LMFDB - Embedded newform 833.2.e.i.324.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(18,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.18"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$833 = 7^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	833.e (of order $3$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [10,-2,2,-10,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - 2x^{9} + 9x^{8} - 10x^{7} + 44x^{6} - 49x^{5} + 99x^{4} - 20x^{3} + 31x^{2} - 3x + 9$ x^10 - 2x^9 + 9x^8 - 10x^7 + 44x^6 - 49x^5 + 99x^4 - 20x^3 + 31x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			324.3
Root			$1.16091 - 2.01076i$ of defining polynomial
Character	$\chi$	$=$	833.324
Dual form			833.2.e.i.18.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438917 + 0.760227i) q^{2} +(-0.453789 - 0.785986i) q^{3} +(0.614704 + 1.06470i) q^{4} +(-1.51909 + 2.63114i) q^{5} +0.796703 q^{6} -2.83488 q^{8} +(1.08815 - 1.88473i) q^{9} +(-1.33351 - 2.30971i) q^{10} +(-2.39089 - 4.14114i) q^{11} +(0.557892 - 0.966297i) q^{12} -4.39933 q^{13} +2.75739 q^{15} +(0.0148720 - 0.0257591i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.955216 + 1.65448i) q^{18} +(1.32183 - 2.28947i) q^{19} -3.73516 q^{20} +4.19761 q^{22} +(4.22941 - 7.32555i) q^{23} +(1.28644 + 2.22818i) q^{24} +(-2.11527 - 3.66376i) q^{25} +(1.93094 - 3.34449i) q^{26} -4.69790 q^{27} +7.04298 q^{29} +(-1.21026 + 2.09624i) q^{30} +(1.71032 + 2.96236i) q^{31} +(-2.82183 - 4.88755i) q^{32} +(-2.16992 + 3.75841i) q^{33} +0.877834 q^{34} +2.67556 q^{36} +(-4.83488 + 8.37426i) q^{37} +(1.16035 + 2.00978i) q^{38} +(1.99637 + 3.45781i) q^{39} +(4.30645 - 7.45898i) q^{40} +1.33675 q^{41} +2.52513 q^{43} +(2.93938 - 5.09115i) q^{44} +(3.30600 + 5.72616i) q^{45} +(3.71272 + 6.43062i) q^{46} +(2.78541 - 4.82448i) q^{47} -0.0269950 q^{48} +3.71372 q^{50} +(-0.453789 + 0.785986i) q^{51} +(-2.70428 - 4.68395i) q^{52} +(-2.58815 - 4.48281i) q^{53} +(2.06199 - 3.57147i) q^{54} +14.5279 q^{55} -2.39933 q^{57} +(-3.09129 + 5.35426i) q^{58} +(-4.64366 - 8.04305i) q^{59} +(1.69498 + 2.93578i) q^{60} +(-3.33162 + 5.77054i) q^{61} -3.00275 q^{62} +5.01368 q^{64} +(6.68297 - 11.5753i) q^{65} +(-1.90483 - 3.29926i) q^{66} +(-2.64126 - 4.57479i) q^{67} +(0.614704 - 1.06470i) q^{68} -7.67704 q^{69} -11.9310 q^{71} +(-3.08478 + 5.34300i) q^{72} +(-6.35773 - 11.0119i) q^{73} +(-4.24423 - 7.35122i) q^{74} +(-1.91977 + 3.32515i) q^{75} +3.25013 q^{76} -3.50496 q^{78} +(-0.970256 + 1.68053i) q^{79} +(0.0451838 + 0.0782607i) q^{80} +(-1.13260 - 1.96172i) q^{81} +(-0.586724 + 1.01624i) q^{82} -4.58417 q^{83} +3.03818 q^{85} +(-1.10832 + 1.91967i) q^{86} +(-3.19603 - 5.53569i) q^{87} +(6.77789 + 11.7397i) q^{88} +(6.69779 - 11.6009i) q^{89} -5.80424 q^{90} +10.3993 q^{92} +(1.55225 - 2.68857i) q^{93} +(2.44513 + 4.23509i) q^{94} +(4.01596 + 6.95584i) q^{95} +(-2.56103 + 4.43583i) q^{96} -15.1668 q^{97} -10.4066 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q - 2 q^{2} + 2 q^{3} - 10 q^{4} - 2 q^{6} + 12 q^{8} - 11 q^{9} - 4 q^{10} + 2 q^{11} + 22 q^{12} + 4 q^{13} + 16 q^{15} - 4 q^{16} - 5 q^{17} + 18 q^{18} - 6 q^{19} - 38 q^{20} + 12 q^{22} + 10 q^{23}+ \cdots - 124 q^{99}+O(q^{100})$ 10 * q - 2 * q^2 + 2 * q^3 - 10 * q^4 - 2 * q^6 + 12 * q^8 - 11 * q^9 - 4 * q^10 + 2 * q^11 + 22 * q^12 + 4 * q^13 + 16 * q^15 - 4 * q^16 - 5 * q^17 + 18 * q^18 - 6 * q^19 - 38 * q^20 + 12 * q^22 + 10 * q^23 - 2 * q^24 - 21 * q^25 + 26 * q^26 - 52 * q^27 - 16 * q^29 + 51 * q^30 - 9 * q^32 - 6 * q^33 + 4 * q^34 + 78 * q^36 - 8 * q^37 - 14 * q^38 - 14 * q^39 - 5 * q^40 + 36 * q^41 + 16 * q^43 + 14 * q^44 - 8 * q^46 + 10 * q^47 - 54 * q^48 + 54 * q^50 + 2 * q^51 - 4 * q^52 - 4 * q^53 - 5 * q^54 - 48 * q^55 + 24 * q^57 - 12 * q^58 - 8 * q^59 + 7 * q^60 - 22 * q^61 + 32 * q^62 - 32 * q^64 + 30 * q^65 - 68 * q^66 - 16 * q^67 - 10 * q^68 - 64 * q^69 - 4 * q^71 - 9 * q^72 - 10 * q^73 + 40 * q^74 + 14 * q^75 + 48 * q^76 + 60 * q^78 - 18 * q^79 + 4 * q^80 - 25 * q^81 + 31 * q^82 - 24 * q^83 - 23 * q^86 + 26 * q^87 + 46 * q^88 - 20 * q^89 + 194 * q^90 + 56 * q^92 + 28 * q^93 + 42 * q^94 + 22 * q^95 + 18 * q^96 + 24 * q^97 - 124 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$ .

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.438917	+	0.760227i	−0.310361	+	0.537561i	−0.978441	−	0.206529i	$-0.933783\pi$
$2$	−0.438917	+	0.760227i	−0.310361	+	0.537561i	0.668079	+	0.744090i	$0.267117\pi$
$3$	−0.453789	−	0.785986i	−0.261995	−	0.453789i	0.704777	−	0.709429i	$-0.251047\pi$
$3$	−0.453789	−	0.785986i	−0.261995	−	0.453789i	−0.966772	+	0.255640i	$0.917714\pi$
$4$	0.614704	+	1.06470i	0.307352	+	0.532349i
$5$	−1.51909	+	2.63114i	−0.679358	+	1.17668i	0.295817	+	0.955245i	$0.404408\pi$
$5$	−1.51909	+	2.63114i	−0.679358	+	1.17668i	−0.975175	+	0.221438i	$0.928925\pi$
$6$	0.796703			0.325253
$7$		0			0
$7$		0			0
$8$	−2.83488			−1.00228
$9$	1.08815	−	1.88473i	0.362717	−	0.628244i
$10$	−1.33351	−	2.30971i	−0.421693	−	0.730393i
$11$	−2.39089	−	4.14114i	−0.720880	−	1.24860i	−0.960647	−	0.277771i	$-0.910404\pi$
$11$	−2.39089	−	4.14114i	−0.720880	−	1.24860i	0.239767	−	0.970830i	$-0.422929\pi$
$12$	0.557892	−	0.966297i	0.161049	−	0.278946i
$13$	−4.39933			−1.22015			−0.610077	−	0.792342i	$-0.708861\pi$
$13$	−4.39933			−1.22015			−0.610077	+	0.792342i	$0.708861\pi$
$14$		0			0
$15$	2.75739			0.711954
$16$	0.0148720	−	0.0257591i	0.00371800	−	0.00643977i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	0.955216	+	1.65448i	0.225147	+	0.389965i
$19$	1.32183	−	2.28947i	0.303248	−	0.525242i	−0.673621	−	0.739077i	$-0.735262\pi$
$19$	1.32183	−	2.28947i	0.303248	−	0.525242i	0.976870	+	0.213835i	$0.0685955\pi$
$20$	−3.73516			−0.835207
$21$		0			0
$22$	4.19761			0.894933
$23$	4.22941	−	7.32555i	0.881892	−	1.52748i	0.0326578	−	0.999467i	$-0.489603\pi$
$23$	4.22941	−	7.32555i	0.881892	−	1.52748i	0.849235	−	0.528016i	$-0.177064\pi$
$24$	1.28644	+	2.22818i	0.262593	+	0.454825i
$25$	−2.11527	−	3.66376i	−0.423054	−	0.732751i
$26$	1.93094	−	3.34449i	0.378688	−	0.655908i
$27$	−4.69790			−0.904111
$28$		0			0
$29$	7.04298			1.30785			0.653925	−	0.756560i	$-0.273121\pi$
$29$	7.04298			1.30785			0.653925	+	0.756560i	$0.273121\pi$
$30$	−1.21026	+	2.09624i	−0.220963	+	0.382719i
$31$	1.71032	+	2.96236i	0.307182	+	0.532055i	0.977745	−	0.209798i	$-0.0672806\pi$
$31$	1.71032	+	2.96236i	0.307182	+	0.532055i	−0.670563	+	0.741853i	$0.733947\pi$
$32$	−2.82183	−	4.88755i	−0.498834	−	0.864005i
$33$	−2.16992	+	3.75841i	−0.377734	+	0.654255i
$34$	0.877834			0.150547
$35$		0			0
$36$	2.67556			0.445927
$37$	−4.83488	+	8.37426i	−0.794850	+	1.37672i	0.128084	+	0.991763i	$0.459117\pi$
$37$	−4.83488	+	8.37426i	−0.794850	+	1.37672i	−0.922934	+	0.384957i	$0.874216\pi$
$38$	1.16035	+	2.00978i	0.188233	+	0.326029i
$39$	1.99637	+	3.45781i	0.319674	+	0.553692i
$40$	4.30645	−	7.45898i	0.680909	−	1.17937i
$41$	1.33675			0.208766			0.104383	−	0.994537i	$-0.466713\pi$
$41$	1.33675			0.208766			0.104383	+	0.994537i	$0.466713\pi$
$42$		0			0
$43$	2.52513			0.385078			0.192539	−	0.981289i	$-0.438328\pi$
$43$	2.52513			0.385078			0.192539	+	0.981289i	$0.438328\pi$
$44$	2.93938	−	5.09115i	0.443128	−	0.767520i
$45$	3.30600	+	5.72616i	0.492829	+	0.853605i
$46$	3.71272	+	6.43062i	0.547410	+	0.948143i
$47$	2.78541	−	4.82448i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$47$	2.78541	−	4.82448i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$48$	−0.0269950			−0.00389639
$49$		0			0
$50$	3.71372			0.525199
$51$	−0.453789	+	0.785986i	−0.0635432	+	0.110060i
$52$	−2.70428	−	4.68395i	−0.375016	−	0.649547i
$53$	−2.58815	−	4.48281i	−0.355510	−	0.615761i	0.631695	−	0.775217i	$-0.282359\pi$
