LMFDB - Embedded newform 1352.2.o.b.1161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1352,2,Mod(361,1352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1352.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (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:	$10.7957743533$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1161.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1352.1161
Dual form			1352.2.o.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} -2.00000i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} -2.00000i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(1.73205 + 1.00000i) q^{15} +(1.50000 + 2.59808i) q^{17} +(-6.06218 + 3.50000i) q^{19} -1.00000i q^{21} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} -8.00000i q^{31} +(0.866025 - 0.500000i) q^{33} +(1.00000 + 1.73205i) q^{35} +(0.866025 + 0.500000i) q^{37} +(9.52628 + 5.50000i) q^{41} +(5.50000 + 9.52628i) q^{43} +(3.46410 - 2.00000i) q^{45} +12.0000i q^{47} +(-3.00000 + 5.19615i) q^{49} -3.00000 q^{51} -6.00000 q^{53} +(-1.00000 + 1.73205i) q^{55} -7.00000i q^{57} +(-7.79423 + 4.50000i) q^{59} +(4.50000 + 7.79423i) q^{61} +(-1.73205 - 1.00000i) q^{63} +(-2.59808 - 1.50000i) q^{67} +(0.500000 + 0.866025i) q^{69} +(4.33013 - 2.50000i) q^{71} -2.00000i q^{73} +(-0.500000 + 0.866025i) q^{75} +1.00000 q^{77} -12.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000i q^{83} +(5.19615 - 3.00000i) q^{85} +(-1.50000 - 2.59808i) q^{87} +(0.866025 + 0.500000i) q^{89} +(6.92820 + 4.00000i) q^{93} +(7.00000 + 12.1244i) q^{95} +(0.866025 - 0.500000i) q^{97} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^9	$ 4 q - 2 q^{3} + 4 q^{9} + 6 q^{17} + 2 q^{23} + 4 q^{25} - 20 q^{27} - 6 q^{29} + 4 q^{35} + 22 q^{43} - 12 q^{49} - 12 q^{51} - 24 q^{53} - 4 q^{55} + 18 q^{61} + 2 q^{69} - 2 q^{75} + 4 q^{77} - 48 q^{79} - 2 q^{81} - 6 q^{87} + 28 q^{95}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^9 + 6 * q^17 + 2 * q^23 + 4 * q^25 - 20 * q^27 - 6 * q^29 + 4 * q^35 + 22 * q^43 - 12 * q^49 - 12 * q^51 - 24 * q^53 - 4 * q^55 + 18 * q^61 + 2 * q^69 - 2 * q^75 + 4 * q^77 - 48 * q^79 - 2 * q^81 - 6 * q^87 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$		0			0
$5$		−	2.00000i		−	0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$		−	2.00000i		−	0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i	0.327327	+	0.944911i	$0.393852\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i	0.363727	−	0.931505i	$-0.381504\pi$
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i	−0.624844	+	0.780750i	$0.714837\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	1.73205	+	1.00000i	0.447214	+	0.258199i
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−6.06218	+	3.50000i	−1.39076	+	0.802955i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−6.06218	+	3.50000i	−1.39076	+	0.802955i	−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$		−	1.00000i		−	0.218218i
$22$		0			0
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$		−	8.00000i		−	1.43684i	−0.695608	−	0.718421i	$-0.744865\pi$
$31$		−	8.00000i		−	1.43684i	0.695608	−	0.718421i	$-0.255135\pi$
$32$		0			0
$33$	0.866025	−	0.500000i	0.150756	−	0.0870388i
$34$		0			0
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$		0			0
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	0.569495	−	0.821995i	$-0.307139\pi$
$37$	0.866025	+	0.500000i	0.142374	+	0.0821995i	−0.427121	+	0.904194i	$0.640472\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.52628	+	5.50000i	1.48775	+	0.858956i	0.999902	−	0.0139704i	$-0.00444706\pi$
$41$	9.52628	+	5.50000i	1.48775	+	0.858956i	0.487852	+	0.872926i	$0.337780\pi$
$42$		0			0
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	0.890947	+	0.454108i	$0.150042\pi$
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	−0.0522047	+	0.998636i	$0.516625\pi$
$44$		0			0
$45$	3.46410	−	2.00000i	0.516398	−	0.298142i
$46$		0			0
$47$			12.0000i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$			12.0000i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$		0			0
$49$	−3.00000	+	5.19615i	−0.428571	+	0.742307i
$50$		0			0
$51$	−3.00000			−0.420084
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$		0			0
$57$		−	7.00000i		−	0.927173i
$58$		0			0
$59$	−7.79423	+	4.50000i	−1.01472	+	0.585850i	−0.912571	−	0.408919i	$-0.865906\pi$
$59$	−7.79423	+	4.50000i	−1.01472	+	0.585850i	−0.102151	+	0.994769i	$0.532573\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$		0			0
$63$	−1.73205	−	1.00000i	−0.218218	−	0.125988i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391996\pi$
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$68$		0			0
$69$	0.500000	+	0.866025i	0.0601929	+	0.104257i
$70$		0			0
$71$	4.33013	−	2.50000i	0.513892	−	0.296695i	−0.220540	−	0.975378i	$-0.570782\pi$
$71$	4.33013	−	2.50000i	0.513892	−	0.296695i	0.734432	+	0.678682i	$0.237449\pi$
$72$		0			0
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	1.00000			0.113961
$78$		0			0
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$	5.19615	−	3.00000i	0.563602	−	0.325396i
$86$		0			0
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$		0			0
$89$	0.866025	+	0.500000i	0.0917985	+	0.0529999i	0.545197	−	0.838308i	$-0.316455\pi$
$89$	0.866025	+	0.500000i	0.0917985	+	0.0529999i	−0.453398	+	0.891308i	$0.649788\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.92820	+	4.00000i	0.718421	+	0.414781i
$94$		0			0
$95$	7.00000	+	12.1244i	0.718185	+	1.24393i
$96$		0			0
$97$	0.866025	−	0.500000i	0.0879316	−	0.0507673i	−0.455389	−	0.890292i	$-0.650500\pi$
$97$	0.866025	−	0.500000i	0.0879316	−	0.0507673i	0.543321	+	0.839525i	$0.317167\pi$
$98$		0			0
$99$		−	2.00000i		−	0.201008i
