LMFDB - Embedded newform 325.2.n.a.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			251.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	325.251
Dual form			325.2.n.a.101.1

$q$-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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$	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	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	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	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		−	1.73205i		−	0.408248i
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	−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	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	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	−0.265340	−	0.964155i	$-0.585484\pi$
$37$	−7.50000	−	4.33013i	−1.23299	−	0.711868i	−0.967653	+	0.252286i	$0.918817\pi$
$38$	−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	0.105601	−	0.994409i	$-0.466323\pi$
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	−0.808383	+	0.588657i	$0.799657\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$		0			0
$46$	−9.00000	+	5.19615i	−1.32698	+	0.766131i
$47$			3.46410i			0.505291i	0.967559	+	0.252646i	$0.0813007\pi$
$47$			3.46410i			0.505291i	−0.967559	+	0.252646i	$0.918699\pi$
$48$	−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	−0.0556984	−	0.998448i	$-0.517739\pi$
$59$	6.00000	−	3.46410i	0.781133	−	0.450988i	0.836832	+	0.547460i	$0.184405\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−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	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	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	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$	−1.50000	+	0.866025i	−0.176777	+	0.102062i
$73$		−	1.73205i		−	0.202721i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$		−	1.73205i		−	0.202721i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	−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	$-0.724969\pi$
$83$		−	13.8564i		−	1.52094i	0.649374	−	0.760469i	$-0.275031\pi$
$84$		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	0.147073	−	0.989126i	$-0.453015\pi$
$89$	−6.00000	−	3.46410i	−0.635999	−	0.367194i	−0.783072	+	0.621932i	$0.786348\pi$
$90$		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	−0.772655	−	0.634826i	$-0.781072\pi$
$97$	−6.00000	+	3.46410i	−0.609208	+	0.351726i	0.163448	+	0.986552i	$0.447739\pi$
$98$	−10.5000	+	6.06218i	−1.06066	+	0.612372i
$99$		0			0
$100$		0			0
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	−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	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$		−	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
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$	−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	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	−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	0.203674	−	0.979039i	$-0.434712\pi$
$137$	13.5000	−	7.79423i	1.15338	−	0.665906i	0.949709	+	0.313133i	$0.101379\pi$
$138$			20.7846i			1.76930i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		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	−0.988492	−	0.151272i	$-0.951663\pi$
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.363241	+	0.931695i	$0.618330\pi$
$150$		0			0
$151$			17.3205i			1.40952i	0.709444	+	0.704761i	$0.248946\pi$
$151$			17.3205i			1.40952i	−0.709444	+	0.704761i	$0.751054\pi$
$152$	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	−0.995375	−	0.0960641i	$-0.969375\pi$
$163$	−18.0000	+	10.3923i	−1.40987	+	0.813988i	−0.414494	+	0.910052i	$0.636041\pi$
$164$		−	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	0.886365	−	0.462988i	$-0.153223\pi$
$167$	12.0000	+	6.92820i	0.928588	+	0.536120i	0.0422232	+	0.999108i	$0.486556\pi$
$168$		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	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$			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	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		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	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	4.50000	+	2.59808i	0.323917	+	0.187014i	0.653137	−	0.757240i	$-0.273452\pi$
