LMFDB - Embedded newform 460.2.g.b.459.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(459,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("460.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			459.8
Root			$-1.14412 + 1.98168i$ of defining polynomial
Character	$\chi$	$=$	460.459
Dual form			460.2.g.b.459.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} -2.82843 q^{3} +(-1.00000 + 1.73205i) q^{4} +2.23607 q^{5} +(-2.00000 - 3.46410i) q^{6} -3.87298i q^{7} -2.82843 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} -2.82843 q^{3} +(-1.00000 + 1.73205i) q^{4} +2.23607 q^{5} +(-2.00000 - 3.46410i) q^{6} -3.87298i q^{7} -2.82843 q^{8} +5.00000 q^{9} +(1.58114 + 2.73861i) q^{10} +(2.82843 - 4.89898i) q^{12} -4.89898i q^{13} +(4.74342 - 2.73861i) q^{14} -6.32456 q^{15} +(-2.00000 - 3.46410i) q^{16} -2.23607 q^{17} +(3.53553 + 6.12372i) q^{18} +6.32456 q^{19} +(-2.23607 + 3.87298i) q^{20} +10.9545i q^{21} +(2.82843 + 3.87298i) q^{23} +8.00000 q^{24} +5.00000 q^{25} +(6.00000 - 3.46410i) q^{26} -5.65685 q^{27} +(6.70820 + 3.87298i) q^{28} +3.00000 q^{29} +(-4.47214 - 7.74597i) q^{30} -1.73205i q^{31} +(2.82843 - 4.89898i) q^{32} +(-1.58114 - 2.73861i) q^{34} -8.66025i q^{35} +(-5.00000 + 8.66025i) q^{36} +6.70820 q^{37} +(4.47214 + 7.74597i) q^{38} +13.8564i q^{39} -6.32456 q^{40} -9.00000 q^{41} +(-13.4164 + 7.74597i) q^{42} -7.74597i q^{43} +11.1803 q^{45} +(-2.74342 + 6.20271i) q^{46} -5.65685 q^{47} +(5.65685 + 9.79796i) q^{48} -8.00000 q^{49} +(3.53553 + 6.12372i) q^{50} +6.32456 q^{51} +(8.48528 + 4.89898i) q^{52} -2.23607 q^{53} +(-4.00000 - 6.92820i) q^{54} +10.9545i q^{56} -17.8885 q^{57} +(2.12132 + 3.67423i) q^{58} -8.66025i q^{59} +(6.32456 - 10.9545i) q^{60} -10.9545i q^{61} +(2.12132 - 1.22474i) q^{62} -19.3649i q^{63} +8.00000 q^{64} -10.9545i q^{65} +11.6190i q^{67} +(2.23607 - 3.87298i) q^{68} +(-8.00000 - 10.9545i) q^{69} +(10.6066 - 6.12372i) q^{70} -1.73205i q^{71} -14.1421 q^{72} -4.89898i q^{73} +(4.74342 + 8.21584i) q^{74} -14.1421 q^{75} +(-6.32456 + 10.9545i) q^{76} +(-16.9706 + 9.79796i) q^{78} +12.6491 q^{79} +(-4.47214 - 7.74597i) q^{80} +1.00000 q^{81} +(-6.36396 - 11.0227i) q^{82} -3.87298i q^{83} +(-18.9737 - 10.9545i) q^{84} -5.00000 q^{85} +(9.48683 - 5.47723i) q^{86} -8.48528 q^{87} +10.9545i q^{89} +(7.90569 + 13.6931i) q^{90} -18.9737 q^{91} +(-9.53663 + 1.02600i) q^{92} +4.89898i q^{93} +(-4.00000 - 6.92820i) q^{94} +14.1421 q^{95} +(-8.00000 + 13.8564i) q^{96} +13.4164 q^{97} +(-5.65685 - 9.79796i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 16 q^{6} + 40 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 16 * q^6 + 40 * q^9	$ 8 q - 8 q^{4} - 16 q^{6} + 40 q^{9} - 16 q^{16} + 64 q^{24} + 40 q^{25} + 48 q^{26} + 24 q^{29} - 40 q^{36} - 72 q^{41} + 16 q^{46} - 64 q^{49} - 32 q^{54} + 64 q^{64} - 64 q^{69} + 8 q^{81} - 40 q^{85} - 32 q^{94} - 64 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 - 16 * q^6 + 40 * q^9 - 16 * q^16 + 64 * q^24 + 40 * q^25 + 48 * q^26 + 24 * q^29 - 40 * q^36 - 72 * q^41 + 16 * q^46 - 64 * q^49 - 32 * q^54 + 64 * q^64 - 64 * q^69 + 8 * q^81 - 40 * q^85 - 32 * q^94 - 64 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.500000	+	0.866025i
$2$	0.707107	+	1.22474i	0.500000	+	0.866025i
$3$	−2.82843			−1.63299			−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−2.82843			−1.63299			−0.816497	+	0.577350i	$0.804087\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	2.23607			1.00000
$5$	2.23607			1.00000
$6$	−2.00000	−	3.46410i	−0.816497	−	1.41421i
$7$		−	3.87298i		−	1.46385i	−0.681385	−	0.731925i	$-0.738622\pi$
$7$		−	3.87298i		−	1.46385i	0.681385	−	0.731925i	$-0.261378\pi$
$8$	−2.82843			−1.00000
$9$	5.00000			1.66667
$10$	1.58114	+	2.73861i	0.500000	+	0.866025i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	2.82843	−	4.89898i	0.816497	−	1.41421i
$13$		−	4.89898i		−	1.35873i	−0.733799	−	0.679366i	$-0.762255\pi$
$13$		−	4.89898i		−	1.35873i	0.733799	−	0.679366i	$-0.237745\pi$
$14$	4.74342	−	2.73861i	1.26773	−	0.731925i
$15$	−6.32456			−1.63299
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−2.23607			−0.542326			−0.271163	−	0.962533i	$-0.587408\pi$
$17$	−2.23607			−0.542326			−0.271163	+	0.962533i	$0.587408\pi$
$18$	3.53553	+	6.12372i	0.833333	+	1.44338i
$19$	6.32456			1.45095			0.725476	−	0.688247i	$-0.241620\pi$
$19$	6.32456			1.45095			0.725476	+	0.688247i	$0.241620\pi$
$20$	−2.23607	+	3.87298i	−0.500000	+	0.866025i
$21$			10.9545i			2.39046i
$22$		0			0
$23$	2.82843	+	3.87298i	0.589768	+	0.807573i
$23$	2.82843	+	3.87298i	0.589768	+	0.807573i
$24$	8.00000			1.63299
$25$	5.00000			1.00000
$26$	6.00000	−	3.46410i	1.17670	−	0.679366i
$27$	−5.65685			−1.08866
$28$	6.70820	+	3.87298i	1.26773	+	0.731925i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−4.47214	−	7.74597i	−0.816497	−	1.41421i
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	2.82843	−	4.89898i	0.500000	−	0.866025i
$33$		0			0
$34$	−1.58114	−	2.73861i	−0.271163	−	0.469668i
$35$		−	8.66025i		−	1.46385i
$36$	−5.00000	+	8.66025i	−0.833333	+	1.44338i
$37$	6.70820			1.10282			0.551411	−	0.834234i	$-0.314090\pi$
$37$	6.70820			1.10282			0.551411	+	0.834234i	$0.314090\pi$
$38$	4.47214	+	7.74597i	0.725476	+	1.25656i
$39$			13.8564i			2.21880i
$40$	−6.32456			−1.00000
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$	−13.4164	+	7.74597i	−2.07020	+	1.19523i
$43$		−	7.74597i		−	1.18125i	−0.806947	−	0.590624i	$-0.798881\pi$
$43$		−	7.74597i		−	1.18125i	0.806947	−	0.590624i	$-0.201119\pi$
$44$		0			0
$45$	11.1803			1.66667
$46$	−2.74342	+	6.20271i	−0.404495	+	0.914540i
$47$	−5.65685			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$47$	−5.65685			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$48$	5.65685	+	9.79796i	0.816497	+	1.41421i
$49$	−8.00000			−1.14286
$50$	3.53553	+	6.12372i	0.500000	+	0.866025i
$51$	6.32456			0.885615
$52$	8.48528	+	4.89898i	1.17670	+	0.679366i
$53$	−2.23607			−0.307148			−0.153574	−	0.988137i	$-0.549078\pi$
$53$	−2.23607			−0.307148			−0.153574	+	0.988137i	$0.549078\pi$
$54$	−4.00000	−	6.92820i	−0.544331	−	0.942809i
$55$		0			0
$56$			10.9545i			1.46385i
$57$	−17.8885			−2.36940
$58$	2.12132	+	3.67423i	0.278543	+	0.482451i
$59$		−	8.66025i		−	1.12747i	−0.825956	−	0.563735i	$-0.809364\pi$
$59$		−	8.66025i		−	1.12747i	0.825956	−	0.563735i	$-0.190636\pi$
$60$	6.32456	−	10.9545i	0.816497	−	1.41421i
$61$		−	10.9545i		−	1.40257i	−0.712879	−	0.701287i	$-0.752609\pi$
$61$		−	10.9545i		−	1.40257i	0.712879	−	0.701287i	$-0.247391\pi$
$62$	2.12132	−	1.22474i	0.269408	−	0.155543i
$63$		−	19.3649i		−	2.43975i
$64$	8.00000			1.00000
$65$		−	10.9545i		−	1.35873i
$66$		0			0
$67$			11.6190i			1.41948i	0.704463	+	0.709740i	$0.251188\pi$
$67$			11.6190i			1.41948i	−0.704463	+	0.709740i	$0.748812\pi$
$68$	2.23607	−	3.87298i	0.271163	−	0.469668i
$69$	−8.00000	−	10.9545i	−0.963087	−	1.31876i
$70$	10.6066	−	6.12372i	1.26773	−	0.731925i
$71$		−	1.73205i		−	0.205557i	−0.994704	−	0.102778i	$-0.967227\pi$
$71$		−	1.73205i		−	0.205557i	0.994704	−	0.102778i	$-0.0327732\pi$
