LMFDB - Embedded newform 1040.2.q.o.321.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(81,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1040.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.q (of order $3$, 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			321.1
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	1040.321
Dual form			1040.2.q.o.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-2.80278 + 4.85455i) q^{11} +3.60555 q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.197224 - 0.341603i) q^{17} +(0.802776 + 1.39045i) q^{19} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(-4.10555 + 7.11102i) q^{29} +4.00000 q^{31} +(2.80278 + 4.85455i) q^{33} +(0.500000 + 0.866025i) q^{35} +(1.80278 - 3.12250i) q^{37} +(1.80278 - 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(2.10555 + 3.64692i) q^{43} +(-1.00000 - 1.73205i) q^{45} +5.21110 q^{47} +(3.00000 - 5.19615i) q^{49} -0.394449 q^{51} +11.2111 q^{53} +(2.80278 - 4.85455i) q^{55} +1.60555 q^{57} +(5.40833 + 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{63} -3.60555 q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-8.40833 - 14.5636i) q^{71} -15.2111 q^{73} +(0.500000 - 0.866025i) q^{75} +5.60555 q^{77} +9.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} -5.21110 q^{83} +(0.197224 + 0.341603i) q^{85} +(4.10555 + 7.11102i) q^{87} +(-4.10555 + 7.11102i) q^{89} +(-1.80278 - 3.12250i) q^{91} +(2.00000 - 3.46410i) q^{93} +(-0.802776 - 1.39045i) q^{95} +(7.80278 + 13.5148i) q^{97} -11.2111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 4 q^{9} - 4 q^{11} - 2 q^{15} - 8 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} + 4 q^{25} + 20 q^{27} - 2 q^{29} + 16 q^{31} + 4 q^{33} + 2 q^{35} - 6 q^{41} - 6 q^{43} - 4 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 4 * q^9 - 4 * q^11 - 2 * q^15 - 8 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 + 4 * q^25 + 20 * q^27 - 2 * q^29 + 16 * q^31 + 4 * q^33 + 2 * q^35 - 6 * q^41 - 6 * q^43 - 4 * q^45 - 8 * q^47 + 12 * q^49 - 16 * q^51 + 16 * q^53 + 4 * q^55 - 8 * q^57 + 2 * q^61 + 4 * q^63 - 14 * q^67 + 6 * q^69 - 12 * q^71 - 32 * q^73 + 2 * q^75 + 8 * q^77 + 8 * q^79 - 2 * q^81 + 8 * q^83 + 8 * q^85 + 2 * q^87 - 2 * q^89 + 8 * q^93 + 4 * q^95 + 24 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	−2.80278	+	4.85455i	−0.845069	+	1.46370i	0.0404929	+	0.999180i	$0.487107\pi$
$11$	−2.80278	+	4.85455i	−0.845069	+	1.46370i	−0.885562	+	0.464522i	$0.846226\pi$
$12$		0			0
$13$	3.60555			1.00000
$13$	3.60555			1.00000
$14$		0			0
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$		0			0
$17$	−0.197224	−	0.341603i	−0.0478339	−	0.0828508i	0.841117	−	0.540853i	$-0.181898\pi$
$17$	−0.197224	−	0.341603i	−0.0478339	−	0.0828508i	−0.888951	+	0.458002i	$0.848565\pi$
$18$		0			0
$19$	0.802776	+	1.39045i	0.184169	+	0.318991i	0.943296	−	0.331952i	$-0.107707\pi$
$19$	0.802776	+	1.39045i	0.184169	+	0.318991i	−0.759127	+	0.650943i	$0.774374\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	−4.10555	+	7.11102i	−0.762382	+	1.32048i	0.179238	+	0.983806i	$0.442637\pi$
$29$	−4.10555	+	7.11102i	−0.762382	+	1.32048i	−0.941620	+	0.336678i	$0.890697\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		0			0
$33$	2.80278	+	4.85455i	0.487901	+	0.845069i
$34$		0			0
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		0			0
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	−0.678929	−	0.734204i	$-0.737556\pi$
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	0.975304	+	0.220868i	$0.0708890\pi$
$38$		0			0
$39$	1.80278	−	3.12250i	0.288675	−	0.500000i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	2.10555	+	3.64692i	0.321094	+	0.556150i	0.980714	−	0.195449i	$-0.0626163\pi$
$43$	2.10555	+	3.64692i	0.321094	+	0.556150i	−0.659620	+	0.751599i	$0.729283\pi$
$44$		0			0
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$		0			0
$47$	5.21110			0.760117			0.380059	−	0.924962i	$-0.375904\pi$
$47$	5.21110			0.760117			0.380059	+	0.924962i	$0.375904\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	−0.394449			−0.0552339
$52$		0			0
$53$	11.2111			1.53996			0.769982	−	0.638066i	$-0.220265\pi$
$53$	11.2111			1.53996			0.769982	+	0.638066i	$0.220265\pi$
$54$		0			0
$55$	2.80278	−	4.85455i	0.377926	−	0.654587i
$56$		0			0
$57$	1.60555			0.212660
$58$		0			0
$59$	5.40833	+	9.36750i	0.704104	+	1.21954i	0.967014	+	0.254724i	$0.0819845\pi$
$59$	5.40833	+	9.36750i	0.704104	+	1.21954i	−0.262910	+	0.964820i	$0.584682\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$		0			0
$65$	−3.60555			−0.447214
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$		0			0
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	−8.40833	−	14.5636i	−0.997885	−	1.72839i	−0.555240	−	0.831690i	$-0.687374\pi$
$71$	−8.40833	−	14.5636i	−0.997885	−	1.72839i	−0.442645	−	0.896697i	$-0.645960\pi$
$72$		0			0
$73$	−15.2111			−1.78032			−0.890162	−	0.455643i	$-0.849409\pi$
$73$	−15.2111			−1.78032			−0.890162	+	0.455643i	$0.849409\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	5.60555			0.638812
$78$		0			0
$79$	9.21110			1.03633			0.518165	−	0.855281i	$-0.326615\pi$
$79$	9.21110			1.03633			0.518165	+	0.855281i	$0.326615\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−5.21110			−0.571993			−0.285996	−	0.958231i	$-0.592325\pi$
$83$	−5.21110			−0.571993			−0.285996	+	0.958231i	$0.592325\pi$
$84$		0			0
$85$	0.197224	+	0.341603i	0.0213920	+	0.0370520i
$86$		0			0
$87$	4.10555	+	7.11102i	0.440161	+	0.762382i
$88$		0			0
$89$	−4.10555	+	7.11102i	−0.435188	+	0.753767i	−0.997311	−	0.0732864i	$-0.976651\pi$
$89$	−4.10555	+	7.11102i	−0.435188	+	0.753767i	0.562123	+	0.827053i	$0.309985\pi$
$90$		0			0
$91$	−1.80278	−	3.12250i	−0.188982	−	0.327327i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$		0			0
$95$	−0.802776	−	1.39045i	−0.0823630	−	0.142657i
$96$		0			0
$97$	7.80278	+	13.5148i	0.792252	+	1.37222i	0.924570	+	0.381013i	$0.124425\pi$
$97$	7.80278	+	13.5148i	0.792252	+	1.37222i	−0.132318	+	0.991207i	$0.542242\pi$
