LMFDB - Embedded newform 30.2.e.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,2,Mod(17,30)] 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("30.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	30.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.239551206064$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	30.17
Dual form			30.2.e.a.23.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(1.00000 + 2.00000i) q^{10} +1.41421i q^{11} +(1.70711 + 0.292893i) q^{12} +1.41421 q^{14} +(3.41421 + 1.82843i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(2.70711 - 1.29289i) q^{18} +4.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(2.00000 - 1.41421i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-2.82843 - 2.82843i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(-4.00000 - 3.00000i) q^{25} +(2.53553 - 4.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} +7.07107 q^{29} +(-3.70711 + 1.12132i) q^{30} -2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.41421 - 0.414214i) q^{33} -2.00000i q^{34} +(-2.82843 + 1.41421i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(6.00000 + 6.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(2.00000 - 1.00000i) q^{40} +5.65685i q^{41} +(-0.414214 + 2.41421i) q^{42} +(6.00000 - 6.00000i) q^{43} +1.41421 q^{44} +(-4.12132 + 5.29289i) q^{45} +4.00000 q^{46} +(0.292893 - 1.70711i) q^{48} -5.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-2.00000 - 2.82843i) q^{51} +(2.82843 + 2.82843i) q^{53} +(1.41421 + 5.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} -1.41421i q^{56} +(-6.82843 - 1.17157i) q^{57} +(-5.00000 + 5.00000i) q^{58} -9.89949 q^{59} +(1.82843 - 3.41421i) q^{60} -6.00000 q^{61} +(1.41421 - 1.41421i) q^{62} +(1.82843 + 3.82843i) q^{63} +1.00000i q^{64} +(2.00000 - 1.41421i) q^{66} +(-4.00000 - 4.00000i) q^{67} +(1.41421 + 1.41421i) q^{68} +(5.65685 - 4.00000i) q^{69} +(1.00000 - 3.00000i) q^{70} -14.1421i q^{71} +(-1.29289 - 2.70711i) q^{72} +(-5.00000 + 5.00000i) q^{73} -8.48528 q^{74} +(6.29289 - 5.94975i) q^{75} +4.00000 q^{76} +(1.41421 - 1.41421i) q^{77} +6.00000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.00000 - 4.00000i) q^{82} +(8.48528 + 8.48528i) q^{83} +(-1.41421 - 2.00000i) q^{84} +(2.00000 + 4.00000i) q^{85} +8.48528i q^{86} +(-2.07107 + 12.0711i) q^{87} +(-1.00000 + 1.00000i) q^{88} -2.82843 q^{89} +(-0.828427 - 6.65685i) q^{90} +(-2.82843 + 2.82843i) q^{92} +(0.585786 - 3.41421i) q^{93} +(8.48528 + 2.82843i) q^{95} +(1.00000 + 1.41421i) q^{96} +(3.00000 + 3.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(1.41421 - 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + 4 q^{10} + 4 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{18} + 8 q^{21} - 4 q^{22} - 16 q^{25} - 4 q^{27} - 4 q^{28} - 12 q^{30} - 8 q^{31} - 4 q^{33} - 4 q^{36} + 24 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^6 - 4 * q^7 + 4 * q^10 + 4 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^18 + 8 * q^21 - 4 * q^22 - 16 * q^25 - 4 * q^27 - 4 * q^28 - 12 * q^30 - 8 * q^31 - 4 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 + 4 * q^42 + 24 * q^43 - 8 * q^45 + 16 * q^46 + 4 * q^48 - 8 * q^51 + 12 * q^55 - 16 * q^57 - 20 * q^58 - 4 * q^60 - 24 * q^61 - 4 * q^63 + 8 * q^66 - 16 * q^67 + 4 * q^70 - 8 * q^72 - 20 * q^73 + 28 * q^75 + 16 * q^76 + 28 * q^81 - 16 * q^82 + 8 * q^85 + 20 * q^87 - 4 * q^88 + 8 * q^90 + 8 * q^93 + 4 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$	1.70711	+	0.292893i	0.492799	+	0.0845510i
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$	1.41421			0.377964
$15$	3.41421	+	1.82843i	0.881546	+	0.472098i
$16$	−1.00000			−0.250000
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$	2.70711	−	1.29289i	0.638071	−	0.304738i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$	2.00000	−	1.41421i	0.436436	−	0.308607i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	0.347801	−	0.937568i	$-0.386929\pi$
$23$	−2.82843	−	2.82843i	−0.589768	−	0.589768i	−0.937568	+	0.347801i	$0.886929\pi$
$24$	−1.41421	+	1.00000i	−0.288675	+	0.204124i
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$		0			0
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	7.07107			1.31306			0.656532	−	0.754298i	$-0.272023\pi$
$29$	7.07107			1.31306			0.656532	+	0.754298i	$0.272023\pi$
$30$	−3.70711	+	1.12132i	−0.676822	+	0.204724i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−2.41421	−	0.414214i	−0.420261	−	0.0721053i
$34$		−	2.00000i		−	0.342997i
$35$	−2.82843	+	1.41421i	−0.478091	+	0.239046i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	0.999909	−	0.0135147i	$-0.00430201\pi$
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	−0.0135147	+	0.999909i	$0.504302\pi$
$38$	−2.82843	−	2.82843i	−0.458831	−	0.458831i
$39$		0			0
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$			5.65685i			0.883452i	0.897150	+	0.441726i	$0.145634\pi$
$41$			5.65685i			0.883452i	−0.897150	+	0.441726i	$0.854366\pi$
$42$	−0.414214	+	2.41421i	−0.0639145	+	0.372521i
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	−0.0816682	−	0.996660i	$-0.526025\pi$
$43$	6.00000	−	6.00000i	0.914991	−	0.914991i	0.996660	+	0.0816682i	$0.0260248\pi$
$44$	1.41421			0.213201
$45$	−4.12132	+	5.29289i	−0.614370	+	0.789018i
$46$	4.00000			0.589768
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	0.292893	−	1.70711i	0.0422755	−	0.246400i
$49$		−	5.00000i		−	0.714286i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$	−2.00000	−	2.82843i	−0.280056	−	0.396059i
$52$		0			0
$53$	2.82843	+	2.82843i	0.388514	+	0.388514i	0.874157	−	0.485643i	$-0.161414\pi$
$53$	2.82843	+	2.82843i	0.388514	+	0.388514i	−0.485643	+	0.874157i	$0.661414\pi$
$54$	1.41421	+	5.00000i	0.192450	+	0.680414i
$55$	3.00000	+	1.00000i	0.404520	+	0.134840i
$56$		−	1.41421i		−	0.188982i
$57$	−6.82843	−	1.17157i	−0.904447	−	0.155179i
$58$	−5.00000	+	5.00000i	−0.656532	+	0.656532i
$59$	−9.89949			−1.28880			−0.644402	−	0.764687i	$-0.722894\pi$
$59$	−9.89949			−1.28880			−0.644402	+	0.764687i	$0.722894\pi$
$60$	1.82843	−	3.41421i	0.236049	−	0.440773i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	1.41421	−	1.41421i	0.179605	−	0.179605i
$63$	1.82843	+	3.82843i	0.230360	+	0.482336i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	2.00000	−	1.41421i	0.246183	−	0.174078i
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	0.419211	−	0.907889i	$-0.362307\pi$
$67$	−4.00000	−	4.00000i	−0.488678	−	0.488678i	−0.907889	+	0.419211i	$0.862307\pi$
$68$	1.41421	+	1.41421i	0.171499	+	0.171499i
$69$	5.65685	−	4.00000i	0.681005	−	0.481543i
$70$	1.00000	−	3.00000i	0.119523	−	0.358569i
$71$		−	14.1421i		−	1.67836i	−0.543852	−	0.839181i	$-0.683035\pi$
$71$		−	14.1421i		−	1.67836i	0.543852	−	0.839181i	$-0.316965\pi$
$72$	−1.29289	−	2.70711i	−0.152369	−	0.319036i
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−5.00000	+	5.00000i	−0.585206	+	0.585206i	0.351123	+	0.936329i	$0.385800\pi$
$74$	−8.48528			−0.986394
$75$	6.29289	−	5.94975i	0.726641	−	0.687018i
$76$	4.00000			0.458831
$77$	1.41421	−	1.41421i	0.161165	−	0.161165i
$78$		0			0
$79$			6.00000i			0.675053i	0.941316	+	0.337526i	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	−4.00000	−	4.00000i	−0.441726	−	0.441726i
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	0.997792	−	0.0664117i	$-0.0211551\pi$
$83$	8.48528	+	8.48528i	0.931381	+	0.931381i	−0.0664117	+	0.997792i	$0.521155\pi$
$84$	−1.41421	−	2.00000i	−0.154303	−	0.218218i
$85$	2.00000	+	4.00000i	0.216930	+	0.433861i
$86$			8.48528i			0.914991i
$87$	−2.07107	+	12.0711i	−0.222042	+	1.29415i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	−2.82843			−0.299813			−0.149906	−	0.988700i	$-0.547897\pi$
$89$	−2.82843			−0.299813			−0.149906	+	0.988700i	$0.547897\pi$
