LMFDB - Embedded newform 975.2.w.d.49.1

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:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.49
Dual form			975.2.w.d.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.866025 + 1.50000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-3.00000 + 1.73205i) q^{11} +2.00000i q^{12} +(-0.866025 + 3.50000i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(-3.00000 - 1.73205i) q^{19} -1.73205i q^{21} +(-5.19615 + 3.00000i) q^{23} +1.00000i q^{27} +(1.73205 + 3.00000i) q^{28} +(3.00000 + 5.19615i) q^{29} -1.73205i q^{31} +(1.73205 - 3.00000i) q^{33} +(-1.00000 - 1.73205i) q^{36} +(-1.00000 - 3.46410i) q^{39} +(-6.00000 + 3.46410i) q^{41} +(0.866025 + 0.500000i) q^{43} +6.92820i q^{44} -3.46410 q^{47} +(3.46410 + 2.00000i) q^{48} +(2.00000 + 3.46410i) q^{49} +(5.19615 + 5.00000i) q^{52} +12.0000i q^{53} +3.46410 q^{57} +(3.00000 + 1.73205i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(0.866025 + 1.50000i) q^{63} -8.00000 q^{64} +(-4.33013 - 7.50000i) q^{67} +(3.00000 - 5.19615i) q^{69} +(-9.00000 - 5.19615i) q^{71} +1.73205 q^{73} +(-6.00000 + 3.46410i) q^{76} -6.00000i q^{77} +11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} -13.8564 q^{83} +(-3.00000 - 1.73205i) q^{84} +(-5.19615 - 3.00000i) q^{87} +(-6.00000 + 3.46410i) q^{89} +(-4.50000 - 4.33013i) q^{91} +12.0000i q^{92} +(0.866025 + 1.50000i) q^{93} +(-2.59808 + 4.50000i) q^{97} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 2 q^{9} - 12 q^{11} - 8 q^{16} - 12 q^{19} + 12 q^{29} - 4 q^{36} - 4 q^{39} - 24 q^{41} + 8 q^{49} + 12 q^{59} - 2 q^{61} - 32 q^{64} + 12 q^{69} - 36 q^{71} - 24 q^{76} + 44 q^{79} - 2 q^{81}+ \cdots - 18 q^{91}+O(q^{100}) $ 4 * q + 4 * q^4 + 2 * q^9 - 12 * q^11 - 8 * q^16 - 12 * q^19 + 12 * q^29 - 4 * q^36 - 4 * q^39 - 24 * q^41 + 8 * q^49 + 12 * q^59 - 2 * q^61 - 32 * q^64 + 12 * q^69 - 36 * q^71 - 24 * q^76 + 44 * q^79 - 2 * q^81 - 12 * q^84 - 24 * q^89 - 18 * q^91

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			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−0.866025	+	1.50000i	−0.327327	+	0.566947i	0.654654	+	0.755929i	$0.272814\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$			2.00000i			0.577350i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		−	1.73205i		−	0.377964i
$22$		0			0
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$	1.73205	+	3.00000i	0.327327	+	0.566947i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		0			0
$33$	1.73205	−	3.00000i	0.301511	−	0.522233i
$34$		0			0
$35$		0			0
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$	−1.00000	−	3.46410i	−0.160128	−	0.554700i
$40$		0			0
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.889032	−	0.457845i	$-0.848621\pi$
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.0480106	+	0.998847i	$0.515288\pi$
$42$		0			0
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	0.564578	−	0.825380i	$-0.309039\pi$
$43$	0.866025	+	0.500000i	0.132068	+	0.0762493i	−0.432511	+	0.901629i	$0.642372\pi$
$44$			6.92820i			1.04447i
$45$		0			0
$46$		0			0
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$	3.46410	+	2.00000i	0.500000	+	0.288675i
$49$	2.00000	+	3.46410i	0.285714	+	0.494872i
$50$		0			0
$51$		0			0
$52$	5.19615	+	5.00000i	0.720577	+	0.693375i
$53$			12.0000i			1.64833i	0.566352	+	0.824163i	$0.308354\pi$
$53$			12.0000i			1.64833i	−0.566352	+	0.824163i	$0.691646\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.46410			0.458831
$58$		0			0
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	0.682406	−	0.730974i	$-0.260934\pi$
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	−0.291839	+	0.956467i	$0.594267\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$		0			0
$63$	0.866025	+	1.50000i	0.109109	+	0.188982i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	−4.33013	−	7.50000i	−0.529009	−	0.916271i	−0.999428	−	0.0338274i	$-0.989230\pi$
$67$	−4.33013	−	7.50000i	−0.529009	−	0.916271i	0.470418	−	0.882443i	$-0.344103\pi$
$68$		0			0
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	−9.00000	−	5.19615i	−1.06810	−	0.616670i	−0.140441	−	0.990089i	$-0.544852\pi$
$71$	−9.00000	−	5.19615i	−1.06810	−	0.616670i	−0.927663	+	0.373419i	$0.878185\pi$
$72$		0			0
$73$	1.73205			0.202721			0.101361	−	0.994850i	$-0.467680\pi$
$73$	1.73205			0.202721			0.101361	+	0.994850i	$0.467680\pi$
$74$		0			0
$75$		0			0
$76$	−6.00000	+	3.46410i	−0.688247	+	0.397360i
$77$		−	6.00000i		−	0.683763i
$78$		0			0
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−13.8564			−1.52094			−0.760469	−	0.649374i	$-0.775031\pi$
$83$	−13.8564			−1.52094			−0.760469	+	0.649374i	$0.775031\pi$
$84$	−3.00000	−	1.73205i	−0.327327	−	0.188982i
$85$		0			0
$86$		0			0
$87$	−5.19615	−	3.00000i	−0.557086	−	0.321634i
$88$		0			0
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	−0.783072	−	0.621932i	$-0.786348\pi$
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	0.147073	+	0.989126i	$0.453015\pi$
$90$		0			0
$91$	−4.50000	−	4.33013i	−0.471728	−	0.453921i
$92$			12.0000i			1.25109i
$93$	0.866025	+	1.50000i	0.0898027	+	0.155543i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.59808	+	4.50000i	−0.263795	+	0.456906i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$	−2.59808	+	4.50000i	−0.263795	+	0.456906i	0.703452	+	0.710742i	$0.251641\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$		0			0
$103$		−	1.00000i		−	0.0985329i	−0.998786	−	0.0492665i	$-0.984312\pi$
$103$		−	1.00000i		−	0.0985329i	0.998786	−	0.0492665i	$-0.0156884\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	−0.227345	−	0.973814i	$-0.573004\pi$
