LMFDB - Embedded newform 1000.2.d.c.501.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(501,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1000.501");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.d (of order $2$, degree $1$, 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:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			501.8
Character	$\chi$	$=$	1000.501
Dual form			1000.2.d.c.501.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26751 + 0.627237i) q^{2} -1.69676i q^{3} +(1.21315 - 1.59005i) q^{4} +(1.06427 + 2.15066i) q^{6} -4.40040 q^{7} +(-0.540334 + 2.77634i) q^{8} +0.120998 q^{9} +O(q^{10})$	\(q+(-1.26751 + 0.627237i) q^{2} -1.69676i q^{3} +(1.21315 - 1.59005i) q^{4} +(1.06427 + 2.15066i) q^{6} -4.40040 q^{7} +(-0.540334 + 2.77634i) q^{8} +0.120998 q^{9} +0.720144i q^{11} +(-2.69794 - 2.05842i) q^{12} +4.59595i q^{13} +(5.57753 - 2.76009i) q^{14} +(-1.05654 - 3.85794i) q^{16} +2.38420 q^{17} +(-0.153366 + 0.0758946i) q^{18} +0.899742i q^{19} +7.46643i q^{21} +(-0.451701 - 0.912788i) q^{22} +8.05029 q^{23} +(4.71078 + 0.916818i) q^{24} +(-2.88275 - 5.82539i) q^{26} -5.29559i q^{27} +(-5.33833 + 6.99687i) q^{28} +1.78194i q^{29} +9.07877 q^{31} +(3.75902 + 4.22727i) q^{32} +1.22191 q^{33} +(-3.02199 + 1.49546i) q^{34} +(0.146789 - 0.192394i) q^{36} +4.74502i q^{37} +(-0.564351 - 1.14043i) q^{38} +7.79823 q^{39} -2.82760 q^{41} +(-4.68322 - 9.46375i) q^{42} -10.7770i q^{43} +(1.14507 + 0.873642i) q^{44} +(-10.2038 + 5.04943i) q^{46} -4.99256 q^{47} +(-6.54601 + 1.79270i) q^{48} +12.3635 q^{49} -4.04541i q^{51} +(7.30780 + 5.57556i) q^{52} -9.74069i q^{53} +(3.32159 + 6.71220i) q^{54} +(2.37768 - 12.2170i) q^{56} +1.52665 q^{57} +(-1.11770 - 2.25863i) q^{58} -6.39947i q^{59} +0.635551i q^{61} +(-11.5074 + 5.69454i) q^{62} -0.532441 q^{63} +(-7.41608 - 3.00030i) q^{64} +(-1.54878 + 0.766429i) q^{66} +1.73643i q^{67} +(2.89238 - 3.79100i) q^{68} -13.6594i q^{69} -8.41146 q^{71} +(-0.0653795 + 0.335932i) q^{72} +13.0770 q^{73} +(-2.97625 - 6.01435i) q^{74} +(1.43064 + 1.09152i) q^{76} -3.16892i q^{77} +(-9.88431 + 4.89133i) q^{78} +7.19828 q^{79} -8.62236 q^{81} +(3.58401 - 1.77358i) q^{82} +0.219648i q^{83} +(11.8720 + 9.05788i) q^{84} +(6.75971 + 13.6599i) q^{86} +3.02354 q^{87} +(-1.99936 - 0.389118i) q^{88} +1.37331 q^{89} -20.2240i q^{91} +(9.76619 - 12.8004i) q^{92} -15.4045i q^{93} +(6.32811 - 3.13152i) q^{94} +(7.17267 - 6.37816i) q^{96} +8.41826 q^{97} +(-15.6708 + 7.75484i) q^{98} +0.0871363i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	$ 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) $ 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.26751	+	0.627237i	−0.896263	+	0.443523i
$2$	−1.26751	+	0.627237i	−0.896263	+	0.443523i
$3$		−	1.69676i		−	0.979626i	−0.871828	−	0.489813i	$-0.837065\pi$
$3$		−	1.69676i		−	0.979626i	0.871828	−	0.489813i	$-0.162935\pi$
$4$	1.21315	−	1.59005i	0.606574	−	0.795027i
$5$		0			0
$5$		0			0
$6$	1.06427	+	2.15066i	0.434487	+	0.878002i
$7$	−4.40040			−1.66319			−0.831597	−	0.555380i	$-0.812573\pi$
$7$	−4.40040			−1.66319			−0.831597	+	0.555380i	$0.812573\pi$
$8$	−0.540334	+	2.77634i	−0.191037	+	0.981583i
$9$	0.120998			0.0403328
$10$		0			0
$11$			0.720144i			0.217132i	0.994089	+	0.108566i	$0.0346258\pi$
$11$			0.720144i			0.217132i	−0.994089	+	0.108566i	$0.965374\pi$
$12$	−2.69794	−	2.05842i	−0.778829	−	0.594216i
$13$			4.59595i			1.27469i	0.770580	+	0.637343i	$0.219967\pi$
$13$			4.59595i			1.27469i	−0.770580	+	0.637343i	$0.780033\pi$
$14$	5.57753	−	2.76009i	1.49066	−	0.737665i
$15$		0			0
$16$	−1.05654	−	3.85794i	−0.264136	−	0.964486i
$17$	2.38420			0.578252			0.289126	−	0.957291i	$-0.406635\pi$
$17$	2.38420			0.578252			0.289126	+	0.957291i	$0.406635\pi$
$18$	−0.153366	+	0.0758946i	−0.0361488	+	0.0178885i
$19$			0.899742i			0.206415i	0.994660	+	0.103208i	$0.0329106\pi$
$19$			0.899742i			0.206415i	−0.994660	+	0.103208i	$0.967089\pi$
$20$		0			0
$21$			7.46643i			1.62931i
$22$	−0.451701	−	0.912788i	−0.0963030	−	0.194607i
$23$	8.05029			1.67860			0.839300	−	0.543668i	$-0.182965\pi$
$23$	8.05029			1.67860			0.839300	+	0.543668i	$0.182965\pi$
$24$	4.71078	+	0.916818i	0.961584	+	0.187145i
$25$		0			0
$26$	−2.88275	−	5.82539i	−0.565353	−	1.14245i
$27$		−	5.29559i		−	1.01914i
$28$	−5.33833	+	6.99687i	−1.00885	+	1.32228i
$29$			1.78194i			0.330899i	0.986218	+	0.165449i	$0.0529075\pi$