$53$	−2.58815	−	4.48281i	−0.355510	−	0.615761i	−0.987205	+	0.159456i	$0.949026\pi$
$54$	2.06199	−	3.57147i	0.280601	−	0.486015i
$55$	14.5279			1.95894
$56$		0			0
$57$	−2.39933			−0.317799
$58$	−3.09129	+	5.35426i	−0.405906	+	0.703049i
$59$	−4.64366	−	8.04305i	−0.604553	−	1.04712i	−0.992122	−	0.125275i	$-0.960019\pi$
$59$	−4.64366	−	8.04305i	−0.604553	−	1.04712i	0.387569	−	0.921841i	$-0.373315\pi$
$60$	1.69498	+	2.93578i	0.218820	+	0.379008i
$61$	−3.33162	+	5.77054i	−0.426571	+	0.738842i	−0.996566	−	0.0828061i	$-0.973612\pi$
$61$	−3.33162	+	5.77054i	−0.426571	+	0.738842i	0.569995	+	0.821648i	$0.306945\pi$
$62$	−3.00275			−0.381350
$63$		0			0
$64$	5.01368			0.626710
$65$	6.68297	−	11.5753i	0.828921	−	1.43573i
$66$	−1.90483	−	3.29926i	−0.234468	−	0.406111i
$67$	−2.64126	−	4.57479i	−0.322681	−	0.558900i	0.658359	−	0.752704i	$-0.271251\pi$
$67$	−2.64126	−	4.57479i	−0.322681	−	0.558900i	−0.981040	+	0.193804i	$0.937917\pi$
$68$	0.614704	−	1.06470i	0.0745438	−	0.129114i
$69$	−7.67704			−0.924206
$70$		0			0
$71$	−11.9310			−1.41595			−0.707973	−	0.706239i	$-0.750390\pi$
$71$	−11.9310			−1.41595			−0.707973	+	0.706239i	$0.750390\pi$
$72$	−3.08478	+	5.34300i	−0.363545	+	0.629678i
$73$	−6.35773	−	11.0119i	−0.744116	−	1.28885i	−0.950606	−	0.310399i	$-0.899537\pi$
$73$	−6.35773	−	11.0119i	−0.744116	−	1.28885i	0.206490	−	0.978449i	$-0.433796\pi$
$74$	−4.24423	−	7.35122i	−0.493381	−	0.854562i
$75$	−1.91977	+	3.32515i	−0.221676	+	0.383955i
$76$	3.25013			0.372816
$77$		0			0
$78$	−3.50496			−0.396858
$79$	−0.970256	+	1.68053i	−0.109162	+	0.189075i	−0.915431	−	0.402475i	$-0.868150\pi$
$79$	−0.970256	+	1.68053i	−0.109162	+	0.189075i	0.806269	+	0.591549i	$0.201483\pi$
$80$	0.0451838	+	0.0782607i	0.00505171	+	0.00874981i
$81$	−1.13260	−	1.96172i	−0.125844	−	0.217968i
$82$	−0.586724	+	1.01624i	−0.0647928	+	0.112224i
$83$	−4.58417			−0.503178			−0.251589	−	0.967834i	$-0.580953\pi$
$83$	−4.58417			−0.503178			−0.251589	+	0.967834i	$0.580953\pi$
$84$		0			0
$85$	3.03818			0.329537
$86$	−1.10832	+	1.91967i	−0.119513	+	0.207003i
$87$	−3.19603	−	5.53569i	−0.342650	−	0.593488i
$88$	6.77789	+	11.7397i	0.722526	+	1.25145i
$89$	6.69779	−	11.6009i	0.709965	−	1.22969i	−0.254905	−	0.966966i	$-0.582044\pi$
$89$	6.69779	−	11.6009i	0.709965	−	1.22969i	0.964870	−	0.262729i	$-0.0846225\pi$
$90$	−5.80424			−0.611820
$91$		0			0
$92$	10.3993			1.08420
$93$	1.55225	−	2.68857i	0.160960	−	0.278792i
$94$	2.44513	+	4.23509i	0.252196	+	0.436816i
$95$	4.01596	+	6.95584i	0.412028	+	0.713654i
$96$	−2.56103	+	4.43583i	−0.261384	+	0.452730i
$97$	−15.1668			−1.53995			−0.769976	−	0.638073i	$-0.779732\pi$
$97$	−15.1668			−1.53995			−0.769976	+	0.638073i	$0.779732\pi$
$98$		0			0
$99$	−10.4066			−1.04590
$100$	2.60053	−	4.50425i	0.260053	−	0.450425i
$101$	−1.62393	−	2.81273i	−0.161587	−	0.279877i	0.773851	−	0.633368i	$-0.218328\pi$
$101$	−1.62393	−	2.81273i	−0.161587	−	0.279877i	−0.935438	+	0.353491i	$0.884995\pi$
$102$	−0.398352	−	0.689965i	−0.0394427	−	0.0683167i
$103$	6.35157	−	11.0012i	0.625839	−	1.08399i	−0.362539	−	0.931969i	$-0.618090\pi$
$103$	6.35157	−	11.0012i	0.625839	−	1.08399i	0.988378	−	0.152016i	$-0.0485767\pi$
$104$	12.4716			1.22294
$105$		0			0
$106$	4.54393			0.441346
$107$	−1.95705	+	3.38971i	−0.189195	+	0.327696i	−0.944982	−	0.327122i	$-0.893921\pi$
$107$	−1.95705	+	3.38971i	−0.189195	+	0.327696i	0.755787	+	0.654818i	$0.227255\pi$
$108$	−2.88782	−	5.00184i	−0.277880	−	0.481303i
$109$	1.78178	+	3.08613i	0.170663	+	0.295598i	0.938652	−	0.344866i	$-0.112076\pi$
$109$	1.78178	+	3.08613i	0.170663	+	0.295598i	−0.767989	+	0.640464i	$0.778742\pi$
$110$	−6.37655	+	11.0445i	−0.607980	+	1.05305i
$111$	8.77607			0.832988
$112$		0			0
$113$	0.966622			0.0909322			0.0454661	−	0.998966i	$-0.485523\pi$
$113$	0.966622			0.0909322			0.0454661	+	0.998966i	$0.485523\pi$
$114$	1.05311	−	1.82403i	0.0986323	−	0.170836i
$115$	12.8497	+	22.2563i	1.19824	+	2.07541i
$116$	4.32935	+	7.49865i	0.401970	+	0.696232i
$117$	−4.78713	+	8.29155i	−0.442570	+	0.766554i
$118$	8.15272			0.750519
$119$		0			0
$120$	−7.81687			−0.713579
$121$	−5.93270	+	10.2757i	−0.539337	+	0.934159i
$122$	−2.92461	−	5.06558i	−0.264782	−	0.458616i
$123$	−0.606604	−	1.05067i	−0.0546957	−	0.0947356i
$124$	−2.10268	+	3.64194i	−0.188826	+	0.327056i
$125$	−2.33775			−0.209095
$126$		0			0
$127$	−5.55875			−0.493260			−0.246630	−	0.969110i	$-0.579323\pi$
$127$	−5.55875			−0.493260			−0.246630	+	0.969110i	$0.579323\pi$
$128$	3.44307	−	5.96357i	0.304327	−	0.527110i
$129$	−1.14587	−	1.98471i	−0.100889	−	0.174744i
$130$	5.86654	+	10.1612i	0.514530	+	0.891192i
$131$	1.75567	−	3.04091i	0.153393	−	0.265685i	−0.779079	−	0.626925i	$-0.784313\pi$
$131$	1.75567	−	3.04091i	0.153393	−	0.265685i	0.932473	+	0.361240i	$0.117646\pi$
$132$	−5.33543			−0.464389
$133$		0			0
$134$	4.63717			0.400590
$135$	7.13653	−	12.3608i	0.614215	−	1.06385i
$136$	1.41744	+	2.45508i	0.121545	+	0.210522i
$137$	0.968898	+	1.67818i	0.0827786	+	0.143377i	0.904442	−	0.426596i	$-0.140287\pi$
$137$	0.968898	+	1.67818i	0.0827786	+	0.143377i	−0.821664	+	0.569972i	$0.806954\pi$
$138$	3.36958	−	5.83629i	0.286838	−	0.496818i
$139$	4.69834			0.398508			0.199254	−	0.979948i	$-0.436148\pi$
$139$	4.69834			0.398508			0.199254	+	0.979948i	$0.436148\pi$
$140$		0			0
$141$	−5.05596			−0.425789
$142$	5.23671	−	9.07024i	0.439455	−	0.761158i
$143$	10.5183	+	18.2182i	0.879585	+	1.52349i
$144$	−0.0323660	−	0.0560595i	−0.00269716	−	0.00467162i
$145$	−10.6989	+	18.5311i	−0.888498	+	1.53892i
$146$	11.1621			0.923780
$147$		0			0
$148$	−11.8881			−0.977194
$149$	−2.12081	+	3.67335i	−0.173743	+	0.300932i	−0.939726	−	0.341929i	$-0.888920\pi$
$149$	−2.12081	+	3.67335i	−0.173743	+	0.300932i	0.765982	+	0.642862i	$0.222253\pi$
$150$	−1.68524	−	2.91893i	−0.137600	−	0.238329i
$151$	−6.22919	−	10.7893i	−0.506924	−	0.878018i	−0.999968	−	0.00801357i	$-0.997449\pi$
$151$	−6.22919	−	10.7893i	−0.506924	−	0.878018i	0.493044	−	0.870004i	$-0.335884\pi$
$152$	−3.74723	+	6.49040i	−0.303941	+	0.526441i
$153$	−2.17630			−0.175944
$154$		0			0
$155$	−10.3925			−0.834746
$156$	−2.45435	+	4.25105i	−0.196505	+	0.340357i
$157$	8.82359	+	15.2829i	0.704199	+	1.21971i	0.966980	+	0.254853i	$0.0820272\pi$
$157$	8.82359	+	15.2829i	0.704199	+	1.21971i	−0.262780	+	0.964856i	$0.584639\pi$
$158$	−0.851724	−	1.47523i	−0.0677595	−	0.117363i
$159$	−2.34895	+	4.06850i	−0.186284	+	0.322653i
$160$	17.1465			1.35555
$161$		0			0
$162$	1.98847			0.156229
$163$	1.33778	−	2.31711i	0.104783	−	0.181490i	−0.808866	−	0.587993i	$-0.799918\pi$
$163$	1.33778	−	2.31711i	0.104783	−	0.181490i	0.913650	+	0.406503i	$0.133252\pi$
$164$	0.821707	+	1.42324i	0.0641645	+	0.111136i
$165$	−6.59261	−	11.4187i	−0.513234	−	0.888947i
$166$	2.01207	−	3.48501i	0.156167	−	0.270489i
$167$	−1.95783			−0.151501			−0.0757507	−	0.997127i	$-0.524135\pi$
$167$	−1.95783			−0.151501			−0.0757507	+	0.997127i	$0.524135\pi$
$168$		0			0
$169$	6.35407			0.488775
$170$	−1.33351	+	2.30971i	−0.102276	+	0.177146i
$171$	−2.87670	−	4.98259i	−0.219987	−	0.381028i
$172$	1.55220	+	2.68850i	0.118354	+	0.204996i
$173$	−3.00866	+	5.21115i	−0.228744	+	0.396196i	−0.957436	−	0.288645i	$-0.906795\pi$
$173$	−3.00866	+	5.21115i	−0.228744	+	0.396196i	0.728692	+	0.684841i	$0.240129\pi$
$174$	5.61117			0.425382
$175$		0			0
$176$	−0.142229			−0.0107209
$177$	−4.21448	+	7.29970i	−0.316780	+	0.548679i
$178$	5.87955	+	10.1837i	0.440691	+	0.763299i
$179$	−0.875558	−	1.51651i	−0.0654423	−	0.113349i	0.831448	−	0.555603i	$-0.187512\pi$
$179$	−0.875558	−	1.51651i	−0.0654423	−	0.113349i	−0.896890	+	0.442253i	$0.854179\pi$
$180$	−4.06442	+	7.03978i	−0.302944	+	0.524714i
