LMFDB - Embedded newform 325.2.m.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(49,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	325.49
Dual form			325.2.m.a.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 1.50000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{6} -1.73205 q^{8} +(0.500000 - 0.866025i) q^{9} -2.00000i q^{12} +(2.59808 + 2.50000i) q^{13} +(2.50000 + 4.33013i) q^{16} +(2.59808 + 1.50000i) q^{17} -1.73205 q^{18} +(3.00000 + 1.73205i) q^{19} +(5.19615 - 3.00000i) q^{23} +(3.00000 - 1.73205i) q^{24} +(1.50000 - 6.06218i) q^{26} -4.00000i q^{27} +(1.50000 + 2.59808i) q^{29} -3.46410i q^{31} +(2.59808 - 4.50000i) q^{32} -5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(4.33013 + 7.50000i) q^{37} -6.00000i q^{38} +(-7.00000 - 1.73205i) q^{39} +(-4.50000 + 2.59808i) q^{41} +(6.92820 + 4.00000i) q^{43} +(-9.00000 - 5.19615i) q^{46} -3.46410 q^{47} +(-8.66025 - 5.00000i) q^{48} +(3.50000 + 6.06218i) q^{49} -6.00000 q^{51} +(-3.46410 + 1.00000i) q^{52} +3.00000i q^{53} +(-6.00000 + 3.46410i) q^{54} -6.92820 q^{57} +(2.59808 - 4.50000i) q^{58} +(-6.00000 - 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-5.19615 + 3.00000i) q^{62} +1.00000 q^{64} +(1.73205 + 3.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} +(-6.00000 + 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-0.866025 + 1.50000i) q^{72} -1.73205 q^{73} +(7.50000 - 12.9904i) q^{74} +(-3.00000 + 1.73205i) q^{76} +(3.46410 + 12.0000i) q^{78} -4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} +(7.79423 + 4.50000i) q^{82} -13.8564 q^{83} -13.8564i q^{86} +(-5.19615 - 3.00000i) q^{87} +(6.00000 - 3.46410i) q^{89} +6.00000i q^{92} +(3.46410 + 6.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} +10.3923i q^{96} +(-3.46410 + 6.00000i) q^{97} +(6.06218 - 10.5000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 12 q^{6} + 2 q^{9} + 10 q^{16} + 12 q^{19} + 12 q^{24} + 6 q^{26} + 6 q^{29} + 2 q^{36} - 28 q^{39} - 18 q^{41} - 36 q^{46} + 14 q^{49} - 24 q^{51} - 24 q^{54} - 24 q^{59} - 2 q^{61} + 4 q^{64}+ \cdots + 12 q^{94}+O(q^{100}) $ 4 * q - 2 * q^4 + 12 * q^6 + 2 * q^9 + 10 * q^16 + 12 * q^19 + 12 * q^24 + 6 * q^26 + 6 * q^29 + 2 * q^36 - 28 * q^39 - 18 * q^41 - 36 * q^46 + 14 * q^49 - 24 * q^51 - 24 * q^54 - 24 * q^59 - 2 * q^61 + 4 * q^64 - 24 * q^69 + 12 * q^71 + 30 * q^74 - 12 * q^76 - 16 * q^79 + 22 * q^81 + 24 * q^89 + 12 * q^94

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 $

$2$	−0.866025	−	1.50000i	−0.612372	−	1.06066i	−0.990839	−	0.135045i	$-0.956882\pi$
$2$	−0.866025	−	1.50000i	−0.612372	−	1.06066i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	−1.73205	+	1.00000i	−1.00000	+	0.577350i	−0.908248	−	0.418432i	$-0.862580\pi$
$3$	−1.73205	+	1.00000i	−1.00000	+	0.577350i	−0.0917517	+	0.995782i	$0.529247\pi$
$4$	−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		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−1.73205			−0.612372
$9$	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	$0.333333\pi$
$12$		−	2.00000i		−	0.577350i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$		0			0
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	0.780801	−	0.624780i	$-0.214811\pi$
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	−0.150675	+	0.988583i	$0.548145\pi$
$18$	−1.73205			−0.408248
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	−0.114708	+	0.993399i	$0.536593\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$	3.00000	−	1.73205i	0.612372	−	0.353553i
$25$		0			0
$26$	1.50000	−	6.06218i	0.294174	−	1.18889i
$27$		−	4.00000i		−	0.769800i
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	2.59808	−	4.50000i	0.459279	−	0.795495i
$33$		0			0
$34$		−	5.19615i		−	0.891133i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	4.33013	+	7.50000i	0.711868	+	1.23299i	0.964155	+	0.265340i	$0.0854841\pi$
$37$	4.33013	+	7.50000i	0.711868	+	1.23299i	−0.252286	+	0.967653i	$0.581183\pi$
$38$		−	6.00000i		−	0.973329i
$39$	−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
$43$	6.92820	+	4.00000i	1.05654	+	0.609994i	0.924473	−	0.381246i	$-0.124505\pi$
$43$	6.92820	+	4.00000i	1.05654	+	0.609994i	0.132068	+	0.991241i	$0.457838\pi$
$44$		0			0
$45$		0			0
$46$	−9.00000	−	5.19615i	−1.32698	−	0.766131i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$	−8.66025	−	5.00000i	−1.25000	−	0.721688i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$		0			0
$51$	−6.00000			−0.840168
$52$	−3.46410	+	1.00000i	−0.480384	+	0.138675i
$53$			3.00000i			0.412082i	0.978543	+	0.206041i	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$	−6.00000	+	3.46410i	−0.816497	+	0.471405i
$55$		0			0
$56$		0			0
$57$	−6.92820			−0.917663
$58$	2.59808	−	4.50000i	0.341144	−	0.590879i
$59$	−6.00000	−	3.46410i	−0.781133	−	0.450988i	0.0556984	−	0.998448i	$-0.482261\pi$
$59$	−6.00000	−	3.46410i	−0.781133	−	0.450988i	−0.836832	+	0.547460i	$0.815595\pi$
$60$		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	$0.187058\pi$
$62$	−5.19615	+	3.00000i	−0.659912	+	0.381000i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	1.73205	+	3.00000i	0.211604	+	0.366508i	0.952217	−	0.305424i	$-0.0987981\pi$
$67$	1.73205	+	3.00000i	0.211604	+	0.366508i	−0.740613	+	0.671932i	$0.765465\pi$
$68$	−2.59808	+	1.50000i	−0.315063	+	0.181902i
$69$	−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	$0.600766\pi$
$72$	−0.866025	+	1.50000i	−0.102062	+	0.176777i
$73$	−1.73205			−0.202721			−0.101361	−	0.994850i	$-0.532320\pi$
$73$	−1.73205			−0.202721			−0.101361	+	0.994850i	$0.532320\pi$
$74$	7.50000	−	12.9904i	0.871857	−	1.51010i
$75$		0			0
$76$	−3.00000	+	1.73205i	−0.344124	+	0.198680i
$77$		0			0
$78$	3.46410	+	12.0000i	0.392232	+	1.35873i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	7.79423	+	4.50000i	0.860729	+	0.496942i
$83$	−13.8564			−1.52094			−0.760469	−	0.649374i	$-0.775031\pi$
$83$	−13.8564			−1.52094			−0.760469	+	0.649374i	$0.775031\pi$
$84$		0			0
$85$		0			0
$86$		−	13.8564i		−	1.49417i
$87$	−5.19615	−	3.00000i	−0.557086	−	0.321634i
$88$		0			0
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$		0			0
$91$		0			0
$92$			6.00000i			0.625543i
$93$	3.46410	+	6.00000i	0.359211	+	0.622171i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$			10.3923i			1.06066i
