LMFDB - Embedded newform 784.2.x.k.165.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 4x^14 + 4x^13 - 13x^12 + 32x^11 - 4x^10 - 34x^9 + 121x^8 - 68x^7 - 16x^6 + 256x^5 - 208x^4 + 128x^3 + 256x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.2
Root			$0.640069 + 1.26108i$ of defining polynomial
Character	$\chi$	$=$	784.165
Dual form			784.2.x.k.765.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14477 - 0.830359i) q^{2} +(-0.261809 - 0.977085i) q^{3} +(0.621007 + 1.90114i) q^{4} +(0.317608 - 1.18533i) q^{5} +(-0.511620 + 1.33594i) q^{6} +(0.867721 - 2.69204i) q^{8} +(1.71192 - 0.988380i) q^{9} +(-1.34784 + 1.09320i) q^{10} +(4.06633 - 1.08957i) q^{11} +(1.69499 - 1.10451i) q^{12} +(-2.02017 + 2.02017i) q^{13} -1.24132 q^{15} +(-3.22870 + 2.36125i) q^{16} +(-0.132279 + 0.229115i) q^{17} +(-2.78047 - 0.290042i) q^{18} +(6.20120 + 1.66161i) q^{19} +(2.45072 - 0.132279i) q^{20} +(-5.55976 - 2.12921i) q^{22} +(1.33906 - 0.773104i) q^{23} +(-2.85753 - 0.143037i) q^{24} +(3.02600 + 1.74706i) q^{25} +(3.99009 - 0.635167i) q^{26} +(-3.55976 - 3.55976i) q^{27} +(-0.328129 + 0.328129i) q^{29} +(1.42103 + 1.03074i) q^{30} +(-3.02017 + 5.23108i) q^{31} +(5.65681 - 0.0221123i) q^{32} +(-2.12921 - 3.68789i) q^{33} +(0.341677 - 0.152445i) q^{34} +(2.94217 + 2.64082i) q^{36} +(2.43357 - 9.08220i) q^{37} +(-5.71923 - 7.05138i) q^{38} +(2.50277 + 1.44498i) q^{39} +(-2.91535 - 1.88355i) q^{40} -11.0327i q^{41} +(3.38407 + 3.38407i) q^{43} +(4.59665 + 7.05405i) q^{44} +(-0.627835 - 2.34311i) q^{45} +(-2.17487 - 0.226869i) q^{46} +(-1.56283 - 2.70690i) q^{47} +(3.15244 + 2.53652i) q^{48} +(-2.01339 - 4.51265i) q^{50} +(0.258496 + 0.0692639i) q^{51} +(-5.09516 - 2.58609i) q^{52} +(-0.588145 + 0.157593i) q^{53} +(1.11923 + 7.03099i) q^{54} -5.16599i q^{55} -6.49412i q^{57} +(0.648097 - 0.103168i) q^{58} +(6.31978 - 1.69338i) q^{59} +(-0.770868 - 2.35993i) q^{60} +(-6.64943 - 1.78171i) q^{61} +(7.80108 - 3.48057i) q^{62} +(-6.49412 - 4.67187i) q^{64} +(1.75294 + 3.03618i) q^{65} +(-0.624819 + 5.98980i) q^{66} +(1.22389 + 4.56764i) q^{67} +(-0.517726 - 0.109200i) q^{68} +(-1.10597 - 1.10597i) q^{69} +9.03885i q^{71} +(-1.17528 - 5.46620i) q^{72} +(-12.8298 - 7.40731i) q^{73} +(-10.3274 + 8.37632i) q^{74} +(0.914793 - 3.41405i) q^{75} +(0.692037 + 12.8212i) q^{76} +(-1.66525 - 3.73237i) q^{78} +(-6.29520 - 10.9036i) q^{79} +(1.77340 + 4.57702i) q^{80} +(0.418932 - 0.725612i) q^{81} +(-9.16111 + 12.6299i) q^{82} +(-0.715276 + 0.715276i) q^{83} +(0.229563 + 0.229563i) q^{85} +(-1.06400 - 6.68399i) q^{86} +(0.406517 + 0.234703i) q^{87} +(0.595277 - 11.8922i) q^{88} +(-9.51968 + 5.49619i) q^{89} +(-1.22690 + 3.20366i) q^{90} +(2.30135 + 2.06564i) q^{92} +(5.90192 + 1.58141i) q^{93} +(-0.458616 + 4.39650i) q^{94} +(3.93910 - 6.82272i) q^{95} +(-1.50261 - 5.52140i) q^{96} -14.2452 q^{97} +(5.88434 - 5.88434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8} - 12 q^{10} + 12 q^{12} - 16 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 12 q^{19} - 16 q^{20} - 8 q^{22} - 8 q^{26} + 24 q^{27} - 32 q^{29} - 20 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8 - 12 * q^10 + 12 * q^12 - 16 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 12 * q^19 - 16 * q^20 - 8 * q^22 - 8 * q^26 + 24 * q^27 - 32 * q^29 - 20 * q^30 - 16 * q^31 + 28 * q^32 + 24 * q^33 - 24 * q^34 + 48 * q^36 - 16 * q^37 + 16 * q^38 - 28 * q^40 - 64 * q^43 + 32 * q^44 + 8 * q^45 - 20 * q^46 - 24 * q^47 + 40 * q^48 - 28 * q^50 - 8 * q^51 - 32 * q^52 + 8 * q^53 + 16 * q^54 - 12 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 + 40 * q^62 - 64 * q^64 + 48 * q^65 + 16 * q^66 - 28 * q^68 + 88 * q^69 - 44 * q^72 + 4 * q^74 - 28 * q^75 - 48 * q^76 + 24 * q^78 + 24 * q^79 + 12 * q^80 - 40 * q^81 - 4 * q^82 - 80 * q^85 + 40 * q^88 - 32 * q^90 + 72 * q^92 - 16 * q^93 - 28 * q^94 - 16 * q^95 - 8 * q^96 - 64 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.14477	−	0.830359i	−0.809476	−	0.587153i
$2$	−1.14477	−	0.830359i	−0.809476	−	0.587153i
$3$	−0.261809	−	0.977085i	−0.151156	−	0.564120i	−0.999404	−	0.0345217i	$-0.989009\pi$
$3$	−0.261809	−	0.977085i	−0.151156	−	0.564120i	0.848248	−	0.529599i	$-0.177657\pi$
$4$	0.621007	+	1.90114i	0.310504	+	0.950572i
$5$	0.317608	−	1.18533i	0.142039	−	0.530095i	−0.857831	−	0.513932i	$-0.828188\pi$
$5$	0.317608	−	1.18533i	0.142039	−	0.530095i	0.999869	−	0.0161629i	$-0.00514502\pi$
$6$	−0.511620	+	1.33594i	−0.208868	+	0.545393i
$7$		0			0
$7$		0			0
$8$	0.867721	−	2.69204i	0.306786	−	0.951779i
$9$	1.71192	−	0.988380i	0.570642	−	0.329460i
$10$	−1.34784	+	1.09320i	−0.426223	+	0.345701i
$11$	4.06633	−	1.08957i	1.22604	−	0.328518i	0.413007	−	0.910728i	$-0.364479\pi$
$11$	4.06633	−	1.08957i	1.22604	−	0.328518i	0.813038	+	0.582210i	$0.197812\pi$
$12$	1.69499	−	1.10451i	0.489303	−	0.318846i
$13$	−2.02017	+	2.02017i	−0.560293	+	0.560293i	−0.929391	−	0.369098i	$-0.879667\pi$
$13$	−2.02017	+	2.02017i	−0.560293	+	0.560293i	0.369098	+	0.929391i	$0.379667\pi$
$14$		0			0
$15$	−1.24132			−0.320507
$16$	−3.22870	+	2.36125i	−0.807175	+	0.590312i
$17$	−0.132279	+	0.229115i	−0.0320825	+	0.0555685i	−0.881621	−	0.471958i	$-0.843547\pi$
$17$	−0.132279	+	0.229115i	−0.0320825	+	0.0555685i	0.849538	+	0.527527i	$0.176881\pi$
$18$	−2.78047	−	0.290042i	−0.655364	−	0.0683636i
$19$	6.20120	+	1.66161i	1.42265	+	0.381199i	0.886424	−	0.462874i	$-0.153182\pi$
$19$	6.20120	+	1.66161i	1.42265	+	0.381199i	0.536228	+	0.844073i	$0.319849\pi$
$20$	2.45072	−	0.132279i	0.547997	−	0.0295786i
$21$		0			0
$22$	−5.55976	−	2.12921i	−1.18534	−	0.453948i
$23$	1.33906	−	0.773104i	0.279212	−	0.161203i	−0.353854	−	0.935301i	$-0.615129\pi$
$23$	1.33906	−	0.773104i	0.279212	−	0.161203i	0.633067	+	0.774097i	$0.281796\pi$
$24$	−2.85753	−	0.143037i	−0.583290	−	0.0291973i
$25$	3.02600	+	1.74706i	0.605200	+	0.349412i
$26$	3.99009	−	0.635167i	0.782521	−	0.124566i
$27$	−3.55976	−	3.55976i	−0.685076	−	0.685076i
$28$		0			0
$29$	−0.328129	+	0.328129i	−0.0609320	+	0.0609320i	−0.736916	−	0.675984i	$-0.763719\pi$
$29$	−0.328129	+	0.328129i	−0.0609320	+	0.0609320i	0.675984	+	0.736916i	$0.263719\pi$
$30$	1.42103	+	1.03074i	0.259443	+	0.188187i
$31$	−3.02017	+	5.23108i	−0.542438	+	0.939530i	0.456326	+	0.889813i	$0.349165\pi$
$31$	−3.02017	+	5.23108i	−0.542438	+	0.939530i	−0.998763	+	0.0497168i	$0.984168\pi$
$32$	5.65681	−	0.0221123i	0.999992	−	0.00390894i
$33$	−2.12921	−	3.68789i	−0.370647	−	0.641980i
$34$	0.341677	−	0.152445i	0.0585972	−	0.0261440i
$35$		0			0
$36$	2.94217	+	2.64082i	0.490362	+	0.440137i
$37$	2.43357	−	9.08220i	0.400076	−	1.49310i	−0.412883	−	0.910784i	$-0.635478\pi$
$37$	2.43357	−	9.08220i	0.400076	−	1.49310i	0.812959	−	0.582320i	$-0.197855\pi$
$38$	−5.71923	−	7.05138i	−0.927782	−	1.14389i
$39$	2.50277	+	1.44498i	0.400764	+	0.231381i
$40$	−2.91535	−	1.88355i	−0.460958	−	0.297815i
$41$		−	11.0327i		−	1.72302i	−0.507741	−	0.861510i	$-0.669519\pi$
$41$		−	11.0327i		−	1.72302i	0.507741	−	0.861510i	$-0.330481\pi$
$42$		0			0
$43$	3.38407	+	3.38407i	0.516066	+	0.516066i	0.916379	−	0.400312i	$-0.131098\pi$
$43$	3.38407	+	3.38407i	0.516066	+	0.516066i	−0.400312	+	0.916379i	$0.631098\pi$
$44$	4.59665	+	7.05405i	0.692971	+	1.06344i
$45$	−0.627835	−	2.34311i	−0.0935921	−	0.349290i
$46$	−2.17487	−	0.226869i	−0.320667	−	0.0334500i
$47$	−1.56283	−	2.70690i	−0.227962	−	0.394842i	0.729242	−	0.684256i	$-0.239873\pi$
$47$	−1.56283	−	2.70690i	−0.227962	−	0.394842i	−0.957204	+	0.289414i	$0.906540\pi$
$48$	3.15244	+	2.53652i	0.455016	+	0.366115i
$49$		0			0
$50$	−2.01339	−	4.51265i	−0.284736	−	0.638185i
$51$	0.258496	+	0.0692639i	0.0361967	+	0.00969889i
$52$	−5.09516	−	2.58609i	−0.706572	−	0.358626i
$53$	−0.588145	+	0.157593i	−0.0807879	+	0.0216471i	−0.298987	−	0.954257i	$-0.596649\pi$
$53$	−0.588145	+	0.157593i	−0.0807879	+	0.0216471i	0.218199	+	0.975904i	$0.429982\pi$
$54$	1.11923	+	7.03099i	0.152309	+	0.956796i
$55$		−	5.16599i		−	0.696582i
$56$		0			0
$57$		−	6.49412i		−	0.860167i
$58$	0.648097	−	0.103168i	0.0850994	−	0.0135466i
$59$	6.31978	−	1.69338i	0.822765	−	0.220459i	0.177210	−	0.984173i	$-0.443293\pi$
$59$	6.31978	−	1.69338i	0.822765	−	0.220459i	0.645555	+	0.763714i	$0.276626\pi$
$60$	−0.770868	−	2.35993i	−0.0995187	−	0.304665i
$61$	−6.64943	−	1.78171i	−0.851372	−	0.228125i	−0.193356	−	0.981129i	$-0.561937\pi$
$61$	−6.64943	−	1.78171i	−0.851372	−	0.228125i	−0.658016	+	0.753004i	$0.728604\pi$
$62$	7.80108	−	3.48057i	0.990738	−	0.442033i
$63$		0			0
$64$	−6.49412	−	4.67187i	−0.811765	−	0.583984i
$65$	1.75294	+	3.03618i	0.217425	+	0.376592i
$66$	−0.624819	+	5.98980i	−0.0769100	+	0.737294i
$67$	1.22389	+	4.56764i	0.149523	+	0.558026i	0.999512	+	0.0312266i	$0.00994134\pi$
$67$	1.22389	+	4.56764i	0.149523	+	0.558026i	−0.849990	+	0.526799i	$0.823392\pi$
$68$	−0.517726	−	0.109200i	−0.0627835	−	0.0132425i