$90$	−0.828427	−	6.65685i	−0.0873239	−	0.701694i
$91$		0			0
$92$	−2.82843	+	2.82843i	−0.294884	+	0.294884i
$93$	0.585786	−	3.41421i	0.0607432	−	0.354037i
$94$		0			0
$95$	8.48528	+	2.82843i	0.870572	+	0.290191i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	0.842812	−	0.538208i	$-0.180899\pi$
$97$	3.00000	+	3.00000i	0.304604	+	0.304604i	−0.538208	+	0.842812i	$0.680899\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	1.41421	−	4.00000i	0.142134	−	0.402015i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		−	9.89949i		−	0.985037i	−0.870302	−	0.492518i	$-0.836076\pi$
$101$		−	9.89949i		−	0.985037i	0.870302	−	0.492518i	$-0.163924\pi$
$102$	3.41421	+	0.585786i	0.338058	+	0.0580015i
$103$	1.00000	−	1.00000i	0.0985329	−	0.0985329i	−0.656122	−	0.754655i	$-0.727804\pi$
$103$	1.00000	−	1.00000i	0.0985329	−	0.0985329i	0.754655	+	0.656122i	$0.227804\pi$
$104$		0			0
$105$	−1.58579	−	5.24264i	−0.154757	−	0.511629i
$106$	−4.00000			−0.388514
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	−0.557047	−	0.830481i	$-0.688066\pi$
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	0.830481	+	0.557047i	$0.188066\pi$
$108$	−4.53553	−	2.53553i	−0.436432	−	0.243982i
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$	−2.82843	+	1.41421i	−0.269680	+	0.134840i
$111$	−12.0000	+	8.48528i	−1.13899	+	0.805387i
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−9.89949	−	9.89949i	−0.931266	−	0.931266i	0.0665190	−	0.997785i	$-0.478811\pi$
$113$	−9.89949	−	9.89949i	−0.931266	−	0.931266i	−0.997785	+	0.0665190i	$0.978811\pi$
$114$	5.65685	−	4.00000i	0.529813	−	0.374634i
$115$	−8.00000	+	4.00000i	−0.746004	+	0.373002i
$116$		−	7.07107i		−	0.656532i
$117$		0			0
$118$	7.00000	−	7.00000i	0.644402	−	0.644402i
$119$	2.82843			0.259281
$120$	1.12132	+	3.70711i	0.102362	+	0.338411i
$121$	9.00000			0.818182
$122$	4.24264	−	4.24264i	0.384111	−	0.384111i
$123$	−9.65685	−	1.65685i	−0.870729	−	0.149394i
$124$			2.00000i			0.179605i
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$	−4.00000	−	1.41421i	−0.356348	−	0.125988i
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	0.324676	−	0.945825i	$-0.394745\pi$
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	−0.945825	+	0.324676i	$0.894745\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	8.48528	+	12.0000i	0.747087	+	1.05654i
$130$		0			0
$131$			18.3848i			1.60629i	0.595787	+	0.803143i	$0.296840\pi$
$131$			18.3848i			1.60629i	−0.595787	+	0.803143i	$0.703160\pi$
$132$	−0.414214	+	2.41421i	−0.0360527	+	0.210130i
$133$	4.00000	−	4.00000i	0.346844	−	0.346844i
$134$	5.65685			0.488678
$135$	−7.82843	−	8.58579i	−0.673764	−	0.738947i
$136$	−2.00000			−0.171499
$137$	4.24264	−	4.24264i	0.362473	−	0.362473i	−0.502249	−	0.864723i	$-0.667494\pi$
$137$	4.24264	−	4.24264i	0.362473	−	0.362473i	0.864723	+	0.502249i	$0.167494\pi$
$138$	−1.17157	+	6.82843i	−0.0997309	+	0.581274i
$139$			8.00000i			0.678551i	0.940687	+	0.339276i	$0.110182\pi$
$139$			8.00000i			0.678551i	−0.940687	+	0.339276i	$0.889818\pi$
$140$	1.41421	+	2.82843i	0.119523	+	0.239046i
$141$		0			0
$142$	10.0000	+	10.0000i	0.839181	+	0.839181i
$143$		0			0
$144$	2.82843	+	1.00000i	0.235702	+	0.0833333i
$145$	5.00000	−	15.0000i	0.415227	−	1.24568i
$146$		−	7.07107i		−	0.585206i
$147$	8.53553	+	1.46447i	0.703999	+	0.120787i
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−12.7279			−1.04271			−0.521356	−	0.853339i	$-0.674574\pi$
$149$	−12.7279			−1.04271			−0.521356	+	0.853339i	$0.674574\pi$
$150$	−0.242641	+	8.65685i	−0.0198115	+	0.706829i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	−2.82843	+	2.82843i	−0.229416	+	0.229416i
$153$	5.41421	−	2.58579i	0.437713	−	0.209048i
$154$			2.00000i			0.161165i
$155$	−1.41421	+	4.24264i	−0.113592	+	0.340777i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	−4.24264	−	4.24264i	−0.337526	−	0.337526i
$159$	−5.65685	+	4.00000i	−0.448618	+	0.317221i
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$			5.65685i			0.445823i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$	5.65685			0.441726
$165$	−2.58579	+	4.82843i	−0.201303	+	0.375893i
$166$	−12.0000			−0.931381
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	−0.453510	−	0.891251i	$-0.649829\pi$
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	0.891251	+	0.453510i	$0.149829\pi$
$168$	2.41421	+	0.414214i	0.186261	+	0.0319573i
$169$			13.0000i			1.00000i
$170$	−4.24264	−	1.41421i	−0.325396	−	0.108465i
$171$	4.00000	−	11.3137i	0.305888	−	0.865181i
$172$	−6.00000	−	6.00000i	−0.457496	−	0.457496i
$173$	1.41421	+	1.41421i	0.107521	+	0.107521i	0.758820	−	0.651300i	$-0.225776\pi$
$173$	1.41421	+	1.41421i	0.107521	+	0.107521i	−0.651300	+	0.758820i	$0.725776\pi$
$174$	−7.07107	−	10.0000i	−0.536056	−	0.758098i
$175$	1.00000	+	7.00000i	0.0755929	+	0.529150i
$176$		−	1.41421i		−	0.106600i
$177$	2.89949	−	16.8995i	0.217939	−	1.27024i
$178$	2.00000	−	2.00000i	0.149906	−	0.149906i
$179$	18.3848			1.37414			0.687071	−	0.726590i	$-0.258896\pi$
$179$	18.3848			1.37414			0.687071	+	0.726590i	$0.258896\pi$
$180$	5.29289	+	4.12132i	0.394509	+	0.307185i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	1.75736	−	10.2426i	0.129908	−	0.757158i
$184$		−	4.00000i		−	0.294884i
$185$	16.9706	−	8.48528i	1.24770	−	0.623850i
$186$	2.00000	+	2.82843i	0.146647	+	0.207390i
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$	−7.07107	+	2.00000i	−0.514344	+	0.145479i
$190$	−8.00000	+	4.00000i	−0.580381	+	0.290191i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	−1.70711	−	0.292893i	−0.123200	−	0.0211377i
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$	−4.24264			−0.304604
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.237785	+	0.971318i	$0.576421\pi$
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.971318	+	0.237785i	$0.923579\pi$
$198$	1.82843	+	3.82843i	0.129941	+	0.272074i
$199$		−	24.0000i		−	1.70131i	−0.525720	−	0.850657i	$-0.676204\pi$
$199$		−	24.0000i		−	1.70131i	0.525720	−	0.850657i	$-0.323796\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$	8.00000	−	5.65685i	0.564276	−	0.399004i
$202$	7.00000	+	7.00000i	0.492518	+	0.492518i
$203$	−7.07107	−	7.07107i	−0.496292	−	0.496292i
$204$	−2.82843	+	2.00000i	−0.198030	+	0.140028i
$205$	12.0000	+	4.00000i	0.838116	+	0.279372i
$206$			1.41421i			0.0985329i
$207$	5.17157	+	10.8284i	0.359449	+	0.752628i
$208$		0			0
$209$	−5.65685			−0.391293
$210$	4.82843	+	2.58579i	0.333193	+	0.178436i
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	2.82843	−	2.82843i	0.194257	−	0.194257i
$213$	24.1421	+	4.14214i	1.65419	+	0.283814i
$214$			4.00000i			0.273434i
$215$	−8.48528	−	16.9706i	−0.578691	−	1.15738i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	2.00000	+	2.00000i	0.135769	+	0.135769i
$218$	7.07107	+	7.07107i	0.478913	+	0.478913i
$219$	−7.07107	−	10.0000i	−0.477818	−	0.675737i
$220$	1.00000	−	3.00000i	0.0674200	−	0.202260i
$221$		0			0
$222$	2.48528	−	14.4853i	0.166801	−	0.972188i
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	−0.941024	−	0.338340i	$-0.890135\pi$
$223$	−9.00000	+	9.00000i	−0.602685	+	0.602685i	0.338340	+	0.941024i	$0.390135\pi$
$224$	−1.41421			−0.0944911
$225$	8.31371	+	12.4853i	0.554247	+	0.832352i
$226$	14.0000			0.931266
$227$	−15.5563	+	15.5563i	−1.03251	+	1.03251i	−0.0330577	+	0.999453i	$0.510525\pi$
$227$	−15.5563	+	15.5563i	−1.03251	+	1.03251i	−0.999453	+	0.0330577i	$0.989475\pi$
$228$	−1.17157	+	6.82843i	−0.0775893	+	0.452224i
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$	2.82843	−	8.48528i	0.186501	−	0.559503i
$231$	2.00000	+	2.82843i	0.131590	+	0.186097i
$232$	5.00000	+	5.00000i	0.328266	+	0.328266i
$233$	12.7279	+	12.7279i	0.833834	+	0.833834i	0.988039	−	0.154205i	$-0.0492816\pi$
$233$	12.7279	+	12.7279i	0.833834	+	0.833834i	−0.154205	+	0.988039i	$0.549282\pi$
