LMFDB - Embedded newform 343.2.c.e.18.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(18,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("343.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 10 x^{10} - 8 x^{9} + 46 x^{8} - 31 x^{7} + 136 x^{6} - 30 x^{5} + 204 x^{4} + \cdots + 1 $ x^12 - 2x^11 + 10x^10 - 8x^9 + 46x^8 - 31x^7 + 136x^6 - 30x^5 + 204x^4 - 90x^3 + 131x^2 + 11*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.6
Root			$-0.0424677 - 0.0735563i$ of defining polynomial
Character	$\chi$	$=$	343.18
Dual form			343.2.c.e.324.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16596 + 2.01950i) q^{2} +(1.47749 - 2.55909i) q^{3} +(-1.71891 + 2.97725i) q^{4} +(0.976432 + 1.69123i) q^{5} +6.89078 q^{6} -3.35289 q^{8} +(-2.86597 - 4.96401i) q^{9} +O(q^{10})$	\(q+(1.16596 + 2.01950i) q^{2} +(1.47749 - 2.55909i) q^{3} +(-1.71891 + 2.97725i) q^{4} +(0.976432 + 1.69123i) q^{5} +6.89078 q^{6} -3.35289 q^{8} +(-2.86597 - 4.96401i) q^{9} +(-2.27696 + 3.94381i) q^{10} +(-1.32551 + 2.29584i) q^{11} +(5.07937 + 8.79772i) q^{12} +1.50061 q^{13} +5.77069 q^{15} +(-0.471502 - 0.816666i) q^{16} +(1.04607 - 1.81185i) q^{17} +(6.68320 - 11.5756i) q^{18} +(-3.19441 - 5.53287i) q^{19} -6.71361 q^{20} -6.18193 q^{22} +(1.06212 + 1.83965i) q^{23} +(-4.95388 + 8.58036i) q^{24} +(0.593160 - 1.02738i) q^{25} +(1.74965 + 3.03048i) q^{26} -8.07285 q^{27} -7.42740 q^{29} +(6.72838 + 11.6539i) q^{30} +(-0.0327336 + 0.0566962i) q^{31} +(-2.25339 + 3.90298i) q^{32} +(3.91685 + 6.78418i) q^{33} +4.87871 q^{34} +19.7054 q^{36} +(-0.268898 - 0.465745i) q^{37} +(7.44908 - 12.9022i) q^{38} +(2.21714 - 3.84020i) q^{39} +(-3.27387 - 5.67051i) q^{40} -11.8724 q^{41} -0.588754 q^{43} +(-4.55686 - 7.89271i) q^{44} +(5.59685 - 9.69403i) q^{45} +(-2.47678 + 4.28991i) q^{46} +(1.51440 + 2.62302i) q^{47} -2.78657 q^{48} +2.76640 q^{50} +(-3.09114 - 5.35401i) q^{51} +(-2.57942 + 4.46768i) q^{52} +(-0.520812 + 0.902072i) q^{53} +(-9.41260 - 16.3031i) q^{54} -5.17707 q^{55} -18.8788 q^{57} +(-8.66004 - 14.9996i) q^{58} +(-1.13570 + 1.96709i) q^{59} +(-9.91931 + 17.1808i) q^{60} +(-5.13835 - 8.89988i) q^{61} -0.152664 q^{62} -12.3954 q^{64} +(1.46524 + 2.53787i) q^{65} +(-9.13376 + 15.8201i) q^{66} +(0.110857 - 0.192010i) q^{67} +(3.59622 + 6.22884i) q^{68} +6.27711 q^{69} +10.7708 q^{71} +(9.60929 + 16.6438i) q^{72} +(5.11036 - 8.85140i) q^{73} +(0.627047 - 1.08608i) q^{74} +(-1.75278 - 3.03591i) q^{75} +21.9636 q^{76} +10.3404 q^{78} +(6.64297 + 11.5060i) q^{79} +(0.920780 - 1.59484i) q^{80} +(-3.32967 + 5.76716i) q^{81} +(-13.8428 - 23.9764i) q^{82} +11.8543 q^{83} +4.08568 q^{85} +(-0.686463 - 1.18899i) q^{86} +(-10.9739 + 19.0074i) q^{87} +(4.44428 - 7.69771i) q^{88} +(1.75510 + 3.03992i) q^{89} +26.1028 q^{90} -7.30279 q^{92} +(0.0967273 + 0.167537i) q^{93} +(-3.53146 + 6.11666i) q^{94} +(6.23824 - 10.8049i) q^{95} +(6.65873 + 11.5333i) q^{96} -14.6497 q^{97} +15.1954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 5 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 12 q^{8} - 9 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 5 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 12 * q^8 - 9 * q^9	$ 12 q + 2 q^{2} + 5 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 12 q^{8} - 9 q^{9} - 2 q^{10} + q^{11} + 7 q^{12} - 14 q^{13} - 10 q^{15} + 8 q^{16} + 26 q^{17} + 18 q^{18} - 3 q^{19} - 28 q^{20} - 12 q^{22} + 9 q^{23} - 9 q^{24} - 15 q^{25} - 16 q^{27} - 4 q^{29} - 13 q^{30} - 2 q^{31} - q^{32} + 18 q^{33} + 26 q^{34} + 46 q^{36} + 2 q^{37} + 5 q^{38} - 7 q^{39} - 24 q^{40} - 56 q^{41} + 10 q^{43} + 12 q^{44} + 3 q^{45} + 12 q^{46} + 18 q^{47} + 26 q^{48} + 10 q^{50} - 13 q^{51} - 14 q^{52} + q^{53} - 32 q^{54} + 44 q^{55} - 52 q^{57} - 24 q^{58} + 5 q^{59} - 21 q^{60} - 17 q^{61} + 12 q^{62} - 36 q^{64} + 14 q^{65} - 58 q^{66} + 22 q^{67} + 7 q^{68} + 40 q^{69} - 4 q^{71} + 18 q^{72} + 12 q^{73} - 23 q^{74} - 27 q^{75} + 98 q^{76} + 42 q^{78} + 2 q^{79} - 16 q^{80} + 30 q^{81} - 35 q^{82} - 14 q^{83} + 74 q^{85} - 3 q^{86} - 25 q^{87} - 14 q^{88} + 39 q^{89} + 94 q^{90} + 22 q^{92} + 22 q^{93} - 16 q^{94} + 11 q^{95} - 28 q^{96} - 70 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 5 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 12 * q^8 - 9 * q^9 - 2 * q^10 + q^11 + 7 * q^12 - 14 * q^13 - 10 * q^15 + 8 * q^16 + 26 * q^17 + 18 * q^18 - 3 * q^19 - 28 * q^20 - 12 * q^22 + 9 * q^23 - 9 * q^24 - 15 * q^25 - 16 * q^27 - 4 * q^29 - 13 * q^30 - 2 * q^31 - q^32 + 18 * q^33 + 26 * q^34 + 46 * q^36 + 2 * q^37 + 5 * q^38 - 7 * q^39 - 24 * q^40 - 56 * q^41 + 10 * q^43 + 12 * q^44 + 3 * q^45 + 12 * q^46 + 18 * q^47 + 26 * q^48 + 10 * q^50 - 13 * q^51 - 14 * q^52 + q^53 - 32 * q^54 + 44 * q^55 - 52 * q^57 - 24 * q^58 + 5 * q^59 - 21 * q^60 - 17 * q^61 + 12 * q^62 - 36 * q^64 + 14 * q^65 - 58 * q^66 + 22 * q^67 + 7 * q^68 + 40 * q^69 - 4 * q^71 + 18 * q^72 + 12 * q^73 - 23 * q^74 - 27 * q^75 + 98 * q^76 + 42 * q^78 + 2 * q^79 - 16 * q^80 + 30 * q^81 - 35 * q^82 - 14 * q^83 + 74 * q^85 - 3 * q^86 - 25 * q^87 - 14 * q^88 + 39 * q^89 + 94 * q^90 + 22 * q^92 + 22 * q^93 - 16 * q^94 + 11 * q^95 - 28 * q^96 - 70 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.16596	+	2.01950i	0.824456	+	1.42800i	0.902334	+	0.431038i	$0.141852\pi$
$2$	1.16596	+	2.01950i	0.824456	+	1.42800i	−0.0778775	+	0.996963i	$0.524814\pi$
$3$	1.47749	−	2.55909i	0.853031	−	1.47749i	−0.0254287	−	0.999677i	$-0.508095\pi$
$3$	1.47749	−	2.55909i	0.853031	−	1.47749i	0.878460	−	0.477816i	$-0.158572\pi$
$4$	−1.71891	+	2.97725i	−0.859457	+	1.48862i
$5$	0.976432	+	1.69123i	0.436674	+	0.756341i	0.997431	−	0.0716394i	$-0.0228231\pi$
$5$	0.976432	+	1.69123i	0.436674	+	0.756341i	−0.560757	+	0.827981i	$0.689490\pi$
$6$	6.89078			2.81315
$7$		0			0
$7$		0			0
$8$	−3.35289			−1.18543
$9$	−2.86597	−	4.96401i	−0.955324	−	1.65467i
$10$	−2.27696	+	3.94381i	−0.720037	+	1.24714i
$11$	−1.32551	+	2.29584i	−0.399655	+	0.692223i	−0.993683	−	0.112221i	$-0.964203\pi$
$11$	−1.32551	+	2.29584i	−0.399655	+	0.692223i	0.594028	+	0.804444i	$0.297537\pi$
$12$	5.07937	+	8.79772i	1.46629	+	2.53968i
$13$	1.50061			0.416194			0.208097	−	0.978108i	$-0.433273\pi$
$13$	1.50061			0.416194			0.208097	+	0.978108i	$0.433273\pi$
$14$		0			0
$15$	5.77069			1.48999
$16$	−0.471502	−	0.816666i	−0.117876	−	0.204166i
$17$	1.04607	−	1.81185i	0.253710	−	0.439439i	−0.710834	−	0.703360i	$-0.751682\pi$
$17$	1.04607	−	1.81185i	0.253710	−	0.439439i	0.964544	+	0.263920i	$0.0850156\pi$
$18$	6.68320	−	11.5756i	1.57525	−	2.72841i
$19$	−3.19441	−	5.53287i	−0.732847	−	1.26933i	−0.955662	−	0.294467i	$-0.904858\pi$
$19$	−3.19441	−	5.53287i	−0.732847	−	1.26933i	0.222815	−	0.974861i	$-0.428475\pi$
$20$	−6.71361			−1.50121
$21$		0			0
$22$	−6.18193			−1.31799
$23$	1.06212	+	1.83965i	0.221468	+	0.383593i	0.955254	−	0.295787i	$-0.0955819\pi$
$23$	1.06212	+	1.83965i	0.221468	+	0.383593i	−0.733786	+	0.679381i	$0.762249\pi$
$24$	−4.95388	+	8.58036i	−1.01121	+	1.75146i
$25$	0.593160	−	1.02738i	0.118632	−	0.205477i
$26$	1.74965	+	3.03048i	0.343134	+	0.594325i
$27$	−8.07285			−1.55362
$28$		0			0
$29$	−7.42740			−1.37923			−0.689617	−	0.724174i	$-0.742221\pi$
$29$	−7.42740			−1.37923			−0.689617	+	0.724174i	$0.742221\pi$
$30$	6.72838	+	11.6539i	1.22843	+	2.12770i
$31$	−0.0327336	+	0.0566962i	−0.00587912	+	0.0101829i	−0.868950	−	0.494900i	$-0.835205\pi$
$31$	−0.0327336	+	0.0566962i	−0.00587912	+	0.0101829i	0.863071	+	0.505083i	$0.168538\pi$
$32$	−2.25339	+	3.90298i	−0.398347	+	0.689957i
$33$	3.91685	+	6.78418i	0.681836	+	1.18097i
$34$	4.87871			0.836693
$35$		0			0
$36$	19.7054			3.28424
$37$	−0.268898	−	0.465745i	−0.0442065	−	0.0765679i	0.843076	−	0.537795i	$-0.180743\pi$
$37$	−0.268898	−	0.465745i	−0.0442065	−	0.0765679i	−0.887282	+	0.461227i	$0.847409\pi$
$38$	7.44908	−	12.9022i	1.20840	−	2.09301i
$39$	2.21714	−	3.84020i	0.355026	−	0.614924i
$40$	−3.27387	−	5.67051i	−0.517645	−	0.896587i
$41$	−11.8724			−1.85416			−0.927082	−	0.374858i	$-0.877691\pi$
$41$	−11.8724			−1.85416			−0.927082	+	0.374858i	$0.877691\pi$
$42$		0			0
$43$	−0.588754			−0.0897842			−0.0448921	−	0.998992i	$-0.514294\pi$
$43$	−0.588754			−0.0897842			−0.0448921	+	0.998992i	$0.514294\pi$
$44$	−4.55686	−	7.89271i	−0.686972	−	1.18987i
$45$	5.59685	−	9.69403i	0.834330	−	1.44510i
