LMFDB - Embedded newform 980.2.q.c.949.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(569,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.569"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	980.949
Dual form			980.2.q.c.569.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 - 1.50000i) q^{3} +(-0.133975 - 2.23205i) q^{5} +(3.00000 + 5.19615i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000i q^{13} +(-3.00000 + 6.00000i) q^{15} +(-4.33013 - 2.50000i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-1.73205 + 1.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -9.00000i q^{27} +1.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(7.79423 - 4.50000i) q^{33} +(8.66025 - 5.00000i) q^{37} +(1.50000 - 2.59808i) q^{39} +6.00000 q^{41} +4.00000i q^{43} +(11.1962 - 7.39230i) q^{45} +(-9.52628 + 5.50000i) q^{47} +(7.50000 + 12.9904i) q^{51} +(5.19615 + 3.00000i) q^{53} +(6.00000 + 3.00000i) q^{55} -24.0000i q^{57} +(5.00000 - 8.66025i) q^{59} +(2.23205 - 0.133975i) q^{65} +(8.66025 + 5.00000i) q^{67} +6.00000 q^{69} +(8.66025 + 5.00000i) q^{73} +(13.7942 + 5.89230i) q^{75} +(-3.50000 - 6.06218i) q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000i q^{83} +(-5.00000 + 10.0000i) q^{85} +(-2.59808 - 1.50000i) q^{87} +(-4.00000 - 6.92820i) q^{89} +(5.19615 - 3.00000i) q^{93} +(14.9282 - 9.85641i) q^{95} -3.00000i q^{97} -18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} + 12 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{31} + 6 q^{39} + 24 q^{41} + 24 q^{45} + 30 q^{51} + 24 q^{55} + 20 q^{59} + 2 q^{65} + 24 q^{69} + 24 q^{75} - 14 q^{79}+ \cdots - 72 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 + 12 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^31 + 6 * q^39 + 24 * q^41 + 24 * q^45 + 30 * q^51 + 24 * q^55 + 20 * q^59 + 2 * q^65 + 24 * q^69 + 24 * q^75 - 14 * q^79 - 18 * q^81 - 20 * q^85 - 16 * q^89 + 32 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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
$2$		0			0
$3$	−2.59808	−	1.50000i	−1.50000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−2.59808	−	1.50000i	−1.50000	−	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	3.00000	+	5.19615i	1.00000	+	1.73205i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$	−3.00000	+	6.00000i	−0.774597	+	1.54919i
$16$		0			0
$17$	−4.33013	−	2.50000i	−1.05021	−	0.606339i	−0.127502	−	0.991838i	$-0.540696\pi$
$17$	−4.33013	−	2.50000i	−1.05021	−	0.606339i	−0.922708	+	0.385499i	$0.874029\pi$
$18$		0			0
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.802955	+	0.596040i	$0.203260\pi$
$19$	4.00000	+	6.92820i	0.917663	+	1.58944i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	−0.669588	−	0.742732i	$-0.733529\pi$
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	0.308431	+	0.951247i	$0.400196\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$		0			0
$27$		−	9.00000i		−	1.73205i
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		0			0
$33$	7.79423	−	4.50000i	1.35680	−	0.783349i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.66025	−	5.00000i	1.42374	−	0.821995i	0.427121	−	0.904194i	$-0.359528\pi$
$37$	8.66025	−	5.00000i	1.42374	−	0.821995i	0.996616	+	0.0821995i	$0.0261945\pi$
$38$		0			0
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		0			0
$45$	11.1962	−	7.39230i	1.66902	−	1.10198i
$46$		0			0
$47$	−9.52628	+	5.50000i	−1.38955	+	0.802257i	−0.993264	−	0.115870i	$-0.963035\pi$
$47$	−9.52628	+	5.50000i	−1.38955	+	0.802257i	−0.396286	+	0.918127i	$0.629701\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	7.50000	+	12.9904i	1.05021	+	1.81902i
$52$		0			0
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	0.812447	−	0.583036i	$-0.198135\pi$
$53$	5.19615	+	3.00000i	0.713746	+	0.412082i	−0.0987002	+	0.995117i	$0.531468\pi$
$54$		0			0
$55$	6.00000	+	3.00000i	0.809040	+	0.404520i
$56$		0			0
$57$		−	24.0000i		−	3.17888i
$58$		0			0
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.23205	−	0.133975i	0.276852	−	0.0166175i
$66$		0			0
$67$	8.66025	+	5.00000i	1.05802	+	0.610847i	0.924883	−	0.380251i	$-0.124162\pi$
$67$	8.66025	+	5.00000i	1.05802	+	0.610847i	0.133135	+	0.991098i	$0.457496\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.912245	−	0.409644i	$-0.134347\pi$
$73$	8.66025	+	5.00000i	1.01361	+	0.585206i	0.101361	+	0.994850i	$0.467680\pi$
$74$		0			0
$75$	13.7942	+	5.89230i	1.59282	+	0.680385i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.50000	−	6.06218i	−0.393781	−	0.682048i	0.599164	−	0.800626i	$-0.295500\pi$
$79$	−3.50000	−	6.06218i	−0.393781	−	0.682048i	−0.992945	+	0.118578i	$0.962166\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$	−5.00000	+	10.0000i	−0.542326	+	1.08465i
$86$		0			0
$87$	−2.59808	−	1.50000i	−0.278543	−	0.160817i
$88$		0			0
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	0.572327	−	0.820025i	$-0.306041\pi$
$89$	−4.00000	−	6.92820i	−0.423999	−	0.734388i	−0.996326	+	0.0856373i	$0.972707\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.19615	−	3.00000i	0.538816	−	0.311086i
$94$		0			0
$95$	14.9282	−	9.85641i	1.53160	−	1.01125i
$96$		0			0
$97$		−	3.00000i		−	0.304604i	−0.988334	−	0.152302i	$-0.951331\pi$
$97$		−	3.00000i		−	0.304604i	0.988334	−	0.152302i	$-0.0486686\pi$
$98$		0			0
$99$	−18.0000			−1.80907
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	−4.33013	+	2.50000i	−0.426660	+	0.246332i	−0.697923	−	0.716173i	$-0.745892\pi$