$100$		0			0
$101$	−8.50000	+	14.7224i	−0.845782	+	1.46494i	0.0391591	+	0.999233i	$0.487532\pi$
$101$	−8.50000	+	14.7224i	−0.845782	+	1.46494i	−0.884941	+	0.465704i	$0.845801\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$	−2.00000			−0.195180
$106$		0			0
$107$	−8.50000	+	14.7224i	−0.821726	+	1.42327i	0.0826699	+	0.996577i	$0.473655\pi$
$107$	−8.50000	+	14.7224i	−0.821726	+	1.42327i	−0.904396	+	0.426694i	$0.859678\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$		0			0
$111$	−0.866025	+	0.500000i	−0.0821995	+	0.0474579i
$112$		0			0
$113$	−5.50000	−	9.52628i	−0.517396	−	0.896157i	−0.999796	−	0.0202056i	$-0.993568\pi$
$113$	−5.50000	−	9.52628i	−0.517396	−	0.896157i	0.482399	−	0.875951i	$-0.339765\pi$
$114$		0			0
$115$	−1.73205	−	1.00000i	−0.161515	−	0.0932505i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.59808	−	1.50000i	−0.238165	−	0.137505i
$120$		0			0
$121$	−5.00000	−	8.66025i	−0.454545	−	0.787296i
$122$		0			0
$123$	−9.52628	+	5.50000i	−0.858956	+	0.495918i
$124$		0			0
$125$		−	12.0000i		−	1.07331i
$126$		0			0
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	−0.419064	−	0.907957i	$-0.637642\pi$
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	0.995846	−	0.0910585i	$-0.0290250\pi$
$128$		0			0
$129$	−11.0000			−0.968496
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	3.50000	−	6.06218i	0.303488	−	0.525657i
$134$		0			0
$135$			10.0000i			0.860663i
$136$		0			0
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	−0.794524	−	0.607233i	$-0.792279\pi$
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	0.128618	+	0.991694i	$0.458946\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$	−10.3923	−	6.00000i	−0.875190	−	0.505291i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	5.19615	+	3.00000i	0.431517	+	0.249136i
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	0.866025	−	0.500000i	0.0709476	−	0.0409616i	−0.464107	−	0.885779i	$-0.653625\pi$
$149$	0.866025	−	0.500000i	0.0709476	−	0.0409616i	0.535054	+	0.844818i	$0.320291\pi$
$150$		0			0
$151$			16.0000i			1.30206i	0.759051	+	0.651031i	$0.225663\pi$
$151$			16.0000i			1.30206i	−0.759051	+	0.651031i	$0.774337\pi$
$152$		0			0
$153$	−3.00000	+	5.19615i	−0.242536	+	0.420084i
$154$		0			0
$155$	−16.0000			−1.28515
$156$		0			0
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$		0			0
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$			1.00000i			0.0788110i
$162$		0			0
$163$	−4.33013	+	2.50000i	−0.339162	+	0.195815i	−0.659901	−	0.751352i	$-0.729402\pi$
$163$	−4.33013	+	2.50000i	−0.339162	+	0.195815i	0.320740	+	0.947167i	$0.396069\pi$
$164$		0			0
$165$	−1.00000	−	1.73205i	−0.0778499	−	0.134840i
$166$		0			0
$167$	6.06218	+	3.50000i	0.469105	+	0.270838i	0.715865	−	0.698239i	$-0.246033\pi$
$167$	6.06218	+	3.50000i	0.469105	+	0.270838i	−0.246760	+	0.969077i	$0.579366\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−12.1244	−	7.00000i	−0.927173	−	0.535303i
$172$		0			0
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$	−0.866025	+	0.500000i	−0.0654654	+	0.0377964i
$176$		0			0
$177$		−	9.00000i		−	0.676481i
$178$		0			0
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$		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
$183$	−9.00000			−0.665299
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$		−	3.00000i		−	0.219382i
$188$		0			0
$189$	4.33013	−	2.50000i	0.314970	−	0.181848i
$190$		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
$193$	4.33013	+	2.50000i	0.311689	+	0.179954i	0.647682	−	0.761911i	$-0.275738\pi$
$193$	4.33013	+	2.50000i	0.311689	+	0.179954i	−0.335993	+	0.941865i	$0.609072\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.2583	−	6.50000i	−0.802123	−	0.463106i	0.0420901	−	0.999114i	$-0.486598\pi$
$197$	−11.2583	−	6.50000i	−0.802123	−	0.463106i	−0.844213	+	0.536008i	$0.819932\pi$
$198$		0			0
$199$	1.50000	+	2.59808i	0.106332	+	0.184173i	0.914282	−	0.405079i	$-0.132756\pi$
$199$	1.50000	+	2.59808i	0.106332	+	0.184173i	−0.807950	+	0.589252i	$0.799423\pi$
$200$		0			0
$201$	2.59808	−	1.50000i	0.183254	−	0.105802i
$202$		0			0
$203$		−	3.00000i		−	0.210559i
$204$		0			0
$205$	11.0000	−	19.0526i	0.768273	−	1.33069i
$206$		0			0
$207$	2.00000			0.139010
$208$		0			0
$209$	7.00000			0.484200
$210$		0			0
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	−0.882723	−	0.469894i	$-0.844292\pi$
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	0.848301	+	0.529514i	$0.177626\pi$
$212$		0			0
$213$			5.00000i			0.342594i
$214$		0			0
$215$	19.0526	−	11.0000i	1.29937	−	0.750194i
$216$		0			0
$217$	4.00000	+	6.92820i	0.271538	+	0.470317i
$218$		0			0
$219$	1.73205	+	1.00000i	0.117041	+	0.0675737i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.866025	+	0.500000i	0.0579934	+	0.0334825i	0.528716	−	0.848799i	$-0.322674\pi$
$223$	0.866025	+	0.500000i	0.0579934	+	0.0334825i	−0.470723	+	0.882281i	$0.656007\pi$
$224$		0			0
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$		0			0
$227$	0.866025	−	0.500000i	0.0574801	−	0.0331862i	−0.470985	−	0.882141i	$-0.656101\pi$
$227$	0.866025	−	0.500000i	0.0574801	−	0.0331862i	0.528465	+	0.848955i	$0.322768\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		0			0
$231$	−0.500000	+	0.866025i	−0.0328976	+	0.0569803i
$232$		0			0
$233$	26.0000			1.70332			0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000			1.70332			0.851658	+	0.524097i	$0.175597\pi$
$234$		0			0
$235$	24.0000			1.56559
$236$		0			0
$237$	6.00000	−	10.3923i	0.389742	−	0.675053i
$238$		0			0
$239$			24.0000i			1.55243i	0.630468	+	0.776215i	$0.282863\pi$
$239$			24.0000i			1.55243i	−0.630468	+	0.776215i	$0.717137\pi$
$240$		0			0
$241$	9.52628	−	5.50000i	0.613642	−	0.354286i	−0.160748	−	0.986996i	$-0.551391\pi$