$97$	−3.46410	+	6.00000i	−0.351726	+	0.609208i	−0.986552	−	0.163448i	$-0.947739\pi$
$97$	−3.46410	+	6.00000i	−0.351726	+	0.609208i	0.634826	+	0.772655i	$0.281072\pi$
$98$	6.06218	−	10.5000i	0.612372	−	1.06066i
$99$		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	$0.785646\pi$
$102$	5.19615	+	9.00000i	0.514496	+	0.891133i
$103$			10.0000i			0.985329i	0.870219	+	0.492665i	$0.163977\pi$
$103$			10.0000i			0.985329i	−0.870219	+	0.492665i	$0.836023\pi$
$104$	−4.50000	−	4.33013i	−0.441261	−	0.424604i
$105$		0			0
$106$	4.50000	−	2.59808i	0.437079	−	0.252347i
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	−0.227345	−	0.973814i	$-0.573004\pi$
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	0.729676	+	0.683793i	$0.239671\pi$
$108$	3.46410	+	2.00000i	0.333333	+	0.192450i
$109$		−	13.8564i		−	1.32720i	−0.748086	−	0.663602i	$-0.769027\pi$
$109$		−	13.8564i		−	1.32720i	0.748086	−	0.663602i	$-0.230973\pi$
$110$		0			0
$111$	−15.0000	−	8.66025i	−1.42374	−	0.821995i
$112$		0			0
$113$	−12.9904	−	7.50000i	−1.22203	−	0.705541i	−0.256681	−	0.966496i	$-0.582629\pi$
$113$	−12.9904	−	7.50000i	−1.22203	−	0.705541i	−0.965351	+	0.260955i	$0.915962\pi$
$114$	6.00000	+	10.3923i	0.561951	+	0.973329i
$115$		0			0
$116$	−3.00000			−0.278543
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$			12.0000i			1.10469i
$119$		0			0
$120$		0			0
$121$	−5.50000	+	9.52628i	−0.500000	+	0.866025i
$122$	1.73205			0.156813
$123$	5.19615	−	9.00000i	0.468521	−	0.811503i
$124$	3.00000	+	1.73205i	0.269408	+	0.155543i
$125$		0			0
$126$		0			0
$127$	−1.73205	+	1.00000i	−0.153695	+	0.0887357i	−0.574875	−	0.818241i	$-0.694949\pi$
$127$	−1.73205	+	1.00000i	−0.153695	+	0.0887357i	0.421180	+	0.906977i	$0.361616\pi$
$128$	−6.06218	−	10.5000i	−0.535826	−	0.928078i
$129$	−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
$137$	7.79423	−	13.5000i	0.665906	−	1.15338i	−0.313133	−	0.949709i	$-0.601379\pi$
$137$	7.79423	−	13.5000i	0.665906	−	1.15338i	0.979039	−	0.203674i	$-0.0652881\pi$
$138$	20.7846			1.76930
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	6.00000	−	3.46410i	0.505291	−	0.291730i
$142$		−	6.00000i		−	0.503509i
$143$		0			0
$144$	5.00000			0.416667
$145$		0			0
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$	−12.1244	−	7.00000i	−1.00000	−	0.577350i
$148$	−8.66025			−0.711868
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.988492	−	0.151272i	$-0.0483370\pi$
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.363241	+	0.931695i	$0.381670\pi$
$150$		0			0
$151$		−	17.3205i		−	1.40952i	−0.709444	−	0.704761i	$-0.751054\pi$
$151$		−	17.3205i		−	1.40952i	0.709444	−	0.704761i	$-0.248946\pi$
$152$	−5.19615	−	3.00000i	−0.421464	−	0.243332i
$153$	2.59808	−	1.50000i	0.210042	−	0.121268i
$154$		0			0
$155$		0			0
$156$	5.00000	−	5.19615i	0.400320	−	0.416025i
$157$		−	13.0000i		−	1.03751i	−0.854922	−	0.518756i	$-0.826395\pi$
$157$		−	13.0000i		−	1.03751i	0.854922	−	0.518756i	$-0.173605\pi$
$158$	3.46410	+	6.00000i	0.275589	+	0.477334i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$		0			0
$162$	9.52628	−	16.5000i	0.748455	−	1.29636i
$163$	10.3923	−	18.0000i	0.813988	−	1.40987i	−0.0960641	−	0.995375i	$-0.530625\pi$
$163$	10.3923	−	18.0000i	0.813988	−	1.40987i	0.910052	−	0.414494i	$-0.136041\pi$
$164$		−	5.19615i		−	0.405751i
$165$		0			0
$166$	12.0000	+	20.7846i	0.931381	+	1.61320i
$167$	−6.92820	−	12.0000i	−0.536120	−	0.928588i	−0.999108	−	0.0422232i	$-0.986556\pi$
$167$	−6.92820	−	12.0000i	−0.536120	−	0.928588i	0.462988	−	0.886365i	$-0.346777\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$	−6.92820	+	4.00000i	−0.528271	+	0.304997i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$			10.3923i			0.787839i
$175$		0			0
$176$		0			0
$177$	13.8564			1.04151
$178$	−10.3923	−	6.00000i	−0.778936	−	0.449719i
$179$		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
$183$		−	2.00000i		−	0.147844i
$184$	−9.00000	+	5.19615i	−0.663489	+	0.383065i
$185$		0			0
$186$	6.00000	−	10.3923i	0.439941	−	0.762001i
$187$		0			0
$188$	1.73205	−	3.00000i	0.126323	−	0.218797i
$189$		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	$0.940925\pi$
$192$	−1.73205	+	1.00000i	−0.125000	+	0.0721688i
$193$	2.59808	+	4.50000i	0.187014	+	0.323917i	0.944253	−	0.329220i	$-0.106786\pi$
$193$	2.59808	+	4.50000i	0.187014	+	0.323917i	−0.757240	+	0.653137i	$0.773452\pi$
$194$	12.0000			0.861550
$195$		0			0
$196$	−7.00000			−0.500000
$197$	6.92820	+	12.0000i	0.493614	+	0.854965i	0.999973	−	0.00735824i	$-0.00234222\pi$
$197$	6.92820	+	12.0000i	0.493614	+	0.854965i	−0.506359	+	0.862323i	$0.669009\pi$
$198$		0			0
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	−0.899291	−	0.437351i	$-0.855917\pi$
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	0.828403	+	0.560133i	$0.189250\pi$
$200$		0			0
$201$	−6.00000	−	3.46410i	−0.423207	−	0.244339i
$202$	2.59808	−	4.50000i	0.182800	−	0.316619i
$203$		0			0
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$		0			0
$206$	15.0000	−	8.66025i	1.04510	−	0.603388i
$207$		−	6.00000i		−	0.417029i
$208$	−4.33013	+	17.5000i	−0.300240	+	1.21341i
$209$		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	$0.945188\pi$
$212$	−2.59808	−	1.50000i	−0.178437	−	0.103020i
$213$	−6.92820			−0.474713
$214$	−9.00000	−	5.19615i	−0.615227	−	0.355202i
$215$		0			0
$216$			6.92820i			0.471405i
$217$		0			0
$218$	−20.7846	+	12.0000i	−1.40771	+	0.812743i
$219$	3.00000	−	1.73205i	0.202721	−	0.117041i
$220$		0			0
$221$	3.00000	+	10.3923i	0.201802	+	0.699062i
$222$			30.0000i			2.01347i
$223$	5.19615	+	9.00000i	0.347960	+	0.602685i	0.985887	−	0.167412i	$-0.0535411\pi$
$223$	5.19615	+	9.00000i	0.347960	+	0.602685i	−0.637927	+	0.770097i	$0.720208\pi$
$224$		0			0
$225$		0			0
$226$			25.9808i			1.72821i
$227$	−12.1244	+	21.0000i	−0.804722	+	1.39382i	0.111757	+	0.993736i	$0.464352\pi$
$227$	−12.1244	+	21.0000i	−0.804722	+	1.39382i	−0.916479	+	0.400083i	$0.868981\pi$
$228$	3.46410	−	6.00000i	0.229416	−	0.397360i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	−2.59808	−	4.50000i	−0.170572	−	0.295439i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$	−4.50000	−	4.33013i	−0.294174	−	0.283069i
$235$		0			0
