LMFDB - Embedded newform 430.2.e.a.221.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

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("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.e (of order $3$, degree $2$, 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:	$3.43356728692$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	430.221
Dual form			430.2.e.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(0.500000 - 0.866025i) q^{10} -6.00000 q^{11} +(-1.50000 + 2.59808i) q^{12} +(-1.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(3.00000 + 5.19615i) q^{18} +(2.00000 - 3.46410i) q^{19} +(-0.500000 + 0.866025i) q^{20} +6.00000 q^{22} +(1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +9.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} -1.00000 q^{32} +(9.00000 - 15.5885i) q^{33} +(-2.00000 - 3.46410i) q^{34} +(-3.00000 - 5.19615i) q^{36} +(4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{40} +5.00000 q^{41} +(-6.50000 + 0.866025i) q^{43} -6.00000 q^{44} +6.00000 q^{45} -3.00000 q^{47} +(-1.50000 + 2.59808i) q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} -12.0000 q^{51} +(-3.00000 + 5.19615i) q^{53} -9.00000 q^{54} +(3.00000 - 5.19615i) q^{55} +(6.00000 + 10.3923i) q^{57} +(4.50000 + 7.79423i) q^{58} +2.00000 q^{59} +(-1.50000 - 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +(2.00000 - 3.46410i) q^{62} +1.00000 q^{64} +(-9.00000 + 15.5885i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-4.00000 - 6.92820i) q^{71} +(3.00000 + 5.19615i) q^{72} +(-4.00000 - 6.92820i) q^{73} +(-4.00000 + 6.92820i) q^{74} +3.00000 q^{75} +(2.00000 - 3.46410i) q^{76} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} -5.00000 q^{82} +(-5.50000 + 9.52628i) q^{83} -4.00000 q^{85} +(6.50000 - 0.866025i) q^{86} +27.0000 q^{87} +6.00000 q^{88} +(-6.50000 + 11.2583i) q^{89} -6.00000 q^{90} +(-6.00000 - 10.3923i) q^{93} +3.00000 q^{94} +(2.00000 + 3.46410i) q^{95} +(1.50000 - 2.59808i) q^{96} -8.00000 q^{97} +(-3.50000 + 6.06218i) q^{98} +(18.0000 + 31.1769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 2 * q^8 - 6 * q^9	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 2 q^{8} - 6 q^{9} + q^{10} - 12 q^{11} - 3 q^{12} - 3 q^{15} + 2 q^{16} + 4 q^{17} + 6 q^{18} + 4 q^{19} - q^{20} + 12 q^{22} + 3 q^{24} - q^{25} + 18 q^{27} - 9 q^{29} + 3 q^{30} - 4 q^{31} - 2 q^{32} + 18 q^{33} - 4 q^{34} - 6 q^{36} + 8 q^{37} - 4 q^{38} + q^{40} + 10 q^{41} - 13 q^{43} - 12 q^{44} + 12 q^{45} - 6 q^{47} - 3 q^{48} + 7 q^{49} + q^{50} - 24 q^{51} - 6 q^{53} - 18 q^{54} + 6 q^{55} + 12 q^{57} + 9 q^{58} + 4 q^{59} - 3 q^{60} + 2 q^{61} + 4 q^{62} + 2 q^{64} - 18 q^{66} - 11 q^{67} + 4 q^{68} - 8 q^{71} + 6 q^{72} - 8 q^{73} - 8 q^{74} + 6 q^{75} + 4 q^{76} - q^{80} - 9 q^{81} - 10 q^{82} - 11 q^{83} - 8 q^{85} + 13 q^{86} + 54 q^{87} + 12 q^{88} - 13 q^{89} - 12 q^{90} - 12 q^{93} + 6 q^{94} + 4 q^{95} + 3 q^{96} - 16 q^{97} - 7 q^{98} + 36 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 2 * q^8 - 6 * q^9 + q^10 - 12 * q^11 - 3 * q^12 - 3 * q^15 + 2 * q^16 + 4 * q^17 + 6 * q^18 + 4 * q^19 - q^20 + 12 * q^22 + 3 * q^24 - q^25 + 18 * q^27 - 9 * q^29 + 3 * q^30 - 4 * q^31 - 2 * q^32 + 18 * q^33 - 4 * q^34 - 6 * q^36 + 8 * q^37 - 4 * q^38 + q^40 + 10 * q^41 - 13 * q^43 - 12 * q^44 + 12 * q^45 - 6 * q^47 - 3 * q^48 + 7 * q^49 + q^50 - 24 * q^51 - 6 * q^53 - 18 * q^54 + 6 * q^55 + 12 * q^57 + 9 * q^58 + 4 * q^59 - 3 * q^60 + 2 * q^61 + 4 * q^62 + 2 * q^64 - 18 * q^66 - 11 * q^67 + 4 * q^68 - 8 * q^71 + 6 * q^72 - 8 * q^73 - 8 * q^74 + 6 * q^75 + 4 * q^76 - q^80 - 9 * q^81 - 10 * q^82 - 11 * q^83 - 8 * q^85 + 13 * q^86 + 54 * q^87 + 12 * q^88 - 13 * q^89 - 12 * q^90 - 12 * q^93 + 6 * q^94 + 4 * q^95 + 3 * q^96 - 16 * q^97 - 7 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.50000	−	2.59808i	0.612372	−	1.06066i
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	−1.00000			−0.353553
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$	−1.50000	+	2.59808i	−0.433013	+	0.750000i
$13$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$13$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$14$		0			0
$15$	−1.50000	−	2.59808i	−0.387298	−	0.670820i
$16$	1.00000			0.250000
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	3.00000	+	5.19615i	0.707107	+	1.22474i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	6.00000			1.27920
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	9.00000			1.73205
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−1.00000			−0.176777
$33$	9.00000	−	15.5885i	1.56670	−	2.71360i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$		0			0
$36$	−3.00000	−	5.19615i	−0.500000	−	0.866025i
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$	−6.50000	+	0.866025i	−0.991241	+	0.132068i
$43$	−6.50000	+	0.866025i	−0.991241	+	0.132068i
$44$	−6.00000			−0.904534
$45$	6.00000			0.894427
$46$		0			0
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.50000	+	2.59808i	−0.216506	+	0.375000i
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−12.0000			−1.68034
$52$		0			0
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	−9.00000			−1.22474
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$		0			0
$57$	6.00000	+	10.3923i	0.794719	+	1.37649i
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	2.00000			0.260378			0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000			0.260378			0.130189	+	0.991489i	$0.458442\pi$
$60$	−1.50000	−	2.59808i	−0.193649	−	0.335410i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	−9.00000	+	15.5885i	−1.10782	+	1.91881i
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$		0			0
$71$	−4.00000	−	6.92820i	−0.474713	−	0.822226i	0.524868	−	0.851184i	$-0.324115\pi$
$71$	−4.00000	−	6.92820i	−0.474713	−	0.822226i	−0.999581	+	0.0289572i	$0.990781\pi$
$72$	3.00000	+	5.19615i	0.353553	+	0.612372i
$73$	−4.00000	−	6.92820i	−0.468165	−	0.810885i	0.531174	−	0.847263i	$-0.321751\pi$
$73$	−4.00000	−	6.92820i	−0.468165	−	0.810885i	−0.999338	+	0.0363782i	$0.988418\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$	3.00000			0.346410
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−5.00000			−0.552158
$83$	−5.50000	+	9.52628i	−0.603703	+	1.04565i	0.388552	+	0.921427i	$0.372976\pi$
$83$	−5.50000	+	9.52628i	−0.603703	+	1.04565i	−0.992255	+	0.124218i	$0.960358\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	6.50000	−	0.866025i	0.700913	−	0.0933859i
$87$	27.0000			2.89470
$88$	6.00000			0.639602
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	0.283164	+	0.959072i	$0.408616\pi$
