LMFDB - Embedded newform 175.2.e.b.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(51,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.51"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	175.51
Dual form			175.2.e.b.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-2.50000 + 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-1.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +7.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(2.50000 + 4.33013i) q^{32} +2.00000 q^{34} +2.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(3.00000 + 5.19615i) q^{38} +(1.00000 + 1.73205i) q^{39} +5.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} -7.00000 q^{43} +(1.50000 + 2.59808i) q^{46} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{54} +(1.50000 - 7.79423i) q^{56} +6.00000 q^{57} +(3.50000 - 6.06218i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-3.50000 + 6.06218i) q^{61} -2.00000 q^{62} +(-4.00000 - 3.46410i) q^{63} +7.00000 q^{64} +(-2.50000 - 4.33013i) q^{67} +(-1.00000 + 1.73205i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(3.00000 - 5.19615i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(4.00000 + 6.92820i) q^{74} -6.00000 q^{76} +2.00000 q^{78} +(1.00000 - 1.73205i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +11.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-3.50000 + 6.06218i) q^{86} +(-3.50000 - 6.06218i) q^{87} +(-4.50000 + 7.79423i) q^{89} +(-1.00000 + 5.19615i) q^{91} -3.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(2.50000 - 4.33013i) q^{96} +16.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} + q^{4} - 2 q^{6} + q^{7} + 6 q^{8} + 2 q^{9} + q^{12} - 4 q^{13} - 4 q^{14} + q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} - 5 q^{21} - 3 q^{23} - 3 q^{24} - 2 q^{26} - 10 q^{27} + 5 q^{28}+ \cdots - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^3 + q^4 - 2 * q^6 + q^7 + 6 * q^8 + 2 * q^9 + q^12 - 4 * q^13 - 4 * q^14 + q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 - 5 * q^21 - 3 * q^23 - 3 * q^24 - 2 * q^26 - 10 * q^27 + 5 * q^28 + 14 * q^29 - 2 * q^31 + 5 * q^32 + 4 * q^34 + 4 * q^36 - 8 * q^37 + 6 * q^38 + 2 * q^39 + 10 * q^41 - q^42 - 14 * q^43 + 3 * q^46 - 2 * q^48 - 13 * q^49 + 2 * q^51 - 2 * q^52 + 6 * q^53 - 5 * q^54 + 3 * q^56 + 12 * q^57 + 7 * q^58 - 10 * q^59 - 7 * q^61 - 4 * q^62 - 8 * q^63 + 14 * q^64 - 5 * q^67 - 2 * q^68 + 6 * q^69 - 4 * q^71 + 6 * q^72 - 6 * q^73 + 8 * q^74 - 12 * q^76 + 4 * q^78 + 2 * q^79 - q^81 + 5 * q^82 + 22 * q^83 - 4 * q^84 - 7 * q^86 - 7 * q^87 - 9 * q^89 - 2 * q^91 - 6 * q^92 - 2 * q^93 + 5 * q^96 + 32 * q^97 - 11 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	3.00000			1.06066
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$		0			0
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$		0			0
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$	−5.00000			−0.962250
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	7.00000			1.29987			0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		0			0
$34$	2.00000			0.342997
$35$		0			0
$36$	2.00000			0.333333
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$		0			0
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$	1.50000	−	7.79423i	0.200446	−	1.04155i
$57$	6.00000			0.794719
$58$	3.50000	−	6.06218i	0.459573	−	0.796003i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−2.00000			−0.254000
$63$	−4.00000	−	3.46410i	−0.503953	−	0.436436i
$64$	7.00000			0.875000
$65$		0			0
$66$		0			0
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	3.00000			0.361158
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	3.00000	−	5.19615i	0.353553	−	0.612372i
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	−6.00000			−0.688247
$77$		0			0
$78$	2.00000			0.226455
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.50000	−	4.33013i	0.276079	−	0.478183i
$83$	11.0000			1.20741			0.603703	−	0.797209i	$-0.293691\pi$
$83$	11.0000			1.20741			0.603703	+	0.797209i	$0.293691\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$		0			0
$86$	−3.50000	+	6.06218i	−0.377415	+	0.653701i
$87$	−3.50000	−	6.06218i	−0.375239	−	0.649934i
$88$		0			0
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$		0			0
$91$	−1.00000	+	5.19615i	−0.104828	+	0.544705i
$92$	−3.00000			−0.312772
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$		0			0
$95$		0			0
$96$	2.50000	−	4.33013i	0.255155	−	0.441942i
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$	−5.50000	+	4.33013i	−0.555584	+	0.437409i
$99$		0			0
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$	−6.00000			−0.588348
$105$		0			0
$106$	6.00000			0.582772
$107$	5.50000	−	9.52628i	0.531705	−	0.920940i	−0.467610	−	0.883935i	$-0.654885\pi$
$107$	5.50000	−	9.52628i	0.531705	−	0.920940i	0.999315	−	0.0370053i	$-0.0117818\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$		0			0
$116$	3.50000	+	6.06218i	0.324967	+	0.562859i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	−10.0000			−0.920575
$119$	5.00000	−	1.73205i	0.458349	−	0.158777i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	3.50000	+	6.06218i	0.316875	+	0.548844i
$123$	−2.50000	−	4.33013i	−0.225417	−	0.390434i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	−5.00000	+	1.73205i	−0.445435	+	0.154303i
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	3.50000	+	6.06218i	0.308158	+	0.533745i
$130$		0			0
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$		0			0
$133$	12.0000	+	10.3923i	1.04053	+	0.901127i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$	1.50000	−	2.59808i	0.127688	−	0.221163i
$139$	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
