.138485\pi$
$353$	−1.74848	−	7.66060i	−0.0930624	−	0.407733i	−0.999906	+	0.0137351i	$0.995628\pi$
$354$		0			0
$355$	17.5958	−	14.9115i	0.933890	−	0.791422i
$356$	−2.71754			−0.144029
$357$		0			0
$358$	−0.498952	+	0.240283i	−0.0263704	+	0.0126993i
$359$	15.4561	−	7.44327i	0.815742	−	0.392841i	0.0209936	−	0.999780i	$-0.493317\pi$
$359$	15.4561	−	7.44327i	0.815742	−	0.392841i	0.794748	+	0.606939i	$0.207603\pi$
$360$		0			0
$361$	−6.24046	−	7.82529i	−0.328445	−	0.411857i
$362$	1.47806	−	6.47580i	0.0776851	−	0.340361i
$363$		0			0
$364$	−0.0612534	+	0.0768094i	−0.00321055	+	0.00402591i
$365$	−1.75890	−	7.70625i	−0.0920652	−	0.403364i
$366$		0			0
$367$	6.04747	−	7.58329i	0.315676	−	0.395845i	−0.598527	−	0.801103i	$-0.704247\pi$
$367$	6.04747	−	7.58329i	0.315676	−	0.395845i	0.914202	+	0.405258i	$0.132818\pi$
$368$	6.44586	+	8.08286i	0.336014	+	0.421348i
$369$		0			0
$370$	−8.05935	+	3.88118i	−0.418985	+	0.201773i
$371$	−0.321181	+	0.402749i	−0.0166749	+	0.0209097i
$372$		0			0
$373$	−13.8849	−	6.68661i	−0.718933	−	0.346220i	0.0383880	−	0.999263i	$-0.487778\pi$
$373$	−13.8849	−	6.68661i	−0.718933	−	0.346220i	−0.757321	+	0.653043i	$0.773492\pi$
$374$	−1.37331	−	0.661351i	−0.0710122	−	0.0341977i
$375$		0			0
$376$	−3.84894	−	16.8633i	−0.198494	−	0.869659i
$377$	4.17046	+	2.00839i	0.214790	+	0.103437i
$378$		0			0
$379$	−9.20691	−	4.43381i	−0.472927	−	0.227750i	0.182210	−	0.983260i	$-0.441675\pi$
$379$	−9.20691	−	4.43381i	−0.472927	−	0.227750i	−0.655137	+	0.755510i	$0.727389\pi$
$380$	−15.0142			−0.770211
$381$		0			0
$382$	−1.43231	+	6.27535i	−0.0732833	+	0.321075i
$383$	−5.20551	−	22.8068i	−0.265989	−	1.16537i	−0.914634	−	0.404283i	$-0.867521\pi$
$383$	−5.20551	−	22.8068i	−0.265989	−	1.16537i	0.648645	−	0.761091i	$-0.275336\pi$
$384$		0			0
$385$	−0.224255	−	0.281207i	−0.0114291	−	0.0143316i
$386$	−2.54948	−	3.19695i	−0.129765	−	0.162721i
$387$		0			0
$388$	−4.94778	+	21.6776i	−0.251185	+	1.10052i
$389$	2.54644	+	11.1567i	0.129110	+	0.565666i	0.997555	+	0.0698818i	$0.0222622\pi$
$389$	2.54644	+	11.1567i	0.129110	+	0.565666i	−0.868446	+	0.495784i	$0.834881\pi$
$390$		0			0
$391$	−2.44001	+	10.6904i	−0.123396	+	0.540635i
$392$	−2.45990	−	10.7775i	−0.124244	−	0.544348i
$393$		0			0
$394$	−0.214303	−	0.103203i	−0.0107965	−	0.00519930i
$395$	21.4659	+	26.9174i	1.08007	+	1.35436i
$396$		0			0
$397$	34.1446	−	16.4432i	1.71367	−	0.825259i	0.722699	−	0.691162i	$-0.242901\pi$
$397$	34.1446	−	16.4432i	1.71367	−	0.825259i	0.990968	−	0.134096i	$-0.0428132\pi$
$398$	−0.382678	−	1.67662i	−0.0191819	−	0.0840414i
$399$		0			0
$400$	4.66972	−	5.85565i	0.233486	−	0.292782i
$401$	12.8322			0.640811			0.320405	−	0.947281i	$-0.396181\pi$
$401$	12.8322			0.640811			0.320405	+	0.947281i	$0.396181\pi$
$402$		0			0
$403$	0.902866	−	3.95572i	0.0449750	−	0.197048i
$404$	8.34897	+	4.02065i	0.415377	+	0.200035i
$405$		0			0
$406$	0.413457	−	0.199110i	0.0205195	−	0.00988169i
$407$	−8.24875	−	3.97239i	−0.408875	−	0.196904i
$408$		0			0
$409$	12.9666			0.641158			0.320579	−	0.947222i	$-0.396123\pi$
$409$	12.9666			0.641158			0.320579	+	0.947222i	$0.396123\pi$
$410$	−3.44303	+	4.31742i	−0.170039	+	0.213222i
$411$		0			0
$412$	−9.52021			−0.469027
$413$	−0.170640	−	0.213976i	−0.00839664	−	0.0105290i
$414$		0			0
$415$	−16.2311	+	20.3531i	−0.796751	+	0.999094i
$416$	0.463823	+	2.03214i	0.0227408	+	0.0996338i
$417$		0			0
$418$	0.894128	+	1.12120i	0.0437332	+	0.0548397i
$419$	5.32066	−	23.3114i	0.259931	−	1.13883i	−0.661393	−	0.750040i	$-0.730034\pi$
$419$	5.32066	−	23.3114i	0.259931	−	1.13883i	0.921324	−	0.388795i	$-0.127108\pi$
$420$		0			0
$421$	13.7293			0.669126			0.334563	−	0.942373i	$-0.391411\pi$
$421$	13.7293			0.669126			0.334563	+	0.942373i	$0.391411\pi$
$422$	−7.98803	+	3.84683i	−0.388851	+	0.187261i
$423$		0			0
$424$	1.59762	+	6.99965i	0.0775875	+	0.339933i
$425$	7.94383			0.385333
$426$		0			0
$427$	−1.76465			−0.0853974
$428$	2.43969	+	10.6890i	0.117927	+	0.516671i
$429$		0			0
$430$	5.17587	−	2.49257i	0.249603	−	0.120202i
$431$	22.1272			1.06583			0.532914	−	0.846169i	$-0.321097\pi$
$431$	22.1272			1.06583			0.532914	+	0.846169i	$0.321097\pi$
$432$		0			0
$433$	5.55412	−	24.3342i	0.266914	−	1.16943i	−0.646667	−	0.762772i	$-0.723838\pi$
$433$	5.55412	−	24.3342i	0.266914	−	1.16943i	0.913582	−	0.406655i	$-0.133305\pi$
$434$	−0.250800	−	0.314494i	−0.0120388	−	0.0150962i
$435$		0			0
$436$	−0.388378	−	1.70160i	−0.0185999	−	0.0814917i
$437$	6.43222	−	8.06575i	0.307695	−	0.385837i
$438$		0			0
$439$	−8.90456	−	11.1660i	−0.424991	−	0.532922i	0.522527	−	0.852622i	$-0.324989\pi$
$439$	−8.90456	−	11.1660i	−0.424991	−	0.532922i	−0.947519	+	0.319700i	$0.896418\pi$
$440$	−5.01298			−0.238984
$441$		0			0
$442$	−0.388425	+	0.487070i	−0.0184755	+	0.0231675i
$443$	33.4096			1.58734			0.793669	−	0.608349i	$-0.208168\pi$
