LMFDB - Embedded newform 28.2.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,2,Mod(9,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("28.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	28.e (of order $3$, degree $2$, 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:	$0.223581125660$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	28.25
Dual form			28.2.e.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(1.50000 + 2.59808i) q^{33} +(7.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(4.50000 + 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} -1.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-5.00000 - 1.73205i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(3.50000 - 6.06218i) q^{67} +3.00000 q^{69} +(0.500000 - 0.866025i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(-7.50000 - 12.9904i) q^{89} +(-4.00000 + 3.46410i) q^{91} +(3.50000 + 6.06218i) q^{93} +(1.50000 - 2.59808i) q^{95} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 - 3 * q^5 - 4 * q^7 + 2 * q^9	$ 2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} + 4 q^{13} + 6 q^{15} - 3 q^{17} + q^{19} - q^{21} - 3 q^{23} - 4 q^{25} - 10 q^{27} - 12 q^{29} + 7 q^{31} + 3 q^{33} + 15 q^{35} + q^{37} - 2 q^{39} + 12 q^{41} - 8 q^{43} + 6 q^{45} + 9 q^{47} + 2 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} - 2 q^{57} - 9 q^{59} + q^{61} - 10 q^{63} - 6 q^{65} + 7 q^{67} + 6 q^{69} + q^{73} - 4 q^{75} + 3 q^{77} + 13 q^{79} - q^{81} + 24 q^{83} + 18 q^{85} + 6 q^{87} - 15 q^{89} - 8 q^{91} + 7 q^{93} + 3 q^{95} - 20 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q - q^3 - 3 * q^5 - 4 * q^7 + 2 * q^9 + 3 * q^11 + 4 * q^13 + 6 * q^15 - 3 * q^17 + q^19 - q^21 - 3 * q^23 - 4 * q^25 - 10 * q^27 - 12 * q^29 + 7 * q^31 + 3 * q^33 + 15 * q^35 + q^37 - 2 * q^39 + 12 * q^41 - 8 * q^43 + 6 * q^45 + 9 * q^47 + 2 * q^49 - 3 * q^51 - 3 * q^53 - 18 * q^55 - 2 * q^57 - 9 * q^59 + q^61 - 10 * q^63 - 6 * q^65 + 7 * q^67 + 6 * q^69 + q^73 - 4 * q^75 + 3 * q^77 + 13 * q^79 - q^81 + 24 * q^83 + 18 * q^85 + 6 * q^87 - 15 * q^89 - 8 * q^91 + 7 * q^93 + 3 * q^95 - 20 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		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	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	−0.500000	−	2.59808i	−0.109109	−	0.566947i
$22$		0			0
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		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
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−4.00000			−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
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$		0			0
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$		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
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$		0			0
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$		0			0
$69$	3.00000			0.361158
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	−0.835281	−	0.549823i	$-0.814695\pi$
$73$	0.500000	−	0.866025i	0.0585206	−	0.101361i	0.893801	+	0.448463i	$0.148028\pi$
$74$		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
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$		0			0
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		0			0
$91$	−4.00000	+	3.46410i	−0.419314	+	0.363137i
$92$		0			0
$93$	3.50000	+	6.06218i	0.362933	+	0.628619i
$94$		0			0
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		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
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	−0.998793	−	0.0491146i	$-0.984360\pi$
$103$	−5.50000	−	9.52628i	−0.541931	−	0.938652i	0.456862	−	0.889538i	$-0.348973\pi$
$104$		0			0
$105$	−6.00000	+	5.19615i	−0.585540	+	0.507093i
$106$		0			0
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$		0			0
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$		0			0
$111$	−1.00000			−0.0949158
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$		0			0
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$		0			0
$119$	−1.50000	−	7.79423i	−0.137505	−	0.714496i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$131$	−1.50000	−	2.59808i	−0.131056	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$132$		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
$137$	10.5000	−	18.1865i	0.897076	−	1.55378i	0.0658609	−	0.997829i	$-0.479021\pi$
$137$	10.5000	−	18.1865i	0.897076	−	1.55378i	0.831215	−	0.555952i	$-0.187646\pi$
$138$		0			0
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$	−9.00000			−0.757937
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$		0			0
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$		0			0
$147$	5.50000	+	4.33013i	0.453632	+	0.357143i
$148$		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
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	0.279554	+	0.960130i	$0.409814\pi$
