LMFDB - Embedded newform 234.2.f.a.133.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(133,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.133"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2] 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:	$1.86849940730$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	234.133
Dual form			234.2.f.a.139.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(-1.50000 - 2.59808i) q^{10} +1.73205i q^{12} +(1.00000 - 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-4.50000 + 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(-4.50000 + 7.79423i) q^{23} -1.73205i q^{24} +(-2.00000 + 3.46410i) q^{25} +(-1.00000 + 3.46410i) q^{26} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} +6.00000 q^{29} +(4.50000 - 2.59808i) q^{30} +(0.500000 + 0.866025i) q^{31} -1.00000 q^{32} +(1.50000 - 2.59808i) q^{34} +(-1.50000 + 2.59808i) q^{35} -3.00000 q^{36} +(-2.50000 - 4.33013i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(6.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(4.50000 - 7.79423i) q^{41} +(1.50000 - 0.866025i) q^{42} +(3.50000 + 6.06218i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(4.50000 - 7.79423i) q^{46} +(1.50000 - 2.59808i) q^{47} +1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(1.00000 - 3.46410i) q^{52} +6.00000 q^{53} +5.19615i q^{54} +(-0.500000 - 0.866025i) q^{56} +(1.50000 + 0.866025i) q^{57} -6.00000 q^{58} -12.0000 q^{59} +(-4.50000 + 2.59808i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-0.500000 - 0.866025i) q^{62} +(-1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(10.5000 - 2.59808i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-13.5000 - 7.79423i) q^{69} +(1.50000 - 2.59808i) q^{70} +(7.50000 - 12.9904i) q^{71} +3.00000 q^{72} +14.0000 q^{73} +(2.50000 + 4.33013i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-6.00000 - 1.73205i) q^{78} +(-2.50000 + 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +9.00000 q^{81} +(-4.50000 + 7.79423i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-1.50000 + 0.866025i) q^{84} -9.00000 q^{85} +(-3.50000 - 6.06218i) q^{86} +10.3923i q^{87} +(-7.50000 - 12.9904i) q^{89} +(4.50000 + 7.79423i) q^{90} +(3.50000 - 0.866025i) q^{91} +(-4.50000 + 7.79423i) q^{92} +(-1.50000 + 0.866025i) q^{93} +(-1.50000 + 2.59808i) q^{94} +3.00000 q^{95} -1.73205i q^{96} +(6.50000 + 11.2583i) q^{97} +(-3.00000 + 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 3 q^{5} + q^{7} - 2 q^{8} - 6 q^{9} - 3 q^{10} + 2 q^{13} - q^{14} - 9 q^{15} + 2 q^{16} - 3 q^{17} + 6 q^{18} + q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{23} - 4 q^{25} - 2 q^{26}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 3 * q^5 + q^7 - 2 * q^8 - 6 * q^9 - 3 * q^10 + 2 * q^13 - q^14 - 9 * q^15 + 2 * q^16 - 3 * q^17 + 6 * q^18 + q^19 + 3 * q^20 - 3 * q^21 - 9 * q^23 - 4 * q^25 - 2 * q^26 + q^28 + 12 * q^29 + 9 * q^30 + q^31 - 2 * q^32 + 3 * q^34 - 3 * q^35 - 6 * q^36 - 5 * q^37 - q^38 + 12 * q^39 - 3 * q^40 + 9 * q^41 + 3 * q^42 + 7 * q^43 - 9 * q^45 + 9 * q^46 + 3 * q^47 + 6 * q^49 + 4 * q^50 - 9 * q^51 + 2 * q^52 + 12 * q^53 - q^56 + 3 * q^57 - 12 * q^58 - 24 * q^59 - 9 * q^60 + 7 * q^61 - q^62 - 3 * q^63 + 2 * q^64 + 21 * q^65 + q^67 - 3 * q^68 - 27 * q^69 + 3 * q^70 + 15 * q^71 + 6 * q^72 + 28 * q^73 + 5 * q^74 - 12 * q^75 + q^76 - 12 * q^78 - 5 * q^79 + 3 * q^80 + 18 * q^81 - 9 * q^82 - 3 * q^83 - 3 * q^84 - 18 * q^85 - 7 * q^86 - 15 * q^89 + 9 * q^90 + 7 * q^91 - 9 * q^92 - 3 * q^93 - 3 * q^94 + 6 * q^95 + 13 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	1.00000			0.500000
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		−	1.73205i		−	0.707107i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000			−0.353553
$9$	−3.00000			−1.00000
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$			1.73205i			0.500000i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	−4.50000	+	2.59808i	−1.16190	+	0.670820i
$16$	1.00000			0.250000
$17$	−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	$0.285189\pi$
$18$	3.00000			0.707107
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$	−1.50000	+	0.866025i	−0.327327	+	0.188982i
$22$		0			0
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.169701	+	0.985496i	$0.554280\pi$
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.768613	+	0.639713i	$0.779053\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$		−	5.19615i		−	1.00000i
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	4.50000	−	2.59808i	0.821584	−	0.474342i
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	−3.00000			−0.500000
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	0.584002	−	0.811752i	$-0.301486\pi$
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	−0.994999	+	0.0998840i	$0.968153\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	6.00000	+	1.73205i	0.960769	+	0.277350i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$	1.50000	−	0.866025i	0.231455	−	0.133631i
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	0.999223	+	0.0394140i	$0.0125491\pi$
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	−0.465478	+	0.885059i	$0.654118\pi$
$44$		0			0
$45$	−4.50000	−	7.79423i	−0.670820	−	1.16190i
$46$	4.50000	−	7.79423i	0.663489	−	1.14920i
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$			1.73205i			0.250000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$			5.19615i			0.707107i
$55$		0			0
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	1.50000	+	0.866025i	0.198680	+	0.114708i
$58$	−6.00000			−0.787839
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$	−4.50000	+	2.59808i	−0.580948	+	0.335410i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	−0.500000	−	0.866025i	−0.0635001	−	0.109985i
$63$	−1.50000	−	2.59808i	−0.188982	−	0.327327i
$64$	1.00000			0.125000
$65$	10.5000	−	2.59808i	1.30236	−	0.322252i
$66$		0			0
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	−0.833866	−	0.551967i	$-0.813877\pi$
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	0.894951	+	0.446165i	$0.147211\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	−13.5000	−	7.79423i	−1.62521	−	0.938315i
$70$	1.50000	−	2.59808i	0.179284	−	0.310530i
$71$	7.50000	−	12.9904i	0.890086	−	1.54167i	0.0503155	−	0.998733i	$-0.483977\pi$
$71$	7.50000	−	12.9904i	0.890086	−	1.54167i	0.839771	−	0.542941i	$-0.182689\pi$
$72$	3.00000			0.353553
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$	−6.00000	−	3.46410i	−0.692820	−	0.400000i
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$		0			0
$78$	−6.00000	−	1.73205i	−0.679366	−	0.196116i
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	9.00000			1.00000
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$	−1.50000	+	0.866025i	−0.163663	+	0.0944911i
$85$	−9.00000			−0.976187
$86$	−3.50000	−	6.06218i	−0.377415	−	0.653701i