$98$		0			0
$99$	−11.2111			−1.12676
$100$		0			0
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$		0			0
$107$	−4.10555	+	7.11102i	−0.396899	+	0.687449i	−0.993342	−	0.115207i	$-0.963247\pi$
$107$	−4.10555	+	7.11102i	−0.396899	+	0.687449i	0.596443	+	0.802656i	$0.296580\pi$
$108$		0			0
$109$	−4.78890			−0.458693			−0.229347	−	0.973345i	$-0.573659\pi$
$109$	−4.78890			−0.458693			−0.229347	+	0.973345i	$0.573659\pi$
$110$		0			0
$111$	−1.80278	−	3.12250i	−0.171112	−	0.296374i
$112$		0			0
$113$	−2.80278	−	4.85455i	−0.263663	−	0.456678i	0.703550	−	0.710646i	$-0.251597\pi$
$113$	−2.80278	−	4.85455i	−0.263663	−	0.456678i	−0.967212	+	0.253969i	$0.918264\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$		0			0
$117$	3.60555	+	6.24500i	0.333333	+	0.577350i
$118$		0			0
$119$	−0.197224	+	0.341603i	−0.0180795	+	0.0313147i
$120$		0			0
$121$	−10.2111	−	17.6861i	−0.928282	−	1.60783i
$122$		0			0
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.10555	−	8.84307i	0.453044	−	0.784696i	−0.545529	−	0.838092i	$-0.683671\pi$
$127$	5.10555	−	8.84307i	0.453044	−	0.784696i	0.998573	+	0.0533960i	$0.0170046\pi$
$128$		0			0
$129$	4.21110			0.370767
$130$		0			0
$131$	6.78890			0.593149			0.296574	−	0.955010i	$-0.404156\pi$
$131$	6.78890			0.593149			0.296574	+	0.955010i	$0.404156\pi$
$132$		0			0
$133$	0.802776	−	1.39045i	0.0696095	−	0.120567i
$134$		0			0
$135$	−5.00000			−0.430331
$136$		0			0
$137$	−2.80278	−	4.85455i	−0.239457	−	0.414752i	0.721101	−	0.692830i	$-0.243636\pi$
$137$	−2.80278	−	4.85455i	−0.239457	−	0.414752i	−0.960559	+	0.278077i	$0.910303\pi$
$138$		0			0
$139$	6.80278	+	11.7828i	0.577004	+	0.999400i	0.995821	+	0.0913293i	$0.0291116\pi$
$139$	6.80278	+	11.7828i	0.577004	+	0.999400i	−0.418817	+	0.908071i	$0.637555\pi$
$140$		0			0
$141$	2.60555	−	4.51295i	0.219427	−	0.380059i
$142$		0			0
$143$	−10.1056	+	17.5033i	−0.845069	+	1.46370i
$144$		0			0
$145$	4.10555	−	7.11102i	0.340947	−	0.590538i
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	−13.2111			−1.07510			−0.537552	−	0.843231i	$-0.680651\pi$
$151$	−13.2111			−1.07510			−0.537552	+	0.843231i	$0.680651\pi$
$152$		0			0
$153$	0.394449	−	0.683205i	0.0318893	−	0.0552339i
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−3.21110			−0.256274			−0.128137	−	0.991756i	$-0.540900\pi$
$157$	−3.21110			−0.256274			−0.128137	+	0.991756i	$0.540900\pi$
$158$		0			0
$159$	5.60555	−	9.70910i	0.444549	−	0.769982i
$160$		0			0
$161$	3.00000			0.236433
$162$		0			0
$163$	−9.10555	−	15.7713i	−0.713202	−	1.23530i	−0.963649	−	0.267172i	$-0.913911\pi$
$163$	−9.10555	−	15.7713i	−0.713202	−	1.23530i	0.250447	−	0.968130i	$-0.419422\pi$
$164$		0			0
$165$	−2.80278	−	4.85455i	−0.218196	−	0.377926i
$166$		0			0
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	−1.60555	+	2.78090i	−0.122780	+	0.212660i
$172$		0			0
$173$	8.40833	+	14.5636i	0.639273	+	1.10725i	0.985593	+	0.169137i	$0.0540981\pi$
$173$	8.40833	+	14.5636i	0.639273	+	1.10725i	−0.346319	+	0.938117i	$0.612569\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$		0			0
$177$	10.8167			0.813029
$178$		0			0
$179$	0.591673	−	1.02481i	0.0442237	−	0.0765977i	−0.843066	−	0.537810i	$-0.819252\pi$
$179$	0.591673	−	1.02481i	0.0442237	−	0.0765977i	0.887290	+	0.461212i	$0.152585\pi$
$180$		0			0
$181$	−25.6333			−1.90531			−0.952654	−	0.304055i	$-0.901659\pi$
$181$	−25.6333			−1.90531			−0.952654	+	0.304055i	$0.901659\pi$
$182$		0			0
$183$	1.00000			0.0739221
$184$		0			0
$185$	−1.80278	+	3.12250i	−0.132543	+	0.229571i
$186$		0			0
$187$	2.21110			0.161692
$188$		0			0
$189$	−2.50000	−	4.33013i	−0.181848	−	0.314970i
$190$		0			0
$191$	−2.40833	−	4.17134i	−0.174260	−	0.301828i	0.765645	−	0.643264i	$-0.222420\pi$
$191$	−2.40833	−	4.17134i	−0.174260	−	0.301828i	−0.939905	+	0.341436i	$0.889087\pi$
$192$		0			0
$193$	−4.19722	+	7.26981i	−0.302123	+	0.523292i	−0.976617	−	0.214988i	$-0.931029\pi$
$193$	−4.19722	+	7.26981i	−0.302123	+	0.523292i	0.674494	+	0.738281i	$0.264362\pi$
$194$		0			0
$195$	−1.80278	+	3.12250i	−0.129099	+	0.223607i
$196$		0			0
$197$	−11.4083	+	19.7598i	−0.812810	+	1.40783i	0.0980804	+	0.995178i	$0.468730\pi$
$197$	−11.4083	+	19.7598i	−0.812810	+	1.40783i	−0.910890	+	0.412649i	$0.864604\pi$
$198$		0			0
$199$	−4.40833	−	7.63545i	−0.312498	−	0.541262i	0.666404	−	0.745590i	$-0.267832\pi$
$199$	−4.40833	−	7.63545i	−0.312498	−	0.541262i	−0.978902	+	0.204328i	$0.934499\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$	8.21110			0.576306
$204$		0			0
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$		0			0
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−8.19722	+	14.1980i	−0.564320	+	0.977431i	0.432792	+	0.901494i	$0.357528\pi$
$211$	−8.19722	+	14.1980i	−0.564320	+	0.977431i	−0.997113	+	0.0759376i	$0.975805\pi$
$212$		0			0
$213$	−16.8167			−1.15226
$214$		0			0
$215$	−2.10555	−	3.64692i	−0.143597	−	0.248718i
$216$		0			0
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$		0			0
$219$	−7.60555	+	13.1732i	−0.513936	+	0.890162i
$220$		0			0
$221$	−0.711103	−	1.23167i	−0.0478339	−	0.0828508i
$222$		0			0
$223$	5.10555	−	8.84307i	0.341893	−	0.592176i	−0.642891	−	0.765957i	$-0.722265\pi$
$223$	5.10555	−	8.84307i	0.341893	−	0.592176i	0.984784	+	0.173781i	$0.0555986\pi$
$224$		0			0
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$		0			0
$227$	0.711103	+	1.23167i	0.0471975	+	0.0817485i	0.888659	−	0.458569i	$-0.151638\pi$
$227$	0.711103	+	1.23167i	0.0471975	+	0.0817485i	−0.841462	+	0.540317i	$0.818304\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$	2.80278	−	4.85455i	0.184409	−	0.319406i
$232$		0			0
$233$	0.788897			0.0516824			0.0258412	−	0.999666i	$-0.491774\pi$
$233$	0.788897			0.0516824			0.0258412	+	0.999666i	$0.491774\pi$
$234$		0			0
$235$	−5.21110			−0.339935
$236$		0			0
$237$	4.60555	−	7.97705i	0.299163	−	0.518165i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−8.10555	−	14.0392i	−0.522124	−	0.904346i	−0.999669	−	0.0257384i	$-0.991806\pi$
