LMFDB - Embedded newform 784.2.x.o.165.5

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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.5
Character	$\chi$	$=$	784.165
Dual form			784.2.x.o.765.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.504093 - 1.32132i) q^{2} +(-0.589510 - 2.20008i) q^{3} +(-1.49178 + 1.33214i) q^{4} +(0.622192 - 2.32205i) q^{5} +(-2.60985 + 1.88798i) q^{6} +(2.51218 + 1.29960i) q^{8} +(-1.89476 + 1.09394i) q^{9} +O(q^{10})$	\(q+(-0.504093 - 1.32132i) q^{2} +(-0.589510 - 2.20008i) q^{3} +(-1.49178 + 1.33214i) q^{4} +(0.622192 - 2.32205i) q^{5} +(-2.60985 + 1.88798i) q^{6} +(2.51218 + 1.29960i) q^{8} +(-1.89476 + 1.09394i) q^{9} +(-3.38182 + 0.348414i) q^{10} +(0.0284448 - 0.00762177i) q^{11} +(3.81023 + 2.49673i) q^{12} +(-4.38886 + 4.38886i) q^{13} -5.47550 q^{15} +(0.450822 - 3.97451i) q^{16} +(-1.36101 + 2.35734i) q^{17} +(2.40059 + 1.95214i) q^{18} +(-5.73909 - 1.53778i) q^{19} +(2.16512 + 4.29284i) q^{20} +(-0.0244096 - 0.0337427i) q^{22} +(-3.33422 + 1.92501i) q^{23} +(1.37828 - 6.29313i) q^{24} +(-0.674681 - 0.389527i) q^{25} +(8.01149 + 3.58670i) q^{26} +(-1.30797 - 1.30797i) q^{27} +(-4.93772 + 4.93772i) q^{29} +(2.76016 + 7.23489i) q^{30} +(1.29224 - 2.23823i) q^{31} +(-5.47887 + 1.40784i) q^{32} +(-0.0335370 - 0.0580879i) q^{33} +(3.80088 + 0.610015i) q^{34} +(1.36929 - 4.15601i) q^{36} +(2.09988 - 7.83686i) q^{37} +(0.861125 + 8.35837i) q^{38} +(12.2431 + 7.06857i) q^{39} +(4.58080 - 5.02481i) q^{40} -0.207557i q^{41} +(-0.278444 - 0.278444i) q^{43} +(-0.0322802 + 0.0492624i) q^{44} +(1.36129 + 5.08039i) q^{45} +(4.22432 + 3.43519i) q^{46} +(1.91470 + 3.31636i) q^{47} +(-9.01002 + 1.35117i) q^{48} +(-0.174589 + 1.08783i) q^{50} +(5.98867 + 1.60466i) q^{51} +(0.700656 - 12.3938i) q^{52} +(1.22448 - 0.328098i) q^{53} +(-1.06891 + 2.38758i) q^{54} -0.0707926i q^{55} +13.5330i q^{57} +(9.01338 + 4.03524i) q^{58} +(0.208496 - 0.0558664i) q^{59} +(8.16824 - 7.29411i) q^{60} +(-5.93409 - 1.59004i) q^{61} +(-3.60883 - 0.579193i) q^{62} +(4.62207 + 6.52966i) q^{64} +(7.46045 + 12.9219i) q^{65} +(-0.0598470 + 0.0735949i) q^{66} +(-3.20844 - 11.9741i) q^{67} +(-1.10997 - 5.32969i) q^{68} +(6.20075 + 6.20075i) q^{69} -7.37112i q^{71} +(-6.18168 + 0.285738i) q^{72} +(3.67756 + 2.12324i) q^{73} +(-11.4135 + 1.17589i) q^{74} +(-0.459261 + 1.71398i) q^{75} +(10.6100 - 5.35122i) q^{76} +(3.16819 - 19.7403i) q^{78} +(-4.51126 - 7.81374i) q^{79} +(-8.94853 - 3.51975i) q^{80} +(-5.38841 + 9.33299i) q^{81} +(-0.274250 + 0.104628i) q^{82} +(7.55784 - 7.55784i) q^{83} +(4.62706 + 4.62706i) q^{85} +(-0.227552 + 0.508276i) q^{86} +(13.7742 + 7.95255i) q^{87} +(0.0813637 + 0.0178197i) q^{88} +(-3.03921 + 1.75469i) q^{89} +(6.02661 - 4.35968i) q^{90} +(2.40955 - 7.31334i) q^{92} +(-5.68608 - 1.52358i) q^{93} +(3.41679 - 4.20169i) q^{94} +(-7.14164 + 12.3697i) q^{95} +(6.32722 + 11.2240i) q^{96} +11.1522 q^{97} +(-0.0455585 + 0.0455585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−0.504093	−	1.32132i	−0.356447	−	0.934315i
$2$	−0.504093	−	1.32132i	−0.356447	−	0.934315i
$3$	−0.589510	−	2.20008i	−0.340354	−	1.27022i	−0.897947	−	0.440104i	$-0.854942\pi$
$3$	−0.589510	−	2.20008i	−0.340354	−	1.27022i	0.557593	−	0.830115i	$-0.311725\pi$
$4$	−1.49178	+	1.33214i	−0.745891	+	0.666068i
$5$	0.622192	−	2.32205i	0.278253	−	1.03845i	−0.675377	−	0.737472i	$-0.736019\pi$
$5$	0.622192	−	2.32205i	0.278253	−	1.03845i	0.953630	−	0.300981i	$-0.0973142\pi$
$6$	−2.60985	+	1.88798i	−1.06547	+	0.770764i
$7$		0			0
$7$		0			0
$8$	2.51218	+	1.29960i	0.888189	+	0.459479i
$9$	−1.89476	+	1.09394i	−0.631588	+	0.364648i
$10$	−3.38182	+	0.348414i	−1.06943	+	0.110178i
$11$	0.0284448	−	0.00762177i	0.00857644	−	0.00229805i	−0.254528	−	0.967065i	$-0.581920\pi$
$11$	0.0284448	−	0.00762177i	0.00857644	−	0.00229805i	0.263105	+	0.964767i	$0.415254\pi$
$12$	3.81023	+	2.49673i	1.09992	+	0.720745i
$13$	−4.38886	+	4.38886i	−1.21725	+	1.21725i	−0.248660	+	0.968591i	$0.579990\pi$
$13$	−4.38886	+	4.38886i	−1.21725	+	1.21725i	−0.968591	+	0.248660i	$0.920010\pi$
$14$		0			0
$15$	−5.47550			−1.41377
$16$	0.450822	−	3.97451i	0.112706	−	0.993628i
$17$	−1.36101	+	2.35734i	−0.330094	+	0.571739i	−0.982530	−	0.186105i	$-0.940414\pi$
$17$	−1.36101	+	2.35734i	−0.330094	+	0.571739i	0.652436	+	0.757844i	$0.273747\pi$
$18$	2.40059	+	1.95214i	0.565824	+	0.460125i
$19$	−5.73909	−	1.53778i	−1.31664	−	0.352792i	−0.468921	−	0.883240i	$-0.655357\pi$
$19$	−5.73909	−	1.53778i	−1.31664	−	0.352792i	−0.847717	+	0.530448i	$0.822024\pi$
$20$	2.16512	+	4.29284i	0.484135	+	0.959908i
$21$		0			0
$22$	−0.0244096	−	0.0337427i	−0.00520415	−	0.00719396i
$23$	−3.33422	+	1.92501i	−0.695233	+	0.401393i	−0.805570	−	0.592501i	$-0.798141\pi$
$23$	−3.33422	+	1.92501i	−0.695233	+	0.401393i	0.110336	+	0.993894i	$0.464807\pi$
$24$	1.37828	−	6.29313i	0.281340	−	1.28458i
$25$	−0.674681	−	0.389527i	−0.134936	−	0.0779054i
$26$	8.01149	+	3.58670i	1.57118	+	0.703410i
$27$	−1.30797	−	1.30797i	−0.251719	−	0.251719i
$28$		0			0
$29$	−4.93772	+	4.93772i	−0.916911	+	0.916911i	−0.996803	−	0.0798926i	$-0.974542\pi$
$29$	−4.93772	+	4.93772i	−0.916911	+	0.916911i	0.0798926	+	0.996803i	$0.474542\pi$
$30$	2.76016	+	7.23489i	0.503934	+	1.32090i
$31$	1.29224	−	2.23823i	0.232094	−	0.401998i	−0.726330	−	0.687346i	$-0.758776\pi$
$31$	1.29224	−	2.23823i	0.232094	−	0.401998i	0.958424	+	0.285348i	$0.0921091\pi$
$32$	−5.47887	+	1.40784i	−0.968536	+	0.248874i
$33$	−0.0335370	−	0.0580879i	−0.00583805	−	0.0101118i
$34$	3.80088	+	0.610015i	0.651846	+	0.104617i
$35$		0			0
$36$	1.36929	−	4.15601i	0.228215	−	0.692668i
$37$	2.09988	−	7.83686i	0.345218	−	1.28837i	−0.547139	−	0.837042i	$-0.684283\pi$
$37$	2.09988	−	7.83686i	0.345218	−	1.28837i	0.892357	−	0.451330i	$-0.149050\pi$
$38$	0.861125	+	8.35837i	0.139693	+	1.35591i
$39$	12.2431	+	7.06857i	1.96047	+	1.13188i
$40$	4.58080	−	5.02481i	0.724289	−	0.794492i
$41$		−	0.207557i		−	0.0324150i	−0.999869	−	0.0162075i	$-0.994841\pi$
$41$		−	0.207557i		−	0.0324150i	0.999869	−	0.0162075i	$-0.00515924\pi$
$42$		0			0
$43$	−0.278444	−	0.278444i	−0.0424623	−	0.0424623i	0.685557	−	0.728019i	$-0.259559\pi$
$43$	−0.278444	−	0.278444i	−0.0424623	−	0.0424623i	−0.728019	+	0.685557i	$0.759559\pi$
$44$	−0.0322802	+	0.0492624i	−0.00486643	+	0.00742659i
$45$	1.36129	+	5.08039i	0.202928	+	0.757339i
$46$	4.22432	+	3.43519i	0.622842	+	0.506492i
$47$	1.91470	+	3.31636i	0.279288	+	0.483741i	0.971208	−	0.238233i	$-0.0765683\pi$
$47$	1.91470	+	3.31636i	0.279288	+	0.483741i	−0.691920	+	0.721974i	$0.743235\pi$
$48$	−9.01002	+	1.35117i	−1.30048	+	0.195025i
$49$		0			0
$50$	−0.174589	+	1.08783i	−0.0246906	+	0.153842i
$51$	5.98867	+	1.60466i	0.838582	+	0.224697i
$52$	0.700656	−	12.3938i	0.0971636	−	1.71871i
$53$	1.22448	−	0.328098i	0.168195	−	0.0450677i	−0.173739	−	0.984792i	$-0.555585\pi$
$53$	1.22448	−	0.328098i	0.168195	−	0.0450677i	0.341934	+	0.939724i	$0.388918\pi$
$54$	−1.06891	+	2.38758i	−0.145460	+	0.324909i
$55$		−	0.0707926i		−	0.00954567i
$56$		0			0
$57$			13.5330i			1.79249i
$58$	9.01338	+	4.03524i	1.18351	+	0.529854i
$59$	0.208496	−	0.0558664i	0.0271439	−	0.00727319i	−0.245222	−	0.969467i	$-0.578861\pi$
$59$	0.208496	−	0.0558664i	0.0271439	−	0.00727319i	0.272365	+	0.962194i	$0.412194\pi$
$60$	8.16824	−	7.29411i	1.05452	−	0.941666i
$61$	−5.93409	−	1.59004i	−0.759783	−	0.203583i	−0.141930	−	0.989877i	$-0.545331\pi$
$61$	−5.93409	−	1.59004i	−0.759783	−	0.203583i	−0.617853	+	0.786294i	$0.711997\pi$
$62$	−3.60883	−	0.579193i	−0.458322	−	0.0735575i
$63$		0			0
$64$	4.62207	+	6.52966i	0.577759	+	0.816208i
$65$	7.46045	+	12.9219i	0.925355	+	1.60276i
$66$	−0.0598470	+	0.0735949i	−0.00736665	+	0.00905890i
$67$	−3.20844	−	11.9741i	−0.391974	−	1.46287i	−0.826874	−	0.562387i	$-0.809883\pi$
$67$	−3.20844	−	11.9741i	−0.391974	−	1.46287i	0.434901	−	0.900479i	$-0.356784\pi$
$68$	−1.10997	−	5.32969i	−0.134604	−	0.646320i
$69$	6.20075	+	6.20075i	0.746482	+	0.746482i
$70$		0			0
$71$		−	7.37112i		−	0.874791i	−0.899269	−	0.437395i	$-0.855901\pi$
$71$		−	7.37112i		−	0.874791i	0.899269	−	0.437395i	$-0.144099\pi$
$72$	−6.18168	+	0.285738i	−0.728517	+	0.0336745i
$73$	3.67756	+	2.12324i	0.430426	+	0.248507i	0.699528	−	0.714605i	$-0.253394\pi$
$73$	3.67756	+	2.12324i	0.430426	+	0.248507i	−0.269102	+	0.963112i	$0.586727\pi$
$74$	−11.4135	+	1.17589i	−1.32680	+	0.136694i
$75$	−0.459261	+	1.71398i	−0.0530308	+	0.197914i
$76$	10.6100	−	5.35122i	1.21705	−	0.613827i
$77$		0			0
$78$	3.16819	−	19.7403i	0.358727	−	2.23515i
$79$	−4.51126	−	7.81374i	−0.507557	−	0.879114i	−0.999962	−	0.00874800i	$-0.997215\pi$
$79$	−4.51126	−	7.81374i	−0.507557	−	0.879114i	0.492405	−	0.870366i	$-0.336118\pi$