$29$			1.78194i			0.330899i	−0.986218	+	0.165449i	$0.947093\pi$
$30$		0			0
$31$	9.07877			1.63059			0.815297	−	0.579042i	$-0.196573\pi$
$31$	9.07877			1.63059			0.815297	+	0.579042i	$0.196573\pi$
$32$	3.75902	+	4.22727i	0.664507	+	0.747282i
$33$	1.22191			0.212708
$34$	−3.02199	+	1.49546i	−0.518266	+	0.256468i
$35$		0			0
$36$	0.146789	−	0.192394i	0.0244648	−	0.0320656i
$37$			4.74502i			0.780076i	0.920799	+	0.390038i	$0.127538\pi$
$37$			4.74502i			0.780076i	−0.920799	+	0.390038i	$0.872462\pi$
$38$	−0.564351	−	1.14043i	−0.0915499	−	0.185002i
$39$	7.79823			1.24872
$40$		0			0
$41$	−2.82760			−0.441597			−0.220799	−	0.975319i	$-0.570866\pi$
$41$	−2.82760			−0.441597			−0.220799	+	0.975319i	$0.570866\pi$
$42$	−4.68322	−	9.46375i	−0.722636	−	1.46029i
$43$		−	10.7770i		−	1.64347i	−0.569868	−	0.821736i	$-0.693006\pi$
$43$		−	10.7770i		−	1.64347i	0.569868	−	0.821736i	$-0.306994\pi$
$44$	1.14507	+	0.873642i	0.172626	+	0.131706i
$45$		0			0
$46$	−10.2038	+	5.04943i	−1.50447	+	0.744498i
$47$	−4.99256			−0.728240			−0.364120	−	0.931352i	$-0.618630\pi$
$47$	−4.99256			−0.728240			−0.364120	+	0.931352i	$0.618630\pi$
$48$	−6.54601	+	1.79270i	−0.944835	+	0.258754i
$49$	12.3635			1.76621
$50$		0			0
$51$		−	4.04541i		−	0.566471i
$52$	7.30780	+	5.57556i	1.01341	+	0.773192i
$53$		−	9.74069i		−	1.33799i	−0.743268	−	0.668994i	$-0.766725\pi$
$53$		−	9.74069i		−	1.33799i	0.743268	−	0.668994i	$-0.233275\pi$
$54$	3.32159	+	6.71220i	0.452011	+	0.913415i
$55$		0			0
$56$	2.37768	−	12.2170i	0.317731	−	1.63256i
$57$	1.52665			0.202210
$58$	−1.11770	−	2.25863i	−0.146761	−	0.296572i
$59$		−	6.39947i		−	0.833141i	−0.909103	−	0.416570i	$-0.863232\pi$
$59$		−	6.39947i		−	0.833141i	0.909103	−	0.416570i	$-0.136768\pi$
$60$		0			0
$61$			0.635551i			0.0813740i	0.999172	+	0.0406870i	$0.0129547\pi$
$61$			0.635551i			0.0813740i	−0.999172	+	0.0406870i	$0.987045\pi$
$62$	−11.5074	+	5.69454i	−1.46144	+	0.723207i
$63$	−0.532441			−0.0670812
$64$	−7.41608	−	3.00030i	−0.927010	−	0.375037i
$65$		0			0
$66$	−1.54878	+	0.766429i	−0.190642	+	0.0943409i
$67$			1.73643i			0.212138i	0.994359	+	0.106069i	$0.0338265\pi$
$67$			1.73643i			0.212138i	−0.994359	+	0.106069i	$0.966174\pi$
$68$	2.89238	−	3.79100i	0.350753	−	0.459726i
$69$		−	13.6594i		−	1.64440i
$70$		0			0
$71$	−8.41146			−0.998257			−0.499128	−	0.866528i	$-0.666346\pi$
$71$	−8.41146			−0.998257			−0.499128	+	0.866528i	$0.666346\pi$
$72$	−0.0653795	+	0.335932i	−0.00770505	+	0.0395900i
$73$	13.0770			1.53055			0.765274	−	0.643705i	$-0.222604\pi$
$73$	13.0770			1.53055			0.765274	+	0.643705i	$0.222604\pi$
$74$	−2.97625	−	6.01435i	−0.345982	−	0.699154i
$75$		0			0
$76$	1.43064	+	1.09152i	0.164106	+	0.125206i
$77$		−	3.16892i		−	0.361132i
$78$	−9.88431	+	4.89133i	−1.11918	+	0.553834i
$79$	7.19828			0.809870			0.404935	−	0.914346i	$-0.367294\pi$
$79$	7.19828			0.809870			0.404935	+	0.914346i	$0.367294\pi$
$80$		0			0
$81$	−8.62236			−0.958040
$82$	3.58401	−	1.77358i	0.395787	−	0.195859i
$83$			0.219648i			0.0241095i	0.999927	+	0.0120548i	$0.00383724\pi$
$83$			0.219648i			0.0241095i	−0.999927	+	0.0120548i	$0.996163\pi$
$84$	11.8720	+	9.05788i	1.29534	+	0.988296i
$85$		0			0
$86$	6.75971	+	13.6599i	0.728918	+	1.47298i
$87$	3.02354			0.324157
$88$	−1.99936	−	0.389118i	−0.213133	−	0.0414802i
$89$	1.37331			0.145571			0.0727853	−	0.997348i	$-0.476811\pi$
$89$	1.37331			0.145571			0.0727853	+	0.997348i	$0.476811\pi$
$90$		0			0
$91$		−	20.2240i		−	2.12005i
$92$	9.76619	−	12.8004i	1.01820	−	1.33453i
$93$		−	15.4045i		−	1.59737i
$94$	6.32811	−	3.13152i	0.652695	−	0.322991i
$95$		0			0
$96$	7.17267	−	6.37816i	0.732057	−	0.650968i
$97$	8.41826			0.854744			0.427372	−	0.904076i	$-0.359439\pi$
$97$	8.41826			0.854744			0.427372	+	0.904076i	$0.359439\pi$
$98$	−15.6708	+	7.75484i	−1.58299	+	0.783357i
$99$			0.0871363i			0.00875752i
$100$		0			0
$101$			17.2981i			1.72122i	0.509264	+	0.860610i	$0.329918\pi$
$101$			17.2981i			1.72122i	−0.509264	+	0.860610i	$0.670082\pi$
$102$	2.53743	+	5.12759i	0.251243	+	0.507707i
$103$	9.40667			0.926867			0.463433	−	0.886132i	$-0.346617\pi$
$103$	9.40667			0.926867			0.463433	+	0.886132i	$0.346617\pi$
$104$	−12.7599	−	2.48335i	−1.25121	−	0.243512i
$105$		0			0
$106$	6.10972	+	12.3464i	0.593428	+	1.19919i
$107$			9.29949i			0.899015i	0.893276	+	0.449508i	$0.148401\pi$
