LMFDB - Embedded newform 1456.2.r.e.417.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1456,2,Mod(417,1456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1456.417"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.r (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-1,0,3,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 728)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			417.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1456.417
Dual form			1456.2.r.e.625.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.50000 + 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} -3.00000 q^{15} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(0.500000 + 2.59808i) q^{21} +(0.500000 + 0.866025i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.00000 q^{27} -2.00000 q^{29} +(4.50000 - 7.79423i) q^{31} +(-1.50000 - 2.59808i) q^{33} +(7.50000 + 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{39} +10.0000 q^{41} -4.00000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-3.50000 - 6.06218i) q^{51} +(0.500000 - 0.866025i) q^{53} -9.00000 q^{55} +1.00000 q^{57} +(-5.50000 + 9.52628i) q^{59} +(0.500000 + 0.866025i) q^{61} +(5.00000 + 1.73205i) q^{63} +(-1.50000 - 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} -1.00000 q^{69} -8.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} -21.0000 q^{85} +(1.00000 - 1.73205i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(4.50000 + 7.79423i) q^{93} +(1.50000 - 2.59808i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 3 q^{5} + 4 q^{7} + 2 q^{9} - 3 q^{11} - 2 q^{13} - 6 q^{15} - 7 q^{17} - q^{19} + q^{21} + q^{23} - 4 q^{25} - 10 q^{27} - 4 q^{29} + 9 q^{31} - 3 q^{33} + 15 q^{35} + 3 q^{37} + q^{39}+ \cdots - 12 q^{99}+O(q^{100}) $ 2 * q - q^3 + 3 * q^5 + 4 * q^7 + 2 * q^9 - 3 * q^11 - 2 * q^13 - 6 * q^15 - 7 * q^17 - q^19 + q^21 + q^23 - 4 * q^25 - 10 * q^27 - 4 * q^29 + 9 * q^31 - 3 * q^33 + 15 * q^35 + 3 * q^37 + q^39 + 20 * q^41 - 8 * q^43 - 6 * q^45 + 3 * q^47 + 2 * q^49 - 7 * q^51 + q^53 - 18 * q^55 + 2 * q^57 - 11 * q^59 + q^61 + 10 * q^63 - 3 * q^65 - 7 * q^67 - 2 * q^69 - 16 * q^71 + 7 * q^73 - 4 * q^75 + 3 * q^77 - 11 * q^79 - q^81 + 8 * q^83 - 42 * q^85 + 2 * q^87 - q^89 - 4 * q^91 + 9 * q^93 + 3 * q^95 + 4 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−3.00000			−0.774597
$16$		0			0
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	0.500000	+	2.59808i	0.109109	+	0.566947i
$22$		0			0
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	−0.105869	−	0.994380i	$-0.533762\pi$
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	0.914093	−	0.405505i	$-0.132904\pi$
$32$		0			0
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$		0			0
$35$	7.50000	+	2.59808i	1.26773	+	0.439155i
$36$		0			0
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	0.962580	−	0.270998i	$-0.0873538\pi$
$37$	1.50000	+	2.59808i	0.246598	+	0.427121i	−0.715981	+	0.698119i	$0.754020\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	−3.50000	−	6.06218i	−0.490098	−	0.848875i
$52$		0			0
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$	1.00000			0.132453
$58$		0			0
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		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
$63$	5.00000	+	1.73205i	0.629941	+	0.218218i
$64$		0			0
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		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
$69$	−1.00000			−0.120386
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$		0			0
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$		0			0
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	−21.0000			−2.27777
$86$		0			0
$87$	1.00000	−	1.73205i	0.107211	−	0.185695i
$88$		0			0
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	0.838308	−	0.545197i	$-0.183545\pi$
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	−0.891308	+	0.453398i	$0.850212\pi$
$90$		0			0
$91$	−2.00000	+	1.73205i	−0.209657	+	0.181568i
$92$		0			0
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$		0			0
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$	−6.00000	+	5.19615i	−0.585540	+	0.507093i
$106$		0			0
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	0.997298	−	0.0734594i	$-0.0234039\pi$
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	−0.562267	+	0.826956i	$0.690071\pi$
$108$		0			0
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$		0			0
$111$	−3.00000			−0.284747
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$		0			0
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$		0			0
$119$	3.50000	+	18.1865i	0.320844	+	1.66716i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$		0			0
$135$	−7.50000	−	12.9904i	−0.645497	−	1.11803i
$136$		0			0
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	−0.676888	−	0.736086i	$-0.736672\pi$
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	0.975913	+	0.218159i	$0.0700052\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$		0			0