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	−0.971274	+	0.237964i	$0.923520\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	−21.0000			−1.68676
$156$		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
$159$	−1.50000	−	2.59808i	−0.118958	−	0.206041i
$160$		0			0
$161$	7.50000	+	2.59808i	0.591083	+	0.204757i
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$		0			0
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$		0			0
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$	−2.00000	−	10.3923i	−0.151186	−	0.785584i
$176$		0			0
$177$	−4.50000	−	7.79423i	−0.338241	−	0.585850i
$178$		0			0
$179$	−10.5000	+	18.1865i	−0.784807	+	1.35933i	0.144308	+	0.989533i	$0.453905\pi$
$179$	−10.5000	+	18.1865i	−0.784807	+	1.35933i	−0.929114	+	0.369792i	$0.879429\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$		0			0
$185$	1.50000	−	2.59808i	0.110282	−	0.191014i
$186$		0			0
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$		0			0
$189$	10.0000	−	8.66025i	0.727393	−	0.629941i
$190$		0			0
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	0.981635	−	0.190767i	$-0.0610975\pi$
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	−0.656027	+	0.754738i	$0.727764\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$		0			0
$195$	6.00000			0.429669
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$	12.0000	−	10.3923i	0.842235	−	0.729397i
$204$		0			0
$205$	−9.00000	−	15.5885i	−0.628587	−	1.08875i
$206$		0			0
$207$	3.00000	−	5.19615i	0.208514	−	0.361158i
$208$		0			0
$209$	3.00000			0.207514
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.00000	+	10.3923i	0.409197	+	0.708749i
$216$		0			0
$217$	3.50000	+	18.1865i	0.237595	+	1.23458i
$218$		0			0
$219$	0.500000	+	0.866025i	0.0337869	+	0.0585206i
$220$		0			0
$221$	−3.00000	+	5.19615i	−0.201802	+	0.349531i
$222$		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
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$		0			0
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	0.625076	−	0.780564i	$-0.285068\pi$
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$230$		0			0
$231$	−7.50000	−	2.59808i	−0.493464	−	0.170941i
$232$		0			0
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$		0			0
$235$	13.5000	−	23.3827i	0.880643	−	1.52532i
$236$		0			0
$237$	−13.0000			−0.844441
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		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
$247$	1.00000	+	1.73205i	0.0636285	+	0.110208i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$		0			0
$255$	−4.50000	+	7.79423i	−0.281801	+	0.488094i
$256$		0			0
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$		0			0
$259$	−2.50000	−	0.866025i	−0.155342	−	0.0538122i
$260$		0			0
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$		0			0
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	−0.816066	−	0.577959i	$-0.803849\pi$
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	0.908560	+	0.417755i	$0.137183\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$		0			0
$267$	15.0000			0.917985
$268$		0			0
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$		0			0
$273$	−1.00000	−	5.19615i	−0.0605228	−	0.314485i
$274$		0			0
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	−0.601975	−	0.798515i	$-0.705619\pi$
$277$	6.50000	−	11.2583i	0.390547	−	0.676448i	0.992522	+	0.122068i	$0.0389525\pi$
$278$		0			0
$279$	14.0000			0.838158
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−14.5000	+	25.1147i	−0.861936	+	1.49292i	0.00812260	+	0.999967i	$0.497414\pi$
$283$	−14.5000	+	25.1147i	−0.861936	+	1.49292i	−0.870058	+	0.492949i	$0.835919\pi$
$284$		0			0
$285$	1.50000	+	2.59808i	0.0888523	+	0.153897i
$286$		0			0
$287$	−12.0000	+	10.3923i	−0.708338	+	0.613438i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$		0			0
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	27.0000			1.57200
$296$		0			0
$297$	−7.50000	+	12.9904i	−0.435194	+	0.753778i
$298$		0			0
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		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
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	11.0000			0.625768
$310$		0			0
$311$	13.5000	−	23.3827i	0.765515	−	1.32591i	−0.174459	−	0.984664i	$-0.555818\pi$
$311$	13.5000	−	23.3827i	0.765515	−	1.32591i	0.939974	−	0.341246i	$-0.110849\pi$
$312$		0			0
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	−0.983118	−	0.182973i	$-0.941428\pi$
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	0.333099	−	0.942892i	$-0.391906\pi$
$314$		0			0
$315$	3.00000	+	15.5885i	0.169031	+	0.878310i
$316$		0			0
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	15.0000			0.837218
$322$		0			0
$323$	−3.00000			−0.166924
$324$		0			0
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$		0			0