$72$	−14.1421			−1.66667
$73$		−	4.89898i		−	0.573382i	−0.958023	−	0.286691i	$-0.907445\pi$
$73$		−	4.89898i		−	0.573382i	0.958023	−	0.286691i	$-0.0925553\pi$
$74$	4.74342	+	8.21584i	0.551411	+	0.955072i
$75$	−14.1421			−1.63299
$76$	−6.32456	+	10.9545i	−0.725476	+	1.25656i
$77$		0			0
$78$	−16.9706	+	9.79796i	−1.92154	+	1.10940i
$79$	12.6491			1.42314			0.711568	−	0.702617i	$-0.247985\pi$
$79$	12.6491			1.42314			0.711568	+	0.702617i	$0.247985\pi$
$80$	−4.47214	−	7.74597i	−0.500000	−	0.866025i
$81$	1.00000			0.111111
$82$	−6.36396	−	11.0227i	−0.702782	−	1.21725i
$83$		−	3.87298i		−	0.425115i	−0.977149	−	0.212558i	$-0.931821\pi$
$83$		−	3.87298i		−	0.425115i	0.977149	−	0.212558i	$-0.0681793\pi$
$84$	−18.9737	−	10.9545i	−2.07020	−	1.19523i
$85$	−5.00000			−0.542326
$86$	9.48683	−	5.47723i	1.02299	−	0.590624i
$87$	−8.48528			−0.909718
$88$		0			0
$89$			10.9545i			1.16117i	0.814200	+	0.580585i	$0.197176\pi$
$89$			10.9545i			1.16117i	−0.814200	+	0.580585i	$0.802824\pi$
$90$	7.90569	+	13.6931i	0.833333	+	1.44338i
$91$	−18.9737			−1.98898
$92$	−9.53663	+	1.02600i	−0.994263	+	0.106967i
$93$			4.89898i			0.508001i
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	14.1421			1.45095
$96$	−8.00000	+	13.8564i	−0.816497	+	1.41421i
$97$	13.4164			1.36223			0.681115	−	0.732177i	$-0.261495\pi$
$97$	13.4164			1.36223			0.681115	+	0.732177i	$0.261495\pi$
$98$	−5.65685	−	9.79796i	−0.571429	−	0.989743i
$99$		0			0
$100$	−5.00000	+	8.66025i	−0.500000	+	0.866025i
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$	4.47214	+	7.74597i	0.442807	+	0.766965i
$103$			7.74597i			0.763233i	0.924321	+	0.381616i	$0.124632\pi$
$103$			7.74597i			0.763233i	−0.924321	+	0.381616i	$0.875368\pi$
$104$			13.8564i			1.35873i
$105$			24.4949i			2.39046i
$106$	−1.58114	−	2.73861i	−0.153574	−	0.265998i
$107$			11.6190i			1.12325i	0.827393	+	0.561623i	$0.189823\pi$
$107$			11.6190i			1.12325i	−0.827393	+	0.561623i	$0.810177\pi$
$108$	5.65685	−	9.79796i	0.544331	−	0.942809i
$109$		−	10.9545i		−	1.04925i	−0.851335	−	0.524623i	$-0.824206\pi$
$109$		−	10.9545i		−	1.04925i	0.851335	−	0.524623i	$-0.175794\pi$
$110$		0			0
$111$	−18.9737			−1.80090
$112$	−13.4164	+	7.74597i	−1.26773	+	0.731925i
$113$	−11.1803			−1.05176			−0.525879	−	0.850559i	$-0.676264\pi$
$113$	−11.1803			−1.05176			−0.525879	+	0.850559i	$0.676264\pi$
$114$	−12.6491	−	21.9089i	−1.18470	−	2.05196i
$115$	6.32456	+	8.66025i	0.589768	+	0.807573i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$		−	24.4949i		−	2.26455i
$118$	10.6066	−	6.12372i	0.976417	−	0.563735i
$119$			8.66025i			0.793884i
$120$	17.8885			1.63299
$121$	−11.0000			−1.00000
$122$	13.4164	−	7.74597i	1.21466	−	0.701287i
$123$	25.4558			2.29528
$124$	3.00000	+	1.73205i	0.269408	+	0.155543i
$125$	11.1803			1.00000
$126$	23.7171	−	13.6931i	2.11289	−	1.21988i
$127$	−8.48528			−0.752947			−0.376473	−	0.926427i	$-0.622863\pi$
$127$	−8.48528			−0.752947			−0.376473	+	0.926427i	$0.622863\pi$
$128$	5.65685	+	9.79796i	0.500000	+	0.866025i
$129$			21.9089i			1.92897i
$130$	13.4164	−	7.74597i	1.17670	−	0.679366i
$131$		−	10.3923i		−	0.907980i	−0.891007	−	0.453990i	$-0.850000\pi$
$131$		−	10.3923i		−	0.907980i	0.891007	−	0.453990i	$-0.150000\pi$
$132$		0			0
$133$		−	24.4949i		−	2.12398i
$134$	−14.2302	+	8.21584i	−1.22931	+	0.709740i
$135$	−12.6491			−1.08866
$136$	6.32456			0.542326
$137$	−4.47214			−0.382080			−0.191040	−	0.981582i	$-0.561186\pi$
$137$	−4.47214			−0.382080			−0.191040	+	0.981582i	$0.561186\pi$
$138$	7.75955	−	17.5439i	0.660537	−	1.49344i
$139$			5.19615i			0.440732i	0.975417	+	0.220366i	$0.0707252\pi$
$139$			5.19615i			0.440732i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	15.0000	+	8.66025i	1.26773	+	0.731925i
$141$	16.0000			1.34744
$142$	2.12132	−	1.22474i	0.178017	−	0.102778i
$143$		0			0
$144$	−10.0000	−	17.3205i	−0.833333	−	1.44338i
$145$	6.70820			0.557086
$146$	6.00000	−	3.46410i	0.496564	−	0.286691i
$147$	22.6274			1.86628
$148$	−6.70820	+	11.6190i	−0.551411	+	0.955072i
$149$			10.9545i			0.897424i	0.893677	+	0.448712i	$0.148117\pi$
$149$			10.9545i			0.897424i	−0.893677	+	0.448712i	$0.851883\pi$
$150$	−10.0000	−	17.3205i	−0.816497	−	1.41421i
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	−17.8885			−1.45095
$153$	−11.1803			−0.903877
$154$		0			0
$155$		−	3.87298i		−	0.311086i
$156$	−24.0000	−	13.8564i	−1.92154	−	1.10940i
$157$	6.70820			0.535373			0.267686	−	0.963506i	$-0.413741\pi$
$157$	6.70820			0.535373			0.267686	+	0.963506i	$0.413741\pi$
$158$	8.94427	+	15.4919i	0.711568	+	1.23247i
$159$	6.32456			0.501570
$160$	6.32456	−	10.9545i	0.500000	−	0.866025i
$161$	15.0000	−	10.9545i	1.18217	−	0.863332i
$162$	0.707107	+	1.22474i	0.0555556	+	0.0962250i
$163$	−16.9706			−1.32924			−0.664619	−	0.747183i	$-0.731406\pi$
$163$	−16.9706			−1.32924			−0.664619	+	0.747183i	$0.731406\pi$
$164$	9.00000	−	15.5885i	0.702782	−	1.21725i
$165$		0			0
$166$	4.74342	−	2.73861i	0.368161	−	0.212558i
$167$	11.3137			0.875481			0.437741	−	0.899101i	$-0.355779\pi$
$167$	11.3137			0.875481			0.437741	+	0.899101i	$0.355779\pi$
$168$		−	30.9839i		−	2.39046i
$169$	−11.0000			−0.846154
$170$	−3.53553	−	6.12372i	−0.271163	−	0.469668i
$171$	31.6228			2.41825
$172$	13.4164	+	7.74597i	1.02299	+	0.590624i
$173$			24.4949i			1.86231i	0.364620	+	0.931156i	$0.381199\pi$
$173$			24.4949i			1.86231i	−0.364620	+	0.931156i	$0.618801\pi$
$174$	−6.00000	−	10.3923i	−0.454859	−	0.787839i
$175$		−	19.3649i		−	1.46385i
$176$		0			0
$177$			24.4949i			1.84115i
$178$	−13.4164	+	7.74597i	−1.00560	+	0.580585i
$179$			3.46410i			0.258919i	0.991585	+	0.129460i	$0.0413242\pi$
$179$			3.46410i			0.258919i	−0.991585	+	0.129460i	$0.958676\pi$
$180$	−11.1803	+	19.3649i	−0.833333	+	1.44338i
$181$			10.9545i			0.814238i	0.913375	+	0.407119i	$0.133467\pi$
$181$			10.9545i			0.814238i	−0.913375	+	0.407119i	$0.866533\pi$
$182$	−13.4164	−	23.2379i	−0.994490	−	1.72251i
$183$			30.9839i			2.29039i
$184$	−8.00000	−	10.9545i	−0.589768	−	0.807573i
$185$	15.0000			1.10282
$186$	−6.00000	+	3.46410i	−0.439941	+	0.254000i
$187$		0			0
$188$	5.65685	−	9.79796i	0.412568	−	0.714590i
$189$			21.9089i			1.59364i
$190$	10.0000	+	17.3205i	0.725476	+	1.25656i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−22.6274			−1.63299
$193$			4.89898i			0.352636i	0.984333	+	0.176318i	$0.0564187\pi$
$193$			4.89898i			0.352636i	−0.984333	+	0.176318i	$0.943581\pi$
$194$	9.48683	+	16.4317i	0.681115	+	1.17973i
$195$			30.9839i			2.21880i
$196$	8.00000	−	13.8564i	0.571429	−	0.989743i
$197$		−	9.79796i		−	0.698076i	−0.937109	−	0.349038i	$-0.886508\pi$
$197$		−	9.79796i		−	0.698076i	0.937109	−	0.349038i	$-0.113492\pi$
$198$		0			0
$199$	−6.32456			−0.448336			−0.224168	−	0.974551i	$-0.571966\pi$
$199$	−6.32456			−0.448336			−0.224168	+	0.974551i	$0.571966\pi$
$200$	−14.1421			−1.00000
$201$		−	32.8634i		−	2.31800i
$202$	2.12132	+	3.67423i	0.149256	+	0.258518i
$203$		−	11.6190i		−	0.815490i
$204$	−6.32456	+	10.9545i	−0.442807	+	0.766965i
$205$	−20.1246			−1.40556
$206$	−9.48683	+	5.47723i	−0.660979	+	0.381616i
$207$	14.1421	+	19.3649i	0.982946	+	1.34595i