$107$			9.29949i			0.899015i	−0.893276	+	0.449508i	$0.851599\pi$
$108$	−8.42028	−	6.42434i	−0.810241	−	0.618182i
$109$			19.0410i			1.82379i	0.410418	+	0.911897i	$0.365383\pi$
$109$			19.0410i			1.82379i	−0.410418	+	0.911897i	$0.634617\pi$
$110$		0			0
$111$	8.05117			0.764183
$112$	4.64921	+	16.9765i	0.439309	+	1.60413i
$113$	6.64364			0.624981			0.312491	−	0.949921i	$-0.398837\pi$
$113$	6.64364			0.624981			0.312491	+	0.949921i	$0.398837\pi$
$114$	−1.93504	+	0.957570i	−0.181233	+	0.0896846i
$115$		0			0
$116$	2.83339	+	2.16176i	0.263074	+	0.200715i
$117$			0.556102i			0.0514116i
$118$	4.01399	+	8.11138i	0.369517	+	0.746713i
$119$	−10.4914			−0.961746
$120$		0			0
$121$	10.4814			0.952854
$122$	−0.398641	−	0.805566i	−0.0360913	−	0.0729325i
$123$			4.79777i			0.432600i
$124$	11.0139	−	14.4357i	0.989077	−	1.29637i
$125$		0			0
$126$	0.674872	−	0.333966i	0.0601224	−	0.0297521i
$127$	2.37460			0.210712			0.105356	−	0.994435i	$-0.466402\pi$
$127$	2.37460			0.210712			0.105356	+	0.994435i	$0.466402\pi$
$128$	11.2818	−	0.848738i	0.997182	−	0.0750185i
$129$	−18.2860			−1.60999
$130$		0			0
$131$		−	13.4494i		−	1.17508i	−0.809196	−	0.587538i	$-0.800097\pi$
$131$		−	13.4494i		−	1.17508i	0.809196	−	0.587538i	$-0.199903\pi$
$132$	1.48236	−	1.94291i	0.129023	−	0.169108i
$133$		−	3.95922i		−	0.343308i
$134$	−1.08915	−	2.20093i	−0.0940882	−	0.190131i
$135$		0			0
$136$	−1.28826	+	6.61933i	−0.110468	+	0.567603i
$137$	18.4004			1.57205			0.786025	−	0.618194i	$-0.212136\pi$
$137$	18.4004			1.57205			0.786025	+	0.618194i	$0.212136\pi$
$138$	8.56769	+	17.3134i	0.729330	+	1.47382i
$139$			9.62833i			0.816665i	0.912833	+	0.408332i	$0.133890\pi$
$139$			9.62833i			0.816665i	−0.912833	+	0.408332i	$0.866110\pi$
$140$		0			0
$141$			8.47119i			0.713403i
$142$	10.6616	−	5.27598i	0.894700	−	0.442750i
$143$	−3.30974			−0.276775
$144$	−0.127840	−	0.466805i	−0.0106533	−	0.0389004i
$145$		0			0
$146$	−16.5752	+	8.20238i	−1.37177	+	0.678833i
$147$		−	20.9779i		−	1.73023i
$148$	7.54484	+	5.75641i	0.620182	+	0.473174i
$149$		−	12.8658i		−	1.05401i	−0.849862	−	0.527005i	$-0.823315\pi$
$149$		−	12.8658i		−	1.05401i	0.849862	−	0.527005i	$-0.176685\pi$
$150$		0			0
$151$	11.5898			0.943167			0.471583	−	0.881821i	$-0.343683\pi$
$151$	11.5898			0.943167			0.471583	+	0.881821i	$0.343683\pi$
$152$	−2.49799	−	0.486161i	−0.202613	−	0.0394329i
$153$	0.288484			0.0233225
$154$	1.98766	+	4.01663i	0.160170	+	0.323669i
$155$		0			0
$156$	9.46041	−	12.3996i	0.757439	−	0.992762i
$157$			19.0105i			1.51721i	0.651553	+	0.758603i	$0.274118\pi$
$157$			19.0105i			1.51721i	−0.651553	+	0.758603i	$0.725882\pi$
$158$	−9.12387	+	4.51502i	−0.725856	+	0.359196i
$159$	−16.5276			−1.31073
$160$		0			0
$161$	−35.4245			−2.79184
$162$	10.9289	−	5.40826i	0.858656	−	0.424913i
$163$			14.3754i			1.12597i	0.826468	+	0.562984i	$0.190347\pi$
$163$			14.3754i			1.12597i	−0.826468	+	0.562984i	$0.809653\pi$
$164$	−3.43030	+	4.49604i	−0.267861	+	0.351082i
$165$		0			0
$166$	−0.137771	−	0.278406i	−0.0106931	−	0.0216085i
$167$	−0.460864			−0.0356627			−0.0178314	−	0.999841i	$-0.505676\pi$
$167$	−0.460864			−0.0356627			−0.0178314	+	0.999841i	$0.505676\pi$
$168$	−20.7293	−	4.03437i	−1.59930	−	0.311258i
$169$	−8.12272			−0.624824
$170$		0			0
$171$			0.108867i			0.00832529i
$172$	−17.1360	−	13.0741i	−1.30660	−	0.996888i
$173$		−	2.96448i		−	0.225385i	−0.993630	−	0.112693i	$-0.964052\pi$
$173$		−	2.96448i		−	0.225385i	0.993630	−	0.112693i	$-0.0359476\pi$
$174$	−3.83235	+	1.89647i	−0.290530	+	0.143771i
$175$		0			0
$176$	2.77828	−	0.760863i	0.209420	−	0.0573522i
$177$	−10.8584			−0.816166
$178$	−1.74068	+	0.861391i	−0.130470	+	0.0645640i
$179$			15.5047i			1.15888i	0.815016	+	0.579438i	$0.196728\pi$
$179$			15.5047i			1.15888i	−0.815016	+	0.579438i	$0.803272\pi$
$180$		0			0
$181$		−	6.57069i		−	0.488395i	−0.969725	−	0.244198i	$-0.921475\pi$
$181$		−	6.57069i		−	0.488395i	0.969725	−	0.244198i	$-0.0785246\pi$
$182$	12.6852	+	25.6340i	0.940292	+	1.90012i
$183$	1.07838			0.0797161
$184$	−4.34984	+	22.3503i	−0.320675	+	1.64769i
$185$		0			0
$186$	9.66227	+	19.5253i	0.708472	+	1.43167i
$187$			1.71697i			0.125557i
$188$	−6.05672	+	7.93844i	−0.441732	+	0.578970i
$189$			23.3027i			1.69502i
$190$		0			0
$191$	1.14661			0.0829657			0.0414829	−	0.999139i	$-0.486792\pi$
$191$	1.14661			0.0829657			0.0414829	+	0.999139i	$0.486792\pi$
