LMFDB - Embedded newform 980.2.x.m.863.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			863.14
Character	$\chi$	$=$	980.863
Dual form			980.2.x.m.67.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13844 - 0.839014i) q^{2} +(1.08292 + 0.290169i) q^{3} +(0.592112 - 1.91034i) q^{4} +(-1.68711 - 1.46754i) q^{5} +(1.47630 - 0.578247i) q^{6} +(-0.928715 - 2.67161i) q^{8} +(-1.50955 - 0.871538i) q^{9} +(-3.15196 - 0.255205i) q^{10} +(-2.58391 + 1.49182i) q^{11} +(1.19553 - 1.89694i) q^{12} +(-4.05418 - 4.05418i) q^{13} +(-1.40118 - 2.07878i) q^{15} +(-3.29881 - 2.26227i) q^{16} +(2.30478 + 0.617565i) q^{17} +(-2.44977 + 0.274334i) q^{18} +(1.25694 - 2.17708i) q^{19} +(-3.80246 + 2.35400i) q^{20} +(-1.68998 + 3.86629i) q^{22} +(1.55254 + 5.79414i) q^{23} +(-0.230511 - 3.16263i) q^{24} +(0.692662 + 4.95179i) q^{25} +(-8.01697 - 1.21395i) q^{26} +(-3.76010 - 3.76010i) q^{27} -2.55433i q^{29} +(-3.33928 - 1.19097i) q^{30} +(3.12248 - 1.80277i) q^{31} +(-5.65359 + 0.192271i) q^{32} +(-3.23105 + 0.865758i) q^{33} +(3.14202 - 1.23068i) q^{34} +(-2.55876 + 2.36770i) q^{36} +(-1.23528 - 4.61014i) q^{37} +(-0.395646 - 3.53308i) q^{38} +(-3.21397 - 5.56676i) q^{39} +(-2.35384 + 5.87021i) q^{40} +7.93727 q^{41} +(7.62646 - 7.62646i) q^{43} +(1.31992 + 5.81947i) q^{44} +(1.26775 + 3.68570i) q^{45} +(6.62884 + 5.29371i) q^{46} +(2.85870 - 0.765987i) q^{47} +(-2.91592 - 3.40708i) q^{48} +(4.94318 + 5.05618i) q^{50} +(2.31671 + 1.33755i) q^{51} +(-10.1454 + 5.34433i) q^{52} +(0.662485 - 2.47243i) q^{53} +(-7.43544 - 1.12589i) q^{54} +(6.54863 + 1.27512i) q^{55} +(1.99289 - 1.99289i) q^{57} +(-2.14312 - 2.90796i) q^{58} +(-1.04694 - 1.81336i) q^{59} +(-4.80083 + 1.44585i) q^{60} +(-0.950478 + 1.64628i) q^{61} +(2.04223 - 4.67216i) q^{62} +(-6.27498 + 4.96233i) q^{64} +(0.890172 + 12.7895i) q^{65} +(-2.95199 + 3.69652i) q^{66} +(-0.805219 + 3.00512i) q^{67} +(2.54445 - 4.03726i) q^{68} +6.72512i q^{69} -8.09721i q^{71} +(-0.926468 + 4.84233i) q^{72} +(-2.52396 + 9.41954i) q^{73} +(-5.27428 - 4.21197i) q^{74} +(-0.686753 + 5.56340i) q^{75} +(-3.41472 - 3.69026i) q^{76} +(-8.32952 - 3.64089i) q^{78} +(4.03058 - 6.98117i) q^{79} +(2.24547 + 8.65782i) q^{80} +(-0.366226 - 0.634322i) q^{81} +(9.03614 - 6.65948i) q^{82} +(5.99790 - 5.99790i) q^{83} +(-2.98212 - 4.42426i) q^{85} +(2.28360 - 15.0810i) q^{86} +(0.741186 - 2.76614i) q^{87} +(6.38527 + 5.51771i) q^{88} +(-1.77990 - 1.02763i) q^{89} +(4.53562 + 3.13230i) q^{90} +(11.9881 + 0.464910i) q^{92} +(3.90452 - 1.04621i) q^{93} +(2.61180 - 3.27052i) q^{94} +(-5.31554 + 1.82837i) q^{95} +(-6.17820 - 1.43228i) q^{96} +(-6.63160 + 6.63160i) q^{97} +5.20071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.13844	−	0.839014i	0.805002	−	0.593272i
$2$	1.13844	−	0.839014i	0.805002	−	0.593272i
$3$	1.08292	+	0.290169i	0.625227	+	0.167529i	0.557503	−	0.830175i	$-0.311760\pi$
$3$	1.08292	+	0.290169i	0.625227	+	0.167529i	0.0677240	+	0.997704i	$0.478426\pi$
$4$	0.592112	−	1.91034i	0.296056	−	0.955171i
$5$	−1.68711	−	1.46754i	−0.754497	−	0.656303i
$5$	−1.68711	−	1.46754i	−0.754497	−	0.656303i
$6$	1.47630	−	0.578247i	0.602699	−	0.236068i
$7$		0			0
$7$		0			0
$8$	−0.928715	−	2.67161i	−0.328350	−	0.944556i
$9$	−1.50955	−	0.871538i	−0.503183	−	0.290513i
$10$	−3.15196	−	0.255205i	−0.996738	−	0.0807029i
$11$	−2.58391	+	1.49182i	−0.779077	+	0.449800i	−0.836103	−	0.548572i	$-0.815172\pi$
$11$	−2.58391	+	1.49182i	−0.779077	+	0.449800i	0.0570261	+	0.998373i	$0.481838\pi$
$12$	1.19553	−	1.89694i	0.345121	−	0.547600i
$13$	−4.05418	−	4.05418i	−1.12443	−	1.12443i	−0.991068	−	0.133359i	$-0.957424\pi$
$13$	−4.05418	−	4.05418i	−1.12443	−	1.12443i	−0.133359	−	0.991068i	$-0.542576\pi$
$14$		0			0
$15$	−1.40118	−	2.07878i	−0.361782	−	0.536738i
$16$	−3.29881	−	2.26227i	−0.824702	−	0.565568i
$17$	2.30478	+	0.617565i	0.558992	+	0.149782i	0.527243	−	0.849714i	$-0.323226\pi$
$17$	2.30478	+	0.617565i	0.558992	+	0.149782i	0.0317490	+	0.999496i	$0.489892\pi$
$18$	−2.44977	+	0.274334i	−0.577416	+	0.0646611i
$19$	1.25694	−	2.17708i	0.288362	−	0.499457i	−0.685057	−	0.728489i	$-0.740223\pi$
$19$	1.25694	−	2.17708i	0.288362	−	0.499457i	0.973419	+	0.229032i	$0.0735561\pi$
$20$	−3.80246	+	2.35400i	−0.850255	+	0.526371i
$21$		0			0
$22$	−1.68998	+	3.86629i	−0.360304	+	0.824295i
$23$	1.55254	+	5.79414i	0.323726	+	1.20816i	0.915586	+	0.402122i	$0.131727\pi$
$23$	1.55254	+	5.79414i	0.323726	+	1.20816i	−0.591860	+	0.806041i	$0.701606\pi$
$24$	−0.230511	−	3.16263i	−0.0470529	−	0.645570i
$25$	0.692662	+	4.95179i	0.138532	+	0.990358i
$26$	−8.01697	−	1.21395i	−1.57226	−	0.238075i
$27$	−3.76010	−	3.76010i	−0.723632	−	0.723632i
$28$		0			0
$29$		−	2.55433i		−	0.474327i	−0.971470	−	0.237163i	$-0.923782\pi$
$29$		−	2.55433i		−	0.474327i	0.971470	−	0.237163i	$-0.0762177\pi$
$30$	−3.33928	−	1.19097i	−0.609667	−	0.217440i
$31$	3.12248	−	1.80277i	0.560815	−	0.323787i	−0.192658	−	0.981266i	$-0.561711\pi$
$31$	3.12248	−	1.80277i	0.560815	−	0.323787i	0.753472	+	0.657479i	$0.228377\pi$
$32$	−5.65359	+	0.192271i	−0.999422	+	0.0339891i
$33$	−3.23105	+	0.865758i	−0.562454	+	0.150709i
$34$	3.14202	−	1.23068i	0.538851	−	0.211060i
$35$		0			0
$36$	−2.55876	+	2.36770i	−0.426460	+	0.394617i
$37$	−1.23528	−	4.61014i	−0.203079	−	0.757903i	−0.990026	−	0.140882i	$-0.955006\pi$
$37$	−1.23528	−	4.61014i	−0.203079	−	0.757903i	0.786947	−	0.617021i	$-0.211661\pi$
$38$	−0.395646	−	3.53308i	−0.0641823	−	0.573141i
$39$	−3.21397	−	5.56676i	−0.514648	−	0.891396i
$40$	−2.35384	+	5.87021i	−0.372175	+	0.928162i
$41$	7.93727			1.23959			0.619797	−	0.784763i	$-0.287215\pi$
$41$	7.93727			1.23959			0.619797	+	0.784763i	$0.287215\pi$
$42$		0			0
$43$	7.62646	−	7.62646i	1.16302	−	1.16302i	0.179215	−	0.983810i	$-0.442644\pi$
$43$	7.62646	−	7.62646i	1.16302	−	1.16302i	0.983810	−	0.179215i	$-0.0573557\pi$
$44$	1.31992	+	5.81947i	0.198986	+	0.877318i
$45$	1.26775	+	3.68570i	0.188986	+	0.549432i
$46$	6.62884	+	5.29371i	0.977369	+	0.780515i
$47$	2.85870	−	0.765987i	0.416985	−	0.111731i	−0.0442256	−	0.999022i	$-0.514082\pi$
$47$	2.85870	−	0.765987i	0.416985	−	0.111731i	0.461210	+	0.887291i	$0.347415\pi$
$48$	−2.91592	−	3.40708i	−0.420876	−	0.491770i
$49$		0			0
$50$	4.94318	+	5.05618i	0.699071	+	0.715053i
$51$	2.31671	+	1.33755i	0.324404	+	0.187295i
$52$	−10.1454	+	5.34433i	−1.40691	+	0.741126i
$53$	0.662485	−	2.47243i	0.0909993	−	0.339614i	−0.905383	−	0.424595i	$-0.860416\pi$
$53$	0.662485	−	2.47243i	0.0909993	−	0.339614i	0.996383	+	0.0849813i	$0.0270830\pi$
$54$	−7.43544	−	1.12589i	−1.01184	−	0.153214i
$55$	6.54863	+	1.27512i	0.883017	+	0.171938i
$56$		0			0
$57$	1.99289	−	1.99289i	0.263965	−	0.263965i
$58$	−2.14312	−	2.90796i	−0.281405	−	0.381834i
$59$	−1.04694	−	1.81336i	−0.136301	−	0.236079i	0.789793	−	0.613374i	$-0.210188\pi$
$59$	−1.04694	−	1.81336i	−0.136301	−	0.236079i	−0.926094	+	0.377294i	$0.876855\pi$
$60$	−4.80083	+	1.44585i	−0.619784	+	0.186659i
$61$	−0.950478	+	1.64628i	−0.121696	+	0.210784i	−0.920437	−	0.390892i	$-0.872167\pi$
$61$	−0.950478	+	1.64628i	−0.121696	+	0.210784i	0.798740	+	0.601676i	$0.205500\pi$
$62$	2.04223	−	4.67216i	0.259363	−	0.593365i
$63$		0			0
$64$	−6.27498	+	4.96233i	−0.784372	+	0.620291i
$65$	0.890172	+	12.7895i	0.110412	+	1.58634i
$66$	−2.95199	+	3.69652i	−0.363365	+	0.455010i
$67$	−0.805219	+	3.00512i	−0.0983732	+	0.367134i	−0.997509	−	0.0705354i	$-0.977529\pi$
$67$	−0.805219	+	3.00512i	−0.0983732	+	0.367134i	0.899136	+	0.437669i	$0.144196\pi$
$68$	2.54445	−	4.03726i	0.308560	−	0.489589i
$69$			6.72512i			0.809609i
$70$		0			0
$71$		−	8.09721i		−	0.960962i	−0.877005	−	0.480481i	$-0.840462\pi$
$71$		−	8.09721i		−	0.960962i	0.877005	−	0.480481i	$-0.159538\pi$
$72$	−0.926468	+	4.84233i	−0.109185	+	0.570674i
$73$	−2.52396	+	9.41954i	−0.295407	+	1.10247i	0.645487	+	0.763771i	$0.276655\pi$
$73$	−2.52396	+	9.41954i	−0.295407	+	1.10247i	−0.940894	+	0.338702i	$0.890012\pi$
$74$	−5.27428	−	4.21197i	−0.613122	−	0.489632i
$75$	−0.686753	+	5.56340i	−0.0792995	+	0.642406i
$76$	−3.41472	−	3.69026i	−0.391695	−	0.423302i
$77$		0			0
$78$	−8.32952	−	3.64089i	−0.943133	−	0.412249i
$79$	4.03058	−	6.98117i	0.453476	−	0.785443i	−0.545123	−	0.838356i	$-0.683517\pi$
$79$	4.03058	−	6.98117i	0.453476	−	0.785443i	0.998599	+	0.0529126i	$0.0168505\pi$
$80$	2.24547	+	8.65782i	0.251051	+	0.967974i
$81$	−0.366226	−	0.634322i	−0.0406918	−	0.0704802i
$82$	9.03614	−	6.65948i	0.997875	−	0.735416i
$83$	5.99790	−	5.99790i	0.658356	−	0.658356i	−0.296635	−	0.954991i	$-0.595865\pi$
$83$	5.99790	−	5.99790i	0.658356	−	0.658356i	0.954991	+	0.296635i	$0.0958646\pi$
$84$		0			0
$85$	−2.98212	−	4.42426i	−0.323456	−	0.479878i