$208$	−16.9706	+	9.79796i	−1.17670	+	0.679366i
$209$		0			0
$210$	−30.0000	+	17.3205i	−2.07020	+	1.19523i
$211$		−	8.66025i		−	0.596196i	−0.954535	−	0.298098i	$-0.903648\pi$
$211$		−	8.66025i		−	0.596196i	0.954535	−	0.298098i	$-0.0963523\pi$
$212$	2.23607	−	3.87298i	0.153574	−	0.265998i
$213$			4.89898i			0.335673i
$214$	−14.2302	+	8.21584i	−0.972760	+	0.561623i
$215$		−	17.3205i		−	1.18125i
$216$	16.0000			1.08866
$217$	−6.70820			−0.455383
$218$	13.4164	−	7.74597i	0.908674	−	0.524623i
$219$			13.8564i			0.936329i
$220$		0			0
$221$			10.9545i			0.736876i
$222$	−13.4164	−	23.2379i	−0.900450	−	1.55963i
$223$	−8.48528			−0.568216			−0.284108	−	0.958792i	$-0.591698\pi$
$223$	−8.48528			−0.568216			−0.284108	+	0.958792i	$0.591698\pi$
$224$	−18.9737	−	10.9545i	−1.26773	−	0.731925i
$225$	25.0000			1.66667
$226$	−7.90569	−	13.6931i	−0.525879	−	0.910849i
$227$		−	7.74597i		−	0.514118i	−0.966396	−	0.257059i	$-0.917247\pi$
$227$		−	7.74597i		−	0.514118i	0.966396	−	0.257059i	$-0.0827534\pi$
$228$	17.8885	−	30.9839i	1.18470	−	2.05196i
$229$		−	10.9545i		−	0.723891i	−0.932199	−	0.361945i	$-0.882113\pi$
$229$		−	10.9545i		−	0.723891i	0.932199	−	0.361945i	$-0.117887\pi$
$230$	−6.13447	+	13.8697i	−0.404495	+	0.914540i
$231$		0			0
$232$	−8.48528			−0.557086
$233$			29.3939i			1.92566i	0.270114	+	0.962828i	$0.412939\pi$
$233$			29.3939i			1.92566i	−0.270114	+	0.962828i	$0.587061\pi$
$234$	30.0000	−	17.3205i	1.96116	−	1.13228i
$235$	−12.6491			−0.825137
$236$	15.0000	+	8.66025i	0.976417	+	0.563735i
$237$	−35.7771			−2.32397
$238$	−10.6066	+	6.12372i	−0.687524	+	0.396942i
$239$			12.1244i			0.784259i	0.919910	+	0.392130i	$0.128262\pi$
$239$			12.1244i			0.784259i	−0.919910	+	0.392130i	$0.871738\pi$
$240$	12.6491	+	21.9089i	0.816497	+	1.41421i
$241$			10.9545i			0.705638i	0.935692	+	0.352819i	$0.114777\pi$
$241$			10.9545i			0.705638i	−0.935692	+	0.352819i	$0.885223\pi$
$242$	−7.77817	−	13.4722i	−0.500000	−	0.866025i
$243$	14.1421			0.907218
$244$	18.9737	+	10.9545i	1.21466	+	0.701287i
$245$	−17.8885			−1.14286
$246$	18.0000	+	31.1769i	1.14764	+	1.98777i
$247$		−	30.9839i		−	1.97146i
$248$			4.89898i			0.311086i
$249$			10.9545i			0.694210i
$250$	7.90569	+	13.6931i	0.500000	+	0.866025i
$251$	18.9737			1.19761			0.598804	−	0.800896i	$-0.295643\pi$
$251$	18.9737			1.19761			0.598804	+	0.800896i	$0.295643\pi$
$252$	33.5410	+	19.3649i	2.11289	+	1.21988i
$253$		0			0
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	14.1421			0.885615
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		−	9.79796i		−	0.611180i	−0.952163	−	0.305590i	$-0.901146\pi$
$257$		−	9.79796i		−	0.611180i	0.952163	−	0.305590i	$-0.0988537\pi$
$258$	−26.8328	+	15.4919i	−1.67054	+	0.964486i
$259$		−	25.9808i		−	1.61437i
$260$	18.9737	+	10.9545i	1.17670	+	0.679366i
$261$	15.0000			0.928477
$262$	12.7279	−	7.34847i	0.786334	−	0.453990i
$263$			11.6190i			0.716455i	0.933634	+	0.358228i	$0.116619\pi$
$263$			11.6190i			0.716455i	−0.933634	+	0.358228i	$0.883381\pi$
$264$		0			0
$265$	−5.00000			−0.307148
$266$	30.0000	−	17.3205i	1.83942	−	1.06199i
$267$		−	30.9839i		−	1.89618i
$268$	−20.1246	−	11.6190i	−1.22931	−	0.709740i
$269$	3.00000			0.182913			0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000			0.182913			0.0914566	+	0.995809i	$0.470848\pi$
$270$	−8.94427	−	15.4919i	−0.544331	−	0.942809i
$271$		−	8.66025i		−	0.526073i	−0.964786	−	0.263036i	$-0.915276\pi$
$271$		−	8.66025i		−	0.526073i	0.964786	−	0.263036i	$-0.0847240\pi$
$272$	4.47214	+	7.74597i	0.271163	+	0.469668i
$273$	53.6656			3.24799
$274$	−3.16228	−	5.47723i	−0.191040	−	0.330891i
$275$		0			0
$276$	26.9737	−	2.90196i	1.62362	−	0.174677i
$277$			9.79796i			0.588702i	0.955697	+	0.294351i	$0.0951035\pi$
$277$			9.79796i			0.588702i	−0.955697	+	0.294351i	$0.904896\pi$
$278$	−6.36396	+	3.67423i	−0.381685	+	0.220366i
$279$		−	8.66025i		−	0.518476i
$280$			24.4949i			1.46385i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	11.3137	+	19.5959i	0.673722	+	1.16692i
$283$			11.6190i			0.690675i	0.938479	+	0.345337i	$0.112236\pi$
$283$			11.6190i			0.690675i	−0.938479	+	0.345337i	$0.887764\pi$
$284$	3.00000	+	1.73205i	0.178017	+	0.102778i
$285$	−40.0000			−2.36940
$286$		0			0
$287$			34.8569i			2.05753i
$288$	14.1421	−	24.4949i	0.833333	−	1.44338i
$289$	−12.0000			−0.705882
$290$	4.74342	+	8.21584i	0.278543	+	0.482451i
$291$	−37.9473			−2.22451
$292$	8.48528	+	4.89898i	0.496564	+	0.286691i
$293$	24.5967			1.43696			0.718479	−	0.695549i	$-0.244839\pi$
$293$	24.5967			1.43696			0.718479	+	0.695549i	$0.244839\pi$
$294$	16.0000	+	27.7128i	0.933139	+	1.61624i
$295$		−	19.3649i		−	1.12747i
$296$	−18.9737			−1.10282
$297$		0			0
$298$	−13.4164	+	7.74597i	−0.777192	+	0.448712i
$299$	18.9737	−	13.8564i	1.09728	−	0.801337i
$300$	14.1421	−	24.4949i	0.816497	−	1.41421i
$301$	−30.0000			−1.72917
$302$	−12.7279	+	7.34847i	−0.732410	+	0.422857i
$303$	−8.48528			−0.487467
$304$	−12.6491	−	21.9089i	−0.725476	−	1.25656i
$305$		−	24.4949i		−	1.40257i
$306$	−7.90569	−	13.6931i	−0.451938	−	0.782780i
$307$	−16.9706			−0.968561			−0.484281	−	0.874913i	$-0.660919\pi$
$307$	−16.9706			−0.968561			−0.484281	+	0.874913i	$0.660919\pi$
$308$		0			0
$309$		−	21.9089i		−	1.24635i
$310$	4.74342	−	2.73861i	0.269408	−	0.155543i
$311$			10.3923i			0.589294i	0.955606	+	0.294647i	$0.0952020\pi$
$311$			10.3923i			0.589294i	−0.955606	+	0.294647i	$0.904798\pi$
$312$		−	39.1918i		−	2.21880i
$313$	−20.1246			−1.13751			−0.568755	−	0.822507i	$-0.692575\pi$
$313$	−20.1246			−1.13751			−0.568755	+	0.822507i	$0.692575\pi$
$314$	4.74342	+	8.21584i	0.267686	+	0.463647i
$315$		−	43.3013i		−	2.43975i
$316$	−12.6491	+	21.9089i	−0.711568	+	1.23247i
$317$			24.4949i			1.37577i	0.725819	+	0.687885i	$0.241461\pi$
$317$			24.4949i			1.37577i	−0.725819	+	0.687885i	$0.758539\pi$
$318$	4.47214	+	7.74597i	0.250785	+	0.434372i
$319$		0			0
$320$	17.8885			1.00000
$321$		−	32.8634i		−	1.83425i
$322$	24.0230	+	10.6252i	1.33875	+	0.592120i
$323$	−14.1421			−0.786889
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$		−	24.4949i		−	1.35873i
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$			30.9839i			1.71341i
$328$	25.4558			1.40556
$329$			21.9089i			1.20788i
$330$		0			0
$331$		−	15.5885i		−	0.856819i	−0.903585	−	0.428410i	$-0.859074\pi$
$331$		−	15.5885i		−	0.856819i	0.903585	−	0.428410i	$-0.140926\pi$
$332$	6.70820	+	3.87298i	0.368161	+	0.212558i
$333$	33.5410			1.83804
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$			25.9808i			1.41948i
$336$	37.9473	−	21.9089i	2.07020	−	1.19523i
$337$	13.4164			0.730838			0.365419	−	0.930843i	$-0.380926\pi$
$337$	13.4164			0.730838			0.365419	+	0.930843i	$0.380926\pi$
$338$	−7.77817	−	13.4722i	−0.423077	−	0.732791i
$339$	31.6228			1.71751
$340$	5.00000	−	8.66025i	0.271163	−	0.469668i
$341$		0			0
$342$	22.3607	+	38.7298i	1.20913	+	2.09427i
$343$			3.87298i			0.209121i
$344$			21.9089i			1.18125i
$345$	−17.8885	−	24.4949i	−0.963087	−	1.31876i
$346$	−30.0000	+	17.3205i	−1.61281	+	0.931156i
$347$	2.82843			0.151838			0.0759190	−	0.997114i	$-0.475811\pi$
