LMFDB - Embedded newform 975.2.w.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

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, 3, 5]))

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

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

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.49
Dual form			975.2.w.c.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 1.50000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{6} +1.73205 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 - 0.866025i) q^{11} +1.00000i q^{12} +(0.866025 - 3.50000i) q^{13} +(2.50000 + 4.33013i) q^{16} +1.73205 q^{18} +(2.59808 + 1.50000i) q^{22} +(2.59808 - 1.50000i) q^{23} +(1.50000 - 0.866025i) q^{24} +(6.00000 - 1.73205i) q^{26} -1.00000i q^{27} +6.92820i q^{31} +(-2.59808 + 4.50000i) q^{32} +(0.866025 - 1.50000i) q^{33} +(0.500000 + 0.866025i) q^{36} +(0.866025 + 1.50000i) q^{37} +(-1.00000 - 3.46410i) q^{39} +(3.00000 - 1.73205i) q^{41} +(-8.66025 - 5.00000i) q^{43} +1.73205i q^{44} +(4.50000 + 2.59808i) q^{46} -3.46410 q^{47} +(4.33013 + 2.50000i) q^{48} +(3.50000 + 6.06218i) q^{49} +(2.59808 + 2.50000i) q^{52} +(1.50000 - 0.866025i) q^{54} +(9.00000 + 5.19615i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-10.3923 + 6.00000i) q^{62} +1.00000 q^{64} +3.00000 q^{66} +(1.73205 + 3.00000i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-7.50000 - 4.33013i) q^{71} +(0.866025 - 1.50000i) q^{72} -8.66025 q^{73} +(-1.50000 + 2.59808i) q^{74} +(4.33013 - 4.50000i) q^{78} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} -8.66025 q^{83} -17.3205i q^{86} +(2.59808 - 1.50000i) q^{88} +(6.00000 - 3.46410i) q^{89} +3.00000i q^{92} +(3.46410 + 6.00000i) q^{93} +(-3.00000 - 5.19615i) q^{94} +5.19615i q^{96} +(-4.33013 + 7.50000i) q^{97} +(-6.06218 + 10.5000i) q^{98} -1.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 6 q^{6} + 2 q^{9} + 6 q^{11} + 10 q^{16} + 6 q^{24} + 24 q^{26} + 2 q^{36} - 4 q^{39} + 12 q^{41} + 18 q^{46} + 14 q^{49} + 6 q^{54} + 36 q^{59} - 14 q^{61} + 4 q^{64} + 12 q^{66} + 6 q^{69}+ \cdots - 12 q^{94}+O(q^{100}) $ 4 * q - 2 * q^4 + 6 * q^6 + 2 * q^9 + 6 * q^11 + 10 * q^16 + 6 * q^24 + 24 * q^26 + 2 * q^36 - 4 * q^39 + 12 * q^41 + 18 * q^46 + 14 * q^49 + 6 * q^54 + 36 * q^59 - 14 * q^61 + 4 * q^64 + 12 * q^66 + 6 * q^69 - 30 * q^71 - 6 * q^74 + 32 * q^79 - 2 * q^81 + 24 * q^89 - 12 * q^94

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−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		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	1.73205			0.612372
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$			1.00000i			0.288675i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$		0			0
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	1.73205			0.408248
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$		0			0
$22$	2.59808	+	1.50000i	0.553912	+	0.319801i
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$		0			0
$26$	6.00000	−	1.73205i	1.17670	−	0.339683i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$			6.92820i			1.24434i	0.782881	+	0.622171i	$0.213749\pi$
$31$			6.92820i			1.24434i	−0.782881	+	0.622171i	$0.786251\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	0.866025	−	1.50000i	0.150756	−	0.261116i
$34$		0			0
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	0.866025	+	1.50000i	0.142374	+	0.246598i	0.928390	−	0.371607i	$-0.121193\pi$
$37$	0.866025	+	1.50000i	0.142374	+	0.246598i	−0.786016	+	0.618206i	$0.787860\pi$
$38$		0			0
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$		0			0
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	−0.247099	−	0.968990i	$-0.579477\pi$
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	0.715621	+	0.698489i	$0.246144\pi$
$42$		0			0
$43$	−8.66025	−	5.00000i	−1.32068	−	0.762493i	−0.336840	−	0.941562i	$-0.609358\pi$
$43$	−8.66025	−	5.00000i	−1.32068	−	0.762493i	−0.983836	+	0.179069i	$0.942691\pi$
$44$			1.73205i			0.261116i
$45$		0			0
$46$	4.50000	+	2.59808i	0.663489	+	0.383065i
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$	4.33013	+	2.50000i	0.625000	+	0.360844i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$		0			0
$51$		0			0
$52$	2.59808	+	2.50000i	0.360288	+	0.346688i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	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	$-0.0968372\pi$
$59$	9.00000	+	5.19615i	1.17170	+	0.676481i	0.217620	+	0.976034i	$0.430171\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−10.3923	+	6.00000i	−1.31982	+	0.762001i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	1.73205	+	3.00000i	0.211604	+	0.366508i	0.952217	−	0.305424i	$-0.0987981\pi$
$67$	1.73205	+	3.00000i	0.211604	+	0.366508i	−0.740613	+	0.671932i	$0.765465\pi$
$68$		0			0
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$	−7.50000	−	4.33013i	−0.890086	−	0.513892i	−0.0161155	−	0.999870i	$-0.505130\pi$
$71$	−7.50000	−	4.33013i	−0.890086	−	0.513892i	−0.873971	+	0.485979i	$0.838463\pi$
$72$	0.866025	−	1.50000i	0.102062	−	0.176777i
$73$	−8.66025			−1.01361			−0.506803	−	0.862062i	$-0.669173\pi$
$73$	−8.66025			−1.01361			−0.506803	+	0.862062i	$0.669173\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$		0			0
$76$		0			0
$77$		0			0
$78$	4.33013	−	4.50000i	0.490290	−	0.509525i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.19615	+	3.00000i	0.573819	+	0.331295i
$83$	−8.66025			−0.950586			−0.475293	−	0.879827i	$-0.657658\pi$
$83$	−8.66025			−0.950586			−0.475293	+	0.879827i	$0.657658\pi$
$84$		0			0
$85$		0			0
$86$		−	17.3205i		−	1.86772i
$87$		0			0
$88$	2.59808	−	1.50000i	0.276956	−	0.159901i
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$		0			0
$91$		0			0
$92$			3.00000i			0.312772i
$93$	3.46410	+	6.00000i	0.359211	+	0.622171i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$			5.19615i			0.530330i
$97$	−4.33013	+	7.50000i	−0.439658	+	0.761510i	−0.997663	−	0.0683279i	$-0.978234\pi$
