LMFDB - Embedded newform 975.2.bc.g.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(751,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("975.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (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:	$7.78541419707$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	975.901
Dual form			975.2.bc.g.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 0.866025i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +(2.50000 - 4.33013i) q^{16} -1.73205i q^{18} +(1.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(6.00000 + 1.73205i) q^{26} -1.00000 q^{27} -6.92820i q^{31} +(4.50000 - 2.59808i) q^{32} +(1.50000 - 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{36} +(1.50000 + 0.866025i) q^{37} +(1.00000 - 3.46410i) q^{39} +(3.00000 + 1.73205i) q^{41} +(5.00000 + 8.66025i) q^{43} +1.73205i q^{44} +(4.50000 - 2.59808i) q^{46} -3.46410i q^{47} +(-2.50000 - 4.33013i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(2.50000 + 2.59808i) q^{52} +(-1.50000 - 0.866025i) q^{54} +(-9.00000 + 5.19615i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(6.00000 - 10.3923i) q^{62} -1.00000 q^{64} +3.00000 q^{66} +(3.00000 + 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(-7.50000 + 4.33013i) q^{71} +(-1.50000 + 0.866025i) q^{72} +8.66025i q^{73} +(1.50000 + 2.59808i) q^{74} +(4.50000 - 4.33013i) q^{78} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} +8.66025i q^{83} +17.3205i q^{86} +(1.50000 - 2.59808i) q^{88} +(-6.00000 - 3.46410i) q^{89} +3.00000 q^{92} +(-6.00000 - 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{94} -5.19615i q^{96} +(7.50000 - 4.33013i) q^{97} +(-10.5000 + 6.06218i) q^{98} -1.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} - q^{9} + 3 q^{11} + 2 q^{12} + 7 q^{13} + 5 q^{16} + 3 q^{22} + 3 q^{23} - 3 q^{24} + 12 q^{26} - 2 q^{27} + 9 q^{32} + 3 q^{33} + q^{36} + 3 q^{37} + 2 q^{39}+ \cdots - 21 q^{98}+O(q^{100}) $ 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 - q^9 + 3 * q^11 + 2 * q^12 + 7 * q^13 + 5 * q^16 + 3 * q^22 + 3 * q^23 - 3 * q^24 + 12 * q^26 - 2 * q^27 + 9 * q^32 + 3 * q^33 + q^36 + 3 * q^37 + 2 * q^39 + 6 * q^41 + 10 * q^43 + 9 * q^46 - 5 * q^48 - 7 * q^49 + 5 * q^52 - 3 * q^54 - 18 * q^59 - 7 * q^61 + 12 * q^62 - 2 * q^64 + 6 * q^66 + 6 * q^67 - 3 * q^69 - 15 * q^71 - 3 * q^72 + 3 * q^74 + 9 * q^78 - 16 * q^79 - q^81 + 6 * q^82 + 3 * q^88 - 12 * q^89 + 6 * q^92 - 12 * q^93 + 6 * q^94 + 15 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	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	$0.456882\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$		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
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$	1.00000			0.288675
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$		0			0
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		−	1.73205i		−	0.408248i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$		0			0
$26$	6.00000	+	1.73205i	1.17670	+	0.339683i
$27$	−1.00000			−0.192450
$28$		0			0
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$		−	6.92820i		−	1.24434i	−0.782881	−	0.622171i	$-0.786251\pi$
$31$		−	6.92820i		−	1.24434i	0.782881	−	0.622171i	$-0.213749\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$		0			0
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	0.618206	−	0.786016i	$-0.287860\pi$
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	−0.371607	+	0.928390i	$0.621193\pi$
$38$		0			0
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$		0			0
$41$	3.00000	+	1.73205i	0.468521	+	0.270501i	0.715621	−	0.698489i	$-0.246144\pi$
$41$	3.00000	+	1.73205i	0.468521	+	0.270501i	−0.247099	+	0.968990i	$0.579477\pi$
$42$		0			0
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$			1.73205i			0.261116i
$45$		0			0
$46$	4.50000	−	2.59808i	0.663489	−	0.383065i
$47$		−	3.46410i		−	0.505291i	−0.967559	−	0.252646i	$-0.918699\pi$
$47$		−	3.46410i		−	0.505291i	0.967559	−	0.252646i	$-0.0813007\pi$
$48$	−2.50000	−	4.33013i	−0.360844	−	0.625000i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$		0			0
$51$		0			0
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−1.50000	−	0.866025i	−0.204124	−	0.117851i
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.954080	−	0.299552i	$-0.903163\pi$
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.217620	+	0.976034i	$0.569829\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$	6.00000	−	10.3923i	0.762001	−	1.31982i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	3.00000	+	1.73205i	0.366508	+	0.211604i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	3.00000	+	1.73205i	0.366508	+	0.211604i	−0.305424	+	0.952217i	$0.598798\pi$
$68$		0			0
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	−7.50000	+	4.33013i	−0.890086	+	0.513892i	−0.873971	−	0.485979i	$-0.838463\pi$
$71$	−7.50000	+	4.33013i	−0.890086	+	0.513892i	−0.0161155	+	0.999870i	$0.505130\pi$
$72$	−1.50000	+	0.866025i	−0.176777	+	0.102062i
$73$			8.66025i			1.01361i	0.862062	+	0.506803i	$0.169173\pi$
$73$			8.66025i			1.01361i	−0.862062	+	0.506803i	$0.830827\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$		0			0
$77$		0			0
$78$	4.50000	−	4.33013i	0.509525	−	0.490290i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$			8.66025i			0.950586i	0.879827	+	0.475293i	$0.157658\pi$
$83$			8.66025i			0.950586i	−0.879827	+	0.475293i	$0.842342\pi$
$84$		0			0
$85$		0			0
$86$			17.3205i			1.86772i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−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
$92$	3.00000			0.312772
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$		0			0
$96$		−	5.19615i		−	0.530330i
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	−0.0683279	−	0.997663i	$-0.521766\pi$