$103$	−4.33013	+	2.50000i	−0.426660	+	0.246332i	0.271263	+	0.962505i	$0.412559\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.92820	−	4.00000i	0.669775	−	0.386695i	−0.126217	−	0.992003i	$-0.540283\pi$
$107$	6.92820	−	4.00000i	0.669775	−	0.386695i	0.795991	+	0.605308i	$0.206950\pi$
$108$		0			0
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$		0			0
$111$	−30.0000			−2.84747
$112$		0			0
$113$			10.0000i			0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$			10.0000i			0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$		0			0
$115$	2.46410	+	3.73205i	0.229779	+	0.348016i
$116$		0			0
$117$	−5.19615	+	3.00000i	−0.480384	+	0.277350i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−15.5885	−	9.00000i	−1.40556	−	0.811503i
$124$		0			0
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$		0			0
$129$	6.00000	−	10.3923i	0.528271	−	0.914991i
$130$		0			0
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	0.906399	−	0.422423i	$-0.138820\pi$
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	−0.819028	+	0.573753i	$0.805487\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−20.0885	+	1.20577i	−1.72894	+	0.103776i
$136$		0			0
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		0			0
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$	33.0000			2.77910
$142$		0			0
$143$	−2.59808	−	1.50000i	−0.217262	−	0.125436i
$144$		0			0
$145$	−0.133975	−	2.23205i	−0.0111260	−	0.185362i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	−0.988969	−	0.148124i	$-0.952676\pi$
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	0.622764	+	0.782410i	$0.286010\pi$
$152$		0			0
$153$		−	30.0000i		−	2.42536i
$154$		0			0
$155$	4.00000	+	2.00000i	0.321288	+	0.160644i
$156$		0			0
$157$	−15.5885	−	9.00000i	−1.24409	−	0.718278i	−0.274169	−	0.961681i	$-0.588403\pi$
$157$	−15.5885	−	9.00000i	−1.24409	−	0.718278i	−0.969925	+	0.243403i	$0.921736\pi$
$158$		0			0
$159$	−9.00000	−	15.5885i	−0.713746	−	1.23625i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.19615	+	3.00000i	−0.406994	+	0.234978i	−0.689497	−	0.724288i	$-0.742169\pi$
$163$	−5.19615	+	3.00000i	−0.406994	+	0.234978i	0.282503	+	0.959266i	$0.408835\pi$
$164$		0			0
$165$	−11.0885	−	16.7942i	−0.863235	−	1.30743i
$166$		0			0
$167$		−	3.00000i		−	0.232147i	−0.993241	−	0.116073i	$-0.962969\pi$
$167$		−	3.00000i		−	0.232147i	0.993241	−	0.116073i	$-0.0370308\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−24.0000	+	41.5692i	−1.83533	+	3.17888i
$172$		0			0
$173$	−7.79423	+	4.50000i	−0.592584	+	0.342129i	−0.766119	−	0.642699i	$-0.777815\pi$
$173$	−7.79423	+	4.50000i	−0.592584	+	0.342129i	0.173534	+	0.984828i	$0.444481\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−25.9808	+	15.0000i	−1.95283	+	1.12747i
$178$		0			0
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.3205	−	18.6603i	−0.905822	−	1.37193i
$186$		0			0
$187$	12.9904	−	7.50000i	0.949951	−	0.548454i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.50000	−	6.06218i	−0.253251	−	0.438644i	0.711168	−	0.703022i	$-0.248167\pi$
$191$	−3.50000	−	6.06218i	−0.253251	−	0.438644i	−0.964419	+	0.264378i	$0.914833\pi$
$192$		0			0
$193$	6.92820	+	4.00000i	0.498703	+	0.287926i	0.728178	−	0.685388i	$-0.240368\pi$
$193$	6.92820	+	4.00000i	0.498703	+	0.287926i	−0.229475	+	0.973315i	$0.573701\pi$
$194$		0			0
$195$	−6.00000	−	3.00000i	−0.429669	−	0.214834i
$196$		0			0
$197$			10.0000i			0.712470i	0.934396	+	0.356235i	$0.115940\pi$
$197$			10.0000i			0.712470i	−0.934396	+	0.356235i	$0.884060\pi$
$198$		0			0
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	0.347879	+	0.937539i	$0.386902\pi$
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	−0.985873	+	0.167497i	$0.946431\pi$
$200$		0			0
$201$	−15.0000	−	25.9808i	−1.05802	−	1.83254i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.803848	−	13.3923i	−0.0561432	−	0.935359i
$206$		0			0
$207$	−10.3923	−	6.00000i	−0.722315	−	0.417029i
$208$		0			0
$209$	−24.0000			−1.66011
$210$		0			0
$211$	−3.00000			−0.206529			−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000			−0.206529			−0.103264	+	0.994654i	$0.532929\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.92820	−	0.535898i	0.608898	−	0.0365480i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−15.0000	−	25.9808i	−1.01361	−	1.75562i
$220$		0			0
$221$	2.50000	−	4.33013i	0.168168	−	0.291276i
$222$		0			0
$223$			19.0000i			1.27233i	0.771551	+	0.636167i	$0.219481\pi$
$223$			19.0000i			1.27233i	−0.771551	+	0.636167i	$0.780519\pi$
$224$		0			0
$225$	−18.0000	−	24.0000i	−1.20000	−	1.60000i
$226$		0			0
$227$	23.3827	+	13.5000i	1.55196	+	0.896026i	0.997982	+	0.0634974i	$0.0202255\pi$
$227$	23.3827	+	13.5000i	1.55196	+	0.896026i	0.553981	+	0.832529i	$0.313108\pi$
$228$		0			0
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	0.872823	+	0.488037i	$0.162287\pi$
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	−0.0137585	+	0.999905i	$0.504380\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.8564	+	8.00000i	−0.907763	+	0.524097i	−0.879711	−	0.475509i	$-0.842264\pi$
$233$	−13.8564	+	8.00000i	−0.907763	+	0.524097i	−0.0280525	+	0.999606i	$0.508931\pi$
$234$		0			0
$235$	13.5526	+	20.5263i	0.884071	+	1.33899i
$236$		0			0
$237$			21.0000i			1.36410i
$238$		0			0