$236$	6.00000	−	3.46410i	0.390567	−	0.225494i
$237$	6.92820	−	4.00000i	0.450035	−	0.259828i
$238$		0			0
$239$		−	20.7846i		−	1.34444i	−0.740349	−	0.672222i	$-0.765340\pi$
$239$		−	20.7846i		−	1.34444i	0.740349	−	0.672222i	$-0.234660\pi$
$240$		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	$0.684433\pi$
$242$	19.0526			1.22474
$243$	−8.66025	−	5.00000i	−0.555556	−	0.320750i
$244$	−0.500000	−	0.866025i	−0.0320092	−	0.0554416i
$245$		0			0
$246$	−18.0000			−1.14764
$247$	3.46410	+	12.0000i	0.220416	+	0.763542i
$248$			6.00000i			0.381000i
$249$	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
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	−0.416775	−	0.909010i	$-0.636840\pi$
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	0.578838	+	0.815442i	$0.303506\pi$
$258$	13.8564	+	24.0000i	0.862662	+	1.49417i
$259$		0			0
$260$		0			0
$261$	3.00000			0.185695
$262$	−15.5885	−	27.0000i	−0.963058	−	1.66807i
$263$	−10.3923	+	6.00000i	−0.640817	+	0.369976i	−0.784929	−	0.619586i	$-0.787301\pi$
$263$	−10.3923	+	6.00000i	−0.640817	+	0.369976i	0.144112	+	0.989561i	$0.453967\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.92820	+	12.0000i	−0.423999	+	0.734388i
$268$	−3.46410			−0.211604
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		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	$0.115860\pi$
$272$			15.0000i			0.909509i
$273$		0			0
$274$	−27.0000			−1.63113
$275$		0			0
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	6.06218	+	3.50000i	0.364241	+	0.210295i	0.670940	−	0.741512i	$-0.265891\pi$
$277$	6.06218	+	3.50000i	0.364241	+	0.210295i	−0.306699	+	0.951807i	$0.599224\pi$
$278$	6.92820			0.415526
$279$	−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	$0.765601\pi$
$282$	−10.3923	−	6.00000i	−0.618853	−	0.357295i
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	−0.599414	−	0.800439i	$-0.704600\pi$
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	0.393494	+	0.919327i	$0.371266\pi$
$284$	−3.00000	+	1.73205i	−0.178017	+	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.59808	−	4.50000i	−0.153093	−	0.265165i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$		−	13.8564i		−	0.812277i
$292$	0.866025	−	1.50000i	0.0506803	−	0.0877809i
$293$	2.59808	−	4.50000i	0.151781	−	0.262893i	−0.780101	−	0.625653i	$-0.784832\pi$
$293$	2.59808	−	4.50000i	0.151781	−	0.262893i	0.931882	+	0.362761i	$0.118166\pi$
$294$			24.2487i			1.41421i
$295$		0			0
$296$	−7.50000	−	12.9904i	−0.435929	−	0.755051i
$297$		0			0
$298$		−	33.0000i		−	1.91164i
$299$	21.0000	+	5.19615i	1.21446	+	0.300501i
$300$		0			0
$301$		0			0
$302$	−25.9808	+	15.0000i	−1.49502	+	0.863153i
$303$	−5.19615	−	3.00000i	−0.298511	−	0.172345i
$304$			17.3205i			0.993399i
$305$		0			0
$306$	−4.50000	−	2.59808i	−0.257248	−	0.148522i
$307$	−17.3205			−0.988534			−0.494267	−	0.869310i	$-0.664563\pi$
$307$	−17.3205			−0.988534			−0.494267	+	0.869310i	$0.664563\pi$
$308$		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	$0.823744\pi$
$312$	12.1244	+	3.00000i	0.686406	+	0.169842i
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	−19.5000	+	11.2583i	−1.10045	+	0.635344i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−5.19615			−0.291845			−0.145922	−	0.989296i	$-0.546615\pi$
$317$	−5.19615			−0.291845			−0.145922	+	0.989296i	$0.546615\pi$
$318$	−5.19615	+	9.00000i	−0.291386	+	0.504695i
$319$		0			0
$320$		0			0
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$		0			0
$323$	5.19615	+	9.00000i	0.289122	+	0.500773i
$324$	−11.0000			−0.611111
$325$		0			0
$326$	−36.0000			−1.99386
$327$	13.8564	+	24.0000i	0.766261	+	1.32720i
$328$	7.79423	−	4.50000i	0.430364	−	0.248471i
$329$		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	$0.942261\pi$
$332$	6.92820	−	12.0000i	0.380235	−	0.658586i
$333$	8.66025			0.474579
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$		0			0
$336$		0			0
$337$		−	23.0000i		−	1.25289i	−0.779466	−	0.626445i	$-0.784509\pi$
$337$		−	23.0000i		−	1.25289i	0.779466	−	0.626445i	$-0.215491\pi$
$338$	19.0526	−	12.0000i	1.03632	−	0.652714i
$339$	30.0000			1.62938
$340$		0			0
$341$		0			0
$342$	−5.19615	−	3.00000i	−0.280976	−	0.162221i
$343$		0			0
$344$	−12.0000	−	6.92820i	−0.646997	−	0.373544i
$345$		0			0
$346$		−	10.3923i		−	0.558694i
$347$	25.9808	+	15.0000i	1.39472	+	0.805242i	0.993833	−	0.110885i	$-0.0353686\pi$
$347$	25.9808	+	15.0000i	1.39472	+	0.805242i	0.400887	+	0.916127i	$0.368702\pi$
$348$	5.19615	−	3.00000i	0.278543	−	0.160817i
$349$	−12.0000	+	6.92820i	−0.642345	+	0.370858i	−0.785517	−	0.618840i	$-0.787603\pi$
$349$	−12.0000	+	6.92820i	−0.642345	+	0.370858i	0.143172	+	0.989698i	$0.454270\pi$
$350$		0			0
$351$	10.0000	−	10.3923i	0.533761	−	0.554700i
$352$		0			0
$353$	−16.4545	−	28.5000i	−0.875784	−	1.51690i	−0.855926	−	0.517099i	$-0.827012\pi$
$353$	−16.4545	−	28.5000i	−0.875784	−	1.51690i	−0.0198582	−	0.999803i	$-0.506321\pi$
$354$	−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	$-0.941475\pi$
$359$		−	6.92820i		−	0.365657i	0.983145	−	0.182828i	$-0.0585252\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$	−9.52628	−	16.5000i	−0.500690	−	0.867221i
$363$		−	22.0000i		−	1.15470i
$364$		0			0
$365$		0			0
$366$	−3.00000	+	1.73205i	−0.156813	+	0.0905357i
$367$	−19.0526	+	11.0000i	−0.994535	+	0.574195i	−0.906627	−	0.421933i	$-0.861352\pi$
$367$	−19.0526	+	11.0000i	−0.994535	+	0.574195i	−0.0879086	+	0.996129i	$0.528018\pi$
$368$	25.9808	+	15.0000i	1.35434	+	0.781929i
$369$			5.19615i			0.270501i
$370$		0			0
$371$		0			0
$372$	−6.92820			−0.359211
$373$	16.4545	+	9.50000i	0.851981	+	0.491891i	0.861319	−	0.508065i	$-0.169639\pi$
$373$	16.4545	+	9.50000i	0.851981	+	0.491891i	−0.00933789	+	0.999956i	$0.502972\pi$
$374$		0			0
$375$		0			0
$376$	6.00000			0.309426
$377$	−2.59808	+	10.5000i	−0.133808	+	0.540778i
$378$		0			0
$379$	21.0000	−	12.1244i	1.07870	−	0.622786i	0.148153	−	0.988964i	$-0.452667\pi$
$379$	21.0000	−	12.1244i	1.07870	−	0.622786i	0.930545	+	0.366178i	$0.119334\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$	31.1769			1.59515
$383$	−10.3923	+	18.0000i	−0.531022	+	0.919757i	0.468323	+	0.883558i	$0.344859\pi$
$383$	−10.3923	+	18.0000i	−0.531022	+	0.919757i	−0.999345	+	0.0361995i	$0.988475\pi$