$97$	7.50000	−	4.33013i	0.761510	−	0.439658i	0.829837	+	0.558005i	$0.188433\pi$
$98$	−10.5000	+	6.06218i	−1.06066	+	0.612372i
$99$		−	1.73205i		−	0.174078i
$100$		0			0
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−1.50000	−	6.06218i	−0.147087	−	0.594445i
$105$		0			0
$106$		0			0
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			8.66025i			0.829502i	0.909935	+	0.414751i	$0.136131\pi$
$109$			8.66025i			0.829502i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	1.50000	−	0.866025i	0.142374	−	0.0821995i
$112$		0			0
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	−18.0000			−1.65703
$119$		0			0
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		−	12.1244i		−	1.09769i
$123$	3.00000	−	1.73205i	0.270501	−	0.156174i
$124$	6.00000	−	3.46410i	0.538816	−	0.311086i
$125$		0			0
$126$		0			0
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$	10.0000			0.880451
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	1.50000	+	0.866025i	0.130558	+	0.0753778i
$133$		0			0
$134$	3.00000	+	5.19615i	0.259161	+	0.448879i
$135$		0			0
$136$		0			0
$137$	−18.0000	+	10.3923i	−1.53784	+	0.887875i	−0.538879	+	0.842383i	$0.681152\pi$
$137$	−18.0000	+	10.3923i	−1.53784	+	0.887875i	−0.998965	+	0.0454914i	$0.985515\pi$
$138$		−	5.19615i		−	0.442326i
$139$	5.00000	+	8.66025i	0.424094	+	0.734553i	0.996335	−	0.0855324i	$-0.0272591\pi$
$139$	5.00000	+	8.66025i	0.424094	+	0.734553i	−0.572241	+	0.820086i	$0.693926\pi$
$140$		0			0
$141$	−3.00000	−	1.73205i	−0.252646	−	0.145865i
$142$	−15.0000			−1.25877
$143$	6.00000	+	1.73205i	0.501745	+	0.144841i
$144$	−5.00000			−0.416667
$145$		0			0
$146$	−7.50000	+	12.9904i	−0.620704	+	1.07509i
$147$	3.50000	+	6.06218i	0.288675	+	0.500000i
$148$			1.73205i			0.142374i
$149$	6.00000	−	3.46410i	0.491539	−	0.283790i	−0.233674	−	0.972315i	$-0.575075\pi$
$149$	6.00000	−	3.46410i	0.491539	−	0.283790i	0.725213	+	0.688525i	$0.241741\pi$
$150$		0			0
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	3.50000	−	0.866025i	0.280224	−	0.0693375i
$157$	−1.00000			−0.0798087			−0.0399043	−	0.999204i	$-0.512705\pi$
$157$	−1.00000			−0.0798087			−0.0399043	+	0.999204i	$0.512705\pi$
$158$	−12.0000	−	6.92820i	−0.954669	−	0.551178i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.50000	+	0.866025i	−0.117851	+	0.0680414i
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	−0.612866	−	0.790186i	$-0.709984\pi$
$163$	−3.00000	+	1.73205i	−0.234978	+	0.135665i	0.377888	+	0.925851i	$0.376650\pi$
$164$			3.46410i			0.270501i
$165$		0			0
$166$	−7.50000	+	12.9904i	−0.582113	+	1.00825i
$167$	−7.50000	−	4.33013i	−0.580367	−	0.335075i	0.180912	−	0.983499i	$-0.442095\pi$
$167$	−7.50000	−	4.33013i	−0.580367	−	0.335075i	−0.761279	+	0.648424i	$0.775428\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$		0			0
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.810745	+	0.585399i	$0.199062\pi$
$173$	12.0000	+	20.7846i	0.912343	+	1.58022i	0.101598	+	0.994826i	$0.467605\pi$
$174$		0			0
$175$		0			0
$176$	7.50000	−	4.33013i	0.565334	−	0.326396i
$177$			10.3923i			0.781133i
$178$	−6.00000	−	10.3923i	−0.449719	−	0.778936i
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$	−4.50000	−	2.59808i	−0.331744	−	0.191533i
$185$		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
$191$	−4.50000	−	7.79423i	−0.325609	−	0.563971i	0.656027	−	0.754738i	$-0.272236\pi$
$191$	−4.50000	−	7.79423i	−0.325609	−	0.563971i	−0.981635	+	0.190767i	$0.938902\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.50000	−	4.33013i	−0.539862	−	0.311689i	0.205161	−	0.978728i	$-0.434228\pi$
$193$	−7.50000	−	4.33013i	−0.539862	−	0.311689i	−0.745023	+	0.667039i	$0.767561\pi$
$194$	15.0000			1.07694
$195$		0			0
$196$	−7.00000			−0.500000
$197$	9.00000	+	5.19615i	0.641223	+	0.370211i	0.785086	−	0.619387i	$-0.212619\pi$
$197$	9.00000	+	5.19615i	0.641223	+	0.370211i	−0.143862	+	0.989598i	$0.545952\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$		0			0
$201$	3.00000	−	1.73205i	0.211604	−	0.122169i
$202$	−27.0000	+	15.5885i	−1.89971	+	1.09680i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	21.0000	+	12.1244i	1.46314	+	0.844744i
$207$	−3.00000			−0.208514
$208$	5.00000	−	17.3205i	0.346688	−	1.20096i
$209$		0			0
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$		0			0
$213$			8.66025i			0.593391i
$214$	18.0000	−	10.3923i	1.23045	−	0.710403i
$215$		0			0
$216$			1.73205i			0.117851i
$217$		0			0
$218$	−7.50000	+	12.9904i	−0.507964	+	0.879820i
$219$	7.50000	+	4.33013i	0.506803	+	0.292603i
$220$		0			0
$221$		0			0
$222$	3.00000			0.201347
$223$	−9.00000	−	5.19615i	−0.602685	−	0.347960i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	−9.00000	−	5.19615i	−0.602685	−	0.347960i	−0.770097	+	0.637927i	$0.779792\pi$
$224$		0			0
$225$		0			0
$226$			10.3923i			0.691286i
$227$	−25.5000	+	14.7224i	−1.69249	+	0.977162i	−0.740000	+	0.672607i	$0.765174\pi$
$227$	−25.5000	+	14.7224i	−1.69249	+	0.977162i	−0.952495	+	0.304555i	$0.901492\pi$
$228$		0			0
$229$		−	25.9808i		−	1.71686i	−0.512933	−	0.858429i	$-0.671441\pi$
$229$		−	25.9808i		−	1.71686i	0.512933	−	0.858429i	$-0.328559\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	−1.50000	−	6.06218i	−0.0980581	−	0.396297i
$235$		0			0
$236$	−9.00000	−	5.19615i	−0.585850	−	0.338241i
$237$	−4.00000	+	6.92820i	−0.259828	+	0.450035i
$238$		0			0
$239$			5.19615i			0.336111i	0.985778	+	0.168056i	$0.0537488\pi$
$239$			5.19615i			0.336111i	−0.985778	+	0.168056i	$0.946251\pi$
$240$		0			0
$241$	18.0000	−	10.3923i	1.15948	−	0.669427i	0.208302	−	0.978065i	$-0.433206\pi$
$241$	18.0000	−	10.3923i	1.15948	−	0.669427i	0.951180	+	0.308637i	$0.0998729\pi$
$242$		−	13.8564i		−	0.890724i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.50000	−	6.06218i	0.224065	−	0.388091i
$245$		0			0