$69$	−1.10597	−	1.10597i	−0.133143	−	0.133143i
$70$		0			0
$71$			9.03885i			1.07271i	0.843991	+	0.536357i	$0.180200\pi$
$71$			9.03885i			1.07271i	−0.843991	+	0.536357i	$0.819800\pi$
$72$	−1.17528	−	5.46620i	−0.138508	−	0.644198i
$73$	−12.8298	−	7.40731i	−1.50162	−	0.866960i	−0.999998	−	0.00187294i	$-0.999404\pi$
$73$	−12.8298	−	7.40731i	−1.50162	−	0.866960i	−0.501621	−	0.865087i	$-0.667263\pi$
$74$	−10.3274	+	8.37632i	−1.20053	+	0.973727i
$75$	0.914793	−	3.41405i	0.105631	−	0.394221i
$76$	0.692037	+	12.8212i	0.0793820	+	1.47070i
$77$		0			0
$78$	−1.66525	−	3.73237i	−0.188553	−	0.422607i
$79$	−6.29520	−	10.9036i	−0.708265	−	1.22675i	−0.965500	−	0.260402i	$-0.916145\pi$
$79$	−6.29520	−	10.9036i	−0.708265	−	1.22675i	0.257235	−	0.966349i	$-0.417189\pi$
$80$	1.77340	+	4.57702i	0.198272	+	0.511726i
$81$	0.418932	−	0.725612i	0.0465480	−	0.0806235i
$82$	−9.16111	+	12.6299i	−1.01168	+	1.39474i
$83$	−0.715276	+	0.715276i	−0.0785117	+	0.0785117i	−0.745272	−	0.666760i	$-0.767680\pi$
$83$	−0.715276	+	0.715276i	−0.0785117	+	0.0785117i	0.666760	+	0.745272i	$0.267680\pi$
$84$		0			0
$85$	0.229563	+	0.229563i	0.0248996	+	0.0248996i
$86$	−1.06400	−	6.68399i	−0.114734	−	0.720753i
$87$	0.406517	+	0.234703i	0.0435832	+	0.0251628i
$88$	0.595277	−	11.8922i	0.0634567	−	1.26771i
$89$	−9.51968	+	5.49619i	−1.00908	+	0.582595i	−0.910923	−	0.412576i	$-0.864629\pi$
$89$	−9.51968	+	5.49619i	−1.00908	+	0.582595i	−0.0981604	+	0.995171i	$0.531296\pi$
$90$	−1.22690	+	3.20366i	−0.129326	+	0.337695i
$91$		0			0
$92$	2.30135	+	2.06564i	0.239932	+	0.215357i
$93$	5.90192	+	1.58141i	0.612000	+	0.163985i
$94$	−0.458616	+	4.39650i	−0.0473026	+	0.453464i
$95$	3.93910	−	6.82272i	0.404143	−	0.699996i
$96$	−1.50261	−	5.52140i	−0.153360	−	0.563525i
$97$	−14.2452			−1.44638			−0.723189	−	0.690650i	$-0.757325\pi$
$97$	−14.2452			−1.44638			−0.723189	+	0.690650i	$0.757325\pi$
$98$		0			0
$99$	5.88434	−	5.88434i	0.591399	−	0.591399i
$100$	−1.44225	+	6.83780i	−0.144225	+	0.683780i
$101$	14.3841	−	3.85421i	1.43127	−	0.383508i	0.541804	−	0.840505i	$-0.317741\pi$
$101$	14.3841	−	3.85421i	1.43127	−	0.383508i	0.889469	+	0.456996i	$0.151075\pi$
$102$	−0.238406	−	0.293936i	−0.0236057	−	0.0291040i
$103$	11.2464	−	6.49311i	1.10814	−	0.639785i	0.169794	−	0.985480i	$-0.445690\pi$
$103$	11.2464	−	6.49311i	1.10814	−	0.639785i	0.938347	+	0.345694i	$0.112357\pi$
$104$	3.68542	+	7.19130i	0.361385	+	0.705165i
$105$		0			0
$106$	0.804151	+	0.307963i	0.0781060	+	0.0299121i
$107$	−0.454354	+	1.69567i	−0.0439241	+	0.163927i	−0.984404	−	0.175922i	$-0.943709\pi$
$107$	−0.454354	+	1.69567i	−0.0439241	+	0.163927i	0.940480	+	0.339849i	$0.110376\pi$
$108$	4.55698	−	8.97825i	0.438495	−	0.863932i
$109$	−4.00927	−	14.9628i	−0.384018	−	1.43318i	−0.839709	−	0.543037i	$-0.817274\pi$
$109$	−4.00927	−	14.9628i	−0.384018	−	1.43318i	0.455691	−	0.890138i	$-0.349392\pi$
$110$	−4.28963	+	5.91389i	−0.409000	+	0.563867i
$111$	−9.51121			−0.902764
$112$		0			0
$113$	7.63302			0.718054			0.359027	−	0.933327i	$-0.383109\pi$
$113$	7.63302			0.718054			0.359027	+	0.933327i	$0.383109\pi$
$114$	−5.39245	+	7.43429i	−0.505050	+	0.696285i
$115$	−0.491088	−	1.83277i	−0.0457942	−	0.170906i
$116$	−0.827590	−	0.420050i	−0.0768398	−	0.0390006i
$117$	−1.46168	+	5.45506i	−0.135132	+	0.504321i
$118$	−8.64082	−	3.30915i	−0.795452	−	0.304632i
$119$		0			0
$120$	−1.07712	+	3.34168i	−0.0983270	+	0.305052i
$121$	5.82160	−	3.36110i	0.529237	−	0.305555i
$122$	6.13262	+	7.56107i	0.555222	+	0.684547i
$123$	−10.7799	+	2.88846i	−0.971990	+	0.260444i
$124$	−11.8206	−	2.49323i	−1.06152	−	0.223899i
$125$	7.37052	−	7.37052i	0.659240	−	0.659240i
$126$		0			0
$127$	−10.7393			−0.952959			−0.476479	−	0.879186i	$-0.658087\pi$
$127$	−10.7393			−0.952959			−0.476479	+	0.879186i	$0.658087\pi$
$128$	3.55496	+	10.7407i	0.314217	+	0.949351i
$129$	2.42055	−	4.19251i	0.213117	−	0.369130i
$130$	0.514403	−	4.93130i	0.0451162	−	0.432504i
$131$	17.6038	+	4.71692i	1.53805	+	0.412120i	0.925636	−	0.378416i	$-0.123531\pi$
$131$	17.6038	+	4.71692i	1.53805	+	0.412120i	0.612416	+	0.790536i	$0.290198\pi$
$132$	5.68896	−	6.33813i	0.495161	−	0.551664i
$133$		0			0
$134$	2.39170	−	6.24518i	0.206611	−	0.539501i
$135$	−5.35009	+	3.08887i	−0.460462	+	0.265848i
$136$	0.502003	+	0.554908i	0.0430464	+	0.0475830i
$137$	−6.35987	−	3.67187i	−0.543360	−	0.313709i	0.203079	−	0.979162i	$-0.434905\pi$
$137$	−6.35987	−	3.67187i	−0.543360	−	0.313709i	−0.746440	+	0.665453i	$0.768238\pi$
$138$	0.347730	+	2.18443i	0.0296008	+	0.185951i
$139$	8.36184	+	8.36184i	0.709242	+	0.709242i	0.966376	−	0.257134i	$-0.0827781\pi$
$139$	8.36184	+	8.36184i	0.709242	+	0.709242i	−0.257134	+	0.966376i	$0.582778\pi$
$140$		0			0
$141$	−2.23571	+	2.23571i	−0.188281	+	0.188281i
$142$	7.50549	−	10.3474i	0.629847	−	0.868337i
$143$	−6.01355	+	10.4158i	−0.502878	+	0.871011i
$144$	−3.19348	+	7.23346i	−0.266123	+	0.602789i
$145$	0.284724	+	0.493157i	0.0236450	+	0.0409544i
$146$	8.53652	+	19.1331i	0.706487	+	1.58346i
$147$		0			0
$148$	18.7778	−	1.01355i	1.54353	−	0.0833132i
$149$	−4.71375	+	17.5919i	−0.386165	+	1.44119i	0.450157	+	0.892949i	$0.351368\pi$
$149$	−4.71375	+	17.5919i	−0.386165	+	1.44119i	−0.836322	+	0.548239i	$0.815299\pi$
$150$	−3.88212	+	3.14871i	−0.316974	+	0.257091i
$151$	11.2731	+	6.50855i	0.917394	+	0.529658i	0.882803	−	0.469744i	$-0.155654\pi$
$151$	11.2731	+	6.50855i	0.917394	+	0.529658i	0.0345916	+	0.999402i	$0.488987\pi$
$152$	9.85401	−	15.2520i	0.799266	−	1.23710i
$153$			0.522969i			0.0422796i
$154$		0			0
$155$	5.24132	+	5.24132i	0.420993	+	0.420993i
$156$	−1.19287	+	5.65547i	−0.0955059	+	0.452800i
$157$	5.36485	+	20.0219i	0.428162	+	1.59792i	0.756921	+	0.653507i	$0.226703\pi$
$157$	5.36485	+	20.0219i	0.428162	+	1.59792i	−0.328759	+	0.944414i	$0.606630\pi$
$158$	−1.84734	+	17.7094i	−0.146966	+	1.40889i
$159$	0.307963	+	0.533408i	0.0244231	+	0.0423020i
$160$	1.77044	−	6.71220i	0.139965	−	0.530646i
$161$		0			0
$162$	−1.08210	+	0.482796i	−0.0850178	+	0.0379321i
$163$	−6.07559	−	1.62795i	−0.475877	−	0.127511i	0.0129051	−	0.999917i	$-0.495892\pi$
$163$	−6.07559	−	1.62795i	−0.475877	−	0.127511i	−0.488782	+	0.872406i	$0.662559\pi$
$164$	20.9748	−	6.85139i	1.63785	−	0.535004i
$165$	−5.04762	+	1.35250i	−0.392956	+	0.105292i
$166$	1.41276	−	0.224892i	0.109652	−	0.0174550i
$167$			5.45765i			0.422326i	0.977451	+	0.211163i	$0.0677250\pi$
$167$			5.45765i			0.422326i	−0.977451	+	0.211163i	$0.932275\pi$
$168$		0			0
$169$			4.83786i			0.372143i
$170$	−0.0721777	−	0.453417i	−0.00553577	−	0.0347755i
$171$	12.2583	−	3.28460i	0.937414	−	0.251179i
$172$	−4.33208	+	8.53515i	−0.330318	+	0.650799i
$173$	−15.8764	−	4.25406i	−1.20706	−	0.323430i	−0.401452	−	0.915880i	$-0.631494\pi$
$173$	−15.8764	−	4.25406i	−1.20706	−	0.323430i	−0.805607	+	0.592450i	$0.798161\pi$
$174$	−0.270482	−	0.606236i	−0.0205052	−	0.0459586i
$175$		0			0
$176$	−10.5562	+	13.1195i	−0.795705	+	0.988921i
$177$	−3.30915	−	5.73162i	−0.248731	−	0.430815i
$178$	15.4617	+	1.61287i	1.15890	+	0.120889i
$179$	4.73701	+	17.6788i	0.354061	+	1.32137i	0.881662	+	0.471882i	$0.156425\pi$
$179$	4.73701	+	17.6788i	0.354061	+	1.32137i	−0.527601	+	0.849492i	$0.676908\pi$
$180$	4.06470	−	2.64869i	0.302965	−	0.197422i
$181$	1.39069	+	1.39069i	0.103369	+	0.103369i	0.756900	−	0.653531i	$-0.226713\pi$
$181$	1.39069	+	1.39069i	0.103369	+	0.103369i	−0.653531	+	0.756900i	$0.726713\pi$
$182$		0			0
$183$			6.96353i			0.514759i
$184$	−0.919299	−	4.27563i	−0.0677716	−	0.315203i
$185$	−9.99247	−	5.76916i	−0.734661	−	0.424157i
$186$	−5.44321	−	6.71107i	−0.399116	−	0.492080i
$187$	−0.288255	+	1.07578i	−0.0210793	+	0.0786691i
$188$	4.17568	−	4.65217i	0.304543	−	0.339295i
$189$		0			0
$190$	−10.1747	+	4.53959i	−0.738149	+	0.329337i
$191$	1.73544	+	3.00587i	0.125572	+	0.217497i	0.921956	−	0.387294i	$-0.126590\pi$
$191$	1.73544	+	3.00587i	0.125572	+	0.217497i	−0.796384	+	0.604791i	$0.793257\pi$
$192$	−2.86460	+	7.56845i	−0.206734	+	0.546206i
$193$	3.79327	−	6.57014i	0.273046	−	0.472929i	−0.696595	−	0.717465i	$-0.745302\pi$
$193$	3.79327	−	6.57014i	0.273046	−	0.472929i	0.969640	+	0.244536i	$0.0786357\pi$
$194$	16.3075	+	11.8286i	1.17081	+	0.849245i
$195$	2.50767	−	2.50767i	0.179578	−	0.179578i
$196$		0			0
$197$	7.82786	+	7.82786i	0.557712	+	0.557712i	0.928655	−	0.370944i	$-0.120966\pi$
$197$	7.82786	+	7.82786i	0.557712	+	0.557712i	−0.370944	+	0.928655i	$0.620966\pi$
$198$	−11.6224	+	1.85011i	−0.825965	+	0.131482i
$199$	17.0344	+	9.83479i	1.20753	+	0.697170i	0.962220	−	0.272274i	$-0.0877757\pi$
$199$	17.0344	+	9.83479i	1.20753	+	0.697170i	0.245314	+	0.969444i	$0.421109\pi$
$200$	7.32887	−	6.63014i	0.518230	−	0.468822i
$201$	4.14254	−	2.39170i	0.292192	−	0.168697i
$202$	−19.6669	−	7.53178i	−1.38376	−	0.529935i
$203$		0			0
$204$	0.0288475	+	0.534452i	0.00201973	+	0.0374192i