$347$	2.82843			0.151838			0.0759190	+	0.997114i	$0.475811\pi$
$348$	8.48528	−	14.6969i	0.454859	−	0.787839i
$349$	23.0000			1.23116			0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000			1.23116			0.615581	+	0.788074i	$0.288921\pi$
$350$	23.7171	−	13.6931i	1.26773	−	0.731925i
$351$			27.7128i			1.47920i
$352$		0			0
$353$		−	29.3939i		−	1.56448i	−0.622978	−	0.782239i	$-0.714078\pi$
$353$		−	29.3939i		−	1.56448i	0.622978	−	0.782239i	$-0.285922\pi$
$354$	−30.0000	+	17.3205i	−1.59448	+	0.920575i
$355$		−	3.87298i		−	0.205557i
$356$	−18.9737	−	10.9545i	−1.00560	−	0.580585i
$357$		−	24.4949i		−	1.29641i
$358$	−4.24264	+	2.44949i	−0.224231	+	0.129460i
$359$	18.9737			1.00139			0.500696	−	0.865623i	$-0.333077\pi$
$359$	18.9737			1.00139			0.500696	+	0.865623i	$0.333077\pi$
$360$	−31.6228			−1.66667
$361$	21.0000			1.10526
$362$	−13.4164	+	7.74597i	−0.705151	+	0.407119i
$363$	31.1127			1.63299
$364$	18.9737	−	32.8634i	0.994490	−	1.72251i
$365$		−	10.9545i		−	0.573382i
$366$	−37.9473	+	21.9089i	−1.98354	+	1.14520i
$367$		−	3.87298i		−	0.202168i	−0.994878	−	0.101084i	$-0.967769\pi$
$367$		−	3.87298i		−	0.202168i	0.994878	−	0.101084i	$-0.0322311\pi$
$368$	7.75955	−	17.5439i	0.404495	−	0.914540i
$369$	−45.0000			−2.34261
$370$	10.6066	+	18.3712i	0.551411	+	0.955072i
$371$			8.66025i			0.449618i
$372$	−8.48528	−	4.89898i	−0.439941	−	0.254000i
$373$	−13.4164			−0.694675			−0.347338	−	0.937740i	$-0.612914\pi$
$373$	−13.4164			−0.694675			−0.347338	+	0.937740i	$0.612914\pi$
$374$		0			0
$375$	−31.6228			−1.63299
$376$	16.0000			0.825137
$377$		−	14.6969i		−	0.756931i
$378$	−26.8328	+	15.4919i	−1.38013	+	0.796819i
$379$	6.32456			0.324871			0.162435	−	0.986719i	$-0.448065\pi$
$379$	6.32456			0.324871			0.162435	+	0.986719i	$0.448065\pi$
$380$	−14.1421	+	24.4949i	−0.725476	+	1.25656i
$381$	24.0000			1.22956
$382$		0			0
$383$		−	3.87298i		−	0.197900i	−0.995092	−	0.0989501i	$-0.968452\pi$
$383$		−	3.87298i		−	0.197900i	0.995092	−	0.0989501i	$-0.0315484\pi$
$384$	−16.0000	−	27.7128i	−0.816497	−	1.41421i
$385$		0			0
$386$	−6.00000	+	3.46410i	−0.305392	+	0.176318i
$387$		−	38.7298i		−	1.96875i
$388$	−13.4164	+	23.2379i	−0.681115	+	1.17973i
$389$		−	21.9089i		−	1.11083i	−0.831575	−	0.555413i	$-0.812560\pi$
$389$		−	21.9089i		−	1.11083i	0.831575	−	0.555413i	$-0.187440\pi$
$390$	−37.9473	+	21.9089i	−1.92154	+	1.10940i
$391$	−6.32456	−	8.66025i	−0.319847	−	0.437968i
$392$	22.6274			1.14286
$393$			29.3939i			1.48272i
$394$	12.0000	−	6.92820i	0.604551	−	0.349038i
$395$	28.2843			1.42314
$396$		0			0
$397$			34.2929i			1.72111i	0.509358	+	0.860555i	$0.329883\pi$
$397$			34.2929i			1.72111i	−0.509358	+	0.860555i	$0.670117\pi$
$398$	−4.47214	−	7.74597i	−0.224168	−	0.388270i
$399$			69.2820i			3.46844i
$400$	−10.0000	−	17.3205i	−0.500000	−	0.866025i
$401$			21.9089i			1.09408i	0.837107	+	0.547039i	$0.184245\pi$
$401$			21.9089i			1.09408i	−0.837107	+	0.547039i	$0.815755\pi$
$402$	40.2492	−	23.2379i	2.00745	−	1.15900i
$403$	−8.48528			−0.422682
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	2.23607			0.111111
$406$	14.2302	−	8.21584i	0.706235	−	0.407745i
$407$		0			0
$408$	−17.8885			−0.885615
$409$	7.00000			0.346128			0.173064	−	0.984911i	$-0.444633\pi$
$409$	7.00000			0.346128			0.173064	+	0.984911i	$0.444633\pi$
$410$	−14.2302	−	24.6475i	−0.702782	−	1.21725i
$411$	12.6491			0.623935
$412$	−13.4164	−	7.74597i	−0.660979	−	0.381616i
$413$	−33.5410			−1.65045
$414$	−13.7171	+	31.0136i	−0.674158	+	1.52423i
$415$		−	8.66025i		−	0.425115i
$416$	−24.0000	−	13.8564i	−1.17670	−	0.679366i
$417$		−	14.6969i		−	0.719712i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−42.4264	−	24.4949i	−2.07020	−	1.19523i
$421$			21.9089i			1.06777i	0.845556	+	0.533887i	$0.179269\pi$
$421$			21.9089i			1.06777i	−0.845556	+	0.533887i	$0.820731\pi$
$422$	10.6066	−	6.12372i	0.516321	−	0.298098i
$423$	−28.2843			−1.37523
$424$	6.32456			0.307148
$425$	−11.1803			−0.542326
$426$	−6.00000	+	3.46410i	−0.290701	+	0.167836i
$427$	−42.4264			−2.05316
$428$	−20.1246	−	11.6190i	−0.972760	−	0.561623i
$429$		0			0
$430$	21.2132	−	12.2474i	1.02299	−	0.590624i
$431$	−18.9737			−0.913929			−0.456965	−	0.889485i	$-0.651063\pi$
$431$	−18.9737			−0.913929			−0.456965	+	0.889485i	$0.651063\pi$
$432$	11.3137	+	19.5959i	0.544331	+	0.942809i
$433$	33.5410			1.61188			0.805939	−	0.591998i	$-0.201661\pi$
$433$	33.5410			1.61188			0.805939	+	0.591998i	$0.201661\pi$
$434$	−4.74342	−	8.21584i	−0.227691	−	0.394373i
$435$	−18.9737			−0.909718
$436$	18.9737	+	10.9545i	0.908674	+	0.524623i
$437$	17.8885	+	24.4949i	0.855725	+	1.17175i
$438$	−16.9706	+	9.79796i	−0.810885	+	0.468165i
$439$			38.1051i			1.81866i	0.416078	+	0.909329i	$0.363404\pi$
$439$			38.1051i			1.81866i	−0.416078	+	0.909329i	$0.636596\pi$
$440$		0			0
$441$	−40.0000			−1.90476
$442$	−13.4164	+	7.74597i	−0.638153	+	0.368438i
$443$	−2.82843			−0.134383			−0.0671913	−	0.997740i	$-0.521404\pi$
$443$	−2.82843			−0.134383			−0.0671913	+	0.997740i	$0.521404\pi$
$444$	18.9737	−	32.8634i	0.900450	−	1.55963i
$445$			24.4949i			1.16117i
$446$	−6.00000	−	10.3923i	−0.284108	−	0.492090i
$447$		−	30.9839i		−	1.46549i
$448$		−	30.9839i		−	1.46385i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	17.6777	+	30.6186i	0.833333	+	1.44338i
$451$		0			0
$452$	11.1803	−	19.3649i	0.525879	−	0.910849i
$453$		−	29.3939i		−	1.38104i
$454$	9.48683	−	5.47723i	0.445239	−	0.257059i
$455$	−42.4264			−1.98898
$456$	50.5964			2.36940
$457$	33.5410			1.56898			0.784491	−	0.620140i	$-0.212924\pi$
$457$	33.5410			1.56898			0.784491	+	0.620140i	$0.212924\pi$
$458$	13.4164	−	7.74597i	0.626908	−	0.361945i
$459$	12.6491			0.590410
$460$	−21.3246	+	2.29420i	−0.994263	+	0.106967i
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$	−8.48528			−0.394344			−0.197172	−	0.980369i	$-0.563176\pi$
$463$	−8.48528			−0.394344			−0.197172	+	0.980369i	$0.563176\pi$
$464$	−6.00000	−	10.3923i	−0.278543	−	0.482451i
$465$			10.9545i			0.508001i
$466$	−36.0000	+	20.7846i	−1.66767	+	0.962828i
$467$		−	19.3649i		−	0.896101i	−0.894008	−	0.448051i	$-0.852118\pi$
$467$		−	19.3649i		−	0.896101i	0.894008	−	0.448051i	$-0.147882\pi$
$468$	42.4264	+	24.4949i	1.96116	+	1.13228i
$469$	45.0000			2.07791
$470$	−8.94427	−	15.4919i	−0.412568	−	0.714590i
$471$	−18.9737			−0.874260
$472$			24.4949i			1.12747i
$473$		0			0
$474$	−25.2982	−	43.8178i	−1.16199	−	2.01262i
$475$	31.6228			1.45095
$476$	−15.0000	−	8.66025i	−0.687524	−	0.396942i
$477$	−11.1803			−0.511913
$478$	−14.8492	+	8.57321i	−0.679189	+	0.392130i
$479$	−37.9473			−1.73386			−0.866929	−	0.498432i	$-0.833909\pi$
$479$	−37.9473			−1.73386			−0.866929	+	0.498432i	$0.833909\pi$
$480$	−17.8885	+	30.9839i	−0.816497	+	1.41421i
$481$		−	32.8634i		−	1.49844i
$482$	−13.4164	+	7.74597i	−0.611101	+	0.352819i
$483$	−42.4264	+	30.9839i	−1.93047	+	1.40981i
$484$	11.0000	−	19.0526i	0.500000	−	0.866025i
$485$	30.0000			1.36223
$486$	10.0000	+	17.3205i	0.453609	+	0.785674i
$487$	−8.48528			−0.384505			−0.192252	−	0.981346i	$-0.561579\pi$
$487$	−8.48528			−0.384505			−0.192252	+	0.981346i	$0.561579\pi$