$246$	6.00000			0.382546
$247$		0			0
$248$	−12.0000			−0.762001
$249$	7.50000	+	4.33013i	0.475293	+	0.274411i
$250$		0			0
$251$	−13.5000	−	23.3827i	−0.852112	−	1.47590i	−0.879298	−	0.476272i	$-0.841988\pi$
$251$	−13.5000	−	23.3827i	−0.852112	−	1.47590i	0.0271858	−	0.999630i	$-0.491345\pi$
$252$		0			0
$253$	4.50000	−	2.59808i	0.282913	−	0.163340i
$254$	3.00000	−	1.73205i	0.188237	−	0.108679i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	15.0000	+	8.66025i	0.933859	+	0.539164i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−18.0000	−	10.3923i	−1.11204	−	0.642039i
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	−0.536614	−	0.843828i	$-0.680297\pi$
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	0.999083	+	0.0428069i	$0.0136300\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$		0			0
$266$		0			0
$267$	−6.00000	+	3.46410i	−0.367194	+	0.212000i
$268$			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
$271$	12.0000	+	6.92820i	0.728948	+	0.420858i	0.818037	−	0.575165i	$-0.195062\pi$
$271$	12.0000	+	6.92820i	0.728948	+	0.420858i	−0.0890891	+	0.996024i	$0.528396\pi$
$272$		0			0
$273$		0			0
$274$	−36.0000			−2.17484
$275$		0			0
$276$	1.50000	−	2.59808i	0.0902894	−	0.156386i
$277$	12.5000	+	21.6506i	0.751052	+	1.30086i	0.947313	+	0.320309i	$0.103787\pi$
$277$	12.5000	+	21.6506i	0.751052	+	1.30086i	−0.196261	+	0.980552i	$0.562880\pi$
$278$			17.3205i			1.03882i
$279$	−6.00000	+	3.46410i	−0.359211	+	0.207390i
$280$		0			0
$281$			13.8564i			0.826604i	0.910594	+	0.413302i	$0.135625\pi$
$281$			13.8564i			0.826604i	−0.910594	+	0.413302i	$0.864375\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	16.0000	−	27.7128i	0.951101	−	1.64736i	0.208053	−	0.978117i	$-0.433287\pi$
$283$	16.0000	−	27.7128i	0.951101	−	1.64736i	0.743048	−	0.669238i	$-0.233379\pi$
$284$	−7.50000	−	4.33013i	−0.445043	−	0.256946i
$285$		0			0
$286$	7.50000	+	7.79423i	0.443484	+	0.460882i
$287$		0			0
$288$	−4.50000	−	2.59808i	−0.265165	−	0.153093i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		−	8.66025i		−	0.507673i
$292$	−7.50000	+	4.33013i	−0.438904	+	0.253402i
$293$	−15.0000	+	8.66025i	−0.876309	+	0.505937i	−0.869440	−	0.494039i	$-0.835520\pi$
$293$	−15.0000	+	8.66025i	−0.876309	+	0.505937i	−0.00686959	+	0.999976i	$0.502187\pi$
$294$			12.1244i			0.707107i
$295$		0			0
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$	−1.50000	−	0.866025i	−0.0870388	−	0.0502519i
$298$	12.0000			0.695141
$299$	3.00000	−	10.3923i	0.173494	−	0.601003i
$300$		0			0
$301$		0			0
$302$	−3.00000	+	5.19615i	−0.172631	+	0.299005i
$303$	9.00000	+	15.5885i	0.517036	+	0.895533i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	31.1769i		−	1.77936i	−0.456584	−	0.889680i	$-0.650927\pi$
$307$		−	31.1769i		−	1.77936i	0.456584	−	0.889680i	$-0.349073\pi$
$308$		0			0
$309$	7.00000	−	12.1244i	0.398216	−	0.689730i
$310$		0			0
$311$	−3.00000			−0.170114			−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000			−0.170114			−0.0850572	+	0.996376i	$0.527107\pi$
$312$	−6.00000	−	1.73205i	−0.339683	−	0.0980581i
$313$	−17.0000			−0.960897			−0.480448	−	0.877023i	$-0.659526\pi$
$313$	−17.0000			−0.960897			−0.480448	+	0.877023i	$0.659526\pi$
$314$	−1.50000	−	0.866025i	−0.0846499	−	0.0488726i
$315$		0			0
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$			27.7128i			1.55651i	0.627950	+	0.778253i	$0.283894\pi$
$317$			27.7128i			1.55651i	−0.627950	+	0.778253i	$0.716106\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$		0			0
$323$		0			0
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−6.00000			−0.332309
$327$	7.50000	+	4.33013i	0.414751	+	0.239457i
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$		0			0
$330$		0			0
$331$	3.00000	−	1.73205i	0.164895	−	0.0952021i	−0.415282	−	0.909693i	$-0.636317\pi$
$331$	3.00000	−	1.73205i	0.164895	−	0.0952021i	0.580176	+	0.814491i	$0.302984\pi$
$332$	−7.50000	+	4.33013i	−0.411616	+	0.237647i
$333$		−	1.73205i		−	0.0949158i
$334$	−7.50000	−	12.9904i	−0.410382	−	0.710802i
$335$		0			0
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	22.5000	+	0.866025i	1.22384	+	0.0471056i
$339$	6.00000			0.325875
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$		0			0
$344$	15.0000	−	8.66025i	0.808746	−	0.466930i
$345$		0			0
$346$			41.5692i			2.23478i
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	0.903475	−	0.428640i	$-0.141007\pi$
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	−0.822951	+	0.568112i	$0.807674\pi$
$348$		0			0
$349$	13.5000	+	7.79423i	0.722638	+	0.417215i	0.815723	−	0.578443i	$-0.196339\pi$
$349$	13.5000	+	7.79423i	0.722638	+	0.417215i	−0.0930846	+	0.995658i	$0.529673\pi$
$350$		0			0
$351$	−3.50000	+	0.866025i	−0.186816	+	0.0462250i
$352$	9.00000			0.479702
$353$	−15.0000	−	8.66025i	−0.798369	−	0.460939i	0.0445312	−	0.999008i	$-0.485821\pi$
$353$	−15.0000	−	8.66025i	−0.798369	−	0.460939i	−0.842901	+	0.538069i	$0.819154\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$		0			0
$356$		−	6.92820i		−	0.367194i
$357$		0			0
$358$	−13.5000	+	7.79423i	−0.713497	+	0.411938i
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$		0			0
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	−10.5000	−	6.06218i	−0.551868	−	0.318621i
$363$	−8.00000			−0.419891
$364$		0			0
$365$		0			0
$366$	−10.5000	−	6.06218i	−0.548844	−	0.316875i
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	−7.50000	−	12.9904i	−0.390965	−	0.677170i
$369$		−	3.46410i		−	0.180334i
$370$		0			0
$371$		0			0
$372$		−	6.92820i		−	0.359211i
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	0.647225	−	0.762299i	$-0.275929\pi$
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	−0.983783	+	0.179364i	$0.942596\pi$
$374$		0			0
$375$		0			0
$376$	−6.00000			−0.309426
$377$		0			0
$378$		0			0