$241$	−8.10555	−	14.0392i	−0.522124	−	0.904346i	0.477544	−	0.878608i	$-0.341527\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$		0			0
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$		0			0
$247$	2.89445	+	5.01333i	0.184169	+	0.318991i
$248$		0			0
$249$	−2.60555	+	4.51295i	−0.165120	+	0.285996i
$250$		0			0
$251$	−14.4083	−	24.9560i	−0.909446	−	1.57521i	−0.814836	−	0.579691i	$-0.803173\pi$
$251$	−14.4083	−	24.9560i	−0.909446	−	1.57521i	−0.0946094	−	0.995514i	$-0.530160\pi$
$252$		0			0
$253$	−8.40833	−	14.5636i	−0.528627	−	0.915609i
$254$		0			0
$255$	0.394449			0.0247013
$256$		0			0
$257$	11.8028	−	20.4430i	0.736237	−	1.27520i	−0.217942	−	0.975962i	$-0.569934\pi$
$257$	11.8028	−	20.4430i	0.736237	−	1.27520i	0.954179	−	0.299238i	$-0.0967324\pi$
$258$		0			0
$259$	−3.60555			−0.224038
$260$		0			0
$261$	−16.4222			−1.01651
$262$		0			0
$263$	13.1056	−	22.6995i	0.808123	−	1.39971i	−0.106040	−	0.994362i	$-0.533817\pi$
$263$	13.1056	−	22.6995i	0.808123	−	1.39971i	0.914162	−	0.405348i	$-0.132850\pi$
$264$		0			0
$265$	−11.2111			−0.688693
$266$		0			0
$267$	4.10555	+	7.11102i	0.251256	+	0.435188i
$268$		0			0
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$		0			0
$271$	0.408327	−	0.707243i	0.0248041	−	0.0429620i	−0.853357	−	0.521327i	$-0.825437\pi$
$271$	0.408327	−	0.707243i	0.0248041	−	0.0429620i	0.878161	+	0.478365i	$0.158770\pi$
$272$		0			0
$273$	−3.60555			−0.218218
$274$		0			0
$275$	−2.80278	+	4.85455i	−0.169014	+	0.292740i
$276$		0			0
$277$	−10.1972	−	17.6621i	−0.612692	−	1.06121i	−0.990785	−	0.135446i	$-0.956753\pi$
$277$	−10.1972	−	17.6621i	−0.612692	−	1.06121i	0.378093	−	0.925768i	$-0.376580\pi$
$278$		0			0
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	−0.782104	−	0.623148i	$-0.785854\pi$
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	0.930714	+	0.365748i	$0.119187\pi$
$284$		0			0
$285$	−1.60555			−0.0951046
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	8.42221	−	14.5877i	0.495424	−	0.858099i
$290$		0			0
$291$	15.6056			0.914814
$292$		0			0
$293$	−8.80278	−	15.2469i	−0.514264	−	0.890731i	−0.999863	−	0.0165493i	$-0.994732\pi$
$293$	−8.80278	−	15.2469i	−0.514264	−	0.890731i	0.485599	−	0.874181i	$-0.338601\pi$
$294$		0			0
$295$	−5.40833	−	9.36750i	−0.314885	−	0.545397i
$296$		0			0
$297$	−14.0139	+	24.2727i	−0.813168	+	1.40845i
$298$		0			0
$299$	−5.40833	+	9.36750i	−0.312772	+	0.541736i
$300$		0			0
$301$	2.10555	−	3.64692i	0.121362	−	0.210205i
$302$		0			0
$303$	−4.50000	−	7.79423i	−0.258518	−	0.447767i
$304$		0			0
$305$	−0.500000	−	0.866025i	−0.0286299	−	0.0495885i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$		0			0
$311$	−5.21110			−0.295495			−0.147747	−	0.989025i	$-0.547202\pi$
$311$	−5.21110			−0.295495			−0.147747	+	0.989025i	$0.547202\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$		0			0
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	−23.0139	−	39.8612i	−1.28853	−	2.23180i
$320$		0			0
$321$	4.10555	+	7.11102i	0.229150	+	0.396899i
$322$		0			0
$323$	0.316654	−	0.548461i	0.0176191	−	0.0305172i
$324$		0			0
$325$	3.60555			0.200000
$326$		0			0
$327$	−2.39445	+	4.14731i	−0.132413	+	0.229347i
$328$		0			0
$329$	−2.60555	−	4.51295i	−0.143649	−	0.248807i
$330$		0			0
$331$	−13.0139	−	22.5407i	−0.715307	−	1.23895i	−0.962841	−	0.270069i	$-0.912953\pi$
$331$	−13.0139	−	22.5407i	−0.715307	−	1.23895i	0.247533	−	0.968879i	$-0.420380\pi$
$332$		0			0
$333$	7.21110			0.395166
$334$		0			0
$335$	3.50000	−	6.06218i	0.191225	−	0.331212i
$336$		0			0
$337$	17.6333			0.960547			0.480274	−	0.877119i	$-0.340537\pi$
$337$	17.6333			0.960547			0.480274	+	0.877119i	$0.340537\pi$
$338$		0			0
$339$	−5.60555			−0.304452
$340$		0			0
$341$	−11.2111	+	19.4182i	−0.607115	+	1.05155i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$		0			0
$347$	10.1056	+	17.5033i	0.542494	+	0.939628i	0.998760	+	0.0497842i	$0.0158534\pi$
$347$	10.1056	+	17.5033i	0.542494	+	0.939628i	−0.456266	+	0.889844i	$0.650813\pi$
$348$		0			0
$349$	9.10555	−	15.7713i	0.487409	−	0.844217i	−0.512486	−	0.858695i	$-0.671275\pi$
$349$	9.10555	−	15.7713i	0.487409	−	0.844217i	0.999895	+	0.0144783i	$0.00460876\pi$
$350$		0			0
$351$	18.0278			0.962250
$352$		0			0
$353$	2.40833	−	4.17134i	0.128182	−	0.222018i	−0.794790	−	0.606884i	$-0.792419\pi$
$353$	2.40833	−	4.17134i	0.128182	−	0.222018i	0.922972	+	0.384866i	$0.125752\pi$
$354$		0			0
$355$	8.40833	+	14.5636i	0.446268	+	0.772958i
$356$		0			0
$357$	0.197224	+	0.341603i	0.0104382	+	0.0180795i
$358$		0			0
$359$	10.4222			0.550063			0.275031	−	0.961435i	$-0.411312\pi$
$359$	10.4222			0.550063			0.275031	+	0.961435i	$0.411312\pi$
$360$		0			0
$361$	8.21110	−	14.2220i	0.432163	−	0.748529i
$362$		0			0
$363$	−20.4222			−1.07189
$364$		0			0
$365$	15.2111			0.796185
$366$		0			0
$367$	−8.71110	+	15.0881i	−0.454716	+	0.787591i	−0.998672	−	0.0515228i	$-0.983593\pi$
$367$	−8.71110	+	15.0881i	−0.454716	+	0.787591i	0.543956	+	0.839114i	$0.316926\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$		0			0
$371$	−5.60555	−	9.70910i	−0.291026	−	0.504071i
$372$		0			0
$373$	13.8028	+	23.9071i	0.714681	+	1.23786i	0.963083	+	0.269206i	$0.0867613\pi$
$373$	13.8028	+	23.9071i	0.714681	+	1.23786i	−0.248402	+	0.968657i	$0.579905\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−14.8028	+	25.6392i	−0.762382	+	1.32048i
$378$		0			0
$379$	1.19722	−	2.07365i	0.0614973	−	0.106516i	−0.833638	−	0.552312i	$-0.813746\pi$
$379$	1.19722	−	2.07365i	0.0614973	−	0.106516i	0.895135	+	0.445795i	$0.147079\pi$
$380$		0			0
$381$	−5.10555	−	8.84307i	−0.261565	−	0.453044i
$382$		0			0
$383$	9.31665	+	16.1369i	0.476059	+	0.824558i	0.999624	−	0.0274277i	$-0.00873162\pi$
$383$	9.31665	+	16.1369i	0.476059	+	0.824558i	−0.523565	+	0.851986i	$0.675398\pi$
$384$		0			0
$385$	−5.60555			−0.285685
$386$		0			0
$387$	−4.21110	+	7.29384i	−0.214062	+	0.370767i
$388$		0			0
$389$	−0.788897			−0.0399987			−0.0199993	−	0.999800i	$-0.506366\pi$
$389$	−0.788897			−0.0399987			−0.0199993	+	0.999800i	$0.506366\pi$
