LMFDB - Embedded newform 234.2.g.b.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(61,234)] 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("234.61"); 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, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.g (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:	$1.86849940730$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	234.211
Dual form			234.2.g.b.61.1

$q$-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} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{10} -1.73205i q^{12} +(-3.50000 + 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(0.500000 - 0.866025i) q^{19} -3.00000 q^{20} +(-1.50000 - 0.866025i) q^{21} +9.00000 q^{23} +(-1.50000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} -5.19615i q^{30} +(0.500000 - 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) 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} -9.00000 q^{41} +(-1.50000 + 0.866025i) q^{42} -7.00000 q^{43} +9.00000 q^{45} +(4.50000 - 7.79423i) q^{46} +(1.50000 + 2.59808i) q^{47} +(-1.50000 + 0.866025i) q^{48} -6.00000 q^{49} -4.00000 q^{50} +(-4.50000 + 2.59808i) q^{51} +(2.50000 + 2.59808i) q^{52} +6.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +1.00000 q^{56} +(1.50000 - 0.866025i) q^{57} +(3.00000 + 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-4.50000 - 2.59808i) q^{60} -7.00000 q^{61} +(-0.500000 - 0.866025i) q^{62} +(-1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 10.3923i) q^{65} -1.00000 q^{67} +3.00000 q^{68} +(13.5000 + 7.79423i) q^{69} +(1.50000 + 2.59808i) q^{70} +(7.50000 - 12.9904i) q^{71} +(-1.50000 - 2.59808i) q^{72} +14.0000 q^{73} -5.00000 q^{74} -6.92820i q^{75} -1.00000 q^{76} +(-4.50000 + 4.33013i) q^{78} +(-2.50000 - 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} +(-1.50000 - 2.59808i) q^{83} +1.73205i q^{84} +(4.50000 + 7.79423i) q^{85} +(-3.50000 + 6.06218i) q^{86} +(-9.00000 + 5.19615i) 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} +3.00000 q^{94} +(-1.50000 - 2.59808i) q^{95} +1.73205i q^{96} -13.0000 q^{97} +(-3.00000 + 5.19615i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{7} - 2 q^{8} + 3 q^{9} - 3 q^{10} - 7 q^{13} - q^{14} + 9 q^{15} - q^{16} - 3 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - 3 q^{21} + 18 q^{23} - 3 q^{24}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 + 3 * q^5 + 3 * q^6 - 2 * q^7 - 2 * q^8 + 3 * q^9 - 3 * q^10 - 7 * q^13 - q^14 + 9 * q^15 - q^16 - 3 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - 3 * q^21 + 18 * q^23 - 3 * q^24 - 4 * q^25 - 2 * q^26 + q^28 - 6 * q^29 + q^31 + q^32 + 3 * q^34 - 3 * q^35 + 3 * q^36 - 5 * q^37 - q^38 - 12 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 - 14 * q^43 + 18 * q^45 + 9 * q^46 + 3 * q^47 - 3 * q^48 - 12 * q^49 - 8 * q^50 - 9 * q^51 + 5 * q^52 + 12 * q^53 + 9 * q^54 + 2 * q^56 + 3 * q^57 + 6 * q^58 + 12 * q^59 - 9 * q^60 - 14 * q^61 - q^62 - 3 * q^63 + 2 * q^64 - 6 * q^65 - 2 * q^67 + 6 * q^68 + 27 * q^69 + 3 * q^70 + 15 * q^71 - 3 * q^72 + 28 * q^73 - 10 * q^74 - 2 * q^76 - 9 * q^78 - 5 * q^79 + 3 * q^80 - 9 * q^81 - 9 * q^82 - 3 * q^83 + 9 * q^85 - 7 * q^86 - 18 * q^87 - 15 * q^89 + 9 * q^90 + 7 * q^91 - 9 * q^92 + 3 * q^93 + 6 * q^94 - 3 * q^95 - 26 * q^97 - 6 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	4.50000	−	2.59808i	1.16190	−	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−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	$0.130073\pi$
$20$	−3.00000			−0.670820
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$		0			0
$23$	9.00000			1.87663			0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000			1.87663			0.938315	+	0.345782i	$0.112386\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−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
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		−	5.19615i		−	0.948683i
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−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
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$	−1.50000	+	0.866025i	−0.231455	+	0.133631i
$43$	−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
$45$	9.00000			1.34164
$46$	4.50000	−	7.79423i	0.663489	−	1.14920i
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	−6.00000			−0.857143
$50$	−4.00000			−0.565685
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	2.50000	+	2.59808i	0.346688	+	0.360288i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		0			0
$56$	1.00000			0.133631
$57$	1.50000	−	0.866025i	0.198680	−	0.114708i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−4.50000	−	2.59808i	−0.580948	−	0.335410i
$61$	−7.00000			−0.896258			−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000			−0.896258			−0.448129	+	0.893969i	$0.647910\pi$
$62$	−0.500000	−	0.866025i	−0.0635001	−	0.109985i
$63$	−1.50000	−	2.59808i	−0.188982	−	0.327327i
$64$	1.00000			0.125000
$65$	−3.00000	+	10.3923i	−0.372104	+	1.28901i
$66$		0			0
$67$	−1.00000			−0.122169			−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000			−0.122169			−0.0610847	+	0.998133i	$0.519456\pi$
$68$	3.00000			0.363803
$69$	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	$-0.182689\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	−5.00000			−0.581238
$75$		−	6.92820i		−	0.800000i
$76$	−1.00000			−0.114708
$77$		0			0
$78$	−4.50000	+	4.33013i	−0.509525	+	0.490290i
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	0.771883	−	0.635764i	$-0.219315\pi$
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	−0.936530	+	0.350588i	$0.885982\pi$