$384$	21.0000	+	12.1244i	1.07165	+	0.618718i
$385$		0			0
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	6.92820	−	4.00000i	0.352180	−	0.203331i
$388$	−3.46410	−	6.00000i	−0.175863	−	0.304604i
$389$	9.00000			0.456318			0.228159	−	0.973624i	$-0.426729\pi$
$389$	9.00000			0.456318			0.228159	+	0.973624i	$0.426729\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	−6.06218	−	10.5000i	−0.306186	−	0.530330i
$393$	−31.1769	+	18.0000i	−1.57267	+	0.907980i
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$		0			0
$396$		0			0
$397$	6.92820	−	12.0000i	0.347717	−	0.602263i	−0.638127	−	0.769931i	$-0.720290\pi$
$397$	6.92820	−	12.0000i	0.347717	−	0.602263i	0.985843	+	0.167668i	$0.0536238\pi$
$398$	3.46410			0.173640
$399$		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	$0.347104\pi$
$402$			12.0000i			0.598506i
$403$	8.66025	−	9.00000i	0.431398	−	0.448322i
$404$	−3.00000			−0.149256
$405$		0			0
$406$		0			0
$407$		0			0
$408$	10.3923			0.514496
$409$	−13.5000	−	7.79423i	−0.667532	−	0.385400i	0.127609	−	0.991825i	$-0.459270\pi$
$409$	−13.5000	−	7.79423i	−0.667532	−	0.385400i	−0.795141	+	0.606425i	$0.792603\pi$
$410$		0			0
$411$			31.1769i			1.53784i
$412$	−8.66025	−	5.00000i	−0.426660	−	0.246332i
$413$		0			0
$414$	−9.00000	+	5.19615i	−0.442326	+	0.255377i
$415$		0			0
$416$	18.0000	−	5.19615i	0.882523	−	0.254762i
$417$		−	8.00000i		−	0.391762i
$418$		0			0
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	0.997665	−	0.0683046i	$-0.0217590\pi$
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	−0.557986	+	0.829851i	$0.688426\pi$
$420$		0			0
$421$		−	15.5885i		−	0.759735i	−0.925041	−	0.379867i	$-0.875970\pi$
$421$		−	15.5885i		−	0.759735i	0.925041	−	0.379867i	$-0.124030\pi$
$422$	−8.66025	+	15.0000i	−0.421575	+	0.730189i
$423$	−1.73205	+	3.00000i	−0.0842152	+	0.145865i
$424$		−	5.19615i		−	0.252347i
$425$		0			0
$426$	6.00000	+	10.3923i	0.290701	+	0.503509i
$427$		0			0
$428$			6.00000i			0.290021i
$429$		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	$0.386696\pi$
$432$	17.3205	−	10.0000i	0.833333	−	0.481125i
$433$	−14.7224	−	8.50000i	−0.707515	−	0.408484i	0.102625	−	0.994720i	$-0.467276\pi$
$433$	−14.7224	−	8.50000i	−0.707515	−	0.408484i	−0.810140	+	0.586236i	$0.800609\pi$
$434$		0			0
$435$		0			0
$436$	12.0000	+	6.92820i	0.574696	+	0.331801i
$437$	20.7846			0.994263
$438$	−5.19615	−	3.00000i	−0.248282	−	0.143346i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$	12.9904	−	13.5000i	0.617889	−	0.642130i
$443$			12.0000i			0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$443$			12.0000i			0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$444$	15.0000	−	8.66025i	0.711868	−	0.410997i
$445$		0			0
$446$	9.00000	−	15.5885i	0.426162	−	0.738135i
$447$	−38.1051			−1.80231
$448$		0			0
$449$	6.00000	+	3.46410i	0.283158	+	0.163481i	0.634852	−	0.772634i	$-0.281061\pi$
$449$	6.00000	+	3.46410i	0.283158	+	0.163481i	−0.351694	+	0.936115i	$0.614394\pi$
$450$		0			0
$451$		0			0
$452$	12.9904	−	7.50000i	0.611016	−	0.352770i
$453$	17.3205	+	30.0000i	0.813788	+	1.40952i
$454$	42.0000			1.97116
$455$		0			0
$456$	12.0000			0.561951
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	0.885570	−	0.464506i	$-0.153768\pi$
$457$	0.866025	+	1.50000i	0.0405110	+	0.0701670i	−0.845059	+	0.534673i	$0.820435\pi$
$458$		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
$463$	−13.8564			−0.643962			−0.321981	−	0.946746i	$-0.604349\pi$
$463$	−13.8564			−0.643962			−0.321981	+	0.946746i	$0.604349\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$		0			0
$466$	−9.00000	+	5.19615i	−0.416917	+	0.240707i
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$	−0.866025	+	3.50000i	−0.0400320	+	0.161788i
$469$		0			0
$470$		0			0
$471$	13.0000	+	22.5167i	0.599008	+	1.03751i
$472$	10.3923	+	6.00000i	0.478345	+	0.276172i
$473$		0			0
$474$	−12.0000	−	6.92820i	−0.551178	−	0.318223i
$475$		0			0
$476$		0			0
$477$	2.59808	+	1.50000i	0.118958	+	0.0686803i
$478$	−31.1769	+	18.0000i	−1.42600	+	0.823301i
$479$	−21.0000	+	12.1244i	−0.959514	+	0.553976i	−0.896024	−	0.444006i	$-0.853557\pi$
$479$	−21.0000	+	12.1244i	−0.959514	+	0.553976i	−0.0634909	+	0.997982i	$0.520223\pi$
$480$		0			0
$481$	−7.50000	+	30.3109i	−0.341971	+	1.38206i
$482$			3.00000i			0.136646i
$483$		0			0
$484$	−5.50000	−	9.52628i	−0.250000	−	0.433013i
$485$		0			0
$486$			17.3205i			0.785674i
$487$	3.46410	−	6.00000i	0.156973	−	0.271886i	−0.776802	−	0.629744i	$-0.783160\pi$
$487$	3.46410	−	6.00000i	0.156973	−	0.271886i	0.933776	+	0.357858i	$0.116493\pi$
$488$	0.866025	−	1.50000i	0.0392031	−	0.0679018i
$489$			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	$0.920614\pi$
$492$	5.19615	+	9.00000i	0.234261	+	0.405751i
$493$			9.00000i			0.405340i
$494$	15.0000	−	15.5885i	0.674882	−	0.701358i
$495$		0			0
$496$	15.0000	−	8.66025i	0.673520	−	0.388857i
$497$		0			0
$498$	−41.5692	−	24.0000i	−1.86276	−	1.07547i
$499$			31.1769i			1.39567i	0.716258	+	0.697835i	$0.245853\pi$
$499$			31.1769i			1.39567i	−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$	24.0000	+	13.8564i	1.07224	+	0.619059i
$502$	−31.1769			−1.39149
$503$	31.1769	+	18.0000i	1.39011	+	0.802580i	0.993327	−	0.115332i	$-0.0367932\pi$
$503$	31.1769	+	18.0000i	1.39011	+	0.802580i	0.396783	+	0.917912i	$0.370127\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−13.8564	−	22.0000i	−0.615385	−	0.977054i
$508$		−	2.00000i		−	0.0887357i
$509$	−16.5000	+	9.52628i	−0.731350	+	0.422245i	−0.818916	−	0.573914i	$-0.805424\pi$
$509$	−16.5000	+	9.52628i	−0.731350	+	0.422245i	0.0875661	+	0.996159i	$0.472091\pi$
$510$		0			0
$511$		0			0
$512$	8.66025			0.382733
$513$	6.92820	−	12.0000i	0.305888	−	0.529813i
$514$	−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	$0.436832\pi$
$522$	−2.59808	−	4.50000i	−0.113715	−	0.196960i
$523$	13.8564	−	8.00000i	0.605898	−	0.349816i	−0.165460	−	0.986216i	$-0.552911\pi$
$523$	13.8564	−	8.00000i	0.605898	−	0.349816i	0.771358	+	0.636401i	$0.219578\pi$
$524$	−9.00000	+	15.5885i	−0.393167	+	0.680985i
$525$		0			0
$526$	18.0000	+	10.3923i	0.784837	+	0.453126i
$527$	5.19615	−	9.00000i	0.226348	−	0.392046i
$528$		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