$141$		0			0
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$		0			0
$144$	−1.00000	−	1.73205i	−0.0833333	−	0.144338i
$145$		0			0
$146$	−6.00000			−0.496564
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$	−8.00000			−0.657596
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	−9.00000	+	15.5885i	−0.729996	+	1.26439i
$153$	4.00000			0.323381
$154$		0			0
$155$		0			0
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	6.00000	+	10.3923i	0.478852	+	0.829396i	0.999706	−	0.0242497i	$-0.00771967\pi$
$157$	6.00000	+	10.3923i	0.478852	+	0.829396i	−0.520854	+	0.853646i	$0.674386\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$	6.00000	+	5.19615i	0.472866	+	0.409514i
$162$	−1.00000			−0.0785674
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	2.50000	+	4.33013i	0.195217	+	0.338126i
$165$		0			0
$166$	5.50000	−	9.52628i	0.426883	−	0.739383i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$	−7.50000	+	2.59808i	−0.578638	+	0.200446i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	6.00000	+	10.3923i	0.458831	+	0.794719i
$172$	−3.50000	−	6.06218i	−0.266872	−	0.462237i
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	−7.00000			−0.530669
$175$		0			0
$176$		0			0
$177$	−5.00000	+	8.66025i	−0.375823	+	0.650945i
$178$	4.50000	+	7.79423i	0.337289	+	0.584202i
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	0.900975	−	0.433872i	$-0.142853\pi$
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	−0.826231	+	0.563331i	$0.809520\pi$
$180$		0			0
$181$	−3.00000			−0.222988			−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000			−0.222988			−0.111494	+	0.993765i	$0.535564\pi$
$182$	4.00000	+	3.46410i	0.296500	+	0.256776i
$183$	7.00000			0.517455
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$		0			0
$189$	−2.50000	+	12.9904i	−0.181848	+	0.944911i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−3.50000	−	6.06218i	−0.252591	−	0.437500i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	8.00000	−	13.8564i	0.574367	−	0.994832i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$		0			0
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$	−9.00000			−0.633238
$203$	3.50000	−	18.1865i	0.245652	−	1.27644i
$204$	2.00000			0.140028
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$		0			0
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	1.00000	+	1.73205i	0.0685189	+	0.118678i
$214$	−5.50000	−	9.52628i	−0.375972	−	0.651203i
$215$		0			0
$216$	−15.0000			−1.02062
$217$	−5.00000	+	1.73205i	−0.339422	+	0.117579i
$218$	−5.00000			−0.338643
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$		0			0
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$	4.00000	−	6.92820i	0.268462	−	0.464991i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$	12.5000	−	4.33013i	0.835191	−	0.289319i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$	3.00000	+	5.19615i	0.198680	+	0.344124i
$229$	11.0000	−	19.0526i	0.726900	−	1.25903i	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	11.0000	−	19.0526i	0.726900	−	1.25903i	0.958187	−	0.286143i	$-0.0923732\pi$
$230$		0			0
$231$		0			0
$232$	21.0000			1.37872
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	−0.540301	−	0.841472i	$-0.681690\pi$
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	0.998886	+	0.0471787i	$0.0150230\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$		0			0
$236$	5.00000	−	8.66025i	0.325472	−	0.563735i
$237$	−2.00000			−0.129914
$238$	1.00000	−	5.19615i	0.0648204	−	0.336817i
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$		0			0
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−7.00000			−0.448129
$245$		0			0
$246$	−5.00000			−0.318788
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$	−5.50000	−	9.52628i	−0.348548	−	0.603703i
$250$		0			0
$251$	30.0000			1.89358			0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000			1.89358			0.946792	+	0.321847i	$0.104304\pi$
$252$	1.00000	−	5.19615i	0.0629941	−	0.327327i
$253$		0			0
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	10.0000	−	17.3205i	0.623783	−	1.08042i	−0.364992	−	0.931011i	$-0.618928\pi$
$257$	10.0000	−	17.3205i	0.623783	−	1.08042i	0.988775	−	0.149413i	$-0.0477384\pi$
$258$	7.00000			0.435801
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$		0			0
$261$	7.00000	−	12.1244i	0.433289	−	0.750479i
$262$	2.00000	+	3.46410i	0.123560	+	0.214013i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$		0			0
$266$	15.0000	−	5.19615i	0.919709	−	0.318597i
$267$	9.00000			0.550791
$268$	2.50000	−	4.33013i	0.152712	−	0.264505i
$269$	5.50000	+	9.52628i	0.335341	+	0.580828i	0.983550	−	0.180635i	$-0.0578152\pi$
$269$	5.50000	+	9.52628i	0.335341	+	0.580828i	−0.648209	+	0.761462i	$0.724482\pi$
$270$		0			0
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$	2.00000			0.121268
$273$	5.00000	−	1.73205i	0.302614	−	0.104828i
$274$		0			0
$275$		0			0
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	4.00000	−	6.92820i	0.239904	−	0.415526i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−14.0000			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$282$		0			0
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$		0			0
$287$	2.50000	−	12.9904i	0.147570	−	0.766798i
$288$	10.0000			0.589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−8.00000	−	13.8564i	−0.468968	−	0.812277i
$292$	3.00000	−	5.19615i	0.175562	−	0.304082i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$	6.50000	+	2.59808i	0.379088	+	0.151523i
$295$		0			0
$296$	−12.0000	+	20.7846i	−0.697486	+	1.20808i
$297$		0			0
$298$	0.500000	+	0.866025i	0.0289642	+	0.0501675i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	−3.50000	+	18.1865i	−0.201737	+	1.04825i
