LMFDB - Embedded newform 1050.2.j.b.743.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(407,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1050.407");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.j (of order $4$, 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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			743.1
Root			$1.14412 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	1050.743
Dual form			1050.2.j.b.407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.58114 + 0.707107i) q^{3} +1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.58114 + 0.707107i) q^{3} +1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} +3.23607i q^{11} +(-0.707107 - 1.58114i) q^{12} +(-4.57649 - 4.57649i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} +(-2.99535 + 0.166925i) q^{18} +0.763932i q^{19} +(-0.618034 + 1.61803i) q^{21} +(2.28825 - 2.28825i) q^{22} +(-1.74806 + 1.74806i) q^{23} +(-0.618034 + 1.61803i) q^{24} +6.47214i q^{26} +(-1.58114 + 4.94975i) q^{27} +(0.707107 + 0.707107i) q^{28} -0.763932 q^{29} +5.23607 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.28825 - 5.11667i) q^{33} -2.00000i q^{34} +(2.23607 + 2.00000i) q^{36} +(5.11667 - 5.11667i) q^{37} +(0.540182 - 0.540182i) q^{38} +(10.4721 + 4.00000i) q^{39} -9.23607i q^{41} +(1.58114 - 0.707107i) q^{42} +(-2.28825 - 2.28825i) q^{43} -3.23607 q^{44} +2.47214 q^{46} +(-7.19859 - 7.19859i) q^{47} +(1.58114 - 0.707107i) q^{48} -1.00000i q^{49} +(-3.23607 - 1.23607i) q^{51} +(4.57649 - 4.57649i) q^{52} +(-7.73877 + 7.73877i) q^{53} +(4.61803 - 2.38197i) q^{54} -1.00000i q^{56} +(-0.540182 - 1.20788i) q^{57} +(0.540182 + 0.540182i) q^{58} -0.291796 q^{59} -12.9443 q^{61} +(-3.70246 - 3.70246i) q^{62} +(-0.166925 - 2.99535i) q^{63} -1.00000i q^{64} +(-2.00000 + 5.23607i) q^{66} +(6.19704 - 6.19704i) q^{67} +(-1.41421 + 1.41421i) q^{68} +(1.52786 - 4.00000i) q^{69} -11.4164i q^{71} +(-0.166925 - 2.99535i) q^{72} +(-2.62210 - 2.62210i) q^{73} -7.23607 q^{74} -0.763932 q^{76} +(2.28825 + 2.28825i) q^{77} +(-4.57649 - 10.2333i) q^{78} -12.9443i q^{79} +(-1.00000 - 8.94427i) q^{81} +(-6.53089 + 6.53089i) q^{82} +(5.11667 - 5.11667i) q^{83} +(-1.61803 - 0.618034i) q^{84} +3.23607i q^{86} +(1.20788 - 0.540182i) q^{87} +(2.28825 + 2.28825i) q^{88} -9.23607 q^{89} -6.47214 q^{91} +(-1.74806 - 1.74806i) q^{92} +(-8.27895 + 3.70246i) q^{93} +10.1803i q^{94} +(-1.61803 - 0.618034i) q^{96} +(10.0270 - 10.0270i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(7.23607 + 6.47214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6} + 16 q^{9}+O(q^{10}) $ 8 * q + 4 * q^6 + 16 * q^9	$ 8 q + 4 q^{6} + 16 q^{9} - 8 q^{14} - 8 q^{16} + 4 q^{21} + 4 q^{24} - 24 q^{29} + 24 q^{31} + 48 q^{39} - 8 q^{44} - 16 q^{46} - 8 q^{51} + 28 q^{54} - 56 q^{59} - 32 q^{61} - 16 q^{66} + 48 q^{69} - 40 q^{74} - 24 q^{76} - 8 q^{81} - 4 q^{84} - 56 q^{89} - 16 q^{91} - 4 q^{96} + 40 q^{99}+O(q^{100}) $ 8 * q + 4 * q^6 + 16 * q^9 - 8 * q^14 - 8 * q^16 + 4 * q^21 + 4 * q^24 - 24 * q^29 + 24 * q^31 + 48 * q^39 - 8 * q^44 - 16 * q^46 - 8 * q^51 + 28 * q^54 - 56 * q^59 - 32 * q^61 - 16 * q^66 + 48 * q^69 - 40 * q^74 - 24 * q^76 - 8 * q^81 - 4 * q^84 - 56 * q^89 - 16 * q^91 - 4 * q^96 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.58114	+	0.707107i	−0.912871	+	0.408248i
$3$	−1.58114	+	0.707107i	−0.912871	+	0.408248i
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	1.61803	+	0.618034i	0.660560	+	0.252311i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.00000	−	2.23607i	0.666667	−	0.745356i
$10$		0			0
$11$			3.23607i			0.975711i	0.872924	+	0.487856i	$0.162221\pi$
$11$			3.23607i			0.975711i	−0.872924	+	0.487856i	$0.837779\pi$
$12$	−0.707107	−	1.58114i	−0.204124	−	0.456435i
$13$	−4.57649	−	4.57649i	−1.26929	−	1.26929i	−0.946455	−	0.322835i	$-0.895364\pi$
$13$	−4.57649	−	4.57649i	−1.26929	−	1.26929i	−0.322835	−	0.946455i	$-0.604636\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	0.857493	−	0.514496i	$-0.172021\pi$
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	−0.514496	+	0.857493i	$0.672021\pi$
$18$	−2.99535	+	0.166925i	−0.706011	+	0.0393447i
$19$			0.763932i			0.175258i	0.996153	+	0.0876290i	$0.0279290\pi$
$19$			0.763932i			0.175258i	−0.996153	+	0.0876290i	$0.972071\pi$
$20$		0			0
$21$	−0.618034	+	1.61803i	−0.134866	+	0.353084i
$22$	2.28825	−	2.28825i	0.487856	−	0.487856i
$23$	−1.74806	+	1.74806i	−0.364497	+	0.364497i	−0.865465	−	0.500969i	$-0.832977\pi$
$23$	−1.74806	+	1.74806i	−0.364497	+	0.364497i	0.500969	+	0.865465i	$0.332977\pi$
$24$	−0.618034	+	1.61803i	−0.126156	+	0.330280i
$25$		0			0
$26$			6.47214i			1.26929i
$27$	−1.58114	+	4.94975i	−0.304290	+	0.952579i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	−0.763932			−0.141859			−0.0709293	−	0.997481i	$-0.522596\pi$
$29$	−0.763932			−0.141859			−0.0709293	+	0.997481i	$0.522596\pi$
$30$		0			0
$31$	5.23607			0.940426			0.470213	−	0.882553i	$-0.344177\pi$
$31$	5.23607			0.940426			0.470213	+	0.882553i	$0.344177\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.28825	−	5.11667i	−0.398332	−	0.890698i
$34$		−	2.00000i		−	0.342997i
$35$		0			0
$36$	2.23607	+	2.00000i	0.372678	+	0.333333i
$37$	5.11667	−	5.11667i	0.841176	−	0.841176i	−0.147836	−	0.989012i	$-0.547231\pi$
$37$	5.11667	−	5.11667i	0.841176	−	0.841176i	0.989012	+	0.147836i	$0.0472308\pi$
$38$	0.540182	−	0.540182i	0.0876290	−	0.0876290i
$39$	10.4721	+	4.00000i	1.67688	+	0.640513i
$40$		0			0
$41$		−	9.23607i		−	1.44243i	−0.692711	−	0.721216i	$-0.743584\pi$
$41$		−	9.23607i		−	1.44243i	0.692711	−	0.721216i	$-0.256416\pi$
$42$	1.58114	−	0.707107i	0.243975	−	0.109109i
$43$	−2.28825	−	2.28825i	−0.348954	−	0.348954i	0.510766	−	0.859720i	$-0.329362\pi$
$43$	−2.28825	−	2.28825i	−0.348954	−	0.348954i	−0.859720	+	0.510766i	$0.829362\pi$
$44$	−3.23607			−0.487856
$45$		0			0
$46$	2.47214			0.364497
$47$	−7.19859	−	7.19859i	−1.05002	−	1.05002i	−0.998681	−	0.0513407i	$-0.983651\pi$
$47$	−7.19859	−	7.19859i	−1.05002	−	1.05002i	−0.0513407	−	0.998681i	$-0.516349\pi$
$48$	1.58114	−	0.707107i	0.228218	−	0.102062i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−3.23607	−	1.23607i	−0.453140	−	0.173084i
$52$	4.57649	−	4.57649i	0.634645	−	0.634645i
$53$	−7.73877	+	7.73877i	−1.06300	+	1.06300i	−0.0651245	+	0.997877i	$0.520744\pi$
$53$	−7.73877	+	7.73877i	−1.06300	+	1.06300i	−0.997877	+	0.0651245i	$0.979256\pi$
$54$	4.61803	−	2.38197i	0.628435	−	0.324145i
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$	−0.540182	−	1.20788i	−0.0715488	−	0.159988i
$58$	0.540182	+	0.540182i	0.0709293	+	0.0709293i
$59$	−0.291796			−0.0379886			−0.0189943	−	0.999820i	$-0.506046\pi$
$59$	−0.291796			−0.0379886			−0.0189943	+	0.999820i	$0.506046\pi$
$60$		0			0
$61$	−12.9443			−1.65734			−0.828672	−	0.559734i	$-0.810903\pi$
$61$	−12.9443			−1.65734			−0.828672	+	0.559734i	$0.810903\pi$
$62$	−3.70246	−	3.70246i	−0.470213	−	0.470213i
$63$	−0.166925	−	2.99535i	−0.0210306	−	0.377379i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.00000	+	5.23607i	−0.246183	+	0.644515i
$67$	6.19704	−	6.19704i	0.757088	−	0.757088i	−0.218703	−	0.975791i	$-0.570183\pi$
$67$	6.19704	−	6.19704i	0.757088	−	0.757088i	0.975791	+	0.218703i	$0.0701826\pi$
$68$	−1.41421	+	1.41421i	−0.171499	+	0.171499i
$69$	1.52786	−	4.00000i	0.183933	−	0.481543i
$70$		0			0
$71$		−	11.4164i		−	1.35488i	−0.735579	−	0.677439i	$-0.763090\pi$
$71$		−	11.4164i		−	1.35488i	0.735579	−	0.677439i	$-0.236910\pi$
$72$	−0.166925	−	2.99535i	−0.0196723	−	0.353006i
$73$	−2.62210	−	2.62210i	−0.306893	−	0.306893i	0.536810	−	0.843703i	$-0.319629\pi$