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	0.729676	+	0.683793i	$0.239671\pi$
$108$	1.73205	+	1.00000i	0.166667	+	0.0962250i
$109$		−	15.5885i		−	1.49310i	−0.665327	−	0.746552i	$-0.731708\pi$
$109$		−	15.5885i		−	1.49310i	0.665327	−	0.746552i	$-0.268292\pi$
$110$		0			0
$111$		0			0
$112$	6.92820			0.654654
$113$	−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
$116$	12.0000			1.11417
$117$	2.59808	+	2.50000i	0.240192	+	0.231125i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	3.46410	−	6.00000i	0.312348	−	0.541002i
$124$	−3.00000	−	1.73205i	−0.269408	−	0.155543i
$125$		0			0
$126$		0			0
$127$	−11.2583	+	6.50000i	−0.999015	+	0.576782i	−0.907957	−	0.419064i	$-0.862358\pi$
$127$	−11.2583	+	6.50000i	−0.999015	+	0.576782i	−0.0910585	+	0.995846i	$0.529025\pi$
$128$		0			0
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$	−3.46410	−	6.00000i	−0.301511	−	0.522233i
$133$	5.19615	−	3.00000i	0.450564	−	0.260133i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$		0			0
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	−0.740308	−	0.672268i	$-0.765320\pi$
$139$	2.50000	−	4.33013i	0.212047	−	0.367277i	0.952355	+	0.304991i	$0.0986536\pi$
$140$		0			0
$141$	3.00000	−	1.73205i	0.252646	−	0.145865i
$142$		0			0
$143$	−3.46410	−	12.0000i	−0.289683	−	1.00349i
$144$	−4.00000			−0.333333
$145$		0			0
$146$		0			0
$147$	−3.46410	−	2.00000i	−0.285714	−	0.164957i
$148$		0			0
$149$	6.00000	+	3.46410i	0.491539	+	0.283790i	0.725213	−	0.688525i	$-0.241741\pi$
$149$	6.00000	+	3.46410i	0.491539	+	0.283790i	−0.233674	+	0.972315i	$0.575075\pi$
$150$		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
$156$	−7.00000	−	1.73205i	−0.560449	−	0.138675i
$157$		−	11.0000i		−	0.877896i	−0.898513	−	0.438948i	$-0.855351\pi$
$157$		−	11.0000i		−	0.877896i	0.898513	−	0.438948i	$-0.144649\pi$
$158$		0			0
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$		0			0
$163$	9.52628	−	16.5000i	0.746156	−	1.29238i	−0.203497	−	0.979076i	$-0.565231\pi$
$163$	9.52628	−	16.5000i	0.746156	−	1.29238i	0.949653	−	0.313304i	$-0.101436\pi$
$164$			13.8564i			1.08200i
$165$		0			0
$166$		0			0
$167$	3.46410	+	6.00000i	0.268060	+	0.464294i	0.968361	−	0.249554i	$-0.0802840\pi$
$167$	3.46410	+	6.00000i	0.268060	+	0.464294i	−0.700301	+	0.713848i	$0.746951\pi$
$168$		0			0
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$	−3.00000	+	1.73205i	−0.229416	+	0.132453i
$172$	1.73205	−	1.00000i	0.132068	−	0.0762493i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$		0			0
$175$		0			0
$176$	12.0000	+	6.92820i	0.904534	+	0.522233i
$177$	−3.46410			−0.260378
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$		−	1.00000i		−	0.0739221i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−3.46410	+	6.00000i	−0.252646	+	0.437595i
$189$	−1.50000	−	0.866025i	−0.109109	−	0.0629941i
$190$		0			0
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	6.92820	−	4.00000i	0.500000	−	0.288675i
$193$	−7.79423	−	13.5000i	−0.561041	−	0.971751i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$	−7.79423	−	13.5000i	−0.561041	−	0.971751i	0.436365	−	0.899770i	$-0.356266\pi$
$194$		0			0
$195$		0			0
$196$	8.00000			0.571429
$197$	−6.92820	−	12.0000i	−0.493614	−	0.854965i	0.506359	−	0.862323i	$-0.330991\pi$
$197$	−6.92820	−	12.0000i	−0.493614	−	0.854965i	−0.999973	+	0.00735824i	$0.997658\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$	7.50000	+	4.33013i	0.529009	+	0.305424i
$202$		0			0
$203$	−10.3923			−0.729397
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.00000i			0.417029i
$208$	13.8564	−	4.00000i	0.960769	−	0.277350i
$209$	12.0000			0.830057
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	20.7846	+	12.0000i	1.42749	+	0.824163i
$213$	10.3923			0.712069
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.59808	+	1.50000i	0.176369	+	0.101827i
$218$		0			0
$219$	−1.50000	+	0.866025i	−0.101361	+	0.0585206i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	8.66025	+	15.0000i	0.579934	+	1.00447i	0.995486	+	0.0949052i	$0.0302548\pi$
$223$	8.66025	+	15.0000i	0.579934	+	1.00447i	−0.415553	+	0.909569i	$0.636412\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.3923	−	18.0000i	0.689761	−	1.19470i	−0.282153	−	0.959369i	$-0.591049\pi$
$227$	10.3923	−	18.0000i	0.689761	−	1.19470i	0.971915	−	0.235333i	$-0.0756180\pi$
$228$	3.46410	−	6.00000i	0.229416	−	0.397360i
$229$			27.7128i			1.83131i	0.401960	+	0.915657i	$0.368329\pi$
$229$			27.7128i			1.83131i	−0.401960	+	0.915657i	$0.631671\pi$
$230$		0			0
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$		0			0
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	−	3.46410i	0.390567	−	0.225494i
$237$	−9.52628	+	5.50000i	−0.618798	+	0.357263i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		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	$0.433206\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$		0			0
$246$		0			0
$247$	8.66025	−	9.00000i	0.551039	−	0.572656i
$248$		0			0
$249$	12.0000	−	6.92820i	0.760469	−	0.439057i
$250$		0			0
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	3.46410			0.218218
$253$	10.3923	−	18.0000i	0.653359	−	1.13165i
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	6.00000			0.371391
$262$		0			0
$263$	10.3923	−	6.00000i	0.640817	−	0.369976i	−0.144112	−	0.989561i	$-0.546033\pi$
$263$	10.3923	−	6.00000i	0.640817	−	0.369976i	0.784929	+	0.619586i	$0.212699\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.46410	−	6.00000i	0.212000	−	0.367194i
$268$	−17.3205			−1.05802