$89$	−6.50000	+	11.2583i	−0.688999	+	1.19338i	−0.972162	+	0.234309i	$0.924717\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$		0			0
$93$	−6.00000	−	10.3923i	−0.622171	−	1.07763i
$94$	3.00000			0.309426
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	−3.50000	+	6.06218i	−0.353553	+	0.612372i
$99$	18.0000	+	31.1769i	1.80907	+	3.13340i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$	12.0000			1.18818
$103$	−7.50000	−	12.9904i	−0.738997	−	1.27998i	−0.952947	−	0.303136i	$-0.901966\pi$
$103$	−7.50000	−	12.9904i	−0.738997	−	1.27998i	0.213950	−	0.976845i	$-0.431367\pi$
$104$		0			0
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−19.0000			−1.83680			−0.918400	−	0.395654i	$-0.870518\pi$
$107$	−19.0000			−1.83680			−0.918400	+	0.395654i	$0.870518\pi$
$108$	9.00000			0.866025
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.0957826	+	0.995402i	$0.530535\pi$
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	12.0000	+	20.7846i	1.13899	+	1.97279i
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−6.00000	−	10.3923i	−0.561951	−	0.973329i
$115$		0			0
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$		0			0
$118$	−2.00000			−0.184115
$119$		0			0
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	25.0000			2.27273
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$	−7.50000	+	12.9904i	−0.676252	+	1.17130i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	19.0000			1.68598			0.842989	−	0.537931i	$-0.180794\pi$
$127$	19.0000			1.68598			0.842989	+	0.537931i	$0.180794\pi$
$128$	−1.00000			−0.0883883
$129$	7.50000	−	18.1865i	0.660338	−	1.60123i
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	9.00000	−	15.5885i	0.783349	−	1.35680i
$133$		0			0
$134$	5.50000	−	9.52628i	0.475128	−	0.822945i
$135$	−4.50000	+	7.79423i	−0.387298	+	0.670820i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	−4.00000			−0.341743			−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000			−0.341743			−0.170872	+	0.985293i	$0.554658\pi$
$138$		0			0
$139$	−9.00000	+	15.5885i	−0.763370	+	1.32220i	0.177734	+	0.984079i	$0.443123\pi$
$139$	−9.00000	+	15.5885i	−0.763370	+	1.32220i	−0.941104	+	0.338117i	$0.890210\pi$
$140$		0			0
$141$	4.50000	−	7.79423i	0.378968	−	0.656392i
$142$	4.00000	+	6.92820i	0.335673	+	0.581402i
$143$		0			0
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	9.00000			0.747409
$146$	4.00000	+	6.92820i	0.331042	+	0.573382i
$147$	10.5000	+	18.1865i	0.866025	+	1.50000i
$148$	4.00000	−	6.92820i	0.328798	−	0.569495i
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	−0.973028	−	0.230689i	$-0.925902\pi$
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	0.686296	+	0.727322i	$0.259235\pi$
$150$	−3.00000			−0.244949
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	12.0000	−	20.7846i	0.970143	−	1.68034i
$154$		0			0
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	0.775113	−	0.631822i	$-0.217693\pi$
$157$	−2.00000	−	3.46410i	−0.159617	−	0.276465i	−0.934731	+	0.355357i	$0.884359\pi$
$158$		0			0
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$	5.00000			0.390434
$165$	9.00000	+	15.5885i	0.700649	+	1.21356i
$166$	5.50000	−	9.52628i	0.426883	−	0.739383i
$167$	−0.500000	+	0.866025i	−0.0386912	+	0.0670151i	−0.884723	−	0.466118i	$-0.845652\pi$
$167$	−0.500000	+	0.866025i	−0.0386912	+	0.0670151i	0.846031	+	0.533133i	$0.178986\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$	4.00000			0.306786
$171$	−24.0000			−1.83533
$172$	−6.50000	+	0.866025i	−0.495620	+	0.0660338i
$173$	−20.0000			−1.52057			−0.760286	−	0.649589i	$-0.774941\pi$
$173$	−20.0000			−1.52057			−0.760286	+	0.649589i	$0.774941\pi$
$174$	−27.0000			−2.04686
$175$		0			0
$176$	−6.00000			−0.452267
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	6.50000	−	11.2583i	0.487196	−	0.843848i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	6.00000			0.447214
$181$	3.00000	+	5.19615i	0.222988	+	0.386227i	0.955714	−	0.294297i	$-0.0950855\pi$
$181$	3.00000	+	5.19615i	0.222988	+	0.386227i	−0.732726	+	0.680524i	$0.761752\pi$
$182$		0			0
$183$	−6.00000			−0.443533
$184$		0			0
$185$	4.00000	+	6.92820i	0.294086	+	0.509372i
$186$	6.00000	+	10.3923i	0.439941	+	0.762001i
$187$	−12.0000	−	20.7846i	−0.877527	−	1.51992i
$188$	−3.00000			−0.218797
$189$		0			0
$190$	−2.00000	−	3.46410i	−0.145095	−	0.251312i
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$	−1.50000	+	2.59808i	−0.108253	+	0.187500i
$193$	−12.0000			−0.863779			−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000			−0.863779			−0.431889	+	0.901927i	$0.642153\pi$
$194$	8.00000			0.574367
$195$		0			0
$196$	3.50000	−	6.06218i	0.250000	−	0.433013i
$197$	7.00000	+	12.1244i	0.498729	+	0.863825i	0.999999	−	0.00146660i	$-0.000466833\pi$
$197$	7.00000	+	12.1244i	0.498729	+	0.863825i	−0.501270	+	0.865291i	$0.667133\pi$
$198$	−18.0000	−	31.1769i	−1.27920	−	2.21565i
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−16.5000	−	28.5788i	−1.16382	−	2.01580i
$202$	7.50000	+	12.9904i	0.527698	+	0.914000i
$203$		0			0
$204$	−12.0000			−0.840168
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	7.50000	+	12.9904i	0.522550	+	0.905083i
$207$		0			0
$208$		0			0
$209$	−12.0000	+	20.7846i	−0.830057	+	1.43770i
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	24.0000			1.64445
$214$	19.0000			1.29881
$215$	2.50000	−	6.06218i	0.170499	−	0.413437i
$216$	−9.00000			−0.612372
$217$		0			0
$218$	9.50000	−	16.4545i	0.643421	−	1.11444i
$219$	24.0000			1.62177
$220$	3.00000	−	5.19615i	0.202260	−	0.350325i
$221$		0			0
$222$	−12.0000	−	20.7846i	−0.805387	−	1.39497i
$223$	23.0000			1.54019			0.770097	−	0.637927i	$-0.220208\pi$
$223$	23.0000			1.54019			0.770097	+	0.637927i	$0.220208\pi$
$224$		0			0
$225$	−3.00000	+	5.19615i	−0.200000	+	0.346410i
$226$	6.00000			0.399114
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	−14.5000	−	25.1147i	−0.958187	−	1.65963i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−14.5000	−	25.1147i	−0.958187	−	1.65963i	−0.231287	−	0.972886i	$-0.574293\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	+	7.79423i	0.295439	+	0.511716i
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	1.50000	−	2.59808i	0.0978492	−	0.169480i
$236$	2.00000			0.130189
$237$		0			0
$238$		0			0
$239$	−11.0000	+	19.0526i	−0.711531	+	1.23241i	0.252752	+	0.967531i	$0.418664\pi$
$239$	−11.0000	+	19.0526i	−0.711531	+	1.23241i	−0.964282	+	0.264876i	$0.914669\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	−25.0000			−1.60706
$243$		0			0
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$	3.50000	+	6.06218i	0.223607	+	0.387298i