$192$	−5.09079	+	12.5833i	−0.367396	+	0.908123i
$193$	15.5981			1.12278			0.561389	−	0.827552i	$-0.310267\pi$
$193$	15.5981			1.12278			0.561389	+	0.827552i	$0.310267\pi$
$194$	−10.6702	+	5.28024i	−0.766076	+	0.379099i
$195$		0			0
$196$	14.9988	−	19.6586i	1.07134	−	1.40419i
$197$		−	17.3637i		−	1.23711i	−0.785740	−	0.618557i	$-0.787718\pi$
$197$		−	17.3637i		−	1.23711i	0.785740	−	0.618557i	$-0.212282\pi$
$198$	−0.0546551	−	0.110446i	−0.00388417	−	0.00784904i
$199$	−9.00089			−0.638056			−0.319028	−	0.947745i	$-0.603356\pi$
$199$	−9.00089			−0.638056			−0.319028	+	0.947745i	$0.603356\pi$
$200$		0			0
$201$	2.94630			0.207816
$202$	−10.8500	−	21.9254i	−0.763401	−	1.54267i
$203$		−	7.84127i		−	0.550349i
$204$	−6.43242	−	4.90769i	−0.450360	−	0.343607i
$205$		0			0
$206$	−11.9230	+	5.90021i	−0.830716	+	0.411087i
$207$	0.974071			0.0677026
$208$	17.7309	−	4.85581i	1.22942	−	0.336690i
$209$	−0.647944			−0.0448192
$210$		0			0
$211$		−	17.9912i		−	1.23856i	−0.785169	−	0.619281i	$-0.787424\pi$
$211$		−	17.9912i		−	1.23856i	0.785169	−	0.619281i	$-0.212576\pi$
$212$	−15.4882	−	11.8169i	−1.06374	−	0.811588i
$213$			14.2722i			0.977918i
$214$	−5.83298	−	11.7872i	−0.398734	−	0.805754i
$215$		0			0
$216$	14.7023	+	2.86139i	1.00037	+	0.194693i
$217$	−39.9502			−2.71200
$218$	−11.9432	−	24.1346i	−0.808895	−	1.63460i
$219$		−	22.1886i		−	1.49936i
$220$		0			0
$221$			10.9576i			0.737090i
$222$	−10.2049	+	5.04999i	−0.684909	+	0.338933i
$223$	6.79501			0.455028			0.227514	−	0.973775i	$-0.426940\pi$
$223$	6.79501			0.455028			0.227514	+	0.973775i	$0.426940\pi$
$224$	−16.5412	−	18.6017i	−1.10520	−	1.24288i
$225$		0			0
$226$	−8.42086	+	4.16714i	−0.560148	+	0.277194i
$227$			26.0338i			1.72792i	0.503557	+	0.863962i	$0.332024\pi$
$227$			26.0338i			1.72792i	−0.503557	+	0.863962i	$0.667976\pi$
$228$	1.85205	−	2.42745i	0.122655	−	0.160762i
$229$		−	13.9303i		−	0.920539i	−0.887779	−	0.460269i	$-0.847753\pi$
$229$		−	13.9303i		−	0.920539i	0.887779	−	0.460269i	$-0.152247\pi$
$230$		0			0
$231$	−5.37691			−0.353774
$232$	−4.94728	−	0.962846i	−0.324805	−	0.0632139i
$233$	−12.5940			−0.825059			−0.412529	−	0.910944i	$-0.635355\pi$
$233$	−12.5940			−0.825059			−0.412529	+	0.910944i	$0.635355\pi$
$234$	−0.348807	−	0.704863i	−0.0228023	−	0.0460783i
$235$		0			0
$236$	−10.1755	−	7.76351i	−0.662369	−	0.505362i
$237$		−	12.2138i		−	0.793369i
$238$	13.2979	−	6.58060i	0.861977	−	0.426557i
$239$	9.25499			0.598656			0.299328	−	0.954150i	$-0.403238\pi$
$239$	9.25499			0.598656			0.299328	+	0.954150i	$0.403238\pi$
$240$		0			0
$241$	−11.8958			−0.766278			−0.383139	−	0.923691i	$-0.625157\pi$
$241$	−11.8958			−0.766278			−0.383139	+	0.923691i	$0.625157\pi$
$242$	−13.2852	+	6.57431i	−0.854007	+	0.422613i
$243$		−	1.25667i		−	0.0806157i
$244$	1.01056	+	0.771018i	0.0646945	+	0.0493594i
$245$		0			0
$246$	−3.00934	−	6.08120i	−0.191868	−	0.387723i
$247$	−4.13517			−0.263114
$248$	−4.90557	+	25.2057i	−0.311504	+	1.60056i
$249$	0.372691			0.0236183
$250$		0			0
$251$		−	18.4410i		−	1.16399i	−0.813193	−	0.581993i	$-0.802273\pi$
$251$		−	18.4410i		−	1.16399i	0.813193	−	0.581993i	$-0.197727\pi$
$252$	−0.645930	+	0.846609i	−0.0406897	+	0.0533314i
$253$			5.79737i			0.364477i
$254$	−3.00982	+	1.48944i	−0.188853	+	0.0934556i
$255$		0			0
$256$	−13.7674	+	8.15216i	−0.860465	+	0.509510i
$257$	−4.04100			−0.252071			−0.126035	−	0.992026i	$-0.540225\pi$
$257$	−4.04100			−0.252071			−0.126035	+	0.992026i	$0.540225\pi$
$258$	23.1776	−	11.4696i	1.44297	−	0.714067i
$259$		−	20.8800i		−	1.29742i
$260$		0			0
$261$			0.215612i			0.0133461i
$262$	8.43593	+	17.0472i	0.521174	+	1.05318i
$263$	−24.1904			−1.49164			−0.745821	−	0.666146i	$-0.767943\pi$
$263$	−24.1904			−1.49164			−0.745821	+	0.666146i	$0.767943\pi$
$264$	−0.660242	+	3.39244i	−0.0406351	+	0.208790i
$265$		0			0
$266$	2.48337	+	5.01834i	0.152265	+	0.307694i
$267$		−	2.33018i		−	0.142605i
$268$	2.76101	+	2.10654i	0.168655	+	0.128677i
$269$		−	7.29938i		−	0.445051i	−0.974927	−	0.222526i	$-0.928570\pi$
$269$		−	7.29938i		−	0.445051i	0.974927	−	0.222526i	$-0.0714301\pi$
$270$		0			0
$271$	7.82918			0.475589			0.237794	−	0.971316i	$-0.423576\pi$
$271$	7.82918			0.475589			0.237794	+	0.971316i	$0.423576\pi$
$272$	−2.51900	−	9.19809i	−0.152737	−	0.557716i
$273$	−34.3153			−2.07686
$274$	−23.3226	+	11.5414i	−1.40897	+	0.697241i
$275$		0			0
