LMFDB - Embedded newform 325.2.n.a.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(101,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,3,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.a.251.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{6} +1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +2.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +(2.50000 + 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.73205i q^{18} +(-3.00000 - 1.73205i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-3.00000 + 1.73205i) q^{24} +(1.50000 - 6.06218i) q^{26} +4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} -3.46410i q^{31} +(4.50000 + 2.59808i) q^{32} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(-7.50000 + 4.33013i) q^{37} -6.00000 q^{38} +(7.00000 + 1.73205i) q^{39} +(-4.50000 + 2.59808i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-9.00000 - 5.19615i) q^{46} -3.46410i q^{47} +(-5.00000 + 8.66025i) q^{48} +(-3.50000 - 6.06218i) q^{49} -6.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +3.00000 q^{53} +(6.00000 - 3.46410i) q^{54} -6.92820i q^{57} +(-4.50000 - 2.59808i) q^{58} +(6.00000 + 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(-3.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-1.50000 - 0.866025i) q^{72} +1.73205i q^{73} +(-7.50000 + 12.9904i) q^{74} +(-3.00000 + 1.73205i) q^{76} +(12.0000 - 3.46410i) q^{78} +4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} +(-4.50000 + 7.79423i) q^{82} +13.8564i q^{83} -13.8564i q^{86} +(3.00000 - 5.19615i) q^{87} +(-6.00000 + 3.46410i) q^{89} -6.00000 q^{92} +(6.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +10.3923i q^{96} +(-6.00000 - 3.46410i) q^{97} +(-10.5000 - 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 2 q^{3} + q^{4} + 6 q^{6} - q^{9} + 4 q^{12} + 5 q^{13} + 5 q^{16} - 3 q^{17} - 6 q^{19} - 6 q^{23} - 6 q^{24} + 3 q^{26} + 8 q^{27} - 3 q^{29} + 9 q^{32} + q^{36} - 15 q^{37} - 12 q^{38}+ \cdots - 21 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + 2 * q^3 + q^4 + 6 * q^6 - q^9 + 4 * q^12 + 5 * q^13 + 5 * q^16 - 3 * q^17 - 6 * q^19 - 6 * q^23 - 6 * q^24 + 3 * q^26 + 8 * q^27 - 3 * q^29 + 9 * q^32 + q^36 - 15 * q^37 - 12 * q^38 + 14 * q^39 - 9 * q^41 + 8 * q^43 - 18 * q^46 - 10 * q^48 - 7 * q^49 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 12 * q^54 - 9 * q^58 + 12 * q^59 - q^61 - 6 * q^62 - 2 * q^64 - 6 * q^67 + 3 * q^68 + 12 * q^69 + 6 * q^71 - 3 * q^72 - 15 * q^74 - 6 * q^76 + 24 * q^78 + 8 * q^79 + 11 * q^81 - 9 * q^82 + 6 * q^87 - 12 * q^89 - 12 * q^92 + 12 * q^93 - 6 * q^94 - 12 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	3.00000	+	1.73205i	1.22474	+	0.707107i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$			1.73205i			0.612372i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	2.00000			0.577350
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$			1.73205i			0.408248i
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−3.00000	+	1.73205i	−0.612372	+	0.353553i
$25$		0			0
$26$	1.50000	−	6.06218i	0.294174	−	1.18889i
$27$	4.00000			0.769800
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$		0			0
$34$			5.19615i			0.891133i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−7.50000	+	4.33013i	−1.23299	+	0.711868i	−0.967653	−	0.252286i	$-0.918817\pi$
$37$	−7.50000	+	4.33013i	−1.23299	+	0.711868i	−0.265340	+	0.964155i	$0.585484\pi$
$38$	−6.00000			−0.973329
$39$	7.00000	+	1.73205i	1.12090	+	0.277350i
$40$		0			0
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$		0			0
$45$		0			0
$46$	−9.00000	−	5.19615i	−1.32698	−	0.766131i
$47$		−	3.46410i		−	0.505291i	−0.967559	−	0.252646i	$-0.918699\pi$
$47$		−	3.46410i		−	0.505291i	0.967559	−	0.252646i	$-0.0813007\pi$
$48$	−5.00000	+	8.66025i	−0.721688	+	1.25000i
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$	−6.00000			−0.840168
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	6.00000	−	3.46410i	0.816497	−	0.471405i
$55$		0			0
$56$		0			0
$57$		−	6.92820i		−	0.917663i
$58$	−4.50000	−	2.59808i	−0.590879	−	0.341144i
$59$	6.00000	+	3.46410i	0.781133	+	0.450988i	0.836832	−	0.547460i	$-0.184405\pi$
$59$	6.00000	+	3.46410i	0.781133	+	0.450988i	−0.0556984	+	0.998448i	$0.517739\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	−3.00000	−	5.19615i	−0.381000	−	0.659912i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	0.305424	+	0.952217i	$0.401202\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$		0			0
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	0.667340	−	0.744753i	$-0.267433\pi$
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	−0.311305	+	0.950310i	$0.600766\pi$
$72$	−1.50000	−	0.866025i	−0.176777	−	0.102062i
$73$			1.73205i			0.202721i	0.994850	+	0.101361i	$0.0323196\pi$
$73$			1.73205i			0.202721i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−7.50000	+	12.9904i	−0.871857	+	1.51010i
$75$		0			0
$76$	−3.00000	+	1.73205i	−0.344124	+	0.198680i
$77$		0			0
$78$	12.0000	−	3.46410i	1.35873	−	0.392232i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$			13.8564i			1.52094i	0.649374	+	0.760469i	$0.275031\pi$
$83$			13.8564i			1.52094i	−0.649374	+	0.760469i	$0.724969\pi$
$84$		0			0
$85$		0			0
$86$		−	13.8564i		−	1.49417i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	−0.783072	−	0.621932i	$-0.786348\pi$
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	0.147073	+	0.989126i	$0.453015\pi$
$90$		0			0
$91$		0			0
$92$	−6.00000			−0.625543
$93$	6.00000	−	3.46410i	0.622171	−	0.359211i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$			10.3923i			1.06066i
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	0.163448	−	0.986552i	$-0.447739\pi$
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	−0.772655	+	0.634826i	$0.781072\pi$
$98$	−10.5000	−	6.06218i	−1.06066	−	0.612372i
$99$		0			0
$100$		0			0
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$	−9.00000	+	5.19615i	−0.891133	+	0.514496i
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	4.50000	+	4.33013i	0.441261	+	0.424604i
$105$		0			0