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$		0			0
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$		0			0
$147$	5.50000	+	4.33013i	0.453632	+	0.357143i
$148$		0			0
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	−0.969724	−	0.244202i	$-0.921474\pi$
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	0.273377	−	0.961907i	$-0.411859\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$	−14.0000			−1.13183
$154$		0			0
$155$	27.0000			2.16869
$156$		0			0
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$		0			0
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$		0			0
$161$	2.50000	+	0.866025i	0.197028	+	0.0682524i
$162$		0			0
$163$	7.50000	+	12.9904i	0.587445	+	1.01749i	0.994566	+	0.104111i	$0.0331996\pi$
$163$	7.50000	+	12.9904i	0.587445	+	1.01749i	−0.407120	+	0.913375i	$0.633467\pi$
$164$		0			0
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$		0			0
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$		0			0
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	0.920722	+	0.390218i	$0.127601\pi$
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	−0.122422	+	0.992478i	$0.539066\pi$
$174$		0			0
$175$	2.00000	+	10.3923i	0.151186	+	0.785584i
$176$		0			0
$177$	−5.50000	−	9.52628i	−0.413405	−	0.716039i
$178$		0			0
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	−0.583920	−	0.811811i	$-0.698482\pi$
$179$	5.50000	−	9.52628i	0.411089	−	0.712028i	0.995009	+	0.0997838i	$0.0318151\pi$
$180$		0			0
$181$	26.0000			1.93256			0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000			1.93256			0.966282	+	0.257485i	$0.0828937\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$	−4.50000	+	7.79423i	−0.330847	+	0.573043i
$186$		0			0
$187$	−10.5000	−	18.1865i	−0.767836	−	1.32993i
$188$		0			0
$189$	−10.0000	+	8.66025i	−0.727393	+	0.629941i
$190$		0			0
$191$	12.5000	+	21.6506i	0.904468	+	1.56658i	0.821629	+	0.570022i	$0.193065\pi$
$191$	12.5000	+	21.6506i	0.904468	+	1.56658i	0.0828388	+	0.996563i	$0.473601\pi$
$192$		0			0
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$		0			0
$195$	3.00000			0.214834
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	−0.940927	−	0.338608i	$-0.890044\pi$
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	0.763707	+	0.645563i	$0.223377\pi$
$200$		0			0
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$		0			0
$203$	−4.00000	+	3.46410i	−0.280745	+	0.243132i
$204$		0			0
$205$	15.0000	+	25.9808i	1.04765	+	1.81458i
$206$		0			0
$207$	−1.00000	+	1.73205i	−0.0695048	+	0.120386i
$208$		0			0
$209$	3.00000			0.207514
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$	4.00000	−	6.92820i	0.274075	−	0.474713i
$214$		0			0
$215$	−6.00000	−	10.3923i	−0.409197	−	0.708749i
$216$		0			0
$217$	−4.50000	−	23.3827i	−0.305480	−	1.58732i
$218$		0			0
$219$	3.50000	+	6.06218i	0.236508	+	0.409644i
$220$		0			0
$221$	3.50000	−	6.06218i	0.235435	−	0.407786i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	−8.00000			−0.533333
$226$		0			0
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	−0.272623	−	0.962121i	$-0.587891\pi$
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	0.969533	−	0.244962i	$-0.0787754\pi$
$228$		0			0
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$		0			0
$231$	−7.50000	−	2.59808i	−0.493464	−	0.170941i
$232$		0			0
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$		0			0
$235$	−4.50000	+	7.79423i	−0.293548	+	0.508439i
$236$		0			0
$237$	11.0000			0.714527
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	−0.378963	−	0.925412i	$-0.623719\pi$
$241$	9.50000	−	16.4545i	0.611949	−	1.05993i	0.990912	−	0.134515i	$-0.0429475\pi$
$242$		0			0
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$		0			0
$245$	19.5000	−	7.79423i	1.24581	−	0.497955i
$246$		0			0
$247$	0.500000	+	0.866025i	0.0318142	+	0.0551039i
$248$		0			0
$249$	−2.00000	+	3.46410i	−0.126745	+	0.219529i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$		0			0
$255$	10.5000	−	18.1865i	0.657536	−	1.13888i
$256$		0			0
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	0.981901	+	0.189396i	$0.0606529\pi$
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	−0.326929	+	0.945049i	$0.606014\pi$
$258$		0			0
$259$	7.50000	+	2.59808i	0.466027	+	0.161437i
$260$		0			0
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$		0			0
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	−0.536614	−	0.843828i	$-0.680297\pi$
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	0.999083	+	0.0428069i	$0.0136300\pi$
$264$		0			0
$265$	3.00000			0.184289
$266$		0			0
$267$	1.00000			0.0611990
$268$		0			0
$269$	12.5000	−	21.6506i	0.762138	−	1.32006i	−0.179608	−	0.983738i	$-0.557483\pi$
$269$	12.5000	−	21.6506i	0.762138	−	1.32006i	0.941746	−	0.336324i	$-0.109184\pi$
$270$		0			0
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	0.998722	−	0.0505395i	$-0.0160941\pi$
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	−0.543130	+	0.839649i	$0.682761\pi$
$272$		0			0
$273$	−0.500000	−	2.59808i	−0.0302614	−	0.157243i