$73$	−2.62210	−	2.62210i	−0.306893	−	0.306893i	−0.843703	+	0.536810i	$0.819629\pi$
$74$	−7.23607			−0.841176
$75$		0			0
$76$	−0.763932			−0.0876290
$77$	2.28825	+	2.28825i	0.260770	+	0.260770i
$78$	−4.57649	−	10.2333i	−0.518186	−	1.15870i
$79$		−	12.9443i		−	1.45634i	−0.685394	−	0.728172i	$-0.740370\pi$
$79$		−	12.9443i		−	1.45634i	0.685394	−	0.728172i	$-0.259630\pi$
$80$		0			0
$81$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$82$	−6.53089	+	6.53089i	−0.721216	+	0.721216i
$83$	5.11667	−	5.11667i	0.561628	−	0.561628i	−0.368142	−	0.929770i	$-0.620006\pi$
$83$	5.11667	−	5.11667i	0.561628	−	0.561628i	0.929770	+	0.368142i	$0.120006\pi$
$84$	−1.61803	−	0.618034i	−0.176542	−	0.0674330i
$85$		0			0
$86$			3.23607i			0.348954i
$87$	1.20788	−	0.540182i	0.129499	−	0.0579135i
$88$	2.28825	+	2.28825i	0.243928	+	0.243928i
$89$	−9.23607			−0.979021			−0.489511	−	0.871997i	$-0.662825\pi$
$89$	−9.23607			−0.979021			−0.489511	+	0.871997i	$0.662825\pi$
$90$		0			0
$91$	−6.47214			−0.678464
$92$	−1.74806	−	1.74806i	−0.182248	−	0.182248i
$93$	−8.27895	+	3.70246i	−0.858487	+	0.383927i
$94$			10.1803i			1.05002i
$95$		0			0
$96$	−1.61803	−	0.618034i	−0.165140	−	0.0630778i
$97$	10.0270	−	10.0270i	1.01809	−	1.01809i	0.0182557	−	0.999833i	$-0.494189\pi$
$97$	10.0270	−	10.0270i	1.01809	−	1.01809i	0.999833	−	0.0182557i	$-0.00581130\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	7.23607	+	6.47214i	0.727252	+	0.650474i
$100$		0			0
$101$		−	16.9443i		−	1.68602i	−0.537899	−	0.843009i	$-0.680782\pi$
$101$		−	16.9443i		−	1.68602i	0.537899	−	0.843009i	$-0.319218\pi$
$102$	1.41421	+	3.16228i	0.140028	+	0.313112i
$103$	−3.90879	−	3.90879i	−0.385145	−	0.385145i	0.487807	−	0.872952i	$-0.337797\pi$
$103$	−3.90879	−	3.90879i	−0.385145	−	0.385145i	−0.872952	+	0.487807i	$0.837797\pi$
$104$	−6.47214			−0.634645
$105$		0			0
$106$	10.9443			1.06300
$107$	11.9814	+	11.9814i	1.15829	+	1.15829i	0.984844	+	0.173443i	$0.0554891\pi$
$107$	11.9814	+	11.9814i	1.15829	+	1.15829i	0.173443	+	0.984844i	$0.444511\pi$
$108$	−4.94975	−	1.58114i	−0.476290	−	0.152145i
$109$			2.94427i			0.282010i	0.990009	+	0.141005i	$0.0450334\pi$
$109$			2.94427i			0.282010i	−0.990009	+	0.141005i	$0.954967\pi$
$110$		0			0
$111$	−4.47214	+	11.7082i	−0.424476	+	1.11129i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−2.49458	+	2.49458i	−0.234670	+	0.234670i	−0.814639	−	0.579969i	$-0.803065\pi$
$113$	−2.49458	+	2.49458i	−0.234670	+	0.234670i	0.579969	+	0.814639i	$0.303065\pi$
$114$	−0.472136	+	1.23607i	−0.0442196	+	0.115768i
$115$		0			0
$116$		−	0.763932i		−	0.0709293i
$117$	−19.3863	+	1.08036i	−1.79227	+	0.0998796i
$118$	0.206331	+	0.206331i	0.0189943	+	0.0189943i
$119$	2.00000			0.183340
$120$		0			0
$121$	0.527864			0.0479876
$122$	9.15298	+	9.15298i	0.828672	+	0.828672i
$123$	6.53089	+	14.6035i	0.588870	+	1.31675i
$124$			5.23607i			0.470213i
$125$		0			0
$126$	−2.00000	+	2.23607i	−0.178174	+	0.199205i
$127$	−10.2333	+	10.2333i	−0.908063	+	0.908063i	−0.996116	−	0.0880532i	$-0.971935\pi$
$127$	−10.2333	+	10.2333i	−0.908063	+	0.908063i	0.0880532	+	0.996116i	$0.471935\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	5.23607	+	2.00000i	0.461010	+	0.176090i
$130$		0			0
$131$		−	8.29180i		−	0.724458i	−0.932089	−	0.362229i	$-0.882016\pi$
$131$		−	8.29180i		−	0.724458i	0.932089	−	0.362229i	$-0.117984\pi$
$132$	5.11667	−	2.28825i	0.445349	−	0.199166i
$133$	0.540182	+	0.540182i	0.0468397	+	0.0468397i
$134$	−8.76393			−0.757088
$135$		0			0
$136$	2.00000			0.171499
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	0.143831	−	0.989602i	$-0.454058\pi$
$137$	−9.89949	−	9.89949i	−0.845771	−	0.845771i	−0.989602	+	0.143831i	$0.954058\pi$
$138$	−3.90879	+	1.74806i	−0.332738	+	0.148805i
$139$		−	1.70820i		−	0.144888i	−0.997372	−	0.0724440i	$-0.976920\pi$
$139$		−	1.70820i		−	0.144888i	0.997372	−	0.0724440i	$-0.0230799\pi$
$140$		0			0
$141$	16.4721	+	6.29180i	1.38720	+	0.529865i
$142$	−8.07262	+	8.07262i	−0.677439	+	0.677439i
$143$	14.8098	−	14.8098i	1.23846	−	1.23846i
$144$	−2.00000	+	2.23607i	−0.166667	+	0.186339i
$145$		0			0
$146$			3.70820i			0.306893i
$147$	0.707107	+	1.58114i	0.0583212	+	0.130410i
$148$	5.11667	+	5.11667i	0.420588	+	0.420588i
$149$	−20.1803			−1.65324			−0.826619	−	0.562762i	$-0.809739\pi$
$149$	−20.1803			−1.65324			−0.826619	+	0.562762i	$0.809739\pi$
$150$		0			0
$151$	5.52786			0.449851			0.224926	−	0.974376i	$-0.427786\pi$
$151$	5.52786			0.449851			0.224926	+	0.974376i	$0.427786\pi$
$152$	0.540182	+	0.540182i	0.0438145	+	0.0438145i
$153$	5.99070	−	0.333851i	0.484320	−	0.0269902i
$154$		−	3.23607i		−	0.260770i
$155$		0			0
$156$	−4.00000	+	10.4721i	−0.320256	+	0.838442i
$157$	3.90879	−	3.90879i	0.311955	−	0.311955i	−0.533711	−	0.845667i	$-0.679203\pi$
$157$	3.90879	−	3.90879i	0.311955	−	0.311955i	0.845667	+	0.533711i	$0.179203\pi$
$158$	−9.15298	+	9.15298i	−0.728172	+	0.728172i
$159$	6.76393	−	17.7082i	0.536415	−	1.40435i
$160$		0			0
$161$			2.47214i			0.194832i
$162$	−5.61745	+	7.03166i	−0.441348	+	0.552460i
$163$	10.3609	+	10.3609i	0.811526	+	0.811526i	0.984863	−	0.173337i	$-0.0554550\pi$
$163$	10.3609	+	10.3609i	0.811526	+	0.811526i	−0.173337	+	0.984863i	$0.555455\pi$
$164$	9.23607			0.721216
$165$		0			0
$166$	−7.23607			−0.561628
$167$	−0.206331	−	0.206331i	−0.0159664	−	0.0159664i	0.699079	−	0.715045i	$-0.253594\pi$
$167$	−0.206331	−	0.206331i	−0.0159664	−	0.0159664i	−0.715045	+	0.699079i	$0.753594\pi$
$168$	0.707107	+	1.58114i	0.0545545	+	0.121988i
$169$			28.8885i			2.22220i
$170$		0			0
$171$	1.70820	+	1.52786i	0.130630	+	0.116839i
$172$	2.28825	−	2.28825i	0.174477	−	0.174477i
$173$	6.32456	−	6.32456i	0.480847	−	0.480847i	−0.424555	−	0.905402i	$-0.639569\pi$
$173$	6.32456	−	6.32456i	0.480847	−	0.480847i	0.905402	+	0.424555i	$0.139569\pi$
$174$	−1.23607	−	0.472136i	−0.0937061	−	0.0357925i
$175$		0			0
$176$		−	3.23607i		−	0.243928i
$177$	0.461370	−	0.206331i	0.0346787	−	0.0155088i
$178$	6.53089	+	6.53089i	0.489511	+	0.489511i
$179$	−8.76393			−0.655047			−0.327524	−	0.944843i	$-0.606214\pi$
$179$	−8.76393			−0.655047			−0.327524	+	0.944843i	$0.606214\pi$
$180$		0			0
$181$	−21.8885			−1.62696			−0.813481	−	0.581591i	$-0.802430\pi$
$181$	−21.8885			−1.62696			−0.813481	+	0.581591i	$0.802430\pi$
$182$	4.57649	+	4.57649i	0.339232	+	0.339232i
$183$	20.4667	−	9.15298i	1.51294	−	0.676608i
$184$			2.47214i			0.182248i
$185$		0			0
$186$	8.47214	+	3.23607i	0.621207	+	0.237280i
$187$	−4.57649	+	4.57649i	−0.334666	+	0.334666i
$188$	7.19859	−	7.19859i	0.525011	−	0.525011i
$189$	2.38197	+	4.61803i	0.173263	+	0.335913i
$190$		0			0
$191$		−	3.05573i		−	0.221105i	−0.993870	−	0.110552i	$-0.964738\pi$
$191$		−	3.05573i		−	0.221105i	0.993870	−	0.110552i	$-0.0352620\pi$
$192$	0.707107	+	1.58114i	0.0510310	+	0.114109i
$193$	5.24419	+	5.24419i	0.377485	+	0.377485i	0.870194	−	0.492709i	$-0.163993\pi$
$193$	5.24419	+	5.24419i	0.377485	+	0.377485i	−0.492709	+	0.870194i	$0.663993\pi$
$194$	−14.1803			−1.01809
$195$		0			0
$196$	1.00000			0.0714286
$197$	−1.41421	−	1.41421i	−0.100759	−	0.100759i	0.654931	−	0.755689i	$-0.272698\pi$
$197$	−1.41421	−	1.41421i	−0.100759	−	0.100759i	−0.755689	+	0.654931i	$0.772698\pi$
$198$	−0.540182	−	9.69316i	−0.0383890	−	0.688863i
$199$		−	2.18034i		−	0.154560i	−0.997009	−	0.0772801i	$-0.975376\pi$
$199$		−	2.18034i		−	0.154560i	0.997009	−	0.0772801i	$-0.0246236\pi$
$200$		0			0
$201$	−5.41641	+	14.1803i	−0.382044	+	1.00020i
$202$	−11.9814	+	11.9814i	−0.843009	+	0.843009i
$203$	−0.540182	+	0.540182i	−0.0379133	+	0.0379133i
$204$	1.23607	−	3.23607i	0.0865421	−	0.226570i
$205$		0			0