$106$	4.50000	−	2.59808i	0.437079	−	0.252347i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$			13.8564i			1.32720i	0.748086	+	0.663602i	$0.230973\pi$
$109$			13.8564i			1.32720i	−0.748086	+	0.663602i	$0.769027\pi$
$110$		0			0
$111$	−15.0000	−	8.66025i	−1.42374	−	0.821995i
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−6.00000	−	10.3923i	−0.561951	−	0.973329i
$115$		0			0
$116$	−3.00000			−0.278543
$117$	1.00000	+	3.46410i	0.0924500	+	0.320256i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$			1.73205i			0.156813i
$123$	−9.00000	−	5.19615i	−0.811503	−	0.468521i
$124$	−3.00000	−	1.73205i	−0.269408	−	0.155543i
$125$		0			0
$126$		0			0
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	−1.00000	−	1.73205i	−0.0887357	−	0.153695i	−0.906977	+	0.421180i	$0.861616\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$	16.0000			1.40872
$130$		0			0
$131$	18.0000			1.57267			0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000			1.57267			0.786334	+	0.617802i	$0.211977\pi$
$132$		0			0
$133$		0			0
$134$	−3.00000	+	5.19615i	−0.259161	+	0.448879i
$135$		0			0
$136$	−4.50000	−	2.59808i	−0.385872	−	0.222783i
$137$	13.5000	+	7.79423i	1.15338	+	0.665906i	0.949709	−	0.313133i	$-0.101379\pi$
$137$	13.5000	+	7.79423i	1.15338	+	0.665906i	0.203674	+	0.979039i	$0.434712\pi$
$138$		−	20.7846i		−	1.76930i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	6.00000	−	3.46410i	0.505291	−	0.291730i
$142$	6.00000			0.503509
$143$		0			0
$144$	−5.00000			−0.416667
$145$		0			0
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$	7.00000	−	12.1244i	0.577350	−	1.00000i
$148$			8.66025i			0.711868i
$149$	−16.5000	−	9.52628i	−1.35173	−	0.780423i	−0.363241	−	0.931695i	$-0.618330\pi$
$149$	−16.5000	−	9.52628i	−1.35173	−	0.780423i	−0.988492	+	0.151272i	$0.951663\pi$
$150$		0			0
$151$		−	17.3205i		−	1.40952i	−0.709444	−	0.704761i	$-0.751054\pi$
$151$		−	17.3205i		−	1.40952i	0.709444	−	0.704761i	$-0.248946\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$		0			0
$155$		0			0
$156$	5.00000	−	5.19615i	0.400320	−	0.416025i
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$	6.00000	−	3.46410i	0.477334	−	0.275589i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$		0			0
$162$	16.5000	+	9.52628i	1.29636	+	0.748455i
$163$	−18.0000	−	10.3923i	−1.40987	−	0.813988i	−0.414494	−	0.910052i	$-0.636041\pi$
$163$	−18.0000	−	10.3923i	−1.40987	−	0.813988i	−0.995375	+	0.0960641i	$0.969375\pi$
$164$			5.19615i			0.405751i
$165$		0			0
$166$	12.0000	+	20.7846i	0.931381	+	1.61320i
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.0422232	−	0.999108i	$-0.486556\pi$
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.886365	+	0.462988i	$0.153223\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		−	10.3923i		−	0.787839i
$175$		0			0
$176$		0			0
$177$			13.8564i			1.04151i
$178$	−6.00000	+	10.3923i	−0.449719	+	0.778936i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$		0			0
$183$	−2.00000			−0.147844
$184$	9.00000	−	5.19615i	0.663489	−	0.383065i
$185$		0			0
$186$	6.00000	−	10.3923i	0.439941	−	0.762001i
$187$		0			0
$188$	−3.00000	−	1.73205i	−0.218797	−	0.126323i
$189$		0			0
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	4.50000	−	2.59808i	0.323917	−	0.187014i	−0.329220	−	0.944253i	$-0.606786\pi$
$193$	4.50000	−	2.59808i	0.323917	−	0.187014i	0.653137	+	0.757240i	$0.273452\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−12.0000	+	6.92820i	−0.854965	+	0.493614i	−0.862323	−	0.506359i	$-0.830991\pi$
$197$	−12.0000	+	6.92820i	−0.854965	+	0.493614i	0.00735824	+	0.999973i	$0.497658\pi$
$198$		0			0
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$		0			0
$201$	−6.00000	−	3.46410i	−0.423207	−	0.244339i
$202$	4.50000	+	2.59808i	0.316619	+	0.182800i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$		0			0
$206$	15.0000	−	8.66025i	1.04510	−	0.603388i
$207$	6.00000			0.417029
$208$	17.5000	+	4.33013i	1.21341	+	0.300240i
$209$		0			0
$210$		0			0
$211$	−5.00000	−	8.66025i	−0.344214	−	0.596196i	0.640996	−	0.767544i	$-0.278521\pi$
$211$	−5.00000	−	8.66025i	−0.344214	−	0.596196i	−0.985211	+	0.171347i	$0.945188\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$			6.92820i			0.474713i
$214$	9.00000	+	5.19615i	0.615227	+	0.355202i
$215$		0			0
$216$			6.92820i			0.471405i
$217$		0			0
$218$	12.0000	+	20.7846i	0.812743	+	1.40771i
$219$	−3.00000	+	1.73205i	−0.202721	+	0.117041i
$220$		0			0
$221$	3.00000	+	10.3923i	0.201802	+	0.699062i
$222$	−30.0000			−2.01347
$223$	9.00000	−	5.19615i	0.602685	−	0.347960i	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	9.00000	−	5.19615i	0.602685	−	0.347960i	0.770097	+	0.637927i	$0.220208\pi$
$224$		0			0
$225$		0			0
$226$			25.9808i			1.72821i
$227$	−21.0000	−	12.1244i	−1.39382	−	0.804722i	−0.400083	−	0.916479i	$-0.631019\pi$
$227$	−21.0000	−	12.1244i	−1.39382	−	0.804722i	−0.993736	+	0.111757i	$0.964352\pi$
$228$	−6.00000	−	3.46410i	−0.397360	−	0.229416i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	−	2.59808i	0.295439	−	0.170572i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	4.50000	+	4.33013i	0.294174	+	0.283069i
$235$		0			0
$236$	6.00000	−	3.46410i	0.390567	−	0.225494i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$		0			0
$239$			20.7846i			1.34444i	0.740349	+	0.672222i	$0.234660\pi$
$239$			20.7846i			1.34444i	−0.740349	+	0.672222i	$0.765340\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$			19.0526i			1.22474i
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$		0			0
$246$	−18.0000			−1.14764
$247$	−12.0000	+	3.46410i	−0.763542	+	0.220416i
$248$	6.00000			0.381000
$249$	−24.0000	+	13.8564i	−1.52094	+	0.878114i
$250$		0			0
$251$	9.00000	−	15.5885i	0.568075	−	0.983935i	−0.428681	−	0.903456i	$-0.641022\pi$
$251$	9.00000	−	15.5885i	0.568075	−	0.983935i	0.996756	−	0.0804789i	$-0.0256450\pi$
$252$		0			0
$253$		0			0
$254$	−3.00000	−	1.73205i	−0.188237	−	0.108679i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$	24.0000	−	13.8564i	1.49417	−	0.862662i
$259$		0			0
$260$		0			0
$261$	3.00000			0.185695
$262$	27.0000	−	15.5885i	1.66807	−	0.963058i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−12.0000	−	6.92820i	−0.734388	−	0.423999i