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−4.50000	+	2.59808i	−0.273356	+	0.157822i	−0.630412	−	0.776261i	$-0.717114\pi$
$271$	−4.50000	+	2.59808i	−0.273356	+	0.157822i	0.357056	+	0.934083i	$0.383781\pi$
$272$		0			0
$273$	6.06218	+	1.50000i	0.366900	+	0.0907841i
$274$		0			0
$275$		0			0
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−8.66025	−	5.00000i	−0.520344	−	0.300421i	0.216731	−	0.976231i	$-0.430460\pi$
$277$	−8.66025	−	5.00000i	−0.520344	−	0.300421i	−0.737075	+	0.675810i	$0.763794\pi$
$278$		0			0
$279$	−1.50000	−	0.866025i	−0.0898027	−	0.0518476i
$280$		0			0
$281$			24.2487i			1.44656i	0.690557	+	0.723278i	$0.257366\pi$
$281$			24.2487i			1.44656i	−0.690557	+	0.723278i	$0.742634\pi$
$282$		0			0
$283$	−9.52628	+	5.50000i	−0.566279	+	0.326941i	−0.755662	−	0.654962i	$-0.772685\pi$
$283$	−9.52628	+	5.50000i	−0.566279	+	0.326941i	0.189383	+	0.981903i	$0.439351\pi$
$284$	−18.0000	+	10.3923i	−1.06810	+	0.616670i
$285$		0			0
$286$		0			0
$287$		−	12.0000i		−	0.708338i
$288$		0			0
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$		−	5.19615i		−	0.304604i
$292$	1.73205	−	3.00000i	0.101361	−	0.175562i
$293$	8.66025	−	15.0000i	0.505937	−	0.876309i	−0.494039	−	0.869440i	$-0.664480\pi$
$293$	8.66025	−	15.0000i	0.505937	−	0.876309i	0.999976	−	0.00686959i	$-0.00218668\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.73205	−	3.00000i	−0.100504	−	0.174078i
$298$		0			0
$299$	−6.00000	−	20.7846i	−0.346989	−	1.20201i
$300$		0			0
$301$	−1.50000	+	0.866025i	−0.0864586	+	0.0499169i
$302$		0			0
$303$	−15.5885	−	9.00000i	−0.895533	−	0.517036i
$304$			13.8564i			0.794719i
$305$		0			0
$306$		0			0
$307$	1.73205			0.0988534			0.0494267	−	0.998778i	$-0.484261\pi$
$307$	1.73205			0.0988534			0.0494267	+	0.998778i	$0.484261\pi$
$308$	−10.3923	−	6.00000i	−0.592157	−	0.341882i
$309$	0.500000	+	0.866025i	0.0284440	+	0.0492665i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$			13.0000i			0.734803i	0.930062	+	0.367402i	$0.119753\pi$
$313$			13.0000i			0.734803i	−0.930062	+	0.367402i	$0.880247\pi$
$314$		0			0
$315$		0			0
$316$	11.0000	−	19.0526i	0.618798	−	1.07179i
$317$	−6.92820			−0.389127			−0.194563	−	0.980890i	$-0.562329\pi$
$317$	−6.92820			−0.389127			−0.194563	+	0.980890i	$0.562329\pi$
$318$		0			0
$319$	−18.0000	−	10.3923i	−1.00781	−	0.581857i
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$		0			0
$323$		0			0
$324$	−2.00000			−0.111111
$325$		0			0
$326$		0			0
$327$	7.79423	+	13.5000i	0.431022	+	0.746552i
$328$		0			0
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	4.50000	+	2.59808i	0.247342	+	0.142803i	0.618547	−	0.785748i	$-0.287722\pi$
$331$	4.50000	+	2.59808i	0.247342	+	0.142803i	−0.371204	+	0.928551i	$0.621055\pi$
$332$	−13.8564	+	24.0000i	−0.760469	+	1.31717i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−6.00000	+	3.46410i	−0.327327	+	0.188982i
$337$			5.00000i			0.272367i	0.990684	+	0.136184i	$0.0434837\pi$
$337$			5.00000i			0.272367i	−0.990684	+	0.136184i	$0.956516\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$		0			0
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$		0			0
$343$	−19.0526			−1.02874
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.175457	−	0.984487i	$-0.556140\pi$
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.940319	+	0.340293i	$0.889474\pi$
$348$	−10.3923	+	6.00000i	−0.557086	+	0.321634i
$349$	16.5000	−	9.52628i	0.883225	−	0.509930i	0.0115044	−	0.999934i	$-0.496338\pi$
$349$	16.5000	−	9.52628i	0.883225	−	0.509930i	0.871720	+	0.490004i	$0.163005\pi$
$350$		0			0
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$		0			0
$353$	5.19615	+	9.00000i	0.276563	+	0.479022i	0.970528	−	0.240987i	$-0.0774711\pi$
$353$	5.19615	+	9.00000i	0.276563	+	0.479022i	−0.693965	+	0.720009i	$0.744138\pi$
$354$		0			0
$355$		0			0
$356$			13.8564i			0.734388i
$357$		0			0
$358$		0			0
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$		0			0
$363$			1.00000i			0.0524864i
$364$	−12.0000	+	3.46410i	−0.628971	+	0.181568i
$365$		0			0
$366$		0			0
$367$	−14.7224	+	8.50000i	−0.768505	+	0.443696i	−0.832341	−	0.554264i	$-0.813000\pi$
$367$	−14.7224	+	8.50000i	−0.768505	+	0.443696i	0.0638362	+	0.997960i	$0.479666\pi$
$368$	20.7846	+	12.0000i	1.08347	+	0.625543i
$369$			6.92820i			0.360668i
$370$		0			0
$371$	−18.0000	−	10.3923i	−0.934513	−	0.539542i
$372$	3.46410			0.179605
$373$	9.52628	+	5.50000i	0.493252	+	0.284779i	0.725923	−	0.687776i	$-0.241413\pi$
$373$	9.52628	+	5.50000i	0.493252	+	0.284779i	−0.232671	+	0.972556i	$0.574746\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−20.7846	+	6.00000i	−1.07046	+	0.309016i
$378$		0			0
$379$	19.5000	−	11.2583i	1.00165	−	0.578302i	0.0929123	−	0.995674i	$-0.470382\pi$
$379$	19.5000	−	11.2583i	1.00165	−	0.578302i	0.908735	+	0.417373i	$0.137049\pi$
$380$		0			0
$381$	6.50000	−	11.2583i	0.333005	−	0.576782i
$382$		0			0
$383$	−13.8564	+	24.0000i	−0.708029	+	1.22634i	0.257558	+	0.966263i	$0.417082\pi$
$383$	−13.8564	+	24.0000i	−0.708029	+	1.22634i	−0.965587	+	0.260080i	$0.916251\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.866025	−	0.500000i	0.0440225	−	0.0254164i
$388$	5.19615	+	9.00000i	0.263795	+	0.456906i
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−5.19615	+	3.00000i	−0.262111	+	0.151330i
$394$		0			0
$395$		0			0
$396$	6.00000	+	3.46410i	0.301511	+	0.174078i
$397$	7.79423	−	13.5000i	0.391181	−	0.677546i	−0.601424	−	0.798930i	$-0.705400\pi$
$397$	7.79423	−	13.5000i	0.391181	−	0.677546i	0.992606	+	0.121384i	$0.0387333\pi$
$398$		0			0
$399$	−3.00000	+	5.19615i	−0.150188	+	0.260133i