$84$			1.73205i			0.188982i
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$	−3.50000	+	6.06218i	−0.377415	+	0.653701i
$87$	−9.00000	+	5.19615i	−0.964901	+	0.557086i
$88$		0			0
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$	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
$94$	3.00000			0.309426
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$			1.73205i			0.176777i
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$			5.19615i			0.514496i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$	−4.50000	+	2.59808i	−0.439155	+	0.253546i
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	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	$0.787012\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	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
$111$		−	8.66025i		−	0.821995i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$		−	1.73205i		−	0.162221i
$115$	13.5000	−	23.3827i	1.25888	−	2.18045i
$116$	6.00000			0.557086
$117$	−7.50000	−	7.79423i	−0.693375	−	0.720577i
$118$	12.0000			1.10469
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	−4.50000	+	2.59808i	−0.410792	+	0.237171i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−3.50000	+	6.06218i	−0.316875	+	0.548844i
$123$	−13.5000	−	7.79423i	−1.21725	−	0.702782i
$124$	−1.00000			−0.0898027
$125$	3.00000			0.268328
$126$	−3.00000			−0.267261
$127$	−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	$0.995624\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−10.5000	−	6.06218i	−0.924473	−	0.533745i
$130$	7.50000	+	7.79423i	0.657794	+	0.683599i
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$		0			0
$133$	−0.500000	+	0.866025i	−0.0433555	+	0.0750939i
$134$	−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
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$	13.5000	−	7.79423i	1.14920	−	0.663489i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	3.00000			0.253546
$141$			5.19615i			0.437595i
$142$	−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
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	−9.00000	−	5.19615i	−0.742307	−	0.428571i
$148$	−2.50000	+	4.33013i	−0.205499	+	0.355934i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	−6.00000	−	3.46410i	−0.489898	−	0.282843i
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	−9.00000			−0.727607
$154$		0			0
$155$	−1.50000	−	2.59808i	−0.120483	−	0.208683i
$156$	1.50000	+	6.06218i	0.120096	+	0.485363i
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$	−5.00000			−0.397779
$159$	9.00000	+	5.19615i	0.713746	+	0.412082i
$160$	3.00000			0.237171
$161$	−9.00000			−0.709299
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−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
$166$	−3.00000			−0.232845
$167$	9.00000			0.696441			0.348220	−	0.937413i	$-0.386786\pi$
$167$	9.00000			0.696441			0.348220	+	0.937413i	$0.386786\pi$
$168$	1.50000	+	0.866025i	0.115728	+	0.0668153i
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	9.00000			0.690268
$171$	3.00000			0.229416
$172$	3.50000	+	6.06218i	0.266872	+	0.462237i
$173$	21.0000			1.59660			0.798300	−	0.602260i	$-0.205733\pi$
$173$	21.0000			1.59660			0.798300	+	0.602260i	$0.205733\pi$
$174$			10.3923i			0.787839i
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$		0			0
$177$			20.7846i			1.56227i
$178$	−15.0000			−1.12430
$179$	−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	$0.804709\pi$
$182$	1.00000	−	3.46410i	0.0741249	−	0.256776i
$183$	−10.5000	−	6.06218i	−0.776182	−	0.448129i
$184$	−9.00000			−0.663489
$185$	−15.0000			−1.10282
$186$		−	1.73205i		−	0.127000i
$187$		0			0
$188$	1.50000	−	2.59808i	0.109399	−	0.189484i
$189$		−	5.19615i		−	0.377964i
$190$	−3.00000			−0.217643
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	23.0000			1.65558			0.827788	−	0.561041i	$-0.189599\pi$
$193$	23.0000			1.65558			0.827788	+	0.561041i	$0.189599\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$	−13.5000	+	12.9904i	−0.966755	+	0.930261i
$196$	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
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$	4.50000	+	2.59808i	0.315063	+	0.181902i
$205$	−13.5000	+	23.3827i	−0.942881	+	1.63312i
$206$	−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
$210$			5.19615i			0.358569i
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	22.5000	−	12.9904i	1.54167	−	0.890086i
$214$	3.00000			0.205076
$215$	−10.5000	+	18.1865i	−0.716094	+	1.24031i
$216$		−	5.19615i		−	0.353553i
$217$	−0.500000	+	0.866025i	−0.0339422	+	0.0587896i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	21.0000	+	12.1244i	1.41905	+	0.819288i
$220$		0			0
$221$	3.00000	−	10.3923i	0.201802	−	0.699062i
$222$	−7.50000	−	4.33013i	−0.503367	−	0.290619i
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	−6.00000			−0.399114
$227$	9.00000			0.597351			0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000			0.597351			0.298675	+	0.954355i	$0.403455\pi$
$228$	−1.50000	−	0.866025i	−0.0993399	−	0.0573539i
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	−0.936728	−	0.350058i	$-0.886162\pi$
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	0.771523	+	0.636201i	$0.219495\pi$
$230$	−13.5000	−	23.3827i	−0.890164	−	1.54181i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	−10.5000	+	2.59808i	−0.686406	+	0.169842i
$235$	9.00000			0.587095
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$		−	8.66025i		−	0.562544i
$238$	−1.50000	−	2.59808i	−0.0972306	−	0.168408i