$46$	−2.47678	+	4.28991i	−0.365181	+	0.632512i
$47$	1.51440	+	2.62302i	0.220898	+	0.382607i	0.955081	−	0.296345i	$-0.0957678\pi$
$47$	1.51440	+	2.62302i	0.220898	+	0.382607i	−0.734183	+	0.678952i	$0.762434\pi$
$48$	−2.78657			−0.402206
$49$		0			0
$50$	2.76640			0.391228
$51$	−3.09114	−	5.35401i	−0.432846	−	0.749711i
$52$	−2.57942	+	4.46768i	−0.357701	+	0.619556i
$53$	−0.520812	+	0.902072i	−0.0715390	+	0.123909i	−0.899576	−	0.436764i	$-0.856124\pi$
$53$	−0.520812	+	0.902072i	−0.0715390	+	0.123909i	0.828037	+	0.560673i	$0.189458\pi$
$54$	−9.41260	−	16.3031i	−1.28089	−	2.21857i
$55$	−5.17707			−0.698075
$56$		0			0
$57$	−18.8788			−2.50056
$58$	−8.66004	−	14.9996i	−1.13712	−	1.96955i
$59$	−1.13570	+	1.96709i	−0.147855	+	0.256093i	−0.930435	−	0.366458i	$-0.880570\pi$
$59$	−1.13570	+	1.96709i	−0.147855	+	0.256093i	0.782579	+	0.622551i	$0.213904\pi$
$60$	−9.91931	+	17.1808i	−1.28058	+	2.21803i
$61$	−5.13835	−	8.89988i	−0.657898	−	1.13951i	−0.981159	−	0.193203i	$-0.938112\pi$
$61$	−5.13835	−	8.89988i	−0.657898	−	1.13951i	0.323260	−	0.946310i	$-0.395221\pi$
$62$	−0.152664			−0.0193883
$63$		0			0
$64$	−12.3954			−1.54943
$65$	1.46524	+	2.53787i	0.181741	+	0.314785i
$66$	−9.13376	+	15.8201i	−1.12429	+	1.94732i
$67$	0.110857	−	0.192010i	0.0135434	−	0.0234578i	−0.859174	−	0.511683i	$-0.829022\pi$
$67$	0.110857	−	0.192010i	0.0135434	−	0.0234578i	0.872718	+	0.488225i	$0.162356\pi$
$68$	3.59622	+	6.22884i	0.436106	+	0.755358i
$69$	6.27711			0.755676
$70$		0			0
$71$	10.7708			1.27826			0.639131	−	0.769098i	$-0.279294\pi$
$71$	10.7708			1.27826			0.639131	+	0.769098i	$0.279294\pi$
$72$	9.60929	+	16.6438i	1.13247	+	1.96149i
$73$	5.11036	−	8.85140i	0.598122	−	1.03598i	−0.394976	−	0.918692i	$-0.629247\pi$
$73$	5.11036	−	8.85140i	0.598122	−	1.03598i	0.993098	−	0.117287i	$-0.0374197\pi$
$74$	0.627047	−	1.08608i	0.0728927	−	0.126254i
$75$	−1.75278	−	3.03591i	−0.202394	−	0.350556i
$76$	21.9636			2.51940
$77$		0			0
$78$	10.3404			1.17081
$79$	6.64297	+	11.5060i	0.747392	+	1.29452i	0.949069	+	0.315069i	$0.102028\pi$
$79$	6.64297	+	11.5060i	0.747392	+	1.29452i	−0.201676	+	0.979452i	$0.564639\pi$
$80$	0.920780	−	1.59484i	0.102946	−	0.178308i
$81$	−3.32967	+	5.76716i	−0.369963	+	0.640795i
$82$	−13.8428	−	23.9764i	−1.52868	−	2.64775i
$83$	11.8543			1.30118			0.650592	−	0.759428i	$-0.274521\pi$
$83$	11.8543			1.30118			0.650592	+	0.759428i	$0.274521\pi$
$84$		0			0
$85$	4.08568			0.443155
$86$	−0.686463	−	1.18899i	−0.0740232	−	0.128212i
$87$	−10.9739	+	19.0074i	−1.17653	+	2.03781i
$88$	4.44428	−	7.69771i	0.473762	−	0.820579i
$89$	1.75510	+	3.03992i	0.186040	+	0.322231i	0.943926	−	0.330156i	$-0.107101\pi$
$89$	1.75510	+	3.03992i	0.186040	+	0.322231i	−0.757886	+	0.652386i	$0.773768\pi$
$90$	26.1028			2.75147
$91$		0			0
$92$	−7.30279			−0.761368
$93$	0.0967273	+	0.167537i	0.0100302	+	0.0173727i
$94$	−3.53146	+	6.11666i	−0.364242	+	0.630886i
$95$	6.23824	−	10.8049i	0.640030	−	1.10856i
$96$	6.65873	+	11.5333i	0.679604	+	1.17711i
$97$	−14.6497			−1.48746			−0.743728	−	0.668483i	$-0.766944\pi$
$97$	−14.6497			−1.48746			−0.743728	+	0.668483i	$0.766944\pi$
$98$		0			0
$99$	15.1954			1.52720
$100$	2.03918	+	3.53197i	0.203918	+	0.353197i
$101$	0.162134	−	0.280825i	0.0161330	−	0.0279431i	−0.857846	−	0.513906i	$-0.828198\pi$
$101$	0.162134	−	0.280825i	0.0161330	−	0.0279431i	0.873979	+	0.485963i	$0.161531\pi$
$102$	7.20827	−	12.4851i	0.713725	−	1.23621i
$103$	5.09857	+	8.83099i	0.502377	+	0.870143i	0.999996	+	0.00274729i	$0.000874490\pi$
$103$	5.09857	+	8.83099i	0.502377	+	0.870143i	−0.497619	+	0.867396i	$0.665792\pi$
$104$	−5.03138			−0.493367
$105$		0			0
$106$	−2.42898			−0.235923
$107$	7.68421	+	13.3094i	0.742861	+	1.28667i	0.951188	+	0.308614i	$0.0998650\pi$
$107$	7.68421	+	13.3094i	0.742861	+	1.28667i	−0.208327	+	0.978059i	$0.566802\pi$
$108$	13.8765	−	24.0349i	1.33527	−	2.31276i
$109$	7.11936	−	12.3311i	0.681911	−	1.18111i	−0.292485	−	0.956270i	$-0.594482\pi$
$109$	7.11936	−	12.3311i	0.681911	−	1.18111i	0.974397	−	0.224835i	$-0.0721844\pi$
$110$	−6.03624	−	10.4551i	−0.575533	−	0.996852i
$111$	−1.58918			−0.150838
$112$		0			0
$113$	−8.22812			−0.774037			−0.387018	−	0.922072i	$-0.626495\pi$
$113$	−8.22812			−0.774037			−0.387018	+	0.922072i	$0.626495\pi$
$114$	−22.0119	−	38.1258i	−2.06161	−	3.57081i
$115$	−2.07418	+	3.59259i	−0.193418	+	0.335010i
$116$	12.7671	−	22.1132i	1.18539	−	2.05316i
$117$	−4.30070	−	7.44903i	−0.397600	−	0.688663i
$118$	−5.29670			−0.487601
$119$		0			0
$120$	−19.3485			−1.76627
$121$	1.98607	+	3.43997i	0.180552	+	0.312725i
$122$	11.9822	−	20.7538i	1.08482	−	1.87896i
$123$	−17.5415	+	30.3827i	−1.58166	+	2.73952i
$124$	−0.112532	−	0.194912i	−0.0101057	−	0.0175036i
$125$	12.0810			1.08056
$126$		0			0
$127$	15.7450			1.39714			0.698572	−	0.715540i	$-0.253819\pi$
$127$	15.7450			1.39714			0.698572	+	0.715540i	$0.253819\pi$
$128$	−9.94577	−	17.2266i	−0.879090	−	1.52263i
$129$	−0.869881	+	1.50668i	−0.0765887	+	0.132656i
$130$	−3.41682	+	5.91811i	−0.299675	+	0.519052i
$131$	4.12975	+	7.15294i	0.360818	+	0.624955i	0.988096	−	0.153840i	$-0.0491641\pi$
$131$	4.12975	+	7.15294i	0.360818	+	0.624955i	−0.627278	+	0.778796i	$0.715831\pi$
$132$	−26.9309			−2.34404
$133$		0			0
$134$	0.517019			0.0446636
$135$	−7.88259	−	13.6531i	−0.678426	−	1.17507i
$136$	−3.50738	+	6.07495i	−0.300755	+	0.520923i
$137$	−0.0390265	+	0.0675959i	−0.00333426	+	0.00577510i	−0.867688	−	0.497110i	$-0.834395\pi$
$137$	−0.0390265	+	0.0675959i	−0.00333426	+	0.00577510i	0.864353	+	0.502885i	$0.167728\pi$
$138$	7.31885	+	12.6766i	0.623022	+	1.07911i
$139$	−15.6375			−1.32635			−0.663177	−	0.748463i	$-0.730792\pi$
$139$	−15.6375			−1.32635			−0.663177	+	0.748463i	$0.730792\pi$
$140$		0			0
$141$	8.95007			0.753732
$142$	12.5583	+	21.7516i	1.05387	+	1.82536i
$143$	−1.98906	+	3.44516i	−0.166334	+	0.288099i
$144$	−2.70262	+	4.68108i	−0.225219	+	0.390090i
$145$	−7.25236	−	12.5614i	−0.602275	−	1.04317i
$146$	23.8339			1.97250
$147$		0			0
$148$	1.84885			0.151974
$149$	3.13283	+	5.42622i	0.256652	+	0.444534i	0.965343	−	0.260985i	$-0.0840474\pi$
$149$	3.13283	+	5.42622i	0.256652	+	0.444534i	−0.708691	+	0.705519i	$0.750714\pi$
$150$	4.08734	−	7.07947i	0.333730	−	0.578037i
$151$	8.16111	−	14.1355i	0.664142	−	1.15033i	−0.315375	−	0.948967i	$-0.602130\pi$
$151$	8.16111	−	14.1355i	0.664142	−	1.15033i	0.979517	−	0.201361i	$-0.0645363\pi$
$152$	10.7105	+	18.5511i	0.868736	+	1.50469i
$153$	−11.9921			−0.969502
$154$		0			0
$155$	−0.127848			−0.0102690
$156$	7.62214	+	13.2019i	0.610260	+	1.05700i
$157$	−6.68319	+	11.5756i	−0.533376	+	0.923835i	0.465864	+	0.884856i	$0.345744\pi$
$157$	−6.68319	+	11.5756i	−0.533376	+	0.923835i	−0.999240	+	0.0389784i	$0.987590\pi$
$158$	−15.4908	+	26.8309i	−1.23238	+	2.13455i
$159$	1.53899	+	2.66561i	0.122050	+	0.211397i
$160$	−8.80113			−0.695790
$161$		0			0
$162$	−15.5290			−1.22008
$163$	5.55818	+	9.62705i	0.435350	+	0.754049i	0.997324	−	0.0731063i	$-0.0232912\pi$
$163$	5.55818	+	9.62705i	0.435350	+	0.754049i	−0.561974	+	0.827155i	$0.689958\pi$
$164$	20.4077	−	35.3472i	1.59357	−	2.76015i
$165$	−7.64908	+	13.2486i	−0.595480	+	1.03140i
$166$	13.8217	+	23.9398i	1.07277	+	1.85809i
$167$	8.91212			0.689640			0.344820	−	0.938669i	$-0.387940\pi$
$167$	8.91212			0.689640			0.344820	+	0.938669i	$0.387940\pi$
$168$		0			0
$169$	−10.7482			−0.826783
$170$	4.76373	+	8.25103i	0.365362	+	0.632825i
$171$	−18.3101	+	31.7141i	−1.40021	+	2.42524i
$172$	1.01202	−	1.75287i	0.0771657	−	0.133655i
$173$	1.62255	+	2.81033i	0.123360	+	0.213666i	0.921091	−	0.389348i	$-0.127300\pi$
$173$	1.62255	+	2.81033i	0.123360	+	0.213666i	−0.797731	+	0.603014i	$0.793966\pi$
$174$	−51.1806			−3.87999
$175$		0			0
$176$	2.49992			0.188438
$177$	3.35597	+	5.81271i	0.252250	+	0.436910i
$178$	−4.09274	+	7.08883i	−0.306764	+	0.531330i
$179$	2.02355	−	3.50490i	0.151248	−	0.261968i	−0.780439	−	0.625232i	$-0.785004\pi$
$179$	2.02355	−	3.50490i	0.151248	−	0.261968i	0.931686	+	0.363264i	$0.118338\pi$
$180$	19.2410	+	33.3264i	1.43414	+	2.48400i
$181$	−8.66577			−0.644121			−0.322061	−	0.946719i	$-0.604376\pi$
$181$	−8.66577			−0.644121			−0.322061	+	0.946719i	$0.604376\pi$
$182$		0			0
$183$	−30.3675			−2.24483
$184$	−3.56118	−	6.16815i	−0.262534	−	0.454722i
$185$	0.525121	−	0.909536i	0.0386077	−	0.0668704i