$86$	2.28360	−	15.0810i	0.246247	−	1.62623i
$87$	0.741186	−	2.76614i	0.0794635	−	0.296562i
$88$	6.38527	+	5.51771i	0.680672	+	0.588190i
$89$	−1.77990	−	1.02763i	−0.188669	−	0.108928i	0.402690	−	0.915336i	$-0.368075\pi$
$89$	−1.77990	−	1.02763i	−0.188669	−	0.108928i	−0.591359	+	0.806408i	$0.701408\pi$
$90$	4.53562	+	3.13230i	0.478096	+	0.330174i
$91$		0			0
$92$	11.9881	+	0.464910i	1.24984	+	0.0484702i
$93$	3.90452	−	1.04621i	0.404880	−	0.108487i
$94$	2.61180	−	3.27052i	0.269387	−	0.337329i
$95$	−5.31554	+	1.82837i	−0.545363	+	0.187586i
$96$	−6.17820	−	1.43228i	−0.630560	−	0.146181i
$97$	−6.63160	+	6.63160i	−0.673337	+	0.673337i	−0.958484	−	0.285147i	$-0.907958\pi$
$97$	−6.63160	+	6.63160i	−0.673337	+	0.673337i	0.285147	+	0.958484i	$0.407958\pi$
$98$		0			0
$99$	5.20071			0.522691
$100$	9.86974	+	1.60879i	0.986974	+	0.160879i
$101$	−3.73273	−	6.46529i	−0.371421	−	0.643320i	0.618363	−	0.785892i	$-0.287796\pi$
$101$	−3.73273	−	6.46529i	−0.371421	−	0.643320i	−0.989784	+	0.142572i	$0.954463\pi$
$102$	3.75967	−	0.421021i	0.372263	−	0.0416873i
$103$	−1.06672	−	3.98105i	−0.105107	−	0.392264i	0.893250	−	0.449560i	$-0.148419\pi$
$103$	−1.06672	−	3.98105i	−0.105107	−	0.392264i	−0.998357	+	0.0572952i	$0.981752\pi$
$104$	−7.06600	+	14.5964i	−0.692878	+	1.43129i
$105$		0			0
$106$	−1.32020	−	3.37056i	−0.128229	−	0.327377i
$107$	10.0616	−	2.69601i	0.972696	−	0.260633i	0.262730	−	0.964869i	$-0.415377\pi$
$107$	10.0616	−	2.69601i	0.972696	−	0.260633i	0.709966	+	0.704236i	$0.248710\pi$
$108$	−9.40948	+	4.95667i	−0.905427	+	0.476956i
$109$	−8.88798	+	5.13148i	−0.851314	+	0.491507i	−0.861094	−	0.508446i	$-0.830220\pi$
$109$	−8.88798	+	5.13148i	−0.851314	+	0.491507i	0.00977974	+	0.999952i	$0.496887\pi$
$110$	8.52510	−	4.04273i	0.812836	−	0.385459i
$111$		−	5.35088i		−	0.507883i
$112$		0			0
$113$	7.35551	+	7.35551i	0.691948	+	0.691948i	0.962660	−	0.270712i	$-0.0872592\pi$
$113$	7.35551	+	7.35551i	0.691948	+	0.691948i	−0.270712	+	0.962660i	$0.587259\pi$
$114$	0.596734	−	3.94086i	0.0558892	−	0.369095i
$115$	5.88383	−	12.0537i	0.548670	−	1.12402i
$116$	−4.87964	−	1.51245i	−0.453063	−	0.140427i
$117$	2.58661	+	9.65335i	0.239132	+	0.892453i
$118$	−2.71332	−	1.18601i	−0.249782	−	0.109181i
$119$		0			0
$120$	−4.25239	+	5.67399i	−0.388188	+	0.517962i
$121$	−1.04895	+	1.81684i	−0.0953593	+	0.165167i
$122$	0.299182	+	2.67166i	0.0270866	+	0.241881i
$123$	8.59546	+	2.30315i	0.775027	+	0.207668i
$124$	−1.59504	−	7.03245i	−0.143239	−	0.631533i
$125$	6.09835	−	9.37071i	0.545453	−	0.838142i
$126$		0			0
$127$	−13.3832	−	13.3832i	−1.18756	−	1.18756i	−0.977739	−	0.209826i	$-0.932710\pi$
$127$	−13.3832	−	13.3832i	−1.18756	−	1.18756i	−0.209826	−	0.977739i	$-0.567290\pi$
$128$	−2.98025	+	10.9141i	−0.263420	+	0.964681i
$129$	10.4718	−	6.04592i	0.921994	−	0.532314i
$130$	11.7440	+	13.8133i	1.03001	+	1.21150i
$131$	13.2990	+	7.67817i	1.16194	+	0.670845i	0.951767	−	0.306820i	$-0.0992651\pi$
$131$	13.2990	+	7.67817i	1.16194	+	0.670845i	0.210170	+	0.977665i	$0.432598\pi$
$132$	−0.259253	+	6.68504i	−0.0225651	+	0.581858i
$133$		0			0
$134$	1.60464	+	4.09675i	0.138620	+	0.353905i
$135$	0.825602	+	11.8618i	0.0710565	+	1.02090i
$136$	−0.490597	−	6.73102i	−0.0420683	−	0.577181i
$137$	−4.55145	−	1.21956i	−0.388857	−	0.104194i	0.0590931	−	0.998252i	$-0.481179\pi$
$137$	−4.55145	−	1.21956i	−0.388857	−	0.104194i	−0.447950	+	0.894059i	$0.647846\pi$
$138$	5.64247	+	7.65617i	0.480319	+	0.651737i
$139$	−10.3065			−0.874185			−0.437093	−	0.899417i	$-0.643992\pi$
$139$	−10.3065			−0.874185			−0.437093	+	0.899417i	$0.643992\pi$
$140$		0			0
$141$	3.31802			0.279428
$142$	−6.79367	−	9.21822i	−0.570112	−	0.773576i
$143$	16.5237	+	4.42752i	1.38178	+	0.370248i
$144$	3.00805	+	6.29005i	0.250671	+	0.524171i
$145$	−3.74857	+	4.30942i	−0.311302	+	0.357878i
$146$	5.02973	+	12.8413i	0.416264	+	1.06275i
$147$		0			0
$148$	−9.53837	−	0.369908i	−0.784049	−	0.0304063i
$149$	8.37658	+	4.83622i	0.686236	+	0.396199i	0.802201	−	0.597055i	$-0.203662\pi$
$149$	8.37658	+	4.83622i	0.686236	+	0.396199i	−0.115964	+	0.993253i	$0.536996\pi$
$150$	3.88594	+	6.90982i	0.317286	+	0.564185i
$151$	−0.955932	+	0.551908i	−0.0777927	+	0.0449136i	−0.538392	−	0.842695i	$-0.680968\pi$
$151$	−0.955932	+	0.551908i	−0.0777927	+	0.0449136i	0.460599	+	0.887608i	$0.347635\pi$
$152$	−6.98365	−	1.33616i	−0.566449	−	0.108377i
$153$	−2.94095	−	2.94095i	−0.237762	−	0.237762i
$154$		0			0
$155$	−7.91360	−	1.54090i	−0.635635	−	0.123768i
$156$	−12.5375	+	2.84364i	−1.00380	+	0.227673i
$157$	−8.39254	−	2.24878i	−0.669798	−	0.179472i	−0.0921341	−	0.995747i	$-0.529369\pi$
$157$	−8.39254	−	2.24878i	−0.669798	−	0.179472i	−0.577664	+	0.816275i	$0.696036\pi$
$158$	−1.26870	−	11.3294i	−0.100933	−	0.901318i
$159$	1.43484	−	2.48522i	0.113790	−	0.197091i
$160$	9.82037	+	7.97247i	0.776369	+	0.630279i
$161$		0			0
$162$	−0.949133	−	0.414872i	−0.0745709	−	0.0325954i
$163$	−0.278958	−	1.04108i	−0.0218496	−	0.0815440i	0.954140	−	0.299360i	$-0.0967733\pi$
$163$	−0.278958	−	1.04108i	−0.0218496	−	0.0815440i	−0.975990	+	0.217816i	$0.930107\pi$
$164$	4.69975	−	15.1629i	0.366989	−	1.18402i
$165$	6.72167	+	3.28107i	0.523281	+	0.255431i
$166$	1.79596	−	11.8606i	0.139393	−	0.920562i
$167$	2.18132	+	2.18132i	0.168796	+	0.168796i	0.786450	−	0.617654i	$-0.211917\pi$
$167$	2.18132	+	2.18132i	0.168796	+	0.168796i	−0.617654	+	0.786450i	$0.711917\pi$
$168$		0			0
$169$			19.8727i			1.52867i
$170$	−7.10699	−	2.53474i	−0.545081	−	0.194405i
$171$	−3.79482	+	2.19094i	−0.290197	+	0.167546i
$172$	−10.0534	−	19.0849i	−0.766566	−	1.45521i
$173$	22.7858	−	6.10543i	1.73237	−	0.464187i	0.751643	−	0.659570i	$-0.229262\pi$
$173$	22.7858	−	6.10543i	1.73237	−	0.464187i	0.980727	+	0.195383i	$0.0625948\pi$
$174$	−1.47703	−	3.77097i	−0.111974	−	0.285876i
$175$		0			0
$176$	11.8987	+	0.924279i	0.896899	+	0.0696701i
$177$	−0.607581	−	2.26752i	−0.0456686	−	0.170437i
$178$	−2.88851	+	0.323465i	−0.216503	+	0.0242448i
$179$	3.53155	+	6.11682i	0.263960	+	0.457193i	0.967291	−	0.253670i	$-0.0816379\pi$
$179$	3.53155	+	6.11682i	0.263960	+	0.457193i	−0.703330	+	0.710863i	$0.748305\pi$
$180$	7.79160	−	0.239496i	0.580751	−	0.0178510i
$181$	2.37419			0.176472			0.0882360	−	0.996100i	$-0.471877\pi$
$181$	2.37419			0.176472			0.0882360	+	0.996100i	$0.471877\pi$
$182$		0			0
$183$	−1.50699	+	1.50699i	−0.111400	+	0.111400i
$184$	14.0378	−	9.52888i	1.03488	−	0.702478i
$185$	−4.68150	+	9.59063i	−0.344191	+	0.705117i
$186$	3.56729	−	4.46700i	0.261567	−	0.327537i
$187$	−6.87664	+	1.84259i	−0.502870	+	0.134744i
$188$	0.229376	−	5.91465i	0.0167290	−	0.431370i
$189$		0			0
$190$	−4.51743	+	6.54131i	−0.327729	+	0.474556i
$191$	−5.46966	−	3.15791i	−0.395771	−	0.228498i	0.288887	−	0.957363i	$-0.406715\pi$
$191$	−5.46966	−	3.15791i	−0.395771	−	0.228498i	−0.684658	+	0.728865i	$0.740048\pi$
$192$	−8.23524	+	3.55302i	−0.594327	+	0.256417i
$193$	5.46675	−	20.4022i	0.393505	−	1.46858i	−0.430806	−	0.902445i	$-0.641771\pi$
$193$	5.46675	−	20.4022i	0.393505	−	1.46858i	0.824311	−	0.566137i	$-0.191563\pi$
$194$	−1.98571	+	13.1137i	−0.142565	+	0.941509i
$195$	−2.74712	+	14.1084i	−0.196726	+	1.01032i
$196$		0			0
$197$	−1.01354	+	1.01354i	−0.0722120	+	0.0722120i	−0.742290	−	0.670078i	$-0.766260\pi$
$197$	−1.01354	+	1.01354i	−0.0722120	+	0.0722120i	0.670078	+	0.742290i	$0.266260\pi$
$198$	5.92072	−	4.36347i	0.420767	−	0.310098i
$199$	4.75738	+	8.24003i	0.337242	+	0.584120i	0.983913	−	0.178649i	$-0.0571727\pi$
$199$	4.75738	+	8.24003i	0.337242	+	0.584120i	−0.646671	+	0.762769i	$0.723839\pi$
$200$	12.5860	−	6.44932i	0.889961	−	0.456036i
$201$	−1.74398	+	3.02067i	−0.123011	+	0.213061i
$202$	−9.67397	−	4.22855i	−0.680658	−	0.297520i
$203$		0			0
$204$	3.92693	−	3.63372i	0.274940	−	0.254412i
$205$	−13.3910	−	11.6482i	−0.935270	−	0.813549i
$206$	−4.55455	−	3.63721i	−0.317331	−	0.253417i
$207$	2.70619	−	10.0996i	0.188093	−	0.701973i
$208$	4.20229	+	22.5456i	0.291377	+	1.56326i
$209$			7.50050i			0.518821i
$210$		0			0
$211$			26.9476i			1.85515i	0.373634	+	0.927576i	$0.378112\pi$
$211$			26.9476i			1.85515i	−0.373634	+	0.927576i	$0.621888\pi$
$212$	−4.33092	−	2.72953i	−0.297448	−	0.187465i
$213$	2.34956	−	8.76866i	0.160989	−	0.600819i
$214$	9.19264	−	11.5111i	0.628396	−	0.786884i
$215$	−24.0588	+	1.67453i	−1.64080	+	0.114202i
$216$	−6.55345	+	13.5376i	−0.445906	+	0.921116i
$217$		0			0
$218$	−5.81310	+	13.2990i	−0.393712	+	0.900725i
$219$	−5.46651	+	9.46827i	−0.369393	+	0.639807i
$220$	6.31344	−	11.7551i	0.425652	−	0.792529i
$221$	−6.84029	−	11.8477i	−0.460128	−	0.796964i
$222$	−4.48946	−	6.09168i	−0.301313	−	0.408847i
$223$	−2.22624	+	2.22624i	−0.149080	+	0.149080i	−0.777707	−	0.628627i	$-0.783617\pi$