$80$	−8.94853	−	3.51975i	−1.00048	−	0.393519i
$81$	−5.38841	+	9.33299i	−0.598712	+	1.03700i
$82$	−0.274250	+	0.104628i	−0.0302859	+	0.0115542i
$83$	7.55784	−	7.55784i	0.829580	−	0.829580i	−0.157878	−	0.987459i	$-0.550465\pi$
$83$	7.55784	−	7.55784i	0.829580	−	0.829580i	0.987459	+	0.157878i	$0.0504653\pi$
$84$		0			0
$85$	4.62706	+	4.62706i	0.501875	+	0.501875i
$86$	−0.227552	+	0.508276i	−0.0245376	+	0.0548088i
$87$	13.7742	+	7.95255i	1.47675	+	0.852603i
$88$	0.0813637	+	0.0178197i	0.00867340	+	0.00189959i
$89$	−3.03921	+	1.75469i	−0.322155	+	0.185996i	−0.652353	−	0.757915i	$-0.726218\pi$
$89$	−3.03921	+	1.75469i	−0.322155	+	0.185996i	0.330198	+	0.943912i	$0.392885\pi$
$90$	6.02661	−	4.35968i	0.635261	−	0.459551i
$91$		0			0
$92$	2.40955	−	7.31334i	0.251213	−	0.762468i
$93$	−5.68608	−	1.52358i	−0.589619	−	0.157988i
$94$	3.41679	−	4.20169i	0.352415	−	0.433371i
$95$	−7.14164	+	12.3697i	−0.732716	+	1.26910i
$96$	6.32722	+	11.2240i	0.645769	+	1.14555i
$97$	11.1522			1.13233			0.566167	−	0.824290i	$-0.308426\pi$
$97$	11.1522			1.13233			0.566167	+	0.824290i	$0.308426\pi$
$98$		0			0
$99$	−0.0455585	+	0.0455585i	−0.00457880	+	0.00457880i
$100$	1.52538	−	0.317678i	0.152538	−	0.0317678i
$101$	−13.8235	+	3.70400i	−1.37549	+	0.368561i	−0.869481	−	0.493967i	$-0.835546\pi$
$101$	−13.8235	+	3.70400i	−1.37549	+	0.368561i	−0.506009	+	0.862528i	$0.668880\pi$
$102$	−0.898574	−	8.72186i	−0.0889721	−	0.863593i
$103$	−3.78718	+	2.18653i	−0.373162	+	0.215445i	−0.674839	−	0.737965i	$-0.735787\pi$
$103$	−3.78718	+	2.18653i	−0.373162	+	0.215445i	0.301677	+	0.953410i	$0.402454\pi$
$104$	−16.7294	+	5.32182i	−1.64045	+	0.521847i
$105$		0			0
$106$	−1.05077	−	1.45254i	−0.102060	−	0.141083i
$107$	4.66945	−	17.4266i	0.451413	−	1.68470i	−0.247011	−	0.969013i	$-0.579448\pi$
$107$	4.66945	−	17.4266i	0.451413	−	1.68470i	0.698424	−	0.715684i	$-0.253885\pi$
$108$	3.69360	+	0.208810i	0.355416	+	0.0200927i
$109$	3.03462	+	11.3254i	0.290664	+	1.08477i	0.944600	+	0.328223i	$0.106450\pi$
$109$	3.03462	+	11.3254i	0.290664	+	1.08477i	−0.653936	+	0.756550i	$0.726884\pi$
$110$	−0.0935398	+	0.0356860i	−0.00891867	+	0.00340253i
$111$	−18.4796			−1.75401
$112$		0			0
$113$	−5.25802			−0.494633			−0.247316	−	0.968935i	$-0.579549\pi$
$113$	−5.25802			−0.494633			−0.247316	+	0.968935i	$0.579549\pi$
$114$	17.8815	−	6.82189i	1.67475	−	0.638929i
$115$	2.39546	+	8.93997i	0.223378	+	0.833657i
$116$	0.788278	−	13.9437i	0.0731898	−	1.29464i
$117$	3.51469	−	13.1170i	0.324934	−	1.21267i
$118$	−0.178919	−	0.247329i	−0.0164708	−	0.0227685i
$119$		0			0
$120$	−13.7554	−	7.11597i	−1.25569	−	0.649596i
$121$	−9.52553	+	5.49957i	−0.865957	+	0.499961i
$122$	0.890385	+	8.64237i	0.0806116	+	0.782443i
$123$	−0.456643	+	0.122357i	−0.0411742	+	0.0110326i
$124$	1.05389	+	5.06039i	0.0946417	+	0.454437i
$125$	7.17502	−	7.17502i	0.641753	−	0.641753i
$126$		0			0
$127$	7.05793			0.626290			0.313145	−	0.949705i	$-0.398617\pi$
$127$	7.05793			0.626290			0.313145	+	0.949705i	$0.398617\pi$
$128$	6.29783	−	9.39879i	0.556655	−	0.830744i
$129$	−0.448454	+	0.776745i	−0.0394842	+	0.0683886i
$130$	13.3132	−	16.3715i	1.16764	−	1.43587i
$131$	−8.52012	−	2.28296i	−0.744407	−	0.199463i	−0.133371	−	0.991066i	$-0.542580\pi$
$131$	−8.52012	−	2.28296i	−0.744407	−	0.199463i	−0.611036	+	0.791603i	$0.709247\pi$
$132$	0.127411	+	0.0419784i	0.0110897	+	0.00365375i
$133$		0			0
$134$	−14.2042	+	10.2754i	−1.22706	+	0.887662i
$135$	−3.85098	+	2.22336i	−0.331440	+	0.191357i
$136$	−6.48271	+	4.15328i	−0.555887	+	0.356141i
$137$	−8.17549	−	4.72012i	−0.698479	−	0.403267i	0.108302	−	0.994118i	$-0.465459\pi$
$137$	−8.17549	−	4.72012i	−0.698479	−	0.403267i	−0.806781	+	0.590851i	$0.798792\pi$
$138$	5.06743	−	11.3189i	0.431368	−	0.963532i
$139$	−9.26594	−	9.26594i	−0.785927	−	0.785927i	0.194897	−	0.980824i	$-0.437563\pi$
$139$	−9.26594	−	9.26594i	−0.785927	−	0.785927i	−0.980824	+	0.194897i	$0.937563\pi$
$140$		0			0
$141$	6.16753	−	6.16753i	0.519400	−	0.519400i
$142$	−9.73962	+	3.71573i	−0.817330	+	0.311817i
$143$	−0.0913895	+	0.158291i	−0.00764237	+	0.0132370i
$144$	3.49369	+	8.02394i	0.291141	+	0.668662i
$145$	8.39343	+	14.5378i	0.697036	+	1.20730i
$146$	0.951653	−	5.92955i	0.0787593	−	0.490733i
$147$		0			0
$148$	7.30721	+	14.4882i	0.600649	+	1.19092i
$149$	−4.10675	+	15.3266i	−0.336438	+	1.25560i	0.565864	+	0.824498i	$0.308543\pi$
$149$	−4.10675	+	15.3266i	−0.336438	+	1.25560i	−0.902302	+	0.431104i	$0.858124\pi$
$150$	2.49623	−	0.257176i	0.203817	−	0.0209983i
$151$	−1.97991	−	1.14310i	−0.161122	−	0.0930241i	0.417271	−	0.908782i	$-0.362987\pi$
$151$	−1.97991	−	1.14310i	−0.161122	−	0.0930241i	−0.578393	+	0.815758i	$0.696320\pi$
$152$	−12.4191	−	11.3217i	−1.00732	−	0.918313i
$153$		−	5.95547i		−	0.481472i
$154$		0			0
$155$	−4.39326	−	4.39326i	−0.352875	−	0.352875i
$156$	−27.6804	+	5.76476i	−2.21620	+	0.461550i
$157$	−1.51721	−	5.66229i	−0.121086	−	0.451900i	0.878584	−	0.477588i	$-0.158489\pi$
$157$	−1.51721	−	5.66229i	−0.121086	−	0.451900i	−0.999670	+	0.0256882i	$0.991822\pi$
$158$	−8.05037	+	9.89968i	−0.640453	+	0.787576i
$159$	−1.44368	−	2.50053i	−0.114492	−	0.198305i
$160$	−0.139825	+	13.5982i	−0.0110542	+	1.07503i
$161$		0			0
$162$	15.0481	+	2.41512i	1.18229	+	0.189750i
$163$	−14.2334	−	3.81383i	−1.11485	−	0.298722i	−0.346050	−	0.938216i	$-0.612477\pi$
$163$	−14.2334	−	3.81383i	−1.11485	−	0.298722i	−0.768796	+	0.639494i	$0.779144\pi$
$164$	0.276495	+	0.309630i	0.0215906	+	0.0241781i
$165$	−0.155750	+	0.0417330i	−0.0121251	+	0.00324891i
$166$	−13.7962	−	6.17648i	−1.07079	−	0.479388i
$167$			15.6157i			1.20838i	0.796841	+	0.604190i	$0.206503\pi$
$167$			15.6157i			1.20838i	−0.796841	+	0.604190i	$0.793497\pi$
$168$		0			0
$169$		−	25.5242i		−	1.96340i
$170$	3.78137	−	8.44630i	0.290018	−	0.647802i
$171$	12.5565	−	3.36450i	0.960218	−	0.257290i
$172$	0.786303	+	0.0444520i	0.0599550	+	0.00338943i
$173$	−1.18182	−	0.316668i	−0.0898522	−	0.0240758i	0.213613	−	0.976918i	$-0.431477\pi$
$173$	−1.18182	−	0.316668i	−0.0898522	−	0.0240758i	−0.303465	+	0.952843i	$0.598144\pi$
$174$	3.56439	−	22.2090i	0.270216	−	1.68366i
$175$		0			0
$176$	−0.0174693	−	0.116490i	−0.00131679	−	0.00878080i
$177$	−0.245822	−	0.425775i	−0.0184771	−	0.0320032i
$178$	3.85055	+	3.13125i	0.288611	+	0.234697i
$179$	0.307054	+	1.14594i	0.0229503	+	0.0856516i	0.976451	−	0.215739i	$-0.0692160\pi$
$179$	0.307054	+	1.14594i	0.0229503	+	0.0856516i	−0.953501	+	0.301390i	$0.902549\pi$
$180$	−8.79851	−	5.76541i	−0.655802	−	0.429728i
$181$	1.91395	+	1.91395i	0.142263	+	0.142263i	0.774651	−	0.632389i	$-0.217925\pi$
$181$	1.91395	+	1.91395i	0.142263	+	0.142263i	−0.632389	+	0.774651i	$0.717925\pi$
$182$		0			0
$183$			13.9928i			1.03438i
$184$	−10.8779	+	0.502814i	−0.801930	+	0.0370679i
$185$	−16.8911	−	9.75206i	−1.24186	−	0.716986i
$186$	0.853171	+	8.28116i	0.0625575	+	0.607204i
$187$	−0.0207466	+	0.0774275i	−0.00151714	+	0.00566206i
$188$	−7.27416	−	2.39664i	−0.530523	−	0.174793i
$189$		0			0
$190$	19.9444	+	3.20094i	1.44692	+	0.232220i
$191$	3.36453	+	5.82754i	0.243449	+	0.421666i	0.961694	−	0.274124i	$-0.0883879\pi$
$191$	3.36453	+	5.82754i	0.243449	+	0.421666i	−0.718246	+	0.695790i	$0.755055\pi$
$192$	11.6410	−	14.0182i	0.840120	−	1.01168i
$193$	9.93003	−	17.1993i	0.714779	−	1.23803i	−0.248265	−	0.968692i	$-0.579860\pi$
$193$	9.93003	−	17.1993i	0.714779	−	1.23803i	0.963045	−	0.269342i	$-0.0868063\pi$
$194$	−5.62174	−	14.7356i	−0.403618	−	1.05796i
$195$	24.0312	−	24.0312i	1.72091	−	1.72091i
$196$		0			0
$197$	9.36967	+	9.36967i	0.667561	+	0.667561i	0.957151	−	0.289590i	$-0.0935188\pi$
$197$	9.36967	+	9.36967i	0.667561	+	0.667561i	−0.289590	+	0.957151i	$0.593519\pi$
$198$	0.0831631	+	0.0372317i	0.00591014	+	0.00264594i
$199$	−4.53338	−	2.61735i	−0.321363	−	0.185539i	0.330637	−	0.943758i	$-0.392736\pi$
$199$	−4.53338	−	2.61735i	−0.321363	−	0.185539i	−0.652000	+	0.758219i	$0.726070\pi$
$200$	−1.18869	−	1.85538i	−0.0840529	−	0.131195i
$201$	−24.4525	+	14.1177i	−1.72475	+	0.995784i
$202$	11.8625	+	16.3981i	0.834642	+	1.15377i
$203$		0			0
$204$	−11.0714	+	5.58393i	−0.775154	+	0.390953i
$205$	−0.481959	−	0.129141i	−0.0336615	−	0.00901957i
$206$	4.79820	+	3.90187i	0.334306	+	0.271856i
$207$	4.21171	−	7.29490i	0.292734	−	0.507030i
$208$	15.4650	+	19.4222i	1.07230	+	1.34669i
$209$	−0.174968			−0.0121028
$210$		0			0
$211$	−3.18196	+	3.18196i	−0.219055	+	0.219055i	−0.808100	−	0.589045i	$-0.799504\pi$
$211$	−3.18196	+	3.18196i	−0.219055	+	0.219055i	0.589045	+	0.808100i	$0.299504\pi$
$212$	−1.38958	+	2.12062i	−0.0954368	+	0.145645i
$213$	−16.2171	+	4.34535i	−1.11118	+	0.297738i
$214$	−25.3800	+	2.61479i	−1.73494	+	0.178743i