$533$	−18.1865	−	4.50000i	−0.787746	−	0.194917i
$534$	24.0000			1.03858
$535$		0			0
$536$	−3.00000	−	5.19615i	−0.129580	−	0.224440i
$537$		0			0
$538$	10.3923			0.448044
$539$		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	$-0.218163\pi$
$542$	−31.1769	−	18.0000i	−1.33916	−	0.773166i
$543$	−19.0526	+	11.0000i	−0.817624	+	0.472055i
$544$	13.5000	−	7.79423i	0.578808	−	0.334175i
$545$		0			0
$546$		0			0
$547$		−	22.0000i		−	0.940652i	−0.882493	−	0.470326i	$-0.844136\pi$
$547$		−	22.0000i		−	0.940652i	0.882493	−	0.470326i	$-0.155864\pi$
$548$	7.79423	+	13.5000i	0.332953	+	0.576691i
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$			10.3923i			0.442727i
$552$	10.3923	−	18.0000i	0.442326	−	0.766131i
$553$		0			0
$554$		−	12.1244i		−	0.515115i
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	−7.79423	−	13.5000i	−0.330252	−	0.572013i	0.652309	−	0.757953i	$-0.273800\pi$
$557$	−7.79423	−	13.5000i	−0.330252	−	0.572013i	−0.982561	+	0.185940i	$0.940467\pi$
$558$			6.00000i			0.254000i
$559$	8.00000	+	27.7128i	0.338364	+	1.17213i
$560$		0			0
$561$		0			0
$562$	33.7750	−	19.5000i	1.42471	−	0.822558i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$			6.92820i			0.291730i
$565$		0			0
$566$	6.00000	+	3.46410i	0.252199	+	0.145607i
$567$		0			0
$568$	−5.19615	−	3.00000i	−0.218026	−	0.125877i
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.0294311	−	0.999567i	$-0.509370\pi$
$570$		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
$573$		−	36.0000i		−	1.50392i
$574$		0			0
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−19.0526			−0.793168			−0.396584	−	0.917998i	$-0.629805\pi$
$577$	−19.0526			−0.793168			−0.396584	+	0.917998i	$0.629805\pi$
$578$	−6.92820	+	12.0000i	−0.288175	+	0.499134i
$579$	−9.00000	−	5.19615i	−0.374027	−	0.215945i
$580$		0			0
$581$		0			0
$582$	−20.7846	+	12.0000i	−0.861550	+	0.497416i
$583$		0			0
$584$	3.00000			0.124141
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−10.3923	−	18.0000i	−0.428936	−	0.742940i	0.567843	−	0.823137i	$-0.307778\pi$
$587$	−10.3923	−	18.0000i	−0.428936	−	0.742940i	−0.996779	+	0.0801976i	$0.974445\pi$
$588$	12.1244	−	7.00000i	0.500000	−	0.288675i
$589$	6.00000	−	10.3923i	0.247226	−	0.428207i
$590$		0			0
$591$	−24.0000	−	13.8564i	−0.987228	−	0.569976i
$592$	−21.6506	+	37.5000i	−0.889836	+	1.54124i
$593$	25.9808			1.06690			0.533451	−	0.845831i	$-0.320895\pi$
$593$	25.9808			1.06690			0.533451	+	0.845831i	$0.320895\pi$
$594$		0			0
$595$		0			0
$596$	−16.5000	+	9.52628i	−0.675866	+	0.390212i
$597$		−	4.00000i		−	0.163709i
$598$	−10.3923	−	36.0000i	−0.424973	−	1.47215i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		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
$603$	3.46410			0.141069
$604$	15.0000	+	8.66025i	0.610341	+	0.352381i
$605$		0			0
$606$			10.3923i			0.422159i
$607$	29.4449	+	17.0000i	1.19513	+	0.690009i	0.959466	−	0.281826i	$-0.0909400\pi$
$607$	29.4449	+	17.0000i	1.19513	+	0.690009i	0.235665	+	0.971834i	$0.424273\pi$
$608$	15.5885	−	9.00000i	0.632195	−	0.364998i
$609$		0			0
$610$		0			0
$611$	−9.00000	−	8.66025i	−0.364101	−	0.350356i
$612$			3.00000i			0.121268i
$613$	6.06218	+	10.5000i	0.244849	+	0.424091i	0.962089	−	0.272735i	$-0.0879283\pi$
$613$	6.06218	+	10.5000i	0.244849	+	0.424091i	−0.717240	+	0.696826i	$0.754595\pi$
$614$	15.0000	+	25.9808i	0.605351	+	1.04850i
$615$		0			0
$616$		0			0
$617$	11.2583	−	19.5000i	0.453243	−	0.785040i	−0.545342	−	0.838214i	$-0.683600\pi$
$617$	11.2583	−	19.5000i	0.453243	−	0.785040i	0.998585	+	0.0531732i	$0.0169335\pi$
$618$	−17.3205	+	30.0000i	−0.696733	+	1.20678i
$619$		−	20.7846i		−	0.835404i	−0.908584	−	0.417702i	$-0.862836\pi$
$619$		−	20.7846i		−	0.835404i	0.908584	−	0.417702i	$-0.137164\pi$
$620$		0			0
$621$	−12.0000	−	20.7846i	−0.481543	−	0.834058i
$622$	25.9808	+	45.0000i	1.04173	+	1.80434i
$623$		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
$628$	11.2583	+	6.50000i	0.449256	+	0.259378i
$629$			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	$-0.749265\pi$
$632$	6.92820			0.275589
$633$	17.3205	+	10.0000i	0.688428	+	0.397464i
$634$	4.50000	+	7.79423i	0.178718	+	0.309548i
$635$		0			0
$636$	6.00000			0.237915
$637$	−6.06218	+	24.5000i	−0.240192	+	0.970725i
$638$		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	$0.940718\pi$
$642$	20.7846			0.820303
$643$	6.92820	−	12.0000i	0.273222	−	0.473234i	−0.696463	−	0.717592i	$-0.745244\pi$
$643$	6.92820	−	12.0000i	0.273222	−	0.473234i	0.969685	+	0.244359i	$0.0785774\pi$
$644$		0			0
$645$		0			0
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	15.5885	−	9.00000i	0.612845	−	0.353827i	−0.161233	−	0.986916i	$-0.551547\pi$
$647$	15.5885	−	9.00000i	0.612845	−	0.353827i	0.774078	+	0.633090i	$0.218214\pi$
$648$	−9.52628	−	16.5000i	−0.374228	−	0.648181i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	10.3923	+	18.0000i	0.406994	+	0.704934i
$653$	25.9808	−	15.0000i	1.01671	−	0.586995i	0.103558	−	0.994623i	$-0.466977\pi$
$653$	25.9808	−	15.0000i	1.01671	−	0.586995i	0.913148	+	0.407628i	$0.133644\pi$
$654$	24.0000	−	41.5692i	0.938474	−	1.62549i
$655$		0			0
$656$	−22.5000	−	12.9904i	−0.878477	−	0.507189i
$657$	−0.866025	+	1.50000i	−0.0337869	+	0.0585206i
$658$		0			0
$659$	−6.00000	+	10.3923i	−0.233727	+	0.404827i	−0.958902	−	0.283738i	$-0.908425\pi$
$659$	−6.00000	+	10.3923i	−0.233727	+	0.404827i	0.725175	+	0.688565i	$0.241759\pi$
$660$		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	$0.969813\pi$
$662$			48.0000i			1.86557i
$663$	−15.5885	−	15.0000i	−0.605406	−	0.582552i
$664$	24.0000			0.931381
$665$		0			0
$666$	−7.50000	−	12.9904i	−0.290619	−	0.503367i
$667$	15.5885	+	9.00000i	0.603587	+	0.348481i
$668$	13.8564			0.536120
$669$	−18.0000	−	10.3923i	−0.695920	−	0.401790i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	16.4545	−	9.50000i	0.634274	−	0.366198i	−0.148132	−	0.988968i	$-0.547326\pi$
$673$	16.4545	−	9.50000i	0.634274	−	0.366198i	0.782405	+	0.622770i	$0.213993\pi$
$674$	−34.5000	+	19.9186i	−1.32889	+	0.767235i
$675$		0			0
$676$	−11.5000	−	6.06218i	−0.442308	−	0.233161i
$677$		−	6.00000i		−	0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$		−	6.00000i		−	0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$	−25.9808	−	45.0000i	−0.997785	−	1.72821i