$241$	9.52628	−	5.50000i	0.613642	−	0.354286i	0.774389	+	0.632709i	$0.218057\pi$
$242$		0			0
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$		0			0
$245$	10.3923	+	6.00000i	0.663940	+	0.383326i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−3.46410	−	2.00000i	−0.219529	−	0.126745i
$250$		0			0
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	0.584643	−	0.811290i	$-0.301234\pi$
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	−0.994920	+	0.100671i	$0.967901\pi$
$252$		0			0
$253$	−0.866025	+	0.500000i	−0.0544466	+	0.0314347i
$254$		0			0
$255$			6.00000i			0.375735i
$256$		0			0
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	−0.994375	−	0.105919i	$-0.966222\pi$
$257$	−6.50000	+	11.2583i	−0.405459	+	0.702275i	0.588916	+	0.808194i	$0.299555\pi$
$258$		0			0
$259$	−1.00000			−0.0621370
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	15.5000	−	26.8468i	0.955771	−	1.65544i	0.223177	−	0.974778i	$-0.428357\pi$
$263$	15.5000	−	26.8468i	0.955771	−	1.65544i	0.732594	−	0.680666i	$-0.238309\pi$
$264$		0			0
$265$			12.0000i			0.737154i
$266$		0			0
$267$	−0.866025	+	0.500000i	−0.0529999	+	0.0305995i
$268$		0			0
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	0.932119	−	0.362151i	$-0.117958\pi$
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	−0.779692	+	0.626164i	$0.784624\pi$
$270$		0			0
$271$	6.06218	+	3.50000i	0.368251	+	0.212610i	0.672694	−	0.739921i	$-0.265137\pi$
$271$	6.06218	+	3.50000i	0.368251	+	0.212610i	−0.304443	+	0.952531i	$0.598470\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.866025	−	0.500000i	−0.0522233	−	0.0301511i
$276$		0			0
$277$	−10.5000	−	18.1865i	−0.630884	−	1.09272i	−0.987371	−	0.158423i	$-0.949359\pi$
$277$	−10.5000	−	18.1865i	−0.630884	−	1.09272i	0.356488	−	0.934300i	$-0.383974\pi$
$278$		0			0
$279$	13.8564	−	8.00000i	0.829561	−	0.478947i
$280$		0			0
$281$			14.0000i			0.835170i	0.908638	+	0.417585i	$0.137123\pi$
$281$			14.0000i			0.835170i	−0.908638	+	0.417585i	$0.862877\pi$
$282$		0			0
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$		0			0
$285$	−14.0000			−0.829288
$286$		0			0
$287$	−11.0000			−0.649309
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$			1.00000i			0.0586210i
$292$		0			0
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	−0.710084	−	0.704117i	$-0.751343\pi$
$293$	−7.79423	+	4.50000i	−0.455344	+	0.262893i	0.254741	+	0.967009i	$0.418010\pi$
$294$		0			0
$295$	9.00000	+	15.5885i	0.524000	+	0.907595i
$296$		0			0
$297$	4.33013	+	2.50000i	0.251259	+	0.145065i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−9.52628	−	5.50000i	−0.549086	−	0.317015i
$302$		0			0
$303$	−8.50000	−	14.7224i	−0.488312	−	0.845782i
$304$		0			0
$305$	15.5885	−	9.00000i	0.892592	−	0.515339i
$306$		0			0
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$		0			0
$309$	−4.00000	+	6.92820i	−0.227552	+	0.394132i
$310$		0			0
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$		0			0
$313$	30.0000			1.69570			0.847850	−	0.530236i	$-0.177897\pi$
$313$	30.0000			1.69570			0.847850	+	0.530236i	$0.177897\pi$
$314$		0			0
$315$	−2.00000	+	3.46410i	−0.112687	+	0.195180i
$316$		0			0
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	2.59808	−	1.50000i	0.145464	−	0.0839839i
$320$		0			0
$321$	−8.50000	−	14.7224i	−0.474424	−	0.821726i
$322$		0			0
$323$	−18.1865	−	10.5000i	−1.01193	−	0.584236i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.66025	+	5.00000i	0.478913	+	0.276501i
$328$		0			0
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	−23.3827	+	13.5000i	−1.28523	+	0.742027i	−0.977799	−	0.209544i	$-0.932802\pi$
$331$	−23.3827	+	13.5000i	−1.28523	+	0.742027i	−0.307429	+	0.951571i	$0.599469\pi$
$332$		0			0
$333$			2.00000i			0.109599i
$334$		0			0
$335$	−3.00000	+	5.19615i	−0.163908	+	0.283896i
$336$		0			0
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$		0			0
$339$	11.0000			0.597438
$340$		0			0
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$		0			0
$343$		−	13.0000i		−	0.701934i
$344$		0			0
$345$	1.73205	−	1.00000i	0.0932505	−	0.0538382i
$346$		0			0
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	−0.959090	−	0.283101i	$-0.908637\pi$
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	0.234372	−	0.972147i	$-0.424697\pi$
$348$		0			0
$349$	7.79423	+	4.50000i	0.417215	+	0.240879i	0.693885	−	0.720086i	$-0.255897\pi$
$349$	7.79423	+	4.50000i	0.417215	+	0.240879i	−0.276670	+	0.960965i	$0.589231\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−21.6506	−	12.5000i	−1.15235	−	0.665308i	−0.202889	−	0.979202i	$-0.565033\pi$
$353$	−21.6506	−	12.5000i	−1.15235	−	0.665308i	−0.949458	+	0.313894i	$0.898366\pi$
$354$		0			0
$355$	−5.00000	−	8.66025i	−0.265372	−	0.459639i
$356$		0			0
$357$	2.59808	−	1.50000i	0.137505	−	0.0793884i
$358$		0			0
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$		0			0
$361$	15.0000	−	25.9808i	0.789474	−	1.36741i
$362$		0			0
$363$	10.0000			0.524864
$364$		0			0
$365$	−4.00000			−0.209370
$366$		0			0
$367$	7.50000	−	12.9904i	0.391497	−	0.678092i	−0.601150	−	0.799136i	$-0.705291\pi$
$367$	7.50000	−	12.9904i	0.391497	−	0.678092i	0.992647	+	0.121044i	$0.0386241\pi$
$368$		0			0
$369$			22.0000i			1.14527i
$370$		0			0
$371$	5.19615	−	3.00000i	0.269771	−	0.155752i
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$		0			0
$375$	10.3923	+	6.00000i	0.536656	+	0.309839i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−12.9904	−	7.50000i	−0.667271	−	0.385249i	0.127771	−	0.991804i	$-0.459218\pi$
$379$	−12.9904	−	7.50000i	−0.667271	−	0.385249i	−0.795042	+	0.606555i	$0.792551\pi$
$380$		0			0
$381$	6.50000	+	11.2583i	0.333005	+	0.576782i
$382$		0			0