$276$	−21.7192	−	16.5709i	−1.30734	−	0.997451i
$277$		−	4.34266i		−	0.260925i	−0.991453	−	0.130463i	$-0.958354\pi$
$277$		−	4.34266i		−	0.260925i	0.991453	−	0.130463i	$-0.0416463\pi$
$278$	−6.03924	−	12.2040i	−0.362210	−	0.731946i
$279$	1.09852			0.0657664
$280$		0			0
$281$	9.84024			0.587020			0.293510	−	0.955956i	$-0.405177\pi$
$281$	9.84024			0.587020			0.293510	+	0.955956i	$0.405177\pi$
$282$	−5.31344	−	10.7373i	−0.316411	−	0.639397i
$283$		−	24.8597i		−	1.47776i	−0.673839	−	0.738879i	$-0.735356\pi$
$283$		−	24.8597i		−	1.47776i	0.673839	−	0.738879i	$-0.264644\pi$
$284$	−10.2043	+	13.3747i	−0.605517	+	0.793641i
$285$		0			0
$286$	4.19512	−	2.07599i	0.248063	−	0.122756i
$287$	12.4426			0.734462
$288$	0.454835	+	0.511492i	0.0268014	+	0.0301400i
$289$	−11.3156			−0.665624
$290$		0			0
$291$		−	14.2838i		−	0.837330i
$292$	15.8643	−	20.7931i	0.928391	−	1.21683i
$293$			21.1433i			1.23521i	0.786490	+	0.617603i	$0.211896\pi$
$293$			21.1433i			1.23521i	−0.786490	+	0.617603i	$0.788104\pi$
$294$	13.1581	+	26.5897i	0.767397	+	1.55074i
$295$		0			0
$296$	−13.1738	−	2.56390i	−0.765710	−	0.149023i
$297$	3.81359			0.221287
$298$	8.06993	+	16.3075i	0.467478	+	0.944671i
$299$			36.9987i			2.13969i
$300$		0			0
$301$			47.4229i			2.73341i
$302$	−14.6902	+	7.26956i	−0.845325	+	0.418316i
$303$	29.3507			1.68615
$304$	3.47115	−	0.950616i	0.199084	−	0.0545215i
$305$		0			0
$306$	−0.365655	+	0.180948i	−0.0209031	+	0.0103441i
$307$			6.81511i			0.388959i	0.980907	+	0.194479i	$0.0623017\pi$
$307$			6.81511i			0.388959i	−0.980907	+	0.194479i	$0.937698\pi$
$308$	−5.03875	−	3.84437i	−0.287110	−	0.219053i
$309$		−	15.9609i		−	0.907983i
$310$		0			0
$311$	−3.23527			−0.183455			−0.0917276	−	0.995784i	$-0.529239\pi$
$311$	−3.23527			−0.183455			−0.0917276	+	0.995784i	$0.529239\pi$
$312$	−4.21365	+	21.6505i	−0.238551	+	1.22572i
$313$	8.18203			0.462476			0.231238	−	0.972897i	$-0.425722\pi$
$313$	8.18203			0.462476			0.231238	+	0.972897i	$0.425722\pi$
$314$	−11.9241	−	24.0960i	−0.672916	−	1.35982i
$315$		0			0
$316$	8.73258	−	11.4456i	0.491246	−	0.643868i
$317$		−	26.3642i		−	1.48076i	−0.672189	−	0.740380i	$-0.734646\pi$
$317$		−	26.3642i		−	1.48076i	0.672189	−	0.740380i	$-0.265354\pi$
$318$	20.9489	−	10.3667i	1.17476	−	0.581338i
$319$	−1.28326			−0.0718486
$320$		0			0
$321$	15.7790			0.880699
$322$	44.9007	−	22.2195i	2.50222	−	1.23825i
$323$			2.14516i			0.119360i
$324$	−10.4602	+	13.7100i	−0.581123	+	0.761668i
$325$		0			0
$326$	−9.01677	−	18.2209i	−0.499393	−	1.00916i
$327$	32.3080			1.78664
$328$	1.52785	−	7.85037i	0.0843614	−	0.433464i
$329$	21.9693			1.21120
$330$		0			0
$331$			30.4387i			1.67306i	0.547920	+	0.836531i	$0.315420\pi$
$331$			30.4387i			1.67306i	−0.547920	+	0.836531i	$0.684580\pi$
$332$	0.349253	+	0.266466i	0.0191677	+	0.0146242i
$333$			0.574139i			0.0314626i
$334$	0.584148	−	0.289071i	0.0319632	−	0.0158172i
$335$		0			0
$336$	28.8050	−	7.88860i	1.57144	−	0.430358i
$337$	−29.5259			−1.60838			−0.804190	−	0.594373i	$-0.797400\pi$
$337$	−29.5259			−1.60838			−0.804190	+	0.594373i	$0.797400\pi$
$338$	10.2956	−	5.09486i	0.560007	−	0.277124i
$339$		−	11.2727i		−	0.612248i
$340$		0			0
$341$			6.53802i			0.354054i
$342$	−0.0682856	−	0.137990i	−0.00369246	−	0.00746165i
$343$	−23.6015			−1.27436
$344$	29.9205	+	5.82316i	1.61320	+	0.313964i
$345$		0			0
$346$	1.85943	+	3.75750i	0.0999637	+	0.202005i
$347$		−	5.89868i		−	0.316658i	−0.987386	−	0.158329i	$-0.949389\pi$
$347$		−	5.89868i		−	0.316658i	0.987386	−	0.158329i	$-0.0506106\pi$
$348$	3.66800	−	4.80759i	0.196625	−	0.257714i
$349$			18.7429i			1.00329i	0.865075	+	0.501643i	$0.167271\pi$
$349$			18.7429i			1.00329i	−0.865075	+	0.501643i	$0.832729\pi$
$350$		0			0
$351$	24.3383			1.29908
$352$	−3.04424	+	2.70703i	−0.162259	+	0.144285i
$353$	−25.1509			−1.33865			−0.669323	−	0.742972i	$-0.733416\pi$
$353$	−25.1509			−1.33865			−0.669323	+	0.742972i	$0.733416\pi$
$354$	13.7631	−	6.81078i	0.731500	−	0.361989i
$355$		0			0
$356$	1.66603	−	2.18364i	0.0882994	−	0.115733i
$357$			17.8014i			0.942151i
$358$	−9.72512	−	19.6523i	−0.513989	−	1.03866i
$359$	1.12502			0.0593764			0.0296882	−	0.999559i	$-0.490549\pi$
$359$	1.12502			0.0593764			0.0296882	+	0.999559i	$0.490549\pi$
$360$		0			0
$361$	18.1905			0.957393
$362$	4.12137	+	8.32839i	0.216615	+	0.437730i
$363$		−	17.7844i		−	0.933440i
$364$	−32.1572	−	24.5347i	−1.68550	−	1.28597i