$488$			30.9839i			1.40257i
$489$	48.0000			2.17064
$490$	−12.6491	−	21.9089i	−0.571429	−	0.989743i
$491$		−	36.3731i		−	1.64149i	−0.571292	−	0.820747i	$-0.693558\pi$
$491$		−	36.3731i		−	1.64149i	0.571292	−	0.820747i	$-0.306442\pi$
$492$	−25.4558	+	44.0908i	−1.14764	+	1.98777i
$493$	−6.70820			−0.302122
$494$	37.9473	−	21.9089i	1.70733	−	0.985728i
$495$		0			0
$496$	−6.00000	+	3.46410i	−0.269408	+	0.155543i
$497$	−6.70820			−0.300904
$498$	−13.4164	+	7.74597i	−0.601204	+	0.347105i
$499$			39.8372i			1.78336i	0.452670	+	0.891678i	$0.350472\pi$
$499$			39.8372i			1.78336i	−0.452670	+	0.891678i	$0.649528\pi$
$500$	−11.1803	+	19.3649i	−0.500000	+	0.866025i
$501$	−32.0000			−1.42965
$502$	13.4164	+	23.2379i	0.598804	+	1.03716i
$503$		−	19.3649i		−	0.863439i	−0.902008	−	0.431719i	$-0.857907\pi$
$503$		−	19.3649i		−	0.863439i	0.902008	−	0.431719i	$-0.142093\pi$
$504$			54.7723i			2.43975i
$505$	6.70820			0.298511
$506$		0			0
$507$	31.1127			1.38176
$508$	8.48528	−	14.6969i	0.376473	−	0.652071i
$509$	−42.0000			−1.86162			−0.930809	−	0.365507i	$-0.880896\pi$
$509$	−42.0000			−1.86162			−0.930809	+	0.365507i	$0.880896\pi$
$510$	10.0000	+	17.3205i	0.442807	+	0.766965i
$511$	−18.9737			−0.839346
$512$	−22.6274			−1.00000
$513$	−35.7771			−1.57960
$514$	12.0000	−	6.92820i	0.529297	−	0.305590i
$515$			17.3205i			0.763233i
$516$	−37.9473	−	21.9089i	−1.67054	−	0.964486i
$517$		0			0
$518$	31.8198	−	18.3712i	1.39808	−	0.807183i
$519$		−	69.2820i		−	3.04114i
$520$			30.9839i			1.35873i
$521$			32.8634i			1.43977i	0.694094	+	0.719885i	$0.255805\pi$
$521$			32.8634i			1.43977i	−0.694094	+	0.719885i	$0.744195\pi$
$522$	10.6066	+	18.3712i	0.464238	+	0.804084i
$523$		−	38.7298i		−	1.69354i	−0.531961	−	0.846769i	$-0.678545\pi$
$523$		−	38.7298i		−	1.69354i	0.531961	−	0.846769i	$-0.321455\pi$
$524$	18.0000	+	10.3923i	0.786334	+	0.453990i
$525$			54.7723i			2.39046i
$526$	−14.2302	+	8.21584i	−0.620468	+	0.358228i
$527$			3.87298i			0.168710i
$528$		0			0
$529$	−7.00000	+	21.9089i	−0.304348	+	0.952561i
$530$	−3.53553	−	6.12372i	−0.153574	−	0.265998i
$531$		−	43.3013i		−	1.87912i
$532$	42.4264	+	24.4949i	1.83942	+	1.06199i
$533$			44.0908i			1.90979i
$534$	37.9473	−	21.9089i	1.64214	−	0.948091i
$535$			25.9808i			1.12325i
$536$		−	32.8634i		−	1.41948i
$537$		−	9.79796i		−	0.422813i
$538$	2.12132	+	3.67423i	0.0914566	+	0.158408i
$539$		0			0
$540$	12.6491	−	21.9089i	0.544331	−	0.942809i
$541$	14.0000			0.601907			0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000			0.601907			0.300954	+	0.953639i	$0.402695\pi$
$542$	10.6066	−	6.12372i	0.455593	−	0.263036i
$543$		−	30.9839i		−	1.32964i
$544$	−6.32456	+	10.9545i	−0.271163	+	0.469668i
$545$		−	24.4949i		−	1.04925i
$546$	37.9473	+	65.7267i	1.62400	+	2.81284i
$547$	33.9411			1.45122			0.725609	−	0.688107i	$-0.241558\pi$
$547$	33.9411			1.45122			0.725609	+	0.688107i	$0.241558\pi$
$548$	4.47214	−	7.74597i	0.191040	−	0.330891i
$549$		−	54.7723i		−	2.33762i
$550$		0			0
$551$	18.9737			0.808305
$552$	22.6274	+	30.9839i	0.963087	+	1.31876i
$553$		−	48.9898i		−	2.08326i
$554$	−12.0000	+	6.92820i	−0.509831	+	0.294351i
$555$	−42.4264			−1.80090
$556$	−9.00000	−	5.19615i	−0.381685	−	0.220366i
$557$	24.5967			1.04220			0.521099	−	0.853496i	$-0.325522\pi$
$557$	24.5967			1.04220			0.521099	+	0.853496i	$0.325522\pi$
$558$	10.6066	−	6.12372i	0.449013	−	0.259238i
$559$	−37.9473			−1.60500
$560$	−30.0000	+	17.3205i	−1.26773	+	0.731925i
$561$		0			0
$562$		0			0
$563$			11.6190i			0.489680i	0.969563	+	0.244840i	$0.0787355\pi$
$563$			11.6190i			0.489680i	−0.969563	+	0.244840i	$0.921265\pi$
$564$	−16.0000	+	27.7128i	−0.673722	+	1.16692i
$565$	−25.0000			−1.05176
$566$	−14.2302	+	8.21584i	−0.598142	+	0.345337i
$567$		−	3.87298i		−	0.162650i
$568$			4.89898i			0.205557i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$	−28.2843	−	48.9898i	−1.18470	−	2.05196i
$571$	6.32456			0.264674			0.132337	−	0.991205i	$-0.457752\pi$
$571$	6.32456			0.264674			0.132337	+	0.991205i	$0.457752\pi$
$572$		0			0
$573$		0			0
$574$	−42.6907	+	24.6475i	−1.78188	+	1.02877i
$575$	14.1421	+	19.3649i	0.589768	+	0.807573i
$576$	40.0000			1.66667
$577$		−	14.6969i		−	0.611842i	−0.952057	−	0.305921i	$-0.901036\pi$
$577$		−	14.6969i		−	0.611842i	0.952057	−	0.305921i	$-0.0989643\pi$
$578$	−8.48528	−	14.6969i	−0.352941	−	0.611312i
$579$		−	13.8564i		−	0.575853i
$580$	−6.70820	+	11.6190i	−0.278543	+	0.482451i
$581$	−15.0000			−0.622305
$582$	−26.8328	−	46.4758i	−1.11226	−	1.92648i
$583$		0			0
$584$			13.8564i			0.573382i
$585$		−	54.7723i		−	2.26455i
$586$	17.3925	+	30.1247i	0.718479	+	1.24444i
$587$	22.6274			0.933933			0.466967	−	0.884275i	$-0.345347\pi$
$587$	22.6274			0.933933			0.466967	+	0.884275i	$0.345347\pi$
$588$	−22.6274	+	39.1918i	−0.933139	+	1.61624i
$589$		−	10.9545i		−	0.451370i
$590$	23.7171	−	13.6931i	0.976417	−	0.563735i
$591$			27.7128i			1.13995i
$592$	−13.4164	−	23.2379i	−0.551411	−	0.955072i
$593$		−	24.4949i		−	1.00588i	−0.864320	−	0.502942i	$-0.832251\pi$
$593$		−	24.4949i		−	1.00588i	0.864320	−	0.502942i	$-0.167749\pi$
$594$		0			0
$595$			19.3649i			0.793884i
$596$	−18.9737	−	10.9545i	−0.777192	−	0.448712i
$597$	17.8885			0.732129
$598$	30.3870	+	13.4399i	1.24262	+	0.549600i
$599$		−	17.3205i		−	0.707697i	−0.935303	−	0.353848i	$-0.884873\pi$
$599$		−	17.3205i		−	0.707697i	0.935303	−	0.353848i	$-0.115127\pi$
$600$	40.0000			1.63299
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	−21.2132	−	36.7423i	−0.864586	−	1.49751i
$603$			58.0948i			2.36580i
$604$	−18.0000	−	10.3923i	−0.732410	−	0.422857i
$605$	−24.5967			−1.00000
$606$	−6.00000	−	10.3923i	−0.243733	−	0.422159i
$607$	−25.4558			−1.03322			−0.516610	−	0.856221i	$-0.672806\pi$
$607$	−25.4558			−1.03322			−0.516610	+	0.856221i	$0.672806\pi$
$608$	17.8885	−	30.9839i	0.725476	−	1.25656i
$609$			32.8634i			1.33169i
$610$	30.0000	−	17.3205i	1.21466	−	0.701287i
$611$			27.7128i			1.12114i
$612$	11.1803	−	19.3649i	0.451938	−	0.782780i
$613$	−13.4164			−0.541884			−0.270942	−	0.962596i	$-0.587335\pi$
$613$	−13.4164			−0.541884			−0.270942	+	0.962596i	$0.587335\pi$
$614$	−12.0000	−	20.7846i	−0.484281	−	0.838799i
$615$	56.9210			2.29528
$616$		0			0
$617$	15.6525			0.630145			0.315072	−	0.949068i	$-0.397971\pi$
$617$	15.6525			0.630145			0.315072	+	0.949068i	$0.397971\pi$
$618$	26.8328	−	15.4919i	1.07937	−	0.623177i
$619$	−6.32456			−0.254205			−0.127103	−	0.991890i	$-0.540568\pi$
$619$	−6.32456			−0.254205			−0.127103	+	0.991890i	$0.540568\pi$
$620$	6.70820	+	3.87298i	0.269408	+	0.155543i
$621$	−16.0000	−	21.9089i	−0.642058	−	0.879174i
$622$	−12.7279	+	7.34847i	−0.510343	+	0.294647i
$623$	42.4264			1.69978
$624$	48.0000	−	27.7128i	1.92154	−	1.10940i
$625$	25.0000			1.00000
$626$	−14.2302	−	24.6475i	−0.568755	−	0.985113i
$627$		0			0
$628$	−6.70820	+	11.6190i	−0.267686	+	0.463647i
$629$	−15.0000			−0.598089
$630$	53.0330	−	30.6186i	2.11289	−	1.21988i
$631$	6.32456			0.251777			0.125888	−	0.992044i	$-0.459822\pi$
$631$	6.32456			0.251777			0.125888	+	0.992044i	$0.459822\pi$
$632$	−35.7771			−1.42314