$443$	33.4096			1.58734			0.793669	+	0.608349i	$0.208168\pi$
$444$		0			0
$445$	−3.66368	−	1.76433i	−0.173675	−	0.0836375i
$446$	8.00253	−	3.85382i	0.378931	−	0.182484i
$447$		0			0
$448$	−0.428475	−	0.206343i	−0.0202436	−	0.00974879i
$449$	−3.04575	+	13.3443i	−0.143738	+	0.629756i	0.850810	+	0.525473i	$0.176112\pi$
$449$	−3.04575	+	13.3443i	−0.143738	+	0.629756i	−0.994548	+	0.104282i	$0.966745\pi$
$450$		0			0
$451$	−5.65197			−0.266141
$452$	−6.24043	+	7.82525i	−0.293525	+	0.368069i
$453$		0			0
$454$	1.73884	+	7.61835i	0.0816077	+	0.357547i
$455$	−0.132447	+	0.0637831i	−0.00620921	+	0.00299020i
$456$		0			0
$457$	4.60689	+	5.77686i	0.215501	+	0.270230i	0.877818	−	0.478993i	$-0.158998\pi$
$457$	4.60689	+	5.77686i	0.215501	+	0.270230i	−0.662317	+	0.749224i	$0.730427\pi$
$458$	0.955384	+	0.460089i	0.0446422	+	0.0214985i
$459$		0			0
$460$	3.83347	+	16.7955i	0.178736	+	0.783096i
$461$	−2.69008	+	11.7860i	−0.125289	+	0.548929i	0.872852	+	0.487985i	$0.162268\pi$
$461$	−2.69008	+	11.7860i	−0.125289	+	0.548929i	−0.998141	+	0.0609433i	$0.980589\pi$
$462$		0			0
$463$	−0.454213	−	1.99004i	−0.0211091	−	0.0924849i	0.963276	−	0.268513i	$-0.0865322\pi$
$463$	−0.454213	−	1.99004i	−0.0211091	−	0.0924849i	−0.984385	+	0.176028i	$0.943675\pi$
$464$	−6.54214	+	28.6630i	−0.303711	+	1.33065i
$465$		0			0
$466$	5.23416	+	6.56343i	0.242468	+	0.304045i
$467$	−17.9069	−	22.4545i	−0.828631	−	1.03907i	−0.998562	−	0.0536140i	$-0.982926\pi$
$467$	−17.9069	−	22.4545i	−0.828631	−	1.03907i	0.169931	−	0.985456i	$-0.445645\pi$
$468$		0			0
$469$	0.265741	+	1.16429i	0.0122708	+	0.0537619i
$470$	2.75129	−	12.0542i	0.126908	−	0.556019i
$471$		0			0
$472$	−3.81446			−0.175575
$473$	5.29751	+	2.55115i	0.243580	+	0.117302i
$474$		0			0
$475$	−6.73366	−	3.24276i	−0.308962	−	0.148788i
$476$	−0.147270	−	0.645232i	−0.00675011	−	0.0295742i
$477$		0			0
$478$	−7.26899	−	3.50056i	−0.332476	−	0.160112i
$479$	11.2597	+	5.42240i	0.514470	+	0.247756i	0.673059	−	0.739589i	$-0.264980\pi$
$479$	11.2597	+	5.42240i	0.514470	+	0.247756i	−0.158589	+	0.987345i	$0.550694\pi$
$480$		0			0
$481$	−2.33306	+	2.92557i	−0.106379	+	0.133394i
$482$	−4.31837	+	2.07962i	−0.196696	+	0.0947239i
$483$		0			0
$484$	11.0178	+	13.8159i	0.500808	+	0.627994i
$485$	−20.7444	+	26.0126i	−0.941953	+	1.18117i
$486$		0			0
$487$	−6.84636	−	29.9959i	−0.310238	−	1.35924i	−0.854118	−	0.520079i	$-0.825902\pi$
$487$	−6.84636	−	29.9959i	−0.310238	−	1.35924i	0.543880	−	0.839163i	$-0.316955\pi$
$488$	−15.3345	+	19.2289i	−0.694162	+	0.870451i
$489$		0			0
$490$	1.75838	−	7.70398i	0.0794356	−	0.348030i
$491$	−9.94483	−	12.4704i	−0.448804	−	0.562783i	0.505036	−	0.863098i	$-0.331479\pi$
$491$	−9.94483	−	12.4704i	−0.448804	−	0.562783i	−0.953840	+	0.300316i	$0.902908\pi$
$492$		0			0
$493$	−28.0949	+	13.5298i	−1.26533	+	0.609350i
$494$	0.528079	−	0.254309i	0.0237594	−	0.0114419i
$495$		0			0
$496$	25.7707			1.15714
$497$	−0.440524	−	0.849045i	−0.0197602	−	0.0380849i
$498$		0			0
$499$	4.74378	+	20.7839i	0.212361	+	0.930413i	0.962958	+	0.269653i	$0.0869089\pi$
$499$	4.74378	+	20.7839i	0.212361	+	0.930413i	−0.750597	+	0.660760i	$0.770234\pi$
$500$	−11.3122	+	5.44765i	−0.505896	+	0.243627i
$501$		0			0
$502$	6.34631			0.283250
$503$	−25.8724	−	32.4429i	−1.15359	−	1.44656i	−0.873659	−	0.486538i	$-0.838260\pi$
$503$	−25.8724	−	32.4429i	−1.15359	−	1.44656i	−0.279932	−	0.960020i	$-0.590312\pi$
$504$		0			0
$505$	8.64537	+	10.8409i	0.384714	+	0.482416i
$506$	1.02593	−	1.28648i	0.0456083	−	0.0571910i
$507$		0			0
$508$	−17.3465	+	21.7518i	−0.769625	+	0.965080i
$509$	−15.0457	+	18.8667i	−0.666888	+	0.836251i	−0.994074	−	0.108709i	$-0.965328\pi$
$509$	−15.0457	+	18.8667i	−0.666888	+	0.836251i	0.327185	+	0.944960i	$0.393900\pi$
$510$		0			0
$511$	−0.327812			−0.0145015
$512$	−20.4947	+	9.86971i	−0.905745	+	0.436184i
$513$		0			0
$514$	−10.3791			−0.457801
$515$	−12.8348	−	6.18089i	−0.565567	−	0.272363i
$516$		0			0
$517$	11.4015	−	5.49070i	0.501439	−	0.241481i
$518$	0.0825495	+	0.361673i	0.00362702	+	0.0158910i
$519$		0			0
$520$	−0.455917	+	1.99750i	−0.0199933	+	0.0875963i
$521$	−12.4294	−	5.98569i	−0.544543	−	0.262238i	0.141326	−	0.989963i	$-0.454863\pi$
$521$	−12.4294	−	5.98569i	−0.544543	−	0.262238i	−0.685869	+	0.727725i	$0.740578\pi$
$522$		0			0
$523$	4.93839	−	6.19255i	0.215941	−	0.270781i	−0.662049	−	0.749461i	$-0.730313\pi$
$523$	4.93839	−	6.19255i	0.215941	−	0.270781i	0.877990	+	0.478679i	$0.158884\pi$
$524$	1.99029	−	8.72003i	0.0869463	−	0.380936i
$525$		0			0
$526$	11.3261	−	5.45436i	0.493841	−	0.237821i
$527$	17.0422	+	21.3702i	0.742368	+	0.930900i
$528$		0			0
$529$	10.0573	+	4.84333i	0.437273	+	0.210580i
$530$	−1.14201	+	5.00347i	−0.0496057	+	0.217337i
$531$		0			0
$532$	−0.138556	+	0.607054i	−0.00600717	+	0.0263191i