$223$	−2.22624	+	2.22624i	−0.149080	+	0.149080i	0.628627	+	0.777707i	$0.283617\pi$
$224$		0			0
$225$	3.27007	−	8.07865i	0.218004	−	0.538577i
$226$	14.5452	+	2.20247i	0.967533	+	0.146506i
$227$	−2.08751	+	7.79070i	−0.138553	+	0.517087i	0.861405	+	0.507919i	$0.169585\pi$
$227$	−2.08751	+	7.79070i	−0.138553	+	0.517087i	−0.999958	+	0.00916824i	$0.997082\pi$
$228$	−2.62709	−	4.98712i	−0.173983	−	0.330280i
$229$	−2.10701	−	1.21648i	−0.139235	−	0.0803873i	0.428764	−	0.903416i	$-0.358949\pi$
$229$	−2.10701	−	1.21648i	−0.139235	−	0.0803873i	−0.567999	+	0.823029i	$0.692282\pi$
$230$	−3.41484	−	18.6591i	−0.225168	−	1.23035i
$231$		0			0
$232$	−6.82416	+	2.37224i	−0.448028	+	0.155745i
$233$	−10.1117	+	2.70941i	−0.662437	+	0.177499i	−0.574346	−	0.818613i	$-0.694743\pi$
$233$	−10.1117	+	2.70941i	−0.662437	+	0.177499i	−0.0880913	+	0.996112i	$0.528077\pi$
$234$	11.0440	+	8.81961i	0.721969	+	0.576556i
$235$	−5.94705	−	2.90295i	−0.387943	−	0.189368i
$236$	−4.08405	+	0.926308i	−0.265849	+	0.0602975i
$237$	6.39053	−	6.39053i	0.415110	−	0.415110i
$238$		0			0
$239$	12.9050			0.834754			0.417377	−	0.908733i	$-0.362949\pi$
$239$	12.9050			0.834754			0.417377	+	0.908733i	$0.362949\pi$
$240$	−0.0805566	+	10.0273i	−0.00519991	+	0.647261i
$241$	1.35695	+	2.35030i	0.0874087	+	0.151396i	0.906415	−	0.422388i	$-0.138808\pi$
$241$	1.35695	+	2.35030i	0.0874087	+	0.151396i	−0.819006	+	0.573784i	$0.805475\pi$
$242$	0.330178	+	2.94846i	0.0212247	+	0.189534i
$243$	3.91634	+	14.6160i	0.251234	+	0.937616i
$244$	2.58216	+	2.79052i	0.165306	+	0.178645i
$245$		0			0
$246$	11.7178	−	4.58970i	0.747101	−	0.292629i
$247$	−13.9221	+	3.73043i	−0.885845	+	0.237361i
$248$	−7.71619	−	6.66780i	−0.489978	−	0.423405i
$249$	8.23568	−	4.75487i	0.521915	−	0.301328i
$250$	−0.919524	−	15.7846i	−0.0581558	−	0.998308i
$251$			3.15358i			0.199052i	0.995035	+	0.0995262i	$0.0317327\pi$
$251$			3.15358i			0.199052i	−0.995035	+	0.0995262i	$0.968267\pi$
$252$		0			0
$253$	−12.6554	−	12.6554i	−0.795640	−	0.795640i
$254$	−26.4647	−	4.00734i	−1.66054	−	0.251443i
$255$	−1.94563	−	5.65646i	−0.121840	−	0.354221i
$256$	5.76424	+	14.9256i	0.360265	+	0.932850i
$257$	−4.26180	−	15.9053i	−0.265844	−	0.992143i	−0.961732	−	0.273993i	$-0.911656\pi$
$257$	−4.26180	−	15.9053i	−0.265844	−	0.992143i	0.695888	−	0.718151i	$-0.255011\pi$
$258$	6.84900	−	15.6690i	0.426400	−	0.975507i
$259$		0			0
$260$	24.9594	+	5.87229i	1.54792	+	0.364184i
$261$	−2.22619	+	3.85588i	−0.137798	+	0.238673i
$262$	21.5822	−	2.41685i	1.33335	−	0.149314i
$263$	28.1947	+	7.55474i	1.73856	+	0.465845i	0.982126	−	0.188227i	$-0.0602739\pi$
$263$	28.1947	+	7.55474i	1.73856	+	0.465845i	0.756432	+	0.654072i	$0.226941\pi$
$264$	5.31370	+	7.82807i	0.327035	+	0.481784i
$265$	−4.74607	+	3.19903i	−0.291549	+	0.196515i
$266$		0			0
$267$	−1.62931	−	1.62931i	−0.0997123	−	0.0997123i
$268$	5.26402	+	3.31761i	0.321551	+	0.202655i
$269$	−5.29203	+	3.05536i	−0.322661	+	0.186288i	−0.652578	−	0.757721i	$-0.726313\pi$
$269$	−5.29203	+	3.05536i	−0.322661	+	0.186288i	0.329917	+	0.944010i	$0.392979\pi$
$270$	10.8921	+	12.8113i	0.662872	+	0.779671i
$271$	19.0699	+	11.0100i	1.15841	+	0.668810i	0.950923	−	0.309428i	$-0.100137\pi$
$271$	19.0699	+	11.0100i	1.15841	+	0.668810i	0.207489	+	0.978237i	$0.433471\pi$
$272$	−6.20594	−	7.25128i	−0.376290	−	0.439673i
$273$		0			0
$274$	−6.20480	+	2.43033i	−0.374846	+	0.146822i
$275$	−9.17695	−	11.7616i	−0.553391	−	0.709253i
$276$	12.8473	+	3.98202i	0.773315	+	0.239690i
$277$	15.8956	+	4.25922i	0.955077	+	0.255912i	0.702515	−	0.711669i	$-0.252060\pi$
$277$	15.8956	+	4.25922i	0.955077	+	0.255912i	0.252561	+	0.967581i	$0.418727\pi$
$278$	−11.7334	+	8.64729i	−0.703721	+	0.518630i
$279$	−6.28472			−0.376257
$280$		0			0
$281$	6.79274			0.405221			0.202610	−	0.979259i	$-0.435057\pi$
$281$	6.79274			0.405221			0.202610	+	0.979259i	$0.435057\pi$
$282$	3.77739	−	2.78387i	0.224940	−	0.165777i
$283$	−12.6003	−	3.37625i	−0.749013	−	0.200697i	−0.135932	−	0.990718i	$-0.543403\pi$
$283$	−12.6003	−	3.37625i	−0.749013	−	0.200697i	−0.613080	+	0.790021i	$0.710070\pi$
$284$	−15.4684	−	4.79446i	−0.917882	−	0.284499i
$285$	−6.28687	+	0.437577i	−0.372402	+	0.0259198i
$286$	22.5261	−	8.82314i	1.33200	−	0.521723i
$287$		0			0
$288$	8.70194	+	4.63707i	0.512767	+	0.273242i
$289$	−9.79179	−	5.65329i	−0.575987	−	0.332546i
$290$	−0.651877	+	8.05115i	−0.0382796	+	0.472780i
$291$	−9.10580	+	5.25724i	−0.533791	+	0.308185i
$292$	16.5001	+	10.3990i	0.965593	+	0.608558i
$293$	1.28839	+	1.28839i	0.0752688	+	0.0752688i	0.743739	−	0.668470i	$-0.233051\pi$
$293$	1.28839	+	1.28839i	0.0752688	+	0.0752688i	−0.668470	+	0.743739i	$0.733051\pi$
$294$		0			0
$295$	−0.894869	+	4.59577i	−0.0521013	+	0.267576i
$296$	−11.1693	+	7.58170i	−0.649200	+	0.440678i
$297$	15.3251	+	4.10636i	0.889255	+	0.238275i
$298$	13.5939	−	1.52230i	0.787475	−	0.0881842i
$299$	17.1962	−	29.7848i	0.994484	−	1.72250i
$300$	10.2214	+	4.60609i	0.590131	+	0.265933i
$301$		0			0
$302$	−0.625218	+	1.43036i	−0.0359772	+	0.0823078i
$303$	−2.16625	−	8.08454i	−0.124448	−	0.464445i
$304$	−9.07156	+	4.33824i	−0.520289	+	0.248815i
$305$	4.01953	−	1.38258i	0.230158	−	0.0791664i
$306$	−5.81561	−	0.880613i	−0.332456	−	0.0503413i
$307$	−11.6465	−	11.6465i	−0.664701	−	0.664701i	0.291783	−	0.956484i	$-0.405751\pi$
$307$	−11.6465	−	11.6465i	−0.664701	−	0.664701i	−0.956484	+	0.291783i	$0.905751\pi$
$308$		0			0
$309$		−	4.62070i		−	0.262863i
$310$	−10.3020	+	4.88538i	−0.585116	+	0.277471i
$311$	−26.1398	+	15.0918i	−1.48225	+	0.855778i	−0.999797	−	0.0201436i	$-0.993588\pi$
$311$	−26.1398	+	15.0918i	−1.48225	+	0.855778i	−0.482454	+	0.875922i	$0.660254\pi$
$312$	−11.8873	+	13.7564i	−0.672988	+	0.778804i
$313$	21.3109	−	5.71023i	1.20456	−	0.322761i	0.399935	−	0.916543i	$-0.369033\pi$
$313$	21.3109	−	5.71023i	1.20456	−	0.322761i	0.804626	+	0.593782i	$0.202366\pi$
$314$	−11.4412	+	4.48135i	−0.645664	+	0.252897i
$315$		0			0
$316$	−10.9499	−	11.8334i	−0.615978	−	0.665682i
$317$	−0.375154	−	1.40009i	−0.0210708	−	0.0786372i	0.954590	−	0.297923i	$-0.0962939\pi$
$317$	−0.375154	−	1.40009i	−0.0210708	−	0.0786372i	−0.975661	+	0.219286i	$0.929627\pi$
$318$	−0.451645	−	4.03314i	−0.0253270	−	0.226167i
$319$	3.81059	+	6.60014i	0.213352	+	0.369537i
$320$	17.8690	+	0.836792i	0.998905	+	0.0467781i
$321$	11.6783			0.651819
$322$		0			0
$323$	4.24147	−	4.24147i	0.236001	−	0.236001i
$324$	−1.42862	+	0.324027i	−0.0793677	+	0.0180015i
$325$	17.2673	−	22.8836i	0.957815	−	1.26935i
$326$	−1.19106	−	0.951167i	−0.0659668	−	0.0526803i
$327$	−11.1140	+	2.97799i	−0.614606	+	0.164683i
$328$	−7.37146	−	21.2053i	−0.407021	−	1.17087i
$329$		0			0
$330$	10.4051	−	1.90426i	0.572782	−	0.104826i
$331$	24.5744	+	14.1881i	1.35073	+	0.779846i	0.988352	−	0.152184i	$-0.0486305\pi$
$331$	24.5744	+	14.1881i	1.35073	+	0.779846i	0.362381	+	0.932030i	$0.381964\pi$
$332$	−7.90661	−	15.0095i	−0.433932	−	0.823752i
$333$	−2.15320	+	8.03583i	−0.117994	+	0.440361i
$334$	4.31348	+	0.653156i	0.236023	+	0.0357391i
$335$	5.76862	−	3.88827i	0.315173	−	0.212439i
$336$		0			0
$337$	−11.7829	+	11.7829i	−0.641857	+	0.641857i	−0.951012	−	0.309155i	$-0.899954\pi$
$337$	−11.7829	+	11.7829i	−0.641857	+	0.641857i	0.309155	+	0.951012i	$0.399954\pi$
$338$	16.6735	+	22.6240i	0.906918	+	1.23058i
$339$	5.83112	+	10.0998i	0.316703	+	0.548546i
$340$	−10.2176	+	3.07721i	−0.554127	+	0.166885i
$341$	−5.37880	+	9.31636i	−0.291279	+	0.504509i
$342$	−2.48197	+	5.67817i	−0.134209	+	0.307041i
$343$		0			0
$344$	−27.4577	−	13.2921i	−1.48042	−	0.716662i
$345$	9.86937	−	11.3460i	0.531349	−	0.610848i
$346$	20.8178	−	26.0683i	1.11917	−	1.40144i
$347$	4.13190	−	15.4205i	0.221812	−	0.827815i	−0.761844	−	0.647760i	$-0.775706\pi$
$347$	4.13190	−	15.4205i	0.221812	−	0.827815i	0.983657	−	0.180055i	$-0.0576274\pi$
$348$	−4.84541	−	3.05379i	−0.259741	−	0.163700i
$349$		−	7.52656i		−	0.402888i	−0.979500	−	0.201444i	$-0.935437\pi$
$349$		−	7.52656i		−	0.402888i	0.979500	−	0.201444i	$-0.0645633\pi$
$350$		0			0
$351$			30.4882i			1.62734i
$352$	14.3215	−	8.93094i	0.763339	−	0.476021i
$353$	−1.45108	+	5.41550i	−0.0772331	+	0.288238i	−0.993730	−	0.111803i	$-0.964337\pi$
$353$	−1.45108	+	5.41550i	−0.0772331	+	0.288238i	0.916497	+	0.400041i	$0.131004\pi$
$354$	−2.59418	−	2.07168i	−0.137879	−	0.110109i
$355$	−11.8830	+	13.6609i	−0.630682	+	0.725043i
$356$	−3.01702	+	2.79175i	−0.159902	+	0.147962i
$357$		0			0
$358$	9.15257	+	4.00064i	0.483728	+	0.211441i
$359$	18.2143	−	31.5480i	0.961311	−	1.66504i	0.242097	−	0.970252i	$-0.422165\pi$
$359$	18.2143	−	31.5480i	0.961311	−	1.66504i	0.719215	−	0.694788i	$-0.244502\pi$