$390$		0			0
$391$	1.18335			0.0598444
$392$		0			0
$393$	3.39445	−	5.87936i	0.171227	−	0.296574i
$394$		0			0
$395$	−9.21110			−0.463461
$396$		0			0
$397$	7.01388	+	12.1484i	0.352016	+	0.609710i	0.986603	−	0.163142i	$-0.0521628\pi$
$397$	7.01388	+	12.1484i	0.352016	+	0.609710i	−0.634586	+	0.772852i	$0.718829\pi$
$398$		0			0
$399$	−0.802776	−	1.39045i	−0.0401890	−	0.0696095i
$400$		0			0
$401$	1.10555	−	1.91487i	0.0552086	−	0.0956241i	−0.837100	−	0.547049i	$-0.815751\pi$
$401$	1.10555	−	1.91487i	0.0552086	−	0.0956241i	0.892309	+	0.451425i	$0.149084\pi$
$402$		0			0
$403$	14.4222			0.718421
$404$		0			0
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$		0			0
$407$	10.1056	+	17.5033i	0.500914	+	0.867608i
$408$		0			0
$409$	3.10555	+	5.37897i	0.153560	+	0.265973i	0.932534	−	0.361083i	$-0.117593\pi$
$409$	3.10555	+	5.37897i	0.153560	+	0.265973i	−0.778974	+	0.627056i	$0.784260\pi$
$410$		0			0
$411$	−5.60555			−0.276501
$412$		0			0
$413$	5.40833	−	9.36750i	0.266126	−	0.460944i
$414$		0			0
$415$	5.21110			0.255803
$416$		0			0
$417$	13.6056			0.666267
$418$		0			0
$419$	−16.6194	+	28.7857i	−0.811912	+	1.40627i	0.0996117	+	0.995026i	$0.468240\pi$
$419$	−16.6194	+	28.7857i	−0.811912	+	1.40627i	−0.911524	+	0.411247i	$0.865093\pi$
$420$		0			0
$421$	3.57779			0.174371			0.0871855	−	0.996192i	$-0.472213\pi$
$421$	3.57779			0.174371			0.0871855	+	0.996192i	$0.472213\pi$
$422$		0			0
$423$	5.21110	+	9.02589i	0.253372	+	0.438854i
$424$		0			0
$425$	−0.197224	−	0.341603i	−0.00956679	−	0.0165702i
$426$		0			0
$427$	0.500000	−	0.866025i	0.0241967	−	0.0419099i
$428$		0			0
$429$	10.1056	+	17.5033i	0.487901	+	0.845069i
$430$		0			0
$431$	−10.6194	+	18.3934i	−0.511520	+	0.885978i	0.488391	+	0.872625i	$0.337584\pi$
$431$	−10.6194	+	18.3934i	−0.511520	+	0.885978i	−0.999911	+	0.0133535i	$0.995749\pi$
$432$		0			0
$433$	1.80278	+	3.12250i	0.0866359	+	0.150058i	0.906087	−	0.423091i	$-0.139055\pi$
$433$	1.80278	+	3.12250i	0.0866359	+	0.150058i	−0.819451	+	0.573149i	$0.805722\pi$
$434$		0			0
$435$	−4.10555	−	7.11102i	−0.196846	−	0.340947i
$436$		0			0
$437$	−4.81665			−0.230412
$438$		0			0
$439$	11.6194	−	20.1254i	0.554565	−	0.960535i	−0.443372	−	0.896338i	$-0.646218\pi$
$439$	11.6194	−	20.1254i	0.554565	−	0.960535i	0.997937	−	0.0641973i	$-0.0204487\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$	22.4222			1.06531			0.532656	−	0.846332i	$-0.321194\pi$
$443$	22.4222			1.06531			0.532656	+	0.846332i	$0.321194\pi$
$444$		0			0
$445$	4.10555	−	7.11102i	0.194622	−	0.337095i
$446$		0			0
$447$	−3.00000			−0.141895
$448$		0			0
$449$	6.31665	+	10.9408i	0.298101	+	0.516327i	0.975702	−	0.219104i	$-0.0703133\pi$
$449$	6.31665	+	10.9408i	0.298101	+	0.516327i	−0.677600	+	0.735430i	$0.736980\pi$
$450$		0			0
$451$	−8.40833	−	14.5636i	−0.395933	−	0.685775i
$452$		0			0
$453$	−6.60555	+	11.4412i	−0.310356	+	0.537552i
$454$		0			0
$455$	1.80278	+	3.12250i	0.0845154	+	0.146385i
$456$		0			0
$457$	2.59167	−	4.48891i	0.121233	−	0.209982i	−0.799021	−	0.601303i	$-0.794648\pi$
$457$	2.59167	−	4.48891i	0.121233	−	0.209982i	0.920254	+	0.391321i	$0.127982\pi$
$458$		0			0
$459$	−0.986122	−	1.70801i	−0.0460282	−	0.0797232i
$460$		0			0
$461$	−10.8944	−	18.8697i	−0.507405	−	0.878851i	−0.999963	−	0.00857184i	$-0.997271\pi$
$461$	−10.8944	−	18.8697i	−0.507405	−	0.878851i	0.492558	−	0.870280i	$-0.336062\pi$
$462$		0			0
$463$	5.57779			0.259222			0.129611	−	0.991565i	$-0.458627\pi$
$463$	5.57779			0.259222			0.129611	+	0.991565i	$0.458627\pi$
$464$		0			0
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$		0			0
$467$	−17.2111			−0.796435			−0.398217	−	0.917291i	$-0.630371\pi$
$467$	−17.2111			−0.796435			−0.398217	+	0.917291i	$0.630371\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$		0			0
$471$	−1.60555	+	2.78090i	−0.0739799	+	0.128137i
$472$		0			0
$473$	−23.6056			−1.08538
$474$		0			0
$475$	0.802776	+	1.39045i	0.0368339	+	0.0637981i
$476$		0			0
$477$	11.2111	+	19.4182i	0.513321	+	0.889098i
$478$		0			0
$479$	−3.59167	+	6.22096i	−0.164108	+	0.284243i	−0.936338	−	0.351100i	$-0.885808\pi$
$479$	−3.59167	+	6.22096i	−0.164108	+	0.284243i	0.772230	+	0.635343i	$0.219141\pi$
$480$		0			0
$481$	6.50000	−	11.2583i	0.296374	−	0.513336i
$482$		0			0
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$		0			0
$485$	−7.80278	−	13.5148i	−0.354306	−	0.613676i
$486$		0			0
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$		0			0
$489$	−18.2111			−0.823535
$490$		0			0
$491$	2.40833	−	4.17134i	0.108686	−	0.188250i	−0.806552	−	0.591163i	$-0.798669\pi$
$491$	2.40833	−	4.17134i	0.108686	−	0.188250i	0.915238	+	0.402913i	$0.132002\pi$
$492$		0			0
$493$	3.23886			0.145871
$494$		0			0
$495$	11.2111			0.503902
$496$		0			0
$497$	−8.40833	+	14.5636i	−0.377165	+	0.653269i
$498$		0			0
$499$	26.4222			1.18282			0.591410	−	0.806371i	$-0.298571\pi$
$499$	26.4222			1.18282			0.591410	+	0.806371i	$0.298571\pi$
$500$		0			0
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$		0			0
$503$	1.50000	+	2.59808i	0.0668817	+	0.115842i	0.897527	−	0.440959i	$-0.145362\pi$
$503$	1.50000	+	2.59808i	0.0668817	+	0.115842i	−0.830645	+	0.556802i	$0.812028\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$		0			0
$507$	6.50000	−	11.2583i	0.288675	−	0.500000i
$508$		0			0
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	−0.897352	−	0.441315i	$-0.854512\pi$
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	0.830866	+	0.556473i	$0.187846\pi$
$510$		0			0
$511$	7.60555	+	13.1732i	0.336450	+	0.582748i
$512$		0			0
$513$	4.01388	+	6.95224i	0.177217	+	0.306949i
$514$		0			0
$515$	−4.00000			−0.176261
$516$		0			0
$517$	−14.6056	+	25.2976i	−0.642351	+	1.11259i
$518$		0			0
$519$	16.8167			0.738169
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$	13.7111	−	23.7483i	0.599545	−	1.03844i	−0.393344	−	0.919392i	$-0.628682\pi$
$523$	13.7111	−	23.7483i	0.599545	−	1.03844i	0.992888	−	0.119050i	$-0.0379850\pi$
$524$		0			0
$525$	−1.00000			−0.0436436
$526$		0			0