$97$	−4.33013	+	7.50000i	−0.439658	+	0.761510i	0.558005	+	0.829837i	$0.311567\pi$
$98$	−6.06218	+	10.5000i	−0.612372	+	1.06066i
$99$		−	1.73205i		−	0.174078i
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$		0			0
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	1.50000	−	6.06218i	0.147087	−	0.594445i
$105$		0			0
$106$		0			0
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.909624	−	0.415432i	$-0.863630\pi$
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.0950377	+	0.995474i	$0.530297\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			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
$113$	−5.19615	−	3.00000i	−0.488813	−	0.282216i	0.235269	−	0.971930i	$-0.424403\pi$
$113$	−5.19615	−	3.00000i	−0.488813	−	0.282216i	−0.724082	+	0.689714i	$0.757736\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.59808	−	2.50000i	−0.240192	−	0.231125i
$118$			18.0000i			1.65703i
$119$		0			0
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	−12.1244			−1.09769
$123$	1.73205	−	3.00000i	0.156174	−	0.270501i
$124$	−6.00000	−	3.46410i	−0.538816	−	0.311086i
$125$		0			0
$126$		0			0
$127$	−1.73205	+	1.00000i	−0.153695	+	0.0887357i	−0.574875	−	0.818241i	$-0.694949\pi$
$127$	−1.73205	+	1.00000i	−0.153695	+	0.0887357i	0.421180	+	0.906977i	$0.361616\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	−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	$0.675644\pi$
$132$	0.866025	+	1.50000i	0.0753778	+	0.130558i
$133$		0			0
$134$	−3.00000	+	5.19615i	−0.259161	+	0.448879i
$135$		0			0
$136$		0			0
$137$	10.3923	−	18.0000i	0.887875	−	1.53784i	0.0454914	−	0.998965i	$-0.485515\pi$
$137$	10.3923	−	18.0000i	0.887875	−	1.53784i	0.842383	−	0.538879i	$-0.181152\pi$
$138$	5.19615			0.442326
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	−0.996335	−	0.0855324i	$-0.972741\pi$
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	0.572241	+	0.820086i	$0.306074\pi$
$140$		0			0
$141$	−3.00000	+	1.73205i	−0.252646	+	0.145865i
$142$		−	15.0000i		−	1.25877i
$143$	−1.73205	−	6.00000i	−0.144841	−	0.501745i
$144$	5.00000			0.416667
$145$		0			0
$146$	−7.50000	−	12.9904i	−0.620704	−	1.07509i
$147$	6.06218	+	3.50000i	0.500000	+	0.288675i
$148$	−1.73205			−0.142374
$149$	−6.00000	−	3.46410i	−0.491539	−	0.283790i	0.233674	−	0.972315i	$-0.424925\pi$
$149$	−6.00000	−	3.46410i	−0.491539	−	0.283790i	−0.725213	+	0.688525i	$0.758259\pi$
$150$		0			0
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	3.50000	+	0.866025i	0.280224	+	0.0693375i
$157$		−	1.00000i		−	0.0798087i	−0.999204	−	0.0399043i	$-0.987295\pi$
$157$		−	1.00000i		−	0.0798087i	0.999204	−	0.0399043i	$-0.0127053\pi$
$158$	6.92820	+	12.0000i	0.551178	+	0.954669i
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.866025	−	1.50000i	0.0680414	−	0.117851i
$163$	−1.73205	+	3.00000i	−0.135665	+	0.234978i	−0.925851	−	0.377888i	$-0.876650\pi$
$163$	−1.73205	+	3.00000i	−0.135665	+	0.234978i	0.790186	+	0.612866i	$0.209984\pi$
$164$			3.46410i			0.270501i
$165$		0			0
$166$	−7.50000	−	12.9904i	−0.582113	−	1.00825i
$167$	−4.33013	−	7.50000i	−0.335075	−	0.580367i	0.648424	−	0.761279i	$-0.275428\pi$
$167$	−4.33013	−	7.50000i	−0.335075	−	0.580367i	−0.983499	+	0.180912i	$0.942095\pi$
$168$		0			0
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$		0			0
$172$	8.66025	−	5.00000i	0.660338	−	0.381246i
$173$	−20.7846	−	12.0000i	−1.58022	−	0.912343i	−0.994826	−	0.101598i	$-0.967605\pi$
$173$	−20.7846	−	12.0000i	−1.58022	−	0.912343i	−0.585399	−	0.810745i	$-0.699062\pi$
$174$		0			0
$175$		0			0
$176$	7.50000	+	4.33013i	0.565334	+	0.326396i
$177$	10.3923			0.781133
$178$	10.3923	+	6.00000i	0.778936	+	0.449719i
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$		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
$183$			7.00000i			0.517455i
$184$	4.50000	−	2.59808i	0.331744	−	0.191533i
$185$		0			0
$186$	−6.00000	+	10.3923i	−0.439941	+	0.762001i
$187$		0			0
$188$	1.73205	−	3.00000i	0.126323	−	0.218797i
$189$		0			0
$190$		0			0
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	−0.981635	−	0.190767i	$-0.938902\pi$
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	0.656027	+	0.754738i	$0.272236\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	4.33013	+	7.50000i	0.311689	+	0.539862i	0.978728	−	0.205161i	$-0.0657718\pi$
$193$	4.33013	+	7.50000i	0.311689	+	0.539862i	−0.667039	+	0.745023i	$0.732439\pi$
$194$	−15.0000			−1.07694
$195$		0			0
$196$	−7.00000			−0.500000
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	0.989598	−	0.143862i	$-0.0459522\pi$
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	−0.619387	+	0.785086i	$0.712619\pi$
$198$	2.59808	−	1.50000i	0.184637	−	0.106600i
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$		0			0
$201$	3.00000	+	1.73205i	0.211604	+	0.122169i
$202$	15.5885	−	27.0000i	1.09680	−	1.89971i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	21.0000	−	12.1244i	1.46314	−	0.844744i
$207$		−	3.00000i		−	0.208514i
$208$	17.3205	−	5.00000i	1.20096	−	0.346688i
$209$		0			0
$210$		0			0
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$		0			0
$213$	−8.66025			−0.593391
$214$	−18.0000	−	10.3923i	−1.23045	−	0.710403i
$215$		0			0
$216$		−	1.73205i		−	0.117851i
$217$		0			0
$218$	−12.9904	+	7.50000i	−0.879820	+	0.507964i
$219$	−7.50000	+	4.33013i	−0.506803	+	0.292603i
$220$		0			0
$221$		0			0
$222$			3.00000i			0.201347i
$223$	5.19615	+	9.00000i	0.347960	+	0.602685i	0.985887	−	0.167412i	$-0.0535411\pi$
$223$	5.19615	+	9.00000i	0.347960	+	0.602685i	−0.637927	+	0.770097i	$0.720208\pi$
$224$		0			0
$225$		0			0
$226$		−	10.3923i		−	0.691286i
$227$	14.7224	−	25.5000i	0.977162	−	1.69249i	0.304555	−	0.952495i	$-0.401492\pi$
$227$	14.7224	−	25.5000i	0.977162	−	1.69249i	0.672607	−	0.740000i	$-0.265174\pi$
$228$		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
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	1.50000	−	6.06218i	0.0980581	−	0.396297i
$235$		0			0
$236$	−9.00000	+	5.19615i	−0.585850	+	0.338241i