$633$			24.4949i			0.973585i
$634$	−30.0000	+	17.3205i	−1.19145	+	0.687885i
$635$	−18.9737			−0.752947
$636$	−6.32456	+	10.9545i	−0.250785	+	0.434372i
$637$			39.1918i			1.55284i
$638$		0			0
$639$		−	8.66025i		−	0.342594i
$640$	12.6491	+	21.9089i	0.500000	+	0.866025i
$641$		−	21.9089i		−	0.865350i	−0.901550	−	0.432675i	$-0.857570\pi$
$641$		−	21.9089i		−	0.865350i	0.901550	−	0.432675i	$-0.142430\pi$
$642$	40.2492	−	23.2379i	1.58851	−	0.917127i
$643$			11.6190i			0.458207i	0.973402	+	0.229103i	$0.0735794\pi$
$643$			11.6190i			0.458207i	−0.973402	+	0.229103i	$0.926421\pi$
$644$	3.97367	+	36.9352i	0.156584	+	1.45545i
$645$			48.9898i			1.92897i
$646$	−10.0000	−	17.3205i	−0.393445	−	0.681466i
$647$	19.7990			0.778379			0.389189	−	0.921158i	$-0.372755\pi$
$647$	19.7990			0.778379			0.389189	+	0.921158i	$0.372755\pi$
$648$	−2.82843			−0.111111
$649$		0			0
$650$	30.0000	−	17.3205i	1.17670	−	0.679366i
$651$	18.9737			0.743637
$652$	16.9706	−	29.3939i	0.664619	−	1.15115i
$653$		−	19.5959i		−	0.766848i	−0.923573	−	0.383424i	$-0.874745\pi$
$653$		−	19.5959i		−	0.766848i	0.923573	−	0.383424i	$-0.125255\pi$
$654$	−37.9473	+	21.9089i	−1.48386	+	0.856706i
$655$		−	23.2379i		−	0.907980i
$656$	18.0000	+	31.1769i	0.702782	+	1.21725i
$657$		−	24.4949i		−	0.955637i
$658$	−26.8328	+	15.4919i	−1.04605	+	0.603938i
$659$	18.9737			0.739109			0.369555	−	0.929209i	$-0.379510\pi$
$659$	18.9737			0.739109			0.369555	+	0.929209i	$0.379510\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	19.0919	−	11.0227i	0.742027	−	0.428410i
$663$		−	30.9839i		−	1.20331i
$664$			10.9545i			0.425115i
$665$		−	54.7723i		−	2.12398i
$666$	23.7171	+	41.0792i	0.919018	+	1.59179i
$667$	8.48528	+	11.6190i	0.328551	+	0.449888i
$668$	−11.3137	+	19.5959i	−0.437741	+	0.758189i
$669$	24.0000			0.927894
$670$	−31.8198	+	18.3712i	−1.22931	+	0.709740i
$671$		0			0
$672$	53.6656	+	30.9839i	2.07020	+	1.19523i
$673$		−	29.3939i		−	1.13305i	−0.824044	−	0.566525i	$-0.808287\pi$
$673$		−	29.3939i		−	1.13305i	0.824044	−	0.566525i	$-0.191713\pi$
$674$	9.48683	+	16.4317i	0.365419	+	0.632925i
$675$	−28.2843			−1.08866
$676$	11.0000	−	19.0526i	0.423077	−	0.732791i
$677$	42.4853			1.63284			0.816421	−	0.577457i	$-0.195955\pi$
$677$	42.4853			1.63284			0.816421	+	0.577457i	$0.195955\pi$
$678$	22.3607	+	38.7298i	0.858757	+	1.48741i
$679$		−	51.9615i		−	1.99410i
$680$	14.1421			0.542326
$681$			21.9089i			0.839551i
$682$		0			0
$683$	2.82843			0.108227			0.0541134	−	0.998535i	$-0.482767\pi$
$683$	2.82843			0.108227			0.0541134	+	0.998535i	$0.482767\pi$
$684$	−31.6228	+	54.7723i	−1.20913	+	2.09427i
$685$	−10.0000			−0.382080
$686$	−4.74342	+	2.73861i	−0.181104	+	0.104561i
$687$			30.9839i			1.18211i
$688$	−26.8328	+	15.4919i	−1.02299	+	0.590624i
$689$			10.9545i			0.417331i
$690$	17.3509	−	39.2294i	0.660537	−	1.49344i
$691$			17.3205i			0.658903i	0.944172	+	0.329452i	$0.106864\pi$
$691$			17.3205i			0.658903i	−0.944172	+	0.329452i	$0.893136\pi$
$692$	−42.4264	−	24.4949i	−1.61281	−	0.931156i
$693$		0			0
$694$	2.00000	+	3.46410i	0.0759190	+	0.131495i
$695$			11.6190i			0.440732i
$696$	24.0000			0.909718
$697$	20.1246			0.762274
$698$	16.2635	+	28.1691i	0.615581	+	1.06622i
$699$		−	83.1384i		−	3.14458i
$700$	33.5410	+	19.3649i	1.26773	+	0.731925i
$701$			21.9089i			0.827488i	0.910393	+	0.413744i	$0.135779\pi$
$701$			21.9089i			0.827488i	−0.910393	+	0.413744i	$0.864221\pi$
$702$	−33.9411	+	19.5959i	−1.28103	+	0.739600i
$703$	42.4264			1.60014
$704$		0			0
$705$	35.7771			1.34744
$706$	36.0000	−	20.7846i	1.35488	−	0.782239i
$707$		−	11.6190i		−	0.436976i
$708$	−42.4264	−	24.4949i	−1.59448	−	0.920575i
$709$			32.8634i			1.23421i	0.786881	+	0.617105i	$0.211694\pi$
$709$			32.8634i			1.23421i	−0.786881	+	0.617105i	$0.788306\pi$
$710$	4.74342	−	2.73861i	0.178017	−	0.102778i
$711$	63.2456			2.37189
$712$		−	30.9839i		−	1.16117i
$713$	6.70820	−	4.89898i	0.251224	−	0.183468i
$714$	30.0000	−	17.3205i	1.12272	−	0.648204i
$715$		0			0
$716$	−6.00000	−	3.46410i	−0.224231	−	0.129460i
$717$		−	34.2929i		−	1.28069i
$718$	13.4164	+	23.2379i	0.500696	+	0.867231i
$719$		−	8.66025i		−	0.322973i	−0.986875	−	0.161486i	$-0.948371\pi$
$719$		−	8.66025i		−	0.322973i	0.986875	−	0.161486i	$-0.0516288\pi$
$720$	−22.3607	−	38.7298i	−0.833333	−	1.44338i
$721$	30.0000			1.11726
$722$	14.8492	+	25.7196i	0.552632	+	0.957186i
$723$		−	30.9839i		−	1.15230i
$724$	−18.9737	−	10.9545i	−0.705151	−	0.407119i
$725$	15.0000			0.557086
$726$	22.0000	+	38.1051i	0.816497	+	1.41421i
$727$			11.6190i			0.430923i	0.976512	+	0.215462i	$0.0691256\pi$
$727$			11.6190i			0.430923i	−0.976512	+	0.215462i	$0.930874\pi$
$728$	53.6656			1.98898
$729$	−43.0000			−1.59259
$730$	13.4164	−	7.74597i	0.496564	−	0.286691i
$731$			17.3205i			0.640622i
$732$	−53.6656	−	30.9839i	−1.98354	−	1.14520i
$733$	−46.9574			−1.73441			−0.867206	−	0.497949i	$-0.834087\pi$
$733$	−46.9574			−1.73441			−0.867206	+	0.497949i	$0.834087\pi$
$734$	4.74342	−	2.73861i	0.175083	−	0.101084i
$735$	50.5964			1.86628
$736$	26.9737	−	2.90196i	0.994263	−	0.106967i
$737$		0			0
$738$	−31.8198	−	55.1135i	−1.17130	−	2.02876i
$739$			39.8372i			1.46543i	0.680534	+	0.732717i	$0.261748\pi$
$739$			39.8372i			1.46543i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	−15.0000	+	25.9808i	−0.551411	+	0.955072i
$741$			87.6356i			3.21937i
$742$	−10.6066	+	6.12372i	−0.389381	+	0.224809i
$743$		−	23.2379i		−	0.852516i	−0.904602	−	0.426258i	$-0.859832\pi$
$743$		−	23.2379i		−	0.852516i	0.904602	−	0.426258i	$-0.140168\pi$
$744$		−	13.8564i		−	0.508001i
$745$			24.4949i			0.897424i
$746$	−9.48683	−	16.4317i	−0.347338	−	0.601606i
$747$		−	19.3649i		−	0.708525i
$748$		0			0
$749$	45.0000			1.64426
$750$	−22.3607	−	38.7298i	−0.816497	−	1.41421i
$751$	−6.32456			−0.230786			−0.115393	−	0.993320i	$-0.536813\pi$
$751$	−6.32456			−0.230786			−0.115393	+	0.993320i	$0.536813\pi$
$752$	11.3137	+	19.5959i	0.412568	+	0.714590i
$753$	−53.6656			−1.95568
$754$	18.0000	−	10.3923i	0.655521	−	0.378465i
$755$			23.2379i			0.845714i
$756$	−37.9473	−	21.9089i	−1.38013	−	0.796819i
$757$	−20.1246			−0.731441			−0.365721	−	0.930725i	$-0.619177\pi$
$757$	−20.1246			−0.731441			−0.365721	+	0.930725i	$0.619177\pi$
$758$	4.47214	+	7.74597i	0.162435	+	0.281346i
$759$		0			0
$760$	−40.0000			−1.45095
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$	16.9706	+	29.3939i	0.614779	+	1.06483i
$763$	−42.4264			−1.53594
$764$		0			0
$765$	−25.0000			−0.903877
$766$	4.74342	−	2.73861i	0.171387	−	0.0989501i
$767$	−42.4264			−1.53193
$768$	22.6274	−	39.1918i	0.816497	−	1.41421i
$769$		−	43.8178i		−	1.58011i	−0.613036	−	0.790055i	$-0.710052\pi$
$769$		−	43.8178i		−	1.58011i	0.613036	−	0.790055i	$-0.289948\pi$
$770$		0			0
$771$			27.7128i			0.998053i
$772$	−8.48528	−	4.89898i	−0.305392	−	0.176318i
$773$	22.3607			0.804258			0.402129	−	0.915583i	$-0.368270\pi$
$773$	22.3607			0.804258			0.402129	+	0.915583i	$0.368270\pi$
$774$	47.4342	−	27.3861i	1.70499	−	0.984374i
$775$		−	8.66025i		−	0.311086i
$776$	−37.9473			−1.36223
$777$			73.4847i			2.63625i
$778$	26.8328	−	15.4919i	0.962003	−	0.555413i