$274$		0			0
$275$	−6.00000	−	10.3923i	−0.361814	−	0.626680i
$276$		0			0
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$		0			0
$279$	18.0000			1.07763
$280$		0			0
$281$	−26.0000			−1.55103			−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000			−1.55103			−0.775515	+	0.631329i	$0.782510\pi$
$282$		0			0
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	−0.880504	−	0.474039i	$-0.842796\pi$
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	0.850782	+	0.525519i	$0.176129\pi$
$284$		0			0
$285$	1.50000	+	2.59808i	0.0888523	+	0.153897i
$286$		0			0
$287$	20.0000	−	17.3205i	1.18056	−	1.02240i
$288$		0			0
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$		0			0
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$		0			0
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$	−33.0000			−1.92133
$296$		0			0
$297$	7.50000	−	12.9904i	0.435194	−	0.753778i
$298$		0			0
$299$	−0.500000	−	0.866025i	−0.0289157	−	0.0500835i
$300$		0			0
$301$	−8.00000	+	6.92820i	−0.461112	+	0.399335i
$302$		0			0
$303$	−7.50000	−	12.9904i	−0.430864	−	0.746278i
$304$		0			0
$305$	−1.50000	+	2.59808i	−0.0858898	+	0.148765i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	−13.0000			−0.739544
$310$		0			0
$311$	7.50000	−	12.9904i	0.425286	−	0.736617i	−0.571161	−	0.820838i	$-0.693507\pi$
$311$	7.50000	−	12.9904i	0.425286	−	0.736617i	0.996447	+	0.0842210i	$0.0268402\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$		0			0
$315$	3.00000	+	15.5885i	0.169031	+	0.878310i
$316$		0			0
$317$	9.50000	+	16.4545i	0.533573	+	0.924176i	0.999231	+	0.0392110i	$0.0124844\pi$
$317$	9.50000	+	16.4545i	0.533573	+	0.924176i	−0.465658	+	0.884965i	$0.654182\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$	−9.00000			−0.502331
$322$		0			0
$323$	7.00000			0.389490
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$		0			0
$327$	3.50000	+	6.06218i	0.193550	+	0.335239i
$328$		0			0
$329$	7.50000	+	2.59808i	0.413488	+	0.143237i
$330$		0			0
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	0.995134	−	0.0985303i	$-0.0314141\pi$
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	−0.582897	+	0.812546i	$0.698081\pi$
$332$		0			0
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$		0			0
$335$	−21.0000			−1.14735
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$		0			0
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$		0			0
$341$	13.5000	+	23.3827i	0.731066	+	1.26624i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$		0			0
$347$	5.50000	−	9.52628i	0.295255	−	0.511397i	−0.679789	−	0.733408i	$-0.737929\pi$
$347$	5.50000	−	9.52628i	0.295255	−	0.511397i	0.975044	+	0.222010i	$0.0712619\pi$
$348$		0			0
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$		0			0
$353$	−2.50000	+	4.33013i	−0.133062	+	0.230469i	−0.924855	−	0.380319i	$-0.875814\pi$
$353$	−2.50000	+	4.33013i	−0.133062	+	0.230469i	0.791794	+	0.610789i	$0.209147\pi$
$354$		0			0
$355$	−12.0000	−	20.7846i	−0.636894	−	1.10313i
$356$		0			0
$357$	−17.5000	−	6.06218i	−0.926198	−	0.320844i
$358$		0			0
$359$	−12.5000	−	21.6506i	−0.659725	−	1.14268i	−0.980687	−	0.195585i	$-0.937340\pi$
$359$	−12.5000	−	21.6506i	−0.659725	−	1.14268i	0.320962	−	0.947092i	$-0.395994\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−2.00000			−0.104973
$364$		0			0
$365$	21.0000			1.09919
$366$		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
$369$	10.0000	+	17.3205i	0.520579	+	0.901670i
$370$		0			0
$371$	−0.500000	−	2.59808i	−0.0259587	−	0.134885i
$372$		0			0
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	0.947444	+	0.319921i	$0.103656\pi$
$373$	14.5000	+	25.1147i	0.750782	+	1.30039i	−0.196663	+	0.980471i	$0.563010\pi$
$374$		0			0
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$		0			0
$377$	2.00000			0.103005
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		0			0
$383$	−0.500000	−	0.866025i	−0.0255488	−	0.0442518i	0.852968	−	0.521963i	$-0.174800\pi$
$383$	−0.500000	−	0.866025i	−0.0255488	−	0.0442518i	−0.878517	+	0.477711i	$0.841467\pi$
$384$		0			0
$385$	−18.0000	+	15.5885i	−0.917365	+	0.794461i
$386$		0			0
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$		0			0
$389$	14.5000	−	25.1147i	0.735179	−	1.27337i	−0.219465	−	0.975620i	$-0.570431\pi$
$389$	14.5000	−	25.1147i	0.735179	−	1.27337i	0.954645	−	0.297747i	$-0.0962353\pi$
$390$		0			0
$391$	−7.00000			−0.354005
$392$		0			0
$393$	15.0000			0.756650
$394$		0			0
$395$	16.5000	−	28.5788i	0.830205	−	1.43796i
$396$		0			0
$397$	11.5000	+	19.9186i	0.577168	+	0.999685i	0.995802	+	0.0915300i	$0.0291757\pi$
$397$	11.5000	+	19.9186i	0.577168	+	0.999685i	−0.418634	+	0.908155i	$0.637491\pi$
$398$		0			0
$399$	2.00000	−	1.73205i	0.100125	−	0.0867110i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		0			0
$403$	−4.50000	+	7.79423i	−0.224161	+	0.388258i
$404$		0			0
$405$	−3.00000			−0.149071
$406$		0			0
$407$	−9.00000			−0.446113
$408$		0			0
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	−0.428063	−	0.903749i	$-0.640804\pi$