$237$	6.92820	−	4.00000i	0.450035	−	0.259828i
$238$		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	0.951180	−	0.308637i	$-0.0998729\pi$
$241$	18.0000	+	10.3923i	1.15948	+	0.669427i	0.208302	+	0.978065i	$0.433206\pi$
$242$	−13.8564			−0.890724
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.50000	−	6.06218i	−0.224065	−	0.388091i
$245$		0			0
$246$	6.00000			0.382546
$247$		0			0
$248$			12.0000i			0.762001i
$249$	−7.50000	+	4.33013i	−0.475293	+	0.274411i
$250$		0			0
$251$	−13.5000	+	23.3827i	−0.852112	+	1.47590i	0.0271858	+	0.999630i	$0.491345\pi$
$251$	−13.5000	+	23.3827i	−0.852112	+	1.47590i	−0.879298	+	0.476272i	$0.841988\pi$
$252$		0			0
$253$	2.59808	−	4.50000i	0.163340	−	0.282913i
$254$	−3.00000	−	1.73205i	−0.188237	−	0.108679i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	−0.653231	−	0.757159i	$-0.726587\pi$
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	0.329104	+	0.944294i	$0.393253\pi$
$258$	−8.66025	−	15.0000i	−0.539164	−	0.933859i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−10.3923	−	18.0000i	−0.642039	−	1.11204i
$263$	12.9904	−	7.50000i	0.801021	−	0.462470i	−0.0428069	−	0.999083i	$-0.513630\pi$
$263$	12.9904	−	7.50000i	0.801021	−	0.462470i	0.843828	+	0.536614i	$0.180297\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$		0			0
$266$		0			0
$267$	3.46410	−	6.00000i	0.212000	−	0.367194i
$268$	−3.46410			−0.211604
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	12.0000	−	6.92820i	0.728948	−	0.420858i	−0.0890891	−	0.996024i	$-0.528396\pi$
$271$	12.0000	−	6.92820i	0.728948	−	0.420858i	0.818037	+	0.575165i	$0.195062\pi$
$272$		0			0
$273$		0			0
$274$	36.0000			2.17484
$275$		0			0
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	21.6506	+	12.5000i	1.30086	+	0.751052i	0.980552	−	0.196261i	$-0.0628800\pi$
$277$	21.6506	+	12.5000i	1.30086	+	0.751052i	0.320309	+	0.947313i	$0.396213\pi$
$278$	−17.3205			−1.03882
$279$	6.00000	+	3.46410i	0.359211	+	0.207390i
$280$		0			0
$281$		−	13.8564i		−	0.826604i	−0.910594	−	0.413302i	$-0.864375\pi$
$281$		−	13.8564i		−	0.826604i	0.910594	−	0.413302i	$-0.135625\pi$
$282$	−5.19615	−	3.00000i	−0.309426	−	0.178647i
$283$	27.7128	−	16.0000i	1.64736	−	0.951101i	0.669238	−	0.743048i	$-0.266621\pi$
$283$	27.7128	−	16.0000i	1.64736	−	0.951101i	0.978117	−	0.208053i	$-0.0667128\pi$
$284$	7.50000	−	4.33013i	0.445043	−	0.256946i
$285$		0			0
$286$	7.50000	−	7.79423i	0.443484	−	0.460882i
$287$		0			0
$288$	2.59808	+	4.50000i	0.153093	+	0.265165i
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$			8.66025i			0.507673i
$292$	4.33013	−	7.50000i	0.253402	−	0.438904i
$293$	−8.66025	+	15.0000i	−0.505937	+	0.876309i	0.494039	+	0.869440i	$0.335520\pi$
$293$	−8.66025	+	15.0000i	−0.505937	+	0.876309i	−0.999976	+	0.00686959i	$0.997813\pi$
$294$			12.1244i			0.707107i
$295$		0			0
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	−0.866025	−	1.50000i	−0.0502519	−	0.0870388i
$298$		−	12.0000i		−	0.695141i
$299$	−3.00000	−	10.3923i	−0.173494	−	0.601003i
$300$		0			0
$301$		0			0
$302$	5.19615	−	3.00000i	0.299005	−	0.172631i
$303$	−15.5885	−	9.00000i	−0.895533	−	0.517036i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−31.1769			−1.77936			−0.889680	−	0.456584i	$-0.849073\pi$
$307$	−31.1769			−1.77936			−0.889680	+	0.456584i	$0.849073\pi$
$308$		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	$0.527107\pi$
$312$	−1.73205	−	6.00000i	−0.0980581	−	0.339683i
$313$			17.0000i			0.960897i	0.877023	+	0.480448i	$0.159526\pi$
$313$			17.0000i			0.960897i	−0.877023	+	0.480448i	$0.840474\pi$
$314$	1.50000	−	0.866025i	0.0846499	−	0.0488726i
$315$		0			0
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	27.7128			1.55651			0.778253	−	0.627950i	$-0.216106\pi$
$317$	27.7128			1.55651			0.778253	+	0.627950i	$0.216106\pi$
$318$		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
$327$	4.33013	+	7.50000i	0.239457	+	0.414751i
$328$	5.19615	−	3.00000i	0.286910	−	0.165647i
$329$		0			0
$330$		0			0
$331$	3.00000	+	1.73205i	0.164895	+	0.0952021i	0.580176	−	0.814491i	$-0.302984\pi$
$331$	3.00000	+	1.73205i	0.164895	+	0.0952021i	−0.415282	+	0.909693i	$0.636317\pi$
$332$	4.33013	−	7.50000i	0.237647	−	0.411616i
$333$	1.73205			0.0949158
$334$	7.50000	−	12.9904i	0.410382	−	0.710802i
$335$		0			0
$336$		0			0
$337$		−	14.0000i		−	0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$		−	14.0000i		−	0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	−0.866025	−	22.5000i	−0.0471056	−	1.22384i
$339$	−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
$347$	2.59808	+	1.50000i	0.139472	+	0.0805242i	0.568112	−	0.822951i	$-0.307674\pi$
$347$	2.59808	+	1.50000i	0.139472	+	0.0805242i	−0.428640	+	0.903475i	$0.641007\pi$
$348$		0			0
$349$	−13.5000	+	7.79423i	−0.722638	+	0.417215i	−0.815723	−	0.578443i	$-0.803661\pi$
$349$	−13.5000	+	7.79423i	−0.722638	+	0.417215i	0.0930846	+	0.995658i	$0.470327\pi$
$350$		0			0
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$			9.00000i			0.479702i
$353$	8.66025	+	15.0000i	0.460939	+	0.798369i	0.999008	−	0.0445312i	$-0.0141794\pi$
$353$	8.66025	+	15.0000i	0.460939	+	0.798369i	−0.538069	+	0.842901i	$0.680846\pi$
$354$	9.00000	+	15.5885i	0.478345	+	0.828517i
$355$		0			0
$356$			6.92820i			0.367194i
$357$		0			0
$358$	−7.79423	+	13.5000i	−0.411938	+	0.713497i
$359$			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
$362$	−6.06218	−	10.5000i	−0.318621	−	0.551868i
$363$			8.00000i			0.419891i
$364$		0			0
$365$		0			0
$366$	−10.5000	+	6.06218i	−0.548844	+	0.316875i
$367$	−24.2487	+	14.0000i	−1.26577	+	0.730794i	−0.974185	−	0.225750i	$-0.927517\pi$
$367$	−24.2487	+	14.0000i	−1.26577	+	0.730794i	−0.291587	+	0.956544i	$0.594183\pi$
$368$	12.9904	+	7.50000i	0.677170	+	0.390965i
$369$		−	3.46410i		−	0.180334i
$370$		0			0
$371$		0			0
$372$	−6.92820			−0.359211
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	0.762299	−	0.647225i	$-0.224071\pi$
$373$	11.2583	+	6.50000i	0.582934	+	0.336557i	−0.179364	+	0.983783i	$0.557404\pi$