$87$			10.3923i			1.11417i
$88$		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	$-0.459195\pi$
$90$	4.50000	+	7.79423i	0.474342	+	0.821584i
$91$	3.50000	−	0.866025i	0.366900	−	0.0907841i
$92$	−4.50000	+	7.79423i	−0.469157	+	0.812605i
$93$	−1.50000	+	0.866025i	−0.155543	+	0.0898027i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	3.00000			0.307794
$96$		−	1.73205i		−	0.176777i
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	0.980622	+	0.195911i	$0.0627665\pi$
$97$	6.50000	+	11.2583i	0.659975	+	1.14311i	−0.320647	+	0.947199i	$0.603900\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−1.00000	+	3.46410i	−0.0980581	+	0.339683i
$105$	−4.50000	−	2.59808i	−0.439155	−	0.253546i
$106$	−6.00000			−0.582772
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		−	5.19615i		−	0.500000i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	7.50000	−	4.33013i	0.711868	−	0.410997i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	−1.50000	−	0.866025i	−0.140488	−	0.0811107i
$115$	−27.0000			−2.51776
$116$	6.00000			0.557086
$117$	−3.00000	+	10.3923i	−0.277350	+	0.960769i
$118$	12.0000			1.10469
$119$	−3.00000			−0.275010
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	−11.0000			−1.00000
$122$	−3.50000	−	6.06218i	−0.316875	−	0.548844i
$123$	13.5000	+	7.79423i	1.21725	+	0.702782i
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$	3.00000			0.268328
$126$	1.50000	+	2.59808i	0.133631	+	0.231455i
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	0.511859	−	0.859069i	$-0.328957\pi$
$127$	−5.50000	−	9.52628i	−0.488046	−	0.845321i	−0.999905	+	0.0137486i	$0.995624\pi$
$128$	−1.00000			−0.0883883
$129$	−10.5000	+	6.06218i	−0.924473	+	0.533745i
$130$	−10.5000	+	2.59808i	−0.920911	+	0.227866i
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$		0			0
$133$	1.00000			0.0867110
$134$	−0.500000	+	0.866025i	−0.0431934	+	0.0748132i
$135$	13.5000	−	7.79423i	1.16190	−	0.670820i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	13.5000	+	7.79423i	1.14920	+	0.663489i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−1.50000	+	2.59808i	−0.126773	+	0.219578i
$141$	4.50000	+	2.59808i	0.378968	+	0.218797i
$142$	−7.50000	+	12.9904i	−0.629386	+	1.09013i
$143$		0			0
$144$	−3.00000			−0.250000
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$	−14.0000			−1.15865
$147$	9.00000	+	5.19615i	0.742307	+	0.428571i
$148$	−2.50000	−	4.33013i	−0.205499	−	0.355934i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	6.00000	+	3.46410i	0.489898	+	0.282843i
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	0.935857	−	0.352381i	$-0.114628\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$		0			0
$155$	−1.50000	+	2.59808i	−0.120483	+	0.208683i
$156$	6.00000	+	1.73205i	0.480384	+	0.138675i
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	−0.975470	−	0.220131i	$-0.929352\pi$
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	0.297097	−	0.954847i	$-0.403982\pi$
$158$	2.50000	−	4.33013i	0.198889	−	0.344486i
$159$			10.3923i			0.824163i
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$	−9.00000			−0.709299
$162$	−9.00000			−0.707107
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	1.50000	−	2.59808i	0.116423	−	0.201650i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$	1.50000	−	0.866025i	0.115728	−	0.0668153i
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	9.00000			0.690268
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$	3.50000	+	6.06218i	0.266872	+	0.462237i
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	−0.920722	−	0.390218i	$-0.872399\pi$
$173$	−10.5000	−	18.1865i	−0.798300	−	1.38270i	0.122422	−	0.992478i	$-0.460934\pi$
$174$		−	10.3923i		−	0.787839i
$175$	−4.00000			−0.302372
$176$		0			0
$177$		−	20.7846i		−	1.56227i
$178$	7.50000	+	12.9904i	0.562149	+	0.973670i
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$	−4.50000	−	7.79423i	−0.335410	−	0.580948i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−3.50000	+	0.866025i	−0.259437	+	0.0641941i
$183$	−10.5000	+	6.06218i	−0.776182	+	0.448129i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	7.50000	−	12.9904i	0.551411	−	0.955072i
$186$	1.50000	−	0.866025i	0.109985	−	0.0635001i
$187$		0			0
$188$	1.50000	−	2.59808i	0.109399	−	0.189484i
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$	−3.00000			−0.217643
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$			1.73205i			0.125000i
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	0.0719816	+	0.997406i	$0.477068\pi$
$193$	−11.5000	+	19.9186i	−0.827788	+	1.43377i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−6.50000	−	11.2583i	−0.466673	−	0.808301i
$195$	4.50000	+	18.1865i	0.322252	+	1.30236i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−10.5000	−	18.1865i	−0.748094	−	1.29574i	−0.948735	−	0.316072i	$-0.897636\pi$
$197$	−10.5000	−	18.1865i	−0.748094	−	1.29574i	0.200641	−	0.979665i	$-0.435697\pi$
$198$		0			0
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	−0.303486	−	0.952836i	$-0.598151\pi$
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	0.976923	−	0.213591i	$-0.0685161\pi$
$200$	2.00000	−	3.46410i	0.141421	−	0.244949i
$201$	1.50000	+	0.866025i	0.105802	+	0.0610847i
$202$	6.00000			0.422159
$203$	3.00000	+	5.19615i	0.210559	+	0.364698i
$204$	−4.50000	−	2.59808i	−0.315063	−	0.181902i
$205$	27.0000			1.88576
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	13.5000	−	23.3827i	0.938315	−	1.62521i
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$		0			0
$210$	4.50000	+	2.59808i	0.310530	+	0.179284i
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$	6.00000			0.412082
$213$	22.5000	+	12.9904i	1.54167	+	0.890086i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	−10.5000	+	18.1865i	−0.716094	+	1.24031i
$216$			5.19615i			0.353553i
$217$	−0.500000	+	0.866025i	−0.0339422	+	0.0587896i
$218$	−2.00000			−0.135457
$219$			24.2487i			1.63858i
$220$		0			0
$221$	7.50000	+	7.79423i	0.504505	+	0.524297i
$222$	−7.50000	+	4.33013i	−0.503367	+	0.290619i
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	−6.00000			−0.399114
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$	1.50000	+	0.866025i	0.0993399	+	0.0573539i
$229$	−2.50000	−	4.33013i	−0.165205	−	0.286143i	0.771523	−	0.636201i	$-0.219495\pi$
$229$	−2.50000	−	4.33013i	−0.165205	−	0.286143i	−0.936728	+	0.350058i	$0.886162\pi$
$230$	27.0000			1.78033
$231$		0			0
$232$	−6.00000			−0.393919
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	3.00000	−	10.3923i	0.196116	−	0.679366i
$235$	9.00000			0.587095
$236$	−12.0000			−0.781133
$237$	−7.50000	−	4.33013i	−0.487177	−	0.281272i
$238$	3.00000			0.194461
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$	−4.50000	+	2.59808i	−0.290474	+	0.167705i
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	11.0000			0.707107