$409$	11.5000	−	19.9186i	0.568638	−	0.984911i	0.996701	−	0.0811615i	$-0.0258630\pi$
$410$		0			0
$411$	3.50000	+	6.06218i	0.172642	+	0.299025i
$412$		0			0
$413$	5.50000	+	28.5788i	0.270637	+	1.40627i
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$		0			0
$417$	−4.00000	+	6.92820i	−0.195881	+	0.339276i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	−14.0000	−	24.2487i	−0.679100	−	1.17624i
$426$		0			0
$427$	2.50000	+	0.866025i	0.120983	+	0.0419099i
$428$		0			0
$429$	1.50000	+	2.59808i	0.0724207	+	0.125436i
$430$		0			0
$431$	−9.50000	+	16.4545i	−0.457599	+	0.792585i	−0.998833	−	0.0482871i	$-0.984624\pi$
$431$	−9.50000	+	16.4545i	−0.457599	+	0.792585i	0.541235	+	0.840872i	$0.317957\pi$
$432$		0			0
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$		0			0
$437$	0.500000	−	0.866025i	0.0239182	−	0.0414276i
$438$		0			0
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	0.770334	−	0.637641i	$-0.220089\pi$
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	−0.937380	+	0.348309i	$0.886756\pi$
$440$		0			0
$441$	13.0000	−	5.19615i	0.619048	−	0.247436i
$442$		0			0
$443$	20.5000	+	35.5070i	0.973984	+	1.68699i	0.683247	+	0.730188i	$0.260567\pi$
$443$	20.5000	+	35.5070i	0.973984	+	1.68699i	0.290738	+	0.956803i	$0.406099\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$	17.0000			0.804072
$448$		0			0
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$		0			0
$451$	−15.0000	+	25.9808i	−0.706322	+	1.22339i
$452$		0			0
$453$	−9.50000	−	16.4545i	−0.446349	−	0.773099i
$454$		0			0
$455$	−7.50000	−	2.59808i	−0.351605	−	0.121800i
$456$		0			0
$457$	13.5000	+	23.3827i	0.631503	+	1.09380i	0.987245	+	0.159211i	$0.0508951\pi$
$457$	13.5000	+	23.3827i	0.631503	+	1.09380i	−0.355741	+	0.934585i	$0.615772\pi$
$458$		0			0
$459$	17.5000	−	30.3109i	0.816830	−	1.41479i
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$	−13.5000	+	23.3827i	−0.626048	+	1.08435i
$466$		0			0
$467$	−11.5000	−	19.9186i	−0.532157	−	0.921722i	−0.999295	−	0.0375381i	$-0.988048\pi$
$467$	−11.5000	−	19.9186i	−0.532157	−	0.921722i	0.467139	−	0.884184i	$-0.345285\pi$
$468$		0			0
$469$	3.50000	+	18.1865i	0.161615	+	0.839776i
$470$		0			0
$471$	6.50000	+	11.2583i	0.299504	+	0.518756i
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	4.00000			0.183533
$476$		0			0
$477$	2.00000			0.0915737
$478$		0			0
$479$	18.5000	−	32.0429i	0.845287	−	1.46408i	−0.0400855	−	0.999196i	$-0.512763\pi$
$479$	18.5000	−	32.0429i	0.845287	−	1.46408i	0.885372	−	0.464883i	$-0.153904\pi$
$480$		0			0
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$		0			0
$483$	−2.00000	+	1.73205i	−0.0910032	+	0.0788110i
$484$		0			0
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		0			0
$487$	−21.5000	+	37.2391i	−0.974258	+	1.68746i	−0.291896	+	0.956450i	$0.594286\pi$
$487$	−21.5000	+	37.2391i	−0.974258	+	1.68746i	−0.682362	+	0.731014i	$0.739047\pi$
$488$		0			0
$489$	−15.0000			−0.678323
$490$		0			0
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$		0			0
$493$	7.00000	−	12.1244i	0.315264	−	0.546054i
$494$		0			0
$495$	−9.00000	−	15.5885i	−0.404520	−	0.700649i
$496$		0			0
$497$	−16.0000	+	13.8564i	−0.717698	+	0.621545i
$498$		0			0
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$		0			0
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	−45.0000			−2.00247
$506$		0			0
$507$	−0.500000	+	0.866025i	−0.0222058	+	0.0384615i
$508$		0			0
$509$	−20.5000	−	35.5070i	−0.908647	−	1.57382i	−0.815946	−	0.578128i	$-0.803783\pi$
$509$	−20.5000	−	35.5070i	−0.908647	−	1.57382i	−0.0927004	−	0.995694i	$-0.529550\pi$
$510$		0			0
$511$	−3.50000	−	18.1865i	−0.154831	−	0.804525i
$512$		0			0
$513$	2.50000	+	4.33013i	0.110378	+	0.191180i
$514$		0			0
$515$	−19.5000	+	33.7750i	−0.859273	+	1.48830i
$516$		0			0
$517$	−9.00000			−0.395820
$518$		0			0
$519$	−21.0000			−0.921798
$520$		0			0
$521$	0.500000	−	0.866025i	0.0219054	−	0.0379413i	−0.854865	−	0.518851i	$-0.826360\pi$
$521$	0.500000	−	0.866025i	0.0219054	−	0.0379413i	0.876770	+	0.480909i	$0.159693\pi$
$522$		0			0
$523$	−13.5000	−	23.3827i	−0.590314	−	1.02245i	−0.994190	−	0.107640i	$-0.965671\pi$
$523$	−13.5000	−	23.3827i	−0.590314	−	1.02245i	0.403876	−	0.914814i	$-0.367663\pi$
$524$		0			0
$525$	−10.0000	−	3.46410i	−0.436436	−	0.151186i
$526$		0			0
$527$	31.5000	+	54.5596i	1.37216	+	2.37665i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	−22.0000			−0.954719
$532$		0			0
$533$	−10.0000			−0.433148
$534$		0			0
$535$	−13.5000	+	23.3827i	−0.583656	+	1.01092i
$536$		0			0
$537$	5.50000	+	9.52628i	0.237343	+	0.411089i
$538$		0			0
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$		0			0
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$542$		0			0
$543$	−13.0000	+	22.5167i	−0.557883	+	0.966282i
$544$		0			0
$545$	21.0000			0.899541
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	1.00000	+	1.73205i	0.0426014	+	0.0737878i
$552$		0			0
$553$	−27.5000	−	9.52628i	−1.16942	−	0.405099i
$554$		0			0