$193$	4.50000	+	2.59808i	0.323917	+	0.187014i	−0.329220	+	0.944253i	$0.606786\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−12.0000	−	6.92820i	−0.854965	−	0.493614i	0.00735824	−	0.999973i	$-0.497658\pi$
$197$	−12.0000	−	6.92820i	−0.854965	−	0.493614i	−0.862323	+	0.506359i	$0.830991\pi$
$198$		0			0
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	0.899291	−	0.437351i	$-0.144083\pi$
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	−0.828403	+	0.560133i	$0.810750\pi$
$200$		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	−0.985211	−	0.171347i	$-0.945188\pi$
$211$	−5.00000	+	8.66025i	−0.344214	+	0.596196i	0.640996	+	0.767544i	$0.278521\pi$
$212$	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	0.770097	−	0.637927i	$-0.220208\pi$
$223$	9.00000	+	5.19615i	0.602685	+	0.347960i	−0.167412	+	0.985887i	$0.553541\pi$
$224$		0			0
$225$		0			0
$226$		−	25.9808i		−	1.72821i
$227$	−21.0000	+	12.1244i	−1.39382	+	0.804722i	−0.993736	−	0.111757i	$-0.964352\pi$
$227$	−21.0000	+	12.1244i	−1.39382	+	0.804722i	−0.400083	+	0.916479i	$0.631019\pi$
$228$	−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	$-0.765340\pi$
$239$		−	20.7846i		−	1.34444i	0.740349	−	0.672222i	$-0.234660\pi$
$240$		0			0
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$		−	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	0.996756	+	0.0804789i	$0.0256450\pi$
$251$	9.00000	+	15.5885i	0.568075	+	0.983935i	−0.428681	+	0.903456i	$0.641022\pi$
$252$		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	−0.815442	−	0.578838i	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$	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	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		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	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$		0			0
$271$	18.0000	+	10.3923i	1.09342	+	0.631288i	0.934485	−	0.356001i	$-0.115860\pi$
$271$	18.0000	+	10.3923i	1.09342	+	0.631288i	0.158937	+	0.987289i	$0.449193\pi$
$272$	−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	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$			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	$-0.765601\pi$
$281$		−	22.5167i		−	1.34323i	0.740900	−	0.671616i	$-0.234399\pi$
$282$	6.00000	+	10.3923i	0.357295	+	0.618853i
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	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	−0.625653	−	0.780101i	$-0.715168\pi$
$293$	−4.50000	+	2.59808i	−0.262893	+	0.151781i	0.362761	+	0.931882i	$0.381834\pi$
$294$			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	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		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	$0.0466150\pi$
$317$			5.19615i			0.291845i	−0.989296	+	0.145922i	$0.953385\pi$
$318$	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	−0.983593	−	0.180400i	$-0.942261\pi$
$331$	−24.0000	+	13.8564i	−1.31916	+	0.761617i	−0.335566	+	0.942017i	$0.608928\pi$
$332$	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	−0.916127	−	0.400887i	$-0.868702\pi$
$347$	−15.0000	−	25.9808i	−0.805242	−	1.39472i	0.110885	−	0.993833i	$-0.464631\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	12.0000	+	6.92820i	0.642345	+	0.370858i	0.785517	−	0.618840i	$-0.212397\pi$
$349$	12.0000	+	6.92820i	0.642345	+	0.370858i	−0.143172	+	0.989698i	$0.545730\pi$
$350$		0			0
$351$	10.0000	+	10.3923i	0.533761	+	0.554700i
$352$		0			0
$353$	−28.5000	−	16.4545i	−1.51690	−	0.875784i	−0.999803	−	0.0198582i	$-0.993679\pi$
$353$	−28.5000	−	16.4545i	−1.51690	−	0.875784i	−0.517099	−	0.855926i	$-0.672988\pi$
$354$	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
$362$	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	0.421933	+	0.906627i	$0.361352\pi$
$367$	−11.0000	+	19.0526i	−0.574195	+	0.994535i	−0.996129	+	0.0879086i	$0.971982\pi$
$368$	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	0.999956	−	0.00933789i	$-0.00297238\pi$
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	−0.508065	+	0.861319i	$0.669639\pi$