$383$	28.5788	−	16.5000i	1.46031	−	0.843111i	0.461285	−	0.887252i	$-0.347389\pi$
$383$	28.5788	−	16.5000i	1.46031	−	0.843111i	0.999025	+	0.0441413i	$0.0140552\pi$
$384$		0			0
$385$		−	2.00000i		−	0.101929i
$386$		0			0
$387$	−11.0000	+	19.0526i	−0.559161	+	0.968496i
$388$		0			0
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	3.00000			0.151717
$392$		0			0
$393$	−6.00000	+	10.3923i	−0.302660	+	0.524222i
$394$		0			0
$395$			24.0000i			1.20757i
$396$		0			0
$397$	16.4545	−	9.50000i	0.825827	−	0.476791i	−0.0265948	−	0.999646i	$-0.508466\pi$
$397$	16.4545	−	9.50000i	0.825827	−	0.476791i	0.852422	+	0.522855i	$0.175133\pi$
$398$		0			0
$399$	3.50000	+	6.06218i	0.175219	+	0.303488i
$400$		0			0
$401$	−23.3827	−	13.5000i	−1.16768	−	0.674158i	−0.214544	−	0.976714i	$-0.568827\pi$
$401$	−23.3827	−	13.5000i	−1.16768	−	0.674158i	−0.953131	+	0.302556i	$0.902160\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	1.73205	+	1.00000i	0.0860663	+	0.0496904i
$406$		0			0
$407$	−0.500000	−	0.866025i	−0.0247841	−	0.0429273i
$408$		0			0
$409$	−30.3109	+	17.5000i	−1.49878	+	0.865319i	−0.999999	−	0.00141047i	$-0.999551\pi$
$409$	−30.3109	+	17.5000i	−1.49878	+	0.865319i	−0.498778	+	0.866730i	$0.666218\pi$
$410$		0			0
$411$		−	9.00000i		−	0.443937i
$412$		0			0
$413$	4.50000	−	7.79423i	0.221431	−	0.383529i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$	−9.00000			−0.440732
$418$		0			0
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$			22.0000i			1.07221i	0.844150	+	0.536107i	$0.180106\pi$
$421$			22.0000i			1.07221i	−0.844150	+	0.536107i	$0.819894\pi$
$422$		0			0
$423$	−20.7846	+	12.0000i	−1.01058	+	0.583460i
$424$		0			0
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$		0			0
$427$	−7.79423	−	4.50000i	−0.377189	−	0.217770i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.52628	−	5.50000i	−0.458865	−	0.264926i	0.252702	−	0.967544i	$-0.418681\pi$
$431$	−9.52628	−	5.50000i	−0.458865	−	0.264926i	−0.711567	+	0.702618i	$0.752014\pi$
$432$		0			0
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	0.998775	−	0.0494752i	$-0.0157549\pi$
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	−0.542234	+	0.840227i	$0.682422\pi$
$434$		0			0
$435$	−5.19615	+	3.00000i	−0.249136	+	0.143839i
$436$		0			0
$437$			7.00000i			0.334855i
$438$		0			0
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	0.0586141	+	0.998281i	$0.481332\pi$
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	−0.893843	+	0.448379i	$0.852001\pi$
$440$		0			0
$441$	−12.0000			−0.571429
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	1.00000	−	1.73205i	0.0474045	−	0.0821071i
$446$		0			0
$447$			1.00000i			0.0472984i
$448$		0			0
$449$	−18.1865	+	10.5000i	−0.858276	+	0.495526i	−0.863434	−	0.504461i	$-0.831691\pi$
$449$	−18.1865	+	10.5000i	−0.858276	+	0.495526i	0.00515887	+	0.999987i	$0.498358\pi$
$450$		0			0
$451$	−5.50000	−	9.52628i	−0.258985	−	0.448575i
$452$		0			0
$453$	−13.8564	−	8.00000i	−0.651031	−	0.375873i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.06218	+	3.50000i	0.283577	+	0.163723i	0.635042	−	0.772478i	$-0.280983\pi$
$457$	6.06218	+	3.50000i	0.283577	+	0.163723i	−0.351465	+	0.936201i	$0.614316\pi$
$458$		0			0
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	−2.59808	+	1.50000i	−0.121004	+	0.0698620i	−0.559281	−	0.828978i	$-0.688923\pi$
$461$	−2.59808	+	1.50000i	−0.121004	+	0.0698620i	0.438276	+	0.898840i	$0.355589\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$	8.00000	−	13.8564i	0.370991	−	0.642575i
$466$		0			0
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	3.00000			0.138527
$470$		0			0
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$		0			0
$473$		−	11.0000i		−	0.505781i
$474$		0			0
$475$	−6.06218	+	3.50000i	−0.278152	+	0.160591i
$476$		0			0
$477$	−6.00000	−	10.3923i	−0.274721	−	0.475831i
$478$		0			0
$479$	23.3827	+	13.5000i	1.06838	+	0.616831i	0.927739	−	0.373230i	$-0.121750\pi$
$479$	23.3827	+	13.5000i	1.06838	+	0.616831i	0.140643	+	0.990060i	$0.455083\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.866025	−	0.500000i	−0.0394055	−	0.0227508i
$484$		0			0
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$		0			0
$487$	11.2583	−	6.50000i	0.510164	−	0.294543i	−0.222737	−	0.974879i	$-0.571499\pi$
$487$	11.2583	−	6.50000i	0.510164	−	0.294543i	0.732901	+	0.680335i	$0.238166\pi$
$488$		0			0
$489$		−	5.00000i		−	0.226108i
$490$		0			0
$491$	−1.50000	+	2.59808i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$491$	−1.50000	+	2.59808i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$		0			0
$495$	−4.00000			−0.179787
$496$		0			0
$497$	−2.50000	+	4.33013i	−0.112140	+	0.194233i
$498$		0			0
$499$		−	36.0000i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$499$		−	36.0000i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$500$		0			0
$501$	−6.06218	+	3.50000i	−0.270838	+	0.156368i
$502$		0			0
$503$	12.5000	+	21.6506i	0.557347	+	0.965354i	0.997717	+	0.0675374i	$0.0215142\pi$
$503$	12.5000	+	21.6506i	0.557347	+	0.965354i	−0.440369	+	0.897817i	$0.645152\pi$
$504$		0			0
$505$	29.4449	+	17.0000i	1.31028	+	0.756490i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.866025	−	0.500000i	−0.0383859	−	0.0221621i	0.480684	−	0.876894i	$-0.340388\pi$
$509$	−0.866025	−	0.500000i	−0.0383859	−	0.0221621i	−0.519070	+	0.854732i	$0.673722\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$		0			0
$513$	30.3109	−	17.5000i	1.33826	−	0.772644i
$514$		0			0
$515$		−	16.0000i		−	0.705044i
$516$		0			0
$517$	6.00000	−	10.3923i	0.263880	−	0.457053i
$518$		0			0
$519$	9.00000			0.395056
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	9.50000	−	16.4545i	0.415406	−	0.719504i	−0.580065	−	0.814570i	$-0.696973\pi$