$374$		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	$-0.414567\pi$
$379$	24.0000	−	13.8564i	1.23280	−	0.711756i	0.967612	+	0.252442i	$0.0812336\pi$
$380$		0			0
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	−15.5885			−0.797575
$383$	11.2583	−	19.5000i	0.575274	−	0.996403i	−0.420738	−	0.907182i	$-0.638229\pi$
$383$	11.2583	−	19.5000i	0.575274	−	0.996403i	0.996012	−	0.0892213i	$-0.0284378\pi$
$384$	10.5000	+	6.06218i	0.535826	+	0.309359i
$385$		0			0
$386$	−7.50000	+	12.9904i	−0.381740	+	0.661193i
$387$	−8.66025	+	5.00000i	−0.440225	+	0.254164i
$388$	−4.33013	−	7.50000i	−0.219829	−	0.380755i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$		0			0
$392$	6.06218	+	10.5000i	0.306186	+	0.530330i
$393$	−10.3923	+	6.00000i	−0.524222	+	0.302660i
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$		0			0
$396$	1.50000	+	0.866025i	0.0753778	+	0.0435194i
$397$	−13.8564	+	24.0000i	−0.695433	+	1.20453i	0.274601	+	0.961558i	$0.411454\pi$
$397$	−13.8564	+	24.0000i	−0.695433	+	1.20453i	−0.970034	+	0.242967i	$0.921879\pi$
$398$	−24.2487			−1.21548
$399$		0			0
$400$		0			0
$401$	24.0000	−	13.8564i	1.19850	−	0.691956i	0.238282	−	0.971196i	$-0.423416\pi$
$401$	24.0000	−	13.8564i	1.19850	−	0.691956i	0.960221	+	0.279240i	$0.0900826\pi$
$402$			6.00000i			0.299253i
$403$	24.2487	+	6.00000i	1.20791	+	0.298881i
$404$	18.0000			0.895533
$405$		0			0
$406$		0			0
$407$	2.59808	+	1.50000i	0.128782	+	0.0743522i
$408$		0			0
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	0.640951	−	0.767582i	$-0.278540\pi$
$409$	6.00000	+	3.46410i	0.296681	+	0.171289i	−0.344270	+	0.938871i	$0.611874\pi$
$410$		0			0
$411$		−	20.7846i		−	1.02523i
$412$	12.1244	+	7.00000i	0.597324	+	0.344865i
$413$		0			0
$414$	4.50000	−	2.59808i	0.221163	−	0.127688i
$415$		0			0
$416$	13.5000	+	12.9904i	0.661892	+	0.636906i
$417$			10.0000i			0.489702i
$418$		0			0
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	0.989000	−	0.147918i	$-0.0472572\pi$
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	−0.622601	+	0.782540i	$0.713924\pi$
$420$		0			0
$421$		−	12.1244i		−	0.590905i	−0.955357	−	0.295452i	$-0.904530\pi$
$421$		−	12.1244i		−	0.590905i	0.955357	−	0.295452i	$-0.0954704\pi$
$422$	−17.3205	+	30.0000i	−0.843149	+	1.46038i
$423$	−1.73205	+	3.00000i	−0.0842152	+	0.145865i
$424$		0			0
$425$		0			0
$426$	−7.50000	−	12.9904i	−0.363376	−	0.629386i
$427$		0			0
$428$		−	12.0000i		−	0.580042i
$429$	−4.50000	−	4.33013i	−0.217262	−	0.209061i
$430$		0			0
$431$	10.5000	−	6.06218i	0.505767	−	0.292005i	−0.225325	−	0.974284i	$-0.572344\pi$
$431$	10.5000	−	6.06218i	0.505767	−	0.292005i	0.731092	+	0.682279i	$0.239011\pi$
$432$	4.33013	−	2.50000i	0.208333	−	0.120281i
$433$	−9.52628	−	5.50000i	−0.457804	−	0.264313i	0.253317	−	0.967383i	$-0.418479\pi$
$433$	−9.52628	−	5.50000i	−0.457804	−	0.264313i	−0.711120	+	0.703070i	$0.751812\pi$
$434$		0			0
$435$		0			0
$436$	−7.50000	−	4.33013i	−0.359185	−	0.207375i
$437$		0			0
$438$	−12.9904	−	7.50000i	−0.620704	−	0.358364i
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	0.814344	−	0.580383i	$-0.197097\pi$
$439$	−2.00000	−	3.46410i	−0.0954548	−	0.165333i	−0.909798	+	0.415051i	$0.863764\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$			27.0000i			1.28281i	0.767203	+	0.641404i	$0.221648\pi$
$443$			27.0000i			1.28281i	−0.767203	+	0.641404i	$0.778352\pi$
$444$	−1.50000	+	0.866025i	−0.0711868	+	0.0410997i
$445$		0			0
$446$	−9.00000	+	15.5885i	−0.426162	+	0.738135i
$447$	−6.92820			−0.327693
$448$		0			0
$449$	15.0000	+	8.66025i	0.707894	+	0.408703i	0.810281	−	0.586042i	$-0.199315\pi$
$449$	15.0000	+	8.66025i	0.707894	+	0.408703i	−0.102387	+	0.994745i	$0.532648\pi$
$450$		0			0
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$	5.19615	−	3.00000i	0.244406	−	0.141108i
$453$	−1.73205	−	3.00000i	−0.0813788	−	0.140952i
$454$	51.0000			2.39355
$455$		0			0
$456$		0			0
$457$	7.79423	+	13.5000i	0.364599	+	0.631503i	0.988712	−	0.149831i	$-0.0478729\pi$
$457$	7.79423	+	13.5000i	0.364599	+	0.631503i	−0.624113	+	0.781334i	$0.714540\pi$
$458$	38.9711	−	22.5000i	1.82100	−	1.05136i
$459$		0			0
$460$		0			0
$461$	−24.0000	−	13.8564i	−1.11779	−	0.645357i	−0.176955	−	0.984219i	$-0.556625\pi$
$461$	−24.0000	−	13.8564i	−1.11779	−	0.645357i	−0.940836	+	0.338862i	$0.889958\pi$
$462$		0			0
$463$	−24.2487			−1.12693			−0.563467	−	0.826139i	$-0.690533\pi$
$463$	−24.2487			−1.12693			−0.563467	+	0.826139i	$0.690533\pi$
$464$		0			0
$465$		0			0
$466$	27.0000	−	15.5885i	1.25075	−	0.722121i
$467$			33.0000i			1.52706i	0.645774	+	0.763529i	$0.276535\pi$
$467$			33.0000i			1.52706i	−0.645774	+	0.763529i	$0.723465\pi$
$468$	3.46410	−	1.00000i	0.160128	−	0.0462250i
$469$		0			0
$470$		0			0
$471$	−0.500000	−	0.866025i	−0.0230388	−	0.0399043i
$472$	15.5885	+	9.00000i	0.717517	+	0.414259i
$473$	−17.3205			−0.796398
$474$	12.0000	+	6.92820i	0.551178	+	0.318223i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−7.79423	+	4.50000i	−0.356500	+	0.205825i
$479$	9.00000	−	5.19615i	0.411220	−	0.237418i	−0.280094	−	0.959973i	$-0.590365\pi$
$479$	9.00000	−	5.19615i	0.411220	−	0.237418i	0.691314	+	0.722554i	$0.257032\pi$
$480$		0			0
$481$	6.00000	−	1.73205i	0.273576	−	0.0789747i
$482$			36.0000i			1.63976i
$483$		0			0
$484$	−4.00000	−	6.92820i	−0.181818	−	0.314918i
$485$		0			0
$486$		−	1.73205i		−	0.0785674i
$487$	−8.66025	+	15.0000i	−0.392434	+	0.679715i	−0.992770	−	0.120033i	$-0.961700\pi$
$487$	−8.66025	+	15.0000i	−0.392434	+	0.679715i	0.600336	+	0.799748i	$0.295033\pi$
$488$	−6.06218	+	10.5000i	−0.274422	+	0.475313i
$489$			3.46410i			0.156652i
$490$		0			0
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	0.991365	+	0.131132i	$0.0418613\pi$
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	−0.382118	+	0.924113i	$0.624805\pi$
$492$	1.73205	+	3.00000i	0.0780869	+	0.135250i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−30.0000	+	17.3205i	−1.34704	+	0.777714i
$497$		0			0