$374$		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	−0.148153	−	0.988964i	$-0.547333\pi$
$379$	−21.0000	−	12.1244i	−1.07870	−	0.622786i	−0.930545	+	0.366178i	$0.880666\pi$
$380$		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	0.0361995	−	0.999345i	$-0.488475\pi$
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.883558	+	0.468323i	$0.155141\pi$
$384$	−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	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$			3.46410i			0.173640i
$399$		0			0
$400$		0			0
$401$	−1.50000	−	0.866025i	−0.0749064	−	0.0432472i	0.462079	−	0.886839i	$-0.347104\pi$
$401$	−1.50000	−	0.866025i	−0.0749064	−	0.0432472i	−0.536985	+	0.843592i	$0.680437\pi$
$402$	−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	−0.127609	−	0.991825i	$-0.540730\pi$
$409$	13.5000	−	7.79423i	0.667532	−	0.385400i	0.795141	+	0.606425i	$0.207397\pi$
$410$		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	−0.997665	−	0.0683046i	$-0.978241\pi$
$419$	−9.00000	+	15.5885i	−0.439679	+	0.761546i	0.557986	+	0.829851i	$0.311574\pi$
$420$		0			0
$421$			15.5885i			0.759735i	0.925041	+	0.379867i	$0.124030\pi$
$421$			15.5885i			0.759735i	−0.925041	+	0.379867i	$0.875970\pi$
$422$	−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	0.348485	−	0.937314i	$-0.386696\pi$
$431$	−6.00000	−	3.46410i	−0.289010	−	0.166860i	−0.637495	+	0.770454i	$0.720029\pi$
$432$	10.0000	−	17.3205i	0.481125	−	0.833333i
$433$	−8.50000	−	14.7224i	−0.408484	−	0.707515i	0.586236	−	0.810140i	$-0.300609\pi$
$433$	−8.50000	−	14.7224i	−0.408484	−	0.707515i	−0.994720	+	0.102625i	$0.967276\pi$
$434$		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	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		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	−0.634852	−	0.772634i	$-0.718939\pi$
$449$	−6.00000	+	3.46410i	−0.283158	+	0.163481i	0.351694	+	0.936115i	$0.385606\pi$
$450$		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	0.464506	−	0.885570i	$-0.346232\pi$
$457$	−1.50000	−	0.866025i	−0.0701670	−	0.0405110i	−0.534673	+	0.845059i	$0.679565\pi$
$458$		0			0
$459$	−6.00000	−	10.3923i	−0.280056	−	0.485071i
$460$		0			0
$461$	19.5000	−	11.2583i	0.908206	−	0.524353i	0.0283522	−	0.999598i	$-0.490974\pi$
$461$	19.5000	−	11.2583i	0.908206	−	0.524353i	0.879853	+	0.475245i	$0.157641\pi$
$462$		0			0
$463$		−	13.8564i		−	0.643962i	−0.946746	−	0.321981i	$-0.895651\pi$
$463$		−	13.8564i		−	0.643962i	0.946746	−	0.321981i	$-0.104349\pi$
$464$	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	0.896024	−	0.444006i	$-0.146443\pi$
$479$	21.0000	+	12.1244i	0.959514	+	0.553976i	0.0634909	+	0.997982i	$0.479777\pi$
$480$		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	−0.357858	−	0.933776i	$-0.616493\pi$
$487$	6.00000	−	3.46410i	0.271886	−	0.156973i	0.629744	+	0.776802i	$0.283160\pi$
$488$	−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	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$	−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	$0.245853\pi$
$499$			31.1769i			1.39567i	−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$	24.0000	−	13.8564i	1.07224	−	0.619059i
$502$			31.1769i			1.39149i
$503$	18.0000	+	31.1769i	0.802580	+	1.39011i	0.917912	+	0.396783i	$0.129873\pi$
$503$	18.0000	+	31.1769i	0.802580	+	1.39011i	−0.115332	+	0.993327i	$0.536793\pi$
$504$		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	0.818916	−	0.573914i	$-0.194576\pi$
$509$	16.5000	+	9.52628i	0.731350	+	0.422245i	−0.0875661	+	0.996159i	$0.527909\pi$
$510$		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	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	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	$0.218163\pi$
$541$			29.4449i			1.26593i	−0.774179	+	0.632967i	$0.781837\pi$
$542$	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	0.757953	−	0.652309i	$-0.226200\pi$
$557$	13.5000	+	7.79423i	0.572013	+	0.330252i	−0.185940	+	0.982561i	$0.559533\pi$
$558$	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	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$			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	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		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	$0.129805\pi$