$523$	9.50000	−	16.4545i	0.415406	−	0.719504i	0.995471	+	0.0950659i	$0.0303062\pi$
$524$		0			0
$525$		−	1.00000i		−	0.0436436i
$526$		0			0
$527$	20.7846	−	12.0000i	0.905392	−	0.522728i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$		0			0
$531$	−15.5885	−	9.00000i	−0.676481	−	0.390567i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	29.4449	+	17.0000i	1.27301	+	0.734974i
$536$		0			0
$537$	4.50000	+	7.79423i	0.194189	+	0.336346i
$538$		0			0
$539$	5.19615	−	3.00000i	0.223814	−	0.129219i
$540$		0			0
$541$			30.0000i			1.28980i	0.764267	+	0.644900i	$0.223101\pi$
$541$			30.0000i			1.28980i	−0.764267	+	0.644900i	$0.776899\pi$
$542$		0			0
$543$	−7.00000	+	12.1244i	−0.300399	+	0.520306i
$544$		0			0
$545$	−20.0000			−0.856706
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$		0			0
$549$	−9.00000	+	15.5885i	−0.384111	+	0.665299i
$550$		0			0
$551$		−	21.0000i		−	0.894630i
$552$		0			0
$553$	10.3923	−	6.00000i	0.441926	−	0.255146i
$554$		0			0
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$		0			0
$557$	−16.4545	−	9.50000i	−0.697199	−	0.402528i	0.109104	−	0.994030i	$-0.465202\pi$
$557$	−16.4545	−	9.50000i	−0.697199	−	0.402528i	−0.806303	+	0.591502i	$0.798535\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.59808	+	1.50000i	0.109691	+	0.0633300i
$562$		0			0
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	0.755482	−	0.655169i	$-0.227403\pi$
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	−0.945134	+	0.326682i	$0.894069\pi$
$564$		0			0
$565$	−19.0526	+	11.0000i	−0.801547	+	0.462773i
$566$		0			0
$567$		−	1.00000i		−	0.0419961i
$568$		0			0
$569$	−8.50000	+	14.7224i	−0.356339	+	0.617196i	−0.987346	−	0.158580i	$-0.949308\pi$
$569$	−8.50000	+	14.7224i	−0.356339	+	0.617196i	0.631008	+	0.775777i	$0.282642\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	7.00000			0.292429
$574$		0			0
$575$	0.500000	−	0.866025i	0.0208514	−	0.0361158i
$576$		0			0
$577$		−	22.0000i		−	0.915872i	−0.888985	−	0.457936i	$-0.848589\pi$
$577$		−	22.0000i		−	0.915872i	0.888985	−	0.457936i	$-0.151411\pi$
$578$		0			0
$579$	−4.33013	+	2.50000i	−0.179954	+	0.103896i
$580$		0			0
$581$	−2.00000	−	3.46410i	−0.0829740	−	0.143715i
$582$		0			0
$583$	5.19615	+	3.00000i	0.215203	+	0.124247i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.1865	+	10.5000i	0.750639	+	0.433381i	0.825925	−	0.563781i	$-0.190654\pi$
$587$	18.1865	+	10.5000i	0.750639	+	0.433381i	−0.0752860	+	0.997162i	$0.523987\pi$
$588$		0			0
$589$	28.0000	+	48.4974i	1.15372	+	1.99830i
$590$		0			0
$591$	11.2583	−	6.50000i	0.463106	−	0.267374i
$592$		0			0
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$		0			0
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$		0			0
$597$	−3.00000			−0.122782
$598$		0			0
$599$	−44.0000			−1.79779			−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000			−1.79779			−0.898896	+	0.438163i	$0.855629\pi$
$600$		0			0
$601$	10.5000	−	18.1865i	0.428304	−	0.741844i	−0.568419	−	0.822739i	$-0.692445\pi$
$601$	10.5000	−	18.1865i	0.428304	−	0.741844i	0.996723	+	0.0808953i	$0.0257779\pi$
$602$		0			0
$603$		−	6.00000i		−	0.244339i
$604$		0			0
$605$	−17.3205	+	10.0000i	−0.704179	+	0.406558i
$606$		0			0
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$		0			0
$609$	2.59808	+	1.50000i	0.105279	+	0.0607831i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	33.7750	+	19.5000i	1.36416	+	0.787598i	0.990174	−	0.139837i	$-0.0446580\pi$
$613$	33.7750	+	19.5000i	1.36416	+	0.787598i	0.373985	+	0.927435i	$0.377991\pi$
$614$		0			0
$615$	11.0000	+	19.0526i	0.443563	+	0.768273i
$616$		0			0
$617$	−40.7032	+	23.5000i	−1.63865	+	0.946074i	−0.657350	+	0.753586i	$0.728323\pi$
$617$	−40.7032	+	23.5000i	−1.63865	+	0.946074i	−0.981299	+	0.192489i	$0.938344\pi$
$618$		0			0
$619$		−	20.0000i		−	0.803868i	−0.915669	−	0.401934i	$-0.868338\pi$
$619$		−	20.0000i		−	0.803868i	0.915669	−	0.401934i	$-0.131662\pi$
$620$		0			0
$621$	−2.50000	+	4.33013i	−0.100322	+	0.173762i
$622$		0			0
$623$	−1.00000			−0.0400642
$624$		0			0
$625$	−19.0000			−0.760000
$626$		0			0
$627$	−3.50000	+	6.06218i	−0.139777	+	0.242100i
$628$		0			0
$629$			3.00000i			0.119618i
$630$		0			0
$631$	23.3827	−	13.5000i	0.930850	−	0.537427i	0.0437697	−	0.999042i	$-0.486063\pi$
$631$	23.3827	−	13.5000i	0.930850	−	0.537427i	0.887080	+	0.461615i	$0.152730\pi$
$632$		0			0
$633$	−0.500000	−	0.866025i	−0.0198732	−	0.0344214i
$634$		0			0
$635$	−22.5167	−	13.0000i	−0.893546	−	0.515889i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	8.66025	+	5.00000i	0.342594	+	0.197797i
$640$		0			0
$641$	5.50000	+	9.52628i	0.217237	+	0.376265i	0.953962	−	0.299927i	$-0.0969622\pi$
$641$	5.50000	+	9.52628i	0.217237	+	0.376265i	−0.736725	+	0.676192i	$0.763629\pi$
$642$		0			0
$643$	−16.4545	+	9.50000i	−0.648901	+	0.374643i	−0.788035	−	0.615630i	$-0.788902\pi$
$643$	−16.4545	+	9.50000i	−0.648901	+	0.374643i	0.139134	+	0.990274i	$0.455568\pi$
$644$		0			0
$645$			22.0000i			0.866249i
$646$		0			0
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	−0.894004	−	0.448059i	$-0.852115\pi$
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	0.835033	+	0.550200i	$0.185449\pi$
$648$		0			0
$649$	9.00000			0.353281
$650$		0			0
$651$	−8.00000			−0.313545
$652$		0			0
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$		0			0
$655$		−	24.0000i		−	0.937758i
$656$		0			0
$657$	3.46410	−	2.00000i	0.135147	−	0.0780274i
$658$		0			0
$659$	14.5000	+	25.1147i	0.564840	+	0.978331i	0.997065	+	0.0765653i	$0.0243954\pi$
$659$	14.5000	+	25.1147i	0.564840	+	0.978331i	−0.432225	+	0.901766i	$0.642271\pi$
$660$		0			0
$661$	21.6506	+	12.5000i	0.842112	+	0.486194i	0.857982	−	0.513680i	$-0.171718\pi$