$360$	8.66936	−	6.80991i	0.456915	−	0.358914i
$361$	6.34021	+	10.9816i	0.333695	+	0.577977i
$362$	2.70288	−	1.99198i	0.142060	−	0.104696i
$363$	−1.66313	+	1.66313i	−0.0872915	+	0.0872915i
$364$		0			0
$365$	18.0817	−	12.1878i	0.946440	−	0.637937i
$366$	−0.451241	+	2.98002i	−0.0235867	+	0.155768i
$367$	8.46227	−	31.5816i	0.441727	−	1.64855i	−0.282709	−	0.959206i	$-0.591233\pi$
$367$	8.46227	−	31.5816i	0.441727	−	1.64855i	0.724436	−	0.689342i	$-0.242100\pi$
$368$	7.98642	−	22.6260i	0.416321	−	1.17946i
$369$	−11.9817	−	6.91763i	−0.623742	−	0.360118i
$370$	2.71704	+	14.8463i	0.141252	+	0.771820i
$371$		0			0
$372$	0.313291	−	8.07844i	0.0162434	−	0.418848i
$373$	25.2614	−	6.76877i	1.30799	−	0.350474i	0.463522	−	0.886086i	$-0.346586\pi$
$373$	25.2614	−	6.76877i	1.30799	−	0.350474i	0.844464	+	0.535612i	$0.179919\pi$
$374$	−6.28272	+	7.86729i	−0.324872	+	0.406808i
$375$	9.32313	−	8.37822i	0.481445	−	0.432649i
$376$	−4.70134	−	6.92595i	−0.242453	−	0.357178i
$377$	−10.3557	+	10.3557i	−0.533346	+	0.533346i
$378$		0			0
$379$	−20.3769			−1.04669			−0.523344	−	0.852121i	$-0.675316\pi$
$379$	−20.3769			−1.04669			−0.523344	+	0.852121i	$0.675316\pi$
$380$	0.345403	+	11.2371i	0.0177188	+	0.576451i
$381$	−10.6096	−	18.3763i	−0.543546	−	0.941449i
$382$	−8.87644	+	0.994015i	−0.454158	+	0.0508582i
$383$	−6.60856	−	24.6635i	−0.337682	−	1.26025i	−0.900932	−	0.433960i	$-0.857116\pi$
$383$	−6.60856	−	24.6635i	−0.337682	−	1.26025i	0.563250	−	0.826286i	$-0.309551\pi$
$384$	−6.39433	+	10.9544i	−0.326309	+	0.559014i
$385$		0			0
$386$	−10.8941	−	27.8134i	−0.554496	−	1.41567i
$387$	−18.1593	+	4.86576i	−0.923088	+	0.247341i
$388$	8.74196	+	16.5953i	0.443806	+	0.842497i
$389$	−15.6310	+	9.02458i	−0.792525	+	0.457564i	−0.840851	−	0.541267i	$-0.817945\pi$
$389$	−15.6310	+	9.02458i	−0.792525	+	0.457564i	0.0483257	+	0.998832i	$0.484611\pi$
$390$	8.70966	+	18.3665i	0.441031	+	0.930022i
$391$			14.3130i			0.723842i
$392$		0			0
$393$	12.1738	+	12.1738i	0.614088	+	0.614088i
$394$	−0.303487	+	2.00424i	−0.0152894	+	0.100972i
$395$	−17.0452	+	5.86295i	−0.857635	+	0.294997i
$396$	3.07940	−	9.93513i	0.154746	−	0.499259i
$397$	−7.78706	−	29.0617i	−0.390821	−	1.45857i	−0.828782	−	0.559571i	$-0.810966\pi$
$397$	−7.78706	−	29.0617i	−0.390821	−	1.45857i	0.437961	−	0.898994i	$-0.355701\pi$
$398$	12.3295	+	5.38931i	0.618022	+	0.270141i
$399$		0			0
$400$	8.91734	−	17.9020i	0.445867	−	0.895099i
$401$	−2.44780	+	4.23972i	−0.122237	+	0.211721i	−0.920650	−	0.390390i	$-0.872340\pi$
$401$	−2.44780	+	4.23972i	−0.122237	+	0.211721i	0.798412	+	0.602111i	$0.205674\pi$
$402$	0.548953	+	4.90209i	0.0273793	+	0.244494i
$403$	−19.9678	−	5.35037i	−0.994669	−	0.266521i
$404$	−14.5611	+	3.30262i	−0.724442	+	0.164312i
$405$	−0.313029	+	1.60762i	−0.0155546	+	0.0798833i
$406$		0			0
$407$	10.0694	+	10.0694i	0.499119	+	0.499119i
$408$	1.42185	−	7.43155i	0.0703922	−	0.367916i
$409$	−29.0499	+	16.7720i	−1.43642	+	0.829320i	−0.997599	−	0.0692530i	$-0.977938\pi$
$409$	−29.0499	+	16.7720i	−1.43642	+	0.829320i	−0.438825	+	0.898573i	$0.644605\pi$
$410$	−25.0180	−	2.02563i	−1.23555	−	0.100039i
$411$	−4.57500	−	2.64138i	−0.225668	−	0.130290i
$412$	−8.23678	−	0.319431i	−0.405797	−	0.0157372i
$413$		0			0
$414$	−5.39289	−	13.7684i	−0.265046	−	0.676680i
$415$	−18.9213	+	1.31695i	−0.928808	+	0.0646467i
$416$	23.7001	+	22.1411i	1.16200	+	1.08556i
$417$	−11.1611	−	2.99062i	−0.546564	−	0.146451i
$418$	6.29303	+	8.53891i	0.307802	+	0.417652i
$419$	36.3735			1.77696			0.888481	−	0.458914i	$-0.151761\pi$
$419$	36.3735			1.77696			0.888481	+	0.458914i	$0.151761\pi$
$420$		0			0
$421$	−33.2473			−1.62038			−0.810188	−	0.586170i	$-0.800635\pi$
$421$	−33.2473			−1.62038			−0.810188	+	0.586170i	$0.800635\pi$
$422$	22.6094	+	30.6784i	1.10061	+	1.49340i
$423$	−4.98294	−	1.33517i	−0.242279	−	0.0649184i
$424$	−7.22062	+	0.526281i	−0.350664	+	0.0255585i
$425$	−1.46162	+	11.8406i	−0.0708988	+	0.574352i
$426$	−4.68219	−	11.9539i	−0.226853	−	0.579171i
$427$		0			0
$428$	0.807325	−	20.8175i	0.0390235	−	1.00625i
$429$	16.6092	+	9.58933i	0.801900	+	0.462977i
$430$	−25.9846	+	22.0920i	−1.25309	+	1.06537i
$431$	−26.9460	+	15.5573i	−1.29794	+	0.749367i	−0.980048	−	0.198759i	$-0.936309\pi$
$431$	−26.9460	+	15.5573i	−1.29794	+	0.749367i	−0.317894	+	0.948126i	$0.602976\pi$
$432$	3.89747	+	20.9102i	0.187517	+	1.00604i
$433$	−7.14603	−	7.14603i	−0.343416	−	0.343416i	0.514234	−	0.857650i	$-0.328076\pi$
$433$	−7.14603	−	7.14603i	−0.343416	−	0.343416i	−0.857650	+	0.514234i	$0.828076\pi$
$434$		0			0
$435$	−5.30988	+	3.57906i	−0.254589	+	0.171603i
$436$	4.54019	+	20.0175i	0.217436	+	0.958664i
$437$	14.5658	+	3.90289i	0.696776	+	0.186700i
$438$	1.72069	+	15.3656i	0.0822178	+	0.734196i
$439$	0.278565	−	0.482489i	0.0132952	−	0.0230280i	−0.859301	−	0.511470i	$-0.829101\pi$
$439$	0.278565	−	0.482489i	0.0132952	−	0.0230280i	0.872596	+	0.488442i	$0.162435\pi$
$440$	−2.67518	−	18.6796i	−0.127534	−	0.890515i
$441$		0			0
$442$	−17.7277	−	7.74889i	−0.843221	−	0.368577i
$443$	−6.31254	−	23.5587i	−0.299918	−	1.11931i	−0.937233	−	0.348705i	$-0.886621\pi$
$443$	−6.31254	−	23.5587i	−0.299918	−	1.11931i	0.637315	−	0.770604i	$-0.280045\pi$
$444$	−10.2220	−	3.16832i	−0.485115	−	0.150362i
$445$	1.49480	+	4.34579i	0.0708604	+	0.206010i
$446$	−0.666606	+	4.40230i	−0.0315647	+	0.208455i
$447$	7.66789	+	7.66789i	0.362679	+	0.362679i
$448$		0			0
$449$		−	8.64441i		−	0.407955i	−0.978976	−	0.203978i	$-0.934613\pi$
$449$		−	8.64441i		−	0.407955i	0.978976	−	0.203978i	$-0.0653870\pi$
$450$	−3.05531	−	11.9407i	−0.144029	−	0.562891i
$451$	−20.5092	+	11.8410i	−0.965738	+	0.557569i
$452$	18.4068	−	9.69625i	0.865784	−	0.456073i
$453$	−1.19535	+	0.320293i	−0.0561624	+	0.0150487i
$454$	4.15999	+	10.6207i	0.195238	+	0.498456i
$455$		0			0
$456$	−7.17505	−	3.47340i	−0.336003	−	0.162657i
$457$	0.707473	+	2.64033i	0.0330942	+	0.123509i	0.980497	−	0.196535i	$-0.0629689\pi$
$457$	0.707473	+	2.64033i	0.0330942	+	0.123509i	−0.947403	+	0.320044i	$0.896302\pi$
$458$	−3.41935	+	0.382911i	−0.159776	+	0.0178923i
$459$	−6.34412	−	10.9883i	−0.296118	−	0.512891i
$460$	−19.5429	−	18.3773i	−0.911192	−	0.856846i
$461$	−38.5986			−1.79772			−0.898858	−	0.438239i	$-0.855602\pi$
$461$	−38.5986			−1.79772			−0.898858	+	0.438239i	$0.855602\pi$
$462$		0			0
$463$	13.5055	−	13.5055i	0.627652	−	0.627652i	−0.319824	−	0.947477i	$-0.603624\pi$
$463$	13.5055	−	13.5055i	0.627652	−	0.627652i	0.947477	+	0.319824i	$0.103624\pi$
$464$	−5.77859	+	8.42623i	−0.268264	+	0.391178i
$465$	−8.12270	−	3.96496i	−0.376681	−	0.183871i
$466$	−9.23833	+	11.5683i	−0.427957	+	0.535893i
$467$	−12.9076	+	3.45858i	−0.597292	+	0.160044i	−0.544784	−	0.838577i	$-0.683388\pi$
$467$	−12.9076	+	3.45858i	−0.597292	+	0.160044i	−0.0525083	+	0.998620i	$0.516722\pi$
$468$	19.9728	+	0.774565i	0.923241	+	0.0358043i
$469$		0			0
$470$	−9.20601	+	1.68481i	−0.424641	+	0.0777144i
$471$	−8.43596	−	4.87051i	−0.388709	−	0.224421i
$472$	−3.87228	+	4.48112i	−0.178236	+	0.206260i
$473$	−8.32876	+	31.0834i	−0.382957	+	1.42921i
$474$	1.91352	−	12.6370i	0.0878911	−	0.580437i
$475$	11.6511	+	4.71612i	0.534589	+	0.216390i
$476$		0			0
$477$	−3.15487	+	3.15487i	−0.144452	+	0.144452i
$478$	14.6916	−	10.8275i	0.671979	−	0.495237i
$479$	3.91630	+	6.78323i	0.178940	+	0.309934i	0.941518	−	0.336963i	$-0.109400\pi$
$479$	3.91630	+	6.78323i	0.178940	+	0.309934i	−0.762578	+	0.646897i	$0.776066\pi$
$480$	8.32136	+	11.4831i	0.379816	+	0.524132i
$481$	−13.6823	+	23.6984i	−0.623858	+	1.08055i
$482$	3.51675	+	1.53719i	0.160183	+	0.0700172i
$483$		0			0
$484$	2.84968	+	3.07963i	0.129531	+	0.139983i
$485$	20.9203	−	1.45609i	0.949944	−	0.0661178i
$486$	16.7216	+	13.3536i	0.758505	+	0.605733i
$487$	0.631456	−	2.35662i	0.0286140	−	0.106789i	−0.950142	−	0.311818i	$-0.899062\pi$
$487$	0.631456	−	2.35662i	0.0286140	−	0.106789i	0.978756	+	0.205029i	$0.0657288\pi$
$488$	5.28093	+	1.01038i	0.239056	+	0.0457379i
$489$		−	1.20836i		−	0.0546439i
$490$		0			0
$491$			33.5206i			1.51276i	0.654130	+	0.756382i	$0.273035\pi$
$491$			33.5206i			1.51276i	−0.654130	+	0.756382i	$0.726965\pi$
$492$	9.48927	−	15.0565i	0.427810	−	0.678801i
$493$	1.57746	−	5.88718i	0.0710454	−	0.265145i
$494$	−12.7197	+	15.9277i	−0.572287	+	0.716623i
$495$	−8.77416	−	7.63224i	−0.394369	−	0.343044i
$496$	−14.3788	−	1.11693i	−0.645628	−	0.0501517i
$497$		0			0
$498$	5.38646	−	12.3230i	0.241373	−	0.552207i
$499$	−10.3462	+	17.9201i	−0.463159	+	0.802216i	−0.999116	−	0.0420297i	$-0.986618\pi$
$499$	−10.3462	+	17.9201i	−0.463159	+	0.802216i	0.535957	+	0.844245i	$0.319951\pi$
$500$	−14.2903	−	17.1984i	−0.639084	−	0.769137i