$533$	−0.514031	+	2.25212i	−0.0222652	+	0.0975501i
$534$		0			0
$535$	−3.65061	+	15.9944i	−0.157830	+	0.691498i
$536$	14.9962	+	7.22178i	0.647736	+	0.311933i
$537$		0			0
$538$	0.647363	+	0.811768i	0.0279098	+	0.0349978i
$539$	7.28686	−	3.50917i	0.313867	−	0.151151i
$540$		0			0
$541$	5.96643	−	26.1406i	0.256517	−	1.12387i	−0.668430	−	0.743775i	$-0.733033\pi$
$541$	5.96643	−	26.1406i	0.256517	−	1.12387i	0.924946	−	0.380098i	$-0.124110\pi$
$542$	−1.25615	+	1.57517i	−0.0539564	+	0.0676592i
$543$		0			0
$544$	−12.6512	−	6.09252i	−0.542418	−	0.261215i
$545$	0.581147	−	2.54617i	0.0248936	−	0.109066i
$546$		0			0
$547$	7.70356	+	33.7515i	0.329381	+	1.44311i	0.820314	+	0.571913i	$0.193799\pi$
$547$	7.70356	+	33.7515i	0.329381	+	1.44311i	−0.490933	+	0.871197i	$0.663344\pi$
$548$	26.5164	−	12.7696i	1.13272	−	0.545491i
$549$		0			0
$550$	−1.07401	−	0.517217i	−0.0457961	−	0.0220542i
$551$	29.3379			1.24983
$552$		0			0
$553$	1.28642	−	0.619509i	0.0547043	−	0.0263442i
$554$	−8.26667			−0.351217
$555$		0			0
$556$	−9.93402	+	12.4569i	−0.421296	+	0.528289i
$557$	−0.0629165	+	0.0788949i	−0.00266586	+	0.00334288i	−0.783163	−	0.621817i	$-0.786395\pi$
$557$	−0.0629165	+	0.0788949i	−0.00266586	+	0.00334288i	0.780497	+	0.625160i	$0.214966\pi$
$558$		0			0
$559$	1.49834	−	1.87886i	0.0633730	−	0.0794672i
$560$	−0.582151	−	0.729995i	−0.0246004	−	0.0308479i
$561$		0			0
$562$	−1.98435	−	2.48829i	−0.0837047	−	0.104962i
$563$	−11.5855			−0.488272			−0.244136	−	0.969741i	$-0.578504\pi$
$563$	−11.5855			−0.488272			−0.244136	+	0.969741i	$0.578504\pi$
$564$		0			0
$565$	−13.4935	+	6.49815i	−0.567678	+	0.273379i
$566$	−0.877047	−	3.84259i	−0.0368650	−	0.161516i
$567$		0			0
$568$	−13.0799	−	2.57781i	−0.548820	−	0.108162i
$569$	−28.0690			−1.17672			−0.588358	−	0.808601i	$-0.700225\pi$
$569$	−28.0690			−1.17672			−0.588358	+	0.808601i	$0.700225\pi$
$570$		0			0
$571$	6.96734	−	3.35529i	0.291574	−	0.140415i	−0.282379	−	0.959303i	$-0.591124\pi$
$571$	6.96734	−	3.35529i	0.291574	−	0.140415i	0.573953	+	0.818888i	$0.305409\pi$
$572$	−0.902562	+	0.434651i	−0.0377380	+	0.0181737i
$573$		0			0
$574$	0.142789	+	0.179052i	0.00595989	+	0.00747347i
$575$	−1.90824	+	8.36053i	−0.0795789	+	0.348658i
$576$		0			0
$577$	4.70290	−	5.89726i	0.195784	−	0.245506i	−0.674243	−	0.738510i	$-0.735530\pi$
$577$	4.70290	−	5.89726i	0.195784	−	0.245506i	0.870027	+	0.493004i	$0.164101\pi$
$578$	0.629091	+	2.75623i	0.0261667	+	0.114644i
$579$		0			0
$580$	−30.5455	+	38.3029i	−1.26833	+	1.59044i
$581$	0.673132	+	0.844081i	0.0279262	+	0.0350184i
$582$		0			0
$583$	−4.73257	+	2.27909i	−0.196003	+	0.0943901i
$584$	−2.84863	+	3.57207i	−0.117877	+	0.147813i
$585$		0			0
$586$	4.54109	+	2.18687i	0.187591	+	0.0903388i
$587$	16.5984	+	7.99337i	0.685089	+	0.329922i	0.743846	−	0.668351i	$-0.232999\pi$
$587$	16.5984	+	7.99337i	0.685089	+	0.329922i	−0.0587569	+	0.998272i	$0.518714\pi$
$588$		0			0
$589$	−5.72239	−	25.0714i	−0.235787	−	1.03305i
$590$	−2.45662	−	1.18305i	−0.101138	−	0.0487053i
$591$		0			0
$592$	−21.4132	−	10.3120i	−0.880077	−	0.423823i
$593$	−2.19087			−0.0899684			−0.0449842	−	0.998988i	$-0.514324\pi$
$593$	−2.19087			−0.0899684			−0.0449842	+	0.998988i	$0.514324\pi$
$594$		0			0
$595$	0.220367	−	0.965489i	0.00903415	−	0.0395812i
$596$	−2.27003	−	9.94565i	−0.0929841	−	0.407390i
$597$		0			0
$598$	−0.419313	−	0.525802i	−0.0171470	−	0.0215016i
$599$	−15.4031	−	19.3149i	−0.629355	−	0.789186i	0.360272	−	0.932847i	$-0.382684\pi$
$599$	−15.4031	−	19.3149i	−0.629355	−	0.789186i	−0.989627	+	0.143661i	$0.954112\pi$
$600$		0			0
$601$	−2.52164	+	11.0480i	−0.102860	+	0.450659i	0.897101	+	0.441825i	$0.145669\pi$
$601$	−2.52164	+	11.0480i	−0.102860	+	0.450659i	−0.999961	+	0.00883344i	$0.997188\pi$
$602$	−0.0530149	−	0.232273i	−0.00216073	−	0.00946676i
$603$		0			0
$604$	0.824145	−	3.61081i	0.0335340	−	0.146922i
$605$	5.88392	+	25.7791i	0.239215	+	1.04807i
$606$		0			0
$607$	23.8727	+	11.4965i	0.968962	+	0.466627i	0.850295	−	0.526307i	$-0.176424\pi$
$607$	23.8727	+	11.4965i	0.968962	+	0.466627i	0.118667	+	0.992934i	$0.462138\pi$
$608$	8.23691	+	10.3288i	0.334051	+	0.418886i
$609$		0			0
$610$	−15.8397	+	7.62799i	−0.641330	+	0.308848i
$611$	−1.15092	−	5.04250i	−0.0465611	−	0.203998i
$612$		0			0
$613$	−6.47878	+	8.12413i	−0.261675	+	0.328130i	−0.895261	−	0.445542i	$-0.853011\pi$
$613$	−6.47878	+	8.12413i	−0.261675	+	0.328130i	0.633586	+	0.773673i	$0.281582\pi$
$614$	−7.54007			−0.304292
$615$		0			0
$616$	−0.0462615	+	0.202685i	−0.00186393	+	0.00816641i
$617$	11.3317	+	5.45704i	0.456195	+	0.219692i	0.647846	−	0.761771i	$-0.275670\pi$
$617$	11.3317	+	5.45704i	0.456195	+	0.219692i	−0.191651	+	0.981463i	$0.561384\pi$
$618$		0			0
$619$	−22.1526	+	10.6682i	−0.890390	+	0.428789i	−0.822409	−	0.568897i	$-0.807370\pi$