$302$	−14.0000			−0.805609
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$		0			0
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	−23.0000			−1.31268			−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000			−1.31268			−0.656340	+	0.754466i	$0.727896\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$		0			0
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	−0.880693	−	0.473688i	$-0.842923\pi$
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	0.0301210	−	0.999546i	$-0.490411\pi$
$312$	3.00000	+	5.19615i	0.169842	+	0.294174i
$313$	12.0000	−	20.7846i	0.678280	−	1.17482i	−0.297218	−	0.954810i	$-0.596059\pi$
$313$	12.0000	−	20.7846i	0.678280	−	1.17482i	0.975499	−	0.220006i	$-0.0706077\pi$
$314$	12.0000			0.677199
$315$		0			0
$316$	2.00000			0.112509
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$		0			0
$320$		0			0
$321$	−11.0000			−0.613960
$322$	7.50000	−	2.59808i	0.417959	−	0.144785i
$323$	−12.0000			−0.667698
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	−2.50000	+	4.33013i	−0.138250	+	0.239457i
$328$	15.0000			0.828236
$329$		0			0
$330$		0			0
$331$	−3.00000	+	5.19615i	−0.164895	+	0.285606i	−0.936618	−	0.350352i	$-0.886062\pi$
$331$	−3.00000	+	5.19615i	−0.164895	+	0.285606i	0.771723	+	0.635959i	$0.219395\pi$
$332$	5.50000	+	9.52628i	0.301852	+	0.522823i
$333$	8.00000	+	13.8564i	0.438397	+	0.759326i
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$		0			0
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$		0			0
$342$	12.0000			0.648886
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−21.0000			−1.13224
$345$		0			0
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	7.50000	+	12.9904i	0.402621	+	0.697360i	0.994041	−	0.109003i	$-0.0347659\pi$
$347$	7.50000	+	12.9904i	0.402621	+	0.697360i	−0.591420	+	0.806363i	$0.701433\pi$
$348$	3.50000	−	6.06218i	0.187620	−	0.324967i
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	10.0000			0.533761
$352$		0			0
$353$	−13.0000	−	22.5167i	−0.691920	−	1.19844i	−0.971208	−	0.238233i	$-0.923432\pi$
$353$	−13.0000	−	22.5167i	−0.691920	−	1.19844i	0.279288	−	0.960207i	$-0.409902\pi$
$354$	5.00000	+	8.66025i	0.265747	+	0.460287i
$355$		0			0
$356$	−9.00000			−0.476999
$357$	−4.00000	−	3.46410i	−0.211702	−	0.183340i
$358$	2.00000			0.105703
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−1.50000	+	2.59808i	−0.0788382	+	0.136552i
$363$	−11.0000			−0.577350
$364$	−5.00000	+	1.73205i	−0.262071	+	0.0907841i
$365$		0			0
$366$	3.50000	−	6.06218i	0.182948	−	0.316875i
$367$	13.5000	+	23.3827i	0.704694	+	1.22057i	0.966802	+	0.255528i	$0.0822492\pi$
$367$	13.5000	+	23.3827i	0.704694	+	1.22057i	−0.262108	+	0.965039i	$0.584418\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$	5.00000	−	8.66025i	0.260290	−	0.450835i
$370$		0			0
$371$	15.0000	−	5.19615i	0.778761	−	0.269771i
$372$	−2.00000			−0.103695
$373$	−12.0000	+	20.7846i	−0.621336	+	1.07619i	0.367901	+	0.929865i	$0.380077\pi$
$373$	−12.0000	+	20.7846i	−0.621336	+	1.07619i	−0.989237	+	0.146321i	$0.953257\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.0000			−0.721037
$378$	10.0000	+	8.66025i	0.514344	+	0.445435i
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$		0			0
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	2.50000	−	4.33013i	0.127744	−	0.221259i	−0.795058	−	0.606533i	$-0.792560\pi$
$383$	2.50000	−	4.33013i	0.127744	−	0.221259i	0.922802	+	0.385274i	$0.125893\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	−4.00000			−0.203595
$387$	−7.00000	+	12.1244i	−0.355830	+	0.616316i
$388$	8.00000	+	13.8564i	0.406138	+	0.703452i
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	0.632189	−	0.774814i	$-0.282157\pi$
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	−0.987103	+	0.160085i	$0.948823\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	−19.5000	−	7.79423i	−0.984899	−	0.393668i
$393$	4.00000			0.201773
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$		0			0
$396$		0			0
$397$	−8.00000	+	13.8564i	−0.401508	+	0.695433i	−0.993908	−	0.110211i	$-0.964847\pi$
$397$	−8.00000	+	13.8564i	−0.401508	+	0.695433i	0.592400	+	0.805644i	$0.298181\pi$
$398$	4.00000			0.200502
$399$	3.00000	−	15.5885i	0.150188	−	0.780399i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	2.50000	+	4.33013i	0.124689	+	0.215967i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$		0			0
$406$	−14.0000	−	12.1244i	−0.694808	−	0.601722i
$407$		0			0
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$		0			0
$411$		0			0
$412$	7.00000			0.344865
$413$	−25.0000	+	8.66025i	−1.23017	+	0.426143i
$414$	6.00000			0.294884
$415$		0			0
$416$	−5.00000	−	8.66025i	−0.245145	−	0.424604i
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	15.0000			0.731055			0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000			0.731055			0.365528	+	0.930800i	$0.380889\pi$
$422$	−5.00000	+	8.66025i	−0.243396	+	0.421575i
$423$		0			0
$424$	9.00000	+	15.5885i	0.437079	+	0.757042i
$425$		0			0
$426$	2.00000			0.0969003
$427$	14.0000	+	12.1244i	0.677507	+	0.586739i
$428$	11.0000			0.531705
$429$		0			0
$430$		0			0
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−1.00000	+	5.19615i	−0.0480015	+	0.249423i
$435$		0			0
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	−9.00000	−	15.5885i	−0.430528	−	0.745697i
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$		0			0
$441$	−11.0000	+	8.66025i	−0.523810	+	0.412393i
$442$	−4.00000			−0.190261
$443$	15.5000	−	26.8468i	0.736427	−	1.27553i	−0.217667	−	0.976023i	$-0.569845\pi$