$234$		0			0
$235$		0			0
$236$			9.89949i			0.644402i
$237$	−10.2426	−	1.75736i	−0.665331	−	0.114153i
$238$	−2.00000	+	2.00000i	−0.129641	+	0.129641i
$239$	8.48528			0.548867			0.274434	−	0.961606i	$-0.411510\pi$
$239$	8.48528			0.548867			0.274434	+	0.961606i	$0.411510\pi$
$240$	−3.41421	−	1.82843i	−0.220387	−	0.118024i
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$	−6.36396	+	6.36396i	−0.409091	+	0.409091i
$243$	−11.7071	+	10.2929i	−0.751011	+	0.660289i
$244$			6.00000i			0.384111i
$245$	−10.6066	−	3.53553i	−0.677631	−	0.225877i
$246$	8.00000	−	5.65685i	0.510061	−	0.360668i
$247$		0			0
$248$	−1.41421	−	1.41421i	−0.0898027	−	0.0898027i
$249$	−16.9706	+	12.0000i	−1.07547	+	0.760469i
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$		−	12.7279i		−	0.803379i	−0.915776	−	0.401690i	$-0.868423\pi$
$251$		−	12.7279i		−	0.803379i	0.915776	−	0.401690i	$-0.131577\pi$
$252$	3.82843	−	1.82843i	0.241168	−	0.115180i
$253$	4.00000	−	4.00000i	0.251478	−	0.251478i
$254$	9.89949			0.621150
$255$	−7.41421	+	2.24264i	−0.464296	+	0.140440i
$256$	1.00000			0.0625000
$257$	9.89949	−	9.89949i	0.617514	−	0.617514i	−0.327379	−	0.944893i	$-0.606166\pi$
$257$	9.89949	−	9.89949i	0.617514	−	0.617514i	0.944893	+	0.327379i	$0.106166\pi$
$258$	−14.4853	−	2.48528i	−0.901814	−	0.154727i
$259$		−	12.0000i		−	0.745644i
$260$		0			0
$261$	−20.0000	−	7.07107i	−1.23797	−	0.437688i
$262$	−13.0000	−	13.0000i	−0.803143	−	0.803143i
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$	−1.41421	−	2.00000i	−0.0870388	−	0.123091i
$265$	8.00000	−	4.00000i	0.491436	−	0.245718i
$266$			5.65685i			0.346844i
$267$	0.828427	−	4.82843i	0.0506989	−	0.295495i
$268$	−4.00000	+	4.00000i	−0.244339	+	0.244339i
$269$	15.5563			0.948487			0.474244	−	0.880394i	$-0.342722\pi$
$269$	15.5563			0.948487			0.474244	+	0.880394i	$0.342722\pi$
$270$	11.6066	+	0.535534i	0.706355	+	0.0325916i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	1.41421	−	1.41421i	0.0857493	−	0.0857493i
$273$		0			0
$274$			6.00000i			0.362473i
$275$	4.24264	−	5.65685i	0.255841	−	0.341121i
$276$	−4.00000	−	5.65685i	−0.240772	−	0.340503i
$277$	−6.00000	−	6.00000i	−0.360505	−	0.360505i	0.503494	−	0.863999i	$-0.332048\pi$
$277$	−6.00000	−	6.00000i	−0.360505	−	0.360505i	−0.863999	+	0.503494i	$0.832048\pi$
$278$	−5.65685	−	5.65685i	−0.339276	−	0.339276i
$279$	5.65685	+	2.00000i	0.338667	+	0.119737i
$280$	−3.00000	−	1.00000i	−0.179284	−	0.0597614i
$281$		−	8.48528i		−	0.506189i	−0.967442	−	0.253095i	$-0.918552\pi$
$281$		−	8.48528i		−	0.506189i	0.967442	−	0.253095i	$-0.0814484\pi$
$282$		0			0
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.211498	−	0.977378i	$-0.432166\pi$
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.977378	−	0.211498i	$-0.0678343\pi$
$284$	−14.1421			−0.839181
$285$	−7.31371	+	13.6569i	−0.433227	+	0.808962i
$286$		0			0
$287$	5.65685	−	5.65685i	0.333914	−	0.333914i
$288$	−2.70711	+	1.29289i	−0.159518	+	0.0761845i
$289$			13.0000i			0.764706i
$290$	7.07107	+	14.1421i	0.415227	+	0.830455i
$291$	−6.00000	+	4.24264i	−0.351726	+	0.248708i
$292$	5.00000	+	5.00000i	0.292603	+	0.292603i
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	−7.07107	+	5.00000i	−0.412393	+	0.291606i
$295$	−7.00000	+	21.0000i	−0.407556	+	1.22267i
$296$			8.48528i			0.493197i
$297$	6.41421	+	3.58579i	0.372190	+	0.208068i
$298$	9.00000	−	9.00000i	0.521356	−	0.521356i
$299$		0			0
$300$	−5.94975	−	6.29289i	−0.343509	−	0.363320i
$301$	−12.0000			−0.691669
$302$	−11.3137	+	11.3137i	−0.651031	+	0.651031i
$303$	16.8995	+	2.89949i	0.970851	+	0.166572i
$304$		−	4.00000i		−	0.229416i
$305$	−4.24264	+	12.7279i	−0.242933	+	0.728799i
$306$	−2.00000	+	5.65685i	−0.114332	+	0.323381i
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.999616	+	0.0276979i	$0.00881765\pi$
$307$	18.0000	+	18.0000i	1.02731	+	1.02731i	0.0276979	+	0.999616i	$0.491182\pi$
$308$	−1.41421	−	1.41421i	−0.0805823	−	0.0805823i
$309$	1.41421	+	2.00000i	0.0804518	+	0.113776i
$310$	−2.00000	−	4.00000i	−0.113592	−	0.227185i
$311$			19.7990i			1.12270i	0.827579	+	0.561349i	$0.189717\pi$
$311$			19.7990i			1.12270i	−0.827579	+	0.561349i	$0.810283\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$		0			0
$315$	9.41421	−	1.17157i	0.530431	−	0.0660107i
$316$	6.00000			0.337526
$317$	12.7279	−	12.7279i	0.714871	−	0.714871i	−0.252679	−	0.967550i	$-0.581312\pi$
$317$	12.7279	−	12.7279i	0.714871	−	0.714871i	0.967550	+	0.252679i	$0.0813116\pi$
$318$	1.17157	−	6.82843i	0.0656985	−	0.382919i
$319$			10.0000i			0.559893i
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$	4.00000	+	5.65685i	0.223258	+	0.315735i
$322$	−4.00000	−	4.00000i	−0.222911	−	0.222911i
$323$	−5.65685	−	5.65685i	−0.314756	−	0.314756i
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$		0			0
$326$		−	5.65685i		−	0.313304i
$327$	17.0711	+	2.92893i	0.944032	+	0.161970i
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$		0			0
$330$	−1.58579	−	5.24264i	−0.0872947	−	0.288598i
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	8.48528	−	8.48528i	0.465690	−	0.465690i
$333$	−10.9706	−	22.9706i	−0.601183	−	1.25878i
$334$			8.00000i			0.437741i
$335$	−11.3137	+	5.65685i	−0.618134	+	0.309067i
$336$	−2.00000	+	1.41421i	−0.109109	+	0.0771517i
$337$	−9.00000	−	9.00000i	−0.490261	−	0.490261i	0.418127	−	0.908388i	$-0.362687\pi$
$337$	−9.00000	−	9.00000i	−0.490261	−	0.490261i	−0.908388	+	0.418127i	$0.862687\pi$
$338$	−9.19239	−	9.19239i	−0.500000	−	0.500000i
$339$	19.7990	−	14.0000i	1.07533	−	0.760376i
$340$	4.00000	−	2.00000i	0.216930	−	0.108465i
$341$		−	2.82843i		−	0.153168i
$342$	5.17157	+	10.8284i	0.279647	+	0.585534i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	8.48528			0.457496
$345$	−4.48528	−	14.8284i	−0.241479	−	0.798336i
$346$	−2.00000			−0.107521
$347$	−9.89949	+	9.89949i	−0.531433	+	0.531433i	−0.920999	−	0.389566i	$-0.872625\pi$
$347$	−9.89949	+	9.89949i	−0.531433	+	0.531433i	0.389566	+	0.920999i	$0.372625\pi$
$348$	12.0711	+	2.07107i	0.647077	+	0.111021i
$349$		−	2.00000i		−	0.107058i	−0.998566	−	0.0535288i	$-0.982953\pi$
$349$		−	2.00000i		−	0.107058i	0.998566	−	0.0535288i	$-0.0170469\pi$
$350$	−5.65685	−	4.24264i	−0.302372	−	0.226779i
$351$		0			0
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−12.7279	−	12.7279i	−0.677439	−	0.677439i	0.281981	−	0.959420i	$-0.409008\pi$
$353$	−12.7279	−	12.7279i	−0.677439	−	0.677439i	−0.959420	+	0.281981i	$0.909008\pi$
$354$	9.89949	+	14.0000i	0.526152	+	0.744092i
$355$	−30.0000	−	10.0000i	−1.59223	−	0.530745i
$356$			2.82843i			0.149906i
$357$	−0.828427	+	4.82843i	−0.0438450	+	0.255547i
$358$	−13.0000	+	13.0000i	−0.687071	+	0.687071i
$359$	−11.3137			−0.597115			−0.298557	−	0.954392i	$-0.596505\pi$
$359$	−11.3137			−0.597115			−0.298557	+	0.954392i	$0.596505\pi$
$360$	−6.65685	+	0.828427i	−0.350847	+	0.0436619i
$361$	3.00000			0.157895
$362$	15.5563	−	15.5563i	0.817624	−	0.817624i
$363$	−2.63604	+	15.3640i	−0.138356	+	0.806399i
$364$		0			0
$365$	7.07107	+	14.1421i	0.370117	+	0.740233i
$366$	6.00000	+	8.48528i	0.313625	+	0.443533i
$367$	−19.0000	−	19.0000i	−0.991792	−	0.991792i	0.00817466	−	0.999967i	$-0.497398\pi$
$367$	−19.0000	−	19.0000i	−0.991792	−	0.991792i	−0.999967	+	0.00817466i	$0.997398\pi$
$368$	2.82843	+	2.82843i	0.147442	+	0.147442i
$369$	5.65685	−	16.0000i	0.294484	−	0.832927i
$370$	−6.00000	+	18.0000i	−0.311925	+	0.935775i
$371$		−	5.65685i		−	0.293689i
$372$	−3.41421	−	0.585786i	−0.177019	−	0.0303716i
$373$	4.00000	−	4.00000i	0.207112	−	0.207112i	−0.595927	−	0.803039i	$-0.703215\pi$
$373$	4.00000	−	4.00000i	0.207112	−	0.207112i	0.803039	+	0.595927i	$0.203215\pi$
$374$	2.82843			0.146254
$375$	−8.17157	−	17.5563i	−0.421978	−	0.906606i
$376$		0			0
$377$		0			0
$378$	3.58579	−	6.41421i	0.184433	−	0.329912i