$205$	−13.0774	−	3.50407i	−0.913364	−	0.244735i
$206$	−18.2662	−	1.90542i	−1.27267	−	0.132757i
$207$	1.52824	−	2.64699i	0.106220	−	0.183979i
$208$	1.75239	−	11.2926i	0.121507	−	0.783002i
$209$	27.0266			1.86947
$210$		0			0
$211$	−1.13890	+	1.13890i	−0.0784048	+	0.0784048i	−0.745222	−	0.666817i	$-0.767656\pi$
$211$	−1.13890	+	1.13890i	−0.0784048	+	0.0784048i	0.666817	+	0.745222i	$0.267656\pi$
$212$	−0.664849	−	1.02028i	−0.0456620	−	0.0700732i
$213$	8.83173	−	2.36645i	0.605140	−	0.162147i
$214$	1.92815	−	1.56388i	0.131806	−	0.106905i
$215$	5.08605	−	2.93643i	0.346865	−	0.200263i
$216$	−12.6719	+	6.49412i	−0.862212	+	0.441869i
$217$		0			0
$218$	−7.83479	+	20.4581i	−0.530639	+	1.38560i
$219$	−3.87860	+	14.4751i	−0.262092	+	0.978140i
$220$	9.82130	−	3.20812i	0.662152	−	0.216291i
$221$	−0.195623	−	0.730076i	−0.0131590	−	0.0491102i
$222$	10.8882	+	7.89772i	0.730766	+	0.530060i
$223$	−8.02710			−0.537534			−0.268767	−	0.963205i	$-0.586616\pi$
$223$	−8.02710			−0.537534			−0.268767	+	0.963205i	$0.586616\pi$
$224$		0			0
$225$	6.90704			0.460469
$226$	−8.73807	−	6.33815i	−0.581248	−	0.421607i
$227$	−1.30829	−	4.88260i	−0.0868342	−	0.324070i	0.908821	−	0.417186i	$-0.136984\pi$
$227$	−1.30829	−	4.88260i	−0.0868342	−	0.324070i	−0.995655	+	0.0931165i	$0.970317\pi$
$228$	12.3463	−	4.03290i	0.817651	−	0.267085i
$229$	0.232826	−	0.868918i	0.0153856	−	0.0574197i	−0.957806	−	0.287415i	$-0.907204\pi$
$229$	0.232826	−	0.868918i	0.0153856	−	0.0574197i	0.973192	+	0.229995i	$0.0738709\pi$
$230$	−0.959669	+	2.50588i	−0.0632787	+	0.165233i
$231$		0			0
$232$	0.598610	+	1.16806i	0.0393007	+	0.0766868i
$233$	21.2724	−	12.2816i	1.39360	−	0.804598i	0.399892	−	0.916562i	$-0.369048\pi$
$233$	21.2724	−	12.2816i	1.39360	−	0.804598i	0.993712	+	0.111965i	$0.0357144\pi$
$234$	6.20295	−	5.03109i	0.405500	−	0.328892i
$235$	−3.70494	+	0.992735i	−0.241683	+	0.0647589i
$236$	7.14399	+	10.9632i	0.465034	+	0.713645i
$237$	−9.00561	+	9.00561i	−0.584977	+	0.584977i
$238$		0			0
$239$	−29.3026			−1.89543			−0.947714	−	0.319122i	$-0.896612\pi$
$239$	−29.3026			−1.89543			−0.947714	+	0.319122i	$0.896612\pi$
$240$	4.00785	−	2.93106i	0.258705	−	0.189199i
$241$	−3.97014	+	6.87649i	−0.255739	+	0.442954i	−0.965096	−	0.261896i	$-0.915652\pi$
$241$	−3.97014	+	6.87649i	−0.255739	+	0.442954i	0.709357	+	0.704850i	$0.248986\pi$
$242$	−9.45533	−	0.986322i	−0.607812	−	0.0634032i
$243$	−15.4068	−	4.12825i	−0.988348	−	0.264827i
$244$	−0.742058	−	13.7480i	−0.0475054	−	0.880124i
$245$		0			0
$246$	14.7390	+	5.64455i	0.939723	+	0.359883i
$247$	−15.8842	+	9.17073i	−1.01069	+	0.583519i
$248$	11.4616	+	12.6695i	0.727812	+	0.804515i
$249$	0.886151	+	0.511620i	0.0561576	+	0.0324226i
$250$	−14.5578	+	2.31739i	−0.920713	+	0.146565i
$251$	6.93336	+	6.93336i	0.437630	+	0.437630i	0.891214	−	0.453584i	$-0.149855\pi$
$251$	6.93336	+	6.93336i	0.437630	+	0.437630i	−0.453584	+	0.891214i	$0.649855\pi$
$252$		0			0
$253$	4.60269	−	4.60269i	0.289369	−	0.289369i
$254$	12.2941	+	8.91748i	0.771397	+	0.559532i
$255$	0.164201	−	0.284404i	0.0102827	−	0.0178101i
$256$	4.84900	−	15.2475i	0.303063	−	0.952971i
$257$	4.15244	+	7.19225i	0.259022	+	0.448640i	0.965980	−	0.258616i	$-0.0832663\pi$
$257$	4.15244	+	7.19225i	0.259022	+	0.448640i	−0.706958	+	0.707256i	$0.749933\pi$
$258$	−6.25226	+	2.78955i	−0.389249	+	0.173670i
$259$		0			0
$260$	−4.68363	+	5.21808i	−0.290466	+	0.323612i
$261$	−0.237416	+	0.886048i	−0.0146957	+	0.0548450i
$262$	−16.2356	−	20.0173i	−1.00304	−	1.23667i
$263$	−11.9975	−	6.92674i	−0.739795	−	0.427121i	0.0821996	−	0.996616i	$-0.473806\pi$
$263$	−11.9975	−	6.92674i	−0.739795	−	0.427121i	−0.821995	+	0.569495i	$0.807139\pi$
$264$	−11.7755	+	2.53184i	−0.724732	+	0.155824i
$265$			0.747198i			0.0459000i
$266$		0			0
$267$	7.86258	+	7.86258i	0.481182	+	0.481182i
$268$	−7.92369	+	5.16334i	−0.484016	+	0.315401i
$269$	0.470782	+	1.75698i	0.0287041	+	0.107125i	0.978792	−	0.204858i	$-0.0656733\pi$
$269$	0.470782	+	1.75698i	0.0287041	+	0.107125i	−0.950088	+	0.311983i	$0.899007\pi$
$270$	8.68951	+	0.906436i	0.528827	+	0.0551640i
$271$	8.18515	+	14.1771i	0.497212	+	0.861197i	0.999995	−	0.00321582i	$-0.00102363\pi$
$271$	8.18515	+	14.1771i	0.497212	+	0.861197i	−0.502782	+	0.864413i	$0.667690\pi$
$272$	−0.113906	−	1.05209i	−0.00690658	−	0.0637921i
$273$		0			0
$274$	4.23163	+	9.48443i	0.255642	+	0.572975i
$275$	14.2083	+	3.80709i	0.856790	+	0.229576i
$276$	1.41579	−	2.78941i	0.0852204	−	0.167903i
$277$	−11.2949	+	3.02645i	−0.678643	+	0.181842i	−0.581645	−	0.813443i	$-0.697591\pi$
$277$	−11.2949	+	3.02645i	−0.678643	+	0.181842i	−0.0969979	+	0.995285i	$0.530924\pi$
$278$	−2.62907	−	16.5157i	−0.157681	−	0.990548i
$279$			11.9403i			0.714846i
$280$		0			0
$281$		−	30.2126i		−	1.80233i	−0.433476	−	0.901165i	$-0.642713\pi$
$281$		−	30.2126i		−	1.80233i	0.433476	−	0.901165i	$-0.357287\pi$
$282$	4.41582	−	0.702937i	0.262958	−	0.0418593i
$283$	16.1296	−	4.32192i	0.958806	−	0.256911i	0.254711	−	0.967017i	$-0.418020\pi$
$283$	16.1296	−	4.32192i	0.958806	−	0.256911i	0.704095	+	0.710106i	$0.251353\pi$
$284$	−17.1842	+	5.61319i	−1.01969	+	0.333082i
$285$	−7.69767	−	2.06258i	−0.455970	−	0.122177i
$286$	15.5330	−	6.93028i	0.918484	−	0.409796i
$287$		0			0
$288$	9.66218	−	5.62894i	0.569349	−	0.331688i
$289$	8.46500	+	14.6618i	0.497941	+	0.862460i
$290$	0.0835528	−	0.800975i	0.00490639	−	0.0470349i
$291$	3.72952	+	13.9188i	0.218628	+	0.815932i
$292$	6.11494	−	28.9914i	0.357850	−	1.69659i
$293$	15.3849	+	15.3849i	0.898793	+	0.898793i	0.995329	−	0.0965365i	$-0.0307765\pi$
$293$	15.3849	+	15.3849i	0.898793	+	0.898793i	−0.0965365	+	0.995329i	$0.530776\pi$
$294$		0			0
$295$		−	8.02885i		−	0.467458i
$296$	−22.3380	−	14.4321i	−1.29837	−	0.838847i
$297$	−18.3538	−	10.5965i	−1.06499	−	0.614874i
$298$	20.0038	−	16.2247i	1.15879	−	0.939870i
$299$	−1.14332	+	4.26691i	−0.0661197	+	0.246762i
$300$	7.05870	−	0.380999i	0.407534	−	0.0219970i
$301$		0			0
$302$	−7.50074	−	16.8116i	−0.431619	−	0.967396i
$303$	−7.53178	−	13.0454i	−0.432690	−	0.749441i
$304$	−23.9453	+	9.27775i	−1.37336	+	0.532115i
$305$	−4.22382	+	7.31587i	−0.241855	+	0.418906i
$306$	0.434252	−	0.598681i	0.0248246	−	0.0342243i
$307$	−8.15291	+	8.15291i	−0.465311	+	0.465311i	−0.900392	−	0.435080i	$-0.856720\pi$
$307$	−8.15291	+	8.15291i	−0.465311	+	0.465311i	0.435080	+	0.900392i	$0.356720\pi$
$308$		0			0
$309$	−9.28874	−	9.28874i	−0.528418	−	0.528418i
$310$	−1.64794	−	10.3523i	−0.0935967	−	0.587971i
$311$	−26.9396	−	15.5536i	−1.52761	−	0.881964i	−0.999462	−	0.0328102i	$-0.989554\pi$
$311$	−26.9396	−	15.5536i	−1.52761	−	0.881964i	−0.528145	−	0.849154i	$-0.677112\pi$
$312$	6.06163	−	5.48372i	0.343172	−	0.310454i
$313$	2.75384	−	1.58993i	0.155656	−	0.0898681i	−0.420149	−	0.907455i	$-0.638022\pi$
$313$	2.75384	−	1.58993i	0.155656	−	0.0898681i	0.575805	+	0.817587i	$0.304689\pi$
$314$	10.4838	−	27.3753i	0.591637	−	1.54488i
$315$		0			0
$316$	16.8200	−	18.7393i	0.946197	−	1.05417i
$317$	−2.14391	−	0.574458i	−0.120414	−	0.0322648i	0.198109	−	0.980180i	$-0.436520\pi$
$317$	−2.14391	−	0.574458i	−0.120414	−	0.0322648i	−0.318523	+	0.947915i	$0.603187\pi$
$318$	0.0903725	−	0.866351i	0.00506784	−	0.0485826i
$319$	−0.976761	+	1.69180i	−0.0546881	+	0.0947226i
$320$	−7.60029	+	6.21384i	−0.424869	+	0.347364i
$321$	1.77577			0.0991139
$322$		0			0
$323$	−1.20099	+	1.20099i	−0.0668248	+	0.0668248i
$324$	1.63965	+	0.345840i	0.0910918	+	0.0192134i
$325$	−9.64237	+	2.58366i	−0.534862	+	0.143316i
$326$	5.60339	+	6.90856i	0.310343	+	0.382630i
$327$	−13.5703	+	7.83479i	−0.750437	+	0.433265i
$328$	−29.7004	−	9.57331i	−1.63993	−	0.528597i
$329$		0			0
$330$	6.90143	+	2.64302i	0.379911	+	0.145494i
$331$	0.717289	−	2.67696i	0.0394258	−	0.147139i	−0.943407	−	0.331637i	$-0.892399\pi$
$331$	0.717289	−	2.67696i	0.0394258	−	0.147139i	0.982833	+	0.184498i	$0.0590658\pi$
$332$	−1.80403	−	0.915651i	−0.0990093	−	0.0502529i
$333$	−4.81058	−	17.9533i	−0.263618	−	0.983837i
$334$	4.53181	−	6.24777i	0.247970	−	0.341863i
$335$	5.80287			0.317045
$336$		0			0
$337$	−28.7067			−1.56375			−0.781876	−	0.623434i	$-0.785737\pi$
$337$	−28.7067			−1.56375			−0.781876	+	0.623434i	$0.785737\pi$
$338$	4.01717	−	5.53825i	0.218505	−	0.301241i
$339$	−1.99839	−	7.45811i	−0.108538	−	0.405069i
$340$	−0.293872	+	0.578993i	−0.0159375	+	0.0314003i
$341$	−6.58136	+	24.5620i	−0.356401	+	1.33011i
$342$	−16.7603	−	6.41866i	−0.906295	−	0.347082i
$343$		0			0
$344$	12.0465	−	6.17362i	0.649503	−	0.332859i
$345$	−1.66220	+	0.959669i	−0.0894896	+	0.0516669i
$346$	14.6424	+	18.0530i	0.787183	+	0.970537i
$347$	−6.03619	+	1.61739i	−0.324039	+	0.0868261i	−0.417172	−	0.908828i	$-0.636979\pi$
$347$	−6.03619	+	1.61739i	−0.324039	+	0.0868261i	0.0931324	+	0.995654i	$0.470312\pi$
$348$	−0.193754	+	0.918599i	−0.0103863	+	0.0492421i
$349$	−7.46427	+	7.46427i	−0.399553	+	0.399553i	−0.878075	−	0.478522i	$-0.841173\pi$