$379$	−24.0000	−	13.8564i	−1.23280	−	0.711756i	−0.265185	−	0.964198i	$-0.585433\pi$
$379$	−24.0000	−	13.8564i	−1.23280	−	0.711756i	−0.967612	+	0.252442i	$0.918766\pi$
$380$		0			0
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$		−	15.5885i		−	0.797575i
$383$	19.5000	−	11.2583i	0.996403	−	0.575274i	0.0892213	−	0.996012i	$-0.471562\pi$
$383$	19.5000	−	11.2583i	0.996403	−	0.575274i	0.907182	+	0.420738i	$0.138229\pi$
$384$	−10.5000	+	6.06218i	−0.535826	+	0.309359i
$385$		0			0
$386$	−7.50000	−	12.9904i	−0.381740	−	0.661193i
$387$	5.00000	−	8.66025i	0.254164	−	0.440225i
$388$	7.50000	+	4.33013i	0.380755	+	0.219829i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$		0			0
$392$	10.5000	+	6.06218i	0.530330	+	0.306186i
$393$	−6.00000	+	10.3923i	−0.302660	+	0.524222i
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$		0			0
$396$	1.50000	−	0.866025i	0.0753778	−	0.0435194i
$397$	24.0000	−	13.8564i	1.20453	−	0.695433i	0.242967	−	0.970034i	$-0.421879\pi$
$397$	24.0000	−	13.8564i	1.20453	−	0.695433i	0.961558	+	0.274601i	$0.0885459\pi$
$398$			24.2487i			1.21548i
$399$		0			0
$400$		0			0
$401$	24.0000	+	13.8564i	1.19850	+	0.691956i	0.960221	−	0.279240i	$-0.0900826\pi$
$401$	24.0000	+	13.8564i	1.19850	+	0.691956i	0.238282	+	0.971196i	$0.423416\pi$
$402$	6.00000			0.299253
$403$	−6.00000	−	24.2487i	−0.298881	−	1.20791i
$404$	−18.0000			−0.895533
$405$		0			0
$406$		0			0
$407$	1.50000	+	2.59808i	0.0743522	+	0.128782i
$408$		0			0
$409$	−6.00000	+	3.46410i	−0.296681	+	0.171289i	−0.640951	−	0.767582i	$-0.721460\pi$
$409$	−6.00000	+	3.46410i	−0.296681	+	0.171289i	0.344270	+	0.938871i	$0.388126\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$	−4.50000	−	2.59808i	−0.221163	−	0.127688i
$415$		0			0
$416$	13.5000	−	12.9904i	0.661892	−	0.636906i
$417$	10.0000			0.489702
$418$		0			0
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	−0.989000	−	0.147918i	$-0.952743\pi$
$419$	−7.50000	+	12.9904i	−0.366399	+	0.634622i	0.622601	+	0.782540i	$0.286076\pi$
$420$		0			0
$421$			12.1244i			0.590905i	0.955357	+	0.295452i	$0.0954704\pi$
$421$			12.1244i			0.590905i	−0.955357	+	0.295452i	$0.904530\pi$
$422$	30.0000	−	17.3205i	1.46038	−	0.843149i
$423$	−3.00000	+	1.73205i	−0.145865	+	0.0842152i
$424$		0			0
$425$		0			0
$426$	−7.50000	+	12.9904i	−0.363376	+	0.629386i
$427$		0			0
$428$	12.0000			0.580042
$429$	4.50000	−	4.33013i	0.217262	−	0.209061i
$430$		0			0
$431$	10.5000	+	6.06218i	0.505767	+	0.292005i	0.731092	−	0.682279i	$-0.239011\pi$
$431$	10.5000	+	6.06218i	0.505767	+	0.292005i	−0.225325	+	0.974284i	$0.572344\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	0.967383	−	0.253317i	$-0.0815214\pi$
$433$	5.50000	+	9.52628i	0.264313	+	0.457804i	−0.703070	+	0.711120i	$0.748188\pi$
$434$		0			0
$435$		0			0
$436$	−7.50000	+	4.33013i	−0.359185	+	0.207375i
$437$		0			0
$438$	7.50000	+	12.9904i	0.358364	+	0.620704i
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$	−27.0000			−1.28281			−0.641404	−	0.767203i	$-0.721648\pi$
$443$	−27.0000			−1.28281			−0.641404	+	0.767203i	$0.721648\pi$
$444$	1.50000	+	0.866025i	0.0711868	+	0.0410997i
$445$		0			0
$446$	−9.00000	−	15.5885i	−0.426162	−	0.738135i
$447$		−	6.92820i		−	0.327693i
$448$		0			0
$449$	−15.0000	+	8.66025i	−0.707894	+	0.408703i	−0.810281	−	0.586042i	$-0.800685\pi$
$449$	−15.0000	+	8.66025i	−0.707894	+	0.408703i	0.102387	+	0.994745i	$0.467352\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	3.00000	+	1.73205i	0.140952	+	0.0813788i
$454$	−51.0000			−2.39355
$455$		0			0
$456$		0			0
$457$	13.5000	+	7.79423i	0.631503	+	0.364599i	0.781334	−	0.624113i	$-0.214540\pi$
$457$	13.5000	+	7.79423i	0.631503	+	0.364599i	−0.149831	+	0.988712i	$0.547873\pi$
$458$	22.5000	−	38.9711i	1.05136	−	1.82100i
$459$		0			0
$460$		0			0
$461$	−24.0000	+	13.8564i	−1.11779	+	0.645357i	−0.940836	−	0.338862i	$-0.889958\pi$
$461$	−24.0000	+	13.8564i	−1.11779	+	0.645357i	−0.176955	+	0.984219i	$0.556625\pi$
$462$		0			0
$463$			24.2487i			1.12693i	0.826139	+	0.563467i	$0.190533\pi$
$463$			24.2487i			1.12693i	−0.826139	+	0.563467i	$0.809467\pi$
$464$		0			0
$465$		0			0
$466$	27.0000	+	15.5885i	1.25075	+	0.722121i
$467$	33.0000			1.52706			0.763529	−	0.645774i	$-0.223465\pi$
$467$	33.0000			1.52706			0.763529	+	0.645774i	$0.223465\pi$
$468$	1.00000	−	3.46410i	0.0462250	−	0.160128i
$469$		0			0
$470$		0			0
$471$	−0.500000	+	0.866025i	−0.0230388	+	0.0399043i
$472$	9.00000	+	15.5885i	0.414259	+	0.717517i
$473$			17.3205i			0.796398i
$474$	−12.0000	+	6.92820i	−0.551178	+	0.318223i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−4.50000	+	7.79423i	−0.205825	+	0.356500i
$479$	−9.00000	−	5.19615i	−0.411220	−	0.237418i	0.280094	−	0.959973i	$-0.409635\pi$
$479$	−9.00000	−	5.19615i	−0.411220	−	0.237418i	−0.691314	+	0.722554i	$0.742968\pi$
$480$		0			0
$481$	6.00000	+	1.73205i	0.273576	+	0.0789747i
$482$	36.0000			1.63976
$483$		0			0
$484$	4.00000	−	6.92820i	0.181818	−	0.314918i
$485$		0			0
$486$			1.73205i			0.0785674i
$487$	15.0000	−	8.66025i	0.679715	−	0.392434i	−0.120033	−	0.992770i	$-0.538300\pi$
$487$	15.0000	−	8.66025i	0.679715	−	0.392434i	0.799748	+	0.600336i	$0.204967\pi$
$488$	−10.5000	+	6.06218i	−0.475313	+	0.274422i
$489$			3.46410i			0.156652i
$490$		0			0
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	−0.382118	−	0.924113i	$-0.624805\pi$
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	0.991365	−	0.131132i	$-0.0418613\pi$
$492$	3.00000	+	1.73205i	0.135250	+	0.0780869i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−30.0000	−	17.3205i	−1.34704	−	0.777714i
$497$		0			0
$498$	7.50000	+	12.9904i	0.336083	+	0.582113i
$499$			38.1051i			1.70582i	0.522059	+	0.852910i	$0.325164\pi$
$499$			38.1051i			1.70582i	−0.522059	+	0.852910i	$0.674836\pi$
$500$		0			0
$501$	−7.50000	+	4.33013i	−0.335075	+	0.193456i