$215$	−0.819807	+	0.473316i	−0.0559104	+	0.0322799i
$216$	−1.58601	−	4.98569i	−0.107914	−	0.339233i
$217$		0			0
$218$	13.4347	−	9.71874i	0.909914	−	0.658236i
$219$	2.50335	−	9.34261i	0.169160	−	0.631315i
$220$	0.0943054	+	0.105607i	0.00635807	+	0.00712003i
$221$	−4.37275	−	16.3193i	−0.294143	−	1.09776i
$222$	9.31545	+	24.4175i	0.625212	+	1.63880i
$223$	−7.91238			−0.529852			−0.264926	−	0.964269i	$-0.585348\pi$
$223$	−7.91238			−0.529852			−0.264926	+	0.964269i	$0.585348\pi$
$224$		0			0
$225$	1.70448			0.113632
$226$	2.65053	+	6.94753i	0.176310	+	0.462143i
$227$	−1.97430	−	7.36819i	−0.131039	−	0.489044i	0.868944	−	0.494911i	$-0.164799\pi$
$227$	−1.97430	−	7.36819i	−0.131039	−	0.489044i	−0.999983	+	0.00586685i	$0.998133\pi$
$228$	−18.0278	−	20.1883i	−1.19392	−	1.33700i
$229$	1.10749	−	4.13322i	0.0731852	−	0.273131i	−0.919630	−	0.392785i	$-0.871512\pi$
$229$	1.10749	−	4.13322i	0.0731852	−	0.273131i	0.992816	+	0.119654i	$0.0381784\pi$
$230$	10.6050	−	7.67174i	0.699276	−	0.505860i
$231$		0			0
$232$	−18.8215	+	5.98735i	−1.23569	+	0.393089i
$233$	−18.3239	+	10.5793i	−1.20044	+	0.693074i	−0.960653	−	0.277751i	$-0.910411\pi$
$233$	−18.3239	+	10.5793i	−1.20044	+	0.693074i	−0.239787	+	0.970826i	$0.577078\pi$
$234$	−19.1035	+	1.96815i	−1.24884	+	0.128662i
$235$	8.89208	−	2.38262i	0.580055	−	0.155425i
$236$	−0.236609	+	0.361086i	−0.0154020	+	0.0235047i
$237$	−14.5314	+	14.5314i	−0.943918	+	0.943918i
$238$		0			0
$239$	−23.1747			−1.49905			−0.749523	−	0.661978i	$-0.769717\pi$
$239$	−23.1747			−1.49905			−0.749523	+	0.661978i	$0.769717\pi$
$240$	−2.46848	+	21.7624i	−0.159340	+	1.40476i
$241$	3.03376	−	5.25462i	0.195421	−	0.338480i	−0.751617	−	0.659600i	$-0.770726\pi$
$241$	3.03376	−	5.25462i	0.195421	−	0.338480i	0.947039	+	0.321120i	$0.104059\pi$
$242$	12.0684	+	9.81399i	0.775789	+	0.630867i
$243$	18.3497	+	4.91679i	1.17714	+	0.315412i
$244$	10.9705	−	5.53304i	0.702315	−	0.354217i
$245$		0			0
$246$	0.391864	+	0.541693i	0.0249843	+	0.0345371i
$247$	31.9372	−	18.4389i	2.03211	−	1.17324i
$248$	6.15515	−	3.94343i	0.390852	−	0.250408i
$249$	−21.0833	−	12.1724i	−1.33610	−	0.771397i
$250$	−13.0974	−	5.86363i	−0.828351	−	0.370849i
$251$	6.15437	+	6.15437i	0.388461	+	0.388461i	0.874138	−	0.485677i	$-0.161427\pi$
$251$	6.15437	+	6.15437i	0.388461	+	0.388461i	−0.485677	+	0.874138i	$0.661427\pi$
$252$		0			0
$253$	−0.0801694	+	0.0801694i	−0.00504020	+	0.00504020i
$254$	−3.55785	−	9.32579i	−0.223239	−	0.585152i
$255$	7.45221	−	12.9076i	0.466676	−	0.808306i
$256$	−15.5935	−	3.58360i	−0.974595	−	0.223975i
$257$	−11.0543	−	19.1467i	−0.689550	−	1.19434i	−0.971983	−	0.235049i	$-0.924475\pi$
$257$	−11.0543	−	19.1467i	−0.689550	−	1.19434i	0.282433	−	0.959287i	$-0.408858\pi$
$258$	1.25239	+	0.201000i	0.0779706	+	0.0125137i
$259$		0			0
$260$	−28.3431	−	9.33828i	−1.75776	−	0.579135i
$261$	3.95423	−	14.7574i	0.244761	−	0.913459i
$262$	1.27841	+	12.4086i	0.0789803	+	0.766609i
$263$	3.81595	+	2.20314i	0.235302	+	0.135852i	0.613016	−	0.790071i	$-0.289956\pi$
$263$	3.81595	+	2.20314i	0.235302	+	0.135852i	−0.377714	+	0.925922i	$0.623290\pi$
$264$	−0.00875988	−	0.189512i	−0.000539133	−	0.0116636i
$265$		−	3.04744i		−	0.187203i
$266$		0			0
$267$	5.65210	+	5.65210i	0.345903	+	0.345903i
$268$	20.7374	+	13.5886i	1.26674	+	0.830056i
$269$	0.219433	+	0.818934i	0.0133791	+	0.0499313i	0.972293	−	0.233767i	$-0.0751053\pi$
$269$	0.219433	+	0.818934i	0.0133791	+	0.0499313i	−0.958914	+	0.283698i	$0.908439\pi$
$270$	4.87903	+	3.96760i	0.296928	+	0.241461i
$271$	5.86644	+	10.1610i	0.356361	+	0.617235i	0.987350	−	0.158557i	$-0.0506840\pi$
$271$	5.86644	+	10.1610i	0.356361	+	0.617235i	−0.630989	+	0.775792i	$0.717351\pi$
$272$	8.75571	+	6.47210i	0.530893	+	0.392429i
$273$		0			0
$274$	−2.11559	+	13.1818i	−0.127808	+	0.796343i
$275$	−0.0221601	−	0.00593777i	−0.00133630	−	0.000358061i
$276$	−17.5104	−	0.989914i	−1.05400	−	0.0595858i
$277$	15.4763	−	4.14686i	0.929880	−	0.249161i	0.238076	−	0.971246i	$-0.423483\pi$
$277$	15.4763	−	4.14686i	0.929880	−	0.249161i	0.691803	+	0.722086i	$0.256816\pi$
$278$	−7.57239	+	16.9142i	−0.454162	+	1.01444i
$279$			5.65456i			0.338529i
$280$		0			0
$281$		−	21.3810i		−	1.27548i	−0.770250	−	0.637742i	$-0.779869\pi$
$281$		−	21.3810i		−	1.27548i	0.770250	−	0.637742i	$-0.220131\pi$
$282$	−11.2583	−	5.04028i	−0.670422	−	0.300144i
$283$	18.6380	−	4.99404i	1.10791	−	0.296865i	0.341931	−	0.939725i	$-0.388919\pi$
$283$	18.6380	−	4.99404i	1.10791	−	0.296865i	0.765983	+	0.642860i	$0.222252\pi$
$284$	9.81934	+	10.9961i	0.582670	+	0.652498i
$285$	31.4244	+	8.42014i	1.86142	+	0.498766i
$286$	0.255222	+	0.0409614i	0.0150916	+	0.00242210i
$287$		0			0
$288$	8.84106	−	8.66110i	0.520965	−	0.510360i
$289$	4.79530	+	8.30570i	0.282076	+	0.488571i
$290$	14.9781	−	18.4188i	0.879545	−	1.08159i
$291$	−6.57434	−	24.5358i	−0.385395	−	1.43831i
$292$	−8.31457	+	1.73160i	−0.486573	+	0.101334i
$293$	19.0966	+	19.0966i	1.11563	+	1.11563i	0.992374	+	0.123260i	$0.0393348\pi$
$293$	19.0966	+	19.0966i	1.11563	+	1.11563i	0.123260	+	0.992374i	$0.460665\pi$
$294$		0			0
$295$		−	0.518899i		−	0.0302115i
$296$	15.4601	−	16.9586i	0.898598	−	0.985697i
$297$	−0.0471740	−	0.0272359i	−0.00273731	−	0.00158039i
$298$	22.3215	−	2.29969i	1.29305	−	0.133217i
$299$	6.18482	−	23.0820i	0.357677	−	1.33487i
$300$	−1.59814	−	3.16869i	−0.0922689	−	0.182944i
$301$		0			0
$302$	−0.512346	+	3.19232i	−0.0294822	+	0.183697i
$303$	16.2982	+	28.2293i	0.936307	+	1.62173i
$304$	−8.69926	+	22.1168i	−0.498937	+	1.26849i
$305$	−7.38429	+	12.7900i	−0.422823	+	0.732352i
$306$	−7.86910	+	3.00211i	−0.449846	+	0.171619i
$307$	−2.51869	+	2.51869i	−0.143749	+	0.143749i	−0.775319	−	0.631570i	$-0.782411\pi$
$307$	−2.51869	+	2.51869i	−0.143749	+	0.143749i	0.631570	+	0.775319i	$0.282411\pi$
$308$		0			0
$309$	7.04312	+	7.04312i	0.400669	+	0.400669i
$310$	−3.59030	+	8.01953i	−0.203915	+	0.455478i
$311$	−2.62390	−	1.51491i	−0.148788	−	0.0859027i	0.423758	−	0.905776i	$-0.360711\pi$
$311$	−2.62390	−	1.51491i	−0.148788	−	0.0859027i	−0.572546	+	0.819873i	$0.694044\pi$
$312$	21.5706	+	33.6687i	1.22119	+	1.90612i
$313$	23.7963	−	13.7388i	1.34504	−	0.776562i	0.357501	−	0.933913i	$-0.383629\pi$
$313$	23.7963	−	13.7388i	1.34504	−	0.776562i	0.987543	+	0.157351i	$0.0502954\pi$
$314$	−6.71690	+	4.85904i	−0.379056	+	0.274211i
$315$		0			0
$316$	17.1388	+	5.64677i	0.964132	+	0.317655i
$317$	8.18443	+	2.19301i	0.459683	+	0.123172i	0.481227	−	0.876596i	$-0.340191\pi$
$317$	8.18443	+	2.19301i	0.459683	+	0.123172i	−0.0215435	+	0.999768i	$0.506858\pi$
$318$	−2.57626	+	3.16807i	−0.144469	+	0.177657i
$319$	−0.102818	+	0.178087i	−0.00575672	+	0.00997094i
$320$	18.0380	−	6.66998i	1.00836	−	0.372863i
$321$	−41.0927			−2.29357
$322$		0			0
$323$	11.4361	−	11.4361i	0.636319	−	0.636319i
$324$	−4.39450	−	21.1009i	−0.244139	−	1.17227i
$325$	4.67066	−	1.25150i	0.259082	−	0.0694207i
$326$	2.13566	+	20.7294i	0.118283	+	1.14810i
$327$	23.1278	−	13.3528i	1.27897	−	0.738413i
$328$	0.269742	−	0.521421i	0.0148940	−	0.0287907i
$329$		0			0
$330$	0.133655	+	0.184758i	0.00735746	+	0.0101706i
$331$	−6.08497	+	22.7094i	−0.334460	+	1.24822i	0.569993	+	0.821650i	$0.306946\pi$
$331$	−6.08497	+	22.7094i	−0.334460	+	1.24822i	−0.904453	+	0.426573i	$0.859721\pi$
$332$	−1.20657	+	21.3427i	−0.0662189	+	1.17133i
$333$	4.59430	+	17.1461i	0.251766	+	0.939603i
$334$	20.6334	−	7.87176i	1.12901	−	0.430723i
$335$	−29.8007			−1.62819
$336$		0			0
$337$	−8.50787			−0.463453			−0.231726	−	0.972781i	$-0.574437\pi$
$337$	−8.50787			−0.463453			−0.231726	+	0.972781i	$0.574437\pi$
$338$	−33.7256	+	12.8665i	−1.83443	+	0.699848i
$339$	3.09966	+	11.5681i	0.168350	+	0.628291i
$340$	−13.0664	−	0.738684i	−0.708627	−	0.0400607i
$341$	0.0196983	−	0.0735152i	0.00106672	−	0.00398107i
$342$	−10.7752	−	14.8951i	−0.582657	−	0.805436i
$343$		0			0
$344$	−0.337634	−	1.06137i	−0.0182040	−	0.0572251i
$345$	18.2565	−	10.5404i	0.982898	−	0.567477i
$346$	0.177327	+	1.72120i	0.00953316	+	0.0925320i
$347$	12.2420	−	3.28024i	0.657187	−	0.176093i	0.0852109	−	0.996363i	$-0.472844\pi$
$347$	12.2420	−	3.28024i	0.657187	−	0.176093i	0.571976	+	0.820270i	$0.306177\pi$
$348$	−31.1420	+	6.48568i	−1.66939	+	0.347669i
$349$	10.5665	−	10.5665i	0.565613	−	0.565613i	−0.365283	−	0.930896i	$-0.619028\pi$
$349$	10.5665	−	10.5665i	0.565613	−	0.565613i	0.930896	+	0.365283i	$0.119028\pi$
$350$		0			0
$351$	11.4810			0.612809
$352$	−0.145115	+	0.0818045i	−0.00773466	+	0.00436019i
$353$	−1.14985	+	1.99161i	−0.0612006	+	0.106003i	−0.895002	−	0.446061i	$-0.852826\pi$
$353$	−1.14985	+	1.99161i	−0.0612006	+	0.106003i	0.833802	+	0.552064i	$0.186160\pi$