$661$	21.6506	+	12.5000i	0.842112	+	0.486194i	−0.0158695	+	0.999874i	$0.505052\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.1244	−	7.00000i	−0.470162	−	0.271448i
$666$		0			0
$667$	1.50000	+	2.59808i	0.0580802	+	0.100598i
$668$		0			0
$669$	−0.866025	+	0.500000i	−0.0334825	+	0.0193311i
$670$		0			0
$671$		−	9.00000i		−	0.347441i
$672$		0			0
$673$	19.5000	−	33.7750i	0.751670	−	1.30193i	−0.195343	−	0.980735i	$-0.562582\pi$
$673$	19.5000	−	33.7750i	0.751670	−	1.30193i	0.947013	−	0.321195i	$-0.104085\pi$
$674$		0			0
$675$	−5.00000			−0.192450
$676$		0			0
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	−0.500000	+	0.866025i	−0.0191882	+	0.0332350i
$680$		0			0
$681$			1.00000i			0.0383201i
$682$		0			0
$683$	−7.79423	+	4.50000i	−0.298238	+	0.172188i	−0.641651	−	0.766997i	$-0.721750\pi$
$683$	−7.79423	+	4.50000i	−0.298238	+	0.172188i	0.343413	+	0.939184i	$0.388417\pi$
$684$		0			0
$685$	9.00000	+	15.5885i	0.343872	+	0.595604i
$686$		0			0
$687$	5.19615	+	3.00000i	0.198246	+	0.114457i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	21.6506	+	12.5000i	0.823629	+	0.475522i	0.851666	−	0.524084i	$-0.175592\pi$
$691$	21.6506	+	12.5000i	0.823629	+	0.475522i	−0.0280373	+	0.999607i	$0.508926\pi$
$692$		0			0
$693$	1.00000	+	1.73205i	0.0379869	+	0.0657952i
$694$		0			0
$695$	15.5885	−	9.00000i	0.591304	−	0.341389i
$696$		0			0
$697$			33.0000i			1.24996i
$698$		0			0
$699$	−13.0000	+	22.5167i	−0.491705	+	0.851658i
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$		0			0
$703$	−7.00000			−0.264010
$704$		0			0
$705$	−12.0000	+	20.7846i	−0.451946	+	0.782794i
$706$		0			0
$707$		−	17.0000i		−	0.639351i
$708$		0			0
$709$	−25.1147	+	14.5000i	−0.943204	+	0.544559i	−0.890963	−	0.454076i	$-0.849970\pi$
$709$	−25.1147	+	14.5000i	−0.943204	+	0.544559i	−0.0522406	+	0.998635i	$0.516636\pi$
$710$		0			0
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$		0			0
$713$	−6.92820	−	4.00000i	−0.259463	−	0.149801i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.7846	−	12.0000i	−0.776215	−	0.448148i
$718$		0			0
$719$	19.5000	+	33.7750i	0.727227	+	1.25959i	0.958051	+	0.286599i	$0.0925247\pi$
$719$	19.5000	+	33.7750i	0.727227	+	1.25959i	−0.230823	+	0.972996i	$0.574142\pi$
$720$		0			0
$721$	−6.92820	+	4.00000i	−0.258020	+	0.148968i
$722$		0			0
$723$			11.0000i			0.409094i
$724$		0			0
$725$	−1.50000	+	2.59808i	−0.0557086	+	0.0964901i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−16.5000	+	28.5788i	−0.610275	+	1.05703i
$732$		0			0
$733$		−	46.0000i		−	1.69905i	−0.527549	−	0.849524i	$-0.676889\pi$
$733$		−	46.0000i		−	1.69905i	0.527549	−	0.849524i	$-0.323111\pi$
$734$		0			0
$735$	−10.3923	+	6.00000i	−0.383326	+	0.221313i
$736$		0			0
$737$	1.50000	+	2.59808i	0.0552532	+	0.0957014i
$738$		0			0
$739$	9.52628	+	5.50000i	0.350430	+	0.202321i	0.664875	−	0.746955i	$-0.268485\pi$
$739$	9.52628	+	5.50000i	0.350430	+	0.202321i	−0.314445	+	0.949276i	$0.601818\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.884072	−	0.467351i	$-0.154791\pi$
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.0372984	+	0.999304i	$0.488125\pi$
$744$		0			0
$745$	−1.00000	−	1.73205i	−0.0366372	−	0.0634574i
$746$		0			0
$747$	−6.92820	+	4.00000i	−0.253490	+	0.146352i
$748$		0			0
$749$		−	17.0000i		−	0.621166i
$750$		0			0
$751$	8.50000	−	14.7224i	0.310169	−	0.537229i	−0.668229	−	0.743955i	$-0.732948\pi$
$751$	8.50000	−	14.7224i	0.310169	−	0.537229i	0.978399	+	0.206726i	$0.0662809\pi$
$752$		0			0
$753$	13.0000			0.473746
$754$		0			0
$755$	32.0000			1.16460
$756$		0			0
$757$	−23.5000	+	40.7032i	−0.854122	+	1.47938i	0.0233351	+	0.999728i	$0.492572\pi$
$757$	−23.5000	+	40.7032i	−0.854122	+	1.47938i	−0.877457	+	0.479655i	$0.840762\pi$
$758$		0			0
$759$		−	1.00000i		−	0.0362977i
$760$		0			0
$761$	2.59808	−	1.50000i	0.0941802	−	0.0543750i	−0.452170	−	0.891932i	$-0.649350\pi$
$761$	2.59808	−	1.50000i	0.0941802	−	0.0543750i	0.546350	+	0.837557i	$0.316017\pi$
$762$		0			0
$763$	5.00000	+	8.66025i	0.181012	+	0.313522i
$764$		0			0
$765$	10.3923	+	6.00000i	0.375735	+	0.216930i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−4.33013	−	2.50000i	−0.156148	−	0.0901523i	0.419890	−	0.907575i	$-0.362069\pi$
$769$	−4.33013	−	2.50000i	−0.156148	−	0.0901523i	−0.576038	+	0.817423i	$0.695402\pi$
$770$		0			0
$771$	−6.50000	−	11.2583i	−0.234092	−	0.405459i
$772$		0			0
$773$	−2.59808	+	1.50000i	−0.0934463	+	0.0539513i	−0.545995	−	0.837788i	$-0.683848\pi$
$773$	−2.59808	+	1.50000i	−0.0934463	+	0.0539513i	0.452549	+	0.891740i	$0.350515\pi$
$774$		0			0
$775$		−	8.00000i		−	0.287368i
$776$		0			0
$777$	0.500000	−	0.866025i	0.0179374	−	0.0310685i
$778$		0			0
$779$	−77.0000			−2.75881
$780$		0			0
$781$	−5.00000			−0.178914
$782$		0			0
$783$	7.50000	−	12.9904i	0.268028	−	0.464238i
$784$		0			0
$785$		−	20.0000i		−	0.713831i
$786$		0			0
$787$	−18.1865	+	10.5000i	−0.648280	+	0.374285i	−0.787797	−	0.615935i	$-0.788778\pi$
$787$	−18.1865	+	10.5000i	−0.648280	+	0.374285i	0.139517	+	0.990220i	$0.455445\pi$
$788$		0			0
$789$	15.5000	+	26.8468i	0.551815	+	0.955771i
$790$		0			0
$791$	9.52628	+	5.50000i	0.338716	+	0.195557i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−10.3923	−	6.00000i	−0.368577	−	0.212798i
$796$		0			0
$797$	11.5000	+	19.9186i	0.407351	+	0.705552i	0.994592	−	0.103860i	$-0.0331193\pi$
$797$	11.5000	+	19.9186i	0.407351	+	0.705552i	−0.587241	+	0.809412i	$0.699786\pi$
$798$		0			0
$799$	−31.1769	+	18.0000i	−1.10296	+	0.636794i
$800$		0			0
$801$			2.00000i			0.0706665i
$802$		0			0
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$	2.00000			0.0704907
$806$		0			0
$807$	−5.00000			−0.176008
$808$		0			0
$809$	−13.5000	+	23.3827i	−0.474635	+	0.822091i	−0.999578	−	0.0290457i	$-0.990753\pi$