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$			5.19615i			0.335410i
$241$	−25.0000			−1.61039			−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000			−1.61039			−0.805196	+	0.593009i	$0.797940\pi$
$242$	11.0000			0.707107
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$	−9.00000	+	15.5885i	−0.574989	+	0.995910i
$246$	−13.5000	+	7.79423i	−0.860729	+	0.496942i
$247$	−1.00000	+	3.46410i	−0.0636285	+	0.220416i
$248$	−0.500000	+	0.866025i	−0.0317500	+	0.0549927i
$249$		−	5.19615i		−	0.329293i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−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
$254$	−11.0000			−0.690201
$255$			15.5885i			0.976187i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0000			0.935674			0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000			0.935674			0.467837	+	0.883815i	$0.345033\pi$
$258$	−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		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	9.00000	−	15.5885i	0.552866	−	0.957591i
$266$	0.500000	+	0.866025i	0.0306570	+	0.0530994i
$267$		−	25.9808i		−	1.59000i
$268$	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
$273$	6.00000	+	1.73205i	0.363137	+	0.104828i
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$		0			0
$276$		−	15.5885i		−	0.938315i
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$	4.00000			0.239904
$279$	3.00000			0.179605
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−1.50000	−	2.59808i	−0.0894825	−	0.154988i	0.817810	−	0.575488i	$-0.195188\pi$
$281$	−1.50000	−	2.59808i	−0.0894825	−	0.154988i	−0.907293	+	0.420500i	$0.861855\pi$
$282$	4.50000	+	2.59808i	0.267971	+	0.154713i
$283$	−1.00000			−0.0594438			−0.0297219	−	0.999558i	$-0.509462\pi$
$283$	−1.00000			−0.0594438			−0.0297219	+	0.999558i	$0.509462\pi$
$284$	−15.0000			−0.890086
$285$		−	5.19615i		−	0.307794i
$286$		0			0
$287$	9.00000			0.531253
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	18.0000			1.05700
$291$	−19.5000	−	11.2583i	−1.14311	−	0.659975i
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	0.940252	−	0.340480i	$-0.110589\pi$
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	−0.764990	+	0.644042i	$0.777256\pi$
$294$	−9.00000	+	5.19615i	−0.524891	+	0.303046i
$295$	36.0000			2.09600
$296$	2.50000	+	4.33013i	0.145310	+	0.251684i
$297$		0			0
$298$	−6.00000			−0.347571
$299$	−31.5000	+	7.79423i	−1.82169	+	0.450752i
$300$	−6.00000	+	3.46410i	−0.346410	+	0.200000i
$301$	7.00000			0.403473
$302$	19.0000			1.09333
$303$	9.00000	−	5.19615i	0.517036	−	0.298511i
$304$	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
$310$	−3.00000			−0.170389
$311$	−13.5000	+	23.3827i	−0.765515	+	1.32591i	0.174459	+	0.984664i	$0.444182\pi$
$311$	−13.5000	+	23.3827i	−0.765515	+	1.32591i	−0.939974	+	0.341246i	$0.889151\pi$
$312$	6.00000	+	1.73205i	0.339683	+	0.0980581i
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$	8.50000	+	14.7224i	0.479683	+	0.830835i
$315$	−9.00000			−0.507093
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	0.711535	−	0.702650i	$-0.248000\pi$
$317$	−4.50000	−	7.79423i	−0.252745	−	0.437767i	−0.964281	+	0.264883i	$0.914667\pi$
$318$	9.00000	−	5.19615i	0.504695	−	0.291386i
$319$		0			0
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$			5.19615i			0.290021i
$322$	−4.50000	+	7.79423i	−0.250775	+	0.434355i
$323$	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
$327$	3.00000	+	1.73205i	0.165900	+	0.0957826i
$328$	9.00000			0.496942
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−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
$335$	−1.50000	+	2.59808i	−0.0819538	+	0.141948i
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	−0.632882	−	0.774248i	$-0.718128\pi$
$337$	6.50000	−	11.2583i	0.354078	−	0.613280i	0.986960	+	0.160968i	$0.0514616\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$		−	10.3923i		−	0.564433i
$340$	4.50000	−	7.79423i	0.244047	−	0.422701i
$341$		0			0
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$	13.0000			0.701934
$344$	7.00000			0.377415
$345$	40.5000	−	23.3827i	2.18045	−	1.25888i
$346$	10.5000	−	18.1865i	0.564483	−	0.977714i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	9.00000	+	5.19615i	0.482451	+	0.278543i
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	4.00000			0.213809
$351$	−4.50000	−	18.1865i	−0.240192	−	0.970725i
$352$		0			0
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$	18.0000	+	10.3923i	0.956689	+	0.552345i
$355$	−22.5000	−	38.9711i	−1.19418	−	2.06837i
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$	4.50000	−	2.59808i	0.238165	−	0.137505i
$358$	−9.00000			−0.475665
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	−9.00000			−0.474342
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$			19.0526i			1.00000i
$364$	−2.50000	−	2.59808i	−0.131036	−	0.136176i
$365$	21.0000	−	36.3731i	1.09919	−	1.90385i
$366$	−10.5000	+	6.06218i	−0.548844	+	0.316875i
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	−0.578101	−	0.815966i	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	−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
$371$	−6.00000			−0.311504
$372$	−1.50000	−	0.866025i	−0.0777714	−	0.0449013i
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$		0			0
$375$	4.50000	+	2.59808i	0.232379	+	0.134164i
$376$	−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	$-0.434129\pi$
$380$	−1.50000	+	2.59808i	−0.0769484	+	0.133278i
$381$		−	19.0526i		−	0.976092i
$382$	1.50000	−	2.59808i	0.0767467	−	0.132929i