$619$	−22.1526	+	10.6682i	−0.890390	+	0.428789i	−0.0679814	+	0.997687i	$0.521656\pi$
$620$	38.6906	+	18.6324i	1.55385	+	0.748297i
$621$		0			0
$622$	−3.69323			−0.148085
$623$	−0.105145	+	0.131848i	−0.00421256	+	0.00528239i
$624$		0			0
$625$	−31.2499			−1.25000
$626$	2.70084	+	3.38674i	0.107947	+	0.135362i
$627$		0			0
$628$	−17.0180	+	21.3399i	−0.679091	+	0.851553i
$629$	−5.60933	−	24.5761i	−0.223659	−	0.979912i
$630$		0			0
$631$	−1.46385	−	1.83560i	−0.0582748	−	0.0730742i	0.751840	−	0.659346i	$-0.229167\pi$
$631$	−1.46385	−	1.83560i	−0.0582748	−	0.0730742i	−0.810115	+	0.586271i	$0.800595\pi$
$632$	4.42820	−	19.4012i	0.176144	−	0.771739i
$633$		0			0
$634$	1.43678			0.0570618
$635$	−37.5079	+	18.0629i	−1.48846	+	0.716803i
$636$		0			0
$637$	−0.735564	−	3.22272i	−0.0291441	−	0.127689i
$638$	4.67936			0.185258
$639$		0			0
$640$	−28.8577			−1.14070
$641$	3.92831	+	17.2111i	0.155159	+	0.679796i	0.991338	+	0.131339i	$0.0419276\pi$
$641$	3.92831	+	17.2111i	0.155159	+	0.679796i	−0.836178	+	0.548457i	$0.815215\pi$
$642$		0			0
$643$	−22.9331	+	11.0440i	−0.904394	+	0.435533i	−0.827474	−	0.561504i	$-0.810223\pi$
$643$	−22.9331	+	11.0440i	−0.904394	+	0.435533i	−0.0769201	+	0.997037i	$0.524509\pi$
$644$	0.714455			0.0281535
$645$		0			0
$646$	−0.878623	+	3.84950i	−0.0345690	+	0.151457i
$647$	−6.83699	−	8.57331i	−0.268790	−	0.337052i	0.629058	−	0.777359i	$-0.283441\pi$
$647$	−6.83699	−	8.57331i	−0.268790	−	0.337052i	−0.897847	+	0.440307i	$0.854870\pi$
$648$		0			0
$649$	−0.620995	−	2.72076i	−0.0243762	−	0.106799i
$650$	−0.303772	+	0.380918i	−0.0119149	+	0.0149409i
$651$		0			0
$652$	20.0882	+	25.1898i	0.786716	+	0.986510i
$653$	30.4504			1.19161			0.595807	−	0.803127i	$-0.296832\pi$
$653$	30.4504			1.19161			0.595807	+	0.803127i	$0.296832\pi$
$654$		0			0
$655$	8.34461	−	10.4638i	0.326051	−	0.408855i
$656$	−14.6721			−0.572850
$657$		0			0
$658$	−0.461986	−	0.222481i	−0.0180101	−	0.00867321i
$659$	35.9646	−	17.3197i	1.40098	−	0.674678i	0.427623	−	0.903957i	$-0.359351\pi$
$659$	35.9646	−	17.3197i	1.40098	−	0.674678i	0.973361	+	0.229279i	$0.0736369\pi$
$660$		0			0
$661$	−26.5437	−	12.7828i	−1.03243	−	0.497192i	−0.160610	−	0.987018i	$-0.551346\pi$
$661$	−26.5437	−	12.7828i	−1.03243	−	0.497192i	−0.871820	+	0.489826i	$0.837060\pi$
$662$	0.0881080	−	0.386026i	0.00342441	−	0.0150033i
$663$		0			0
$664$	15.0471			0.583941
$665$	−0.580919	+	0.728450i	−0.0225271	+	0.0282481i
$666$		0			0
$667$	−7.49064	−	32.8186i	−0.290039	−	1.27074i
$668$	−19.9374	+	9.60136i	−0.771402	+	0.371488i
$669$		0			0
$670$	7.41815	+	9.30206i	0.286588	+	0.359370i
$671$	−16.2119	−	7.80725i	−0.625854	−	0.301396i
$672$		0			0
$673$	−1.94289	−	8.51236i	−0.0748930	−	0.328128i	0.923578	−	0.383411i	$-0.125251\pi$
$673$	−1.94289	−	8.51236i	−0.0748930	−	0.328128i	−0.998471	+	0.0552837i	$0.982394\pi$
$674$	2.53838	−	11.1214i	0.0977749	−	0.428380i
$675$		0			0
$676$	−5.20061	−	22.7853i	−0.200023	−	0.876360i
$677$	9.75382	−	42.7343i	0.374870	−	1.64241i	−0.338023	−	0.941138i	$-0.609758\pi$
$677$	9.75382	−	42.7343i	0.374870	−	1.64241i	0.712893	−	0.701273i	$-0.247385\pi$
$678$		0			0
$679$	0.860307	+	1.07879i	0.0330156	+	0.0414002i
$680$	−8.60571	−	10.7912i	−0.330014	−	0.413824i
$681$		0			0
$682$	−0.912716	−	3.99887i	−0.0349497	−	0.153125i
$683$	−4.54964	+	19.9333i	−0.174087	+	0.762725i	0.810201	+	0.586153i	$0.199358\pi$
$683$	−4.54964	+	19.9333i	−0.174087	+	0.762725i	−0.984288	+	0.176572i	$0.943499\pi$
$684$		0			0
$685$	44.0388			1.68264
$686$	−0.591066	−	0.284642i	−0.0225670	−	0.0108677i
$687$		0			0
$688$	13.7520	+	6.62260i	0.524289	+	0.252484i
$689$	0.477724	+	2.09305i	0.0181998	+	0.0797387i
$690$		0			0
$691$	31.5250	+	15.1816i	1.19927	+	0.577537i	0.923467	−	0.383678i	$-0.125343\pi$
$691$	31.5250	+	15.1816i	1.19927	+	0.577537i	0.275801	+	0.961215i	$0.411057\pi$
$692$	27.1764	+	13.0875i	1.03309	+	0.497511i
$693$		0			0
$694$	−1.21875	+	1.52826i	−0.0462631	+	0.0580121i
$695$	−21.4801	+	10.3443i	−0.814787	+	0.392381i
$696$		0			0
$697$	−9.70266	−	12.1667i	−0.367514	−	0.460848i
$698$	−5.69768	+	7.14467i	−0.215661	+	0.270430i
$699$		0			0
$700$	−0.115174	−	0.504612i	−0.00435318	−	0.0190725i
$701$	31.6365	−	39.6709i	1.19489	−	1.49835i	0.373847	−	0.927490i	$-0.378038\pi$
$701$	31.6365	−	39.6709i	1.19489	−	1.49835i	0.821047	−	0.570860i	$-0.193390\pi$
$702$		0			0
$703$	−5.27743	+	23.1219i	−0.199042	+	0.872059i
$704$	−3.02351	−	3.79136i	−0.113953	−	0.142892i
$705$		0			0
$706$	−2.92504	+	1.40862i	−0.110085	+	0.0530143i
$707$	0.518104	−	0.249506i	0.0194853	−	0.00938364i
$708$		0			0
$709$	−12.7113			−0.477383			−0.238692	−	0.971095i	$-0.576719\pi$
$709$	−12.7113			−0.477383			−0.238692	+	0.971095i	$0.576719\pi$
$710$	−7.62432	−	5.71688i	−0.286136	−	0.214551i
$711$		0			0
$712$	0.523015	+	2.29148i	0.0196008	+	0.0858768i