$498$	−12.9904	−	7.50000i	−0.582113	−	0.336083i
$499$			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
$502$	−46.7654			−2.08724
$503$	7.79423	+	4.50000i	0.347527	+	0.200645i	0.663596	−	0.748091i	$-0.269030\pi$
$503$	7.79423	+	4.50000i	0.347527	+	0.200645i	−0.316068	+	0.948736i	$0.602363\pi$
$504$		0			0
$505$		0			0
$506$	9.00000			0.400099
$507$	−12.9904	+	0.500000i	−0.576923	+	0.0222058i
$508$		−	2.00000i		−	0.0887357i
$509$	27.0000	−	15.5885i	1.19675	−	0.690946i	0.236924	−	0.971528i	$-0.423861\pi$
$509$	27.0000	−	15.5885i	1.19675	−	0.690946i	0.959830	+	0.280582i	$0.0905275\pi$
$510$		0			0
$511$		0			0
$512$	−8.66025			−0.382733
$513$		0			0
$514$	−9.00000	−	5.19615i	−0.396973	−	0.229192i
$515$		0			0
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−5.19615	+	3.00000i	−0.228527	+	0.131940i
$518$		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
$523$	−17.3205	+	10.0000i	−0.757373	+	0.437269i	−0.828352	−	0.560208i	$-0.810721\pi$
$523$	−17.3205	+	10.0000i	−0.757373	+	0.437269i	0.0709788	+	0.997478i	$0.477388\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$		0			0
$526$	22.5000	+	12.9904i	0.981047	+	0.566408i
$527$		0			0
$528$	8.66025			0.376889
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$	9.00000	−	5.19615i	0.390567	−	0.225494i
$532$		0			0
$533$	−3.46410	−	12.0000i	−0.150047	−	0.519778i
$534$	12.0000			0.519291
$535$		0			0
$536$	3.00000	+	5.19615i	0.129580	+	0.224440i
$537$	7.79423	+	4.50000i	0.336346	+	0.194189i
$538$	−10.3923			−0.448044
$539$	10.5000	+	6.06218i	0.452267	+	0.261116i
$540$		0			0
$541$		−	29.4449i		−	1.26593i	−0.774179	−	0.632967i	$-0.781837\pi$
$541$		−	29.4449i		−	1.26593i	0.774179	−	0.632967i	$-0.218163\pi$
$542$	20.7846	+	12.0000i	0.892775	+	0.515444i
$543$	−6.06218	+	3.50000i	−0.260153	+	0.150199i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$	10.3923	+	18.0000i	0.443937	+	0.768922i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$		0			0
$551$		0			0
$552$	2.59808	−	4.50000i	0.110581	−	0.191533i
$553$		0			0
$554$			43.3013i			1.83969i
$555$		0			0
$556$	−5.00000	−	8.66025i	−0.212047	−	0.367277i
$557$	−8.66025	−	15.0000i	−0.366947	−	0.635570i	0.622140	−	0.782906i	$-0.286264\pi$
$557$	−8.66025	−	15.0000i	−0.366947	−	0.635570i	−0.989087	+	0.147336i	$0.952930\pi$
$558$			12.0000i			0.508001i
$559$	−25.0000	+	25.9808i	−1.05739	+	1.09887i
$560$		0			0
$561$		0			0
$562$	20.7846	−	12.0000i	0.876746	−	0.506189i
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	0.831614	−	0.555354i	$-0.187417\pi$
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	−0.0651433	+	0.997876i	$0.520750\pi$
$564$		−	3.46410i		−	0.145865i
$565$		0			0
$566$	48.0000	+	27.7128i	2.01759	+	1.16486i
$567$		0			0
$568$	−12.9904	−	7.50000i	−0.545064	−	0.314693i
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−14.0000			−0.585882			−0.292941	−	0.956131i	$-0.594634\pi$
$571$	−14.0000			−0.585882			−0.292941	+	0.956131i	$0.594634\pi$
$572$	6.06218	+	1.50000i	0.253472	+	0.0627182i
$573$			9.00000i			0.375980i
$574$		0			0
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	29.4449			1.22581			0.612903	−	0.790158i	$-0.290002\pi$
$577$	29.4449			1.22581			0.612903	+	0.790158i	$0.290002\pi$
$578$	14.7224	−	25.5000i	0.612372	−	1.06066i
$579$	7.50000	+	4.33013i	0.311689	+	0.179954i
$580$		0			0
$581$		0			0
$582$	−12.9904	+	7.50000i	−0.538469	+	0.310885i
$583$		0			0
$584$	−15.0000			−0.620704
$585$		0			0
$586$	−30.0000			−1.23929
$587$	2.59808	+	4.50000i	0.107234	+	0.185735i	0.914649	−	0.404249i	$-0.132467\pi$
$587$	2.59808	+	4.50000i	0.107234	+	0.185735i	−0.807415	+	0.589984i	$0.799134\pi$
$588$	−6.06218	+	3.50000i	−0.250000	+	0.144338i
$589$		0			0
$590$		0			0
$591$	9.00000	+	5.19615i	0.370211	+	0.213741i
$592$	−4.33013	+	7.50000i	−0.177967	+	0.308248i
$593$	−13.8564			−0.569014			−0.284507	−	0.958674i	$-0.591830\pi$
$593$	−13.8564			−0.569014			−0.284507	+	0.958674i	$0.591830\pi$
$594$	1.50000	−	2.59808i	0.0615457	−	0.106600i
$595$		0			0
$596$	6.00000	−	3.46410i	0.245770	−	0.141895i
$597$			14.0000i			0.572982i
$598$	12.9904	−	13.5000i	0.531216	−	0.552056i
$599$	9.00000			0.367730			0.183865	−	0.982952i	$-0.441139\pi$
$599$	9.00000			0.367730			0.183865	+	0.982952i	$0.441139\pi$
$600$		0			0
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$	3.46410			0.141069
$604$	3.00000	+	1.73205i	0.122068	+	0.0704761i
$605$		0			0
$606$		−	31.1769i		−	1.26648i
$607$	−27.7128	−	16.0000i	−1.12483	−	0.649420i	−0.182199	−	0.983262i	$-0.558322\pi$
$607$	−27.7128	−	16.0000i	−1.12483	−	0.649420i	−0.942629	+	0.333842i	$0.891655\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.00000	+	12.1244i	−0.121367	+	0.490499i
$612$		0			0
$613$	−3.46410	−	6.00000i	−0.139914	−	0.242338i	0.787550	−	0.616251i	$-0.211349\pi$
$613$	−3.46410	−	6.00000i	−0.139914	−	0.242338i	−0.927464	+	0.373913i	$0.878016\pi$
$614$	−27.0000	−	46.7654i	−1.08963	−	1.88730i
$615$		0			0
$616$		0			0
$617$	22.5167	−	39.0000i	0.906487	−	1.57008i	0.0875775	−	0.996158i	$-0.472087\pi$
$617$	22.5167	−	39.0000i	0.906487	−	1.57008i	0.818909	−	0.573923i	$-0.194579\pi$
$618$	12.1244	−	21.0000i	0.487713	−	0.844744i
$619$		−	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
$622$	−2.59808	−	4.50000i	−0.104173	−	0.180434i
$623$		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
$628$	0.866025	+	0.500000i	0.0345582	+	0.0199522i
$629$		0			0
$630$		0			0
$631$	42.0000	+	24.2487i	1.67199	+	0.965326i	0.966521	+	0.256589i	$0.0825987\pi$
$631$	42.0000	+	24.2487i	1.67199	+	0.965326i	0.705473	+	0.708737i	$0.250735\pi$
$632$	13.8564			0.551178
$633$	17.3205	+	10.0000i	0.688428	+	0.397464i
$634$	24.0000	+	41.5692i	0.953162	+	1.65092i
$635$		0			0
$636$		0			0
$637$	24.2487	−	7.00000i	0.960769	−	0.277350i
$638$		0			0
$639$	−7.50000	+	4.33013i	−0.296695	+	0.171297i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$	−20.7846			−0.820303
$643$	−8.66025	+	15.0000i	−0.341527	+	0.591542i	−0.984717	−	0.174165i	$-0.944277\pi$