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$	2.82843	−	8.48528i	0.145095	−	0.435286i
$381$	14.0000	−	9.89949i	0.717242	−	0.507166i
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$	16.9706	+	16.9706i	0.867155	+	0.867155i	0.992157	−	0.125001i	$-0.0398935\pi$
$383$	16.9706	+	16.9706i	0.867155	+	0.867155i	−0.125001	+	0.992157i	$0.539894\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$	−2.00000	−	4.00000i	−0.101929	−	0.203859i
$386$		−	21.2132i		−	1.07972i
$387$	−22.9706	+	10.9706i	−1.16766	+	0.557665i
$388$	3.00000	−	3.00000i	0.152302	−	0.152302i
$389$	−4.24264			−0.215110			−0.107555	−	0.994199i	$-0.534302\pi$
$389$	−4.24264			−0.215110			−0.107555	+	0.994199i	$0.534302\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	−31.3848	−	5.38478i	−1.58315	−	0.271626i
$394$		−	24.0000i		−	1.20910i
$395$	12.7279	+	4.24264i	0.640411	+	0.213470i
$396$	−4.00000	−	1.41421i	−0.201008	−	0.0710669i
$397$	22.0000	+	22.0000i	1.10415	+	1.10415i	0.993905	+	0.110244i	$0.0351632\pi$
$397$	22.0000	+	22.0000i	1.10415	+	1.10415i	0.110244	+	0.993905i	$0.464837\pi$
$398$	16.9706	+	16.9706i	0.850657	+	0.850657i
$399$	5.65685	+	8.00000i	0.283197	+	0.400501i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$			8.48528i			0.423735i	0.977298	+	0.211867i	$0.0679545\pi$
$401$			8.48528i			0.423735i	−0.977298	+	0.211867i	$0.932046\pi$
$402$	−1.65685	+	9.65685i	−0.0826364	+	0.481640i
$403$		0			0
$404$	−9.89949			−0.492518
$405$	16.9497	−	10.8492i	0.842240	−	0.539103i
$406$	10.0000			0.496292
$407$	−8.48528	+	8.48528i	−0.420600	+	0.420600i
$408$	0.585786	−	3.41421i	0.0290008	−	0.169029i
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$	−11.3137	+	5.65685i	−0.558744	+	0.279372i
$411$	6.00000	+	8.48528i	0.295958	+	0.418548i
$412$	−1.00000	−	1.00000i	−0.0492665	−	0.0492665i
$413$	9.89949	+	9.89949i	0.487122	+	0.487122i
$414$	−11.3137	−	4.00000i	−0.556038	−	0.196589i
$415$	24.0000	−	12.0000i	1.17811	−	0.589057i
$416$		0			0
$417$	−13.6569	−	2.34315i	−0.668779	−	0.114744i
$418$	4.00000	−	4.00000i	0.195646	−	0.195646i
$419$	−21.2132			−1.03633			−0.518166	−	0.855280i	$-0.673385\pi$
$419$	−21.2132			−1.03633			−0.518166	+	0.855280i	$0.673385\pi$
$420$	−5.24264	+	1.58579i	−0.255815	+	0.0773785i
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	−5.65685	+	5.65685i	−0.275371	+	0.275371i
$423$		0			0
$424$			4.00000i			0.194257i
$425$	9.89949	−	1.41421i	0.480196	−	0.0685994i
$426$	−20.0000	+	14.1421i	−0.969003	+	0.685189i
$427$	6.00000	+	6.00000i	0.290360	+	0.290360i
$428$	−2.82843	−	2.82843i	−0.136717	−	0.136717i
$429$		0			0
$430$	18.0000	+	6.00000i	0.868037	+	0.289346i
$431$		−	11.3137i		−	0.544962i	−0.962161	−	0.272481i	$-0.912156\pi$
$431$		−	11.3137i		−	0.544962i	0.962161	−	0.272481i	$-0.0878442\pi$
$432$	−2.53553	+	4.53553i	−0.121991	+	0.218216i
$433$	−1.00000	+	1.00000i	−0.0480569	+	0.0480569i	−0.730727	−	0.682670i	$-0.760819\pi$
$433$	−1.00000	+	1.00000i	−0.0480569	+	0.0480569i	0.682670	+	0.730727i	$0.260819\pi$
$434$	−2.82843			−0.135769
$435$	24.1421	+	12.9289i	1.15753	+	0.619895i
$436$	−10.0000			−0.478913
$437$	11.3137	−	11.3137i	0.541208	−	0.541208i
$438$	12.0711	+	2.07107i	0.576778	+	0.0989594i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	1.41421	+	2.82843i	0.0674200	+	0.134840i
$441$	−5.00000	+	14.1421i	−0.238095	+	0.673435i
$442$		0			0
$443$	4.24264	+	4.24264i	0.201574	+	0.201574i	0.800674	−	0.599100i	$-0.204475\pi$
$443$	4.24264	+	4.24264i	0.201574	+	0.201574i	−0.599100	+	0.800674i	$0.704475\pi$
$444$	8.48528	+	12.0000i	0.402694	+	0.569495i
$445$	−2.00000	+	6.00000i	−0.0948091	+	0.284427i
$446$		−	12.7279i		−	0.602685i
$447$	3.72792	−	21.7279i	0.176325	−	1.02770i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	−14.1421			−0.667409			−0.333704	−	0.942678i	$-0.608299\pi$
$449$	−14.1421			−0.667409			−0.333704	+	0.942678i	$0.608299\pi$
$450$	−14.7071	−	2.94975i	−0.693300	−	0.139052i
$451$	−8.00000			−0.376705
$452$	−9.89949	+	9.89949i	−0.465633	+	0.465633i
$453$	−4.68629	+	27.3137i	−0.220181	+	1.28331i
$454$		−	22.0000i		−	1.03251i
$455$		0			0
$456$	−4.00000	−	5.65685i	−0.187317	−	0.264906i
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	0.263099	−	0.964769i	$-0.415256\pi$
$457$	−15.0000	−	15.0000i	−0.701670	−	0.701670i	−0.964769	+	0.263099i	$0.915256\pi$
$458$	4.24264	+	4.24264i	0.198246	+	0.198246i
$459$	2.82843	+	10.0000i	0.132020	+	0.466760i
$460$	4.00000	+	8.00000i	0.186501	+	0.373002i
$461$		−	7.07107i		−	0.329332i	−0.986349	−	0.164666i	$-0.947345\pi$
$461$		−	7.07107i		−	0.329332i	0.986349	−	0.164666i	$-0.0526547\pi$
$462$	−3.41421	−	0.585786i	−0.158844	−	0.0272533i
$463$	5.00000	−	5.00000i	0.232370	−	0.232370i	−0.581311	−	0.813681i	$-0.697460\pi$
$463$	5.00000	−	5.00000i	0.232370	−	0.232370i	0.813681	+	0.581311i	$0.197460\pi$
$464$	−7.07107			−0.328266
$465$	−6.82843	−	3.65685i	−0.316661	−	0.169583i
$466$	−18.0000			−0.833834
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	−0.0805616	−	0.996750i	$-0.525671\pi$
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	0.996750	+	0.0805616i	$0.0256714\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$		0			0
$471$		0			0
$472$	−7.00000	−	7.00000i	−0.322201	−	0.322201i
$473$	8.48528	+	8.48528i	0.390154	+	0.390154i
$474$	8.48528	−	6.00000i	0.389742	−	0.275589i
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$		−	2.82843i		−	0.129641i
$477$	−5.17157	−	10.8284i	−0.236790	−	0.495800i
$478$	−6.00000	+	6.00000i	−0.274434	+	0.274434i
$479$	−31.1127			−1.42158			−0.710788	−	0.703407i	$-0.751661\pi$
$479$	−31.1127			−1.42158			−0.710788	+	0.703407i	$0.751661\pi$
$480$	3.70711	−	1.12132i	0.169206	−	0.0511810i
$481$		0			0
$482$	−2.82843	+	2.82843i	−0.128831	+	0.128831i
$483$	−9.65685	−	1.65685i	−0.439402	−	0.0753895i
$484$		−	9.00000i		−	0.409091i
$485$	8.48528	−	4.24264i	0.385297	−	0.192648i
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$	9.00000	+	9.00000i	0.407829	+	0.407829i	0.880981	−	0.473152i	$-0.156884\pi$
$487$	9.00000	+	9.00000i	0.407829	+	0.407829i	−0.473152	+	0.880981i	$0.656884\pi$
$488$	−4.24264	−	4.24264i	−0.192055	−	0.192055i
$489$	−5.65685	−	8.00000i	−0.255812	−	0.361773i
$490$	10.0000	−	5.00000i	0.451754	−	0.225877i
$491$		−	26.8701i		−	1.21263i	−0.795225	−	0.606314i	$-0.792647\pi$
$491$		−	26.8701i		−	1.21263i	0.795225	−	0.606314i	$-0.207353\pi$
$492$	−1.65685	+	9.65685i	−0.0746968	+	0.435365i
$493$	−10.0000	+	10.0000i	−0.450377	+	0.450377i
$494$		0			0
$495$	−7.48528	−	5.82843i	−0.336438	−	0.261968i
$496$	2.00000			0.0898027
$497$	−14.1421	+	14.1421i	−0.634361	+	0.634361i
$498$	3.51472	−	20.4853i	0.157498	−	0.917967i
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$	8.00000	+	11.3137i	0.357414	+	0.505459i
$502$	9.00000	+	9.00000i	0.401690	+	0.401690i
$503$	−8.48528	−	8.48528i	−0.378340	−	0.378340i	0.492163	−	0.870503i	$-0.336206\pi$
$503$	−8.48528	−	8.48528i	−0.378340	−	0.378340i	−0.870503	+	0.492163i	$0.836206\pi$
$504$	−1.41421	+	4.00000i	−0.0629941	+	0.178174i
$505$	−21.0000	−	7.00000i	−0.934488	−	0.311496i
$506$			5.65685i			0.251478i
$507$	−22.1924	−	3.80761i	−0.985599	−	0.169102i
$508$	−7.00000	+	7.00000i	−0.310575	+	0.310575i
$509$	24.0416			1.06563			0.532813	−	0.846233i	$-0.321135\pi$
$509$	24.0416			1.06563			0.532813	+	0.846233i	$0.321135\pi$
$510$	3.65685	−	6.82843i	0.161928	−	0.302368i
$511$	10.0000			0.442374
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	18.1421	+	10.1421i	0.800995	+	0.447786i
$514$			14.0000i			0.617514i
$515$	−1.41421	−	2.82843i	−0.0623177	−	0.124635i
$516$	12.0000	−	8.48528i	0.528271	−	0.373544i
$517$		0			0
$518$	8.48528	+	8.48528i	0.372822	+	0.372822i
$519$	−2.82843	+	2.00000i	−0.124154	+	0.0877903i
$520$		0			0
$521$			25.4558i			1.11524i	0.830096	+	0.557620i	$0.188286\pi$