$181$	2.76491			0.205514			0.102757	−	0.994707i	$-0.467234\pi$
$181$	2.76491			0.205514			0.102757	+	0.994707i	$0.467234\pi$
$182$		0			0
$183$	6.04742			0.447038
$184$	−11.9899	+	20.7671i	−0.883906	+	1.53097i
$185$	−14.6893	−	25.4425i	−1.07998	−	1.87057i
$186$	1.36261	+	2.36012i	0.0999118	+	0.173052i
$187$	−2.39089	+	4.14114i	−0.174839	+	0.302830i
$188$	6.84881			0.499501
$189$		0			0
$190$	−7.05069			−0.511511
$191$	−9.42303	+	16.3212i	−0.681827	+	1.18096i	0.292596	+	0.956236i	$0.405481\pi$
$191$	−9.42303	+	16.3212i	−0.681827	+	1.18096i	−0.974423	+	0.224723i	$0.927852\pi$
$192$	−2.27516	−	3.94068i	−0.164195	−	0.284394i
$193$	−5.95533	−	10.3149i	−0.428674	−	0.742485i	0.568082	−	0.822972i	$-0.307686\pi$
$193$	−5.95533	−	10.3149i	−0.428674	−	0.742485i	−0.996756	+	0.0804869i	$0.974352\pi$
$194$	6.65695	−	11.5302i	0.477941	−	0.827819i
$195$	−12.1306			−0.868693
$196$		0			0
$197$	−17.2682			−1.23031			−0.615153	−	0.788408i	$-0.710906\pi$
$197$	−17.2682			−1.23031			−0.615153	+	0.788408i	$0.710906\pi$
$198$	4.56763	−	7.91137i	0.324607	−	0.562237i
$199$	7.62257	+	13.2027i	0.540350	+	0.935913i	0.998884	+	0.0472365i	$0.0150414\pi$
$199$	7.62257	+	13.2027i	0.540350	+	0.935913i	−0.458534	+	0.888677i	$0.651625\pi$
$200$	5.99655	+	10.3863i	0.424020	+	0.734424i
$201$	−2.39715	+	4.15198i	−0.169082	+	0.292858i
$202$	2.85108			0.200601
$203$		0			0
$204$	−1.11578			−0.0781204
$205$	−2.03065	+	3.51719i	−0.141827	+	0.245651i
$206$	5.57563	+	9.65727i	0.388472	+	0.672854i
$207$	−9.20447	−	15.9426i	−0.639755	−	1.10809i
$208$	−0.0654268	+	0.113323i	−0.00453653	+	0.00785750i
$209$	−12.6414			−0.874423
$210$		0			0
$211$	8.51331			0.586080			0.293040	−	0.956100i	$-0.405333\pi$
$211$	8.51331			0.586080			0.293040	+	0.956100i	$0.405333\pi$
$212$	3.18189	−	5.51120i	0.218533	−	0.378511i
$213$	5.41415	+	9.37758i	0.370971	+	0.642541i
$214$	−1.71797	−	2.97560i	−0.117438	−	0.203408i
$215$	−3.83589	+	6.64396i	−0.261606	+	0.453115i
$216$	13.3180			0.906175
$217$		0			0
$218$	−3.12821			−0.211869
$219$	−5.77014	+	9.99418i	−0.389910	+	0.675344i
$220$	8.93036	+	15.4678i	0.602085	+	1.04284i
$221$	2.19966	+	3.80993i	0.147965	+	0.256284i
$222$	−3.85197	+	6.67180i	−0.258527	+	0.447782i
$223$	−2.49093			−0.166805			−0.0834027	−	0.996516i	$-0.526579\pi$
$223$	−2.49093			−0.166805			−0.0834027	+	0.996516i	$0.526579\pi$
$224$		0			0
$225$	−9.20694			−0.613796
$226$	−0.424267	+	0.734852i	−0.0282218	+	0.0488816i
$227$	8.49210	+	14.7087i	0.563640	+	0.976253i	0.997175	+	0.0751165i	$0.0239329\pi$
$227$	8.49210	+	14.7087i	0.563640	+	0.976253i	−0.433535	+	0.901137i	$0.642734\pi$
$228$	−1.47487	−	2.55456i	−0.0976759	−	0.169180i
$229$	8.16515	−	14.1425i	0.539568	−	0.934560i	−0.459359	−	0.888251i	$-0.651921\pi$
$229$	8.16515	−	14.1425i	0.539568	−	0.934560i	0.998927	−	0.0463089i	$-0.0147459\pi$
$230$	−22.5598			−1.48755
$231$		0			0
$232$	−19.9660			−1.31083
$233$	2.88912	−	5.00411i	0.189273	−	0.327830i	−0.755735	−	0.654877i	$-0.772720\pi$
$233$	2.88912	−	5.00411i	0.189273	−	0.327830i	0.945008	+	0.327047i	$0.106054\pi$
$234$	−4.20231	−	7.27861i	−0.274713	−	0.475818i
$235$	8.46259	+	14.6576i	0.552038	+	0.956158i
$236$	5.70895	−	9.88818i	0.371621	−	0.643666i
$237$	1.76117			0.114400
$238$		0			0
$239$	7.44275			0.481432			0.240716	−	0.970596i	$-0.422618\pi$
$239$	7.44275			0.481432			0.240716	+	0.970596i	$0.422618\pi$
$240$	0.0410079	−	0.0710277i	0.00264705	−	0.00458482i
$241$	−10.9518	−	18.9691i	−0.705467	−	1.22190i	−0.966523	−	0.256581i	$-0.917404\pi$
$241$	−10.9518	−	18.9691i	−0.705467	−	1.22190i	0.261056	−	0.965324i	$-0.415929\pi$
$242$	−5.20793	−	9.02040i	−0.334778	−	0.579853i
$243$	−8.07477	+	13.9859i	−0.517997	+	0.897197i
$244$	−8.19184			−0.524429
$245$		0			0
$246$	1.06500			0.0679016
$247$	−5.81516	+	10.0721i	−0.370010	+	0.640875i
$248$	−4.84855	−	8.39793i	−0.307883	−	0.533269i
$249$	2.08025	+	3.60309i	0.131830	+	0.228337i
$250$	1.02608	−	1.77722i	0.0648949	−	0.112401i
$251$	16.5769			1.04632			0.523162	−	0.852233i	$-0.324752\pi$
$251$	16.5769			1.04632			0.523162	+	0.852233i	$0.324752\pi$
$252$		0			0
$253$	−40.4482			−2.54296
$254$	2.43983	−	4.22591i	0.153089	−	0.265157i
$255$	−1.37869	−	2.38797i	−0.0863371	−	0.149540i
$256$	8.03613	+	13.9190i	0.502258	+	0.869936i
$257$	−6.05791	+	10.4926i	−0.377882	+	0.654511i	−0.990754	−	0.135672i	$-0.956681\pi$
$257$	−6.05791	+	10.4926i	−0.377882	+	0.654511i	0.612872	+	0.790182i	$0.290014\pi$
$258$	2.01178			0.125248
$259$		0			0
$260$	16.4322			1.01908
$261$	7.66383	−	13.2741i	0.474379	−	0.821649i
$262$	1.54119	+	2.66941i	0.0952148	+	0.164917i
$263$	−1.60067	−	2.77245i	−0.0987018	−	0.170956i	0.812446	−	0.583037i	$-0.198136\pi$
$263$	−1.60067	−	2.77245i	−0.0987018	−	0.170956i	−0.911148	+	0.412080i	$0.864802\pi$
$264$	6.15147	−	10.6547i	0.378597	−	0.655749i
$265$	15.7265			0.966074
$266$		0			0
$267$	−12.1575			−0.744030
$268$	3.24718	−	5.62428i	0.198353	−	0.343558i
$269$	−7.72002	−	13.3715i	−0.470698	−	0.815273i	0.528740	−	0.848784i	$-0.322664\pi$
$269$	−7.72002	−	13.3715i	−0.470698	−	0.815273i	−0.999438	+	0.0335109i	$0.989331\pi$
$270$	6.26469	+	10.8508i	0.381257	+	0.660357i
$271$	12.4439	−	21.5534i	0.755912	−	1.30928i	−0.189007	−	0.981976i	$-0.560527\pi$
$271$	12.4439	−	21.5534i	0.755912	−	1.30928i	0.944919	−	0.327303i	$-0.106140\pi$
$272$	−0.0297440			−0.00180349
$273$		0			0
$274$	−1.70106			−0.102765
$275$	−10.1148	+	17.5193i	−0.609943	+	1.05645i
$276$	−4.71910	−	8.17372i	−0.284056	−	0.492000i
$277$	5.64352	+	9.77486i	0.339086	+	0.587315i	0.984261	−	0.176720i	$-0.0565488\pi$
$277$	5.64352	+	9.77486i	0.339086	+	0.587315i	−0.645175	+	0.764035i	$0.723216\pi$
$278$	−2.06218	+	3.57181i	−0.123682	+	0.214223i
$279$	7.44433			0.445680
$280$		0			0
$281$	13.0332			0.777495			0.388747	−	0.921344i	$-0.372908\pi$
$281$	13.0332			0.777495			0.388747	+	0.921344i	$0.372908\pi$
$282$	2.21915	−	3.84368i	0.132148	−	0.228888i
$283$	−10.8595	−	18.8092i	−0.645531	−	1.11809i	−0.984179	−	0.177179i	$-0.943303\pi$
$283$	−10.8595	−	18.8092i	−0.645531	−	1.11809i	0.338648	−	0.940913i	$-0.390031\pi$
$284$	−7.33401	−	12.7029i	−0.435194	−	0.753777i
$285$	3.64479	−	6.31297i	0.215899	−	0.373948i
$286$	−18.4667			−1.09196
$287$		0			0
$288$	−12.2823			−0.723742
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−9.39189	−	16.2672i	−0.551511	−	0.955244i
$291$	6.88251	+	11.9209i	0.403460	+	0.698813i
$292$	7.81624	−	13.5381i	0.457411	−	0.792259i
$293$	−28.9400			−1.69069			−0.845346	−	0.534219i	$-0.820606\pi$
$293$	−28.9400			−1.69069			−0.845346	+	0.534219i	$0.820606\pi$
$294$		0			0
$295$	28.2165			1.64283
$296$	13.7063	−	23.7401i	0.796665	−	1.37986i
$297$	11.2322	+	19.4547i	0.651756	+	1.12887i
$298$	−1.86172	−	3.22459i	−0.107846	−	0.186795i
$299$	−18.6065	+	32.2275i	−1.07604	+	1.86376i
$300$	−4.72037			−0.272531
$301$		0			0
$302$	10.9364			0.629318
$303$	−1.47384	+	2.55277i	−0.0846701	+	0.146653i
$304$	−0.0393165	−	0.0680981i	−0.00225495	−	0.00390570i
$305$	−10.1221	−	17.5319i	−0.579588	−	1.00388i
$306$	0.955216	−	1.65448i	0.0546061	−	0.0945805i
$307$	−11.5836			−0.661110			−0.330555	−	0.943787i	$-0.607236\pi$
$307$	−11.5836			−0.661110			−0.330555	+	0.943787i	$0.607236\pi$
$308$		0			0
$309$	−11.5291			−0.655867
$310$	4.56145	−	7.90066i	0.259073	−	0.448727i
$311$	7.89996	+	13.6831i	0.447966	+	0.775900i	0.998254	−	0.0590756i	$-0.0188153\pi$
$311$	7.89996	+	13.6831i	0.447966	+	0.775900i	−0.550288	+	0.834975i	$0.685482\pi$
$312$	−5.65947	−	9.80248i	−0.320404	−	0.554956i
$313$	−10.1329	+	17.5507i	−0.572745	+	0.992024i	0.423537	+	0.905879i	$0.360788\pi$
$313$	−10.1329	+	17.5507i	−0.572745	+	0.992024i	−0.996283	+	0.0861453i	$0.972545\pi$