$643$	−8.66025	+	15.0000i	−0.341527	+	0.591542i	0.643189	+	0.765707i	$0.277611\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−28.5788	+	16.5000i	−1.12355	+	0.648682i	−0.942305	−	0.334756i	$-0.891346\pi$
$647$	−28.5788	+	16.5000i	−1.12355	+	0.648682i	−0.181245	+	0.983438i	$0.558013\pi$
$648$	−0.866025	−	1.50000i	−0.0340207	−	0.0589256i
$649$	18.0000			0.706562
$650$		0			0
$651$		0			0
$652$	−1.73205	−	3.00000i	−0.0678323	−	0.117489i
$653$	41.5692	−	24.0000i	1.62673	−	0.939193i	0.641669	−	0.766982i	$-0.278242\pi$
$653$	41.5692	−	24.0000i	1.62673	−	0.939193i	0.985060	−	0.172211i	$-0.0550911\pi$
$654$	−7.50000	+	12.9904i	−0.293273	+	0.507964i
$655$		0			0
$656$	15.0000	+	8.66025i	0.585652	+	0.338126i
$657$	−4.33013	+	7.50000i	−0.168934	+	0.292603i
$658$		0			0
$659$	16.5000	−	28.5788i	0.642749	−	1.11327i	−0.342068	−	0.939675i	$-0.611127\pi$
$659$	16.5000	−	28.5788i	0.642749	−	1.11327i	0.984817	−	0.173598i	$-0.0555394\pi$
$660$		0			0
$661$	−12.0000	+	6.92820i	−0.466746	+	0.269476i	−0.714877	−	0.699251i	$-0.753517\pi$
$661$	−12.0000	+	6.92820i	−0.466746	+	0.269476i	0.248131	+	0.968727i	$0.420184\pi$
$662$			6.00000i			0.233197i
$663$		0			0
$664$	−15.0000			−0.582113
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$		0			0
$668$	8.66025			0.335075
$669$	9.00000	+	5.19615i	0.347960	+	0.200895i
$670$		0			0
$671$			12.1244i			0.468056i
$672$		0			0
$673$	−14.7224	+	8.50000i	−0.567508	+	0.327651i	−0.756153	−	0.654394i	$-0.772924\pi$
$673$	−14.7224	+	8.50000i	−0.567508	+	0.327651i	0.188645	+	0.982045i	$0.439590\pi$
$674$	21.0000	−	12.1244i	0.808890	−	0.467013i
$675$		0			0
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$		−	36.0000i		−	1.38359i	−0.722093	−	0.691796i	$-0.756820\pi$
$677$		−	36.0000i		−	1.38359i	0.722093	−	0.691796i	$-0.243180\pi$
$678$	−5.19615	−	9.00000i	−0.199557	−	0.345643i
$679$		0			0
$680$		0			0
$681$		−	29.4449i		−	1.12833i
$682$	−10.3923	+	18.0000i	−0.397942	+	0.689256i
$683$	23.3827	−	40.5000i	0.894714	−	1.54969i	0.0605550	−	0.998165i	$-0.480713\pi$
$683$	23.3827	−	40.5000i	0.894714	−	1.54969i	0.834159	−	0.551525i	$-0.185954\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−12.9904	−	22.5000i	−0.495614	−	0.858429i
$688$		−	50.0000i		−	1.90623i
$689$		0			0
$690$		0			0
$691$	−12.0000	+	6.92820i	−0.456502	+	0.263561i	−0.710572	−	0.703624i	$-0.751564\pi$
$691$	−12.0000	+	6.92820i	−0.456502	+	0.263561i	0.254071	+	0.967186i	$0.418230\pi$
$692$	20.7846	−	12.0000i	0.790112	−	0.456172i
$693$		0			0
$694$			5.19615i			0.197243i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−23.3827	−	13.5000i	−0.885048	−	0.510983i
$699$	−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	$0.308281\pi$
$702$	−1.73205	−	6.00000i	−0.0653720	−	0.226455i
$703$		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
$708$	−5.19615	+	9.00000i	−0.195283	+	0.338241i
$709$	−25.5000	−	14.7224i	−0.957673	−	0.552913i	−0.0622167	−	0.998063i	$-0.519817\pi$
$709$	−25.5000	−	14.7224i	−0.957673	−	0.552913i	−0.895456	+	0.445150i	$0.853150\pi$
$710$		0			0
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$	10.3923	−	6.00000i	0.389468	−	0.224860i
$713$	10.3923	+	18.0000i	0.389195	+	0.674105i
$714$		0			0
$715$		0			0
$716$	−9.00000			−0.336346
$717$	2.59808	+	4.50000i	0.0970269	+	0.168056i
$718$	−36.3731	+	21.0000i	−1.35743	+	0.783713i
$719$	22.5000	−	38.9711i	0.839108	−	1.45338i	−0.0515326	−	0.998671i	$-0.516411\pi$
$719$	22.5000	−	38.9711i	0.839108	−	1.45338i	0.890641	−	0.454707i	$-0.150256\pi$
$720$		0			0
$721$		0			0
$722$	16.4545	−	28.5000i	0.612372	−	1.06066i
$723$	20.7846			0.772988
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$		0			0
$726$	−12.0000	+	6.92820i	−0.445362	+	0.257130i
$727$		−	26.0000i		−	0.964287i	−0.876092	−	0.482143i	$-0.839858\pi$
$727$		−	26.0000i		−	0.964287i	0.876092	−	0.482143i	$-0.160142\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$	−6.06218	−	3.50000i	−0.224065	−	0.129364i
$733$	1.73205			0.0639748			0.0319874	−	0.999488i	$-0.489816\pi$
$733$	1.73205			0.0639748			0.0319874	+	0.999488i	$0.489816\pi$
$734$	−42.0000	−	24.2487i	−1.55025	−	0.895036i
$735$		0			0
$736$			15.5885i			0.574598i
$737$	5.19615	+	3.00000i	0.191403	+	0.110506i
$738$	5.19615	−	3.00000i	0.191273	−	0.110432i
$739$	−39.0000	+	22.5167i	−1.43464	+	0.828289i	−0.997470	−	0.0710909i	$-0.977352\pi$
$739$	−39.0000	+	22.5167i	−1.43464	+	0.828289i	−0.437168	+	0.899380i	$0.644019\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.66025	+	15.0000i	0.317714	+	0.550297i	0.980011	−	0.198945i	$-0.0637515\pi$
$743$	8.66025	+	15.0000i	0.317714	+	0.550297i	−0.662297	+	0.749242i	$0.730418\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$		0			0
$746$			22.5167i			0.824394i
$747$	−4.33013	+	7.50000i	−0.158431	+	0.274411i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	0.709580	−	0.704625i	$-0.248885\pi$
$751$	−7.00000	−	12.1244i	−0.255434	−	0.442424i	−0.965013	+	0.262201i	$0.915552\pi$
$752$	−8.66025	−	15.0000i	−0.315807	−	0.546994i
$753$			27.0000i			0.983935i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.73205	+	1.00000i	−0.0629525	+	0.0363456i	−0.531146	−	0.847280i	$-0.678238\pi$
$757$	−1.73205	+	1.00000i	−0.0629525	+	0.0363456i	0.468193	+	0.883626i	$0.344905\pi$
$758$	41.5692	+	24.0000i	1.50986	+	0.871719i
$759$		−	5.19615i		−	0.188608i
$760$		0			0
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	0.604792	−	0.796383i	$-0.293256\pi$
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	−0.387292	+	0.921957i	$0.626590\pi$
$762$	−3.46410			−0.125491
$763$		0			0
$764$	−4.50000	−	7.79423i	−0.162804	−	0.281985i
$765$		0			0
$766$	39.0000			1.40913
$767$	25.9808	−	27.0000i	0.938111	−	0.974913i
$768$			19.0000i			0.685603i
$769$	42.0000	−	24.2487i	1.51456	−	0.874431i	0.514704	−	0.857368i	$-0.327902\pi$
$769$	42.0000	−	24.2487i	1.51456	−	0.874431i	0.999854	−	0.0170631i	$-0.00543163\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	−8.66025			−0.311689