$527$	−0.788897	−	1.36641i	−0.0343649	−	0.0595218i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−10.8167	+	18.7350i	−0.469403	+	0.813029i
$532$		0			0
$533$	−5.40833	+	9.36750i	−0.234261	+	0.405751i
$534$		0			0
$535$	4.10555	−	7.11102i	0.177498	−	0.307436i
$536$		0			0
$537$	−0.591673	−	1.02481i	−0.0255326	−	0.0442237i
$538$		0			0
$539$	16.8167	+	29.1273i	0.724345	+	1.25460i
$540$		0			0
$541$	17.6333			0.758115			0.379058	−	0.925373i	$-0.376248\pi$
$541$	17.6333			0.758115			0.379058	+	0.925373i	$0.376248\pi$
$542$		0			0
$543$	−12.8167	+	22.1991i	−0.550015	+	0.952654i
$544$		0			0
$545$	4.78890			0.205134
$546$		0			0
$547$	24.8444			1.06227			0.531135	−	0.847287i	$-0.321766\pi$
$547$	24.8444			1.06227			0.531135	+	0.847287i	$0.321766\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	−13.1833			−0.561629
$552$		0			0
$553$	−4.60555	−	7.97705i	−0.195848	−	0.339219i
$554$		0			0
$555$	1.80278	+	3.12250i	0.0765236	+	0.132543i
$556$		0			0
$557$	−2.80278	+	4.85455i	−0.118757	+	0.205694i	−0.919276	−	0.393615i	$-0.871224\pi$
$557$	−2.80278	+	4.85455i	−0.118757	+	0.205694i	0.800518	+	0.599309i	$0.204558\pi$
$558$		0			0
$559$	7.59167	+	13.1492i	0.321094	+	0.556150i
$560$		0			0
$561$	1.10555	−	1.91487i	0.0466764	−	0.0808459i
$562$		0			0
$563$	−9.71110	−	16.8201i	−0.409274	−	0.708884i	0.585534	−	0.810648i	$-0.300885\pi$
$563$	−9.71110	−	16.8201i	−0.409274	−	0.708884i	−0.994809	+	0.101764i	$0.967551\pi$
$564$		0			0
$565$	2.80278	+	4.85455i	0.117914	+	0.204232i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	−0.711103	+	1.23167i	−0.0298110	+	0.0516341i	−0.880546	−	0.473961i	$-0.842824\pi$
$569$	−0.711103	+	1.23167i	−0.0298110	+	0.0516341i	0.850735	+	0.525595i	$0.176157\pi$
$570$		0			0
$571$	36.8444			1.54189			0.770945	−	0.636901i	$-0.219784\pi$
$571$	36.8444			1.54189			0.770945	+	0.636901i	$0.219784\pi$
$572$		0			0
$573$	−4.81665			−0.201219
$574$		0			0
$575$	−1.50000	+	2.59808i	−0.0625543	+	0.108347i
$576$		0			0
$577$	29.6333			1.23365			0.616825	−	0.787100i	$-0.288418\pi$
$577$	29.6333			1.23365			0.616825	+	0.787100i	$0.288418\pi$
$578$		0			0
$579$	4.19722	+	7.26981i	0.174431	+	0.302123i
$580$		0			0
$581$	2.60555	+	4.51295i	0.108096	+	0.187229i
$582$		0			0
$583$	−31.4222	+	54.4249i	−1.30137	+	2.25405i
$584$		0			0
$585$	−3.60555	−	6.24500i	−0.149071	−	0.258199i
$586$		0			0
$587$	−2.28890	+	3.96449i	−0.0944729	+	0.163632i	−0.909389	−	0.415948i	$-0.863450\pi$
$587$	−2.28890	+	3.96449i	−0.0944729	+	0.163632i	0.814916	+	0.579580i	$0.196783\pi$
$588$		0			0
$589$	3.21110	+	5.56179i	0.132311	+	0.229170i
$590$		0			0
$591$	11.4083	+	19.7598i	0.469276	+	0.812810i
$592$		0			0
$593$	35.2111			1.44595			0.722973	−	0.690876i	$-0.242775\pi$
$593$	35.2111			1.44595			0.722973	+	0.690876i	$0.242775\pi$
$594$		0			0
$595$	0.197224	−	0.341603i	0.00808541	−	0.0140043i
$596$		0			0
$597$	−8.81665			−0.360842
$598$		0			0
$599$	6.78890			0.277387			0.138693	−	0.990335i	$-0.455710\pi$
$599$	6.78890			0.277387			0.138693	+	0.990335i	$0.455710\pi$
$600$		0			0
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	0.420623	+	0.907235i	$0.361811\pi$
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	−0.996001	+	0.0893475i	$0.971522\pi$
$602$		0			0
$603$	−14.0000			−0.570124
$604$		0			0
$605$	10.2111	+	17.6861i	0.415140	+	0.719044i
$606$		0			0
$607$	−9.89445	−	17.1377i	−0.401603	−	0.695597i	0.592316	−	0.805706i	$-0.298214\pi$
$607$	−9.89445	−	17.1377i	−0.401603	−	0.695597i	−0.993920	+	0.110108i	$0.964880\pi$
$608$		0			0
$609$	4.10555	−	7.11102i	0.166365	−	0.288153i
$610$		0			0
$611$	18.7889			0.760117
$612$		0			0
$613$	−0.802776	+	1.39045i	−0.0324238	+	0.0561597i	−0.881782	−	0.471657i	$-0.843656\pi$
$613$	−0.802776	+	1.39045i	−0.0324238	+	0.0561597i	0.849358	+	0.527817i	$0.176989\pi$
$614$		0			0
$615$	−1.50000	−	2.59808i	−0.0604858	−	0.104765i
$616$		0			0
$617$	−13.2250	−	22.9063i	−0.532418	−	0.922174i	−0.999284	−	0.0378463i	$-0.987950\pi$
$617$	−13.2250	−	22.9063i	−0.532418	−	0.922174i	0.466866	−	0.884328i	$-0.345383\pi$
$618$		0			0
$619$	14.4222			0.579677			0.289839	−	0.957076i	$-0.406398\pi$
$619$	14.4222			0.579677			0.289839	+	0.957076i	$0.406398\pi$
$620$		0			0
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$		0			0
$623$	8.21110			0.328971
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$		0			0
$629$	−1.42221			−0.0567070
$630$		0			0
$631$	0.0138782	+	0.0240377i	0.000552482	+	0.000956927i	0.866302	−	0.499521i	$-0.166491\pi$
$631$	0.0138782	+	0.0240377i	0.000552482	+	0.000956927i	−0.865749	+	0.500478i	$0.833157\pi$
$632$		0			0
$633$	8.19722	+	14.1980i	0.325810	+	0.564320i
$634$		0			0
$635$	−5.10555	+	8.84307i	−0.202608	+	0.350927i
$636$		0			0
$637$	10.8167	−	18.7350i	0.428571	−	0.742307i
$638$		0			0
$639$	16.8167	−	29.1273i	0.665257	−	1.15226i
$640$		0			0
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	0.991569	−	0.129579i	$-0.0413627\pi$
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	−0.608004	+	0.793934i	$0.708029\pi$
$642$		0			0
$643$	−20.3167	−	35.1895i	−0.801211	−	1.38774i	−0.918820	−	0.394678i	$-0.870856\pi$
$643$	−20.3167	−	35.1895i	−0.801211	−	1.38774i	0.117609	−	0.993060i	$-0.462477\pi$
$644$		0			0
$645$	−4.21110			−0.165812
$646$		0			0
$647$	5.28890	−	9.16064i	0.207928	−	0.360142i	−0.743134	−	0.669143i	$-0.766661\pi$
$647$	5.28890	−	9.16064i	0.207928	−	0.360142i	0.951062	+	0.309001i	$0.0999947\pi$
$648$		0			0
$649$	−60.6333			−2.38007
$650$		0			0
$651$	−4.00000			−0.156772
$652$		0			0
$653$	14.4083	−	24.9560i	0.563841	−	0.976602i	−0.433315	−	0.901243i	$-0.642656\pi$
$653$	14.4083	−	24.9560i	0.563841	−	0.976602i	0.997156	−	0.0753594i	$-0.0240104\pi$
$654$		0			0
$655$	−6.78890			−0.265264
$656$		0			0
$657$	−15.2111	−	26.3464i	−0.593442	−	1.02787i
$658$		0			0
$659$	−6.59167	−	11.4171i	−0.256775	−	0.444748i	0.708601	−	0.705609i	$-0.249327\pi$
$659$	−6.59167	−	11.4171i	−0.256775	−	0.444748i	−0.965376	+	0.260862i	$0.915993\pi$
$660$		0			0