$243$			15.5885i			1.00000i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$	18.0000			1.14998
$246$	−13.5000	−	7.79423i	−0.860729	−	0.496942i
$247$	−2.50000	−	2.59808i	−0.159071	−	0.165312i
$248$	−0.500000	−	0.866025i	−0.0317500	−	0.0549927i
$249$	−4.50000	−	2.59808i	−0.285176	−	0.164646i
$250$	−3.00000			−0.189737
$251$	−13.5000	+	23.3827i	−0.852112	+	1.47590i	0.0271858	+	0.999630i	$0.491345\pi$
$251$	−13.5000	+	23.3827i	−0.852112	+	1.47590i	−0.879298	+	0.476272i	$0.841988\pi$
$252$	−1.50000	−	2.59808i	−0.0944911	−	0.163663i
$253$		0			0
$254$	5.50000	+	9.52628i	0.345101	+	0.597732i
$255$		−	15.5885i		−	0.976187i
$256$	1.00000			0.0625000
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$	10.5000	−	6.06218i	0.653701	−	0.377415i
$259$	2.50000	−	4.33013i	0.155342	−	0.269061i
$260$	10.5000	−	2.59808i	0.651182	−	0.161126i
$261$	−18.0000			−1.11417
$262$	−7.50000	−	12.9904i	−0.463352	−	0.802548i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	9.00000	+	15.5885i	0.552866	+	0.957591i
$266$	−1.00000			−0.0613139
$267$	22.5000	−	12.9904i	1.37698	−	0.794998i
$268$	0.500000	−	0.866025i	0.0305424	−	0.0529009i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$	−13.5000	+	7.79423i	−0.821584	+	0.474342i
$271$	−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	$0.941766\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	1.50000	+	6.06218i	0.0907841	+	0.366900i
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$		0			0
$276$	−13.5000	−	7.79423i	−0.812605	−	0.469157i
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$	4.00000			0.239904
$279$	−1.50000	−	2.59808i	−0.0898027	−	0.155543i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−1.50000	+	2.59808i	−0.0894825	+	0.154988i	−0.907293	−	0.420500i	$-0.861855\pi$
$281$	−1.50000	+	2.59808i	−0.0894825	+	0.154988i	0.817810	+	0.575488i	$0.195188\pi$
$282$	−4.50000	−	2.59808i	−0.267971	−	0.154713i
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	−0.850782	−	0.525519i	$-0.823871\pi$
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	0.880504	+	0.474039i	$0.157204\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$			5.19615i			0.307794i
$286$		0			0
$287$	9.00000			0.531253
$288$	3.00000			0.176777
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−9.00000	−	15.5885i	−0.528498	−	0.915386i
$291$	−19.5000	+	11.2583i	−1.14311	+	0.659975i
$292$	14.0000			0.819288
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	−9.00000	−	5.19615i	−0.524891	−	0.303046i
$295$	−18.0000	−	31.1769i	−1.04800	−	1.81519i
$296$	2.50000	+	4.33013i	0.145310	+	0.251684i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	22.5000	+	23.3827i	1.30121	+	1.35226i
$300$	−6.00000	−	3.46410i	−0.346410	−	0.200000i
$301$	−3.50000	+	6.06218i	−0.201737	+	0.349418i
$302$	−9.50000	+	16.4545i	−0.546664	+	0.946849i
$303$		−	10.3923i		−	0.597022i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	−10.5000	+	18.1865i	−0.601228	+	1.04136i
$306$	−4.50000	+	7.79423i	−0.257248	+	0.445566i
$307$	−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
$309$	−19.5000	+	11.2583i	−1.10932	+	0.640464i
$310$	1.50000	−	2.59808i	0.0851943	−	0.147561i
$311$	−13.5000	−	23.3827i	−0.765515	−	1.32591i	−0.939974	−	0.341246i	$-0.889151\pi$
$311$	−13.5000	−	23.3827i	−0.765515	−	1.32591i	0.174459	−	0.984664i	$-0.444182\pi$
$312$	−6.00000	−	1.73205i	−0.339683	−	0.0980581i
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	8.50000	+	14.7224i	0.479683	+	0.830835i
$315$	4.50000	−	7.79423i	0.253546	−	0.439155i
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	−0.964281	−	0.264883i	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$		−	10.3923i		−	0.582772i
$319$		0			0
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$	9.00000			0.501550
$323$	1.50000	+	2.59808i	0.0834622	+	0.144561i
$324$	9.00000			0.500000
$325$	10.0000	+	10.3923i	0.554700	+	0.576461i
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$			3.46410i			0.191565i
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$	3.00000			0.165395
$330$		0			0
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	0.789104	−	0.614260i	$-0.210545\pi$
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	−0.926516	+	0.376254i	$0.877212\pi$
$332$	−1.50000	+	2.59808i	−0.0823232	+	0.142588i
$333$	7.50000	+	12.9904i	0.410997	+	0.711868i
$334$	4.50000	−	7.79423i	0.246229	−	0.426481i
$335$	3.00000			0.163908
$336$	−1.50000	+	0.866025i	−0.0818317	+	0.0472456i
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$			10.3923i			0.564433i
$340$	−9.00000			−0.488094
$341$		0			0
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$	13.0000			0.701934
$344$	−3.50000	−	6.06218i	−0.188707	−	0.326851i
$345$		−	46.7654i		−	2.51776i
$346$	10.5000	+	18.1865i	0.564483	+	0.977714i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$			10.3923i			0.557086i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	4.00000			0.213809
$351$	−18.0000	−	5.19615i	−0.960769	−	0.277350i
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$			20.7846i			1.10469i
$355$	45.0000			2.38835
$356$	−7.50000	−	12.9904i	−0.397499	−	0.688489i
$357$		−	5.19615i		−	0.275010i
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	4.50000	+	7.79423i	0.237171	+	0.410792i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	22.0000			1.15629
$363$		−	19.0526i		−	1.00000i
$364$	3.50000	−	0.866025i	0.183450	−	0.0453921i
$365$	21.0000	+	36.3731i	1.09919	+	1.90385i
$366$	10.5000	−	6.06218i	0.548844	−	0.316875i
$367$	−16.0000			−0.835193			−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000			−0.835193			−0.417597	+	0.908633i	$0.637127\pi$
$368$	−4.50000	+	7.79423i	−0.234579	+	0.406302i
$369$	−13.5000	+	23.3827i	−0.702782	+	1.21725i
$370$	−7.50000	+	12.9904i	−0.389906	+	0.675338i
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$	−1.50000	+	0.866025i	−0.0777714	+	0.0449013i
$373$	14.0000			0.724893			0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000			0.724893			0.362446	+	0.932005i	$0.381942\pi$
$374$		0			0
$375$			5.19615i			0.268328i
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	6.00000	−	20.7846i	0.309016	−	1.07046i
$378$	−4.50000	+	2.59808i	−0.231455	+	0.133631i
$379$	−14.5000	−	25.1147i	−0.744815	−	1.29006i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−14.5000	−	25.1147i	−0.744815	−	1.29006i	0.205466	−	0.978664i	$-0.434129\pi$
$380$	3.00000			0.153897
$381$	16.5000	−	9.52628i	0.845321	−	0.488046i
$382$	1.50000	+	2.59808i	0.0767467	+	0.132929i
$383$	−36.0000			−1.83951			−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000			−1.83951			−0.919757	+	0.392488i	$0.871614\pi$
$384$		−	1.73205i		−	0.0883883i
$385$		0			0
$386$	11.5000	−	19.9186i	0.585335	−	1.01383i
$387$	−10.5000	−	18.1865i	−0.533745	−	0.924473i
$388$	6.50000	+	11.2583i	0.329988	+	0.571555i