$186$	−0.225560	+	0.390681i	−0.0165388	+	0.0286461i
$187$	2.77316	+	4.80325i	0.202793	+	0.351248i
$188$	−10.4125			−0.759410
$189$		0			0
$190$	29.0941			2.11071
$191$	−7.60823	−	13.1778i	−0.550512	−	0.953515i	−0.998238	−	0.0593438i	$-0.981099\pi$
$191$	−7.60823	−	13.1778i	−0.550512	−	0.953515i	0.447726	−	0.894171i	$-0.352234\pi$
$192$	−18.3142	+	31.7211i	−1.32171	+	2.28927i
$193$	−5.13578	+	8.89544i	−0.369682	+	0.640308i	−0.989516	−	0.144425i	$-0.953867\pi$
$193$	−5.13578	+	8.89544i	−0.369682	+	0.640308i	0.619834	+	0.784733i	$0.287200\pi$
$194$	−17.0810	−	29.5851i	−1.22634	−	2.12409i
$195$	8.65954			0.620123
$196$		0			0
$197$	7.72522			0.550399			0.275200	−	0.961387i	$-0.411256\pi$
$197$	7.72522			0.550399			0.275200	+	0.961387i	$0.411256\pi$
$198$	17.7172	+	30.6872i	1.25911	+	2.18084i
$199$	−7.38462	+	12.7905i	−0.523482	+	0.906698i	0.476144	+	0.879367i	$0.342034\pi$
$199$	−7.38462	+	12.7905i	−0.523482	+	0.906698i	−0.999626	+	0.0273306i	$0.991299\pi$
$200$	−1.98880	+	3.44471i	−0.140630	+	0.243578i
$201$	−0.327581	−	0.567387i	−0.0231058	−	0.0400204i
$202$	0.756167			0.0532037
$203$		0			0
$204$	21.2536			1.48805
$205$	−11.5926	−	20.0790i	−0.809665	−	1.40238i
$206$	−11.8894	+	20.5931i	−0.828376	+	1.43479i
$207$	6.08802	−	10.5448i	0.423147	−	0.732912i
$208$	−0.707540	−	1.22550i	−0.0490591	−	0.0849728i
$209$	16.9368			1.17154
$210$		0			0
$211$	−4.88834			−0.336527			−0.168264	−	0.985742i	$-0.553816\pi$
$211$	−4.88834			−0.336527			−0.168264	+	0.985742i	$0.553816\pi$
$212$	−1.79046	−	3.10117i	−0.122969	−	0.212989i
$213$	15.9138	−	27.5635i	1.09040	−	1.88862i
$214$	−17.9189	+	31.0365i	−1.22491	+	2.12161i
$215$	−0.574879	−	0.995719i	−0.0392064	−	0.0679075i
$216$	27.0674			1.84170
$217$		0			0
$218$	33.2035			2.24883
$219$	−15.1010	−	26.1558i	−1.02043	−	1.76744i
$220$	8.89893	−	15.4134i	0.599966	−	1.03917i
$221$	1.56975	−	2.71888i	0.105593	−	0.182892i
$222$	−1.85291	−	3.20934i	−0.124359	−	0.215397i
$223$	−1.74696			−0.116985			−0.0584925	−	0.998288i	$-0.518629\pi$
$223$	−1.74696			−0.116985			−0.0584925	+	0.998288i	$0.518629\pi$
$224$		0			0
$225$	−6.79992			−0.453328
$226$	−9.59364	−	16.6167i	−0.638160	−	1.10532i
$227$	11.8470	−	20.5196i	0.786311	−	1.36193i	−0.141902	−	0.989881i	$-0.545322\pi$
$227$	11.8470	−	20.5196i	0.786311	−	1.36193i	0.928213	−	0.372050i	$-0.121345\pi$
$228$	32.4511	−	56.2070i	2.14913	−	3.72240i
$229$	6.59550	+	11.4237i	0.435843	+	0.754902i	0.997364	−	0.0725606i	$-0.0231171\pi$
$229$	6.59550	+	11.4237i	0.435843	+	0.754902i	−0.561521	+	0.827462i	$0.689784\pi$
$230$	−9.67363			−0.637860
$231$		0			0
$232$	24.9033			1.63498
$233$	−10.6450	−	18.4377i	−0.697379	−	1.20790i	−0.969372	−	0.245597i	$-0.921016\pi$
$233$	−10.6450	−	18.4377i	−0.697379	−	1.20790i	0.271993	−	0.962299i	$-0.412317\pi$
$234$	10.0289	−	17.3705i	0.655608	−	1.13555i
$235$	−2.95742	+	5.12240i	−0.192921	+	0.334149i
$236$	−3.90433	−	6.76250i	−0.254150	−	0.440202i
$237$	39.2598			2.55020
$238$		0			0
$239$	−11.2612			−0.728429			−0.364215	−	0.931315i	$-0.618663\pi$
$239$	−11.2612			−0.728429			−0.364215	+	0.931315i	$0.618663\pi$
$240$	−2.72089	−	4.71272i	−0.175633	−	0.304205i
$241$	4.63025	−	8.01982i	0.298260	−	0.516602i	−0.677478	−	0.735543i	$-0.736927\pi$
$241$	4.63025	−	8.01982i	0.298260	−	0.516602i	0.975738	+	0.218941i	$0.0702603\pi$
$242$	−4.63135	+	8.02173i	−0.297714	+	0.515656i
$243$	−2.27015	−	3.93201i	−0.145630	−	0.252239i
$244$	35.3295			2.26174
$245$		0			0
$246$	−81.8104			−5.21604
$247$	−4.79355	−	8.30267i	−0.305006	−	0.528287i
$248$	0.109752	−	0.190096i	0.00696927	−	0.0120711i
$249$	17.5147	−	30.3364i	1.10995	−	1.92249i
$250$	14.0860	+	24.3976i	0.890876	+	1.54304i
$251$	19.8599			1.25355			0.626773	−	0.779202i	$-0.284375\pi$
$251$	19.8599			1.25355			0.626773	+	0.779202i	$0.284375\pi$
$252$		0			0
$253$	−5.63140			−0.354043
$254$	18.3580	+	31.7970i	1.15188	+	1.99512i
$255$	6.03657	−	10.4556i	0.378025	−	0.654758i
$256$	10.7973	−	18.7014i	0.674829	−	1.16884i
$257$	12.5787	+	21.7869i	0.784637	+	1.35903i	0.929216	+	0.369538i	$0.120484\pi$
$257$	12.5787	+	21.7869i	0.784637	+	1.35903i	−0.144579	+	0.989493i	$0.546183\pi$
$258$	−4.05698			−0.252576
$259$		0			0
$260$	−10.0745			−0.624794
$261$	21.2867	+	36.8697i	1.31762	+	2.28218i
$262$	−9.63023	+	16.6801i	−0.594958	+	1.03050i
$263$	5.16429	−	8.94481i	0.318444	−	0.551560i	−0.661720	−	0.749751i	$-0.730173\pi$
$263$	5.16429	−	8.94481i	0.318444	−	0.551560i	0.980163	+	0.198191i	$0.0635065\pi$
$264$	−13.1328	−	22.7466i	−0.808267	−	1.39996i
$265$	−2.03415			−0.124957
$266$		0			0
$267$	10.3726			0.634792
$268$	0.381108	+	0.660098i	0.0232799	+	0.0403219i
$269$	−0.224165	+	0.388265i	−0.0136676	+	0.0236729i	−0.872778	−	0.488117i	$-0.837684\pi$
$269$	−0.224165	+	0.388265i	−0.0136676	+	0.0236729i	0.859111	+	0.511790i	$0.171017\pi$
$270$	18.3815	−	31.8378i	1.11866	−	1.93758i
$271$	−11.9815	−	20.7526i	−0.727825	−	1.26063i	−0.957801	−	0.287433i	$-0.907198\pi$
$271$	−11.9815	−	20.7526i	−0.727825	−	1.26063i	0.229976	−	0.973196i	$-0.426135\pi$
$272$	−1.97291			−0.119625
$273$		0			0
$274$	−0.182013			−0.0109958
$275$	1.57247	+	2.72361i	0.0948238	+	0.164240i
$276$	−10.7898	+	18.6885i	−0.649471	+	1.12492i
$277$	−7.58787	+	13.1426i	−0.455911	+	0.789661i	−0.998740	−	0.0501822i	$-0.984020\pi$
$277$	−7.58787	+	13.1426i	−0.455911	+	0.789661i	0.542829	+	0.839843i	$0.317353\pi$
$278$	−18.2326	−	31.5798i	−1.09352	−	1.89403i
$279$	0.375254			0.0224659
$280$		0			0
$281$	10.0320			0.598460			0.299230	−	0.954181i	$-0.403270\pi$
$281$	10.0320			0.598460			0.299230	+	0.954181i	$0.403270\pi$
$282$	10.4354	+	18.0747i	0.621419	+	1.07633i
$283$	−1.05153	+	1.82130i	−0.0625068	+	0.108265i	−0.895585	−	0.444890i	$-0.853243\pi$
$283$	−1.05153	+	1.82130i	−0.0625068	+	0.108265i	0.833079	+	0.553155i	$0.186576\pi$
$284$	−18.5141	+	32.0674i	−1.09861	+	1.90285i
$285$	−18.4339	−	31.9285i	−1.09193	−	1.89128i
$286$	−9.27666			−0.548540
$287$		0			0
$288$	25.8326			1.52220
$289$	6.31146	+	10.9318i	0.371262	+	0.643045i
$290$	16.9119	−	29.2922i	0.993100	−	1.72010i
$291$	−21.6449	+	37.4900i	−1.26885	+	2.19770i
$292$	17.5685	+	30.4296i	1.02812	+	1.78076i
$293$	−18.6487			−1.08947			−0.544735	−	0.838608i	$-0.683370\pi$
$293$	−18.6487			−1.08947			−0.544735	+	0.838608i	$0.683370\pi$
$294$		0			0
$295$	−4.43573			−0.258258
$296$	0.901585	+	1.56159i	0.0524036	+	0.0907657i
$297$	10.7006	−	18.5340i	0.620913	−	1.07545i
$298$	−7.30550	+	12.6535i	−0.423196	+	0.732997i
$299$	1.59383	+	2.76059i	0.0921735	+	0.159649i
$300$	12.0515			0.695795
$301$		0			0
$302$	38.0620			2.19022
$303$	−0.479104	−	0.829833i	−0.0275238	−	0.0476727i
$304$	−3.01234	+	5.21752i	−0.172769	+	0.299246i
$305$	10.0345	−	17.3803i	0.574574	−	0.995191i
$306$	−13.9823	−	24.2180i	−0.799312	−	1.38445i
$307$	−9.72652			−0.555122			−0.277561	−	0.960708i	$-0.589526\pi$
$307$	−9.72652			−0.555122			−0.277561	+	0.960708i	$0.589526\pi$
$308$		0			0
$309$	30.1324			1.71417
$310$	−0.149066	−	0.258190i	−0.00846637	−	0.0146642i
$311$	−13.9213	+	24.1124i	−0.789406	+	1.36729i	0.136925	+	0.990581i	$0.456278\pi$
$311$	−13.9213	+	24.1124i	−0.789406	+	1.36729i	−0.926331	+	0.376710i	$0.877055\pi$
$312$	−7.43383	+	12.8758i	−0.420858	+	0.728947i
$313$	10.1075	+	17.5067i	0.571311	+	0.989540i	0.996432	+	0.0844030i	$0.0268983\pi$
$313$	10.1075	+	17.5067i	0.571311	+	0.989540i	−0.425121	+	0.905137i	$0.639768\pi$
$314$	−31.1692			−1.75898
$315$		0			0
$316$	−45.6748			−2.56941
$317$	−5.92676	−	10.2654i	−0.332880	−	0.576565i	0.650195	−	0.759767i	$-0.274687\pi$
$317$	−5.92676	−	10.2654i	−0.332880	−	0.576565i	−0.983075	+	0.183202i	$0.941354\pi$
$318$	−3.58880	+	6.21598i	−0.201250	+	0.348575i
$319$	9.84506	−	17.0522i	0.551218	−	0.954737i
$320$	−12.1033	−	20.9635i	−0.676595	−	1.17190i
$321$	45.4135			2.53473
$322$		0			0
$323$	−13.3663			−0.743723
$324$	−11.4468	−	19.8265i	−0.635935	−	1.10147i
$325$	0.890101	−	1.54170i	0.0493739	−	0.0855182i
$326$	−12.9612	+	22.4495i	−0.717855	+	1.24336i
$327$	−21.0376	−	36.4382i	−1.16338	−	2.01504i
$328$	39.8070			2.19798
$329$		0			0
$330$	−35.6740			−1.96379
$331$	−6.34278	−	10.9860i	−0.348631	−	0.603846i	0.637376	−	0.770553i	$-0.280020\pi$
$331$	−6.34278	−	10.9860i	−0.348631	−	0.603846i	−0.986006	+	0.166707i	$0.946687\pi$
$332$	−20.3766	+	35.2933i	−1.11831	+	1.93697i
$333$	−1.54131	+	2.66962i	−0.0844631	+	0.146294i