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$		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	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$	4.50000	+	18.1865i	0.227866	+	0.920911i
$391$	−13.5000	+	23.3827i	−0.682724	+	1.18251i
$392$	6.00000			0.303046
$393$	22.5000	−	12.9904i	1.13497	−	0.655278i
$394$	−21.0000			−1.05796
$395$	−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
$399$	−1.50000	+	0.866025i	−0.0750939	+	0.0433555i
$400$	4.00000			0.200000
$401$	−9.00000			−0.449439			−0.224719	−	0.974424i	$-0.572147\pi$
$401$	−9.00000			−0.449439			−0.224719	+	0.974424i	$0.572147\pi$
$402$	−1.50000	+	0.866025i	−0.0748132	+	0.0431934i
$403$	−1.00000	+	3.46410i	−0.0498135	+	0.172559i
$404$	−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
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	13.5000	+	23.3827i	0.666717	+	1.15479i
$411$	4.50000	+	2.59808i	0.221969	+	0.128154i
$412$	−13.0000			−0.640464
$413$	−6.00000	−	10.3923i	−0.295241	−	0.511372i
$414$	27.0000			1.32698
$415$	−9.00000			−0.441793
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$			6.92820i			0.339276i
$418$		0			0
$419$	−21.0000			−1.02592			−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000			−1.02592			−0.512959	+	0.858413i	$0.671451\pi$
$420$	4.50000	+	2.59808i	0.219578	+	0.126773i
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	0.999109	−	0.0422075i	$-0.0134391\pi$
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−6.00000			−0.291386
$425$	12.0000			0.582086
$426$		−	25.9808i		−	1.25877i
$427$	7.00000			0.338754
$428$	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	$0.763785\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−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
$435$			31.1769i			1.49482i
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	4.50000	−	7.79423i	0.215264	−	0.372849i
$438$	21.0000	−	12.1244i	1.00342	−	0.579324i
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	0.177325	+	0.984152i	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$		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	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$	−7.50000	+	4.33013i	−0.355934	+	0.205499i
$445$	−45.0000			−2.13320
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$		−	10.3923i		−	0.491539i
$448$	−1.00000			−0.0472456
$449$	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
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$			32.9090i			1.54620i
$454$	4.50000	−	7.79423i	0.211195	−	0.365801i
$455$	3.00000	−	10.3923i	0.140642	−	0.487199i
$456$	−1.50000	+	0.866025i	−0.0702439	+	0.0405554i
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	2.50000	+	4.33013i	0.116817	+	0.202334i
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$	−27.0000			−1.25888
$461$	−27.0000			−1.25752			−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000			−1.25752			−0.628758	+	0.777601i	$0.716436\pi$
$462$		0			0
$463$	−5.50000	+	9.52628i	−0.255607	+	0.442724i	−0.965060	−	0.262029i	$-0.915609\pi$
$463$	−5.50000	+	9.52628i	−0.255607	+	0.442724i	0.709453	+	0.704752i	$0.248942\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		−	5.19615i		−	0.240966i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	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
$470$	4.50000	−	7.79423i	0.207570	−	0.359521i
$471$	−25.5000	+	14.7224i	−1.17498	+	0.678374i
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$		0			0
$474$	−7.50000	−	4.33013i	−0.344486	−	0.198889i
$475$	−4.00000			−0.183533
$476$	−3.00000			−0.137505
$477$	9.00000	+	15.5885i	0.412082	+	0.713746i
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	4.50000	+	2.59808i	0.205396	+	0.118585i
$481$	12.5000	+	12.9904i	0.569951	+	0.592310i
$482$	−12.5000	+	21.6506i	−0.569359	+	0.986159i
$483$	−13.5000	−	7.79423i	−0.614271	−	0.354650i
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	−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	$0.0250088\pi$
$488$	7.00000			0.316875
$489$	−16.5000	+	9.52628i	−0.746156	+	0.430793i
$490$	9.00000	+	15.5885i	0.406579	+	0.704215i
$491$	15.0000			0.676941			0.338470	−	0.940977i	$-0.390091\pi$
$491$	15.0000			0.676941			0.338470	+	0.940977i	$0.390091\pi$
$492$			15.5885i			0.702782i
$493$	−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
$497$	−7.50000	+	12.9904i	−0.336421	+	0.582698i
$498$	−4.50000	−	2.59808i	−0.201650	−	0.116423i
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$	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
$507$	22.5000	+	0.866025i	0.999260	+	0.0384615i
$508$	−5.50000	+	9.52628i	−0.244023	+	0.422660i
$509$	−39.0000			−1.72864			−0.864322	−	0.502938i	$-0.832252\pi$
$509$	−39.0000			−1.72864			−0.864322	+	0.502938i	$0.832252\pi$
$510$	13.5000	+	7.79423i	0.597790	+	0.345134i
$511$	−14.0000			−0.619324
$512$	−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
$516$			12.1244i			0.533745i
$517$		0			0
$518$	5.00000			0.219687
$519$	31.5000	+	18.1865i	1.38270	+	0.798300i
$520$	3.00000	−	10.3923i	0.131559	−	0.455733i
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	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	$0.444037\pi$
$524$	−15.0000			−0.655278
$525$			6.92820i			0.302372i
$526$		0			0
$527$	1.50000	+	2.59808i	0.0653410	+	0.113174i
$528$		0			0
$529$	58.0000			2.52174
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$	−18.0000	+	31.1769i	−0.781133	+	1.35296i
$532$	1.00000			0.0433555
$533$	31.5000	−	7.79423i	1.36442	−	0.337606i
$534$	−22.5000	−	12.9904i	−0.973670	−	0.562149i
$535$	9.00000			0.389104
$536$	1.00000			0.0431934