$327$	0.500000	+	0.866025i	0.0276501	+	0.0478913i
$328$		0			0
$329$	−22.5000	−	7.79423i	−1.24047	−	0.429710i
$330$		0			0
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	0.987504	−	0.157593i	$-0.0503735\pi$
$331$	6.50000	+	11.2583i	0.357272	+	0.618814i	−0.630232	+	0.776407i	$0.717040\pi$
$332$		0			0
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$		0			0
$335$	−21.0000			−1.14735
$336$		0			0
$337$	−34.0000			−1.85210			−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−34.0000			−1.85210			−0.926049	+	0.377403i	$0.876817\pi$
$338$		0			0
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	−10.5000	−	18.1865i	−0.568607	−	0.984856i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	−4.50000	−	7.79423i	−0.242272	−	0.419627i
$346$		0			0
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	−0.961162	−	0.275983i	$-0.910997\pi$
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	0.719590	+	0.694399i	$0.244330\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−10.0000			−0.533761
$352$		0			0
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	7.50000	+	2.59808i	0.396942	+	0.137505i
$358$		0			0
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−2.00000			−0.104973
$364$		0			0
$365$	−3.00000			−0.157027
$366$		0			0
$367$	−2.50000	+	4.33013i	−0.130499	+	0.226031i	−0.923869	−	0.382709i	$-0.874991\pi$
$367$	−2.50000	+	4.33013i	−0.130499	+	0.226031i	0.793370	+	0.608740i	$0.208325\pi$
$368$		0			0
$369$	6.00000	+	10.3923i	0.312348	+	0.541002i
$370$		0			0
$371$	−1.50000	−	7.79423i	−0.0778761	−	0.404656i
$372$		0			0
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	0.983783	+	0.179364i	$0.0574041\pi$
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	−0.336557	+	0.941663i	$0.609263\pi$
$374$		0			0
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$		0			0
$383$	16.5000	+	28.5788i	0.843111	+	1.46031i	0.887252	+	0.461285i	$0.152611\pi$
$383$	16.5000	+	28.5788i	0.843111	+	1.46031i	−0.0441413	+	0.999025i	$0.514055\pi$
$384$		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
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	−0.991100	−	0.133120i	$-0.957501\pi$
$389$	−7.50000	+	12.9904i	−0.380265	+	0.658638i	0.610835	+	0.791758i	$0.290834\pi$
$390$		0			0
$391$	9.00000			0.455150
$392$		0			0
$393$	3.00000			0.151330
$394$		0			0
$395$	19.5000	−	33.7750i	0.981151	−	1.69940i
$396$		0			0
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.785853	+	0.618414i	$0.212224\pi$
$397$	18.5000	+	32.0429i	0.928488	+	1.60819i	0.142636	+	0.989775i	$0.454442\pi$
$398$		0			0
$399$	2.00000	−	1.73205i	0.100125	−	0.0867110i
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	7.00000	−	12.1244i	0.348695	−	0.603957i
$404$		0			0
$405$	3.00000			0.149071
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	−0.969363	−	0.245633i	$-0.921004\pi$
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	0.697406	+	0.716677i	$0.254338\pi$
$410$		0			0
$411$	10.5000	+	18.1865i	0.517927	+	0.897076i
$412$		0			0
$413$	−4.50000	−	23.3827i	−0.221431	−	1.15059i
$414$		0			0
$415$	−18.0000	−	31.1769i	−0.883585	−	1.53041i
$416$		0			0
$417$	−10.0000	+	17.3205i	−0.489702	+	0.848189i
$418$		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	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$	−9.00000	+	15.5885i	−0.437595	+	0.757937i
$424$		0			0
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$		0			0
$427$	−2.50000	−	0.866025i	−0.120983	−	0.0419099i
$428$		0			0
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	−0.626907	−	0.779094i	$-0.715679\pi$
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	0.988169	+	0.153370i	$0.0490126\pi$
$432$		0			0
$433$	−10.0000			−0.480569			−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000			−0.480569			−0.240285	+	0.970702i	$0.577241\pi$
$434$		0			0
$435$	−18.0000			−0.863034
$436$		0			0
$437$	1.50000	−	2.59808i	0.0717547	−	0.124283i
$438$		0			0
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$		0			0
$441$	13.0000	−	5.19615i	0.619048	−	0.247436i
$442$		0			0
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$		0			0
$445$	−22.5000	+	38.9711i	−1.06660	+	1.84741i
$446$		0			0
$447$	3.00000			0.141895
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$		0			0
$453$	−8.50000	−	14.7224i	−0.399365	−	0.691720i
$454$		0			0
$455$	15.0000	+	5.19615i	0.703211	+	0.243599i
$456$		0			0
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	−0.999014	−	0.0443868i	$-0.985867\pi$
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	0.461067	−	0.887365i	$-0.347467\pi$
$458$		0			0
$459$	7.50000	−	12.9904i	0.350070	−	0.606339i
$460$		0			0
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	10.5000	−	18.1865i	0.486926	−	0.843380i
$466$		0			0
$467$	10.5000	+	18.1865i	0.485882	+	0.841572i	0.999868	−	0.0162260i	$-0.00516512\pi$