$577$			19.0526i			0.793168i	−0.917998	+	0.396584i	$0.870195\pi$
$578$	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	0.823137	−	0.567843i	$-0.192222\pi$
$587$	18.0000	+	10.3923i	0.742940	+	0.428936i	−0.0801976	+	0.996779i	$0.525555\pi$
$588$	−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	$0.179105\pi$
$593$			25.9808i			1.06690i	−0.845831	+	0.533451i	$0.820895\pi$
$594$		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	0.490049	+	0.871695i	$0.336979\pi$
$601$	−12.5000	+	21.6506i	−0.509886	+	0.883148i	−0.999934	+	0.0114528i	$0.996354\pi$
$602$		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	−0.971834	−	0.235665i	$-0.924273\pi$
$607$	−17.0000	−	29.4449i	−0.690009	−	1.19513i	0.281826	−	0.959466i	$-0.409060\pi$
$608$	−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	0.696826	−	0.717240i	$-0.254595\pi$
$613$	10.5000	+	6.06218i	0.424091	+	0.244849i	−0.272735	+	0.962089i	$0.587928\pi$
$614$	−15.0000	+	25.9808i	−0.605351	+	1.04850i
$615$		0			0
$616$		0			0
$617$	19.5000	−	11.2583i	0.785040	−	0.453243i	−0.0531732	−	0.998585i	$-0.516934\pi$
$617$	19.5000	−	11.2583i	0.785040	−	0.453243i	0.838214	+	0.545342i	$0.183600\pi$
$618$	30.0000	−	17.3205i	1.20678	−	0.696733i
$619$		−	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
$622$	−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	−0.705473	+	0.708737i	$0.749265\pi$
$631$	−42.0000	+	24.2487i	−1.67199	+	0.965326i	−0.966521	+	0.256589i	$0.917401\pi$
$632$		−	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	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		−	20.7846i		−	0.820303i
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	−0.717592	−	0.696463i	$-0.754756\pi$
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	0.244359	+	0.969685i	$0.421423\pi$
$644$		0			0
$645$		0			0
$646$	9.00000	+	15.5885i	0.354100	+	0.613320i
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	−0.633090	−	0.774078i	$-0.718214\pi$
$647$	9.00000	−	15.5885i	0.353827	−	0.612845i	0.986916	+	0.161233i	$0.0515470\pi$
$648$	−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	0.407628	+	0.913148i	$0.366356\pi$
$653$	−15.0000	+	25.9808i	−0.586995	+	1.01671i	−0.994623	+	0.103558i	$0.966977\pi$
$654$	−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	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$	−40.5000	−	23.3827i	−1.57527	−	0.909481i	−0.995506	−	0.0946945i	$-0.969813\pi$
$661$	−40.5000	−	23.3827i	−1.57527	−	0.909481i	−0.579761	−	0.814787i	$-0.696854\pi$
$662$	−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	−0.988968	−	0.148132i	$-0.952674\pi$
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	0.622770	+	0.782405i	$0.286007\pi$
$674$	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	−0.844708	−	0.535227i	$-0.820226\pi$
$683$	−21.0000	+	12.1244i	−0.803543	+	0.463926i	0.0411658	+	0.999152i	$0.486893\pi$
$684$			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	0.710572	−	0.703624i	$-0.248436\pi$
$691$	12.0000	+	6.92820i	0.456502	+	0.263561i	−0.254071	+	0.967186i	$0.581770\pi$
$692$	−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	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−4.50000	+	2.59808i	−0.169001	+	0.0975728i	0.413114	+	0.910679i	$0.364441\pi$
$710$		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	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		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	$-0.928117\pi$
$733$		−	12.1244i		−	0.447823i	0.974609	−	0.223912i	$-0.0718827\pi$
$734$	−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	0.130951	−	0.991389i	$-0.458197\pi$
$739$	−18.0000	−	10.3923i	−0.662141	−	0.382287i	−0.793092	+	0.609102i	$0.791530\pi$
$740$		0			0
$741$	−18.0000	+	17.3205i	−0.661247	+	0.636285i
$742$		0			0
$743$	30.0000	+	17.3205i	1.10059	+	0.635428i	0.936377	−	0.350997i	$-0.114157\pi$
$743$	30.0000	+	17.3205i	1.10059	+	0.635428i	0.164216	+	0.986424i	$0.447490\pi$
$744$	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	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	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	−0.999505	−	0.0314762i	$-0.989979\pi$