$365$		0			0
$366$	−1.36685	+	0.676399i	−0.0714466	+	0.0353560i
$367$	6.86079			0.358130			0.179065	−	0.983837i	$-0.442693\pi$
$367$	6.86079			0.358130			0.179065	+	0.983837i	$0.442693\pi$
$368$	−8.50547	−	31.0575i	−0.443378	−	1.61899i
$369$	−0.342135			−0.0178108
$370$		0			0
$371$			42.8629i			2.22533i
$372$	−24.4940	−	18.6880i	−1.26995	−	0.968925i
$373$			7.89076i			0.408568i	0.978912	+	0.204284i	$0.0654866\pi$
$373$			7.89076i			0.408568i	−0.978912	+	0.204284i	$0.934513\pi$
$374$	−1.07694	−	2.17627i	−0.0556874	−	0.112532i
$375$		0			0
$376$	2.69765	−	13.8610i	0.139121	−	0.714828i
$377$	−8.18972			−0.421792
$378$	−14.6163	−	29.5363i	−0.751782	−	1.51919i
$379$		−	4.36955i		−	0.224449i	−0.993683	−	0.112224i	$-0.964202\pi$
$379$		−	4.36955i		−	0.224449i	0.993683	−	0.112224i	$-0.0357976\pi$
$380$		0			0
$381$		−	4.02913i		−	0.206419i
$382$	−1.45333	+	0.719195i	−0.0743591	+	0.0367972i
$383$	−12.3406			−0.630574			−0.315287	−	0.948996i	$-0.602101\pi$
$383$	−12.3406			−0.630574			−0.315287	+	0.948996i	$0.602101\pi$
$384$	−1.44011	−	19.1426i	−0.0734901	−	0.976866i
$385$		0			0
$386$	−19.7707	+	9.78371i	−1.00630	+	0.497978i
$387$		−	1.30400i		−	0.0662858i
$388$	10.2126	−	13.3855i	0.518466	−	0.679545i
$389$			18.1641i			0.920957i	0.887671	+	0.460478i	$0.152322\pi$
$389$			18.1641i			0.920957i	−0.887671	+	0.460478i	$0.847678\pi$
$390$		0			0
$391$	19.1935			0.970655
$392$	−6.68042	+	34.3252i	−0.337412	+	1.73369i
$393$	−22.8204			−1.15114
$394$	10.8912	+	22.0086i	0.548689	+	1.10878i
$395$		0			0
$396$	0.138551	+	0.105709i	0.00696247	+	0.00531209i
$397$			19.0559i			0.956389i	0.878254	+	0.478194i	$0.158709\pi$
$397$			19.0559i			0.956389i	−0.878254	+	0.478194i	$0.841291\pi$
$398$	11.4087	−	5.64569i	0.571866	−	0.282993i
$399$	−6.71786			−0.336314
$400$		0			0
$401$	−16.6574			−0.831833			−0.415917	−	0.909403i	$-0.636539\pi$
$401$	−16.6574			−0.831833			−0.415917	+	0.909403i	$0.636539\pi$
$402$	−3.73446	+	1.84803i	−0.186258	+	0.0921712i
$403$			41.7255i			2.07850i
$404$	27.5048	+	20.9851i	1.36842	+	1.04405i
$405$		0			0
$406$	4.91833	+	9.93886i	0.244093	+	0.493257i
$407$	−3.41710			−0.169379
$408$	11.2314	+	2.18587i	0.556038	+	0.108217i
$409$	−25.0986			−1.24105			−0.620523	−	0.784188i	$-0.713080\pi$
$409$	−25.0986			−1.24105			−0.620523	+	0.784188i	$0.713080\pi$
$410$		0			0
$411$		−	31.2211i		−	1.54002i
$412$	11.4117	−	14.9571i	0.562214	−	0.736884i
$413$			28.1602i			1.38567i
$414$	−1.23464	+	0.610973i	−0.0606793	+	0.0300277i
$415$		0			0
$416$	−19.4283	+	17.2762i	−0.952550	+	0.847037i
$417$	16.3370			0.800026
$418$	0.821274	−	0.406414i	0.0401698	−	0.0198784i
$419$			16.2968i			0.796149i	0.917353	+	0.398074i	$0.130321\pi$
$419$			16.2968i			0.796149i	−0.917353	+	0.398074i	$0.869679\pi$
$420$		0			0
$421$		−	13.3488i		−	0.650579i	−0.945614	−	0.325290i	$-0.894538\pi$
$421$		−	13.3488i		−	0.650579i	0.945614	−	0.325290i	$-0.105462\pi$
$422$	11.2847	+	22.8039i	0.549331	+	1.11008i
$423$	−0.604092			−0.0293719
$424$	27.0434	+	5.26323i	1.31335	+	0.255605i
$425$		0			0
$426$	−8.95208	−	18.0902i	−0.433729	−	0.876472i
$427$		−	2.79668i		−	0.135341i
$428$	14.7867	+	11.2817i	0.714741	+	0.545320i
$429$			5.61585i			0.271136i
$430$		0			0
$431$	−26.1490			−1.25955			−0.629777	−	0.776776i	$-0.716854\pi$
$431$	−26.1490			−1.25955			−0.629777	+	0.776776i	$0.716854\pi$
$432$	−20.4301	+	5.59502i	−0.982943	+	0.269190i
$433$	15.8230			0.760403			0.380201	−	0.924904i	$-0.375855\pi$
$433$	15.8230			0.760403			0.380201	+	0.924904i	$0.375855\pi$
$434$	50.6371	−	25.0582i	2.43066	−	1.20283i
$435$		0			0
$436$	30.2762	+	23.0995i	1.44997	+	1.10627i
$437$			7.24318i			0.346488i
$438$	13.9175	+	28.1242i	0.665003	+	1.34382i
$439$	19.9204			0.950748			0.475374	−	0.879784i	$-0.342313\pi$
$439$	19.9204			0.950748			0.475374	+	0.879784i	$0.342313\pi$
$440$		0			0
$441$	1.49596			0.0712363
$442$	−6.87303	−	13.8889i	−0.326917	−	0.660627i
$443$		−	4.42692i		−	0.210329i	−0.994455	−	0.105165i	$-0.966463\pi$
$443$		−	4.42692i		−	0.210329i	0.994455	−	0.105165i	$-0.0335369\pi$
$444$	9.76726	−	12.8018i	0.463534	−	0.607546i
$445$		0			0
$446$	−8.61273	+	4.26208i	−0.407824	+	0.201815i
$447$	−21.8303			−1.03254
$448$	32.6337	+	13.2025i	1.54180	+	0.623760i
$449$	7.08837			0.334521			0.167260	−	0.985913i	$-0.446508\pi$
$449$	7.08837			0.334521			0.167260	+	0.985913i	$0.446508\pi$