$537$		−	15.5885i		−	0.672692i
$538$	10.5000	+	18.1865i	0.452687	+	0.784077i
$539$		0			0
$540$		−	15.5885i		−	0.670820i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	−11.0000			−0.472490
$543$	−33.0000	−	19.0526i	−1.41617	−	0.817624i
$544$	−3.00000			−0.128624
$545$	3.00000	−	5.19615i	0.128506	−	0.222579i
$546$	4.50000	−	4.33013i	0.192582	−	0.185312i
$547$	12.5000	+	21.6506i	0.534461	+	0.925714i	0.999189	+	0.0402607i	$0.0128188\pi$
$547$	12.5000	+	21.6506i	0.534461	+	0.925714i	−0.464728	+	0.885454i	$0.653848\pi$
$548$	−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
$553$	2.50000	+	4.33013i	0.106311	+	0.184136i
$554$	8.50000	−	14.7224i	0.361130	−	0.625496i
$555$	−22.5000	−	12.9904i	−0.955072	−	0.551411i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−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
$562$	−3.00000			−0.126547
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	4.50000	−	2.59808i	0.189484	−	0.109399i
$565$	−18.0000			−0.757266
$566$	−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
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$	−4.50000	−	2.59808i	−0.188484	−	0.108821i
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$		0			0
$573$	4.50000	+	2.59808i	0.187990	+	0.108536i
$574$	4.50000	−	7.79423i	0.187826	−	0.325325i
$575$	−18.0000	−	31.1769i	−0.750652	−	1.30017i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	8.00000			0.332756
$579$	34.5000	+	19.9186i	1.43377	+	0.827788i
$580$	9.00000	−	15.5885i	0.373705	−	0.647275i
$581$	1.50000	+	2.59808i	0.0622305	+	0.107786i
$582$	−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
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	−0.715226	−	0.698893i	$-0.753676\pi$
$587$	6.00000	−	10.3923i	0.247647	−	0.428936i	0.962872	+	0.269957i	$0.0870095\pi$
$588$			10.3923i			0.428571i
$589$	−0.500000	−	0.866025i	−0.0206021	−	0.0356840i
$590$	18.0000	−	31.1769i	0.741048	−	1.28353i
$591$		−	36.3731i		−	1.49619i
$592$	5.00000			0.205499
$593$	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
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$	28.5000	−	16.4545i	1.16643	−	0.673437i
$598$	−9.00000	+	31.1769i	−0.368037	+	1.27492i
$599$	16.5000	−	28.5788i	0.674172	−	1.16770i	−0.302539	−	0.953137i	$-0.597834\pi$
$599$	16.5000	−	28.5788i	0.674172	−	1.16770i	0.976710	−	0.214563i	$-0.0688326\pi$
$600$			6.92820i			0.282843i
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	0.949799	+	0.312861i	$0.101287\pi$
$602$	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
$605$	33.0000			1.34164
$606$		−	10.3923i		−	0.422159i
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	1.00000			0.0405554
$609$	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	$0.618008\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$	−40.5000	+	23.3827i	−1.63312	+	0.942881i
$616$		0			0
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$		−	22.5167i		−	0.905753i
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$			46.7654i			1.87663i
$622$	13.5000	+	23.3827i	0.541301	+	0.937560i
$623$	7.50000	+	12.9904i	0.300481	+	0.520449i
$624$	4.50000	−	4.33013i	0.180144	−	0.173344i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	1.00000			0.0399680
$627$		0			0
$628$	17.0000			0.678374
$629$	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
$634$	−9.00000			−0.357436
$635$	−33.0000			−1.30957
$636$		−	10.3923i		−	0.412082i
$637$	21.0000	−	5.19615i	0.832050	−	0.205879i
$638$		0			0
$639$	45.0000			1.78017
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	27.0000			1.06644			0.533218	−	0.845978i	$-0.320983\pi$
$641$	27.0000			1.06644			0.533218	+	0.845978i	$0.320983\pi$
$642$	4.50000	+	2.59808i	0.177601	+	0.102538i
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	0.979541	−	0.201243i	$-0.0644981\pi$
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	−0.664052	+	0.747686i	$0.731165\pi$
$644$	4.50000	+	7.79423i	0.177325	+	0.307136i
$645$	−31.5000	+	18.1865i	−1.24031	+	0.716094i
$646$	3.00000			0.118033
$647$	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	$0.697885\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$		0			0
$650$	14.0000	−	3.46410i	0.549125	−	0.135873i
$651$	−1.50000	+	0.866025i	−0.0587896	+	0.0339422i
$652$	11.0000			0.430793
$653$	21.0000			0.821794			0.410897	−	0.911682i	$-0.365216\pi$
$653$	21.0000			0.821794			0.410897	+	0.911682i	$0.365216\pi$
$654$	3.00000	−	1.73205i	0.117309	−	0.0677285i
$655$	−22.5000	−	38.9711i	−0.879148	−	1.52273i
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	21.0000	+	36.3731i	0.819288	+	1.41905i
$658$	−3.00000			−0.116952
$659$	21.0000			0.818044			0.409022	−	0.912525i	$-0.365870\pi$
$659$	21.0000			0.818044			0.409022	+	0.912525i	$0.365870\pi$
$660$		0			0
$661$	5.00000			0.194477			0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000			0.194477			0.0972387	+	0.995261i	$0.468999\pi$
$662$	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
$669$	−12.0000	+	6.92820i	−0.463947	+	0.267860i
$670$	1.50000	+	2.59808i	0.0579501	+	0.100372i
$671$		0			0
$672$		−	1.73205i		−	0.0668153i
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	−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	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$	−9.00000	−	5.19615i	−0.345643	−	0.199557i
$679$	13.0000			0.498894
$680$	−4.50000	−	7.79423i	−0.172567	−	0.298895i
$681$	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
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	−7.50000	+	4.33013i	−0.286143	+	0.165205i
$688$	3.50000	−	6.06218i	0.133436	−	0.231118i