$773$	17.3205	−	30.0000i	0.622975	−	1.07903i	−0.365953	−	0.930633i	$-0.619257\pi$
$773$	17.3205	−	30.0000i	0.622975	−	1.07903i	0.988929	−	0.148392i	$-0.0474097\pi$
$774$	−15.0000	−	8.66025i	−0.539164	−	0.311286i
$775$		0			0
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$		0			0
$778$	−25.9808	−	45.0000i	−0.931455	−	1.61333i
$779$		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		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	−10.3923			−0.370211
$789$	7.50000	−	12.9904i	0.267007	−	0.462470i
$790$		0			0
$791$		0			0
$792$		−	3.00000i		−	0.106600i
$793$	18.1865	+	17.5000i	0.645823	+	0.621443i
$794$	−48.0000			−1.70346
$795$		0			0
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	−15.5885	−	9.00000i	−0.552171	−	0.318796i	0.197826	−	0.980237i	$-0.436612\pi$
$797$	−15.5885	−	9.00000i	−0.552171	−	0.318796i	−0.749997	+	0.661441i	$0.769945\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		−	6.92820i		−	0.244796i
$802$	41.5692	+	24.0000i	1.46786	+	0.847469i
$803$	−12.9904	+	7.50000i	−0.458421	+	0.264669i
$804$	−3.00000	+	1.73205i	−0.105802	+	0.0610847i
$805$		0			0
$806$	12.0000	+	41.5692i	0.422682	+	1.46421i
$807$			6.00000i			0.211210i
$808$	−15.5885	−	27.0000i	−0.548400	−	0.949857i
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$		0			0
$811$		−	13.8564i		−	0.486564i	−0.969956	−	0.243282i	$-0.921776\pi$
$811$		−	13.8564i		−	0.486564i	0.969956	−	0.243282i	$-0.0782241\pi$
$812$		0			0
$813$	6.92820	−	12.0000i	0.242983	−	0.420858i
$814$			5.19615i			0.182125i
$815$		0			0
$816$		0			0
$817$		0			0
$818$			12.0000i			0.419570i
$819$		0			0
$820$		0			0
$821$	12.0000	−	6.92820i	0.418803	−	0.241796i	−0.275762	−	0.961226i	$-0.588930\pi$
$821$	12.0000	−	6.92820i	0.418803	−	0.241796i	0.694565	+	0.719430i	$0.255597\pi$
$822$	31.1769	−	18.0000i	1.08742	−	0.627822i
$823$	−3.46410	−	2.00000i	−0.120751	−	0.0697156i	0.438408	−	0.898776i	$-0.355543\pi$
$823$	−3.46410	−	2.00000i	−0.120751	−	0.0697156i	−0.559159	+	0.829060i	$0.688876\pi$
$824$		−	24.2487i		−	0.844744i
$825$		0			0
$826$		0			0
$827$	−8.66025			−0.301147			−0.150573	−	0.988599i	$-0.548112\pi$
$827$	−8.66025			−0.301147			−0.150573	+	0.988599i	$0.548112\pi$
$828$	2.59808	+	1.50000i	0.0902894	+	0.0521286i
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$		0			0
$831$	25.0000			0.867240
$832$	0.866025	−	3.50000i	0.0300240	−	0.121341i
$833$		0			0
$834$	−15.0000	+	8.66025i	−0.519408	+	0.299880i
$835$		0			0
$836$		0			0
$837$	6.92820			0.239474
$838$	−12.9904	+	22.5000i	−0.448745	+	0.777250i
$839$	7.50000	+	4.33013i	0.258929	+	0.149493i	0.623846	−	0.781547i	$-0.285569\pi$
$839$	7.50000	+	4.33013i	0.258929	+	0.149493i	−0.364917	+	0.931040i	$0.618903\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	18.1865	−	10.5000i	0.626749	−	0.361854i
$843$	−6.92820	−	12.0000i	−0.238620	−	0.413302i
$844$	−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
$852$	4.33013	−	7.50000i	0.148348	−	0.256946i
$853$	−41.5692			−1.42330			−0.711651	−	0.702533i	$-0.752052\pi$
$853$	−41.5692			−1.42330			−0.711651	+	0.702533i	$0.752052\pi$
$854$		0			0
$855$		0			0
$856$	−18.0000	+	10.3923i	−0.615227	+	0.355202i
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$	2.59808	−	10.5000i	0.0886969	−	0.358464i
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$		0			0
$861$		0			0
$862$	18.1865	+	10.5000i	0.619436	+	0.357631i
$863$	25.9808			0.884395			0.442198	−	0.896918i	$-0.354199\pi$
$863$	25.9808			0.884395			0.442198	+	0.896918i	$0.354199\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		0			0
$866$		−	19.0526i		−	0.647432i
$867$	−14.7224	−	8.50000i	−0.500000	−	0.288675i
$868$		0			0
$869$	12.0000	−	6.92820i	0.407072	−	0.235023i
$870$		0			0
$871$	12.0000	−	3.46410i	0.406604	−	0.117377i
$872$			15.0000i			0.507964i
$873$	4.33013	+	7.50000i	0.146553	+	0.253837i
$874$		0			0
$875$		0			0
$876$		−	8.66025i		−	0.292603i
$877$	19.9186	−	34.5000i	0.672603	−	1.16498i	−0.304561	−	0.952493i	$-0.598510\pi$
$877$	19.9186	−	34.5000i	0.672603	−	1.16498i	0.977163	−	0.212489i	$-0.0681571\pi$
$878$	3.46410	−	6.00000i	0.116908	−	0.202490i
$879$			17.3205i			0.584206i
$880$		0			0
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	0.747074	−	0.664741i	$-0.231458\pi$
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	−0.949219	+	0.314615i	$0.898125\pi$
$882$	6.06218	+	10.5000i	0.204124	+	0.353553i
$883$			2.00000i			0.0673054i	0.999434	+	0.0336527i	$0.0107140\pi$
$883$			2.00000i			0.0673054i	−0.999434	+	0.0336527i	$0.989286\pi$
$884$		0			0
$885$		0			0
$886$	−40.5000	+	23.3827i	−1.36062	+	0.785557i
$887$	−20.7846	+	12.0000i	−0.697879	+	0.402921i	−0.806557	−	0.591156i	$-0.798672\pi$
$887$	−20.7846	+	12.0000i	−0.697879	+	0.402921i	0.108678	+	0.994077i	$0.465338\pi$
$888$	2.59808	+	1.50000i	0.0871857	+	0.0503367i
$889$		0			0
$890$		0			0
$891$	−1.50000	−	0.866025i	−0.0502519	−	0.0290129i
$892$	−10.3923			−0.347960
$893$		0			0
$894$	−6.00000	−	10.3923i	−0.200670	−	0.347571i
$895$		0			0
$896$		0			0
$897$	−7.79423	−	7.50000i	−0.260242	−	0.250418i
$898$			30.0000i			1.00111i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	10.3923			0.346026
$903$		0			0
$904$	−9.00000	−	5.19615i	−0.299336	−	0.172821i
$905$		0			0
$906$	3.00000	−	5.19615i	0.0996683	−	0.172631i
$907$	−6.92820	+	4.00000i	−0.230047	+	0.132818i	−0.610594	−	0.791944i	$-0.709069\pi$
$907$	−6.92820	+	4.00000i	−0.230047	+	0.132818i	0.380547	+	0.924762i	$0.375736\pi$
$908$	14.7224	+	25.5000i	0.488581	+	0.846247i
$909$	−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
$913$	−12.9904	+	7.50000i	−0.429919	+	0.248214i
$914$	−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	$-0.843835\pi$
$919$	−1.00000	+	1.73205i	−0.0329870	+	0.0571351i	0.849061	+	0.528295i	$0.177169\pi$
$920$		0			0
$921$	−27.0000	+	15.5885i	−0.889680	+	0.513657i
$922$		−	48.0000i		−	1.58080i
$923$	−21.6506	+	22.5000i	−0.712639	+	0.740597i
$924$		0			0
$925$		0			0
$926$	−21.0000	−	36.3731i	−0.690103	−	1.19529i