$713$	−26.5850	+	12.8026i	−0.995614	+	0.479463i
$714$		0			0
$715$	−1.49899			−0.0560590
$716$	−1.52872	−	1.91696i	−0.0571311	−	0.0716402i
$717$		0			0
$718$	−4.41927	−	5.54159i	−0.164926	−	0.206810i
$719$	7.77941	−	9.75507i	0.290123	−	0.363803i	−0.615315	−	0.788281i	$-0.710971\pi$
$719$	7.77941	−	9.75507i	0.290123	−	0.363803i	0.905438	+	0.424479i	$0.139543\pi$
$720$		0			0
$721$	−0.368350	+	0.461896i	−0.0137181	+	0.0172019i
$722$	−2.57839	+	3.23319i	−0.0959576	+	0.120327i
$723$		0			0
$724$	29.4084			1.09296
$725$	−21.9719	+	10.5811i	−0.816016	+	0.392973i
$726$		0			0
$727$	9.36147			0.347198			0.173599	−	0.984816i	$-0.444460\pi$
$727$	9.36147			0.347198			0.173599	+	0.984816i	$0.444460\pi$
$728$	0.0765558	+	0.0368673i	0.00283735	+	0.00136639i
$729$		0			0
$730$	−2.94247	+	1.41702i	−0.108906	+	0.0524462i
$731$	3.60242	+	15.7832i	0.133240	+	0.583764i
$732$		0			0
$733$	−7.67153	+	33.6112i	−0.283355	+	1.24146i	0.610107	+	0.792319i	$0.291126\pi$
$733$	−7.67153	+	33.6112i	−0.283355	+	1.24146i	−0.893462	+	0.449139i	$0.851731\pi$
$734$	−3.61065	−	1.73880i	−0.133272	−	0.0641802i
$735$		0			0
$736$	9.45113	−	11.8513i	0.348373	−	0.436846i
$737$	−2.70972	+	11.8721i	−0.0998140	+	0.437314i
$738$		0			0
$739$	−33.2907	+	16.0320i	−1.22462	+	0.589745i	−0.930594	−	0.366053i	$-0.880709\pi$
$739$	−33.2907	+	16.0320i	−1.22462	+	0.589745i	−0.294024	+	0.955798i	$0.594995\pi$
$740$	−24.6928	−	30.9638i	−0.907725	−	1.13825i
$741$		0			0
$742$	0.191762	+	0.0923476i	0.00703980	+	0.00339019i
$743$	−10.2717	+	45.0031i	−0.376831	+	1.65100i	0.330267	+	0.943888i	$0.392861\pi$
$743$	−10.2717	+	45.0031i	−0.376831	+	1.65100i	−0.707098	+	0.707116i	$0.749996\pi$
$744$		0			0
$745$	3.39674	−	14.8821i	0.124447	−	0.545238i
$746$	−1.41689	+	6.20778i	−0.0518759	+	0.227283i
$747$		0			0
$748$	1.50169	−	6.57934i	0.0549073	−	0.240564i
$749$	0.612997	+	0.295204i	0.0223984	+	0.0107865i
$750$		0			0
$751$	−9.37009	−	11.7497i	−0.341919	−	0.428753i	0.580907	−	0.813970i	$-0.302698\pi$
$751$	−9.37009	−	11.7497i	−0.341919	−	0.428753i	−0.922826	+	0.385217i	$0.874127\pi$
$752$	29.5976	−	14.2535i	1.07931	−	0.519771i
$753$		0			0
$754$	0.425576	−	1.86457i	0.0154985	−	0.0679036i
$755$	3.45536	−	4.33288i	0.125753	−	0.157690i
$756$		0			0
$757$	6.99341	+	3.36785i	0.254180	+	0.122407i	0.556635	−	0.830757i	$-0.312092\pi$
$757$	6.99341	+	3.36785i	0.254180	+	0.122407i	−0.302455	+	0.953164i	$0.597806\pi$
$758$	−0.939520	+	4.11631i	−0.0341249	+	0.149511i
$759$		0			0
$760$	2.88961	+	12.6602i	0.104817	+	0.459234i
$761$	−29.2085	+	14.0661i	−1.05881	+	0.509894i	−0.880483	−	0.474078i	$-0.842782\pi$
$761$	−29.2085	+	14.0661i	−1.05881	+	0.509894i	−0.178323	+	0.983972i	$0.557067\pi$
$762$		0			0
$763$	−0.0975840	−	0.0469940i	−0.00353278	−	0.00170130i
$764$	−28.4981			−1.03103
$765$		0			0
$766$	−8.70830	+	4.19370i	−0.314644	+	0.151524i
$767$	−1.14061			−0.0411849
$768$		0			0
$769$	24.5956	−	30.8419i	0.886939	−	1.11219i	−0.106095	−	0.994356i	$-0.533835\pi$
$769$	24.5956	−	30.8419i	0.886939	−	1.11219i	0.993034	−	0.117830i	$-0.0375938\pi$
$770$	−0.0926561	+	0.116187i	−0.00333909	+	0.00418709i
$771$		0			0
$772$	11.2876	−	14.1543i	0.406251	−	0.509423i
$773$	−12.1955	−	15.2927i	−0.438643	−	0.550041i	0.512542	−	0.858662i	$-0.328704\pi$
$773$	−12.1955	−	15.2927i	−0.438643	−	0.550041i	−0.951185	+	0.308621i	$0.900132\pi$
$774$		0			0
$775$	13.3280	+	16.7128i	0.478756	+	0.600342i
$776$	19.2312			0.690360
$777$		0			0
$778$	4.25994	−	2.05148i	0.152726	−	0.0735491i
$779$	3.25794	+	14.2740i	0.116728	+	0.511419i
$780$		0			0
$781$	−0.290725	−	9.74920i	−0.0104030	−	0.348854i
$782$	4.53055			0.162012
$783$		0			0
$784$	18.9162	−	9.10956i	0.675579	−	0.325341i
$785$	−36.7976	+	17.7208i	−1.31336	+	0.632482i
$786$		0			0
$787$	7.46367	+	9.35914i	0.266051	+	0.333617i	0.896855	−	0.442325i	$-0.145846\pi$
$787$	7.46367	+	9.35914i	0.266051	+	0.333617i	−0.630804	+	0.775942i	$0.717275\pi$
$788$	0.234337	−	1.02670i	0.00834792	−	0.0365746i
$789$		0			0
$790$	8.86913	−	11.1215i	0.315550	−	0.395687i
$791$	0.138210	+	0.605539i	0.00491419	+	0.0215305i
$792$		0			0
$793$	−4.58536	+	5.74986i	−0.162831	+	0.204183i
$794$	−9.76276	−	12.2421i	−0.346467	−	0.434456i
$795$		0			0
$796$	6.85998	−	3.30359i	0.243146	−	0.117093i
$797$	23.1637	−	29.0463i	0.820499	−	1.02887i	−0.178491	−	0.983942i	$-0.557121\pi$
$797$	23.1637	−	29.0463i	0.820499	−	1.02887i	0.998990	−	0.0449320i	$-0.0143071\pi$
$798$		0			0
$799$	31.3925	+	15.1178i	1.11059	+	0.534830i
$800$	−9.89406	−	4.76473i	−0.349808	−	0.168459i
$801$		0			0
$802$	−1.17979	−	5.16899i	−0.0416598	−	0.182523i
$803$	−3.01162	−	1.45032i	−0.106278	−	0.0511807i
$804$		0			0
$805$	0.963198	+	0.463852i	0.0339483	+	0.0163486i
$806$	−1.67642			−0.0590495
$807$		0			0
$808$	1.78345	−	7.81380i	0.0627415	−	0.274889i