$349$	−7.46427	+	7.46427i	−0.399553	+	0.399553i	0.478522	+	0.878075i	$0.341173\pi$
$350$		0			0
$351$	14.3826			0.767686
$352$	22.9784	−	6.25341i	1.22475	−	0.333308i
$353$	3.35343	−	5.80832i	0.178485	−	0.309146i	−0.762877	−	0.646544i	$-0.776214\pi$
$353$	3.35343	−	5.80832i	0.178485	−	0.309146i	0.941362	+	0.337399i	$0.109547\pi$
$354$	−0.971077	+	9.30919i	−0.0516122	+	0.494778i
$355$	10.7140	+	2.87081i	0.568641	+	0.152367i
$356$	−16.3608	−	14.6851i	−0.867122	−	0.778309i
$357$		0			0
$358$	9.25693	−	24.1716i	0.489244	−	1.27751i
$359$	10.1793	−	5.87700i	0.537241	−	0.310176i	−0.206719	−	0.978400i	$-0.566279\pi$
$359$	10.1793	−	5.87700i	0.537241	−	0.310176i	0.743960	+	0.668224i	$0.232945\pi$
$360$	−6.85252	−	0.343012i	−0.361160	−	0.0180783i
$361$	19.2394	+	11.1079i	1.01260	+	0.584626i
$362$	−0.437251	−	2.74680i	−0.0229814	−	0.144368i
$363$	−4.80823	−	4.80823i	−0.252367	−	0.252367i
$364$		0			0
$365$	−12.8550	+	12.8550i	−0.672859	+	0.672859i
$366$	5.78223	−	7.97165i	0.302242	−	0.416685i
$367$	−17.2352	+	29.8522i	−0.899669	+	1.55827i	−0.0717506	+	0.997423i	$0.522859\pi$
$367$	−17.2352	+	29.8522i	−0.899669	+	1.55827i	−0.827918	+	0.560849i	$0.810475\pi$
$368$	−2.49792	+	5.65797i	−0.130213	+	0.294942i
$369$	−10.9045	−	18.8872i	−0.567666	−	0.983226i
$370$	6.64863	+	14.9017i	0.345646	+	0.774703i
$371$		0			0
$372$	0.658638	+	12.2025i	0.0341488	+	0.632668i
$373$	−3.22012	+	12.0177i	−0.166732	+	0.622251i	0.831081	+	0.556151i	$0.187722\pi$
$373$	−3.22012	+	12.0177i	−0.166732	+	0.622251i	−0.997813	+	0.0660999i	$0.978944\pi$
$374$	1.22327	−	0.992172i	0.0632540	−	0.0513040i
$375$	−9.13130	−	5.27196i	−0.471538	−	0.272243i
$376$	−8.64318	+	1.85836i	−0.445738	+	0.0958378i
$377$		−	1.32575i		−	0.0682795i
$378$		0			0
$379$	−0.171601	−	0.171601i	−0.00881456	−	0.00881456i	0.702686	−	0.711500i	$-0.251984\pi$
$379$	−0.171601	−	0.171601i	−0.00881456	−	0.00881456i	−0.711500	+	0.702686i	$0.751984\pi$
$380$	15.4172	+	3.25184i	0.790885	+	0.166816i
$381$	2.81165	+	10.4932i	0.144045	+	0.537583i
$382$	0.509269	−	4.88208i	0.0260564	−	0.249789i
$383$	−10.8580	−	18.8067i	−0.554819	−	0.960975i	−0.997918	−	0.0645023i	$-0.979454\pi$
$383$	−10.8580	−	18.8067i	−0.554819	−	0.960975i	0.443098	−	0.896473i	$-0.353879\pi$
$384$	9.56384	−	6.28551i	0.488053	−	0.320756i
$385$		0			0
$386$	−9.79800	+	4.37153i	−0.498705	+	0.222505i
$387$	9.13803	+	2.44853i	0.464512	+	0.124466i
$388$	−8.84636	−	27.0821i	−0.449106	−	1.37489i
$389$	−15.4798	+	4.14779i	−0.784856	+	0.210302i	−0.628925	−	0.777466i	$-0.716505\pi$
$389$	−15.4798	+	4.14779i	−0.784856	+	0.210302i	−0.155931	+	0.987768i	$0.549838\pi$
$390$	−4.95298	+	0.788445i	−0.250804	+	0.0399244i
$391$			0.409063i			0.0206872i
$392$		0			0
$393$		−	18.4353i		−	0.929940i
$394$	−2.46118	−	15.4611i	−0.123993	−	0.778916i
$395$	−14.9238	+	3.99881i	−0.750896	+	0.201202i
$396$	14.8412	+	7.53277i	0.745799	+	0.378536i
$397$	20.1457	+	5.39802i	1.01108	+	0.270919i	0.726082	−	0.687608i	$-0.241339\pi$
$397$	20.1457	+	5.39802i	1.01108	+	0.270919i	0.285001	+	0.958527i	$0.408006\pi$
$398$	−11.3341	−	25.4032i	−0.568125	−	1.27335i
$399$		0			0
$400$	−13.8953	+	1.50440i	−0.694764	+	0.0752200i
$401$	0.0734423	+	0.127206i	0.00366753	+	0.00635235i	0.867853	−	0.496820i	$-0.165499\pi$
$401$	0.0734423	+	0.127206i	0.00366753	+	0.00635235i	−0.864186	+	0.503173i	$0.832166\pi$
$402$	−6.72824	−	0.701849i	−0.335574	−	0.0350050i
$403$	−4.46641	−	16.6689i	−0.222488	−	0.830336i
$404$	16.2601	+	24.9528i	0.808968	+	1.24145i
$405$	−0.727032	−	0.727032i	−0.0361265	−	0.0361265i
$406$		0			0
$407$		−	39.5828i		−	1.96205i
$408$	0.410764	−	0.635780i	0.0203358	−	0.0314758i
$409$	−1.96730	−	1.13582i	−0.0972768	−	0.0561628i	0.450572	−	0.892740i	$-0.351220\pi$
$409$	−1.96730	−	1.13582i	−0.0972768	−	0.0561628i	−0.547849	+	0.836577i	$0.684553\pi$
$410$	12.0610	+	14.8703i	0.595649	+	0.734391i
$411$	−1.92266	+	7.17546i	−0.0948378	+	0.353939i
$412$	19.3284	+	17.3488i	0.952244	+	0.854712i
$413$		0			0
$414$	−3.94744	+	1.76121i	−0.194006	+	0.0865590i
$415$	0.620660	+	1.07501i	0.0304670	+	0.0527704i
$416$	−11.3830	+	11.4724i	−0.558099	+	0.562479i
$417$	5.98102	−	10.3594i	0.292892	−	0.507304i
$418$	−30.9393	−	22.4417i	−1.51329	−	1.09766i
$419$	19.3654	−	19.3654i	0.946061	−	0.946061i	−0.0525570	−	0.998618i	$-0.516737\pi$
$419$	19.3654	−	19.3654i	0.946061	−	0.946061i	0.998618	+	0.0525570i	$0.0167371\pi$
$420$		0			0
$421$	8.11005	+	8.11005i	0.395260	+	0.395260i	0.876557	−	0.481298i	$-0.159834\pi$
$421$	8.11005	+	8.11005i	0.395260	+	0.395260i	−0.481298	+	0.876557i	$0.659834\pi$
$422$	2.24947	−	0.358084i	0.109502	−	0.0174313i
$423$	−5.35090	−	3.08934i	−0.260170	−	0.150209i
$424$	−0.0860995	+	1.72005i	−0.00418136	+	0.0835332i
$425$	−0.800554	+	0.462200i	−0.0388326	+	0.0224200i
$426$	−12.0753	−	4.62446i	−0.585051	−	0.224056i
$427$		0			0
$428$	−3.50588	+	0.189233i	−0.169463	+	0.00914690i
$429$	11.7515	+	3.14880i	0.567368	+	0.152026i
$430$	−8.26066	−	0.861701i	−0.398364	−	0.0415549i
$431$	5.38288	−	9.32343i	0.259284	−	0.449094i	−0.706766	−	0.707447i	$-0.749847\pi$
$431$	5.38288	−	9.32343i	0.259284	−	0.449094i	0.966050	+	0.258354i	$0.0831800\pi$
$432$	19.8989	+	3.08791i	0.957384	+	0.148567i
$433$	4.99439			0.240015			0.120008	−	0.992773i	$-0.461708\pi$
$433$	4.99439			0.240015			0.120008	+	0.992773i	$0.461708\pi$
$434$		0			0
$435$	0.407313	−	0.407313i	0.0195291	−	0.0195291i
$436$	25.9566	−	16.9142i	1.24310	−	0.810043i
$437$	9.58835	−	2.56919i	0.458673	−	0.122901i
$438$	16.4597	−	13.3501i	0.786475	−	0.637893i
$439$	−1.47159	+	0.849621i	−0.0702350	+	0.0405502i	−0.534706	−	0.845038i	$-0.679578\pi$
$439$	−1.47159	+	0.849621i	−0.0702350	+	0.0405502i	0.464471	+	0.885588i	$0.346244\pi$
$440$	−13.9070	−	4.48264i	−0.662992	−	0.213701i
$441$		0			0
$442$	−0.382281	+	0.998208i	−0.0181833	+	0.0474799i
$443$	−2.89267	+	10.7956i	−0.137435	+	0.512913i	0.862541	+	0.505987i	$0.168872\pi$
$443$	−2.89267	+	10.7956i	−0.137435	+	0.512913i	−0.999976	+	0.00692670i	$0.997795\pi$
$444$	−5.90653	−	18.0822i	−0.280312	−	0.858143i
$445$	3.49126	+	13.0296i	0.165502	+	0.617661i
$446$	9.18920	+	6.66537i	0.435121	+	0.315615i
$447$	18.4229			0.871375
$448$		0			0
$449$	4.05419			0.191329			0.0956646	−	0.995414i	$-0.469502\pi$
$449$	4.05419			0.191329			0.0956646	+	0.995414i	$0.469502\pi$
$450$	−7.90699	−	5.73533i	−0.372739	−	0.270366i
$451$	−12.0209	−	44.8626i	−0.566042	−	2.11250i
$452$	4.74016	+	14.5115i	0.222958	+	0.682562i
$453$	3.40799	−	12.7188i	0.160122	−	0.597582i
$454$	−2.55662	+	6.67582i	−0.119988	+	0.313312i
$455$		0			0
$456$	−17.4824	−	5.63508i	−0.818689	−	0.263887i
$457$	−8.79002	+	5.07492i	−0.411180	+	0.237395i	−0.691296	−	0.722571i	$-0.742960\pi$
$457$	−8.79002	+	5.07492i	−0.411180	+	0.237395i	0.280117	+	0.959966i	$0.409627\pi$
$458$	−0.988047	+	0.801384i	−0.0461684	+	0.0374462i
$459$	1.28647	−	0.344710i	0.0600475	−	0.0160897i
$460$	3.17938	−	2.07179i	0.148239	−	0.0965977i
$461$	1.02609	−	1.02609i	0.0477897	−	0.0477897i	−0.682808	−	0.730598i	$-0.739241\pi$
$461$	1.02609	−	1.02609i	0.0477897	−	0.0477897i	0.730598	+	0.682808i	$0.239241\pi$
$462$		0			0
$463$	10.5945			0.492369			0.246185	−	0.969223i	$-0.420823\pi$
$463$	10.5945			0.492369			0.246185	+	0.969223i	$0.420823\pi$
$464$	0.284635	−	1.83422i	0.0132139	−	0.0851517i
$465$	3.74899	−	6.49344i	0.173855	−	0.301126i
$466$	−34.5503	−	3.60407i	−1.60051	−	0.166955i
$467$	−12.6595	−	3.39211i	−0.585812	−	0.156968i	−0.0462738	−	0.998929i	$-0.514735\pi$
$467$	−12.6595	−	3.39211i	−0.585812	−	0.156968i	−0.539539	+	0.841961i	$0.681401\pi$
$468$	−11.2786	+	0.608770i	−0.521352	+	0.0281404i
$469$		0			0
$470$	5.06564	+	1.93997i	0.233660	+	0.0894843i
$471$	18.1585	−	10.4838i	0.836701	−	0.483069i
$472$	0.925163	−	18.4825i	0.0425841	−	0.850724i
$473$	17.4479	+	10.0736i	0.802257	+	0.463184i
$474$	17.7873	−	2.83148i	0.816996	−	0.130054i
$475$	15.8619	+	15.8619i	0.727793	+	0.727793i
$476$		0			0
$477$	−0.851098	+	0.851098i	−0.0389691	+	0.0389691i
$478$	33.5448	+	24.3317i	1.53430	+	1.11291i
$479$	−16.7383	+	28.9916i	−0.764792	+	1.32466i	0.175564	+	0.984468i	$0.443825\pi$
$479$	−16.7383	+	28.9916i	−0.764792	+	1.32466i	−0.940356	+	0.340191i	$0.889508\pi$
$480$	−7.02191	+	0.0274484i	−0.320505	+	0.00125284i
$481$	13.4313	+	23.2638i	0.612416	+	1.06074i
$482$	10.2549	−	4.57537i	0.467096	−	0.208402i
$483$		0			0
$484$	10.0052	+	8.98044i	0.454782	+	0.408202i
$485$	−4.52438	+	16.8852i	−0.205441	+	0.766718i
$486$	14.2094	+	17.5191i	0.644550	+	0.794682i
$487$	19.9401	+	11.5124i	0.903571	+	0.521677i	0.878357	−	0.478005i	$-0.158640\pi$
$487$	19.9401	+	11.5124i	0.903571	+	0.521677i	0.0252137	+	0.999682i	$0.491973\pi$
$488$	−10.5663	+	16.3545i	−0.478313	+	0.740333i
$489$			6.36258i			0.287726i
$490$		0			0
$491$	−21.9341	−	21.9341i	−0.989874	−	0.989874i	0.0100754	−	0.999949i	$-0.496793\pi$