$400$		0			0
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	6.06218	+	1.50000i	0.301979	+	0.0747203i
$404$	36.0000			1.79107
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$		0			0
$411$		0			0
$412$	−1.73205	−	1.00000i	−0.0853320	−	0.0492665i
$413$	−5.19615	+	3.00000i	−0.255686	+	0.147620i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			5.00000i			0.244851i
$418$		0			0
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$			12.1244i			0.590905i	0.955357	+	0.295452i	$0.0954704\pi$
$421$			12.1244i			0.590905i	−0.955357	+	0.295452i	$0.904530\pi$
$422$		0			0
$423$	−1.73205	+	3.00000i	−0.0842152	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.866025	−	1.50000i	−0.0419099	−	0.0725901i
$428$		−	12.0000i		−	0.580042i
$429$	9.00000	+	8.66025i	0.434524	+	0.418121i
$430$		0			0
$431$	18.0000	−	10.3923i	0.867029	−	0.500580i	0.000669521	−	1.00000i	$-0.499787\pi$
$431$	18.0000	−	10.3923i	0.867029	−	0.500580i	0.866360	+	0.499420i	$0.166454\pi$
$432$	3.46410	−	2.00000i	0.166667	−	0.0962250i
$433$	19.9186	+	11.5000i	0.957226	+	0.552655i	0.895318	−	0.445427i	$-0.146948\pi$
$433$	19.9186	+	11.5000i	0.957226	+	0.552655i	0.0619079	+	0.998082i	$0.480282\pi$
$434$		0			0
$435$		0			0
$436$	−27.0000	−	15.5885i	−1.29307	−	0.746552i
$437$	20.7846			0.994263
$438$		0			0
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	0.893843	+	0.448379i	$0.147999\pi$
$439$	17.5000	+	30.3109i	0.835229	+	1.44666i	−0.0586141	+	0.998281i	$0.518668\pi$
$440$		0			0
$441$	4.00000			0.190476
$442$		0			0
$443$			24.0000i			1.14027i	0.821549	+	0.570137i	$0.193110\pi$
$443$			24.0000i			1.14027i	−0.821549	+	0.570137i	$0.806890\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.92820			−0.327693
$448$	6.92820	−	12.0000i	0.327327	−	0.566947i
$449$	−33.0000	−	19.0526i	−1.55737	−	0.899146i	−0.997508	−	0.0705577i	$-0.977522\pi$
$449$	−33.0000	−	19.0526i	−1.55737	−	0.899146i	−0.559859	−	0.828588i	$-0.689145\pi$
$450$		0			0
$451$	12.0000	−	20.7846i	0.565058	−	0.978709i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	−1.73205	−	3.00000i	−0.0813788	−	0.140952i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.1865	+	31.5000i	0.850730	+	1.47351i	0.880550	+	0.473953i	$0.157173\pi$
$457$	18.1865	+	31.5000i	0.850730	+	1.47351i	−0.0298202	+	0.999555i	$0.509493\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−36.0000	−	20.7846i	−1.67669	−	0.968036i	−0.963750	−	0.266808i	$-0.914031\pi$
$461$	−36.0000	−	20.7846i	−1.67669	−	0.968036i	−0.712938	−	0.701228i	$-0.752636\pi$
$462$		0			0
$463$	−36.3731			−1.69040			−0.845200	−	0.534450i	$-0.820519\pi$
$463$	−36.3731			−1.69040			−0.845200	+	0.534450i	$0.820519\pi$
$464$	12.0000	−	20.7846i	0.557086	−	0.964901i
$465$		0			0
$466$		0			0
$467$		−	6.00000i		−	0.277647i	−0.990317	−	0.138823i	$-0.955668\pi$
$467$		−	6.00000i		−	0.277647i	0.990317	−	0.138823i	$-0.0443321\pi$
$468$	6.92820	−	2.00000i	0.320256	−	0.0924500i
$469$	15.0000			0.692636
$470$		0			0
$471$	5.50000	+	9.52628i	0.253427	+	0.438948i
$472$		0			0
$473$	−3.46410			−0.159280
$474$		0			0
$475$		0			0
$476$		0			0
$477$	10.3923	+	6.00000i	0.475831	+	0.274721i
$478$		0			0
$479$	−30.0000	+	17.3205i	−1.37073	+	0.791394i	−0.991021	−	0.133710i	$-0.957311\pi$
$479$	−30.0000	+	17.3205i	−1.37073	+	0.791394i	−0.379714	+	0.925104i	$0.623978\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	5.19615	+	9.00000i	0.236433	+	0.409514i
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$		0			0
$487$	−12.1244	+	21.0000i	−0.549407	+	0.951601i	0.448908	+	0.893578i	$0.351813\pi$
$487$	−12.1244	+	21.0000i	−0.549407	+	0.951601i	−0.998315	+	0.0580230i	$0.981520\pi$
$488$		0			0
$489$			19.0526i			0.861586i
$490$		0			0
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	0.790358	−	0.612646i	$-0.209895\pi$
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	−0.925746	+	0.378147i	$0.876561\pi$
$492$	−6.92820	−	12.0000i	−0.312348	−	0.541002i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−6.00000	+	3.46410i	−0.269408	+	0.155543i
$497$	15.5885	−	9.00000i	0.699238	−	0.403705i
$498$		0			0
$499$			31.1769i			1.39567i	0.716258	+	0.697835i	$0.245853\pi$
$499$			31.1769i			1.39567i	−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$	−6.00000	−	3.46410i	−0.268060	−	0.154765i
$502$		0			0
$503$	25.9808	+	15.0000i	1.15842	+	0.668817i	0.950926	−	0.309418i	$-0.100134\pi$
$503$	25.9808	+	15.0000i	1.15842	+	0.668817i	0.207499	+	0.978235i	$0.433468\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.9904	−	0.500000i	0.576923	−	0.0222058i
$508$			26.0000i			1.15356i
$509$	15.0000	−	8.66025i	0.664863	−	0.383859i	−0.129264	−	0.991610i	$-0.541262\pi$
$509$	15.0000	−	8.66025i	0.664863	−	0.383859i	0.794128	+	0.607751i	$0.207928\pi$
$510$		0			0
$511$	−1.50000	+	2.59808i	−0.0663561	+	0.114932i
$512$		0			0
$513$	1.73205	−	3.00000i	0.0764719	−	0.132453i
$514$		0			0
$515$		0			0
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	10.3923	−	6.00000i	0.457053	−	0.263880i
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$		0			0
$523$	−24.2487	+	14.0000i	−1.06032	+	0.612177i	−0.925521	−	0.378695i	$-0.876373\pi$
$523$	−24.2487	+	14.0000i	−1.06032	+	0.612177i	−0.134801	+	0.990873i	$0.543039\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−13.8564			−0.603023
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	3.00000	−	1.73205i	0.130189	−	0.0751646i
$532$		−	12.0000i		−	0.520266i
$533$	−6.92820	−	24.0000i	−0.300094	−	1.03956i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.3923	−	6.00000i	−0.448461	−	0.258919i
$538$		0			0