$443$	15.5000	−	26.8468i	0.736427	−	1.27553i	0.954094	−	0.299506i	$-0.0968220\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$		0			0
$446$		0			0
$447$	1.00000			0.0472984
$448$	3.50000	−	18.1865i	0.165359	−	0.859233i
$449$	31.0000			1.46298			0.731490	−	0.681852i	$-0.238825\pi$
$449$	31.0000			1.46298			0.731490	+	0.681852i	$0.238825\pi$
$450$		0			0
$451$		0			0
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	−7.00000	+	12.1244i	−0.328889	+	0.569652i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	18.0000			0.842927
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	−0.200118	−	0.979772i	$-0.564132\pi$
$457$	16.0000	−	27.7128i	0.748448	−	1.29635i	0.948566	−	0.316579i	$-0.102534\pi$
$458$	−11.0000	−	19.0526i	−0.513996	−	0.890268i
$459$	−5.00000	−	8.66025i	−0.233380	−	0.404226i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	−3.00000			−0.139422			−0.0697109	−	0.997567i	$-0.522208\pi$
$463$	−3.00000			−0.139422			−0.0697109	+	0.997567i	$0.522208\pi$
$464$	3.50000	−	6.06218i	0.162483	−	0.281430i
$465$		0			0
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	−0.829231	−	0.558906i	$-0.811221\pi$
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	0.898642	+	0.438682i	$0.144554\pi$
$468$	−4.00000			−0.184900
$469$	−12.5000	+	4.33013i	−0.577196	+	0.199947i
$470$		0			0
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$	−15.0000	−	25.9808i	−0.690431	−	1.19586i
$473$		0			0
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$		0			0
$476$	4.00000	+	3.46410i	0.183340	+	0.158777i
$477$	12.0000			0.549442
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−21.0000	−	36.3731i	−0.959514	−	1.66193i	−0.723681	−	0.690134i	$-0.757551\pi$
$479$	−21.0000	−	36.3731i	−0.959514	−	1.66193i	−0.235833	−	0.971794i	$-0.575782\pi$
$480$		0			0
$481$	8.00000	−	13.8564i	0.364769	−	0.631798i
$482$	14.0000			0.637683
$483$	1.50000	−	7.79423i	0.0682524	−	0.354650i
$484$	11.0000			0.500000
$485$		0			0
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	0.697459	−	0.716625i	$-0.254314\pi$
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	−0.969345	+	0.245705i	$0.920981\pi$
$488$	−10.5000	+	18.1865i	−0.475313	+	0.823266i
$489$	4.00000			0.180886
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$	2.50000	−	4.33013i	0.112709	−	0.195217i
$493$	7.00000	+	12.1244i	0.315264	+	0.546054i
$494$	−6.00000	−	10.3923i	−0.269953	−	0.467572i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	−1.00000	+	5.19615i	−0.0448561	+	0.233079i
$498$	−11.0000			−0.492922
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	−0.987648	−	0.156687i	$-0.949919\pi$
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	0.629519	+	0.776985i	$0.283252\pi$
$500$		0			0
$501$	−1.50000	−	2.59808i	−0.0670151	−	0.116073i
$502$	15.0000	−	25.9808i	0.669483	−	1.15958i
$503$	15.0000			0.668817			0.334408	−	0.942428i	$-0.391463\pi$
$503$	15.0000			0.668817			0.334408	+	0.942428i	$0.391463\pi$
$504$	−12.0000	−	10.3923i	−0.534522	−	0.462910i
$505$		0			0
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	0.394684	+	0.918817i	$0.370854\pi$
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	−0.993061	+	0.117602i	$0.962479\pi$
$510$		0			0
$511$	−15.0000	+	5.19615i	−0.663561	+	0.229864i
$512$	11.0000			0.486136
$513$	15.0000	−	25.9808i	0.662266	−	1.14708i
$514$	−10.0000	−	17.3205i	−0.441081	−	0.763975i
$515$		0			0
$516$	−3.50000	+	6.06218i	−0.154079	+	0.266872i
$517$		0			0
$518$	20.0000	−	6.92820i	0.878750	−	0.304408i
$519$	12.0000			0.526742
$520$		0			0
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$	−7.00000	−	12.1244i	−0.306382	−	0.530669i
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−9.00000			−0.392419
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	−20.0000			−0.867926
$532$	−3.00000	+	15.5885i	−0.130066	+	0.675845i
$533$	−10.0000			−0.433148
$534$	4.50000	−	7.79423i	0.194734	−	0.337289i
$535$		0			0
$536$	−7.50000	−	12.9904i	−0.323951	−	0.561099i
$537$	1.00000	−	1.73205i	0.0431532	−	0.0747435i
$538$	11.0000			0.474244
$539$		0			0
$540$		0			0
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$	1.50000	+	2.59808i	0.0643712	+	0.111494i
$544$	−5.00000	+	8.66025i	−0.214373	+	0.371305i
$545$		0			0
$546$	1.00000	−	5.19615i	0.0427960	−	0.222375i
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$		0			0
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$		0			0
$551$	−21.0000	+	36.3731i	−0.894630	+	1.54954i
$552$	9.00000			0.383065
$553$	−4.00000	−	3.46410i	−0.170097	−	0.147309i
$554$	10.0000			0.424859
$555$		0			0
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	−22.0000	−	38.1051i	−0.932170	−	1.61457i	−0.779604	−	0.626272i	$-0.784580\pi$
$557$	−22.0000	−	38.1051i	−0.932170	−	1.61457i	−0.152566	−	0.988293i	$-0.548754\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	14.0000			0.592137
$560$		0			0
$561$		0			0
$562$	−7.00000	+	12.1244i	−0.295277	+	0.511435i
$563$	16.5000	+	28.5788i	0.695392	+	1.20445i	0.970048	+	0.242912i	$0.0781026\pi$
$563$	16.5000	+	28.5788i	0.695392	+	1.20445i	−0.274656	+	0.961542i	$0.588564\pi$
$564$		0			0
$565$		0			0
$566$	16.0000			0.672530
$567$	−2.50000	+	0.866025i	−0.104990	+	0.0363696i
$568$	−6.00000			−0.251754
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	9.00000	+	15.5885i	0.376638	+	0.652357i	0.990571	−	0.137002i	$-0.0437466\pi$
$571$	9.00000	+	15.5885i	0.376638	+	0.652357i	−0.613933	+	0.789359i	$0.710413\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$	−10.0000	−	8.66025i	−0.417392	−	0.361472i
$575$		0			0
$576$	7.00000	−	12.1244i	0.291667	−	0.505181i
$577$	−16.0000	−	27.7128i	−0.666089	−	1.15370i	−0.978989	−	0.203913i	$-0.934634\pi$