$491$	−21.9341	−	21.9341i	−0.989874	−	0.989874i	−0.999949	+	0.0100754i	$0.996793\pi$
$492$	−12.1858	−	18.7004i	−0.549377	−	0.843078i
$493$	−0.0317744	−	0.118584i	−0.00143105	−	0.00534074i
$494$	25.7987	+	2.69117i	1.16074	+	0.121081i
$495$	−5.10597	−	8.84379i	−0.229496	−	0.397499i
$496$	−2.60068	−	24.0209i	−0.116774	−	1.07857i
$497$		0			0
$498$	−0.589613	−	1.32151i	−0.0264212	−	0.0592184i
$499$	−8.36254	−	2.24074i	−0.374359	−	0.100309i	0.0667336	−	0.997771i	$-0.478742\pi$
$499$	−8.36254	−	2.24074i	−0.374359	−	0.100309i	−0.441092	+	0.897462i	$0.645409\pi$
$500$	18.5896	+	9.43528i	0.831351	+	0.421959i
$501$	5.33259	−	1.42886i	0.238242	−	0.0638369i
$502$	−2.17994	−	13.6943i	−0.0972954	−	0.611206i
$503$		−	11.5286i		−	0.514034i	−0.966407	−	0.257017i	$-0.917260\pi$
$503$		−	11.5286i		−	0.514034i	0.966407	−	0.257017i	$-0.0827396\pi$
$504$		0			0
$505$		−	18.2740i		−	0.813183i
$506$	−9.09092	+	1.44715i	−0.404141	+	0.0643335i
$507$	4.72701	−	1.26660i	0.209934	−	0.0562516i
$508$	−6.66918	−	20.4170i	−0.295897	−	0.905856i
$509$	24.4978	+	6.56418i	1.08585	+	0.290952i	0.756989	−	0.653427i	$-0.226669\pi$
$509$	24.4978	+	6.56418i	1.08585	+	0.290952i	0.328859	+	0.944379i	$0.393336\pi$
$510$	−0.424131	+	0.189233i	−0.0187808	+	0.00837936i
$511$		0			0
$512$	−18.2119	+	13.4285i	−0.804861	+	0.593463i
$513$	−16.1598	−	27.9897i	−0.713475	−	1.23577i
$514$	1.21854	−	11.6815i	0.0537476	−	0.515249i
$515$	−4.12453	−	15.3929i	−0.181748	−	0.678294i
$516$	9.47374	+	1.99823i	0.417058	+	0.0879671i
$517$	−9.30435	−	9.30435i	−0.409205	−	0.409205i
$518$		0			0
$519$			16.6263i			0.729815i
$520$	9.69457	−	2.08442i	0.425135	−	0.0914079i
$521$	−0.249004	−	0.143762i	−0.0109091	−	0.00629835i	0.494536	−	0.869157i	$-0.335338\pi$
$521$	−0.249004	−	0.143762i	−0.0109091	−	0.00629835i	−0.505445	+	0.862859i	$0.668672\pi$
$522$	1.00752	−	0.817183i	0.0440982	−	0.0357671i
$523$	−1.40664	+	5.24964i	−0.0615079	+	0.229551i	−0.989837	−	0.142210i	$-0.954579\pi$
$523$	−1.40664	+	5.24964i	−0.0615079	+	0.229551i	0.928329	+	0.371761i	$0.121246\pi$
$524$	1.96454	+	36.3966i	0.0858211	+	1.58999i
$525$		0			0
$526$	7.98268	+	17.8917i	0.348062	+	0.780117i
$527$	−0.799011	−	1.38393i	−0.0348055	−	0.0602848i
$528$	15.5826	+	6.87951i	0.678145	+	0.299392i
$529$	−10.3046	+	17.8481i	−0.448027	+	0.776005i
$530$	0.620442	−	0.855371i	0.0269503	−	0.0371549i
$531$	9.14529	−	9.14529i	0.396872	−	0.396872i
$532$		0			0
$533$	22.2879	+	22.2879i	0.965396	+	0.965396i
$534$	−2.47210	−	15.5296i	−0.106978	−	0.672033i
$535$	1.86562	+	1.07712i	0.0806580	+	0.0465679i
$536$	13.3582	+	0.668664i	0.576988	+	0.0288819i
$537$	16.0335	−	9.25693i	0.691896	−	0.399466i
$538$	0.919989	−	2.40226i	0.0396635	−	0.103569i
$539$		0			0
$540$	−9.19484	−	8.25308i	−0.395683	−	0.355156i
$541$	−35.9992	−	9.64594i	−1.54772	−	0.414712i	−0.618972	−	0.785413i	$-0.712451\pi$
$541$	−35.9992	−	9.64594i	−1.54772	−	0.414712i	−0.928752	+	0.370701i	$0.879117\pi$
$542$	2.40195	−	23.0262i	0.103172	−	0.989058i
$543$	0.994727	−	1.72292i	0.0426878	−	0.0739375i
$544$	−0.743213	+	1.29898i	−0.0318650	+	0.0556934i
$545$	−19.0092			−0.814264
$546$		0			0
$547$	10.4205	−	10.4205i	0.445550	−	0.445550i	−0.448322	−	0.893872i	$-0.647978\pi$
$547$	10.4205	−	10.4205i	0.445550	−	0.445550i	0.893872	+	0.448322i	$0.147978\pi$
$548$	3.03123	−	14.3713i	0.129488	−	0.613911i
$549$	−13.1443	+	3.52201i	−0.560986	+	0.150316i
$550$	−13.1040	−	16.1562i	−0.558755	−	0.688903i
$551$	−2.58001	+	1.48957i	−0.109912	+	0.0634578i
$552$	−3.93697	+	2.01763i	−0.167569	+	0.0858761i
$553$		0			0
$554$	15.4431	+	5.91420i	0.656114	+	0.251270i
$555$	−3.02084	+	11.2739i	−0.128227	+	0.478551i
$556$	−10.7043	+	21.0898i	−0.453964	+	0.894408i
$557$	2.83567	+	10.5829i	0.120151	+	0.448411i	0.999621	−	0.0275450i	$-0.00876897\pi$
$557$	2.83567	+	10.5829i	0.120151	+	0.448411i	−0.879469	+	0.475956i	$0.842102\pi$
$558$	9.91473	−	13.6689i	0.419724	−	0.578651i
$559$	−13.6728			−0.578297
$560$		0			0
$561$	1.12660			0.0475651
$562$	−25.0873	+	34.5865i	−1.05824	+	1.45894i
$563$	5.14520	+	19.2022i	0.216844	+	0.809274i	0.985509	+	0.169622i	$0.0542548\pi$
$563$	5.14520	+	19.2022i	0.216844	+	0.809274i	−0.768665	+	0.639652i	$0.779079\pi$
$564$	−5.63880	−	2.86202i	−0.237436	−	0.120513i
$565$	2.42431	−	9.04763i	0.101991	−	0.380637i
$566$	−22.0535	−	8.44576i	−0.926977	−	0.355002i
$567$		0			0
$568$	24.3329	+	7.84320i	1.02099	+	0.329093i
$569$	−23.3519	+	13.4822i	−0.978963	+	0.565205i	−0.901957	−	0.431826i	$-0.857869\pi$
$569$	−23.3519	+	13.4822i	−0.978963	+	0.565205i	−0.0770061	+	0.997031i	$0.524536\pi$
$570$	7.09939	+	8.75302i	0.297361	+	0.366624i
$571$	−29.7973	+	7.98417i	−1.24698	+	0.334127i	−0.821169	−	0.570686i	$-0.806678\pi$
$571$	−29.7973	+	7.98417i	−1.24698	+	0.334127i	−0.425810	+	0.904813i	$0.640011\pi$
$572$	−23.5363	−	4.96435i	−0.984104	−	0.207570i
$573$	2.48264	−	2.48264i	0.103714	−	0.103714i
$574$		0			0
$575$	5.40264			0.225306
$576$	−15.7350	−	1.57923i	−0.655626	−	0.0658013i
$577$	−4.08125	+	7.06893i	−0.169905	+	0.294283i	−0.938386	−	0.345589i	$-0.887679\pi$
$577$	−4.08125	+	7.06893i	−0.169905	+	0.294283i	0.768482	+	0.639872i	$0.221013\pi$
$578$	2.48407	−	23.8134i	0.103324	−	0.990508i
$579$	−7.41269	−	1.98623i	−0.308061	−	0.0825447i
$580$	−0.760746	+	0.847555i	−0.0315883	+	0.0351928i
$581$		0			0
$582$	7.28811	−	19.0306i	0.302102	−	0.788845i
$583$	−2.21988	+	1.28165i	−0.0919382	+	0.0530805i
$584$	−31.0735	+	28.1109i	−1.28583	+	1.16324i
$585$	6.00180	+	3.46514i	0.248144	+	0.143266i
$586$	−4.83720	−	30.3871i	−0.199823	−	1.25528i
$587$	−0.0166226	−	0.0166226i	−0.000686087	−	0.000686087i	0.706764	−	0.707450i	$-0.250154\pi$
$587$	−0.0166226	−	0.0166226i	−0.000686087	−	0.000686087i	−0.707450	+	0.706764i	$0.750154\pi$
$588$		0			0
$589$	−27.4206	+	27.4206i	−1.12985	+	1.12985i
$590$	−6.66683	+	9.19120i	−0.274469	+	0.378396i
$591$	5.59908	−	9.69789i	0.230315	−	0.398918i
$592$	13.5881	+	35.0700i	0.558467	+	1.44137i
$593$	−8.35729	−	14.4753i	−0.343193	−	0.594427i	0.641831	−	0.766846i	$-0.278175\pi$
$593$	−8.35729	−	14.4753i	−0.343193	−	0.594427i	−0.985024	+	0.172419i	$0.944842\pi$
$594$	12.2119	+	27.3708i	0.501062	+	1.12304i
$595$		0			0
$596$	−36.3721	+	1.96321i	−1.48986	+	0.0804163i
$597$	5.14968	−	19.2189i	0.210762	−	0.786575i
$598$	4.85191	−	3.93528i	0.198409	−	0.160926i
$599$	−15.2174	−	8.78578i	−0.621767	−	0.358977i	0.155790	−	0.987790i	$-0.450208\pi$
$599$	−15.2174	−	8.78578i	−0.621767	−	0.358977i	−0.777556	+	0.628813i	$0.783541\pi$
$600$	−8.39697	−	5.42510i	−0.342805	−	0.221479i
$601$		−	6.99237i		−	0.285225i	−0.989779	−	0.142612i	$-0.954450\pi$
$601$		−	6.99237i		−	0.285225i	0.989779	−	0.142612i	$-0.0455503\pi$
$602$		0			0
$603$	6.60978	+	6.60978i	0.269171	+	0.269171i
$604$	−5.37299	+	25.4737i	−0.218624	+	1.03651i
$605$	−2.13503	−	7.96802i	−0.0868011	−	0.323946i
$606$	−2.21022	+	21.1881i	−0.0897839	+	0.860709i
$607$	3.12773	+	5.41738i	0.126951	+	0.219885i	0.922494	−	0.386012i	$-0.126148\pi$
$607$	3.12773	+	5.41738i	0.126951	+	0.219885i	−0.795543	+	0.605897i	$0.792814\pi$
$608$	35.1157	+	9.26227i	1.42413	+	0.375635i
$609$		0			0
$610$	10.9101	−	4.86772i	0.441738	−	0.197088i
$611$	8.62557	+	2.31121i	0.348953	+	0.0935017i
$612$	−0.994240	+	0.324768i	−0.0401898	+	0.0131280i
$613$	7.78494	−	2.08597i	0.314431	−	0.0842514i	−0.0981525	−	0.995171i	$-0.531293\pi$
$613$	7.78494	−	2.08597i	0.314431	−	0.0842514i	0.412583	+	0.910920i	$0.364627\pi$
$614$	16.1031	−	2.56338i	0.649867	−	0.103450i
$615$			13.6951i			0.552240i
$616$		0			0
$617$			44.4895i			1.79108i	0.444980	+	0.895541i	$0.353211\pi$
$617$			44.4895i			1.79108i	−0.444980	+	0.895541i	$0.646789\pi$
$618$	2.92050	+	18.3465i	0.117480	+	0.738003i
$619$	18.9538	−	5.07865i	0.761816	−	0.204128i	0.143063	−	0.989714i	$-0.454305\pi$
$619$	18.9538	−	5.07865i	0.761816	−	0.204128i	0.618753	+	0.785586i	$0.287638\pi$
$620$	−6.70961	+	13.2194i	−0.269464	+	0.530904i
$621$	−7.51878	−	2.01465i	−0.301718	−	0.0808451i
$622$	17.9247	+	40.1749i	0.718714	+	1.61087i
$623$		0			0
$624$	−11.4926	+	1.24427i	−0.460074	+	0.0498108i
$625$	2.33975	+	4.05256i	0.0935899	+	0.162103i
$626$	−4.47273	−	0.466568i	−0.178766	−	0.0186478i
$627$	−7.07580	−	26.4072i	−0.282580	−	1.05460i
$628$	−34.7329	+	22.6331i	−1.38599	+	0.903159i
$629$	1.75895	+	1.75895i	0.0701341	+	0.0701341i
$630$		0			0
$631$			8.64101i			0.343993i	0.985098	+	0.171997i	$0.0550218\pi$
$631$			8.64101i			0.343993i	−0.985098	+	0.171997i	$0.944978\pi$
$632$	−34.8154	+	7.48562i	−1.38488	+	0.297762i
$633$	1.41097	+	0.814625i	0.0560811	+	0.0323784i
$634$	1.97728	+	2.43784i	0.0785277	+	0.0968188i
$635$	−3.41088	+	12.7296i	−0.135357	+	0.505159i
$636$	−0.822839	+	0.916733i	−0.0326277	+	0.0363508i
$637$		0			0
$638$	2.52297	−	1.12566i	0.0998853	−	0.0445654i
$639$	8.93382	+	15.4738i	0.353417	+	0.612136i
$640$	13.8603	−	0.802470i	0.547877	−	0.0317204i