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	−0.957263	−	0.289220i	$-0.906604\pi$
$389$	−4.50000	+	7.79423i	−0.228159	+	0.395183i	0.729103	+	0.684403i	$0.239937\pi$
$390$	−4.50000	−	18.1865i	−0.227866	−	0.920911i
$391$	−13.5000	−	23.3827i	−0.682724	−	1.18251i
$392$	−3.00000	+	5.19615i	−0.151523	+	0.262445i
$393$	−22.5000	+	12.9904i	−1.13497	+	0.655278i
$394$	10.5000	+	18.1865i	0.528982	+	0.916224i
$395$	−15.0000			−0.754732
$396$		0			0
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	−9.50000	+	16.4545i	−0.476192	+	0.824789i
$399$			1.73205i			0.0867110i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$	−1.50000	−	0.866025i	−0.0748132	−	0.0431934i
$403$	3.50000	−	0.866025i	0.174347	−	0.0431398i
$404$	−6.00000			−0.298511
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$	−3.00000	−	5.19615i	−0.148888	−	0.257881i
$407$		0			0
$408$	4.50000	+	2.59808i	0.222783	+	0.128624i
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	−27.0000			−1.33343
$411$	4.50000	−	2.59808i	0.221969	−	0.128154i
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	−6.00000	−	10.3923i	−0.295241	−	0.511372i
$414$	−13.5000	+	23.3827i	−0.663489	+	1.14920i
$415$	−9.00000			−0.441793
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$		−	6.92820i		−	0.339276i
$418$		0			0
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	−0.486928	−	0.873442i	$-0.661883\pi$
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	0.999887	−	0.0150285i	$-0.00478389\pi$
$420$	−4.50000	−	2.59808i	−0.219578	−	0.126773i
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	0.999109	+	0.0422075i	$0.0134391\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−6.00000			−0.291386
$425$	−6.00000	−	10.3923i	−0.291043	−	0.504101i
$426$	−22.5000	−	12.9904i	−1.09013	−	0.629386i
$427$	−3.50000	+	6.06218i	−0.169377	+	0.293369i
$428$	1.50000	+	2.59808i	0.0725052	+	0.125583i
$429$		0			0
$430$	10.5000	−	18.1865i	0.506355	−	0.877033i
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	0.953815	−	0.300395i	$-0.0971186\pi$
$431$	4.50000	+	7.79423i	0.216757	+	0.375435i	−0.737057	+	0.675830i	$0.763785\pi$
$432$		−	5.19615i		−	0.250000i
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	−0.967383	−	0.253317i	$-0.918479\pi$
$433$	−5.50000	+	9.52628i	−0.264313	+	0.457804i	0.703070	+	0.711120i	$0.251812\pi$
$434$	0.500000	−	0.866025i	0.0240008	−	0.0415705i
$435$	−27.0000	+	15.5885i	−1.29455	+	0.747409i
$436$	2.00000			0.0957826
$437$	4.50000	+	7.79423i	0.215264	+	0.372849i
$438$		−	24.2487i		−	1.15865i
$439$	32.0000			1.52728			0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000			1.52728			0.763638	+	0.645644i	$0.223411\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$	−7.50000	−	7.79423i	−0.356739	−	0.370734i
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$	7.50000	−	4.33013i	0.355934	−	0.205499i
$445$	22.5000	−	38.9711i	1.06660	−	1.84741i
$446$	−8.00000			−0.378811
$447$			10.3923i			0.491539i
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	−0.740087	−	0.672511i	$-0.765216\pi$
$449$	4.50000	−	7.79423i	0.212368	−	0.367832i	0.952455	+	0.304679i	$0.0985491\pi$
$450$	−6.00000	+	10.3923i	−0.282843	+	0.489898i
$451$		0			0
$452$	6.00000			0.282216
$453$	28.5000	+	16.4545i	1.33905	+	0.773099i
$454$	4.50000	+	7.79423i	0.211195	+	0.365801i
$455$	7.50000	+	7.79423i	0.351605	+	0.365399i
$456$	−1.50000	−	0.866025i	−0.0702439	−	0.0405554i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	2.50000	+	4.33013i	0.116817	+	0.202334i
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$	−27.0000			−1.25888
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	0.987801	+	0.155719i	$0.0497696\pi$
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	−0.359044	+	0.933321i	$0.616897\pi$
$462$		0			0
$463$	−5.50000	−	9.52628i	−0.255607	−	0.442724i	0.709453	−	0.704752i	$-0.248942\pi$
$463$	−5.50000	−	9.52628i	−0.255607	−	0.442724i	−0.965060	+	0.262029i	$0.915609\pi$
$464$	6.00000			0.278543
$465$	−4.50000	−	2.59808i	−0.208683	−	0.120483i
$466$	−6.00000			−0.277945
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$	−3.00000	+	10.3923i	−0.138675	+	0.480384i
$469$	1.00000			0.0461757
$470$	−9.00000			−0.415139
$471$	25.5000	−	14.7224i	1.17498	−	0.678374i
$472$	12.0000			0.552345
$473$		0			0
$474$	7.50000	+	4.33013i	0.344486	+	0.198889i
$475$	2.00000	+	3.46410i	0.0917663	+	0.158944i
$476$	−3.00000			−0.137505
$477$	−18.0000			−0.824163
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	4.50000	−	2.59808i	0.205396	−	0.118585i
$481$	−17.5000	+	4.33013i	−0.797931	+	0.197437i
$482$	−12.5000	−	21.6506i	−0.569359	−	0.986159i
$483$		−	15.5885i		−	0.709299i
$484$	−11.0000			−0.500000
$485$	−19.5000	+	33.7750i	−0.885449	+	1.53364i
$486$		−	15.5885i		−	0.707107i
$487$	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	$0.0250088\pi$
$488$	−3.50000	−	6.06218i	−0.158438	−	0.274422i
$489$	−16.5000	−	9.52628i	−0.746156	−	0.430793i
$490$	−18.0000			−0.813157
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$	13.5000	+	7.79423i	0.608627	+	0.351391i
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	2.50000	+	2.59808i	0.112480	+	0.116893i
$495$		0			0
$496$	0.500000	+	0.866025i	0.0224507	+	0.0388857i
$497$	15.0000			0.672842
$498$	4.50000	+	2.59808i	0.201650	+	0.116423i
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	0.804627	−	0.593780i	$-0.202365\pi$
$499$	−2.50000	−	4.33013i	−0.111915	−	0.193843i	−0.916542	+	0.399937i	$0.869032\pi$
$500$	3.00000			0.134164
$501$	−13.5000	−	7.79423i	−0.603136	−	0.348220i
$502$	13.5000	−	23.3827i	0.602534	−	1.04362i
$503$	19.5000	−	33.7750i	0.869462	−	1.50595i	0.00691465	−	0.999976i	$-0.497799\pi$
$503$	19.5000	−	33.7750i	0.869462	−	1.50595i	0.862547	−	0.505976i	$-0.168868\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−9.00000	−	15.5885i	−0.400495	−	0.693677i
$506$		0			0
$507$	12.0000	−	19.0526i	0.532939	−	0.846154i
$508$	−5.50000	−	9.52628i	−0.244023	−	0.422660i
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	−0.00339621	−	0.999994i	$-0.501081\pi$
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	0.867719	−	0.497056i	$-0.165586\pi$
$510$			15.5885i			0.690268i
$511$	7.00000	+	12.1244i	0.309662	+	0.536350i
$512$	−1.00000			−0.0441942
$513$	−4.50000	−	2.59808i	−0.198680	−	0.114708i
$514$	7.50000	−	12.9904i	0.330811	−	0.572981i
$515$	−19.5000	+	33.7750i	−0.859273	+	1.48830i
$516$	−10.5000	+	6.06218i	−0.462237	+	0.266872i
$517$		0			0
$518$	−2.50000	+	4.33013i	−0.109844	+	0.190255i
$519$	31.5000	−	18.1865i	1.38270	−	0.798300i
$520$	−10.5000	+	2.59808i	−0.460455	+	0.113933i
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	18.0000			0.787839
$523$	21.5000	+	37.2391i	0.940129	+	1.62835i	0.765222	+	0.643767i	$0.222629\pi$
$523$	21.5000	+	37.2391i	0.940129	+	1.62835i	0.174908	+	0.984585i	$0.444037\pi$
$524$	7.50000	+	12.9904i	0.327639	+	0.567487i
$525$		−	6.92820i		−	0.302372i