$501$	1.72926	+	2.99516i	0.0772575	+	0.133814i
$502$	2.64590	+	3.59018i	0.118092	+	0.160238i
$503$	4.35918	−	4.35918i	0.194366	−	0.194366i	−0.603214	−	0.797580i	$-0.706113\pi$
$503$	4.35918	−	4.35918i	0.194366	−	0.194366i	0.797580	+	0.603214i	$0.206113\pi$
$504$		0			0
$505$	−3.19053	+	16.3856i	−0.141977	+	0.729148i
$506$	−25.0256	−	3.78943i	−1.11252	−	0.168460i
$507$	−5.76644	+	21.5207i	−0.256097	+	0.955766i
$508$	−33.4908	+	17.6421i	−1.48591	+	0.782741i
$509$	26.4887	+	15.2933i	1.17409	+	0.677862i	0.954640	−	0.297761i	$-0.0962400\pi$
$509$	26.4887	+	15.2933i	1.17409	+	0.677862i	0.219451	+	0.975623i	$0.429573\pi$
$510$	−6.96083	−	4.80715i	−0.308231	−	0.212864i
$511$		0			0
$512$	19.0851	+	12.1557i	0.843448	+	0.537211i
$513$	−12.9123	+	3.45983i	−0.570091	+	0.152755i
$514$	−18.1966	−	14.5316i	−0.802616	−	0.640959i
$515$	−4.04267	+	8.28191i	−0.178141	+	0.364944i
$516$	−5.34927	−	23.5847i	−0.235488	−	1.03826i
$517$	−6.24391	+	6.24391i	−0.274607	+	0.274607i
$518$		0			0
$519$	26.4469			1.16089
$520$	33.3418	−	14.2560i	1.46213	−	0.625167i
$521$	4.68273	+	8.11072i	0.205154	+	0.355337i	0.950182	−	0.311696i	$-0.100897\pi$
$521$	4.68273	+	8.11072i	0.205154	+	0.355337i	−0.745028	+	0.667033i	$0.767564\pi$
$522$	0.700739	+	6.25752i	0.0306705	+	0.273884i
$523$	−8.46836	−	31.6043i	−0.370296	−	1.38196i	−0.860098	−	0.510128i	$-0.829598\pi$
$523$	−8.46836	−	31.6043i	−0.370296	−	1.38196i	0.489803	−	0.871833i	$-0.337069\pi$
$524$	22.5424	−	20.8592i	0.984770	−	0.911240i
$525$		0			0
$526$	38.4366	−	15.0551i	1.67592	−	0.656432i
$527$	8.30998	−	2.22665i	0.361988	−	0.0969945i
$528$	12.6172	+	4.45356i	0.549093	+	0.193816i
$529$	−11.2432	+	6.49124i	−0.488833	+	0.282228i
$530$	−2.71910	+	7.62393i	−0.118110	+	0.331162i
$531$			3.64981i			0.158388i
$532$		0			0
$533$	−32.1791	−	32.1791i	−1.39383	−	1.39383i
$534$	−3.22190	−	0.487867i	−0.139425	−	0.0211120i
$535$	−20.9316	−	10.2174i	−0.904951	−	0.441736i
$536$	8.77632	−	0.639670i	0.379079	−	0.0276295i
$537$	2.04949	+	7.64880i	0.0884420	+	0.330070i
$538$	−3.46120	+	7.91844i	−0.149223	+	0.341388i
$539$		0			0
$540$	23.1489	+	5.44633i	0.996170	+	0.234373i
$541$	2.73095	−	4.73015i	0.117413	−	0.203365i	−0.801329	−	0.598224i	$-0.795873\pi$
$541$	2.73095	−	4.73015i	0.117413	−	0.203365i	0.918742	+	0.394859i	$0.129207\pi$
$542$	30.9475	−	3.46561i	1.32931	−	0.148861i
$543$	2.57107	+	0.688915i	0.110335	+	0.0295642i
$544$	−13.1490	−	3.04831i	−0.563760	−	0.130695i
$545$	22.5256	+	4.38610i	0.964892	+	0.187880i
$546$		0			0
$547$	4.64823	+	4.64823i	0.198744	+	0.198744i	0.799461	−	0.600718i	$-0.205118\pi$
$547$	4.64823	+	4.64823i	0.198744	+	0.198744i	−0.600718	+	0.799461i	$0.705118\pi$
$548$	−5.02474	+	7.97271i	−0.214646	+	0.340577i
$549$	2.86959	−	1.65676i	0.122471	−	0.0707087i
$550$	−20.3156	−	5.69038i	−0.866261	−	0.242639i
$551$	−5.56098	−	3.21064i	−0.236906	−	0.136778i
$552$	17.9669	−	6.24572i	0.764721	−	0.265835i
$553$		0			0
$554$	21.6699	−	8.48777i	0.920664	−	0.360611i
$555$	−7.85262	+	9.02750i	−0.333325	+	0.383196i
$556$	−6.10260	+	19.6889i	−0.258808	+	0.834996i
$557$	−12.0516	−	3.22921i	−0.510642	−	0.136826i	−0.00570726	−	0.999984i	$-0.501817\pi$
$557$	−12.0516	−	3.22921i	−0.510642	−	0.136826i	−0.504934	+	0.863158i	$0.668483\pi$
$558$	−7.15481	+	5.27297i	−0.302887	+	0.223223i
$559$	−61.8381			−2.61547
$560$		0			0
$561$	−7.98155			−0.336981
$562$	7.73316	−	5.69920i	0.326204	−	0.240406i
$563$	18.3414	+	4.91456i	0.772997	+	0.207124i	0.623695	−	0.781668i	$-0.285631\pi$
$563$	18.3414	+	4.91456i	0.772997	+	0.207124i	0.149302	+	0.988792i	$0.452297\pi$
$564$	1.96464	−	6.33856i	0.0827264	−	0.266901i
$565$	−1.61504	−	23.2040i	−0.0679453	−	0.976201i
$566$	−17.1775	+	6.72818i	−0.722025	+	0.282807i
$567$		0			0
$568$	−21.6326	+	7.52000i	−0.907682	+	0.315532i
$569$	−19.5330	−	11.2774i	−0.818868	−	0.472773i	0.0311582	−	0.999514i	$-0.490080\pi$
$569$	−19.5330	−	11.2774i	−0.818868	−	0.472773i	−0.850026	+	0.526741i	$0.823414\pi$
$570$	−6.79012	+	5.77292i	−0.284407	+	0.241801i
$571$	22.8480	−	13.1913i	0.956158	−	0.552038i	0.0611692	−	0.998127i	$-0.480517\pi$
$571$	22.8480	−	13.1913i	0.956158	−	0.552038i	0.894988	+	0.446090i	$0.147184\pi$
$572$	18.2420	−	28.9443i	0.762735	−	1.21022i
$573$	−5.00690	−	5.00690i	−0.209166	−	0.209166i
$574$		0			0
$575$	−27.6160	+	11.7012i	−1.15167	+	0.487975i
$576$	13.7972	−	2.02199i	0.574885	−	0.0842496i
$577$	−30.8143	−	8.25666i	−1.28282	−	0.343729i	−0.447888	−	0.894090i	$-0.647824\pi$
$577$	−30.8143	−	8.25666i	−1.28282	−	0.343729i	−0.834927	+	0.550360i	$0.814490\pi$
$578$	−15.8906	+	1.77948i	−0.660961	+	0.0740168i
$579$	11.8402	−	20.5077i	0.492060	−	0.852273i
$580$	6.01290	+	9.71272i	0.249672	+	0.403299i
$581$		0			0
$582$	−5.95556	+	13.6250i	−0.246866	+	0.564773i
$583$	1.97662	+	7.37683i	0.0818630	+	0.305517i
$584$	27.5093	−	2.00504i	1.13834	−	0.0829693i
$585$	9.80278	−	20.0822i	0.405295	−	0.830296i
$586$	2.54775	+	0.385785i	0.105246	+	0.0159366i
$587$	14.8860	+	14.8860i	0.614410	+	0.614410i	0.944092	−	0.329682i	$-0.106942\pi$
$587$	14.8860	+	14.8860i	0.614410	+	0.614410i	−0.329682	+	0.944092i	$0.606942\pi$
$588$		0			0
$589$		−	9.06388i		−	0.373471i
$590$	2.83715	+	5.98283i	0.116804	+	0.246309i
$591$	−1.39169	+	0.803493i	−0.0572465	+	0.0330513i
$592$	−6.35444	+	18.0025i	−0.261166	+	0.739899i
$593$	−31.8592	+	8.53664i	−1.30830	+	0.350558i	−0.844582	−	0.535426i	$-0.820151\pi$
$593$	−31.8592	+	8.53664i	−1.30830	+	0.350558i	−0.463717	+	0.885984i	$0.653484\pi$
$594$	20.8921	−	8.18314i	0.857214	−	0.335758i
$595$		0			0
$596$	14.1987	−	13.1385i	0.581602	−	0.538176i
$597$	2.76089	+	10.3038i	0.112996	+	0.421705i
$598$	−5.41285	−	48.3362i	−0.221348	−	1.97661i
$599$	8.79228	+	15.2287i	0.359243	+	0.622227i	0.987835	−	0.155509i	$-0.0497016\pi$
$599$	8.79228	+	15.2287i	0.359243	+	0.622227i	−0.628592	+	0.777736i	$0.716368\pi$
$600$	15.5010	−	3.33208i	0.632827	−	0.136032i
$601$	17.7704			0.724871			0.362436	−	0.932009i	$-0.381945\pi$
$601$	17.7704			0.724871			0.362436	+	0.932009i	$0.381945\pi$
$602$		0			0
$603$	3.83460	−	3.83460i	0.156157	−	0.156157i
$604$	0.488313	+	2.15295i	0.0198692	+	0.0876022i
$605$	4.43598	−	1.52582i	0.180348	−	0.0620336i
$606$	−9.24919	−	7.38629i	−0.375723	−	0.300048i
$607$	9.32548	−	2.49876i	0.378510	−	0.101421i	−0.0645477	−	0.997915i	$-0.520560\pi$
$607$	9.32548	−	2.49876i	0.378510	−	0.101421i	0.443057	+	0.896493i	$0.353894\pi$
$608$	−6.68762	+	12.5500i	−0.271219	+	0.508970i
$609$		0			0
$610$	3.41601	−	4.94644i	0.138310	−	0.200275i
$611$	−14.6951	−	8.48424i	−0.594502	−	0.343236i
$612$	−7.35960	+	3.87685i	−0.297494	+	0.156712i
$613$	2.25362	−	8.41064i	0.0910230	−	0.339702i	−0.905364	−	0.424637i	$-0.860402\pi$
$613$	2.25362	−	8.41064i	0.0910230	−	0.339702i	0.996386	+	0.0849350i	$0.0270683\pi$
$614$	−23.0305	−	3.48733i	−0.929435	−	0.140737i
$615$	−11.1215	−	16.4998i	−0.448463	−	0.665337i
$616$		0			0
$617$	21.0055	−	21.0055i	0.845648	−	0.845648i	−0.143938	−	0.989587i	$-0.545977\pi$
$617$	21.0055	−	21.0055i	0.845648	−	0.845648i	0.989587	+	0.143938i	$0.0459767\pi$
$618$	−3.87683	−	5.26041i	−0.155949	−	0.211605i
$619$	7.01153	+	12.1443i	0.281817	+	0.488121i	0.971832	−	0.235673i	$-0.0757296\pi$
$619$	7.01153	+	12.1443i	0.281817	+	0.488121i	−0.690015	+	0.723795i	$0.742396\pi$
$620$	−7.62939	+	14.2053i	−0.306404	+	0.570498i
$621$	15.9489	−	27.6243i	0.640006	−	1.10852i
$622$	−17.0965	+	39.1128i	−0.685505	+	1.56828i
$623$		0			0
$624$	−1.99127	+	25.6346i	−0.0797144	+	1.02620i
$625$	−24.0404	+	6.85984i	−0.961618	+	0.274393i
$626$	19.4703	−	24.3809i	0.778189	−	0.974456i
$627$	−2.17641	+	8.12248i	−0.0869175	+	0.324381i
$628$	−9.26525	+	14.7011i	−0.369724	+	0.586637i
$629$		−	11.3883i		−	0.454080i
$630$		0			0
$631$		−	25.9447i		−	1.03284i	−0.856334	−	0.516422i	$-0.827264\pi$
$631$		−	25.9447i		−	1.03284i	0.856334	−	0.516422i	$-0.172736\pi$
$632$	−22.3942	−	4.28461i	−0.890794	−	0.170433i
$633$	−7.81936	+	29.1823i	−0.310792	+	1.15989i
$634$	−1.60179	−	1.27917i	−0.0636152	−	0.0508024i
$635$	2.93853	+	42.2192i	0.116612	+	1.67542i
$636$	−3.89803	−	4.21257i	−0.154567	−	0.167039i
$637$		0			0
$638$	9.87576	+	4.31676i	0.390985	+	0.170902i
$639$	−7.05703	+	12.2231i	−0.279172	+	0.483540i
$640$	21.0449	−	14.0397i	0.831873	−	0.554966i
$641$	−2.50802	−	4.34403i	−0.0990610	−	0.171579i	0.812235	−	0.583330i	$-0.198251\pi$
$641$	−2.50802	−	4.34403i	−0.0990610	−	0.171579i	−0.911296	+	0.411751i	$0.864917\pi$
$642$	13.2951	−	9.79825i	0.524716	−	0.386706i
$643$	5.68565	−	5.68565i	0.224220	−	0.224220i	−0.586053	−	0.810273i	$-0.699319\pi$
$643$	5.68565	−	5.68565i	0.224220	−	0.224220i	0.810273	+	0.586053i	$0.199319\pi$
$644$		0			0
$645$	−26.5397	−	5.16771i	−1.04500	−	0.203478i