$502$		−	46.7654i		−	2.08724i
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$		0			0
$505$		0			0
$506$	9.00000			0.400099
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	2.00000			0.0887357
$509$	−27.0000	−	15.5885i	−1.19675	−	0.690946i	−0.236924	−	0.971528i	$-0.576139\pi$
$509$	−27.0000	−	15.5885i	−1.19675	−	0.690946i	−0.959830	+	0.280582i	$0.909473\pi$
$510$		0			0
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	9.00000	−	5.19615i	0.396973	−	0.229192i
$515$		0			0
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$	3.00000	−	5.19615i	0.131940	−	0.228527i
$518$		0			0
$519$	24.0000			1.05348
$520$		0			0
$521$	−12.0000			−0.525730			−0.262865	−	0.964833i	$-0.584667\pi$
$521$	−12.0000			−0.525730			−0.262865	+	0.964833i	$0.584667\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	22.5000	−	12.9904i	0.981047	−	0.566408i
$527$		0			0
$528$		−	8.66025i		−	0.376889i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	9.00000	+	5.19615i	0.390567	+	0.225494i
$532$		0			0
$533$	12.0000	+	3.46410i	0.519778	+	0.150047i
$534$	−12.0000			−0.519291
$535$		0			0
$536$	3.00000	−	5.19615i	0.129580	−	0.224440i
$537$	4.50000	+	7.79423i	0.194189	+	0.336346i
$538$			10.3923i			0.448044i
$539$	−10.5000	+	6.06218i	−0.452267	+	0.261116i
$540$		0			0
$541$			29.4449i			1.26593i	0.774179	+	0.632967i	$0.218163\pi$
$541$			29.4449i			1.26593i	−0.774179	+	0.632967i	$0.781837\pi$
$542$	12.0000	+	20.7846i	0.515444	+	0.892775i
$543$	−3.50000	+	6.06218i	−0.150199	+	0.260153i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$	−18.0000	−	10.3923i	−0.768922	−	0.443937i
$549$	−3.50000	+	6.06218i	−0.149376	+	0.258727i
$550$		0			0
$551$		0			0
$552$	−4.50000	+	2.59808i	−0.191533	+	0.110581i
$553$		0			0
$554$			43.3013i			1.83969i
$555$		0			0
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$	−15.0000	−	8.66025i	−0.635570	−	0.366947i	0.147336	−	0.989087i	$-0.452930\pi$
$557$	−15.0000	−	8.66025i	−0.635570	−	0.366947i	−0.782906	+	0.622140i	$0.786264\pi$
$558$	−12.0000			−0.508001
$559$	25.0000	+	25.9808i	1.05739	+	1.09887i
$560$		0			0
$561$		0			0
$562$	−12.0000	+	20.7846i	−0.506189	+	0.876746i
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	0.555354	−	0.831614i	$-0.312583\pi$
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	−0.997876	+	0.0651433i	$0.979250\pi$
$564$		−	3.46410i		−	0.145865i
$565$		0			0
$566$	48.0000	−	27.7128i	2.01759	−	1.16486i
$567$		0			0
$568$	7.50000	+	12.9904i	0.314693	+	0.545064i
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	−14.0000			−0.585882			−0.292941	−	0.956131i	$-0.594634\pi$
$571$	−14.0000			−0.585882			−0.292941	+	0.956131i	$0.594634\pi$
$572$	1.50000	+	6.06218i	0.0627182	+	0.253472i
$573$	−9.00000			−0.375980
$574$		0			0
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			29.4449i			1.22581i	0.790158	+	0.612903i	$0.209998\pi$
$577$			29.4449i			1.22581i	−0.790158	+	0.612903i	$0.790002\pi$
$578$	25.5000	−	14.7224i	1.06066	−	0.612372i
$579$	−7.50000	+	4.33013i	−0.311689	+	0.179954i
$580$		0			0
$581$		0			0
$582$	7.50000	−	12.9904i	0.310885	−	0.538469i
$583$		0			0
$584$	15.0000			0.620704
$585$		0			0
$586$	−30.0000			−1.23929
$587$	4.50000	+	2.59808i	0.185735	+	0.107234i	0.589984	−	0.807415i	$-0.299134\pi$
$587$	4.50000	+	2.59808i	0.185735	+	0.107234i	−0.404249	+	0.914649i	$0.632467\pi$
$588$	−3.50000	+	6.06218i	−0.144338	+	0.250000i
$589$		0			0
$590$		0			0
$591$	9.00000	−	5.19615i	0.370211	−	0.213741i
$592$	7.50000	−	4.33013i	0.308248	−	0.177967i
$593$			13.8564i			0.569014i	0.958674	+	0.284507i	$0.0918300\pi$
$593$			13.8564i			0.569014i	−0.958674	+	0.284507i	$0.908170\pi$
$594$	−1.50000	−	2.59808i	−0.0615457	−	0.106600i
$595$		0			0
$596$	6.00000	+	3.46410i	0.245770	+	0.141895i
$597$	14.0000			0.572982
$598$	13.5000	−	12.9904i	0.552056	−	0.531216i
$599$	−9.00000			−0.367730			−0.183865	−	0.982952i	$-0.558861\pi$
$599$	−9.00000			−0.367730			−0.183865	+	0.982952i	$0.558861\pi$
$600$		0			0
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$		−	3.46410i		−	0.141069i
$604$	−3.00000	+	1.73205i	−0.122068	+	0.0704761i
$605$		0			0
$606$			31.1769i			1.26648i
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.00000	−	12.1244i	−0.121367	−	0.490499i
$612$		0			0
$613$	6.00000	+	3.46410i	0.242338	+	0.139914i	0.616251	−	0.787550i	$-0.288651\pi$
$613$	6.00000	+	3.46410i	0.242338	+	0.139914i	−0.373913	+	0.927464i	$0.621984\pi$
$614$	27.0000	−	46.7654i	1.08963	−	1.88730i
$615$		0			0
$616$		0			0
$617$	−39.0000	+	22.5167i	−1.57008	+	0.906487i	−0.573923	+	0.818909i	$0.694579\pi$
$617$	−39.0000	+	22.5167i	−1.57008	+	0.906487i	−0.996158	+	0.0875775i	$0.972087\pi$
$618$	21.0000	−	12.1244i	0.844744	−	0.487713i
$619$		−	27.7128i		−	1.11387i	−0.830555	−	0.556936i	$-0.811977\pi$
$619$		−	27.7128i		−	1.11387i	0.830555	−	0.556936i	$-0.188023\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$	−4.50000	−	2.59808i	−0.180434	−	0.104173i
$623$		0			0
$624$	−12.5000	−	12.9904i	−0.500400	−	0.520031i
$625$		0			0
$626$	−25.5000	−	14.7224i	−1.01918	−	0.588427i
$627$		0			0
$628$	−0.500000	−	0.866025i	−0.0199522	−	0.0345582i
$629$		0			0
$630$		0			0
$631$	42.0000	−	24.2487i	1.67199	−	0.965326i	0.705473	−	0.708737i	$-0.250735\pi$
$631$	42.0000	−	24.2487i	1.67199	−	0.965326i	0.966521	−	0.256589i	$-0.0825987\pi$
$632$			13.8564i			0.551178i
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	−24.0000	+	41.5692i	−0.953162	+	1.65092i
$635$		0			0
$636$		0			0
$637$	−7.00000	+	24.2487i	−0.277350	+	0.960769i
$638$		0			0
$639$	7.50000	+	4.33013i	0.296695	+	0.171297i
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$		−	20.7846i		−	0.820303i
$643$	−15.0000	+	8.66025i	−0.591542	+	0.341527i	−0.765707	−	0.643189i	$-0.777611\pi$