$526$		0			0
$527$	−3.00000			−0.130682
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$	36.0000			1.56227
$532$	1.00000			0.0433555
$533$	−22.5000	−	23.3827i	−0.974583	−	1.01282i
$534$	−22.5000	+	12.9904i	−0.973670	+	0.562149i
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$	−0.500000	+	0.866025i	−0.0215967	+	0.0374066i
$537$	13.5000	−	7.79423i	0.582568	−	0.336346i
$538$	10.5000	−	18.1865i	0.452687	−	0.784077i
$539$		0			0
$540$	13.5000	−	7.79423i	0.580948	−	0.335410i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	5.50000	+	9.52628i	0.236245	+	0.409189i
$543$		−	38.1051i		−	1.63525i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	3.00000	+	5.19615i	0.128506	+	0.222579i
$546$	−1.50000	−	6.06218i	−0.0641941	−	0.259437i
$547$	12.5000	−	21.6506i	0.534461	−	0.925714i	−0.464728	−	0.885454i	$-0.653848\pi$
$547$	12.5000	−	21.6506i	0.534461	−	0.925714i	0.999189	−	0.0402607i	$-0.0128188\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$	−10.5000	−	18.1865i	−0.448129	−	0.776182i
$550$		0			0
$551$	3.00000	−	5.19615i	0.127804	−	0.221364i
$552$	13.5000	+	7.79423i	0.574598	+	0.331744i
$553$	−5.00000			−0.212622
$554$	8.50000	+	14.7224i	0.361130	+	0.625496i
$555$	22.5000	+	12.9904i	0.955072	+	0.551411i
$556$	−4.00000			−0.169638
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$	1.50000	+	2.59808i	0.0635001	+	0.109985i
$559$	24.5000	−	6.06218i	1.03624	−	0.256403i
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$		0			0
$562$	1.50000	−	2.59808i	0.0632737	−	0.109593i
$563$	−36.0000			−1.51722			−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000			−1.51722			−0.758610	+	0.651546i	$0.774121\pi$
$564$	4.50000	+	2.59808i	0.189484	+	0.109399i
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$	−0.500000	+	0.866025i	−0.0210166	+	0.0364018i
$567$	4.50000	+	7.79423i	0.188982	+	0.327327i
$568$	−7.50000	+	12.9904i	−0.314693	+	0.545064i
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		−	5.19615i		−	0.217643i
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365228\pi$
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$572$		0			0
$573$	4.50000	−	2.59808i	0.187990	−	0.108536i
$574$	−9.00000			−0.375653
$575$	−18.0000	−	31.1769i	−0.750652	−	1.30017i
$576$	−3.00000			−0.125000
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−34.5000	−	19.9186i	−1.43377	−	0.827788i
$580$	9.00000	+	15.5885i	0.373705	+	0.647275i
$581$	−3.00000			−0.124461
$582$	19.5000	−	11.2583i	0.808301	−	0.466673i
$583$		0			0
$584$	−14.0000			−0.579324
$585$	−31.5000	+	7.79423i	−1.30236	+	0.322252i
$586$	6.00000			0.247858
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	9.00000	+	5.19615i	0.371154	+	0.214286i
$589$	1.00000			0.0412043
$590$	18.0000	+	31.1769i	0.741048	+	1.28353i
$591$	31.5000	−	18.1865i	1.29574	−	0.748094i
$592$	−2.50000	−	4.33013i	−0.102749	−	0.177967i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	−4.50000	−	7.79423i	−0.184482	−	0.319532i
$596$	6.00000			0.245770
$597$	28.5000	+	16.4545i	1.16643	+	0.673437i
$598$	−22.5000	−	23.3827i	−0.920093	−	0.956189i
$599$	16.5000	+	28.5788i	0.674172	+	1.16770i	0.976710	+	0.214563i	$0.0688326\pi$
$599$	16.5000	+	28.5788i	0.674172	+	1.16770i	−0.302539	+	0.953137i	$0.597834\pi$
$600$	6.00000	+	3.46410i	0.244949	+	0.141421i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	3.50000	−	6.06218i	0.142649	−	0.247076i
$603$	−1.50000	+	2.59808i	−0.0610847	+	0.105802i
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$	−16.5000	−	28.5788i	−0.670820	−	1.16190i
$606$			10.3923i			0.422159i
$607$	8.00000			0.324710			0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000			0.324710			0.162355	+	0.986732i	$0.448091\pi$
$608$	−0.500000	+	0.866025i	−0.0202777	+	0.0351220i
$609$	−9.00000	+	5.19615i	−0.364698	+	0.210559i
$610$	10.5000	−	18.1865i	0.425133	−	0.736351i
$611$	−7.50000	−	7.79423i	−0.303418	−	0.315321i
$612$	4.50000	−	7.79423i	0.181902	−	0.315063i
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	28.0000			1.12999
$615$			46.7654i			1.88576i
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	19.5000	−	11.2583i	0.784405	−	0.452876i
$619$	−17.5000	+	30.3109i	−0.703384	+	1.21830i	0.263887	+	0.964554i	$0.414995\pi$
$619$	−17.5000	+	30.3109i	−0.703384	+	1.21830i	−0.967271	+	0.253744i	$0.918338\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$	40.5000	+	23.3827i	1.62521	+	0.938315i
$622$	13.5000	+	23.3827i	0.541301	+	0.937560i
$623$	7.50000	−	12.9904i	0.300481	−	0.520449i
$624$	6.00000	+	1.73205i	0.240192	+	0.0693375i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$		0			0
$628$	−8.50000	−	14.7224i	−0.339187	−	0.587489i
$629$	15.0000			0.598089
$630$	−4.50000	+	7.79423i	−0.179284	+	0.310530i
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	0.418559	+	0.908190i	$0.362535\pi$
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	−0.995795	+	0.0916122i	$0.970798\pi$
$632$	2.50000	−	4.33013i	0.0994447	−	0.172243i
$633$	19.5000	+	11.2583i	0.775055	+	0.447478i
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	16.5000	−	28.5788i	0.654783	−	1.13412i
$636$			10.3923i			0.412082i
$637$	−15.0000	−	15.5885i	−0.594322	−	0.617637i
$638$		0			0
$639$	−22.5000	+	38.9711i	−0.890086	+	1.54167i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$	4.50000	−	2.59808i	0.177601	−	0.102538i
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$	−9.00000			−0.354650
$645$	−31.5000	−	18.1865i	−1.24031	−	0.716094i
$646$	−1.50000	−	2.59808i	−0.0590167	−	0.102220i
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	0.995194	−	0.0979182i	$-0.0312184\pi$
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	−0.582397	+	0.812905i	$0.697885\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$	−10.0000	−	10.3923i	−0.392232	−	0.407620i
$651$	−1.50000	−	0.866025i	−0.0587896	−	0.0339422i
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	−0.994988	−	0.0999939i	$-0.968118\pi$
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	0.584091	+	0.811688i	$0.301451\pi$
$654$		−	3.46410i		−	0.135457i
$655$	−22.5000	+	38.9711i	−0.879148	+	1.52273i
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	−42.0000			−1.63858
$658$	−3.00000			−0.116952
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967463\pi$
$660$		0			0
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	−0.910541	−	0.413419i	$-0.864334\pi$
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	0.813302	+	0.581842i	$0.197668\pi$
$662$	2.50000	+	4.33013i	0.0971653	+	0.168295i
$663$	−13.5000	+	12.9904i	−0.524297	+	0.504505i
$664$	1.50000	−	2.59808i	0.0582113	−	0.100825i
$665$	1.50000	+	2.59808i	0.0581675	+	0.100749i
$666$	−7.50000	−	12.9904i	−0.290619	−	0.503367i
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$	−4.50000	+	7.79423i	−0.174110	+	0.301568i
$669$			13.8564i			0.535720i
$670$	−3.00000			−0.115900