$354$	−0.438669	+	0.539440i	−0.0233150	+	0.0286709i
$355$	−17.1161	−	4.58625i	−0.908430	−	0.243413i
$356$	2.19635	−	6.66625i	0.116406	−	0.353311i
$357$		0			0
$358$	1.35937	−	0.983376i	0.0718450	−	0.0519731i
$359$	6.94555	−	4.01001i	0.366572	−	0.211640i	−0.305388	−	0.952228i	$-0.598786\pi$
$359$	6.94555	−	4.01001i	0.366572	−	0.211640i	0.671960	+	0.740588i	$0.265453\pi$
$360$	−3.18269	+	14.5320i	−0.167743	+	0.765902i
$361$	14.1179	+	8.15098i	0.743048	+	0.428999i
$362$	1.56413	−	3.49375i	0.0822091	−	0.183627i
$363$	17.7149	+	17.7149i	0.929791	+	0.929791i
$364$		0			0
$365$	7.21843	−	7.21843i	0.377830	−	0.377830i
$366$	18.4890	−	7.05369i	0.966437	−	0.368702i
$367$	7.61255	−	13.1853i	0.397372	−	0.688269i	−0.596029	−	0.802963i	$-0.703256\pi$
$367$	7.61255	−	13.1853i	0.397372	−	0.688269i	0.993401	+	0.114694i	$0.0365889\pi$
$368$	6.14785	+	14.1198i	0.320479	+	0.736043i
$369$	0.227056	+	0.393272i	0.0118201	+	0.0204729i
$370$	−4.37095	+	27.2345i	−0.227235	+	1.41585i
$371$		0			0
$372$	10.5120	−	5.30179i	0.545022	−	0.274885i
$373$	−2.91375	+	10.8743i	−0.150868	+	0.563048i	0.848556	+	0.529106i	$0.177473\pi$
$373$	−2.91375	+	10.8743i	−0.150868	+	0.563048i	−0.999424	+	0.0339416i	$0.989194\pi$
$374$	0.112765	−	0.0116176i	0.00583093	−	0.000600734i
$375$	−20.0154	−	11.5559i	−1.03359	−	0.596744i
$376$	0.500120	+	10.8196i	0.0257917	+	0.557980i
$377$		−	43.3419i		−	2.23222i
$378$		0			0
$379$	2.15234	+	2.15234i	0.110558	+	0.110558i	0.760222	−	0.649663i	$-0.225090\pi$
$379$	2.15234	+	2.15234i	0.110558	+	0.110558i	−0.649663	+	0.760222i	$0.725090\pi$
$380$	−5.82434	−	27.9665i	−0.298783	−	1.43465i
$381$	−4.16072	−	15.5280i	−0.213160	−	0.795525i
$382$	6.00401	−	7.38324i	0.307192	−	0.377760i
$383$	15.2044	+	26.3347i	0.776906	+	1.34564i	0.933717	+	0.358012i	$0.116545\pi$
$383$	15.2044	+	26.3347i	0.776906	+	1.34564i	−0.156811	+	0.987629i	$0.550121\pi$
$384$	−24.3908	−	8.31507i	−1.24469	−	0.424326i
$385$		0			0
$386$	−27.7315	−	4.45072i	−1.41150	−	0.226535i
$387$	0.832187	+	0.222984i	0.0423025	+	0.0113349i
$388$	−16.6366	+	14.8563i	−0.844598	+	0.754212i
$389$	0.711187	−	0.190562i	0.0360586	−	0.00966187i	−0.240745	−	0.970588i	$-0.577392\pi$
$389$	0.711187	−	0.190562i	0.0360586	−	0.00966187i	0.276803	+	0.960927i	$0.410725\pi$
$390$	−43.8669	−	19.6390i	−2.22129	−	0.994458i
$391$		−	10.4799i		−	0.529989i
$392$		0			0
$393$			20.0908i			1.01345i
$394$	7.65717	−	17.1035i	0.385762	−	0.861663i
$395$	−20.9508	+	5.61375i	−1.05415	+	0.282458i
$396$	0.00727315	−	0.128653i	0.000365490	−	0.00646508i
$397$	−16.3947	−	4.39295i	−0.822827	−	0.220476i	−0.177245	−	0.984167i	$-0.556719\pi$
$397$	−16.3947	−	4.39295i	−0.822827	−	0.220476i	−0.645582	+	0.763691i	$0.723385\pi$
$398$	−1.17312	+	7.30944i	−0.0588030	+	0.366389i
$399$		0			0
$400$	−1.85234	+	2.50592i	−0.0926171	+	0.125296i
$401$	−14.7845	−	25.6075i	−0.738302	−	1.27878i	−0.953260	−	0.302153i	$-0.902295\pi$
$401$	−14.7845	−	25.6075i	−0.738302	−	1.27878i	0.214958	−	0.976623i	$-0.431039\pi$
$402$	30.9803	+	25.1930i	1.54516	+	1.25651i
$403$	4.15180	+	15.4947i	0.206816	+	0.771848i
$404$	15.6874	−	23.9403i	0.780478	−	1.19108i
$405$	18.3191	+	18.3191i	0.910283	+	0.910283i
$406$		0			0
$407$		−	0.238923i		−	0.0118430i
$408$	12.9592	+	11.8141i	0.641575	+	0.584884i
$409$	14.1848	+	8.18961i	0.701394	+	0.404950i	0.807866	−	0.589366i	$-0.200622\pi$
$409$	14.1848	+	8.18961i	0.701394	+	0.404950i	−0.106472	+	0.994316i	$0.533956\pi$
$410$	0.0723159	+	0.701922i	0.00357143	+	0.0346655i
$411$	−5.56512	+	20.7693i	−0.274507	+	1.02447i
$412$	2.73689	−	8.30686i	0.134837	−	0.409250i
$413$		0			0
$414$	−11.7620	−	1.88772i	−0.578071	−	0.0927764i
$415$	−12.8473	−	22.2521i	−0.630648	−	1.09231i
$416$	17.8672	−	30.2248i	0.876009	−	1.48189i
$417$	−14.9235	+	25.8482i	−0.730805	+	1.26579i
$418$	0.0882001	+	0.231189i	0.00431401	+	0.0113078i
$419$	−25.7529	+	25.7529i	−1.25811	+	1.25811i	−0.306115	+	0.951995i	$0.599029\pi$
$419$	−25.7529	+	25.7529i	−1.25811	+	1.25811i	−0.951995	+	0.306115i	$0.900971\pi$
$420$		0			0
$421$	−21.6928	−	21.6928i	−1.05724	−	1.05724i	−0.998259	−	0.0589820i	$-0.981215\pi$
$421$	−21.6928	−	21.6928i	−1.05724	−	1.05724i	−0.0589820	−	0.998259i	$-0.518785\pi$
$422$	5.80839	+	2.60039i	0.282748	+	0.126585i
$423$	−7.25582	−	4.18915i	−0.352790	−	0.203683i
$424$	3.50250	+	0.767093i	0.170096	+	0.0372534i
$425$	1.83650	−	1.06030i	0.0890832	−	0.0514322i
$426$	13.9165	+	19.2375i	0.674257	+	0.932060i
$427$		0			0
$428$	16.2489	+	32.2171i	0.785419	+	1.55727i
$429$	0.402129	+	0.107750i	0.0194150	+	0.00520222i
$430$	1.03866	+	0.844634i	0.0500887	+	0.0407319i
$431$	−13.2778	+	22.9977i	−0.639567	+	1.10776i	0.345961	+	0.938249i	$0.387553\pi$
$431$	−13.2778	+	22.9977i	−0.639567	+	1.10776i	−0.985528	+	0.169513i	$0.945780\pi$
$432$	−5.78820	+	4.60888i	−0.278485	+	0.221745i
$433$	−29.2189			−1.40417			−0.702085	−	0.712093i	$-0.747747\pi$
$433$	−29.2189			−1.40417			−0.702085	+	0.712093i	$0.747747\pi$
$434$		0			0
$435$	27.0365	−	27.0365i	1.29630	−	1.29630i
$436$	−19.6139	−	12.8524i	−0.939336	−	0.615520i
$437$	22.0957	−	5.92052i	1.05698	−	0.283217i
$438$	−13.6065	+	1.40182i	−0.650144	+	0.0669815i
$439$	−3.28383	+	1.89592i	−0.156729	+	0.0904874i	−0.576313	−	0.817229i	$-0.695509\pi$
$439$	−3.28383	+	1.89592i	−0.156729	+	0.0904874i	0.419584	+	0.907716i	$0.362176\pi$
$440$	0.0920022	−	0.177844i	0.00438603	−	0.00847836i
$441$		0			0
$442$	−19.3588	+	14.0043i	−0.920804	+	0.666115i
$443$	−0.965694	+	3.60402i	−0.0458815	+	0.171232i	−0.985065	−	0.172184i	$-0.944918\pi$
$443$	−0.965694	+	3.60402i	−0.0458815	+	0.171232i	0.939183	+	0.343416i	$0.111584\pi$
$444$	27.5676	−	24.6174i	1.30830	−	1.16829i
$445$	2.18351	+	8.14895i	0.103508	+	0.386298i
$446$	3.98857	+	10.4548i	0.188864	+	0.495049i
$447$	36.1407			1.70940
$448$		0			0
$449$	18.7626			0.885460			0.442730	−	0.896655i	$-0.354010\pi$
$449$	18.7626			0.885460			0.442730	+	0.896655i	$0.354010\pi$
$450$	−0.859217	−	2.25217i	−0.0405039	−	0.106168i
$451$	−0.00158195	−	0.00590393i	−7.44913e−5	−	0.000278005i
$452$	7.84381	−	7.00440i	0.368942	−	0.329459i
$453$	−1.34774	+	5.02983i	−0.0633222	+	0.236322i
$454$	−8.74051	+	6.32293i	−0.410213	+	0.296750i
$455$		0			0
$456$	−17.5875	+	33.9973i	−0.823612	+	1.59207i
$457$	15.8043	−	9.12461i	0.739294	−	0.426831i	−0.0825187	−	0.996590i	$-0.526296\pi$
$457$	15.8043	−	9.12461i	0.739294	−	0.426831i	0.821812	+	0.569758i	$0.192963\pi$
$458$	−6.01959	+	0.620172i	−0.281277	+	0.0289787i
$459$	4.86349	−	1.30317i	0.227008	−	0.0608266i
$460$	−15.4828	−	10.1454i	−0.721888	−	0.473032i
$461$	−7.85090	+	7.85090i	−0.365653	+	0.365653i	−0.865889	−	0.500236i	$-0.833247\pi$
$461$	−7.85090	+	7.85090i	−0.365653	+	0.365653i	0.500236	+	0.865889i	$0.333247\pi$
$462$		0			0
$463$	2.40372			0.111710			0.0558551	−	0.998439i	$-0.482212\pi$
$463$	2.40372			0.111710			0.0558551	+	0.998439i	$0.482212\pi$
$464$	17.3990	+	21.8511i	0.807728	+	1.01441i
$465$	−7.07567	+	12.2554i	−0.328126	+	0.568331i
$466$	23.2156	+	18.8788i	1.07544	+	0.874545i
$467$	7.33384	+	1.96510i	0.339369	+	0.0909338i	0.424479	−	0.905438i	$-0.360457\pi$
$467$	7.33384	+	1.96510i	0.339369	+	0.0909338i	−0.0851094	+	0.996372i	$0.527124\pi$
$468$	12.2305	+	24.2498i	0.565355	+	1.12095i
$469$		0			0
$470$	−7.63064	−	10.5482i	−0.351975	−	0.486553i
$471$	−11.5631	+	6.67596i	−0.532800	+	0.307612i
$472$	0.596384	+	0.130616i	0.0274508	+	0.00601209i
$473$	−0.0100425	−	0.00579805i	−0.000461756	−	0.000266595i
$474$	26.5259	+	11.8755i	1.21837	+	0.545460i
$475$	3.27305	+	3.27305i	0.150178	+	0.150178i
$476$		0			0
$477$	−1.96117	+	1.96117i	−0.0897960	+	0.0897960i
$478$	11.6822	+	30.6212i	0.534331	+	1.40058i
$479$	−17.2984	+	29.9617i	−0.790385	+	1.36899i	0.135344	+	0.990799i	$0.456786\pi$
$479$	−17.2984	+	29.9617i	−0.790385	+	1.36899i	−0.925729	+	0.378188i	$0.876547\pi$
$480$	29.9995	−	7.70863i	1.36928	−	0.351849i
$481$	25.1788	+	43.6109i	1.14805	+	1.98849i
$482$	−8.47234	−	1.35975i	−0.385904	−	0.0619350i
$483$		0			0
$484$	6.88383	−	20.8935i	0.312901	−	0.949703i
$485$	6.93881	−	25.8960i	0.315075	−	1.17588i
$486$	−2.75330	−	26.7244i	−0.124892	−	1.21224i
$487$	4.11458	+	2.37555i	0.186449	+	0.107647i	0.590319	−	0.807170i	$-0.299002\pi$
$487$	4.11458	+	2.37555i	0.186449	+	0.107647i	−0.403870	+	0.914816i	$0.632335\pi$
$488$	−12.8411	−	11.7064i	−0.581288	−	0.529924i
$489$			33.5630i			1.51777i
$490$		0			0
$491$	−16.3309	−	16.3309i	−0.737003	−	0.737003i	0.234994	−	0.971997i	$-0.424493\pi$
$491$	−16.3309	−	16.3309i	−0.737003	−	0.737003i	−0.971997	+	0.234994i	$0.924493\pi$
$492$	0.518216	−	0.790842i	0.0233630	−	0.0356539i
$493$	−4.91959	−	18.3602i	−0.221567	−	0.826900i
$494$	−40.4631	−	32.9044i	−1.82052	−	1.48044i