$643$	−15.0000	+	8.66025i	−0.591542	+	0.341527i	0.174165	+	0.984717i	$0.444277\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.5000	−	28.5788i	0.648682	−	1.12355i	−0.334756	−	0.942305i	$-0.608654\pi$
$647$	16.5000	−	28.5788i	0.648682	−	1.12355i	0.983438	−	0.181245i	$-0.0580128\pi$
$648$	1.50000	+	0.866025i	0.0589256	+	0.0340207i
$649$	−18.0000			−0.706562
$650$		0			0
$651$		0			0
$652$	−3.00000	−	1.73205i	−0.117489	−	0.0678323i
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.172211	−	0.985060i	$-0.444909\pi$
$653$	24.0000	−	41.5692i	0.939193	−	1.62673i	0.766982	−	0.641669i	$-0.221758\pi$
$654$	7.50000	+	12.9904i	0.293273	+	0.507964i
$655$		0			0
$656$	15.0000	−	8.66025i	0.585652	−	0.338126i
$657$	7.50000	−	4.33013i	0.292603	−	0.168934i
$658$		0			0
$659$	−16.5000	−	28.5788i	−0.642749	−	1.11327i	−0.984817	−	0.173598i	$-0.944461\pi$
$659$	−16.5000	−	28.5788i	−0.642749	−	1.11327i	0.342068	−	0.939675i	$-0.388873\pi$
$660$		0			0
$661$	−12.0000	−	6.92820i	−0.466746	−	0.269476i	0.248131	−	0.968727i	$-0.420184\pi$
$661$	−12.0000	−	6.92820i	−0.466746	−	0.269476i	−0.714877	+	0.699251i	$0.753517\pi$
$662$	6.00000			0.233197
$663$		0			0
$664$	15.0000			0.582113
$665$		0			0
$666$	1.50000	−	2.59808i	0.0581238	−	0.100673i
$667$		0			0
$668$		−	8.66025i		−	0.335075i
$669$	−9.00000	+	5.19615i	−0.347960	+	0.200895i
$670$		0			0
$671$		−	12.1244i		−	0.468056i
$672$		0			0
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	−0.982045	−	0.188645i	$-0.939590\pi$
$673$	−8.50000	+	14.7224i	−0.327651	+	0.567508i	0.654394	+	0.756153i	$0.272924\pi$
$674$	−21.0000	−	12.1244i	−0.808890	−	0.467013i
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	−36.0000			−1.38359			−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000			−1.38359			−0.691796	+	0.722093i	$0.743180\pi$
$678$	9.00000	+	5.19615i	0.345643	+	0.199557i
$679$		0			0
$680$		0			0
$681$			29.4449i			1.12833i
$682$	18.0000	−	10.3923i	0.689256	−	0.397942i
$683$	40.5000	−	23.3827i	1.54969	−	0.894714i	0.551525	−	0.834159i	$-0.314046\pi$
$683$	40.5000	−	23.3827i	1.54969	−	0.894714i	0.998165	−	0.0605550i	$-0.0192870\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−22.5000	−	12.9904i	−0.858429	−	0.495614i
$688$	50.0000			1.90623
$689$		0			0
$690$		0			0
$691$	−12.0000	−	6.92820i	−0.456502	−	0.263561i	0.254071	−	0.967186i	$-0.418230\pi$
$691$	−12.0000	−	6.92820i	−0.456502	−	0.263561i	−0.710572	+	0.703624i	$0.751564\pi$
$692$	−12.0000	+	20.7846i	−0.456172	+	0.790112i
$693$		0			0
$694$			5.19615i			0.197243i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	13.5000	+	23.3827i	0.510983	+	0.885048i
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	−6.00000	−	1.73205i	−0.226455	−	0.0653720i
$703$		0			0
$704$	−1.50000	−	0.866025i	−0.0565334	−	0.0326396i
$705$		0			0
$706$	−15.0000	−	25.9808i	−0.564532	−	0.977799i
$707$		0			0
$708$	−9.00000	+	5.19615i	−0.338241	+	0.195283i
$709$	25.5000	−	14.7224i	0.957673	−	0.552913i	0.0622167	−	0.998063i	$-0.480183\pi$
$709$	25.5000	−	14.7224i	0.957673	−	0.552913i	0.895456	+	0.445150i	$0.146850\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	−18.0000	−	10.3923i	−0.674105	−	0.389195i
$714$		0			0
$715$		0			0
$716$	−9.00000			−0.336346
$717$	4.50000	+	2.59808i	0.168056	+	0.0970269i
$718$	−21.0000	+	36.3731i	−0.783713	+	1.35743i
$719$	−22.5000	−	38.9711i	−0.839108	−	1.45338i	−0.890641	−	0.454707i	$-0.849744\pi$
$719$	−22.5000	−	38.9711i	−0.839108	−	1.45338i	0.0515326	−	0.998671i	$-0.483589\pi$
$720$		0			0
$721$		0			0
$722$	−28.5000	+	16.4545i	−1.06066	+	0.612372i
$723$		−	20.7846i		−	0.772988i
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$		0			0
$726$	−12.0000	−	6.92820i	−0.445362	−	0.257130i
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	−3.50000	−	6.06218i	−0.129364	−	0.224065i
$733$		−	1.73205i		−	0.0639748i	−0.999488	−	0.0319874i	$-0.989816\pi$
$733$		−	1.73205i		−	0.0639748i	0.999488	−	0.0319874i	$-0.0101836\pi$
$734$	42.0000	−	24.2487i	1.55025	−	0.895036i
$735$		0			0
$736$		−	15.5885i		−	0.574598i
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	39.0000	+	22.5167i	1.43464	+	0.828289i	0.997470	−	0.0710909i	$-0.0226481\pi$
$739$	39.0000	+	22.5167i	1.43464	+	0.828289i	0.437168	+	0.899380i	$0.355981\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.0000	−	8.66025i	−0.550297	−	0.317714i	0.198945	−	0.980011i	$-0.436248\pi$
$743$	−15.0000	−	8.66025i	−0.550297	−	0.317714i	−0.749242	+	0.662297i	$0.769582\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$		0			0
$746$		−	22.5167i		−	0.824394i
$747$	7.50000	−	4.33013i	0.274411	−	0.158431i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	−0.965013	−	0.262201i	$-0.915552\pi$
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	0.709580	+	0.704625i	$0.248885\pi$
$752$	−15.0000	−	8.66025i	−0.546994	−	0.315807i
$753$	−27.0000			−0.983935
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	−0.847280	−	0.531146i	$-0.821762\pi$
$757$	1.00000	−	1.73205i	0.0363456	−	0.0629525i	0.883626	+	0.468193i	$0.155095\pi$
$758$	−24.0000	−	41.5692i	−0.871719	−	1.50986i
$759$		−	5.19615i		−	0.188608i
$760$		0			0
$761$	6.00000	−	3.46410i	0.217500	−	0.125574i	−0.387292	−	0.921957i	$-0.626590\pi$
$761$	6.00000	−	3.46410i	0.217500	−	0.125574i	0.604792	+	0.796383i	$0.293256\pi$
$762$		−	3.46410i		−	0.125491i
$763$		0			0
$764$	4.50000	−	7.79423i	0.162804	−	0.281985i
$765$		0			0
$766$	39.0000			1.40913
$767$	−27.0000	+	25.9808i	−0.974913	+	0.938111i
$768$	−19.0000			−0.685603
$769$	−42.0000	−	24.2487i	−1.51456	−	0.874431i	−0.999854	−	0.0170631i	$-0.994568\pi$
$769$	−42.0000	−	24.2487i	−1.51456	−	0.874431i	−0.514704	−	0.857368i	$-0.672098\pi$
$770$		0			0
$771$	−3.00000	−	5.19615i	−0.108042	−	0.187135i
$772$		−	8.66025i		−	0.311689i
$773$	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	$0.119257\pi$