$757$	−13.0000	+	22.5167i	−0.472493	+	0.818382i	0.527011	+	0.849858i	$0.323312\pi$
$758$	−21.0000	−	36.3731i	−0.762754	−	1.32113i
$759$		0			0
$760$		0			0
$761$	30.0000	−	17.3205i	1.08750	−	0.627868i	0.154590	−	0.987979i	$-0.450594\pi$
$761$	30.0000	−	17.3205i	1.08750	−	0.627868i	0.932910	+	0.360111i	$0.117261\pi$
$762$			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	0.604266	−	0.796782i	$-0.293466\pi$
$769$	6.00000	+	3.46410i	0.216366	+	0.124919i	−0.387901	+	0.921701i	$0.626800\pi$
$770$		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	0.148392	−	0.988929i	$-0.452590\pi$
$773$	30.0000	−	17.3205i	1.07903	−	0.622975i	0.930633	+	0.365953i	$0.119257\pi$
$774$	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	−0.955161	−	0.296087i	$-0.904318\pi$
$787$	−33.0000	+	19.0526i	−1.17632	+	0.679150i	−0.221162	+	0.975237i	$0.570985\pi$
$788$		−	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	0.950726	+	0.310031i	$0.100340\pi$
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	−0.206868	+	0.978369i	$0.566327\pi$
$798$		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	0.415357	+	0.909659i	$0.363657\pi$
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	−0.995466	+	0.0951198i	$0.969677\pi$
$810$		0			0
$811$		−	38.1051i		−	1.33805i	−0.743239	−	0.669026i	$-0.766712\pi$
$811$		−	38.1051i		−	1.33805i	0.743239	−	0.669026i	$-0.233288\pi$
$812$		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	−0.284034	−	0.958814i	$-0.591673\pi$
$821$	−36.0000	−	20.7846i	−1.25641	−	0.725388i	−0.972375	+	0.233426i	$0.925006\pi$
$822$	27.0000	−	46.7654i	0.941733	−	1.63113i
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$		−	17.3205i		−	0.603388i
$825$		0			0
$826$		0			0
$827$		−	20.7846i		−	0.722752i	−0.932420	−	0.361376i	$-0.882307\pi$
$827$		−	20.7846i		−	0.722752i	0.932420	−	0.361376i	$-0.117693\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$		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	0.358688	−	0.933458i	$-0.383224\pi$
$839$	39.0000	−	22.5167i	1.34643	−	0.777361i	0.987742	+	0.156096i	$0.0498910\pi$
$840$		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	$-0.853281\pi$
$853$		−	25.9808i		−	0.889564i	0.895639	−	0.444782i	$-0.146719\pi$
$854$		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	$0.156351\pi$
$863$			27.7128i			0.943355i	−0.881771	+	0.471678i	$0.843649\pi$
$864$	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	−0.666692	−	0.745334i	$-0.732290\pi$
$877$	−10.5000	+	6.06218i	−0.354560	+	0.204705i	0.312132	+	0.950039i	$0.398957\pi$
$878$	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	−0.998678	−	0.0513987i	$-0.983632\pi$
$881$	−13.5000	+	23.3827i	−0.454827	+	0.787783i	0.543852	+	0.839181i	$0.316965\pi$
$882$	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	−0.387768	−	0.921757i	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	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	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	−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	0.625573	−	0.780165i	$-0.284865\pi$
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	−0.988430	+	0.151680i	$0.951532\pi$
$920$		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	−0.985108	−	0.171935i	$-0.944998\pi$
$929$	−40.5000	+	23.3827i	−1.32876	+	0.767161i	−0.343654	+	0.939096i	$0.611665\pi$
$930$		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	$0.110014\pi$
$941$			20.7846i			0.677559i	−0.940866	+	0.338779i	$0.889986\pi$
$942$	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	0.723510	−	0.690314i	$-0.242528\pi$
$947$	15.0000	+	8.66025i	0.487435	+	0.281420i	−0.236075	+	0.971735i	$0.575861\pi$
$948$	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	0.813337	−	0.581793i	$-0.197649\pi$
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	−0.910516	+	0.413473i	$0.864315\pi$
$954$		−	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	$-0.604213\pi$