$239$	−5.00000			−0.323423			−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000			−0.323423			−0.161712	+	0.986838i	$0.551701\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.92820	+	4.00000i	−0.440831	+	0.254514i
$248$		0			0
$249$	18.0000	−	31.1769i	1.14070	−	1.97576i
$250$		0			0
$251$	−2.00000			−0.126239			−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000			−0.126239			−0.0631194	+	0.998006i	$0.520105\pi$
$252$		0			0
$253$		−	6.00000i		−	0.377217i
$254$		0			0
$255$	27.9904	−	18.4808i	1.75283	−	1.15731i
$256$		0			0
$257$	−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	$0.393253\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$		0			0
$265$	6.00000	−	12.0000i	0.368577	−	0.737154i
$266$		0			0
$267$			24.0000i			1.46878i
$268$		0			0
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	−0.894900	−	0.446267i	$-0.852753\pi$
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	0.833929	+	0.551872i	$0.186086\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.89230	−	13.7942i	0.355319	−	0.831823i
$276$		0			0
$277$	12.1244	+	7.00000i	0.728482	+	0.420589i	0.817867	−	0.575408i	$-0.195157\pi$
$277$	12.1244	+	7.00000i	0.728482	+	0.420589i	−0.0893846	+	0.995997i	$0.528490\pi$
$278$		0			0
$279$	−12.0000			−0.718421
$280$		0			0
$281$	15.0000			0.894825			0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000			0.894825			0.447412	+	0.894328i	$0.352346\pi$
$282$		0			0
$283$	6.06218	+	3.50000i	0.360359	+	0.208053i	0.669238	−	0.743048i	$-0.266621\pi$
$283$	6.06218	+	3.50000i	0.360359	+	0.208053i	−0.308879	+	0.951101i	$0.599954\pi$
$284$		0			0
$285$	−53.5692	+	3.21539i	−3.17317	+	0.190463i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−4.50000	+	7.79423i	−0.263795	+	0.456906i
$292$		0			0
$293$			15.0000i			0.876309i	0.898900	+	0.438155i	$0.144368\pi$
$293$			15.0000i			0.876309i	−0.898900	+	0.438155i	$0.855632\pi$
$294$		0			0
$295$	−20.0000	−	10.0000i	−1.16445	−	0.582223i
$296$		0			0
$297$	23.3827	+	13.5000i	1.35680	+	0.783349i
$298$		0			0
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	31.1769	−	18.0000i	1.79107	−	1.03407i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			19.0000i			1.08439i	0.840254	+	0.542194i	$0.182406\pi$
$307$			19.0000i			1.08439i	−0.840254	+	0.542194i	$0.817594\pi$
$308$		0			0
$309$	15.0000			0.853320
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−6.06218	+	3.50000i	−0.342655	+	0.197832i	−0.661445	−	0.749993i	$-0.730057\pi$
$313$	−6.06218	+	3.50000i	−0.342655	+	0.197832i	0.318791	+	0.947825i	$0.396723\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	24.2487	−	14.0000i	1.36194	−	0.786318i	0.372061	−	0.928208i	$-0.378651\pi$
$317$	24.2487	−	14.0000i	1.36194	−	0.786318i	0.989882	+	0.141890i	$0.0453179\pi$
$318$		0			0
$319$	−1.50000	+	2.59808i	−0.0839839	+	0.145464i
$320$		0			0
$321$	−24.0000			−1.33955
$322$		0			0
$323$		−	40.0000i		−	2.22566i
$324$		0			0
$325$	−0.598076	−	4.96410i	−0.0331753	−	0.275359i
$326$		0			0
$327$	18.1865	−	10.5000i	1.00572	−	0.580651i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$		0			0
$333$	51.9615	+	30.0000i	2.84747	+	1.64399i
$334$		0			0
$335$	10.0000	−	20.0000i	0.546358	−	1.09272i
$336$		0			0
$337$			22.0000i			1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$			22.0000i			1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$		0			0
$339$	15.0000	−	25.9808i	0.814688	−	1.41108i
$340$		0			0
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.803848	−	13.3923i	−0.0432777	−	0.721017i
$346$		0			0
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	0.0193540	−	0.999813i	$-0.493839\pi$
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	−0.856186	+	0.516667i	$0.827172\pi$
$348$		0			0
$349$	36.0000			1.92704			0.963518	−	0.267644i	$-0.0862451\pi$
$349$	36.0000			1.92704			0.963518	+	0.267644i	$0.0862451\pi$
$350$		0			0
$351$	9.00000			0.480384
$352$		0			0
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	0.692869	−	0.721063i	$-0.256346\pi$
$353$	7.79423	+	4.50000i	0.414845	+	0.239511i	−0.278024	+	0.960574i	$0.589680\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.0000	+	24.2487i	0.738892	+	1.27980i	0.952995	+	0.302987i	$0.0979839\pi$
$359$	14.0000	+	24.2487i	0.738892	+	1.27980i	−0.214103	+	0.976811i	$0.568683\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$		−	6.00000i		−	0.314918i
$364$		0			0
$365$	10.0000	−	20.0000i	0.523424	−	1.04685i
$366$		0			0
$367$	16.4545	+	9.50000i	0.858917	+	0.495896i	0.863649	−	0.504093i	$-0.168173\pi$
$367$	16.4545	+	9.50000i	0.858917	+	0.495896i	−0.00473247	+	0.999989i	$0.501506\pi$
$368$		0			0
$369$	18.0000	+	31.1769i	0.937043	+	1.62301i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−27.7128	+	16.0000i	−1.43492	+	0.828449i	−0.997490	−	0.0708063i	$-0.977443\pi$
$373$	−27.7128	+	16.0000i	−1.43492	+	0.828449i	−0.437425	+	0.899255i	$0.644109\pi$
$374$		0			0
$375$	11.3038	−	31.5788i	0.583728	−	1.63072i
$376$		0			0
$377$			1.00000i			0.0515026i
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	−3.00000	+	5.19615i	−0.153695	+	0.266207i
$382$		0			0
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−20.7846	+	12.0000i	−1.05654	+	0.609994i
$388$		0			0
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	−0.729103	−	0.684403i	$-0.760063\pi$
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	0.957263	+	0.289220i	$0.0933960\pi$
$390$		0			0
$391$	10.0000			0.505722
$392$		0			0
$393$		−	6.00000i		−	0.302660i