$577$	−16.0000	−	27.7128i	−0.666089	−	1.15370i	0.312900	−	0.949786i	$-0.398699\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−2.00000	+	3.46410i	−0.0831172	+	0.143963i
$580$		0			0
$581$	5.50000	−	28.5788i	0.228178	−	1.18565i
$582$	−16.0000			−0.663221
$583$		0			0
$584$	−9.00000	−	15.5885i	−0.372423	−	0.645055i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$	36.0000			1.48588			0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000			1.48588			0.742940	+	0.669359i	$0.233431\pi$
$588$	−5.50000	+	4.33013i	−0.226816	+	0.178571i
$589$	12.0000			0.494451
$590$		0			0
$591$	−4.00000	−	6.92820i	−0.164538	−	0.284988i
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	11.0000	−	19.0526i	0.451716	−	0.782395i	−0.546777	−	0.837278i	$-0.684145\pi$
$593$	11.0000	−	19.0526i	0.451716	−	0.782395i	0.998493	+	0.0548835i	$0.0174787\pi$
$594$		0			0
$595$		0			0
$596$	−1.00000			−0.0409616
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	22.0000	+	38.1051i	0.898896	+	1.55693i	0.828908	+	0.559385i	$0.188963\pi$
$599$	22.0000	+	38.1051i	0.898896	+	1.55693i	0.0699877	+	0.997548i	$0.477704\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$	14.0000	+	12.1244i	0.570597	+	0.494152i
$603$	−10.0000			−0.407231
$604$	7.00000	−	12.1244i	0.284826	−	0.493333i
$605$		0			0
$606$	4.50000	+	7.79423i	0.182800	+	0.316619i
$607$	−16.5000	+	28.5788i	−0.669714	+	1.15998i	0.308270	+	0.951299i	$0.400250\pi$
$607$	−16.5000	+	28.5788i	−0.669714	+	1.15998i	−0.977984	+	0.208680i	$0.933083\pi$
$608$	−30.0000			−1.21666
$609$	−17.5000	+	6.06218i	−0.709136	+	0.245652i
$610$		0			0
$611$		0			0
$612$	2.00000	+	3.46410i	0.0808452	+	0.140028i
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−17.0000	−	29.4449i	−0.686624	−	1.18927i	0.286300	−	0.958140i	$-0.407575\pi$
$614$	−11.5000	+	19.9186i	−0.464102	+	0.803849i
$615$		0			0
$616$		0			0
$617$	4.00000			0.161034			0.0805170	−	0.996753i	$-0.474343\pi$
$617$	4.00000			0.161034			0.0805170	+	0.996753i	$0.474343\pi$
$618$	−3.50000	+	6.06218i	−0.140791	+	0.243857i
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	−0.997259	−	0.0739910i	$-0.976426\pi$
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	0.434551	−	0.900647i	$-0.356907\pi$
$620$		0			0
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$	−30.0000			−1.20289
$623$	18.0000	+	15.5885i	0.721155	+	0.624538i
$624$	2.00000			0.0800641
$625$		0			0
$626$	−12.0000	−	20.7846i	−0.479616	−	0.830720i
$627$		0			0
$628$	−6.00000	+	10.3923i	−0.239426	+	0.414698i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$	3.00000	−	5.19615i	0.119334	−	0.206692i
$633$	5.00000	+	8.66025i	0.198732	+	0.344214i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$		0			0
$636$	6.00000			0.237915
$637$	13.0000	+	5.19615i	0.515079	+	0.205879i
$638$		0			0
$639$	−2.00000	+	3.46410i	−0.0791188	+	0.137038i
$640$		0			0
$641$	5.50000	+	9.52628i	0.217237	+	0.376265i	0.953962	−	0.299927i	$-0.0969622\pi$
$641$	5.50000	+	9.52628i	0.217237	+	0.376265i	−0.736725	+	0.676192i	$0.763629\pi$
$642$	−5.50000	+	9.52628i	−0.217068	+	0.375972i
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$	−1.50000	+	7.79423i	−0.0591083	+	0.307136i
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	23.5000	+	40.7032i	0.923880	+	1.60021i	0.793352	+	0.608763i	$0.208334\pi$
$647$	23.5000	+	40.7032i	0.923880	+	1.60021i	0.130528	+	0.991445i	$0.458333\pi$
$648$	−1.50000	−	2.59808i	−0.0589256	−	0.102062i
$649$		0			0
$650$		0			0
$651$	4.00000	+	3.46410i	0.156772	+	0.135769i
$652$	−4.00000			−0.156652
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	0.491220	+	0.871036i	$0.336551\pi$
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	−0.999949	+	0.0101092i	$0.996782\pi$
$654$	2.50000	+	4.33013i	0.0977577	+	0.169321i
$655$		0			0
$656$	2.50000	−	4.33013i	0.0976086	−	0.169063i
$657$	−12.0000			−0.468165
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$		0			0
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	0.940172	−	0.340701i	$-0.110665\pi$
$661$	4.50000	+	7.79423i	0.175030	+	0.303160i	−0.765142	+	0.643862i	$0.777331\pi$
$662$	3.00000	+	5.19615i	0.116598	+	0.201954i
$663$	−2.00000	+	3.46410i	−0.0776736	+	0.134535i
$664$	33.0000			1.28065
$665$		0			0
$666$	16.0000			0.619987
$667$	−10.5000	+	18.1865i	−0.406562	+	0.704185i
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−10.0000	−	8.66025i	−0.385758	−	0.334077i
$673$	36.0000			1.38770			0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000			1.38770			0.693849	+	0.720121i	$0.255914\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$		0			0
$676$	−4.50000	−	7.79423i	−0.173077	−	0.299778i
$677$	−7.00000	+	12.1244i	−0.269032	+	0.465977i	−0.968612	−	0.248577i	$-0.920037\pi$
$677$	−7.00000	+	12.1244i	−0.269032	+	0.465977i	0.699580	+	0.714554i	$0.253370\pi$
$678$	−6.00000			−0.230429
$679$	8.00000	−	41.5692i	0.307012	−	1.59528i
$680$		0			0
$681$	−10.0000	+	17.3205i	−0.383201	+	0.663723i
$682$		0			0
$683$	17.5000	+	30.3109i	0.669619	+	1.15981i	0.978011	+	0.208555i	$0.0668759\pi$
$683$	17.5000	+	30.3109i	0.669619	+	1.15981i	−0.308392	+	0.951259i	$0.599791\pi$
$684$	−6.00000	+	10.3923i	−0.229416	+	0.397360i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−22.0000			−0.839352
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	15.0000			0.569392
$695$		0			0
$696$	−10.5000	−	18.1865i	−0.398001	−	0.689359i
$697$	5.00000	+	8.66025i	0.189389	+	0.328031i
$698$	−8.50000	+	14.7224i	−0.321730	+	0.557252i
$699$	−14.0000			−0.529529
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$	5.00000	−	8.66025i	0.188713	−	0.326860i
$703$	−24.0000	−	41.5692i	−0.905177	−	1.56781i
$704$		0			0