$206$			5.52786i			0.385145i
$207$	0.412662	+	7.40492i	0.0286820	+	0.514677i
$208$	4.57649	+	4.57649i	0.317323	+	0.317323i
$209$	−2.47214			−0.171001
$210$		0			0
$211$	26.8328			1.84725			0.923624	−	0.383301i	$-0.125213\pi$
$211$	26.8328			1.84725			0.923624	+	0.383301i	$0.125213\pi$
$212$	−7.73877	−	7.73877i	−0.531501	−	0.531501i
$213$	8.07262	+	18.0509i	0.553127	+	1.23683i
$214$		−	16.9443i		−	1.15829i
$215$		0			0
$216$	2.38197	+	4.61803i	0.162072	+	0.314217i
$217$	3.70246	−	3.70246i	0.251339	−	0.251339i
$218$	2.08191	−	2.08191i	0.141005	−	0.141005i
$219$	6.00000	+	2.29180i	0.405442	+	0.154865i
$220$		0			0
$221$		−	12.9443i		−	0.870726i
$222$	11.4412	−	5.11667i	0.767885	−	0.343409i
$223$	3.49613	+	3.49613i	0.234118	+	0.234118i	0.814409	−	0.580291i	$-0.197061\pi$
$223$	3.49613	+	3.49613i	0.234118	+	0.234118i	−0.580291	+	0.814409i	$0.697061\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	3.52786			0.234670
$227$	2.28825	+	2.28825i	0.151876	+	0.151876i	0.778955	−	0.627079i	$-0.215750\pi$
$227$	2.28825	+	2.28825i	0.151876	+	0.151876i	−0.627079	+	0.778955i	$0.715750\pi$
$228$	1.20788	−	0.540182i	0.0799940	−	0.0357744i
$229$		−	8.94427i		−	0.591054i	−0.955334	−	0.295527i	$-0.904505\pi$
$229$		−	8.94427i		−	0.591054i	0.955334	−	0.295527i	$-0.0954953\pi$
$230$		0			0
$231$	−5.23607	−	2.00000i	−0.344508	−	0.131590i
$232$	−0.540182	+	0.540182i	−0.0354647	+	0.0354647i
$233$	−5.99070	+	5.99070i	−0.392464	+	0.392464i	−0.875565	−	0.483101i	$-0.839511\pi$
$233$	−5.99070	+	5.99070i	−0.392464	+	0.392464i	0.483101	+	0.875565i	$0.339511\pi$
$234$	14.4721	+	12.9443i	0.946073	+	0.846194i
$235$		0			0
$236$		−	0.291796i		−	0.0189943i
$237$	9.15298	+	20.4667i	0.594550	+	1.32945i
$238$	−1.41421	−	1.41421i	−0.0916698	−	0.0916698i
$239$	30.8328			1.99441			0.997205	−	0.0747204i	$-0.0238064\pi$
$239$	30.8328			1.99441			0.997205	+	0.0747204i	$0.0238064\pi$
$240$		0			0
$241$	27.8885			1.79646			0.898230	−	0.439527i	$-0.144854\pi$
$241$	27.8885			1.79646			0.898230	+	0.439527i	$0.144854\pi$
$242$	−0.373256	−	0.373256i	−0.0239938	−	0.0239938i
$243$	7.90569	+	13.4350i	0.507151	+	0.861858i
$244$		−	12.9443i		−	0.828672i
$245$		0			0
$246$	5.70820	−	14.9443i	0.363942	−	0.952812i
$247$	3.49613	−	3.49613i	0.222453	−	0.222453i
$248$	3.70246	−	3.70246i	0.235106	−	0.235106i
$249$	−4.47214	+	11.7082i	−0.283410	+	0.741977i
$250$		0			0
$251$			27.1246i			1.71209i	0.516901	+	0.856045i	$0.327086\pi$
$251$			27.1246i			1.71209i	−0.516901	+	0.856045i	$0.672914\pi$
$252$	2.99535	−	0.166925i	0.188689	−	0.0105153i
$253$	−5.65685	−	5.65685i	−0.355643	−	0.355643i
$254$	14.4721			0.908063
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.41421	−	1.41421i	−0.0882162	−	0.0882162i	0.661622	−	0.749838i	$-0.269869\pi$
$257$	−1.41421	−	1.41421i	−0.0882162	−	0.0882162i	−0.749838	+	0.661622i	$0.769869\pi$
$258$	−2.28825	−	5.11667i	−0.142460	−	0.318550i
$259$		−	7.23607i		−	0.449627i
$260$		0			0
$261$	−1.52786	+	1.70820i	−0.0945724	+	0.105735i
$262$	−5.86319	+	5.86319i	−0.362229	+	0.362229i
$263$	−9.56564	+	9.56564i	−0.589843	+	0.589843i	−0.937589	−	0.347746i	$-0.886947\pi$
$263$	−9.56564	+	9.56564i	−0.589843	+	0.589843i	0.347746	+	0.937589i	$0.386947\pi$
$264$	−5.23607	−	2.00000i	−0.322258	−	0.123091i
$265$		0			0
$266$		−	0.763932i		−	0.0468397i
$267$	14.6035	−	6.53089i	0.893720	−	0.399684i
$268$	6.19704	+	6.19704i	0.378544	+	0.378544i
$269$	−26.4721			−1.61403			−0.807017	−	0.590528i	$-0.798920\pi$
$269$	−26.4721			−1.61403			−0.807017	+	0.590528i	$0.798920\pi$
$270$		0			0
$271$	−14.7639			−0.896845			−0.448423	−	0.893822i	$-0.648014\pi$
$271$	−14.7639			−0.896845			−0.448423	+	0.893822i	$0.648014\pi$
$272$	−1.41421	−	1.41421i	−0.0857493	−	0.0857493i
$273$	10.2333	−	4.57649i	0.619350	−	0.276982i
$274$			14.0000i			0.845771i
$275$		0			0
$276$	4.00000	+	1.52786i	0.240772	+	0.0919666i
$277$	−22.3423	+	22.3423i	−1.34242	+	1.34242i	−0.448770	+	0.893647i	$0.648138\pi$
$277$	−22.3423	+	22.3423i	−1.34242	+	1.34242i	−0.893647	+	0.448770i	$0.851862\pi$
$278$	−1.20788	+	1.20788i	−0.0724440	+	0.0724440i
$279$	10.4721	−	11.7082i	0.626950	−	0.700952i
$280$		0			0
$281$		−	12.3607i		−	0.737376i	−0.929553	−	0.368688i	$-0.879807\pi$
$281$		−	12.3607i		−	0.737376i	0.929553	−	0.368688i	$-0.120193\pi$
$282$	−7.19859	−	16.0965i	−0.428670	−	0.958534i
$283$	−11.1074	−	11.1074i	−0.660265	−	0.660265i	0.295177	−	0.955442i	$-0.404621\pi$
$283$	−11.1074	−	11.1074i	−0.660265	−	0.660265i	−0.955442	+	0.295177i	$0.904621\pi$
$284$	11.4164			0.677439
$285$		0			0
$286$	−20.9443			−1.23846
$287$	−6.53089	−	6.53089i	−0.385506	−	0.385506i
$288$	2.99535	−	0.166925i	0.176503	−	0.00983617i
$289$		−	13.0000i		−	0.764706i
$290$		0			0
$291$	−8.76393	+	22.9443i	−0.513751	+	1.34502i
$292$	2.62210	−	2.62210i	0.153447	−	0.153447i
$293$	−2.16073	+	2.16073i	−0.126231	+	0.126231i	−0.767400	−	0.641169i	$-0.778450\pi$
$293$	−2.16073	+	2.16073i	−0.126231	+	0.126231i	0.641169	+	0.767400i	$0.278450\pi$
$294$	0.618034	−	1.61803i	0.0360445	−	0.0943657i
$295$		0			0
$296$		−	7.23607i		−	0.420588i
$297$	−16.0177	−	5.11667i	−0.929442	−	0.296899i
$298$	14.2697	+	14.2697i	0.826619	+	0.826619i
$299$	16.0000			0.925304
$300$		0			0
$301$	−3.23607			−0.186524
$302$	−3.90879	−	3.90879i	−0.224926	−	0.224926i
$303$	11.9814	+	26.7912i	0.688314	+	1.53912i
$304$		−	0.763932i		−	0.0438145i
$305$		0			0
$306$	−4.47214	−	4.00000i	−0.255655	−	0.228665i
$307$	−12.1877	+	12.1877i	−0.695591	+	0.695591i	−0.963456	−	0.267865i	$-0.913682\pi$
$307$	−12.1877	+	12.1877i	−0.695591	+	0.695591i	0.267865	+	0.963456i	$0.413682\pi$
$308$	−2.28825	+	2.28825i	−0.130385	+	0.130385i
$309$	8.94427	+	3.41641i	0.508822	+	0.194353i
$310$		0			0
$311$			8.00000i			0.453638i	0.973937	+	0.226819i	$0.0728326\pi$
$311$			8.00000i			0.453638i	−0.973937	+	0.226819i	$0.927167\pi$
$312$	10.2333	−	4.57649i	0.579349	−	0.259093i
$313$	6.53089	+	6.53089i	0.369148	+	0.369148i	0.867166	−	0.498019i	$-0.165939\pi$
$313$	6.53089	+	6.53089i	0.369148	+	0.369148i	−0.498019	+	0.867166i	$0.665939\pi$
$314$	−5.52786			−0.311955
$315$		0			0
$316$	12.9443			0.728172
$317$	19.0525	+	19.0525i	1.07009	+	1.07009i	0.997351	+	0.0727430i	$0.0231753\pi$
$317$	19.0525	+	19.0525i	1.07009	+	1.07009i	0.0727430	+	0.997351i	$0.476825\pi$
$318$	−17.3044	+	7.73877i	−0.970383	+	0.433969i
$319$		−	2.47214i		−	0.138413i
$320$		0			0
$321$	−27.4164	−	10.4721i	−1.53023	−	0.584498i
$322$	1.74806	−	1.74806i	0.0974158	−	0.0974158i
$323$	−1.08036	+	1.08036i	−0.0601130	+	0.0601130i
$324$	8.94427	−	1.00000i	0.496904	−	0.0555556i
$325$		0			0
$326$		−	14.6525i		−	0.811526i
$327$	−2.08191	−	4.65530i	−0.115130	−	0.257439i
$328$	−6.53089	−	6.53089i	−0.360608	−	0.360608i
$329$	−10.1803			−0.561260
$330$		0			0
$331$	−26.4721			−1.45504			−0.727520	−	0.686086i	$-0.759327\pi$
$331$	−26.4721			−1.45504			−0.727520	+	0.686086i	$0.759327\pi$
$332$	5.11667	+	5.11667i	0.280814	+	0.280814i
$333$	−1.20788	−	21.6746i	−0.0661916	−	1.18776i
$334$			0.291796i			0.0159664i
$335$		0			0
$336$	0.618034	−	1.61803i	0.0337165	−	0.0882710i
$337$	15.8902	−	15.8902i	0.865594	−	0.865594i	−0.126387	−	0.991981i	$-0.540338\pi$
$337$	15.8902	−	15.8902i	0.865594	−	0.865594i	0.991981	+	0.126387i	$0.0403380\pi$
$338$	20.4273	−	20.4273i	1.11110	−	1.11110i
$339$	2.18034	−	5.70820i	0.118420	−	0.310027i
$340$		0			0
$341$			16.9443i			0.917584i
$342$	−0.127520	−	2.28825i	−0.00689547	−	0.123734i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−3.23607			−0.174477
$345$		0			0
$346$	−8.94427			−0.480847
$347$	−10.9010	−	10.9010i	−0.585199	−	0.585199i	0.351128	−	0.936327i	$-0.385798\pi$