$394$		0			0
$395$	−13.0622	+	8.62436i	−0.657229	+	0.433938i
$396$		0			0
$397$	14.7224	−	8.50000i	0.738898	−	0.426603i	−0.0827707	−	0.996569i	$-0.526377\pi$
$397$	14.7224	−	8.50000i	0.738898	−	0.426603i	0.821668	+	0.569966i	$0.193044\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		0			0
$403$	−1.73205	−	1.00000i	−0.0862796	−	0.0498135i
$404$		0			0
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		0			0
$407$			30.0000i			1.48704i
$408$		0			0
$409$	−2.00000	+	3.46410i	−0.0988936	+	0.171289i	−0.911227	−	0.411905i	$-0.864864\pi$
$409$	−2.00000	+	3.46410i	−0.0988936	+	0.171289i	0.812333	+	0.583193i	$0.198197\pi$
$410$		0			0
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	26.7846	−	1.60770i	1.31480	−	0.0789187i
$416$		0			0
$417$	−25.9808	−	15.0000i	−1.27228	−	0.734553i
$418$		0			0
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$		0			0
$423$	−57.1577	−	33.0000i	−2.77910	−	1.60451i
$424$		0			0
$425$	22.9904	+	9.82051i	1.11520	+	0.476365i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	4.50000	+	7.79423i	0.217262	+	0.376309i
$430$		0			0
$431$	18.5000	−	32.0429i	0.891114	−	1.54345i	0.0525716	−	0.998617i	$-0.483258\pi$
$431$	18.5000	−	32.0429i	0.891114	−	1.54345i	0.838542	−	0.544837i	$-0.183408\pi$
$432$		0			0
$433$		−	38.0000i		−	1.82616i	−0.407777	−	0.913082i	$-0.633696\pi$
$433$		−	38.0000i		−	1.82616i	0.407777	−	0.913082i	$-0.366304\pi$
$434$		0			0
$435$	−3.00000	+	6.00000i	−0.143839	+	0.287678i
$436$		0			0
$437$	−13.8564	−	8.00000i	−0.662842	−	0.382692i
$438$		0			0
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	−0.989401	−	0.145210i	$-0.953614\pi$
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	0.368945	−	0.929451i	$-0.379719\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.3923	+	6.00000i	−0.493753	+	0.285069i	−0.726130	−	0.687557i	$-0.758683\pi$
$443$	−10.3923	+	6.00000i	−0.493753	+	0.285069i	0.232377	+	0.972626i	$0.425350\pi$
$444$		0			0
$445$	−14.9282	+	9.85641i	−0.707665	+	0.467238i
$446$		0			0
$447$			18.0000i			0.851371i
$448$		0			0
$449$	−11.0000			−0.519122			−0.259561	−	0.965727i	$-0.583578\pi$
$449$	−11.0000			−0.519122			−0.259561	+	0.965727i	$0.583578\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$		0			0
$453$	23.3827	−	13.5000i	1.09861	−	0.634285i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.0526	+	11.0000i	−0.891241	+	0.514558i	−0.874348	−	0.485299i	$-0.838711\pi$
$457$	−19.0526	+	11.0000i	−0.891241	+	0.514558i	−0.0168929	+	0.999857i	$0.505377\pi$
$458$		0			0
$459$	−22.5000	+	38.9711i	−1.05021	+	1.81902i
$460$		0			0
$461$	−28.0000			−1.30409			−0.652045	−	0.758180i	$-0.726089\pi$
$461$	−28.0000			−1.30409			−0.652045	+	0.758180i	$0.726089\pi$
$462$		0			0
$463$		−	4.00000i		−	0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$		−	4.00000i		−	0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$		0			0
$465$	−7.39230	−	11.1962i	−0.342810	−	0.519209i
$466$		0			0
$467$	19.9186	−	11.5000i	0.921722	−	0.532157i	0.0375381	−	0.999295i	$-0.488048\pi$
$467$	19.9186	−	11.5000i	0.921722	−	0.532157i	0.884184	+	0.467139i	$0.154715\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	27.0000	+	46.7654i	1.24409	+	2.15483i
$472$		0			0
$473$	−10.3923	−	6.00000i	−0.477839	−	0.275880i
$474$		0			0
$475$	−24.0000	−	32.0000i	−1.10120	−	1.46826i
$476$		0			0
$477$			36.0000i			1.64833i
$478$		0			0
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	5.00000	+	8.66025i	0.227980	+	0.394874i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.69615	+	0.401924i	−0.304057	+	0.0182504i
$486$		0			0
$487$	22.5167	+	13.0000i	1.02033	+	0.589086i	0.914199	−	0.405266i	$-0.132821\pi$
$487$	22.5167	+	13.0000i	1.02033	+	0.589086i	0.106129	+	0.994352i	$0.466154\pi$
$488$		0			0
$489$	18.0000			0.813988
$490$		0			0
$491$	33.0000			1.48927			0.744635	−	0.667472i	$-0.232624\pi$
$491$	33.0000			1.48927			0.744635	+	0.667472i	$0.232624\pi$
$492$		0			0
$493$	−4.33013	−	2.50000i	−0.195019	−	0.112594i
$494$		0			0
$495$	2.41154	+	40.1769i	0.108391	+	1.80582i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$500$		0			0
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$		0			0
$503$			1.00000i			0.0445878i	0.999751	+	0.0222939i	$0.00709696\pi$
$503$			1.00000i			0.0445878i	−0.999751	+	0.0222939i	$0.992903\pi$
$504$		0			0
$505$	24.0000	+	12.0000i	1.06799	+	0.533993i
$506$		0			0
$507$	−31.1769	−	18.0000i	−1.38462	−	0.799408i
$508$		0			0
$509$	−13.0000	−	22.5167i	−0.576215	−	0.998033i	−0.995908	−	0.0903676i	$-0.971196\pi$
$509$	−13.0000	−	22.5167i	−0.576215	−	0.998033i	0.419694	−	0.907666i	$-0.362138\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	62.3538	−	36.0000i	2.75299	−	1.58944i
$514$		0			0
$515$	6.16025	+	9.33013i	0.271453	+	0.411135i
$516$		0			0
$517$		−	33.0000i		−	1.45134i
$518$		0			0
$519$	27.0000			1.18517
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		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	$0.477388\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.66025	−	5.00000i	0.377247	−	0.217803i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	60.0000			2.60378
$532$		0			0
$533$			6.00000i			0.259889i
$534$		0			0
$535$	−9.85641	−	14.9282i	−0.426130	−	0.645403i
$536$		0			0
$537$	−10.3923	+	6.00000i	−0.448461	+	0.258919i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	−25.9808	−	15.0000i	−1.11494	−	0.643712i