$927$	−12.1244	−	7.00000i	−0.398216	−	0.229910i
$928$		0			0
$929$	27.0000	+	15.5885i	0.885841	+	0.511441i	0.872580	−	0.488471i	$-0.162445\pi$
$929$	27.0000	+	15.5885i	0.885841	+	0.511441i	0.0132613	+	0.999912i	$0.495779\pi$
$930$		0			0
$931$		0			0
$932$	15.5885	+	9.00000i	0.510617	+	0.294805i
$933$	−2.59808	+	1.50000i	−0.0850572	+	0.0491078i
$934$	−49.5000	+	28.5788i	−1.61969	+	0.935128i
$935$		0			0
$936$	−4.50000	−	4.33013i	−0.147087	−	0.141535i
$937$		−	47.0000i		−	1.53542i	−0.640796	−	0.767712i	$-0.721395\pi$
$937$		−	47.0000i		−	1.53542i	0.640796	−	0.767712i	$-0.278605\pi$
$938$		0			0
$939$	8.50000	+	14.7224i	0.277387	+	0.480448i
$940$		0			0
$941$		−	31.1769i		−	1.01634i	−0.861257	−	0.508169i	$-0.830322\pi$
$941$		−	31.1769i		−	1.01634i	0.861257	−	0.508169i	$-0.169678\pi$
$942$	0.866025	−	1.50000i	0.0282166	−	0.0488726i
$943$	5.19615	−	9.00000i	0.169210	−	0.293080i
$944$			51.9615i			1.69120i
$945$		0			0
$946$	−15.0000	−	25.9808i	−0.487692	−	0.844707i
$947$	−7.79423	−	13.5000i	−0.253278	−	0.438691i	0.711148	−	0.703042i	$-0.248176\pi$
$947$	−7.79423	−	13.5000i	−0.253278	−	0.438691i	−0.964426	+	0.264351i	$0.914842\pi$
$948$			8.00000i			0.259828i
$949$	−7.50000	+	30.3109i	−0.243460	+	0.983933i
$950$		0			0
$951$	24.0000	−	13.8564i	0.778253	−	0.449325i
$952$		0			0
$953$	10.3923	+	6.00000i	0.336640	+	0.194359i	0.658785	−	0.752331i	$-0.271071\pi$
$953$	10.3923	+	6.00000i	0.336640	+	0.194359i	−0.322145	+	0.946690i	$0.604404\pi$
$954$		0			0
$955$		0			0
$956$	−4.50000	−	2.59808i	−0.145540	−	0.0840278i
$957$		0			0
$958$	15.5885	+	9.00000i	0.503640	+	0.290777i
$959$		0			0
$960$		0			0
$961$	−17.0000			−0.548387
$962$	7.79423	+	7.50000i	0.251296	+	0.241810i
$963$			12.0000i			0.386695i
$964$	−18.0000	+	10.3923i	−0.579741	+	0.334714i
$965$		0			0
$966$		0			0
$967$	20.7846			0.668388			0.334194	−	0.942504i	$-0.391536\pi$
$967$	20.7846			0.668388			0.334194	+	0.942504i	$0.391536\pi$
$968$	−6.92820	+	12.0000i	−0.222681	+	0.385695i
$969$		0			0
$970$		0			0
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	0.167258	+	0.985913i	$0.446509\pi$
$971$	−24.0000	+	41.5692i	−0.770197	+	1.33402i	−0.937455	+	0.348107i	$0.886825\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$		0			0
$974$	−30.0000			−0.961262
$975$		0			0
$976$	−35.0000			−1.12032
$977$	3.46410	+	6.00000i	0.110826	+	0.191957i	0.916104	−	0.400941i	$-0.131317\pi$
$977$	3.46410	+	6.00000i	0.110826	+	0.191957i	−0.805277	+	0.592898i	$0.797984\pi$
$978$	−5.19615	+	3.00000i	−0.166155	+	0.0959294i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	7.50000	+	4.33013i	0.239457	+	0.138250i
$982$	−23.3827	+	40.5000i	−0.746171	+	1.29241i
$983$	10.3923			0.331463			0.165732	−	0.986171i	$-0.447001\pi$
$983$	10.3923			0.331463			0.165732	+	0.986171i	$0.447001\pi$
$984$	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	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$	−31.1769	−	18.0000i	−0.989868	−	0.571501i
$993$	3.46410			0.109930
$994$		0			0
$995$		0			0
$996$		−	8.66025i		−	0.274411i
$997$	8.66025	+	5.00000i	0.274273	+	0.158352i	0.630828	−	0.775923i	$-0.282715\pi$
$997$	8.66025	+	5.00000i	0.274273	+	0.158352i	−0.356555	+	0.934274i	$0.616049\pi$
$998$	−57.1577	+	33.0000i	−1.80929	+	1.04460i
$999$	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.w.c.49.2		4
5.2	odd	4		975.2.bc.a.751.1	✓	2
5.3	odd	4		975.2.bc.g.751.1	yes	2
5.4	even	2	inner	975.2.w.c.49.1		4
13.4	even	6	inner	975.2.w.c.199.1		4
65.4	even	6	inner	975.2.w.c.199.2		4
65.17	odd	12		975.2.bc.a.901.1	yes	2
65.43	odd	12		975.2.bc.g.901.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.c.49.1		4	5.4	even	2	inner
975.2.w.c.49.2		4	1.1	even	1	trivial
975.2.w.c.199.1		4	13.4	even	6	inner
975.2.w.c.199.2		4	65.4	even	6	inner
975.2.bc.a.751.1	✓	2	5.2	odd	4
975.2.bc.a.901.1	yes	2	65.17	odd	12
975.2.bc.g.751.1	yes	2	5.3	odd	4
975.2.bc.g.901.1	yes	2	65.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{6} +1.73205 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 - 0.866025i) q^{11} +1.00000i q^{12} +(0.866025 - 3.50000i) q^{13} +(2.50000 + 4.33013i) q^{16} +1.73205 q^{18} +(2.59808 + 1.50000i) q^{22} +(2.59808 - 1.50000i) q^{23} +(1.50000 - 0.866025i) q^{24} +(6.00000 - 1.73205i) q^{26} -1.00000i q^{27} +6.92820i q^{31} +(-2.59808 + 4.50000i) q^{32} +(0.866025 - 1.50000i) q^{33} +(0.500000 + 0.866025i) q^{36} +(0.866025 + 1.50000i) q^{37} +(-1.00000 - 3.46410i) q^{39} +(3.00000 - 1.73205i) q^{41} +(-8.66025 - 5.00000i) q^{43} +1.73205i q^{44} +(4.50000 + 2.59808i) q^{46} -3.46410 q^{47} +(4.33013 + 2.50000i) q^{48} +(3.50000 + 6.06218i) q^{49} +(2.59808 + 2.50000i) q^{52} +(1.50000 - 0.866025i) q^{54} +(9.00000 + 5.19615i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(-10.3923 + 6.00000i) q^{62} +1.00000 q^{64} +3.00000 q^{66} +(1.73205 + 3.00000i) q^{67} +(1.50000 - 2.59808i) q^{69} +(-7.50000 - 4.33013i) q^{71} +(0.866025 - 1.50000i) q^{72} -8.66025 q^{73} +(-1.50000 + 2.59808i) q^{74} +(4.33013 - 4.50000i) q^{78} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} -8.66025 q^{83} -17.3205i q^{86} +(2.59808 - 1.50000i) q^{88} +(6.00000 - 3.46410i) q^{89} +3.00000i q^{92} +(3.46410 + 6.00000i) q^{93} +(-3.00000 - 5.19615i) q^{94} +5.19615i q^{96} +(-4.33013 + 7.50000i) q^{97} +(-6.06218 + 10.5000i) q^{98} -1.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 6 q^{6} + 2 q^{9} + 6 q^{11} + 10 q^{16} + 6 q^{24} + 24 q^{26} + 2 q^{36} - 4 q^{39} + 12 q^{41} + 18 q^{46} + 14 q^{49} + 6 q^{54} + 36 q^{59} - 14 q^{61} + 4 q^{64} + 12 q^{66} + 6 q^{69}+ \cdots - 12 q^{94}+O(q^{100}) \) 4 * q - 2 * q^4 + 6 * q^6 + 2 * q^9 + 6 * q^11 + 10 * q^16 + 6 * q^24 + 24 * q^26 + 2 * q^36 - 4 * q^39 + 12 * q^41 + 18 * q^46 + 14 * q^49 + 6 * q^54 + 36 * q^59 - 14 * q^61 + 4 * q^64 + 12 * q^66 + 6 * q^69 - 30 * q^71 - 6 * q^74 + 32 * q^79 - 2 * q^81 + 24 * q^89 - 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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