$679$		0			0
$680$		0			0
$681$		−	48.4974i		−	1.85843i
$682$		0			0
$683$	12.1244	−	21.0000i	0.463926	−	0.803543i	−0.535227	−	0.844708i	$-0.679774\pi$
$683$	12.1244	−	21.0000i	0.463926	−	0.803543i	0.999152	+	0.0411658i	$0.0131072\pi$
$684$			3.46410i			0.132453i
$685$		0			0
$686$		0			0
$687$		0			0
$688$			40.0000i			1.52499i
$689$	−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	$0.248436\pi$
$692$	−5.19615	+	3.00000i	−0.197528	+	0.114043i
$693$		0			0
$694$		−	51.9615i		−	1.97243i
$695$		0			0
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	−15.5885			−0.590455
$698$	20.7846	+	12.0000i	0.786709	+	0.454207i
$699$	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	$0.389598\pi$
$702$	−24.2487	−	6.00000i	−0.915209	−	0.226455i
$703$			30.0000i			1.13147i
$704$		0			0
$705$		0			0
$706$	−28.5000	+	49.3634i	−1.07261	+	1.85782i
$707$		0			0
$708$	−6.92820	+	12.0000i	−0.260378	+	0.450988i
$709$	4.50000	+	2.59808i	0.169001	+	0.0975728i	0.582115	−	0.813107i	$-0.302225\pi$
$709$	4.50000	+	2.59808i	0.169001	+	0.0975728i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	−10.3923	+	6.00000i	−0.389468	+	0.224860i
$713$	−10.3923	−	18.0000i	−0.389195	−	0.674105i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	20.7846	+	36.0000i	0.776215	+	1.34444i
$718$	−10.3923	+	6.00000i	−0.387837	+	0.223918i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		0			0
$721$		0			0
$722$	−6.06218	+	10.5000i	−0.225611	+	0.390770i
$723$	3.46410			0.128831
$724$	−5.50000	+	9.52628i	−0.204406	+	0.354041i
$725$		0			0
$726$	−33.0000	+	19.0526i	−1.22474	+	0.707107i
$727$		−	32.0000i		−	1.18681i	−0.804902	−	0.593407i	$-0.797782\pi$
$727$		−	32.0000i		−	1.18681i	0.804902	−	0.593407i	$-0.202218\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	1.73205	+	1.00000i	0.0640184	+	0.0369611i
$733$	−12.1244			−0.447823			−0.223912	−	0.974609i	$-0.571883\pi$
$733$	−12.1244			−0.447823			−0.223912	+	0.974609i	$0.571883\pi$
$734$	33.0000	+	19.0526i	1.21805	+	0.703243i
$735$		0			0
$736$		−	31.1769i		−	1.14920i
$737$		0			0
$738$	7.79423	−	4.50000i	0.286910	−	0.165647i
$739$	18.0000	−	10.3923i	0.662141	−	0.382287i	−0.130951	−	0.991389i	$-0.541803\pi$
$739$	18.0000	−	10.3923i	0.662141	−	0.382287i	0.793092	+	0.609102i	$0.208470\pi$
$740$		0			0
$741$	−18.0000	−	17.3205i	−0.661247	−	0.636285i
$742$		0			0
$743$	17.3205	+	30.0000i	0.635428	+	1.10059i	0.986424	+	0.164216i	$0.0525096\pi$
$743$	17.3205	+	30.0000i	0.635428	+	1.10059i	−0.350997	+	0.936377i	$0.614157\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$		0			0
$746$		−	32.9090i		−	1.20488i
$747$	−6.92820	+	12.0000i	−0.253490	+	0.439057i
$748$		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	$0.739038\pi$
$752$	−8.66025	−	15.0000i	−0.315807	−	0.546994i
$753$			36.0000i			1.31191i
$754$	18.0000	−	5.19615i	0.655521	−	0.189233i
$755$		0			0
$756$		0			0
$757$	−22.5167	+	13.0000i	−0.818382	+	0.472493i	−0.849858	−	0.527011i	$-0.823312\pi$
$757$	−22.5167	+	13.0000i	−0.818382	+	0.472493i	0.0314762	+	0.999505i	$0.489979\pi$
$758$	−36.3731	−	21.0000i	−1.32113	−	0.762754i
$759$		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	$0.450594\pi$
$762$	−6.92820			−0.250982
$763$		0			0
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$		0			0
$766$	36.0000			1.30073
$767$	−6.92820	−	24.0000i	−0.250163	−	0.866590i
$768$		−	38.0000i		−	1.37121i
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	−0.604266	−	0.796782i	$-0.706534\pi$
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	0.387901	+	0.921701i	$0.373200\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	−5.19615			−0.187014
$773$	−17.3205	+	30.0000i	−0.622975	+	1.07903i	0.365953	+	0.930633i	$0.380743\pi$
$773$	−17.3205	+	30.0000i	−0.622975	+	1.07903i	−0.988929	+	0.148392i	$0.952590\pi$
$774$	−12.0000	−	6.92820i	−0.431331	−	0.249029i
$775$		0			0
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$		0			0
$778$	−7.79423	−	13.5000i	−0.279437	−	0.483998i
$779$	−18.0000			−0.644917
$780$		0			0
$781$		0			0
$782$	−15.5885	−	27.0000i	−0.557442	−	0.965518i
$783$	10.3923	−	6.00000i	0.371391	−	0.214423i
$784$	−17.5000	+	30.3109i	−0.625000	+	1.08253i
$785$		0			0
$786$	54.0000	+	31.1769i	1.92612	+	1.11204i
$787$	−19.0526	+	33.0000i	−0.679150	+	1.17632i	0.296087	+	0.955161i	$0.404318\pi$
$787$	−19.0526	+	33.0000i	−0.679150	+	1.17632i	−0.975237	+	0.221162i	$0.929015\pi$
$788$	−13.8564			−0.493614
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.46410	+	1.00000i	−0.123014	+	0.0355110i
$794$	−24.0000			−0.851728
$795$		0			0
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.310031	−	0.950726i	$-0.600340\pi$
$797$	−36.3731	−	21.0000i	−1.28840	−	0.743858i	−0.978369	+	0.206868i	$0.933673\pi$
$798$		0			0
$799$	−9.00000	−	5.19615i	−0.318397	−	0.183827i
$800$		0			0
$801$		−	6.92820i		−	0.244796i
$802$	2.59808	+	1.50000i	0.0917413	+	0.0529668i
$803$		0			0
$804$	6.00000	−	3.46410i	0.211604	−	0.122169i
$805$		0			0
$806$	−21.0000	−	5.19615i	−0.739693	−	0.183027i
$807$		−	12.0000i		−	0.422420i
$808$	−2.59808	−	4.50000i	−0.0914000	−	0.158309i
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$		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
$813$	−20.7846	+	36.0000i	−0.728948	+	1.26258i
$814$		0			0
$815$		0			0
$816$	−15.0000	−	25.9808i	−0.525105	−	0.909509i
$817$	13.8564	+	24.0000i	0.484774	+	0.839654i
$818$			27.0000i			0.944033i
$819$		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	$0.591673\pi$
$822$	46.7654	−	27.0000i	1.63113	−	0.941733i
$823$	−3.46410	−	2.00000i	−0.120751	−	0.0697156i	0.438408	−	0.898776i	$-0.355543\pi$
$823$	−3.46410	−	2.00000i	−0.120751	−	0.0697156i	−0.559159	+	0.829060i	$0.688876\pi$
$824$		−	17.3205i		−	0.603388i
$825$		0			0
$826$		0			0
$827$	20.7846			0.722752			0.361376	−	0.932420i	$-0.382307\pi$
$827$	20.7846			0.722752			0.361376	+	0.932420i	$0.382307\pi$
$828$	5.19615	+	3.00000i	0.180579	+	0.104257i
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	−14.0000			−0.485655
$832$	2.59808	+	2.50000i	0.0900721	+	0.0866719i
$833$			21.0000i			0.727607i
$834$	−12.0000	+	6.92820i	−0.415526	+	0.239904i
$835$		0			0
$836$		0			0
$837$	−13.8564			−0.478947
$838$	15.5885	−	27.0000i	0.538494	−	0.932700i