$641$	−7.54432	+	13.0672i	−0.297983	+	0.516122i	−0.975674	−	0.219225i	$-0.929647\pi$
$641$	−7.54432	+	13.0672i	−0.297983	+	0.516122i	0.677691	+	0.735346i	$0.262981\pi$
$642$	−2.03285	−	1.47453i	−0.0802304	−	0.0581950i
$643$	−12.3557	+	12.3557i	−0.487261	+	0.487261i	−0.907441	−	0.420180i	$-0.861967\pi$
$643$	−12.3557	+	12.3557i	−0.487261	+	0.487261i	0.420180	+	0.907441i	$0.361967\pi$
$644$		0			0
$645$	−4.20072	−	4.20072i	−0.165403	−	0.165403i
$646$	2.37211	−	0.377607i	0.0933295	−	0.0148567i
$647$	35.3412	+	20.4042i	1.38941	+	0.802173i	0.993248	−	0.116009i	$-0.0370103\pi$
$647$	35.3412	+	20.4042i	1.38941	+	0.802173i	0.396157	+	0.918183i	$0.370344\pi$
$648$	−1.58986	−	1.75741i	−0.0624555	−	0.0690376i
$649$	23.8533	−	13.7717i	0.936323	−	0.540586i
$650$	13.1837	+	5.04892i	0.517107	+	0.198035i
$651$		0			0
$652$	−0.678019	−	12.5615i	−0.0265533	−	0.491948i
$653$	13.5015	+	3.61772i	0.528356	+	0.141572i	0.513129	−	0.858312i	$-0.328486\pi$
$653$	13.5015	+	3.61772i	0.528356	+	0.141572i	0.0152268	+	0.999884i	$0.495153\pi$
$654$	22.0405	+	2.29913i	0.861853	+	0.0899033i
$655$	11.1822	−	19.3682i	0.436925	−	0.756776i
$656$	26.0510	+	35.6213i	1.01712	+	1.39078i
$657$	−29.2850			−1.14252
$658$		0			0
$659$	−2.71835	+	2.71835i	−0.105892	+	0.105892i	−0.758068	−	0.652176i	$-0.773856\pi$
$659$	−2.71835	+	2.71835i	−0.105892	+	0.105892i	0.652176	+	0.758068i	$0.273856\pi$
$660$	−5.70591	−	8.75633i	−0.222102	−	0.340840i
$661$	13.3501	−	3.57716i	0.519260	−	0.139135i	0.0103356	−	0.999947i	$-0.496710\pi$
$661$	13.3501	−	3.57716i	0.519260	−	0.139135i	0.508924	+	0.860811i	$0.330043\pi$
$662$	−3.04397	+	2.46890i	−0.118307	+	0.0959565i
$663$	−0.662130	+	0.382281i	−0.0257150	+	0.0148466i
$664$	1.30489	+	2.54621i	0.0506395	+	0.0988121i
$665$		0			0
$666$	−9.40070	+	24.5470i	−0.364270	+	0.951177i
$667$	−0.185705	+	0.693060i	−0.00719053	+	0.0268354i
$668$	−10.3758	+	3.38924i	−0.401451	+	0.131134i
$669$	2.10157	+	7.84316i	0.0812513	+	0.303234i
$670$	−6.64296	−	4.81847i	−0.256640	−	0.186154i
$671$	−28.9801			−1.11876
$672$		0			0
$673$	−19.1036			−0.736391			−0.368195	−	0.929748i	$-0.620024\pi$
$673$	−19.1036			−0.736391			−0.368195	+	0.929748i	$0.620024\pi$
$674$	32.8626	+	23.8369i	1.26582	+	0.918161i
$675$	−4.55271	−	16.9909i	−0.175234	−	0.653981i
$676$	−9.19748	+	3.00435i	−0.353749	+	0.115552i
$677$	3.81488	−	14.2373i	0.146618	−	0.547186i	−0.853060	−	0.521813i	$-0.825256\pi$
$677$	3.81488	−	14.2373i	0.146618	−	0.547186i	0.999678	−	0.0253729i	$-0.00807731\pi$
$678$	−3.90520	+	10.1972i	−0.149978	+	0.391622i
$679$		0			0
$680$	0.817189	−	0.418796i	0.0313378	−	0.0160601i
$681$	−4.42820	+	2.55662i	−0.169689	+	0.0979699i
$682$	27.9294	−	22.6530i	1.06947	−	0.867427i
$683$	47.8769	−	12.8286i	1.83196	−	0.490872i	0.833830	−	0.552022i	$-0.186143\pi$
$683$	47.8769	−	12.8286i	1.83196	−	0.490872i	0.998129	+	0.0611498i	$0.0194767\pi$
$684$	13.8570	+	21.2650i	0.529835	+	0.813088i
$685$	−6.37232	+	6.37232i	−0.243474	+	0.243474i
$686$		0			0
$687$	−0.909963			−0.0347172
$688$	−18.9168	−	2.93552i	−0.721196	−	0.111916i
$689$	0.869786	−	1.50651i	0.0331362	−	0.0573936i
$690$	2.69971	+	0.281617i	0.102776	+	0.0107210i
$691$	−5.48399	−	1.46943i	−0.208621	−	0.0558997i	0.152995	−	0.988227i	$-0.451108\pi$
$691$	−5.48399	−	1.46943i	−0.208621	−	0.0558997i	−0.361616	+	0.932327i	$0.617775\pi$
$692$	−1.77176	−	32.8251i	−0.0673522	−	1.24782i
$693$		0			0
$694$	8.25308	+	3.16066i	0.313282	+	0.119977i
$695$	12.5673	−	7.25574i	0.476705	−	0.275226i
$696$	0.984571	−	0.890702i	0.0373201	−	0.0337620i
$697$	2.52775	+	1.45940i	0.0957455	+	0.0552787i
$698$	14.7429	−	2.34686i	0.558027	−	0.0888301i
$699$	−17.5695	−	17.5695i	−0.664541	−	0.664541i
$700$		0			0
$701$	6.91144	−	6.91144i	0.261041	−	0.261041i	−0.564436	−	0.825477i	$-0.690906\pi$
$701$	6.91144	−	6.91144i	0.261041	−	0.261041i	0.825477	+	0.564436i	$0.190906\pi$
$702$	−16.4648	−	11.9427i	−0.621424	−	0.450749i
$703$	30.1821	−	52.2769i	1.13834	−	1.97166i
$704$	−31.4976	−	11.9216i	−1.18711	−	0.449311i
$705$	1.93997	+	3.36013i	0.0730636	+	0.126550i
$706$	−8.66191	+	3.86465i	−0.325995	+	0.145448i
$707$		0			0
$708$	8.84163	−	9.85056i	0.332289	−	0.370207i
$709$	6.77484	−	25.2840i	0.254434	−	0.949562i	−0.713970	−	0.700176i	$-0.753105\pi$
$709$	6.77484	−	25.2840i	0.254434	−	0.949562i	0.968404	−	0.249385i	$-0.0802286\pi$
$710$	−9.88130	−	12.1829i	−0.370839	−	0.457216i
$711$	−21.5538	−	12.4441i	−0.808331	−	0.466690i
$712$	6.53552	+	30.3965i	0.244929	+	1.13916i
$713$			9.33961i			0.349771i
$714$		0			0
$715$	10.4362	+	10.4362i	0.390290	+	0.390290i
$716$	−30.6682	+	19.9844i	−1.14612	+	0.746852i
$717$	7.67169	+	28.6311i	0.286504	+	1.06925i
$718$	−16.5330	−	1.72462i	−0.617005	−	0.0643622i
$719$	−7.26709	−	12.5870i	−0.271017	−	0.469415i	0.698106	−	0.715995i	$-0.254027\pi$
$719$	−7.26709	−	12.5870i	−0.271017	−	0.469415i	−0.969122	+	0.246580i	$0.920693\pi$
$720$	7.55976	+	6.08273i	0.281736	+	0.226690i
$721$		0			0
$722$	−12.8012	−	28.6917i	−0.476413	−	1.06779i
$723$	7.75834	+	2.07884i	0.288536	+	0.0773129i
$724$	−1.78027	+	3.50753i	−0.0661634	+	0.130356i
$725$	−1.56618	+	0.419656i	−0.0581664	+	0.0155856i
$726$	1.51177	+	9.49689i	0.0561071	+	0.352463i
$727$		−	35.2605i		−	1.30774i	−0.756607	−	0.653870i	$-0.773144\pi$
$727$		−	35.2605i		−	1.30774i	0.756607	−	0.653870i	$-0.226856\pi$
$728$		0			0
$729$			13.6210i			0.504481i
$730$	25.3902	−	4.04177i	0.939734	−	0.149593i
$731$	−1.22298	+	0.327697i	−0.0452337	+	0.0121203i
$732$	−13.2387	+	4.32440i	−0.489315	+	0.159834i
$733$	6.39419	+	1.71332i	0.236175	+	0.0632828i	0.374965	−	0.927039i	$-0.377655\pi$
$733$	6.39419	+	1.71332i	0.236175	+	0.0632828i	−0.138790	+	0.990322i	$0.544321\pi$
$734$	44.5184	−	19.8626i	1.64320	−	0.733141i
$735$		0			0
$736$	7.55769	−	4.40291i	0.278580	−	0.162294i
$737$	9.95352	+	17.2400i	0.366643	+	0.635044i
$738$	−3.19995	+	30.6762i	−0.117792	+	1.12921i
$739$	4.06431	+	15.1682i	0.149508	+	0.557972i	0.999513	+	0.0311973i	$0.00993203\pi$
$739$	4.06431	+	15.1682i	0.149508	+	0.557972i	−0.850005	+	0.526774i	$0.823401\pi$
$740$	4.76260	−	22.5798i	0.175077	−	0.830051i
$741$	13.1192	+	13.1192i	0.481946	+	0.481946i
$742$		0			0
$743$		−	9.88941i		−	0.362807i	−0.983409	−	0.181404i	$-0.941936\pi$
$743$		−	9.88941i		−	0.362807i	0.983409	−	0.181404i	$-0.0580641\pi$
$744$	9.37844	−	14.5160i	0.343830	−	0.532181i
$745$	19.3551	+	11.1747i	0.709116	+	0.409408i
$746$	13.6653	−	11.0836i	0.500321	−	0.405800i
$747$	−0.517534	+	1.93146i	−0.0189356	+	0.0706686i
$748$	−2.22423	+	0.120054i	−0.0813258	+	0.00438963i
$749$		0			0
$750$	6.07564	+	13.6175i	0.221851	+	0.497239i
$751$	1.95848	+	3.39219i	0.0714659	+	0.123783i	0.899544	−	0.436830i	$-0.143899\pi$
$751$	1.95848	+	3.39219i	0.0714659	+	0.123783i	−0.828078	+	0.560613i	$0.810566\pi$
$752$	11.4376	+	5.04954i	0.417086	+	0.184138i
$753$	4.95926	−	8.58970i	0.180726	−	0.313026i
$754$	−1.10085	+	1.51768i	−0.0400905	+	0.0552707i
$755$	11.2952	−	11.2952i	0.411074	−	0.411074i
$756$		0			0
$757$	30.8256	+	30.8256i	1.12037	+	1.12037i	0.991685	+	0.128689i	$0.0410770\pi$
$757$	30.8256	+	30.8256i	1.12037	+	1.12037i	0.128689	+	0.991685i	$0.458923\pi$
$758$	0.0539537	+	0.338935i	0.00195969	+	0.0123107i
$759$	−5.70225	−	3.29220i	−0.206979	−	0.119499i
$760$	−14.9490	−	16.5244i	−0.542256	−	0.599403i
$761$	26.7482	−	15.4431i	0.969622	−	0.559812i	0.0705012	−	0.997512i	$-0.477540\pi$
$761$	26.7482	−	15.4431i	0.969622	−	0.559812i	0.899121	+	0.437700i	$0.144207\pi$
$762$	5.49444	−	14.3470i	0.199042	−	0.519737i
$763$		0			0
$764$	−4.63688	+	5.16599i	−0.167756	+	0.186899i
$765$	0.619890	+	0.166099i	0.0224122	+	0.00600533i
$766$	−3.18631	+	30.5454i	−0.115126	+	1.10365i
$767$	−9.34610	+	16.1879i	−0.337468	+	0.584512i
$768$	−16.1676	−	0.745947i	−0.583400	−	0.0269170i
$769$	32.1016			1.15761			0.578807	−	0.815465i	$-0.303519\pi$
$769$	32.1016			1.15761			0.578807	+	0.815465i	$0.303519\pi$
$770$		0			0
$771$	5.94029	−	5.94029i	0.213934	−	0.213934i
$772$	14.8464	+	3.13145i	0.534335	+	0.112703i
$773$	42.3105	−	11.3371i	1.52180	−	0.407766i	0.601469	−	0.798896i	$-0.294582\pi$
$773$	42.3105	−	11.3371i	1.52180	−	0.407766i	0.920335	+	0.391130i	$0.127916\pi$
$774$	−8.42781	−	10.3909i	−0.302931	−	0.373492i
$775$	−18.2780	+	10.5528i	−0.656566	+	0.379069i
$776$	−12.3608	+	38.3485i	−0.443728	+	1.37663i
$777$		0			0
$778$	21.1650	+	8.10550i	0.758801	+	0.290596i
$779$	18.3320	−	68.4160i	0.656812	−	2.45126i
$780$	6.32472	+	3.21016i	0.226461	+	0.114942i
$781$	9.84846	+	36.7550i	0.352406	+	1.31520i
$782$	0.339669	−	0.468284i	0.0121465	−	0.0167458i
$783$	2.33612			0.0834860
$784$		0			0
$785$	25.4364			0.907865
$786$	−15.3080	+	21.1043i	−0.546017	+	0.752765i
$787$	8.96793	+	33.4688i	0.319672	+	1.19303i	0.919560	+	0.392949i	$0.128545\pi$
$787$	8.96793	+	33.4688i	0.319672	+	1.19303i	−0.599888	+	0.800084i	$0.704788\pi$