$555$	−4.50000	−	7.79423i	−0.191014	−	0.330847i
$556$		0			0
$557$	3.50000	−	6.06218i	0.148300	−	0.256863i	−0.782299	−	0.622903i	$-0.785953\pi$
$557$	3.50000	−	6.06218i	0.148300	−	0.256863i	0.930599	+	0.366040i	$0.119287\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$	21.0000			0.886621
$562$		0			0
$563$	15.5000	−	26.8468i	0.653247	−	1.13146i	−0.329083	−	0.944301i	$-0.606740\pi$
$563$	15.5000	−	26.8468i	0.653247	−	1.13146i	0.982330	−	0.187156i	$-0.0599271\pi$
$564$		0			0
$565$	−27.0000	−	46.7654i	−1.13590	−	1.96743i
$566$		0			0
$567$	0.500000	+	2.59808i	0.0209980	+	0.109109i
$568$		0			0
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	0.997703	−	0.0677445i	$-0.0215803\pi$
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	−0.557520	+	0.830164i	$0.688247\pi$
$570$		0			0
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$		0			0
$573$	−25.0000			−1.04439
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	1.50000	−	2.59808i	0.0624458	−	0.108159i	−0.833112	−	0.553104i	$-0.813443\pi$
$577$	1.50000	−	2.59808i	0.0624458	−	0.108159i	0.895558	+	0.444945i	$0.146777\pi$
$578$		0			0
$579$	11.5000	+	19.9186i	0.477924	+	0.827788i
$580$		0			0
$581$	8.00000	−	6.92820i	0.331896	−	0.287430i
$582$		0			0
$583$	1.50000	+	2.59808i	0.0621237	+	0.107601i
$584$		0			0
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$		0			0
$587$	36.0000			1.48588			0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000			1.48588			0.742940	+	0.669359i	$0.233431\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	−16.5000	−	28.5788i	−0.677574	−	1.17359i	−0.975709	−	0.219069i	$-0.929698\pi$
$593$	−16.5000	−	28.5788i	−0.677574	−	1.17359i	0.298136	−	0.954524i	$-0.403635\pi$
$594$		0			0
$595$	−42.0000	+	36.3731i	−1.72183	+	1.49115i
$596$		0			0
$597$	−2.50000	−	4.33013i	−0.102318	−	0.177220i
$598$		0			0
$599$	17.5000	−	30.3109i	0.715031	−	1.23847i	−0.247917	−	0.968781i	$-0.579746\pi$
$599$	17.5000	−	30.3109i	0.715031	−	1.23847i	0.962948	−	0.269688i	$-0.0869206\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$	−14.0000			−0.570124
$604$		0			0
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$		0			0
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	0.999964	+	0.00851879i	$0.00271165\pi$
$607$	12.5000	+	21.6506i	0.507359	+	0.878772i	−0.492604	+	0.870253i	$0.663955\pi$
$608$		0			0
$609$	−1.00000	−	5.19615i	−0.0405220	−	0.210559i
$610$		0			0
$611$	−1.50000	−	2.59808i	−0.0606835	−	0.105107i
$612$		0			0
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	0.409145	+	0.912470i	$0.365827\pi$
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	−0.994794	+	0.101905i	$0.967506\pi$
$614$		0			0
$615$	−30.0000			−1.20972
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$	−15.5000	+	26.8468i	−0.622998	+	1.07906i	0.365927	+	0.930644i	$0.380752\pi$
$619$	−15.5000	+	26.8468i	−0.622998	+	1.07906i	−0.988924	+	0.148420i	$0.952581\pi$
$620$		0			0
$621$	−2.50000	−	4.33013i	−0.100322	−	0.173762i
$622$		0			0
$623$	−2.50000	−	0.866025i	−0.100160	−	0.0346966i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$	−1.50000	+	2.59808i	−0.0599042	+	0.103757i
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$		0			0
$635$	6.00000	+	10.3923i	0.238103	+	0.412406i
$636$		0			0
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$		0			0
$639$	−8.00000	−	13.8564i	−0.316475	−	0.548151i
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$		0			0
$645$	12.0000			0.472500
$646$		0			0
$647$	−8.50000	+	14.7224i	−0.334169	+	0.578799i	−0.983325	−	0.181857i	$-0.941789\pi$
$647$	−8.50000	+	14.7224i	−0.334169	+	0.578799i	0.649155	+	0.760656i	$0.275122\pi$
$648$		0			0
$649$	−16.5000	−	28.5788i	−0.647682	−	1.12182i
$650$		0			0
$651$	22.5000	+	7.79423i	0.881845	+	0.305480i
$652$		0			0
$653$	−9.50000	−	16.4545i	−0.371764	−	0.643914i	0.618073	−	0.786121i	$-0.287914\pi$
$653$	−9.50000	−	16.4545i	−0.371764	−	0.643914i	−0.989837	+	0.142207i	$0.954580\pi$
$654$		0			0
$655$	22.5000	−	38.9711i	0.879148	−	1.52273i
$656$		0			0
$657$	14.0000			0.546192
$658$		0			0
$659$	44.0000			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$660$		0			0
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	0.241605	+	0.970375i	$0.422326\pi$
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	−0.961172	+	0.275951i	$0.911007\pi$
$662$		0			0
$663$	3.50000	+	6.06218i	0.135929	+	0.235435i
$664$		0			0
$665$	−1.50000	−	7.79423i	−0.0581675	−	0.302247i
$666$		0			0
$667$	−1.00000	−	1.73205i	−0.0387202	−	0.0670653i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	−3.00000			−0.115814
$672$		0			0
$673$	−30.0000			−1.15642			−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000			−1.15642			−0.578208	+	0.815890i	$0.696248\pi$
$674$		0			0
$675$	10.0000	−	17.3205i	0.384900	−	0.666667i
$676$		0			0
$677$	−5.50000	−	9.52628i	−0.211382	−	0.366125i	0.740765	−	0.671764i	$-0.234463\pi$
$677$	−5.50000	−	9.52628i	−0.211382	−	0.366125i	−0.952147	+	0.305639i	$0.901130\pi$
$678$		0			0
$679$	4.00000	−	3.46410i	0.153506	−	0.132940i