$521$			25.4558i			1.11524i	−0.830096	+	0.557620i	$0.811714\pi$
$522$	19.1421	−	9.14214i	0.837829	−	0.400140i
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$	18.3848			0.803143
$525$	−12.2426	−	0.343146i	−0.534313	−	0.0149761i
$526$	8.00000			0.348817
$527$	2.82843	−	2.82843i	0.123208	−	0.123208i
$528$	2.41421	+	0.414214i	0.105065	+	0.0180263i
$529$		−	7.00000i		−	0.304348i
$530$	−2.82843	+	8.48528i	−0.122859	+	0.368577i
$531$	28.0000	+	9.89949i	1.21510	+	0.429601i
$532$	−4.00000	−	4.00000i	−0.173422	−	0.173422i
$533$		0			0
$534$	2.82843	+	4.00000i	0.122398	+	0.173097i
$535$	−4.00000	−	8.00000i	−0.172935	−	0.345870i
$536$		−	5.65685i		−	0.244339i
$537$	−5.38478	+	31.3848i	−0.232370	+	1.35435i
$538$	−11.0000	+	11.0000i	−0.474244	+	0.474244i
$539$	7.07107			0.304572
$540$	−8.58579	+	7.82843i	−0.369473	+	0.336882i
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$		0			0
$543$	6.44365	−	37.5563i	0.276524	−	1.61170i
$544$			2.00000i			0.0857493i
$545$	−21.2132	−	7.07107i	−0.908674	−	0.302891i
$546$		0			0
$547$	6.00000	+	6.00000i	0.256541	+	0.256541i	0.823646	−	0.567104i	$-0.191936\pi$
$547$	6.00000	+	6.00000i	0.256541	+	0.256541i	−0.567104	+	0.823646i	$0.691936\pi$
$548$	−4.24264	−	4.24264i	−0.181237	−	0.181237i
$549$	16.9706	+	6.00000i	0.724286	+	0.256074i
$550$	1.00000	+	7.00000i	0.0426401	+	0.298481i
$551$			28.2843i			1.20495i
$552$	6.82843	+	1.17157i	0.290637	+	0.0498655i
$553$	6.00000	−	6.00000i	0.255146	−	0.255146i
$554$	8.48528			0.360505
$555$	9.51472	+	31.4558i	0.403877	+	1.33523i
$556$	8.00000			0.339276
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$	−5.41421	+	2.58579i	−0.229202	+	0.109465i
$559$		0			0
$560$	2.82843	−	1.41421i	0.119523	−	0.0597614i
$561$	4.00000	−	2.82843i	0.168880	−	0.119416i
$562$	6.00000	+	6.00000i	0.253095	+	0.253095i
$563$	−21.2132	−	21.2132i	−0.894030	−	0.894030i	0.100870	−	0.994900i	$-0.467837\pi$
$563$	−21.2132	−	21.2132i	−0.894030	−	0.894030i	−0.994900	+	0.100870i	$0.967837\pi$
$564$		0			0
$565$	−28.0000	+	14.0000i	−1.17797	+	0.588984i
$566$			28.2843i			1.18888i
$567$	−1.34315	−	12.6569i	−0.0564068	−	0.531538i
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$	14.1421			0.592869			0.296435	−	0.955053i	$-0.404202\pi$
$569$	14.1421			0.592869			0.296435	+	0.955053i	$0.404202\pi$
$570$	−4.48528	−	14.8284i	−0.187868	−	0.621094i
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$	−4.82843	−	0.828427i	−0.201710	−	0.0346080i
$574$			8.00000i			0.333914i
$575$	2.82843	+	19.7990i	0.117954	+	0.825675i
$576$	1.00000	−	2.82843i	0.0416667	−	0.117851i
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	0.923880	−	0.382683i	$-0.125000\pi$
$577$	13.0000	+	13.0000i	0.541197	+	0.541197i	−0.382683	+	0.923880i	$0.625000\pi$
$578$	−9.19239	−	9.19239i	−0.382353	−	0.382353i
$579$	−21.2132	−	30.0000i	−0.881591	−	1.24676i
$580$	−15.0000	−	5.00000i	−0.622841	−	0.207614i
$581$		−	16.9706i		−	0.704058i
$582$	1.24264	−	7.24264i	0.0515091	−	0.300217i
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	−7.07107			−0.292603
$585$		0			0
$586$		0			0
$587$	25.4558	−	25.4558i	1.05068	−	1.05068i	0.0520296	−	0.998646i	$-0.483431\pi$
$587$	25.4558	−	25.4558i	1.05068	−	1.05068i	0.998646	−	0.0520296i	$-0.0165690\pi$
$588$	1.46447	−	8.53553i	0.0603936	−	0.351999i
$589$		−	8.00000i		−	0.329634i
$590$	−9.89949	−	19.7990i	−0.407556	−	0.815112i
$591$	−24.0000	−	33.9411i	−0.987228	−	1.39615i
$592$	−6.00000	−	6.00000i	−0.246598	−	0.246598i
$593$	−15.5563	−	15.5563i	−0.638823	−	0.638823i	0.311442	−	0.950265i	$-0.399188\pi$
$593$	−15.5563	−	15.5563i	−0.638823	−	0.638823i	−0.950265	+	0.311442i	$0.899188\pi$
$594$	−7.07107	+	2.00000i	−0.290129	+	0.0820610i
$595$	2.00000	−	6.00000i	0.0819920	−	0.245976i
$596$			12.7279i			0.521356i
$597$	40.9706	+	7.02944i	1.67681	+	0.287696i
$598$		0			0
$599$	45.2548			1.84906			0.924531	−	0.381106i	$-0.124457\pi$
$599$	45.2548			1.84906			0.924531	+	0.381106i	$0.124457\pi$
$600$	8.65685	+	0.242641i	0.353415	+	0.00990576i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	8.48528	−	8.48528i	0.345834	−	0.345834i
$603$	7.31371	+	15.3137i	0.297837	+	0.623622i
$604$		−	16.0000i		−	0.651031i
$605$	6.36396	−	19.0919i	0.258732	−	0.776195i
$606$	−14.0000	+	9.89949i	−0.568711	+	0.402139i
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	0.765364	−	0.643598i	$-0.222559\pi$
$607$	3.00000	+	3.00000i	0.121766	+	0.121766i	−0.643598	+	0.765364i	$0.722559\pi$
$608$	2.82843	+	2.82843i	0.114708	+	0.114708i
$609$	14.1421	−	10.0000i	0.573068	−	0.405220i
$610$	−6.00000	−	12.0000i	−0.242933	−	0.485866i
$611$		0			0
$612$	−2.58579	−	5.41421i	−0.104524	−	0.218857i
$613$	18.0000	−	18.0000i	0.727013	−	0.727013i	−0.243011	−	0.970024i	$-0.578135\pi$
$613$	18.0000	−	18.0000i	0.727013	−	0.727013i	0.970024	+	0.243011i	$0.0781350\pi$
$614$	−25.4558			−1.02731
$615$	−10.3431	+	19.3137i	−0.417076	+	0.778804i
$616$	2.00000			0.0805823
$617$	−21.2132	+	21.2132i	−0.854011	+	0.854011i	−0.990624	−	0.136613i	$-0.956378\pi$
$617$	−21.2132	+	21.2132i	−0.854011	+	0.854011i	0.136613	+	0.990624i	$0.456378\pi$
$618$	−2.41421	−	0.414214i	−0.0971139	−	0.0166621i
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$	4.24264	+	1.41421i	0.170389	+	0.0567962i
$621$	−20.0000	+	5.65685i	−0.802572	+	0.227002i
$622$	−14.0000	−	14.0000i	−0.561349	−	0.561349i
$623$	2.82843	+	2.82843i	0.113319	+	0.113319i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			12.7279i			0.508710i
$627$	1.65685	−	9.65685i	0.0661684	−	0.385658i
$628$		0			0
$629$	−16.9706			−0.676661
$630$	−5.82843	+	7.48528i	−0.232210	+	0.298221i
$631$	−14.0000			−0.557331			−0.278666	−	0.960388i	$-0.589892\pi$
$631$	−14.0000			−0.557331			−0.278666	+	0.960388i	$0.589892\pi$
$632$	−4.24264	+	4.24264i	−0.168763	+	0.168763i
$633$	−2.34315	+	13.6569i	−0.0931317	+	0.542811i
$634$			18.0000i			0.714871i
$635$	−19.7990	+	9.89949i	−0.785699	+	0.392849i
$636$	4.00000	+	5.65685i	0.158610	+	0.224309i
$637$		0			0
$638$	−7.07107	−	7.07107i	−0.279946	−	0.279946i
$639$	−14.1421	+	40.0000i	−0.559454	+	1.58238i
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$		−	5.65685i		−	0.223432i	−0.993740	−	0.111716i	$-0.964365\pi$
$641$		−	5.65685i		−	0.223432i	0.993740	−	0.111716i	$-0.0356347\pi$
$642$	−6.82843	−	1.17157i	−0.269497	−	0.0462383i
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	−0.0521706	−	0.998638i	$-0.516614\pi$
$643$	24.0000	−	24.0000i	0.946468	−	0.946468i	0.998638	+	0.0521706i	$0.0166140\pi$
$644$	5.65685			0.222911
$645$	31.4558	−	9.51472i	1.23857	−	0.374642i
$646$	8.00000			0.314756
$647$	−19.7990	+	19.7990i	−0.778379	+	0.778379i	−0.979555	−	0.201176i	$-0.935524\pi$
$647$	−19.7990	+	19.7990i	−0.778379	+	0.778379i	0.201176	+	0.979555i	$0.435524\pi$
$648$	0.949747	+	8.94975i	0.0373096	+	0.351579i
$649$		−	14.0000i		−	0.549548i
$650$		0			0
$651$	−4.00000	+	2.82843i	−0.156772	+	0.110855i
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	0.619203	−	0.785231i	$-0.287456\pi$
$653$	−4.24264	−	4.24264i	−0.166027	−	0.166027i	−0.785231	+	0.619203i	$0.787456\pi$
$654$	−14.1421	+	10.0000i	−0.553001	+	0.391031i
$655$	39.0000	+	13.0000i	1.52386	+	0.507952i
$656$		−	5.65685i		−	0.220863i
$657$	19.1421	−	9.14214i	0.746806	−	0.356669i
$658$		0			0
$659$	35.3553			1.37725			0.688624	−	0.725118i	$-0.258215\pi$
$659$	35.3553			1.37725			0.688624	+	0.725118i	$0.258215\pi$
$660$	4.82843	+	2.58579i	0.187946	+	0.100652i
$661$	50.0000			1.94477			0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000			1.94477			0.972387	+	0.233373i	$0.0749763\pi$
$662$	5.65685	−	5.65685i	0.219860	−	0.219860i
$663$		0			0
$664$			12.0000i			0.465690i
$665$	−5.65685	−	11.3137i	−0.219363	−	0.438727i
$666$	24.0000	+	8.48528i	0.929981	+	0.328798i
$667$	−20.0000	−	20.0000i	−0.774403	−	0.774403i
$668$	−5.65685	−	5.65685i	−0.218870	−	0.218870i