$347$	−10.9010	−	10.9010i	−0.585199	−	0.585199i	−0.936327	+	0.351128i	$0.885798\pi$
$348$	0.540182	+	1.20788i	0.0289568	+	0.0647493i
$349$		−	4.00000i		−	0.214115i	−0.994253	−	0.107058i	$-0.965857\pi$
$349$		−	4.00000i		−	0.214115i	0.994253	−	0.107058i	$-0.0341429\pi$
$350$		0			0
$351$	29.8885	−	15.4164i	1.59533	−	0.822867i
$352$	−2.28825	+	2.28825i	−0.121964	+	0.121964i
$353$	24.0416	−	24.0416i	1.27961	−	1.27961i	0.338719	−	0.940887i	$-0.390006\pi$
$353$	24.0416	−	24.0416i	1.27961	−	1.27961i	0.940887	−	0.338719i	$-0.109994\pi$
$354$	−0.472136	−	0.180340i	−0.0250937	−	0.00958496i
$355$		0			0
$356$		−	9.23607i		−	0.489511i
$357$	−3.16228	+	1.41421i	−0.167365	+	0.0748481i
$358$	6.19704	+	6.19704i	0.327524	+	0.327524i
$359$	11.4164			0.602535			0.301267	−	0.953540i	$-0.402590\pi$
$359$	11.4164			0.602535			0.301267	+	0.953540i	$0.402590\pi$
$360$		0			0
$361$	18.4164			0.969285
$362$	15.4775	+	15.4775i	0.813481	+	0.813481i
$363$	−0.834626	+	0.373256i	−0.0438065	+	0.0195909i
$364$		−	6.47214i		−	0.339232i
$365$		0			0
$366$	−20.9443	−	8.00000i	−1.09477	−	0.418167i
$367$	−14.8098	+	14.8098i	−0.773067	+	0.773067i	−0.978642	−	0.205574i	$-0.934094\pi$
$367$	−14.8098	+	14.8098i	−0.773067	+	0.773067i	0.205574	+	0.978642i	$0.434094\pi$
$368$	1.74806	−	1.74806i	0.0911241	−	0.0911241i
$369$	−20.6525	−	18.4721i	−1.07512	−	0.961621i
$370$		0			0
$371$			10.9443i			0.568198i
$372$	−3.70246	−	8.27895i	−0.191964	−	0.429244i
$373$	−16.4304	−	16.4304i	−0.850733	−	0.850733i	0.139491	−	0.990223i	$-0.455454\pi$
$373$	−16.4304	−	16.4304i	−0.850733	−	0.850733i	−0.990223	+	0.139491i	$0.955454\pi$
$374$	6.47214			0.334666
$375$		0			0
$376$	−10.1803			−0.525011
$377$	3.49613	+	3.49613i	0.180060	+	0.180060i
$378$	1.58114	−	4.94975i	0.0813250	−	0.254588i
$379$			28.3607i			1.45679i	0.685157	+	0.728395i	$0.259733\pi$
$379$			28.3607i			1.45679i	−0.685157	+	0.728395i	$0.740267\pi$
$380$		0			0
$381$	8.94427	−	23.4164i	0.458229	−	1.19966i
$382$	−2.16073	+	2.16073i	−0.110552	+	0.110552i
$383$	−8.94665	+	8.94665i	−0.457153	+	0.457153i	−0.897720	−	0.440567i	$-0.854777\pi$
$383$	−8.94665	+	8.94665i	−0.457153	+	0.457153i	0.440567	+	0.897720i	$0.354777\pi$
$384$	0.618034	−	1.61803i	0.0315389	−	0.0825700i
$385$		0			0
$386$		−	7.41641i		−	0.377485i
$387$	−9.69316	+	0.540182i	−0.492731	+	0.0274590i
$388$	10.0270	+	10.0270i	0.509045	+	0.509045i
$389$	23.2361			1.17812			0.589058	−	0.808091i	$-0.299499\pi$
$389$	23.2361			1.17812			0.589058	+	0.808091i	$0.299499\pi$
$390$		0			0
$391$	−4.94427			−0.250043
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	5.86319	+	13.1105i	0.295759	+	0.661336i
$394$			2.00000i			0.100759i
$395$		0			0
$396$	−6.47214	+	7.23607i	−0.325237	+	0.363626i
$397$	0.412662	−	0.412662i	0.0207109	−	0.0207109i	−0.696675	−	0.717386i	$-0.745338\pi$
$397$	0.412662	−	0.412662i	0.0207109	−	0.0207109i	0.717386	+	0.696675i	$0.245338\pi$
$398$	−1.54173	+	1.54173i	−0.0772801	+	0.0772801i
$399$	−1.23607	−	0.472136i	−0.0618808	−	0.0236364i
$400$		0			0
$401$		−	3.05573i		−	0.152596i	−0.997085	−	0.0762979i	$-0.975690\pi$
$401$		−	3.05573i		−	0.152596i	0.997085	−	0.0762979i	$-0.0243100\pi$
$402$	13.8570	−	6.19704i	0.691124	−	0.309080i
$403$	−23.9628	−	23.9628i	−1.19367	−	1.19367i
$404$	16.9443			0.843009
$405$		0			0
$406$	0.763932			0.0379133
$407$	16.5579	+	16.5579i	0.820745	+	0.820745i
$408$	−3.16228	+	1.41421i	−0.156556	+	0.0700140i
$409$		−	4.11146i		−	0.203298i	−0.994820	−	0.101649i	$-0.967588\pi$
$409$		−	4.11146i		−	0.203298i	0.994820	−	0.101649i	$-0.0324119\pi$
$410$		0			0
$411$	22.6525	+	8.65248i	1.11736	+	0.426795i
$412$	3.90879	−	3.90879i	0.192572	−	0.192572i
$413$	−0.206331	+	0.206331i	−0.0101529	+	0.0101529i
$414$	4.94427	−	5.52786i	0.242998	−	0.271680i
$415$		0			0
$416$		−	6.47214i		−	0.317323i
$417$	1.20788	+	2.70091i	0.0591503	+	0.132264i
$418$	1.74806	+	1.74806i	0.0855006	+	0.0855006i
$419$	−19.1246			−0.934298			−0.467149	−	0.884178i	$-0.654719\pi$
$419$	−19.1246			−0.934298			−0.467149	+	0.884178i	$0.654719\pi$
$420$		0			0
$421$	10.9443			0.533391			0.266696	−	0.963781i	$-0.414068\pi$
$421$	10.9443			0.533391			0.266696	+	0.963781i	$0.414068\pi$
$422$	−18.9737	−	18.9737i	−0.923624	−	0.923624i
$423$	−30.4937	+	1.69936i	−1.48265	+	0.0826255i
$424$			10.9443i			0.531501i
$425$		0			0
$426$	7.05573	−	18.4721i	0.341851	−	0.894978i
$427$	−9.15298	+	9.15298i	−0.442944	+	0.442944i
$428$	−11.9814	+	11.9814i	−0.579143	+	0.579143i
$429$	−12.9443	+	33.8885i	−0.624955	+	1.63615i
$430$		0			0
$431$			12.5836i			0.606130i	0.952970	+	0.303065i	$0.0980100\pi$
$431$			12.5836i			0.606130i	−0.952970	+	0.303065i	$0.901990\pi$
$432$	1.58114	−	4.94975i	0.0760726	−	0.238145i
$433$	4.78282	+	4.78282i	0.229848	+	0.229848i	0.812629	−	0.582781i	$-0.198036\pi$
$433$	4.78282	+	4.78282i	0.229848	+	0.229848i	−0.582781	+	0.812629i	$0.698036\pi$
$434$	−5.23607			−0.251339
$435$		0			0
$436$	−2.94427			−0.141005
$437$	−1.33540	−	1.33540i	−0.0638809	−	0.0638809i
$438$	−2.62210	−	5.86319i	−0.125289	−	0.280154i
$439$			9.81966i			0.468667i	0.972156	+	0.234333i	$0.0752907\pi$
$439$			9.81966i			0.468667i	−0.972156	+	0.234333i	$0.924709\pi$
$440$		0			0
$441$	−2.23607	−	2.00000i	−0.106479	−	0.0952381i
$442$	−9.15298	+	9.15298i	−0.435363	+	0.435363i
$443$	−6.32456	+	6.32456i	−0.300489	+	0.300489i	−0.841205	−	0.540716i	$-0.818153\pi$
$443$	−6.32456	+	6.32456i	−0.300489	+	0.300489i	0.540716	+	0.841205i	$0.318153\pi$
$444$	−11.7082	−	4.47214i	−0.555647	−	0.212238i
$445$		0			0
$446$		−	4.94427i		−	0.234118i
$447$	31.9079	−	14.2697i	1.50919	−	0.674932i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$	−35.4164			−1.67140			−0.835702	−	0.549183i	$-0.814939\pi$
$449$	−35.4164			−1.67140			−0.835702	+	0.549183i	$0.814939\pi$
$450$		0			0
$451$	29.8885			1.40740
$452$	−2.49458	−	2.49458i	−0.117335	−	0.117335i
$453$	−8.74032	+	3.90879i	−0.410656	+	0.183651i
$454$		−	3.23607i		−	0.151876i
$455$		0			0
$456$	−1.23607	−	0.472136i	−0.0578842	−	0.0221098i
$457$	3.08347	−	3.08347i	0.144238	−	0.144238i	−0.631300	−	0.775539i	$-0.717478\pi$
$457$	3.08347	−	3.08347i	0.144238	−	0.144238i	0.775539	+	0.631300i	$0.217478\pi$
$458$	−6.32456	+	6.32456i	−0.295527	+	0.295527i
$459$	−9.23607	+	4.76393i	−0.431103	+	0.222361i
$460$		0			0
$461$			20.3607i			0.948291i	0.880446	+	0.474146i	$0.157243\pi$
$461$			20.3607i			0.948291i	−0.880446	+	0.474146i	$0.842757\pi$
$462$	2.28825	+	5.11667i	0.106459	+	0.238049i
$463$	−14.8098	−	14.8098i	−0.688271	−	0.688271i	0.273578	−	0.961850i	$-0.411793\pi$
$463$	−14.8098	−	14.8098i	−0.688271	−	0.688271i	−0.961850	+	0.273578i	$0.911793\pi$
$464$	0.763932			0.0354647
$465$		0			0
$466$	8.47214			0.392464
$467$	5.11667	+	5.11667i	0.236771	+	0.236771i	0.815512	−	0.578740i	$-0.196456\pi$
$467$	5.11667	+	5.11667i	0.236771	+	0.236771i	−0.578740	+	0.815512i	$0.696456\pi$
$468$	−1.08036	−	19.3863i	−0.0499398	−	0.896133i
$469$		−	8.76393i		−	0.404681i
$470$		0			0
$471$	−3.41641	+	8.94427i	−0.157420	+	0.412130i
$472$	−0.206331	+	0.206331i	−0.00949715	+	0.00949715i
$473$	7.40492	−	7.40492i	0.340479	−	0.340479i
$474$	8.00000	−	20.9443i	0.367452	−	0.962002i
$475$		0			0
$476$			2.00000i			0.0916698i
$477$	1.82688	+	32.7820i	0.0836469	+	1.50098i
$478$	−21.8021	−	21.8021i	−0.997205	−	0.997205i
$479$	5.52786			0.252575			0.126287	−	0.991994i	$-0.459694\pi$
$479$	5.52786			0.252575			0.126287	+	0.991994i	$0.459694\pi$
$480$		0			0
$481$	−46.8328			−2.13539
$482$	−19.7202	−	19.7202i	−0.898230	−	0.898230i
$483$	−1.74806	−	3.90879i	−0.0795397	−	0.177856i
$484$			0.527864i			0.0239938i
$485$		0			0
$486$	3.90983	−	15.0902i	0.177353	−	0.684504i