$680$		0			0
$681$	10.5000	+	18.1865i	0.402361	+	0.696909i
$682$		0			0
$683$	0.500000	−	0.866025i	0.0191320	−	0.0331375i	−0.856301	−	0.516477i	$-0.827243\pi$
$683$	0.500000	−	0.866025i	0.0191320	−	0.0331375i	0.875433	+	0.483340i	$0.160576\pi$
$684$		0			0
$685$	21.0000			0.802369
$686$		0			0
$687$	−19.0000			−0.724895
$688$		0			0
$689$	−0.500000	+	0.866025i	−0.0190485	+	0.0329929i
$690$		0			0
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	−0.967132	−	0.254273i	$-0.918164\pi$
$691$	−18.5000	−	32.0429i	−0.703773	−	1.21897i	0.263359	−	0.964698i	$-0.415170\pi$
$692$		0			0
$693$	−12.0000	+	10.3923i	−0.455842	+	0.394771i
$694$		0			0
$695$	12.0000	+	20.7846i	0.455186	+	0.788405i
$696$		0			0
$697$	−35.0000	+	60.6218i	−1.32572	+	2.29621i
$698$		0			0
$699$	3.00000			0.113470
$700$		0			0
$701$	10.0000			0.377695			0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000			0.377695			0.188847	+	0.982006i	$0.439525\pi$
$702$		0			0
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$		0			0
$705$	−4.50000	−	7.79423i	−0.169480	−	0.293548i
$706$		0			0
$707$	7.50000	+	38.9711i	0.282067	+	1.46566i
$708$		0			0
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	0.598680	−	0.800988i	$-0.295692\pi$
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	−0.993016	+	0.117978i	$0.962359\pi$
$710$		0			0
$711$	11.0000	−	19.0526i	0.412532	−	0.714527i
$712$		0			0
$713$	9.00000			0.337053
$714$		0			0
$715$	9.00000			0.336581
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.5000	+	35.5070i	0.764521	+	1.32419i	0.940499	+	0.339795i	$0.110358\pi$
$719$	20.5000	+	35.5070i	0.764521	+	1.32419i	−0.175978	+	0.984394i	$0.556309\pi$
$720$		0			0
$721$	32.5000	+	11.2583i	1.21036	+	0.419282i
$722$		0			0
$723$	9.50000	+	16.4545i	0.353309	+	0.611949i
$724$		0			0
$725$	4.00000	−	6.92820i	0.148556	−	0.257307i
$726$		0			0
$727$	24.0000			0.890111			0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000			0.890111			0.445055	+	0.895503i	$0.353184\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	14.0000	−	24.2487i	0.517809	−	0.896871i
$732$		0			0
$733$	13.5000	+	23.3827i	0.498634	+	0.863659i	0.999999	−	0.00157675i	$-0.000501894\pi$
$733$	13.5000	+	23.3827i	0.498634	+	0.863659i	−0.501365	+	0.865236i	$0.667169\pi$
$734$		0			0
$735$	−3.00000	+	20.7846i	−0.110657	+	0.766652i
$736$		0			0
$737$	−10.5000	−	18.1865i	−0.386772	−	0.669910i
$738$		0			0
$739$	−21.5000	+	37.2391i	−0.790890	+	1.36986i	0.134526	+	0.990910i	$0.457049\pi$
$739$	−21.5000	+	37.2391i	−0.790890	+	1.36986i	−0.925416	+	0.378952i	$0.876285\pi$
$740$		0			0
$741$	−1.00000			−0.0367359
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	25.5000	−	44.1673i	0.934248	−	1.61816i
$746$		0			0
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$		0			0
$749$	22.5000	+	7.79423i	0.822132	+	0.284795i
$750$		0			0
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	0.959906	−	0.280321i	$-0.0904408\pi$
$751$	6.50000	+	11.2583i	0.237188	+	0.410822i	−0.722718	+	0.691143i	$0.757107\pi$
$752$		0			0
$753$	6.00000	−	10.3923i	0.218652	−	0.378717i
$754$		0			0
$755$	−57.0000			−2.07444
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$	1.50000	−	2.59808i	0.0544466	−	0.0943042i
$760$		0			0
$761$	9.50000	+	16.4545i	0.344375	+	0.596475i	0.985240	−	0.171179i	$-0.0547576\pi$
$761$	9.50000	+	16.4545i	0.344375	+	0.596475i	−0.640865	+	0.767653i	$0.721424\pi$
$762$		0			0
$763$	−3.50000	−	18.1865i	−0.126709	−	0.658397i
$764$		0			0
$765$	−21.0000	−	36.3731i	−0.759257	−	1.31507i
$766$		0			0
$767$	5.50000	−	9.52628i	0.198593	−	0.343974i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−21.0000			−0.756297
$772$		0			0
$773$	1.50000	−	2.59808i	0.0539513	−	0.0934463i	−0.837788	−	0.545995i	$-0.816152\pi$
$773$	1.50000	−	2.59808i	0.0539513	−	0.0934463i	0.891740	+	0.452549i	$0.149485\pi$
$774$		0			0
$775$	18.0000	+	31.1769i	0.646579	+	1.11991i
$776$		0			0
$777$	−6.00000	+	5.19615i	−0.215249	+	0.186411i
$778$		0			0
$779$	−5.00000	−	8.66025i	−0.179144	−	0.310286i
$780$		0			0
$781$	12.0000	−	20.7846i	0.429394	−	0.743732i
$782$		0			0
$783$	10.0000			0.357371
$784$		0			0
$785$	39.0000			1.39197
$786$		0			0
$787$	−17.5000	+	30.3109i	−0.623808	+	1.08047i	0.364963	+	0.931022i	$0.381082\pi$
$787$	−17.5000	+	30.3109i	−0.623808	+	1.08047i	−0.988770	+	0.149444i	$0.952252\pi$
$788$		0			0
$789$	7.50000	+	12.9904i	0.267007	+	0.462470i
$790$		0			0
$791$	−36.0000	+	31.1769i	−1.28001	+	1.10852i
$792$		0			0
$793$	−0.500000	−	0.866025i	−0.0177555	−	0.0307535i
$794$		0			0
$795$	−1.50000	+	2.59808i	−0.0531995	+	0.0921443i
$796$		0			0
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$	−21.0000			−0.742927
$800$		0			0
$801$	1.00000	−	1.73205i	0.0353333	−	0.0611990i
$802$		0			0
$803$	10.5000	+	18.1865i	0.370537	+	0.641789i
$804$		0			0
$805$	1.50000	+	7.79423i	0.0528681	+	0.274710i
$806$		0			0
$807$	12.5000	+	21.6506i	0.440021	+	0.762138i
$808$		0			0
$809$	−5.50000	+	9.52628i	−0.193370	+	0.334926i	−0.946365	−	0.323100i	$-0.895275\pi$