$539$	−12.0000	−	6.92820i	−0.516877	−	0.298419i
$540$		0			0
$541$			29.4449i			1.26593i	0.774179	+	0.632967i	$0.218163\pi$
$541$			29.4449i			1.26593i	−0.774179	+	0.632967i	$0.781837\pi$
$542$		0			0
$543$	−12.1244	+	7.00000i	−0.520306	+	0.300399i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			19.0000i			0.812381i	0.913788	+	0.406191i	$0.133143\pi$
$547$			19.0000i			0.812381i	−0.913788	+	0.406191i	$0.866857\pi$
$548$		0			0
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$		−	20.7846i		−	0.885454i
$552$		0			0
$553$	−9.52628	+	16.5000i	−0.405099	+	0.701651i
$554$		0			0
$555$		0			0
$556$	−5.00000	−	8.66025i	−0.212047	−	0.367277i
$557$	13.8564	+	24.0000i	0.587115	+	1.01691i	0.994608	+	0.103704i	$0.0330696\pi$
$557$	13.8564	+	24.0000i	0.587115	+	1.01691i	−0.407493	+	0.913208i	$0.633597\pi$
$558$		0			0
$559$	−2.50000	+	2.59808i	−0.105739	+	0.109887i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	36.3731	+	21.0000i	1.53294	+	0.885044i	0.999224	+	0.0393818i	$0.0125389\pi$
$563$	36.3731	+	21.0000i	1.53294	+	0.885044i	0.533718	+	0.845663i	$0.320794\pi$
$564$		−	6.92820i		−	0.291730i
$565$		0			0
$566$		0			0
$567$	1.73205			0.0727393
$568$		0			0
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$		0			0
$571$	−44.0000			−1.84134			−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000			−1.84134			−0.920671	+	0.390339i	$0.872358\pi$
$572$	−24.2487	−	6.00000i	−1.01389	−	0.250873i
$573$			18.0000i			0.751961i
$574$		0			0
$575$		0			0
$576$	−4.00000	+	6.92820i	−0.166667	+	0.288675i
$577$	34.6410			1.44212			0.721062	−	0.692870i	$-0.243654\pi$
$577$	34.6410			1.44212			0.721062	+	0.692870i	$0.243654\pi$
$578$		0			0
$579$	13.5000	+	7.79423i	0.561041	+	0.323917i
$580$		0			0
$581$	12.0000	−	20.7846i	0.497844	−	0.862291i
$582$		0			0
$583$	−20.7846	−	36.0000i	−0.860811	−	1.49097i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.5885	+	27.0000i	0.643404	+	1.11441i	0.984668	+	0.174441i	$0.0558120\pi$
$587$	15.5885	+	27.0000i	0.643404	+	1.11441i	−0.341263	+	0.939968i	$0.610855\pi$
$588$	−6.92820	+	4.00000i	−0.285714	+	0.164957i
$589$	−3.00000	+	5.19615i	−0.123613	+	0.214104i
$590$		0			0
$591$	12.0000	+	6.92820i	0.493614	+	0.284988i
$592$		0			0
$593$	3.46410			0.142254			0.0711268	−	0.997467i	$-0.477341\pi$
$593$	3.46410			0.142254			0.0711268	+	0.997467i	$0.477341\pi$
$594$		0			0
$595$		0			0
$596$	12.0000	−	6.92820i	0.491539	−	0.283790i
$597$			7.00000i			0.286491i
$598$		0			0
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	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
$603$	−8.66025			−0.352673
$604$	6.00000	+	3.46410i	0.244137	+	0.140952i
$605$		0			0
$606$		0			0
$607$	6.92820	+	4.00000i	0.281207	+	0.162355i	0.633970	−	0.773358i	$-0.281424\pi$
$607$	6.92820	+	4.00000i	0.281207	+	0.162355i	−0.352763	+	0.935713i	$0.614758\pi$
$608$		0			0
$609$	9.00000	−	5.19615i	0.364698	−	0.210559i
$610$		0			0
$611$	3.00000	−	12.1244i	0.121367	−	0.490499i
$612$		0			0
$613$	4.33013	+	7.50000i	0.174892	+	0.302922i	0.940124	−	0.340833i	$-0.110709\pi$
$613$	4.33013	+	7.50000i	0.174892	+	0.302922i	−0.765232	+	0.643755i	$0.777376\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.19615	+	9.00000i	−0.209189	+	0.362326i	−0.951459	−	0.307774i	$-0.900416\pi$
$617$	−5.19615	+	9.00000i	−0.209189	+	0.362326i	0.742270	+	0.670101i	$0.233749\pi$
$618$		0			0
$619$			25.9808i			1.04425i	0.852867	+	0.522127i	$0.174861\pi$
$619$			25.9808i			1.04425i	−0.852867	+	0.522127i	$0.825139\pi$
$620$		0			0
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$		0			0
$623$		−	12.0000i		−	0.480770i
$624$	−10.0000	+	10.3923i	−0.400320	+	0.416025i
$625$		0			0
$626$		0			0
$627$	−10.3923	+	6.00000i	−0.415029	+	0.239617i
$628$	−19.0526	−	11.0000i	−0.760280	−	0.438948i
$629$		0			0
$630$		0			0
$631$	1.50000	+	0.866025i	0.0597141	+	0.0344759i	0.529560	−	0.848273i	$-0.322357\pi$
$631$	1.50000	+	0.866025i	0.0597141	+	0.0344759i	−0.469846	+	0.882749i	$0.655690\pi$
$632$		0			0
$633$	11.2583	+	6.50000i	0.447478	+	0.258352i
$634$		0			0
$635$		0			0
$636$	−24.0000			−0.951662
$637$	−13.8564	+	4.00000i	−0.549011	+	0.158486i
$638$		0			0
$639$	−9.00000	+	5.19615i	−0.356034	+	0.205557i
$640$		0			0
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		0			0
$643$	−9.52628	+	16.5000i	−0.375680	+	0.650696i	−0.990429	−	0.138027i	$-0.955924\pi$
$643$	−9.52628	+	16.5000i	−0.375680	+	0.650696i	0.614749	+	0.788723i	$0.289257\pi$
$644$	−18.0000	−	10.3923i	−0.709299	−	0.409514i
$645$		0			0
$646$		0			0
$647$	15.5885	−	9.00000i	0.612845	−	0.353827i	−0.161233	−	0.986916i	$-0.551547\pi$
$647$	15.5885	−	9.00000i	0.612845	−	0.353827i	0.774078	+	0.633090i	$0.218214\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$		0			0
$651$	−3.00000			−0.117579
$652$	−19.0526	−	33.0000i	−0.746156	−	1.29238i
$653$	31.1769	−	18.0000i	1.22005	−	0.704394i	0.255119	−	0.966910i	$-0.417885\pi$
$653$	31.1769	−	18.0000i	1.22005	−	0.704394i	0.964928	+	0.262515i	$0.0845520\pi$
$654$		0			0
$655$		0			0
$656$	24.0000	+	13.8564i	0.937043	+	0.541002i
$657$	0.866025	−	1.50000i	0.0337869	−	0.0585206i
$658$		0			0
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.160108	−	0.987099i	$-0.448816\pi$
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.774799	−	0.632207i	$-0.217851\pi$
$660$		0			0
$661$	−22.5000	+	12.9904i	−0.875149	+	0.505267i	−0.869056	−	0.494714i	$-0.835273\pi$
$661$	−22.5000	+	12.9904i	−0.875149	+	0.505267i	−0.00609283	+	0.999981i	$0.501939\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−31.1769	−	18.0000i	−1.20717	−	0.696963i
$668$	13.8564			0.536120