$661$	−19.3167	+	33.4574i	−0.751331	+	1.30134i	0.195847	+	0.980634i	$0.437254\pi$
$661$	−19.3167	+	33.4574i	−0.751331	+	1.30134i	−0.947178	+	0.320709i	$0.896079\pi$
$662$		0			0
$663$	−1.42221			−0.0552339
$664$		0			0
$665$	−0.802776	+	1.39045i	−0.0311303	+	0.0539193i
$666$		0			0
$667$	−12.3167	−	21.3331i	−0.476903	−	0.826020i
$668$		0			0
$669$	−5.10555	−	8.84307i	−0.197392	−	0.341893i
$670$		0			0
$671$	−5.60555			−0.216400
$672$		0			0
$673$	5.19722	−	9.00186i	0.200338	−	0.346996i	−0.748299	−	0.663361i	$-0.769129\pi$
$673$	5.19722	−	9.00186i	0.200338	−	0.346996i	0.948637	+	0.316365i	$0.102463\pi$
$674$		0			0
$675$	5.00000			0.192450
$676$		0			0
$677$	33.6333			1.29263			0.646317	−	0.763069i	$-0.276309\pi$
$677$	33.6333			1.29263			0.646317	+	0.763069i	$0.276309\pi$
$678$		0			0
$679$	7.80278	−	13.5148i	0.299443	−	0.518651i
$680$		0			0
$681$	1.42221			0.0544990
$682$		0			0
$683$	10.8944	+	18.8697i	0.416864	+	0.722030i	0.995622	−	0.0934691i	$-0.0297956\pi$
$683$	10.8944	+	18.8697i	0.416864	+	0.722030i	−0.578758	+	0.815500i	$0.696462\pi$
$684$		0			0
$685$	2.80278	+	4.85455i	0.107089	+	0.185483i
$686$		0			0
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$		0			0
$689$	40.4222			1.53996
$690$		0			0
$691$	3.01388	−	5.22019i	0.114653	−	0.198585i	−0.802988	−	0.595995i	$-0.796758\pi$
$691$	3.01388	−	5.22019i	0.114653	−	0.198585i	0.917641	+	0.397410i	$0.130091\pi$
$692$		0			0
$693$	5.60555	+	9.70910i	0.212937	+	0.368818i
$694$		0			0
$695$	−6.80278	−	11.7828i	−0.258044	−	0.446945i
$696$		0			0
$697$	1.18335			0.0448224
$698$		0			0
$699$	0.394449	−	0.683205i	0.0149194	−	0.0258412i
$700$		0			0
$701$	−7.57779			−0.286209			−0.143105	−	0.989708i	$-0.545709\pi$
$701$	−7.57779			−0.286209			−0.143105	+	0.989708i	$0.545709\pi$
$702$		0			0
$703$	5.78890			0.218332
$704$		0			0
$705$	−2.60555	+	4.51295i	−0.0981307	+	0.169967i
$706$		0			0
$707$	−9.00000			−0.338480
$708$		0			0
$709$	−21.9222	−	37.9704i	−0.823306	−	1.42601i	−0.903207	−	0.429205i	$-0.858794\pi$
$709$	−21.9222	−	37.9704i	−0.823306	−	1.42601i	0.0799016	−	0.996803i	$-0.474539\pi$
$710$		0			0
$711$	9.21110	+	15.9541i	0.345443	+	0.598325i
$712$		0			0
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	10.1056	−	17.5033i	0.377926	−	0.654587i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.19722	−	15.9301i	−0.342999	−	0.594091i	0.641989	−	0.766713i	$-0.278109\pi$
$719$	−9.19722	−	15.9301i	−0.342999	−	0.594091i	−0.984988	+	0.172622i	$0.944776\pi$
$720$		0			0
$721$	−2.00000	−	3.46410i	−0.0744839	−	0.129010i
$722$		0			0
$723$	−16.2111			−0.602897
$724$		0			0
$725$	−4.10555	+	7.11102i	−0.152476	+	0.264097i
$726$		0			0
$727$	−42.4222			−1.57335			−0.786676	−	0.617366i	$-0.788200\pi$
$727$	−42.4222			−1.57335			−0.786676	+	0.617366i	$0.788200\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	0.830532	−	1.43852i	0.0307183	−	0.0532057i
$732$		0			0
$733$	10.8444			0.400547			0.200274	−	0.979740i	$-0.435817\pi$
$733$	10.8444			0.400547			0.200274	+	0.979740i	$0.435817\pi$
$734$		0			0
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$		0			0
$737$	−19.6194	−	33.9818i	−0.722691	−	1.25174i
$738$		0			0
$739$	−14.1972	+	24.5903i	−0.522253	+	0.904569i	0.477411	+	0.878680i	$0.341575\pi$
$739$	−14.1972	+	24.5903i	−0.522253	+	0.904569i	−0.999665	+	0.0258895i	$0.991758\pi$
$740$		0			0
$741$	5.78890			0.212660
$742$		0			0
$743$	−3.31665	+	5.74461i	−0.121676	+	0.210749i	−0.920429	−	0.390910i	$-0.872160\pi$
$743$	−3.31665	+	5.74461i	−0.121676	+	0.210749i	0.798753	+	0.601660i	$0.205494\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$		0			0
$747$	−5.21110	−	9.02589i	−0.190664	−	0.330240i
$748$		0			0
$749$	8.21110			0.300027
$750$		0			0
$751$	−9.22498	+	15.9781i	−0.336624	+	0.583050i	−0.983795	−	0.179294i	$-0.942619\pi$
$751$	−9.22498	+	15.9781i	−0.336624	+	0.583050i	0.647171	+	0.762345i	$0.275952\pi$
$752$		0			0
$753$	−28.8167			−1.05014
$754$		0			0
$755$	13.2111			0.480801
$756$		0			0
$757$	10.4083	−	18.0278i	0.378297	−	0.655230i	−0.612518	−	0.790457i	$-0.709843\pi$
$757$	10.4083	−	18.0278i	0.378297	−	0.655230i	0.990815	+	0.135227i	$0.0431764\pi$
$758$		0			0
$759$	−16.8167			−0.610406
$760$		0			0
$761$	12.3167	+	21.3331i	0.446478	+	0.773323i	0.998154	−	0.0607356i	$-0.0193447\pi$
$761$	12.3167	+	21.3331i	0.446478	+	0.773323i	−0.551676	+	0.834059i	$0.686011\pi$
$762$		0			0
$763$	2.39445	+	4.14731i	0.0866849	+	0.150143i
$764$		0			0
$765$	−0.394449	+	0.683205i	−0.0142613	+	0.0247013i
$766$		0			0
$767$	19.5000	+	33.7750i	0.704104	+	1.21954i
$768$		0			0
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$770$		0			0
$771$	−11.8028	−	20.4430i	−0.425067	−	0.736237i
$772$		0			0
$773$	−14.8028	−	25.6392i	−0.532419	−	0.922176i	−0.999284	−	0.0378477i	$-0.987950\pi$
$773$	−14.8028	−	25.6392i	−0.532419	−	0.922176i	0.466865	−	0.884329i	$-0.345384\pi$
$774$		0			0
$775$	4.00000			0.143684
$776$		0			0
$777$	−1.80278	+	3.12250i	−0.0646742	+	0.112019i
$778$		0			0
$779$	−4.81665			−0.172575
$780$		0			0
$781$	94.2666			3.37312
$782$		0			0
$783$	−20.5278	+	35.5551i	−0.733602	+	1.27064i
$784$		0			0
$785$	3.21110			0.114609
$786$		0			0
$787$	−14.3167	−	24.7972i	−0.510334	−	0.883924i	−0.999928	−	0.0119736i	$-0.996189\pi$
$787$	−14.3167	−	24.7972i	−0.510334	−	0.883924i	0.489595	−	0.871950i	$-0.337145\pi$
$788$		0			0
$789$	−13.1056	−	22.6995i	−0.466570	−	0.808123i
$790$		0			0
$791$	−2.80278	+	4.85455i	−0.0996552	+	0.172608i
$792$		0			0
$793$	1.80278	+	3.12250i	0.0640184	+	0.110883i
$794$		0			0
$795$	−5.60555	+	9.70910i	−0.198808	+	0.344346i
$796$		0			0
$797$	−25.2250	−	43.6909i	−0.893515	−	1.54761i	−0.835632	−	0.549289i	$-0.814898\pi$
$797$	−25.2250	−	43.6909i	−0.893515	−	1.54761i	−0.0578825	−	0.998323i	$-0.518435\pi$
$798$		0			0
$799$	−1.02776	−	1.78013i	−0.0363594	−	0.0629763i
$800$		0			0
$801$	−16.4222			−0.580250
$802$		0			0
$803$	42.6333	−	73.8431i	1.50450	−	2.60586i
$804$		0			0
$805$	−3.00000			−0.105736
$806$		0			0
$807$	9.00000			0.316815
$808$		0			0