$544$		0			0
$545$	14.0000	+	7.00000i	0.599694	+	0.299847i
$546$		0			0
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	4.01924	+	66.9615i	0.170607	+	2.84236i
$556$		0			0
$557$	−17.3205	−	10.0000i	−0.733893	−	0.423714i	0.0859514	−	0.996299i	$-0.472607\pi$
$557$	−17.3205	−	10.0000i	−0.733893	−	0.423714i	−0.819845	+	0.572586i	$0.805940\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$		0			0
$561$	−45.0000			−1.89990
$562$		0			0
$563$	13.8564	+	8.00000i	0.583978	+	0.337160i	0.762713	−	0.646737i	$-0.223867\pi$
$563$	13.8564	+	8.00000i	0.583978	+	0.337160i	−0.178735	+	0.983897i	$0.557200\pi$
$564$		0			0
$565$	22.3205	−	1.33975i	0.939031	−	0.0563635i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$			21.0000i			0.877288i
$574$		0			0
$575$	8.00000	−	6.00000i	0.333623	−	0.250217i
$576$		0			0
$577$	14.7224	+	8.50000i	0.612903	+	0.353860i	0.774101	−	0.633062i	$-0.218202\pi$
$577$	14.7224	+	8.50000i	0.612903	+	0.353860i	−0.161198	+	0.986922i	$0.551536\pi$
$578$		0			0
$579$	−12.0000	−	20.7846i	−0.498703	−	0.863779i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−15.5885	+	9.00000i	−0.645608	+	0.372742i
$584$		0			0
$585$	7.39230	+	11.1962i	0.305634	+	0.462904i
$586$		0			0
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$		0			0
$591$	15.0000	−	25.9808i	0.617018	−	1.06871i
$592$		0			0
$593$	−2.59808	+	1.50000i	−0.106690	+	0.0615976i	−0.552396	−	0.833582i	$-0.686286\pi$
$593$	−2.59808	+	1.50000i	−0.106690	+	0.0615976i	0.445705	+	0.895180i	$0.352953\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	46.7654	−	27.0000i	1.91398	−	1.10504i
$598$		0			0
$599$	−10.5000	+	18.1865i	−0.429018	+	0.743082i	−0.996786	−	0.0801071i	$-0.974474\pi$
$599$	−10.5000	+	18.1865i	−0.429018	+	0.743082i	0.567768	+	0.823189i	$0.307807\pi$
$600$		0			0
$601$	−8.00000			−0.326327			−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000			−0.326327			−0.163163	+	0.986599i	$0.552170\pi$
$602$		0			0
$603$			60.0000i			2.44339i
$604$		0			0
$605$	3.73205	−	2.46410i	0.151729	−	0.100180i
$606$		0			0
$607$	−4.33013	+	2.50000i	−0.175754	+	0.101472i	−0.585296	−	0.810819i	$-0.699022\pi$
$607$	−4.33013	+	2.50000i	−0.175754	+	0.101472i	0.409542	+	0.912291i	$0.365689\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.50000	−	9.52628i	−0.222506	−	0.385392i
$612$		0			0
$613$	−10.3923	−	6.00000i	−0.419741	−	0.242338i	0.275225	−	0.961380i	$-0.411248\pi$
$613$	−10.3923	−	6.00000i	−0.419741	−	0.242338i	−0.694967	+	0.719042i	$0.744581\pi$
$614$		0			0
$615$	−18.0000	+	36.0000i	−0.725830	+	1.45166i
$616$		0			0
$617$		−	34.0000i		−	1.36879i	−0.729112	−	0.684394i	$-0.760067\pi$
$617$		−	34.0000i		−	1.36879i	0.729112	−	0.684394i	$-0.239933\pi$
$618$		0			0
$619$	1.00000	−	1.73205i	0.0401934	−	0.0696170i	−0.845229	−	0.534404i	$-0.820536\pi$
$619$	1.00000	−	1.73205i	0.0401934	−	0.0696170i	0.885422	+	0.464787i	$0.153869\pi$
$620$		0			0
$621$	9.00000	+	15.5885i	0.361158	+	0.625543i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		0			0
$627$	62.3538	+	36.0000i	2.49017	+	1.43770i
$628$		0			0
$629$	−50.0000			−1.99363
$630$		0			0
$631$	15.0000			0.597141			0.298570	−	0.954388i	$-0.403490\pi$
$631$	15.0000			0.597141			0.298570	+	0.954388i	$0.403490\pi$
$632$		0			0
$633$	7.79423	+	4.50000i	0.309793	+	0.178859i
$634$		0			0
$635$	−4.46410	+	0.267949i	−0.177152	+	0.0106332i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	−0.486409	−	0.873731i	$-0.661693\pi$
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	0.999878	−	0.0156233i	$-0.00497325\pi$
$642$		0			0
$643$		−	5.00000i		−	0.197181i	−0.995128	−	0.0985904i	$-0.968567\pi$
$643$		−	5.00000i		−	0.197181i	0.995128	−	0.0985904i	$-0.0314334\pi$
$644$		0			0
$645$	−24.0000	−	12.0000i	−0.944999	−	0.472500i
$646$		0			0
$647$	−20.7846	−	12.0000i	−0.817127	−	0.471769i	0.0322975	−	0.999478i	$-0.489718\pi$
$647$	−20.7846	−	12.0000i	−0.817127	−	0.471769i	−0.849425	+	0.527710i	$0.823051\pi$
$648$		0			0
$649$	15.0000	+	25.9808i	0.588802	+	1.01983i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.964928	−	0.262515i	$-0.915448\pi$
$653$	−31.1769	+	18.0000i	−1.22005	+	0.704394i	−0.255119	+	0.966910i	$0.582115\pi$
$654$		0			0
$655$	3.73205	−	2.46410i	0.145823	−	0.0962804i
$656$		0			0
$657$			60.0000i			2.34082i
$658$		0			0
$659$	−39.0000			−1.51922			−0.759612	−	0.650376i	$-0.774611\pi$
$659$	−39.0000			−1.51922			−0.759612	+	0.650376i	$0.774611\pi$
$660$		0			0
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	−0.454099	−	0.890951i	$-0.650039\pi$
$661$	14.0000	−	24.2487i	0.544537	−	0.943166i	0.998636	−	0.0522143i	$-0.0166279\pi$
$662$		0			0
$663$	−12.9904	+	7.50000i	−0.504505	+	0.291276i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.73205	+	1.00000i	−0.0670653	+	0.0387202i
$668$		0			0
$669$	28.5000	−	49.3634i	1.10187	−	1.90850i
$670$		0			0
$671$		0			0
$672$		0			0
$673$			16.0000i			0.616755i	0.951264	+	0.308377i	$0.0997859\pi$
$673$			16.0000i			0.616755i	−0.951264	+	0.308377i	$0.900214\pi$
$674$		0			0
$675$	5.38269	+	44.6769i	0.207180	+	1.71962i
$676$		0			0
$677$	9.52628	−	5.50000i	0.366125	−	0.211382i	−0.305639	−	0.952147i	$-0.598870\pi$
$677$	9.52628	−	5.50000i	0.366125	−	0.211382i	0.671764	+	0.740765i	$0.265537\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−40.5000	−	70.1481i	−1.55196	−	2.68808i
$682$		0			0
$683$	34.6410	+	20.0000i	1.32550	+	0.765279i	0.984600	−	0.174820i	$-0.0559345\pi$