$314$	−15.4913			−0.874225
$315$		0			0
$316$	−2.38568			−0.134205
$317$	−3.18268	+	5.51257i	−0.178757	+	0.309617i	−0.941455	−	0.337138i	$-0.890541\pi$
$317$	−3.18268	+	5.51257i	−0.178757	+	0.309617i	0.762698	+	0.646755i	$0.223874\pi$
$318$	−2.06199	−	3.57147i	−0.115631	−	0.200278i
$319$	−16.8390	−	29.1660i	−0.942803	−	1.63298i
$320$	−7.61624	+	13.1917i	−0.425761	+	0.737439i
$321$	3.55235			0.198273
$322$		0			0
$323$	−2.64366			−0.147097
$324$	1.39242	−	2.41175i	0.0773569	−	0.133986i
$325$	9.30577	+	16.1181i	0.516191	+	0.894069i
$326$	1.17435	+	2.03404i	0.0650414	+	0.112655i
$327$	1.61710	−	2.80091i	0.0894260	−	0.154890i
$328$	−3.78954			−0.209242
$329$		0			0
$330$	11.5744			0.637151
$331$	−12.2955	+	21.2965i	−0.675823	+	1.17056i	0.300405	+	0.953812i	$0.402878\pi$
$331$	−12.2955	+	21.2965i	−0.675823	+	1.17056i	−0.976228	+	0.216748i	$0.930455\pi$
$332$	−2.81791	−	4.88076i	−0.154653	−	0.267866i
$333$	10.5222	+	18.2249i	0.576611	+	0.998720i
$334$	0.859325	−	1.48839i	0.0470202	−	0.0814413i
$335$	16.0492			0.876863
$336$		0			0
$337$	7.11956			0.387827			0.193913	−	0.981019i	$-0.437882\pi$
$337$	7.11956			0.387827			0.193913	+	0.981019i	$0.437882\pi$
$338$	−2.78891	+	4.83053i	−0.151697	+	0.262746i
$339$	−0.438643	−	0.759751i	−0.0238238	−	0.0412640i
$340$	1.86758	+	3.23474i	0.101284	+	0.175429i
$341$	8.17836	−	14.1653i	0.442883	−	0.767096i
$342$	5.05053			0.273101
$343$		0			0
$344$	−7.15844			−0.385957
$345$	11.6621	−	20.1994i	0.627867	−	1.08750i
$346$	−2.64110	−	4.57453i	−0.141987	−	0.245928i
$347$	−0.757387	−	1.31183i	−0.0406586	−	0.0704228i	0.844980	−	0.534798i	$-0.179612\pi$
$347$	−0.757387	−	1.31183i	−0.0406586	−	0.0704228i	−0.885639	+	0.464375i	$0.846279\pi$
$348$	3.92922	−	6.80561i	0.210628	−	0.364819i
$349$	24.7937			1.32717			0.663587	−	0.748099i	$-0.269033\pi$
$349$	24.7937			1.32717			0.663587	+	0.748099i	$0.269033\pi$
$350$		0			0
$351$	20.6676			1.10315
$352$	−13.4934	+	23.3712i	−0.719199	+	1.24569i
$353$	5.92082	+	10.2552i	0.315133	+	0.545827i	0.979466	−	0.201610i	$-0.0646174\pi$
$353$	5.92082	+	10.2552i	0.315133	+	0.545827i	−0.664332	+	0.747437i	$0.731284\pi$
$354$	−3.69962	−	6.40792i	−0.196632	−	0.340577i
$355$	18.1242	−	31.3921i	0.961934	−	1.66612i
$356$	16.4686			0.872836
$357$		0			0
$358$	1.53719			0.0812430
$359$	13.3371	−	23.1006i	0.703907	−	1.21920i	−0.263177	−	0.964747i	$-0.584770\pi$
$359$	13.3371	−	23.1006i	0.703907	−	1.21920i	0.967085	−	0.254455i	$-0.0818962\pi$
$360$	−9.37212	−	16.2330i	−0.493954	−	0.855554i
$361$	6.00554	+	10.4019i	0.316081	+	0.547468i
$362$	−1.21356	+	2.10195i	−0.0637835	+	0.110476i
$363$	10.7688			0.565215
$364$		0			0
$365$	38.6319			2.02209
$366$	−2.65431	+	4.59741i	−0.138743	+	0.240310i
$367$	14.3449	+	24.8460i	0.748796	+	1.29695i	0.948400	+	0.317076i	$0.102701\pi$
$367$	14.3449	+	24.8460i	0.748796	+	1.29695i	−0.199604	+	0.979877i	$0.563966\pi$
$368$	−0.125799	−	0.217891i	−0.00655775	−	0.0113584i
$369$	1.45459	−	2.51942i	0.0757229	−	0.131156i
$370$	25.7895			1.34073
$371$		0			0
$372$	3.81668			0.197886
$373$	13.4473	−	23.2914i	0.696275	−	1.20598i	−0.273474	−	0.961879i	$-0.588173\pi$
$373$	13.4473	−	23.2914i	0.696275	−	1.20598i	0.969749	−	0.244104i	$-0.0784939\pi$
$374$	−2.09880	−	3.63524i	−0.108527	−	0.187974i
$375$	1.06085	+	1.83744i	0.0547818	+	0.0948849i
$376$	−7.89632	+	13.6768i	−0.407222	+	0.705329i
$377$	−30.9844			−1.59578
$378$		0			0
$379$	0.960453			0.0493351			0.0246676	−	0.999696i	$-0.492147\pi$
$379$	0.960453			0.0493351			0.0246676	+	0.999696i	$0.492147\pi$
$380$	−4.93724	+	8.55156i	−0.253275	+	0.438686i
$381$	2.52250	+	4.36910i	0.129232	+	0.223836i
$382$	−8.27186	−	14.3273i	−0.423225	−	0.733048i
$383$	5.49563	−	9.51871i	0.280814	−	0.486384i	−0.690772	−	0.723073i	$-0.742729\pi$
$383$	5.49563	−	9.51871i	0.280814	−	0.486384i	0.971585	+	0.236689i	$0.0760624\pi$
$384$	−6.24970			−0.318929
$385$		0			0
$386$	10.4556			0.532175
$387$	2.74772	−	4.75919i	0.139674	−	0.241923i
$388$	−9.32306	−	16.1480i	−0.473307	−	0.819791i
$389$	12.7119	+	22.0177i	0.644520	+	1.11634i	0.984412	+	0.175878i	$0.0562763\pi$
$389$	12.7119	+	22.0177i	0.644520	+	1.11634i	−0.339892	+	0.940465i	$0.610390\pi$
$390$	5.32435	−	9.22204i	0.269609	−	0.466976i
$391$	−8.45881			−0.427781
$392$		0			0
$393$	−3.18681			−0.160753
$394$	7.57930	−	13.1277i	0.381839	−	0.661365i
$395$	−2.94781	−	5.10576i	−0.148321	−	0.256899i
$396$	−6.39697	−	11.0799i	−0.321460	−	0.556785i
$397$	7.50702	−	13.0025i	0.376767	−	0.652579i	−0.613823	−	0.789444i	$-0.710369\pi$
$397$	7.50702	−	13.0025i	0.376767	−	0.652579i	0.990590	+	0.136865i	$0.0437026\pi$
$398$	−13.3827			−0.670815
$399$		0			0
$400$	−0.125833			−0.00629166
$401$	5.53278	−	9.58306i	0.276294	−	0.478555i	−0.694167	−	0.719814i	$-0.744227\pi$
$401$	5.53278	−	9.58306i	0.276294	−	0.478555i	0.970461	+	0.241259i	$0.0775603\pi$
$402$	−2.10430	−	3.64475i	−0.104953	−	0.181784i
$403$	−7.52424	−	13.0324i	−0.374809	−	0.649188i
$404$	1.99647	−	3.45799i	0.0993282	−	0.172041i
$405$	6.88207			0.341973
$406$		0			0
$407$	46.2387			2.29197
$408$	1.28644	−	2.22818i	0.0636882	−	0.110311i
$409$	−14.2825	−	24.7380i	−0.706225	−	1.22322i	−0.966248	−	0.257615i	$-0.917063\pi$
$409$	−14.2825	−	24.7380i	−0.706225	−	1.22322i	0.260023	−	0.965602i	$-0.416270\pi$
$410$	−1.78257	−	3.08751i	−0.0880350	−	0.152481i
$411$	0.879351	−	1.52308i	0.0433752	−	0.0751280i
$412$	15.6173			0.769411
$413$		0			0
$414$	16.1600			0.794220
$415$	6.96377	−	12.0616i	0.341838	−	0.592081i
$416$	12.4141	+	21.5019i	0.608654	+	1.05422i
$417$	−2.13206	−	3.69283i	−0.104407	−	0.180839i
$418$	5.54852	−	9.61032i	0.271387	−	0.470056i
$419$	−1.98566			−0.0970057			−0.0485029	−	0.998823i	$-0.515445\pi$
$419$	−1.98566			−0.0970057			−0.0485029	+	0.998823i	$0.515445\pi$
$420$		0			0
$421$	25.1984			1.22810			0.614048	−	0.789269i	$-0.289540\pi$
$421$	25.1984			1.22810			0.614048	+	0.789269i	$0.289540\pi$
$422$	−3.73664	+	6.47204i	−0.181897	+	0.315054i
$423$	−6.06190	−	10.4995i	−0.294740	−	0.510504i
$424$	7.33711	+	12.7082i	0.356321	+	0.617167i
$425$	−2.11527	+	3.66376i	−0.102606	+	0.177718i
$426$	−9.50544			−0.460540
$427$		0			0
$428$	−4.81202			−0.232598
$429$	9.54618	−	16.5345i	0.460894	−	0.798292i
$430$	−3.36728	−	5.83230i	−0.162385	−	0.281258i
$431$	13.7492	+	23.8143i	0.662275	+	1.14709i	0.980017	+	0.198916i	$0.0637422\pi$
$431$	13.7492	+	23.8143i	0.662275	+	1.14709i	−0.317742	+	0.948177i	$0.602925\pi$
$432$	−0.0698672	+	0.121013i	−0.00336148	+	0.00582226i
$433$	28.1977			1.35509			0.677547	−	0.735480i	$-0.263043\pi$
$433$	28.1977			1.35509			0.677547	+	0.735480i	$0.263043\pi$
$434$		0			0
$435$	19.4202			0.931129
$436$	−2.19053	+	3.79411i	−0.104907	+	0.181705i
$437$	−11.1811	−	19.3662i	−0.534865	−	0.926413i
$438$	−5.06523	−	8.77323i	−0.242026	−	0.419201i
$439$	−3.15649	+	5.46720i	−0.150651	+	0.260935i	−0.931467	−	0.363826i	$-0.881470\pi$
$439$	−3.15649	+	5.46720i	−0.150651	+	0.260935i	0.780816	+	0.624761i	$0.214804\pi$
$440$	−41.1849			−1.96341
$441$		0			0
$442$	−3.86188			−0.183691
$443$	−13.2278	+	22.9113i	−0.628473	+	1.08855i	0.359385	+	0.933189i	$0.382986\pi$
$443$	−13.2278	+	22.9113i	−0.628473	+	1.08855i	−0.987858	+	0.155358i	$0.950347\pi$
$444$	5.39468	+	9.34386i	0.256020	+	0.443440i
$445$	20.3491	+	35.2457i	0.964640	+	1.67081i
$446$	1.09331	−	1.89367i	0.0517699	−	0.0896681i
$447$	3.84960			0.182080
$448$		0			0
$449$	−34.5555			−1.63077			−0.815387	−	0.578916i	$-0.803476\pi$
$449$	−34.5555			−1.63077			−0.815387	+	0.578916i	$0.803476\pi$
$450$	4.04108	−	6.99936i	0.190498	−	0.329953i
$451$	−3.19603	−	5.53569i	−0.150495	−	0.260665i
$452$	0.594186	+	1.02916i	0.0279482	+	0.0484076i