$779$	−56.9210			−2.03941
$780$	−53.6656	−	30.9839i	−1.92154	−	1.10940i
$781$		0			0
$782$	6.13447	−	13.8697i	0.219368	−	0.495979i
$783$	−16.9706			−0.606478
$784$	16.0000	+	27.7128i	0.571429	+	0.989743i
$785$	15.0000			0.535373
$786$	−36.0000	+	20.7846i	−1.28408	+	0.741362i
$787$		−	19.3649i		−	0.690285i	−0.938550	−	0.345142i	$-0.887831\pi$
$787$		−	19.3649i		−	0.690285i	0.938550	−	0.345142i	$-0.112169\pi$
$788$	16.9706	+	9.79796i	0.604551	+	0.349038i
$789$		−	32.8634i		−	1.16997i
$790$	20.0000	+	34.6410i	0.711568	+	1.23247i
$791$			43.3013i			1.53962i
$792$		0			0
$793$	−53.6656			−1.90572
$794$	−42.0000	+	24.2487i	−1.49052	+	0.860555i
$795$	14.1421			0.501570
$796$	6.32456	−	10.9545i	0.224168	−	0.388270i
$797$	−38.0132			−1.34650			−0.673248	−	0.739417i	$-0.735101\pi$
$797$	−38.0132			−1.34650			−0.673248	+	0.739417i	$0.735101\pi$
$798$	−84.8528	+	48.9898i	−3.00376	+	1.73422i
$799$	12.6491			0.447493
$800$	14.1421	−	24.4949i	0.500000	−	0.866025i
$801$			54.7723i			1.93528i
$802$	−26.8328	+	15.4919i	−0.947500	+	0.547039i
$803$		0			0
$804$	56.9210	+	32.8634i	2.00745	+	1.15900i
$805$	33.5410	−	24.4949i	1.18217	−	0.863332i
$806$	−6.00000	−	10.3923i	−0.211341	−	0.366053i
$807$	−8.48528			−0.298696
$808$	−8.48528			−0.298511
$809$	−21.0000			−0.738321			−0.369160	−	0.929366i	$-0.620355\pi$
$809$	−21.0000			−0.738321			−0.369160	+	0.929366i	$0.620355\pi$
$810$	1.58114	+	2.73861i	0.0555556	+	0.0962250i
$811$		−	15.5885i		−	0.547385i	−0.961817	−	0.273692i	$-0.911755\pi$
$811$		−	15.5885i		−	0.547385i	0.961817	−	0.273692i	$-0.0882450\pi$
$812$	20.1246	+	11.6190i	0.706235	+	0.407745i
$813$			24.4949i			0.859074i
$814$		0			0
$815$	−37.9473			−1.32924
$816$	−12.6491	−	21.9089i	−0.442807	−	0.766965i
$817$		−	48.9898i		−	1.71394i
$818$	4.94975	+	8.57321i	0.173064	+	0.299755i
$819$	−94.8683			−3.31497
$820$	20.1246	−	34.8569i	0.702782	−	1.21725i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$	8.94427	+	15.4919i	0.311967	+	0.540343i
$823$	25.4558			0.887335			0.443667	−	0.896191i	$-0.353677\pi$
$823$	25.4558			0.887335			0.443667	+	0.896191i	$0.353677\pi$
$824$		−	21.9089i		−	0.763233i
$825$		0			0
$826$	−23.7171	−	41.0792i	−0.825223	−	1.42933i
$827$			42.6028i			1.48145i	0.671811	+	0.740723i	$0.265517\pi$
$827$			42.6028i			1.48145i	−0.671811	+	0.740723i	$0.734483\pi$
$828$	−47.6832	+	5.12998i	−1.65710	+	0.178279i
$829$	31.0000			1.07667			0.538337	−	0.842729i	$-0.319053\pi$
$829$	31.0000			1.07667			0.538337	+	0.842729i	$0.319053\pi$
$830$	10.6066	−	6.12372i	0.368161	−	0.212558i
$831$		−	27.7128i		−	0.961347i
$832$		−	39.1918i		−	1.35873i
$833$	17.8885			0.619801
$834$	18.0000	−	10.3923i	0.623289	−	0.359856i
$835$	25.2982			0.875481
$836$		0			0
$837$			9.79796i			0.338667i
$838$		0			0
$839$	−18.9737			−0.655044			−0.327522	−	0.944844i	$-0.606214\pi$
$839$	−18.9737			−0.655044			−0.327522	+	0.944844i	$0.606214\pi$
$840$		−	69.2820i		−	2.39046i
$841$	−20.0000			−0.689655
$842$	−26.8328	+	15.4919i	−0.924720	+	0.533887i
$843$		0			0
$844$	15.0000	+	8.66025i	0.516321	+	0.298098i
$845$	−24.5967			−0.846154
$846$	−20.0000	−	34.6410i	−0.687614	−	1.19098i
$847$			42.6028i			1.46385i
$848$	4.47214	+	7.74597i	0.153574	+	0.265998i
$849$		−	32.8634i		−	1.12787i
$850$	−7.90569	−	13.6931i	−0.271163	−	0.469668i
$851$	18.9737	+	25.9808i	0.650409	+	0.890609i
$852$	−8.48528	−	4.89898i	−0.290701	−	0.167836i
$853$			24.4949i			0.838689i	0.907827	+	0.419345i	$0.137740\pi$
$853$			24.4949i			0.838689i	−0.907827	+	0.419345i	$0.862260\pi$
$854$	−30.0000	−	51.9615i	−1.02658	−	1.77809i
$855$	70.7107			2.41825
$856$		−	32.8634i		−	1.12325i
$857$			39.1918i			1.33877i	0.742917	+	0.669384i	$0.233442\pi$
$857$			39.1918i			1.33877i	−0.742917	+	0.669384i	$0.766558\pi$
$858$		0			0
$859$			12.1244i			0.413678i	0.978375	+	0.206839i	$0.0663176\pi$
$859$			12.1244i			0.413678i	−0.978375	+	0.206839i	$0.933682\pi$
$860$	30.0000	+	17.3205i	1.02299	+	0.590624i
$861$		−	98.5901i		−	3.35994i
$862$	−13.4164	−	23.2379i	−0.456965	−	0.791486i
$863$	45.2548			1.54049			0.770246	−	0.637747i	$-0.220133\pi$
$863$	45.2548			1.54049			0.770246	+	0.637747i	$0.220133\pi$
$864$	−16.0000	+	27.7128i	−0.544331	+	0.942809i
$865$			54.7723i			1.86231i
$866$	23.7171	+	41.0792i	0.805939	+	1.39593i
$867$	33.9411			1.15270
$868$	6.70820	−	11.6190i	0.227691	−	0.394373i
$869$		0			0
$870$	−13.4164	−	23.2379i	−0.454859	−	0.787839i
$871$	56.9210			1.92869
$872$			30.9839i			1.04925i
$873$	67.0820			2.27038
$874$	−17.3509	+	39.2294i	−0.586903	+	1.32695i
$875$		−	43.3013i		−	1.46385i
$876$	−24.0000	−	13.8564i	−0.810885	−	0.468165i
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$	−46.6690	+	26.9444i	−1.57500	+	0.909329i
$879$	−69.5701			−2.34654
$880$		0			0
$881$		−	10.9545i		−	0.369065i	−0.982826	−	0.184532i	$-0.940923\pi$
$881$		−	10.9545i		−	0.369065i	0.982826	−	0.184532i	$-0.0590771\pi$
$882$	−28.2843	−	48.9898i	−0.952381	−	1.64957i
$883$	8.48528			0.285552			0.142776	−	0.989755i	$-0.454397\pi$
$883$	8.48528			0.285552			0.142776	+	0.989755i	$0.454397\pi$
$884$	−18.9737	−	10.9545i	−0.638153	−	0.368438i
$885$			54.7723i			1.84115i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$	−36.7696			−1.23460			−0.617300	−	0.786728i	$-0.711774\pi$
$887$	−36.7696			−1.23460			−0.617300	+	0.786728i	$0.711774\pi$
$888$	53.6656			1.80090
$889$			32.8634i			1.10220i
$890$	−30.0000	+	17.3205i	−1.00560	+	0.580585i
$891$		0			0
$892$	8.48528	−	14.6969i	0.284108	−	0.492090i
$893$	−35.7771			−1.19723
$894$	37.9473	−	21.9089i	1.26915	−	0.732743i
$895$			7.74597i			0.258919i
$896$	37.9473	−	21.9089i	1.26773	−	0.731925i
$897$	−53.6656	+	39.1918i	−1.79184	+	1.30858i
$898$	−6.36396	−	11.0227i	−0.212368	−	0.367832i
$899$		−	5.19615i		−	0.173301i
$900$	−25.0000	+	43.3013i	−0.833333	+	1.44338i
$901$	5.00000			0.166574
$902$		0			0
$903$	84.8528			2.82372
$904$	31.6228			1.05176
$905$			24.4949i			0.814238i
$906$	36.0000	−	20.7846i	1.19602	−	0.690522i
$907$			58.0948i			1.92900i	0.264075	+	0.964502i	$0.414933\pi$
$907$			58.0948i			1.92900i	−0.264075	+	0.964502i	$0.585067\pi$
$908$	13.4164	+	7.74597i	0.445239	+	0.257059i
$909$	15.0000			0.497519
$910$	−30.0000	−	51.9615i	−0.994490	−	1.72251i
$911$	−18.9737			−0.628626			−0.314313	−	0.949319i	$-0.601774\pi$
$911$	−18.9737			−0.628626			−0.314313	+	0.949319i	$0.601774\pi$
$912$	35.7771	+	61.9677i	1.18470	+	2.05196i
$913$		0			0
$914$	23.7171	+	41.0792i	0.784491	+	1.35878i
$915$			69.2820i			2.29039i
$916$	18.9737	+	10.9545i	0.626908	+	0.361945i
$917$	−40.2492			−1.32915
$918$	8.94427	+	15.4919i	0.295205	+	0.511310i
$919$	44.2719			1.46039			0.730197	−	0.683236i	$-0.239428\pi$
$919$	44.2719			1.46039			0.730197	+	0.683236i	$0.239428\pi$
$920$	−17.8885	−	24.4949i	−0.589768	−	0.807573i
$921$	48.0000			1.58165
$922$	4.24264	+	7.34847i	0.139724	+	0.242009i
$923$	−8.48528			−0.279296
$924$		0			0
$925$	33.5410			1.10282
$926$	−6.00000	−	10.3923i	−0.197172	−	0.341512i
$927$			38.7298i			1.27205i
$928$	8.48528	−	14.6969i	0.278543	−	0.482451i
$929$	3.00000			0.0984268			0.0492134	−	0.998788i	$-0.484329\pi$