$646$	1.27003	−	8.38732i	0.0499685	−	0.329995i
$647$	−5.04946	+	18.8448i	−0.198515	+	0.740867i	0.792814	+	0.609463i	$0.208615\pi$
$647$	−5.04946	+	18.8448i	−0.198515	+	0.740867i	−0.991329	+	0.131404i	$0.958052\pi$
$648$	−1.35454	+	1.56752i	−0.0532113	+	0.0615779i
$649$	5.41041	+	3.12370i	0.212377	+	0.122616i
$650$	0.458155	−	40.5392i	0.0179703	−	1.59008i
$651$		0			0
$652$	−2.15400	−	0.0835344i	−0.0843572	−	0.00327146i
$653$	25.9460	−	6.95220i	1.01534	−	0.272061i	0.287483	−	0.957786i	$-0.407181\pi$
$653$	25.9460	−	6.95220i	1.01534	−	0.272061i	0.727861	+	0.685725i	$0.240515\pi$
$654$	−10.1541	+	12.7151i	−0.397057	+	0.497199i
$655$	−11.1688	−	32.4707i	−0.436401	−	1.26873i
$656$	−26.1835	−	17.9563i	−1.02229	−	0.701074i
$657$	12.0195	−	12.0195i	0.468926	−	0.468926i
$658$		0			0
$659$	2.47864			0.0965543			0.0482771	−	0.998834i	$-0.484627\pi$
$659$	2.47864			0.0965543			0.0482771	+	0.998834i	$0.484627\pi$
$660$	10.2479	−	10.8979i	0.398901	−	0.424201i
$661$	6.04270	+	10.4663i	0.235034	+	0.407091i	0.959283	−	0.282448i	$-0.0911466\pi$
$661$	6.04270	+	10.4663i	0.235034	+	0.407091i	−0.724249	+	0.689539i	$0.757813\pi$
$662$	39.8806	−	4.46597i	1.55000	−	0.173575i
$663$	−3.96968	−	14.8150i	−0.154169	−	0.575368i
$664$	−21.5944	−	10.4537i	−0.838025	−	0.405682i
$665$		0			0
$666$	4.29088	+	10.9549i	0.166268	+	0.424494i
$667$	14.8001	−	3.96569i	0.573064	−	0.153552i
$668$	5.45866	−	2.87548i	0.211202	−	0.111256i
$669$	−3.05684	+	1.76487i	−0.118184	+	0.0682337i
$670$	3.30494	−	9.26653i	0.127681	−	0.357997i
$671$		−	5.67177i		−	0.218956i
$672$		0			0
$673$	34.0874	+	34.0874i	1.31397	+	1.31397i	0.918461	+	0.395511i	$0.129432\pi$
$673$	34.0874	+	34.0874i	1.31397	+	1.31397i	0.395511	+	0.918461i	$0.370568\pi$
$674$	−3.52817	+	23.3003i	−0.135900	+	0.897492i
$675$	16.0147	−	21.2237i	0.616408	−	0.816901i
$676$	37.9637	+	11.7669i	1.46014	+	0.452572i
$677$	8.74919	+	32.6524i	0.336259	+	1.25493i	0.902498	+	0.430693i	$0.141731\pi$
$677$	8.74919	+	32.6524i	0.336259	+	1.25493i	−0.566240	+	0.824241i	$0.691602\pi$
$678$	15.1123	+	6.60567i	0.580384	+	0.253689i
$679$		0			0
$680$	−9.05035	+	12.0759i	−0.347065	+	0.463091i
$681$	−4.52124	+	7.83101i	−0.173254	+	0.300085i
$682$	1.69308	+	15.1191i	0.0648316	+	0.578938i
$683$	7.23810	+	1.93944i	0.276958	+	0.0742107i	0.394625	−	0.918842i	$-0.370875\pi$
$683$	7.23810	+	1.93944i	0.276958	+	0.0742107i	−0.117666	+	0.993053i	$0.537541\pi$
$684$	1.93849	+	8.54669i	0.0741199	+	0.326791i
$685$	5.88904	+	8.73696i	0.225009	+	0.333822i
$686$		0			0
$687$	−1.92874	−	1.92874i	−0.0735862	−	0.0735862i
$688$	−42.4114	+	7.90508i	−1.61692	+	0.301379i
$689$	−12.7095	+	7.33783i	−0.484193	+	0.279549i
$690$	1.71628	−	21.1973i	0.0653378	−	0.806968i
$691$	16.5249	+	9.54066i	0.628637	+	0.362944i	0.780224	−	0.625500i	$-0.215105\pi$
$691$	16.5249	+	9.54066i	0.628637	+	0.362944i	−0.151587	+	0.988444i	$0.548438\pi$
$692$	1.82828	−	47.1437i	0.0695009	−	1.79213i
$693$		0			0
$694$	−8.23405	−	21.0221i	−0.312560	−	0.797987i
$695$	17.3882	+	15.1252i	0.659570	+	0.573730i
$696$	−8.07840	+	0.588802i	−0.306211	+	0.0223185i
$697$	18.2937	+	4.90178i	0.692923	+	0.185668i
$698$	−6.31489	−	8.56857i	−0.239022	−	0.324325i
$699$	−11.7363			−0.443909
$700$		0			0
$701$	−30.0384			−1.13454			−0.567268	−	0.823533i	$-0.692000\pi$
$701$	−30.0384			−1.13454			−0.567268	+	0.823533i	$0.692000\pi$
$702$	25.5800	+	34.7092i	0.965457	+	1.31001i
$703$	−11.5893	−	3.10535i	−0.437100	−	0.117121i
$704$	8.81106	−	22.1833i	0.332079	−	0.836065i
$705$	−5.59786	−	4.86933i	−0.210828	−	0.183389i
$706$	2.89170	+	7.38272i	0.108831	+	0.277852i
$707$		0			0
$708$	−4.69150	−	0.181941i	−0.176317	−	0.00683777i
$709$	−23.7012	−	13.6839i	−0.890117	−	0.513909i	−0.0161363	−	0.999870i	$-0.505137\pi$
$709$	−23.7012	−	13.6839i	−0.890117	−	0.513909i	−0.873981	+	0.485960i	$0.838470\pi$
$710$	−2.06645	+	25.5221i	−0.0775524	+	0.957827i
$711$	−12.1687	+	7.02562i	−0.456363	+	0.263481i
$712$	−1.09239	+	5.70957i	−0.0409391	+	0.213975i
$713$	15.2933	+	15.2933i	0.572737	+	0.572737i
$714$		0			0
$715$	−21.3797	−	31.7189i	−0.799557	−	1.18622i
$716$	13.7763	−	3.12462i	0.514844	−	0.116772i
$717$	13.9751	+	3.74462i	0.521911	+	0.139846i
$718$	−5.73329	−	51.1977i	−0.213965	−	1.91068i
$719$	−21.7523	+	37.6760i	−0.811223	+	1.40508i	0.100786	+	0.994908i	$0.467864\pi$
$719$	−21.7523	+	37.6760i	−0.811223	+	1.40508i	−0.912009	+	0.410171i	$0.865469\pi$
$720$	4.15598	−	15.0264i	0.154884	−	0.560001i
$721$		0			0
$722$	16.4317	+	7.18238i	0.611523	+	0.267300i
$723$	0.787488	+	2.93894i	0.0292870	+	0.109300i
$724$	1.40579	−	4.53551i	0.0522456	−	0.168561i
$725$	12.6485	−	1.76929i	0.469753	−	0.0657097i
$726$	−0.497991	+	3.28876i	−0.0184822	+	0.122057i
$727$	14.9542	+	14.9542i	0.554620	+	0.554620i	0.927771	−	0.373151i	$-0.121723\pi$
$727$	14.9542	+	14.9542i	0.554620	+	0.554620i	−0.373151	+	0.927771i	$0.621723\pi$
$728$		0			0
$729$			19.1618i			0.709695i
$730$	10.3593	−	29.0459i	0.383416	−	1.07504i
$731$	22.2872	−	12.8675i	0.824322	−	0.475922i
$732$	1.98656	+	3.77118i	0.0734255	+	0.139387i
$733$	−30.6917	+	8.22383i	−1.13363	+	0.303754i	−0.776385	−	0.630259i	$-0.782949\pi$
$733$	−30.6917	+	8.22383i	−1.13363	+	0.303754i	−0.357240	+	0.934013i	$0.616282\pi$
$734$	−16.8636	−	43.0539i	−0.622446	−	1.58915i
$735$		0			0
$736$	−9.89144	−	32.4592i	−0.364603	−	1.19646i
$737$	−2.40248	−	8.96619i	−0.0884966	−	0.330274i
$738$	−19.4445	+	2.17746i	−0.715761	+	0.0801535i
$739$	0.495453	+	0.858149i	0.0182255	+	0.0315675i	0.874994	−	0.484133i	$-0.160865\pi$
$739$	0.495453	+	0.858149i	0.0182255	+	0.0315675i	−0.856769	+	0.515701i	$0.827532\pi$
$740$	15.5494	+	14.6220i	0.571607	+	0.537515i
$741$	−16.1591			−0.593619
$742$		0			0
$743$	−9.00016	+	9.00016i	−0.330184	+	0.330184i	−0.852656	−	0.522472i	$-0.825010\pi$
$743$	−9.00016	+	9.00016i	−0.330184	+	0.330184i	0.522472	+	0.852656i	$0.325010\pi$
$744$	−6.42126	−	9.45971i	−0.235415	−	0.346810i
$745$	−7.03485	−	20.4522i	−0.257737	−	0.749310i
$746$	23.0796	−	28.9005i	0.845005	−	1.05812i
$747$	−14.2815	+	3.82673i	−0.522534	+	0.140013i
$748$	−0.551767	+	14.2278i	−0.0201746	+	0.520218i
$749$		0			0
$750$	3.58443	−	17.3604i	0.130885	−	0.633911i
$751$	11.3279	+	6.54015i	0.413360	+	0.238653i	0.692232	−	0.721675i	$-0.256627\pi$
$751$	11.3279	+	6.54015i	0.413360	+	0.238653i	−0.278872	+	0.960328i	$0.589961\pi$
$752$	−11.1632	−	3.94032i	−0.407079	−	0.143689i
$753$	−0.915071	+	3.41509i	−0.0333470	+	0.124453i
$754$	−3.10082	+	20.4780i	−0.112925	+	0.745763i
$755$	2.42271	+	0.471740i	0.0881713	+	0.0171684i
$756$		0			0
$757$	3.92981	−	3.92981i	0.142831	−	0.142831i	−0.632076	−	0.774907i	$-0.717797\pi$
$757$	3.92981	−	3.92981i	0.142831	−	0.142831i	0.774907	+	0.632076i	$0.217797\pi$
$758$	−23.1979	+	17.0965i	−0.842586	+	0.620971i
$759$	−10.0327	−	17.3771i	−0.364162	−	0.630748i
$760$	9.82130	+	12.5030i	0.356256	+	0.453532i
$761$	−11.1617	+	19.3326i	−0.404612	+	0.700808i	−0.994276	−	0.106840i	$-0.965927\pi$
$761$	−11.1617	+	19.3326i	−0.404612	+	0.700808i	0.589665	+	0.807648i	$0.299260\pi$
$762$	−27.4964	−	12.0189i	−0.996091	−	0.435397i
$763$		0			0
$764$	−9.27134	+	8.57908i	−0.335425	+	0.310380i
$765$	0.645742	+	9.27767i	0.0233469	+	0.335435i
$766$	−28.2165	−	22.5334i	−1.01950	−	0.814163i
$767$	−3.10719	+	11.5962i	−0.112194	+	0.418714i
$768$	1.91130	+	17.8359i	0.0689681	+	0.643598i
$769$		−	27.9731i		−	1.00873i	−0.863489	−	0.504367i	$-0.831726\pi$
$769$		−	27.9731i		−	1.00873i	0.863489	−	0.504367i	$-0.168274\pi$
$770$		0			0
$771$		−	18.4608i		−	0.664851i
$772$	−35.7382	−	22.5237i	−1.28625	−	0.810647i
$773$	11.5257	−	43.0144i	0.414550	−	1.54712i	−0.371186	−	0.928559i	$-0.621049\pi$
$773$	11.5257	−	43.0144i	0.414550	−	1.54712i	0.785736	−	0.618562i	$-0.212285\pi$
$774$	−16.5909	+	20.7753i	−0.596347	+	0.746752i
$775$	11.0898	+	14.2132i	0.398356	+	0.510552i
$776$	23.8759	+	11.5582i	0.857094	+	0.414914i
$777$		0			0
$778$	−10.2233	+	23.3886i	−0.366524	+	0.838523i
$779$	9.97667	−	17.2801i	0.357451	−	0.619124i
$780$	25.3252	+	13.6017i	0.906787	+	0.487018i
$781$	12.0796	+	20.9224i	0.432241	+	0.748663i
$782$	12.0088	+	16.2946i	0.429435	+	0.582694i
$783$	−9.60453	+	9.60453i	−0.343238	+	0.343238i
$784$		0			0
$785$	10.8590	+	16.1103i	0.387573	+	0.575001i
$786$	24.0732	+	3.64522i	0.858663	+	0.130021i
$787$	10.4742	−	39.0901i	0.373363	−	1.39341i	−0.482358	−	0.875974i	$-0.660220\pi$
$787$	10.4742	−	39.0901i	0.373363	−	1.39341i	0.855722	−	0.517437i	$-0.173114\pi$
$788$	1.33608	+	2.53635i	0.0475960	+	0.0903536i
$789$	28.3405	+	16.3624i	1.00895	+	0.582518i
$790$	−14.4859	+	20.9758i	−0.515384	+	0.746285i
$791$		0			0
$792$	−4.82998	−	13.8943i	−0.171626	−	0.493711i