$705$		0			0
$706$	−26.0000			−0.978523
$707$	−22.5000	+	7.79423i	−0.846200	+	0.293132i
$708$	−10.0000			−0.375823
$709$	24.5000	−	42.4352i	0.920117	−	1.59369i	0.120885	−	0.992667i	$-0.461427\pi$
$709$	24.5000	−	42.4352i	0.920117	−	1.59369i	0.799232	−	0.601023i	$-0.205240\pi$
$710$		0			0
$711$	−2.00000	−	3.46410i	−0.0750059	−	0.129914i
$712$	−13.5000	+	23.3827i	−0.505934	+	0.876303i
$713$	6.00000			0.224702
$714$	−5.00000	+	1.73205i	−0.187120	+	0.0648204i
$715$		0			0
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	5.00000	+	8.66025i	0.186598	+	0.323198i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	−14.0000	−	12.1244i	−0.521387	−	0.451535i
$722$	−17.0000			−0.632674
$723$	7.00000	−	12.1244i	0.260333	−	0.450910i
$724$	−1.50000	−	2.59808i	−0.0557471	−	0.0965567i
$725$		0			0
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$	47.0000			1.74313			0.871567	−	0.490277i	$-0.163104\pi$
$727$	47.0000			1.74313			0.871567	+	0.490277i	$0.163104\pi$
$728$	−3.00000	+	15.5885i	−0.111187	+	0.577747i
$729$	13.0000			0.481481
$730$		0			0
$731$	−7.00000	−	12.1244i	−0.258904	−	0.448435i
$732$	3.50000	+	6.06218i	0.129364	+	0.224065i
$733$	−8.00000	+	13.8564i	−0.295487	+	0.511798i	−0.975098	−	0.221774i	$-0.928815\pi$
$733$	−8.00000	+	13.8564i	−0.295487	+	0.511798i	0.679611	+	0.733572i	$0.262148\pi$
$734$	27.0000			0.996588
$735$		0			0
$736$	−15.0000			−0.552907
$737$		0			0
$738$	−5.00000	−	8.66025i	−0.184053	−	0.318788i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	−12.0000			−0.440831
$742$	3.00000	−	15.5885i	0.110133	−	0.572270i
$743$	49.0000			1.79764			0.898818	−	0.438322i	$-0.144427\pi$
$743$	49.0000			1.79764			0.898818	+	0.438322i	$0.144427\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$		0			0
$746$	12.0000	+	20.7846i	0.439351	+	0.760979i
$747$	11.0000	−	19.0526i	0.402469	−	0.697097i
$748$		0			0
$749$	−22.0000	−	19.0526i	−0.803863	−	0.696165i
$750$		0			0
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$		0			0
$753$	−15.0000	−	25.9808i	−0.546630	−	0.946792i
$754$	−7.00000	+	12.1244i	−0.254925	+	0.441543i
$755$		0			0
$756$	−12.5000	+	4.33013i	−0.454621	+	0.157485i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−5.00000	+	8.66025i	−0.181608	+	0.314555i
$759$		0			0
$760$		0			0
$761$	−7.00000	+	12.1244i	−0.253750	+	0.439508i	−0.964555	−	0.263881i	$-0.914997\pi$
$761$	−7.00000	+	12.1244i	−0.253750	+	0.439508i	0.710805	+	0.703389i	$0.248331\pi$
$762$	16.0000			0.579619
$763$	−12.5000	+	4.33013i	−0.452530	+	0.156761i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−2.50000	−	4.33013i	−0.0903287	−	0.156454i
$767$	10.0000	+	17.3205i	0.361079	+	0.625407i
$768$	8.50000	−	14.7224i	0.306717	−	0.531250i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$		0			0
$771$	−20.0000			−0.720282
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	7.00000	+	12.1244i	0.251610	+	0.435801i
$775$		0			0
$776$	48.0000			1.72310
$777$	4.00000	−	20.7846i	0.143499	−	0.745644i
$778$	−14.0000			−0.501924
$779$	−15.0000	+	25.9808i	−0.537431	+	0.930857i
$780$		0			0
$781$		0			0
$782$	−3.00000	+	5.19615i	−0.107280	+	0.185814i
$783$	−35.0000			−1.25080
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$		0			0
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	0.673820	−	0.738896i	$-0.264652\pi$
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	−0.976812	+	0.214097i	$0.931319\pi$
$788$	4.00000	+	6.92820i	0.142494	+	0.246807i
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$		0			0
$791$	3.00000	−	15.5885i	0.106668	−	0.554262i
$792$		0			0
$793$	7.00000	−	12.1244i	0.248577	−	0.430548i
$794$	8.00000	+	13.8564i	0.283909	+	0.491745i
$795$		0			0
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	−40.0000			−1.41687			−0.708436	−	0.705775i	$-0.750599\pi$
$797$	−40.0000			−1.41687			−0.708436	+	0.705775i	$0.750599\pi$
$798$	−12.0000	−	10.3923i	−0.424795	−	0.367884i
$799$		0			0
$800$		0			0
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	1.50000	+	2.59808i	0.0529668	+	0.0917413i
$803$		0			0
$804$	−5.00000			−0.176336
$805$		0			0
$806$	4.00000			0.140894
$807$	5.50000	−	9.52628i	0.193609	−	0.335341i
$808$	−13.5000	−	23.3827i	−0.474928	−	0.822600i
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	0.776012	−	0.630718i	$-0.217239\pi$
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	−0.934224	+	0.356687i	$0.883906\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$	17.5000	−	6.06218i	0.614130	−	0.212741i
$813$	−2.00000			−0.0701431
$814$		0			0
$815$		0			0
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	21.0000	−	36.3731i	0.734697	−	1.27253i
$818$	25.0000			0.874105
$819$	8.00000	+	6.92820i	0.279543	+	0.242091i
$820$		0			0
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	12.5000	+	21.6506i	0.435723	+	0.754694i	0.997354	−	0.0726937i	$-0.0231595\pi$
$823$	12.5000	+	21.6506i	0.435723	+	0.754694i	−0.561632	+	0.827387i	$0.689826\pi$
$824$	10.5000	−	18.1865i	0.365785	−	0.633558i
$825$		0			0
$826$	−5.00000	+	25.9808i	−0.173972	+	0.903986i
$827$	39.0000			1.35616			0.678081	−	0.734987i	$-0.262812\pi$
$827$	39.0000			1.35616			0.678081	+	0.734987i	$0.262812\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	15.0000	+	25.9808i	0.520972	+	0.902349i	0.999703	+	0.0243876i	$0.00776357\pi$
$829$	15.0000	+	25.9808i	0.520972	+	0.902349i	−0.478731	+	0.877962i	$0.658903\pi$
$830$		0			0
$831$	5.00000	−	8.66025i	0.173448	−	0.300421i
$832$	−14.0000			−0.485363
$833$	−2.00000	−	13.8564i	−0.0692959	−	0.480096i
$834$	−8.00000			−0.277017
$835$		0			0
$836$		0			0
$837$	5.00000	+	8.66025i	0.172825	+	0.299342i
$838$	12.0000	−	20.7846i	0.414533	−	0.717992i