$246$	7.50000	−	12.9904i	0.478183	−	0.828236i
$247$		0			0
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−16.5000	−	28.5788i	−1.04565	−	1.81111i
$250$	−1.00000			−0.0632456
$251$	−5.00000	−	8.66025i	−0.315597	−	0.546630i	0.663967	−	0.747762i	$-0.268872\pi$
$251$	−5.00000	−	8.66025i	−0.315597	−	0.546630i	−0.979564	+	0.201131i	$0.935538\pi$
$252$		0			0
$253$		0			0
$254$	−19.0000			−1.19217
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$	1.00000			0.0625000
$257$	12.0000			0.748539			0.374270	−	0.927320i	$-0.377893\pi$
$257$	12.0000			0.748539			0.374270	+	0.927320i	$0.377893\pi$
$258$	−7.50000	+	18.1865i	−0.466930	+	1.13224i
$259$		0			0
$260$		0			0
$261$	−27.0000	+	46.7654i	−1.67126	+	2.89470i
$262$	−12.0000			−0.741362
$263$	−2.50000	+	4.33013i	−0.154157	+	0.267007i	−0.932752	−	0.360520i	$-0.882599\pi$
$263$	−2.50000	+	4.33013i	−0.154157	+	0.267007i	0.778595	+	0.627527i	$0.215933\pi$
$264$	−9.00000	+	15.5885i	−0.553912	+	0.959403i
$265$	−3.00000	−	5.19615i	−0.184289	−	0.319197i
$266$		0			0
$267$	−19.5000	−	33.7750i	−1.19338	−	2.06700i
$268$	−5.50000	+	9.52628i	−0.335966	+	0.581910i
$269$	27.0000			1.64622			0.823110	−	0.567883i	$-0.192237\pi$
$269$	27.0000			1.64622			0.823110	+	0.567883i	$0.192237\pi$
$270$	4.50000	−	7.79423i	0.273861	−	0.474342i
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	0.991658	+	0.128897i	$0.0411435\pi$
$271$	10.0000	+	17.3205i	0.607457	+	1.05215i	−0.384201	+	0.923249i	$0.625523\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$		0			0
$274$	4.00000			0.241649
$275$	3.00000	+	5.19615i	0.180907	+	0.313340i
$276$		0			0
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	−0.988044	−	0.154172i	$-0.950729\pi$
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	0.627539	+	0.778585i	$0.284062\pi$
$278$	9.00000	−	15.5885i	0.539784	−	0.934934i
$279$	24.0000			1.43684
$280$		0			0
$281$	7.00000	−	12.1244i	0.417585	−	0.723278i	−0.578111	−	0.815958i	$-0.696210\pi$
$281$	7.00000	−	12.1244i	0.417585	−	0.723278i	0.995696	+	0.0926797i	$0.0295433\pi$
$282$	−4.50000	+	7.79423i	−0.267971	+	0.464140i
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$	−4.00000	−	6.92820i	−0.237356	−	0.411113i
$285$	−12.0000			−0.710819
$286$		0			0
$287$		0			0
$288$	3.00000	+	5.19615i	0.176777	+	0.306186i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−9.00000			−0.528498
$291$	12.0000	−	20.7846i	0.703452	−	1.21842i
$292$	−4.00000	−	6.92820i	−0.234082	−	0.405442i
$293$	2.00000			0.116841			0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000			0.116841			0.0584206	+	0.998292i	$0.481394\pi$
$294$	−10.5000	−	18.1865i	−0.612372	−	1.06066i
$295$	−1.00000	+	1.73205i	−0.0582223	+	0.100844i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	−54.0000			−3.13340
$298$	3.50000	−	6.06218i	0.202750	−	0.351173i
$299$		0			0
$300$	3.00000			0.173205
$301$		0			0
$302$	10.0000			0.575435
$303$	45.0000			2.58518
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−2.00000			−0.114520
$306$	−12.0000	+	20.7846i	−0.685994	+	1.18818i
$307$	10.5000	−	18.1865i	0.599267	−	1.03796i	−0.393663	−	0.919255i	$-0.628792\pi$
$307$	10.5000	−	18.1865i	0.599267	−	1.03796i	0.992930	−	0.118705i	$-0.0378744\pi$
$308$		0			0
$309$	45.0000			2.55996
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$		0			0
$313$	−17.0000	+	29.4449i	−0.960897	+	1.66432i	−0.240640	+	0.970614i	$0.577357\pi$
$313$	−17.0000	+	29.4449i	−0.960897	+	1.66432i	−0.720257	+	0.693708i	$0.755976\pi$
$314$	2.00000	+	3.46410i	0.112867	+	0.195491i
$315$		0			0
$316$		0			0
$317$	22.0000			1.23564			0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000			1.23564			0.617822	+	0.786318i	$0.288015\pi$
$318$	9.00000	+	15.5885i	0.504695	+	0.874157i
$319$	27.0000	+	46.7654i	1.51171	+	2.61836i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	28.5000	−	49.3634i	1.59071	−	2.75520i
$322$		0			0
$323$	16.0000			0.890264
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$		0			0
$326$	5.50000	+	9.52628i	0.304617	+	0.527612i
$327$	−28.5000	−	49.3634i	−1.57605	−	2.72980i
$328$	−5.00000			−0.276079
$329$		0			0
$330$	−9.00000	−	15.5885i	−0.495434	−	0.858116i
$331$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$331$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$332$	−5.50000	+	9.52628i	−0.301852	+	0.522823i
$333$	−48.0000			−2.63038
$334$	0.500000	−	0.866025i	0.0273588	−	0.0473868i
$335$	−5.50000	−	9.52628i	−0.300497	−	0.520476i
$336$		0			0
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	0.954164	−	0.299285i	$-0.0967480\pi$
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	−0.736270	+	0.676688i	$0.763415\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$	−4.00000			−0.216930
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$	24.0000			1.29777
$343$		0			0
$344$	6.50000	−	0.866025i	0.350457	−	0.0466930i
$345$		0			0
$346$	20.0000			1.07521
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	−0.234372	−	0.972147i	$-0.575303\pi$
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	0.959090	−	0.283101i	$-0.0913633\pi$
$348$	27.0000			1.44735
$349$	3.50000	−	6.06218i	0.187351	−	0.324501i	−0.757015	−	0.653397i	$-0.773343\pi$
$349$	3.50000	−	6.06218i	0.187351	−	0.324501i	0.944366	+	0.328896i	$0.106677\pi$
$350$		0			0
$351$		0			0
$352$	6.00000			0.319801
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$	8.00000			0.424596
$356$	−6.50000	+	11.2583i	−0.344499	+	0.596690i
$357$		0			0
$358$		0			0
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	0.775934	−	0.630814i	$-0.217279\pi$
$359$	−3.00000	−	5.19615i	−0.158334	−	0.274242i	−0.934268	+	0.356572i	$0.883946\pi$
$360$	−6.00000			−0.316228
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−3.00000	−	5.19615i	−0.157676	−	0.273104i
$363$	−37.5000	+	64.9519i	−1.96824	+	3.40909i
$364$		0			0
$365$	8.00000			0.418739
$366$	6.00000			0.313625
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$	−15.0000	−	25.9808i	−0.780869	−	1.35250i
$370$	−4.00000	−	6.92820i	−0.207950	−	0.360180i
$371$		0			0
$372$	−6.00000	−	10.3923i	−0.311086	−	0.538816i
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$	12.0000	+	20.7846i	0.620505	+	1.07475i
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$	3.00000			0.154713
$377$		0			0
$378$		0			0
$379$	−30.0000			−1.54100			−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000			−1.54100			−0.770498	+	0.637442i	$0.779993\pi$
$380$	2.00000	+	3.46410i	0.102598	+	0.177705i
$381$	−28.5000	+	49.3634i	−1.46010	+	2.52897i
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	1.00000			0.0510976			0.0255488	−	0.999674i	$-0.491867\pi$