$839$	−39.0000	−	22.5167i	−1.34643	−	0.777361i	−0.358688	−	0.933458i	$-0.616776\pi$
$839$	−39.0000	−	22.5167i	−1.34643	−	0.777361i	−0.987742	+	0.156096i	$0.950109\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−23.3827	+	13.5000i	−0.805821	+	0.465241i
$843$	−22.5167	−	39.0000i	−0.775515	−	1.34323i
$844$	10.0000			0.344214
$845$		0			0
$846$	6.00000			0.206284
$847$		0			0
$848$	−12.9904	+	7.50000i	−0.446092	+	0.257551i
$849$	4.00000	−	6.92820i	0.137280	−	0.237775i
$850$		0			0
$851$	45.0000	+	25.9808i	1.54258	+	0.890609i
$852$	3.46410	−	6.00000i	0.118678	−	0.205557i
$853$	−25.9808			−0.889564			−0.444782	−	0.895639i	$-0.646719\pi$
$853$	−25.9808			−0.889564			−0.444782	+	0.895639i	$0.646719\pi$
$854$		0			0
$855$		0			0
$856$	−9.00000	+	5.19615i	−0.307614	+	0.177601i
$857$			3.00000i			0.102478i	0.998686	+	0.0512390i	$0.0163170\pi$
$857$			3.00000i			0.102478i	−0.998686	+	0.0512390i	$0.983683\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$		0			0
$861$		0			0
$862$	10.3923	+	6.00000i	0.353963	+	0.204361i
$863$	27.7128			0.943355			0.471678	−	0.881771i	$-0.343649\pi$
$863$	27.7128			0.943355			0.471678	+	0.881771i	$0.343649\pi$
$864$	−18.0000	−	10.3923i	−0.612372	−	0.353553i
$865$		0			0
$866$			29.4449i			1.00058i
$867$	13.8564	+	8.00000i	0.470588	+	0.271694i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−3.00000	+	12.1244i	−0.101651	+	0.410818i
$872$			24.0000i			0.812743i
$873$	3.46410	+	6.00000i	0.117242	+	0.203069i
$874$	−18.0000	−	31.1769i	−0.608859	−	1.05457i
$875$		0			0
$876$			3.46410i			0.117041i
$877$	−6.06218	+	10.5000i	−0.204705	+	0.354560i	−0.950039	−	0.312132i	$-0.898957\pi$
$877$	−6.06218	+	10.5000i	−0.204705	+	0.354560i	0.745334	+	0.666692i	$0.232290\pi$
$878$	−24.2487	+	42.0000i	−0.818354	+	1.41743i
$879$			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	$0.983632\pi$
$882$	−6.06218	−	10.5000i	−0.204124	−	0.353553i
$883$		−	10.0000i		−	0.336527i	−0.985742	−	0.168263i	$-0.946184\pi$
$883$		−	10.0000i		−	0.336527i	0.985742	−	0.168263i	$-0.0538159\pi$
$884$	−10.5000	−	2.59808i	−0.353153	−	0.0873828i
$885$		0			0
$886$	18.0000	−	10.3923i	0.604722	−	0.349136i
$887$	31.1769	−	18.0000i	1.04682	−	0.604381i	0.125061	−	0.992149i	$-0.460087\pi$
$887$	31.1769	−	18.0000i	1.04682	−	0.604381i	0.921757	+	0.387768i	$0.126754\pi$
$888$	25.9808	+	15.0000i	0.871857	+	0.503367i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−10.3923			−0.347960
$893$	−10.3923	−	6.00000i	−0.347765	−	0.200782i
$894$	33.0000	+	57.1577i	1.10369	+	1.91164i
$895$		0			0
$896$		0			0
$897$	−41.5692	+	12.0000i	−1.38796	+	0.400668i
$898$		−	12.0000i		−	0.400445i
$899$	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
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	−0.0401089	−	0.999195i	$-0.512770\pi$
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	0.845274	+	0.534333i	$0.179437\pi$
$908$	−12.1244	−	21.0000i	−0.402361	−	0.696909i
$909$	3.00000			0.0995037
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−17.3205	−	30.0000i	−0.573539	−	0.993399i
$913$		0			0
$914$	1.50000	−	2.59808i	0.0496156	−	0.0859367i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−20.7846			−0.685994
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	−0.625573	−	0.780165i	$-0.715135\pi$
$919$	11.0000	−	19.0526i	0.362857	−	0.628486i	0.988430	+	0.151680i	$0.0484682\pi$
$920$		0			0
$921$	30.0000	−	17.3205i	0.988534	−	0.570730i
$922$		−	39.0000i		−	1.28440i
$923$	3.46410	+	12.0000i	0.114022	+	0.394985i
$924$		0			0
$925$		0			0
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	8.66025	+	5.00000i	0.284440	+	0.164222i
$928$	15.5885			0.511716
$929$	40.5000	+	23.3827i	1.32876	+	0.767161i	0.985108	−	0.171935i	$-0.0550020\pi$
$929$	40.5000	+	23.3827i	1.32876	+	0.767161i	0.343654	+	0.939096i	$0.388335\pi$
$930$		0			0
$931$			24.2487i			0.794719i
$932$	5.19615	+	3.00000i	0.170206	+	0.0982683i
$933$	51.9615	−	30.0000i	1.70114	−	0.982156i
$934$	18.0000	−	10.3923i	0.588978	−	0.340047i
$935$		0			0
$936$	−6.00000	+	1.73205i	−0.196116	+	0.0566139i
$937$			7.00000i			0.228680i	0.993442	+	0.114340i	$0.0364753\pi$
$937$			7.00000i			0.228680i	−0.993442	+	0.114340i	$0.963525\pi$
$938$		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	$-0.110014\pi$
$942$	22.5167	−	39.0000i	0.733632	−	1.27069i
$943$	−15.5885	+	27.0000i	−0.507630	+	0.879241i
$944$		−	34.6410i		−	1.12747i
$945$		0			0
$946$		0			0
$947$	−8.66025	−	15.0000i	−0.281420	−	0.487435i	0.690314	−	0.723510i	$-0.257472\pi$
$947$	−8.66025	−	15.0000i	−0.281420	−	0.487435i	−0.971735	+	0.236075i	$0.924139\pi$
$948$			8.00000i			0.259828i
$949$	−4.50000	−	4.33013i	−0.146076	−	0.140562i
$950$		0			0
$951$	9.00000	−	5.19615i	0.291845	−	0.168497i
$952$		0			0
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	0.413473	−	0.910516i	$-0.364315\pi$
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	−0.581793	+	0.813337i	$0.697649\pi$
$954$		−	5.19615i		−	0.168232i
$955$		0			0
$956$	18.0000	+	10.3923i	0.582162	+	0.336111i
$957$		0			0
$958$	36.3731	+	21.0000i	1.17516	+	0.678479i
$959$		0			0
$960$		0			0
$961$	19.0000			0.612903
$962$	51.9615	−	15.0000i	1.67531	−	0.483619i
$963$		−	6.00000i		−	0.193347i
$964$	1.50000	−	0.866025i	0.0483117	−	0.0278928i
$965$		0			0
$966$		0			0
$967$	58.8897			1.89377			0.946883	−	0.321578i	$-0.104213\pi$
$967$	58.8897			1.89377			0.946883	+	0.321578i	$0.104213\pi$
$968$	9.52628	−	16.5000i	0.306186	−	0.530330i
$969$	−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	$0.197359\pi$
$972$	8.66025	−	5.00000i	0.277778	−	0.160375i
$973$		0			0
$974$	−12.0000			−0.384505
$975$		0			0
$976$	−5.00000			−0.160046
$977$	21.6506	+	37.5000i	0.692665	+	1.19973i	0.970961	+	0.239236i	$0.0768970\pi$
$977$	21.6506	+	37.5000i	0.692665	+	1.19973i	−0.278296	+	0.960495i	$0.589770\pi$
$978$	62.3538	−	36.0000i	1.99386	−	1.15115i
$979$		0			0
$980$		0			0
$981$	−12.0000	−	6.92820i	−0.383131	−	0.221201i
$982$	−10.3923	+	18.0000i	−0.331632	+	0.574403i
$983$	−51.9615			−1.65732			−0.828658	−	0.559756i	$-0.810895\pi$
$983$	−51.9615			−1.65732			−0.828658	+	0.559756i	$0.810895\pi$
$984$	−9.00000	+	15.5885i	−0.286910	+	0.496942i
$985$		0			0
$986$	13.5000	−	7.79423i	0.429928	−	0.248219i