$495$	0.0774431	+	0.134135i	0.00348081	+	0.00602893i
$496$	−8.31330	−	6.14508i	−0.373278	−	0.275922i
$497$		0			0
$498$	−5.45578	+	33.9938i	−0.244479	+	1.52330i
$499$	−19.5147	−	5.22895i	−0.873599	−	0.234080i	−0.205955	−	0.978561i	$-0.566030\pi$
$499$	−19.5147	−	5.22895i	−0.873599	−	0.234080i	−0.667643	+	0.744481i	$0.732697\pi$
$500$	−1.14545	+	20.2617i	−0.0512261	+	0.906129i
$501$	34.3558	−	9.20562i	1.53491	−	0.411277i
$502$	5.02953	−	11.2343i	0.224479	−	0.501411i
$503$		−	7.84369i		−	0.349733i	−0.984592	−	0.174866i	$-0.944051\pi$
$503$		−	7.84369i		−	0.349733i	0.984592	−	0.174866i	$-0.0559493\pi$
$504$		0			0
$505$			34.4035i			1.53094i
$506$	0.146342	+	0.0655167i	0.00650571	+	0.00291257i
$507$	−56.1553	+	15.0468i	−2.49394	+	0.668250i
$508$	−10.5289	+	9.40212i	−0.467144	+	0.417152i
$509$	21.0090	+	5.62933i	0.931206	+	0.249516i	0.692369	−	0.721544i	$-0.256567\pi$
$509$	21.0090	+	5.62933i	0.931206	+	0.249516i	0.238837	+	0.971060i	$0.423234\pi$
$510$	−20.8117	−	3.34014i	−0.921558	−	0.147904i
$511$		0			0
$512$	3.12549	+	22.4105i	0.138128	+	0.990414i
$513$	5.49518	+	9.51793i	0.242618	+	0.420227i
$514$	−19.7265	+	24.2580i	−0.870098	+	1.06998i
$515$	2.72088	+	10.1545i	0.119896	+	0.447459i
$516$	−0.365736	−	1.75614i	−0.0161006	−	0.0773096i
$517$	0.0797399	+	0.0797399i	0.00350696	+	0.00350696i
$518$		0			0
$519$			2.78678i			0.122326i
$520$	1.94867	+	42.1577i	0.0854548	+	1.84874i
$521$	6.01150	+	3.47074i	0.263369	+	0.152056i	0.625870	−	0.779927i	$-0.284744\pi$
$521$	6.01150	+	3.47074i	0.263369	+	0.152056i	−0.362502	+	0.931983i	$0.618077\pi$
$522$	−21.4926	+	2.21428i	−0.940704	+	0.0969165i
$523$	−1.85202	+	6.91185i	−0.0809833	+	0.302234i	−0.994523	−	0.104515i	$-0.966671\pi$
$523$	−1.85202	+	6.91185i	−0.0809833	+	0.302234i	0.913540	+	0.406749i	$0.133338\pi$
$524$	15.7514	−	7.94430i	0.688102	−	0.347048i
$525$		0			0
$526$	0.987465	−	6.15269i	0.0430555	−	0.268270i
$527$	3.51751	+	6.09251i	0.153225	+	0.265394i
$528$	−0.245990	+	0.107106i	−0.0107054	+	0.00466120i
$529$	−4.08864	+	7.08173i	−0.177767	+	0.307902i
$530$	−4.02665	+	1.53619i	−0.174906	+	0.0667279i
$531$	−0.333937	+	0.333937i	−0.0144916	+	0.0144916i
$532$		0			0
$533$	0.910940	+	0.910940i	0.0394572	+	0.0394572i
$534$	4.61906	−	10.3174i	0.199886	−	0.446479i
$535$	−37.5603	−	21.6854i	−1.62387	−	0.937543i
$536$	7.50135	−	34.2507i	0.324009	−	1.47940i
$537$	2.34015	−	1.35109i	0.100985	−	0.0583037i
$538$	0.971461	−	0.702760i	0.0418827	−	0.0302981i
$539$		0			0
$540$	2.78299	−	8.44681i	0.119761	−	0.363493i
$541$	42.7523	+	11.4554i	1.83806	+	0.492508i	0.998696	−	0.0510566i	$-0.0162589\pi$
$541$	42.7523	+	11.4554i	1.83806	+	0.492508i	0.839368	+	0.543564i	$0.182926\pi$
$542$	10.4687	−	12.8735i	0.449668	−	0.552965i
$543$	3.08255	−	5.33914i	0.132285	−	0.229124i
$544$	4.13804	−	14.8316i	0.177417	−	0.635901i
$545$	28.1862			1.20736
$546$		0			0
$547$	1.52168	−	1.52168i	0.0650623	−	0.0650623i	−0.673827	−	0.738889i	$-0.735351\pi$
$547$	1.52168	−	1.52168i	0.0650623	−	0.0650623i	0.738889	+	0.673827i	$0.235351\pi$
$548$	18.4839	−	3.84948i	0.789592	−	0.164442i
$549$	12.9831	−	3.47882i	0.554106	−	0.148472i
$550$	0.00332502	+	0.0322738i	0.000141779	+	0.00137616i
$551$	35.9311	−	20.7449i	1.53072	−	0.883761i
$552$	7.51887	+	23.6359i	0.320024	+	1.00601i
$553$		0			0
$554$	−13.2808	−	18.3587i	−0.564248	−	0.779988i
$555$	−11.4979	+	42.9107i	−0.488058	+	1.82146i
$556$	26.1663	+	1.47925i	1.10970	+	0.0627344i
$557$	−11.9596	−	44.6337i	−0.506743	−	1.89119i	−0.450508	−	0.892773i	$-0.648757\pi$
$557$	−11.9596	−	44.6337i	−0.506743	−	1.89119i	−0.0562353	−	0.998418i	$-0.517910\pi$
$558$	7.47149	−	2.85042i	0.316293	−	0.120668i
$559$	2.44410			0.103375
$560$		0			0
$561$	0.182577			0.00770841
$562$	−28.2512	+	10.7780i	−1.19170	+	0.454643i
$563$	−0.438376	−	1.63604i	−0.0184754	−	0.0689510i	0.956073	−	0.293130i	$-0.0946968\pi$
$563$	−0.438376	−	1.63604i	−0.0184754	−	0.0689510i	−0.974548	+	0.224179i	$0.928030\pi$
$564$	−0.984611	+	17.4166i	−0.0414596	+	0.733371i
$565$	−3.27150	+	12.2094i	−0.137633	+	0.513653i
$566$	−15.9940	−	22.1093i	−0.672278	−	0.929325i
$567$		0			0
$568$	9.57952	−	18.5176i	0.401948	−	0.776979i
$569$	−4.81619	+	2.78063i	−0.201905	+	0.116570i	−0.597544	−	0.801836i	$-0.703857\pi$
$569$	−4.81619	+	2.78063i	−0.201905	+	0.116570i	0.395639	+	0.918406i	$0.370523\pi$
$570$	−4.71509	−	45.7662i	−0.197493	−	1.91694i
$571$	−11.9127	+	3.19199i	−0.498529	+	0.133581i	−0.499317	−	0.866419i	$-0.666416\pi$
$571$	−11.9127	+	3.19199i	−0.498529	+	0.133581i	0.000788088		1.00000i	$0.499749\pi$
$572$	−0.0745325	−	0.357879i	−0.00311636	−	0.0149637i
$573$	10.8376	−	10.8376i	0.452749	−	0.452749i
$574$		0			0
$575$	2.99938			0.125083
$576$	−15.9008	−	7.31589i	−0.662534	−	0.304829i
$577$	14.2426	−	24.6689i	0.592927	−	1.02698i	−0.400909	−	0.916118i	$-0.631305\pi$
$577$	14.2426	−	24.6689i	0.592927	−	1.02698i	0.993836	−	0.110862i	$-0.0353612\pi$
$578$	8.55722	−	10.5230i	0.355934	−	0.437698i
$579$	−43.6938	−	11.7077i	−1.81585	−	0.486556i
$580$	−31.8876	−	10.5061i	−1.32406	−	0.436242i
$581$		0			0
$582$	−29.1056	+	21.0551i	−1.20646	+	0.872763i
$583$	0.0323293	−	0.0186654i	0.00133894	−	0.000773040i
$584$	6.47932	+	10.1133i	0.268116	+	0.418492i
$585$	−28.2716	−	16.3226i	−1.16889	−	0.674857i
$586$	15.6063	−	34.8592i	0.644689	−	1.44002i
$587$	−15.1948	−	15.1948i	−0.627157	−	0.627157i	0.320195	−	0.947352i	$-0.396252\pi$
$587$	−15.1948	−	15.1948i	−0.627157	−	0.627157i	−0.947352	+	0.320195i	$0.896252\pi$
$588$		0			0
$589$	−10.8582	+	10.8582i	−0.447405	+	0.447405i
$590$	−0.685633	+	0.261573i	−0.0282271	+	0.0107688i
$591$	15.0905	−	26.1376i	0.620741	−	1.07516i
$592$	−30.2010	−	11.8790i	−1.24125	−	0.488225i
$593$	−15.3004	−	26.5011i	−0.628313	−	1.08827i	−0.987890	−	0.155155i	$-0.950412\pi$
$593$	−15.3004	−	26.5011i	−0.628313	−	1.08827i	0.359577	−	0.933115i	$-0.382921\pi$
$594$	−0.0122073	+	0.0760614i	−0.000500873	+	0.00312084i
$595$		0			0
$596$	−14.2907	−	28.3347i	−0.585372	−	1.16063i
$597$	−3.08591	+	11.5168i	−0.126298	+	0.471350i
$598$	−33.6165	+	3.46336i	−1.37468	+	0.141627i
$599$	11.2663	+	6.50461i	0.460329	+	0.265771i	0.712183	−	0.701994i	$-0.247707\pi$
$599$	11.2663	+	6.50461i	0.460329	+	0.265771i	−0.251853	+	0.967765i	$0.581040\pi$
$600$	−3.38124	+	3.70898i	−0.138039	+	0.151418i
$601$		−	39.6831i		−	1.61871i	−0.587322	−	0.809353i	$-0.699818\pi$
$601$		−	39.6831i		−	1.61871i	0.587322	−	0.809353i	$-0.300182\pi$
$602$		0			0
$603$	19.1782	+	19.1782i	0.780996	+	0.780996i
$604$	4.47635	−	0.932252i	0.182140	−	0.0379328i
$605$	6.84358	+	25.5406i	0.278231	+	1.03837i
$606$	29.0842	−	35.7653i	1.18146	−	1.45287i
$607$	−0.982401	−	1.70157i	−0.0398744	−	0.0690645i	0.845399	−	0.534135i	$-0.179362\pi$
$607$	−0.982401	−	1.70157i	−0.0398744	−	0.0690645i	−0.885274	+	0.465070i	$0.846029\pi$
$608$	33.6087	+	0.345586i	1.36301	+	0.0140154i
$609$		0			0
$610$	20.6220	+	3.30970i	0.834962	+	0.134006i
$611$	−22.9584	−	6.15168i	−0.928797	−	0.248870i
$612$	7.93351	+	8.88426i	0.320693	+	0.359125i
$613$	4.85993	−	1.30222i	0.196291	−	0.0525960i	−0.159334	−	0.987225i	$-0.550935\pi$
$613$	4.85993	−	1.30222i	0.196291	−	0.0525960i	0.355625	+	0.934629i	$0.384268\pi$
$614$	4.59765	+	2.05835i	0.185546	+	0.0830681i
$615$			1.13648i			0.0458273i
$616$		0			0
$617$		−	21.7544i		−	0.875798i	−0.899024	−	0.437899i	$-0.855723\pi$
$617$		−	21.7544i		−	0.875798i	0.899024	−	0.437899i	$-0.144277\pi$
$618$	5.75584	−	12.8566i	0.231534	−	0.517169i
$619$	41.5607	−	11.1362i	1.67047	−	0.447600i	0.705230	−	0.708979i	$-0.250844\pi$
$619$	41.5607	−	11.1362i	1.67047	−	0.447600i	0.965236	+	0.261378i	$0.0841771\pi$
$620$	12.4062	+	0.701360i	0.498246	+	0.0281673i
$621$	6.87892	+	1.84320i	0.276041	+	0.0739651i
$622$	−0.678994	+	4.23067i	−0.0272252	+	0.169635i
$623$		0			0
$624$	33.6136	−	45.4738i	1.34562	−	1.82041i
$625$	−14.1442	−	24.4984i	−0.565767	−	0.979937i
$626$	−30.1489	−	24.5169i	−1.20499	−	0.979892i
$627$	0.103146	+	0.384944i	0.00411923	+	0.0153732i
$628$	9.80629	+	6.42578i	0.391314	+	0.256416i
$629$	15.6162	+	15.6162i	0.622658	+	0.622658i
$630$		0			0
$631$		−	15.4311i		−	0.614303i	−0.951661	−	0.307152i	$-0.900624\pi$
$631$		−	15.4311i		−	0.614303i	0.951661	−	0.307152i	$-0.0993758\pi$
$632$	−1.17834	−	25.4923i	−0.0468719	−	1.01403i
$633$	8.87636	+	5.12477i	0.352804	+	0.203691i
$634$	−1.22804	−	11.9197i	−0.0487716	−	0.473393i
$635$	4.39139	−	16.3889i	0.174267	−	0.650373i
$636$	5.48471	+	1.80706i	0.217483	+	0.0716547i
$637$		0			0
$638$	0.287140	+	0.0460840i	0.0113680	+	0.00182448i
$639$	8.06358	+	13.9665i	0.318990	+	0.552507i
$640$	−17.9060	−	20.4718i	−0.707798	−	0.809217i
$641$	7.89923	−	13.6819i	0.312001	−	0.540402i	−0.666794	−	0.745242i	$-0.732334\pi$