$383$	1.00000			0.0510976			0.0255488	+	0.999674i	$0.491867\pi$
$384$	1.50000	−	2.59808i	0.0765466	−	0.132583i
$385$		0			0
$386$	12.0000			0.610784
$387$	24.0000	+	31.1769i	1.21999	+	1.58481i
$388$	−8.00000			−0.406138
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$		0			0
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$	−18.0000	+	31.1769i	−0.907980	+	1.57267i
$394$	−7.00000	−	12.1244i	−0.352655	−	0.610816i
$395$		0			0
$396$	18.0000	+	31.1769i	0.904534	+	1.56670i
$397$	−19.0000	+	32.9090i	−0.953583	+	1.65165i	−0.216004	+	0.976392i	$0.569302\pi$
$397$	−19.0000	+	32.9090i	−0.953583	+	1.65165i	−0.737579	+	0.675261i	$0.764031\pi$
$398$	2.00000			0.100251
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	5.00000	+	8.66025i	0.249688	+	0.432472i	0.963439	−	0.267927i	$-0.0863386\pi$
$401$	5.00000	+	8.66025i	0.249688	+	0.432472i	−0.713751	+	0.700399i	$0.753005\pi$
$402$	16.5000	+	28.5788i	0.822945	+	1.42538i
$403$		0			0
$404$	−7.50000	−	12.9904i	−0.373139	−	0.646296i
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$		0			0
$407$	−24.0000	+	41.5692i	−1.18964	+	2.06051i
$408$	12.0000			0.594089
$409$	−17.0000			−0.840596			−0.420298	−	0.907386i	$-0.638074\pi$
$409$	−17.0000			−0.840596			−0.420298	+	0.907386i	$0.638074\pi$
$410$	2.50000	−	4.33013i	0.123466	−	0.213850i
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$	−7.50000	−	12.9904i	−0.369498	−	0.639990i
$413$		0			0
$414$		0			0
$415$	−5.50000	−	9.52628i	−0.269984	−	0.467627i
$416$		0			0
$417$	−27.0000	−	46.7654i	−1.32220	−	2.29011i
$418$	12.0000	−	20.7846i	0.586939	−	1.01661i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	0.999109	−	0.0422075i	$-0.0134391\pi$
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	−0.536107	+	0.844150i	$0.680106\pi$
$422$	4.00000			0.194717
$423$	9.00000	+	15.5885i	0.437595	+	0.757937i
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	−24.0000			−1.16280
$427$		0			0
$428$	−19.0000			−0.918400
$429$		0			0
$430$	−2.50000	+	6.06218i	−0.120561	+	0.292344i
$431$	30.0000			1.44505			0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000			1.44505			0.722525	+	0.691345i	$0.242982\pi$
$432$	9.00000			0.433013
$433$	−14.0000	+	24.2487i	−0.672797	+	1.16532i	0.304311	+	0.952573i	$0.401574\pi$
$433$	−14.0000	+	24.2487i	−0.672797	+	1.16532i	−0.977108	+	0.212746i	$0.931759\pi$
$434$		0			0
$435$	−13.5000	+	23.3827i	−0.647275	+	1.12111i
$436$	−9.50000	+	16.4545i	−0.454967	+	0.788027i
$437$		0			0
$438$	−24.0000			−1.14676
$439$	−17.0000	−	29.4449i	−0.811366	−	1.40533i	−0.911908	−	0.410394i	$-0.865391\pi$
$439$	−17.0000	−	29.4449i	−0.811366	−	1.40533i	0.100543	−	0.994933i	$-0.467942\pi$
$440$	−3.00000	+	5.19615i	−0.143019	+	0.247717i
$441$	−42.0000			−2.00000
$442$		0			0
$443$	−13.5000	−	23.3827i	−0.641404	−	1.11094i	−0.985119	−	0.171871i	$-0.945019\pi$
$443$	−13.5000	−	23.3827i	−0.641404	−	1.11094i	0.343715	−	0.939074i	$-0.388315\pi$
$444$	12.0000	+	20.7846i	0.569495	+	0.986394i
$445$	−6.50000	−	11.2583i	−0.308130	−	0.533696i
$446$	−23.0000			−1.08908
$447$	−10.5000	−	18.1865i	−0.496633	−	0.860194i
$448$		0			0
$449$	−3.50000	+	6.06218i	−0.165175	+	0.286092i	−0.936717	−	0.350086i	$-0.886152\pi$
$449$	−3.50000	+	6.06218i	−0.165175	+	0.286092i	0.771542	+	0.636178i	$0.219486\pi$
$450$	3.00000	−	5.19615i	0.141421	−	0.244949i
$451$	−30.0000			−1.41264
$452$	−6.00000			−0.282216
$453$	15.0000	−	25.9808i	0.704761	−	1.22068i
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$		0			0
$456$	−6.00000	−	10.3923i	−0.280976	−	0.486664i
$457$	−30.0000			−1.40334			−0.701670	−	0.712502i	$-0.747562\pi$
$457$	−30.0000			−1.40334			−0.701670	+	0.712502i	$0.747562\pi$
$458$	14.5000	+	25.1147i	0.677541	+	1.17353i
$459$	18.0000	+	31.1769i	0.840168	+	1.45521i
$460$		0			0
$461$	2.50000	−	4.33013i	0.116437	−	0.201674i	−0.801917	−	0.597436i	$-0.796186\pi$
$461$	2.50000	−	4.33013i	0.116437	−	0.201674i	0.918353	+	0.395762i	$0.129519\pi$
$462$		0			0
$463$	8.50000	−	14.7224i	0.395029	−	0.684209i	−0.598076	−	0.801439i	$-0.704068\pi$
$463$	8.50000	−	14.7224i	0.395029	−	0.684209i	0.993105	+	0.117230i	$0.0374014\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$	12.0000			0.556487
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−2.00000	+	3.46410i	−0.0925490	+	0.160300i	−0.908583	−	0.417704i	$-0.862835\pi$
$467$	−2.00000	+	3.46410i	−0.0925490	+	0.160300i	0.816034	+	0.578004i	$0.196168\pi$
$468$		0			0
$469$		0			0
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	12.0000			0.552931
$472$	−2.00000			−0.0920575
$473$	39.0000	−	5.19615i	1.79322	−	0.238919i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	36.0000			1.64833
$478$	11.0000	−	19.0526i	0.503128	−	0.871444i
$479$	−17.0000	+	29.4449i	−0.776750	+	1.34537i	0.157056	+	0.987590i	$0.449800\pi$
$479$	−17.0000	+	29.4449i	−0.776750	+	1.34537i	−0.933806	+	0.357780i	$0.883534\pi$
$480$	1.50000	+	2.59808i	0.0684653	+	0.118585i
$481$		0			0
$482$	−5.50000	−	9.52628i	−0.250518	−	0.433910i
$483$		0			0
$484$	25.0000			1.13636
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$		0			0
$487$	11.5000	+	19.9186i	0.521115	+	0.902597i	0.999698	+	0.0245553i	$0.00781698\pi$
$487$	11.5000	+	19.9186i	0.521115	+	0.902597i	−0.478584	+	0.878042i	$0.658850\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	33.0000			1.49231
$490$	−3.50000	−	6.06218i	−0.158114	−	0.273861i
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$	−7.50000	+	12.9904i	−0.338126	+	0.585652i
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$		0			0
$495$	−36.0000			−1.61808
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$		0			0
$498$	16.5000	+	28.5788i	0.739383	+	1.28065i
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	0.925329	−	0.379165i	$-0.123789\pi$
$499$	3.00000	+	5.19615i	0.134298	+	0.232612i	−0.791031	+	0.611776i	$0.790455\pi$
$500$	1.00000			0.0447214
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$	5.00000	+	8.66025i	0.223161	+	0.386526i
$503$	−12.5000	−	21.6506i	−0.557347	−	0.965354i	−0.997717	−	0.0675374i	$-0.978486\pi$
$503$	−12.5000	−	21.6506i	−0.557347	−	0.965354i	0.440369	−	0.897817i	$-0.354848\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$		0			0
$507$	19.5000	+	33.7750i	0.866025	+	1.50000i
$508$	19.0000			0.842989
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	0.748894	−	0.662690i	$-0.230585\pi$
$509$	−4.50000	−	7.79423i	−0.199459	−	0.345473i	−0.948353	+	0.317217i	$0.897252\pi$
$510$	−6.00000	+	10.3923i	−0.265684	+	0.460179i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	18.0000	−	31.1769i	0.794719	−	1.37649i