$453$	−5.65347	+	9.79210i	−0.265623	+	0.460073i
$454$	−14.9093			−0.699728
$455$		0			0
$456$	6.80181			0.318524
$457$	−13.2961	+	23.0295i	−0.621965	+	1.07728i	0.367154	+	0.930160i	$0.380332\pi$
$457$	−13.2961	+	23.0295i	−0.621965	+	1.07728i	−0.989119	+	0.147115i	$0.953001\pi$
$458$	7.16765	+	12.4147i	0.334922	+	0.580102i
$459$	2.34895	+	4.06850i	0.109640	+	0.189901i
$460$	−15.7975	+	27.3621i	−0.736563	+	1.27576i
$461$	−0.310199			−0.0144474			−0.00722371	−	0.999974i	$-0.502299\pi$
$461$	−0.310199			−0.0144474			−0.00722371	+	0.999974i	$0.502299\pi$
$462$		0			0
$463$	22.4654			1.04406			0.522028	−	0.852928i	$-0.325175\pi$
$463$	22.4654			1.04406			0.522028	+	0.852928i	$0.325175\pi$
$464$	0.104743	−	0.181421i	0.00486258	−	0.00842224i
$465$	4.71600	+	8.16836i	0.218699	+	0.378799i
$466$	2.53617	+	4.39278i	0.117486	+	0.203492i
$467$	5.80628	−	10.0568i	0.268682	−	0.465372i	−0.699839	−	0.714300i	$-0.746745\pi$
$467$	5.80628	−	10.0568i	0.268682	−	0.465372i	0.968522	+	0.248929i	$0.0800785\pi$
$468$	−11.7707			−0.544099
$469$		0			0
$470$	−14.8575			−0.685325
$471$	8.00810	−	13.8704i	0.368994	−	0.639116i
$472$	13.1642	+	22.8011i	0.605933	+	1.04951i
$473$	−6.03730	−	10.4569i	−0.277595	−	0.480809i
$474$	−0.773006	+	1.33889i	−0.0355053	+	0.0614971i
$475$	−11.1841			−0.513162
$476$		0			0
$477$	−11.2652			−0.515798
$478$	−3.26675	+	5.65818i	−0.149418	+	0.258799i
$479$	−15.8988	−	27.5376i	−0.726435	−	1.25822i	−0.958380	−	0.285494i	$-0.907842\pi$
$479$	−15.8988	−	27.5376i	−0.726435	−	1.25822i	0.231945	−	0.972729i	$-0.425491\pi$
$480$	−7.78087	−	13.4769i	−0.355147	−	0.615132i
$481$	21.2702	−	36.8411i	0.969839	−	1.67981i
$482$	19.2277			0.875799
$483$		0			0
$484$	−14.5874			−0.663064
$485$	23.0397	−	39.9059i	1.04618	−	1.81203i
$486$	−7.08831	−	12.2773i	−0.321532	−	0.556910i
$487$	11.5083	+	19.9329i	0.521490	+	0.903248i	0.999688	+	0.0249951i	$0.00795703\pi$
$487$	11.5083	+	19.9329i	0.521490	+	0.903248i	−0.478197	+	0.878252i	$0.658710\pi$
$488$	9.44477	−	16.3588i	0.427544	−	0.740529i
$489$	−2.42829			−0.109811
$490$		0			0
$491$	−33.3176			−1.50360			−0.751802	−	0.659389i	$-0.770815\pi$
$491$	−33.3176			−1.50360			−0.751802	+	0.659389i	$0.770815\pi$
$492$	0.745763	−	1.29170i	0.0336216	−	0.0582343i
$493$	−3.52149	−	6.09940i	−0.158600	−	0.274703i
$494$	−5.10474	−	8.84167i	−0.229673	−	0.397806i
$495$	15.8086	−	27.3812i	0.710542	−	1.23069i
$496$	0.101743			0.00456841
$497$		0			0
$498$	−3.65222			−0.163660
$499$	−18.5118	+	32.0634i	−0.828703	+	1.43536i	0.0703537	+	0.997522i	$0.477587\pi$
$499$	−18.5118	+	32.0634i	−0.828703	+	1.43536i	−0.899056	+	0.437833i	$0.855746\pi$
$500$	−1.43702	−	2.48900i	−0.0642656	−	0.111311i
$501$	0.888442	+	1.53883i	0.0396926	+	0.0687497i
$502$	−7.27589	+	12.6022i	−0.324739	+	0.562464i
$503$	−12.4172			−0.553654			−0.276827	−	0.960920i	$-0.589283\pi$
$503$	−12.4172			−0.553654			−0.276827	+	0.960920i	$0.589283\pi$
$504$		0			0
$505$	9.86759			0.439102
$506$	17.7534	−	30.7498i	0.789235	−	1.36699i
$507$	−2.88341	−	4.99421i	−0.128057	−	0.221801i
$508$	−3.41699	−	5.91839i	−0.151604	−	0.262586i
$509$	−5.96285	+	10.3280i	−0.264299	+	0.457779i	−0.967380	−	0.253331i	$-0.918474\pi$
$509$	−5.96285	+	10.3280i	−0.264299	+	0.457779i	0.703081	+	0.711110i	$0.251807\pi$
$510$	2.42053			0.107183
$511$		0			0
$512$	−0.336507			−0.0148716
$513$	−6.20982	+	10.7557i	−0.274170	+	0.474877i
$514$	−5.31784	−	9.21077i	−0.234560	−	0.406270i
$515$	19.2972	+	33.4238i	0.850337	+	1.47283i
$516$	1.40875	−	2.44002i	0.0620166	−	0.107416i
$517$	−26.6385			−1.17156
$518$		0			0
$519$	5.46119			0.239719
$520$	−18.9455	+	32.8145i	−0.830813	+	1.43901i
$521$	−13.1990	−	22.8613i	−0.578259	−	1.00157i	−0.995679	−	0.0928600i	$-0.970399\pi$
$521$	−13.1990	−	22.8613i	−0.578259	−	1.00157i	0.417420	−	0.908713i	$-0.362934\pi$
$522$	6.72757	+	11.6525i	0.294458	+	0.510016i
$523$	−6.81358	+	11.8015i	−0.297937	+	0.516042i	−0.975664	−	0.219272i	$-0.929632\pi$
$523$	−6.81358	+	11.8015i	−0.297937	+	0.516042i	0.677727	+	0.735314i	$0.262965\pi$
$524$	4.31686			0.188583
$525$		0			0
$526$	2.81025			0.122533
$527$	1.71032	−	2.96236i	0.0745026	−	0.129042i
$528$	0.0645421	+	0.111790i	0.00280883	+	0.00486504i
$529$	−24.2758	−	42.0469i	−1.05547	−	1.82812i
$530$	−6.90265	+	11.9557i	−0.299832	+	0.519324i
$531$	−20.2120			−0.877126
$532$		0			0
$533$	−5.88081			−0.254726
$534$	5.33615	−	9.24249i	0.230918	−	0.399962i
$535$	−5.94587	−	10.2986i	−0.257062	−	0.445245i
$536$	7.48766	+	12.9690i	0.323417	+	0.560175i
$537$	−0.794637	+	1.37635i	−0.0342911	+	0.0593940i
$538$	13.5538			0.584346
$539$		0			0
$540$	17.5474			0.755120
$541$	−13.1679	+	22.8075i	−0.566132	+	0.980570i	0.430811	+	0.902442i	$0.358227\pi$
$541$	−13.1679	+	22.8075i	−0.566132	+	0.980570i	−0.996943	+	0.0781276i	$0.975106\pi$
$542$	10.9237	+	18.9204i	0.469212	+	0.812699i
$543$	−1.25468	−	2.17318i	−0.0538436	−	0.0932599i
$544$	−2.82183	+	4.88755i	−0.120985	+	0.209552i
$545$	−10.8267			−0.463766
$546$		0			0
$547$	−2.25139			−0.0962624			−0.0481312	−	0.998841i	$-0.515327\pi$
$547$	−2.25139			−0.0962624			−0.0481312	+	0.998841i	$0.515327\pi$
$548$	−1.19117	+	2.06317i	−0.0508843	+	0.0881342i
$549$	7.25062	+	12.5584i	0.309449	+	0.535981i
$550$	−8.87908	−	15.3790i	−0.378605	−	0.655764i
$551$	9.30962	−	16.1247i	0.396603	−	0.686937i
$552$	21.7635			0.926316
$553$		0			0
$554$	−9.90815			−0.420957
$555$	−13.3316	+	23.0911i	−0.565897	+	0.980162i
$556$	2.88809	+	5.00231i	0.122482	+	0.212145i
$557$	−15.1678	−	26.2713i	−0.642679	−	1.11315i	−0.984832	−	0.173508i	$-0.944490\pi$
$557$	−15.1678	−	26.2713i	−0.642679	−	1.11315i	0.342154	−	0.939644i	$-0.388844\pi$
$558$	−3.26744	+	5.65938i	−0.138322	+	0.239581i
$559$	−11.1089			−0.469854
$560$		0			0
$561$	4.33984			0.183228
$562$	−5.72049	+	9.90818i	−0.241304	+	0.417951i
$563$	−5.49336	−	9.51478i	−0.231518	−	0.401000i	0.726737	−	0.686915i	$-0.241036\pi$
$563$	−5.49336	−	9.51478i	−0.231518	−	0.401000i	−0.958255	+	0.285915i	$0.907702\pi$
$564$	−3.10792	−	5.38307i	−0.130867	−	0.226668i
$565$	−1.46839	+	2.54332i	−0.0617755	+	0.106998i
$566$	19.0657			0.801391
$567$		0			0
$568$	33.8229			1.41918
$569$	14.4240	−	24.9831i	0.604684	−	1.04734i	−0.387417	−	0.921905i	$-0.626633\pi$
$569$	14.4240	−	24.9831i	0.604684	−	1.04734i	0.992101	−	0.125440i	$-0.0400341\pi$
$570$	3.19952	+	5.54174i	0.134013	+	0.232118i
$571$	5.25823	+	9.10753i	0.220050	+	0.381138i	0.954823	−	0.297175i	$-0.0960446\pi$
$571$	5.25823	+	9.10753i	0.220050	+	0.381138i	−0.734773	+	0.678313i	$0.762711\pi$
$572$	−12.9313	+	22.3976i	−0.540684	+	0.936492i
$573$	17.1043			0.714542
$574$		0			0
$575$	−35.7854			−1.49235
$576$	5.45564	−	9.44945i	0.227319	−	0.393727i
$577$	18.4144	+	31.8947i	0.766601	+	1.32779i	0.939396	+	0.342835i	$0.111387\pi$
$577$	18.4144	+	31.8947i	0.766601	+	1.32779i	−0.172794	+	0.984958i	$0.555280\pi$
$578$	−0.438917	−	0.760227i	−0.0182565	−	0.0316213i
$579$	−5.40493	+	9.36161i	−0.224621	+	0.389055i
$580$	−26.3067			−1.09233
$581$		0			0
$582$	−12.0834			−0.500873
$583$	−12.3760	+	21.4358i	−0.512560	+	0.887780i
$584$	18.0234	+	31.2175i	0.745815	+	1.29179i
$585$	−14.5442	−	25.1912i	−0.601327	−	1.04153i
$586$	12.7023	−	22.0010i	0.524726	−	0.908851i
$587$	30.1420			1.24409			0.622047	−	0.782980i	$-0.286301\pi$
$587$	30.1420			1.24409			0.622047	+	0.782980i	$0.286301\pi$
$588$		0			0
$589$	9.04298			0.372610
$590$	−12.3847	+	21.4510i	−0.509871	+	0.883122i
$591$	7.83611	+	13.5725i	0.322334	+	0.558300i
$592$	0.143809	+	0.249084i	0.00591051	+	0.0102373i
$593$	3.94462	−	6.83229i	0.161986	−	0.280568i	−0.773595	−	0.633681i	$-0.781543\pi$
$593$	3.94462	−	6.83229i	0.161986	−	0.280568i	0.935581	+	0.353112i	$0.114877\pi$