$774$	15.0000	−	8.66025i	0.539164	−	0.311286i
$775$		0			0
$776$	−7.50000	−	12.9904i	−0.269234	−	0.466328i
$777$		0			0
$778$	45.0000	+	25.9808i	1.61333	+	0.931455i
$779$		0			0
$780$		0			0
$781$	−15.0000			−0.536742
$782$		0			0
$783$		0			0
$784$	17.5000	+	30.3109i	0.625000	+	1.08253i
$785$		0			0
$786$	−18.0000	+	10.3923i	−0.642039	+	0.370681i
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$			10.3923i			0.370211i
$789$	−7.50000	−	12.9904i	−0.267007	−	0.462470i
$790$		0			0
$791$		0			0
$792$	−3.00000			−0.106600
$793$	−17.5000	−	18.1865i	−0.621443	−	0.645823i
$794$	48.0000			1.70346
$795$		0			0
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			6.92820i			0.244796i
$802$	24.0000	+	41.5692i	0.847469	+	1.46786i
$803$	−7.50000	+	12.9904i	−0.264669	+	0.458421i
$804$	3.00000	+	1.73205i	0.105802	+	0.0610847i
$805$		0			0
$806$	12.0000	−	41.5692i	0.422682	−	1.46421i
$807$	6.00000			0.211210
$808$	27.0000	+	15.5885i	0.949857	+	0.548400i
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$		0			0
$811$			13.8564i			0.486564i	0.969956	+	0.243282i	$0.0782241\pi$
$811$			13.8564i			0.486564i	−0.969956	+	0.243282i	$0.921776\pi$
$812$		0			0
$813$	12.0000	−	6.92820i	0.420858	−	0.242983i
$814$			5.19615i			0.182125i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−12.0000			−0.419570
$819$		0			0
$820$		0			0
$821$	12.0000	+	6.92820i	0.418803	+	0.241796i	0.694565	−	0.719430i	$-0.255597\pi$
$821$	12.0000	+	6.92820i	0.418803	+	0.241796i	−0.275762	+	0.961226i	$0.588930\pi$
$822$	−18.0000	+	31.1769i	−0.627822	+	1.08742i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$		−	24.2487i		−	0.844744i
$825$		0			0
$826$		0			0
$827$		−	8.66025i		−	0.301147i	−0.988599	−	0.150573i	$-0.951888\pi$
$827$		−	8.66025i		−	0.301147i	0.988599	−	0.150573i	$-0.0481119\pi$
$828$	−1.50000	−	2.59808i	−0.0521286	−	0.0902894i
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$		0			0
$831$	25.0000			0.867240
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$		0			0
$834$	15.0000	+	8.66025i	0.519408	+	0.299880i
$835$		0			0
$836$		0			0
$837$			6.92820i			0.239474i
$838$	−22.5000	+	12.9904i	−0.777250	+	0.448745i
$839$	−7.50000	+	4.33013i	−0.258929	+	0.149493i	−0.623846	−	0.781547i	$-0.714431\pi$
$839$	−7.50000	+	4.33013i	−0.258929	+	0.149493i	0.364917	+	0.931040i	$0.381097\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−10.5000	+	18.1865i	−0.361854	+	0.626749i
$843$	12.0000	+	6.92820i	0.413302	+	0.238620i
$844$	20.0000			0.688428
$845$		0			0
$846$	−6.00000			−0.206284
$847$		0			0
$848$		0			0
$849$	−16.0000	−	27.7128i	−0.549119	−	0.951101i
$850$		0			0
$851$	4.50000	−	2.59808i	0.154258	−	0.0890609i
$852$	−7.50000	+	4.33013i	−0.256946	+	0.148348i
$853$			41.5692i			1.42330i	0.702533	+	0.711651i	$0.252052\pi$
$853$			41.5692i			1.42330i	−0.702533	+	0.711651i	$0.747948\pi$
$854$		0			0
$855$		0			0
$856$	−18.0000	−	10.3923i	−0.615227	−	0.355202i
$857$	−12.0000			−0.409912			−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000			−0.409912			−0.204956	+	0.978771i	$0.565705\pi$
$858$	10.5000	−	2.59808i	0.358464	−	0.0886969i
$859$	−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
$862$	10.5000	+	18.1865i	0.357631	+	0.619436i
$863$		−	25.9808i		−	0.884395i	−0.896918	−	0.442198i	$-0.854199\pi$
$863$		−	25.9808i		−	0.884395i	0.896918	−	0.442198i	$-0.145801\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		0			0
$866$			19.0526i			0.647432i
$867$	−8.50000	−	14.7224i	−0.288675	−	0.500000i
$868$		0			0
$869$	−12.0000	−	6.92820i	−0.407072	−	0.235023i
$870$		0			0
$871$	12.0000	+	3.46410i	0.406604	+	0.117377i
$872$	15.0000			0.507964
$873$	−7.50000	−	4.33013i	−0.253837	−	0.146553i
$874$		0			0
$875$		0			0
$876$			8.66025i			0.292603i
$877$	−34.5000	+	19.9186i	−1.16498	+	0.672603i	−0.952493	−	0.304561i	$-0.901490\pi$
$877$	−34.5000	+	19.9186i	−1.16498	+	0.672603i	−0.212489	+	0.977163i	$0.568157\pi$
$878$	6.00000	−	3.46410i	0.202490	−	0.116908i
$879$			17.3205i			0.584206i
$880$		0			0
$881$	−6.00000	+	10.3923i	−0.202145	+	0.350126i	−0.949219	−	0.314615i	$-0.898125\pi$
$881$	−6.00000	+	10.3923i	−0.202145	+	0.350126i	0.747074	+	0.664741i	$0.231458\pi$
$882$	10.5000	+	6.06218i	0.353553	+	0.204124i
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		0			0
$885$		0			0
$886$	−40.5000	−	23.3827i	−1.36062	−	0.785557i
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	−1.50000	−	2.59808i	−0.0503367	−	0.0871857i
$889$		0			0
$890$		0			0
$891$	−1.50000	+	0.866025i	−0.0502519	+	0.0290129i
$892$		−	10.3923i		−	0.347960i
$893$		0			0
$894$	6.00000	−	10.3923i	0.200670	−	0.347571i
$895$		0			0
$896$		0			0
$897$	−7.50000	−	7.79423i	−0.250418	−	0.260242i
$898$	−30.0000			−1.00111
$899$		0			0
$900$		0			0
$901$		0			0
$902$			10.3923i			0.346026i
$903$		0			0
$904$	9.00000	−	5.19615i	0.299336	−	0.172821i
$905$		0			0
$906$	3.00000	+	5.19615i	0.0996683	+	0.172631i
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$	−25.5000	−	14.7224i	−0.846247	−	0.488581i
$909$	18.0000			0.597022
$910$		0			0
$911$	−57.0000			−1.88849			−0.944247	−	0.329238i	$-0.893208\pi$
$911$	−57.0000			−1.88849			−0.944247	+	0.329238i	$0.893208\pi$
$912$		0			0
$913$	−7.50000	+	12.9904i	−0.248214	+	0.429919i
$914$	13.5000	+	23.3827i	0.446540	+	0.773431i
$915$		0			0
$916$	22.5000	−	12.9904i	0.743421	−	0.429214i
$917$		0			0
$918$		0			0
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	0.882048	−	0.471160i	$-0.156165\pi$
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	−0.849061	+	0.528295i	$0.822831\pi$
$920$		0			0
$921$	−27.0000	−	15.5885i	−0.889680	−	0.513657i
$922$	−48.0000			−1.58080
$923$	−22.5000	+	21.6506i	−0.740597	+	0.712639i
$924$		0			0
$925$		0			0
$926$	−21.0000	+	36.3731i	−0.690103	+	1.19529i
$927$	−7.00000	−	12.1244i	−0.229910	−	0.398216i