$450$		0			0
$451$		−	2.03628i		−	0.0958847i
$452$	8.05972	−	10.5637i	0.379098	−	0.496877i
$453$		−	19.6652i		−	0.923951i
$454$	−16.3294	−	32.9980i	−0.766375	−	1.54867i
$455$		0			0
$456$	−0.824900	+	4.23849i	−0.0386295	+	0.198485i
$457$	27.7894			1.29993			0.649967	−	0.759962i	$-0.274783\pi$
$457$	27.7894			1.29993			0.649967	+	0.759962i	$0.274783\pi$
$458$	8.73758	+	17.6567i	0.408280	+	0.825045i
$459$		−	12.6257i		−	0.589319i
$460$		0			0
$461$		−	21.0565i		−	0.980701i	−0.871525	−	0.490350i	$-0.836869\pi$
$461$		−	21.0565i		−	0.980701i	0.871525	−	0.490350i	$-0.163131\pi$
$462$	6.81527	−	3.37259i	0.317075	−	0.156907i
$463$	−30.0661			−1.39729			−0.698645	−	0.715468i	$-0.746213\pi$
$463$	−30.0661			−1.39729			−0.698645	+	0.715468i	$0.746213\pi$
$464$	6.87464	−	1.88270i	0.319147	−	0.0874022i
$465$		0			0
$466$	15.9630	−	7.89940i	0.739469	−	0.365933i
$467$		−	0.930499i		−	0.0430583i	−0.999768	−	0.0215292i	$-0.993147\pi$
$467$		−	0.930499i		−	0.0430583i	0.999768	−	0.0215292i	$-0.00685348\pi$
$468$	0.884232	+	0.674634i	0.0408736	+	0.0311850i
$469$		−	7.64096i		−	0.352827i
$470$		0			0
$471$	32.2564			1.48629
$472$	17.7671	+	3.45785i	0.817797	+	0.159161i
$473$	7.76097			0.356850
$474$	7.66092	+	15.4810i	0.351878	+	0.711067i
$475$		0			0
$476$	−12.7276	+	16.6819i	−0.583370	+	0.764614i
$477$		−	1.17861i		−	0.0539647i
$478$	−11.7308	+	5.80507i	−0.536553	+	0.265518i
$479$	−12.3798			−0.565648			−0.282824	−	0.959172i	$-0.591271\pi$
$479$	−12.3798			−0.565648			−0.282824	+	0.959172i	$0.591271\pi$
$480$		0			0
$481$	−21.8079			−0.994353
$482$	15.0781	−	7.46151i	0.686787	−	0.339862i
$483$			60.1069i			2.73496i
$484$	12.7155	−	16.6660i	0.577977	−	0.757544i
$485$		0			0
$486$	0.788232	+	1.59284i	0.0357549	+	0.0722528i
$487$	−30.0601			−1.36215			−0.681076	−	0.732212i	$-0.738488\pi$
$487$	−30.0601			−1.36215			−0.681076	+	0.732212i	$0.738488\pi$
$488$	−1.76450	−	0.343410i	−0.0798754	−	0.0155454i
$489$	24.3916			1.10303
$490$		0			0
$491$			7.77369i			0.350822i	0.984495	+	0.175411i	$0.0561253\pi$
$491$			7.77369i			0.350822i	−0.984495	+	0.175411i	$0.943875\pi$
$492$	7.62871	+	5.82040i	0.343929	+	0.262404i
$493$			4.24851i			0.191343i
$494$	5.24135	−	2.59373i	0.235820	−	0.116697i
$495$		0			0
$496$	−9.59210	−	35.0254i	−0.430698	−	1.57269i
$497$	37.0138			1.66029
$498$	−0.472388	+	0.233765i	−0.0211682	+	0.0104753i
$499$			3.02886i			0.135590i	0.997699	+	0.0677952i	$0.0215964\pi$
$499$			3.02886i			0.135590i	−0.997699	+	0.0677952i	$0.978404\pi$
$500$		0			0
$501$			0.781976i			0.0349361i
$502$	11.5669	+	23.3741i	0.516255	+	1.04324i
$503$	−18.5947			−0.829096			−0.414548	−	0.910027i	$-0.636060\pi$
$503$	−18.5947			−0.829096			−0.414548	+	0.910027i	$0.636060\pi$
$504$	0.287696	−	1.47823i	0.0128150	−	0.0658458i
$505$		0			0
$506$	−3.63632	−	7.34820i	−0.161654	−	0.326667i
$507$			13.7823i			0.612094i
$508$	2.88074	−	3.77574i	0.127812	−	0.167521i
$509$		−	35.8471i		−	1.58889i	−0.607334	−	0.794446i	$-0.707761\pi$
$509$		−	35.8471i		−	1.58889i	0.607334	−	0.794446i	$-0.292239\pi$
$510$		0			0
$511$	−57.5440			−2.54560
$512$	12.3370	−	18.9684i	0.545223	−	0.838291i
$513$	4.76467			0.210365
$514$	5.12199	−	2.53466i	0.225921	−	0.111799i
$515$		0			0
$516$	−22.1836	+	29.0756i	−0.976577	+	1.27998i
$517$		−	3.59537i		−	0.158124i
$518$	13.0967	+	26.4655i	0.575435	+	1.16283i
$519$	−5.03002			−0.220794
$520$		0			0
$521$	8.00169			0.350560			0.175280	−	0.984519i	$-0.443917\pi$
$521$	8.00169			0.350560			0.175280	+	0.984519i	$0.443917\pi$
$522$	−0.135240	−	0.273290i	−0.00591929	−	0.0119616i
$523$			23.5586i			1.03015i	0.857146	+	0.515073i	$0.172235\pi$
$523$			23.5586i			1.03015i	−0.857146	+	0.515073i	$0.827765\pi$
$524$	−21.3852	−	16.3161i	−0.934217	−	0.712771i
$525$		0			0
$526$	30.6615	−	15.1731i	1.33690	−	0.661578i
$527$	21.6456			0.942895
$528$	−1.29100	−	4.71407i	−0.0561837	−	0.205154i
$529$	41.8071			1.81770
$530$		0			0
$531$		−	0.774326i		−	0.0336029i
$532$	−6.29538	−	4.80313i	−0.272939	−	0.208242i
$533$		−	12.9955i		−	0.562898i
$534$	1.46158	+	2.95352i	0.0632486	+	0.127811i
$535$		0			0
$536$	−4.82090	−	0.938250i	−0.208231	−	0.0405262i
$537$	26.3078			1.13527
$538$	4.57844	+	9.25202i	0.197391	+	0.398883i
$539$			8.90350i			0.383501i
$540$		0			0
$541$		−	14.5520i		−	0.625638i	−0.949813	−	0.312819i	$-0.898727\pi$
$541$		−	14.5520i		−	0.625638i	0.949813	−	0.312819i	$-0.101273\pi$