$487$	11.5687	−	11.5687i	0.524230	−	0.524230i	−0.394616	−	0.918846i	$-0.629122\pi$
$487$	11.5687	−	11.5687i	0.524230	−	0.524230i	0.918846	+	0.394616i	$0.129122\pi$
$488$	−9.15298	+	9.15298i	−0.414336	+	0.414336i
$489$	−23.7082	−	9.05573i	−1.07212	−	0.409514i
$490$		0			0
$491$			21.7082i			0.979678i	0.871813	+	0.489839i	$0.162944\pi$
$491$			21.7082i			0.979678i	−0.871813	+	0.489839i	$0.837056\pi$
$492$	−14.6035	+	6.53089i	−0.658377	+	0.294435i
$493$	−1.08036	−	1.08036i	−0.0486571	−	0.0486571i
$494$	−4.94427			−0.222453
$495$		0			0
$496$	−5.23607			−0.235106
$497$	−8.07262	−	8.07262i	−0.362106	−	0.362106i
$498$	11.4412	−	5.11667i	0.512694	−	0.229284i
$499$		−	12.0000i		−	0.537194i	−0.963253	−	0.268597i	$-0.913440\pi$
$499$		−	12.0000i		−	0.537194i	0.963253	−	0.268597i	$-0.0865599\pi$
$500$		0			0
$501$	0.472136	+	0.180340i	0.0210935	+	0.00805699i
$502$	19.1800	−	19.1800i	0.856045	−	0.856045i
$503$	−28.3330	+	28.3330i	−1.26331	+	1.26331i	−0.313824	+	0.949481i	$0.601610\pi$
$503$	−28.3330	+	28.3330i	−1.26331	+	1.26331i	−0.949481	+	0.313824i	$0.898390\pi$
$504$	−2.23607	−	2.00000i	−0.0996024	−	0.0890871i
$505$		0			0
$506$			8.00000i			0.355643i
$507$	−20.4273	−	45.6768i	−0.907208	−	2.02858i
$508$	−10.2333	−	10.2333i	−0.454031	−	0.454031i
$509$	−37.3050			−1.65351			−0.826756	−	0.562560i	$-0.809817\pi$
$509$	−37.3050			−1.65351			−0.826756	+	0.562560i	$0.809817\pi$
$510$		0			0
$511$	−3.70820			−0.164041
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.78127	−	1.20788i	−0.166947	−	0.0533293i
$514$			2.00000i			0.0882162i
$515$		0			0
$516$	−2.00000	+	5.23607i	−0.0880451	+	0.230505i
$517$	23.2951	−	23.2951i	1.02452	−	1.02452i
$518$	−5.11667	+	5.11667i	−0.224814	+	0.224814i
$519$	−5.52786	+	14.4721i	−0.242646	+	0.635256i
$520$		0			0
$521$			12.2918i			0.538513i	0.963068	+	0.269257i	$0.0867780\pi$
$521$			12.2918i			0.538513i	−0.963068	+	0.269257i	$0.913222\pi$
$522$	2.28825	−	0.127520i	0.100154	−	0.00558138i
$523$	−19.8477	−	19.8477i	−0.867879	−	0.867879i	0.124358	−	0.992237i	$-0.460313\pi$
$523$	−19.8477	−	19.8477i	−0.867879	−	0.867879i	−0.992237	+	0.124358i	$0.960313\pi$
$524$	8.29180			0.362229
$525$		0			0
$526$	13.5279			0.589843
$527$	7.40492	+	7.40492i	0.322563	+	0.322563i
$528$	2.28825	+	5.11667i	0.0995831	+	0.222675i
$529$			16.8885i			0.734285i
$530$		0			0
$531$	−0.583592	+	0.652476i	−0.0253257	+	0.0283150i
$532$	−0.540182	+	0.540182i	−0.0234198	+	0.0234198i
$533$	−42.2688	+	42.2688i	−1.83086	+	1.83086i
$534$	−14.9443	−	5.70820i	−0.646702	−	0.247018i
$535$		0			0
$536$		−	8.76393i		−	0.378544i
$537$	13.8570	−	6.19704i	0.597973	−	0.267422i
$538$	18.7186	+	18.7186i	0.807017	+	0.807017i
$539$	3.23607			0.139387
$540$		0			0
$541$	6.00000			0.257960			0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000			0.257960			0.128980	+	0.991647i	$0.458830\pi$
$542$	10.4397	+	10.4397i	0.448423	+	0.448423i
$543$	34.6088	−	15.4775i	1.48521	−	0.664205i
$544$			2.00000i			0.0857493i
$545$		0			0
$546$	−10.4721	−	4.00000i	−0.448166	−	0.171184i
$547$	18.4335	−	18.4335i	0.788159	−	0.788159i	−0.193033	−	0.981192i	$-0.561833\pi$
$547$	18.4335	−	18.4335i	0.788159	−	0.788159i	0.981192	+	0.193033i	$0.0618325\pi$
$548$	9.89949	−	9.89949i	0.422885	−	0.422885i
$549$	−25.8885	+	28.9443i	−1.10490	+	1.23531i
$550$		0			0
$551$		−	0.583592i		−	0.0248619i
$552$	−1.74806	−	3.90879i	−0.0744025	−	0.166369i
$553$	−9.15298	−	9.15298i	−0.389224	−	0.389224i
$554$	31.5967			1.34242
$555$		0			0
$556$	1.70820			0.0724440
$557$	−26.0447	−	26.0447i	−1.10355	−	1.10355i	−0.993979	−	0.109572i	$-0.965052\pi$
$557$	−26.0447	−	26.0447i	−1.10355	−	1.10355i	−0.109572	−	0.993979i	$-0.534948\pi$
$558$	−15.6839	+	0.874032i	−0.663951	+	0.0370007i
$559$			20.9443i			0.885848i
$560$		0			0
$561$	4.00000	−	10.4721i	0.168880	−	0.442134i
$562$	−8.74032	+	8.74032i	−0.368688	+	0.368688i
$563$	26.6637	−	26.6637i	1.12374	−	1.12374i	0.132568	−	0.991174i	$-0.457678\pi$
$563$	26.6637	−	26.6637i	1.12374	−	1.12374i	0.991174	−	0.132568i	$-0.0423224\pi$
$564$	−6.29180	+	16.4721i	−0.264932	+	0.693602i
$565$		0			0
$566$			15.7082i			0.660265i
$567$	−7.03166	−	5.61745i	−0.295302	−	0.235911i
$568$	−8.07262	−	8.07262i	−0.338720	−	0.338720i
$569$	11.0557			0.463480			0.231740	−	0.972778i	$-0.425558\pi$
$569$	11.0557			0.463480			0.231740	+	0.972778i	$0.425558\pi$
$570$		0			0
$571$	23.4164			0.979946			0.489973	−	0.871738i	$-0.337007\pi$
$571$	23.4164			0.979946			0.489973	+	0.871738i	$0.337007\pi$
$572$	14.8098	+	14.8098i	0.619230	+	0.619230i
$573$	2.16073	+	4.83153i	0.0902656	+	0.201840i
$574$			9.23607i			0.385506i
$575$		0			0
$576$	−2.23607	−	2.00000i	−0.0931695	−	0.0833333i
$577$	10.4397	−	10.4397i	0.434609	−	0.434609i	−0.455584	−	0.890193i	$-0.650569\pi$
$577$	10.4397	−	10.4397i	0.434609	−	0.434609i	0.890193	+	0.455584i	$0.150569\pi$
$578$	−9.19239	+	9.19239i	−0.382353	+	0.382353i
$579$	−12.0000	−	4.58359i	−0.498703	−	0.190488i
$580$		0			0
$581$		−	7.23607i		−	0.300203i
$582$	22.4211	−	10.0270i	0.929384	−	0.415633i
$583$	−25.0432	−	25.0432i	−1.03718	−	1.03718i
$584$	−3.70820			−0.153447
$585$		0			0
$586$	3.05573			0.126231
$587$	−16.4304	−	16.4304i	−0.678154	−	0.678154i	0.281428	−	0.959582i	$-0.409192\pi$
$587$	−16.4304	−	16.4304i	−0.678154	−	0.678154i	−0.959582	+	0.281428i	$0.909192\pi$
$588$	−1.58114	+	0.707107i	−0.0652051	+	0.0291606i
$589$			4.00000i			0.164817i
$590$		0			0
$591$	3.23607	+	1.23607i	0.133114	+	0.0508450i
$592$	−5.11667	+	5.11667i	−0.210294	+	0.210294i
$593$	24.7093	−	24.7093i	1.01469	−	1.01469i	0.0148002	−	0.999890i	$-0.495289\pi$
$593$	24.7093	−	24.7093i	1.01469	−	1.01469i	0.999890	−	0.0148002i	$-0.00471121\pi$
$594$	7.70820	+	14.9443i	0.316271	+	0.613171i
$595$		0			0
$596$		−	20.1803i		−	0.826619i
$597$	1.54173	+	3.44742i	0.0630989	+	0.141094i
$598$	−11.3137	−	11.3137i	−0.462652	−	0.462652i
$599$	20.9443			0.855760			0.427880	−	0.903836i	$-0.359261\pi$
$599$	20.9443			0.855760			0.427880	+	0.903836i	$0.359261\pi$
$600$		0			0
$601$	18.0000			0.734235			0.367118	−	0.930175i	$-0.380345\pi$
$601$	18.0000			0.734235			0.367118	+	0.930175i	$0.380345\pi$
$602$	2.28825	+	2.28825i	0.0932619	+	0.0932619i
$603$	−1.46292	−	26.2511i	−0.0595748	−	1.06903i
$604$			5.52786i			0.224926i
$605$		0			0
$606$	10.4721	−	27.4164i	0.425401	−	1.11372i
$607$	22.6274	−	22.6274i	0.918419	−	0.918419i	−0.0784959	−	0.996914i	$-0.525012\pi$
$607$	22.6274	−	22.6274i	0.918419	−	0.918419i	0.996914	+	0.0784959i	$0.0250118\pi$
$608$	−0.540182	+	0.540182i	−0.0219073	+	0.0219073i
$609$	0.472136	−	1.23607i	0.0191319	−	0.0500880i
$610$		0			0
$611$			65.8885i			2.66557i
$612$	0.333851	+	5.99070i	0.0134951	+	0.242160i
$613$	11.8539	+	11.8539i	0.478774	+	0.478774i	0.904739	−	0.425965i	$-0.140065\pi$
$613$	11.8539	+	11.8539i	0.478774	+	0.478774i	−0.425965	+	0.904739i	$0.640065\pi$
$614$	17.2361			0.695591
$615$		0			0
$616$	3.23607			0.130385
$617$	−22.9613	−	22.9613i	−0.924386	−	0.924386i	0.0729498	−	0.997336i	$-0.476759\pi$
$617$	−22.9613	−	22.9613i	−0.924386	−	0.924386i	−0.997336	+	0.0729498i	$0.976759\pi$
$618$	−3.90879	−	8.74032i	−0.157235	−	0.351587i
$619$		−	7.23607i		−	0.290842i	−0.989370	−	0.145421i	$-0.953546\pi$
$619$		−	7.23607i		−	0.290842i	0.989370	−	0.145421i	$-0.0464537\pi$
$620$		0			0
$621$	−5.88854	−	11.4164i	−0.236299	−	0.458125i
$622$	5.65685	−	5.65685i	0.226819	−	0.226819i
$623$	−6.53089	+	6.53089i	−0.261654	+	0.261654i
$624$	−10.4721	−	4.00000i	−0.419221	−	0.160128i
$625$		0			0
$626$		−	9.23607i		−	0.369148i
$627$	3.90879	−	1.74806i	0.156102	−	0.0698110i
$628$	3.90879	+	3.90879i	0.155978	+	0.155978i