$928$		0			0
$929$	−27.0000	+	15.5885i	−0.885841	+	0.511441i	−0.872580	−	0.488471i	$-0.837555\pi$
$929$	−27.0000	+	15.5885i	−0.885841	+	0.511441i	−0.0132613	+	0.999912i	$0.504221\pi$
$930$		0			0
$931$		0			0
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$	−1.50000	+	2.59808i	−0.0491078	+	0.0850572i
$934$	49.5000	+	28.5788i	1.61969	+	0.935128i
$935$		0			0
$936$	−4.50000	+	4.33013i	−0.147087	+	0.141535i
$937$	−47.0000			−1.53542			−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000			−1.53542			−0.767712	+	0.640796i	$0.778605\pi$
$938$		0			0
$939$	−8.50000	+	14.7224i	−0.277387	+	0.480448i
$940$		0			0
$941$			31.1769i			1.01634i	0.861257	+	0.508169i	$0.169678\pi$
$941$			31.1769i			1.01634i	−0.861257	+	0.508169i	$0.830322\pi$
$942$	−1.50000	+	0.866025i	−0.0488726	+	0.0282166i
$943$	9.00000	−	5.19615i	0.293080	−	0.169210i
$944$			51.9615i			1.69120i
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	−13.5000	−	7.79423i	−0.438691	−	0.253278i	0.264351	−	0.964426i	$-0.414842\pi$
$947$	−13.5000	−	7.79423i	−0.438691	−	0.253278i	−0.703042	+	0.711148i	$0.748176\pi$
$948$	−8.00000			−0.259828
$949$	7.50000	+	30.3109i	0.243460	+	0.983933i
$950$		0			0
$951$	24.0000	+	13.8564i	0.778253	+	0.449325i
$952$		0			0
$953$	−6.00000	−	10.3923i	−0.194359	−	0.336640i	0.752331	−	0.658785i	$-0.228929\pi$
$953$	−6.00000	−	10.3923i	−0.194359	−	0.336640i	−0.946690	+	0.322145i	$0.895596\pi$
$954$		0			0
$955$		0			0
$956$	−4.50000	+	2.59808i	−0.145540	+	0.0840278i
$957$		0			0
$958$	−9.00000	−	15.5885i	−0.290777	−	0.503640i
$959$		0			0
$960$		0			0
$961$	−17.0000			−0.548387
$962$	7.50000	+	7.79423i	0.241810	+	0.251296i
$963$	−12.0000			−0.386695
$964$	18.0000	+	10.3923i	0.579741	+	0.334714i
$965$		0			0
$966$		0			0
$967$			20.7846i			0.668388i	0.942504	+	0.334194i	$0.108464\pi$
$967$			20.7846i			0.668388i	−0.942504	+	0.334194i	$0.891536\pi$
$968$	−12.0000	+	6.92820i	−0.385695	+	0.222681i
$969$		0			0
$970$		0			0
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$		0			0
$974$	30.0000			0.961262
$975$		0			0
$976$	−35.0000			−1.12032
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	0.592898	−	0.805277i	$-0.297984\pi$
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	−0.400941	+	0.916104i	$0.631317\pi$
$978$	−3.00000	+	5.19615i	−0.0959294	+	0.166155i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	7.50000	−	4.33013i	0.239457	−	0.138250i
$982$	40.5000	−	23.3827i	1.29241	−	0.746171i
$983$		−	10.3923i		−	0.331463i	−0.986171	−	0.165732i	$-0.947001\pi$
$983$		−	10.3923i		−	0.331463i	0.986171	−	0.165732i	$-0.0529985\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30.0000			0.953945
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	−18.0000	−	31.1769i	−0.571501	−	0.989868i
$993$		−	3.46410i		−	0.109930i
$994$		0			0
$995$		0			0
$996$			8.66025i			0.274411i
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−33.0000	+	57.1577i	−1.04460	+	1.80929i
$999$	−1.50000	−	0.866025i	−0.0474579	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.g.901.1	yes	2
5.2	odd	4		975.2.w.c.199.1		4
5.3	odd	4		975.2.w.c.199.2		4
5.4	even	2		975.2.bc.a.901.1	yes	2
13.10	even	6	inner	975.2.bc.g.751.1	yes	2
65.23	odd	12		975.2.w.c.49.1		4
65.49	even	6		975.2.bc.a.751.1	✓	2
65.62	odd	12		975.2.w.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.c.49.1		4	65.23	odd	12
975.2.w.c.49.2		4	65.62	odd	12
975.2.w.c.199.1		4	5.2	odd	4
975.2.w.c.199.2		4	5.3	odd	4
975.2.bc.a.751.1	✓	2	65.49	even	6
975.2.bc.a.901.1	yes	2	5.4	even	2
975.2.bc.g.751.1	yes	2	13.10	even	6	inner
975.2.bc.g.901.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 0.866025i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +(2.50000 - 4.33013i) q^{16} -1.73205i q^{18} +(1.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(6.00000 + 1.73205i) q^{26} -1.00000 q^{27} -6.92820i q^{31} +(4.50000 - 2.59808i) q^{32} +(1.50000 - 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{36} +(1.50000 + 0.866025i) q^{37} +(1.00000 - 3.46410i) q^{39} +(3.00000 + 1.73205i) q^{41} +(5.00000 + 8.66025i) q^{43} +1.73205i q^{44} +(4.50000 - 2.59808i) q^{46} -3.46410i q^{47} +(-2.50000 - 4.33013i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(2.50000 + 2.59808i) q^{52} +(-1.50000 - 0.866025i) q^{54} +(-9.00000 + 5.19615i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(6.00000 - 10.3923i) q^{62} -1.00000 q^{64} +3.00000 q^{66} +(3.00000 + 1.73205i) q^{67} +(-1.50000 - 2.59808i) q^{69} +(-7.50000 + 4.33013i) q^{71} +(-1.50000 + 0.866025i) q^{72} +8.66025i q^{73} +(1.50000 + 2.59808i) q^{74} +(4.50000 - 4.33013i) q^{78} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} +8.66025i q^{83} +17.3205i q^{86} +(1.50000 - 2.59808i) q^{88} +(-6.00000 - 3.46410i) q^{89} +3.00000 q^{92} +(-6.00000 - 3.46410i) q^{93} +(3.00000 - 5.19615i) q^{94} -5.19615i q^{96} +(7.50000 - 4.33013i) q^{97} +(-10.5000 + 6.06218i) q^{98} -1.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + q^{3} + q^{4} + 3 q^{6} - q^{9} + 3 q^{11} + 2 q^{12} + 7 q^{13} + 5 q^{16} + 3 q^{22} + 3 q^{23} - 3 q^{24} + 12 q^{26} - 2 q^{27} + 9 q^{32} + 3 q^{33} + q^{36} + 3 q^{37} + 2 q^{39}+ \cdots - 21 q^{98}+O(q^{100}) \) 2 * q + 3 * q^2 + q^3 + q^4 + 3 * q^6 - q^9 + 3 * q^11 + 2 * q^12 + 7 * q^13 + 5 * q^16 + 3 * q^22 + 3 * q^23 - 3 * q^24 + 12 * q^26 - 2 * q^27 + 9 * q^32 + 3 * q^33 + q^36 + 3 * q^37 + 2 * q^39 + 6 * q^41 + 10 * q^43 + 9 * q^46 - 5 * q^48 - 7 * q^49 + 5 * q^52 - 3 * q^54 - 18 * q^59 - 7 * q^61 + 12 * q^62 - 2 * q^64 + 6 * q^66 + 6 * q^67 - 3 * q^69 - 15 * q^71 - 3 * q^72 + 3 * q^74 + 9 * q^78 - 16 * q^79 - q^81 + 6 * q^82 + 3 * q^88 - 12 * q^89 + 6 * q^92 - 12 * q^93 + 6 * q^94 + 15 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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