$669$	−15.0000	−	8.66025i	−0.579934	−	0.334825i
$670$		0			0
$671$		−	3.46410i		−	0.133730i
$672$		0			0
$673$	−0.866025	+	0.500000i	−0.0333828	+	0.0192736i	−0.516599	−	0.856228i	$-0.672802\pi$
$673$	−0.866025	+	0.500000i	−0.0333828	+	0.0192736i	0.483216	+	0.875501i	$0.339469\pi$
$674$		0			0
$675$		0			0
$676$	−22.0000	+	13.8564i	−0.846154	+	0.532939i
$677$		−	48.0000i		−	1.84479i	−0.386248	−	0.922395i	$-0.626229\pi$
$677$		−	48.0000i		−	1.84479i	0.386248	−	0.922395i	$-0.373771\pi$
$678$		0			0
$679$	−4.50000	−	7.79423i	−0.172694	−	0.299115i
$680$		0			0
$681$			20.7846i			0.796468i
$682$		0			0
$683$	−12.1244	+	21.0000i	−0.463926	+	0.803543i	−0.999152	−	0.0411658i	$-0.986893\pi$
$683$	−12.1244	+	21.0000i	−0.463926	+	0.803543i	0.535227	+	0.844708i	$0.320226\pi$
$684$			6.92820i			0.264906i
$685$		0			0
$686$		0			0
$687$	−13.8564	−	24.0000i	−0.528655	−	0.915657i
$688$		−	4.00000i		−	0.152499i
$689$	−42.0000	−	10.3923i	−1.60007	−	0.395915i
$690$		0			0
$691$	37.5000	−	21.6506i	1.42657	−	0.823629i	0.429719	−	0.902963i	$-0.358613\pi$
$691$	37.5000	−	21.6506i	1.42657	−	0.823629i	0.996848	+	0.0793336i	$0.0252792\pi$
$692$	10.3923	−	6.00000i	0.395056	−	0.228086i
$693$	−5.19615	−	3.00000i	−0.197386	−	0.113961i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$		0			0
$704$	24.0000	−	13.8564i	0.904534	−	0.522233i
$705$		0			0
$706$		0			0
$707$	−31.1769			−1.17253
$708$	−3.46410	+	6.00000i	−0.130189	+	0.225494i
$709$	16.5000	+	9.52628i	0.619671	+	0.357767i	0.776741	−	0.629821i	$-0.216872\pi$
$709$	16.5000	+	9.52628i	0.619671	+	0.357767i	−0.157070	+	0.987587i	$0.550205\pi$
$710$		0			0
$711$	5.50000	−	9.52628i	0.206266	−	0.357263i
$712$		0			0
$713$	5.19615	+	9.00000i	0.194597	+	0.337053i
$714$		0			0
$715$		0			0
$716$	24.0000			0.896922
$717$		0			0
$718$		0			0
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	1.50000	+	0.866025i	0.0558629	+	0.0322525i
$722$		0			0
$723$	−20.7846			−0.772988
$724$	14.0000	−	24.2487i	0.520306	−	0.901196i
$725$		0			0
$726$		0			0
$727$			35.0000i			1.29808i	0.760755	+	0.649039i	$0.224829\pi$
$727$			35.0000i			1.29808i	−0.760755	+	0.649039i	$0.775171\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$	−1.73205	−	1.00000i	−0.0640184	−	0.0369611i
$733$	39.8372			1.47142			0.735710	−	0.677297i	$-0.236849\pi$
$733$	39.8372			1.47142			0.735710	+	0.677297i	$0.236849\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.9808	+	15.0000i	0.957014	+	0.552532i
$738$		0			0
$739$	−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
$741$	−3.00000	+	12.1244i	−0.110208	+	0.445399i
$742$		0			0
$743$	−5.19615	−	9.00000i	−0.190628	−	0.330178i	0.754830	−	0.655920i	$-0.227719\pi$
$743$	−5.19615	−	9.00000i	−0.190628	−	0.330178i	−0.945459	+	0.325742i	$0.894386\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−6.92820	+	12.0000i	−0.253490	+	0.439057i
$748$		0			0
$749$			10.3923i			0.379727i
$750$		0			0
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	6.92820	+	12.0000i	0.252646	+	0.437595i
$753$		−	12.0000i		−	0.437304i
$754$		0			0
$755$		0			0
$756$	−3.00000	+	1.73205i	−0.109109	+	0.0629941i
$757$	−29.4449	+	17.0000i	−1.07019	+	0.617876i	−0.928234	−	0.371997i	$-0.878673\pi$
$757$	−29.4449	+	17.0000i	−1.07019	+	0.617876i	−0.141958	+	0.989873i	$0.545340\pi$
$758$		0			0
$759$			20.7846i			0.754434i
$760$		0			0
$761$	−18.0000	−	10.3923i	−0.652499	−	0.376721i	0.136914	−	0.990583i	$-0.456282\pi$
$761$	−18.0000	−	10.3923i	−0.652499	−	0.376721i	−0.789413	+	0.613862i	$0.789615\pi$
$762$		0			0
$763$	23.3827	+	13.5000i	0.846510	+	0.488733i
$764$	−18.0000	−	31.1769i	−0.651217	−	1.12794i
$765$		0			0
$766$		0			0
$767$	−8.66025	+	9.00000i	−0.312704	+	0.324971i
$768$		−	16.0000i		−	0.577350i
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	−0.387901	−	0.921701i	$-0.626800\pi$
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	0.604266	+	0.796782i	$0.293466\pi$
$770$		0			0
$771$		0			0
$772$	−31.1769			−1.12208
$773$	25.9808	−	45.0000i	0.934463	−	1.61854i	0.158874	−	0.987299i	$-0.449213\pi$
$773$	25.9808	−	45.0000i	0.934463	−	1.61854i	0.775589	−	0.631239i	$-0.217453\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.0000			0.859889
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$	−5.19615	+	3.00000i	−0.185695	+	0.107211i
$784$	8.00000	−	13.8564i	0.285714	−	0.494872i
$785$		0			0
$786$		0			0
$787$	16.4545	−	28.5000i	0.586539	−	1.01592i	−0.408143	−	0.912918i	$-0.633823\pi$
$787$	16.4545	−	28.5000i	0.586539	−	1.01592i	0.994682	−	0.102997i	$-0.0328433\pi$
$788$	−27.7128			−0.987228
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$	9.00000	−	5.19615i	0.320003	−	0.184754i
$792$		0			0
$793$	−2.59808	−	2.50000i	−0.0922604	−	0.0887776i
$794$		0			0
$795$		0			0
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	10.3923	+	6.00000i	0.368114	+	0.212531i	0.672634	−	0.739975i	$-0.265163\pi$
$797$	10.3923	+	6.00000i	0.368114	+	0.212531i	−0.304520	+	0.952506i	$0.598496\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			6.92820i			0.244796i
$802$		0			0
$803$	−5.19615	+	3.00000i	−0.183368	+	0.105868i
$804$	15.0000	−	8.66025i	0.529009	−	0.305424i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$		0			0
$811$			25.9808i			0.912308i	0.889901	+	0.456154i	$0.150773\pi$
$811$			25.9808i			0.912308i	−0.889901	+	0.456154i	$0.849227\pi$
$812$	−10.3923	+	18.0000i	−0.364698	+	0.631676i
$813$	2.59808	−	4.50000i	0.0911185	−	0.157822i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.73205	−	3.00000i	−0.0605968	−	0.104957i
$818$		0			0
$819$	−6.00000	+	1.73205i	−0.209657	+	0.0605228i