$629$	14.4721			0.577042
$630$		0			0
$631$	7.41641			0.295243			0.147621	−	0.989044i	$-0.452838\pi$
$631$	7.41641			0.295243			0.147621	+	0.989044i	$0.452838\pi$
$632$	−9.15298	−	9.15298i	−0.364086	−	0.364086i
$633$	−42.4264	+	18.9737i	−1.68630	+	0.754136i
$634$		−	26.9443i		−	1.07009i
$635$		0			0
$636$	17.7082	+	6.76393i	0.702176	+	0.268207i
$637$	−4.57649	+	4.57649i	−0.181327	+	0.181327i
$638$	−1.74806	+	1.74806i	−0.0692065	+	0.0692065i
$639$	−25.5279	−	22.8328i	−1.00987	−	0.903252i
$640$		0			0
$641$		−	11.0557i		−	0.436675i	−0.975873	−	0.218338i	$-0.929937\pi$
$641$		−	11.0557i		−	0.436675i	0.975873	−	0.218338i	$-0.0700634\pi$
$642$	11.9814	+	26.7912i	0.472869	+	1.05737i
$643$	1.12907	+	1.12907i	0.0445262	+	0.0445262i	0.729019	−	0.684493i	$-0.239976\pi$
$643$	1.12907	+	1.12907i	0.0445262	+	0.0445262i	−0.684493	+	0.729019i	$0.739976\pi$
$644$	−2.47214			−0.0974158
$645$		0			0
$646$	1.52786			0.0601130
$647$	0.618993	+	0.618993i	0.0243351	+	0.0243351i	0.719170	−	0.694835i	$-0.244522\pi$
$647$	0.618993	+	0.618993i	0.0243351	+	0.0243351i	−0.694835	+	0.719170i	$0.744522\pi$
$648$	−7.03166	−	5.61745i	−0.276230	−	0.220674i
$649$		−	0.944272i		−	0.0370659i
$650$		0			0
$651$	−3.23607	+	8.47214i	−0.126832	+	0.332049i
$652$	−10.3609	+	10.3609i	−0.405763	+	0.405763i
$653$	20.5455	−	20.5455i	0.804008	−	0.804008i	−0.179712	−	0.983719i	$-0.557516\pi$
$653$	20.5455	−	20.5455i	0.804008	−	0.804008i	0.983719	+	0.179712i	$0.0575165\pi$
$654$	−1.81966	+	4.76393i	−0.0711543	+	0.186284i
$655$		0			0
$656$			9.23607i			0.360608i
$657$	−11.1074	+	0.618993i	−0.433340	+	0.0241492i
$658$	7.19859	+	7.19859i	0.280630	+	0.280630i
$659$	19.2361			0.749331			0.374665	−	0.927160i	$-0.377758\pi$
$659$	19.2361			0.749331			0.374665	+	0.927160i	$0.377758\pi$
$660$		0			0
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$	18.7186	+	18.7186i	0.727520	+	0.727520i
$663$	9.15298	+	20.4667i	0.355472	+	0.794860i
$664$		−	7.23607i		−	0.280814i
$665$		0			0
$666$	−14.4721	+	16.1803i	−0.560784	+	0.626975i
$667$	1.33540	−	1.33540i	0.0517070	−	0.0517070i
$668$	0.206331	−	0.206331i	0.00798319	−	0.00798319i
$669$	−8.00000	−	3.05573i	−0.309298	−	0.118141i
$670$		0			0
$671$		−	41.8885i		−	1.61709i
$672$	−1.58114	+	0.707107i	−0.0609938	+	0.0272772i
$673$	24.6305	+	24.6305i	0.949437	+	0.949437i	0.998782	−	0.0493450i	$-0.0157134\pi$
$673$	24.6305	+	24.6305i	0.949437	+	0.949437i	−0.0493450	+	0.998782i	$0.515713\pi$
$674$	−22.4721			−0.865594
$675$		0			0
$676$	−28.8885			−1.11110
$677$	21.1344	+	21.1344i	0.812261	+	0.812261i	0.984972	−	0.172712i	$-0.0552529\pi$
$677$	21.1344	+	21.1344i	0.812261	+	0.812261i	−0.172712	+	0.984972i	$0.555253\pi$
$678$	−5.57804	+	2.49458i	−0.214223	+	0.0958036i
$679$		−	14.1803i		−	0.544191i
$680$		0			0
$681$	−5.23607	−	2.00000i	−0.200647	−	0.0766402i
$682$	11.9814	−	11.9814i	0.458792	−	0.458792i
$683$	13.3168	−	13.3168i	0.509554	−	0.509554i	−0.404836	−	0.914389i	$-0.632671\pi$
$683$	13.3168	−	13.3168i	0.509554	−	0.509554i	0.914389	+	0.404836i	$0.132671\pi$
$684$	−1.52786	+	1.70820i	−0.0584193	+	0.0653148i
$685$		0			0
$686$			1.00000i			0.0381802i
$687$	6.32456	+	14.1421i	0.241297	+	0.539556i
$688$	2.28825	+	2.28825i	0.0872385	+	0.0872385i
$689$	70.8328			2.69852
$690$		0			0
$691$	−2.87539			−0.109385			−0.0546925	−	0.998503i	$-0.517418\pi$
$691$	−2.87539			−0.109385			−0.0546925	+	0.998503i	$0.517418\pi$
$692$	6.32456	+	6.32456i	0.240424	+	0.240424i
$693$	9.69316	−	0.540182i	0.368213	−	0.0205198i
$694$			15.4164i			0.585199i
$695$		0			0
$696$	0.472136	−	1.23607i	0.0178963	−	0.0468530i
$697$	13.0618	−	13.0618i	0.494750	−	0.494750i
$698$	−2.82843	+	2.82843i	−0.107058	+	0.107058i
$699$	5.23607	−	13.7082i	0.198046	−	0.518492i
$700$		0			0
$701$			6.87539i			0.259680i	0.991535	+	0.129840i	$0.0414463\pi$
$701$			6.87539i			0.259680i	−0.991535	+	0.129840i	$0.958554\pi$
$702$	−32.0354	−	10.2333i	−1.20910	−	0.386233i
$703$	3.90879	+	3.90879i	0.147423	+	0.147423i
$704$	3.23607			0.121964
$705$		0			0
$706$	−34.0000			−1.27961
$707$	−11.9814	−	11.9814i	−0.450607	−	0.450607i
$708$	0.206331	+	0.461370i	0.00775439	+	0.0173393i
$709$		−	9.05573i		−	0.340095i	−0.985436	−	0.170048i	$-0.945608\pi$
$709$		−	9.05573i		−	0.340095i	0.985436	−	0.170048i	$-0.0543921\pi$
$710$		0			0
$711$	−28.9443	−	25.8885i	−1.08550	−	0.970896i
$712$	−6.53089	+	6.53089i	−0.244755	+	0.244755i
$713$	−9.15298	+	9.15298i	−0.342782	+	0.342782i
$714$	3.23607	+	1.23607i	0.121107	+	0.0462587i
$715$		0			0
$716$		−	8.76393i		−	0.327524i
$717$	−48.7510	+	21.8021i	−1.82064	+	0.814214i
$718$	−8.07262	−	8.07262i	−0.301267	−	0.301267i
$719$	23.4164			0.873285			0.436642	−	0.899635i	$-0.356168\pi$
$719$	23.4164			0.873285			0.436642	+	0.899635i	$0.356168\pi$
$720$		0			0
$721$	−5.52786			−0.205868
$722$	−13.0224	−	13.0224i	−0.484642	−	0.484642i
$723$	−44.0957	+	19.7202i	−1.63994	+	0.733401i
$724$		−	21.8885i		−	0.813481i
$725$		0			0
$726$	0.854102	+	0.326238i	0.0316987	+	0.0121078i
$727$	−22.2148	+	22.2148i	−0.823900	+	0.823900i	−0.986665	−	0.162765i	$-0.947959\pi$
$727$	−22.2148	+	22.2148i	−0.823900	+	0.823900i	0.162765	+	0.986665i	$0.447959\pi$
$728$	−4.57649	+	4.57649i	−0.169616	+	0.169616i
$729$	−22.0000	−	15.6525i	−0.814815	−	0.579721i
$730$		0			0
$731$		−	6.47214i		−	0.239381i
$732$	9.15298	+	20.4667i	0.338304	+	0.756471i
$733$	4.32145	+	4.32145i	0.159616	+	0.159616i	0.782397	−	0.622780i	$-0.213997\pi$
$733$	4.32145	+	4.32145i	0.159616	+	0.159616i	−0.622780	+	0.782397i	$0.713997\pi$
$734$	20.9443			0.773067
$735$		0			0
$736$	−2.47214			−0.0911241
$737$	20.0540	+	20.0540i	0.738700	+	0.738700i
$738$	1.54173	+	27.6653i	0.0567520	+	1.01837i
$739$		−	44.3607i		−	1.63183i	−0.578169	−	0.815917i	$-0.696233\pi$
$739$		−	44.3607i		−	1.63183i	0.578169	−	0.815917i	$-0.303767\pi$
$740$		0			0
$741$	−3.05573	+	8.00000i	−0.112255	+	0.293887i
$742$	7.73877	−	7.73877i	0.284099	−	0.284099i
$743$	−13.4744	+	13.4744i	−0.494329	+	0.494329i	−0.909667	−	0.415338i	$-0.863663\pi$
$743$	−13.4744	+	13.4744i	−0.494329	+	0.494329i	0.415338	+	0.909667i	$0.363663\pi$
$744$	−3.23607	+	8.47214i	−0.118640	+	0.310604i
$745$		0			0
$746$			23.2361i			0.850733i
$747$	−1.20788	−	21.6746i	−0.0441941	−	0.793031i
$748$	−4.57649	−	4.57649i	−0.167333	−	0.167333i
$749$	16.9443			0.619130
$750$		0			0
$751$	−15.4164			−0.562553			−0.281276	−	0.959627i	$-0.590758\pi$
$751$	−15.4164			−0.562553			−0.281276	+	0.959627i	$0.590758\pi$
$752$	7.19859	+	7.19859i	0.262505	+	0.262505i
$753$	−19.1800	−	42.8878i	−0.698958	−	1.56292i
$754$		−	4.94427i		−	0.180060i
$755$		0			0
$756$	−4.61803	+	2.38197i	−0.167956	+	0.0866313i
$757$	8.35776	−	8.35776i	0.303768	−	0.303768i	−0.538718	−	0.842486i	$-0.681091\pi$
$757$	8.35776	−	8.35776i	0.303768	−	0.303768i	0.842486	+	0.538718i	$0.181091\pi$
$758$	20.0540	−	20.0540i	0.728395	−	0.728395i
$759$	12.9443	+	4.94427i	0.469847	+	0.179466i
$760$		0			0
$761$			14.7639i			0.535192i	0.963531	+	0.267596i	$0.0862293\pi$
$761$			14.7639i			0.535192i	−0.963531	+	0.267596i	$0.913771\pi$
$762$	−22.8825	+	10.2333i	−0.828944	+	0.370715i
$763$	2.08191	+	2.08191i	0.0753704	+	0.0753704i
$764$	3.05573			0.110552
$765$		0			0
$766$	12.6525			0.457153
$767$	1.33540	+	1.33540i	0.0482186	+	0.0482186i
$768$	−1.58114	+	0.707107i	−0.0570544	+	0.0255155i
$769$			29.0557i			1.04778i	0.851787	+	0.523888i	$0.175519\pi$
$769$			29.0557i			1.04778i	−0.851787	+	0.523888i	$0.824481\pi$
$770$		0			0
$771$	3.23607	+	1.23607i	0.116544	+	0.0445159i
$772$	−5.24419	+	5.24419i	−0.188743	+	0.188743i
$773$	2.16073	−	2.16073i	0.0777159	−	0.0777159i	−0.667180	−	0.744896i	$-0.732499\pi$