$793$	10.5277	−	2.82089i	0.373850	−	0.100173i
$794$	−33.2483	−	26.5517i	−1.17994	−	0.942285i
$795$	−6.06789	+	2.08715i	−0.215206	+	0.0740235i
$796$	18.5582	−	4.20920i	0.657777	−	0.149191i
$797$	−3.10654	+	3.10654i	−0.110039	+	0.110039i	−0.759983	−	0.649943i	$-0.774793\pi$
$797$	−3.10654	+	3.10654i	−0.110039	+	0.110039i	0.649943	+	0.759983i	$0.274793\pi$
$798$		0			0
$799$	7.06174			0.249826
$800$	−4.86811	−	27.8622i	−0.172114	−	0.985077i
$801$	1.79123	+	3.10250i	0.0632900	+	0.109622i
$802$	0.770494	+	6.88042i	0.0272071	+	0.242956i
$803$	−7.53057	−	28.1045i	−0.265748	−	0.991786i
$804$	4.73787	+	5.12018i	0.167092	+	0.180575i
$805$		0			0
$806$	−27.2213	+	10.6622i	−0.958830	+	0.375560i
$807$	−6.61744	+	1.77314i	−0.232945	+	0.0624174i
$808$	−13.8061	+	15.9768i	−0.485696	+	0.562062i
$809$	26.5415	−	15.3237i	0.933148	−	0.538753i	0.0453422	−	0.998972i	$-0.485562\pi$
$809$	26.5415	−	15.3237i	0.933148	−	0.538753i	0.887806	+	0.460218i	$0.152229\pi$
$810$	0.992448	+	2.09282i	0.0348711	+	0.0735343i
$811$		−	47.0428i		−	1.65190i	−0.563747	−	0.825948i	$-0.690641\pi$
$811$		−	47.0428i		−	1.65190i	0.563747	−	0.825948i	$-0.309359\pi$
$812$		0			0
$813$	17.4565	+	17.4565i	0.612225	+	0.612225i
$814$	19.9117	+	3.01508i	0.697906	+	0.105678i
$815$	−1.05720	+	2.16580i	−0.0370321	+	0.0758647i
$816$	−4.61647	−	9.65336i	−0.161609	−	0.337935i
$817$	−7.01744	−	26.1894i	−0.245509	−	0.916253i
$818$	−18.9998	+	43.4672i	−0.664312	+	1.51979i
$819$		0			0
$820$	−30.1811	+	18.6844i	−1.05397	+	0.652486i
$821$	0.415401	−	0.719496i	0.0144976	−	0.0251106i	−0.858686	−	0.512503i	$-0.828718\pi$
$821$	0.415401	−	0.719496i	0.0144976	−	0.0251106i	0.873183	+	0.487392i	$0.162052\pi$
$822$	−7.42454	+	0.831426i	−0.258961	+	0.0289993i
$823$	0.223479	+	0.0598810i	0.00778999	+	0.00208732i	0.262712	−	0.964874i	$-0.415383\pi$
$823$	0.223479	+	0.0598810i	0.00778999	+	0.00208732i	−0.254922	+	0.966962i	$0.582050\pi$
$824$	−9.64512	+	6.54712i	−0.336004	+	0.228080i
$825$	−6.52508	−	15.3998i	−0.227174	−	0.536153i
$826$		0			0
$827$	−0.00150949	−	0.00150949i	−5.24902e−5	−	5.24902e-5i	0.707081	−	0.707133i	$-0.250012\pi$
$827$	−0.00150949	−	0.00150949i	−5.24902e−5	−	5.24902e-5i	−0.707133	+	0.707081i	$0.750012\pi$
$828$	−17.6914	−	11.1499i	−0.614818	−	0.387485i
$829$	36.8314	−	21.2646i	1.27921	−	0.738551i	0.302506	−	0.953148i	$-0.402177\pi$
$829$	36.8314	−	21.2646i	1.27921	−	0.738551i	0.976703	+	0.214596i	$0.0688435\pi$
$830$	−20.4359	+	17.3745i	−0.709339	+	0.603077i
$831$	15.9779	+	9.22484i	0.554267	+	0.320006i
$832$	45.5580	+	5.32172i	1.57944	+	0.184497i
$833$		0			0
$834$	−15.2155	+	5.95970i	−0.526870	+	0.206368i
$835$	−0.478951	−	6.88130i	−0.0165748	−	0.238137i
$836$	14.3285	+	4.44114i	0.495562	+	0.153600i
$837$	−18.5194	−	4.96227i	−0.640126	−	0.171521i
$838$	41.4092	−	30.5179i	1.43046	−	1.05422i
$839$	49.4733			1.70801			0.854004	−	0.520267i	$-0.174168\pi$
$839$	49.4733			1.70801			0.854004	+	0.520267i	$0.174168\pi$
$840$		0			0
$841$	22.4754			0.775014
$842$	−37.8502	+	27.8950i	−1.30441	+	0.961324i
$843$	7.35602	+	1.97104i	0.253355	+	0.0678862i
$844$	51.4792	+	15.9560i	1.77199	+	0.549229i
$845$	29.1640	−	33.5274i	1.00327	−	1.15338i
$846$	−6.79303	+	2.66073i	−0.233549	+	0.0914778i
$847$		0			0
$848$	−7.77872	+	6.65734i	−0.267122	+	0.228614i
$849$	−12.6655	−	7.31245i	−0.434680	−	0.250963i
$850$	8.27043	+	14.7062i	0.283674	+	0.504417i
$851$	24.7940	−	14.3148i	0.849928	−	0.490706i
$852$	−15.3599	−	9.68049i	−0.526223	−	0.331648i
$853$	−9.16674	−	9.16674i	−0.313863	−	0.313863i	0.532541	−	0.846404i	$-0.321237\pi$
$853$	−9.16674	−	9.16674i	−0.313863	−	0.313863i	−0.846404	+	0.532541i	$0.821237\pi$
$854$		0			0
$855$	9.61757	+	1.87269i	0.328914	+	0.0640448i
$856$	−16.5471	−	24.3769i	−0.565568	−	0.833187i
$857$	21.7101	+	5.81720i	0.741602	+	0.198712i	0.609790	−	0.792563i	$-0.291254\pi$
$857$	21.7101	+	5.81720i	0.741602	+	0.198712i	0.131812	+	0.991275i	$0.457920\pi$
$858$	26.9542	−	3.01843i	0.920203	−	0.103048i
$859$	4.05858	−	7.02967i	0.138477	−	0.239849i	−0.788443	−	0.615107i	$-0.789113\pi$
$859$	4.05858	−	7.02967i	0.138477	−	0.239849i	0.926920	+	0.375258i	$0.122446\pi$
$860$	−11.0466	+	46.9520i	−0.376685	+	1.60105i
$861$		0			0
$862$	−17.6237	+	40.3191i	−0.600267	+	1.37328i
$863$	0.125947	+	0.470041i	0.00428729	+	0.0160004i	0.968036	−	0.250810i	$-0.0806969\pi$
$863$	0.125947	+	0.470041i	0.00428729	+	0.0160004i	−0.963749	+	0.266810i	$0.914030\pi$
$864$	21.9810	+	20.5351i	0.747809	+	0.698618i
$865$	−47.4020	−	23.1385i	−1.61172	−	0.786732i
$866$	−14.1310	−	2.13974i	−0.480190	−	0.0727114i
$867$	−8.96335	−	8.96335i	−0.304411	−	0.304411i
$868$		0			0
$869$			24.0516i			0.815895i
$870$	−3.04212	+	8.52963i	−0.103138	+	0.289181i
$871$	15.4478	−	8.91879i	0.523428	−	0.302202i
$872$	21.9637	+	18.9795i	0.743785	+	0.642728i
$873$	15.7904	−	4.23103i	0.534424	−	0.143199i
$874$	19.8569	−	7.77766i	0.671670	−	0.263083i
$875$		0			0
$876$	14.8508	+	16.0492i	0.501763	+	0.542251i
$877$	4.62691	+	17.2678i	0.156240	+	0.583094i	0.998996	+	0.0447988i	$0.0142647\pi$
$877$	4.62691	+	17.2678i	0.156240	+	0.583094i	−0.842757	+	0.538295i	$0.819069\pi$
$878$	−0.0876839	−	0.783007i	−0.00295919	−	0.0264252i
$879$	1.02138	+	1.76909i	0.0344504	+	0.0596698i
$880$	−18.7180	−	19.0212i	−0.630983	−	0.641203i
$881$	5.27459			0.177705			0.0888527	−	0.996045i	$-0.471680\pi$
$881$	5.27459			0.177705			0.0888527	+	0.996045i	$0.471680\pi$
$882$		0			0
$883$	5.20270	−	5.20270i	0.175085	−	0.175085i	−0.614124	−	0.789209i	$-0.710491\pi$
$883$	5.20270	−	5.20270i	0.175085	−	0.175085i	0.789209	+	0.614124i	$0.210491\pi$
$884$	−26.6834	+	6.05210i	−0.897461	+	0.203554i
$885$	−2.30262	+	4.71720i	−0.0774018	+	0.158567i
$886$	−26.9526	−	21.5240i	−0.905489	−	0.723113i
$887$	43.1849	−	11.5714i	1.45001	−	0.388528i	0.553981	−	0.832529i	$-0.313108\pi$
$887$	43.1849	−	11.5714i	1.45001	−	0.388528i	0.896026	+	0.444001i	$0.146441\pi$
$888$	−14.2954	+	4.96944i	−0.479724	+	0.166764i
$889$		0			0
$890$	5.34792	+	3.69328i	0.179263	+	0.123799i
$891$	1.89259	+	1.09269i	0.0634040	+	0.0366063i
$892$	2.93470	+	5.57107i	0.0982610	+	0.186533i
$893$	1.92560	−	7.18643i	0.0644377	−	0.240485i
$894$	15.1629	+	2.29600i	0.507124	+	0.0767898i
$895$	3.01857	−	15.5024i	0.100900	−	0.518189i
$896$		0			0
$897$	27.2648	−	27.2648i	0.910346	−	0.910346i
$898$	−7.25278	−	9.84119i	−0.242028	−	0.328405i
$899$	−4.60486	−	7.97585i	−0.153581	−	0.266009i
$900$	−13.4967	−	11.0304i	−0.449891	−	0.367680i
$901$	3.05377	−	5.28929i	0.101736	−	0.176212i
$902$	−13.4138	+	30.6877i	−0.446631	+	1.02179i
$903$		0			0
$904$	12.8199	−	26.4822i	0.426382	−	0.880785i
$905$	−4.00551	−	3.48421i	−0.133148	−	0.115819i
$906$	−1.09211	+	1.36755i	−0.0362829	+	0.0454338i
$907$	2.53267	−	9.45206i	0.0840960	−	0.313851i	−0.911045	−	0.412306i	$-0.864723\pi$
$907$	2.53267	−	9.45206i	0.0840960	−	0.313851i	0.995141	+	0.0984553i	$0.0313902\pi$
$908$	13.6469	+	8.60083i	0.452887	+	0.285429i
$909$			13.0129i			0.431610i
$910$		0			0
$911$		−	5.81294i		−	0.192591i	−0.995353	−	0.0962957i	$-0.969301\pi$
$911$		−	5.81294i		−	0.192591i	0.995353	−	0.0962957i	$-0.0306994\pi$
$912$	−11.0826	+	2.06570i	−0.366982	+	0.0684021i
$913$	−6.55024	+	24.4458i	−0.216781	+	0.809038i
$914$	3.02069	+	2.41228i	0.0999155	+	0.0797913i
$915$	4.75403	−	0.330889i	0.157163	−	0.0109389i
$916$	−3.57148	+	3.30481i	−0.118005	+	0.109194i
$917$		0			0
$918$	−16.4418	−	7.18681i	−0.542660	−	0.237200i
$919$	−10.6688	+	18.4789i	−0.351930	+	0.609561i	−0.986588	−	0.163232i	$-0.947808\pi$
$919$	−10.6688	+	18.4789i	−0.351930	+	0.609561i	0.634657	+	0.772794i	$0.281141\pi$
$920$	−37.6673	−	4.52479i	−1.24185	−	0.149178i
$921$	−9.23283	−	15.9917i	−0.304232	−	0.526946i
$922$	−43.9424	+	32.3848i	−1.44717	+	1.06654i
$923$	−32.8275	+	32.8275i	−1.08053	+	1.08053i
$924$		0			0
$925$	21.9728	−	9.31014i	0.722462	−	0.306115i
$926$	4.04396	−	26.7065i	0.132893	−	0.877630i
$927$	−1.85937	+	6.93927i	−0.0610698	+	0.227916i
$928$	0.491124	+	14.4411i	0.0161219	+	0.474053i
$929$	−12.5925	−	7.27026i	−0.413145	−	0.238529i	0.278995	−	0.960293i	$-0.409999\pi$
$929$	−12.5925	−	7.27026i	−0.413145	−	0.238529i	−0.692140	+	0.721763i	$0.743332\pi$
$930$	−12.5739	+	2.30117i	−0.412315	+	0.0754584i
$931$		0			0
$932$	−0.811338	+	20.9210i	−0.0265763	+	0.685290i
$933$	−32.6866	+	8.75834i	−1.07011	+	0.286735i
$934$	−11.7928	+	14.7670i	−0.385872	+	0.483192i
$935$	14.3057	+	6.98309i	0.467847	+	0.228371i
$936$	23.3878	−	15.8756i	0.764453	−	0.518911i
$937$	−5.05360	+	5.05360i	−0.165094	+	0.165094i	−0.784819	−	0.619725i	$-0.787244\pi$
$937$	−5.05360	+	5.05360i	−0.165094	+	0.165094i	0.619725	+	0.784819i	$0.287244\pi$
$938$		0			0