$929$	3.00000			0.0984268			0.0492134	+	0.998788i	$0.484329\pi$
$930$	−13.4164	+	7.74597i	−0.439941	+	0.254000i
$931$	−50.5964			−1.65823
$932$	−50.9117	−	29.3939i	−1.66767	−	0.962828i
$933$		−	29.3939i		−	0.962312i
$934$	23.7171	−	13.6931i	0.776047	−	0.448051i
$935$		0			0
$936$			69.2820i			2.26455i
$937$	13.4164			0.438295			0.219147	−	0.975692i	$-0.429672\pi$
$937$	13.4164			0.438295			0.219147	+	0.975692i	$0.429672\pi$
$938$	31.8198	+	55.1135i	1.03895	+	1.79952i
$939$	56.9210			1.85755
$940$	12.6491	−	21.9089i	0.412568	−	0.714590i
$941$		−	10.9545i		−	0.357105i	−0.983930	−	0.178552i	$-0.942859\pi$
$941$		−	10.9545i		−	0.357105i	0.983930	−	0.178552i	$-0.0571414\pi$
$942$	−13.4164	−	23.2379i	−0.437130	−	0.757132i
$943$	−25.4558	−	34.8569i	−0.828956	−	1.13510i
$944$	−30.0000	+	17.3205i	−0.976417	+	0.563735i
$945$			48.9898i			1.59364i
$946$		0			0
$947$	22.6274			0.735292			0.367646	−	0.929966i	$-0.380164\pi$
$947$	22.6274			0.735292			0.367646	+	0.929966i	$0.380164\pi$
$948$	35.7771	−	61.9677i	1.16199	−	2.01262i
$949$	−24.0000			−0.779073
$950$	22.3607	+	38.7298i	0.725476	+	1.25656i
$951$		−	69.2820i		−	2.24662i
$952$		−	24.4949i		−	0.793884i
$953$	−4.47214			−0.144867			−0.0724333	−	0.997373i	$-0.523076\pi$
$953$	−4.47214			−0.144867			−0.0724333	+	0.997373i	$0.523076\pi$
$954$	−7.90569	−	13.6931i	−0.255956	−	0.443329i
$955$		0			0
$956$	−21.0000	−	12.1244i	−0.679189	−	0.392130i
$957$		0			0
$958$	−26.8328	−	46.4758i	−0.866929	−	1.50156i
$959$			17.3205i			0.559308i
$960$	−50.5964			−1.63299
$961$	28.0000			0.903226
$962$	40.2492	−	23.2379i	1.29769	−	0.749220i
$963$			58.0948i			1.87208i
$964$	−18.9737	−	10.9545i	−0.611101	−	0.352819i
$965$			10.9545i			0.352636i
$966$	−67.9473	−	30.0526i	−2.18617	−	0.966927i
$967$	50.9117			1.63721			0.818605	−	0.574357i	$-0.194748\pi$
$967$	50.9117			1.63721			0.818605	+	0.574357i	$0.194748\pi$
$968$	31.1127			1.00000
$969$	40.0000			1.28499
$970$	21.2132	+	36.7423i	0.681115	+	1.17973i
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	−14.1421	+	24.4949i	−0.453609	+	0.785674i
$973$	20.1246			0.645165
$974$	−6.00000	−	10.3923i	−0.192252	−	0.332991i
$975$			69.2820i			2.21880i
$976$	−37.9473	+	21.9089i	−1.21466	+	0.701287i
$977$	24.5967			0.786920			0.393460	−	0.919342i	$-0.371278\pi$
$977$	24.5967			0.786920			0.393460	+	0.919342i	$0.371278\pi$
$978$	33.9411	+	58.7878i	1.08532	+	1.87983i
$979$		0			0
$980$	17.8885	−	30.9839i	0.571429	−	0.989743i
$981$		−	54.7723i		−	1.74874i
$982$	44.5477	−	25.7196i	1.42158	−	0.820747i
$983$			42.6028i			1.35882i	0.733759	+	0.679409i	$0.237764\pi$
$983$			42.6028i			1.35882i	−0.733759	+	0.679409i	$0.762236\pi$
$984$	−72.0000			−2.29528
$985$		−	21.9089i		−	0.698076i
$986$	−4.74342	−	8.21584i	−0.151061	−	0.261646i
$987$		−	61.9677i		−	1.97245i
$988$	53.6656	+	30.9839i	1.70733	+	0.985728i
$989$	30.0000	−	21.9089i	0.953945	−	0.696663i
$990$		0			0
$991$		−	8.66025i		−	0.275102i	−0.990495	−	0.137551i	$-0.956077\pi$
$991$		−	8.66025i		−	0.275102i	0.990495	−	0.137551i	$-0.0439231\pi$
$992$	−8.48528	−	4.89898i	−0.269408	−	0.155543i
$993$			44.0908i			1.39918i
$994$	−4.74342	−	8.21584i	−0.150452	−	0.260591i
$995$	−14.1421			−0.448336
$996$	−18.9737	−	10.9545i	−0.601204	−	0.347105i
$997$		−	48.9898i		−	1.55152i	−0.631027	−	0.775761i	$-0.717366\pi$
$997$		−	48.9898i		−	1.55152i	0.631027	−	0.775761i	$-0.282634\pi$
$998$	−48.7904	+	28.1691i	−1.54443	+	0.891678i
$999$	−37.9473			−1.20060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.g.b.459.8	yes	8
4.3	odd	2	inner	460.2.g.b.459.4	yes	8
5.4	even	2	inner	460.2.g.b.459.1	✓	8
20.19	odd	2	inner	460.2.g.b.459.5	yes	8
23.22	odd	2	inner	460.2.g.b.459.7	yes	8
92.91	even	2	inner	460.2.g.b.459.3	yes	8
115.114	odd	2	inner	460.2.g.b.459.2	yes	8
460.459	even	2	inner	460.2.g.b.459.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.g.b.459.1	✓	8	5.4	even	2	inner
460.2.g.b.459.2	yes	8	115.114	odd	2	inner
460.2.g.b.459.3	yes	8	92.91	even	2	inner
460.2.g.b.459.4	yes	8	4.3	odd	2	inner
460.2.g.b.459.5	yes	8	20.19	odd	2	inner
460.2.g.b.459.6	yes	8	460.459	even	2	inner
460.2.g.b.459.7	yes	8	23.22	odd	2	inner
460.2.g.b.459.8	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} -2.82843 q^{3} +(-1.00000 + 1.73205i) q^{4} +2.23607 q^{5} +(-2.00000 - 3.46410i) q^{6} -3.87298i q^{7} -2.82843 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} -2.82843 q^{3} +(-1.00000 + 1.73205i) q^{4} +2.23607 q^{5} +(-2.00000 - 3.46410i) q^{6} -3.87298i q^{7} -2.82843 q^{8} +5.00000 q^{9} +(1.58114 + 2.73861i) q^{10} +(2.82843 - 4.89898i) q^{12} -4.89898i q^{13} +(4.74342 - 2.73861i) q^{14} -6.32456 q^{15} +(-2.00000 - 3.46410i) q^{16} -2.23607 q^{17} +(3.53553 + 6.12372i) q^{18} +6.32456 q^{19} +(-2.23607 + 3.87298i) q^{20} +10.9545i q^{21} +(2.82843 + 3.87298i) q^{23} +8.00000 q^{24} +5.00000 q^{25} +(6.00000 - 3.46410i) q^{26} -5.65685 q^{27} +(6.70820 + 3.87298i) q^{28} +3.00000 q^{29} +(-4.47214 - 7.74597i) q^{30} -1.73205i q^{31} +(2.82843 - 4.89898i) q^{32} +(-1.58114 - 2.73861i) q^{34} -8.66025i q^{35} +(-5.00000 + 8.66025i) q^{36} +6.70820 q^{37} +(4.47214 + 7.74597i) q^{38} +13.8564i q^{39} -6.32456 q^{40} -9.00000 q^{41} +(-13.4164 + 7.74597i) q^{42} -7.74597i q^{43} +11.1803 q^{45} +(-2.74342 + 6.20271i) q^{46} -5.65685 q^{47} +(5.65685 + 9.79796i) q^{48} -8.00000 q^{49} +(3.53553 + 6.12372i) q^{50} +6.32456 q^{51} +(8.48528 + 4.89898i) q^{52} -2.23607 q^{53} +(-4.00000 - 6.92820i) q^{54} +10.9545i q^{56} -17.8885 q^{57} +(2.12132 + 3.67423i) q^{58} -8.66025i q^{59} +(6.32456 - 10.9545i) q^{60} -10.9545i q^{61} +(2.12132 - 1.22474i) q^{62} -19.3649i q^{63} +8.00000 q^{64} -10.9545i q^{65} +11.6190i q^{67} +(2.23607 - 3.87298i) q^{68} +(-8.00000 - 10.9545i) q^{69} +(10.6066 - 6.12372i) q^{70} -1.73205i q^{71} -14.1421 q^{72} -4.89898i q^{73} +(4.74342 + 8.21584i) q^{74} -14.1421 q^{75} +(-6.32456 + 10.9545i) q^{76} +(-16.9706 + 9.79796i) q^{78} +12.6491 q^{79} +(-4.47214 - 7.74597i) q^{80} +1.00000 q^{81} +(-6.36396 - 11.0227i) q^{82} -3.87298i q^{83} +(-18.9737 - 10.9545i) q^{84} -5.00000 q^{85} +(9.48683 - 5.47723i) q^{86} -8.48528 q^{87} +10.9545i q^{89} +(7.90569 + 13.6931i) q^{90} -18.9737 q^{91} +(-9.53663 + 1.02600i) q^{92} +4.89898i q^{93} +(-4.00000 - 6.92820i) q^{94} +14.1421 q^{95} +(-8.00000 + 13.8564i) q^{96} +13.4164 q^{97} +(-5.65685 - 9.79796i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 16 q^{6} + 40 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 16 * q^6 + 40 * q^9	\( 8 q - 8 q^{4} - 16 q^{6} + 40 q^{9} - 16 q^{16} + 64 q^{24} + 40 q^{25} + 48 q^{26} + 24 q^{29} - 40 q^{36} - 72 q^{41} + 16 q^{46} - 64 q^{49} - 32 q^{54} + 64 q^{64} - 64 q^{69} + 8 q^{81} - 40 q^{85} - 32 q^{94} - 64 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 - 16 * q^6 + 40 * q^9 - 16 * q^16 + 64 * q^24 + 40 * q^25 + 48 * q^26 + 24 * q^29 - 40 * q^36 - 72 * q^41 + 16 * q^46 - 64 * q^49 - 32 * q^54 + 64 * q^64 - 64 * q^69 + 8 * q^81 - 40 * q^85 - 32 * q^94 - 64 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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