$788$	−10.0207	+	19.7430i	−0.356974	+	0.703317i
$789$	−3.62697	+	13.5360i	−0.129123	+	0.481895i
$790$	20.4047	+	7.81435i	0.725968	+	0.278022i
$791$		0			0
$792$	−10.7349	−	20.9468i	−0.381448	−	0.744313i
$793$	17.0323	−	9.83360i	0.604835	−	0.349201i
$794$	−18.5799	−	22.9077i	−0.659377	−	0.812962i
$795$	0.730076	−	0.195623i	0.0258931	−	0.00693804i
$796$	−8.11890	+	38.4922i	−0.287767	+	1.36432i
$797$	−10.8522	+	10.8522i	−0.384403	+	0.384403i	−0.872686	−	0.488283i	$-0.837624\pi$
$797$	−10.8522	+	10.8522i	−0.384403	+	0.384403i	0.488283	+	0.872686i	$0.337624\pi$
$798$		0			0
$799$	0.826921			0.0292544
$800$	17.1561	+	9.81588i	0.606561	+	0.347044i
$801$	−10.8646	+	18.8181i	−0.383883	+	0.664906i
$802$	0.0215518	−	0.206605i	0.000761020	−	0.00729548i
$803$	−60.2412	−	16.1416i	−2.12586	−	0.569624i
$804$	7.11951	+	6.39031i	0.251086	+	0.225369i
$805$		0			0
$806$	−8.72813	+	22.7908i	−0.307435	+	0.802772i
$807$	1.59347	−	0.919989i	0.0560927	−	0.0323851i
$808$	2.10571	−	42.0669i	0.0740787	−	1.47991i
$809$	−34.7775	−	20.0788i	−1.22271	−	0.705932i	−0.257216	−	0.966354i	$-0.582805\pi$
$809$	−34.7775	−	20.0788i	−1.22271	−	0.705932i	−0.965495	+	0.260422i	$0.916138\pi$
$810$	0.228589	+	1.43598i	0.00803178	+	0.0504553i
$811$	−15.7147	−	15.7147i	−0.551819	−	0.551819i	0.375147	−	0.926966i	$-0.377592\pi$
$811$	−15.7147	−	15.7147i	−0.551819	−	0.551819i	−0.926966	+	0.375147i	$0.877592\pi$
$812$		0			0
$813$	11.7093	−	11.7093i	0.410662	−	0.410662i
$814$	−32.8679	+	45.3133i	−1.15202	+	1.58823i
$815$	−3.85931	+	6.68452i	−0.135186	+	0.234149i
$816$	−0.998157	+	0.386742i	−0.0349425	+	0.0135387i
$817$	15.3623	+	26.6083i	0.537459	+	0.930907i
$818$	1.30897	+	2.93382i	0.0457671	+	0.102579i
$819$		0			0
$820$	−1.45940	−	27.0380i	−0.0509644	−	0.944209i
$821$	−0.837392	+	3.12519i	−0.0292252	+	0.109070i	−0.978998	−	0.203871i	$-0.934648\pi$
$821$	−0.837392	+	3.12519i	−0.0292252	+	0.109070i	0.949773	+	0.312941i	$0.101314\pi$
$822$	8.15922	−	6.61777i	0.284585	−	0.230821i
$823$	9.16184	+	5.28959i	0.319362	+	0.184384i	0.651108	−	0.758985i	$-0.274304\pi$
$823$	9.16184	+	5.28959i	0.319362	+	0.184384i	−0.331746	+	0.943369i	$0.607638\pi$
$824$	−7.72096	−	35.9099i	−0.268973	−	1.25098i
$825$		−	14.8794i		−	0.518034i
$826$		0			0
$827$	16.8200	+	16.8200i	0.584887	+	0.584887i	0.936242	−	0.351355i	$-0.114279\pi$
$827$	16.8200	+	16.8200i	0.584887	+	0.584887i	−0.351355	+	0.936242i	$0.614279\pi$
$828$	5.98137	+	1.26161i	0.207867	+	0.0438439i
$829$	2.00157	+	7.46997i	0.0695175	+	0.259443i	0.991934	−	0.126753i	$-0.0404556\pi$
$829$	2.00157	+	7.46997i	0.0695175	+	0.259443i	−0.922417	+	0.386196i	$0.873789\pi$
$830$	0.182134	−	1.74602i	0.00632196	−	0.0606051i
$831$	5.91420	+	10.2437i	0.205161	+	0.355350i
$832$	22.5572	−	3.68125i	0.782029	−	0.127624i
$833$		0			0
$834$	−15.4490	+	6.89280i	−0.534954	+	0.238678i
$835$	6.46911	+	1.73339i	0.223873	+	0.0599865i
$836$	16.7837	+	51.3814i	0.580476	+	1.77706i
$837$	29.3724	−	7.87032i	1.01526	−	0.272038i
$838$	−38.2492	+	6.08873i	−1.32130	+	0.210332i
$839$			6.99735i			0.241575i	0.992678	+	0.120788i	$0.0385420\pi$
$839$			6.99735i			0.241575i	−0.992678	+	0.120788i	$0.961458\pi$
$840$		0			0
$841$			28.7847i			0.992575i
$842$	−2.54991	−	16.0184i	−0.0878756	−	0.552031i
$843$	−29.5202	+	7.90993i	−1.01673	+	0.272432i
$844$	−2.87247	−	1.45794i	−0.0988745	−	0.0501845i
$845$	5.73446	+	1.53654i	0.197271	+	0.0528587i
$846$	3.56030	+	7.97976i	0.122406	+	0.274350i
$847$		0			0
$848$	1.52683	−	1.89758i	0.0524315	−	0.0651631i
$849$	−8.44576	−	14.6285i	−0.289858	−	0.502048i
$850$	1.30024	+	0.135634i	0.0445980	+	0.00465219i
$851$	−3.76280	−	14.0430i	−0.128987	−	0.481387i
$852$	9.98354	+	15.3208i	0.342030	+	0.524882i
$853$	−32.6377	−	32.6377i	−1.11749	−	1.11749i	−0.992108	−	0.125384i	$-0.959984\pi$
$853$	−32.6377	−	32.6377i	−1.11749	−	1.11749i	−0.125384	−	0.992108i	$-0.540016\pi$
$854$		0			0
$855$		−	15.5733i		−	0.532596i
$856$	4.17056	+	2.69451i	0.142547	+	0.0920965i
$857$	37.8047	+	21.8266i	1.29139	+	0.745582i	0.978900	−	0.204341i	$-0.0655051\pi$
$857$	37.8047	+	21.8266i	1.29139	+	0.745582i	0.312486	+	0.949923i	$0.398838\pi$
$858$	−10.8382	−	13.3626i	−0.370008	−	0.456193i
$859$	2.42878	−	9.06433i	0.0828689	−	0.309271i	−0.912033	−	0.410116i	$-0.865488\pi$
$859$	2.42878	−	9.06433i	0.0828689	−	0.309271i	0.994902	+	0.100845i	$0.0321547\pi$
$860$	8.74105	+	7.84576i	0.298067	+	0.267538i
$861$		0			0
$862$	−13.9040	+	6.20347i	−0.473571	+	0.211291i
$863$	4.05796	+	7.02860i	0.138135	+	0.239256i	0.926791	−	0.375579i	$-0.122556\pi$
$863$	4.05796	+	7.02860i	0.138135	+	0.239256i	−0.788656	+	0.614835i	$0.789223\pi$
$864$	−20.2156	−	20.0582i	−0.687748	−	0.682392i
$865$	−10.0849	+	17.4676i	−0.342898	+	0.593916i
$866$	−5.71744	−	4.14714i	−0.194287	−	0.140926i
$867$	12.1096	−	12.1096i	0.411265	−	0.411265i
$868$		0			0
$869$	−37.4786	−	37.4786i	−1.27137	−	1.27137i
$870$	−0.804496	+	0.128064i	−0.0272750	+	0.00434179i
$871$	−11.6999	−	6.75491i	−0.396434	−	0.228881i
$872$	−43.7593	−	2.19043i	−1.48188	−	0.0741772i
$873$	−24.3867	+	14.0797i	−0.825364	+	0.476524i
$874$	−13.1098	−	5.02063i	−0.443446	−	0.169825i
$875$		0			0
$876$	−29.9280	+	1.61539i	−1.01117	+	0.0545789i
$877$	−31.7089	−	8.49639i	−1.07074	−	0.286903i	−0.319940	−	0.947438i	$-0.603663\pi$
$877$	−31.7089	−	8.49639i	−1.07074	−	0.286903i	−0.750795	+	0.660535i	$0.770329\pi$
$878$	2.39012	+	0.249323i	0.0806627	+	0.00841424i
$879$	11.0044	−	19.0602i	0.371170	−	0.642885i
$880$	12.1982	+	16.6794i	0.411201	+	0.562264i
$881$	−12.2614			−0.413096			−0.206548	−	0.978436i	$-0.566223\pi$
$881$	−12.2614			−0.413096			−0.206548	+	0.978436i	$0.566223\pi$
$882$		0			0
$883$	4.12180	−	4.12180i	0.138710	−	0.138710i	−0.634342	−	0.773052i	$-0.718729\pi$
$883$	4.12180	−	4.12180i	0.138710	−	0.138710i	0.773052	+	0.634342i	$0.218729\pi$
$884$	1.26650	−	0.825290i	0.0425969	−	0.0277575i
$885$	−7.84487	+	2.10203i	−0.263702	+	0.0706588i
$886$	12.2757	−	9.95653i	0.412409	−	0.334496i
$887$	−20.6829	+	11.9413i	−0.694465	+	0.400949i	−0.805283	−	0.592891i	$-0.797986\pi$
$887$	−20.6829	+	11.9413i	−0.694465	+	0.400949i	0.110818	+	0.993841i	$0.464653\pi$
$888$	−8.25308	+	25.6045i	−0.276955	+	0.859232i
$889$		0			0
$890$	6.82252	−	17.8149i	0.228692	−	0.597157i
$891$	0.912912	−	3.40703i	0.0305837	−	0.114140i
$892$	−4.98489	−	15.2607i	−0.166906	−	0.510965i
$893$	−5.19362	−	19.3829i	−0.173798	−	0.648622i
$894$	−21.0901	−	15.2976i	−0.705357	−	0.511630i
$895$	22.4597			0.750744
$896$		0			0
$897$	4.46847			0.149198
$898$	−4.64113	−	3.36644i	−0.154876	−	0.112339i
$899$	−0.725465	−	2.70747i	−0.0241956	−	0.0902992i
$900$	4.28932	+	13.1313i	0.142977	+	0.437709i
$901$	0.0416926	−	0.155599i	0.00138898	−	0.00518375i
$902$	−23.4909	+	61.3392i	−0.782161	+	2.04237i
$903$		0			0
$904$	6.62333	−	20.5484i	0.220289	−	0.683428i
$905$	2.09012	−	1.20673i	0.0694779	−	0.0401131i
$906$	−14.4626	+	11.7303i	−0.480486	+	0.389712i
$907$	−46.2279	+	12.3867i	−1.53497	+	0.411295i	−0.924637	−	0.380849i	$-0.875632\pi$
$907$	−46.2279	+	12.3867i	−1.53497	+	0.411295i	−0.610335	+	0.792143i	$0.708965\pi$
$908$	8.47008	−	5.51938i	0.281089	−	0.183167i
$909$	20.8151	−	20.8151i	0.690393	−	0.690393i
$910$		0			0
$911$	0.866439			0.0287064			0.0143532	−	0.999897i	$-0.495431\pi$
$911$	0.866439			0.0287064			0.0143532	+	0.999897i	$0.495431\pi$
$912$	15.3342	+	20.9676i	0.507767	+	0.694306i
$913$	−2.12921	+	3.68789i	−0.0704664	+	0.122051i
$914$	14.2766	+	1.48924i	0.472227	+	0.0492598i
$915$	8.25407	+	2.21167i	0.272871	+	0.0731156i
$916$	1.79653	−	0.0969689i	0.0593589	−	0.00320394i
$917$		0			0
$918$	−1.75895	−	0.673622i	−0.0580541	−	0.0222328i
$919$	28.1635	−	16.2602i	0.929028	−	0.536375i	0.0425240	−	0.999095i	$-0.486460\pi$
$919$	28.1635	−	16.2602i	0.929028	−	0.536375i	0.886504	+	0.462721i	$0.153127\pi$
$920$	−5.36000	−	0.268301i	−0.176714	−	0.00884564i
$921$	10.1006	+	5.83158i	0.332826	+	0.192157i
$922$	−2.02666	+	0.322616i	−0.0667445	+	0.0106248i
$923$	−18.2600	−	18.2600i	−0.601034	−	0.601034i
$924$		0			0
$925$	23.2311	−	23.2311i	0.763835	−	0.763835i
$926$	−12.1283	−	8.79726i	−0.398561	−	0.289096i
$927$	12.8353	−	22.2314i	0.421568	−	0.730176i
$928$	−1.84891	+	1.86342i	−0.0606933	+	0.0611697i
$929$	−5.10083	−	8.83489i	−0.167353	−	0.289863i	0.770136	−	0.637880i	$-0.220189\pi$
$929$	−5.10083	−	8.83489i	−0.167353	−	0.289863i	−0.937488	+	0.348017i	$0.886855\pi$
$930$	−9.68363	+	4.32050i	−0.317539	+	0.141675i
$931$		0			0
$932$	36.5595	+	32.8150i	1.19755	+	1.07489i
$933$	−8.14415	+	30.3944i	−0.266628	+	0.995068i
$934$	11.6756	+	14.3951i	0.382037	+	0.471023i
$935$	1.18360	+	0.683354i	0.0387080	+	0.0223481i
$936$	13.4169	+	8.66837i	0.438545	+	0.283334i
$937$			5.06532i			0.165477i	0.996571	+	0.0827384i	$0.0263666\pi$
$937$			5.06532i			0.165477i	−0.996571	+	0.0827384i	$0.973633\pi$
$938$		0			0