$683$	34.6410	+	20.0000i	1.32550	+	0.765279i	0.340901	+	0.940099i	$0.389268\pi$
$684$		0			0
$685$	−4.00000	+	8.00000i	−0.152832	+	0.305664i
$686$		0			0
$687$		−	78.0000i		−	2.97589i
$688$		0			0
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	0.942420	+	0.334431i	$0.108544\pi$
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	−0.181584	+	0.983375i	$0.558123\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.33975	−	22.3205i	−0.0508195	−	0.846665i
$696$		0			0
$697$	−25.9808	−	15.0000i	−0.984092	−	0.568166i
$698$		0			0
$699$	48.0000			1.81553
$700$		0			0
$701$	−25.0000			−0.944237			−0.472118	−	0.881535i	$-0.656511\pi$
$701$	−25.0000			−0.944237			−0.472118	+	0.881535i	$0.656511\pi$
$702$		0			0
$703$	69.2820	+	40.0000i	2.61302	+	1.50863i
$704$		0			0
$705$	−4.42116	−	73.6577i	−0.166511	−	2.77411i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	7.50000	+	12.9904i	0.281668	+	0.487864i	0.971796	−	0.235824i	$-0.0757789\pi$
$709$	7.50000	+	12.9904i	0.281668	+	0.487864i	−0.690127	+	0.723688i	$0.742446\pi$
$710$		0			0
$711$	21.0000	−	36.3731i	0.787562	−	1.36410i
$712$		0			0
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$	−3.00000	+	6.00000i	−0.112194	+	0.224387i
$716$		0			0
$717$	12.9904	+	7.50000i	0.485135	+	0.280093i
$718$		0			0
$719$	−1.00000	−	1.73205i	−0.0372937	−	0.0645946i	0.846776	−	0.531949i	$-0.178540\pi$
$719$	−1.00000	−	1.73205i	−0.0372937	−	0.0645946i	−0.884070	+	0.467355i	$0.845207\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	46.7654	−	27.0000i	1.73922	−	1.00414i
$724$		0			0
$725$	−4.96410	+	0.598076i	−0.184362	+	0.0222120i
$726$		0			0
$727$		−	28.0000i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$727$		−	28.0000i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$		0			0
$733$	35.5070	−	20.5000i	1.31148	−	0.757185i	0.329141	−	0.944281i	$-0.393241\pi$
$733$	35.5070	−	20.5000i	1.31148	−	0.757185i	0.982342	+	0.187096i	$0.0599076\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−25.9808	+	15.0000i	−0.957014	+	0.552532i
$738$		0			0
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$		0			0
$741$	24.0000			0.881662
$742$		0			0
$743$		−	30.0000i		−	1.10059i	−0.834969	−	0.550297i	$-0.814515\pi$
$743$		−	30.0000i		−	1.10059i	0.834969	−	0.550297i	$-0.185485\pi$
$744$		0			0
$745$	−11.1962	+	7.39230i	−0.410195	+	0.270833i
$746$		0			0
$747$	−62.3538	+	36.0000i	−2.28141	+	1.31717i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$		0			0
$753$	5.19615	+	3.00000i	0.189358	+	0.109326i
$754$		0			0
$755$	18.0000	+	9.00000i	0.655087	+	0.327544i
$756$		0			0
$757$		−	48.0000i		−	1.74459i	−0.488980	−	0.872295i	$-0.662631\pi$
$757$		−	48.0000i		−	1.74459i	0.488980	−	0.872295i	$-0.337369\pi$
$758$		0			0
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$		0			0
$761$	−19.0000	−	32.9090i	−0.688749	−	1.19295i	−0.972243	−	0.233975i	$-0.924827\pi$
$761$	−19.0000	−	32.9090i	−0.688749	−	1.19295i	0.283493	−	0.958974i	$-0.408507\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−66.9615	+	4.01924i	−2.42100	+	0.145316i
$766$		0			0
$767$	8.66025	+	5.00000i	0.312704	+	0.180540i
$768$		0			0
$769$	16.0000			0.576975			0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000			0.576975			0.288487	+	0.957484i	$0.406848\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$		0			0
$773$	23.3827	+	13.5000i	0.841017	+	0.485561i	0.857610	−	0.514301i	$-0.171949\pi$
$773$	23.3827	+	13.5000i	0.841017	+	0.485561i	−0.0165929	+	0.999862i	$0.505282\pi$
$774$		0			0
$775$	3.92820	−	9.19615i	0.141105	−	0.330336i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.0000	+	41.5692i	0.859889	+	1.48937i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	9.00000i		−	0.321634i
$784$		0			0
$785$	−18.0000	+	36.0000i	−0.642448	+	1.28490i
$786$		0			0
$787$	2.59808	+	1.50000i	0.0926114	+	0.0534692i	0.545590	−	0.838052i	$-0.316305\pi$
$787$	2.59808	+	1.50000i	0.0926114	+	0.0534692i	−0.452979	+	0.891521i	$0.649639\pi$
$788$		0			0
$789$	36.0000	+	62.3538i	1.28163	+	2.21986i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−33.5885	+	22.1769i	−1.19126	+	0.786534i
$796$		0			0
$797$		−	43.0000i		−	1.52314i	−0.648084	−	0.761569i	$-0.724429\pi$
$797$		−	43.0000i		−	1.52314i	0.648084	−	0.761569i	$-0.275571\pi$
$798$		0			0
$799$	55.0000			1.94576
$800$		0			0
$801$	24.0000	−	41.5692i	0.847998	−	1.46878i
$802$		0			0
$803$	−25.9808	+	15.0000i	−0.916841	+	0.529339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.19615	−	3.00000i	0.182913	−	0.105605i
$808$		0			0
$809$	−5.50000	+	9.52628i	−0.193370	+	0.334926i	−0.946365	−	0.323100i	$-0.895275\pi$
$809$	−5.50000	+	9.52628i	−0.193370	+	0.334926i	0.752995	+	0.658026i	$0.228608\pi$
$810$		0			0
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.39230	+	11.1962i	0.258941	+	0.392184i
$816$		0			0
$817$	−27.7128	+	16.0000i	−0.969549	+	0.559769i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	−0.928846	−	0.370465i	$-0.879198\pi$
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	0.143591	−	0.989637i	$-0.454135\pi$
$822$		0			0
$823$	−15.5885	−	9.00000i	−0.543379	−	0.313720i	0.203068	−	0.979165i	$-0.434909\pi$
$823$	−15.5885	−	9.00000i	−0.543379	−	0.313720i	−0.746447	+	0.665444i	$0.768242\pi$
$824$		0			0
$825$	−36.0000	+	27.0000i	−1.25336	+	0.940019i
$826$		0			0
$827$		−	22.0000i		−	0.765015i	−0.923952	−	0.382507i	$-0.875061\pi$