$689$	−21.0000	+	5.19615i	−0.800036	+	0.197958i
$690$		−	46.7654i		−	1.78033i
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$	−10.5000	−	18.1865i	−0.399150	−	0.691348i
$693$		0			0
$694$	12.0000			0.455514
$695$	12.0000			0.455186
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$	−5.00000	−	8.66025i	−0.189253	−	0.327795i
$699$	9.00000	+	5.19615i	0.340411	+	0.196537i
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	−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
$705$	13.5000	+	7.79423i	0.508439	+	0.293548i
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$	18.0000	−	10.3923i	0.676481	−	0.390567i
$709$	−19.0000			−0.713560			−0.356780	−	0.934188i	$-0.616125\pi$
$709$	−19.0000			−0.713560			−0.356780	+	0.934188i	$0.616125\pi$
$710$	−45.0000			−1.68882
$711$	7.50000	−	12.9904i	0.281272	−	0.487177i
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	4.50000	−	7.79423i	0.168526	−	0.291896i
$714$		−	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
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$	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
$722$	18.0000			0.669891
$723$	−37.5000	−	21.6506i	−1.39464	−	0.805196i
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	24.0000			0.891338
$726$	16.5000	+	9.52628i	0.612372	+	0.353553i
$727$	15.5000	+	26.8468i	0.574863	+	0.995692i	0.996056	+	0.0887213i	$0.0282781\pi$
$727$	15.5000	+	26.8468i	0.574863	+	0.995692i	−0.421193	+	0.906971i	$0.638389\pi$
$728$	−3.50000	+	0.866025i	−0.129719	+	0.0320970i
$729$	−27.0000			−1.00000
$730$	−21.0000	−	36.3731i	−0.777245	−	1.34623i
$731$	10.5000	−	18.1865i	0.388357	−	0.672653i
$732$			12.1244i			0.448129i
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	−0.635515	−	0.772088i	$-0.719212\pi$
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	0.986406	+	0.164328i	$0.0525456\pi$
$734$	−8.00000	−	13.8564i	−0.295285	−	0.511449i
$735$	−27.0000	+	15.5885i	−0.995910	+	0.574989i
$736$	4.50000	+	7.79423i	0.165872	+	0.287299i
$737$		0			0
$738$	−27.0000			−0.993884
$739$	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
$743$	−27.0000			−0.990534			−0.495267	−	0.868741i	$-0.664930\pi$
$743$	−27.0000			−0.990534			−0.495267	+	0.868741i	$0.664930\pi$
$744$	−1.50000	+	0.866025i	−0.0549927	+	0.0317500i
$745$	−18.0000			−0.659469
$746$	−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
$750$	4.50000	−	2.59808i	0.164317	−	0.0948683i
$751$	53.0000			1.93400			0.966999	−	0.254781i	$-0.0820034\pi$
$751$	53.0000			1.93400			0.966999	+	0.254781i	$0.0820034\pi$
$752$	−3.00000			−0.109399
$753$	−40.5000	+	23.3827i	−1.47590	+	0.852112i
$754$	−15.0000	−	15.5885i	−0.546268	−	0.567698i
$755$	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	$0.792731\pi$
$758$	−29.0000			−1.05333
$759$		0			0
$760$	1.50000	+	2.59808i	0.0544107	+	0.0942421i
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	−16.5000	−	9.52628i	−0.597732	−	0.345101i
$763$	−2.00000			−0.0724049
$764$	−1.50000	−	2.59808i	−0.0542681	−	0.0939951i
$765$	−13.5000	+	23.3827i	−0.488094	+	0.845403i
$766$	36.0000			1.30073
$767$	−30.0000	−	31.1769i	−1.08324	−	1.12573i
$768$		−	1.73205i		−	0.0625000i
$769$	47.0000			1.69486			0.847432	−	0.530904i	$-0.178148\pi$
$769$	47.0000			1.69486			0.847432	+	0.530904i	$0.178148\pi$
$770$		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	$0.149485\pi$
$774$	−21.0000			−0.754829
$775$	−4.00000			−0.143684
$776$	13.0000			0.466673
$777$			8.66025i			0.310685i
$778$	−9.00000			−0.322666
$779$	−4.50000	+	7.79423i	−0.161229	+	0.279257i
$780$	18.0000	+	5.19615i	0.644503	+	0.186052i
$781$		0			0
$782$	13.5000	+	23.3827i	0.482759	+	0.836163i
$783$	−27.0000	−	15.5885i	−0.964901	−	0.557086i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	25.5000	+	44.1673i	0.910134	+	1.57640i
$786$		−	25.9808i		−	0.926703i
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	0.785885	−	0.618373i	$-0.212208\pi$
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	−0.928469	+	0.371409i	$0.878875\pi$
$788$	−10.5000	+	18.1865i	−0.374047	+	0.647868i
$789$		0			0
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$	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
$796$	−19.0000			−0.673437
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	−0.999331	−	0.0365596i	$-0.988360\pi$
$797$	−15.0000	−	25.9808i	−0.531327	−	0.920286i	0.468004	−	0.883726i	$-0.344973\pi$
$798$			1.73205i			0.0613139i
$799$	−9.00000			−0.318397
$800$	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
$804$			1.73205i			0.0610847i
$805$	−13.5000	+	23.3827i	−0.475812	+	0.824131i
$806$	2.50000	+	2.59808i	0.0880587	+	0.0915133i
$807$	−31.5000	+	18.1865i	−1.10885	+	0.640196i
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	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	$0.542864\pi$
$810$	27.0000			0.948683
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−6.00000			−0.210559
$813$		−	19.0526i		−	0.668202i
$814$		0			0
$815$	16.5000	+	28.5788i	0.577970	+	1.00107i
$816$		−	5.19615i		−	0.181902i
$817$	−3.50000	+	6.06218i	−0.122449	+	0.212089i
$818$	−14.0000			−0.489499
$819$	7.50000	+	7.79423i	0.262071	+	0.272352i
$820$	27.0000			0.942881
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$	4.50000	−	2.59808i	0.156956	−	0.0906183i
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	−6.50000	+	11.2583i	−0.226438	+	0.392203i
$825$		0			0
$826$	−12.0000			−0.417533
$827$	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	$-0.538790\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$	25.5000	+	14.7224i	0.884585	+	0.510716i