$641$	7.89923	−	13.6819i	0.312001	−	0.540402i	0.978795	+	0.204840i	$0.0656674\pi$
$642$	20.7145	+	54.2967i	0.817538	+	2.14292i
$643$	15.9560	−	15.9560i	0.629244	−	0.629244i	−0.318634	−	0.947878i	$-0.603224\pi$
$643$	15.9560	−	15.9560i	0.629244	−	0.629244i	0.947878	+	0.318634i	$0.103224\pi$
$644$		0			0
$645$	1.52462	+	1.52462i	0.0600318	+	0.0600318i
$646$	−20.8755	−	9.34587i	−0.821337	−	0.367708i
$647$	−12.7953	−	7.38738i	−0.503036	−	0.290428i	0.226931	−	0.973911i	$-0.427131\pi$
$647$	−12.7953	−	7.38738i	−0.503036	−	0.290428i	−0.729966	+	0.683483i	$0.760464\pi$
$648$	−25.6658	+	16.4433i	−1.00825	+	0.645956i
$649$	0.00550484	−	0.00317822i	0.000216084	−	0.000124756i
$650$	−4.00808	−	5.54057i	−0.157210	−	0.217319i
$651$		0			0
$652$	26.3137	−	13.2714i	1.03052	−	0.519750i
$653$	−5.87011	−	1.57289i	−0.229715	−	0.0615520i	0.142125	−	0.989849i	$-0.454606\pi$
$653$	−5.87011	−	1.57289i	−0.229715	−	0.0615520i	−0.371840	+	0.928297i	$0.621273\pi$
$654$	−29.3019	−	23.8282i	−1.14580	−	0.931755i
$655$	−10.6023	+	18.3637i	−0.414267	+	0.717531i
$656$	−0.824940	−	0.0935715i	−0.0322085	−	0.00365335i
$657$	−9.29082			−0.362469
$658$		0			0
$659$	−16.6838	+	16.6838i	−0.649907	+	0.649907i	−0.952970	−	0.303063i	$-0.901991\pi$
$659$	−16.6838	+	16.6838i	−0.649907	+	0.649907i	0.303063	+	0.952970i	$0.401991\pi$
$660$	0.176750	−	0.269736i	0.00687999	−	0.0104995i
$661$	39.5975	−	10.6101i	1.54016	−	0.412686i	0.613845	−	0.789427i	$-0.289622\pi$
$661$	39.5975	−	10.6101i	1.54016	−	0.412686i	0.926319	+	0.376741i	$0.122955\pi$
$662$	33.0738	−	3.40745i	1.28545	−	0.132434i
$663$	−33.3261	+	19.2408i	−1.29428	+	0.747251i
$664$	28.8088	−	9.16444i	1.11800	−	0.355649i
$665$		0			0
$666$	20.3396	−	14.7138i	0.788144	−	0.570148i
$667$	6.95827	−	25.9686i	0.269425	−	1.00551i
$668$	−20.8022	−	23.2952i	−0.804863	−	0.901319i
$669$	4.66443	+	17.4079i	0.180337	+	0.673028i
$670$	15.0223	+	39.3763i	0.580363	+	1.52124i
$671$	−0.180913			−0.00698407
$672$		0			0
$673$	−1.26298			−0.0486841			−0.0243421	−	0.999704i	$-0.507749\pi$
$673$	−1.26298			−0.0486841			−0.0243421	+	0.999704i	$0.507749\pi$
$674$	4.28875	+	11.2416i	0.165197	+	0.433011i
$675$	0.372972	+	1.39195i	0.0143557	+	0.0535762i
$676$	34.0017	+	38.0765i	1.30776	+	1.46448i
$677$	5.45778	−	20.3687i	0.209759	−	0.782833i	−0.778186	−	0.628033i	$-0.783860\pi$
$677$	5.45778	−	20.3687i	0.209759	−	0.782833i	0.987946	−	0.154800i	$-0.0494732\pi$
$678$	13.7226	−	9.92702i	0.527014	−	0.381245i
$679$		0			0
$680$	5.61066	+	17.6373i	0.215159	+	0.676361i
$681$	−15.0467	+	8.68724i	−0.576593	+	0.332896i
$682$	−0.107067	+	0.0110306i	−0.00409981	+	0.000422385i
$683$	−37.8876	+	10.1519i	−1.44973	+	0.388453i	−0.895929	−	0.444197i	$-0.853489\pi$
$683$	−37.8876	+	10.1519i	−1.44973	+	0.388453i	−0.553798	+	0.832651i	$0.686822\pi$
$684$	−14.2495	+	21.7460i	−0.544845	+	0.831481i
$685$	−16.0471	+	16.0471i	−0.613128	+	0.613128i
$686$		0			0
$687$	−9.74631			−0.371845
$688$	−1.23221	+	0.981150i	−0.0469775	+	0.0374060i
$689$	−3.93408	+	6.81403i	−0.149877	+	0.259594i
$690$	−23.1303	−	18.8094i	−0.880554	−	0.716062i
$691$	−12.9202	−	3.46195i	−0.491507	−	0.131699i	0.00454863	−	0.999990i	$-0.498552\pi$
$691$	−12.9202	−	3.46195i	−0.491507	−	0.131699i	−0.496056	+	0.868291i	$0.665219\pi$
$692$	2.18486	−	1.10195i	0.0830560	−	0.0418898i
$693$		0			0
$694$	−10.5054	−	14.5221i	−0.398779	−	0.551252i
$695$	−27.2812	+	15.7508i	−1.03483	+	0.597462i
$696$	24.2681	+	37.8792i	0.919881	+	1.43581i
$697$	0.489284	+	0.282488i	0.0185329	+	0.0107000i
$698$	−19.2883	−	8.63527i	−0.730073	−	0.326850i
$699$	34.0775	+	34.0775i	1.28893	+	1.28893i
$700$		0			0
$701$	−26.5854	+	26.5854i	−1.00412	+	1.00412i	−0.00412374	+	0.999991i	$0.501313\pi$
$701$	−26.5854	+	26.5854i	−1.00412	+	1.00412i	−0.999991	+	0.00412374i	$0.998687\pi$
$702$	−5.78748	−	15.1701i	−0.218434	−	0.572557i
$703$	−24.1028	+	41.7473i	−0.909054	+	1.57453i
$704$	0.181241	+	0.150507i	0.00683080	+	0.00567244i
$705$	−10.4839	−	18.1587i	−0.394848	−	0.683897i
$706$	3.21119	+	0.515373i	0.120855	+	0.0193963i
$707$		0			0
$708$	0.933903	+	0.307696i	0.0350982	+	0.0115639i
$709$	2.14928	−	8.02123i	0.0807180	−	0.301244i	−0.913751	−	0.406275i	$-0.866828\pi$
$709$	2.14928	−	8.02123i	0.0807180	−	0.301244i	0.994469	+	0.105031i	$0.0334942\pi$
$710$	2.56820	+	24.9278i	0.0963828	+	0.935524i
$711$	17.0956	+	9.87013i	0.641134	+	0.370159i
$712$	−9.91542	+	0.458324i	−0.371596	+	0.0171764i
$713$			9.95034i			0.372643i
$714$		0			0
$715$	0.310699	+	0.310699i	0.0116195	+	0.0116195i
$716$	−1.98461	−	1.30045i	−0.0741682	−	0.0486002i
$717$	13.6617	+	50.9862i	0.510206	+	1.90412i
$718$	−8.79971	−	7.15588i	−0.328402	−	0.267055i
$719$	−16.9795	−	29.4094i	−0.633230	−	1.09679i	−0.986887	−	0.161411i	$-0.948395\pi$
$719$	−16.9795	−	29.4094i	−0.633230	−	1.09679i	0.353657	−	0.935375i	$-0.384938\pi$
$720$	20.8058	−	3.12010i	0.775385	−	0.116279i
$721$		0			0
$722$	3.65333	−	22.7631i	0.135963	−	0.847156i
$723$	−13.3490	−	3.57686i	−0.496456	−	0.133025i
$724$	−5.40484	−	0.305551i	−0.200869	−	0.0113557i
$725$	5.25476	−	1.40801i	0.195157	−	0.0522921i
$726$	14.4771	−	32.3370i	0.537297	−	1.20014i
$727$		−	8.94504i		−	0.331753i	−0.986147	−	0.165877i	$-0.946955\pi$
$727$		−	8.94504i		−	0.331753i	0.986147	−	0.165877i	$-0.0530454\pi$
$728$		0			0
$729$		−	10.9390i		−	0.405147i
$730$	−13.1766	−	5.89911i	−0.487689	−	0.218336i
$731$	1.03535	−	0.277422i	0.0382939	−	0.0102608i
$732$	−18.6404	−	20.8743i	−0.688968	−	0.771535i
$733$	−32.0933	−	8.59937i	−1.18539	−	0.317625i	−0.388329	−	0.921521i	$-0.626948\pi$
$733$	−32.0933	−	8.59937i	−1.18539	−	0.317625i	−0.797063	+	0.603896i	$0.793614\pi$
$734$	−21.2595	−	3.41200i	−0.784702	−	0.125939i
$735$		0			0
$736$	15.5576	−	15.2410i	0.573462	−	0.561789i
$737$	−0.182527	−	0.316146i	−0.00672348	−	0.0116454i
$738$	0.405182	−	0.498260i	0.0149150	−	0.0183412i
$739$	−13.7240	−	51.2188i	−0.504847	−	1.88411i	−0.465828	−	0.884875i	$-0.654243\pi$
$739$	−13.7240	−	51.2188i	−0.504847	−	1.88411i	−0.0390191	−	0.999238i	$-0.512423\pi$
$740$	38.1889	−	7.95327i	1.40385	−	0.292368i
$741$	−59.3945	−	59.3945i	−2.18191	−	2.18191i
$742$		0			0
$743$			36.7472i			1.34812i	0.738675	+	0.674062i	$0.235452\pi$
$743$			36.7472i			1.34812i	−0.738675	+	0.674062i	$0.764548\pi$
$744$	−12.3044	−	11.2171i	−0.451101	−	0.411240i
$745$	33.0340	+	19.0722i	1.21027	+	0.698750i
$746$	15.8372	−	1.63163i	0.579841	−	0.0597384i
$747$	−6.05248	+	22.5882i	−0.221449	+	0.826458i
$748$	−0.0721945	−	0.143142i	−0.00263969	−	0.00523380i
$749$		0			0
$750$	−5.17944	+	32.2720i	−0.189126	+	1.17841i
$751$	−0.273033	−	0.472907i	−0.00996312	−	0.0172566i	0.861001	−	0.508603i	$-0.169838\pi$
$751$	−0.273033	−	0.472907i	−0.00996312	−	0.0172566i	−0.870964	+	0.491347i	$0.836505\pi$
$752$	14.0441	−	6.11492i	0.512136	−	0.222988i
$753$	9.91206	−	17.1682i	0.361216	−	0.625644i
$754$	−57.2686	+	21.8483i	−2.08560	+	0.795669i
$755$	−3.88622	+	3.88622i	−0.141434	+	0.141434i
$756$		0			0
$757$	−1.43871	−	1.43871i	−0.0522908	−	0.0522908i	0.680478	−	0.732769i	$-0.261772\pi$
$757$	−1.43871	−	1.43871i	−0.0522908	−	0.0522908i	−0.732769	+	0.680478i	$0.761772\pi$
$758$	1.75896	−	3.92892i	0.0638882	−	0.142705i
$759$	0.223640	+	0.129119i	0.00811761	+	0.00468671i
$760$	−34.0167	+	21.7935i	−1.23392	+	0.790535i
$761$	−44.8946	+	25.9199i	−1.62743	+	0.939596i	−0.642571	+	0.766226i	$0.722132\pi$
$761$	−44.8946	+	25.9199i	−1.62743	+	0.939596i	−0.984857	+	0.173369i	$0.944535\pi$
$762$	−18.4201	+	13.3252i	−0.667291	+	0.482721i
$763$		0			0
$764$	−12.7822	−	4.21139i	−0.462444	−	0.152363i
$765$	−13.8289	−	3.70545i	−0.499986	−	0.133971i
$766$	27.1322	−	33.3650i	0.980327	−	1.20553i
$767$	−0.669871	+	1.16025i	−0.0241877	+	0.0418942i
$768$	1.30832	+	36.4196i	0.0472101	+	1.31418i
$769$	−14.1856			−0.511545			−0.255773	−	0.966737i	$-0.582330\pi$
$769$	−14.1856			−0.511545			−0.255773	+	0.966737i	$0.582330\pi$
$770$		0			0
$771$	−35.6076	+	35.6076i	−1.28238	+	1.28238i
$772$	8.09841	+	38.8858i	0.291468	+	1.39953i
$773$	−4.71890	+	1.26443i	−0.169727	+	0.0454782i	−0.342682	−	0.939452i	$-0.611335\pi$
$773$	−4.71890	+	1.26443i	−0.169727	+	0.0454782i	0.172955	+	0.984930i	$0.444669\pi$
$774$	−0.124866	−	1.21199i	−0.00448822	−	0.0435641i
$775$	−1.74370	+	1.00673i	−0.0626356	+	0.0361627i
$776$	28.0163	+	14.4934i	1.00573	+	0.520284i
$777$		0			0
$778$	−0.610298	−	0.843646i	−0.0218802	−	0.0302462i
$779$	−0.319179	+	1.19119i	−0.0114358	+	0.0426788i
$780$	−3.83644	+	67.8621i	−0.137367	+	2.42985i
$781$	−0.0561809	−	0.209670i	−0.00201031	−	0.00750259i
$782$	−13.8473	+	5.28282i	−0.495177	+	0.188913i
$783$	12.9168			0.461607
$784$		0			0
$785$	−14.0921			−0.502970