$669$	−12.7279	−	18.0000i	−0.492090	−	0.695920i
$670$	4.00000	−	12.0000i	0.154533	−	0.463600i
$671$		−	8.48528i		−	0.327571i
$672$	0.414214	−	2.41421i	0.0159786	−	0.0931303i
$673$	13.0000	−	13.0000i	0.501113	−	0.501113i	−0.410671	−	0.911784i	$-0.634705\pi$
$673$	13.0000	−	13.0000i	0.501113	−	0.501113i	0.911784	+	0.410671i	$0.134705\pi$
$674$	12.7279			0.490261
$675$	−23.7487	+	10.5355i	−0.914089	+	0.405513i
$676$	13.0000			0.500000
$677$	−18.3848	+	18.3848i	−0.706584	+	0.706584i	−0.965815	−	0.259231i	$-0.916531\pi$
$677$	−18.3848	+	18.3848i	−0.706584	+	0.706584i	0.259231	+	0.965815i	$0.416531\pi$
$678$	−4.10051	+	23.8995i	−0.157479	+	0.917855i
$679$		−	6.00000i		−	0.230259i
$680$	−1.41421	+	4.24264i	−0.0542326	+	0.162698i
$681$	−22.0000	−	31.1127i	−0.843042	−	1.19224i
$682$	2.00000	+	2.00000i	0.0765840	+	0.0765840i
$683$	25.4558	+	25.4558i	0.974041	+	0.974041i	0.999671	−	0.0256307i	$-0.00815939\pi$
$683$	25.4558	+	25.4558i	0.974041	+	0.974041i	−0.0256307	+	0.999671i	$0.508159\pi$
$684$	−11.3137	−	4.00000i	−0.432590	−	0.152944i
$685$	−6.00000	−	12.0000i	−0.229248	−	0.458496i
$686$		−	16.9706i		−	0.647939i
$687$	10.2426	+	1.75736i	0.390781	+	0.0670474i
$688$	−6.00000	+	6.00000i	−0.228748	+	0.228748i
$689$		0			0
$690$	13.6569	+	7.31371i	0.519908	+	0.278428i
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	1.41421	−	1.41421i	0.0537603	−	0.0537603i
$693$	−5.41421	+	2.58579i	−0.205669	+	0.0982259i
$694$		−	14.0000i		−	0.531433i
$695$	16.9706	+	5.65685i	0.643730	+	0.214577i
$696$	−10.0000	+	7.07107i	−0.379049	+	0.268028i
$697$	−8.00000	−	8.00000i	−0.303022	−	0.303022i
$698$	1.41421	+	1.41421i	0.0535288	+	0.0535288i
$699$	−25.4558	+	18.0000i	−0.962828	+	0.680823i
$700$	7.00000	−	1.00000i	0.264575	−	0.0377964i
$701$			26.8701i			1.01487i	0.861691	+	0.507434i	$0.169406\pi$
$701$			26.8701i			1.01487i	−0.861691	+	0.507434i	$0.830594\pi$
$702$		0			0
$703$	−24.0000	+	24.0000i	−0.905177	+	0.905177i
$704$	−1.41421			−0.0533002
$705$		0			0
$706$	18.0000			0.677439
$707$	−9.89949	+	9.89949i	−0.372309	+	0.372309i
$708$	−16.8995	−	2.89949i	−0.635122	−	0.108970i
$709$			10.0000i			0.375558i	0.982211	+	0.187779i	$0.0601289\pi$
$709$			10.0000i			0.375558i	−0.982211	+	0.187779i	$0.939871\pi$
$710$	28.2843	−	14.1421i	1.06149	−	0.530745i
$711$	6.00000	−	16.9706i	0.225018	−	0.636446i
$712$	−2.00000	−	2.00000i	−0.0749532	−	0.0749532i
$713$	5.65685	+	5.65685i	0.211851	+	0.211851i
$714$	−2.82843	−	4.00000i	−0.105851	−	0.149696i
$715$		0			0
$716$		−	18.3848i		−	0.687071i
$717$	−2.48528	+	14.4853i	−0.0928145	+	0.540963i
$718$	8.00000	−	8.00000i	0.298557	−	0.298557i
$719$	−22.6274			−0.843860			−0.421930	−	0.906628i	$-0.638647\pi$
$719$	−22.6274			−0.843860			−0.421930	+	0.906628i	$0.638647\pi$
$720$	4.12132	−	5.29289i	0.153593	−	0.197254i
$721$	−2.00000			−0.0744839
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$	−1.17157	+	6.82843i	−0.0435713	+	0.253952i
$724$			22.0000i			0.817624i
$725$	−28.2843	−	21.2132i	−1.05045	−	0.787839i
$726$	−9.00000	−	12.7279i	−0.334021	−	0.472377i
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	0.649283	−	0.760547i	$-0.275069\pi$
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	−0.760547	+	0.649283i	$0.775069\pi$
$728$		0			0
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	−15.0000	−	5.00000i	−0.555175	−	0.185058i
$731$			16.9706i			0.627679i
$732$	−10.2426	−	1.75736i	−0.378579	−	0.0649539i
$733$	−26.0000	+	26.0000i	−0.960332	+	0.960332i	−0.999243	−	0.0389108i	$-0.987611\pi$
$733$	−26.0000	+	26.0000i	−0.960332	+	0.960332i	0.0389108	+	0.999243i	$0.487611\pi$
$734$	26.8701			0.991792
$735$	9.14214	−	17.0711i	0.337213	−	0.629676i
$736$	−4.00000			−0.147442
$737$	5.65685	−	5.65685i	0.208373	−	0.208373i
$738$	7.31371	+	15.3137i	0.269221	+	0.563705i
$739$		−	40.0000i		−	1.47142i	−0.677295	−	0.735712i	$-0.736848\pi$
$739$		−	40.0000i		−	1.47142i	0.677295	−	0.735712i	$-0.263152\pi$
$740$	−8.48528	−	16.9706i	−0.311925	−	0.623850i
$741$		0			0
$742$	4.00000	+	4.00000i	0.146845	+	0.146845i
$743$	36.7696	+	36.7696i	1.34894	+	1.34894i	0.886810	+	0.462134i	$0.152916\pi$
$743$	36.7696	+	36.7696i	1.34894	+	1.34894i	0.462134	+	0.886810i	$0.347084\pi$
$744$	2.82843	−	2.00000i	0.103695	−	0.0733236i
$745$	−9.00000	+	27.0000i	−0.329734	+	0.989203i
$746$			5.65685i			0.207112i
$747$	−15.5147	−	32.4853i	−0.567654	−	1.18857i
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	−5.65685			−0.206697
$750$	18.1924	+	6.63604i	0.664292	+	0.242314i
$751$	−30.0000			−1.09472			−0.547358	−	0.836899i	$-0.684366\pi$
$751$	−30.0000			−1.09472			−0.547358	+	0.836899i	$0.684366\pi$
$752$		0			0
$753$	21.7279	+	3.72792i	0.791809	+	0.135853i
$754$		0			0
$755$	11.3137	−	33.9411i	0.411748	−	1.23524i
$756$	2.00000	+	7.07107i	0.0727393	+	0.257172i
$757$	−30.0000	−	30.0000i	−1.09037	−	1.09037i	−0.995489	−	0.0948798i	$-0.969753\pi$
$757$	−30.0000	−	30.0000i	−1.09037	−	1.09037i	−0.0948798	−	0.995489i	$-0.530247\pi$
$758$	−11.3137	−	11.3137i	−0.410932	−	0.410932i
$759$	5.65685	+	8.00000i	0.205331	+	0.290382i
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$		−	36.7696i		−	1.33290i	−0.745552	−	0.666448i	$-0.767814\pi$
$761$		−	36.7696i		−	1.33290i	0.745552	−	0.666448i	$-0.232186\pi$
$762$	−2.89949	+	16.8995i	−0.105038	+	0.612204i
$763$	−10.0000	+	10.0000i	−0.362024	+	0.362024i
$764$	2.82843			0.102329
$765$	−1.65685	−	13.3137i	−0.0599037	−	0.481358i
$766$	−24.0000			−0.867155
$767$		0			0
$768$	−0.292893	+	1.70711i	−0.0105689	+	0.0615999i
$769$		−	22.0000i		−	0.793340i	−0.917961	−	0.396670i	$-0.870166\pi$
$769$		−	22.0000i		−	0.793340i	0.917961	−	0.396670i	$-0.129834\pi$
$770$	4.24264	+	1.41421i	0.152894	+	0.0509647i
$771$	14.0000	+	19.7990i	0.504198	+	0.713043i
$772$	15.0000	+	15.0000i	0.539862	+	0.539862i
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.997499	−	0.0706813i	$-0.977483\pi$
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.0706813	−	0.997499i	$-0.522517\pi$
$774$	8.48528	−	24.0000i	0.304997	−	0.862662i
$775$	8.00000	+	6.00000i	0.287368	+	0.215526i
$776$			4.24264i			0.152302i
$777$	20.4853	+	3.51472i	0.734905	+	0.126090i
$778$	3.00000	−	3.00000i	0.107555	−	0.107555i
$779$	−22.6274			−0.810711
$780$		0			0
$781$	20.0000			0.715656
$782$	−5.65685	+	5.65685i	−0.202289	+	0.202289i
$783$	17.9289	−	32.0711i	0.640728	−	1.14613i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	26.0000	−	18.3848i	0.927389	−	0.655763i
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	0.999998	−	0.00190598i	$-0.000606691\pi$
$787$	28.0000	+	28.0000i	0.998092	+	0.998092i	−0.00190598	+	0.999998i	$0.500607\pi$
$788$	16.9706	+	16.9706i	0.604551	+	0.604551i
$789$	11.3137	−	8.00000i	0.402779	−	0.284808i
$790$	−12.0000	+	6.00000i	−0.426941	+	0.213470i
$791$			19.7990i			0.703971i
$792$	3.82843	−	1.82843i	0.136037	−	0.0649703i
$793$		0			0
$794$	−31.1127			−1.10415
$795$	4.48528	+	14.8284i	0.159077	+	0.525910i
$796$	−24.0000			−0.850657
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$	−9.65685	−	1.65685i	−0.341849	−	0.0586520i
$799$		0			0
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$	8.00000	+	2.82843i	0.282666	+	0.0999376i
$802$	−6.00000	−	6.00000i	−0.211867	−	0.211867i
$803$	−7.07107	−	7.07107i	−0.249533	−	0.249533i
$804$	−5.65685	−	8.00000i	−0.199502	−	0.282138i
$805$	12.0000	+	4.00000i	0.422944	+	0.140981i
$806$		0			0
$807$	−4.55635	+	26.5563i	−0.160391	+	0.934828i
$808$	7.00000	−	7.00000i	0.246259	−	0.246259i
$809$	22.6274			0.795538			0.397769	−	0.917486i	$-0.369785\pi$
$809$	22.6274			0.795538			0.397769	+	0.917486i	$0.369785\pi$
$810$	−4.31371	+	19.6569i	−0.151568	+	0.690671i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−7.07107	+	7.07107i	−0.248146	+	0.248146i
$813$		0			0
$814$		−	12.0000i		−	0.420600i