$820$		0			0
$821$	21.0000	−	12.1244i	0.732905	−	0.423143i	−0.0865789	−	0.996245i	$-0.527593\pi$
$821$	21.0000	−	12.1244i	0.732905	−	0.423143i	0.819484	+	0.573102i	$0.194260\pi$
$822$		0			0
$823$	−27.7128	−	16.0000i	−0.966008	−	0.557725i	−0.0679910	−	0.997686i	$-0.521659\pi$
$823$	−27.7128	−	16.0000i	−0.966008	−	0.557725i	−0.898017	+	0.439961i	$0.854992\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−48.4974			−1.68642			−0.843210	−	0.537584i	$-0.819337\pi$
$827$	−48.4974			−1.68642			−0.843210	+	0.537584i	$0.819337\pi$
$828$	10.3923	+	6.00000i	0.361158	+	0.208514i
$829$	15.5000	+	26.8468i	0.538337	+	0.932427i	0.998994	+	0.0448490i	$0.0142807\pi$
$829$	15.5000	+	26.8468i	0.538337	+	0.932427i	−0.460657	+	0.887578i	$0.652386\pi$
$830$		0			0
$831$	10.0000			0.346896
$832$	6.92820	−	28.0000i	0.240192	−	0.970725i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$	1.73205			0.0598684
$838$		0			0
$839$	−27.0000	−	15.5885i	−0.932144	−	0.538173i	−0.0446547	−	0.999002i	$-0.514219\pi$
$839$	−27.0000	−	15.5885i	−0.932144	−	0.538173i	−0.887489	+	0.460829i	$0.847552\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$		0			0
$843$	−12.1244	−	21.0000i	−0.417585	−	0.723278i
$844$	−26.0000			−0.894957
$845$		0			0
$846$		0			0
$847$	0.866025	+	1.50000i	0.0297570	+	0.0515406i
$848$	41.5692	−	24.0000i	1.42749	−	0.824163i
$849$	5.50000	−	9.52628i	0.188760	−	0.326941i
$850$		0			0
$851$		0			0
$852$	10.3923	−	18.0000i	0.356034	−	0.616670i
$853$	−25.9808			−0.889564			−0.444782	−	0.895639i	$-0.646719\pi$
$853$	−25.9808			−0.889564			−0.444782	+	0.895639i	$0.646719\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$		0			0
$859$	−13.0000			−0.443554			−0.221777	−	0.975097i	$-0.571186\pi$
$859$	−13.0000			−0.443554			−0.221777	+	0.975097i	$0.571186\pi$
$860$		0			0
$861$	6.00000	+	10.3923i	0.204479	+	0.354169i
$862$		0			0
$863$	−17.3205			−0.589597			−0.294798	−	0.955559i	$-0.595253\pi$
$863$	−17.3205			−0.589597			−0.294798	+	0.955559i	$0.595253\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	14.7224	+	8.50000i	0.500000	+	0.288675i
$868$	5.19615	−	3.00000i	0.176369	−	0.101827i
$869$	−33.0000	+	19.0526i	−1.11945	+	0.646314i
$870$		0			0
$871$	30.0000	−	8.66025i	1.01651	−	0.293442i
$872$		0			0
$873$	2.59808	+	4.50000i	0.0879316	+	0.152302i
$874$		0			0
$875$		0			0
$876$			3.46410i			0.117041i
$877$	20.7846	−	36.0000i	0.701846	−	1.21563i	−0.265971	−	0.963981i	$-0.585693\pi$
$877$	20.7846	−	36.0000i	0.701846	−	1.21563i	0.967818	−	0.251653i	$-0.0809741\pi$
$878$		0			0
$879$			17.3205i			0.584206i
$880$		0			0
$881$	6.00000	+	10.3923i	0.202145	+	0.350126i	0.949219	−	0.314615i	$-0.101875\pi$
$881$	6.00000	+	10.3923i	0.202145	+	0.350126i	−0.747074	+	0.664741i	$0.768542\pi$
$882$		0			0
$883$		−	5.00000i		−	0.168263i	−0.996455	−	0.0841317i	$-0.973188\pi$
$883$		−	5.00000i		−	0.168263i	0.996455	−	0.0841317i	$-0.0268116\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	36.3731	−	21.0000i	1.22129	−	0.705111i	0.256096	−	0.966651i	$-0.417564\pi$
$887$	36.3731	−	21.0000i	1.22129	−	0.705111i	0.965193	+	0.261540i	$0.0842305\pi$
$888$		0			0
$889$		−	22.5167i		−	0.755185i
$890$		0			0
$891$	3.00000	+	1.73205i	0.100504	+	0.0580259i
$892$	34.6410			1.15987
$893$	10.3923	+	6.00000i	0.347765	+	0.200782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	15.5885	+	15.0000i	0.520483	+	0.500835i
$898$		0			0
$899$	9.00000	−	5.19615i	0.300167	−	0.173301i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	0.866025	−	1.50000i	0.0288195	−	0.0499169i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	38.1051	−	22.0000i	1.26526	−	0.730498i	0.291172	−	0.956671i	$-0.405955\pi$
$907$	38.1051	−	22.0000i	1.26526	−	0.730498i	0.974087	+	0.226173i	$0.0726213\pi$
$908$	−20.7846	−	36.0000i	−0.689761	−	1.19470i
$909$	18.0000			0.597022
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	−6.92820	−	12.0000i	−0.229416	−	0.397360i
$913$	41.5692	−	24.0000i	1.37574	−	0.794284i
$914$		0			0
$915$		0			0
$916$	48.0000	+	27.7128i	1.58596	+	0.915657i
$917$	−5.19615	+	9.00000i	−0.171592	+	0.297206i
$918$		0			0
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$		0			0
$921$	−1.50000	+	0.866025i	−0.0494267	+	0.0285365i
$922$		0			0
$923$	25.9808	−	27.0000i	0.855167	−	0.888716i
$924$	12.0000			0.394771
$925$		0			0
$926$		0			0
$927$	−0.866025	−	0.500000i	−0.0284440	−	0.0164222i
$928$		0			0
$929$	18.0000	+	10.3923i	0.590561	+	0.340960i	0.765319	−	0.643651i	$-0.222581\pi$
$929$	18.0000	+	10.3923i	0.590561	+	0.340960i	−0.174758	+	0.984611i	$0.555914\pi$
$930$		0			0
$931$		−	13.8564i		−	0.454125i
$932$	−31.1769	−	18.0000i	−1.02123	−	0.589610i
$933$	20.7846	−	12.0000i	0.680458	−	0.392862i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			14.0000i			0.457360i	0.973502	+	0.228680i	$0.0734410\pi$
$937$			14.0000i			0.457360i	−0.973502	+	0.228680i	$0.926559\pi$
$938$		0			0
$939$	−6.50000	−	11.2583i	−0.212119	−	0.367402i
$940$		0			0
$941$			10.3923i			0.338779i	0.985549	+	0.169390i	$0.0541797\pi$
$941$			10.3923i			0.338779i	−0.985549	+	0.169390i	$0.945820\pi$
$942$		0			0
$943$	20.7846	−	36.0000i	0.676840	−	1.17232i
$944$		−	13.8564i		−	0.450988i
$945$		0			0
$946$		0			0
$947$	24.2487	+	42.0000i	0.787977	+	1.36482i	0.927204	+	0.374556i	$0.122205\pi$
$947$	24.2487	+	42.0000i	0.787977	+	1.36482i	−0.139227	+	0.990260i	$0.544462\pi$
$948$			22.0000i			0.714527i
$949$	−1.50000	+	6.06218i	−0.0486921	+	0.196787i
$950$		0			0
$951$	6.00000	−	3.46410i	0.194563	−	0.112331i
$952$		0			0
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	0.413473	−	0.910516i	$-0.364315\pi$