$827$		−	22.0000i		−	0.765015i	0.923952	−	0.382507i	$-0.124939\pi$
$828$		0			0
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$		0			0
$831$	−21.0000	−	36.3731i	−0.728482	−	1.26177i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−6.69615	+	0.401924i	−0.231730	+	0.0139091i
$836$		0			0
$837$	15.5885	+	9.00000i	0.538816	+	0.311086i
$838$		0			0
$839$	−46.0000			−1.58810			−0.794048	−	0.607855i	$-0.792030\pi$
$839$	−46.0000			−1.58810			−0.794048	+	0.607855i	$0.792030\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	−38.9711	−	22.5000i	−1.34224	−	0.774941i
$844$		0			0
$845$	−1.60770	−	26.7846i	−0.0553064	−	0.921419i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−10.5000	−	18.1865i	−0.360359	−	0.624160i
$850$		0			0
$851$	−10.0000	+	17.3205i	−0.342796	+	0.593739i
$852$		0			0
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$		0			0
$855$	96.0000	+	48.0000i	3.28313	+	1.64157i
$856$		0			0
$857$	−19.0526	−	11.0000i	−0.650823	−	0.375753i	0.137948	−	0.990439i	$-0.455949\pi$
$857$	−19.0526	−	11.0000i	−0.650823	−	0.375753i	−0.788771	+	0.614687i	$0.789283\pi$
$858$		0			0
$859$	−12.0000	−	20.7846i	−0.409435	−	0.709162i	0.585392	−	0.810751i	$-0.300941\pi$
$859$	−12.0000	−	20.7846i	−0.409435	−	0.709162i	−0.994826	+	0.101589i	$0.967607\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−39.8372	+	23.0000i	−1.35607	+	0.782929i	−0.989092	−	0.147299i	$-0.952942\pi$
$863$	−39.8372	+	23.0000i	−1.35607	+	0.782929i	−0.366981	+	0.930228i	$0.619609\pi$
$864$		0			0
$865$	11.0885	+	16.7942i	0.377019	+	0.571021i
$866$		0			0
$867$		−	24.0000i		−	0.815083i
$868$		0			0
$869$	21.0000			0.712376
$870$		0			0
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$		0			0
$873$	15.5885	−	9.00000i	0.527589	−	0.304604i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	34.6410	−	20.0000i	1.16974	−	0.675352i	0.216124	−	0.976366i	$-0.430658\pi$
$877$	34.6410	−	20.0000i	1.16974	−	0.675352i	0.953620	+	0.301014i	$0.0973250\pi$
$878$		0			0
$879$	22.5000	−	38.9711i	0.758906	−	1.31446i
$880$		0			0
$881$	48.0000			1.61716			0.808581	−	0.588386i	$-0.200236\pi$
$881$	48.0000			1.61716			0.808581	+	0.588386i	$0.200236\pi$
$882$		0			0
$883$		−	4.00000i		−	0.134611i	−0.997732	−	0.0673054i	$-0.978560\pi$
$883$		−	4.00000i		−	0.134611i	0.997732	−	0.0673054i	$-0.0214402\pi$
$884$		0			0
$885$	36.9615	+	55.9808i	1.24245	+	1.88177i
$886$		0			0
$887$	−10.3923	+	6.00000i	−0.348939	+	0.201460i	−0.664218	−	0.747539i	$-0.731235\pi$
$887$	−10.3923	+	6.00000i	−0.348939	+	0.201460i	0.315279	+	0.948999i	$0.397902\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−13.5000	−	23.3827i	−0.452267	−	0.783349i
$892$		0			0
$893$	−76.2102	−	44.0000i	−2.55028	−	1.47240i
$894$		0			0
$895$	−8.00000	−	4.00000i	−0.267411	−	0.133705i
$896$		0			0
$897$			6.00000i			0.200334i
$898$		0			0
$899$	−1.00000	+	1.73205i	−0.0333519	+	0.0577671i
$900$		0			0
$901$	−15.0000	−	25.9808i	−0.499722	−	0.865545i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.33975	−	22.3205i	−0.0445347	−	0.741959i
$906$		0			0
$907$	−32.9090	−	19.0000i	−1.09272	−	0.630885i	−0.158424	−	0.987371i	$-0.550641\pi$
$907$	−32.9090	−	19.0000i	−1.09272	−	0.630885i	−0.934300	+	0.356487i	$0.883975\pi$
$908$		0			0
$909$	−72.0000			−2.38809
$910$		0			0
$911$	−52.0000			−1.72284			−0.861418	−	0.507896i	$-0.830423\pi$
$911$	−52.0000			−1.72284			−0.861418	+	0.507896i	$0.830423\pi$
$912$		0			0
$913$	−31.1769	−	18.0000i	−1.03181	−	0.595713i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−27.5000	−	47.6314i	−0.907141	−	1.57121i	−0.818017	−	0.575194i	$-0.804926\pi$
$919$	−27.5000	−	47.6314i	−0.907141	−	1.57121i	−0.0891245	−	0.996020i	$-0.528407\pi$
$920$		0			0
$921$	28.5000	−	49.3634i	0.939107	−	1.62658i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−40.0000	+	30.0000i	−1.31519	+	0.986394i
$926$		0			0
$927$	−25.9808	−	15.0000i	−0.853320	−	0.492665i
$928$		0			0
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	0.975050	−	0.221985i	$-0.0712536\pi$
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	−0.679770	+	0.733426i	$0.737920\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−31.1769	+	18.0000i	−1.02069	+	0.589294i
$934$		0			0
$935$	−18.4808	−	27.9904i	−0.604386	−	0.915383i
$936$		0			0
$937$		−	7.00000i		−	0.228680i	−0.993442	−	0.114340i	$-0.963525\pi$
$937$		−	7.00000i		−	0.228680i	0.993442	−	0.114340i	$-0.0364753\pi$
$938$		0			0
$939$	21.0000			0.685309
$940$		0			0
$941$	−20.0000	+	34.6410i	−0.651981	+	1.12926i	0.330660	+	0.943750i	$0.392729\pi$
$941$	−20.0000	+	34.6410i	−0.651981	+	1.12926i	−0.982641	+	0.185515i	$0.940605\pi$
$942$		0			0
$943$	−10.3923	+	6.00000i	−0.338420	+	0.195387i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.19615	−	3.00000i	0.168852	−	0.0974869i	−0.413192	−	0.910644i	$-0.635586\pi$
$947$	5.19615	−	3.00000i	0.168852	−	0.0974869i	0.582045	+	0.813157i	$0.302253\pi$
$948$		0			0
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$		0			0
$951$	−84.0000			−2.72389
$952$		0			0
$953$			42.0000i			1.36051i	0.732974	+	0.680257i	$0.238132\pi$
$953$			42.0000i			1.36051i	−0.732974	+	0.680257i	$0.761868\pi$
$954$		0			0
$955$	−13.0622	+	8.62436i	−0.422682	+	0.279078i
$956$		0			0
$957$	7.79423	−	4.50000i	0.251952	−	0.145464i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	41.5692	+	24.0000i	1.33955	+	0.773389i
$964$		0			0
$965$	8.00000	−	16.0000i	0.257529	−	0.515058i