$967$		−	58.8897i		−	1.89377i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	−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	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	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	−0.239236	−	0.970961i	$-0.576897\pi$
$977$	−37.5000	−	21.6506i	−1.19973	−	0.692665i	−0.960495	+	0.278296i	$0.910230\pi$
$978$	−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	$-0.689105\pi$
$983$		−	51.9615i		−	1.65732i	0.559756	−	0.828658i	$-0.310895\pi$
$984$	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	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	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	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$	−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.251.1		2
5.2	odd	4		325.2.m.a.199.1		4
5.3	odd	4		325.2.m.a.199.2		4
5.4	even	2		13.2.e.a.4.1	✓	2
13.6	odd	12		4225.2.a.v.1.1		2
13.7	odd	12		4225.2.a.v.1.2		2
13.10	even	6	inner	325.2.n.a.101.1		2
15.14	odd	2		117.2.q.c.82.1		2
20.19	odd	2		208.2.w.b.17.1		2
35.4	even	6		637.2.u.c.30.1		2
35.9	even	6		637.2.k.a.459.1		2
35.19	odd	6		637.2.k.c.459.1		2
35.24	odd	6		637.2.u.b.30.1		2
35.34	odd	2		637.2.q.a.589.1		2
40.19	odd	2		832.2.w.a.641.1		2
40.29	even	2		832.2.w.d.641.1		2
60.59	even	2		1872.2.by.d.433.1		2
65.4	even	6		169.2.b.a.168.1		2
65.9	even	6		169.2.b.a.168.2		2
65.19	odd	12		169.2.a.a.1.2		2
65.23	odd	12		325.2.m.a.49.1		4
65.24	odd	12		169.2.c.a.146.2		4
65.29	even	6		169.2.e.a.23.1		2
65.34	odd	4		169.2.c.a.22.2		4
65.44	odd	4		169.2.c.a.22.1		4
65.49	even	6		13.2.e.a.10.1	yes	2
65.54	odd	12		169.2.c.a.146.1		4
65.59	odd	12		169.2.a.a.1.1		2
65.62	odd	12		325.2.m.a.49.2		4
65.64	even	2		169.2.e.a.147.1		2
195.59	even	12		1521.2.a.k.1.2		2
195.74	odd	6		1521.2.b.a.1351.1		2
195.134	odd	6		1521.2.b.a.1351.2		2
195.149	even	12		1521.2.a.k.1.1		2
195.179	odd	6		117.2.q.c.10.1		2
260.19	even	12		2704.2.a.o.1.1		2
260.59	even	12		2704.2.a.o.1.2		2
260.139	odd	6		2704.2.f.b.337.1		2
260.179	odd	6		208.2.w.b.49.1		2
260.199	odd	6		2704.2.f.b.337.2		2
455.114	even	6		637.2.u.c.361.1		2
455.179	even	6		637.2.k.a.569.1		2
455.244	odd	6		637.2.q.a.491.1		2
455.279	even	12		8281.2.a.q.1.2		2
455.374	odd	6		637.2.k.c.569.1		2
455.384	even	12		8281.2.a.q.1.1		2
455.439	odd	6		637.2.u.b.361.1		2
520.179	odd	6		832.2.w.a.257.1		2
520.309	even	6		832.2.w.d.257.1		2
780.179	even	6		1872.2.by.d.1297.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.2.e.a.4.1	✓	2	5.4	even	2
13.2.e.a.10.1	yes	2	65.49	even	6
117.2.q.c.10.1		2	195.179	odd	6
117.2.q.c.82.1		2	15.14	odd	2
169.2.a.a.1.1		2	65.59	odd	12
169.2.a.a.1.2		2	65.19	odd	12
169.2.b.a.168.1		2	65.4	even	6
169.2.b.a.168.2		2	65.9	even	6
169.2.c.a.22.1		4	65.44	odd	4
169.2.c.a.22.2		4	65.34	odd	4
169.2.c.a.146.1		4	65.54	odd	12
169.2.c.a.146.2		4	65.24	odd	12
169.2.e.a.23.1		2	65.29	even	6
169.2.e.a.147.1		2	65.64	even	2
208.2.w.b.17.1		2	20.19	odd	2
208.2.w.b.49.1		2	260.179	odd	6
325.2.m.a.49.1		4	65.23	odd	12
325.2.m.a.49.2		4	65.62	odd	12
325.2.m.a.199.1		4	5.2	odd	4
325.2.m.a.199.2		4	5.3	odd	4
325.2.n.a.101.1		2	13.10	even	6	inner
325.2.n.a.251.1		2	1.1	even	1	trivial
637.2.k.a.459.1		2	35.9	even	6
637.2.k.a.569.1		2	455.179	even	6
637.2.k.c.459.1		2	35.19	odd	6
637.2.k.c.569.1		2	455.374	odd	6
637.2.q.a.491.1		2	455.244	odd	6
637.2.q.a.589.1		2	35.34	odd	2
637.2.u.b.30.1		2	35.24	odd	6
637.2.u.b.361.1		2	455.439	odd	6
637.2.u.c.30.1		2	35.4	even	6
637.2.u.c.361.1		2	455.114	even	6
832.2.w.a.257.1		2	520.179	odd	6
832.2.w.a.641.1		2	40.19	odd	2
832.2.w.d.257.1		2	520.309	even	6
832.2.w.d.641.1		2	40.29	even	2
1521.2.a.k.1.1		2	195.149	even	12
1521.2.a.k.1.2		2	195.59	even	12
1521.2.b.a.1351.1		2	195.74	odd	6
1521.2.b.a.1351.2		2	195.134	odd	6
1872.2.by.d.433.1		2	60.59	even	2
1872.2.by.d.1297.1		2	780.179	even	6
2704.2.a.o.1.1		2	260.19	even	12
2704.2.a.o.1.2		2	260.59	even	12
2704.2.f.b.337.1		2	260.139	odd	6
2704.2.f.b.337.2		2	260.199	odd	6
4225.2.a.v.1.1		2	13.6	odd	12
4225.2.a.v.1.2		2	13.7	odd	12
8281.2.a.q.1.1		2	455.384	even	12
8281.2.a.q.1.2		2	455.279	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 $\F_{q}$

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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