$467$	10.5000	+	18.1865i	0.485882	+	0.841572i	−0.513986	+	0.857798i	$0.671832\pi$
$468$		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
$477$	−6.00000			−0.274721
$478$		0			0
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	−0.829721	−	0.558179i	$-0.811500\pi$
$479$	1.50000	−	2.59808i	0.0685367	−	0.118709i	0.898257	+	0.439470i	$0.144834\pi$
$480$		0			0
$481$	1.00000	+	1.73205i	0.0455961	+	0.0789747i
$482$		0			0
$483$	−6.00000	+	5.19615i	−0.273009	+	0.236433i
$484$		0			0
$485$	15.0000	+	25.9808i	0.681115	+	1.17973i
$486$		0			0
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	0.996915	+	0.0784867i	$0.0250088\pi$
$488$		0			0
$489$	11.0000			0.497437
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$		0			0
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$		0			0
$495$	−9.00000	−	15.5885i	−0.404520	−	0.700649i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	0.716258	−	0.697835i	$-0.245853\pi$
$499$	−5.50000	−	9.52628i	−0.246214	−	0.426455i	−0.962472	+	0.271380i	$0.912520\pi$
$500$		0			0
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	45.0000			2.00247
$506$		0			0
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$		0			0
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	0.500000	+	2.59808i	0.0221187	+	0.114932i
$512$		0			0
$513$	−2.50000	−	4.33013i	−0.110378	−	0.191180i
$514$		0			0
$515$	−16.5000	+	28.5788i	−0.727077	+	1.25933i
$516$		0			0
$517$	27.0000			1.18746
$518$		0			0
$519$	−9.00000			−0.395056
$520$		0			0
$521$	−19.5000	+	33.7750i	−0.854311	+	1.47971i	0.0229727	+	0.999736i	$0.492687\pi$
$521$	−19.5000	+	33.7750i	−0.854311	+	1.47971i	−0.877283	+	0.479973i	$0.840646\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		0			0
$525$	10.0000	+	3.46410i	0.436436	+	0.151186i
$526$		0			0
$527$	10.5000	+	18.1865i	0.457387	+	0.792218i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	12.0000			0.519778
$534$		0			0
$535$	−22.5000	+	38.9711i	−0.972760	+	1.68487i
$536$		0			0
$537$	−10.5000	−	18.1865i	−0.453108	−	0.784807i
$538$		0			0
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$		0			0
$541$	−17.5000	−	30.3109i	−0.752384	−	1.30317i	−0.946664	−	0.322221i	$-0.895571\pi$
$541$	−17.5000	−	30.3109i	−0.752384	−	1.30317i	0.194281	−	0.980946i	$-0.437763\pi$
$542$		0			0
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$		0			0
$545$	−3.00000			−0.128506
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$		0			0
$553$	−32.5000	−	11.2583i	−1.38204	−	0.478753i
$554$		0			0
$555$	1.50000	+	2.59808i	0.0636715	+	0.110282i
$556$		0			0
$557$	16.5000	−	28.5788i	0.699127	−	1.21092i	−0.269642	−	0.962961i	$-0.586905\pi$
$557$	16.5000	−	28.5788i	0.699127	−	1.21092i	0.968769	−	0.247964i	$-0.0797613\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	−9.00000			−0.379980
$562$		0			0
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	−0.945134	−	0.326682i	$-0.894069\pi$
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	0.755482	+	0.655169i	$0.227403\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$		0			0
$567$	−0.500000	−	2.59808i	−0.0209980	−	0.109109i
$568$		0			0
$569$	4.50000	+	7.79423i	0.188650	+	0.326751i	0.944800	−	0.327647i	$-0.106256\pi$
$569$	4.50000	+	7.79423i	0.188650	+	0.326751i	−0.756151	+	0.654398i	$0.772922\pi$
$570$		0			0
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	0.384957	+	0.922934i	$0.374216\pi$
$571$	−14.5000	+	25.1147i	−0.606806	+	1.05102i	−0.991763	+	0.128085i	$0.959117\pi$
$572$		0			0
$573$	−9.00000			−0.375980
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	−0.855430	−	0.517918i	$-0.826707\pi$
$577$	0.500000	−	0.866025i	0.0208153	−	0.0360531i	0.876245	+	0.481865i	$0.160040\pi$
$578$		0			0
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$	−24.0000	+	20.7846i	−0.995688	+	0.862291i
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$		0			0
$585$	6.00000	−	10.3923i	0.248069	−	0.429669i
$586$		0			0
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	7.00000			0.288430
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$		0			0
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$		0			0
$595$	−18.0000	+	15.5885i	−0.737928	+	0.639064i
$596$		0			0
$597$	3.50000	+	6.06218i	0.143245	+	0.248108i
$598$		0			0
$599$	13.5000	−	23.3827i	0.551595	−	0.955391i	−0.446565	−	0.894751i	$-0.647353\pi$
$599$	13.5000	−	23.3827i	0.551595	−	0.955391i	0.998160	−	0.0606393i	$-0.0193139\pi$
$600$		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
$607$	−23.5000	−	40.7032i	−0.953836	−	1.65209i	−0.737011	−	0.675881i	$-0.763763\pi$
$607$	−23.5000	−	40.7032i	−0.953836	−	1.65209i	−0.216825	−	0.976210i	$-0.569570\pi$
$608$		0			0
$609$	3.00000	+	15.5885i	0.121566	+	0.631676i
$610$		0			0
$611$	9.00000	+	15.5885i	0.364101	+	0.630641i
$612$		0			0
$613$	12.5000	−	21.6506i	0.504870	−	0.874461i	−0.495114	−	0.868828i	$-0.664874\pi$