$809$	2.69087	+	11.7895i	0.0946059	+	0.414496i	0.999948	−	0.0101872i	$-0.00324274\pi$
$809$	2.69087	+	11.7895i	0.0946059	+	0.414496i	−0.905342	+	0.424683i	$0.860386\pi$
$810$		0			0
$811$	2.28426	+	2.86437i	0.0802111	+	0.100582i	0.820318	−	0.571908i	$-0.193796\pi$
$811$	2.28426	+	2.86437i	0.0802111	+	0.100582i	−0.740107	+	0.672489i	$0.765225\pi$
$812$	1.26678	+	1.58849i	0.0444552	+	0.0557451i
$813$		0			0
$814$	−0.841745	+	3.68792i	−0.0295031	+	0.129262i
$815$	10.7279	+	47.0020i	0.375782	+	1.64641i
$816$		0			0
$817$	3.38927	−	14.8493i	0.118575	−	0.519513i
$818$	−1.19214	−	5.22313i	−0.0416823	−	0.182622i
$819$		0			0
$820$	−22.0279	−	10.6081i	−0.769246	−	0.370449i
$821$	−28.9360	−	36.2846i	−1.00987	−	1.26634i	−0.963582	−	0.267412i	$-0.913832\pi$
$821$	−28.9360	−	36.2846i	−1.00987	−	1.26634i	−0.0462900	−	0.998928i	$-0.514740\pi$
$822$		0			0
$823$	−28.6162	+	13.7808i	−0.997499	+	0.480370i	−0.860089	−	0.510144i	$-0.829592\pi$
$823$	−28.6162	+	13.7808i	−0.997499	+	0.480370i	−0.137410	+	0.990514i	$0.543878\pi$
$824$	1.83225	+	8.02761i	0.0638294	+	0.279655i
$825$		0			0
$826$	−0.0705036	+	0.0884088i	−0.00245314	+	0.00307613i
$827$	49.6274			1.72572			0.862858	−	0.505447i	$-0.168672\pi$
$827$	49.6274			1.72572			0.862858	+	0.505447i	$0.168672\pi$
$828$		0			0
$829$	−1.44258	+	6.32037i	−0.0501030	+	0.219516i	−0.993781	−	0.111349i	$-0.964483\pi$
$829$	−1.44258	+	6.32037i	−0.0501030	+	0.219516i	0.943678	+	0.330864i	$0.107340\pi$
$830$	9.69077	+	4.66683i	0.336372	+	0.161988i
$831$		0			0
$832$	−1.78571	+	0.859953i	−0.0619084	+	0.0298135i
$833$	20.0633	+	9.66197i	0.695152	+	0.334767i
$834$		0			0
$835$	−33.1124			−1.14590
$836$	−3.95868	+	4.96403i	−0.136914	+	0.171685i
$837$		0			0
$838$	−9.87930			−0.341275
$839$	17.6970	+	22.1914i	0.610970	+	0.766132i	0.987043	−	0.160458i	$-0.0512972\pi$
$839$	17.6970	+	22.1914i	0.610970	+	0.766132i	−0.376073	+	0.926590i	$0.622726\pi$
$840$		0			0
$841$	41.6051	−	52.1711i	1.43466	−	1.79900i
$842$	−1.26227	−	5.53035i	−0.0435006	−	0.190588i
$843$		0			0
$844$	−24.4743	−	30.6898i	−0.842440	−	1.05639i
$845$	7.78189	−	34.0947i	0.267705	−	1.17289i
$846$		0			0
$847$	1.09660			0.0376797
$848$	−12.2854	+	5.91635i	−0.421883	+	0.203168i
$849$		0			0
$850$	−0.730352	−	3.19988i	−0.0250509	−	0.109755i
$851$	27.2127			0.932838
$852$		0			0
$853$	16.1919			0.554399			0.277199	−	0.960812i	$-0.410594\pi$
$853$	16.1919			0.554399			0.277199	+	0.960812i	$0.410594\pi$
$854$	0.162241	+	0.710825i	0.00555178	+	0.0243239i
$855$		0			0
$856$	8.54360	−	4.11438i	0.292014	−	0.140627i
$857$	48.1901			1.64614			0.823071	−	0.567938i	$-0.192259\pi$
$857$	48.1901			1.64614			0.823071	+	0.567938i	$0.192259\pi$
$858$		0			0
$859$	−3.82673	+	16.7660i	−0.130566	+	0.572049i	0.866744	+	0.498753i	$0.166209\pi$
$859$	−3.82673	+	16.7660i	−0.130566	+	0.572049i	−0.997310	+	0.0732953i	$0.976648\pi$
$860$	15.8582	+	19.8856i	0.540760	+	0.678092i
$861$		0			0
$862$	−2.03436	−	8.91312i	−0.0692906	−	0.303582i
$863$	20.1551	−	25.2737i	0.686088	−	0.860327i	−0.309811	−	0.950798i	$-0.600266\pi$
$863$	20.1551	−	25.2737i	0.686088	−	0.860327i	0.995899	+	0.0904712i	$0.0288373\pi$
$864$		0			0
$865$	28.1412	+	35.2880i	0.956830	+	1.19983i
$866$	−10.3128			−0.350443
$867$		0			0
$868$	1.11040	−	1.39240i	0.0376894	−	0.0472610i
$869$	14.5593			0.493890
$870$		0			0
$871$	4.48418	+	2.15947i	0.151941	+	0.0731708i
$872$	−1.36007	+	0.654975i	−0.0460578	+	0.0221802i
$873$		0			0
$874$	−3.84037	−	1.84942i	−0.129902	−	0.0625576i
$875$	−0.173377	+	0.759615i	−0.00586122	+	0.0256797i
$876$		0			0
$877$	−38.3378			−1.29457			−0.647287	−	0.762246i	$-0.724097\pi$
$877$	−38.3378			−1.29457			−0.647287	+	0.762246i	$0.724097\pi$
$878$	−3.67912	+	4.61347i	−0.124164	+	0.155697i
$879$		0			0
$880$	−2.11857	−	9.28208i	−0.0714171	−	0.312899i
$881$	26.9583	−	12.9824i	0.908249	−	0.437389i	0.0793874	−	0.996844i	$-0.474704\pi$
$881$	26.9583	−	12.9824i	0.908249	−	0.437389i	0.828861	+	0.559454i	$0.188989\pi$
$882$		0			0
$883$	12.4006	+	15.5499i	0.417314	+	0.523296i	0.945407	−	0.325891i	$-0.105664\pi$
$883$	12.4006	+	15.5499i	0.417314	+	0.523296i	−0.528093	+	0.849187i	$0.677093\pi$
$884$	−2.48507	−	1.19675i	−0.0835819	−	0.0402509i
$885$		0			0
$886$	−3.07166	−	13.4578i	−0.103195	−	0.452125i
$887$	−5.08331	+	22.2714i	−0.170681	+	0.747802i	0.815039	+	0.579406i	$0.196716\pi$
$887$	−5.08331	+	22.2714i	−0.170681	+	0.747802i	−0.985720	+	0.168395i	$0.946142\pi$
$888$		0			0
$889$	0.384182	+	1.68321i	0.0128851	+	0.0564532i
$890$	−0.373861	+	1.63799i	−0.0125318	+	0.0549056i
$891$		0			0
$892$	24.5187	+	30.7455i	0.820948	+	1.02944i
$893$	−20.4388	−	25.6295i	−0.683960	−	0.857659i
$894$		0			0
$895$	−0.816398	−	3.57687i	−0.0272892	−	0.119562i
$896$	−0.266309	+	1.16678i	−0.00889677	+	0.0389793i
$897$		0			0
$898$	5.65528			0.188719
$899$	−75.6019	−	36.4080i	−2.52147	−	1.21427i