$939$	−2.27447	−	2.27447i	−0.0742247	−	0.0742247i
$940$	−4.18812	−	6.42712i	−0.136602	−	0.209630i
$941$	−10.7693	−	40.1915i	−0.351069	−	1.31021i	−0.885360	−	0.464906i	$-0.846088\pi$
$941$	−10.7693	−	40.1915i	−0.351069	−	1.31021i	0.534292	−	0.845300i	$-0.320578\pi$
$942$	−29.4927	−	3.07650i	−0.960925	−	0.100238i
$943$	−8.52943	−	14.7734i	−0.277757	−	0.481088i
$944$	−16.4062	+	20.3900i	−0.533976	+	0.663638i
$945$		0			0
$946$	−11.6092	−	26.0200i	−0.377449	−	0.845984i
$947$	−25.9598	−	6.95589i	−0.843579	−	0.226036i	−0.188950	−	0.981987i	$-0.560508\pi$
$947$	−25.9598	−	6.95589i	−0.843579	−	0.226036i	−0.654629	+	0.755951i	$0.727175\pi$
$948$	−22.7135	−	11.5284i	−0.737701	−	0.374425i
$949$	40.8824	−	10.9544i	1.32710	−	0.355595i
$950$	−4.98719	−	31.3293i	−0.161806	−	1.01646i
$951$			2.24518i			0.0728049i
$952$		0			0
$953$			39.1113i			1.26694i	0.773767	+	0.633470i	$0.218370\pi$
$953$			39.1113i			1.26694i	−0.773767	+	0.633470i	$0.781630\pi$
$954$	1.68103	−	0.267596i	0.0544254	−	0.00866375i
$955$	4.11414	−	1.10238i	0.133130	−	0.0356722i
$956$	−18.1971	−	55.7085i	−0.588537	−	1.80174i
$957$	1.90876	+	0.511450i	0.0617013	+	0.0165328i
$958$	43.2349	−	19.2900i	1.39686	−	0.623230i
$959$		0			0
$960$	8.06128	+	5.79928i	0.260177	+	0.187171i
$961$	−2.74280	−	4.75066i	−0.0884773	−	0.153247i
$962$	3.94145	−	37.7845i	0.127077	−	1.21822i
$963$	0.898150	+	3.35194i	0.0289425	+	0.108015i
$964$	−15.5387	−	3.27747i	−0.500468	−	0.105560i
$965$	−6.58300	−	6.58300i	−0.211914	−	0.211914i
$966$		0			0
$967$			53.9124i			1.73371i	0.498565	+	0.866853i	$0.333861\pi$
$967$			53.9124i			1.73371i	−0.498565	+	0.866853i	$0.666139\pi$
$968$	−3.99669	−	18.5885i	−0.128458	−	0.597456i
$969$	1.48790	+	0.859038i	0.0477982	+	0.0275963i
$970$	19.2002	−	15.5729i	0.616480	−	0.500015i
$971$	9.55711	−	35.6676i	0.306702	−	1.14463i	−0.624768	−	0.780811i	$-0.714806\pi$
$971$	9.55711	−	35.6676i	0.306702	−	1.14463i	0.931470	−	0.363818i	$-0.118527\pi$
$972$	−1.71936	−	31.8543i	−0.0551485	−	1.02173i
$973$		0			0
$974$	−13.2674	−	29.7365i	−0.425115	−	0.952819i
$975$	5.04892	+	8.74499i	0.161695	+	0.280064i
$976$	25.6761	−	9.94836i	0.821871	−	0.318439i
$977$	28.5378	−	49.4289i	0.913004	−	1.58137i	0.103207	−	0.994660i	$-0.467090\pi$
$977$	28.5378	−	49.4289i	0.913004	−	1.58137i	0.809797	−	0.586710i	$-0.199577\pi$
$978$	5.28323	−	7.28371i	0.168939	−	0.232907i
$979$	−32.7217	+	32.7217i	−1.04579	+	1.04579i
$980$		0			0
$981$	−21.6525	−	21.6525i	−0.691311	−	0.691311i
$982$	6.89638	+	43.3228i	0.220072	+	1.38249i
$983$	−40.3197	−	23.2786i	−1.28600	−	0.742471i	−0.308060	−	0.951367i	$-0.599680\pi$
$983$	−40.3197	−	23.2786i	−1.28600	−	0.742471i	−0.977938	+	0.208896i	$0.933013\pi$
$984$	−1.57809	+	31.5262i	−0.0503075	+	1.00502i
$985$	11.7648	−	6.79239i	0.374857	−	0.216424i
$986$	−0.0620926	+	0.162136i	−0.00197743	+	0.00516345i
$987$		0			0
$988$	−27.2991	−	24.5030i	−0.868499	−	0.779544i
$989$	7.14771	+	1.91522i	0.227284	+	0.0609005i
$990$	−1.49836	+	14.3639i	−0.0476209	+	0.456515i
$991$	−26.4721	+	45.8511i	−0.840915	+	1.45651i	0.0482069	+	0.998837i	$0.484649\pi$
$991$	−26.4721	+	45.8511i	−0.840915	+	1.45651i	−0.889122	+	0.457670i	$0.848684\pi$
$992$	−16.9688	+	29.6580i	−0.538761	+	0.941643i
$993$	−2.80341			−0.0889635
$994$		0			0
$995$	17.0677	−	17.0677i	0.541082	−	0.541082i
$996$	−0.422356	+	2.00242i	−0.0133829	+	0.0634491i
$997$	−21.9178	+	5.87285i	−0.694143	+	0.185995i	−0.588606	−	0.808420i	$-0.700323\pi$
$997$	−21.9178	+	5.87285i	−0.694143	+	0.185995i	−0.105537	+	0.994415i	$0.533656\pi$
$998$	7.71259	+	9.50905i	0.244138	+	0.301004i
$999$	−40.9933	+	23.6675i	−1.29697	+	0.748807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.k.165.2		16
7.2	even	3	inner	784.2.x.k.373.2		16
7.3	odd	6		784.2.m.g.197.4		8
7.4	even	3		112.2.m.c.85.4	yes	8
7.5	odd	6		784.2.x.j.373.2		16
7.6	odd	2		784.2.x.j.165.2		16
16.13	even	4	inner	784.2.x.k.557.2		16
28.11	odd	6		448.2.m.c.113.3		8
56.11	odd	6		896.2.m.f.225.2		8
56.53	even	6		896.2.m.e.225.3		8
112.11	odd	12		896.2.m.f.673.2		8
112.13	odd	4		784.2.x.j.557.2		16
112.45	odd	12		784.2.m.g.589.4		8
112.53	even	12		896.2.m.e.673.3		8
112.61	odd	12		784.2.x.j.765.2		16
112.67	odd	12		448.2.m.c.337.3		8
112.93	even	12	inner	784.2.x.k.765.2		16
112.109	even	12		112.2.m.c.29.4	✓	8
224.67	odd	24		7168.2.a.bd.1.5		8
224.109	even	24		7168.2.a.bc.1.5		8
224.179	odd	24		7168.2.a.bd.1.4		8
224.221	even	24		7168.2.a.bc.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.4	✓	8	112.109	even	12
112.2.m.c.85.4	yes	8	7.4	even	3
448.2.m.c.113.3		8	28.11	odd	6
448.2.m.c.337.3		8	112.67	odd	12
784.2.m.g.197.4		8	7.3	odd	6
784.2.m.g.589.4		8	112.45	odd	12
784.2.x.j.165.2		16	7.6	odd	2
784.2.x.j.373.2		16	7.5	odd	6
784.2.x.j.557.2		16	112.13	odd	4
784.2.x.j.765.2		16	112.61	odd	12
784.2.x.k.165.2		16	1.1	even	1	trivial
784.2.x.k.373.2		16	7.2	even	3	inner
784.2.x.k.557.2		16	16.13	even	4	inner
784.2.x.k.765.2		16	112.93	even	12	inner
896.2.m.e.225.3		8	56.53	even	6
896.2.m.e.673.3		8	112.53	even	12
896.2.m.f.225.2		8	56.11	odd	6
896.2.m.f.673.2		8	112.11	odd	12
7168.2.a.bc.1.4		8	224.221	even	24
7168.2.a.bc.1.5		8	224.109	even	24
7168.2.a.bd.1.4		8	224.179	odd	24
7168.2.a.bd.1.5		8	224.67	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.14477 - 0.830359i) q^{2} +(-0.261809 - 0.977085i) q^{3} +(0.621007 + 1.90114i) q^{4} +(0.317608 - 1.18533i) q^{5} +(-0.511620 + 1.33594i) q^{6} +(0.867721 - 2.69204i) q^{8} +(1.71192 - 0.988380i) q^{9} +(-1.34784 + 1.09320i) q^{10} +(4.06633 - 1.08957i) q^{11} +(1.69499 - 1.10451i) q^{12} +(-2.02017 + 2.02017i) q^{13} -1.24132 q^{15} +(-3.22870 + 2.36125i) q^{16} +(-0.132279 + 0.229115i) q^{17} +(-2.78047 - 0.290042i) q^{18} +(6.20120 + 1.66161i) q^{19} +(2.45072 - 0.132279i) q^{20} +(-5.55976 - 2.12921i) q^{22} +(1.33906 - 0.773104i) q^{23} +(-2.85753 - 0.143037i) q^{24} +(3.02600 + 1.74706i) q^{25} +(3.99009 - 0.635167i) q^{26} +(-3.55976 - 3.55976i) q^{27} +(-0.328129 + 0.328129i) q^{29} +(1.42103 + 1.03074i) q^{30} +(-3.02017 + 5.23108i) q^{31} +(5.65681 - 0.0221123i) q^{32} +(-2.12921 - 3.68789i) q^{33} +(0.341677 - 0.152445i) q^{34} +(2.94217 + 2.64082i) q^{36} +(2.43357 - 9.08220i) q^{37} +(-5.71923 - 7.05138i) q^{38} +(2.50277 + 1.44498i) q^{39} +(-2.91535 - 1.88355i) q^{40} -11.0327i q^{41} +(3.38407 + 3.38407i) q^{43} +(4.59665 + 7.05405i) q^{44} +(-0.627835 - 2.34311i) q^{45} +(-2.17487 - 0.226869i) q^{46} +(-1.56283 - 2.70690i) q^{47} +(3.15244 + 2.53652i) q^{48} +(-2.01339 - 4.51265i) q^{50} +(0.258496 + 0.0692639i) q^{51} +(-5.09516 - 2.58609i) q^{52} +(-0.588145 + 0.157593i) q^{53} +(1.11923 + 7.03099i) q^{54} -5.16599i q^{55} -6.49412i q^{57} +(0.648097 - 0.103168i) q^{58} +(6.31978 - 1.69338i) q^{59} +(-0.770868 - 2.35993i) q^{60} +(-6.64943 - 1.78171i) q^{61} +(7.80108 - 3.48057i) q^{62} +(-6.49412 - 4.67187i) q^{64} +(1.75294 + 3.03618i) q^{65} +(-0.624819 + 5.98980i) q^{66} +(1.22389 + 4.56764i) q^{67} +(-0.517726 - 0.109200i) q^{68} +(-1.10597 - 1.10597i) q^{69} +9.03885i q^{71} +(-1.17528 - 5.46620i) q^{72} +(-12.8298 - 7.40731i) q^{73} +(-10.3274 + 8.37632i) q^{74} +(0.914793 - 3.41405i) q^{75} +(0.692037 + 12.8212i) q^{76} +(-1.66525 - 3.73237i) q^{78} +(-6.29520 - 10.9036i) q^{79} +(1.77340 + 4.57702i) q^{80} +(0.418932 - 0.725612i) q^{81} +(-9.16111 + 12.6299i) q^{82} +(-0.715276 + 0.715276i) q^{83} +(0.229563 + 0.229563i) q^{85} +(-1.06400 - 6.68399i) q^{86} +(0.406517 + 0.234703i) q^{87} +(0.595277 - 11.8922i) q^{88} +(-9.51968 + 5.49619i) q^{89} +(-1.22690 + 3.20366i) q^{90} +(2.30135 + 2.06564i) q^{92} +(5.90192 + 1.58141i) q^{93} +(-0.458616 + 4.39650i) q^{94} +(3.93910 - 6.82272i) q^{95} +(-1.50261 - 5.52140i) q^{96} -14.2452 q^{97} +(5.88434 - 5.88434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} + 4 q^{5} - 32 q^{6} - 8 q^{8} - 12 q^{10} + 12 q^{12} - 16 q^{15} - 8 q^{16} - 24 q^{17} - 6 q^{18} + 12 q^{19} - 16 q^{20} - 8 q^{22} - 8 q^{26} + 24 q^{27} - 32 q^{29} - 20 q^{30}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 + 4 * q^5 - 32 * q^6 - 8 * q^8 - 12 * q^10 + 12 * q^12 - 16 * q^15 - 8 * q^16 - 24 * q^17 - 6 * q^18 + 12 * q^19 - 16 * q^20 - 8 * q^22 - 8 * q^26 + 24 * q^27 - 32 * q^29 - 20 * q^30 - 16 * q^31 + 28 * q^32 + 24 * q^33 - 24 * q^34 + 48 * q^36 - 16 * q^37 + 16 * q^38 - 28 * q^40 - 64 * q^43 + 32 * q^44 + 8 * q^45 - 20 * q^46 - 24 * q^47 + 40 * q^48 - 28 * q^50 - 8 * q^51 - 32 * q^52 + 8 * q^53 + 16 * q^54 - 12 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 + 40 * q^62 - 64 * q^64 + 48 * q^65 + 16 * q^66 - 28 * q^68 + 88 * q^69 - 44 * q^72 + 4 * q^74 - 28 * q^75 - 48 * q^76 + 24 * q^78 + 24 * q^79 + 12 * q^80 - 40 * q^81 - 4 * q^82 - 80 * q^85 + 40 * q^88 - 32 * q^90 + 72 * q^92 - 16 * q^93 - 28 * q^94 - 16 * q^95 - 8 * q^96 - 64 * q^97 + 96 * q^99

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