$671$		0			0
$672$	1.50000	−	0.866025i	0.0578638	−	0.0334077i
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$	18.0000	+	10.3923i	0.692820	+	0.400000i
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	0.352549	+	0.935793i	$0.385315\pi$
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	−0.986695	+	0.162581i	$0.948018\pi$
$678$		−	10.3923i		−	0.399114i
$679$	−6.50000	+	11.2583i	−0.249447	+	0.432055i
$680$	9.00000			0.345134
$681$	13.5000	−	7.79423i	0.517321	−	0.298675i
$682$		0			0
$683$	10.5000	−	18.1865i	0.401771	−	0.695888i	−0.592168	−	0.805814i	$-0.701728\pi$
$683$	10.5000	−	18.1865i	0.401771	−	0.695888i	0.993940	+	0.109926i	$0.0350613\pi$
$684$	−1.50000	+	2.59808i	−0.0573539	+	0.0993399i
$685$	4.50000	−	7.79423i	0.171936	−	0.297802i
$686$	−13.0000			−0.496342
$687$	7.50000	−	4.33013i	0.286143	−	0.165205i
$688$	3.50000	+	6.06218i	0.133436	+	0.231118i
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$			46.7654i			1.78033i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−10.5000	−	18.1865i	−0.399150	−	0.691348i
$693$		0			0
$694$	12.0000			0.455514
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$		−	10.3923i		−	0.393919i
$697$	13.5000	+	23.3827i	0.511349	+	0.885682i
$698$	10.0000			0.378506
$699$			10.3923i			0.393073i
$700$	−4.00000			−0.151186
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	18.0000	+	5.19615i	0.679366	+	0.196116i
$703$	−5.00000			−0.188579
$704$		0			0
$705$			15.5885i			0.587095i
$706$	−6.00000			−0.225813
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$		−	20.7846i		−	0.781133i
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	0.987421	−	0.158114i	$-0.0505412\pi$
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	−0.630641	+	0.776075i	$0.717208\pi$
$710$	−45.0000			−1.68882
$711$	7.50000	−	12.9904i	0.281272	−	0.487177i
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	−9.00000			−0.337053
$714$			5.19615i			0.194461i
$715$		0			0
$716$	−4.50000	−	7.79423i	−0.168173	−	0.291284i
$717$	22.5000	−	12.9904i	0.840278	−	0.485135i
$718$	−24.0000			−0.895672
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	−0.496527	−	0.868021i	$-0.665392\pi$
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	0.999992	−	0.00400572i	$-0.00127506\pi$
$720$	−4.50000	−	7.79423i	−0.167705	−	0.290474i
$721$	−6.50000	+	11.2583i	−0.242073	+	0.419282i
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$	−37.5000	+	21.6506i	−1.39464	+	0.805196i
$724$	−22.0000			−0.817624
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$			19.0526i			0.707107i
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	−0.421193	−	0.906971i	$-0.638389\pi$
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	0.996056	−	0.0887213i	$-0.0282781\pi$
$728$	−3.50000	+	0.866025i	−0.129719	+	0.0320970i
$729$	−27.0000			−1.00000
$730$	−21.0000	−	36.3731i	−0.777245	−	1.34623i
$731$	−21.0000			−0.776713
$732$	−10.5000	+	6.06218i	−0.388091	+	0.224065i
$733$	9.50000	+	16.4545i	0.350891	+	0.607760i	0.986406	−	0.164328i	$-0.0525456\pi$
$733$	9.50000	+	16.4545i	0.350891	+	0.607760i	−0.635515	+	0.772088i	$0.719212\pi$
$734$	16.0000			0.590571
$735$			31.1769i			1.14998i
$736$	4.50000	−	7.79423i	0.165872	−	0.287299i
$737$		0			0
$738$	13.5000	−	23.3827i	0.496942	−	0.860729i
$739$	3.50000	+	6.06218i	0.128750	+	0.223001i	0.923192	−	0.384338i	$-0.125570\pi$
$739$	3.50000	+	6.06218i	0.128750	+	0.223001i	−0.794443	+	0.607339i	$0.792237\pi$
$740$	7.50000	−	12.9904i	0.275705	−	0.477536i
$741$	4.50000	−	4.33013i	0.165312	−	0.159071i
$742$	−3.00000	−	5.19615i	−0.110133	−	0.190757i
$743$	13.5000	−	23.3827i	0.495267	−	0.857828i	−0.504718	−	0.863284i	$-0.668404\pi$
$743$	13.5000	−	23.3827i	0.495267	−	0.857828i	0.999985	+	0.00545664i	$0.00173691\pi$
$744$	1.50000	−	0.866025i	0.0549927	−	0.0317500i
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	−14.0000			−0.512576
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$		0			0
$749$	−1.50000	+	2.59808i	−0.0548088	+	0.0949316i
$750$		−	5.19615i		−	0.189737i
$751$	−26.5000	+	45.8993i	−0.966999	+	1.67489i	−0.262852	+	0.964836i	$0.584663\pi$
$751$	−26.5000	+	45.8993i	−0.966999	+	1.67489i	−0.704146	+	0.710055i	$0.748670\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	−40.5000	−	23.3827i	−1.47590	−	0.852112i
$754$	−6.00000	+	20.7846i	−0.218507	+	0.756931i
$755$	57.0000			2.07444
$756$	4.50000	−	2.59808i	0.163663	−	0.0944911i
$757$	3.50000	+	6.06218i	0.127210	+	0.220334i	0.922595	−	0.385771i	$-0.126065\pi$
$757$	3.50000	+	6.06218i	0.127210	+	0.220334i	−0.795385	+	0.606105i	$0.792731\pi$
$758$	14.5000	+	25.1147i	0.526664	+	0.912208i
$759$		0			0
$760$	−3.00000			−0.108821
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$	−16.5000	+	9.52628i	−0.597732	+	0.345101i
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$	−1.50000	−	2.59808i	−0.0542681	−	0.0939951i
$765$	27.0000			0.976187
$766$	36.0000			1.30073
$767$	−12.0000	+	41.5692i	−0.433295	+	1.50098i
$768$			1.73205i			0.0625000i
$769$	−23.5000	+	40.7032i	−0.847432	+	1.46779i	0.0360609	+	0.999350i	$0.488519\pi$
$769$	−23.5000	+	40.7032i	−0.847432	+	1.46779i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	−22.5000	−	12.9904i	−0.810318	−	0.467837i
$772$	−11.5000	+	19.9186i	−0.413894	+	0.716886i
$773$	1.50000	−	2.59808i	0.0539513	−	0.0934463i	−0.837788	−	0.545995i	$-0.816152\pi$
$773$	1.50000	−	2.59808i	0.0539513	−	0.0934463i	0.891740	+	0.452549i	$0.149485\pi$
$774$	10.5000	+	18.1865i	0.377415	+	0.653701i
$775$	−4.00000			−0.143684
$776$	−6.50000	−	11.2583i	−0.233336	−	0.404151i
$777$	7.50000	+	4.33013i	0.269061	+	0.155342i
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	−4.50000	−	7.79423i	−0.161229	−	0.279257i
$780$	4.50000	+	18.1865i	0.161126	+	0.651182i
$781$		0			0
$782$	13.5000	+	23.3827i	0.482759	+	0.836163i
$783$		−	31.1769i		−	1.11417i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	25.5000	−	44.1673i	0.910134	−	1.57640i
$786$	22.5000	−	12.9904i	0.802548	−	0.463352i
$787$	8.00000			0.285169			0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000			0.285169			0.142585	+	0.989783i	$0.454459\pi$
$788$	−10.5000	−	18.1865i	−0.374047	−	0.647868i
$789$		0			0
$790$	15.0000			0.533676
$791$	3.00000	+	5.19615i	0.106668	+	0.184754i
$792$		0			0
$793$	24.5000	−	6.06218i	0.870021	−	0.215274i
$794$	−3.50000	+	6.06218i	−0.124210	+	0.215139i
$795$	−27.0000	+	15.5885i	−0.957591	+	0.552866i
$796$	9.50000	−	16.4545i	0.336719	−	0.583214i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$		−	1.73205i		−	0.0613139i
$799$	4.50000	+	7.79423i	0.159199	+	0.275740i
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	22.5000	+	38.9711i	0.794998	+	1.37698i
$802$	−4.50000	+	7.79423i	−0.158901	+	0.275224i
$803$		0			0
$804$	1.50000	+	0.866025i	0.0529009	+	0.0305424i
$805$	−13.5000	−	23.3827i	−0.475812	−	0.824131i
$806$	−3.50000	+	0.866025i	−0.123282	+	0.0305044i