$900$		0			0
$901$	−13.0304	−	6.27512i	−0.434106	−	0.209055i
$902$	0.519639	+	2.27669i	0.0173021	+	0.0758054i
$903$		0			0
$904$	7.79941	+	3.75600i	0.259405	+	0.124923i
$905$	39.6473	+	19.0931i	1.31792	+	0.634676i
$906$		0			0
$907$	21.2712	−	26.6732i	0.706298	−	0.885670i	−0.291178	−	0.956669i	$-0.594047\pi$
$907$	21.2712	−	26.6732i	0.706298	−	0.885670i	0.997476	+	0.0709987i	$0.0226186\pi$
$908$	−31.1709	+	15.0111i	−1.03444	+	0.498161i
$909$		0			0
$910$	0.0378698	+	0.0474872i	0.00125537	+	0.00157419i
$911$	32.3377	−	40.5502i	1.07140	−	1.34349i	0.135671	−	0.990754i	$-0.456681\pi$
$911$	32.3377	−	40.5502i	1.07140	−	1.34349i	0.935724	−	0.352733i	$-0.114748\pi$
$912$		0			0
$913$	2.44967	+	10.7327i	0.0810723	+	0.355201i
$914$	1.90344	−	2.38684i	0.0629602	−	0.0789496i
$915$		0			0
$916$	−1.04470	+	4.57712i	−0.0345178	+	0.151232i
$917$	−0.346067	−	0.433954i	−0.0114281	−	0.0143304i
$918$		0			0
$919$	20.7524	−	9.99382i	0.684558	−	0.329666i	−0.0590751	−	0.998254i	$-0.518815\pi$
$919$	20.7524	−	9.99382i	0.684558	−	0.329666i	0.743633	+	0.668588i	$0.233101\pi$
$920$	13.4245	−	6.46490i	0.442593	−	0.213141i
$921$		0			0
$922$	4.99488			0.164498
$923$	−3.91117	−	0.770820i	−0.128738	−	0.0253718i
$924$		0			0
$925$	−4.38684	−	19.2200i	−0.144238	−	0.631950i
$926$	−0.759853	+	0.365926i	−0.0249703	+	0.0120251i
$927$		0			0
$928$	43.1074			1.41507
$929$	17.5865	+	22.0527i	0.576993	+	0.723527i	0.981597	−	0.190965i	$-0.0611619\pi$
$929$	17.5865	+	22.0527i	0.576993	+	0.723527i	−0.404603	+	0.914492i	$0.632590\pi$
$930$		0			0
$931$	−13.0627	−	16.3801i	−0.428113	−	0.536837i
$932$	−23.1739	+	29.0591i	−0.759085	+	0.951862i
$933$		0			0
$934$	−7.39862	+	9.27758i	−0.242090	+	0.303572i
$935$	6.29608	−	7.89504i	0.205904	−	0.258195i
$936$		0			0
$937$	−25.9041			−0.846250			−0.423125	−	0.906071i	$-0.639067\pi$
$937$	−25.9041			−0.846250			−0.423125	+	0.906071i	$0.639067\pi$
$938$	0.444559	−	0.214088i	0.0145154	−	0.00699023i
$939$		0			0
$940$	54.7415			1.78547
$941$	−19.7116	−	9.49259i	−0.642579	−	0.309450i	0.0840688	−	0.996460i	$-0.473208\pi$
$941$	−19.7116	−	9.49259i	−0.642579	−	0.309450i	−0.726648	+	0.687010i	$0.758923\pi$
$942$		0			0
$943$	15.1357	−	7.28896i	0.492886	−	0.237361i
$944$	−1.61206	−	7.06290i	−0.0524681	−	0.229878i
$945$		0			0
$946$	0.540585	−	2.36846i	0.0175759	−	0.0770052i
$947$	−1.65914	−	0.799000i	−0.0539148	−	0.0259640i	0.406732	−	0.913547i	$-0.366668\pi$
$947$	−1.65914	−	0.799000i	−0.0539148	−	0.0259640i	−0.460647	+	0.887583i	$0.652383\pi$
$948$		0			0
$949$	−0.851802	+	1.06813i	−0.0276507	+	0.0346728i
$950$	−0.687138	+	3.01055i	−0.0222937	+	0.0976750i
$951$		0			0
$952$	−0.515728	+	0.248361i	−0.0167148	+	0.00804944i
$953$	−30.5617	−	38.3231i	−0.989990	−	1.24141i	−0.970376	−	0.241601i	$-0.922328\pi$
$953$	−30.5617	−	38.3231i	−0.989990	−	1.24141i	−0.0196143	−	0.999808i	$-0.506244\pi$
$954$		0			0
$955$	−38.4200	−	18.5021i	−1.24324	−	0.598714i
$956$	7.94852	−	34.8247i	0.257073	−	1.12631i
$957$		0			0
$958$	1.14900	−	5.03410i	0.0371225	−	0.162644i
$959$	0.406406	−	1.78058i	0.0131235	−	0.0574979i
$960$		0			0
$961$	−9.46896	+	41.4862i	−0.305450	+	1.33827i
$962$	1.39296	+	0.670814i	0.0449108	+	0.0216279i
$963$		0			0
$964$	−13.2309	−	16.5910i	−0.426139	−	0.534362i
$965$	24.4070	−	11.7538i	0.785690	−	0.378368i
$966$		0			0
$967$	12.5211	−	54.8586i	0.402652	−	1.76413i	−0.213937	−	0.976847i	$-0.568629\pi$
$967$	12.5211	−	54.8586i	0.402652	−	1.76413i	0.616589	−	0.787285i	$-0.288514\pi$
$968$	9.52931	−	11.9494i	0.306283	−	0.384067i
$969$		0			0
$970$	12.3854	+	5.96452i	0.397673	+	0.191509i
$971$	−8.03843	+	35.2187i	−0.257965	+	1.13022i	0.665457	+	0.746436i	$0.268237\pi$
$971$	−8.03843	+	35.2187i	−0.257965	+	1.13022i	−0.923423	+	0.383785i	$0.874621\pi$
$972$		0			0
$973$	0.220014	+	0.963946i	0.00705334	+	0.0309027i
$974$	−11.4533	+	5.51561i	−0.366987	+	0.176732i
$975$		0			0
$976$	−42.0851	−	20.2671i	−1.34711	−	0.648734i
$977$	0.221193			0.00707659			0.00353830	−	0.999994i	$-0.498874\pi$
$977$	0.221193			0.00707659			0.00353830	+	0.999994i	$0.498874\pi$
$978$		0			0
$979$	−1.54930	+	0.746106i	−0.0495160	+	0.0238456i
$980$	34.9859			1.11758
$981$		0			0
$982$	−4.10893	+	5.15244i	−0.131121	+	0.164421i
$983$	−36.3636	+	45.5985i	−1.15982	+	1.45437i	−0.292741	+	0.956192i	$0.594567\pi$
$983$	−36.3636	+	45.5985i	−1.15982	+	1.45437i	−0.867077	+	0.498174i	$0.834004\pi$
$984$		0			0
$985$	0.982496	−	1.23201i	0.0313049	−	0.0392552i
$986$	8.03300	+	10.0731i	0.255823	+	0.320792i
$987$		0			0
$988$	1.61797	+	2.02887i	0.0514744	+	0.0645468i
$989$	−17.4765			−0.555720
$990$		0			0
$991$	36.5626	−	17.6076i	1.16145	−	0.559325i	0.248997	−	0.968504i	$-0.419899\pi$
$991$	36.5626	−	17.6076i	1.16145	−	0.559325i	0.912454	+	0.409179i	$0.134185\pi$
$992$	−8.40815	−	36.8385i	−0.266959	−	1.16962i