$334$	10.3911	+	17.9980i	0.568578	+	0.984807i
$335$	0.432978			0.0236561
$336$		0			0
$337$	28.8310			1.57053			0.785264	−	0.619162i	$-0.212527\pi$
$337$	28.8310			1.57053			0.785264	+	0.619162i	$0.212527\pi$
$338$	−12.5319	−	21.7059i	−0.681646	−	1.18065i
$339$	−12.1570	+	21.0565i	−0.660277	+	1.14363i
$340$	−7.02294	+	12.1641i	−0.380872	+	0.659690i
$341$	−0.0867771	−	0.150302i	−0.00469924	−	0.00813933i
$342$	−85.3954			−4.61766
$343$		0			0
$344$	1.97403			0.106433
$345$	6.12917	+	10.6160i	0.329984	+	0.571548i
$346$	−3.78364	+	6.55345i	−0.203410	+	0.352316i
$347$	−7.78744	+	13.4882i	−0.418052	+	0.724087i	−0.995743	−	0.0921682i	$-0.970620\pi$
$347$	−7.78744	+	13.4882i	−0.418052	+	0.724087i	0.577692	+	0.816255i	$0.303954\pi$
$348$	−37.7265	−	65.3442i	−2.02235	−	3.50282i
$349$	−9.08484			−0.486300			−0.243150	−	0.969989i	$-0.578181\pi$
$349$	−9.08484			−0.486300			−0.243150	+	0.969989i	$0.578181\pi$
$350$		0			0
$351$	−12.1142			−0.646608
$352$	−5.97376	−	10.3469i	−0.318402	−	0.551489i
$353$	11.4961	−	19.9118i	0.611876	−	1.05980i	−0.379048	−	0.925377i	$-0.623749\pi$
$353$	11.4961	−	19.9118i	0.611876	−	1.05980i	0.990924	−	0.134423i	$-0.0429181\pi$
$354$	−7.82584	+	13.5548i	−0.415939	+	0.720427i
$355$	10.5170	+	18.2159i	0.558183	+	0.966802i
$356$	−12.0674			−0.639573
$357$		0			0
$358$	9.43751			0.498788
$359$	7.05815	+	12.2251i	0.372515	+	0.645214i	0.989952	−	0.141406i	$-0.0451623\pi$
$359$	7.05815	+	12.2251i	0.372515	+	0.645214i	−0.617437	+	0.786620i	$0.711829\pi$
$360$	−18.7656	+	32.5031i	−0.989037	+	1.71306i
$361$	−10.9084	+	18.8940i	−0.574129	+	0.994420i
$362$	−10.1039	−	17.5005i	−0.531050	−	0.919806i
$363$	11.7376			0.616065
$364$		0			0
$365$	19.9597			1.04474
$366$	−35.4072	−	61.3271i	−1.85077	−	3.20562i
$367$	6.59459	−	11.4222i	0.344235	−	0.596232i	−0.640980	−	0.767558i	$-0.721472\pi$
$367$	6.59459	−	11.4222i	0.344235	−	0.596232i	0.985214	+	0.171326i	$0.0548051\pi$
$368$	1.00159	−	1.73480i	0.0522113	−	0.0904326i
$369$	34.0261	+	58.9349i	1.77133	+	3.06803i
$370$	2.44907			0.127321
$371$		0			0
$372$	−0.665063			−0.0344819
$373$	−4.57714	−	7.92784i	−0.236995	−	0.410488i	0.722855	−	0.690999i	$-0.242829\pi$
$373$	−4.57714	−	7.92784i	−0.236995	−	0.410488i	−0.959851	+	0.280511i	$0.909496\pi$
$374$	−6.46676	+	11.2008i	−0.334388	+	0.579178i
$375$	17.8497	−	30.9165i	0.921753	−	1.59652i
$376$	−5.07763	−	8.79471i	−0.261859	−	0.453552i
$377$	−11.1456			−0.574029
$378$		0			0
$379$	3.07480			0.157942			0.0789710	−	0.996877i	$-0.474837\pi$
$379$	3.07480			0.157942			0.0789710	+	0.996877i	$0.474837\pi$
$380$	21.4460	+	37.1456i	1.10016	+	1.90553i
$381$	23.2632	−	40.2930i	1.19181	−	2.06427i
$382$	17.7417	−	30.7296i	0.907746	−	1.57226i
$383$	0.546606	+	0.946749i	0.0279303	+	0.0483766i	0.879653	−	0.475617i	$-0.157775\pi$
$383$	0.546606	+	0.946749i	0.0279303	+	0.0483766i	−0.851722	+	0.523993i	$0.824442\pi$
$384$	−58.7792			−2.99956
$385$		0			0
$386$	−23.9524			−1.21915
$387$	1.68735	+	2.92258i	0.0857730	+	0.148563i
$388$	25.1816	−	43.6159i	1.27840	−	2.21426i
$389$	5.91674	−	10.2481i	0.299991	−	0.519599i	−0.676143	−	0.736771i	$-0.736350\pi$
$389$	5.91674	−	10.2481i	0.299991	−	0.519599i	0.976133	+	0.217172i	$0.0696831\pi$
$390$	10.0967	+	17.4879i	0.511264	+	0.885536i
$391$	4.44424			0.224755
$392$		0			0
$393$	24.4067			1.23116
$394$	9.00728	+	15.6011i	0.453780	+	0.785971i
$395$	−12.9728	+	22.4696i	−0.652733	+	1.13057i
$396$	−26.1197	+	45.2406i	−1.31256	+	2.27342i
$397$	−14.1305	−	24.4747i	−0.709188	−	1.22835i	−0.965159	−	0.261665i	$-0.915728\pi$
$397$	−14.1305	−	24.4747i	−0.709188	−	1.22835i	0.255971	−	0.966684i	$-0.417605\pi$
$398$	−34.4406			−1.72635
$399$		0			0
$400$	−1.11871			−0.0559353
$401$	3.33128	+	5.76995i	0.166356	+	0.288138i	0.937136	−	0.348964i	$-0.113466\pi$
$401$	3.33128	+	5.76995i	0.166356	+	0.288138i	−0.770780	+	0.637102i	$0.780133\pi$
$402$	0.763892	−	1.32310i	0.0380995	−	0.0659902i
$403$	−0.0491203	+	0.0850788i	−0.00244686	+	0.00423808i
$404$	0.557390	+	0.965427i	0.0277312	+	0.0480318i
$405$	−13.0048			−0.646213
$406$		0			0
$407$	1.42570			0.0706694
$408$	10.3642	+	17.9514i	0.513107	+	0.888727i
$409$	5.87779	−	10.1806i	0.290638	−	0.503400i	−0.683323	−	0.730116i	$-0.739466\pi$
$409$	5.87779	−	10.1806i	0.290638	−	0.503400i	0.973961	+	0.226717i	$0.0727991\pi$
$410$	27.0330	−	46.8226i	1.33507	−	2.31240i
$411$	0.115323	+	0.199745i	0.00568845	+	0.00985268i
$412$	−35.0560			−1.72709
$413$		0			0
$414$	28.3935			1.39546
$415$	11.5750	+	20.0484i	0.568193	+	0.984139i
$416$	−3.38145	+	5.85685i	−0.165789	+	0.287156i
$417$	−23.1043	+	40.0177i	−1.13142	+	1.95968i
$418$	19.7476	+	34.2038i	0.965887	+	1.67296i
$419$	−6.77442			−0.330952			−0.165476	−	0.986214i	$-0.552916\pi$
$419$	−6.77442			−0.330952			−0.165476	+	0.986214i	$0.552916\pi$
$420$		0			0
$421$	−1.52728			−0.0744351			−0.0372175	−	0.999307i	$-0.511849\pi$
$421$	−1.52728			−0.0744351			−0.0372175	+	0.999307i	$0.511849\pi$
$422$	−5.69960	−	9.87199i	−0.277452	−	0.480561i
$423$	8.68047	−	15.0350i	0.422059	−	0.731027i
$424$	1.74623	−	3.02455i	0.0848042	−	0.146885i
$425$	−1.24098	−	2.14944i	−0.0601964	−	0.104263i
$426$	74.2193			3.59594
$427$		0			0
$428$	−52.8340			−2.55383
$429$	5.87766	+	10.1804i	0.283776	+	0.491515i
$430$	1.34057	−	2.32193i	0.0646480	−	0.111974i
$431$	−1.89230	+	3.27757i	−0.0911491	+	0.157875i	−0.907995	−	0.418981i	$-0.862387\pi$
$431$	−1.89230	+	3.27757i	−0.0911491	+	0.157875i	0.816846	+	0.576856i	$0.195721\pi$
$432$	3.80637	+	6.59282i	0.183134	+	0.317197i
$433$	−3.53219			−0.169746			−0.0848730	−	0.996392i	$-0.527048\pi$
$433$	−3.53219			−0.169746			−0.0848730	+	0.996392i	$0.527048\pi$
$434$		0			0
$435$	−42.8612			−2.05504
$436$	24.4751	+	42.3922i	1.17215	+	2.03022i
$437$	6.78570	−	11.7532i	0.324604	−	0.562230i
$438$	35.2144	−	60.9931i	1.68261	−	2.91436i
$439$	5.72398	+	9.91422i	0.273190	+	0.473180i	0.969677	−	0.244390i	$-0.0785877\pi$
$439$	5.72398	+	9.91422i	0.273190	+	0.473180i	−0.696487	+	0.717570i	$0.745254\pi$
$440$	17.3581			0.827517
$441$		0			0
$442$	7.32104			0.348226
$443$	6.76047	+	11.7095i	0.321200	+	0.556334i	0.980736	−	0.195339i	$-0.0625806\pi$
$443$	6.76047	+	11.7095i	0.321200	+	0.556334i	−0.659536	+	0.751673i	$0.729247\pi$
$444$	2.73166	−	4.73138i	0.129639	−	0.224541i
$445$	−3.42747	+	5.93655i	−0.162478	+	0.281419i
$446$	−2.03688	−	3.52798i	−0.0964490	−	0.167055i
$447$	18.5150			0.875727
$448$		0			0
$449$	−18.0667			−0.852621			−0.426310	−	0.904577i	$-0.640187\pi$
$449$	−18.0667			−0.852621			−0.426310	+	0.904577i	$0.640187\pi$
$450$	−7.92842	−	13.7324i	−0.373749	−	0.647353i
$451$	15.7370	−	27.2573i	0.741026	−	1.28349i
$452$	14.1434	−	24.4972i	0.665251	−	1.15225i
$453$	−24.1160	−	41.7701i	−1.13307	−	1.96253i
$454$	55.2523			2.59312
$455$		0			0
$456$	63.2987			2.96424
$457$	−13.9458	−	24.1548i	−0.652357	−	1.12992i	−0.982549	−	0.186002i	$-0.940447\pi$
$457$	−13.9458	−	24.1548i	−0.652357	−	1.12992i	0.330192	−	0.943914i	$-0.392886\pi$
$458$	−15.3801	+	26.6392i	−0.718667	+	1.24477i
$459$	−8.44481	+	14.6268i	−0.394170	+	0.682722i
$460$	−7.13068	−	12.3507i	−0.332469	−	0.575854i
$461$	−27.9948			−1.30385			−0.651925	−	0.758284i	$-0.726038\pi$
$461$	−27.9948			−1.30385			−0.651925	+	0.758284i	$0.726038\pi$
$462$		0			0
$463$	−37.3527			−1.73593			−0.867964	−	0.496627i	$-0.834572\pi$
$463$	−37.3527			−1.73593			−0.867964	+	0.496627i	$0.834572\pi$
$464$	3.50204	+	6.06571i	0.162578	+	0.281593i
$465$	−0.188895	+	0.327176i	−0.00875981	+	0.0151724i
$466$	24.8233	−	42.9952i	1.14992	−	1.99172i
$467$	−14.4331	−	24.9989i	−0.667886	−	1.15681i	−0.978494	−	0.206275i	$-0.933866\pi$
$467$	−14.4331	−	24.9989i	−0.667886	−	1.15681i	0.310608	−	0.950538i	$-0.399467\pi$
$468$	29.5701			1.36688
$469$		0			0
$470$	−13.7929			−0.636220
$471$	19.7487	+	34.2058i	0.909973	+	1.57612i
$472$	3.80787	−	6.59543i	0.175272	−	0.303579i
$473$	0.780397	−	1.35169i	0.0358827	−	0.0621507i
$474$	45.7752	+	79.2850i	2.10253	+	3.64168i
$475$	−7.57918			−0.347757
$476$		0			0
$477$	5.97052			0.273372
$478$	−13.1301	−	22.7421i	−0.600558	−	1.04020i
$479$	12.5486	−	21.7349i	0.573362	−	0.993092i	−0.422856	−	0.906197i	$-0.638972\pi$
$479$	12.5486	−	21.7349i	0.573362	−	0.993092i	0.996217	−	0.0868948i	$-0.0276944\pi$
$480$	−13.0036	+	22.5229i	−0.593531	+	1.02803i
$481$	−0.403510	−	0.698900i	−0.0183985	−	0.0318671i