$268$			3.46410i			0.211604i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	18.0000	−	10.3923i	1.09342	−	0.631288i	0.158937	−	0.987289i	$-0.449193\pi$
$271$	18.0000	−	10.3923i	1.09342	−	0.631288i	0.934485	+	0.356001i	$0.115860\pi$
$272$	−15.0000			−0.909509
$273$		0			0
$274$	27.0000			1.63113
$275$		0			0
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$		−	6.92820i		−	0.415526i
$279$	3.00000	+	1.73205i	0.179605	+	0.103695i
$280$		0			0
$281$			22.5167i			1.34323i	0.740900	+	0.671616i	$0.234399\pi$
$281$			22.5167i			1.34323i	−0.740900	+	0.671616i	$0.765601\pi$
$282$	6.00000	−	10.3923i	0.357295	−	0.618853i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	3.00000	−	1.73205i	0.178017	−	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.50000	+	2.59808i	−0.265165	+	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		−	13.8564i		−	0.812277i
$292$	1.50000	+	0.866025i	0.0877809	+	0.0506803i
$293$	−4.50000	−	2.59808i	−0.262893	−	0.151781i	0.362761	−	0.931882i	$-0.381834\pi$
$293$	−4.50000	−	2.59808i	−0.262893	−	0.151781i	−0.625653	+	0.780101i	$0.715168\pi$
$294$		−	24.2487i		−	1.41421i
$295$		0			0
$296$	−7.50000	−	12.9904i	−0.435929	−	0.755051i
$297$		0			0
$298$	−33.0000			−1.91164
$299$	−21.0000	−	5.19615i	−1.21446	−	0.300501i
$300$		0			0
$301$		0			0
$302$	−15.0000	−	25.9808i	−0.863153	−	1.49502i
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		−	17.3205i		−	0.993399i
$305$		0			0
$306$	−4.50000	−	2.59808i	−0.257248	−	0.148522i
$307$		−	17.3205i		−	0.988534i	−0.869310	−	0.494267i	$-0.835437\pi$
$307$		−	17.3205i		−	0.988534i	0.869310	−	0.494267i	$-0.164563\pi$
$308$		0			0
$309$	10.0000	+	17.3205i	0.568880	+	0.985329i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	−3.00000	+	12.1244i	−0.169842	+	0.686406i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	19.5000	−	11.2583i	1.10045	−	0.635344i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$		−	5.19615i		−	0.291845i	−0.989296	−	0.145922i	$-0.953385\pi$
$317$		−	5.19615i		−	0.291845i	0.989296	−	0.145922i	$-0.0466150\pi$
$318$	9.00000	+	5.19615i	0.504695	+	0.291386i
$319$		0			0
$320$		0			0
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$		0			0
$323$	9.00000	−	5.19615i	0.500773	−	0.289122i
$324$	11.0000			0.611111
$325$		0			0
$326$	−36.0000			−1.99386
$327$	−24.0000	+	13.8564i	−1.32720	+	0.766261i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$	−24.0000	−	13.8564i	−1.31916	−	0.761617i	−0.335566	−	0.942017i	$-0.608928\pi$
$331$	−24.0000	−	13.8564i	−1.31916	−	0.761617i	−0.983593	+	0.180400i	$0.942261\pi$
$332$	12.0000	+	6.92820i	0.658586	+	0.380235i
$333$		−	8.66025i		−	0.474579i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$		0			0
$336$		0			0
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$	−12.0000	−	19.0526i	−0.652714	−	1.03632i
$339$	−30.0000			−1.62938
$340$		0			0
$341$		0			0
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$		0			0
$344$	12.0000	+	6.92820i	0.646997	+	0.373544i
$345$		0			0
$346$		−	10.3923i		−	0.558694i
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	−0.143172	−	0.989698i	$-0.545730\pi$
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	0.785517	+	0.618840i	$0.212397\pi$
$350$		0			0
$351$	10.0000	−	10.3923i	0.533761	−	0.554700i
$352$		0			0
$353$	−28.5000	+	16.4545i	−1.51690	+	0.875784i	−0.517099	+	0.855926i	$0.672988\pi$
$353$	−28.5000	+	16.4545i	−1.51690	+	0.875784i	−0.999803	+	0.0198582i	$0.993679\pi$
$354$	12.0000	+	20.7846i	0.637793	+	1.10469i
$355$		0			0
$356$			6.92820i			0.367194i
$357$		0			0
$358$		0			0
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$	16.5000	−	9.52628i	0.867221	−	0.500690i
$363$	−22.0000			−1.15470
$364$		0			0
$365$		0			0
$366$	−3.00000	+	1.73205i	−0.156813	+	0.0905357i
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$	15.0000	−	25.9808i	0.781929	−	1.35434i
$369$		−	5.19615i		−	0.270501i
$370$		0			0
$371$		0			0
$372$		−	6.92820i		−	0.359211i
$373$	9.50000	−	16.4545i	0.491891	−	0.851981i	−0.508065	−	0.861319i	$-0.669639\pi$
$373$	9.50000	−	16.4545i	0.491891	−	0.851981i	0.999956	+	0.00933789i	$0.00297238\pi$
$374$		0			0
$375$		0			0
$376$	6.00000			0.309426
$377$	−10.5000	−	2.59808i	−0.540778	−	0.133808i
$378$		0			0
$379$	−21.0000	+	12.1244i	−1.07870	+	0.622786i	−0.930545	−	0.366178i	$-0.880666\pi$
$379$	−21.0000	+	12.1244i	−1.07870	+	0.622786i	−0.148153	+	0.988964i	$0.547333\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$			31.1769i			1.59515i
$383$	18.0000	+	10.3923i	0.919757	+	0.531022i	0.883558	−	0.468323i	$-0.155141\pi$
$383$	18.0000	+	10.3923i	0.919757	+	0.531022i	0.0361995	+	0.999345i	$0.488475\pi$
$384$	−21.0000	−	12.1244i	−1.07165	−	0.618718i
$385$		0			0
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	−6.00000	+	3.46410i	−0.304604	+	0.175863i
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	10.5000	−	6.06218i	0.530330	−	0.306186i
$393$	18.0000	+	31.1769i	0.907980	+	1.57267i
$394$	−12.0000	+	20.7846i	−0.604551	+	1.04711i
$395$		0			0
$396$		0			0
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	0.769931	−	0.638127i	$-0.220290\pi$
$397$	12.0000	+	6.92820i	0.602263	+	0.347717i	−0.167668	+	0.985843i	$0.553624\pi$
$398$		−	3.46410i		−	0.173640i
$399$		0			0
$400$		0			0
$401$	−1.50000	+	0.866025i	−0.0749064	+	0.0432472i	−0.536985	−	0.843592i	$-0.680437\pi$
$401$	−1.50000	+	0.866025i	−0.0749064	+	0.0432472i	0.462079	+	0.886839i	$0.347104\pi$
$402$	−12.0000			−0.598506
$403$	−9.00000	−	8.66025i	−0.448322	−	0.431398i
$404$	3.00000			0.149256
$405$		0			0
$406$		0			0
$407$		0			0
$408$		−	10.3923i		−	0.514496i
$409$	13.5000	+	7.79423i	0.667532	+	0.385400i	0.795141	−	0.606425i	$-0.207397\pi$
$409$	13.5000	+	7.79423i	0.667532	+	0.385400i	−0.127609	+	0.991825i	$0.540730\pi$
$410$		0			0
$411$			31.1769i			1.53784i
$412$	5.00000	−	8.66025i	0.246332	−	0.426660i
$413$		0			0
$414$	9.00000	−	5.19615i	0.442326	−	0.255377i
$415$		0			0
$416$	18.0000	−	5.19615i	0.882523	−	0.254762i
$417$	8.00000			0.391762
$418$		0			0
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	0.557986	−	0.829851i	$-0.311574\pi$