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	−0.581793	+	0.813337i	$0.697649\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	20.7846			0.671871
$958$		0			0
$959$		0			0
$960$		0			0
$961$	28.0000			0.903226
$962$		0			0
$963$		−	6.00000i		−	0.193347i
$964$	36.0000	−	20.7846i	1.15948	−	0.669427i
$965$		0			0
$966$		0			0
$967$	24.2487			0.779786			0.389893	−	0.920860i	$-0.372512\pi$
$967$	24.2487			0.779786			0.389893	+	0.920860i	$0.372512\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	1.73205	−	1.00000i	0.0555556	−	0.0320750i
$973$	4.33013	+	7.50000i	0.138817	+	0.240439i
$974$		0			0
$975$		0			0
$976$	4.00000			0.128037
$977$	13.8564	+	24.0000i	0.443306	+	0.767828i	0.997932	−	0.0642712i	$-0.0204723\pi$
$977$	13.8564	+	24.0000i	0.443306	+	0.767828i	−0.554627	+	0.832099i	$0.687139\pi$
$978$		0			0
$979$	12.0000	−	20.7846i	0.383522	−	0.664279i
$980$		0			0
$981$	−13.5000	−	7.79423i	−0.431022	−	0.248851i
$982$		0			0
$983$	−10.3923			−0.331463			−0.165732	−	0.986171i	$-0.552999\pi$
$983$	−10.3923			−0.331463			−0.165732	+	0.986171i	$0.552999\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			6.00000i			0.190982i
$988$	−6.92820	−	24.0000i	−0.220416	−	0.763542i
$989$	−6.00000			−0.190789
$990$		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	$0.751545\pi$
$992$		0			0
$993$	−5.19615			−0.164895
$994$		0			0
$995$		0			0
$996$		−	27.7128i		−	0.878114i
$997$	30.3109	+	17.5000i	0.959955	+	0.554231i	0.896159	−	0.443732i	$-0.146346\pi$
$997$	30.3109	+	17.5000i	0.959955	+	0.554231i	0.0637961	+	0.997963i	$0.479679\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.w.d.49.1		4
5.2	odd	4		39.2.j.a.10.1	yes	2
5.3	odd	4		975.2.bc.c.751.1		2
5.4	even	2	inner	975.2.w.d.49.2		4
13.4	even	6	inner	975.2.w.d.199.2		4
15.2	even	4		117.2.q.a.10.1		2
20.7	even	4		624.2.bv.b.49.1		2
60.47	odd	4		1872.2.by.f.1297.1		2
65.2	even	12		507.2.a.e.1.1		2
65.4	even	6	inner	975.2.w.d.199.1		4
65.7	even	12		507.2.e.f.22.2		4
65.12	odd	4		507.2.j.b.361.1		2
65.17	odd	12		39.2.j.a.4.1	✓	2
65.22	odd	12		507.2.j.b.316.1		2
65.32	even	12		507.2.e.f.22.1		4
65.37	even	12		507.2.a.e.1.2		2
65.42	odd	12		507.2.b.c.337.1		2
65.43	odd	12		975.2.bc.c.901.1		2
65.47	even	4		507.2.e.f.484.2		4
65.57	even	4		507.2.e.f.484.1		4
65.62	odd	12		507.2.b.c.337.2		2
195.2	odd	12		1521.2.a.h.1.2		2
195.17	even	12		117.2.q.a.82.1		2
195.62	even	12		1521.2.b.f.1351.1		2
195.107	even	12		1521.2.b.f.1351.2		2
195.167	odd	12		1521.2.a.h.1.1		2
260.67	odd	12		8112.2.a.bu.1.1		2
260.147	even	12		624.2.bv.b.433.1		2
260.167	odd	12		8112.2.a.bu.1.2		2
780.407	odd	12		1872.2.by.f.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.j.a.4.1	✓	2	65.17	odd	12
39.2.j.a.10.1	yes	2	5.2	odd	4
117.2.q.a.10.1		2	15.2	even	4
117.2.q.a.82.1		2	195.17	even	12
507.2.a.e.1.1		2	65.2	even	12
507.2.a.e.1.2		2	65.37	even	12
507.2.b.c.337.1		2	65.42	odd	12
507.2.b.c.337.2		2	65.62	odd	12
507.2.e.f.22.1		4	65.32	even	12
507.2.e.f.22.2		4	65.7	even	12
507.2.e.f.484.1		4	65.57	even	4
507.2.e.f.484.2		4	65.47	even	4
507.2.j.b.316.1		2	65.22	odd	12
507.2.j.b.361.1		2	65.12	odd	4
624.2.bv.b.49.1		2	20.7	even	4
624.2.bv.b.433.1		2	260.147	even	12
975.2.w.d.49.1		4	1.1	even	1	trivial
975.2.w.d.49.2		4	5.4	even	2	inner
975.2.w.d.199.1		4	65.4	even	6	inner
975.2.w.d.199.2		4	13.4	even	6	inner
975.2.bc.c.751.1		2	5.3	odd	4
975.2.bc.c.901.1		2	65.43	odd	12
1521.2.a.h.1.1		2	195.167	odd	12
1521.2.a.h.1.2		2	195.2	odd	12
1521.2.b.f.1351.1		2	195.62	even	12
1521.2.b.f.1351.2		2	195.107	even	12
1872.2.by.f.433.1		2	780.407	odd	12
1872.2.by.f.1297.1		2	60.47	odd	4
8112.2.a.bu.1.1		2	260.67	odd	12
8112.2.a.bu.1.2		2	260.167	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.866025 + 1.50000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-3.00000 + 1.73205i) q^{11} +2.00000i q^{12} +(-0.866025 + 3.50000i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(-3.00000 - 1.73205i) q^{19} -1.73205i q^{21} +(-5.19615 + 3.00000i) q^{23} +1.00000i q^{27} +(1.73205 + 3.00000i) q^{28} +(3.00000 + 5.19615i) q^{29} -1.73205i q^{31} +(1.73205 - 3.00000i) q^{33} +(-1.00000 - 1.73205i) q^{36} +(-1.00000 - 3.46410i) q^{39} +(-6.00000 + 3.46410i) q^{41} +(0.866025 + 0.500000i) q^{43} +6.92820i q^{44} -3.46410 q^{47} +(3.46410 + 2.00000i) q^{48} +(2.00000 + 3.46410i) q^{49} +(5.19615 + 5.00000i) q^{52} +12.0000i q^{53} +3.46410 q^{57} +(3.00000 + 1.73205i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(0.866025 + 1.50000i) q^{63} -8.00000 q^{64} +(-4.33013 - 7.50000i) q^{67} +(3.00000 - 5.19615i) q^{69} +(-9.00000 - 5.19615i) q^{71} +1.73205 q^{73} +(-6.00000 + 3.46410i) q^{76} -6.00000i q^{77} +11.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} -13.8564 q^{83} +(-3.00000 - 1.73205i) q^{84} +(-5.19615 - 3.00000i) q^{87} +(-6.00000 + 3.46410i) q^{89} +(-4.50000 - 4.33013i) q^{91} +12.0000i q^{92} +(0.866025 + 1.50000i) q^{93} +(-2.59808 + 4.50000i) q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 2 q^{9} - 12 q^{11} - 8 q^{16} - 12 q^{19} + 12 q^{29} - 4 q^{36} - 4 q^{39} - 24 q^{41} + 8 q^{49} + 12 q^{59} - 2 q^{61} - 32 q^{64} + 12 q^{69} - 36 q^{71} - 24 q^{76} + 44 q^{79} - 2 q^{81}+ \cdots - 18 q^{91}+O(q^{100}) \) 4 * q + 4 * q^4 + 2 * q^9 - 12 * q^11 - 8 * q^16 - 12 * q^19 + 12 * q^29 - 4 * q^36 - 4 * q^39 - 24 * q^41 + 8 * q^49 + 12 * q^59 - 2 * q^61 - 32 * q^64 + 12 * q^69 - 36 * q^71 - 24 * q^76 + 44 * q^79 - 2 * q^81 - 12 * q^84 - 24 * q^89 - 18 * q^91

Introduction

L-functions

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