$482$	21.5947			0.983611
$483$		0			0
$484$	−13.6555			−0.620706
$485$	−14.3045	−	24.7761i	−0.649533	−	1.12502i
$486$	5.29379	−	9.16912i	0.240131	−	0.415920i
$487$	20.5117	−	35.5273i	0.929474	−	1.60990i	0.145270	−	0.989392i	$-0.453595\pi$
$487$	20.5117	−	35.5273i	0.929474	−	1.60990i	0.784204	−	0.620504i	$-0.213072\pi$
$488$	17.2283	+	29.8404i	0.779890	+	1.35081i
$489$	32.8487			1.48547
$490$		0			0
$491$	0.985019			0.0444533			0.0222266	−	0.999753i	$-0.492924\pi$
$491$	0.985019			0.0444533			0.0222266	+	0.999753i	$0.492924\pi$
$492$	−60.3045	−	104.450i	−2.71874	−	4.70899i
$493$	−7.76962	+	13.4574i	−0.349926	+	0.606090i
$494$	11.1782	−	19.3611i	0.502929	−	0.871099i
$495$	14.8373	+	25.6990i	0.666888	+	1.15508i
$496$	0.0617358			0.00277202
$497$		0			0
$498$	81.6856			3.66042
$499$	4.84056	+	8.38410i	0.216693	+	0.375324i	0.953795	−	0.300458i	$-0.0971395\pi$
$499$	4.84056	+	8.38410i	0.216693	+	0.375324i	−0.737102	+	0.675782i	$0.763806\pi$
$500$	−20.7663	+	35.9682i	−0.928696	+	1.60855i
$501$	13.1676	−	22.8069i	0.588284	−	1.01894i
$502$	23.1558	+	40.1070i	1.03349	+	1.79007i
$503$	12.4080			0.553243			0.276622	−	0.960979i	$-0.410785\pi$
$503$	12.4080			0.553243			0.276622	+	0.960979i	$0.410785\pi$
$504$		0			0
$505$	0.633252			0.0281794
$506$	−6.56597	−	11.3726i	−0.291893	−	0.505573i
$507$	−15.8804	+	27.5056i	−0.705271	+	1.22157i
$508$	−27.0643	+	46.8768i	−1.20079	+	2.07982i
$509$	6.85993	+	11.8817i	0.304061	+	0.526649i	0.977052	−	0.213002i	$-0.0683240\pi$
$509$	6.85993	+	11.8817i	0.304061	+	0.526649i	−0.672991	+	0.739651i	$0.734991\pi$
$510$	28.1535			1.24666
$511$		0			0
$512$	10.5735			0.467287
$513$	25.7880	+	44.6661i	1.13857	+	1.97206i
$514$	−29.3324	+	50.8053i	−1.29380	+	2.24092i
$515$	−9.95682	+	17.2457i	−0.438750	+	0.759937i
$516$	−2.99050	−	5.17970i	−0.131649	−	0.228023i
$517$	−8.02939			−0.353132
$518$		0			0
$519$	9.58920			0.420919
$520$	−4.91280	−	8.50922i	−0.215441	−	0.373154i
$521$	−17.0517	+	29.5344i	−0.747049	+	1.29393i	0.202183	+	0.979348i	$0.435196\pi$
$521$	−17.0517	+	29.5344i	−0.747049	+	1.29393i	−0.949232	+	0.314578i	$0.898137\pi$
$522$	−49.6388	+	85.9770i	−2.17263	+	3.76311i
$523$	2.62279	+	4.54280i	0.114687	+	0.198643i	0.917654	−	0.397379i	$-0.130080\pi$
$523$	2.62279	+	4.54280i	0.114687	+	0.198643i	−0.802968	+	0.596022i	$0.796747\pi$
$524$	−28.3948			−1.24043
$525$		0			0
$526$	24.0854			1.05017
$527$	0.0684835	+	0.118617i	0.00298319	+	0.00516704i
$528$	3.69361	−	6.39752i	0.160744	−	0.278416i
$529$	9.24379	−	16.0107i	0.401904	−	0.696118i
$530$	−2.37173	−	4.10796i	−0.103021	−	0.178438i
$531$	13.0195			0.564999
$532$		0			0
$533$	−17.8159			−0.771692
$534$	12.0940	+	20.9474i	0.523358	+	0.906483i
$535$	−15.0062	+	25.9915i	−0.648776	+	1.12371i
$536$	−0.371692	+	0.643789i	−0.0160547	+	0.0278075i
$537$	−5.97958	−	10.3569i	−0.258038	−	0.446934i
$538$	−1.04547			−0.0450732
$539$		0			0
$540$	54.1980			2.33231
$541$	−21.8311	−	37.8126i	−0.938593	−	1.62569i	−0.768099	−	0.640332i	$-0.778797\pi$
$541$	−21.8311	−	37.8126i	−0.938593	−	1.62569i	−0.170494	−	0.985359i	$-0.554536\pi$
$542$	27.9399	−	48.3933i	1.20012	−	2.07867i
$543$	−12.8036	+	22.1765i	−0.549456	+	0.951685i
$544$	4.71443	+	8.16563i	0.202129	+	0.350098i
$545$	27.8063			1.19109
$546$		0			0
$547$	−36.2818			−1.55130			−0.775648	−	0.631166i	$-0.782577\pi$
$547$	−36.2818			−1.55130			−0.775648	+	0.631166i	$0.782577\pi$
$548$	−0.134166	−	0.232383i	−0.00573130	−	0.00992691i
$549$	−29.4527	+	51.0136i	−1.25701	+	2.17721i
$550$	−3.66688	+	6.35122i	−0.156356	+	0.270817i
$551$	23.7261	+	41.0949i	1.01077	+	1.75070i
$552$	−21.0465			−0.895798
$553$		0			0
$554$	−35.3885			−1.50352
$555$	−1.55173	−	2.68767i	−0.0658671	−	0.114085i
$556$	26.8795	−	46.5566i	1.13994	−	1.97444i
$557$	3.59546	−	6.22753i	0.152345	−	0.263869i	−0.779744	−	0.626098i	$-0.784651\pi$
$557$	3.59546	−	6.22753i	0.152345	−	0.263869i	0.932089	+	0.362229i	$0.117984\pi$
$558$	0.437530	+	0.757825i	0.0185221	+	0.0320813i
$559$	−0.883490			−0.0373676
$560$		0			0
$561$	16.3893			0.691956
$562$	11.6969	+	20.2596i	0.493404	+	0.854601i
$563$	5.84949	−	10.1316i	0.246527	−	0.426996i	−0.716033	−	0.698066i	$-0.754044\pi$
$563$	5.84949	−	10.1316i	0.246527	−	0.426996i	0.962560	+	0.271070i	$0.0873774\pi$
$564$	−15.3844	+	26.6466i	−0.647800	+	1.12202i
$565$	−8.03421	−	13.9157i	−0.338002	−	0.585436i
$566$	−4.90414			−0.206136
$567$		0			0
$568$	−36.1134			−1.51528
$569$	−12.1443	−	21.0345i	−0.509115	−	0.881814i	−0.999944	−	0.0105577i	$-0.996639\pi$
$569$	−12.1443	−	21.0345i	−0.509115	−	0.881814i	0.490829	−	0.871256i	$-0.336694\pi$
$570$	42.9863	−	74.4545i	1.80050	−	3.11856i
$571$	−0.792386	+	1.37245i	−0.0331603	+	0.0574354i	−0.882129	−	0.471007i	$-0.843891\pi$
$571$	−0.792386	+	1.37245i	−0.0331603	+	0.0574354i	0.848969	+	0.528443i	$0.177224\pi$
$572$	−6.83806	−	11.8439i	−0.285914	−	0.495217i
$573$	−44.9644			−1.87842
$574$		0			0
$575$	2.52004			0.105093
$576$	35.5250	+	61.5310i	1.48021	+	2.56379i
$577$	−8.95001	+	15.5019i	−0.372594	+	0.645352i	−0.989964	−	0.141321i	$-0.954865\pi$
$577$	−8.95001	+	15.5019i	−0.372594	+	0.645352i	0.617370	+	0.786673i	$0.288198\pi$
$578$	−14.7178	+	25.4919i	−0.612179	+	1.06032i
$579$	15.1762	+	26.2859i	0.630700	+	1.09240i
$580$	49.8647			2.07052
$581$		0			0
$582$	−100.948			−4.18443
$583$	−1.38068	−	2.39140i	−0.0571818	−	0.0990418i
$584$	−17.1345	+	29.6778i	−0.709030	+	1.22808i
$585$	8.39869	−	14.5470i	0.347243	−	0.601442i
$586$	−21.7436	−	37.6611i	−0.898221	−	1.55576i
$587$	1.07134			0.0442189			0.0221094	−	0.999756i	$-0.492962\pi$
$587$	1.07134			0.0442189			0.0221094	+	0.999756i	$0.492962\pi$
$588$		0			0
$589$	0.418257			0.0172340
$590$	−5.17187	−	8.95794i	−0.212923	−	0.368793i
$591$	11.4140	−	19.7696i	0.469508	−	0.813211i
$592$	−0.253572	+	0.439199i	−0.0104217	+	0.0180510i
$593$	−2.60519	−	4.51231i	−0.106982	−	0.185299i	0.807564	−	0.589780i	$-0.200785\pi$
$593$	−2.60519	−	4.51231i	−0.106982	−	0.185299i	−0.914546	+	0.404481i	$0.867452\pi$
$594$	49.9058			2.04766
$595$		0			0
$596$	−21.5403			−0.882324
$597$	21.8215	+	37.7959i	0.893093	+	1.54688i
$598$	−3.71668	+	6.43747i	−0.151986	+	0.263248i
$599$	−9.67984	+	16.7660i	−0.395508	+	0.685039i	−0.993166	−	0.116712i	$-0.962765\pi$
$599$	−9.67984	+	16.7660i	−0.395508	+	0.685039i	0.597658	+	0.801751i	$0.296098\pi$
$600$	5.87688	+	10.1791i	0.239923	+	0.415559i
$601$	15.0693			0.614689			0.307345	−	0.951598i	$-0.400560\pi$
$601$	15.0693			0.614689			0.307345	+	0.951598i	$0.400560\pi$
$602$		0			0
$603$	−1.27085			−0.0517532
$604$	28.0565	+	48.5953i	1.14160	+	1.97731i
$605$	−3.87853	+	6.71780i	−0.157684	+	0.273118i
$606$	1.11723	−	1.93510i	0.0453844	−	0.0786081i
$607$	−15.4831	−	26.8175i	−0.628440	−	1.08849i	−0.987865	−	0.155316i	$-0.950361\pi$
$607$	−15.4831	−	26.8175i	−0.628440	−	1.08849i	0.359425	−	0.933174i	$-0.382973\pi$
$608$	28.7930			1.16771
$609$		0			0
$610$	46.7992			1.89484
$611$	2.27252	+	3.93613i	0.0919365	+	0.159239i
$612$	20.6134	−	35.7034i	0.833246	−	1.44322i
$613$	−1.87717	+	3.25135i	−0.0758182	+	0.131321i	−0.901442	−	0.432900i	$-0.857490\pi$
$613$	−1.87717	+	3.25135i	−0.0758182	+	0.131321i	0.825624	+	0.564221i	$0.190824\pi$
$614$	−11.3407	−	19.6427i	−0.457674	−	0.792714i
$615$	−68.5122			−2.76268
$616$		0			0
$617$	28.0758			1.13029			0.565145	−	0.824991i	$-0.308820\pi$
$617$	28.0758			1.13029			0.565145	+	0.824991i	$0.308820\pi$
$618$	35.1331	+	60.8524i	1.41326	+	2.44784i
$619$	−9.68370	+	16.7727i	−0.389221	+	0.674150i	−0.992345	−	0.123497i	$-0.960589\pi$
$619$	−9.68370	+	16.7727i	−0.389221	+	0.674150i	0.603124	+	0.797647i	$0.293922\pi$
$620$	0.219761	−	0.380636i	0.00882580	−	0.0152867i
$621$	−8.57436	−	14.8512i	−0.344077	−	0.595959i
$622$	−64.9267			−2.60332
$623$		0			0
$624$	−4.18154			−0.167396
$625$	8.83052	+	15.2949i	0.353221	+	0.611796i
$626$	−23.5699	+	40.8242i	−0.942042	+	1.63166i
$627$	25.0240	−	43.3429i	0.999363	−	1.73095i
$628$	−22.9756	−	39.7950i	−0.916828	−	1.58799i
$629$	−1.12515			−0.0448626
$630$		0			0
$631$	40.7248			1.62123			0.810615	−	0.585580i	$-0.199133\pi$
$631$	40.7248			1.62123			0.810615	+	0.585580i	$0.199133\pi$
$632$	−22.2732	−	38.5782i	−0.885979	−	1.53456i
$633$	−7.22249	+	12.5097i	−0.287068	+	0.497217i
$634$	13.8207	−	23.9381i	0.548890	−	0.950705i
$635$	15.3739	+	26.6284i	0.610096	+	1.05672i