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	−0.997665	+	0.0683046i	$0.978241\pi$
$420$		0			0
$421$		−	15.5885i		−	0.759735i	−0.925041	−	0.379867i	$-0.875970\pi$
$421$		−	15.5885i		−	0.759735i	0.925041	−	0.379867i	$-0.124030\pi$
$422$	−15.0000	−	8.66025i	−0.730189	−	0.421575i
$423$	3.00000	+	1.73205i	0.145865	+	0.0842152i
$424$			5.19615i			0.252347i
$425$		0			0
$426$	6.00000	+	10.3923i	0.290701	+	0.503509i
$427$		0			0
$428$	6.00000			0.290021
$429$		0			0
$430$		0			0
$431$	−6.00000	+	3.46410i	−0.289010	+	0.166860i	−0.637495	−	0.770454i	$-0.720029\pi$
$431$	−6.00000	+	3.46410i	−0.289010	+	0.166860i	0.348485	+	0.937314i	$0.386696\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	−8.50000	+	14.7224i	−0.408484	+	0.707515i	−0.994720	−	0.102625i	$-0.967276\pi$
$433$	−8.50000	+	14.7224i	−0.408484	+	0.707515i	0.586236	+	0.810140i	$0.300609\pi$
$434$		0			0
$435$		0			0
$436$	12.0000	+	6.92820i	0.574696	+	0.331801i
$437$			20.7846i			0.994263i
$438$	−3.00000	+	5.19615i	−0.143346	+	0.248282i
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$	13.5000	+	12.9904i	0.642130	+	0.617889i
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$	−15.0000	+	8.66025i	−0.711868	+	0.410997i
$445$		0			0
$446$	9.00000	−	15.5885i	0.426162	−	0.738135i
$447$		−	38.1051i		−	1.80231i
$448$		0			0
$449$	−6.00000	−	3.46410i	−0.283158	−	0.163481i	0.351694	−	0.936115i	$-0.385606\pi$
$449$	−6.00000	−	3.46410i	−0.283158	−	0.163481i	−0.634852	+	0.772634i	$0.718939\pi$
$450$		0			0
$451$		0			0
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$	30.0000	−	17.3205i	1.40952	−	0.813788i
$454$	−42.0000			−1.97116
$455$		0			0
$456$	12.0000			0.561951
$457$	−1.50000	+	0.866025i	−0.0701670	+	0.0405110i	−0.534673	−	0.845059i	$-0.679565\pi$
$457$	−1.50000	+	0.866025i	−0.0701670	+	0.0405110i	0.464506	+	0.885570i	$0.346232\pi$
$458$		0			0
$459$	−6.00000	+	10.3923i	−0.280056	+	0.485071i
$460$		0			0
$461$	19.5000	+	11.2583i	0.908206	+	0.524353i	0.879853	−	0.475245i	$-0.157641\pi$
$461$	19.5000	+	11.2583i	0.908206	+	0.524353i	0.0283522	+	0.999598i	$0.490974\pi$
$462$		0			0
$463$			13.8564i			0.643962i	0.946746	+	0.321981i	$0.104349\pi$
$463$			13.8564i			0.643962i	−0.946746	+	0.321981i	$0.895651\pi$
$464$	7.50000	−	12.9904i	0.348179	−	0.603063i
$465$		0			0
$466$	−9.00000	+	5.19615i	−0.416917	+	0.240707i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	3.50000	+	0.866025i	0.161788	+	0.0400320i
$469$		0			0
$470$		0			0
$471$	13.0000	+	22.5167i	0.599008	+	1.03751i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$		0			0
$474$	12.0000	+	6.92820i	0.551178	+	0.318223i
$475$		0			0
$476$		0			0
$477$	−1.50000	+	2.59808i	−0.0686803	+	0.118958i
$478$	18.0000	+	31.1769i	0.823301	+	1.42600i
$479$	21.0000	−	12.1244i	0.959514	−	0.553976i	0.0634909	−	0.997982i	$-0.479777\pi$
$479$	21.0000	−	12.1244i	0.959514	−	0.553976i	0.896024	+	0.444006i	$0.146443\pi$
$480$		0			0
$481$	−7.50000	+	30.3109i	−0.341971	+	1.38206i
$482$	−3.00000			−0.136646
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$		0			0
$486$			17.3205i			0.785674i
$487$	6.00000	+	3.46410i	0.271886	+	0.156973i	0.629744	−	0.776802i	$-0.283160\pi$
$487$	6.00000	+	3.46410i	0.271886	+	0.156973i	−0.357858	+	0.933776i	$0.616493\pi$
$488$	−1.50000	−	0.866025i	−0.0679018	−	0.0392031i
$489$		−	41.5692i		−	1.87983i
$490$		0			0
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$	−9.00000	+	5.19615i	−0.405751	+	0.234261i
$493$	9.00000			0.405340
$494$	−15.0000	+	15.5885i	−0.674882	+	0.701358i
$495$		0			0
$496$	15.0000	−	8.66025i	0.673520	−	0.388857i
$497$		0			0
$498$	−24.0000	+	41.5692i	−1.07547	+	1.86276i
$499$		−	31.1769i		−	1.39567i	−0.716258	−	0.697835i	$-0.754147\pi$
$499$		−	31.1769i		−	1.39567i	0.716258	−	0.697835i	$-0.245853\pi$
$500$		0			0
$501$	24.0000	+	13.8564i	1.07224	+	0.619059i
$502$		−	31.1769i		−	1.39149i
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	−0.115332	−	0.993327i	$-0.536793\pi$
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	0.917912	−	0.396783i	$-0.129873\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	22.0000	−	13.8564i	0.977054	−	0.615385i
$508$	−2.00000			−0.0887357
$509$	16.5000	−	9.52628i	0.731350	−	0.422245i	−0.0875661	−	0.996159i	$-0.527909\pi$
$509$	16.5000	−	9.52628i	0.731350	−	0.422245i	0.818916	+	0.573914i	$0.194576\pi$
$510$		0			0
$511$		0			0
$512$			8.66025i			0.382733i
$513$	−12.0000	−	6.92820i	−0.529813	−	0.305888i
$514$	4.50000	+	2.59808i	0.198486	+	0.114596i
$515$		0			0
$516$	8.00000	−	13.8564i	0.352180	−	0.609994i
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$	4.50000	−	2.59808i	0.196960	−	0.113715i
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	0.636401	−	0.771358i	$-0.280422\pi$
$523$	−8.00000	−	13.8564i	−0.349816	−	0.605898i	−0.986216	+	0.165460i	$0.947089\pi$
$524$	9.00000	−	15.5885i	0.393167	−	0.680985i
$525$		0			0
$526$	18.0000	+	10.3923i	0.784837	+	0.453126i
$527$	9.00000	+	5.19615i	0.392046	+	0.226348i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−6.00000	+	3.46410i	−0.260378	+	0.150329i
$532$		0			0
$533$	−4.50000	+	18.1865i	−0.194917	+	0.787746i
$534$	−24.0000			−1.03858
$535$		0			0
$536$	−3.00000	−	5.19615i	−0.129580	−	0.224440i
$537$		0			0
$538$		−	10.3923i		−	0.448044i
$539$		0			0
$540$		0			0
$541$		−	29.4449i		−	1.26593i	−0.774179	−	0.632967i	$-0.781837\pi$
$541$		−	29.4449i		−	1.26593i	0.774179	−	0.632967i	$-0.218163\pi$
$542$	18.0000	−	31.1769i	0.773166	−	1.33916i
$543$	11.0000	+	19.0526i	0.472055	+	0.817624i
$544$	−13.5000	+	7.79423i	−0.578808	+	0.334175i
$545$		0			0
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$	13.5000	−	7.79423i	0.576691	−	0.332953i
$549$	−0.500000	−	0.866025i	−0.0213395	−	0.0369611i
$550$		0			0
$551$			10.3923i			0.442727i
$552$	18.0000	+	10.3923i	0.766131	+	0.442326i
$553$		0			0
$554$			12.1244i			0.515115i
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	13.5000	−	7.79423i	0.572013	−	0.330252i	−0.185940	−	0.982561i	$-0.559533\pi$
$557$	13.5000	−	7.79423i	0.572013	−	0.330252i	0.757953	+	0.652309i	$0.226200\pi$
$558$	6.00000			0.254000
$559$	−8.00000	−	27.7128i	−0.338364	−	1.17213i