$809$	−5.50000	+	9.52628i	−0.193370	+	0.334926i	0.752995	+	0.658026i	$0.228608\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−15.0000			−0.526073
$814$		0			0
$815$	−22.5000	+	38.9711i	−0.788141	+	1.36510i
$816$		0			0
$817$	2.00000	+	3.46410i	0.0699711	+	0.121194i
$818$		0			0
$819$	−5.00000	−	1.73205i	−0.174714	−	0.0605228i
$820$		0			0
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	−0.928846	−	0.370465i	$-0.879198\pi$
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	0.143591	−	0.989637i	$-0.454135\pi$
$822$		0			0
$823$	11.5000	−	19.9186i	0.400865	−	0.694318i	−0.592966	−	0.805228i	$-0.702043\pi$
$823$	11.5000	−	19.9186i	0.400865	−	0.694318i	0.993831	+	0.110910i	$0.0353764\pi$
$824$		0			0
$825$	12.0000			0.417786
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	−0.966371	−	0.257152i	$-0.917216\pi$
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	0.705885	+	0.708326i	$0.250549\pi$
$830$		0			0
$831$	−3.50000	−	6.06218i	−0.121414	−	0.210295i
$832$		0			0
$833$	38.5000	+	30.3109i	1.33395	+	1.05021i
$834$		0			0
$835$	12.0000	+	20.7846i	0.415277	+	0.719281i
$836$		0			0
$837$	−22.5000	+	38.9711i	−0.777714	+	1.34704i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	13.0000	−	22.5167i	0.447744	−	0.775515i
$844$		0			0
$845$	1.50000	+	2.59808i	0.0516016	+	0.0893765i
$846$		0			0
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$		0			0
$849$	−0.500000	−	0.866025i	−0.0171600	−	0.0297219i
$850$		0			0
$851$	−1.50000	+	2.59808i	−0.0514193	+	0.0890609i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	6.00000			0.205196
$856$		0			0
$857$	−5.50000	+	9.52628i	−0.187876	+	0.325412i	−0.944542	−	0.328391i	$-0.893494\pi$
$857$	−5.50000	+	9.52628i	−0.187876	+	0.325412i	0.756666	+	0.653802i	$0.226827\pi$
$858$		0			0
$859$	−13.5000	−	23.3827i	−0.460614	−	0.797807i	0.538378	−	0.842704i	$-0.319037\pi$
$859$	−13.5000	−	23.3827i	−0.460614	−	0.797807i	−0.998992	+	0.0448968i	$0.985704\pi$
$860$		0			0
$861$	5.00000	+	25.9808i	0.170400	+	0.885422i
$862$		0			0
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	0.630106	−	0.776509i	$-0.283012\pi$
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	−0.987530	+	0.157433i	$0.949678\pi$
$864$		0			0
$865$	−31.5000	+	54.5596i	−1.07103	+	1.85508i
$866$		0			0
$867$	32.0000			1.08678
$868$		0			0
$869$	33.0000			1.11945
$870$		0			0
$871$	3.50000	−	6.06218i	0.118593	−	0.205409i
$872$		0			0
$873$	2.00000	+	3.46410i	0.0676897	+	0.117242i
$874$		0			0
$875$	6.00000	−	5.19615i	0.202837	−	0.175662i
$876$		0			0
$877$	5.50000	+	9.52628i	0.185722	+	0.321680i	0.943820	−	0.330461i	$-0.107204\pi$
$877$	5.50000	+	9.52628i	0.185722	+	0.321680i	−0.758098	+	0.652141i	$0.773871\pi$
$878$		0			0
$879$	−7.00000	+	12.1244i	−0.236104	+	0.408944i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		0			0
$885$	16.5000	−	28.5788i	0.554641	−	0.960667i
$886$		0			0
$887$	2.50000	+	4.33013i	0.0839418	+	0.145391i	0.904940	−	0.425540i	$-0.139916\pi$
$887$	2.50000	+	4.33013i	0.0839418	+	0.145391i	−0.820998	+	0.570931i	$0.806582\pi$
$888$		0			0
$889$	8.00000	−	6.92820i	0.268311	−	0.232364i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		0			0
$893$	1.50000	−	2.59808i	0.0501956	−	0.0869413i
$894$		0			0
$895$	33.0000			1.10307
$896$		0			0
$897$	1.00000			0.0333890
$898$		0			0
$899$	−9.00000	+	15.5885i	−0.300167	+	0.519904i
$900$		0			0
$901$	3.50000	+	6.06218i	0.116602	+	0.201960i
$902$		0			0
$903$	−2.00000	−	10.3923i	−0.0665558	−	0.345834i
$904$		0			0
$905$	39.0000	+	67.5500i	1.29640	+	2.24544i
$906$		0			0
$907$	−8.50000	+	14.7224i	−0.282238	+	0.488850i	−0.971936	−	0.235247i	$-0.924410\pi$
$907$	−8.50000	+	14.7224i	−0.282238	+	0.488850i	0.689698	+	0.724097i	$0.257743\pi$
$908$		0			0
$909$	−30.0000			−0.995037
$910$		0			0
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$		0			0
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$		0			0
$915$	−1.50000	−	2.59808i	−0.0495885	−	0.0858898i
$916$		0			0
$917$	−37.5000	−	12.9904i	−1.23836	−	0.428980i
$918$		0			0
$919$	−15.5000	−	26.8468i	−0.511298	−	0.885594i	−0.999914	−	0.0130951i	$-0.995832\pi$
$919$	−15.5000	−	26.8468i	−0.511298	−	0.885594i	0.488616	−	0.872499i	$-0.337502\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.00000			0.263323
$924$		0			0
$925$	−12.0000			−0.394558
$926$		0			0
$927$	−13.0000	+	22.5167i	−0.426976	+	0.739544i
$928$		0			0
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	0.962431	−	0.271526i	$-0.0875283\pi$
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	−0.716364	+	0.697727i	$0.754195\pi$
$930$		0			0
$931$	−6.50000	+	2.59808i	−0.213029	+	0.0851485i
$932$		0			0
$933$	7.50000	+	12.9904i	0.245539	+	0.425286i
$934$		0			0
$935$	31.5000	−	54.5596i	1.03016	−	1.78429i
$936$		0			0
$937$	54.0000			1.76410			0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000			1.76410			0.882052	+	0.471153i	$0.156162\pi$
$938$		0			0
$939$	19.0000			0.620042
$940$		0			0