$809$	−8.52776	+	14.7705i	−0.299820	+	0.519303i	−0.976095	−	0.217346i	$-0.930260\pi$
$809$	−8.52776	+	14.7705i	−0.299820	+	0.519303i	0.676275	+	0.736650i	$0.263593\pi$
$810$		0			0
$811$	17.5778			0.617240			0.308620	−	0.951185i	$-0.400133\pi$
$811$	17.5778			0.617240			0.308620	+	0.951185i	$0.400133\pi$
$812$		0			0
$813$	−0.408327	−	0.707243i	−0.0143207	−	0.0248041i
$814$		0			0
$815$	9.10555	+	15.7713i	0.318954	+	0.552444i
$816$		0			0
$817$	−3.38057	+	5.85532i	−0.118271	+	0.204852i
$818$		0			0
$819$	3.60555	−	6.24500i	0.125988	−	0.218218i
$820$		0			0
$821$	3.71110	−	6.42782i	0.129518	−	0.224332i	−0.793972	−	0.607955i	$-0.791990\pi$
$821$	3.71110	−	6.42782i	0.129518	−	0.224332i	0.923490	+	0.383622i	$0.125324\pi$
$822$		0			0
$823$	13.3167	+	23.0651i	0.464189	+	0.804000i	0.999165	−	0.0408682i	$-0.0130124\pi$
$823$	13.3167	+	23.0651i	0.464189	+	0.804000i	−0.534975	+	0.844868i	$0.679679\pi$
$824$		0			0
$825$	2.80278	+	4.85455i	0.0975801	+	0.169014i
$826$		0			0
$827$	13.5778			0.472146			0.236073	−	0.971735i	$-0.424140\pi$
$827$	13.5778			0.472146			0.236073	+	0.971735i	$0.424140\pi$
$828$		0			0
$829$	−0.288897	+	0.500385i	−0.0100338	+	0.0173791i	−0.870999	−	0.491285i	$-0.836527\pi$
$829$	−0.288897	+	0.500385i	−0.0100338	+	0.0173791i	0.860965	+	0.508664i	$0.169861\pi$
$830$		0			0
$831$	−20.3944			−0.707476
$832$		0			0
$833$	−2.36669			−0.0820010
$834$		0			0
$835$	−4.50000	+	7.79423i	−0.155729	+	0.269730i
$836$		0			0
$837$	20.0000			0.691301
$838$		0			0
$839$	8.01388	+	13.8804i	0.276670	+	0.479206i	0.970555	−	0.240879i	$-0.0774358\pi$
$839$	8.01388	+	13.8804i	0.276670	+	0.479206i	−0.693885	+	0.720086i	$0.744103\pi$
$840$		0			0
$841$	−19.2111	−	33.2746i	−0.662452	−	1.14740i
$842$		0			0
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$		0			0
$845$	−13.0000			−0.447214
$846$		0			0
$847$	−10.2111	+	17.6861i	−0.350858	+	0.607703i
$848$		0			0
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$		0			0
$851$	5.40833	+	9.36750i	0.185395	+	0.321114i
$852$		0			0
$853$	32.7889			1.12267			0.561335	−	0.827589i	$-0.310288\pi$
$853$	32.7889			1.12267			0.561335	+	0.827589i	$0.310288\pi$
$854$		0			0
$855$	1.60555	−	2.78090i	0.0549087	−	0.0951046i
$856$		0			0
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	−25.2111			−0.860192			−0.430096	−	0.902783i	$-0.641520\pi$
$859$	−25.2111			−0.860192			−0.430096	+	0.902783i	$0.641520\pi$
$860$		0			0
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$		0			0
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	−8.40833	−	14.5636i	−0.285892	−	0.495179i
$866$		0			0
$867$	−8.42221	−	14.5877i	−0.286033	−	0.495424i
$868$		0			0
$869$	−25.8167	+	44.7158i	−0.875770	+	1.51688i
$870$		0			0
$871$	−12.6194	+	21.8575i	−0.427593	+	0.740613i
$872$		0			0
$873$	−15.6056	+	27.0296i	−0.528168	+	0.914814i
$874$		0			0
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	19.0139	+	32.9330i	0.642053	+	1.11207i	0.984974	+	0.172704i	$0.0552504\pi$
$877$	19.0139	+	32.9330i	0.642053	+	1.11207i	−0.342921	+	0.939364i	$0.611416\pi$
$878$		0			0
$879$	−17.6056			−0.593821
$880$		0			0
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	0.388423	+	0.921481i	$0.373020\pi$
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	−0.992238	+	0.124356i	$0.960313\pi$
$882$		0			0
$883$	31.6333			1.06455			0.532273	−	0.846573i	$-0.321338\pi$
$883$	31.6333			1.06455			0.532273	+	0.846573i	$0.321338\pi$
$884$		0			0
$885$	−10.8167			−0.363598
$886$		0			0
$887$	17.5278	−	30.3590i	0.588524	−	1.01935i	−0.405901	−	0.913917i	$-0.633042\pi$
$887$	17.5278	−	30.3590i	0.588524	−	1.01935i	0.994426	−	0.105437i	$-0.0336243\pi$
$888$		0			0
$889$	−10.2111			−0.342469
$890$		0			0
$891$	−2.80278	−	4.85455i	−0.0938965	−	0.162634i
$892$		0			0
$893$	4.18335	+	7.24577i	0.139990	+	0.242470i
$894$		0			0
$895$	−0.591673	+	1.02481i	−0.0197775	+	0.0342555i
$896$		0			0
$897$	5.40833	+	9.36750i	0.180579	+	0.312772i
$898$		0			0
$899$	−16.4222	+	28.4441i	−0.547711	+	0.948664i
$900$		0			0
$901$	−2.21110	−	3.82974i	−0.0736625	−	0.127587i
$902$		0			0
$903$	−2.10555	−	3.64692i	−0.0700684	−	0.121362i
$904$		0			0
$905$	25.6333			0.852080
$906$		0			0
$907$	24.1333	−	41.8001i	0.801333	−	1.38795i	−0.117405	−	0.993084i	$-0.537458\pi$
$907$	24.1333	−	41.8001i	0.801333	−	1.38795i	0.918739	−	0.394866i	$-0.129209\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	14.6056	−	25.2976i	0.483373	−	0.837227i
$914$		0			0
$915$	−1.00000			−0.0330590
$916$		0			0
$917$	−3.39445	−	5.87936i	−0.112095	−	0.194153i
$918$		0			0
$919$	−8.59167	−	14.8812i	−0.283413	−	0.490886i	0.688810	−	0.724942i	$-0.258133\pi$
$919$	−8.59167	−	14.8812i	−0.283413	−	0.490886i	−0.972223	+	0.234056i	$0.924800\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$		0			0
$923$	−30.3167	−	52.5100i	−0.997885	−	1.72839i
$924$		0			0
$925$	1.80278	−	3.12250i	0.0592749	−	0.102667i
$926$		0			0
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	−6.71110	−	11.6240i	−0.220184	−	0.381370i	0.734680	−	0.678414i	$-0.237332\pi$
$929$	−6.71110	−	11.6240i	−0.220184	−	0.381370i	−0.954864	+	0.297044i	$0.903999\pi$
$930$		0			0
$931$	9.63331			0.315719
$932$		0			0
$933$	−2.60555	+	4.51295i	−0.0853019	+	0.147747i
$934$		0			0
$935$	−2.21110			−0.0723108
$936$		0			0
$937$	−46.4777			−1.51836			−0.759180	−	0.650880i	$-0.774400\pi$
$937$	−46.4777			−1.51836			−0.759180	+	0.650880i	$0.774400\pi$
$938$		0			0
$939$	7.00000	−	12.1244i	0.228436	−	0.395663i
$940$		0			0
$941$	33.6333			1.09641			0.548207	−	0.836343i	$-0.315311\pi$
$941$	33.6333			1.09641			0.548207	+	0.836343i	$0.315311\pi$
$942$		0			0
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$		0			0
$945$	2.50000	+	4.33013i	0.0813250	+	0.140859i
$946$		0			0
$947$	12.3167	−	21.3331i	0.400237	−	0.693232i	−0.593517	−	0.804822i	$-0.702261\pi$
$947$	12.3167	−	21.3331i	0.400237	−	0.693232i	0.993754	+	0.111590i	$0.0355943\pi$
$948$		0			0
$949$	−54.8444			−1.78032
$950$		0			0
$951$	3.00000	−	5.19615i	0.0972817	−	0.168497i
$952$		0			0