$786$	26.5464	−	10.1276i	0.946879	−	0.361241i
$787$	−7.22492	−	26.9638i	−0.257541	−	0.961154i	−0.966659	−	0.256065i	$-0.917574\pi$
$787$	−7.22492	−	26.9638i	−0.257541	−	0.961154i	0.709119	−	0.705089i	$-0.249093\pi$
$788$	−26.4592	−	1.49581i	−0.942569	−	0.0532862i
$789$	2.59755	−	9.69419i	0.0924752	−	0.345122i
$790$	17.9787	+	24.8529i	0.639654	+	0.884226i
$791$		0			0
$792$	−0.173659	+	0.0552431i	−0.00617070	+	0.00196298i
$793$	33.0223	−	19.0655i	1.17266	−	0.677034i
$794$	2.45996	+	23.8771i	0.0873005	+	0.847368i
$795$	−6.70462	+	1.79650i	−0.237788	+	0.0637152i
$796$	10.2495	−	2.13457i	0.363283	−	0.0756579i
$797$	17.1613	−	17.1613i	0.607884	−	0.607884i	−0.334509	−	0.942393i	$-0.608570\pi$
$797$	17.1613	−	17.1613i	0.607884	−	0.607884i	0.942393	+	0.334509i	$0.108570\pi$
$798$		0			0
$799$	−10.4237			−0.368765
$800$	4.24488	+	1.18432i	0.150079	+	0.0418722i
$801$	3.83906	−	6.64944i	0.135646	−	0.234946i
$802$	−26.3830	+	32.4436i	−0.931614	+	1.14562i
$803$	0.120790	+	0.0323657i	0.00426260	+	0.00114216i
$804$	17.6712	−	53.6346i	0.623213	−	1.89155i
$805$		0			0
$806$	18.3806	−	13.2967i	0.647430	−	0.468355i
$807$	1.67237	−	0.965541i	0.0588701	−	0.0339886i
$808$	−39.5408	−	8.65996i	−1.39104	−	0.304656i
$809$	44.9216	+	25.9355i	1.57936	+	0.911844i	0.994948	+	0.100388i	$0.0320083\pi$
$809$	44.9216	+	25.9355i	1.57936	+	0.911844i	0.584413	+	0.811457i	$0.301325\pi$
$810$	14.9709	−	33.4399i	0.526023	−	1.17496i
$811$	−28.9865	−	28.9865i	−1.01785	−	1.01785i	−0.999838	−	0.0180155i	$-0.994265\pi$
$811$	−28.9865	−	28.9865i	−1.01785	−	1.01785i	−0.0180155	−	0.999838i	$-0.505735\pi$
$812$		0			0
$813$	18.8967	−	18.8967i	0.662734	−	0.662734i
$814$	−0.315694	+	0.120439i	−0.0110651	+	0.00422139i
$815$	−17.7118	+	30.6778i	−0.620418	+	1.07460i
$816$	9.07757	−	23.0786i	0.317779	−	0.807914i
$817$	1.16983	+	2.02620i	0.0409271	+	0.0708878i
$818$	3.67064	−	22.8710i	0.128341	−	0.799667i
$819$		0			0
$820$	0.891011	−	0.449386i	0.0311155	−	0.0156933i
$821$	1.65236	−	6.16671i	0.0576679	−	0.215220i	−0.931079	−	0.364818i	$-0.881131\pi$
$821$	1.65236	−	6.16671i	0.0576679	−	0.215220i	0.988747	+	0.149598i	$0.0477980\pi$
$822$	30.2483	−	3.11634i	1.05503	−	0.108695i
$823$	−24.1611	−	13.9494i	−0.842202	−	0.486245i	0.0158104	−	0.999875i	$-0.494967\pi$
$823$	−24.1611	−	13.9494i	−0.842202	−	0.486245i	−0.858012	+	0.513630i	$0.828301\pi$
$824$	−12.3557	+	0.571121i	−0.430431	+	0.0198960i
$825$			0.0522544i			0.00181926i
$826$		0			0
$827$	33.3036	+	33.3036i	1.15808	+	1.15808i	0.984888	+	0.173190i	$0.0554075\pi$
$827$	33.3036	+	33.3036i	1.15808	+	1.15808i	0.173190	+	0.984888i	$0.444592\pi$
$828$	3.43485	+	16.4930i	0.119369	+	0.573170i
$829$	−2.68229	−	10.0105i	−0.0931599	−	0.347678i	0.903574	−	0.428432i	$-0.140934\pi$
$829$	−2.68229	−	10.0105i	−0.0931599	−	0.347678i	−0.996734	+	0.0807543i	$0.974267\pi$
$830$	−22.9260	+	28.1925i	−0.795773	+	0.978576i
$831$	−18.2469	−	31.6045i	−0.632976	−	1.09635i
$832$	−48.9434	−	8.37216i	−1.69681	−	0.290252i
$833$		0			0
$834$	41.6766	+	6.68881i	1.44314	+	0.231614i
$835$	36.2605	+	9.71597i	1.25485	+	0.336235i
$836$	0.261014	−	0.233081i	0.00902736	−	0.00806129i
$837$	−4.61775	+	1.23732i	−0.159613	+	0.0427681i
$838$	47.0096	+	21.0460i	1.62392	+	0.727021i
$839$			26.9095i			0.929018i	0.885568	+	0.464509i	$0.153769\pi$
$839$			26.9095i			0.929018i	−0.885568	+	0.464509i	$0.846231\pi$
$840$		0			0
$841$		−	19.7621i		−	0.681451i
$842$	−17.7280	+	39.5983i	−0.610946	+	1.36465i
$843$	−47.0399	+	12.6043i	−1.62014	+	0.434116i
$844$	0.507981	−	8.98558i	0.0174854	−	0.309297i
$845$	−59.2685	−	15.8809i	−2.03890	−	0.546321i
$846$	−1.87761	+	11.6990i	−0.0645535	+	0.402219i
$847$		0			0
$848$	−0.752007	−	5.01461i	−0.0258240	−	0.172203i
$849$	−21.9746	−	38.0611i	−0.754166	−	1.30625i
$850$	−2.32676	−	1.89211i	−0.0798073	−	0.0648989i
$851$	8.08459	+	30.1721i	0.277136	+	1.03429i
$852$	18.4037	−	28.0857i	0.630501	−	0.962199i
$853$	−16.4841	−	16.4841i	−0.564406	−	0.564406i	0.366150	−	0.930556i	$-0.380676\pi$
$853$	−16.4841	−	16.4841i	−0.564406	−	0.564406i	−0.930556	+	0.366150i	$0.880676\pi$
$854$		0			0
$855$		−	31.2502i		−	1.06873i
$856$	34.3782	−	37.7104i	1.17502	−	1.28891i
$857$	−7.09763	−	4.09782i	−0.242450	−	0.139979i	0.373852	−	0.927488i	$-0.378037\pi$
$857$	−7.09763	−	4.09782i	−0.242450	−	0.139979i	−0.616302	+	0.787510i	$0.711370\pi$
$858$	−0.0603377	−	0.585657i	−0.00205989	−	0.0199940i
$859$	4.24615	−	15.8468i	0.144877	−	0.540687i	−0.854884	−	0.518819i	$-0.826372\pi$
$859$	4.24615	−	15.8468i	0.144877	−	0.540687i	0.999761	−	0.0218682i	$-0.00696143\pi$
$860$	0.592451	−	1.79818i	0.0202024	−	0.0613174i
$861$		0			0
$862$	37.0806	+	5.95119i	1.26297	+	0.202698i
$863$	11.8882	+	20.5910i	0.404680	+	0.700927i	0.994284	−	0.106766i	$-0.0340495\pi$
$863$	11.8882	+	20.5910i	0.404680	+	0.700927i	−0.589604	+	0.807693i	$0.700716\pi$
$864$	9.00760	+	5.32477i	0.306445	+	0.181152i
$865$	−1.47064	+	2.54722i	−0.0500033	+	0.0866082i
$866$	14.7290	+	38.6076i	0.500513	+	1.31194i
$867$	15.4463	−	15.4463i	0.524585	−	0.524585i
$868$		0			0
$869$	−0.187877	−	0.187877i	−0.00637328	−	0.00637328i
$870$	−49.3527	−	22.0950i	−1.67321	−	0.749090i
$871$	66.6339	+	38.4711i	2.25780	+	1.30354i
$872$	−7.09496	+	32.3951i	−0.240266	+	1.09704i
$873$	−21.1308	+	12.1999i	−0.715169	+	0.412903i
$874$	−18.9612	−	26.2110i	−0.641371	−	0.886600i
$875$		0			0
$876$	8.71120	+	17.2719i	0.294324	+	0.583565i
$877$	−50.2984	−	13.4774i	−1.69846	−	0.455100i	−0.725907	−	0.687793i	$-0.758580\pi$
$877$	−50.2984	−	13.4774i	−1.69846	−	0.455100i	−0.972550	+	0.232693i	$0.925246\pi$
$878$	4.16048	+	3.38328i	0.140409	+	0.114180i
$879$	30.7564	−	53.2717i	1.03739	−	1.79681i
$880$	−0.281366	−	0.0319149i	−0.00948485	−	0.00107585i
$881$	41.6166			1.40210			0.701050	−	0.713112i	$-0.252715\pi$
$881$	41.6166			1.40210			0.701050	+	0.713112i	$0.252715\pi$
$882$		0			0
$883$	−7.97461	+	7.97461i	−0.268367	+	0.268367i	−0.828442	−	0.560075i	$-0.810772\pi$
$883$	−7.97461	+	7.97461i	−0.268367	+	0.268367i	0.560075	+	0.828442i	$0.310772\pi$
$884$	28.2628	+	18.5198i	0.950579	+	0.622887i
$885$	−1.14162	+	0.305897i	−0.0383752	+	0.0102826i
$886$	5.24887	−	0.540767i	0.176339	−	0.0181674i
$887$	−24.1323	+	13.9328i	−0.810284	+	0.467818i	−0.847055	−	0.531506i	$-0.821626\pi$
$887$	−24.1323	+	13.9328i	−0.810284	+	0.467818i	0.0367704	+	0.999324i	$0.488293\pi$
$888$	−46.4241	−	24.0162i	−1.55789	−	0.805930i
$889$		0			0
$890$	9.66670	−	6.99294i	0.324029	−	0.234404i
$891$	−0.0821384	+	0.306545i	−0.00275174	+	0.0102696i
$892$	11.8035	−	10.5404i	0.395212	−	0.352918i
$893$	−5.88880	−	21.9773i	−0.197061	−	0.735442i
$894$	−18.2183	−	47.7535i	−0.609310	−	1.59712i
$895$	2.85198			0.0953312
$896$		0			0
$897$	−54.4284			−1.81731
$898$	−9.45807	−	24.7914i	−0.315620	−	0.827299i
$899$	4.67101	+	17.4325i	0.155787	+	0.581405i
$900$	−2.54271	+	2.27060i	−0.0847571	+	0.0756868i
$901$	−0.893089	+	3.33305i	−0.0297531	+	0.111040i
$902$	−0.00700354	+	0.00506640i	−0.000233193	+	0.000168693i
$903$		0			0
$904$	−13.2091	−	6.83333i	−0.439327	−	0.227273i
$905$	5.63514	−	3.25345i	0.187318	−	0.108148i
$906$	7.32540	−	0.754703i	0.243370	−	0.0250733i
$907$	48.4340	−	12.9779i	1.60823	−	0.430923i	0.660712	−	0.750639i	$-0.270254\pi$
$907$	48.4340	−	12.9779i	1.60823	−	0.430923i	0.947513	+	0.319717i	$0.103588\pi$
$908$	12.7607	+	8.36168i	0.423477	+	0.277492i
$909$	22.1403	−	22.1403i	0.734348	−	0.734348i
$910$		0			0
$911$	53.4186			1.76984			0.884919	−	0.465746i	$-0.154214\pi$
$911$	53.4186			1.76984			0.884919	+	0.465746i	$0.154214\pi$
$912$	53.7872	+	6.10099i	1.78107	+	0.202024i
$913$	0.157377	−	0.272585i	0.00520843	−	0.00902126i
$914$	−20.0234	−	16.2829i	−0.662315	−	0.538591i
$915$	32.4921	+	8.70624i	1.07416	+	0.287819i
$916$	3.85388	+	7.64120i	0.127336	+	0.252472i
$917$		0			0
$918$	−4.17355	−	5.76931i	−0.137748	−	0.190416i
$919$	−38.4269	+	22.1858i	−1.26759	+	0.731841i	−0.974531	−	0.224254i	$-0.928005\pi$
$919$	−38.4269	+	22.1858i	−1.26759	+	0.731841i	−0.293055	+	0.956096i	$0.594672\pi$
$920$	−5.60059	+	25.5719i	−0.184646	+	0.843082i
$921$	7.02612	+	4.05653i	0.231519	+	0.133667i
$922$	14.3311	+	6.41598i	0.471971	+	0.211299i
$923$	32.3508	+	32.3508i	1.06484	+	1.06484i
$924$		0			0
$925$	−4.46942	+	4.46942i	−0.146954	+	0.146954i
$926$	−1.21170	−	3.17608i	−0.0398188	−	0.104373i
$927$	4.78387	−	8.28591i	0.157123	−	0.272145i
$928$	20.1016	−	34.0046i	0.659866	−	1.11626i
$929$	19.1351	+	33.1430i	0.627804	+	1.08739i	0.987992	+	0.154508i	$0.0493792\pi$
$929$	19.1351	+	33.1430i	0.627804	+	1.08739i	−0.360188	+	0.932880i	$0.617287\pi$
$930$	19.7601	+	3.17137i	0.647961	+	0.103993i
$931$		0			0
$932$	13.2422	−	40.1920i	0.433762	−	1.31653i