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	9.00000	−	15.5885i	0.311832	−	0.540108i
$834$	6.00000	+	3.46410i	0.207763	+	0.119952i
$835$	13.5000	−	23.3827i	0.467187	−	0.809191i
$836$		0			0
$837$	4.50000	+	2.59808i	0.155543	+	0.0898027i
$838$	−10.5000	+	18.1865i	−0.362716	+	0.628243i
$839$	−57.0000			−1.96786			−0.983929	−	0.178559i	$-0.942857\pi$
$839$	−57.0000			−1.96786			−0.983929	+	0.178559i	$0.942857\pi$
$840$	4.50000	−	2.59808i	0.155265	−	0.0896421i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	19.0000			0.654783
$843$		−	5.19615i		−	0.178965i
$844$	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
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	−1.50000	−	0.866025i	−0.0514799	−	0.0297219i
$850$	6.00000	−	10.3923i	0.205798	−	0.356453i
$851$	−22.5000	−	38.9711i	−0.771290	−	1.33591i
$852$	−22.5000	−	12.9904i	−0.770837	−	0.445043i
$853$	9.50000	+	16.4545i	0.325274	+	0.563391i	0.981568	−	0.191115i	$-0.0612102\pi$
$853$	9.50000	+	16.4545i	0.325274	+	0.563391i	−0.656294	+	0.754505i	$0.727877\pi$
$854$	3.50000	−	6.06218i	0.119768	−	0.207443i
$855$	4.50000	−	7.79423i	0.153897	−	0.266557i
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	0.997176	+	0.0751033i	$0.0239287\pi$
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	−0.433546	+	0.901131i	$0.642738\pi$
$858$		0			0
$859$	−20.5000	+	35.5070i	−0.699451	+	1.21148i	0.269206	+	0.963083i	$0.413239\pi$
$859$	−20.5000	+	35.5070i	−0.699451	+	1.21148i	−0.968657	+	0.248402i	$0.920095\pi$
$860$	21.0000			0.716094
$861$	13.5000	+	7.79423i	0.460079	+	0.265627i
$862$	9.00000			0.306541
$863$	−12.0000			−0.408485			−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000			−0.408485			−0.204242	+	0.978920i	$0.565473\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	31.5000	−	54.5596i	1.07103	−	1.85508i
$866$	5.50000	+	9.52628i	0.186898	+	0.323716i
$867$			13.8564i			0.470588i
$868$	1.00000			0.0339422
$869$		0			0
$870$	27.0000	+	15.5885i	0.915386	+	0.528498i
$871$	3.50000	−	0.866025i	0.118593	−	0.0293442i
$872$	−2.00000			−0.0677285
$873$	−19.5000	−	33.7750i	−0.659975	−	1.14311i
$874$	−4.50000	−	7.79423i	−0.152215	−	0.263644i
$875$	−3.00000			−0.101419
$876$		−	24.2487i		−	0.819288i
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$	16.0000	+	27.7128i	0.539974	+	0.935262i
$879$			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	$0.559488\pi$
$882$	−18.0000			−0.606092
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	−10.5000	+	2.59808i	−0.353153	+	0.0873828i
$885$	54.0000	+	31.1769i	1.81519	+	1.04800i
$886$	9.00000			0.302361
$887$	9.00000			0.302190			0.151095	−	0.988519i	$-0.451720\pi$
$887$	9.00000			0.302190			0.151095	+	0.988519i	$0.451720\pi$
$888$			8.66025i			0.290619i
$889$	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
$893$	3.00000			0.100391
$894$	−9.00000	−	5.19615i	−0.301005	−	0.173785i
$895$	−27.0000			−0.902510
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	−54.0000	−	15.5885i	−1.80301	−	0.520483i
$898$	−4.50000	−	7.79423i	−0.150167	−	0.260097i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$	−12.0000			−0.400000
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$		0			0
$903$	10.5000	+	6.06218i	0.349418	+	0.201737i
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	−33.0000	+	57.1577i	−1.09696	+	1.89999i
$906$	28.5000	+	16.4545i	0.946849	+	0.546664i
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	0.979531	−	0.201291i	$-0.0645138\pi$
$908$	−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	0.963106	−	0.269122i	$-0.0867336\pi$
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	−0.714620	+	0.699513i	$0.753400\pi$
$912$			1.73205i			0.0573539i
$913$		0			0
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$	−31.5000	+	18.1865i	−1.04136	+	0.601228i
$916$	5.00000			0.165205
$917$	−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	$-0.0842858\pi$
$920$	−13.5000	+	23.3827i	−0.445082	+	0.770904i
$921$	−42.0000	−	24.2487i	−1.38395	−	0.799022i
$922$	−13.5000	+	23.3827i	−0.444599	+	0.770068i
$923$	−15.0000	+	51.9615i	−0.493731	+	1.71033i
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	5.50000	+	9.52628i	0.180741	+	0.313053i
$927$	39.0000			1.28093
$928$	−6.00000			−0.196960
$929$	−21.0000			−0.688988			−0.344494	−	0.938789i	$-0.611949\pi$
$929$	−21.0000			−0.688988			−0.344494	+	0.938789i	$0.611949\pi$
$930$	−4.50000	−	2.59808i	−0.147561	−	0.0851943i
$931$	−3.00000	+	5.19615i	−0.0983210	+	0.170297i
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$	−40.5000	+	23.3827i	−1.32591	+	0.765515i
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$	7.50000	+	7.79423i	0.245145	+	0.254762i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	0.500000	−	0.866025i	0.0163256	−	0.0282767i
$939$			1.73205i			0.0565233i
$940$	−4.50000	−	7.79423i	−0.146774	−	0.254220i
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	−0.717496	−	0.696563i	$-0.754712\pi$
$941$	7.50000	−	12.9904i	0.244493	−	0.423474i	0.961989	+	0.273088i	$0.0880451\pi$
$942$			29.4449i			0.959366i
$943$	−81.0000			−2.63772
$944$	−12.0000			−0.390567
$945$	−13.5000	−	7.79423i	−0.439155	−	0.253546i
$946$		0			0
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$	−7.50000	+	4.33013i	−0.243589	+	0.140636i
$949$	−49.0000	+	12.1244i	−1.59061	+	0.393573i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$		−	15.5885i		−	0.505490i
$952$	−1.50000	+	2.59808i	−0.0486153	+	0.0842041i
$953$	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
$956$	15.0000			0.485135