$807$	−31.5000	−	18.1865i	−1.10885	−	0.640196i
$808$	6.00000			0.211079
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	0.925312	+	0.379206i	$0.123803\pi$
$809$	22.5000	+	38.9711i	0.791058	+	1.37015i	−0.134255	+	0.990947i	$0.542864\pi$
$810$	−13.5000	−	23.3827i	−0.474342	−	0.821584i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	16.5000	−	9.52628i	0.578680	−	0.334101i
$814$		0			0
$815$	−33.0000			−1.15594
$816$	−4.50000	−	2.59808i	−0.157532	−	0.0909509i
$817$	7.00000			0.244899
$818$	−14.0000			−0.489499
$819$	−10.5000	+	2.59808i	−0.366900	+	0.0907841i
$820$	27.0000			0.942881
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$	−4.50000	+	2.59808i	−0.156956	+	0.0906183i
$823$	−16.0000			−0.557725			−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000			−0.557725			−0.278862	+	0.960331i	$0.589957\pi$
$824$	−6.50000	−	11.2583i	−0.226438	−	0.392203i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	13.5000	−	23.3827i	0.469157	−	0.812605i
$829$	−26.5000	−	45.8993i	−0.920383	−	1.59415i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−26.5000	−	45.8993i	−0.920383	−	1.59415i	−0.121560	−	0.992584i	$-0.538790\pi$
$830$	9.00000			0.312395
$831$	25.5000	−	14.7224i	0.884585	−	0.510716i
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$	9.00000	+	15.5885i	0.311832	+	0.540108i
$834$			6.92820i			0.239904i
$835$	−27.0000			−0.934374
$836$		0			0
$837$	4.50000	−	2.59808i	0.155543	−	0.0898027i
$838$	−10.5000	+	18.1865i	−0.362716	+	0.628243i
$839$	28.5000	+	49.3634i	0.983929	+	1.70422i	0.646601	+	0.762828i	$0.276190\pi$
$839$	28.5000	+	49.3634i	0.983929	+	1.70422i	0.337328	+	0.941387i	$0.390477\pi$
$840$	4.50000	+	2.59808i	0.155265	+	0.0896421i
$841$	7.00000			0.241379
$842$	−9.50000	+	16.4545i	−0.327392	+	0.567059i
$843$	−4.50000	−	2.59808i	−0.154988	−	0.0894825i
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$	1.50000	−	38.9711i	0.0516016	−	1.34065i
$846$	4.50000	−	7.79423i	0.154713	−	0.267971i
$847$	−5.50000	−	9.52628i	−0.188982	−	0.327327i
$848$	6.00000			0.206041
$849$	1.50000	+	0.866025i	0.0514799	+	0.0297219i
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$	45.0000			1.54258
$852$	22.5000	+	12.9904i	0.770837	+	0.445043i
$853$	9.50000	−	16.4545i	0.325274	−	0.563391i	−0.656294	−	0.754505i	$-0.727877\pi$
$853$	9.50000	−	16.4545i	0.325274	−	0.563391i	0.981568	+	0.191115i	$0.0612102\pi$
$854$	3.50000	−	6.06218i	0.119768	−	0.207443i
$855$	−9.00000			−0.307794
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	16.5000	−	28.5788i	0.563629	−	0.976235i	−0.433546	−	0.901131i	$-0.642738\pi$
$857$	16.5000	−	28.5788i	0.563629	−	0.976235i	0.997176	−	0.0751033i	$-0.0239287\pi$
$858$		0			0
$859$	−20.5000	−	35.5070i	−0.699451	−	1.21148i	−0.968657	−	0.248402i	$-0.920095\pi$
$859$	−20.5000	−	35.5070i	−0.699451	−	1.21148i	0.269206	−	0.963083i	$-0.413239\pi$
$860$	−10.5000	+	18.1865i	−0.358047	+	0.620156i
$861$			15.5885i			0.531253i
$862$	−4.50000	−	7.79423i	−0.153271	−	0.265472i
$863$	−12.0000			−0.408485			−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000			−0.408485			−0.204242	+	0.978920i	$0.565473\pi$
$864$			5.19615i			0.176777i
$865$	31.5000	−	54.5596i	1.07103	−	1.85508i
$866$	5.50000	−	9.52628i	0.186898	−	0.323716i
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	−0.500000	+	0.866025i	−0.0169711	+	0.0293948i
$869$		0			0
$870$	27.0000	−	15.5885i	0.915386	−	0.528498i
$871$	−2.50000	−	2.59808i	−0.0847093	−	0.0880325i
$872$	−2.00000			−0.0677285
$873$	−19.5000	−	33.7750i	−0.659975	−	1.14311i
$874$	−4.50000	−	7.79423i	−0.152215	−	0.263644i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$			24.2487i			0.819288i
$877$	−10.0000			−0.337676			−0.168838	−	0.985644i	$-0.554001\pi$
$877$	−10.0000			−0.337676			−0.168838	+	0.985644i	$0.554001\pi$
$878$	−32.0000			−1.07995
$879$		−	10.3923i		−	0.350524i
$880$		0			0
$881$	22.5000	+	38.9711i	0.758044	+	1.31297i	0.943847	+	0.330384i	$0.107178\pi$
$881$	22.5000	+	38.9711i	0.758044	+	1.31297i	−0.185802	+	0.982587i	$0.559488\pi$
$882$	9.00000	−	15.5885i	0.303046	−	0.524891i
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	7.50000	+	7.79423i	0.252252	+	0.262148i
$885$	54.0000	−	31.1769i	1.81519	−	1.04800i
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−4.50000	+	7.79423i	−0.151095	+	0.261705i	−0.931630	−	0.363407i	$-0.881613\pi$
$887$	−4.50000	+	7.79423i	−0.151095	+	0.261705i	0.780535	+	0.625112i	$0.214947\pi$
$888$	−7.50000	+	4.33013i	−0.251684	+	0.145310i
$889$	5.50000	−	9.52628i	0.184464	−	0.319501i
$890$	−22.5000	+	38.9711i	−0.754202	+	1.30632i
$891$		0			0
$892$	8.00000			0.267860
$893$	−1.50000	−	2.59808i	−0.0501956	−	0.0869413i
$894$		−	10.3923i		−	0.347571i
$895$	13.5000	−	23.3827i	0.451255	−	0.781597i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	−40.5000	+	38.9711i	−1.35226	+	1.30121i
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		0			0
$903$	−10.5000	−	6.06218i	−0.349418	−	0.201737i
$904$	−6.00000			−0.199557
$905$	−33.0000	−	57.1577i	−1.09696	−	1.89999i
$906$	−28.5000	−	16.4545i	−0.946849	−	0.546664i
$907$	−40.0000			−1.32818			−0.664089	−	0.747653i	$-0.731180\pi$
$907$	−40.0000			−1.32818			−0.664089	+	0.747653i	$0.731180\pi$
$908$	−4.50000	−	7.79423i	−0.149338	−	0.258661i
$909$	18.0000			0.597022
$910$	−7.50000	−	7.79423i	−0.248623	−	0.258376i
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$	1.50000	+	0.866025i	0.0496700	+	0.0286770i
$913$		0			0
$914$	10.0000			0.330771
$915$	−31.5000	−	18.1865i	−1.04136	−	0.601228i
$916$	−2.50000	−	4.33013i	−0.0826023	−	0.143071i
$917$	−7.50000	+	12.9904i	−0.247672	+	0.428980i
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	21.5000	−	37.2391i	0.709220	−	1.22840i	−0.255927	−	0.966696i	$-0.582381\pi$
$919$	21.5000	−	37.2391i	0.709220	−	1.22840i	0.965147	−	0.261708i	$-0.0842858\pi$
$920$	27.0000			0.890164
$921$		−	48.4974i		−	1.59804i
$922$	−13.5000	−	23.3827i	−0.444599	−	0.770068i
$923$	−37.5000	−	38.9711i	−1.23433	−	1.28275i
$924$		0			0
$925$	20.0000			0.657596
$926$	5.50000	+	9.52628i	0.180741	+	0.313053i
$927$	−19.5000	−	33.7750i	−0.640464	−	1.10932i
$928$	−6.00000			−0.196960
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$	4.50000	+	2.59808i	0.147561	+	0.0851943i
$931$	−3.00000	−	5.19615i	−0.0983210	−	0.170297i
$932$	6.00000			0.196537
$933$	40.5000	−	23.3827i	1.32591	−	0.765515i
$934$	−12.0000			−0.392652
$935$		0			0
$936$	3.00000	−	10.3923i	0.0980581	−	0.339683i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	−1.00000			−0.0326512
$939$	1.50000	+	0.866025i	0.0489506	+	0.0282617i
$940$	9.00000			0.293548
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	0.961989	−	0.273088i	$-0.0880451\pi$
$941$	7.50000	+	12.9904i	0.244493	+	0.423474i	−0.717496	+	0.696563i	$0.754712\pi$
$942$	−25.5000	+	14.7224i	−0.830835	+	0.479683i
$943$	40.5000	+	70.1481i	1.31886	+	2.28434i