$594$	−19.7199			−0.809119
$595$		0			0
$596$	−5.21467			−0.213601
$597$	6.91808	−	11.9825i	0.283138	−	0.490410i
$598$	−16.3335	−	28.2904i	−0.667925	−	1.15688i
$599$	−14.9029	−	25.8126i	−0.608917	−	1.05468i	−0.991419	−	0.130721i	$-0.958271\pi$
$599$	−14.9029	−	25.8126i	−0.608917	−	1.05468i	0.382502	−	0.923955i	$-0.375062\pi$
$600$	5.44234	−	9.42640i	0.222182	−	0.384831i
$601$	11.9432			0.487175			0.243587	−	0.969879i	$-0.421676\pi$
$601$	11.9432			0.487175			0.243587	+	0.969879i	$0.421676\pi$
$602$		0			0
$603$	−11.4963			−0.468167
$604$	7.65820	−	13.2644i	0.311608	−	0.539721i
$605$	−18.0246	−	31.2196i	−0.732805	−	1.26926i
$606$	−1.29379	−	2.24091i	−0.0525566	−	0.0910308i
$607$	2.33641	−	4.04677i	0.0948318	−	0.164253i	−0.814707	−	0.579873i	$-0.803102\pi$
$607$	2.33641	−	4.04677i	0.0948318	−	0.164253i	0.909538	+	0.415620i	$0.136435\pi$
$608$	−14.9199			−0.605082
$609$		0			0
$610$	17.7710			0.719527
$611$	−12.2539	+	21.2244i	−0.495741	+	0.858649i
$612$	−1.33778	−	2.31710i	−0.0540766	−	0.0936634i
$613$	−21.1947	−	36.7103i	−0.856046	−	1.48271i	−0.875672	−	0.482907i	$-0.839581\pi$
$613$	−21.1947	−	36.7103i	−0.856046	−	1.48271i	0.0196261	−	0.999807i	$-0.493752\pi$
$614$	5.08424	−	8.80615i	0.205183	−	0.355387i
$615$	3.68595			0.148632
$616$		0			0
$617$	−23.2809			−0.937255			−0.468628	−	0.883396i	$-0.655251\pi$
$617$	−23.2809			−0.937255			−0.468628	+	0.883396i	$0.655251\pi$
$618$	5.06032	−	8.76473i	0.203556	−	0.352569i
$619$	21.6101	+	37.4297i	0.868582	+	1.50443i	0.863446	+	0.504441i	$0.168302\pi$
$619$	21.6101	+	37.4297i	0.868582	+	1.50443i	0.00513615	+	0.999987i	$0.498365\pi$
$620$	−6.38831	−	11.0649i	−0.256561	−	0.444376i
$621$	−19.8693	+	34.4147i	−0.797329	+	1.38101i
$622$	−13.8697			−0.556125
$623$		0			0
$624$	0.118760			0.00475420
$625$	14.1276	−	24.4697i	0.565104	−	0.978790i
$626$	−8.89501	−	15.4066i	−0.355516	−	0.615772i
$627$	5.73652	+	9.93595i	0.229095	+	0.396804i
$628$	−10.8478	+	18.7889i	−0.432874	+	0.749760i
$629$	9.66977			0.385559
$630$		0			0
$631$	30.6825			1.22145			0.610725	−	0.791843i	$-0.290878\pi$
$631$	30.6825			1.22145			0.610725	+	0.791843i	$0.290878\pi$
$632$	2.75056	−	4.76412i	0.109412	−	0.189506i
$633$	−3.86325	−	6.69134i	−0.153550	−	0.265957i
$634$	−2.79387	−	4.83912i	−0.110959	−	0.192186i
$635$	8.44425	−	14.6259i	0.335100	−	0.580410i
$636$	−5.77563			−0.229019
$637$		0			0
$638$	29.5637			1.17044
$639$	−12.9827	+	22.4867i	−0.513588	+	0.889560i
$640$	10.4607	+	18.1184i	0.413494	+	0.716192i
$641$	10.6781	+	18.4950i	0.421758	+	0.730507i	0.996112	−	0.0881008i	$-0.0280798\pi$
$641$	10.6781	+	18.4950i	0.421758	+	0.730507i	−0.574353	+	0.818608i	$0.694746\pi$
$642$	−1.55919	+	2.70059i	−0.0615362	+	0.106584i
$643$	22.7013			0.895253			0.447626	−	0.894221i	$-0.352269\pi$
$643$	22.7013			0.895253			0.447626	+	0.894221i	$0.352269\pi$
$644$		0			0
$645$	6.96275			0.274158
$646$	1.16035	−	2.00978i	0.0456532	−	0.0790737i
$647$	−17.6315	−	30.5386i	−0.693165	−	1.20060i	−0.970795	−	0.239909i	$-0.922882\pi$
$647$	−17.6315	−	30.5386i	−0.693165	−	1.20060i	0.277630	−	0.960688i	$-0.410451\pi$
$648$	3.21078	+	5.56124i	0.126131	+	0.218466i
$649$	−22.2049	+	38.4601i	−0.871620	+	1.50969i
$650$	−16.3378			−0.640823
$651$		0			0
$652$	3.28936			0.128821
$653$	15.0296	−	26.0321i	0.588155	−	1.01871i	−0.406319	−	0.913731i	$-0.633188\pi$
$653$	15.0296	−	26.0321i	0.588155	−	1.01871i	0.994474	−	0.104983i	$-0.0334789\pi$
$654$	1.41955	+	2.45873i	0.0555088	+	0.0961440i
$655$	5.33404	+	9.23883i	0.208418	+	0.360991i
$656$	0.0198802	−	0.0344335i	0.000776191	−	0.00134440i
$657$	−27.6727			−1.07961
$658$		0			0
$659$	−18.9747			−0.739148			−0.369574	−	0.929201i	$-0.620496\pi$
$659$	−18.9747			−0.739148			−0.369574	+	0.929201i	$0.620496\pi$
$660$	8.10500	−	14.0383i	0.315487	−	0.546439i
$661$	−12.9019	−	22.3467i	−0.501825	−	0.869187i	−0.999998	−	0.00210905i	$-0.999329\pi$
$661$	−12.9019	−	22.3467i	−0.501825	−	0.869187i	0.498172	−	0.867078i	$-0.334005\pi$
$662$	−10.7934	−	18.6948i	−0.419498	−	0.726593i
$663$	1.99637	−	3.45781i	0.0775324	−	0.134290i
$664$	12.9956			0.504327
$665$		0			0
$666$	−18.4734			−0.715831
$667$	29.7876	−	51.5937i	1.15338	−	1.99772i
$668$	−1.20348	−	2.08450i	−0.0465642	−	0.0806516i
$669$	1.13036	+	1.95784i	0.0437022	+	0.0756944i
$670$	−7.04428	+	12.2011i	−0.272144	+	0.471368i
$671$	31.8622			1.23003
$672$		0			0
$673$	4.38401			0.168991			0.0844956	−	0.996424i	$-0.473072\pi$
$673$	4.38401			0.168991			0.0844956	+	0.996424i	$0.473072\pi$
$674$	−3.12489	+	5.41248i	−0.120366	+	0.208481i
$675$	9.93733	+	17.2120i	0.382488	+	0.662489i
$676$	3.90587	+	6.76517i	0.150226	+	0.260199i
$677$	16.0557	−	27.8094i	0.617073	−	1.06880i	−0.372945	−	0.927854i	$-0.621652\pi$
$677$	16.0557	−	27.8094i	0.617073	−	1.06880i	0.990017	−	0.140947i	$-0.0450148\pi$
$678$	0.770111			0.0295759
$679$		0			0
$680$	−8.61289			−0.330289
$681$	7.70724	−	13.3493i	0.295342	−	0.511548i
$682$	7.17924	+	12.4348i	0.274907	+	0.476153i
$683$	9.35466	+	16.2027i	0.357946	+	0.619981i	0.987618	−	0.156881i	$-0.0501438\pi$
$683$	9.35466	+	16.2027i	0.357946	+	0.619981i	−0.629672	+	0.776861i	$0.716811\pi$
$684$	3.53663	−	6.12563i	0.135227	−	0.234219i
$685$	−5.88738			−0.224945
$686$		0			0
$687$	−14.8210			−0.565457
$688$	0.0375537	−	0.0650449i	0.00143172	−	0.00247981i
$689$	11.3861	+	19.7213i	0.433777	+	0.751323i
$690$	10.2374	+	17.7317i	0.389731	+	0.675034i
$691$	20.4566	−	35.4318i	0.778205	−	1.34789i	−0.154771	−	0.987950i	$-0.549464\pi$
$691$	20.4566	−	35.4318i	0.778205	−	1.34789i	0.932976	−	0.359940i	$-0.117203\pi$
$692$	−7.39773			−0.281220
$693$		0			0
$694$	1.32972			0.0504755
$695$	−7.13721	+	12.3620i	−0.270730	+	0.468918i
$696$	9.06037	+	15.6930i	0.343433	+	0.594843i
$697$	−0.668377	−	1.15766i	−0.0253166	−	0.0438496i
$698$	−10.8824	+	18.8488i	−0.411903	+	0.713438i
$699$	−5.24421			−0.198354
$700$		0			0
$701$	−17.6240			−0.665649			−0.332825	−	0.942989i	$-0.608002\pi$
$701$	−17.6240			−0.665649			−0.332825	+	0.942989i	$0.608002\pi$
$702$	−9.07136	+	15.7121i	−0.342376	+	0.593013i
$703$	12.7818	+	22.1387i	0.482074	+	0.834977i
$704$	−11.9872	−	20.7624i	−0.451783	−	0.782511i
$705$	7.68046	−	13.3029i	0.289263	−	0.501018i
$706$	−10.3950			−0.391221
$707$		0			0
$708$	−10.3626			−0.389451
$709$	4.09345	−	7.09007i	0.153733	−	0.266273i	−0.778864	−	0.627193i	$-0.784204\pi$
$709$	4.09345	−	7.09007i	0.153733	−	0.266273i	0.932597	+	0.360920i	$0.117537\pi$
$710$	15.9101	+	27.5570i	0.597094	+	1.03420i
$711$	2.11157	+	3.65735i	0.0791901	+	0.137161i
$712$	−18.9875	+	32.8873i	−0.711585	+	1.23250i
$713$	28.9345			1.08361
$714$		0			0
$715$	−63.9130			−2.39021
$716$	1.07642	−	1.86441i	0.0402276	−	0.0696763i
$717$	−3.37744	−	5.84990i	−0.126133	−	0.218468i
$718$	11.7078	+	20.2785i	0.436931	+	0.756787i
$719$	−21.3047	+	36.9008i	−0.794530	+	1.37617i	0.128607	+	0.991696i	$0.458949\pi$
$719$	−21.3047	+	36.9008i	−0.794530	+	1.37617i	−0.923137	+	0.384470i	$0.874384\pi$
$720$	0.196667			0.00732936
$721$		0			0
$722$	−10.5437			−0.392397
$723$	−9.93961	+	17.2159i	−0.369658	+	0.640267i
$724$	1.69960	+	2.94379i	0.0631650	+	0.109405i
$725$	−14.8978	−	25.8038i	−0.553291	−	0.958329i
$726$	−4.72660	+	8.18672i	−0.175421	+	0.303838i
$727$	−10.5470			−0.391166			−0.195583	−	0.980687i	$-0.562660\pi$
$727$	−10.5470			−0.391166			−0.195583	+	0.980687i	$0.562660\pi$
$728$		0			0
$729$	7.86138			0.291162
$730$	−16.9562	+	29.3690i	−0.627577	+	1.08700i
$731$	−1.26256	−	2.18682i	−0.0466976	−	0.0808826i
$732$	3.71737	+	6.43867i	0.137398	+	0.237980i
$733$	−3.30745	+	5.72868i	−0.122164	+	0.211594i	−0.920621	−	0.390458i	$-0.872317\pi$
$733$	−3.30745	+	5.72868i	−0.122164	+	0.211594i	0.798457	+	0.602052i	$0.205650\pi$