$514$	−12.0000			−0.529297
$515$	15.0000			0.660979
$516$	7.50000	−	18.1865i	0.330169	−	0.800617i
$517$	18.0000			0.791639
$518$		0			0
$519$	30.0000	−	51.9615i	1.31685	−	2.28086i
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	27.0000	−	46.7654i	1.18176	−	2.04686i
$523$	−13.5000	−	23.3827i	−0.590314	−	1.02245i	−0.994190	−	0.107640i	$-0.965671\pi$
$523$	−13.5000	−	23.3827i	−0.590314	−	1.02245i	0.403876	−	0.914814i	$-0.367663\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	2.50000	−	4.33013i	0.109005	−	0.188803i
$527$	−16.0000			−0.696971
$528$	9.00000	−	15.5885i	0.391675	−	0.678401i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$		0			0
$533$		0			0
$534$	19.5000	+	33.7750i	0.843848	+	1.46159i
$535$	9.50000	−	16.4545i	0.410721	−	0.711389i
$536$	5.50000	−	9.52628i	0.237564	−	0.411473i
$537$		0			0
$538$	−27.0000			−1.16405
$539$	−21.0000	+	36.3731i	−0.904534	+	1.56670i
$540$	−4.50000	+	7.79423i	−0.193649	+	0.335410i
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	−10.0000	−	17.3205i	−0.429537	−	0.743980i
$543$	−18.0000			−0.772454
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$	−9.50000	−	16.4545i	−0.406935	−	0.704833i
$546$		0			0
$547$	−13.5000	+	23.3827i	−0.577218	+	0.999771i	0.418578	+	0.908181i	$0.362529\pi$
$547$	−13.5000	+	23.3827i	−0.577218	+	0.999771i	−0.995797	+	0.0915908i	$0.970805\pi$
$548$	−4.00000			−0.170872
$549$	6.00000	−	10.3923i	0.256074	−	0.443533i
$550$	−3.00000	−	5.19615i	−0.127920	−	0.221565i
$551$	−36.0000			−1.53365
$552$		0			0
$553$		0			0
$554$	6.00000	−	10.3923i	0.254916	−	0.441527i
$555$	−24.0000			−1.01874
$556$	−9.00000	+	15.5885i	−0.381685	+	0.661098i
$557$	−38.0000			−1.61011			−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000			−1.61011			−0.805056	+	0.593199i	$0.797865\pi$
$558$	−24.0000			−1.01600
$559$		0			0
$560$		0			0
$561$	72.0000			3.03984
$562$	−7.00000	+	12.1244i	−0.295277	+	0.511435i
$563$	21.0000			0.885044			0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000			0.885044			0.442522	+	0.896758i	$0.354084\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$	−8.00000	−	13.8564i	−0.336265	−	0.582428i
$567$		0			0
$568$	4.00000	+	6.92820i	0.167836	+	0.290701i
$569$	20.5000	−	35.5070i	0.859405	−	1.48853i	−0.0130929	−	0.999914i	$-0.504168\pi$
$569$	20.5000	−	35.5070i	0.859405	−	1.48853i	0.872498	−	0.488618i	$-0.162499\pi$
$570$	12.0000			0.502625
$571$	19.0000	−	32.9090i	0.795125	−	1.37720i	−0.127634	−	0.991821i	$-0.540738\pi$
$571$	19.0000	−	32.9090i	0.795125	−	1.37720i	0.922760	−	0.385376i	$-0.125928\pi$
$572$		0			0
$573$	18.0000	+	31.1769i	0.751961	+	1.30243i
$574$		0			0
$575$		0			0
$576$	−3.00000	−	5.19615i	−0.125000	−	0.216506i
$577$	−16.0000	−	27.7128i	−0.666089	−	1.15370i	−0.978989	−	0.203913i	$-0.934634\pi$
$577$	−16.0000	−	27.7128i	−0.666089	−	1.15370i	0.312900	−	0.949786i	$-0.398699\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	18.0000	−	31.1769i	0.748054	−	1.29567i
$580$	9.00000			0.373705
$581$		0			0
$582$	−12.0000	+	20.7846i	−0.497416	+	0.861550i
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	4.00000	+	6.92820i	0.165521	+	0.286691i
$585$		0			0
$586$	−2.00000			−0.0826192
$587$	−11.5000	−	19.9186i	−0.474656	−	0.822128i	0.524923	−	0.851150i	$-0.324094\pi$
$587$	−11.5000	−	19.9186i	−0.474656	−	0.822128i	−0.999579	+	0.0290218i	$0.990761\pi$
$588$	10.5000	+	18.1865i	0.433013	+	0.750000i
$589$	8.00000	+	13.8564i	0.329634	+	0.570943i
$590$	1.00000	−	1.73205i	0.0411693	−	0.0713074i
$591$	−42.0000			−1.72765
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$	54.0000			2.21565
$595$		0			0
$596$	−3.50000	+	6.06218i	−0.143366	+	0.248316i
$597$	3.00000	−	5.19615i	0.122782	−	0.212664i
$598$		0			0
$599$	2.00000	−	3.46410i	0.0817178	−	0.141539i	−0.822270	−	0.569097i	$-0.807293\pi$
$599$	2.00000	−	3.46410i	0.0817178	−	0.141539i	0.903988	+	0.427558i	$0.140626\pi$
$600$	−3.00000			−0.122474
$601$	−23.0000			−0.938190			−0.469095	−	0.883148i	$-0.655420\pi$
$601$	−23.0000			−0.938190			−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$	66.0000			2.68773
$604$	−10.0000			−0.406894
$605$	−12.5000	+	21.6506i	−0.508197	+	0.880223i
$606$	−45.0000			−1.82800
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	−2.00000	+	3.46410i	−0.0811107	+	0.140488i
$609$		0			0
$610$	2.00000			0.0809776
$611$		0			0
$612$	12.0000	−	20.7846i	0.485071	−	0.840168i
$613$	−32.0000			−1.29247			−0.646234	−	0.763139i	$-0.723657\pi$
$613$	−32.0000			−1.29247			−0.646234	+	0.763139i	$0.723657\pi$
$614$	−10.5000	+	18.1865i	−0.423746	+	0.733949i
$615$	−7.50000	−	12.9904i	−0.302429	−	0.523823i
$616$		0			0
$617$	18.0000	+	31.1769i	0.724653	+	1.25514i	0.959117	+	0.283011i	$0.0913331\pi$
$617$	18.0000	+	31.1769i	0.724653	+	1.25514i	−0.234464	+	0.972125i	$0.575334\pi$
$618$	−45.0000			−1.81017
$619$	3.00000	+	5.19615i	0.120580	+	0.208851i	0.919997	−	0.391926i	$-0.128191\pi$
$619$	3.00000	+	5.19615i	0.120580	+	0.208851i	−0.799416	+	0.600777i	$0.794858\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$		0			0
$622$	4.00000	−	6.92820i	0.160385	−	0.277796i
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	17.0000	−	29.4449i	0.679457	−	1.17685i
$627$	−36.0000	−	62.3538i	−1.43770	−	2.49017i
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$	32.0000			1.27592
$630$		0			0
$631$	5.00000	+	8.66025i	0.199047	+	0.344759i	0.948220	−	0.317615i	$-0.102882\pi$
$631$	5.00000	+	8.66025i	0.199047	+	0.344759i	−0.749173	+	0.662375i	$0.769549\pi$
$632$		0			0
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$	−22.0000			−0.873732
$635$	−9.50000	+	16.4545i	−0.376996	+	0.652976i
$636$	−9.00000	−	15.5885i	−0.356873	−	0.618123i
$637$		0			0
$638$	−27.0000	−	46.7654i	−1.06894	−	1.85146i
$639$	−24.0000	+	41.5692i	−0.949425	+	1.64445i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	45.0000			1.77739			0.888697	−	0.458496i	$-0.151612\pi$
$641$	45.0000			1.77739			0.888697	+	0.458496i	$0.151612\pi$
$642$	−28.5000	+	49.3634i	−1.12481	+	1.94822i
$643$	−33.0000			−1.30139			−0.650696	−	0.759338i	$-0.725523\pi$
$643$	−33.0000			−1.30139			−0.650696	+	0.759338i	$0.725523\pi$
$644$		0			0
$645$	12.0000	+	15.5885i	0.472500	+	0.613795i
$646$	−16.0000			−0.629512
$647$	17.0000			0.668339			0.334169	−	0.942513i	$-0.391544\pi$
$647$	17.0000			0.668339			0.334169	+	0.942513i	$0.391544\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−12.0000			−0.471041
$650$		0			0
$651$		0			0
$652$	−5.50000	−	9.52628i	−0.215397	−	0.373078i
$653$	14.0000			0.547862			0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000			0.547862			0.273931	+	0.961749i	$0.411676\pi$