$944$	−12.0000			−0.390567
$945$	13.5000	+	7.79423i	0.439155	+	0.253546i
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	−7.50000	−	4.33013i	−0.243589	−	0.140636i
$949$	14.0000	−	48.4974i	0.454459	−	1.57429i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	−13.5000	−	7.79423i	−0.437767	−	0.252745i
$952$	3.00000			0.0972306
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	−0.783890	−	0.620899i	$-0.786768\pi$
$953$	4.50000	−	7.79423i	0.145769	−	0.252480i	0.929660	+	0.368419i	$0.120101\pi$
$954$	18.0000			0.582772
$955$	4.50000	−	7.79423i	0.145617	−	0.252215i
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$		0			0
$958$		0			0
$959$	1.50000	−	2.59808i	0.0484375	−	0.0838963i
$960$	−4.50000	+	2.59808i	−0.145237	+	0.0838525i
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	17.5000	−	4.33013i	0.564223	−	0.139609i
$963$	−4.50000	−	7.79423i	−0.145010	−	0.251166i
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$	−69.0000			−2.22119
$966$			15.5885i			0.501550i
$967$	6.50000	+	11.2583i	0.209026	+	0.362043i	0.951408	−	0.307933i	$-0.0996374\pi$
$967$	6.50000	+	11.2583i	0.209026	+	0.362043i	−0.742382	+	0.669977i	$0.766304\pi$
$968$	11.0000			0.353553
$969$	−4.50000	+	2.59808i	−0.144561	+	0.0834622i
$970$	19.5000	−	33.7750i	0.626107	−	1.08445i
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$			15.5885i			0.500000i
$973$	−2.00000	−	3.46410i	−0.0641171	−	0.111054i
$974$	−9.50000	+	16.4545i	−0.304400	+	0.527236i
$975$	−18.0000	+	17.3205i	−0.576461	+	0.554700i
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	−0.889022	−	0.457864i	$-0.848615\pi$
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	0.841033	+	0.540984i	$0.181948\pi$
$978$	16.5000	+	9.52628i	0.527612	+	0.304617i
$979$		0			0
$980$	18.0000			0.574989
$981$	−6.00000			−0.191565
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	−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	$0.990257\pi$
$984$	−13.5000	−	7.79423i	−0.430364	−	0.248471i
$985$	31.5000	−	54.5596i	1.00367	−	1.73841i
$986$	9.00000	−	15.5885i	0.286618	−	0.496438i
$987$			5.19615i			0.165395i
$988$	−2.50000	−	2.59808i	−0.0795356	−	0.0826558i
$989$	−63.0000			−2.00328
$990$		0			0
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	0.993364	−	0.115015i	$-0.0366917\pi$
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	−0.596288	+	0.802771i	$0.703358\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$	7.50000	−	4.33013i	0.238005	−	0.137412i
$994$	−15.0000			−0.475771
$995$	57.0000			1.80702
$996$	−4.50000	−	2.59808i	−0.142588	−	0.0823232i
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	0.999945	−	0.0104877i	$-0.00333839\pi$
$997$	15.5000	+	26.8468i	0.490890	+	0.850246i	−0.509055	+	0.860734i	$0.670005\pi$
$998$	2.50000	+	4.33013i	0.0791361	+	0.137068i
$999$	−22.5000	+	12.9904i	−0.711868	+	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.f.a.133.1	✓	2
3.2	odd	2		702.2.f.b.289.1		2
9.4	even	3		234.2.g.b.211.1	yes	2
9.5	odd	6		702.2.g.a.523.1		2
13.9	even	3		234.2.g.b.61.1	yes	2
39.35	odd	6		702.2.g.a.451.1		2
117.22	even	3	inner	234.2.f.a.139.1	yes	2
117.113	odd	6		702.2.f.b.685.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.a.133.1	✓	2	1.1	even	1	trivial
234.2.f.a.139.1	yes	2	117.22	even	3	inner
234.2.g.b.61.1	yes	2	13.9	even	3
234.2.g.b.211.1	yes	2	9.4	even	3
702.2.f.b.289.1		2	3.2	odd	2
702.2.f.b.685.1		2	117.113	odd	6
702.2.g.a.451.1		2	39.35	odd	6
702.2.g.a.523.1		2	9.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(1.50000 + 2.59808i) q^{5} -1.73205i q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(-1.50000 - 2.59808i) q^{10} +1.73205i q^{12} +(1.00000 - 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-4.50000 + 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(-4.50000 + 7.79423i) q^{23} -1.73205i q^{24} +(-2.00000 + 3.46410i) q^{25} +(-1.00000 + 3.46410i) q^{26} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} +6.00000 q^{29} +(4.50000 - 2.59808i) q^{30} +(0.500000 + 0.866025i) q^{31} -1.00000 q^{32} +(1.50000 - 2.59808i) q^{34} +(-1.50000 + 2.59808i) q^{35} -3.00000 q^{36} +(-2.50000 - 4.33013i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(6.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(4.50000 - 7.79423i) q^{41} +(1.50000 - 0.866025i) q^{42} +(3.50000 + 6.06218i) q^{43} +(-4.50000 - 7.79423i) q^{45} +(4.50000 - 7.79423i) q^{46} +(1.50000 - 2.59808i) q^{47} +1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(1.00000 - 3.46410i) q^{52} +6.00000 q^{53} +5.19615i q^{54} +(-0.500000 - 0.866025i) q^{56} +(1.50000 + 0.866025i) q^{57} -6.00000 q^{58} -12.0000 q^{59} +(-4.50000 + 2.59808i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-0.500000 - 0.866025i) q^{62} +(-1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(10.5000 - 2.59808i) q^{65} +(0.500000 - 0.866025i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-13.5000 - 7.79423i) q^{69} +(1.50000 - 2.59808i) q^{70} +(7.50000 - 12.9904i) q^{71} +3.00000 q^{72} +14.0000 q^{73} +(2.50000 + 4.33013i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-6.00000 - 1.73205i) q^{78} +(-2.50000 + 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +9.00000 q^{81} +(-4.50000 + 7.79423i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-1.50000 + 0.866025i) q^{84} -9.00000 q^{85} +(-3.50000 - 6.06218i) q^{86} +10.3923i q^{87} +(-7.50000 - 12.9904i) q^{89} +(4.50000 + 7.79423i) q^{90} +(3.50000 - 0.866025i) q^{91} +(-4.50000 + 7.79423i) q^{92} +(-1.50000 + 0.866025i) q^{93} +(-1.50000 + 2.59808i) q^{94} +3.00000 q^{95} -1.73205i q^{96} +(6.50000 + 11.2583i) q^{97} +(-3.00000 + 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 3 q^{5} + q^{7} - 2 q^{8} - 6 q^{9} - 3 q^{10} + 2 q^{13} - q^{14} - 9 q^{15} + 2 q^{16} - 3 q^{17} + 6 q^{18} + q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{23} - 4 q^{25} - 2 q^{26}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 3 * q^5 + q^7 - 2 * q^8 - 6 * q^9 - 3 * q^10 + 2 * q^13 - q^14 - 9 * q^15 + 2 * q^16 - 3 * q^17 + 6 * q^18 + q^19 + 3 * q^20 - 3 * q^21 - 9 * q^23 - 4 * q^25 - 2 * q^26 + q^28 + 12 * q^29 + 9 * q^30 + q^31 - 2 * q^32 + 3 * q^34 - 3 * q^35 - 6 * q^36 - 5 * q^37 - q^38 + 12 * q^39 - 3 * q^40 + 9 * q^41 + 3 * q^42 + 7 * q^43 - 9 * q^45 + 9 * q^46 + 3 * q^47 + 6 * q^49 + 4 * q^50 - 9 * q^51 + 2 * q^52 + 12 * q^53 - q^56 + 3 * q^57 - 12 * q^58 - 24 * q^59 - 9 * q^60 + 7 * q^61 - q^62 - 3 * q^63 + 2 * q^64 + 21 * q^65 + q^67 - 3 * q^68 - 27 * q^69 + 3 * q^70 + 15 * q^71 + 6 * q^72 + 28 * q^73 + 5 * q^74 - 12 * q^75 + q^76 - 12 * q^78 - 5 * q^79 + 3 * q^80 + 18 * q^81 - 9 * q^82 - 3 * q^83 - 3 * q^84 - 18 * q^85 - 7 * q^86 - 15 * q^89 + 9 * q^90 + 7 * q^91 - 9 * q^92 - 3 * q^93 - 3 * q^94 + 6 * q^95 + 13 * q^97 - 6 * q^98

Introduction

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