$933$	−1.78611	+	6.66586i	−0.0584746	+	0.218230i
$934$	−1.10041	−	10.6809i	−0.0360065	−	0.349491i
$935$	0.166882	+	0.0963495i	0.00545763	+	0.00315097i
$936$	25.8764	−	28.3846i	0.845798	−	0.927779i
$937$			28.5675i			0.933259i	0.884453	+	0.466629i	$0.154532\pi$
$937$			28.5675i			0.933259i	−0.884453	+	0.466629i	$0.845468\pi$
$938$		0			0
$939$	−44.2546	−	44.2546i	−1.44419	−	1.44419i
$940$	−10.0910	+	15.3998i	−0.329134	+	0.502287i
$941$	−6.08780	−	22.7200i	−0.198457	−	0.740650i	−0.991345	−	0.131283i	$-0.958090\pi$
$941$	−6.08780	−	22.7200i	−0.198457	−	0.740650i	0.792888	−	0.609367i	$-0.208576\pi$
$942$	14.6500	+	11.9133i	0.477322	+	0.388155i
$943$	0.399551	+	0.692043i	0.0130112	+	0.0225360i
$944$	−0.128047	−	0.853858i	−0.00416758	−	0.0277907i
$945$		0			0
$946$	−0.00259873	+	0.0161922i	−8.44920e−5	+	0.000526453i
$947$	38.9640	+	10.4404i	1.26616	+	0.339267i	0.828559	−	0.559902i	$-0.189161\pi$
$947$	38.9640	+	10.4404i	1.26616	+	0.339267i	0.437602	+	0.899169i	$0.355828\pi$
$948$	2.31986	−	41.0356i	0.0753456	−	1.33277i
$949$	−25.4589	+	6.82169i	−0.826431	+	0.221442i
$950$	2.67483	−	5.97466i	0.0867829	−	0.193844i
$951$		−	19.2992i		−	0.625820i
$952$		0			0
$953$		−	13.3303i		−	0.431812i	−0.976414	−	0.215906i	$-0.930730\pi$
$953$		−	13.3303i		−	0.431812i	0.976414	−	0.215906i	$-0.0692704\pi$
$954$	3.57996	+	1.60273i	0.115905	+	0.0518903i
$955$	15.6252	−	4.18677i	0.505621	−	0.135481i
$956$	34.5716	−	30.8719i	1.11812	−	0.998468i
$957$	0.452418	+	0.121225i	0.0146246	+	0.00391865i
$958$	48.3091	+	7.75328i	1.56080	+	0.250497i
$959$		0			0
$960$	−25.3081	−	35.7531i	−0.816816	−	1.15393i
$961$	12.1602	+	21.0621i	0.392265	+	0.679423i
$962$	44.9316	−	55.2532i	1.44865	−	1.78144i
$963$	10.2162	+	38.1275i	0.329213	+	1.22864i
$964$	2.47417	+	11.8801i	0.0796878	+	0.382633i
$965$	−33.7594	−	33.7594i	−1.08675	−	1.08675i
$966$		0			0
$967$		−	16.7779i		−	0.539540i	−0.962925	−	0.269770i	$-0.913052\pi$
$967$		−	16.7779i		−	0.539540i	0.962925	−	0.269770i	$-0.0869476\pi$
$968$	−31.0771	+	1.43649i	−0.998855	+	0.0461704i
$969$	−31.9019	−	18.4186i	−1.02484	−	0.591690i
$970$	−37.7148	+	3.88558i	−1.21095	+	0.124759i
$971$	0.0819563	−	0.305865i	0.00263010	−	0.00981568i	−0.964598	−	0.263724i	$-0.915049\pi$
$971$	0.0819563	−	0.305865i	0.00263010	−	0.00981568i	0.967228	+	0.253908i	$0.0817160\pi$
$972$	−33.9236	+	17.1096i	−1.08810	+	0.548790i
$973$		0			0
$974$	1.06474	−	6.63418i	0.0341165	−	0.212573i
$975$	−5.50680	−	9.53806i	−0.176359	−	0.305463i
$976$	−8.99484	+	22.8683i	−0.287918	+	0.731997i
$977$	−3.58053	+	6.20166i	−0.114551	+	0.198409i	−0.917600	−	0.397504i	$-0.869876\pi$
$977$	−3.58053	+	6.20166i	−0.114551	+	0.198409i	0.803049	+	0.595913i	$0.203210\pi$
$978$	44.3475	−	16.9188i	1.41808	−	0.541005i
$979$	−0.0730759	+	0.0730759i	−0.00233552	+	0.00233552i
$980$		0			0
$981$	−18.1392	−	18.1392i	−0.579140	−	0.579140i
$982$	−13.3461	+	29.8106i	−0.425890	+	0.951295i
$983$	12.8516	+	7.41988i	0.409903	+	0.236657i	0.690748	−	0.723096i	$-0.257281\pi$
$983$	12.8516	+	7.41988i	0.409903	+	0.236657i	−0.280845	+	0.959753i	$0.590615\pi$
$984$	−1.30619	−	0.286072i	−0.0416397	−	0.00911964i
$985$	27.5866	−	15.9271i	0.878982	−	0.507481i
$986$	−21.7798	+	15.7556i	−0.693609	+	0.501760i
$987$		0			0
$988$	−23.0801	+	70.0516i	−0.734276	+	2.22864i
$989$	1.46440	+	0.392385i	0.0465653	+	0.0124771i
$990$	0.138197	−	0.169944i	0.00439220	−	0.00540117i
$991$	−0.108889	+	0.188601i	−0.00345898	+	0.00599112i	−0.867750	−	0.497001i	$-0.834434\pi$
$991$	−0.108889	+	0.188601i	−0.00345898	+	0.00599112i	0.864291	+	0.502993i	$0.167768\pi$
$992$	−3.92895	+	14.0822i	−0.124744	+	0.447111i
$993$	53.5497			1.69935
$994$		0			0
$995$	−8.89826	+	8.89826i	−0.282094	+	0.282094i
$996$	47.6670	−	9.92721i	1.51039	−	0.314556i
$997$	−22.1242	+	5.92816i	−0.700680	+	0.187747i	−0.591535	−	0.806279i	$-0.701478\pi$
$997$	−22.1242	+	5.92816i	−0.700680	+	0.187747i	−0.109145	+	0.994026i	$0.534811\pi$
$998$	2.92810	+	28.4211i	0.0926873	+	0.899654i
$999$	−12.9969	+	7.50379i	−0.411205	+	0.237409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.165.5		48
7.2	even	3	inner	784.2.x.o.373.4		48
7.3	odd	6		784.2.m.j.197.12		24
7.4	even	3		784.2.m.k.197.12		24
7.5	odd	6		112.2.w.c.37.4	✓	48
7.6	odd	2		112.2.w.c.53.5	yes	48
16.13	even	4	inner	784.2.x.o.557.4		48
28.19	even	6		448.2.ba.c.177.10		48
28.27	even	2		448.2.ba.c.305.3		48
56.5	odd	6		896.2.ba.f.737.10		48
56.13	odd	2		896.2.ba.f.865.3		48
56.19	even	6		896.2.ba.e.737.3		48
56.27	even	2		896.2.ba.e.865.10		48
112.5	odd	12		896.2.ba.f.289.3		48
112.13	odd	4		112.2.w.c.109.4	yes	48
112.19	even	12		448.2.ba.c.401.3		48
112.27	even	4		896.2.ba.e.417.3		48
112.45	odd	12		784.2.m.j.589.12		24
112.61	odd	12		112.2.w.c.93.5	yes	48
112.69	odd	4		896.2.ba.f.417.10		48
112.75	even	12		896.2.ba.e.289.10		48
112.83	even	4		448.2.ba.c.81.10		48
112.93	even	12	inner	784.2.x.o.765.5		48
112.109	even	12		784.2.m.k.589.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.4	✓	48	7.5	odd	6
112.2.w.c.53.5	yes	48	7.6	odd	2
112.2.w.c.93.5	yes	48	112.61	odd	12
112.2.w.c.109.4	yes	48	112.13	odd	4
448.2.ba.c.81.10		48	112.83	even	4
448.2.ba.c.177.10		48	28.19	even	6
448.2.ba.c.305.3		48	28.27	even	2
448.2.ba.c.401.3		48	112.19	even	12
784.2.m.j.197.12		24	7.3	odd	6
784.2.m.j.589.12		24	112.45	odd	12
784.2.m.k.197.12		24	7.4	even	3
784.2.m.k.589.12		24	112.109	even	12
784.2.x.o.165.5		48	1.1	even	1	trivial
784.2.x.o.373.4		48	7.2	even	3	inner
784.2.x.o.557.4		48	16.13	even	4	inner
784.2.x.o.765.5		48	112.93	even	12	inner
896.2.ba.e.289.10		48	112.75	even	12
896.2.ba.e.417.3		48	112.27	even	4
896.2.ba.e.737.3		48	56.19	even	6
896.2.ba.e.865.10		48	56.27	even	2
896.2.ba.f.289.3		48	112.5	odd	12
896.2.ba.f.417.10		48	112.69	odd	4
896.2.ba.f.737.10		48	56.5	odd	6
896.2.ba.f.865.3		48	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.504093 - 1.32132i) q^{2} +(-0.589510 - 2.20008i) q^{3} +(-1.49178 + 1.33214i) q^{4} +(0.622192 - 2.32205i) q^{5} +(-2.60985 + 1.88798i) q^{6} +(2.51218 + 1.29960i) q^{8} +(-1.89476 + 1.09394i) q^{9} +O(q^{10})\)	\(q+(-0.504093 - 1.32132i) q^{2} +(-0.589510 - 2.20008i) q^{3} +(-1.49178 + 1.33214i) q^{4} +(0.622192 - 2.32205i) q^{5} +(-2.60985 + 1.88798i) q^{6} +(2.51218 + 1.29960i) q^{8} +(-1.89476 + 1.09394i) q^{9} +(-3.38182 + 0.348414i) q^{10} +(0.0284448 - 0.00762177i) q^{11} +(3.81023 + 2.49673i) q^{12} +(-4.38886 + 4.38886i) q^{13} -5.47550 q^{15} +(0.450822 - 3.97451i) q^{16} +(-1.36101 + 2.35734i) q^{17} +(2.40059 + 1.95214i) q^{18} +(-5.73909 - 1.53778i) q^{19} +(2.16512 + 4.29284i) q^{20} +(-0.0244096 - 0.0337427i) q^{22} +(-3.33422 + 1.92501i) q^{23} +(1.37828 - 6.29313i) q^{24} +(-0.674681 - 0.389527i) q^{25} +(8.01149 + 3.58670i) q^{26} +(-1.30797 - 1.30797i) q^{27} +(-4.93772 + 4.93772i) q^{29} +(2.76016 + 7.23489i) q^{30} +(1.29224 - 2.23823i) q^{31} +(-5.47887 + 1.40784i) q^{32} +(-0.0335370 - 0.0580879i) q^{33} +(3.80088 + 0.610015i) q^{34} +(1.36929 - 4.15601i) q^{36} +(2.09988 - 7.83686i) q^{37} +(0.861125 + 8.35837i) q^{38} +(12.2431 + 7.06857i) q^{39} +(4.58080 - 5.02481i) q^{40} -0.207557i q^{41} +(-0.278444 - 0.278444i) q^{43} +(-0.0322802 + 0.0492624i) q^{44} +(1.36129 + 5.08039i) q^{45} +(4.22432 + 3.43519i) q^{46} +(1.91470 + 3.31636i) q^{47} +(-9.01002 + 1.35117i) q^{48} +(-0.174589 + 1.08783i) q^{50} +(5.98867 + 1.60466i) q^{51} +(0.700656 - 12.3938i) q^{52} +(1.22448 - 0.328098i) q^{53} +(-1.06891 + 2.38758i) q^{54} -0.0707926i q^{55} +13.5330i q^{57} +(9.01338 + 4.03524i) q^{58} +(0.208496 - 0.0558664i) q^{59} +(8.16824 - 7.29411i) q^{60} +(-5.93409 - 1.59004i) q^{61} +(-3.60883 - 0.579193i) q^{62} +(4.62207 + 6.52966i) q^{64} +(7.46045 + 12.9219i) q^{65} +(-0.0598470 + 0.0735949i) q^{66} +(-3.20844 - 11.9741i) q^{67} +(-1.10997 - 5.32969i) q^{68} +(6.20075 + 6.20075i) q^{69} -7.37112i q^{71} +(-6.18168 + 0.285738i) q^{72} +(3.67756 + 2.12324i) q^{73} +(-11.4135 + 1.17589i) q^{74} +(-0.459261 + 1.71398i) q^{75} +(10.6100 - 5.35122i) q^{76} +(3.16819 - 19.7403i) q^{78} +(-4.51126 - 7.81374i) q^{79} +(-8.94853 - 3.51975i) q^{80} +(-5.38841 + 9.33299i) q^{81} +(-0.274250 + 0.104628i) q^{82} +(7.55784 - 7.55784i) q^{83} +(4.62706 + 4.62706i) q^{85} +(-0.227552 + 0.508276i) q^{86} +(13.7742 + 7.95255i) q^{87} +(0.0813637 + 0.0178197i) q^{88} +(-3.03921 + 1.75469i) q^{89} +(6.02661 - 4.35968i) q^{90} +(2.40955 - 7.31334i) q^{92} +(-5.68608 - 1.52358i) q^{93} +(3.41679 - 4.20169i) q^{94} +(-7.14164 + 12.3697i) q^{95} +(6.32722 + 11.2240i) q^{96} +11.1522 q^{97} +(-0.0455585 + 0.0455585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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