$654$	28.5000	+	49.3634i	1.11444	+	1.93026i
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$	5.00000			0.195217
$657$	−24.0000	+	41.5692i	−0.936329	+	1.62177i
$658$		0			0
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	0.918523	−	0.395367i	$-0.129383\pi$
$659$	3.00000	+	5.19615i	0.116863	+	0.202413i	−0.801660	+	0.597781i	$0.796049\pi$
$660$	9.00000	+	15.5885i	0.350325	+	0.606780i
$661$	−26.0000			−1.01128			−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000			−1.01128			−0.505641	+	0.862744i	$0.668744\pi$
$662$		0			0
$663$		0			0
$664$	5.50000	−	9.52628i	0.213441	−	0.369691i
$665$		0			0
$666$	48.0000			1.85996
$667$		0			0
$668$	−0.500000	+	0.866025i	−0.0193456	+	0.0335075i
$669$	−34.5000	+	59.7558i	−1.33385	+	2.31029i
$670$	5.50000	+	9.52628i	0.212484	+	0.368032i
$671$	−6.00000	−	10.3923i	−0.231627	−	0.401190i
$672$		0			0
$673$	−8.00000	−	13.8564i	−0.308377	−	0.534125i	0.669630	−	0.742695i	$-0.266453\pi$
$673$	−8.00000	−	13.8564i	−0.308377	−	0.534125i	−0.978008	+	0.208569i	$0.933119\pi$
$674$	−4.00000	−	6.92820i	−0.154074	−	0.266864i
$675$	−4.50000	−	7.79423i	−0.173205	−	0.300000i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	14.0000			0.538064			0.269032	−	0.963131i	$-0.413296\pi$
$677$	14.0000			0.538064			0.269032	+	0.963131i	$0.413296\pi$
$678$	−9.00000	+	15.5885i	−0.345643	+	0.598671i
$679$		0			0
$680$	4.00000			0.153393
$681$	4.50000	+	7.79423i	0.172440	+	0.298675i
$682$	−12.0000	+	20.7846i	−0.459504	+	0.795884i
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$	−24.0000			−0.917663
$685$	2.00000	−	3.46410i	0.0764161	−	0.132357i
$686$		0			0
$687$	87.0000			3.31926
$688$	−6.50000	+	0.866025i	−0.247810	+	0.0330169i
$689$		0			0
$690$		0			0
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	−0.995785	−	0.0917209i	$-0.970763\pi$
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	0.577325	+	0.816514i	$0.304097\pi$
$692$	−20.0000			−0.760286
$693$		0			0
$694$	−13.5000	+	23.3827i	−0.512453	+	0.887595i
$695$	−9.00000	−	15.5885i	−0.341389	−	0.591304i
$696$	−27.0000			−1.02343
$697$	10.0000	+	17.3205i	0.378777	+	0.656061i
$698$	−3.50000	+	6.06218i	−0.132477	+	0.229457i
$699$	18.0000			0.680823
$700$		0			0
$701$	13.5000	+	23.3827i	0.509888	+	0.883152i	0.999934	+	0.0114555i	$0.00364648\pi$
$701$	13.5000	+	23.3827i	0.509888	+	0.883152i	−0.490046	+	0.871696i	$0.663020\pi$
$702$		0			0
$703$	−16.0000	−	27.7128i	−0.603451	−	1.04521i
$704$	−6.00000			−0.226134
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$		0			0
$707$		0			0
$708$	−3.00000	+	5.19615i	−0.112747	+	0.195283i
$709$	5.00000			0.187779			0.0938895	−	0.995583i	$-0.470070\pi$
$709$	5.00000			0.187779			0.0938895	+	0.995583i	$0.470070\pi$
$710$	−8.00000			−0.300235
$711$		0			0
$712$	6.50000	−	11.2583i	0.243598	−	0.421924i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−33.0000	−	57.1577i	−1.23241	−	2.13459i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$	6.00000			0.223607
$721$		0			0
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$	−33.0000			−1.22728
$724$	3.00000	+	5.19615i	0.111494	+	0.193113i
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$	37.5000	−	64.9519i	1.39176	−	2.41059i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−8.00000			−0.296093
$731$	−16.0000	−	20.7846i	−0.591781	−	0.768747i
$732$	−6.00000			−0.221766
$733$	10.0000			0.369358			0.184679	−	0.982799i	$-0.440875\pi$
$733$	10.0000			0.369358			0.184679	+	0.982799i	$0.440875\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$	−21.0000			−0.774597
$736$		0			0
$737$	33.0000	−	57.1577i	1.21557	−	2.10543i
$738$	15.0000	+	25.9808i	0.552158	+	0.956365i
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	4.00000	+	6.92820i	0.147043	+	0.254686i
$741$		0			0
$742$		0			0
$743$	−22.0000	+	38.1051i	−0.807102	+	1.39794i	0.107761	+	0.994177i	$0.465632\pi$
$743$	−22.0000	+	38.1051i	−0.807102	+	1.39794i	−0.914863	+	0.403764i	$0.867702\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	−3.50000	−	6.06218i	−0.128230	−	0.222101i
$746$	−16.0000	−	27.7128i	−0.585802	−	1.01464i
$747$	66.0000			2.41481
$748$	−12.0000	−	20.7846i	−0.438763	−	0.759961i
$749$		0			0
$750$	1.50000	−	2.59808i	0.0547723	−	0.0948683i
$751$	−25.0000	+	43.3013i	−0.912263	+	1.58009i	−0.101403	+	0.994845i	$0.532333\pi$
$751$	−25.0000	+	43.3013i	−0.912263	+	1.58009i	−0.810860	+	0.585240i	$0.801000\pi$
$752$	−3.00000			−0.109399
$753$	30.0000			1.09326
$754$		0			0
$755$	5.00000	−	8.66025i	0.181969	−	0.315179i
$756$		0			0
$757$	−5.00000	−	8.66025i	−0.181728	−	0.314762i	0.760741	−	0.649056i	$-0.224836\pi$
$757$	−5.00000	−	8.66025i	−0.181728	−	0.314762i	−0.942469	+	0.334293i	$0.891502\pi$
$758$	30.0000			1.08965
$759$		0			0
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$	28.5000	−	49.3634i	1.03245	−	1.78825i
$763$		0			0
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$	12.0000	+	20.7846i	0.433861	+	0.751469i
$766$	−1.00000			−0.0361315
$767$		0			0
$768$	−1.50000	+	2.59808i	−0.0541266	+	0.0937500i
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	−0.999364	−	0.0356685i	$-0.988644\pi$
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	0.530572	+	0.847640i	$0.321977\pi$
$770$		0			0
$771$	−18.0000	+	31.1769i	−0.648254	+	1.12281i
$772$	−12.0000			−0.431889
$773$	4.00000			0.143870			0.0719350	−	0.997409i	$-0.477083\pi$
$773$	4.00000			0.143870			0.0719350	+	0.997409i	$0.477083\pi$
$774$	−24.0000	−	31.1769i	−0.862662	−	1.12063i
$775$	4.00000			0.143684
$776$	8.00000			0.287183
$777$		0			0
$778$	−18.0000			−0.645331
$779$	10.0000	−	17.3205i	0.358287	−	0.620572i
$780$		0			0
$781$	24.0000	+	41.5692i	0.858788	+	1.48746i
$782$		0			0
$783$	−40.5000	−	70.1481i	−1.44735	−	2.50689i
$784$	3.50000	−	6.06218i	0.125000	−	0.216506i
$785$	4.00000			0.142766
$786$	18.0000	−	31.1769i	0.642039	−	1.11204i
$787$	13.5000	+	23.3827i	0.481223	+	0.833503i	0.999768	−	0.0215477i	$-0.00685939\pi$
$787$	13.5000	+	23.3827i	0.481223	+	0.833503i	−0.518545	+	0.855050i	$0.673526\pi$
$788$	7.00000	+	12.1244i	0.249365	+	0.431912i
$789$	−7.50000	−	12.9904i	−0.267007	−	0.462470i
$790$		0			0
$791$		0			0
$792$	−18.0000	−	31.1769i	−0.639602	−	1.10782i
$793$		0			0
$794$	19.0000	−	32.9090i	0.674285	−	1.16790i
$795$	18.0000			0.638394
$796$	−2.00000			−0.0708881
$797$	19.0000	−	32.9090i	0.673015	−	1.16570i	−0.304030	−	0.952662i	$-0.598332\pi$
$797$	19.0000	−	32.9090i	0.673015	−	1.16570i	0.977045	−	0.213033i	$-0.0683342\pi$
$798$		0			0
$799$	−6.00000	−	10.3923i	−0.212265	−	0.367653i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	78.0000			2.75599