$734$	−25.1848			−0.929589
$735$		0			0
$736$	−47.7387			−1.75967
$737$	−12.6299	+	21.8756i	−0.465228	+	0.805799i
$738$	1.27689	+	2.21164i	0.0470029	+	0.0814114i
$739$	0.417188	+	0.722591i	0.0153465	+	0.0265809i	0.873597	−	0.486651i	$-0.161782\pi$
$739$	0.417188	+	0.722591i	0.0153465	+	0.0265809i	−0.858250	+	0.513232i	$0.828448\pi$
$740$	18.0591	−	31.2792i	0.663865	−	1.14985i
$741$	10.5554			0.387763
$742$		0			0
$743$	52.9082			1.94101			0.970506	−	0.241077i	$-0.0775006\pi$
$743$	52.9082			1.94101			0.970506	+	0.241077i	$0.0775006\pi$
$744$	−4.40044	+	7.62178i	−0.161328	+	0.279428i
$745$	−6.44340	−	11.1603i	−0.236068	−	0.408882i
$746$	11.8045	+	20.4460i	0.432193	+	0.748581i
$747$	−4.98827	+	8.63993i	−0.182511	+	0.316119i
$748$	−5.87875			−0.214948
$749$		0			0
$750$	−1.86249			−0.0680086
$751$	−17.6840	+	30.6297i	−0.645300	+	1.11769i	0.338932	+	0.940811i	$0.389934\pi$
$751$	−17.6840	+	30.6297i	−0.645300	+	1.11769i	−0.984232	+	0.176881i	$0.943399\pi$
$752$	−0.0828493	−	0.143499i	−0.00302120	−	0.00523288i
$753$	−7.52242	−	13.0292i	−0.274132	−	0.474811i
$754$	13.5996	−	23.5552i	0.495267	−	0.857828i
$755$	37.8508			1.37753
$756$		0			0
$757$	−19.6550			−0.714372			−0.357186	−	0.934033i	$-0.616264\pi$
$757$	−19.6550			−0.714372			−0.357186	+	0.934033i	$0.616264\pi$
$758$	−0.421559	+	0.730162i	−0.0153117	+	0.0265207i
$759$	18.3549	+	31.7917i	0.666242	+	1.15397i
$760$	−11.3848	−	19.7190i	−0.412969	−	0.715283i
$761$	3.40388	−	5.89569i	0.123390	−	0.213719i	−0.797712	−	0.603038i	$-0.793957\pi$
$761$	3.40388	−	5.89569i	0.123390	−	0.213719i	0.921103	+	0.389320i	$0.127290\pi$
$762$	−4.42868			−0.160434
$763$		0			0
$764$	−23.1695			−0.838243
$765$	3.30600	−	5.72616i	0.119529	−	0.207030i
$766$	4.82425	+	8.35585i	0.174307	+	0.301909i
$767$	20.4290	+	35.3840i	0.737647	+	1.27764i
$768$	7.29341	−	12.6326i	0.263178	−	0.455838i
$769$	44.3645			1.59983			0.799913	−	0.600116i	$-0.204879\pi$
$769$	44.3645			1.59983			0.799913	+	0.600116i	$0.204879\pi$
$770$		0			0
$771$	10.9961			0.396013
$772$	7.32153	−	12.6813i	0.263508	−	0.456408i
$773$	12.8487	+	22.2546i	0.462135	+	0.800441i	0.999067	−	0.0431843i	$-0.0137503\pi$
$773$	12.8487	+	22.2546i	0.462135	+	0.800441i	−0.536932	+	0.843625i	$0.680417\pi$
$774$	2.41204	+	4.17778i	0.0866990	+	0.150167i
$775$	7.23557	−	12.5324i	0.259909	−	0.450176i
$776$	42.9960			1.54347
$777$		0			0
$778$	−22.3179			−0.800137
$779$	1.76696	−	3.06046i	0.0633079	−	0.109652i
$780$	−7.45675	−	12.9155i	−0.266994	−	0.462448i
$781$	28.5256	+	49.4079i	1.02073	+	1.76795i
$782$	3.71272	−	6.43062i	0.132767	−	0.229958i
$783$	−33.0872			−1.18244
$784$		0			0
$785$	−53.6153			−1.91361
$786$	1.39875	−	2.42270i	0.0498916	−	0.0864149i
$787$	−12.8283	−	22.2193i	−0.457279	−	0.792031i	0.541537	−	0.840677i	$-0.317843\pi$
$787$	−12.8283	−	22.2193i	−0.457279	−	0.792031i	−0.998816	+	0.0486462i	$0.984509\pi$
$788$	−10.6148	−	18.3854i	−0.378137	−	0.654952i
$789$	−1.45274	+	2.51621i	−0.0517188	+	0.0895796i
$790$	5.17538			0.184132
$791$		0			0
$792$	29.5015			1.04829
$793$	14.6569	−	25.3865i	0.520482	−	0.901501i
$794$	6.58992	+	11.4141i	0.233867	+	0.405070i
$795$	−7.13653	−	12.3608i	−0.253107	−	0.438394i
$796$	−9.37124	+	16.2315i	−0.332155	+	0.575309i
$797$	20.3683			0.721483			0.360741	−	0.932666i	$-0.382524\pi$
$797$	20.3683			0.721483			0.360741	+	0.932666i	$0.382524\pi$
$798$		0			0
$799$	−5.57082			−0.197082
$800$	−11.9379	+	20.6770i	−0.422067	+	0.731042i
$801$	−14.5764	−	25.2471i	−0.515032	−	0.892062i
$802$	4.85687	+	8.41234i	0.171502	+	0.297050i
$803$	−30.4013	+	52.6566i	−1.07284	+	1.85821i
$804$	−5.89414			−0.207870
$805$		0			0
$806$	13.2101			0.465305
$807$	−7.00652	+	12.1357i	−0.246641	+	0.427195i
$808$	4.60365	+	7.97376i	0.161956	+	0.280516i
$809$	18.2740	+	31.6515i	0.642480	+	1.11281i	0.984877	+	0.173252i	$0.0554277\pi$
$809$	18.2740	+	31.6515i	0.642480	+	1.11281i	−0.342398	+	0.939555i	$0.611239\pi$
$810$	−3.02066	+	5.23193i	−0.106135	+	0.183831i
$811$	7.33037			0.257404			0.128702	−	0.991683i	$-0.458919\pi$
$811$	7.33037			0.257404			0.128702	+	0.991683i	$0.458919\pi$
$812$		0			0
$813$	−22.5876			−0.792182
$814$	−20.2950	+	35.1519i	−0.711338	+	1.23207i
$815$	4.06443	+	7.03980i	0.142371	+	0.246593i
$816$	0.0134975	+	0.0233784i	0.000472507	+	0.000818406i
$817$	3.33778	−	5.78121i	0.116774	−	0.202259i
$818$	25.0754			0.876739
$819$		0			0
$820$	−4.99299			−0.174363
$821$	−0.881607	+	1.52699i	−0.0307683	+	0.0532922i	−0.881000	−	0.473117i	$-0.843129\pi$
$821$	−0.881607	+	1.52699i	−0.0307683	+	0.0532922i	0.850231	+	0.526409i	$0.176462\pi$
$822$	0.771924	+	1.33701i	0.0269240	+	0.0466337i
$823$	−0.318161	−	0.551072i	−0.0110904	−	0.0192092i	0.860427	−	0.509574i	$-0.170197\pi$
$823$	−0.318161	−	0.551072i	−0.0110904	−	0.0192092i	−0.871517	+	0.490365i	$0.836864\pi$
$824$	−18.0060	+	31.1873i	−0.627268	+	1.08646i
$825$	18.3599			0.639209
$826$		0			0
$827$	−6.81869			−0.237109			−0.118554	−	0.992948i	$-0.537826\pi$
$827$	−6.81869			−0.237109			−0.118554	+	0.992948i	$0.537826\pi$
$828$	11.3160	−	19.5999i	0.393259	−	0.681145i
$829$	−25.4740	−	44.1223i	−0.884749	−	1.53243i	−0.846001	−	0.533181i	$-0.820997\pi$
$829$	−25.4740	−	44.1223i	−0.884749	−	1.53243i	−0.0387473	−	0.999249i	$-0.512337\pi$
$830$	6.11303	+	10.5881i	0.212187	+	0.367518i
$831$	5.12193	−	8.87145i	0.177678	−	0.307747i
$832$	−22.0568			−0.764683
$833$		0			0
$834$	3.74318			0.129616
$835$	2.97412	−	5.15133i	0.102924	−	0.178269i
$836$	−7.77071	−	13.4593i	−0.268755	−	0.465498i
$837$	−8.03489	−	13.9168i	−0.277727	−	0.481037i
$838$	0.871539	−	1.50955i	0.0301068	−	0.0521466i
$839$	2.95064			0.101867			0.0509336	−	0.998702i	$-0.483780\pi$
$839$	2.95064			0.101867			0.0509336	+	0.998702i	$0.483780\pi$
$840$		0			0
$841$	20.6036			0.710470
$842$	−11.0600	+	19.1565i	−0.381153	+	0.660177i
$843$	−5.91432	−	10.2439i	−0.203700	−	0.352819i
$844$	5.23316	+	9.06410i	0.180133	+	0.311999i
$845$	−9.65241	+	16.7185i	−0.332053	+	0.575133i
$846$	10.6427			0.365903
$847$		0			0
$848$	−0.153964			−0.00528714
$849$	−9.85586	+	17.0708i	−0.338252	+	0.585870i
$850$	−1.85686	−	3.21617i	−0.0636897	−	0.110314i
$851$	40.8974	+	70.8363i	1.40194	+	2.42824i
$852$	−6.65619	+	11.5289i	−0.228037	+	0.394972i
$853$	−28.8764			−0.988709			−0.494355	−	0.869260i	$-0.664596\pi$
$853$	−28.8764			−0.988709			−0.494355	+	0.869260i	$0.664596\pi$
$854$		0			0
$855$	17.4799			0.597799
$856$	5.54801	−	9.60943i	0.189627	−	0.328444i
$857$	4.91988	+	8.52149i	0.168060	+	0.291089i	0.937738	−	0.347344i	$-0.112916\pi$
$857$	4.91988	+	8.52149i	0.168060	+	0.291089i	−0.769678	+	0.638433i	$0.779583\pi$
$858$	8.37997	+	14.5145i	0.286087	+	0.495518i
$859$	5.56719	−	9.64266i	0.189950	−	0.329003i	−0.755283	−	0.655398i	$-0.772501\pi$
$859$	5.56719	−	9.64266i	0.189950	−	0.329003i	0.945233	+	0.326395i	$0.105834\pi$
$860$	−9.43175			−0.321620
$861$		0			0
$862$	−24.1390			−0.822178
$863$	−11.3515	+	19.6613i	−0.386409	+	0.669280i	−0.991964	−	0.126524i	$-0.959618\pi$
$863$	−11.3515	+	19.6613i	−0.386409	+	0.669280i	0.605555	+	0.795804i	$0.292951\pi$
$864$	13.2567	+	22.9612i	0.451001	+	0.781157i
$865$	−9.14085	−	15.8324i	−0.310798	−	0.538318i
$866$	−12.3764	+	21.4366i	−0.420569	+	0.728446i
$867$	0.907578			0.0308230
$868$		0			0
$869$	9.27910			0.314772
$870$	−8.52387	+	14.7638i	−0.288986	+	0.500539i
$871$	11.6197	+	20.1260i	0.393720	+	0.681943i
$872$	−5.05114	−	8.74882i	−0.171053	−	0.296273i
$873$	−16.5037	+	28.5853i	−0.558567	+	0.967466i
$874$	19.6303			0.664005
$875$		0			0
$876$	−14.1877			−0.479358
$877$	−0.778586	+	1.34855i	−0.0262910	+	0.0455373i	−0.878872	−	0.477059i	$-0.841703\pi$
$877$	−0.778586	+	1.34855i	−0.0262910	+	0.0455373i	0.852581	+	0.522596i	$0.175036\pi$