$613$	12.5000	−	21.6506i	0.504870	−	0.874461i	0.999984	−	0.00563283i	$-0.00179300\pi$
$614$		0			0
$615$	18.0000			0.725830
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	15.5000	−	26.8468i	0.622998	−	1.07906i	−0.365927	−	0.930644i	$-0.619248\pi$
$619$	15.5000	−	26.8468i	0.622998	−	1.07906i	0.988924	−	0.148420i	$-0.0474187\pi$
$620$		0			0
$621$	7.50000	+	12.9904i	0.300965	+	0.521286i
$622$		0			0
$623$	37.5000	+	12.9904i	1.50241	+	0.520449i
$624$		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
$629$	−3.00000			−0.119618
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$		0			0
$635$	−12.0000	−	20.7846i	−0.476205	−	0.824812i
$636$		0			0
$637$	2.00000	−	13.8564i	0.0792429	−	0.549011i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	−0.975271	−	0.221013i	$-0.929064\pi$
$641$	−7.50000	+	12.9904i	−0.296232	+	0.513089i	0.679039	+	0.734103i	$0.262397\pi$
$642$		0			0
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$		0			0
$645$	−12.0000			−0.472500
$646$		0			0
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	−0.995194	−	0.0979182i	$-0.968782\pi$
$647$	−10.5000	+	18.1865i	−0.412798	+	0.714986i	0.582397	+	0.812905i	$0.302115\pi$
$648$		0			0
$649$	13.5000	+	23.3827i	0.529921	+	0.917851i
$650$		0			0
$651$	−17.5000	−	6.06218i	−0.685879	−	0.237595i
$652$		0			0
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	−0.941248	−	0.337715i	$-0.890346\pi$
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	0.178154	−	0.984003i	$-0.442987\pi$
$654$		0			0
$655$	−4.50000	+	7.79423i	−0.175830	+	0.304546i
$656$		0			0
$657$	2.00000			0.0780274
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	0.739014	+	0.673690i	$0.235292\pi$
$662$		0			0
$663$	−3.00000	−	5.19615i	−0.116510	−	0.201802i
$664$		0			0
$665$	1.50000	+	7.79423i	0.0581675	+	0.302247i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	3.00000			0.115814
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$		0			0
$675$	10.0000	−	17.3205i	0.384900	−	0.666667i
$676$		0			0
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$		0			0
$679$	20.0000	−	17.3205i	0.767530	−	0.664700i
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$		0			0
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	−0.993940	−	0.109926i	$-0.964939\pi$
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	0.592168	+	0.805814i	$0.298272\pi$
$684$		0			0
$685$	−63.0000			−2.40711
$686$		0			0
$687$	11.0000			0.419676
$688$		0			0
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	0.962768	−	0.270330i	$-0.0871327\pi$
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	−0.715496	+	0.698617i	$0.753799\pi$
$692$		0			0
$693$	−12.0000	+	10.3923i	−0.455842	+	0.394771i
$694$		0			0
$695$	−30.0000	−	51.9615i	−1.13796	−	1.97101i
$696$		0			0
$697$	−9.00000	+	15.5885i	−0.340899	+	0.590455i
$698$		0			0
$699$	−21.0000			−0.794293
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−0.500000	+	0.866025i	−0.0188579	+	0.0326628i
$704$		0			0
$705$	13.5000	+	23.3827i	0.508439	+	0.880643i
$706$		0			0
$707$	−7.50000	−	38.9711i	−0.282067	−	1.46566i
$708$		0			0
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	−13.0000	+	22.5167i	−0.487538	+	0.844441i
$712$		0			0
$713$	−21.0000			−0.786456
$714$		0			0
$715$	−18.0000			−0.673162
$716$		0			0
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$		0			0
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	0.992659	−	0.120950i	$-0.0385939\pi$
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	−0.601075	+	0.799193i	$0.705261\pi$
$720$		0			0
$721$	27.5000	+	9.52628i	1.02415	+	0.354777i
$722$		0			0
$723$	0.500000	+	0.866025i	0.0185952	+	0.0322078i
$724$		0			0
$725$	12.0000	−	20.7846i	0.445669	−	0.771921i
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$		0			0
$733$	12.5000	+	21.6506i	0.461698	+	0.799684i	0.999046	−	0.0436764i	$-0.0139070\pi$
$733$	12.5000	+	21.6506i	0.461698	+	0.799684i	−0.537348	+	0.843361i	$0.680574\pi$
$734$		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
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	−0.636691	−	0.771119i	$-0.719697\pi$
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	0.986154	+	0.165831i	$0.0530307\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	−48.0000			−1.76095			−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000			−1.76095			−0.880475	+	0.474093i	$0.842776\pi$
$744$		0			0
$745$	−4.50000	+	7.79423i	−0.164867	+	0.285558i
$746$		0			0
$747$	12.0000	+	20.7846i	0.439057	+	0.760469i
$748$		0			0
$749$	37.5000	+	12.9904i	1.37022	+	0.474658i
$750$		0			0
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	0.998752	−	0.0499348i	$-0.0159013\pi$
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	−0.542621	+	0.839978i	$0.682568\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	51.0000			1.85608