$560$		0			0
$561$		0			0
$562$	19.5000	+	33.7750i	0.822558	+	1.42471i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		−	6.92820i		−	0.291730i
$565$		0			0
$566$	6.00000	+	3.46410i	0.252199	+	0.145607i
$567$		0			0
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	21.0000	+	36.3731i	0.880366	+	1.52484i	0.850935	+	0.525271i	$0.176036\pi$
$569$	21.0000	+	36.3731i	0.880366	+	1.52484i	0.0294311	+	0.999567i	$0.490630\pi$
$570$		0			0
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$		0			0
$573$	−36.0000			−1.50392
$574$		0			0
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	19.0526i		−	0.793168i	−0.917998	−	0.396584i	$-0.870195\pi$
$577$		−	19.0526i		−	0.793168i	0.917998	−	0.396584i	$-0.129805\pi$
$578$	12.0000	+	6.92820i	0.499134	+	0.288175i
$579$	9.00000	+	5.19615i	0.374027	+	0.215945i
$580$		0			0
$581$		0			0
$582$	−12.0000	−	20.7846i	−0.497416	−	0.861550i
$583$		0			0
$584$	−3.00000			−0.124141
$585$		0			0
$586$	−9.00000			−0.371787
$587$	18.0000	−	10.3923i	0.742940	−	0.428936i	−0.0801976	−	0.996779i	$-0.525555\pi$
$587$	18.0000	−	10.3923i	0.742940	−	0.428936i	0.823137	+	0.567843i	$0.192222\pi$
$588$	−7.00000	−	12.1244i	−0.288675	−	0.500000i
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$		0			0
$591$	−24.0000	−	13.8564i	−0.987228	−	0.569976i
$592$	−37.5000	−	21.6506i	−1.54124	−	0.889836i
$593$		−	25.9808i		−	1.06690i	−0.845831	−	0.533451i	$-0.820895\pi$
$593$		−	25.9808i		−	1.06690i	0.845831	−	0.533451i	$-0.179105\pi$
$594$		0			0
$595$		0			0
$596$	−16.5000	+	9.52628i	−0.675866	+	0.390212i
$597$	4.00000			0.163709
$598$	−36.0000	+	10.3923i	−1.47215	+	0.424973i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	−0.999934	−	0.0114528i	$-0.996354\pi$
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	0.490049	−	0.871695i	$-0.336979\pi$
$602$		0			0
$603$		−	3.46410i		−	0.141069i
$604$	−15.0000	−	8.66025i	−0.610341	−	0.352381i
$605$		0			0
$606$			10.3923i			0.422159i
$607$	−17.0000	+	29.4449i	−0.690009	+	1.19513i	0.281826	+	0.959466i	$0.409060\pi$
$607$	−17.0000	+	29.4449i	−0.690009	+	1.19513i	−0.971834	+	0.235665i	$0.924273\pi$
$608$	−9.00000	−	15.5885i	−0.364998	−	0.632195i
$609$		0			0
$610$		0			0
$611$	−9.00000	−	8.66025i	−0.364101	−	0.350356i
$612$	−3.00000			−0.121268
$613$	10.5000	−	6.06218i	0.424091	−	0.244849i	−0.272735	−	0.962089i	$-0.587928\pi$
$613$	10.5000	−	6.06218i	0.424091	−	0.244849i	0.696826	+	0.717240i	$0.254595\pi$
$614$	−15.0000	−	25.9808i	−0.605351	−	1.04850i
$615$		0			0
$616$		0			0
$617$	19.5000	+	11.2583i	0.785040	+	0.453243i	0.838214	−	0.545342i	$-0.183600\pi$
$617$	19.5000	+	11.2583i	0.785040	+	0.453243i	−0.0531732	+	0.998585i	$0.516934\pi$
$618$	30.0000	+	17.3205i	1.20678	+	0.696733i
$619$			20.7846i			0.835404i	0.908584	+	0.417702i	$0.137164\pi$
$619$			20.7846i			0.835404i	−0.908584	+	0.417702i	$0.862836\pi$
$620$		0			0
$621$	−12.0000	−	20.7846i	−0.481543	−	0.834058i
$622$	−45.0000	+	25.9808i	−1.80434	+	1.04173i
$623$		0			0
$624$	10.0000	+	34.6410i	0.400320	+	1.38675i
$625$		0			0
$626$	−15.0000	+	8.66025i	−0.599521	+	0.346133i
$627$		0			0
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$		−	25.9808i		−	1.03592i
$630$		0			0
$631$	−42.0000	−	24.2487i	−1.67199	−	0.965326i	−0.966521	−	0.256589i	$-0.917401\pi$
$631$	−42.0000	−	24.2487i	−1.67199	−	0.965326i	−0.705473	−	0.708737i	$-0.749265\pi$
$632$			6.92820i			0.275589i
$633$	10.0000	−	17.3205i	0.397464	−	0.688428i
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$		0			0
$636$	6.00000			0.237915
$637$	−24.5000	−	6.06218i	−0.970725	−	0.240192i
$638$		0			0
$639$	−3.00000	+	1.73205i	−0.118678	+	0.0685189i
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$			20.7846i			0.820303i
$643$	−12.0000	−	6.92820i	−0.473234	−	0.273222i	0.244359	−	0.969685i	$-0.421423\pi$
$643$	−12.0000	−	6.92820i	−0.473234	−	0.273222i	−0.717592	+	0.696463i	$0.754756\pi$
$644$		0			0
$645$		0			0
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$	−16.5000	+	9.52628i	−0.648181	+	0.374228i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−18.0000	+	10.3923i	−0.704934	+	0.406994i
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$	−24.0000	+	41.5692i	−0.938474	+	1.62549i
$655$		0			0
$656$	−22.5000	−	12.9904i	−0.878477	−	0.507189i
$657$	−1.50000	−	0.866025i	−0.0585206	−	0.0337869i
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	−40.5000	+	23.3827i	−1.57527	+	0.909481i	−0.579761	+	0.814787i	$0.696854\pi$
$661$	−40.5000	+	23.3827i	−1.57527	+	0.909481i	−0.995506	+	0.0946945i	$0.969813\pi$
$662$	−48.0000			−1.86557
$663$	−15.0000	+	15.5885i	−0.582552	+	0.605406i
$664$	−24.0000			−0.931381
$665$		0			0
$666$	−7.50000	−	12.9904i	−0.290619	−	0.503367i
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$		−	13.8564i		−	0.536120i
$669$	18.0000	+	10.3923i	0.695920	+	0.401790i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	0.622770	−	0.782405i	$-0.286007\pi$
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	−0.988968	+	0.148132i	$0.952674\pi$
$674$	34.5000	−	19.9186i	1.32889	−	0.767235i
$675$		0			0
$676$	−11.5000	−	6.06218i	−0.442308	−	0.233161i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	−45.0000	+	25.9808i	−1.72821	+	0.997785i
$679$		0			0
$680$		0			0
$681$		−	48.4974i		−	1.85843i
$682$		0			0
$683$	−21.0000	−	12.1244i	−0.803543	−	0.463926i	0.0411658	−	0.999152i	$-0.486893\pi$
$683$	−21.0000	−	12.1244i	−0.803543	−	0.463926i	−0.844708	+	0.535227i	$0.820226\pi$
$684$		−	3.46410i		−	0.132453i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	40.0000			1.52499
$689$	7.50000	−	7.79423i	0.285727	−	0.296936i
$690$		0			0
$691$	12.0000	−	6.92820i	0.456502	−	0.263561i	−0.254071	−	0.967186i	$-0.581770\pi$
$691$	12.0000	−	6.92820i	0.456502	−	0.263561i	0.710572	+	0.703624i	$0.248436\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$		0			0
$694$			51.9615i			1.97243i
$695$		0			0
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$		−	15.5885i		−	0.590455i
$698$	12.0000	−	20.7846i	0.454207	−	0.786709i
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	6.00000	−	24.2487i	0.226455	−	0.915209i