$878$	−2.77088	−	4.79930i	−0.0935125	−	0.161968i
$879$	13.1327	+	22.7464i	0.442954	+	0.767218i
$880$	0.216059	−	0.374225i	0.00728335	−	0.0126151i
$881$	−10.3326			−0.348113			−0.174056	−	0.984736i	$-0.555687\pi$
$881$	−10.3326			−0.348113			−0.174056	+	0.984736i	$0.555687\pi$
$882$		0			0
$883$	23.6160			0.794743			0.397371	−	0.917658i	$-0.369922\pi$
$883$	23.6160			0.794743			0.397371	+	0.917658i	$0.369922\pi$
$884$	−2.70428	+	4.68395i	−0.0909548	+	0.157538i
$885$	−12.8044	−	22.1778i	−0.430414	−	0.745499i
$886$	−11.6118	−	20.1123i	−0.390107	−	0.675686i
$887$	−6.96298	+	12.0602i	−0.233794	+	0.404943i	−0.958922	−	0.283672i	$-0.908447\pi$
$887$	−6.96298	+	12.0602i	−0.233794	+	0.404943i	0.725128	+	0.688615i	$0.241781\pi$
$888$	−24.8791			−0.834889
$889$		0			0
$890$	−35.7263			−1.19755
$891$	−5.41583	+	9.38049i	−0.181437	+	0.314258i
$892$	−1.53119	−	2.65209i	−0.0512679	−	0.0887986i
$893$	−7.36368	−	12.7543i	−0.246416	−	0.426805i
$894$	−1.68965	+	2.92657i	−0.0565105	+	0.0978791i
$895$	5.32021			0.177835
$896$		0			0
$897$	33.7738			1.12767
$898$	15.1670	−	26.2700i	0.506129	−	0.876641i
$899$	12.0457	+	20.8638i	0.401748	+	0.695847i
$900$	−5.65954	−	9.80261i	−0.188651	−	0.326754i
$901$	−2.58815	+	4.48281i	−0.0862238	+	0.149344i
$902$	5.61117			0.186831
$903$		0			0
$904$	−2.74026			−0.0911398
$905$	−4.20014	+	7.27486i	−0.139617	+	0.241824i
$906$	−4.96281	−	8.59584i	−0.164878	−	0.285578i
$907$	−5.68139	−	9.84046i	−0.188648	−	0.326747i	0.756152	−	0.654396i	$-0.227077\pi$
$907$	−5.68139	−	9.84046i	−0.188648	−	0.326747i	−0.944800	+	0.327649i	$0.893744\pi$
$908$	−10.4402	+	18.0830i	−0.346472	+	0.600106i
$909$	−7.06832			−0.234442
$910$		0			0
$911$	4.75507			0.157543			0.0787713	−	0.996893i	$-0.474900\pi$
$911$	4.75507			0.157543			0.0787713	+	0.996893i	$0.474900\pi$
$912$	−0.0356828	+	0.0618044i	−0.00118157	+	0.00204655i
$913$	10.9602	+	18.9837i	0.362731	+	0.628269i
$914$	−11.6718	−	20.2161i	−0.386068	−	0.668689i
$915$	−9.18657	+	15.9116i	−0.303699	+	0.526022i
$916$	20.0766			0.663349
$917$		0			0
$918$	−4.12398			−0.136111
$919$	16.3152	−	28.2587i	0.538187	−	0.932168i	−0.460815	−	0.887496i	$-0.652443\pi$
$919$	16.3152	−	28.2587i	0.538187	−	0.932168i	0.999002	−	0.0446712i	$-0.0142240\pi$
$920$	−36.4274	−	63.0941i	−1.20098	−	2.08015i
$921$	5.25651	+	9.10454i	0.173208	+	0.300005i
$922$	0.136152	−	0.235822i	0.00448392	−	0.00776637i
$923$	52.4882			1.72767
$924$		0			0
$925$	40.9084			1.34506
$926$	−9.86046	+	17.0788i	−0.324035	+	0.561245i
$927$	−13.8229	−	23.9420i	−0.454005	−	0.786360i
$928$	−19.8741	−	34.4229i	−0.652399	−	1.12999i
$929$	23.6773	−	41.0103i	0.776827	−	1.34550i	−0.156934	−	0.987609i	$-0.550161\pi$
$929$	23.6773	−	41.0103i	0.776827	−	1.34550i	0.933762	−	0.357895i	$-0.116506\pi$
$930$	−8.27974			−0.271503
$931$		0			0
$932$	7.10382			0.232693
$933$	7.16983	−	12.4185i	0.234730	−	0.406564i
$934$	5.09695	+	8.82817i	0.166777	+	0.288867i
$935$	−7.26395	−	12.5815i	−0.237557	−	0.411460i
$936$	13.5710	−	23.5056i	0.443581	−	0.768304i
$937$	−51.6525			−1.68741			−0.843707	−	0.536803i	$-0.819632\pi$
$937$	−51.6525			−1.68741			−0.843707	+	0.536803i	$0.819632\pi$
$938$		0			0
$939$	18.3928			0.600226
$940$	−10.4040	+	18.0202i	−0.339340	+	0.587754i
$941$	27.3620	+	47.3923i	0.891975	+	1.54495i	0.837504	+	0.546431i	$0.184014\pi$
$941$	27.3620	+	47.3923i	0.891975	+	1.54495i	0.0544710	+	0.998515i	$0.482653\pi$
$942$	7.02979	+	12.1759i	0.229043	+	0.396714i
$943$	5.65367	−	9.79245i	0.184109	−	0.318886i
$944$	−0.276242			−0.00899091
$945$		0			0
$946$	10.5995			0.344619
$947$	18.4864	−	32.0194i	0.600727	−	1.04049i	−0.391984	−	0.919972i	$-0.628211\pi$
$947$	18.4864	−	32.0194i	0.600727	−	1.04049i	0.992711	−	0.120518i	$-0.0384555\pi$
$948$	1.08260	+	1.87511i	0.0351611	+	0.0609007i
$949$	27.9697	+	48.4450i	0.907936	+	1.57259i
$950$	4.90890	−	8.50246i	0.159266	−	0.275856i
$951$	5.77707			0.187334
$952$		0			0
$953$	−7.91313			−0.256331			−0.128166	−	0.991753i	$-0.540909\pi$
$953$	−7.91313			−0.256331			−0.128166	+	0.991753i	$0.540909\pi$
$954$	4.94449	−	8.56410i	0.160084	−	0.277273i
$955$	−28.6289	−	49.5867i	−0.926409	−	1.60459i
$956$	4.57509	+	7.92428i	0.147969	+	0.256290i
$957$	−15.2827	+	26.4704i	−0.494020	+	0.855667i
$958$	27.9130			0.901830
$959$		0			0
$960$	13.8247			0.446189
$961$	9.64963	−	16.7137i	0.311279	−	0.539150i
$962$	18.6717	+	32.3404i	0.602001	+	1.04270i
$963$	4.25913	+	7.37703i	0.137249	+	0.237722i
$964$	13.4642	−	23.3207i	0.433653	−	0.751109i
$965$	36.1867			1.16489
$966$		0			0
$967$	8.05906			0.259162			0.129581	−	0.991569i	$-0.458637\pi$
$967$	8.05906			0.259162			0.129581	+	0.991569i	$0.458637\pi$
$968$	16.8185	−	29.1305i	0.540568	−	0.936291i
$969$	1.19966	+	2.07788i	0.0385387	+	0.0667510i
$970$	20.2250	+	35.0308i	0.649386	+	1.12477i
$971$	0.905965	−	1.56918i	0.0290738	−	0.0503573i	−0.851122	−	0.524967i	$-0.824078\pi$
$971$	0.905965	−	1.56918i	0.0290738	−	0.0503573i	0.880196	+	0.474610i	$0.157411\pi$
$972$	−19.8544			−0.636829
$973$		0			0
$974$	−20.2047			−0.647401
$975$	8.44571	−	14.6284i	0.270479	−	0.468484i
$976$	0.0990958	+	0.171639i	0.00317198	+	0.00549403i
$977$	−7.59669	−	13.1579i	−0.243040	−	0.420957i	0.718539	−	0.695487i	$-0.244811\pi$
$977$	−7.59669	−	13.1579i	−0.243040	−	0.420957i	−0.961579	+	0.274530i	$0.911478\pi$
$978$	1.06582	−	1.84605i	0.0340811	−	0.0590301i
$979$	−64.0547			−2.04720
$980$		0			0
$981$	7.75538			0.247610
$982$	14.6237	−	25.3290i	0.466661	−	0.808280i
$983$	−5.82360	−	10.0868i	−0.185744	−	0.321718i	0.758083	−	0.652158i	$-0.226136\pi$
$983$	−5.82360	−	10.0868i	−0.185744	−	0.321718i	−0.943827	+	0.330440i	$0.892803\pi$
$984$	1.71965	+	2.97853i	0.0548205	+	0.0949519i
$985$	26.2319	−	45.4350i	0.835818	−	1.44768i
$986$	6.18257			0.196893
$987$		0			0
$988$	−14.2984			−0.454892
$989$	10.6798	−	18.4979i	0.339597	−	0.588200i
$990$	13.8773	+	24.0362i	0.441049	+	0.763920i
$991$	23.5879	+	40.8555i	0.749296	+	1.29782i	0.948161	+	0.317792i	$0.102941\pi$
$991$	23.5879	+	40.8555i	0.749296	+	1.29782i	−0.198865	+	0.980027i	$0.563725\pi$
$992$	9.65244	−	16.7185i	0.306465	−	0.530814i
$993$	22.3183			0.708249
$994$		0			0
$995$	−46.3175			−1.46836
$996$	−2.55747	+	4.42967i	−0.0810365	+	0.140359i
$997$	−19.8787	−	34.4309i	−0.629564	−	1.09044i	−0.987639	−	0.156744i	$-0.949900\pi$
$997$	−19.8787	−	34.4309i	−0.629564	−	1.09044i	0.358075	−	0.933693i	$-0.383433\pi$
$998$	−16.2503	−	28.1464i	−0.514394	−	0.890957i
$999$	22.7138	−	39.3414i	0.718633	−	1.24471i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.e.i.324.3		10
7.2	even	3		119.2.a.b.1.3	✓	5
7.3	odd	6		833.2.e.h.18.3		10
7.4	even	3	inner	833.2.e.i.18.3		10
7.5	odd	6		833.2.a.g.1.3		5
7.6	odd	2		833.2.e.h.324.3		10
21.2	odd	6		1071.2.a.m.1.3		5
21.5	even	6		7497.2.a.br.1.3		5
28.23	odd	6		1904.2.a.t.1.2		5
35.9	even	6		2975.2.a.m.1.3		5
56.37	even	6		7616.2.a.bt.1.2		5
56.51	odd	6		7616.2.a.bq.1.4		5
119.16	even	6		2023.2.a.j.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.3	✓	5	7.2	even	3
833.2.a.g.1.3		5	7.5	odd	6
833.2.e.h.18.3		10	7.3	odd	6
833.2.e.h.324.3		10	7.6	odd	2
833.2.e.i.18.3		10	7.4	even	3	inner
833.2.e.i.324.3		10	1.1	even	1	trivial
1071.2.a.m.1.3		5	21.2	odd	6
1904.2.a.t.1.2		5	28.23	odd	6
2023.2.a.j.1.3		5	119.16	even	6
2975.2.a.m.1.3		5	35.9	even	6
7497.2.a.br.1.3		5	21.5	even	6
7616.2.a.bq.1.4		5	56.51	odd	6
7616.2.a.bt.1.2		5	56.37	even	6

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

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	833.2.e.i.324.3

Level	$833$
Weight	$2$
Character	833.324
Analytic conductor	$6.652$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$