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$	4.50000	−	7.79423i	0.163340	−	0.282913i
$760$		0			0
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	0.837557	−	0.546350i	$-0.183983\pi$
$761$	−1.50000	−	2.59808i	−0.0543750	−	0.0941802i	−0.891932	+	0.452170i	$0.850650\pi$
$762$		0			0
$763$	0.500000	+	2.59808i	0.0181012	+	0.0940567i
$764$		0			0
$765$	9.00000	+	15.5885i	0.325396	+	0.563602i
$766$		0			0
$767$	−9.00000	+	15.5885i	−0.324971	+	0.562867i
$768$		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
$771$	3.00000			0.108042
$772$		0			0
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	−0.400298	−	0.916385i	$-0.631093\pi$
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	0.993762	−	0.111524i	$-0.0355733\pi$
$774$		0			0
$775$	14.0000	+	24.2487i	0.502895	+	0.871039i
$776$		0			0
$777$	2.00000	−	1.73205i	0.0717496	−	0.0621370i
$778$		0			0
$779$	3.00000	+	5.19615i	0.107486	+	0.186171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	30.0000			1.07211
$784$		0			0
$785$	−39.0000			−1.39197
$786$		0			0
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$		0			0
$789$	1.50000	+	2.59808i	0.0534014	+	0.0924940i
$790$		0			0
$791$	−12.0000	+	10.3923i	−0.426671	+	0.369508i
$792$		0			0
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$		0			0
$795$	−4.50000	+	7.79423i	−0.159599	+	0.276433i
$796$		0			0
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$		0			0
$799$	−27.0000			−0.955191
$800$		0			0
$801$	15.0000	−	25.9808i	0.529999	−	0.917985i
$802$		0			0
$803$	−1.50000	−	2.59808i	−0.0529339	−	0.0916841i
$804$		0			0
$805$	−4.50000	−	23.3827i	−0.158604	−	0.824131i
$806$		0			0
$807$	−1.50000	−	2.59808i	−0.0528025	−	0.0914566i
$808$		0			0
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	−0.415357	−	0.909659i	$-0.636343\pi$
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	0.995466	−	0.0951198i	$-0.0303234\pi$
$810$		0			0
$811$	−52.0000			−1.82597			−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000			−1.82597			−0.912983	+	0.407997i	$0.866228\pi$
$812$		0			0
$813$	11.0000			0.385787
$814$		0			0
$815$	−16.5000	+	28.5788i	−0.577970	+	1.00107i
$816$		0			0
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$		0			0
$819$	−10.0000	−	3.46410i	−0.349428	−	0.121046i
$820$		0			0
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	0.528302	−	0.849056i	$-0.322829\pi$
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	−0.999456	+	0.0329950i	$0.989495\pi$
$822$		0			0
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−2.50000	+	4.33013i	−0.0871445	+	0.150939i	0.819159	+	0.573567i	$0.194441\pi$
$824$		0			0
$825$	−12.0000			−0.417786
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	0.500000	−	0.866025i	0.0173657	−	0.0300783i	−0.857212	−	0.514964i	$-0.827805\pi$
$829$	0.500000	−	0.866025i	0.0173657	−	0.0300783i	0.874578	+	0.484885i	$0.161139\pi$
$830$		0			0
$831$	6.50000	+	11.2583i	0.225483	+	0.390547i
$832$		0			0
$833$	16.5000	+	12.9904i	0.571691	+	0.450090i
$834$		0			0
$835$	18.0000	+	31.1769i	0.622916	+	1.07892i
$836$		0			0
$837$	−17.5000	+	30.3109i	−0.604888	+	1.04770i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−15.0000	+	25.9808i	−0.516627	+	0.894825i
$844$		0			0
$845$	13.5000	+	23.3827i	0.464414	+	0.804389i
$846$		0			0
$847$	−5.00000	−	1.73205i	−0.171802	−	0.0595140i
$848$		0			0
$849$	−14.5000	−	25.1147i	−0.497639	−	0.861936i
$850$		0			0
$851$	1.50000	−	2.59808i	0.0514193	−	0.0890609i
$852$		0			0
$853$	−22.0000			−0.753266			−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000			−0.753266			−0.376633	+	0.926363i	$0.622918\pi$
$854$		0			0
$855$	6.00000			0.205196
$856$		0			0
$857$	−7.50000	+	12.9904i	−0.256195	+	0.443743i	−0.965219	−	0.261441i	$-0.915802\pi$
$857$	−7.50000	+	12.9904i	−0.256195	+	0.443743i	0.709024	+	0.705184i	$0.249136\pi$
$858$		0			0
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	0.600387	−	0.799709i	$-0.295013\pi$
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	−0.992762	+	0.120096i	$0.961680\pi$
$860$		0			0
$861$	−3.00000	−	15.5885i	−0.102240	−	0.531253i
$862$		0			0
$863$	−25.5000	−	44.1673i	−0.868030	−	1.50347i	−0.864007	−	0.503480i	$-0.832053\pi$
$863$	−25.5000	−	44.1673i	−0.868030	−	1.50347i	−0.00402340	−	0.999992i	$-0.501281\pi$
$864$		0			0
$865$	13.5000	−	23.3827i	0.459014	−	0.795035i
$866$		0			0
$867$	−8.00000			−0.271694
$868$		0			0
$869$	39.0000			1.32298
$870$		0			0
$871$	7.00000	−	12.1244i	0.237186	−	0.410818i
$872$		0			0
$873$	−10.0000	−	17.3205i	−0.338449	−	0.586210i
$874$		0			0
$875$	6.00000	−	5.19615i	0.202837	−	0.175662i
$876$		0			0
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$		0			0
$879$	−3.00000	+	5.19615i	−0.101187	+	0.175262i
$880$		0			0
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$		0			0
$885$	−13.5000	+	23.3827i	−0.453798	+	0.786000i