$703$	30.0000			1.13147
$704$		0			0
$705$		0			0
$706$	−28.5000	+	49.3634i	−1.07261	+	1.85782i
$707$		0			0
$708$	12.0000	+	6.92820i	0.450988	+	0.260378i
$709$	−4.50000	−	2.59808i	−0.169001	−	0.0975728i	0.413114	−	0.910679i	$-0.364441\pi$
$709$	−4.50000	−	2.59808i	−0.169001	−	0.0975728i	−0.582115	+	0.813107i	$0.697775\pi$
$710$		0			0
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	−6.00000	−	10.3923i	−0.224860	−	0.389468i
$713$	−18.0000	+	10.3923i	−0.674105	+	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−36.0000	+	20.7846i	−1.34444	+	0.776215i
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$		0			0
$721$		0			0
$722$	−10.5000	−	6.06218i	−0.390770	−	0.225611i
$723$		−	3.46410i		−	0.128831i
$724$	5.50000	−	9.52628i	0.204406	−	0.354041i
$725$		0			0
$726$	−33.0000	+	19.0526i	−1.22474	+	0.707107i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$			12.1244i			0.447823i	0.974609	+	0.223912i	$0.0718827\pi$
$733$			12.1244i			0.447823i	−0.974609	+	0.223912i	$0.928117\pi$
$734$	−33.0000	−	19.0526i	−1.21805	−	0.703243i
$735$		0			0
$736$		−	31.1769i		−	1.14920i
$737$		0			0
$738$	−4.50000	−	7.79423i	−0.165647	−	0.286910i
$739$	−18.0000	+	10.3923i	−0.662141	+	0.382287i	−0.793092	−	0.609102i	$-0.791530\pi$
$739$	−18.0000	+	10.3923i	−0.662141	+	0.382287i	0.130951	+	0.991389i	$0.458197\pi$
$740$		0			0
$741$	−18.0000	−	17.3205i	−0.661247	−	0.636285i
$742$		0			0
$743$	30.0000	−	17.3205i	1.10059	−	0.635428i	0.164216	−	0.986424i	$-0.447490\pi$
$743$	30.0000	−	17.3205i	1.10059	−	0.635428i	0.936377	+	0.350997i	$0.114157\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$		0			0
$746$		−	32.9090i		−	1.20488i
$747$	−12.0000	−	6.92820i	−0.439057	−	0.253490i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	15.0000	−	8.66025i	0.546994	−	0.315807i
$753$	36.0000			1.31191
$754$	−18.0000	+	5.19615i	−0.655521	+	0.189233i
$755$		0			0
$756$		0			0
$757$	−13.0000	−	22.5167i	−0.472493	−	0.818382i	0.527011	−	0.849858i	$-0.323312\pi$
$757$	−13.0000	−	22.5167i	−0.472493	−	0.818382i	−0.999505	+	0.0314762i	$0.989979\pi$
$758$	−21.0000	+	36.3731i	−0.762754	+	1.32113i
$759$		0			0
$760$		0			0
$761$	30.0000	+	17.3205i	1.08750	+	0.627868i	0.932910	−	0.360111i	$-0.117261\pi$
$761$	30.0000	+	17.3205i	1.08750	+	0.627868i	0.154590	+	0.987979i	$0.450594\pi$
$762$		−	6.92820i		−	0.250982i
$763$		0			0
$764$	9.00000	+	15.5885i	0.325609	+	0.563971i
$765$		0			0
$766$	36.0000			1.30073
$767$	24.0000	−	6.92820i	0.866590	−	0.250163i
$768$	−38.0000			−1.37121
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	−0.387901	−	0.921701i	$-0.626800\pi$
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	0.604266	+	0.796782i	$0.293466\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$		−	5.19615i		−	0.187014i
$773$	30.0000	+	17.3205i	1.07903	+	0.622975i	0.930633	−	0.365953i	$-0.119257\pi$
$773$	30.0000	+	17.3205i	1.07903	+	0.622975i	0.148392	+	0.988929i	$0.452590\pi$
$774$	12.0000	+	6.92820i	0.431331	+	0.249029i
$775$		0			0
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$		0			0
$778$	−13.5000	+	7.79423i	−0.483998	+	0.279437i
$779$	18.0000			0.644917
$780$		0			0
$781$		0			0
$782$	27.0000	−	15.5885i	0.965518	−	0.557442i
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$	17.5000	−	30.3109i	0.625000	−	1.08253i
$785$		0			0
$786$	54.0000	+	31.1769i	1.92612	+	1.11204i
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.221162	−	0.975237i	$-0.570985\pi$
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.955161	+	0.296087i	$0.904318\pi$
$788$			13.8564i			0.493614i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.00000	+	3.46410i	0.0355110	+	0.123014i
$794$	24.0000			0.851728
$795$		0			0
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	−0.206868	−	0.978369i	$-0.566327\pi$
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	0.950726	−	0.310031i	$-0.100340\pi$
$798$		0			0
$799$	9.00000	+	5.19615i	0.318397	+	0.183827i
$800$		0			0
$801$		−	6.92820i		−	0.244796i
$802$	−1.50000	+	2.59808i	−0.0529668	+	0.0917413i
$803$		0			0
$804$	−6.00000	+	3.46410i	−0.211604	+	0.122169i
$805$		0			0
$806$	−21.0000	−	5.19615i	−0.739693	−	0.183027i
$807$	12.0000			0.422420
$808$	−4.50000	+	2.59808i	−0.158309	+	0.0914000i
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	−0.995466	−	0.0951198i	$-0.969677\pi$
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	0.415357	−	0.909659i	$-0.363657\pi$
$810$		0			0
$811$			38.1051i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$811$			38.1051i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$812$		0			0
$813$	36.0000	+	20.7846i	1.26258	+	0.728948i
$814$		0			0
$815$		0			0
$816$	−15.0000	−	25.9808i	−0.525105	−	0.909509i
$817$	−24.0000	+	13.8564i	−0.839654	+	0.484774i
$818$	27.0000			0.944033
$819$		0			0
$820$		0			0
$821$	−36.0000	+	20.7846i	−1.25641	+	0.725388i	−0.972375	−	0.233426i	$-0.925006\pi$
$821$	−36.0000	+	20.7846i	−1.25641	+	0.725388i	−0.284034	+	0.958814i	$0.591673\pi$
$822$	27.0000	+	46.7654i	0.941733	+	1.63113i
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	−0.898776	−	0.438408i	$-0.855543\pi$
$823$	−2.00000	+	3.46410i	−0.0697156	+	0.120751i	0.829060	+	0.559159i	$0.188876\pi$
$824$			17.3205i			0.603388i
$825$		0			0
$826$		0			0
$827$			20.7846i			0.722752i	0.932420	+	0.361376i	$0.117693\pi$
$827$			20.7846i			0.722752i	−0.932420	+	0.361376i	$0.882307\pi$
$828$	3.00000	−	5.19615i	0.104257	−	0.180579i
$829$	−12.5000	−	21.6506i	−0.434143	−	0.751958i	0.563082	−	0.826401i	$-0.309615\pi$
$829$	−12.5000	−	21.6506i	−0.434143	−	0.751958i	−0.997225	+	0.0744432i	$0.976282\pi$
$830$		0			0
$831$	−14.0000			−0.485655
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$	21.0000			0.727607
$834$	12.0000	−	6.92820i	0.415526	−	0.239904i
$835$		0			0
$836$		0			0
$837$		−	13.8564i		−	0.478947i
$838$	−27.0000	−	15.5885i	−0.932700	−	0.538494i
$839$	39.0000	+	22.5167i	1.34643	+	0.777361i	0.987742	−	0.156096i	$-0.0498910\pi$
$839$	39.0000	+	22.5167i	1.34643	+	0.777361i	0.358688	+	0.933458i	$0.383224\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−13.5000	−	23.3827i	−0.465241	−	0.805821i