$987$		0			0
$988$	−12.1244	−	3.00000i	−0.385727	−	0.0954427i
$989$	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	$0.843446\pi$
$992$	−15.5885	−	9.00000i	−0.494934	−	0.285750i
$993$	55.4256			1.75888
$994$		0			0
$995$		0			0
$996$			27.7128i			0.878114i
$997$	−14.7224	−	8.50000i	−0.466264	−	0.269198i	0.248410	−	0.968655i	$-0.420092\pi$
$997$	−14.7224	−	8.50000i	−0.466264	−	0.269198i	−0.714675	+	0.699457i	$0.753425\pi$
$998$	46.7654	−	27.0000i	1.48033	−	0.854670i
$999$	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.m.a.49.1		4
5.2	odd	4		325.2.n.a.101.1		2
5.3	odd	4		13.2.e.a.10.1	yes	2
5.4	even	2	inner	325.2.m.a.49.2		4
13.4	even	6	inner	325.2.m.a.199.2		4
15.8	even	4		117.2.q.c.10.1		2
20.3	even	4		208.2.w.b.49.1		2
35.3	even	12		637.2.k.c.569.1		2
35.13	even	4		637.2.q.a.491.1		2
35.18	odd	12		637.2.k.a.569.1		2
35.23	odd	12		637.2.u.c.361.1		2
35.33	even	12		637.2.u.b.361.1		2
40.3	even	4		832.2.w.a.257.1		2
40.13	odd	4		832.2.w.d.257.1		2
60.23	odd	4		1872.2.by.d.1297.1		2
65.2	even	12		4225.2.a.v.1.2		2
65.3	odd	12		169.2.b.a.168.1		2
65.4	even	6	inner	325.2.m.a.199.1		4
65.8	even	4		169.2.c.a.146.1		4
65.17	odd	12		325.2.n.a.251.1		2
65.18	even	4		169.2.c.a.146.2		4
65.23	odd	12		169.2.b.a.168.2		2
65.28	even	12		169.2.a.a.1.1		2
65.33	even	12		169.2.c.a.22.1		4
65.37	even	12		4225.2.a.v.1.1		2
65.38	odd	4		169.2.e.a.23.1		2
65.43	odd	12		13.2.e.a.4.1	✓	2
65.48	odd	12		169.2.e.a.147.1		2
65.58	even	12		169.2.c.a.22.2		4
65.63	even	12		169.2.a.a.1.2		2
195.23	even	12		1521.2.b.a.1351.1		2
195.68	even	12		1521.2.b.a.1351.2		2
195.128	odd	12		1521.2.a.k.1.1		2
195.158	odd	12		1521.2.a.k.1.2		2
195.173	even	12		117.2.q.c.82.1		2
260.3	even	12		2704.2.f.b.337.2		2
260.23	even	12		2704.2.f.b.337.1		2
260.43	even	12		208.2.w.b.17.1		2
260.63	odd	12		2704.2.a.o.1.1		2
260.223	odd	12		2704.2.a.o.1.2		2
455.108	even	12		637.2.u.b.30.1		2
455.173	even	12		637.2.k.c.459.1		2
455.223	odd	12		8281.2.a.q.1.1		2
455.258	odd	12		8281.2.a.q.1.2		2
455.303	odd	12		637.2.k.a.459.1		2
455.368	odd	12		637.2.u.c.30.1		2
455.433	even	12		637.2.q.a.589.1		2
520.43	even	12		832.2.w.a.641.1		2
520.173	odd	12		832.2.w.d.641.1		2
780.563	odd	12		1872.2.by.d.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.2.e.a.4.1	✓	2	65.43	odd	12
13.2.e.a.10.1	yes	2	5.3	odd	4
117.2.q.c.10.1		2	15.8	even	4
117.2.q.c.82.1		2	195.173	even	12
169.2.a.a.1.1		2	65.28	even	12
169.2.a.a.1.2		2	65.63	even	12
169.2.b.a.168.1		2	65.3	odd	12
169.2.b.a.168.2		2	65.23	odd	12
169.2.c.a.22.1		4	65.33	even	12
169.2.c.a.22.2		4	65.58	even	12
169.2.c.a.146.1		4	65.8	even	4
169.2.c.a.146.2		4	65.18	even	4
169.2.e.a.23.1		2	65.38	odd	4
169.2.e.a.147.1		2	65.48	odd	12
208.2.w.b.17.1		2	260.43	even	12
208.2.w.b.49.1		2	20.3	even	4
325.2.m.a.49.1		4	1.1	even	1	trivial
325.2.m.a.49.2		4	5.4	even	2	inner
325.2.m.a.199.1		4	65.4	even	6	inner
325.2.m.a.199.2		4	13.4	even	6	inner
325.2.n.a.101.1		2	5.2	odd	4
325.2.n.a.251.1		2	65.17	odd	12
637.2.k.a.459.1		2	455.303	odd	12
637.2.k.a.569.1		2	35.18	odd	12
637.2.k.c.459.1		2	455.173	even	12
637.2.k.c.569.1		2	35.3	even	12
637.2.q.a.491.1		2	35.13	even	4
637.2.q.a.589.1		2	455.433	even	12
637.2.u.b.30.1		2	455.108	even	12
637.2.u.b.361.1		2	35.33	even	12
637.2.u.c.30.1		2	455.368	odd	12
637.2.u.c.361.1		2	35.23	odd	12
832.2.w.a.257.1		2	40.3	even	4
832.2.w.a.641.1		2	520.43	even	12
832.2.w.d.257.1		2	40.13	odd	4
832.2.w.d.641.1		2	520.173	odd	12
1521.2.a.k.1.1		2	195.128	odd	12
1521.2.a.k.1.2		2	195.158	odd	12
1521.2.b.a.1351.1		2	195.23	even	12
1521.2.b.a.1351.2		2	195.68	even	12
1872.2.by.d.433.1		2	780.563	odd	12
1872.2.by.d.1297.1		2	60.23	odd	4
2704.2.a.o.1.1		2	260.63	odd	12
2704.2.a.o.1.2		2	260.223	odd	12
2704.2.f.b.337.1		2	260.23	even	12
2704.2.f.b.337.2		2	260.3	even	12
4225.2.a.v.1.1		2	65.37	even	12
4225.2.a.v.1.2		2	65.2	even	12
8281.2.a.q.1.1		2	455.223	odd	12
8281.2.a.q.1.2		2	455.258	odd	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.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(3.00000 + 1.73205i) q^{6} -1.73205 q^{8} +(0.500000 - 0.866025i) q^{9} -2.00000i q^{12} +(2.59808 + 2.50000i) q^{13} +(2.50000 + 4.33013i) q^{16} +(2.59808 + 1.50000i) q^{17} -1.73205 q^{18} +(3.00000 + 1.73205i) q^{19} +(5.19615 - 3.00000i) q^{23} +(3.00000 - 1.73205i) q^{24} +(1.50000 - 6.06218i) q^{26} -4.00000i q^{27} +(1.50000 + 2.59808i) q^{29} -3.46410i q^{31} +(2.59808 - 4.50000i) q^{32} -5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(4.33013 + 7.50000i) q^{37} -6.00000i q^{38} +(-7.00000 - 1.73205i) q^{39} +(-4.50000 + 2.59808i) q^{41} +(6.92820 + 4.00000i) q^{43} +(-9.00000 - 5.19615i) q^{46} -3.46410 q^{47} +(-8.66025 - 5.00000i) q^{48} +(3.50000 + 6.06218i) q^{49} -6.00000 q^{51} +(-3.46410 + 1.00000i) q^{52} +3.00000i q^{53} +(-6.00000 + 3.46410i) q^{54} -6.92820 q^{57} +(2.59808 - 4.50000i) q^{58} +(-6.00000 - 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-5.19615 + 3.00000i) q^{62} +1.00000 q^{64} +(1.73205 + 3.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} +(-6.00000 + 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-0.866025 + 1.50000i) q^{72} -1.73205 q^{73} +(7.50000 - 12.9904i) q^{74} +(-3.00000 + 1.73205i) q^{76} +(3.46410 + 12.0000i) q^{78} -4.00000 q^{79} +(5.50000 + 9.52628i) q^{81} +(7.79423 + 4.50000i) q^{82} -13.8564 q^{83} -13.8564i q^{86} +(-5.19615 - 3.00000i) q^{87} +(6.00000 - 3.46410i) q^{89} +6.00000i q^{92} +(3.46410 + 6.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} +10.3923i q^{96} +(-3.46410 + 6.00000i) q^{97} +(6.06218 - 10.5000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 12 q^{6} + 2 q^{9} + 10 q^{16} + 12 q^{19} + 12 q^{24} + 6 q^{26} + 6 q^{29} + 2 q^{36} - 28 q^{39} - 18 q^{41} - 36 q^{46} + 14 q^{49} - 24 q^{51} - 24 q^{54} - 24 q^{59} - 2 q^{61} + 4 q^{64}+ \cdots + 12 q^{94}+O(q^{100}) \) 4 * q - 2 * q^4 + 12 * q^6 + 2 * q^9 + 10 * q^16 + 12 * q^19 + 12 * q^24 + 6 * q^26 + 6 * q^29 + 2 * q^36 - 28 * q^39 - 18 * q^41 - 36 * q^46 + 14 * q^49 - 24 * q^51 - 24 * q^54 - 24 * q^59 - 2 * q^61 + 4 * q^64 - 24 * q^69 + 12 * q^71 + 30 * q^74 - 12 * q^76 - 16 * q^79 + 22 * q^81 + 24 * q^89 + 12 * q^94

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