$886$		0			0
$887$	−19.5000	−	33.7750i	−0.654746	−	1.13405i	−0.981957	−	0.189102i	$-0.939442\pi$
$887$	−19.5000	−	33.7750i	−0.654746	−	1.13405i	0.327212	−	0.944951i	$-0.393891\pi$
$888$		0			0
$889$	−16.0000	+	13.8564i	−0.536623	+	0.464729i
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$		0			0
$893$	−4.50000	+	7.79423i	−0.150587	+	0.260824i
$894$		0			0
$895$	63.0000			2.10586
$896$		0			0
$897$	6.00000			0.200334
$898$		0			0
$899$	−21.0000	+	36.3731i	−0.700389	+	1.21311i
$900$		0			0
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$		0			0
$903$	2.00000	+	10.3923i	0.0665558	+	0.345834i
$904$		0			0
$905$	15.0000	+	25.9808i	0.498617	+	0.863630i
$906$		0			0
$907$	−20.5000	+	35.5070i	−0.680691	+	1.17899i	0.294079	+	0.955781i	$0.404987\pi$
$907$	−20.5000	+	35.5070i	−0.680691	+	1.17899i	−0.974770	+	0.223211i	$0.928346\pi$
$908$		0			0
$909$	−30.0000			−0.995037
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	18.0000	−	31.1769i	0.595713	−	1.03181i
$914$		0			0
$915$	1.50000	+	2.59808i	0.0495885	+	0.0858898i
$916$		0			0
$917$	7.50000	+	2.59808i	0.247672	+	0.0857960i
$918$		0			0
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	0.874154	−	0.485648i	$-0.161416\pi$
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	−0.857661	+	0.514216i	$0.828083\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	11.0000	−	19.0526i	0.361287	−	0.625768i
$928$		0			0
$929$	4.50000	+	7.79423i	0.147640	+	0.255720i	0.930355	−	0.366660i	$-0.119499\pi$
$929$	4.50000	+	7.79423i	0.147640	+	0.255720i	−0.782715	+	0.622381i	$0.786166\pi$
$930$		0			0
$931$	6.50000	−	2.59808i	0.213029	−	0.0851485i
$932$		0			0
$933$	13.5000	+	23.3827i	0.441970	+	0.765515i
$934$		0			0
$935$	13.5000	−	23.3827i	0.441497	−	0.764696i
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$	23.0000			0.750577
$940$		0			0
$941$	−13.5000	+	23.3827i	−0.440087	+	0.762254i	−0.997695	−	0.0678506i	$-0.978386\pi$
$941$	−13.5000	+	23.3827i	−0.440087	+	0.762254i	0.557608	+	0.830104i	$0.311719\pi$
$942$		0			0
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$		0			0
$945$	−37.5000	−	12.9904i	−1.21988	−	0.422577i
$946$		0			0
$947$	22.5000	+	38.9711i	0.731152	+	1.26639i	0.956391	+	0.292089i	$0.0943502\pi$
$947$	22.5000	+	38.9711i	0.731152	+	1.26639i	−0.225240	+	0.974303i	$0.572316\pi$
$948$		0			0
$949$	1.00000	−	1.73205i	0.0324614	−	0.0562247i
$950$		0			0
$951$	−9.00000			−0.291845
$952$		0			0
$953$	−18.0000			−0.583077			−0.291539	−	0.956559i	$-0.594167\pi$
$953$	−18.0000			−0.583077			−0.291539	+	0.956559i	$0.594167\pi$
$954$		0			0
$955$	13.5000	−	23.3827i	0.436850	−	0.756646i
$956$		0			0
$957$	−9.00000	−	15.5885i	−0.290929	−	0.503903i
$958$		0			0
$959$	10.5000	+	54.5596i	0.339063	+	1.76182i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$	15.0000	−	25.9808i	0.483368	−	0.837218i
$964$		0			0
$965$	33.0000			1.06231
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$		0			0
$969$	1.50000	−	2.59808i	0.0481869	−	0.0834622i
$970$		0			0
$971$	−25.5000	−	44.1673i	−0.818334	−	1.41740i	−0.906909	−	0.421326i	$-0.861565\pi$
$971$	−25.5000	−	44.1673i	−0.818334	−	1.41740i	0.0885751	−	0.996070i	$-0.471769\pi$
$972$		0			0
$973$	−40.0000	+	34.6410i	−1.28234	+	1.11054i
$974$		0			0
$975$	−4.00000	−	6.92820i	−0.128103	−	0.221880i
$976$		0			0
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	−0.997037	−	0.0769208i	$-0.975491\pi$
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	0.565134	+	0.824999i	$0.308824\pi$
$978$		0			0
$979$	−45.0000			−1.43821
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	−16.5000	+	28.5788i	−0.526268	+	0.911523i	0.473263	+	0.880921i	$0.343076\pi$
$983$	−16.5000	+	28.5788i	−0.526268	+	0.911523i	−0.999532	+	0.0306024i	$0.990257\pi$
$984$		0			0
$985$	−27.0000	−	46.7654i	−0.860292	−	1.49007i
$986$		0			0
$987$	18.0000	−	15.5885i	0.572946	−	0.496186i
$988$		0			0
$989$	6.00000	+	10.3923i	0.190789	+	0.330456i
$990$		0			0
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	−0.674761	−	0.738036i	$-0.735753\pi$
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	0.976539	+	0.215342i	$0.0690867\pi$
$992$		0			0
$993$	−13.0000			−0.412543
$994$		0			0
$995$	−21.0000			−0.665745
$996$		0			0
$997$	−29.5000	+	51.0955i	−0.934274	+	1.61821i	−0.158352	+	0.987383i	$0.550618\pi$
$997$	−29.5000	+	51.0955i	−0.934274	+	1.61821i	−0.775923	+	0.630828i	$0.782715\pi$
$998$		0			0
$999$	−2.50000	−	4.33013i	−0.0790965	−	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.2.e.a.25.1	yes	2
3.2	odd	2		252.2.k.c.109.1		2
4.3	odd	2		112.2.i.b.81.1		2
5.2	odd	4		700.2.r.b.249.2		4
5.3	odd	4		700.2.r.b.249.1		4
5.4	even	2		700.2.i.c.501.1		2
7.2	even	3	inner	28.2.e.a.9.1	✓	2
7.3	odd	6		196.2.a.a.1.1		1
7.4	even	3		196.2.a.b.1.1		1
7.5	odd	6		196.2.e.a.177.1		2
7.6	odd	2		196.2.e.a.165.1		2