$843$	−39.0000	+	22.5167i	−1.34323	+	0.775515i
$844$	−10.0000			−0.344214
$845$		0			0
$846$	6.00000			0.206284
$847$		0			0
$848$	7.50000	+	12.9904i	0.257551	+	0.446092i
$849$	−4.00000	+	6.92820i	−0.137280	+	0.237775i
$850$		0			0
$851$	45.0000	+	25.9808i	1.54258	+	0.890609i
$852$	6.00000	+	3.46410i	0.205557	+	0.118678i
$853$			25.9808i			0.889564i	0.895639	+	0.444782i	$0.146719\pi$
$853$			25.9808i			0.889564i	−0.895639	+	0.444782i	$0.853281\pi$
$854$		0			0
$855$		0			0
$856$	−9.00000	+	5.19615i	−0.307614	+	0.177601i
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$		0			0
$859$	−14.0000			−0.477674			−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000			−0.477674			−0.238837	+	0.971060i	$0.576766\pi$
$860$		0			0
$861$		0			0
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$		−	27.7128i		−	0.943355i	−0.881771	−	0.471678i	$-0.843649\pi$
$863$		−	27.7128i		−	0.943355i	0.881771	−	0.471678i	$-0.156351\pi$
$864$	18.0000	+	10.3923i	0.612372	+	0.353553i
$865$		0			0
$866$			29.4449i			1.00058i
$867$	−8.00000	+	13.8564i	−0.271694	+	0.470588i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−3.00000	+	12.1244i	−0.101651	+	0.410818i
$872$	−24.0000			−0.812743
$873$	6.00000	−	3.46410i	0.203069	−	0.117242i
$874$	18.0000	+	31.1769i	0.608859	+	1.05457i
$875$		0			0
$876$			3.46410i			0.117041i
$877$	−10.5000	−	6.06218i	−0.354560	−	0.204705i	0.312132	−	0.950039i	$-0.398957\pi$
$877$	−10.5000	−	6.06218i	−0.354560	−	0.204705i	−0.666692	+	0.745334i	$0.732290\pi$
$878$	42.0000	+	24.2487i	1.41743	+	0.818354i
$879$		−	10.3923i		−	0.350524i
$880$		0			0
$881$	−13.5000	−	23.3827i	−0.454827	−	0.787783i	0.543852	−	0.839181i	$-0.316965\pi$
$881$	−13.5000	−	23.3827i	−0.454827	−	0.787783i	−0.998678	+	0.0513987i	$0.983632\pi$
$882$	10.5000	−	6.06218i	0.353553	−	0.204124i
$883$	−10.0000			−0.336527			−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000			−0.336527			−0.168263	+	0.985742i	$0.553816\pi$
$884$	10.5000	+	2.59808i	0.353153	+	0.0873828i
$885$		0			0
$886$	18.0000	−	10.3923i	0.604722	−	0.349136i
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$	15.0000	−	25.9808i	0.503367	−	0.871857i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		−	10.3923i		−	0.347960i
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$	−33.0000	−	57.1577i	−1.10369	−	1.91164i
$895$		0			0
$896$		0			0
$897$	−12.0000	−	41.5692i	−0.400668	−	1.38796i
$898$	−12.0000			−0.400445
$899$	−9.00000	+	5.19615i	−0.300167	+	0.173301i
$900$		0			0
$901$	−4.50000	+	7.79423i	−0.149917	+	0.259663i
$902$		0			0
$903$		0			0
$904$	−22.5000	−	12.9904i	−0.748339	−	0.432054i
$905$		0			0
$906$	30.0000	−	51.9615i	0.996683	−	1.72631i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	−21.0000	+	12.1244i	−0.696909	+	0.402361i
$909$	−3.00000			−0.0995037
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	30.0000	−	17.3205i	0.993399	−	0.573539i
$913$		0			0
$914$	−1.50000	+	2.59808i	−0.0496156	+	0.0859367i
$915$		0			0
$916$		0			0
$917$		0			0
$918$			20.7846i			0.685994i
$919$	−11.0000	+	19.0526i	−0.362857	+	0.628486i	−0.988430	−	0.151680i	$-0.951532\pi$
$919$	−11.0000	+	19.0526i	−0.362857	+	0.628486i	0.625573	+	0.780165i	$0.284865\pi$
$920$		0			0
$921$	30.0000	−	17.3205i	0.988534	−	0.570730i
$922$	39.0000			1.28440
$923$	12.0000	−	3.46410i	0.394985	−	0.114022i
$924$		0			0
$925$		0			0
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	−5.00000	+	8.66025i	−0.164222	+	0.284440i
$928$		−	15.5885i		−	0.511716i
$929$	−40.5000	−	23.3827i	−1.32876	−	0.767161i	−0.343654	−	0.939096i	$-0.611665\pi$
$929$	−40.5000	−	23.3827i	−1.32876	−	0.767161i	−0.985108	+	0.171935i	$0.944998\pi$
$930$		0			0
$931$			24.2487i			0.794719i
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$	−30.0000	−	51.9615i	−0.982156	−	1.70114i
$934$	−18.0000	+	10.3923i	−0.588978	+	0.340047i
$935$		0			0
$936$	−6.00000	+	1.73205i	−0.196116	+	0.0566139i
$937$	−7.00000			−0.228680			−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$		0			0
$939$	−10.0000	−	17.3205i	−0.326338	−	0.565233i
$940$		0			0
$941$		−	20.7846i		−	0.677559i	−0.940866	−	0.338779i	$-0.889986\pi$
$941$		−	20.7846i		−	0.677559i	0.940866	−	0.338779i	$-0.110014\pi$
$942$	39.0000	+	22.5167i	1.27069	+	0.733632i
$943$	27.0000	+	15.5885i	0.879241	+	0.507630i
$944$			34.6410i			1.12747i
$945$		0			0
$946$		0			0
$947$	15.0000	−	8.66025i	0.487435	−	0.281420i	−0.236075	−	0.971735i	$-0.575861\pi$
$947$	15.0000	−	8.66025i	0.487435	−	0.281420i	0.723510	+	0.690314i	$0.242528\pi$
$948$	8.00000			0.259828
$949$	4.50000	+	4.33013i	0.146076	+	0.140562i
$950$		0			0
$951$	9.00000	−	5.19615i	0.291845	−	0.168497i
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$			5.19615i			0.168232i
$955$		0			0
$956$	18.0000	+	10.3923i	0.582162	+	0.336111i
$957$		0			0
$958$	21.0000	−	36.3731i	0.678479	−	1.17516i
$959$		0			0
$960$		0			0
$961$	19.0000			0.612903
$962$	15.0000	+	51.9615i	0.483619	+	1.67531i
$963$	−6.00000			−0.193347
$964$	−1.50000	+	0.866025i	−0.0483117	+	0.0278928i
$965$		0			0
$966$		0			0
$967$			58.8897i			1.89377i	0.321578	+	0.946883i	$0.395787\pi$
$967$			58.8897i			1.89377i	−0.321578	+	0.946883i	$0.604213\pi$
$968$	−16.5000	−	9.52628i	−0.530330	−	0.306186i
$969$	18.0000	+	10.3923i	0.578243	+	0.333849i
$970$		0			0
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$	5.00000	+	8.66025i	0.160375	+	0.277778i
$973$		0			0
$974$	12.0000			0.384505
$975$		0			0
$976$	−5.00000			−0.160046
$977$	−37.5000	+	21.6506i	−1.19973	+	0.692665i	−0.960495	−	0.278296i	$-0.910230\pi$
$977$	−37.5000	+	21.6506i	−1.19973	+	0.692665i	−0.239236	+	0.970961i	$0.576897\pi$
$978$	−36.0000	−	62.3538i	−1.15115	−	1.99386i
$979$		0			0
$980$		0			0
$981$	−12.0000	−	6.92820i	−0.383131	−	0.221201i
$982$	−18.0000	−	10.3923i	−0.574403	−	0.331632i
$983$			51.9615i			1.65732i	0.559756	+	0.828658i	$0.310895\pi$
$983$			51.9615i			1.65732i	−0.559756	+	0.828658i	$0.689105\pi$
$984$	9.00000	−	15.5885i	0.286910	−	0.496942i
$985$		0			0
$986$	13.5000	−	7.79423i	0.429928	−	0.248219i
$987$		0			0
$988$	−3.00000	+	12.1244i	−0.0954427	+	0.385727i
$989$	−48.0000			−1.52631