$636$	−10.5816			−0.419587
$637$		0			0
$638$	45.9157			1.81782
$639$	−30.8689	−	53.4664i	−1.22115	−	2.11510i
$640$	19.4227	−	33.6412i	0.767751	−	1.32978i
$641$	−0.353256	+	0.611858i	−0.0139528	+	0.0241669i	−0.872917	−	0.487868i	$-0.837775\pi$
$641$	−0.353256	+	0.611858i	−0.0139528	+	0.0241669i	0.858965	+	0.512035i	$0.171108\pi$
$642$	52.9502	+	91.7124i	2.08978	+	3.61960i
$643$	−16.5495			−0.652650			−0.326325	−	0.945258i	$-0.605810\pi$
$643$	−16.5495			−0.652650			−0.326325	+	0.945258i	$0.605810\pi$
$644$		0			0
$645$	−3.39752			−0.133777
$646$	−15.5846	−	26.9933i	−0.613168	−	1.06204i
$647$	−5.87980	+	10.1841i	−0.231159	+	0.400379i	−0.958149	−	0.286269i	$-0.907585\pi$
$647$	−5.87980	+	10.1841i	−0.231159	+	0.400379i	0.726991	+	0.686647i	$0.240918\pi$
$648$	11.1640	−	19.3367i	0.438564	−	0.759616i
$649$	−3.01075	−	5.21477i	−0.118182	−	0.204698i
$650$	4.15128			0.162827
$651$		0			0
$652$	−38.2161			−1.49666
$653$	−11.2938	−	19.5615i	−0.441962	−	0.765501i	0.555873	−	0.831267i	$-0.312384\pi$
$653$	−11.2938	−	19.5615i	−0.441962	−	0.765501i	−0.997835	+	0.0657661i	$0.979051\pi$
$654$	49.0579	−	84.9709i	1.91832	−	3.32262i
$655$	−8.06485	+	13.9687i	−0.315120	+	0.545803i
$656$	5.59788	+	9.69582i	0.218561	+	0.378558i
$657$	−58.5846			−2.28560
$658$		0			0
$659$	18.0135			0.701705			0.350852	−	0.936431i	$-0.385892\pi$
$659$	18.0135			0.701705			0.350852	+	0.936431i	$0.385892\pi$
$660$	−26.2962	−	45.5464i	−1.02358	−	1.77289i
$661$	18.8440	−	32.6388i	0.732948	−	1.26950i	−0.222670	−	0.974894i	$-0.571477\pi$
$661$	18.8440	−	32.6388i	0.732948	−	1.26950i	0.955618	−	0.294609i	$-0.0951893\pi$
$662$	14.7908	−	25.6185i	0.574862	−	0.995690i
$663$	−4.63859	−	8.03427i	−0.180148	−	0.312025i
$664$	−39.7463			−1.54246
$665$		0			0
$666$	−7.18839			−0.278545
$667$	−7.88881	−	13.6638i	−0.305456	−	0.529065i
$668$	−15.3192	+	26.5336i	−0.592716	+	1.02661i
$669$	−2.58112	+	4.47063i	−0.0997918	+	0.172844i
$670$	0.504834	+	0.874398i	0.0195034	+	0.0337809i
$671$	27.2436			1.05173
$672$		0			0
$673$	−18.7754			−0.723738			−0.361869	−	0.932229i	$-0.617861\pi$
$673$	−18.7754			−0.723738			−0.361869	+	0.932229i	$0.617861\pi$
$674$	33.6158	+	58.2242i	1.29483	+	2.24271i
$675$	−4.78850	+	8.29392i	−0.184309	+	0.319233i
$676$	18.4752	−	32.0000i	0.710584	−	1.23077i
$677$	−1.92831	−	3.33993i	−0.0741110	−	0.128364i	0.826588	−	0.562807i	$-0.190279\pi$
$677$	−1.92831	−	3.33993i	−0.0741110	−	0.128364i	−0.900699	+	0.434443i	$0.856945\pi$
$678$	−56.6982			−2.17748
$679$		0			0
$680$	−13.6989			−0.525327
$681$	−35.0076	−	60.6350i	−1.34150	−	2.32354i
$682$	0.202357	−	0.350492i	0.00774864	−	0.0134210i
$683$	−20.0272	+	34.6881i	−0.766318	+	1.32730i	0.173228	+	0.984882i	$0.444580\pi$
$683$	−20.0272	+	34.6881i	−0.766318	+	1.32730i	−0.939547	+	0.342421i	$0.888753\pi$
$684$	−62.9471	−	109.028i	−2.40684	−	4.16878i
$685$	−0.152427			−0.00582393
$686$		0			0
$687$	38.9792			1.48715
$688$	0.277599	+	0.480816i	0.0105834	+	0.0183309i
$689$	−0.781534	+	1.35366i	−0.0297741	+	0.0515702i
$690$	−14.2927	+	24.7557i	−0.544114	+	0.942434i
$691$	−16.9118	−	29.2921i	−0.643356	−	1.11433i	−0.984679	−	0.174379i	$-0.944208\pi$
$691$	−16.9118	−	29.2921i	−0.643356	−	1.11433i	0.341323	−	0.939946i	$-0.389125\pi$
$692$	−11.1561			−0.424090
$693$		0			0
$694$	−36.3193			−1.37866
$695$	−15.2689	−	26.4466i	−0.579184	−	1.00318i
$696$	36.7944	−	63.7298i	1.39469	−	2.41567i
$697$	−12.4195	+	21.5111i	−0.470421	+	0.814793i
$698$	−10.5925	−	18.3468i	−0.400934	−	0.694437i
$699$	−62.9118			−2.37954
$700$		0			0
$701$	41.0095			1.54891			0.774453	−	0.632631i	$-0.218025\pi$
$701$	41.0095			1.54891			0.774453	+	0.632631i	$0.218025\pi$
$702$	−14.1246	−	24.4646i	−0.533100	−	0.923356i
$703$	−1.71794	+	2.97555i	−0.0647932	+	0.112225i
$704$	16.4302	−	28.4580i	0.619237	−	1.07255i
$705$	8.73914	+	15.1366i	0.329135	+	0.570079i
$706$	53.6159			2.01786
$707$		0			0
$708$	−23.0745			−0.867193
$709$	12.4320	+	21.5328i	0.466893	+	0.808683i	0.999285	−	0.0378152i	$-0.0120398\pi$
$709$	12.4320	+	21.5328i	0.466893	+	0.808683i	−0.532391	+	0.846498i	$0.678707\pi$
$710$	−24.5247	+	42.4780i	−0.920395	+	1.59417i
$711$	38.0771	−	65.9515i	1.42800	−	2.47337i
$712$	−5.88465	−	10.1925i	−0.220537	−	0.381981i
$713$	−0.139068			−0.00520815
$714$		0			0
$715$	−7.76875			−0.290535
$716$	6.95663	+	12.0492i	0.259982	+	0.450301i
$717$	−16.6384	+	28.8186i	−0.621373	+	1.07625i
$718$	−16.4590	+	28.5078i	−0.614244	+	1.06390i
$719$	10.0775	+	17.4547i	0.375827	+	0.650951i	0.990450	−	0.137869i	$-0.0440254\pi$
$719$	10.0775	+	17.4547i	0.375827	+	0.650951i	−0.614623	+	0.788821i	$0.710692\pi$
$720$	−10.5557			−0.393388
$721$		0			0
$722$	−50.8752			−1.89338
$723$	−13.6823	−	23.6985i	−0.508851	−	0.881355i
$724$	14.8957	−	25.8001i	0.553595	−	0.958854i
$725$	−4.40564	+	7.63079i	−0.163621	+	0.283401i
$726$	13.6856	+	23.7041i	0.507919	+	0.879741i
$727$	−39.6430			−1.47028			−0.735138	−	0.677918i	$-0.762883\pi$
$727$	−39.6430			−1.47028			−0.735138	+	0.677918i	$0.762883\pi$
$728$		0			0
$729$	−33.3945			−1.23683
$730$	23.2721	+	40.3085i	0.861341	+	1.49189i
$731$	−0.615881	+	1.06674i	−0.0227792	+	0.0394547i
$732$	52.1991	−	90.4116i	1.92934	−	3.34171i
$733$	−2.34660	−	4.06444i	−0.0866738	−	0.150123i	0.819429	−	0.573180i	$-0.194290\pi$
$733$	−2.34660	−	4.06444i	−0.0866738	−	0.150123i	−0.906103	+	0.423057i	$0.860957\pi$
$734$	30.7560			1.13523
$735$		0			0
$736$	−9.57350			−0.352884
$737$	0.293883	+	0.509021i	0.0108253	+	0.0187500i
$738$	−79.3460	+	137.431i	−2.92076	+	5.05891i
$739$	−12.2117	+	21.1514i	−0.449216	+	0.778066i	−0.998335	−	0.0576786i	$-0.981630\pi$
$739$	−12.2117	+	21.1514i	−0.449216	+	0.778066i	0.549119	+	0.835744i	$0.314963\pi$
$740$	1.80528	+	3.12683i	0.0663632	+	0.114945i
$741$	−28.3298			−1.04072
$742$		0			0
$743$	28.1516			1.03278			0.516391	−	0.856353i	$-0.327275\pi$
$743$	28.1516			1.03278			0.516391	+	0.856353i	$0.327275\pi$
$744$	−0.324316	−	0.561732i	−0.0118900	−	0.0205941i
$745$	−6.11800	+	10.5967i	−0.224146	+	0.388232i
$746$	10.6735	−	18.4871i	0.390785	−	0.676859i
$747$	−33.9742	−	58.8451i	−1.24305	−	2.15303i
$748$	−19.0673			−0.697168
$749$		0			0
$750$	83.2478			3.03978
$751$	14.3535	+	24.8610i	0.523766	+	0.907190i	0.999617	+	0.0276640i	$0.00880686\pi$
$751$	14.3535	+	24.8610i	0.523766	+	0.907190i	−0.475851	+	0.879526i	$0.657860\pi$
$752$	1.42809	−	2.47352i	0.0520770	−	0.0902000i
$753$	29.3429	−	50.8234i	1.06931	−	1.85211i
$754$	−12.9953	−	22.5086i	−0.473262	−	0.819713i
$755$	31.8751			1.16005
$756$		0			0
$757$	−34.9823			−1.27145			−0.635726	−	0.771915i	$-0.719299\pi$
$757$	−34.9823			−1.27145			−0.635726	+	0.771915i	$0.719299\pi$
$758$	3.58509	+	6.20956i	0.130216	+	0.225541i
$759$	−8.32035	+	14.4113i	−0.302009	+	0.523096i
$760$	−20.9161	+	36.2278i	−0.758708	+	1.31412i
$761$	23.6431	+	40.9510i	0.857060	+	1.48447i	0.874721	+	0.484628i	$0.161045\pi$
$761$	23.6431	+	40.9510i	0.857060	+	1.48447i	−0.0176605	+	0.999844i	$0.505622\pi$
$762$	108.495			3.93037
$763$		0			0
$764$	52.3116			1.89257
$765$	−11.7095	−	20.2814i	−0.423356	−	0.733274i
$766$	−1.27464	+	2.20774i	−0.0460546	+	0.0797688i
$767$	−1.70424	+	2.95183i	−0.0615365	+	0.106584i
$768$	−31.9057	−	55.2624i	−1.15130	−	1.99411i
$769$	41.8758			1.51008			0.755040	−	0.655678i	$-0.227617\pi$
$769$	41.8758			1.51008			0.755040	+	0.655678i	$0.227617\pi$
$770$		0			0
$771$	74.3397			2.67728
$772$	−17.6559	−	30.5810i	−0.635451	−	1.10063i
$773$	−10.5471	+	18.2681i	−0.379353	+	0.657059i	−0.990968	−	0.134097i	$-0.957187\pi$
$773$	−10.5471	+	18.2681i	−0.379353	+	0.657059i	0.611615	+	0.791155i	$0.290520\pi$
$774$	−3.93477	+	6.81521i	−0.141432	+	0.244968i
$775$	0.0388325	+	0.0672599i	0.00139491	+	0.00241605i
$776$	49.1190			1.76327
$777$		0			0
$778$	27.5947			0.989317
$779$	37.9254	+	65.6887i	1.35882	+	2.35354i
$780$	−14.8850	+	25.7816i	−0.532969	+	0.923129i
$781$	−14.2768	+	24.7281i	−0.510863	+	0.884841i
$782$	5.18179	+	8.97513i	0.185300	+	0.320950i
$783$	59.9603			2.14281
$784$		0			0
$785$	−26.1027			−0.931646
$786$	28.4572	+	49.2893i	1.01503	+	1.75809i
$787$	20.1250	−	34.8576i	0.717380	−	1.24254i	−0.244654	−	0.969610i	$-0.578674\pi$
$787$	20.1250	−	34.8576i	0.717380	−	1.24254i	0.962034	−	0.272928i	$-0.0879922\pi$
$788$	−13.2790	+	22.9999i	−0.473045	+	0.819337i
$789$	−15.2604	−	26.4318i	−0.543284	−	0.940996i