$939$	24.7350			0.807195
$940$	−9.06695	+	9.64203i	−0.295731	+	0.314488i
$941$	−1.44742	−	2.50700i	−0.0471845	−	0.0817259i	0.841469	−	0.540306i	$-0.181692\pi$
$941$	−1.44742	−	2.50700i	−0.0471845	−	0.0817259i	−0.888653	+	0.458580i	$0.848358\pi$
$942$	−13.6903	+	1.53309i	−0.446054	+	0.0499507i
$943$	12.3229	+	45.9897i	0.401289	+	1.49763i
$944$	−0.648650	+	8.35040i	−0.0211118	+	0.271782i
$945$		0			0
$946$	16.5975	+	42.3746i	0.539632	+	1.37772i
$947$	32.5747	−	8.72837i	1.05854	−	0.283634i	0.312761	−	0.949832i	$-0.398746\pi$
$947$	32.5747	−	8.72837i	1.05854	−	0.283634i	0.745775	+	0.666198i	$0.232079\pi$
$948$	−8.42419	−	15.9920i	−0.273605	−	0.519396i
$949$	48.4211	−	27.9559i	1.57181	−	0.907487i
$950$	17.2210	−	4.40639i	0.558723	−	0.142962i
$951$		−	1.62505i		−	0.0526960i
$952$		0			0
$953$	23.9098	+	23.9098i	0.774513	+	0.774513i	0.978892	−	0.204379i	$-0.0655173\pi$
$953$	23.9098	+	23.9098i	0.774513	+	0.774513i	−0.204379	+	0.978892i	$0.565517\pi$
$954$	−0.944666	+	6.23862i	−0.0305847	+	0.201983i
$955$	4.59355	+	13.3547i	0.148644	+	0.432147i
$956$	7.64120	−	24.6529i	0.247134	−	0.797333i
$957$	2.21143	+	8.25317i	0.0714854	+	0.266787i
$958$	10.1497	+	4.43650i	0.327922	+	0.143337i
$959$		0			0
$960$	19.1079	+	6.09120i	0.616706	+	0.196592i
$961$	−9.00006	+	15.5886i	−0.290325	+	0.502857i
$962$	4.30677	+	38.4589i	0.138856	+	1.23997i
$963$	−17.5382	−	4.69935i	−0.565161	−	0.151435i
$964$	5.29334	−	1.20059i	0.170487	−	0.0386684i
$965$	−39.1640	+	26.3980i	−1.26073	+	0.849782i
$966$		0			0
$967$	−2.13618	−	2.13618i	−0.0686949	−	0.0686949i	0.671925	−	0.740620i	$-0.265468\pi$
$967$	−2.13618	−	2.13618i	−0.0686949	−	0.0686949i	−0.740620	+	0.671925i	$0.765468\pi$
$968$	5.82806	+	1.11506i	0.187321	+	0.0358395i
$969$	5.82393	−	3.36245i	0.187092	−	0.108017i
$970$	22.5950	−	19.2101i	0.725481	−	0.616800i
$971$	14.3494	+	8.28465i	0.460495	+	0.265867i	0.712252	−	0.701923i	$-0.247675\pi$
$971$	14.3494	+	8.28465i	0.460495	+	0.265867i	−0.251757	+	0.967790i	$0.581008\pi$
$972$	30.2404	+	1.17276i	0.969963	+	0.0376162i
$973$		0			0
$974$	−1.25836	−	3.21269i	−0.0403206	−	0.102941i
$975$	25.3392	−	19.7708i	0.811505	−	0.633172i
$976$	6.85977	−	3.28051i	0.219576	−	0.105006i
$977$	0.302331	+	0.0810094i	0.00967243	+	0.00259172i	0.263652	−	0.964618i	$-0.415073\pi$
$977$	0.302331	+	0.0810094i	0.00967243	+	0.00259172i	−0.253980	+	0.967210i	$0.581740\pi$
$978$	−1.01383	−	1.37565i	−0.0324187	−	0.0439885i
$979$	6.13213			0.195984
$980$		0			0
$981$	17.8891			0.571156
$982$	28.1242	+	38.1613i	0.897481	+	1.21778i
$983$	55.7548	+	14.9395i	1.77830	+	0.476495i	0.990272	−	0.139142i	$-0.0444343\pi$
$983$	55.7548	+	14.9395i	1.77830	+	0.476495i	0.788030	+	0.615636i	$0.211101\pi$
$984$	−1.82963	−	25.1027i	−0.0583265	−	0.800244i
$985$	3.19737	−	0.222543i	0.101877	−	0.00709081i
$986$	−3.14357	−	8.02574i	−0.100112	−	0.255592i
$987$		0			0
$988$	−1.11708	+	28.8049i	−0.0355391	+	0.916405i
$989$	56.0292	+	32.3485i	1.78162	+	1.02862i
$990$	−16.3924	−	1.32725i	−0.520986	−	0.0421827i
$991$	−19.0262	+	10.9848i	−0.604386	+	0.348942i	−0.770765	−	0.637120i	$-0.780126\pi$
$991$	−19.0262	+	10.9848i	−0.604386	+	0.348942i	0.166379	+	0.986062i	$0.446792\pi$
$992$	−17.3066	+	10.7925i	−0.549486	+	0.342661i
$993$	22.4953	+	22.4953i	0.713868	+	0.713868i
$994$		0			0
$995$	4.06634	−	20.8834i	0.128912	−	0.662050i
$996$	−4.20698	−	18.5484i	−0.133303	−	0.587728i
$997$	−8.14653	−	2.18286i	−0.258003	−	0.0691317i	0.127499	−	0.991839i	$-0.459305\pi$
$997$	−8.14653	−	2.18286i	−0.258003	−	0.0691317i	−0.385502	+	0.922707i	$0.625972\pi$
$998$	3.25667	+	29.0817i	0.103088	+	0.920565i
$999$	−12.6898	+	21.9794i	−0.401488	+	0.695397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.863.14		72
4.3	odd	2	inner	980.2.x.m.863.2		72
5.2	odd	4	inner	980.2.x.m.667.13		72
7.2	even	3		980.2.k.j.883.3		36
7.3	odd	6		140.2.w.b.123.10	yes	72
7.4	even	3	inner	980.2.x.m.263.10		72
7.5	odd	6		980.2.k.k.883.3		36
7.6	odd	2		140.2.w.b.23.14	yes	72
20.7	even	4	inner	980.2.x.m.667.10		72
28.3	even	6		140.2.w.b.123.13	yes	72
28.11	odd	6	inner	980.2.x.m.263.13		72
28.19	even	6		980.2.k.k.883.13		36
28.23	odd	6		980.2.k.j.883.13		36
28.27	even	2		140.2.w.b.23.2	✓	72
35.2	odd	12		980.2.k.j.687.13		36
35.3	even	12		700.2.be.e.207.17		72
35.12	even	12		980.2.k.k.687.13		36
35.13	even	4		700.2.be.e.107.6		72
35.17	even	12		140.2.w.b.67.2	yes	72
35.24	odd	6		700.2.be.e.543.9		72
35.27	even	4		140.2.w.b.107.13	yes	72
35.32	odd	12	inner	980.2.x.m.67.2		72
35.34	odd	2		700.2.be.e.443.5		72
140.3	odd	12		700.2.be.e.207.5		72
140.27	odd	4		140.2.w.b.107.10	yes	72
140.47	odd	12		980.2.k.k.687.3		36
140.59	even	6		700.2.be.e.543.6		72
140.67	even	12	inner	980.2.x.m.67.14		72
140.83	odd	4		700.2.be.e.107.9		72
140.87	odd	12		140.2.w.b.67.14	yes	72
140.107	even	12		980.2.k.j.687.3		36
140.139	even	2		700.2.be.e.443.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.2	✓	72	28.27	even	2
140.2.w.b.23.14	yes	72	7.6	odd	2
140.2.w.b.67.2	yes	72	35.17	even	12
140.2.w.b.67.14	yes	72	140.87	odd	12
140.2.w.b.107.10	yes	72	140.27	odd	4
140.2.w.b.107.13	yes	72	35.27	even	4
140.2.w.b.123.10	yes	72	7.3	odd	6
140.2.w.b.123.13	yes	72	28.3	even	6
700.2.be.e.107.6		72	35.13	even	4
700.2.be.e.107.9		72	140.83	odd	4
700.2.be.e.207.5		72	140.3	odd	12
700.2.be.e.207.17		72	35.3	even	12
700.2.be.e.443.5		72	35.34	odd	2
700.2.be.e.443.17		72	140.139	even	2
700.2.be.e.543.6		72	140.59	even	6
700.2.be.e.543.9		72	35.24	odd	6
980.2.k.j.687.3		36	140.107	even	12
980.2.k.j.687.13		36	35.2	odd	12
980.2.k.j.883.3		36	7.2	even	3
980.2.k.j.883.13		36	28.23	odd	6
980.2.k.k.687.3		36	140.47	odd	12
980.2.k.k.687.13		36	35.12	even	12
980.2.k.k.883.3		36	7.5	odd	6
980.2.k.k.883.13		36	28.19	even	6
980.2.x.m.67.2		72	35.32	odd	12	inner
980.2.x.m.67.14		72	140.67	even	12	inner
980.2.x.m.263.10		72	7.4	even	3	inner
980.2.x.m.263.13		72	28.11	odd	6	inner
980.2.x.m.667.10		72	20.7	even	4	inner
980.2.x.m.667.13		72	5.2	odd	4	inner
980.2.x.m.863.2		72	4.3	odd	2	inner
980.2.x.m.863.14		72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13844 - 0.839014i) q^{2} +(1.08292 + 0.290169i) q^{3} +(0.592112 - 1.91034i) q^{4} +(-1.68711 - 1.46754i) q^{5} +(1.47630 - 0.578247i) q^{6} +(-0.928715 - 2.67161i) q^{8} +(-1.50955 - 0.871538i) q^{9} +(-3.15196 - 0.255205i) q^{10} +(-2.58391 + 1.49182i) q^{11} +(1.19553 - 1.89694i) q^{12} +(-4.05418 - 4.05418i) q^{13} +(-1.40118 - 2.07878i) q^{15} +(-3.29881 - 2.26227i) q^{16} +(2.30478 + 0.617565i) q^{17} +(-2.44977 + 0.274334i) q^{18} +(1.25694 - 2.17708i) q^{19} +(-3.80246 + 2.35400i) q^{20} +(-1.68998 + 3.86629i) q^{22} +(1.55254 + 5.79414i) q^{23} +(-0.230511 - 3.16263i) q^{24} +(0.692662 + 4.95179i) q^{25} +(-8.01697 - 1.21395i) q^{26} +(-3.76010 - 3.76010i) q^{27} -2.55433i q^{29} +(-3.33928 - 1.19097i) q^{30} +(3.12248 - 1.80277i) q^{31} +(-5.65359 + 0.192271i) q^{32} +(-3.23105 + 0.865758i) q^{33} +(3.14202 - 1.23068i) q^{34} +(-2.55876 + 2.36770i) q^{36} +(-1.23528 - 4.61014i) q^{37} +(-0.395646 - 3.53308i) q^{38} +(-3.21397 - 5.56676i) q^{39} +(-2.35384 + 5.87021i) q^{40} +7.93727 q^{41} +(7.62646 - 7.62646i) q^{43} +(1.31992 + 5.81947i) q^{44} +(1.26775 + 3.68570i) q^{45} +(6.62884 + 5.29371i) q^{46} +(2.85870 - 0.765987i) q^{47} +(-2.91592 - 3.40708i) q^{48} +(4.94318 + 5.05618i) q^{50} +(2.31671 + 1.33755i) q^{51} +(-10.1454 + 5.34433i) q^{52} +(0.662485 - 2.47243i) q^{53} +(-7.43544 - 1.12589i) q^{54} +(6.54863 + 1.27512i) q^{55} +(1.99289 - 1.99289i) q^{57} +(-2.14312 - 2.90796i) q^{58} +(-1.04694 - 1.81336i) q^{59} +(-4.80083 + 1.44585i) q^{60} +(-0.950478 + 1.64628i) q^{61} +(2.04223 - 4.67216i) q^{62} +(-6.27498 + 4.96233i) q^{64} +(0.890172 + 12.7895i) q^{65} +(-2.95199 + 3.69652i) q^{66} +(-0.805219 + 3.00512i) q^{67} +(2.54445 - 4.03726i) q^{68} +6.72512i q^{69} -8.09721i q^{71} +(-0.926468 + 4.84233i) q^{72} +(-2.52396 + 9.41954i) q^{73} +(-5.27428 - 4.21197i) q^{74} +(-0.686753 + 5.56340i) q^{75} +(-3.41472 - 3.69026i) q^{76} +(-8.32952 - 3.64089i) q^{78} +(4.03058 - 6.98117i) q^{79} +(2.24547 + 8.65782i) q^{80} +(-0.366226 - 0.634322i) q^{81} +(9.03614 - 6.65948i) q^{82} +(5.99790 - 5.99790i) q^{83} +(-2.98212 - 4.42426i) q^{85} +(2.28360 - 15.0810i) q^{86} +(0.741186 - 2.76614i) q^{87} +(6.38527 + 5.51771i) q^{88} +(-1.77990 - 1.02763i) q^{89} +(4.53562 + 3.13230i) q^{90} +(11.9881 + 0.464910i) q^{92} +(3.90452 - 1.04621i) q^{93} +(2.61180 - 3.27052i) q^{94} +(-5.31554 + 1.82837i) q^{95} +(-6.17820 - 1.43228i) q^{96} +(-6.63160 + 6.63160i) q^{97} +5.20071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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