$953$	−25.2250	−	43.6909i	−0.817117	−	1.41529i	−0.907798	−	0.419409i	$-0.862237\pi$
$953$	−25.2250	−	43.6909i	−0.817117	−	1.41529i	0.0906803	−	0.995880i	$-0.471096\pi$
$954$		0			0
$955$	2.40833	+	4.17134i	0.0779316	+	0.134982i
$956$		0			0
$957$	−46.0278			−1.48787
$958$		0			0
$959$	−2.80278	+	4.85455i	−0.0905063	+	0.156762i
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−16.4222			−0.529198
$964$		0			0
$965$	4.19722	−	7.26981i	0.135113	−	0.234023i
$966$		0			0
$967$	−56.4777			−1.81620			−0.908100	−	0.418752i	$-0.862468\pi$
$967$	−56.4777			−1.81620			−0.908100	+	0.418752i	$0.862468\pi$
$968$		0			0
$969$	−0.316654	−	0.548461i	−0.0101724	−	0.0176191i
$970$		0			0
$971$	−3.98612	−	6.90417i	−0.127921	−	0.221565i	0.794950	−	0.606675i	$-0.207497\pi$
$971$	−3.98612	−	6.90417i	−0.127921	−	0.221565i	−0.922871	+	0.385110i	$0.874164\pi$
$972$		0			0
$973$	6.80278	−	11.7828i	0.218087	−	0.377738i
$974$		0			0
$975$	1.80278	−	3.12250i	0.0577350	−	0.100000i
$976$		0			0
$977$	−3.59167	+	6.22096i	−0.114908	+	0.199026i	−0.917743	−	0.397175i	$-0.869991\pi$
$977$	−3.59167	+	6.22096i	−0.114908	+	0.199026i	0.802835	+	0.596201i	$0.203324\pi$
$978$		0			0
$979$	−23.0139	−	39.8612i	−0.735527	−	1.27397i
$980$		0			0
$981$	−4.78890	−	8.29461i	−0.152898	−	0.264827i
$982$		0			0
$983$	10.4222			0.332417			0.166208	−	0.986091i	$-0.446848\pi$
$983$	10.4222			0.332417			0.166208	+	0.986091i	$0.446848\pi$
$984$		0			0
$985$	11.4083	−	19.7598i	0.363500	−	0.629600i
$986$		0			0
$987$	−5.21110			−0.165871
$988$		0			0
$989$	−12.6333			−0.401716
$990$		0			0
$991$	1.98612	−	3.44006i	0.0630912	−	0.109277i	−0.832754	−	0.553642i	$-0.813237\pi$
$991$	1.98612	−	3.44006i	0.0630912	−	0.109277i	0.895846	+	0.444365i	$0.146571\pi$
$992$		0			0
$993$	−26.0278			−0.825966
$994$		0			0
$995$	4.40833	+	7.63545i	0.139753	+	0.242060i
$996$		0			0
$997$	−23.2250	−	40.2268i	−0.735543	−	1.27400i	−0.954485	−	0.298259i	$-0.903594\pi$
$997$	−23.2250	−	40.2268i	−0.735543	−	1.27400i	0.218942	−	0.975738i	$-0.429739\pi$
$998$		0			0
$999$	9.01388	−	15.6125i	0.285186	−	0.493957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.q.o.321.1		4
4.3	odd	2		65.2.e.b.61.1	yes	4
12.11	even	2		585.2.j.d.451.2		4
13.3	even	3	inner	1040.2.q.o.81.1		4
20.3	even	4		325.2.o.b.74.3		8
20.7	even	4		325.2.o.b.74.2		8
20.19	odd	2		325.2.e.a.126.2		4
52.3	odd	6		65.2.e.b.16.1	✓	4
52.7	even	12		845.2.c.d.506.3		4
52.11	even	12		845.2.m.d.361.3		8
52.15	even	12		845.2.m.d.361.2		8
52.19	even	12		845.2.c.d.506.2		4
52.23	odd	6		845.2.e.d.146.2		4
52.31	even	4		845.2.m.d.316.3		8
52.35	odd	6		845.2.a.c.1.2		2
52.43	odd	6		845.2.a.f.1.1		2
52.47	even	4		845.2.m.d.316.2		8
52.51	odd	2		845.2.e.d.191.2		4
156.35	even	6		7605.2.a.bg.1.1		2
156.95	even	6		7605.2.a.bb.1.2		2
156.107	even	6		585.2.j.d.406.2		4
260.3	even	12		325.2.o.b.224.2		8
260.107	even	12		325.2.o.b.224.3		8
260.139	odd	6		4225.2.a.x.1.1		2
260.159	odd	6		325.2.e.a.276.2		4
260.199	odd	6		4225.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.1	✓	4	52.3	odd	6
65.2.e.b.61.1	yes	4	4.3	odd	2
325.2.e.a.126.2		4	20.19	odd	2
325.2.e.a.276.2		4	260.159	odd	6
325.2.o.b.74.2		8	20.7	even	4
325.2.o.b.74.3		8	20.3	even	4
325.2.o.b.224.2		8	260.3	even	12
325.2.o.b.224.3		8	260.107	even	12
585.2.j.d.406.2		4	156.107	even	6
585.2.j.d.451.2		4	12.11	even	2
845.2.a.c.1.2		2	52.35	odd	6
845.2.a.f.1.1		2	52.43	odd	6
845.2.c.d.506.2		4	52.19	even	12
845.2.c.d.506.3		4	52.7	even	12
845.2.e.d.146.2		4	52.23	odd	6
845.2.e.d.191.2		4	52.51	odd	2
845.2.m.d.316.2		8	52.47	even	4
845.2.m.d.316.3		8	52.31	even	4
845.2.m.d.361.2		8	52.15	even	12
845.2.m.d.361.3		8	52.11	even	12
1040.2.q.o.81.1		4	13.3	even	3	inner
1040.2.q.o.321.1		4	1.1	even	1	trivial
4225.2.a.t.1.2		2	260.199	odd	6
4225.2.a.x.1.1		2	260.139	odd	6
7605.2.a.bb.1.2		2	156.95	even	6
7605.2.a.bg.1.1		2	156.35	even	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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -1.00000 q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-2.80278 + 4.85455i) q^{11} +3.60555 q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.197224 - 0.341603i) q^{17} +(0.802776 + 1.39045i) q^{19} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +1.00000 q^{25} +5.00000 q^{27} +(-4.10555 + 7.11102i) q^{29} +4.00000 q^{31} +(2.80278 + 4.85455i) q^{33} +(0.500000 + 0.866025i) q^{35} +(1.80278 - 3.12250i) q^{37} +(1.80278 - 3.12250i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(2.10555 + 3.64692i) q^{43} +(-1.00000 - 1.73205i) q^{45} +5.21110 q^{47} +(3.00000 - 5.19615i) q^{49} -0.394449 q^{51} +11.2111 q^{53} +(2.80278 - 4.85455i) q^{55} +1.60555 q^{57} +(5.40833 + 9.36750i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{63} -3.60555 q^{65} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-8.40833 - 14.5636i) q^{71} -15.2111 q^{73} +(0.500000 - 0.866025i) q^{75} +5.60555 q^{77} +9.21110 q^{79} +(-0.500000 + 0.866025i) q^{81} -5.21110 q^{83} +(0.197224 + 0.341603i) q^{85} +(4.10555 + 7.11102i) q^{87} +(-4.10555 + 7.11102i) q^{89} +(-1.80278 - 3.12250i) q^{91} +(2.00000 - 3.46410i) q^{93} +(-0.802776 - 1.39045i) q^{95} +(7.80278 + 13.5148i) q^{97} -11.2111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} + 4 q^{9} - 4 q^{11} - 2 q^{15} - 8 q^{17} - 4 q^{19} - 4 q^{21} - 6 q^{23} + 4 q^{25} + 20 q^{27} - 2 q^{29} + 16 q^{31} + 4 q^{33} + 2 q^{35} - 6 q^{41} - 6 q^{43} - 4 q^{45}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 + 4 * q^9 - 4 * q^11 - 2 * q^15 - 8 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 + 4 * q^25 + 20 * q^27 - 2 * q^29 + 16 * q^31 + 4 * q^33 + 2 * q^35 - 6 * q^41 - 6 * q^43 - 4 * q^45 - 8 * q^47 + 12 * q^49 - 16 * q^51 + 16 * q^53 + 4 * q^55 - 8 * q^57 + 2 * q^61 + 4 * q^63 - 14 * q^67 + 6 * q^69 - 12 * q^71 - 32 * q^73 + 2 * q^75 + 8 * q^77 + 8 * q^79 - 2 * q^81 + 8 * q^83 + 8 * q^85 + 2 * q^87 - 2 * q^89 + 8 * q^93 + 4 * q^95 + 24 * q^97 - 16 * q^99

Introduction

L-functions

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