$790$	−60.5030			−2.15260
$791$		0			0
$792$	−50.9487			−1.81038
$793$	−7.71065	−	13.3552i	−0.273813	−	0.474259i
$794$	32.9511	−	57.0729i	1.16939	−	2.02544i
$795$	−3.00544	+	5.20558i	−0.106592	+	0.184623i
$796$	−25.3871	−	43.9717i	−0.899821	−	1.55854i
$797$	5.32667			0.188680			0.0943401	−	0.995540i	$-0.469926\pi$
$797$	5.32667			0.188680			0.0943401	+	0.995540i	$0.469926\pi$
$798$		0			0
$799$	6.33671			0.224177
$800$	2.67324	+	4.63019i	0.0945134	+	0.163702i
$801$	10.0601	−	17.4246i	0.355457	−	0.615669i
$802$	−7.76827	+	13.4550i	−0.274307	+	0.475114i
$803$	13.5476	+	23.4652i	0.478085	+	0.828068i
$804$	2.25234			0.0794338
$805$		0			0
$806$	−0.229089			−0.00806930
$807$	0.662403	+	1.14732i	0.0233177	+	0.0403874i
$808$	−0.543619	+	0.941575i	−0.0191244	+	0.0331245i
$809$	−19.1829	+	33.2257i	−0.674434	+	1.16815i	0.302200	+	0.953244i	$0.402279\pi$
$809$	−19.1829	+	33.2257i	−0.674434	+	1.16815i	−0.976634	+	0.214909i	$0.931054\pi$
$810$	−15.1630	−	26.2631i	−0.532775	−	0.922793i
$811$	−33.5120			−1.17676			−0.588382	−	0.808583i	$-0.700235\pi$
$811$	−33.5120			−1.17676			−0.588382	+	0.808583i	$0.700235\pi$
$812$		0			0
$813$	−70.8104			−2.48343
$814$	1.66231	+	2.87920i	0.0582639	+	0.100916i
$815$	−10.8544	+	18.8003i	−0.380212	+	0.658547i
$816$	−2.91496	+	5.04885i	−0.102044	+	0.176745i
$817$	1.88072	+	3.25750i	0.0657981	+	0.113966i
$818$	27.4130			0.958473
$819$		0			0
$820$	79.7070			2.78349
$821$	18.4938	+	32.0321i	0.645437	+	1.11793i	0.984200	+	0.177058i	$0.0566580\pi$
$821$	18.4938	+	32.0321i	0.645437	+	1.11793i	−0.338763	+	0.940872i	$0.610009\pi$
$822$	−0.268923	+	0.465788i	−0.00937976	+	0.0162462i
$823$	−4.05472	+	7.02298i	−0.141339	+	0.244806i	−0.928001	−	0.372578i	$-0.878474\pi$
$823$	−4.05472	+	7.02298i	−0.141339	+	0.244806i	0.786662	+	0.617384i	$0.211807\pi$
$824$	−17.0950	−	29.6094i	−0.595531	−	1.03149i
$825$	9.29328			0.323551
$826$		0			0
$827$	−47.9413			−1.66708			−0.833541	−	0.552458i	$-0.813690\pi$
$827$	−47.9413			−1.66708			−0.833541	+	0.552458i	$0.813690\pi$
$828$	20.9296	+	36.2511i	0.727353	+	1.25981i
$829$	14.7347	−	25.5213i	0.511758	−	0.886391i	−0.488149	−	0.872760i	$-0.662328\pi$
$829$	14.7347	−	25.5213i	0.511758	−	0.886391i	0.999907	−	0.0136310i	$-0.00433901\pi$
$830$	−26.9918	+	46.7512i	−0.936900	+	1.62276i
$831$	22.4221	+	38.8361i	0.777812	+	1.34721i
$832$	−18.6007			−0.644863
$833$		0			0
$834$	−107.754			−3.73123
$835$	8.70208	+	15.0724i	0.301148	+	0.521603i
$836$	−29.1129	+	50.4250i	−1.00689	+	1.74399i
$837$	0.264253	−	0.457700i	0.00913393	−	0.0158204i
$838$	−7.89869	−	13.6809i	−0.272856	−	0.472600i
$839$	−42.6216			−1.47146			−0.735731	−	0.677274i	$-0.763161\pi$
$839$	−42.6216			−1.47146			−0.735731	+	0.677274i	$0.763161\pi$
$840$		0			0
$841$	26.1663			0.902287
$842$	−1.78074	−	3.08434i	−0.0613685	−	0.106293i
$843$	14.8222	−	25.6728i	0.510505	−	0.884220i
$844$	8.40264	−	14.5538i	0.289231	−	0.500962i
$845$	−10.4949	−	18.1776i	−0.361034	−	0.625330i
$846$	40.4842			1.39188
$847$		0			0
$848$	0.982255			0.0337308
$849$	3.10725	+	5.38191i	0.106640	+	0.184707i
$850$	2.89386	−	5.01231i	0.0992586	−	0.171921i
$851$	0.571205	−	0.989355i	0.0195806	−	0.0339147i
$852$	54.7089	+	94.7587i	1.87430	+	3.24638i
$853$	44.8312			1.53499			0.767496	−	0.641054i	$-0.221502\pi$
$853$	44.8312			1.53499			0.767496	+	0.641054i	$0.221502\pi$
$854$		0			0
$855$	−71.5145			−2.44574
$856$	−25.7643	−	44.6251i	−0.880607	−	1.52526i
$857$	16.2744	−	28.1882i	0.555924	−	0.962889i	−0.441907	−	0.897061i	$-0.645698\pi$
$857$	16.2744	−	28.1882i	0.555924	−	0.962889i	0.997831	−	0.0658280i	$-0.0209689\pi$
$858$	−13.7062	+	23.7398i	−0.467922	+	0.810465i
$859$	−17.4416	−	30.2097i	−0.595099	−	1.03074i	−0.993533	−	0.113544i	$-0.963780\pi$
$859$	−17.4416	−	30.2097i	−0.595099	−	1.03074i	0.398434	−	0.917197i	$-0.369554\pi$
$860$	3.95267			0.134785
$861$		0			0
$862$	−8.82539			−0.300594
$863$	0.830104	+	1.43778i	0.0282571	+	0.0489427i	0.879808	−	0.475329i	$-0.157671\pi$
$863$	0.830104	+	1.43778i	0.0282571	+	0.0489427i	−0.851551	+	0.524272i	$0.824338\pi$
$864$	18.1913	−	31.5082i	0.618880	−	1.07193i
$865$	−3.16861	+	5.48820i	−0.107736	+	0.186604i
$866$	−4.11838	−	7.13324i	−0.139948	−	0.242397i
$867$	37.3005			1.26679
$868$		0			0
$869$	−35.2212			−1.19480
$870$	−49.9744	−	86.5581i	−1.69429	−	2.93460i
$871$	0.166353	−	0.288132i	0.00563666	−	0.00976298i
$872$	−23.8705	+	41.3449i	−0.808356	+	1.40011i
$873$	41.9857	+	72.7214i	1.42100	+	2.46125i
$874$	31.6473			1.07049
$875$		0			0
$876$	103.830			3.50808
$877$	−15.2991	−	26.4988i	−0.516613	−	0.894799i	−0.999814	−	0.0192900i	$-0.993859\pi$
$877$	−15.2991	−	26.4988i	−0.516613	−	0.894799i	0.483201	−	0.875509i	$-0.339474\pi$
$878$	−13.3478	+	23.1191i	−0.450467	+	0.780232i
$879$	−27.5534	+	47.7238i	−0.929352	+	1.60969i
$880$	2.44100	+	4.22793i	0.0822860	+	0.142524i
$881$	−51.9678			−1.75084			−0.875419	−	0.483365i	$-0.839414\pi$
$881$	−51.9678			−1.75084			−0.875419	+	0.483365i	$0.839414\pi$
$882$		0			0
$883$	22.8041			0.767420			0.383710	−	0.923454i	$-0.374646\pi$
$883$	22.8041			0.767420			0.383710	+	0.923454i	$0.374646\pi$
$884$	5.39653	+	9.34706i	0.181505	+	0.314376i
$885$	−6.55376	+	11.3514i	−0.220302	+	0.381574i
$886$	−15.7649	+	27.3055i	−0.529630	+	0.917347i
$887$	−7.46042	−	12.9218i	−0.250496	−	0.433872i	0.713166	−	0.700995i	$-0.247260\pi$
$887$	−7.46042	−	12.9218i	−0.250496	−	0.433872i	−0.963663	+	0.267123i	$0.913927\pi$
$888$	5.32834			0.178808
$889$		0			0
$890$	−15.9851			−0.535823
$891$	−8.82699	−	15.2888i	−0.295715	−	0.512194i
$892$	3.00287	−	5.20112i	0.100543	−	0.174146i
$893$	9.67523	−	16.7580i	0.323769	−	0.560785i
$894$	21.5876	+	37.3909i	0.721999	+	1.25054i
$895$	7.90346			0.264183
$896$		0			0
$897$	9.41949			0.314508
$898$	−21.0650	−	36.4857i	−0.702949	−	1.21754i
$899$	0.243125	−	0.421106i	0.00810869	−	0.0140447i
$900$	11.6885	−	20.2450i	0.389616	−	0.674835i
$901$	1.08962	+	1.88727i	0.0363004	+	0.0628741i
$902$	73.3947			2.44377
$903$		0			0
$904$	27.5880			0.917564
$905$	−8.46153	−	14.6558i	−0.281271	−	0.487175i
$906$	56.2364	−	97.4043i	1.86833	−	3.23604i
$907$	20.8103	−	36.0446i	0.690996	−	1.19684i	−0.280516	−	0.959849i	$-0.590505\pi$
$907$	20.8103	−	36.0446i	0.690996	−	1.19684i	0.971512	−	0.236991i	$-0.0761612\pi$
$908$	40.7278	+	70.5427i	1.35160	+	2.34104i
$909$	−1.85869			−0.0616488
$910$		0			0
$911$	21.8850			0.725083			0.362541	−	0.931968i	$-0.381909\pi$
$911$	21.8850			0.725083			0.362541	+	0.931968i	$0.381909\pi$
$912$	8.90142	+	15.4177i	0.294755	+	0.510531i
$913$	−15.7130	+	27.2157i	−0.520024	+	0.900709i
$914$	32.5204	−	56.3270i	1.07568	−	1.86313i
$915$	−29.6518	−	51.3584i	−0.980259	−	1.69786i
$916$	−45.3484			−1.49835
$917$		0			0
$918$	−39.3852			−1.29990
$919$	−2.22819	−	3.85934i	−0.0735012	−	0.127308i	0.826932	−	0.562301i	$-0.190084\pi$
$919$	−2.22819	−	3.85934i	−0.0735012	−	0.127308i	−0.900434	+	0.434994i	$0.856751\pi$
$920$	6.95450	−	12.0456i	0.229283	−	0.397130i
$921$	−14.3709	+	24.8911i	−0.473536	+	0.820189i
$922$	−32.6408	−	56.5355i	−1.07497	−	1.86190i
$923$	16.1628			0.532005
$924$		0			0
$925$	−0.637998			−0.0209772
$926$	−43.5517	−	75.4337i	−1.43120	−	2.47891i
$927$	29.2247	−	50.6187i	0.959866	−	1.66254i
$928$	16.7368	−	28.9890i	0.549413	−	0.951612i
$929$	9.03746	+	15.6533i	0.296509	+	0.513569i	0.975335	−	0.220730i	$-0.0708440\pi$
$929$	9.03746	+	15.6533i	0.296509	+	0.513569i	−0.678825	+	0.734300i	$0.737511\pi$
$930$	−0.880975			−0.0288883
$931$		0			0
$932$	73.1916			2.39747
$933$	41.1373	+	71.2519i	1.34678	+	2.33268i
$934$	33.6569	−	58.2954i	1.10129	−	1.90748i
$935$	−5.41560	+	9.38009i	−0.177109	+	0.306762i
$936$	14.4198	+	24.9758i	0.471326	+	0.816360i
$937$	23.0218			0.752088			0.376044	−	0.926602i	$-0.377284\pi$
$937$	23.0218			0.752088			0.376044	+	0.926602i	$0.377284\pi$
$938$		0			0
$939$	59.7352			1.94938
$940$	−10.1671	−	17.6099i	−0.331614	−	0.574373i
$941$	−5.61938	+	9.73304i	−0.183186	+	0.317288i	−0.942964	−	0.332895i	$-0.891975\pi$
$941$	−5.61938	+	9.73304i	−0.183186	+	0.317288i	0.759777	+	0.650183i	$0.225308\pi$
$942$	−46.0523	+	79.7650i	−1.50047	+	2.59888i
$943$	−12.6100	−	21.8411i	−0.410638	−	0.711245i
$944$	2.14194			0.0697141
$945$		0			0
$946$	3.63964			0.118335
$947$	−4.30336	−	7.45364i	−0.139840	−	0.242211i	0.787596	−	0.616192i	$-0.211326\pi$