$809$	−13.5000	+	23.3827i	−0.474635	+	0.822091i	0.524943	+	0.851137i	$0.324086\pi$
$810$		0			0
$811$		−	32.0000i		−	1.12367i	−0.827249	−	0.561836i	$-0.810095\pi$
$811$		−	32.0000i		−	1.12367i	0.827249	−	0.561836i	$-0.189905\pi$
$812$		0			0
$813$	−6.06218	+	3.50000i	−0.212610	+	0.122750i
$814$		0			0
$815$	5.00000	+	8.66025i	0.175142	+	0.303355i
$816$		0			0
$817$	−66.6840	−	38.5000i	−2.33298	−	1.34694i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.33013	−	2.50000i	−0.151122	−	0.0872506i	0.422532	−	0.906348i	$-0.361141\pi$
$821$	−4.33013	−	2.50000i	−0.151122	−	0.0872506i	−0.573654	+	0.819097i	$0.694475\pi$
$822$		0			0
$823$	−14.5000	−	25.1147i	−0.505438	−	0.875445i	−0.999980	−	0.00629095i	$-0.997998\pi$
$823$	−14.5000	−	25.1147i	−0.505438	−	0.875445i	0.494542	−	0.869154i	$-0.335336\pi$
$824$		0			0
$825$	0.866025	−	0.500000i	0.0301511	−	0.0174078i
$826$		0			0
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$		0			0
$829$	1.50000	−	2.59808i	0.0520972	−	0.0902349i	−0.838801	−	0.544438i	$-0.816743\pi$
$829$	1.50000	−	2.59808i	0.0520972	−	0.0902349i	0.890898	+	0.454204i	$0.150076\pi$
$830$		0			0
$831$	21.0000			0.728482
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	7.00000	−	12.1244i	0.242245	−	0.419581i
$836$		0			0
$837$			40.0000i			1.38260i
$838$		0			0
$839$	23.3827	−	13.5000i	0.807260	−	0.466072i	−0.0387435	−	0.999249i	$-0.512336\pi$
$839$	23.3827	−	13.5000i	0.807260	−	0.466072i	0.846003	+	0.533177i	$0.179002\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$	−12.1244	−	7.00000i	−0.417585	−	0.241093i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	8.66025	+	5.00000i	0.297570	+	0.171802i
$848$		0			0
$849$	12.5000	+	21.6506i	0.428999	+	0.743048i
$850$		0			0
$851$	0.866025	−	0.500000i	0.0296870	−	0.0171398i
$852$		0			0
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$	−14.0000	+	24.2487i	−0.478790	+	0.829288i
$856$		0			0
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$		0			0
$861$	5.50000	−	9.52628i	0.187439	−	0.324655i
$862$		0			0
$863$			16.0000i			0.544646i	0.962206	+	0.272323i	$0.0877920\pi$
$863$			16.0000i			0.544646i	−0.962206	+	0.272323i	$0.912208\pi$
$864$		0			0
$865$	−15.5885	+	9.00000i	−0.530023	+	0.306009i
$866$		0			0
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$		0			0
$869$	10.3923	+	6.00000i	0.352535	+	0.203536i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.73205	+	1.00000i	0.0586210	+	0.0338449i
$874$		0			0
$875$	6.00000	+	10.3923i	0.202837	+	0.351324i
$876$		0			0
$877$	0.866025	−	0.500000i	0.0292436	−	0.0168838i	−0.485307	−	0.874344i	$-0.661292\pi$
$877$	0.866025	−	0.500000i	0.0292436	−	0.0168838i	0.514551	+	0.857460i	$0.327959\pi$
$878$		0			0
$879$		−	9.00000i		−	0.303562i
$880$		0			0
$881$	−22.5000	+	38.9711i	−0.758044	+	1.31297i	0.185802	+	0.982587i	$0.440512\pi$
$881$	−22.5000	+	38.9711i	−0.758044	+	1.31297i	−0.943847	+	0.330384i	$0.892822\pi$
$882$		0			0
$883$	12.0000			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$884$		0			0
$885$	−18.0000			−0.605063
$886$		0			0
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	−0.545302	−	0.838240i	$-0.683585\pi$
$887$	13.5000	−	23.3827i	0.453286	−	0.785114i	0.998588	+	0.0531258i	$0.0169184\pi$
$888$		0			0
$889$			13.0000i			0.436006i
$890$		0			0
$891$	0.866025	−	0.500000i	0.0290129	−	0.0167506i
$892$		0			0
$893$	−42.0000	−	72.7461i	−1.40548	−	2.43436i
$894$		0			0
$895$	−15.5885	−	9.00000i	−0.521065	−	0.300837i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	20.7846	+	12.0000i	0.693206	+	0.400222i
$900$		0			0
$901$	−9.00000	−	15.5885i	−0.299833	−	0.519327i
$902$		0			0
$903$	9.52628	−	5.50000i	0.317015	−	0.183029i
$904$		0			0
$905$		−	28.0000i		−	0.930751i
$906$		0			0
$907$	12.5000	−	21.6506i	0.415056	−	0.718898i	−0.580379	−	0.814347i	$-0.697095\pi$
$907$	12.5000	−	21.6506i	0.415056	−	0.718898i	0.995434	+	0.0954492i	$0.0304288\pi$
$908$		0			0
$909$	−34.0000			−1.12771
$910$		0			0
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$	2.00000	−	3.46410i	0.0661903	−	0.114645i
$914$		0			0
$915$			18.0000i			0.595062i
$916$		0			0
$917$	−10.3923	+	6.00000i	−0.343184	+	0.198137i
$918$		0			0
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	0.715402	−	0.698713i	$-0.246244\pi$
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	−0.962804	+	0.270200i	$0.912910\pi$
$920$		0			0
$921$	17.3205	+	10.0000i	0.570730	+	0.329511i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.866025	+	0.500000i	0.0284747	+	0.0164399i
$926$		0			0
$927$	8.00000	+	13.8564i	0.262754	+	0.455104i
$928$		0			0
$929$	4.33013	−	2.50000i	0.142067	−	0.0820223i	−0.427282	−	0.904118i	$-0.640529\pi$
$929$	4.33013	−	2.50000i	0.142067	−	0.0820223i	0.569349	+	0.822096i	$0.307195\pi$
$930$		0			0
$931$		−	42.0000i		−	1.37649i
$932$		0			0
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$		0			0
$935$	−6.00000			−0.196221
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$	−15.0000	+	25.9808i	−0.489506	+	0.847850i
$940$		0			0
$941$		−	14.0000i		−	0.456387i	−0.973616	−	0.228193i	$-0.926718\pi$
$941$		−	14.0000i		−	0.456387i	0.973616	−	0.228193i	$-0.0732819\pi$
$942$		0			0
$943$	9.52628	−	5.50000i	0.310218	−	0.179105i
$944$		0			0
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$		0			0
$947$	33.7750	+	19.5000i	1.09754	+	0.633665i	0.935574	−	0.353131i	$-0.114883\pi$
$947$	33.7750	+	19.5000i	1.09754	+	0.633665i	0.161966	+	0.986796i	$0.448217\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−1.73205	−	1.00000i	−0.0561656	−	0.0324272i
$952$		0			0
$953$	−4.50000	−	7.79423i	−0.145769	−	0.252480i	0.783890	−	0.620899i	$-0.213232\pi$
$953$	−4.50000	−	7.79423i	−0.145769	−	0.252480i	−0.929660	+	0.368419i	$0.879899\pi$