$839$	48.0000			1.65714			0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000			1.65714			0.828572	+	0.559883i	$0.189154\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	7.50000	−	12.9904i	0.258467	−	0.447678i
$843$	7.00000	+	12.1244i	0.241093	+	0.417585i
$844$	−5.00000	−	8.66025i	−0.172107	−	0.298098i
$845$		0			0
$846$		0			0
$847$	−22.0000	−	19.0526i	−0.755929	−	0.654654i
$848$	6.00000			0.206041
$849$	8.00000	−	13.8564i	0.274559	−	0.475551i
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	17.5000	−	6.06218i	0.598838	−	0.207443i
$855$		0			0
$856$	16.5000	−	28.5788i	0.563958	−	0.976805i
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$		0			0
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	−0.452636	−	0.891695i	$-0.649516\pi$
$859$	16.0000	−	27.7128i	0.545913	−	0.945549i	0.998549	−	0.0538535i	$-0.0171504\pi$
$860$		0			0
$861$	−12.5000	+	4.33013i	−0.425999	+	0.147570i
$862$	32.0000			1.08992
$863$	−4.50000	+	7.79423i	−0.153182	+	0.265319i	−0.932395	−	0.361440i	$-0.882285\pi$
$863$	−4.50000	+	7.79423i	−0.153182	+	0.265319i	0.779214	+	0.626758i	$0.215619\pi$
$864$	−12.5000	−	21.6506i	−0.425259	−	0.736570i
$865$		0			0
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$	−13.0000			−0.441503
$868$	−4.00000	−	3.46410i	−0.135769	−	0.117579i
$869$		0			0
$870$		0			0
$871$	5.00000	+	8.66025i	0.169419	+	0.293442i
$872$	−7.50000	−	12.9904i	−0.253982	−	0.439910i
$873$	16.0000	−	27.7128i	0.541518	−	0.937937i
$874$	−18.0000			−0.608859
$875$		0			0
$876$	−6.00000			−0.202721
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	12.0000	+	20.7846i	0.404980	+	0.701447i
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$		0			0
$881$	−43.0000			−1.44871			−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000			−1.44871			−0.724353	+	0.689429i	$0.757862\pi$
$882$	2.00000	+	13.8564i	0.0673435	+	0.466569i
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$		0			0
$886$	−15.5000	−	26.8468i	−0.520733	−	0.901935i
$887$	21.5000	−	37.2391i	0.721899	−	1.25037i	−0.238338	−	0.971182i	$-0.576603\pi$
$887$	21.5000	−	37.2391i	0.721899	−	1.25037i	0.960238	−	0.279184i	$-0.0900640\pi$
$888$	24.0000			0.805387
$889$	−8.00000	+	41.5692i	−0.268311	+	1.39419i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	0.500000	−	0.866025i	0.0167225	−	0.0289642i
$895$		0			0
$896$	6.00000	+	5.19615i	0.200446	+	0.173591i
$897$	−6.00000			−0.200334
$898$	15.5000	−	26.8468i	0.517242	−	0.895889i
$899$	−7.00000	−	12.1244i	−0.233463	−	0.404370i
$900$		0			0
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$	17.5000	−	6.06218i	0.582364	−	0.201737i
$904$	18.0000			0.598671
$905$		0			0
$906$	7.00000	+	12.1244i	0.232559	+	0.402805i
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268820\pi$
$907$	−9.50000	−	16.4545i	−0.315442	−	0.546362i	−0.979531	+	0.201291i	$0.935486\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	3.00000	−	5.19615i	0.0993399	−	0.172062i
$913$		0			0
$914$	−16.0000	−	27.7128i	−0.529233	−	0.916658i
$915$		0			0
$916$	22.0000			0.726900
$917$	8.00000	+	6.92820i	0.264183	+	0.228789i
$918$	−10.0000			−0.330049
$919$	−17.0000	+	29.4449i	−0.560778	+	0.971296i	0.436650	+	0.899631i	$0.356165\pi$
$919$	−17.0000	+	29.4449i	−0.560778	+	0.971296i	−0.997429	+	0.0716652i	$0.977169\pi$
$920$		0			0
$921$	11.5000	+	19.9186i	0.378938	+	0.656340i
$922$	9.00000	−	15.5885i	0.296399	−	0.513378i
$923$	4.00000			0.131662
$924$		0			0
$925$		0			0
$926$	−1.50000	+	2.59808i	−0.0492931	+	0.0853781i
$927$	−7.00000	−	12.1244i	−0.229910	−	0.398216i
$928$	17.5000	+	30.3109i	0.574466	+	0.995004i
$929$	14.5000	−	25.1147i	0.475730	−	0.823988i	−0.523884	−	0.851790i	$-0.675517\pi$
$929$	14.5000	−	25.1147i	0.475730	−	0.823988i	0.999613	+	0.0278019i	$0.00885076\pi$
$930$		0			0
$931$	33.0000	−	25.9808i	1.08153	−	0.851485i
$932$	14.0000			0.458585
$933$	−15.0000	+	25.9808i	−0.491078	+	0.850572i
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$		0			0
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	−2.50000	+	12.9904i	−0.0816279	+	0.424151i
$939$	−24.0000			−0.783210
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$	−6.00000	−	10.3923i	−0.195491	−	0.338600i
$943$	−7.50000	+	12.9904i	−0.244234	+	0.423025i
$944$	−10.0000			−0.325472
$945$		0			0
$946$		0			0
$947$	−28.5000	+	49.3634i	−0.926126	+	1.60410i	−0.136385	+	0.990656i	$0.543548\pi$
$947$	−28.5000	+	49.3634i	−0.926126	+	1.60410i	−0.789741	+	0.613441i	$0.789785\pi$
$948$	−1.00000	−	1.73205i	−0.0324785	−	0.0562544i
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$		0			0
$951$	6.00000			0.194563
$952$	15.0000	−	5.19615i	0.486153	−	0.168408i
$953$	−60.0000			−1.94359			−0.971795	−	0.235826i	$-0.924220\pi$
$953$	−60.0000			−1.94359			−0.971795	+	0.235826i	$0.924220\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$		0			0
$956$	−9.00000	−	15.5885i	−0.291081	−	0.504167i
$957$		0			0
$958$	−42.0000			−1.35696
$959$		0			0
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−8.00000	−	13.8564i	−0.257930	−	0.446748i
$963$	−11.0000	−	19.0526i	−0.354470	−	0.613960i
$964$	−7.00000	+	12.1244i	−0.225455	+	0.390499i
$965$		0			0
$966$	−6.00000	−	5.19615i	−0.193047	−	0.167183i
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$	16.5000	−	28.5788i	0.530330	−	0.918559i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	16.0000	−	27.7128i	0.513464	−	0.889346i	−0.486414	−	0.873729i	$-0.661695\pi$
$971$	16.0000	−	27.7128i	0.513464	−	0.889346i	0.999878	−	0.0156178i	$-0.00497150\pi$
$972$	−16.0000			−0.513200
$973$	4.00000	−	20.7846i	0.128234	−	0.666324i
$974$	−12.0000			−0.384505
$975$		0			0