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	−0.557608	−	0.830104i	$-0.688281\pi$
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	0.997695	+	0.0678506i	$0.0216141\pi$
$942$		0			0
$943$	5.00000	+	8.66025i	0.162822	+	0.282017i
$944$		0			0
$945$	−37.5000	−	12.9904i	−1.21988	−	0.422577i
$946$		0			0
$947$	11.5000	+	19.9186i	0.373700	+	0.647267i	0.990132	−	0.140141i	$-0.0447557\pi$
$947$	11.5000	+	19.9186i	0.373700	+	0.647267i	−0.616432	+	0.787408i	$0.711422\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$		0			0
$951$	−19.0000			−0.616117
$952$		0			0
$953$	−50.0000			−1.61966			−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000			−1.61966			−0.809829	+	0.586665i	$0.800440\pi$
$954$		0			0
$955$	−37.5000	+	64.9519i	−1.21347	+	2.10179i
$956$		0			0
$957$	3.00000	+	5.19615i	0.0969762	+	0.167968i
$958$		0			0
$959$	−3.50000	−	18.1865i	−0.113021	−	0.587274i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$		0			0
$963$	−9.00000	+	15.5885i	−0.290021	+	0.502331i
$964$		0			0
$965$	69.0000			2.22119
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$	−3.50000	+	6.06218i	−0.112436	+	0.194745i
$970$		0			0
$971$	4.50000	+	7.79423i	0.144412	+	0.250129i	0.929153	−	0.369694i	$-0.120538\pi$
$971$	4.50000	+	7.79423i	0.144412	+	0.250129i	−0.784741	+	0.619823i	$0.787204\pi$
$972$		0			0
$973$	16.0000	−	13.8564i	0.512936	−	0.444216i
$974$		0			0
$975$	2.00000	+	3.46410i	0.0640513	+	0.110940i
$976$		0			0
$977$	−8.50000	+	14.7224i	−0.271939	+	0.471012i	−0.969358	−	0.245651i	$-0.920998\pi$
$977$	−8.50000	+	14.7224i	−0.271939	+	0.471012i	0.697419	+	0.716663i	$0.254332\pi$
$978$		0			0
$979$	3.00000			0.0958804
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	−13.5000	+	23.3827i	−0.430583	+	0.745792i	−0.996924	−	0.0783795i	$-0.975025\pi$
$983$	−13.5000	+	23.3827i	−0.430583	+	0.745792i	0.566340	+	0.824171i	$0.308359\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$	−6.00000	+	5.19615i	−0.190982	+	0.165395i
$988$		0			0
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$		0			0
$991$	25.5000	−	44.1673i	0.810034	−	1.40302i	−0.102805	−	0.994702i	$-0.532782\pi$
$991$	25.5000	−	44.1673i	0.810034	−	1.40302i	0.912839	−	0.408319i	$-0.133885\pi$
$992$		0			0
$993$	−15.0000			−0.476011
$994$		0			0
$995$	−15.0000			−0.475532
$996$		0			0
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	−0.916112	−	0.400923i	$-0.868689\pi$
$997$	−3.50000	+	6.06218i	−0.110846	+	0.191991i	0.805266	+	0.592914i	$0.202023\pi$
$998$		0			0
$999$	−7.50000	−	12.9904i	−0.237289	−	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.r.e.417.1		2
4.3	odd	2		728.2.r.c.417.1	✓	2
7.2	even	3	inner	1456.2.r.e.625.1		2
28.3	even	6		5096.2.a.j.1.1		1
28.11	odd	6		5096.2.a.b.1.1		1
28.23	odd	6		728.2.r.c.625.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.r.c.417.1	✓	2	4.3	odd	2
728.2.r.c.625.1	yes	2	28.23	odd	6
1456.2.r.e.417.1		2	1.1	even	1	trivial
1456.2.r.e.625.1		2	7.2	even	3	inner
5096.2.a.b.1.1		1	28.11	odd	6
5096.2.a.j.1.1		1	28.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.r (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.50000 + 2.59808i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} -3.00000 q^{15} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(0.500000 + 2.59808i) q^{21} +(0.500000 + 0.866025i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.00000 q^{27} -2.00000 q^{29} +(4.50000 - 7.79423i) q^{31} +(-1.50000 - 2.59808i) q^{33} +(7.50000 + 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{39} +10.0000 q^{41} -4.00000 q^{43} +(-3.00000 + 5.19615i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-3.50000 - 6.06218i) q^{51} +(0.500000 - 0.866025i) q^{53} -9.00000 q^{55} +1.00000 q^{57} +(-5.50000 + 9.52628i) q^{59} +(0.500000 + 0.866025i) q^{61} +(5.00000 + 1.73205i) q^{63} +(-1.50000 - 2.59808i) q^{65} +(-3.50000 + 6.06218i) q^{67} -1.00000 q^{69} -8.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} -21.0000 q^{85} +(1.00000 - 1.73205i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(-2.00000 + 1.73205i) q^{91} +(4.50000 + 7.79423i) q^{93} +(1.50000 - 2.59808i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 3 q^{5} + 4 q^{7} + 2 q^{9} - 3 q^{11} - 2 q^{13} - 6 q^{15} - 7 q^{17} - q^{19} + q^{21} + q^{23} - 4 q^{25} - 10 q^{27} - 4 q^{29} + 9 q^{31} - 3 q^{33} + 15 q^{35} + 3 q^{37} + q^{39}+ \cdots - 12 q^{99}+O(q^{100}) \) 2 * q - q^3 + 3 * q^5 + 4 * q^7 + 2 * q^9 - 3 * q^11 - 2 * q^13 - 6 * q^15 - 7 * q^17 - q^19 + q^21 + q^23 - 4 * q^25 - 10 * q^27 - 4 * q^29 + 9 * q^31 - 3 * q^33 + 15 * q^35 + 3 * q^37 + q^39 + 20 * q^41 - 8 * q^43 - 6 * q^45 + 3 * q^47 + 2 * q^49 - 7 * q^51 + q^53 - 18 * q^55 + 2 * q^57 - 11 * q^59 + q^61 + 10 * q^63 - 3 * q^65 - 7 * q^67 - 2 * q^69 - 16 * q^71 + 7 * q^73 - 4 * q^75 + 3 * q^77 - 11 * q^79 - q^81 + 8 * q^83 - 42 * q^85 + 2 * q^87 - q^89 - 4 * q^91 + 9 * q^93 + 3 * q^95 + 4 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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