$957$		0			0
$958$		0			0
$959$	−3.00000			−0.0968751
$960$	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
$965$	34.5000	−	59.7558i	1.11059	−	1.92361i
$966$	−13.5000	+	7.79423i	−0.434355	+	0.250775i
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	−0.742382	−	0.669977i	$-0.766304\pi$
$967$	6.50000	−	11.2583i	0.209026	−	0.362043i	0.951408	+	0.307933i	$0.0996374\pi$
$968$	−5.50000	−	9.52628i	−0.176777	−	0.306186i
$969$			5.19615i			0.166924i
$970$	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	$0.244039\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	−2.00000	−	3.46410i	−0.0641171	−	0.111054i
$974$	−9.50000	−	16.4545i	−0.304400	−	0.527236i
$975$	6.00000	+	24.2487i	0.192154	+	0.776580i
$976$	3.50000	−	6.06218i	0.112032	−	0.194046i
$977$	3.00000			0.0959785			0.0479893	−	0.998848i	$-0.484719\pi$
$977$	3.00000			0.0959785			0.0479893	+	0.998848i	$0.484719\pi$
$978$			19.0526i			0.609234i
$979$		0			0
$980$	18.0000			0.574989
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	−0.999532	−	0.0306024i	$-0.990257\pi$
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	0.473263	−	0.880921i	$-0.343076\pi$
$984$	13.5000	+	7.79423i	0.430364	+	0.248471i
$985$	−63.0000			−2.00735
$986$	−18.0000			−0.573237
$987$		−	5.19615i		−	0.165395i
$988$	3.50000	−	0.866025i	0.111350	−	0.0275519i
$989$	−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	$0.703358\pi$
$992$	1.00000			0.0317500
$993$	7.50000	+	4.33013i	0.238005	+	0.137412i
$994$	7.50000	+	12.9904i	0.237886	+	0.412030i
$995$	−28.5000	−	49.3634i	−0.903511	−	1.56493i
$996$	−4.50000	+	2.59808i	−0.142588	+	0.0823232i
$997$	−31.0000			−0.981780			−0.490890	−	0.871222i	$-0.663328\pi$
$997$	−31.0000			−0.981780			−0.490890	+	0.871222i	$0.663328\pi$
$998$	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.g.b.211.1	yes	2
3.2	odd	2		702.2.g.a.523.1		2
9.2	odd	6		702.2.f.b.289.1		2
9.7	even	3		234.2.f.a.133.1	✓	2
13.9	even	3		234.2.f.a.139.1	yes	2
39.35	odd	6		702.2.f.b.685.1		2
117.61	even	3	inner	234.2.g.b.61.1	yes	2
117.74	odd	6		702.2.g.a.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.f.a.133.1	✓	2	9.7	even	3
234.2.f.a.139.1	yes	2	13.9	even	3
234.2.g.b.61.1	yes	2	117.61	even	3	inner
234.2.g.b.211.1	yes	2	1.1	even	1	trivial
702.2.f.b.289.1		2	9.2	odd	6
702.2.f.b.685.1		2	39.35	odd	6
702.2.g.a.451.1		2	117.74	odd	6
702.2.g.a.523.1		2	3.2	odd	2

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.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(1.50000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{10} -1.73205i q^{12} +(-3.50000 + 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +3.00000 q^{18} +(0.500000 - 0.866025i) q^{19} -3.00000 q^{20} +(-1.50000 - 0.866025i) q^{21} +9.00000 q^{23} +(-1.50000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(0.500000 + 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} -5.19615i q^{30} +(0.500000 - 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{34} +(-1.50000 + 2.59808i) q^{35} +(1.50000 - 2.59808i) 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} -9.00000 q^{41} +(-1.50000 + 0.866025i) q^{42} -7.00000 q^{43} +9.00000 q^{45} +(4.50000 - 7.79423i) q^{46} +(1.50000 + 2.59808i) q^{47} +(-1.50000 + 0.866025i) q^{48} -6.00000 q^{49} -4.00000 q^{50} +(-4.50000 + 2.59808i) q^{51} +(2.50000 + 2.59808i) q^{52} +6.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +1.00000 q^{56} +(1.50000 - 0.866025i) q^{57} +(3.00000 + 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-4.50000 - 2.59808i) q^{60} -7.00000 q^{61} +(-0.500000 - 0.866025i) q^{62} +(-1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-3.00000 + 10.3923i) q^{65} -1.00000 q^{67} +3.00000 q^{68} +(13.5000 + 7.79423i) q^{69} +(1.50000 + 2.59808i) q^{70} +(7.50000 - 12.9904i) q^{71} +(-1.50000 - 2.59808i) q^{72} +14.0000 q^{73} -5.00000 q^{74} -6.92820i q^{75} -1.00000 q^{76} +(-4.50000 + 4.33013i) q^{78} +(-2.50000 - 4.33013i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} +(-1.50000 - 2.59808i) q^{83} +1.73205i q^{84} +(4.50000 + 7.79423i) q^{85} +(-3.50000 + 6.06218i) q^{86} +(-9.00000 + 5.19615i) 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} +3.00000 q^{94} +(-1.50000 - 2.59808i) q^{95} +1.73205i q^{96} -13.0000 q^{97} +(-3.00000 + 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{7} - 2 q^{8} + 3 q^{9} - 3 q^{10} - 7 q^{13} - q^{14} + 9 q^{15} - q^{16} - 3 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - 3 q^{21} + 18 q^{23} - 3 q^{24}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 + 3 * q^5 + 3 * q^6 - 2 * q^7 - 2 * q^8 + 3 * q^9 - 3 * q^10 - 7 * q^13 - q^14 + 9 * q^15 - q^16 - 3 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - 3 * q^21 + 18 * q^23 - 3 * q^24 - 4 * q^25 - 2 * q^26 + q^28 - 6 * q^29 + q^31 + q^32 + 3 * q^34 - 3 * q^35 + 3 * q^36 - 5 * q^37 - q^38 - 12 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 - 14 * q^43 + 18 * q^45 + 9 * q^46 + 3 * q^47 - 3 * q^48 - 12 * q^49 - 8 * q^50 - 9 * q^51 + 5 * q^52 + 12 * q^53 + 9 * q^54 + 2 * q^56 + 3 * q^57 + 6 * q^58 + 12 * q^59 - 9 * q^60 - 14 * q^61 - q^62 - 3 * q^63 + 2 * q^64 - 6 * q^65 - 2 * q^67 + 6 * q^68 + 27 * q^69 + 3 * q^70 + 15 * q^71 - 3 * q^72 + 28 * q^73 - 10 * q^74 - 2 * q^76 - 9 * q^78 - 5 * q^79 + 3 * q^80 - 9 * q^81 - 9 * q^82 - 3 * q^83 + 9 * q^85 - 7 * q^86 - 18 * q^87 - 15 * q^89 + 9 * q^90 + 7 * q^91 - 9 * q^92 + 3 * q^93 + 6 * q^94 - 3 * q^95 - 26 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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