$993$		0			0
$994$	−0.301505	+	0.255510i	−0.00956316	+	0.00810427i
$995$	11.3932			0.361188
$996$		0			0
$997$	−43.8083	+	21.0970i	−1.38742	+	0.668148i	−0.970569	−	0.240825i	$-0.922582\pi$
$997$	−43.8083	+	21.0970i	−1.38742	+	0.668148i	−0.416855	+	0.908973i	$0.636868\pi$
$998$	7.93587	−	3.82171i	0.251206	−	0.120974i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.j.c.91.2		30
3.2	odd	2		71.2.d.a.20.4	✓	30
71.32	even	7	inner	639.2.j.c.316.2		30
213.23	even	14		5041.2.a.m.1.5		15
213.32	odd	14		71.2.d.a.32.4	yes	30
213.119	odd	14		5041.2.a.l.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.d.a.20.4	✓	30	3.2	odd	2
71.2.d.a.32.4	yes	30	213.32	odd	14
639.2.j.c.91.2		30	1.1	even	1	trivial
639.2.j.c.316.2		30	71.32	even	7	inner
5041.2.a.l.1.5		15	213.119	odd	14
5041.2.a.m.1.5		15	213.23	even	14

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:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.j (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0919395 - 0.402813i) q^{2} +(1.64813 - 0.793699i) q^{4} +2.73724 q^{5} +(0.0252603 - 0.110672i) q^{7} +(-0.986458 - 1.23698i) q^{8} +O(q^{10})\)	\(q+(-0.0919395 - 0.402813i) q^{2} +(1.64813 - 0.793699i) q^{4} +2.73724 q^{5} +(0.0252603 - 0.110672i) q^{7} +(-0.986458 - 1.23698i) q^{8} +(-0.251661 - 1.10260i) q^{10} +(0.721709 - 0.904995i) q^{11} +(-0.294972 - 0.369884i) q^{13} -0.0469027 q^{14} +(1.87351 - 2.34931i) q^{16} +3.18709 q^{17} +(-2.70157 - 1.30101i) q^{19} +(4.51134 - 2.17255i) q^{20} +(-0.430897 - 0.207509i) q^{22} +(-0.765590 + 3.35427i) q^{23} +2.49250 q^{25} +(-0.121874 + 0.152826i) q^{26} +(-0.0462083 - 0.202452i) q^{28} +(-8.81520 + 4.24518i) q^{29} +(5.34724 + 6.70523i) q^{31} +(-3.96953 - 1.91162i) q^{32} +(-0.293020 - 1.28380i) q^{34} +(0.0691435 - 0.302937i) q^{35} +(-1.76001 - 7.71113i) q^{37} +(-0.275682 + 1.20784i) q^{38} +(-2.70018 - 3.38591i) q^{40} +(-3.04436 - 3.81751i) q^{41} +(1.13032 + 4.95224i) q^{43} +(0.471179 - 2.06437i) q^{44} +1.42153 q^{46} +(9.84988 + 4.74345i) q^{47} +(6.29517 + 3.03159i) q^{49} +(-0.229159 - 1.00401i) q^{50} +(-0.779730 - 0.375498i) q^{52} +(-4.08850 - 1.96892i) q^{53} +(1.97549 - 2.47719i) q^{55} +(-0.161818 + 0.0779273i) q^{56} +(2.52048 + 3.16058i) q^{58} +(1.50319 - 1.88494i) q^{59} +(-3.45910 - 15.1553i) q^{61} +(2.20933 - 2.77042i) q^{62} +(0.932224 - 4.08434i) q^{64} +(-0.807411 - 1.01246i) q^{65} +(-9.47831 + 4.56452i) q^{67} +(5.25275 - 2.52959i) q^{68} -0.128384 q^{70} +(6.42831 - 5.44765i) q^{71} +(-0.642582 - 2.81533i) q^{73} +(-2.94433 + 1.41791i) q^{74} -5.48515 q^{76} +(-0.0819274 - 0.102734i) q^{77} +(7.84217 + 9.83378i) q^{79} +(5.12825 - 6.43062i) q^{80} +(-1.25785 + 1.57729i) q^{82} +(-5.92971 + 7.43562i) q^{83} +8.72385 q^{85} +(1.89091 - 0.910612i) q^{86} -1.83140 q^{88} +(-1.33846 - 0.644566i) q^{89} +(-0.0483870 + 0.0233020i) q^{91} +(1.40049 + 6.13593i) q^{92} +(1.00513 - 4.40377i) q^{94} +(-7.39485 - 3.56117i) q^{95} +(-7.57856 + 9.50321i) q^{97} +(0.642392 - 2.81450i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 7 q^{4} + 10 q^{5} - 3 q^{7} - 17 q^{8}+O(q^{10}) \) 30 * q + 3 * q^2 - 7 * q^4 + 10 * q^5 - 3 * q^7 - 17 * q^8	\( 30 q + 3 q^{2} - 7 q^{4} + 10 q^{5} - 3 q^{7} - 17 q^{8} - 22 q^{10} - 7 q^{11} + q^{13} + 2 q^{14} - 15 q^{16} + 24 q^{17} + q^{19} - 8 q^{20} + 19 q^{22} - 21 q^{23} + 12 q^{25} + 32 q^{26} + 13 q^{28} + 11 q^{29} - 30 q^{31} + 5 q^{32} + 15 q^{34} + 44 q^{35} + 37 q^{37} - 24 q^{38} + 10 q^{40} - 16 q^{41} - 43 q^{43} - 33 q^{44} - 54 q^{46} + 16 q^{47} - 8 q^{49} - 20 q^{50} - 53 q^{52} - 65 q^{53} + 13 q^{55} + 21 q^{56} - 12 q^{58} - 30 q^{59} - 18 q^{61} - 8 q^{62} + 17 q^{64} - 14 q^{65} + 29 q^{67} + 13 q^{68} + 64 q^{70} + 5 q^{71} - 61 q^{73} + 35 q^{74} - 58 q^{76} + 82 q^{77} + 55 q^{79} + 22 q^{80} + 18 q^{82} - 45 q^{83} - 22 q^{85} + 89 q^{86} + 112 q^{88} + 8 q^{89} + 35 q^{91} - 17 q^{92} + q^{94} - 50 q^{95} - 26 q^{97} - 7 q^{98}+O(q^{100}) \) 30 * q + 3 * q^2 - 7 * q^4 + 10 * q^5 - 3 * q^7 - 17 * q^8 - 22 * q^10 - 7 * q^11 + q^13 + 2 * q^14 - 15 * q^16 + 24 * q^17 + q^19 - 8 * q^20 + 19 * q^22 - 21 * q^23 + 12 * q^25 + 32 * q^26 + 13 * q^28 + 11 * q^29 - 30 * q^31 + 5 * q^32 + 15 * q^34 + 44 * q^35 + 37 * q^37 - 24 * q^38 + 10 * q^40 - 16 * q^41 - 43 * q^43 - 33 * q^44 - 54 * q^46 + 16 * q^47 - 8 * q^49 - 20 * q^50 - 53 * q^52 - 65 * q^53 + 13 * q^55 + 21 * q^56 - 12 * q^58 - 30 * q^59 - 18 * q^61 - 8 * q^62 + 17 * q^64 - 14 * q^65 + 29 * q^67 + 13 * q^68 + 64 * q^70 + 5 * q^71 - 61 * q^73 + 35 * q^74 - 58 * q^76 + 82 * q^77 + 55 * q^79 + 22 * q^80 + 18 * q^82 - 45 * q^83 - 22 * q^85 + 89 * q^86 + 112 * q^88 + 8 * q^89 + 35 * q^91 - 17 * q^92 + q^94 - 50 * q^95 - 26 * q^97 - 7 * q^98

Introduction

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