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	9.00000	−	15.5885i	0.285750	−	0.494934i
$993$		−	55.4256i		−	1.75888i
$994$		0			0
$995$		0			0
$996$			27.7128i			0.878114i
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	−27.0000	−	46.7654i	−0.854670	−	1.48033i
$999$	−30.0000	+	17.3205i	−0.949158	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.a.101.1		2
5.2	odd	4		325.2.m.a.49.2		4
5.3	odd	4		325.2.m.a.49.1		4
5.4	even	2		13.2.e.a.10.1	yes	2
13.2	odd	12		4225.2.a.v.1.2		2
13.4	even	6	inner	325.2.n.a.251.1		2
13.11	odd	12		4225.2.a.v.1.1		2
15.14	odd	2		117.2.q.c.10.1		2
20.19	odd	2		208.2.w.b.49.1		2
35.4	even	6		637.2.k.a.569.1		2
35.9	even	6		637.2.u.c.361.1		2
35.19	odd	6		637.2.u.b.361.1		2
35.24	odd	6		637.2.k.c.569.1		2
35.34	odd	2		637.2.q.a.491.1		2
40.19	odd	2		832.2.w.a.257.1		2
40.29	even	2		832.2.w.d.257.1		2
60.59	even	2		1872.2.by.d.1297.1		2
65.4	even	6		13.2.e.a.4.1	✓	2
65.9	even	6		169.2.e.a.147.1		2
65.17	odd	12		325.2.m.a.199.1		4
65.19	odd	12		169.2.c.a.22.2		4
65.24	odd	12		169.2.a.a.1.2		2
65.29	even	6		169.2.b.a.168.1		2
65.34	odd	4		169.2.c.a.146.1		4
65.43	odd	12		325.2.m.a.199.2		4
65.44	odd	4		169.2.c.a.146.2		4
65.49	even	6		169.2.b.a.168.2		2
65.54	odd	12		169.2.a.a.1.1		2
65.59	odd	12		169.2.c.a.22.1		4
65.64	even	2		169.2.e.a.23.1		2
195.29	odd	6		1521.2.b.a.1351.2		2
195.89	even	12		1521.2.a.k.1.1		2
195.119	even	12		1521.2.a.k.1.2		2
195.134	odd	6		117.2.q.c.82.1		2
195.179	odd	6		1521.2.b.a.1351.1		2
260.119	even	12		2704.2.a.o.1.2		2
260.159	odd	6		2704.2.f.b.337.2		2
260.179	odd	6		2704.2.f.b.337.1		2
260.199	odd	6		208.2.w.b.17.1		2
260.219	even	12		2704.2.a.o.1.1		2
455.4	even	6		637.2.u.c.30.1		2
455.69	odd	6		637.2.q.a.589.1		2
455.199	odd	6		637.2.u.b.30.1		2
455.264	odd	6		637.2.k.c.459.1		2
455.314	even	12		8281.2.a.q.1.1		2
455.349	even	12		8281.2.a.q.1.2		2
455.394	even	6		637.2.k.a.459.1		2
520.69	even	6		832.2.w.d.641.1		2
520.459	odd	6		832.2.w.a.641.1		2
780.719	even	6		1872.2.by.d.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.2.e.a.4.1	✓	2	65.4	even	6
13.2.e.a.10.1	yes	2	5.4	even	2
117.2.q.c.10.1		2	15.14	odd	2
117.2.q.c.82.1		2	195.134	odd	6
169.2.a.a.1.1		2	65.54	odd	12
169.2.a.a.1.2		2	65.24	odd	12
169.2.b.a.168.1		2	65.29	even	6
169.2.b.a.168.2		2	65.49	even	6
169.2.c.a.22.1		4	65.59	odd	12
169.2.c.a.22.2		4	65.19	odd	12
169.2.c.a.146.1		4	65.34	odd	4
169.2.c.a.146.2		4	65.44	odd	4
169.2.e.a.23.1		2	65.64	even	2
169.2.e.a.147.1		2	65.9	even	6
208.2.w.b.17.1		2	260.199	odd	6
208.2.w.b.49.1		2	20.19	odd	2
325.2.m.a.49.1		4	5.3	odd	4
325.2.m.a.49.2		4	5.2	odd	4
325.2.m.a.199.1		4	65.17	odd	12
325.2.m.a.199.2		4	65.43	odd	12
325.2.n.a.101.1		2	1.1	even	1	trivial
325.2.n.a.251.1		2	13.4	even	6	inner
637.2.k.a.459.1		2	455.394	even	6
637.2.k.a.569.1		2	35.4	even	6
637.2.k.c.459.1		2	455.264	odd	6
637.2.k.c.569.1		2	35.24	odd	6
637.2.q.a.491.1		2	35.34	odd	2
637.2.q.a.589.1		2	455.69	odd	6
637.2.u.b.30.1		2	455.199	odd	6
637.2.u.b.361.1		2	35.19	odd	6
637.2.u.c.30.1		2	455.4	even	6
637.2.u.c.361.1		2	35.9	even	6
832.2.w.a.257.1		2	40.19	odd	2
832.2.w.a.641.1		2	520.459	odd	6
832.2.w.d.257.1		2	40.29	even	2
832.2.w.d.641.1		2	520.69	even	6
1521.2.a.k.1.1		2	195.89	even	12
1521.2.a.k.1.2		2	195.119	even	12
1521.2.b.a.1351.1		2	195.179	odd	6
1521.2.b.a.1351.2		2	195.29	odd	6
1872.2.by.d.433.1		2	780.719	even	6
1872.2.by.d.1297.1		2	60.59	even	2
2704.2.a.o.1.1		2	260.219	even	12
2704.2.a.o.1.2		2	260.119	even	12
2704.2.f.b.337.1		2	260.179	odd	6
2704.2.f.b.337.2		2	260.159	odd	6
4225.2.a.v.1.1		2	13.11	odd	12
4225.2.a.v.1.2		2	13.2	odd	12
8281.2.a.q.1.1		2	455.314	even	12
8281.2.a.q.1.2		2	455.349	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{6} +1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +2.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +(2.50000 + 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.73205i q^{18} +(-3.00000 - 1.73205i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-3.00000 + 1.73205i) q^{24} +(1.50000 - 6.06218i) q^{26} +4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} -3.46410i q^{31} +(4.50000 + 2.59808i) q^{32} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(-7.50000 + 4.33013i) q^{37} -6.00000 q^{38} +(7.00000 + 1.73205i) q^{39} +(-4.50000 + 2.59808i) q^{41} +(4.00000 - 6.92820i) q^{43} +(-9.00000 - 5.19615i) q^{46} -3.46410i q^{47} +(-5.00000 + 8.66025i) q^{48} +(-3.50000 - 6.06218i) q^{49} -6.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +3.00000 q^{53} +(6.00000 - 3.46410i) q^{54} -6.92820i q^{57} +(-4.50000 - 2.59808i) q^{58} +(6.00000 + 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(-3.00000 + 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-1.50000 - 0.866025i) q^{72} +1.73205i q^{73} +(-7.50000 + 12.9904i) q^{74} +(-3.00000 + 1.73205i) q^{76} +(12.0000 - 3.46410i) q^{78} +4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} +(-4.50000 + 7.79423i) q^{82} +13.8564i q^{83} -13.8564i q^{86} +(3.00000 - 5.19615i) q^{87} +(-6.00000 + 3.46410i) q^{89} -6.00000 q^{92} +(6.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +10.3923i q^{96} +(-6.00000 - 3.46410i) q^{97} +(-10.5000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 2 q^{3} + q^{4} + 6 q^{6} - q^{9} + 4 q^{12} + 5 q^{13} + 5 q^{16} - 3 q^{17} - 6 q^{19} - 6 q^{23} - 6 q^{24} + 3 q^{26} + 8 q^{27} - 3 q^{29} + 9 q^{32} + q^{36} - 15 q^{37} - 12 q^{38}+ \cdots - 21 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + 2 * q^3 + q^4 + 6 * q^6 - q^9 + 4 * q^12 + 5 * q^13 + 5 * q^16 - 3 * q^17 - 6 * q^19 - 6 * q^23 - 6 * q^24 + 3 * q^26 + 8 * q^27 - 3 * q^29 + 9 * q^32 + q^36 - 15 * q^37 - 12 * q^38 + 14 * q^39 - 9 * q^41 + 8 * q^43 - 18 * q^46 - 10 * q^48 - 7 * q^49 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 12 * q^54 - 9 * q^58 + 12 * q^59 - q^61 - 6 * q^62 - 2 * q^64 - 6 * q^67 + 3 * q^68 + 12 * q^69 + 6 * q^71 - 3 * q^72 - 15 * q^74 - 6 * q^76 + 24 * q^78 + 8 * q^79 + 11 * q^81 - 9 * q^82 + 6 * q^87 - 12 * q^89 - 12 * q^92 + 12 * q^93 - 6 * q^94 - 12 * q^97 - 21 * q^98

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