$947$	−4.30336	−	7.45364i	−0.139840	−	0.242211i	−0.927436	+	0.373982i	$0.877992\pi$
$948$	−67.4841	+	116.886i	−2.19178	+	3.79628i
$949$	7.66865	−	13.2825i	0.248935	−	0.431168i
$950$	−8.83700	−	15.3061i	−0.286710	−	0.496597i
$951$	−35.0270			−1.13583
$952$		0			0
$953$	−16.0513			−0.519951			−0.259976	−	0.965615i	$-0.583715\pi$
$953$	−16.0513			−0.519951			−0.259976	+	0.965615i	$0.583715\pi$
$954$	6.96138	+	12.0575i	0.225383	+	0.390375i
$955$	14.8578	−	25.7345i	0.480788	−	0.832750i
$956$	19.3571	−	33.5275i	0.626054	−	1.08436i
$957$	−29.0920	−	50.3889i	−0.940412	−	1.62884i
$958$	58.5247			1.89085
$959$		0			0
$960$	−71.5302			−2.30863
$961$	15.4979	+	26.8431i	0.499931	+	0.865906i
$962$	0.940952	−	1.62978i	0.0303375	−	0.0525461i
$963$	44.0455	−	76.2890i	1.41935	−	2.45838i
$964$	15.9180	+	27.5708i	0.512684	+	0.887995i
$965$	−20.0590			−0.645721
$966$		0			0
$967$	15.6295			0.502610			0.251305	−	0.967908i	$-0.419140\pi$
$967$	15.6295			0.502610			0.251305	+	0.967908i	$0.419140\pi$
$968$	−6.65908	−	11.5339i	−0.214031	−	0.370712i
$969$	−19.7487	+	34.2057i	−0.634419	+	1.09885i
$970$	33.3568	−	57.7757i	1.07102	−	1.85507i
$971$	2.51655	+	4.35880i	0.0807600	+	0.139880i	0.903577	−	0.428427i	$-0.140932\pi$
$971$	2.51655	+	4.35880i	0.0807600	+	0.139880i	−0.822817	+	0.568307i	$0.807599\pi$
$972$	15.6088			0.500651
$973$		0			0
$974$	95.6631			3.06524
$975$	−2.63024	−	4.55570i	−0.0842350	−	0.145899i
$976$	−4.84549	+	8.39263i	−0.155100	+	0.268642i
$977$	−8.52966	+	14.7738i	−0.272888	+	0.472656i	−0.969600	−	0.244695i	$-0.921312\pi$
$977$	−8.52966	+	14.7738i	−0.272888	+	0.472656i	0.696712	+	0.717351i	$0.254646\pi$
$978$	38.3002	+	66.3378i	1.22470	+	2.12125i
$979$	−9.30557			−0.297407
$980$		0			0
$981$	−81.6156			−2.60578
$982$	1.14849	+	1.98924i	0.0366498	+	0.0634793i
$983$	13.4435	−	23.2848i	0.428781	−	0.742670i	−0.567985	−	0.823039i	$-0.692277\pi$
$983$	13.4435	−	23.2848i	0.428781	−	0.742670i	0.996765	+	0.0803695i	$0.0256100\pi$
$984$	58.8146	−	101.870i	1.87494	−	3.24749i
$985$	7.54316	+	13.0651i	0.240345	+	0.416290i
$986$	−36.2362			−1.15400
$987$		0			0
$988$	32.9588			1.04856
$989$	−0.625329	−	1.08310i	−0.0198843	−	0.0344406i
$990$	−34.5994	+	59.9279i	−1.09964	+	1.90463i
$991$	−15.0189	+	26.0136i	−0.477092	+	0.826348i	−0.999655	−	0.0262528i	$-0.991643\pi$
$991$	−15.0189	+	26.0136i	−0.477092	+	0.826348i	0.522563	+	0.852601i	$0.324976\pi$
$992$	−0.147523	−	0.255517i	−0.00468386	−	0.00811268i
$993$	−37.4857			−1.18957
$994$		0			0
$995$	−28.8423			−0.914364
$996$	60.2126	+	104.291i	1.90791	+	3.30459i
$997$	−21.3033	+	36.8985i	−0.674684	+	1.16859i	0.301878	+	0.953347i	$0.402387\pi$
$997$	−21.3033	+	36.8985i	−0.674684	+	1.16859i	−0.976561	+	0.215240i	$0.930947\pi$
$998$	−11.2878	+	19.5510i	−0.357308	+	0.618876i
$999$	2.17077	+	3.75989i	0.0686802	+	0.118958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.c.e.18.6		12
7.2	even	3	inner	343.2.c.e.324.6		12
7.3	odd	6		343.2.a.d.1.1	yes	6
7.4	even	3		343.2.a.c.1.1	✓	6
7.5	odd	6		343.2.c.d.324.6		12
7.6	odd	2		343.2.c.d.18.6		12
21.11	odd	6		3087.2.a.k.1.6		6
21.17	even	6		3087.2.a.j.1.6		6
28.3	even	6		5488.2.a.h.1.1		6
28.11	odd	6		5488.2.a.p.1.6		6
35.4	even	6		8575.2.a.o.1.6		6
35.24	odd	6		8575.2.a.n.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.2.a.c.1.1	✓	6	7.4	even	3
343.2.a.d.1.1	yes	6	7.3	odd	6
343.2.c.d.18.6		12	7.6	odd	2
343.2.c.d.324.6		12	7.5	odd	6
343.2.c.e.18.6		12	1.1	even	1	trivial
343.2.c.e.324.6		12	7.2	even	3	inner
3087.2.a.j.1.6		6	21.17	even	6
3087.2.a.k.1.6		6	21.11	odd	6
5488.2.a.h.1.1		6	28.3	even	6
5488.2.a.p.1.6		6	28.11	odd	6
8575.2.a.n.1.6		6	35.24	odd	6
8575.2.a.o.1.6		6	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16596 + 2.01950i) q^{2} +(1.47749 - 2.55909i) q^{3} +(-1.71891 + 2.97725i) q^{4} +(0.976432 + 1.69123i) q^{5} +6.89078 q^{6} -3.35289 q^{8} +(-2.86597 - 4.96401i) q^{9} +O(q^{10})\)	\(q+(1.16596 + 2.01950i) q^{2} +(1.47749 - 2.55909i) q^{3} +(-1.71891 + 2.97725i) q^{4} +(0.976432 + 1.69123i) q^{5} +6.89078 q^{6} -3.35289 q^{8} +(-2.86597 - 4.96401i) q^{9} +(-2.27696 + 3.94381i) q^{10} +(-1.32551 + 2.29584i) q^{11} +(5.07937 + 8.79772i) q^{12} +1.50061 q^{13} +5.77069 q^{15} +(-0.471502 - 0.816666i) q^{16} +(1.04607 - 1.81185i) q^{17} +(6.68320 - 11.5756i) q^{18} +(-3.19441 - 5.53287i) q^{19} -6.71361 q^{20} -6.18193 q^{22} +(1.06212 + 1.83965i) q^{23} +(-4.95388 + 8.58036i) q^{24} +(0.593160 - 1.02738i) q^{25} +(1.74965 + 3.03048i) q^{26} -8.07285 q^{27} -7.42740 q^{29} +(6.72838 + 11.6539i) q^{30} +(-0.0327336 + 0.0566962i) q^{31} +(-2.25339 + 3.90298i) q^{32} +(3.91685 + 6.78418i) q^{33} +4.87871 q^{34} +19.7054 q^{36} +(-0.268898 - 0.465745i) q^{37} +(7.44908 - 12.9022i) q^{38} +(2.21714 - 3.84020i) q^{39} +(-3.27387 - 5.67051i) q^{40} -11.8724 q^{41} -0.588754 q^{43} +(-4.55686 - 7.89271i) q^{44} +(5.59685 - 9.69403i) q^{45} +(-2.47678 + 4.28991i) q^{46} +(1.51440 + 2.62302i) q^{47} -2.78657 q^{48} +2.76640 q^{50} +(-3.09114 - 5.35401i) q^{51} +(-2.57942 + 4.46768i) q^{52} +(-0.520812 + 0.902072i) q^{53} +(-9.41260 - 16.3031i) q^{54} -5.17707 q^{55} -18.8788 q^{57} +(-8.66004 - 14.9996i) q^{58} +(-1.13570 + 1.96709i) q^{59} +(-9.91931 + 17.1808i) q^{60} +(-5.13835 - 8.89988i) q^{61} -0.152664 q^{62} -12.3954 q^{64} +(1.46524 + 2.53787i) q^{65} +(-9.13376 + 15.8201i) q^{66} +(0.110857 - 0.192010i) q^{67} +(3.59622 + 6.22884i) q^{68} +6.27711 q^{69} +10.7708 q^{71} +(9.60929 + 16.6438i) q^{72} +(5.11036 - 8.85140i) q^{73} +(0.627047 - 1.08608i) q^{74} +(-1.75278 - 3.03591i) q^{75} +21.9636 q^{76} +10.3404 q^{78} +(6.64297 + 11.5060i) q^{79} +(0.920780 - 1.59484i) q^{80} +(-3.32967 + 5.76716i) q^{81} +(-13.8428 - 23.9764i) q^{82} +11.8543 q^{83} +4.08568 q^{85} +(-0.686463 - 1.18899i) q^{86} +(-10.9739 + 19.0074i) q^{87} +(4.44428 - 7.69771i) q^{88} +(1.75510 + 3.03992i) q^{89} +26.1028 q^{90} -7.30279 q^{92} +(0.0967273 + 0.167537i) q^{93} +(-3.53146 + 6.11666i) q^{94} +(6.23824 - 10.8049i) q^{95} +(6.65873 + 11.5333i) q^{96} -14.6497 q^{97} +15.1954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 5 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 12 q^{8} - 9 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 5 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 12 * q^8 - 9 * q^9	\( 12 q + 2 q^{2} + 5 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 12 q^{8} - 9 q^{9} - 2 q^{10} + q^{11} + 7 q^{12} - 14 q^{13} - 10 q^{15} + 8 q^{16} + 26 q^{17} + 18 q^{18} - 3 q^{19} - 28 q^{20} - 12 q^{22} + 9 q^{23} - 9 q^{24} - 15 q^{25} - 16 q^{27} - 4 q^{29} - 13 q^{30} - 2 q^{31} - q^{32} + 18 q^{33} + 26 q^{34} + 46 q^{36} + 2 q^{37} + 5 q^{38} - 7 q^{39} - 24 q^{40} - 56 q^{41} + 10 q^{43} + 12 q^{44} + 3 q^{45} + 12 q^{46} + 18 q^{47} + 26 q^{48} + 10 q^{50} - 13 q^{51} - 14 q^{52} + q^{53} - 32 q^{54} + 44 q^{55} - 52 q^{57} - 24 q^{58} + 5 q^{59} - 21 q^{60} - 17 q^{61} + 12 q^{62} - 36 q^{64} + 14 q^{65} - 58 q^{66} + 22 q^{67} + 7 q^{68} + 40 q^{69} - 4 q^{71} + 18 q^{72} + 12 q^{73} - 23 q^{74} - 27 q^{75} + 98 q^{76} + 42 q^{78} + 2 q^{79} - 16 q^{80} + 30 q^{81} - 35 q^{82} - 14 q^{83} + 74 q^{85} - 3 q^{86} - 25 q^{87} - 14 q^{88} + 39 q^{89} + 94 q^{90} + 22 q^{92} + 22 q^{93} - 16 q^{94} + 11 q^{95} - 28 q^{96} - 70 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 5 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 12 * q^8 - 9 * q^9 - 2 * q^10 + q^11 + 7 * q^12 - 14 * q^13 - 10 * q^15 + 8 * q^16 + 26 * q^17 + 18 * q^18 - 3 * q^19 - 28 * q^20 - 12 * q^22 + 9 * q^23 - 9 * q^24 - 15 * q^25 - 16 * q^27 - 4 * q^29 - 13 * q^30 - 2 * q^31 - q^32 + 18 * q^33 + 26 * q^34 + 46 * q^36 + 2 * q^37 + 5 * q^38 - 7 * q^39 - 24 * q^40 - 56 * q^41 + 10 * q^43 + 12 * q^44 + 3 * q^45 + 12 * q^46 + 18 * q^47 + 26 * q^48 + 10 * q^50 - 13 * q^51 - 14 * q^52 + q^53 - 32 * q^54 + 44 * q^55 - 52 * q^57 - 24 * q^58 + 5 * q^59 - 21 * q^60 - 17 * q^61 + 12 * q^62 - 36 * q^64 + 14 * q^65 - 58 * q^66 + 22 * q^67 + 7 * q^68 + 40 * q^69 - 4 * q^71 + 18 * q^72 + 12 * q^73 - 23 * q^74 - 27 * q^75 + 98 * q^76 + 42 * q^78 + 2 * q^79 - 16 * q^80 + 30 * q^81 - 35 * q^82 - 14 * q^83 + 74 * q^85 - 3 * q^86 - 25 * q^87 - 14 * q^88 + 39 * q^89 + 94 * q^90 + 22 * q^92 + 22 * q^93 - 16 * q^94 + 11 * q^95 - 28 * q^96 - 70 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more