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	30.0000	+	51.9615i	0.959785	+	1.66240i	0.723017	+	0.690830i	$0.242755\pi$
$977$	30.0000	+	51.9615i	0.959785	+	1.66240i	0.236768	+	0.971566i	$0.423912\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	−13.0000	+	22.5167i	−0.414847	+	0.718536i
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$	−7.50000	−	12.9904i	−0.239091	−	0.414118i
$985$		0			0
$986$	14.0000			0.445851
$987$		0			0
$988$	12.0000			0.381771
$989$	10.5000	−	18.1865i	0.333881	−	0.578298i
$990$		0			0
$991$	25.0000	+	43.3013i	0.794151	+	1.37551i	0.923377	+	0.383895i	$0.125418\pi$
$991$	25.0000	+	43.3013i	0.794151	+	1.37551i	−0.129226	+	0.991615i	$0.541249\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$	6.00000			0.190404
$994$	4.00000	+	3.46410i	0.126872	+	0.109875i
$995$		0			0
$996$	5.50000	−	9.52628i	0.174274	−	0.301852i
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	8.00000	+	13.8564i	0.253236	+	0.438617i
$999$	20.0000	−	34.6410i	0.632772	−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.e.b.51.1		2
5.2	odd	4		35.2.j.a.9.2	yes	4
5.3	odd	4		35.2.j.a.9.1	yes	4
5.4	even	2		175.2.e.a.51.1		2
7.2	even	3		1225.2.a.d.1.1		1
7.4	even	3	inner	175.2.e.b.151.1		2
7.5	odd	6		1225.2.a.b.1.1		1
15.2	even	4		315.2.bf.a.289.1		4
15.8	even	4		315.2.bf.a.289.2		4
20.3	even	4		560.2.bw.b.289.1		4
20.7	even	4		560.2.bw.b.289.2		4
35.2	odd	12		245.2.b.c.99.1		2
35.3	even	12		245.2.j.c.214.2		4
35.4	even	6		175.2.e.a.151.1		2
35.9	even	6		1225.2.a.f.1.1		1
35.12	even	12		245.2.b.b.99.1		2
35.13	even	4		245.2.j.c.79.1		4
35.17	even	12		245.2.j.c.214.1		4
35.18	odd	12		35.2.j.a.4.2	yes	4
35.19	odd	6		1225.2.a.g.1.1		1
35.23	odd	12		245.2.b.c.99.2		2
35.27	even	4		245.2.j.c.79.2		4
35.32	odd	12		35.2.j.a.4.1	✓	4
35.33	even	12		245.2.b.b.99.2		2
105.2	even	12		2205.2.d.d.1324.2		2
105.23	even	12		2205.2.d.d.1324.1		2
105.32	even	12		315.2.bf.a.109.2		4
105.47	odd	12		2205.2.d.e.1324.2		2
105.53	even	12		315.2.bf.a.109.1		4
105.68	odd	12		2205.2.d.e.1324.1		2
140.67	even	12		560.2.bw.b.529.1		4
140.123	even	12		560.2.bw.b.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.j.a.4.1	✓	4	35.32	odd	12
35.2.j.a.4.2	yes	4	35.18	odd	12
35.2.j.a.9.1	yes	4	5.3	odd	4
35.2.j.a.9.2	yes	4	5.2	odd	4
175.2.e.a.51.1		2	5.4	even	2
175.2.e.a.151.1		2	35.4	even	6
175.2.e.b.51.1		2	1.1	even	1	trivial
175.2.e.b.151.1		2	7.4	even	3	inner
245.2.b.b.99.1		2	35.12	even	12
245.2.b.b.99.2		2	35.33	even	12
245.2.b.c.99.1		2	35.2	odd	12
245.2.b.c.99.2		2	35.23	odd	12
245.2.j.c.79.1		4	35.13	even	4
245.2.j.c.79.2		4	35.27	even	4
245.2.j.c.214.1		4	35.17	even	12
245.2.j.c.214.2		4	35.3	even	12
315.2.bf.a.109.1		4	105.53	even	12
315.2.bf.a.109.2		4	105.32	even	12
315.2.bf.a.289.1		4	15.2	even	4
315.2.bf.a.289.2		4	15.8	even	4
560.2.bw.b.289.1		4	20.3	even	4
560.2.bw.b.289.2		4	20.7	even	4
560.2.bw.b.529.1		4	140.67	even	12
560.2.bw.b.529.2		4	140.123	even	12
1225.2.a.b.1.1		1	7.5	odd	6
1225.2.a.d.1.1		1	7.2	even	3
1225.2.a.f.1.1		1	35.9	even	6
1225.2.a.g.1.1		1	35.19	odd	6
2205.2.d.d.1324.1		2	105.23	even	12
2205.2.d.d.1324.2		2	105.2	even	12
2205.2.d.e.1324.1		2	105.68	odd	12
2205.2.d.e.1324.2		2	105.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-2.50000 + 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(-1.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +7.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(2.50000 + 4.33013i) q^{32} +2.00000 q^{34} +2.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(3.00000 + 5.19615i) q^{38} +(1.00000 + 1.73205i) q^{39} +5.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} -7.00000 q^{43} +(1.50000 + 2.59808i) q^{46} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-2.50000 + 4.33013i) q^{54} +(1.50000 - 7.79423i) q^{56} +6.00000 q^{57} +(3.50000 - 6.06218i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-3.50000 + 6.06218i) q^{61} -2.00000 q^{62} +(-4.00000 - 3.46410i) q^{63} +7.00000 q^{64} +(-2.50000 - 4.33013i) q^{67} +(-1.00000 + 1.73205i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(3.00000 - 5.19615i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(4.00000 + 6.92820i) q^{74} -6.00000 q^{76} +2.00000 q^{78} +(1.00000 - 1.73205i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +11.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-3.50000 + 6.06218i) q^{86} +(-3.50000 - 6.06218i) q^{87} +(-4.50000 + 7.79423i) q^{89} +(-1.00000 + 5.19615i) q^{91} -3.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(2.50000 - 4.33013i) q^{96} +16.0000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} + q^{4} - 2 q^{6} + q^{7} + 6 q^{8} + 2 q^{9} + q^{12} - 4 q^{13} - 4 q^{14} + q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} - 5 q^{21} - 3 q^{23} - 3 q^{24} - 2 q^{26} - 10 q^{27} + 5 q^{28}+ \cdots - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^3 + q^4 - 2 * q^6 + q^7 + 6 * q^8 + 2 * q^9 + q^12 - 4 * q^13 - 4 * q^14 + q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 - 5 * q^21 - 3 * q^23 - 3 * q^24 - 2 * q^26 - 10 * q^27 + 5 * q^28 + 14 * q^29 - 2 * q^31 + 5 * q^32 + 4 * q^34 + 4 * q^36 - 8 * q^37 + 6 * q^38 + 2 * q^39 + 10 * q^41 - q^42 - 14 * q^43 + 3 * q^46 - 2 * q^48 - 13 * q^49 + 2 * q^51 - 2 * q^52 + 6 * q^53 - 5 * q^54 + 3 * q^56 + 12 * q^57 + 7 * q^58 - 10 * q^59 - 7 * q^61 - 4 * q^62 - 8 * q^63 + 14 * q^64 - 5 * q^67 - 2 * q^68 + 6 * q^69 - 4 * q^71 + 6 * q^72 - 6 * q^73 + 8 * q^74 - 12 * q^76 + 4 * q^78 + 2 * q^79 - q^81 + 5 * q^82 + 22 * q^83 - 4 * q^84 - 7 * q^86 - 7 * q^87 - 9 * q^89 - 2 * q^91 - 6 * q^92 - 2 * q^93 + 5 * q^96 + 32 * q^97 - 11 * q^98

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