$954$		0			0
$955$	−12.1244	+	7.00000i	−0.392335	+	0.226515i
$956$		0			0
$957$			3.00000i			0.0969762i
$958$		0			0
$959$	4.50000	−	7.79423i	0.145313	−	0.251689i
$960$		0			0
$961$	−33.0000			−1.06452
$962$		0			0
$963$	−34.0000			−1.09563
$964$		0			0
$965$	5.00000	−	8.66025i	0.160956	−	0.278783i
$966$		0			0
$967$			16.0000i			0.514525i	0.966342	+	0.257263i	$0.0828206\pi$
$967$			16.0000i			0.514525i	−0.966342	+	0.257263i	$0.917179\pi$
$968$		0			0
$969$	18.1865	−	10.5000i	0.584236	−	0.337309i
$970$		0			0
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	0.563914	−	0.825833i	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$		0			0
$973$	−7.79423	−	4.50000i	−0.249871	−	0.144263i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.79423	−	4.50000i	−0.249359	−	0.143968i	0.370111	−	0.928987i	$-0.379319\pi$
$977$	−7.79423	−	4.50000i	−0.249359	−	0.143968i	−0.619471	+	0.785020i	$0.712653\pi$
$978$		0			0
$979$	−0.500000	−	0.866025i	−0.0159801	−	0.0276783i
$980$		0			0
$981$	17.3205	−	10.0000i	0.553001	−	0.319275i
$982$		0			0
$983$			32.0000i			1.02064i	0.859984	+	0.510321i	$0.170473\pi$
$983$			32.0000i			1.02064i	−0.859984	+	0.510321i	$0.829527\pi$
$984$		0			0
$985$	−13.0000	+	22.5167i	−0.414214	+	0.717440i
$986$		0			0
$987$	12.0000			0.381964
$988$		0			0
$989$	11.0000			0.349780
$990$		0			0
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	−0.950603	−	0.310409i	$-0.899534\pi$
$991$	−6.50000	+	11.2583i	−0.206479	+	0.357633i	0.744124	+	0.668042i	$0.232867\pi$
$992$		0			0
$993$		−	27.0000i		−	0.856819i
$994$		0			0
$995$	5.19615	−	3.00000i	0.164729	−	0.0951064i
$996$		0			0
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	0.993213	−	0.116310i	$-0.0371066\pi$
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	−0.597334	+	0.801993i	$0.703773\pi$
$998$		0			0
$999$	−4.33013	−	2.50000i	−0.136999	−	0.0790965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.b.1161.1		4
13.2	odd	12		1352.2.i.a.1329.1		2
13.3	even	3	inner	1352.2.o.b.361.1		4
13.4	even	6		1352.2.f.a.337.2		2
13.5	odd	4		1352.2.i.a.529.1		2
13.6	odd	12		1352.2.a.a.1.1		1
13.7	odd	12		1352.2.a.c.1.1		1
13.8	odd	4		104.2.i.a.9.1	✓	2
13.9	even	3		1352.2.f.a.337.1		2
13.10	even	6	inner	1352.2.o.b.361.2		4
13.11	odd	12		104.2.i.a.81.1	yes	2
13.12	even	2	inner	1352.2.o.b.1161.2		4
39.8	even	4		936.2.t.c.217.1		2
39.11	even	12		936.2.t.c.289.1		2
52.7	even	12		2704.2.a.e.1.1		1
52.11	even	12		208.2.i.c.81.1		2
52.19	even	12		2704.2.a.c.1.1		1
52.35	odd	6		2704.2.f.c.337.1		2
52.43	odd	6		2704.2.f.c.337.2		2
52.47	even	4		208.2.i.c.113.1		2
104.11	even	12		832.2.i.d.705.1		2
104.21	odd	4		832.2.i.g.321.1		2
104.37	odd	12		832.2.i.g.705.1		2
104.99	even	4		832.2.i.d.321.1		2
156.11	odd	12		1872.2.t.d.289.1		2
156.47	odd	4		1872.2.t.d.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.i.a.9.1	✓	2	13.8	odd	4
104.2.i.a.81.1	yes	2	13.11	odd	12
208.2.i.c.81.1		2	52.11	even	12
208.2.i.c.113.1		2	52.47	even	4
832.2.i.d.321.1		2	104.99	even	4
832.2.i.d.705.1		2	104.11	even	12
832.2.i.g.321.1		2	104.21	odd	4
832.2.i.g.705.1		2	104.37	odd	12
936.2.t.c.217.1		2	39.8	even	4
936.2.t.c.289.1		2	39.11	even	12
1352.2.a.a.1.1		1	13.6	odd	12
1352.2.a.c.1.1		1	13.7	odd	12
1352.2.f.a.337.1		2	13.9	even	3
1352.2.f.a.337.2		2	13.4	even	6
1352.2.i.a.529.1		2	13.5	odd	4
1352.2.i.a.1329.1		2	13.2	odd	12
1352.2.o.b.361.1		4	13.3	even	3	inner
1352.2.o.b.361.2		4	13.10	even	6	inner
1352.2.o.b.1161.1		4	1.1	even	1	trivial
1352.2.o.b.1161.2		4	13.12	even	2	inner
1872.2.t.d.289.1		2	156.11	odd	12
1872.2.t.d.1153.1		2	156.47	odd	4
2704.2.a.c.1.1		1	52.19	even	12
2704.2.a.e.1.1		1	52.7	even	12
2704.2.f.c.337.1		2	52.35	odd	6
2704.2.f.c.337.2		2	52.43	odd	6

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:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -2.00000i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} -2.00000i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(1.73205 + 1.00000i) q^{15} +(1.50000 + 2.59808i) q^{17} +(-6.06218 + 3.50000i) q^{19} -1.00000i q^{21} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{25} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} -8.00000i q^{31} +(0.866025 - 0.500000i) q^{33} +(1.00000 + 1.73205i) q^{35} +(0.866025 + 0.500000i) q^{37} +(9.52628 + 5.50000i) q^{41} +(5.50000 + 9.52628i) q^{43} +(3.46410 - 2.00000i) q^{45} +12.0000i q^{47} +(-3.00000 + 5.19615i) q^{49} -3.00000 q^{51} -6.00000 q^{53} +(-1.00000 + 1.73205i) q^{55} -7.00000i q^{57} +(-7.79423 + 4.50000i) q^{59} +(4.50000 + 7.79423i) q^{61} +(-1.73205 - 1.00000i) q^{63} +(-2.59808 - 1.50000i) q^{67} +(0.500000 + 0.866025i) q^{69} +(4.33013 - 2.50000i) q^{71} -2.00000i q^{73} +(-0.500000 + 0.866025i) q^{75} +1.00000 q^{77} -12.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000i q^{83} +(5.19615 - 3.00000i) q^{85} +(-1.50000 - 2.59808i) q^{87} +(0.866025 + 0.500000i) q^{89} +(6.92820 + 4.00000i) q^{93} +(7.00000 + 12.1244i) q^{95} +(0.866025 - 0.500000i) q^{97} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^9	\( 4 q - 2 q^{3} + 4 q^{9} + 6 q^{17} + 2 q^{23} + 4 q^{25} - 20 q^{27} - 6 q^{29} + 4 q^{35} + 22 q^{43} - 12 q^{49} - 12 q^{51} - 24 q^{53} - 4 q^{55} + 18 q^{61} + 2 q^{69} - 2 q^{75} + 4 q^{77} - 48 q^{79} - 2 q^{81} - 6 q^{87} + 28 q^{95}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^9 + 6 * q^17 + 2 * q^23 + 4 * q^25 - 20 * q^27 - 6 * q^29 + 4 * q^35 + 22 * q^43 - 12 * q^49 - 12 * q^51 - 24 * q^53 - 4 * q^55 + 18 * q^61 + 2 * q^69 - 2 * q^75 + 4 * q^77 - 48 * q^79 - 2 * q^81 - 6 * q^87 + 28 * q^95

Introduction

L-functions

Modular forms

Varieties

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