$815$	5.65685	+	11.3137i	0.198151	+	0.396302i
$816$	2.00000	+	2.82843i	0.0700140	+	0.0990148i
$817$	24.0000	+	24.0000i	0.839654	+	0.839654i
$818$		0			0
$819$		0			0
$820$	4.00000	−	12.0000i	0.139686	−	0.419058i
$821$			43.8406i			1.53005i	0.644002	+	0.765024i	$0.277273\pi$
$821$			43.8406i			1.53005i	−0.644002	+	0.765024i	$0.722727\pi$
$822$	−10.2426	−	1.75736i	−0.357253	−	0.0612949i
$823$	−25.0000	+	25.0000i	−0.871445	+	0.871445i	−0.992630	−	0.121185i	$-0.961331\pi$
$823$	−25.0000	+	25.0000i	−0.871445	+	0.871445i	0.121185	+	0.992630i	$0.461331\pi$
$824$	1.41421			0.0492665
$825$	8.41421	+	8.89949i	0.292945	+	0.309841i
$826$	−14.0000			−0.487122
$827$	12.7279	−	12.7279i	0.442593	−	0.442593i	−0.450289	−	0.892883i	$-0.648679\pi$
$827$	12.7279	−	12.7279i	0.442593	−	0.442593i	0.892883	+	0.450289i	$0.148679\pi$
$828$	10.8284	−	5.17157i	0.376314	−	0.179725i
$829$			14.0000i			0.486240i	0.969996	+	0.243120i	$0.0781709\pi$
$829$			14.0000i			0.486240i	−0.969996	+	0.243120i	$0.921829\pi$
$830$	−8.48528	+	25.4558i	−0.294528	+	0.883585i
$831$	12.0000	−	8.48528i	0.416275	−	0.294351i
$832$		0			0
$833$	7.07107	+	7.07107i	0.244998	+	0.244998i
$834$	11.3137	−	8.00000i	0.391762	−	0.277017i
$835$	−8.00000	−	16.0000i	−0.276851	−	0.553703i
$836$			5.65685i			0.195646i
$837$	−5.07107	+	9.07107i	−0.175282	+	0.313542i
$838$	15.0000	−	15.0000i	0.518166	−	0.518166i
$839$	5.65685			0.195296			0.0976481	−	0.995221i	$-0.468868\pi$
$839$	5.65685			0.195296			0.0976481	+	0.995221i	$0.468868\pi$
$840$	2.58579	−	4.82843i	0.0892181	−	0.166597i
$841$	21.0000			0.724138
$842$	−9.89949	+	9.89949i	−0.341159	+	0.341159i
$843$	14.4853	+	2.48528i	0.498900	+	0.0855976i
$844$		−	8.00000i		−	0.275371i
$845$	27.5772	+	9.19239i	0.948683	+	0.316228i
$846$		0			0
$847$	−9.00000	−	9.00000i	−0.309244	−	0.309244i
$848$	−2.82843	−	2.82843i	−0.0971286	−	0.0971286i
$849$	28.2843	+	40.0000i	0.970714	+	1.37280i
$850$	−6.00000	+	8.00000i	−0.205798	+	0.274398i
$851$		−	33.9411i		−	1.16349i
$852$	4.14214	−	24.1421i	0.141907	−	0.827096i
$853$	−2.00000	+	2.00000i	−0.0684787	+	0.0684787i	−0.740517	−	0.672038i	$-0.765419\pi$
$853$	−2.00000	+	2.00000i	−0.0684787	+	0.0684787i	0.672038	+	0.740517i	$0.265419\pi$
$854$	−8.48528			−0.290360
$855$	−21.1716	−	16.4853i	−0.724053	−	0.563785i
$856$	4.00000			0.136717
$857$	38.1838	−	38.1838i	1.30433	−	1.30433i	0.378892	−	0.925441i	$-0.376305\pi$
$857$	38.1838	−	38.1838i	1.30433	−	1.30433i	0.925441	−	0.378892i	$-0.123695\pi$
$858$		0			0
$859$			32.0000i			1.09183i	0.837842	+	0.545913i	$0.183817\pi$
$859$			32.0000i			1.09183i	−0.837842	+	0.545913i	$0.816183\pi$
$860$	−16.9706	+	8.48528i	−0.578691	+	0.289346i
$861$	8.00000	+	11.3137i	0.272639	+	0.385570i
$862$	8.00000	+	8.00000i	0.272481	+	0.272481i
$863$	−36.7696	−	36.7696i	−1.25165	−	1.25165i	−0.954980	−	0.296670i	$-0.904124\pi$
$863$	−36.7696	−	36.7696i	−1.25165	−	1.25165i	−0.296670	−	0.954980i	$-0.595876\pi$
$864$	−1.41421	−	5.00000i	−0.0481125	−	0.170103i
$865$	4.00000	−	2.00000i	0.136004	−	0.0680020i
$866$		−	1.41421i		−	0.0480569i
$867$	−22.1924	−	3.80761i	−0.753693	−	0.129313i
$868$	2.00000	−	2.00000i	0.0678844	−	0.0678844i
$869$	−8.48528			−0.287843
$870$	−26.2132	+	7.92893i	−0.888711	+	0.268816i
$871$		0			0
$872$	7.07107	−	7.07107i	0.239457	−	0.239457i
$873$	−5.48528	−	11.4853i	−0.185649	−	0.388718i
$874$			16.0000i			0.541208i
$875$	15.5563	+	2.82843i	0.525901	+	0.0956183i
$876$	−10.0000	+	7.07107i	−0.337869	+	0.238909i
$877$	−36.0000	−	36.0000i	−1.21563	−	1.21563i	−0.969146	−	0.246488i	$-0.920724\pi$
$877$	−36.0000	−	36.0000i	−1.21563	−	1.21563i	−0.246488	−	0.969146i	$-0.579276\pi$
$878$	11.3137	+	11.3137i	0.381819	+	0.381819i
$879$		0			0
$880$	−3.00000	−	1.00000i	−0.101130	−	0.0337100i
$881$		−	19.7990i		−	0.667045i	−0.942742	−	0.333522i	$-0.891763\pi$
$881$		−	19.7990i		−	0.667045i	0.942742	−	0.333522i	$-0.108237\pi$
$882$	−6.46447	−	13.5355i	−0.217670	−	0.455765i
$883$	4.00000	−	4.00000i	0.134611	−	0.134611i	−0.636591	−	0.771202i	$-0.719656\pi$
$883$	4.00000	−	4.00000i	0.134611	−	0.134611i	0.771202	+	0.636591i	$0.219656\pi$
$884$		0			0
$885$	−33.7990	−	18.1005i	−1.13614	−	0.608442i
$886$	−6.00000			−0.201574
$887$	−8.48528	+	8.48528i	−0.284908	+	0.284908i	−0.835063	−	0.550155i	$-0.814569\pi$
$887$	−8.48528	+	8.48528i	−0.284908	+	0.284908i	0.550155	+	0.835063i	$0.314569\pi$
$888$	−14.4853	−	2.48528i	−0.486094	−	0.0834006i
$889$			14.0000i			0.469545i
$890$	−2.82843	−	5.65685i	−0.0948091	−	0.189618i
$891$	−8.00000	+	9.89949i	−0.268010	+	0.331646i
$892$	9.00000	+	9.00000i	0.301342	+	0.301342i
$893$		0			0
$894$	12.7279	+	18.0000i	0.425685	+	0.602010i
$895$	13.0000	−	39.0000i	0.434542	−	1.30363i
$896$			1.41421i			0.0472456i
$897$		0			0
$898$	10.0000	−	10.0000i	0.333704	−	0.333704i
$899$	−14.1421			−0.471667
$900$	12.4853	−	8.31371i	0.416176	−	0.277124i
$901$	−8.00000			−0.266519
$902$	5.65685	−	5.65685i	0.188353	−	0.188353i
$903$	3.51472	−	20.4853i	0.116963	−	0.681707i
$904$		−	14.0000i		−	0.465633i
$905$	−15.5563	+	46.6690i	−0.517111	+	1.55133i
$906$	−16.0000	−	22.6274i	−0.531564	−	0.751746i
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	0.970718	−	0.240220i	$-0.0772197\pi$
$907$	22.0000	+	22.0000i	0.730498	+	0.730498i	−0.240220	+	0.970718i	$0.577220\pi$
$908$	15.5563	+	15.5563i	0.516256	+	0.516256i
$909$	−9.89949	+	28.0000i	−0.328346	+	0.928701i
$910$		0			0
$911$		−	39.5980i		−	1.31194i	−0.754787	−	0.655970i	$-0.772260\pi$
$911$		−	39.5980i		−	1.31194i	0.754787	−	0.655970i	$-0.227740\pi$
$912$	6.82843	+	1.17157i	0.226112	+	0.0387947i
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$	21.2132			0.701670
$915$	−20.4853	−	10.9706i	−0.677223	−	0.362676i
$916$	−6.00000			−0.198246
$917$	18.3848	−	18.3848i	0.607119	−	0.607119i
$918$	−9.07107	−	5.07107i	−0.299390	−	0.167370i
$919$		−	34.0000i		−	1.12156i	−0.827966	−	0.560778i	$-0.810502\pi$
$919$		−	34.0000i		−	1.12156i	0.827966	−	0.560778i	$-0.189498\pi$
$920$	−8.48528	−	2.82843i	−0.279751	−	0.0932505i
$921$	−36.0000	+	25.4558i	−1.18624	+	0.838799i
$922$	5.00000	+	5.00000i	0.164666	+	0.164666i
$923$		0			0
$924$	2.82843	−	2.00000i	0.0930484	−	0.0657952i
$925$	−6.00000	−	42.0000i	−0.197279	−	1.38095i
$926$			7.07107i			0.232370i
$927$	−3.82843	+	1.82843i	−0.125742	+	0.0600534i
$928$	5.00000	−	5.00000i	0.164133	−	0.164133i
$929$	2.82843			0.0927977			0.0463988	−	0.998923i	$-0.485225\pi$
$929$	2.82843			0.0927977			0.0463988	+	0.998923i	$0.485225\pi$
$930$	7.41421	−	2.24264i	0.243122	−	0.0735391i
$931$	20.0000			0.655474
$932$	12.7279	−	12.7279i	0.416917	−	0.416917i
$933$	−33.7990	−	5.79899i	−1.10653	−	0.189850i
$934$			28.0000i			0.916188i
$935$	−5.65685	+	2.82843i	−0.184999	+	0.0924995i
$936$		0			0
$937$	−5.00000	−	5.00000i	−0.163343	−	0.163343i	0.620703	−	0.784046i	$-0.286847\pi$
$937$	−5.00000	−	5.00000i	−0.163343	−	0.163343i	−0.784046	+	0.620703i	$0.786847\pi$
$938$	−5.65685	−	5.65685i	−0.184703	−	0.184703i
$939$	12.7279	+	18.0000i	0.415360	+	0.587408i
$940$		0			0
$941$			12.7279i			0.414918i	0.978244	+	0.207459i	$0.0665194\pi$
$941$			12.7279i			0.414918i	−0.978244	+	0.207459i	$0.933481\pi$
$942$		0			0
$943$	16.0000	−	16.0000i	0.521032	−	0.521032i
$944$	9.89949			0.322201
$945$	−0.757359	+	16.4142i	−0.0246369	+	0.533954i
$946$	−12.0000			−0.390154
$947$	18.3848	−	18.3848i	0.597425	−	0.597425i	−0.342202	−	0.939627i	$-0.611173\pi$
$947$	18.3848	−	18.3848i	0.597425	−	0.597425i	0.939627	+	0.342202i	$0.111173\pi$
$948$	−1.75736	+	10.2426i	−0.0570764	+	0.332666i
$949$		0			0
$950$	2.82843	+	19.7990i	0.0917663	+	0.642364i
$951$	18.0000	+	25.4558i	0.583690	+	0.825462i
$952$	2.00000	+	2.00000i	0.0648204	+	0.0648204i
$953$	4.24264	+	4.24264i	0.137433	+	0.137433i	0.772476	−	0.635044i	$-0.219018\pi$
$953$	4.24264	+	4.24264i	0.137433	+	0.137433i	−0.635044	+	0.772476i	$0.719018\pi$