$773$	2.16073	−	2.16073i	0.0777159	−	0.0777159i	0.744896	+	0.667180i	$0.232499\pi$
$774$	7.23607	+	6.47214i	0.260095	+	0.232636i
$775$		0			0
$776$		−	14.1803i		−	0.509045i
$777$	5.11667	+	11.4412i	0.183560	+	0.410452i
$778$	−16.4304	−	16.4304i	−0.589058	−	0.589058i
$779$	7.05573			0.252798
$780$		0			0
$781$	36.9443			1.32197
$782$	3.49613	+	3.49613i	0.125021	+	0.125021i
$783$	1.20788	−	3.78127i	0.0431662	−	0.135132i
$784$			1.00000i			0.0357143i
$785$		0			0
$786$	5.12461	−	13.4164i	0.182789	−	0.478547i
$787$	−13.5231	+	13.5231i	−0.482048	+	0.482048i	−0.905785	−	0.423737i	$-0.860718\pi$
$787$	−13.5231	+	13.5231i	−0.482048	+	0.482048i	0.423737	+	0.905785i	$0.360718\pi$
$788$	1.41421	−	1.41421i	0.0503793	−	0.0503793i
$789$	8.36068	−	21.8885i	0.297648	−	0.779253i
$790$		0			0
$791$			3.52786i			0.125436i
$792$	9.69316	−	0.540182i	0.344432	−	0.0191945i
$793$	59.2393	+	59.2393i	2.10365	+	2.10365i
$794$	−0.583592			−0.0207109
$795$		0			0
$796$	2.18034			0.0772801
$797$	32.4481	+	32.4481i	1.14937	+	1.14937i	0.986677	+	0.162694i	$0.0520184\pi$
$797$	32.4481	+	32.4481i	1.14937	+	1.14937i	0.162694	+	0.986677i	$0.447982\pi$
$798$	0.540182	+	1.20788i	0.0191222	+	0.0427586i
$799$		−	20.3607i		−	0.720309i
$800$		0			0
$801$	−18.4721	+	20.6525i	−0.652681	+	0.729719i
$802$	−2.16073	+	2.16073i	−0.0762979	+	0.0762979i
$803$	8.48528	−	8.48528i	0.299439	−	0.299439i
$804$	−14.1803	−	5.41641i	−0.500102	−	0.191022i
$805$		0			0
$806$			33.8885i			1.19367i
$807$	41.8561	−	18.7186i	1.47341	−	0.658927i
$808$	−11.9814	−	11.9814i	−0.421505	−	0.421505i
$809$	−39.4164			−1.38581			−0.692904	−	0.721030i	$-0.743669\pi$
$809$	−39.4164			−1.38581			−0.692904	+	0.721030i	$0.743669\pi$
$810$		0			0
$811$	32.5410			1.14267			0.571335	−	0.820717i	$-0.306426\pi$
$811$	32.5410			1.14267			0.571335	+	0.820717i	$0.306426\pi$
$812$	−0.540182	−	0.540182i	−0.0189567	−	0.0189567i
$813$	23.3438	−	10.4397i	0.818704	−	0.366135i
$814$		−	23.4164i		−	0.820745i
$815$		0			0
$816$	3.23607	+	1.23607i	0.113285	+	0.0432710i
$817$	1.74806	−	1.74806i	0.0611570	−	0.0611570i
$818$	−2.90724	+	2.90724i	−0.101649	+	0.101649i
$819$	−12.9443	+	14.4721i	−0.452309	+	0.505697i
$820$		0			0
$821$		−	47.5967i		−	1.66114i	−0.556916	−	0.830569i	$-0.688015\pi$
$821$		−	47.5967i		−	1.66114i	0.556916	−	0.830569i	$-0.311985\pi$
$822$	−9.89949	−	22.1359i	−0.345285	−	0.772080i
$823$	−19.6414	−	19.6414i	−0.684655	−	0.684655i	0.276390	−	0.961045i	$-0.410862\pi$
$823$	−19.6414	−	19.6414i	−0.684655	−	0.684655i	−0.961045	+	0.276390i	$0.910862\pi$
$824$	−5.52786			−0.192572
$825$		0			0
$826$	0.291796			0.0101529
$827$	−7.14988	−	7.14988i	−0.248626	−	0.248626i	0.571781	−	0.820406i	$-0.306253\pi$
$827$	−7.14988	−	7.14988i	−0.248626	−	0.248626i	−0.820406	+	0.571781i	$0.806253\pi$
$828$	−7.40492	+	0.412662i	−0.257339	+	0.0143410i
$829$			25.8885i			0.899146i	0.893244	+	0.449573i	$0.148424\pi$
$829$			25.8885i			0.899146i	−0.893244	+	0.449573i	$0.851576\pi$
$830$		0			0
$831$	19.5279	−	51.1246i	0.677414	−	1.77349i
$832$	−4.57649	+	4.57649i	−0.158661	+	0.158661i
$833$	1.41421	−	1.41421i	0.0489996	−	0.0489996i
$834$	1.05573	−	2.76393i	0.0365569	−	0.0957071i
$835$		0			0
$836$		−	2.47214i		−	0.0855006i
$837$	−8.27895	+	25.9172i	−0.286162	+	0.895830i
$838$	13.5231	+	13.5231i	0.467149	+	0.467149i
$839$	52.3607			1.80769			0.903846	−	0.427859i	$-0.140732\pi$
$839$	52.3607			1.80769			0.903846	+	0.427859i	$0.140732\pi$
$840$		0			0
$841$	−28.4164			−0.979876
$842$	−7.73877	−	7.73877i	−0.266696	−	0.266696i
$843$	8.74032	+	19.5440i	0.301033	+	0.673129i
$844$			26.8328i			0.923624i
$845$		0			0
$846$	22.7639	+	20.3607i	0.782640	+	0.700015i
$847$	0.373256	−	0.373256i	0.0128252	−	0.0128252i
$848$	7.73877	−	7.73877i	0.265750	−	0.265750i
$849$	25.4164	+	9.70820i	0.872289	+	0.333185i
$850$		0			0
$851$			17.8885i			0.613211i
$852$	−18.0509	+	8.07262i	−0.618415	+	0.276563i
$853$	−16.5579	−	16.5579i	−0.566932	−	0.566932i	0.364336	−	0.931268i	$-0.381296\pi$
$853$	−16.5579	−	16.5579i	−0.566932	−	0.566932i	−0.931268	+	0.364336i	$0.881296\pi$
$854$	12.9443			0.442944
$855$		0			0
$856$	16.9443			0.579143
$857$	−17.5595	−	17.5595i	−0.599819	−	0.599819i	0.340445	−	0.940264i	$-0.389422\pi$
$857$	−17.5595	−	17.5595i	−0.599819	−	0.599819i	−0.940264	+	0.340445i	$0.889422\pi$
$858$	33.1158	−	14.8098i	1.13055	−	0.505599i
$859$			32.5410i			1.11029i	0.831755	+	0.555143i	$0.187336\pi$
$859$			32.5410i			1.11029i	−0.831755	+	0.555143i	$0.812664\pi$
$860$		0			0
$861$	14.9443	+	5.70820i	0.509299	+	0.194535i
$862$	8.89794	−	8.89794i	0.303065	−	0.303065i
$863$	9.15298	−	9.15298i	0.311571	−	0.311571i	−0.533947	−	0.845518i	$-0.679292\pi$
$863$	9.15298	−	9.15298i	0.311571	−	0.311571i	0.845518	+	0.533947i	$0.179292\pi$
$864$	−4.61803	+	2.38197i	−0.157109	+	0.0810361i
$865$		0			0
$866$		−	6.76393i		−	0.229848i
$867$	9.19239	+	20.5548i	0.312190	+	0.698078i
$868$	3.70246	+	3.70246i	0.125670	+	0.125670i
$869$	41.8885			1.42097
$870$		0			0
$871$	−56.7214			−1.92193
$872$	2.08191	+	2.08191i	0.0705025	+	0.0705025i
$873$	−2.36706	−	42.4751i	−0.0801127	−	1.43756i
$874$			1.88854i			0.0638809i
$875$		0			0
$876$	−2.29180	+	6.00000i	−0.0774326	+	0.202721i
$877$	16.4304	−	16.4304i	0.554815	−	0.554815i	−0.373012	−	0.927827i	$-0.621675\pi$
$877$	16.4304	−	16.4304i	0.554815	−	0.554815i	0.927827	+	0.373012i	$0.121675\pi$
$878$	6.94355	−	6.94355i	0.234333	−	0.234333i
$879$	1.88854	−	4.94427i	0.0636990	−	0.166766i
$880$		0			0
$881$			36.2918i			1.22270i	0.791360	+	0.611351i	$0.209374\pi$
$881$			36.2918i			1.22270i	−0.791360	+	0.611351i	$0.790626\pi$
$882$	0.166925	+	2.99535i	0.00562067	+	0.100859i
$883$	36.8971	+	36.8971i	1.24169	+	1.24169i	0.959301	+	0.282384i	$0.0911252\pi$
$883$	36.8971	+	36.8971i	1.24169	+	1.24169i	0.282384	+	0.959301i	$0.408875\pi$
$884$	12.9443			0.435363
$885$		0			0
$886$	8.94427			0.300489
$887$	−24.1692	−	24.1692i	−0.811521	−	0.811521i	0.173341	−	0.984862i	$-0.444544\pi$
$887$	−24.1692	−	24.1692i	−0.811521	−	0.811521i	−0.984862	+	0.173341i	$0.944544\pi$
$888$	5.11667	+	11.4412i	0.171704	+	0.383942i
$889$			14.4721i			0.485380i
$890$		0			0
$891$	28.9443	−	3.23607i	0.969670	−	0.108412i
$892$	−3.49613	+	3.49613i	−0.117059	+	0.117059i
$893$	5.49923	−	5.49923i	0.184025	−	0.184025i
$894$	−32.6525	−	12.4721i	−1.09206	−	0.417131i
$895$		0			0
$896$			1.00000i			0.0334077i
$897$	−25.2982	+	11.3137i	−0.844683	+	0.377754i
$898$	25.0432	+	25.0432i	0.835702	+	0.835702i
$899$	−4.00000			−0.133407
$900$		0			0
$901$	−21.8885			−0.729213
$902$	−21.1344	−	21.1344i	−0.703698	−	0.703698i
$903$	5.11667	−	2.28825i	0.170272	−	0.0761480i
$904$			3.52786i			0.117335i
$905$		0			0
$906$	8.94427	+	3.41641i	0.297154	+	0.113503i
$907$	−17.5107	+	17.5107i	−0.581435	+	0.581435i	−0.935297	−	0.353863i	$-0.884868\pi$
$907$	−17.5107	+	17.5107i	−0.581435	+	0.581435i	0.353863	+	0.935297i	$0.384868\pi$
$908$	−2.28825	+	2.28825i	−0.0759381	+	0.0759381i
$909$	−37.8885	−	33.8885i	−1.25668	−	1.12401i
$910$		0			0
$911$		−	35.0557i		−	1.16145i	−0.814100	−	0.580724i	$-0.802770\pi$
$911$		−	35.0557i		−	1.16145i	0.814100	−	0.580724i	$-0.197230\pi$
$912$	0.540182	+	1.20788i	0.0178872	+	0.0399970i
$913$	16.5579	+	16.5579i	0.547987	+	0.547987i
$914$	−4.36068			−0.144238
$915$		0			0
$916$	8.94427			0.295527
$917$	−5.86319	−	5.86319i	−0.193619	−	0.193619i
$918$	9.89949	+	3.16228i	0.326732	+	0.104371i
$919$		−	20.3607i		−	0.671637i	−0.941927	−	0.335818i	$-0.890987\pi$
$919$		−	20.3607i		−	0.671637i	0.941927	−	0.335818i	$-0.109013\pi$
$920$		0			0
$921$	10.6525	−	27.8885i	0.351011	−	0.918959i
$922$	14.3972	−	14.3972i	0.474146	−	0.474146i