8.3	odd	2		448.2.i.c.193.1		2
8.5	even	2		448.2.i.e.193.1		2
9.2	odd	6		2268.2.l.a.109.1		2
9.4	even	3		2268.2.i.a.865.1		2
9.5	odd	6		2268.2.i.h.865.1		2
9.7	even	3		2268.2.l.h.109.1		2
12.11	even	2		1008.2.s.p.865.1		2
21.2	odd	6		252.2.k.c.37.1		2
21.5	even	6		1764.2.k.b.1549.1		2
21.11	odd	6		1764.2.a.a.1.1		1
21.17	even	6		1764.2.a.j.1.1		1
21.20	even	2		1764.2.k.b.361.1		2
28.3	even	6		784.2.a.g.1.1		1
28.11	odd	6		784.2.a.d.1.1		1
28.19	even	6		784.2.i.d.177.1		2
28.23	odd	6		112.2.i.b.65.1		2
28.27	even	2		784.2.i.d.753.1		2
35.2	odd	12		700.2.r.b.149.1		4
35.3	even	12		4900.2.e.h.2549.1		2
35.4	even	6		4900.2.a.g.1.1		1
35.9	even	6		700.2.i.c.401.1		2
35.17	even	12		4900.2.e.h.2549.2		2
35.18	odd	12		4900.2.e.i.2549.2		2
35.23	odd	12		700.2.r.b.149.2		4
35.24	odd	6		4900.2.a.n.1.1		1
35.32	odd	12		4900.2.e.i.2549.1		2
56.3	even	6		3136.2.a.k.1.1		1
56.11	odd	6		3136.2.a.s.1.1		1
56.37	even	6		448.2.i.e.65.1		2
56.45	odd	6		3136.2.a.v.1.1		1
56.51	odd	6		448.2.i.c.65.1		2
56.53	even	6		3136.2.a.h.1.1		1
63.2	odd	6		2268.2.i.h.2053.1		2
63.16	even	3		2268.2.i.a.2053.1		2
63.23	odd	6		2268.2.l.a.541.1		2
63.58	even	3		2268.2.l.h.541.1		2
84.11	even	6		7056.2.a.f.1.1		1
84.23	even	6		1008.2.s.p.289.1		2
84.59	odd	6		7056.2.a.bw.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.2.e.a.9.1	✓	2	7.2	even	3	inner
28.2.e.a.25.1	yes	2	1.1	even	1	trivial
112.2.i.b.65.1		2	28.23	odd	6
112.2.i.b.81.1		2	4.3	odd	2
196.2.a.a.1.1		1	7.3	odd	6
196.2.a.b.1.1		1	7.4	even	3
196.2.e.a.165.1		2	7.6	odd	2
196.2.e.a.177.1		2	7.5	odd	6
252.2.k.c.37.1		2	21.2	odd	6
252.2.k.c.109.1		2	3.2	odd	2
448.2.i.c.65.1		2	56.51	odd	6
448.2.i.c.193.1		2	8.3	odd	2
448.2.i.e.65.1		2	56.37	even	6
448.2.i.e.193.1		2	8.5	even	2
700.2.i.c.401.1		2	35.9	even	6
700.2.i.c.501.1		2	5.4	even	2
700.2.r.b.149.1		4	35.2	odd	12
700.2.r.b.149.2		4	35.23	odd	12
700.2.r.b.249.1		4	5.3	odd	4
700.2.r.b.249.2		4	5.2	odd	4
784.2.a.d.1.1		1	28.11	odd	6
784.2.a.g.1.1		1	28.3	even	6
784.2.i.d.177.1		2	28.19	even	6
784.2.i.d.753.1		2	28.27	even	2
1008.2.s.p.289.1		2	84.23	even	6
1008.2.s.p.865.1		2	12.11	even	2
1764.2.a.a.1.1		1	21.11	odd	6
1764.2.a.j.1.1		1	21.17	even	6
1764.2.k.b.361.1		2	21.20	even	2
1764.2.k.b.1549.1		2	21.5	even	6
2268.2.i.a.865.1		2	9.4	even	3
2268.2.i.a.2053.1		2	63.16	even	3
2268.2.i.h.865.1		2	9.5	odd	6
2268.2.i.h.2053.1		2	63.2	odd	6
2268.2.l.a.109.1		2	9.2	odd	6
2268.2.l.a.541.1		2	63.23	odd	6
2268.2.l.h.109.1		2	9.7	even	3
2268.2.l.h.541.1		2	63.58	even	3
3136.2.a.h.1.1		1	56.53	even	6
3136.2.a.k.1.1		1	56.3	even	6
3136.2.a.s.1.1		1	56.11	odd	6
3136.2.a.v.1.1		1	56.45	odd	6
4900.2.a.g.1.1		1	35.4	even	6
4900.2.a.n.1.1		1	35.24	odd	6
4900.2.e.h.2549.1		2	35.3	even	12
4900.2.e.h.2549.2		2	35.17	even	12
4900.2.e.i.2549.1		2	35.32	odd	12
4900.2.e.i.2549.2		2	35.18	odd	12
7056.2.a.f.1.1		1	84.11	even	6
7056.2.a.bw.1.1		1	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	28.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(1.50000 + 2.59808i) q^{33} +(7.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(4.50000 + 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} -1.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-5.00000 - 1.73205i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(3.50000 - 6.06218i) q^{67} +3.00000 q^{69} +(0.500000 - 0.866025i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(-7.50000 - 12.9904i) q^{89} +(-4.00000 + 3.46410i) q^{91} +(3.50000 + 6.06218i) q^{93} +(1.50000 - 2.59808i) q^{95} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 - 3 * q^5 - 4 * q^7 + 2 * q^9	\( 2 q - q^{3} - 3 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} + 4 q^{13} + 6 q^{15} - 3 q^{17} + q^{19} - q^{21} - 3 q^{23} - 4 q^{25} - 10 q^{27} - 12 q^{29} + 7 q^{31} + 3 q^{33} + 15 q^{35} + q^{37} - 2 q^{39} + 12 q^{41} - 8 q^{43} + 6 q^{45} + 9 q^{47} + 2 q^{49} - 3 q^{51} - 3 q^{53} - 18 q^{55} - 2 q^{57} - 9 q^{59} + q^{61} - 10 q^{63} - 6 q^{65} + 7 q^{67} + 6 q^{69} + q^{73} - 4 q^{75} + 3 q^{77} + 13 q^{79} - q^{81} + 24 q^{83} + 18 q^{85} + 6 q^{87} - 15 q^{89} - 8 q^{91} + 7 q^{93} + 3 q^{95} - 20 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q - q^3 - 3 * q^5 - 4 * q^7 + 2 * q^9 + 3 * q^11 + 4 * q^13 + 6 * q^15 - 3 * q^17 + q^19 - q^21 - 3 * q^23 - 4 * q^25 - 10 * q^27 - 12 * q^29 + 7 * q^31 + 3 * q^33 + 15 * q^35 + q^37 - 2 * q^39 + 12 * q^41 - 8 * q^43 + 6 * q^45 + 9 * q^47 + 2 * q^49 - 3 * q^51 - 3 * q^53 - 18 * q^55 - 2 * q^57 - 9 * q^59 + q^61 - 10 * q^63 - 6 * q^65 + 7 * q^67 + 6 * q^69 + q^73 - 4 * q^75 + 3 * q^77 + 13 * q^79 - q^81 + 24 * q^83 + 18 * q^85 + 6 * q^87 - 15 * q^89 - 8 * q^91 + 7 * q^93 + 3 * q^95 - 20 * q^97 + 12 * q^99

Introduction

L-functions

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Varieties

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