$802$	−5.00000	−	8.66025i	−0.176556	−	0.305804i
$803$	24.0000	+	41.5692i	0.846942	+	1.46695i
$804$	−16.5000	−	28.5788i	−0.581910	−	1.00790i
$805$		0			0
$806$		0			0
$807$	−40.5000	+	70.1481i	−1.42567	+	2.46933i
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	−55.0000			−1.93370			−0.966849	−	0.255351i	$-0.917809\pi$
$809$	−55.0000			−1.93370			−0.966849	+	0.255351i	$0.917809\pi$
$810$	4.50000	+	7.79423i	0.158114	+	0.273861i
$811$	−1.00000	+	1.73205i	−0.0351147	+	0.0608205i	−0.883049	−	0.469281i	$-0.844513\pi$
$811$	−1.00000	+	1.73205i	−0.0351147	+	0.0608205i	0.847934	+	0.530102i	$0.177846\pi$
$812$		0			0
$813$	−60.0000			−2.10429
$814$	24.0000	−	41.5692i	0.841200	−	1.45700i
$815$	11.0000			0.385313
$816$	−12.0000			−0.420084
$817$	−10.0000	+	24.2487i	−0.349856	+	0.848355i
$818$	17.0000			0.594391
$819$		0			0
$820$	−2.50000	+	4.33013i	−0.0873038	+	0.151215i
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$	−6.00000	+	10.3923i	−0.209274	+	0.362473i
$823$	22.5000	−	38.9711i	0.784301	−	1.35845i	−0.145115	−	0.989415i	$-0.546355\pi$
$823$	22.5000	−	38.9711i	0.784301	−	1.35845i	0.929416	−	0.369034i	$-0.120311\pi$
$824$	7.50000	+	12.9904i	0.261275	+	0.452541i
$825$	−18.0000			−0.626680
$826$		0			0
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	−0.742646	−	0.669684i	$-0.766429\pi$
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	0.951286	+	0.308308i	$0.0997628\pi$
$828$		0			0
$829$	0.500000	−	0.866025i	0.0173657	−	0.0300783i	−0.857212	−	0.514964i	$-0.827805\pi$
$829$	0.500000	−	0.866025i	0.0173657	−	0.0300783i	0.874578	+	0.484885i	$0.161139\pi$
$830$	5.50000	+	9.52628i	0.190908	+	0.330662i
$831$	−18.0000	−	31.1769i	−0.624413	−	1.08152i
$832$		0			0
$833$	28.0000			0.970143
$834$	27.0000	+	46.7654i	0.934934	+	1.61935i
$835$	−0.500000	−	0.866025i	−0.0173032	−	0.0299700i
$836$	−12.0000	+	20.7846i	−0.415029	+	0.718851i
$837$	−18.0000	+	31.1769i	−0.622171	+	1.07763i
$838$	12.0000			0.414533
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	−9.50000	−	16.4545i	−0.327392	−	0.567059i
$843$	21.0000	+	36.3731i	0.723278	+	1.25275i
$844$	−4.00000			−0.137686
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$	−9.00000	−	15.5885i	−0.309426	−	0.535942i
$847$		0			0
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	−48.0000			−1.64736
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$		0			0
$852$	24.0000			0.822226
$853$	−11.0000	−	19.0526i	−0.376633	−	0.652347i	0.613937	−	0.789355i	$-0.289585\pi$
$853$	−11.0000	−	19.0526i	−0.376633	−	0.652347i	−0.990570	+	0.137008i	$0.956251\pi$
$854$		0			0
$855$	12.0000	−	20.7846i	0.410391	−	0.710819i
$856$	19.0000			0.649407
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	−0.938699	−	0.344739i	$-0.887967\pi$
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	0.767902	+	0.640567i	$0.221301\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	2.50000	−	6.06218i	0.0852493	−	0.206719i
$861$		0			0
$862$	−30.0000			−1.02180
$863$	−8.00000	+	13.8564i	−0.272323	+	0.471678i	−0.969456	−	0.245264i	$-0.921125\pi$
$863$	−8.00000	+	13.8564i	−0.272323	+	0.471678i	0.697133	+	0.716942i	$0.254459\pi$
$864$	−9.00000			−0.306186
$865$	10.0000	−	17.3205i	0.340010	−	0.588915i
$866$	14.0000	−	24.2487i	0.475739	−	0.824005i
$867$	1.50000	+	2.59808i	0.0509427	+	0.0882353i
$868$		0			0
$869$		0			0
$870$	13.5000	−	23.3827i	0.457693	−	0.792747i
$871$		0			0
$872$	9.50000	−	16.4545i	0.321711	−	0.557219i
$873$	24.0000	+	41.5692i	0.812277	+	1.40690i
$874$		0			0
$875$		0			0
$876$	24.0000			0.810885
$877$	12.0000	+	20.7846i	0.405211	+	0.701846i	0.994346	−	0.106188i	$-0.0338646\pi$
$877$	12.0000	+	20.7846i	0.405211	+	0.701846i	−0.589135	+	0.808035i	$0.700531\pi$
$878$	17.0000	+	29.4449i	0.573722	+	0.993716i
$879$	−3.00000	+	5.19615i	−0.101187	+	0.175262i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	−19.0000			−0.640126			−0.320063	−	0.947396i	$-0.603704\pi$
$881$	−19.0000			−0.640126			−0.320063	+	0.947396i	$0.603704\pi$
$882$	42.0000			1.41421
$883$	−0.500000	+	0.866025i	−0.0168263	+	0.0291441i	−0.874316	−	0.485357i	$-0.838690\pi$
$883$	−0.500000	+	0.866025i	−0.0168263	+	0.0291441i	0.857490	+	0.514501i	$0.172023\pi$
$884$		0			0
$885$	−3.00000	−	5.19615i	−0.100844	−	0.174667i
$886$	13.5000	+	23.3827i	0.453541	+	0.785557i
$887$	16.0000			0.537227			0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000			0.537227			0.268614	+	0.963248i	$0.413434\pi$
$888$	−12.0000	−	20.7846i	−0.402694	−	0.697486i
$889$		0			0
$890$	6.50000	+	11.2583i	0.217880	+	0.377380i
$891$	27.0000	−	46.7654i	0.904534	−	1.56670i
$892$	23.0000			0.770097
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$	10.5000	+	18.1865i	0.351173	+	0.608249i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	3.50000	−	6.06218i	0.116797	−	0.202297i
$899$	36.0000			1.20067
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	−24.0000			−0.799556
$902$	30.0000			0.998891
$903$		0			0
$904$	6.00000			0.199557
$905$	−6.00000			−0.199447
$906$	−15.0000	+	25.9808i	−0.498342	+	0.863153i
$907$	4.00000			0.132818			0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000			0.132818			0.0664089	+	0.997792i	$0.478846\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$	−45.0000	+	77.9423i	−1.49256	+	2.58518i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	6.00000	+	10.3923i	0.198680	+	0.344124i
$913$	33.0000	−	57.1577i	1.09214	−	1.89164i
$914$	30.0000			0.992312
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	−14.5000	−	25.1147i	−0.479093	−	0.829814i
$917$		0			0
$918$	−18.0000	−	31.1769i	−0.594089	−	1.02899i
$919$	−18.0000			−0.593765			−0.296883	−	0.954914i	$-0.595947\pi$
$919$	−18.0000			−0.593765			−0.296883	+	0.954914i	$0.595947\pi$
$920$		0			0
$921$	31.5000	+	54.5596i	1.03796	+	1.79780i
$922$	−2.50000	+	4.33013i	−0.0823331	+	0.142605i
$923$		0			0
$924$		0			0
$925$	−8.00000			−0.263038
$926$	−8.50000	+	14.7224i	−0.279327	+	0.483809i
$927$	−45.0000	+	77.9423i	−1.47799	+	2.55996i
$928$	4.50000	+	7.79423i	0.147720	+	0.255858i
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$	−12.0000			−0.393496
$931$	−14.0000	−	24.2487i	−0.458831	−	0.794719i
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$	2.00000	−	3.46410i	0.0654420	−	0.113349i
$935$	24.0000			0.784884
$936$		0			0
$937$	−2.00000	−	3.46410i	−0.0653372	−	0.113167i	0.831506	−	0.555515i	$-0.187479\pi$
$937$	−2.00000	−	3.46410i	−0.0653372	−	0.113167i	−0.896843	+	0.442348i	$0.854146\pi$
$938$		0			0
$939$	−51.0000	−	88.3346i	−1.66432	−	2.88269i