$954$	11.3137	+	4.00000i	0.366295	+	0.129505i
$955$	6.00000	+	2.00000i	0.194155	+	0.0647185i
$956$		−	8.48528i		−	0.274434i
$957$	−17.0711	−	2.92893i	−0.551829	−	0.0946789i
$958$	22.0000	−	22.0000i	0.710788	−	0.710788i
$959$	−8.48528			−0.274004
$960$	−1.82843	+	3.41421i	−0.0590122	+	0.110193i
$961$	−27.0000			−0.870968
$962$		0			0
$963$	−10.8284	+	5.17157i	−0.348941	+	0.166652i
$964$		−	4.00000i		−	0.128831i
$965$	21.2132	+	42.4264i	0.682877	+	1.36575i
$966$	8.00000	−	5.65685i	0.257396	−	0.182006i
$967$	19.0000	+	19.0000i	0.610999	+	0.610999i	0.943206	−	0.332208i	$-0.107793\pi$
$967$	19.0000	+	19.0000i	0.610999	+	0.610999i	−0.332208	+	0.943206i	$0.607793\pi$
$968$	6.36396	+	6.36396i	0.204545	+	0.204545i
$969$	11.3137	−	8.00000i	0.363449	−	0.256997i
$970$	−3.00000	+	9.00000i	−0.0963242	+	0.288973i
$971$			41.0122i			1.31614i	0.752955	+	0.658072i	$0.228628\pi$
$971$			41.0122i			1.31614i	−0.752955	+	0.658072i	$0.771372\pi$
$972$	10.2929	+	11.7071i	0.330145	+	0.375506i
$973$	8.00000	−	8.00000i	0.256468	−	0.256468i
$974$	−12.7279			−0.407829
$975$		0			0
$976$	6.00000			0.192055
$977$	−4.24264	+	4.24264i	−0.135734	+	0.135734i	−0.771709	−	0.635975i	$-0.780598\pi$
$977$	−4.24264	+	4.24264i	−0.135734	+	0.135734i	0.635975	+	0.771709i	$0.280598\pi$
$978$	9.65685	+	1.65685i	0.308792	+	0.0529804i
$979$		−	4.00000i		−	0.127841i
$980$	−3.53553	+	10.6066i	−0.112938	+	0.338815i
$981$	−10.0000	+	28.2843i	−0.319275	+	0.903047i
$982$	19.0000	+	19.0000i	0.606314	+	0.606314i
$983$	−14.1421	−	14.1421i	−0.451064	−	0.451064i	0.444644	−	0.895708i	$-0.353330\pi$
$983$	−14.1421	−	14.1421i	−0.451064	−	0.451064i	−0.895708	+	0.444644i	$0.853330\pi$
$984$	−5.65685	−	8.00000i	−0.180334	−	0.255031i
$985$	24.0000	+	48.0000i	0.764704	+	1.52941i
$986$		−	14.1421i		−	0.450377i
$987$		0			0
$988$		0			0
$989$	−33.9411			−1.07927
$990$	9.41421	−	1.17157i	0.299203	−	0.0372350i
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$	−1.41421	+	1.41421i	−0.0449013	+	0.0449013i
$993$	2.34315	−	13.6569i	0.0743575	−	0.433387i
$994$		−	20.0000i		−	0.634361i
$995$	−50.9117	−	16.9706i	−1.61401	−	0.538003i
$996$	12.0000	+	16.9706i	0.380235	+	0.537733i
$997$	−8.00000	−	8.00000i	−0.253363	−	0.253363i	0.568985	−	0.822348i	$-0.307336\pi$
$997$	−8.00000	−	8.00000i	−0.253363	−	0.253363i	−0.822348	+	0.568985i	$0.807336\pi$
$998$	−14.1421	−	14.1421i	−0.447661	−	0.447661i
$999$	42.4264	−	12.0000i	1.34231	−	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.2.e.a.17.1	✓	4
3.2	odd	2	inner	30.2.e.a.17.2	yes	4
4.3	odd	2		240.2.v.e.17.1		4
5.2	odd	4		150.2.e.a.143.1		4
5.3	odd	4	inner	30.2.e.a.23.2	yes	4
5.4	even	2		150.2.e.a.107.2		4
8.3	odd	2		960.2.v.c.257.2		4
8.5	even	2		960.2.v.k.257.1		4
9.2	odd	6		810.2.m.f.377.1		8
9.4	even	3		810.2.m.f.107.1		8
9.5	odd	6		810.2.m.f.107.2		8
9.7	even	3		810.2.m.f.377.2		8
12.11	even	2		240.2.v.e.17.2		4
15.2	even	4		150.2.e.a.143.2		4
15.8	even	4	inner	30.2.e.a.23.1	yes	4
15.14	odd	2		150.2.e.a.107.1		4
20.3	even	4		240.2.v.e.113.2		4
20.7	even	4		1200.2.v.b.593.1		4
20.19	odd	2		1200.2.v.b.257.2		4
24.5	odd	2		960.2.v.k.257.2		4
24.11	even	2		960.2.v.c.257.1		4
40.3	even	4		960.2.v.c.833.1		4
40.13	odd	4		960.2.v.k.833.2		4
45.13	odd	12		810.2.m.f.593.1		8
45.23	even	12		810.2.m.f.593.2		8
45.38	even	12		810.2.m.f.53.1		8
45.43	odd	12		810.2.m.f.53.2		8
60.23	odd	4		240.2.v.e.113.1		4
60.47	odd	4		1200.2.v.b.593.2		4
60.59	even	2		1200.2.v.b.257.1		4
120.53	even	4		960.2.v.k.833.1		4
120.83	odd	4		960.2.v.c.833.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.e.a.17.1	✓	4	1.1	even	1	trivial
30.2.e.a.17.2	yes	4	3.2	odd	2	inner
30.2.e.a.23.1	yes	4	15.8	even	4	inner
30.2.e.a.23.2	yes	4	5.3	odd	4	inner
150.2.e.a.107.1		4	15.14	odd	2
150.2.e.a.107.2		4	5.4	even	2
150.2.e.a.143.1		4	5.2	odd	4
150.2.e.a.143.2		4	15.2	even	4
240.2.v.e.17.1		4	4.3	odd	2
240.2.v.e.17.2		4	12.11	even	2
240.2.v.e.113.1		4	60.23	odd	4
240.2.v.e.113.2		4	20.3	even	4
810.2.m.f.53.1		8	45.38	even	12
810.2.m.f.53.2		8	45.43	odd	12
810.2.m.f.107.1		8	9.4	even	3
810.2.m.f.107.2		8	9.5	odd	6
810.2.m.f.377.1		8	9.2	odd	6
810.2.m.f.377.2		8	9.7	even	3
810.2.m.f.593.1		8	45.13	odd	12
810.2.m.f.593.2		8	45.23	even	12
960.2.v.c.257.1		4	24.11	even	2
960.2.v.c.257.2		4	8.3	odd	2
960.2.v.c.833.1		4	40.3	even	4
960.2.v.c.833.2		4	120.83	odd	4
960.2.v.k.257.1		4	8.5	even	2
960.2.v.k.257.2		4	24.5	odd	2
960.2.v.k.833.1		4	120.53	even	4
960.2.v.k.833.2		4	40.13	odd	4
1200.2.v.b.257.1		4	60.59	even	2
1200.2.v.b.257.2		4	20.19	odd	2
1200.2.v.b.593.1		4	20.7	even	4
1200.2.v.b.593.2		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	30.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(1.00000 + 2.00000i) q^{10} +1.41421i q^{11} +(1.70711 + 0.292893i) q^{12} +1.41421 q^{14} +(3.41421 + 1.82843i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(2.70711 - 1.29289i) q^{18} +4.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(2.00000 - 1.41421i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-2.82843 - 2.82843i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(-4.00000 - 3.00000i) q^{25} +(2.53553 - 4.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} +7.07107 q^{29} +(-3.70711 + 1.12132i) q^{30} -2.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.41421 - 0.414214i) q^{33} -2.00000i q^{34} +(-2.82843 + 1.41421i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(6.00000 + 6.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(2.00000 - 1.00000i) q^{40} +5.65685i q^{41} +(-0.414214 + 2.41421i) q^{42} +(6.00000 - 6.00000i) q^{43} +1.41421 q^{44} +(-4.12132 + 5.29289i) q^{45} +4.00000 q^{46} +(0.292893 - 1.70711i) q^{48} -5.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-2.00000 - 2.82843i) q^{51} +(2.82843 + 2.82843i) q^{53} +(1.41421 + 5.00000i) q^{54} +(3.00000 + 1.00000i) q^{55} -1.41421i q^{56} +(-6.82843 - 1.17157i) q^{57} +(-5.00000 + 5.00000i) q^{58} -9.89949 q^{59} +(1.82843 - 3.41421i) q^{60} -6.00000 q^{61} +(1.41421 - 1.41421i) q^{62} +(1.82843 + 3.82843i) q^{63} +1.00000i q^{64} +(2.00000 - 1.41421i) q^{66} +(-4.00000 - 4.00000i) q^{67} +(1.41421 + 1.41421i) q^{68} +(5.65685 - 4.00000i) q^{69} +(1.00000 - 3.00000i) q^{70} -14.1421i q^{71} +(-1.29289 - 2.70711i) q^{72} +(-5.00000 + 5.00000i) q^{73} -8.48528 q^{74} +(6.29289 - 5.94975i) q^{75} +4.00000 q^{76} +(1.41421 - 1.41421i) q^{77} +6.00000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(7.00000 + 5.65685i) q^{81} +(-4.00000 - 4.00000i) q^{82} +(8.48528 + 8.48528i) q^{83} +(-1.41421 - 2.00000i) q^{84} +(2.00000 + 4.00000i) q^{85} +8.48528i q^{86} +(-2.07107 + 12.0711i) q^{87} +(-1.00000 + 1.00000i) q^{88} -2.82843 q^{89} +(-0.828427 - 6.65685i) q^{90} +(-2.82843 + 2.82843i) q^{92} +(0.585786 - 3.41421i) q^{93} +(8.48528 + 2.82843i) q^{95} +(1.00000 + 1.41421i) q^{96} +(3.00000 + 3.00000i) q^{97} +(3.53553 + 3.53553i) q^{98} +(1.41421 - 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{6} - 4 q^{7} + 4 q^{10} + 4 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{18} + 8 q^{21} - 4 q^{22} - 16 q^{25} - 4 q^{27} - 4 q^{28} - 12 q^{30} - 8 q^{31} - 4 q^{33} - 4 q^{36} + 24 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^6 - 4 * q^7 + 4 * q^10 + 4 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^18 + 8 * q^21 - 4 * q^22 - 16 * q^25 - 4 * q^27 - 4 * q^28 - 12 * q^30 - 8 * q^31 - 4 * q^33 - 4 * q^36 + 24 * q^37 + 8 * q^40 + 4 * q^42 + 24 * q^43 - 8 * q^45 + 16 * q^46 + 4 * q^48 - 8 * q^51 + 12 * q^55 - 16 * q^57 - 20 * q^58 - 4 * q^60 - 24 * q^61 - 4 * q^63 + 8 * q^66 - 16 * q^67 + 4 * q^70 - 8 * q^72 - 20 * q^73 + 28 * q^75 + 16 * q^76 + 28 * q^81 - 16 * q^82 + 8 * q^85 + 20 * q^87 - 4 * q^88 + 8 * q^90 + 8 * q^93 + 4 * q^96 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more