$966$		0			0
$967$			8.00000i			0.257263i	0.991692	+	0.128631i	$0.0410584\pi$
$967$			8.00000i			0.257263i	−0.991692	+	0.128631i	$0.958942\pi$
$968$		0			0
$969$	−60.0000	+	103.923i	−1.92748	+	3.33849i
$970$		0			0
$971$	9.00000	+	15.5885i	0.288824	+	0.500257i	0.973529	−	0.228562i	$-0.0734025\pi$
$971$	9.00000	+	15.5885i	0.288824	+	0.500257i	−0.684706	+	0.728820i	$0.740069\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.89230	+	13.7942i	−0.188705	+	0.441769i
$976$		0			0
$977$	51.9615	+	30.0000i	1.66240	+	0.959785i	0.971566	+	0.236768i	$0.0760881\pi$
$977$	51.9615	+	30.0000i	1.66240	+	0.959785i	0.690830	+	0.723017i	$0.257245\pi$
$978$		0			0
$979$	24.0000			0.767043
$980$		0			0
$981$	−42.0000			−1.34096
$982$		0			0
$983$	−11.2583	−	6.50000i	−0.359085	−	0.207318i	0.309594	−	0.950869i	$-0.399807\pi$
$983$	−11.2583	−	6.50000i	−0.359085	−	0.207318i	−0.668679	+	0.743551i	$0.733140\pi$
$984$		0			0
$985$	22.3205	−	1.33975i	0.711191	−	0.0426879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.00000	−	6.92820i	−0.127193	−	0.220304i
$990$		0			0
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$		0			0
$993$			60.0000i			1.90404i
$994$		0			0
$995$	36.0000	+	18.0000i	1.14128	+	0.570638i
$996$		0			0
$997$	−45.8993	−	26.5000i	−1.45365	−	0.839263i	−0.454961	−	0.890511i	$-0.650347\pi$
$997$	−45.8993	−	26.5000i	−1.45365	−	0.839263i	−0.998686	+	0.0512480i	$0.983680\pi$
$998$		0			0
$999$	−45.0000	−	77.9423i	−1.42374	−	2.46598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.q.c.949.1		4
5.4	even	2	inner	980.2.q.c.949.2		4
7.2	even	3	inner	980.2.q.c.569.2		4
7.3	odd	6		140.2.e.a.29.1	✓	2
7.4	even	3		980.2.e.b.589.2		2
7.5	odd	6		980.2.q.f.569.1		4
7.6	odd	2		980.2.q.f.949.2		4
21.17	even	6		1260.2.k.c.1009.2		2
28.3	even	6		560.2.g.a.449.2		2
35.3	even	12		700.2.a.j.1.1		1
35.4	even	6		980.2.e.b.589.1		2
35.9	even	6	inner	980.2.q.c.569.1		4
35.17	even	12		700.2.a.a.1.1		1
35.18	odd	12		4900.2.a.b.1.1		1
35.19	odd	6		980.2.q.f.569.2		4
35.24	odd	6		140.2.e.a.29.2	yes	2
35.32	odd	12		4900.2.a.w.1.1		1
35.34	odd	2		980.2.q.f.949.1		4
56.3	even	6		2240.2.g.f.449.1		2
56.45	odd	6		2240.2.g.e.449.2		2
84.59	odd	6		5040.2.t.s.1009.2		2
105.17	odd	12		6300.2.a.c.1.1		1
105.38	odd	12		6300.2.a.t.1.1		1
105.59	even	6		1260.2.k.c.1009.1		2
140.3	odd	12		2800.2.a.a.1.1		1
140.59	even	6		560.2.g.a.449.1		2
140.87	odd	12		2800.2.a.bf.1.1		1
280.59	even	6		2240.2.g.f.449.2		2
280.269	odd	6		2240.2.g.e.449.1		2
420.59	odd	6		5040.2.t.s.1009.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.e.a.29.1	✓	2	7.3	odd	6
140.2.e.a.29.2	yes	2	35.24	odd	6
560.2.g.a.449.1		2	140.59	even	6
560.2.g.a.449.2		2	28.3	even	6
700.2.a.a.1.1		1	35.17	even	12
700.2.a.j.1.1		1	35.3	even	12
980.2.e.b.589.1		2	35.4	even	6
980.2.e.b.589.2		2	7.4	even	3
980.2.q.c.569.1		4	35.9	even	6	inner
980.2.q.c.569.2		4	7.2	even	3	inner
980.2.q.c.949.1		4	1.1	even	1	trivial
980.2.q.c.949.2		4	5.4	even	2	inner
980.2.q.f.569.1		4	7.5	odd	6
980.2.q.f.569.2		4	35.19	odd	6
980.2.q.f.949.1		4	35.34	odd	2
980.2.q.f.949.2		4	7.6	odd	2
1260.2.k.c.1009.1		2	105.59	even	6
1260.2.k.c.1009.2		2	21.17	even	6
2240.2.g.e.449.1		2	280.269	odd	6
2240.2.g.e.449.2		2	56.45	odd	6
2240.2.g.f.449.1		2	56.3	even	6
2240.2.g.f.449.2		2	280.59	even	6
2800.2.a.a.1.1		1	140.3	odd	12
2800.2.a.bf.1.1		1	140.87	odd	12
4900.2.a.b.1.1		1	35.18	odd	12
4900.2.a.w.1.1		1	35.32	odd	12
5040.2.t.s.1009.1		2	420.59	odd	6
5040.2.t.s.1009.2		2	84.59	odd	6
6300.2.a.c.1.1		1	105.17	odd	12
6300.2.a.t.1.1		1	105.38	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 - 1.50000i) q^{3} +(-0.133975 - 2.23205i) q^{5} +(3.00000 + 5.19615i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000i q^{13} +(-3.00000 + 6.00000i) q^{15} +(-4.33013 - 2.50000i) q^{17} +(4.00000 + 6.92820i) q^{19} +(-1.73205 + 1.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -9.00000i q^{27} +1.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(7.79423 - 4.50000i) q^{33} +(8.66025 - 5.00000i) q^{37} +(1.50000 - 2.59808i) q^{39} +6.00000 q^{41} +4.00000i q^{43} +(11.1962 - 7.39230i) q^{45} +(-9.52628 + 5.50000i) q^{47} +(7.50000 + 12.9904i) q^{51} +(5.19615 + 3.00000i) q^{53} +(6.00000 + 3.00000i) q^{55} -24.0000i q^{57} +(5.00000 - 8.66025i) q^{59} +(2.23205 - 0.133975i) q^{65} +(8.66025 + 5.00000i) q^{67} +6.00000 q^{69} +(8.66025 + 5.00000i) q^{73} +(13.7942 + 5.89230i) q^{75} +(-3.50000 - 6.06218i) q^{79} +(-4.50000 + 7.79423i) q^{81} +12.0000i q^{83} +(-5.00000 + 10.0000i) q^{85} +(-2.59808 - 1.50000i) q^{87} +(-4.00000 - 6.92820i) q^{89} +(5.19615 - 3.00000i) q^{93} +(14.9282 - 9.85641i) q^{95} -3.00000i q^{97} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 12 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{31} + 6 q^{39} + 24 q^{41} + 24 q^{45} + 30 q^{51} + 24 q^{55} + 20 q^{59} + 2 q^{65} + 24 q^{69} + 24 q^{75} - 14 q^{79}+ \cdots - 72 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 + 12 * q^9 - 6 * q^11 - 12 * q^15 + 16 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^31 + 6 * q^39 + 24 * q^41 + 24 * q^45 + 30 * q^51 + 24 * q^55 + 20 * q^59 + 2 * q^65 + 24 * q^69 + 24 * q^75 - 14 * q^79 - 18 * q^81 - 20 * q^85 - 16 * q^89 + 32 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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Database

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