$940$	1.50000	−	2.59808i	0.0489246	−	0.0847399i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$	−12.0000			−0.390981
$943$		0			0
$944$	2.00000			0.0650945
$945$		0			0
$946$	−39.0000	+	5.19615i	−1.26800	+	0.168941i
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$		0			0
$950$	4.00000			0.129777
$951$	−33.0000	+	57.1577i	−1.07010	+	1.85346i
$952$		0			0
$953$	13.0000	+	22.5167i	0.421111	+	0.729386i	0.996048	−	0.0888114i	$-0.0283068\pi$
$953$	13.0000	+	22.5167i	0.421111	+	0.729386i	−0.574937	+	0.818198i	$0.694974\pi$
$954$	−36.0000			−1.16554
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	−11.0000	+	19.0526i	−0.355765	+	0.616204i
$957$	−162.000			−5.23672
$958$	17.0000	−	29.4449i	0.549245	−	0.951320i
$959$		0			0
$960$	−1.50000	−	2.59808i	−0.0484123	−	0.0838525i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	57.0000	+	98.7269i	1.83680	+	3.18143i
$964$	5.50000	+	9.52628i	0.177143	+	0.306821i
$965$	6.00000	−	10.3923i	0.193147	−	0.334540i
$966$		0			0
$967$	24.0000			0.771788			0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000			0.771788			0.385894	+	0.922543i	$0.373893\pi$
$968$	−25.0000			−0.803530
$969$	−24.0000	+	41.5692i	−0.770991	+	1.33540i
$970$	−4.00000	+	6.92820i	−0.128432	+	0.222451i
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	0.684706	−	0.728820i	$-0.259931\pi$
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	−0.973529	+	0.228562i	$0.926597\pi$
$972$		0			0
$973$		0			0
$974$	−11.5000	−	19.9186i	−0.368484	−	0.638233i
$975$		0			0
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	−0.420075	−	0.907489i	$-0.637996\pi$
$977$	18.0000	−	31.1769i	0.575871	−	0.997438i	0.995946	−	0.0899487i	$-0.0286703\pi$
$978$	−33.0000			−1.05522
$979$	39.0000	−	67.5500i	1.24645	−	2.15891i
$980$	3.50000	+	6.06218i	0.111803	+	0.193649i
$981$	114.000			3.63974
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$	10.5000	−	18.1865i	0.334898	−	0.580060i	−0.648567	−	0.761157i	$-0.724631\pi$
$983$	10.5000	−	18.1865i	0.334898	−	0.580060i	0.983465	+	0.181097i	$0.0579648\pi$
$984$	7.50000	−	12.9904i	0.239091	−	0.414118i
$985$	−14.0000			−0.446077
$986$	−18.0000	+	31.1769i	−0.573237	+	0.992875i
$987$		0			0
$988$		0			0
$989$		0			0
$990$	36.0000			1.14416
$991$	10.0000			0.317660			0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000			0.317660			0.158830	+	0.987306i	$0.449228\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		0			0
$994$		0			0
$995$	1.00000	−	1.73205i	0.0317021	−	0.0549097i
$996$	−16.5000	−	28.5788i	−0.522823	−	0.905555i
$997$	28.0000			0.886769			0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000			0.886769			0.443384	+	0.896332i	$0.353778\pi$
$998$	−3.00000	−	5.19615i	−0.0949633	−	0.164481i
$999$	36.0000	−	62.3538i	1.13899	−	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.a.221.1	✓	2
43.36	even	3	inner	430.2.e.a.251.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.a.221.1	✓	2	1.1	even	1	trivial
430.2.e.a.251.1	yes	2	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 - 2.59808i) q^{6} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(0.500000 - 0.866025i) q^{10} -6.00000 q^{11} +(-1.50000 + 2.59808i) q^{12} +(-1.50000 - 2.59808i) q^{15} +1.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(3.00000 + 5.19615i) q^{18} +(2.00000 - 3.46410i) q^{19} +(-0.500000 + 0.866025i) q^{20} +6.00000 q^{22} +(1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +9.00000 q^{27} +(-4.50000 - 7.79423i) q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} -1.00000 q^{32} +(9.00000 - 15.5885i) q^{33} +(-2.00000 - 3.46410i) q^{34} +(-3.00000 - 5.19615i) q^{36} +(4.00000 - 6.92820i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{40} +5.00000 q^{41} +(-6.50000 + 0.866025i) q^{43} -6.00000 q^{44} +6.00000 q^{45} -3.00000 q^{47} +(-1.50000 + 2.59808i) q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} -12.0000 q^{51} +(-3.00000 + 5.19615i) q^{53} -9.00000 q^{54} +(3.00000 - 5.19615i) q^{55} +(6.00000 + 10.3923i) q^{57} +(4.50000 + 7.79423i) q^{58} +2.00000 q^{59} +(-1.50000 - 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +(2.00000 - 3.46410i) q^{62} +1.00000 q^{64} +(-9.00000 + 15.5885i) q^{66} +(-5.50000 + 9.52628i) q^{67} +(2.00000 + 3.46410i) q^{68} +(-4.00000 - 6.92820i) q^{71} +(3.00000 + 5.19615i) q^{72} +(-4.00000 - 6.92820i) q^{73} +(-4.00000 + 6.92820i) q^{74} +3.00000 q^{75} +(2.00000 - 3.46410i) q^{76} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} -5.00000 q^{82} +(-5.50000 + 9.52628i) q^{83} -4.00000 q^{85} +(6.50000 - 0.866025i) q^{86} +27.0000 q^{87} +6.00000 q^{88} +(-6.50000 + 11.2583i) q^{89} -6.00000 q^{90} +(-6.00000 - 10.3923i) q^{93} +3.00000 q^{94} +(2.00000 + 3.46410i) q^{95} +(1.50000 - 2.59808i) q^{96} -8.00000 q^{97} +(-3.50000 + 6.06218i) q^{98} +(18.0000 + 31.1769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 2 * q^8 - 6 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - 2 q^{8} - 6 q^{9} + q^{10} - 12 q^{11} - 3 q^{12} - 3 q^{15} + 2 q^{16} + 4 q^{17} + 6 q^{18} + 4 q^{19} - q^{20} + 12 q^{22} + 3 q^{24} - q^{25} + 18 q^{27} - 9 q^{29} + 3 q^{30} - 4 q^{31} - 2 q^{32} + 18 q^{33} - 4 q^{34} - 6 q^{36} + 8 q^{37} - 4 q^{38} + q^{40} + 10 q^{41} - 13 q^{43} - 12 q^{44} + 12 q^{45} - 6 q^{47} - 3 q^{48} + 7 q^{49} + q^{50} - 24 q^{51} - 6 q^{53} - 18 q^{54} + 6 q^{55} + 12 q^{57} + 9 q^{58} + 4 q^{59} - 3 q^{60} + 2 q^{61} + 4 q^{62} + 2 q^{64} - 18 q^{66} - 11 q^{67} + 4 q^{68} - 8 q^{71} + 6 q^{72} - 8 q^{73} - 8 q^{74} + 6 q^{75} + 4 q^{76} - q^{80} - 9 q^{81} - 10 q^{82} - 11 q^{83} - 8 q^{85} + 13 q^{86} + 54 q^{87} + 12 q^{88} - 13 q^{89} - 12 q^{90} - 12 q^{93} + 6 q^{94} + 4 q^{95} + 3 q^{96} - 16 q^{97} - 7 q^{98} + 36 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - 2 * q^8 - 6 * q^9 + q^10 - 12 * q^11 - 3 * q^12 - 3 * q^15 + 2 * q^16 + 4 * q^17 + 6 * q^18 + 4 * q^19 - q^20 + 12 * q^22 + 3 * q^24 - q^25 + 18 * q^27 - 9 * q^29 + 3 * q^30 - 4 * q^31 - 2 * q^32 + 18 * q^33 - 4 * q^34 - 6 * q^36 + 8 * q^37 - 4 * q^38 + q^40 + 10 * q^41 - 13 * q^43 - 12 * q^44 + 12 * q^45 - 6 * q^47 - 3 * q^48 + 7 * q^49 + q^50 - 24 * q^51 - 6 * q^53 - 18 * q^54 + 6 * q^55 + 12 * q^57 + 9 * q^58 + 4 * q^59 - 3 * q^60 + 2 * q^61 + 4 * q^62 + 2 * q^64 - 18 * q^66 - 11 * q^67 + 4 * q^68 - 8 * q^71 + 6 * q^72 - 8 * q^73 - 8 * q^74 + 6 * q^75 + 4 * q^76 - q^80 - 9 * q^81 - 10 * q^82 - 11 * q^83 - 8 * q^85 + 13 * q^86 + 54 * q^87 + 12 * q^88 - 13 * q^89 - 12 * q^90 - 12 * q^93 + 6 * q^94 + 4 * q^95 + 3 * q^96 - 16 * q^97 - 7 * q^98 + 36 * q^99

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