$923$	−52.2471	+	52.2471i	−1.71973	+	1.71973i
$924$	2.00000	−	5.23607i	0.0657952	−	0.172254i
$925$		0			0
$926$			20.9443i			0.688271i
$927$	−16.5579	+	0.922740i	−0.543833	+	0.0303068i
$928$	−0.540182	−	0.540182i	−0.0177323	−	0.0177323i
$929$	14.1803			0.465242			0.232621	−	0.972567i	$-0.425270\pi$
$929$	14.1803			0.465242			0.232621	+	0.972567i	$0.425270\pi$
$930$		0			0
$931$	0.763932			0.0250369
$932$	−5.99070	−	5.99070i	−0.196232	−	0.196232i
$933$	−5.65685	−	12.6491i	−0.185197	−	0.414113i
$934$		−	7.23607i		−	0.236771i
$935$		0			0
$936$	−12.9443	+	14.4721i	−0.423097	+	0.473037i
$937$	−8.27895	+	8.27895i	−0.270462	+	0.270462i	−0.829286	−	0.558824i	$-0.811253\pi$
$937$	−8.27895	+	8.27895i	−0.270462	+	0.270462i	0.558824	+	0.829286i	$0.311253\pi$
$938$	−6.19704	+	6.19704i	−0.202340	+	0.202340i
$939$	−14.9443	−	5.70820i	−0.487688	−	0.186280i
$940$		0			0
$941$		−	7.05573i		−	0.230010i	−0.993365	−	0.115005i	$-0.963312\pi$
$941$		−	7.05573i		−	0.230010i	0.993365	−	0.115005i	$-0.0366884\pi$
$942$	8.74032	−	3.90879i	0.284775	−	0.127355i
$943$	16.1452	+	16.1452i	0.525761	+	0.525761i
$944$	0.291796			0.00949715
$945$		0			0
$946$	−10.4721			−0.340479
$947$	18.7186	+	18.7186i	0.608274	+	0.608274i	0.942495	−	0.334221i	$-0.108473\pi$
$947$	18.7186	+	18.7186i	0.608274	+	0.608274i	−0.334221	+	0.942495i	$0.608473\pi$
$948$	−20.4667	+	9.15298i	−0.664727	+	0.297275i
$949$			24.0000i			0.779073i
$950$		0			0
$951$	−43.5967	−	16.6525i	−1.41372	−	0.539994i
$952$	1.41421	−	1.41421i	0.0458349	−	0.0458349i
$953$	−22.9613	+	22.9613i	−0.743788	+	0.743788i	−0.973305	−	0.229516i	$-0.926286\pi$
$953$	−22.9613	+	22.9613i	−0.743788	+	0.743788i	0.229516	+	0.973305i	$0.426286\pi$
$954$	21.8885	−	24.4721i	0.708668	−	0.792315i
$955$		0			0
$956$			30.8328i			0.997205i
$957$	1.74806	+	3.90879i	0.0565069	+	0.126353i
$958$	−3.90879	−	3.90879i	−0.126287	−	0.126287i
$959$	−14.0000			−0.452084
$960$		0			0
$961$	−3.58359			−0.115600
$962$	33.1158	+	33.1158i	1.06770	+	1.06770i
$963$	50.7541	−	2.82843i	1.63553	−	0.0911448i
$964$			27.8885i			0.898230i
$965$		0			0
$966$	−1.52786	+	4.00000i	−0.0491582	+	0.128698i
$967$	−16.9706	+	16.9706i	−0.545737	+	0.545737i	−0.925205	−	0.379468i	$-0.876107\pi$
$967$	−16.9706	+	16.9706i	−0.545737	+	0.545737i	0.379468	+	0.925205i	$0.376107\pi$
$968$	0.373256	−	0.373256i	0.0119969	−	0.0119969i
$969$	0.944272	−	2.47214i	0.0303344	−	0.0794164i
$970$		0			0
$971$			48.6525i			1.56133i	0.624948	+	0.780666i	$0.285120\pi$
$971$			48.6525i			1.56133i	−0.624948	+	0.780666i	$0.714880\pi$
$972$	−13.4350	+	7.90569i	−0.430929	+	0.253575i
$973$	−1.20788	−	1.20788i	−0.0387229	−	0.0387229i
$974$	−16.3607			−0.524230
$975$		0			0
$976$	12.9443			0.414336
$977$	27.7928	+	27.7928i	0.889170	+	0.889170i	0.994443	−	0.105273i	$-0.0335716\pi$
$977$	27.7928	+	27.7928i	0.889170	+	0.889170i	−0.105273	+	0.994443i	$0.533572\pi$
$978$	10.3609	+	23.1676i	0.331304	+	0.740818i
$979$		−	29.8885i		−	0.955242i
$980$		0			0
$981$	6.58359	+	5.88854i	0.210198	+	0.188007i
$982$	15.3500	−	15.3500i	0.489839	−	0.489839i
$983$	29.8260	−	29.8260i	0.951302	−	0.951302i	−0.0475663	−	0.998868i	$-0.515147\pi$
$983$	29.8260	−	29.8260i	0.951302	−	0.951302i	0.998868	+	0.0475663i	$0.0151465\pi$
$984$	14.9443	+	5.70820i	0.476406	+	0.181971i
$985$		0			0
$986$			1.52786i			0.0486571i
$987$	16.0965	−	7.19859i	0.512358	−	0.229134i
$988$	3.49613	+	3.49613i	0.111227	+	0.111227i
$989$	8.00000			0.254385
$990$		0			0
$991$	−43.1935			−1.37209			−0.686043	−	0.727561i	$-0.740654\pi$
$991$	−43.1935			−1.37209			−0.686043	+	0.727561i	$0.740654\pi$
$992$	3.70246	+	3.70246i	0.117553	+	0.117553i
$993$	41.8561	−	18.7186i	1.32826	−	0.594018i
$994$			11.4164i			0.362106i
$995$		0			0
$996$	−11.7082	−	4.47214i	−0.370989	−	0.141705i
$997$	−6.99226	+	6.99226i	−0.221447	+	0.221447i	−0.809108	−	0.587661i	$-0.800049\pi$
$997$	−6.99226	+	6.99226i	−0.221447	+	0.221447i	0.587661	+	0.809108i	$0.300049\pi$
$998$	−8.48528	+	8.48528i	−0.268597	+	0.268597i
$999$	17.2361	+	33.4164i	0.545325	+	1.05725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.b.743.1	yes	8
3.2	odd	2		1050.2.j.a.743.3	yes	8
5.2	odd	4		1050.2.j.a.407.4	yes	8
5.3	odd	4		1050.2.j.a.407.1	✓	8
5.4	even	2	inner	1050.2.j.b.743.4	yes	8
15.2	even	4	inner	1050.2.j.b.407.1	yes	8
15.8	even	4	inner	1050.2.j.b.407.4	yes	8
15.14	odd	2		1050.2.j.a.743.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.j.a.407.1	✓	8	5.3	odd	4
1050.2.j.a.407.4	yes	8	5.2	odd	4
1050.2.j.a.743.2	yes	8	15.14	odd	2
1050.2.j.a.743.3	yes	8	3.2	odd	2
1050.2.j.b.407.1	yes	8	15.2	even	4	inner
1050.2.j.b.407.4	yes	8	15.8	even	4	inner
1050.2.j.b.743.1	yes	8	1.1	even	1	trivial
1050.2.j.b.743.4	yes	8	5.4	even	2	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.58114 + 0.707107i) q^{3} +1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.58114 + 0.707107i) q^{3} +1.00000i q^{4} +(1.61803 + 0.618034i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} +3.23607i q^{11} +(-0.707107 - 1.58114i) q^{12} +(-4.57649 - 4.57649i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} +(-2.99535 + 0.166925i) q^{18} +0.763932i q^{19} +(-0.618034 + 1.61803i) q^{21} +(2.28825 - 2.28825i) q^{22} +(-1.74806 + 1.74806i) q^{23} +(-0.618034 + 1.61803i) q^{24} +6.47214i q^{26} +(-1.58114 + 4.94975i) q^{27} +(0.707107 + 0.707107i) q^{28} -0.763932 q^{29} +5.23607 q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.28825 - 5.11667i) q^{33} -2.00000i q^{34} +(2.23607 + 2.00000i) q^{36} +(5.11667 - 5.11667i) q^{37} +(0.540182 - 0.540182i) q^{38} +(10.4721 + 4.00000i) q^{39} -9.23607i q^{41} +(1.58114 - 0.707107i) q^{42} +(-2.28825 - 2.28825i) q^{43} -3.23607 q^{44} +2.47214 q^{46} +(-7.19859 - 7.19859i) q^{47} +(1.58114 - 0.707107i) q^{48} -1.00000i q^{49} +(-3.23607 - 1.23607i) q^{51} +(4.57649 - 4.57649i) q^{52} +(-7.73877 + 7.73877i) q^{53} +(4.61803 - 2.38197i) q^{54} -1.00000i q^{56} +(-0.540182 - 1.20788i) q^{57} +(0.540182 + 0.540182i) q^{58} -0.291796 q^{59} -12.9443 q^{61} +(-3.70246 - 3.70246i) q^{62} +(-0.166925 - 2.99535i) q^{63} -1.00000i q^{64} +(-2.00000 + 5.23607i) q^{66} +(6.19704 - 6.19704i) q^{67} +(-1.41421 + 1.41421i) q^{68} +(1.52786 - 4.00000i) q^{69} -11.4164i q^{71} +(-0.166925 - 2.99535i) q^{72} +(-2.62210 - 2.62210i) q^{73} -7.23607 q^{74} -0.763932 q^{76} +(2.28825 + 2.28825i) q^{77} +(-4.57649 - 10.2333i) q^{78} -12.9443i q^{79} +(-1.00000 - 8.94427i) q^{81} +(-6.53089 + 6.53089i) q^{82} +(5.11667 - 5.11667i) q^{83} +(-1.61803 - 0.618034i) q^{84} +3.23607i q^{86} +(1.20788 - 0.540182i) q^{87} +(2.28825 + 2.28825i) q^{88} -9.23607 q^{89} -6.47214 q^{91} +(-1.74806 - 1.74806i) q^{92} +(-8.27895 + 3.70246i) q^{93} +10.1803i q^{94} +(-1.61803 - 0.618034i) q^{96} +(10.0270 - 10.0270i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(7.23607 + 6.47214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6} + 16 q^{9}+O(q^{10}) \) 8 * q + 4 * q^6 + 16 * q^9	\( 8 q + 4 q^{6} + 16 q^{9} - 8 q^{14} - 8 q^{16} + 4 q^{21} + 4 q^{24} - 24 q^{29} + 24 q^{31} + 48 q^{39} - 8 q^{44} - 16 q^{46} - 8 q^{51} + 28 q^{54} - 56 q^{59} - 32 q^{61} - 16 q^{66} + 48 q^{69} - 40 q^{74} - 24 q^{76} - 8 q^{81} - 4 q^{84} - 56 q^{89} - 16 q^{91} - 4 q^{96} + 40 q^{99}+O(q^{100}) \) 8 * q + 4 * q^6 + 16 * q^9 - 8 * q^14 - 8 * q^16 + 4 * q^21 + 4 * q^24 - 24 * q^29 + 24 * q^31 + 48 * q^39 - 8 * q^44 - 16 * q^46 - 8 * q^51 + 28 * q^54 - 56 * q^59 - 32 * q^61 - 16 * q^66 + 48 * q^69 - 40 * q^74 - 24 * q^76 - 8 * q^81 - 4 * q^84 - 56 * q^89 - 16 * q^91 - 4 * q^96 + 40 * q^99

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