$542$	−9.92354	+	4.91075i	−0.426253	+	0.210935i
$543$	−11.1489			−0.478445
$544$	8.96223	+	10.0786i	0.384253	+	0.432118i
$545$		0			0
$546$	43.4949	−	21.5238i	1.86141	−	0.921134i
$547$		−	7.00697i		−	0.299597i	−0.988717	−	0.149798i	$-0.952138\pi$
$547$		−	7.00697i		−	0.299597i	0.988717	−	0.149798i	$-0.0478624\pi$
$548$	22.3224	−	29.2576i	0.953565	−	1.24982i
$549$			0.0769007i			0.00328204i
$550$		0			0
$551$	−1.60329			−0.0683025
$552$	37.9231	+	7.38065i	1.61412	+	0.314141i
$553$	−31.6753			−1.34697
$554$	2.72388	+	5.50436i	0.115726	+	0.233858i
$555$		0			0
$556$	15.3096	+	11.6806i	0.649270	+	0.495368i
$557$		−	30.8696i		−	1.30799i	−0.756501	−	0.653993i	$-0.773093\pi$
$557$		−	30.8696i		−	1.30799i	0.756501	−	0.653993i	$-0.226907\pi$
$558$	−1.39238	+	0.689029i	−0.0589440	+	0.0291689i
$559$	49.5304			2.09491
$560$		0			0
$561$	2.91328			0.122999
$562$	−12.4726	+	6.17216i	−0.526124	+	0.260357i
$563$			19.5281i			0.823011i	0.911407	+	0.411505i	$0.134997\pi$
$563$			19.5281i			0.823011i	−0.911407	+	0.411505i	$0.865003\pi$
$564$	13.4696	+	10.2768i	0.567175	+	0.432732i
$565$		0			0
$566$	15.5929	+	31.5099i	0.655420	+	1.32446i
$567$	37.9418			1.59341
$568$	4.54500	−	23.3530i	0.190704	−	0.979872i
$569$	−2.43721			−0.102173			−0.0510866	−	0.998694i	$-0.516268\pi$
$569$	−2.43721			−0.102173			−0.0510866	+	0.998694i	$0.516268\pi$
$570$		0			0
$571$		−	3.60054i		−	0.150678i	−0.997158	−	0.0753389i	$-0.975996\pi$
$571$		−	3.60054i		−	0.150678i	0.997158	−	0.0753389i	$-0.0240039\pi$
$572$	−4.01521	+	5.26267i	−0.167884	+	0.220043i
$573$		−	1.94552i		−	0.0812754i
$574$	−15.7710	+	7.80444i	−0.658271	+	0.325751i
$575$		0			0
$576$	−0.897333	−	0.363031i	−0.0373889	−	0.0151263i
$577$	−22.5193			−0.937490			−0.468745	−	0.883334i	$-0.655294\pi$
$577$	−22.5193			−0.937490			−0.468745	+	0.883334i	$0.655294\pi$
$578$	14.3426	−	7.09757i	0.596574	−	0.295220i
$579$		−	26.4663i		−	1.09990i
$580$		0			0
$581$		−	0.966540i		−	0.0400988i
$582$	8.95931	+	18.1048i	0.371375	+	0.750468i
$583$	7.01470			0.290519
$584$	−7.06595	+	36.3061i	−0.292391	+	1.50236i
$585$		0			0
$586$	−13.2619	−	26.7993i	−0.547843	−	1.10707i
$587$		−	10.2171i		−	0.421703i	−0.977518	−	0.210851i	$-0.932376\pi$
$587$		−	10.2171i		−	0.421703i	0.977518	−	0.210851i	$-0.0676236\pi$
$588$	−33.3560	−	25.4493i	−1.37558	−	1.04951i
$589$			8.16855i			0.336579i
$590$		0			0
$591$	−29.4621			−1.21191
$592$	18.3060	−	5.01331i	0.752373	−	0.206046i
$593$	45.8240			1.88177			0.940883	−	0.338733i	$-0.109998\pi$
$593$	45.8240			1.88177			0.940883	+	0.338733i	$0.109998\pi$
$594$	−4.83375	+	2.39202i	−0.198331	+	0.0981459i
$595$		0			0
$596$	−20.4574	−	15.6082i	−0.837967	−	0.639336i
$597$			15.2724i			0.625056i
$598$	−23.2069	−	46.8961i	−0.949002	−	1.91772i
$599$	46.4420			1.89757			0.948785	−	0.315923i	$-0.102314\pi$
$599$	46.4420			1.89757			0.948785	+	0.315923i	$0.102314\pi$
$600$		0			0
$601$	27.7642			1.13253			0.566263	−	0.824225i	$-0.308389\pi$
$601$	27.7642			1.13253			0.566263	+	0.824225i	$0.308389\pi$
$602$	−29.7454	−	60.1089i	−1.21233	−	2.44986i
$603$			0.210105i			0.00855612i
$604$	14.0602	−	18.4284i	0.572101	−	0.749843i
$605$		0			0
$606$	−37.2022	+	18.4098i	−1.51124	+	0.747848i
$607$	−15.2919			−0.620681			−0.310340	−	0.950625i	$-0.600443\pi$
$607$	−15.2919			−0.620681			−0.310340	+	0.950625i	$0.600443\pi$
$608$	−3.80345	+	3.38215i	−0.154250	+	0.137164i
$609$	−13.3048			−0.539136
$610$		0			0
$611$		−	22.9455i		−	0.928277i
$612$	0.349974	−	0.458705i	0.0141468	−	0.0185420i
$613$		−	19.6201i		−	0.792448i	−0.918154	−	0.396224i	$-0.870320\pi$
$613$		−	19.6201i		−	0.792448i	0.918154	−	0.396224i	$-0.129680\pi$
$614$	−4.27468	−	8.63819i	−0.172512	−	0.348609i
$615$		0			0
$616$	8.79799	+	1.71228i	0.354481	+	0.0689896i
$617$	−11.2105			−0.451316			−0.225658	−	0.974207i	$-0.572453\pi$
$617$	−11.2105			−0.451316			−0.225658	+	0.974207i	$0.572453\pi$
$618$	10.0113	+	20.2305i	0.402712	+	0.813791i
$619$		−	18.3211i		−	0.736388i	−0.929749	−	0.368194i	$-0.879976\pi$
$619$		−	18.3211i		−	0.736388i	0.929749	−	0.368194i	$-0.120024\pi$
$620$		0			0
$621$		−	42.6310i		−	1.71072i
$622$	4.10073	−	2.02928i	0.164424	−	0.0813667i
$623$	−6.04311			−0.242112
$624$	−8.23915	−	30.0851i	−0.329830	−	1.20437i
$625$		0			0
$626$	−10.3708	+	5.13207i	−0.414500	+	0.205119i
$627$			1.09941i			0.0439061i
$628$	30.2278	+	23.0626i	1.20622	+	0.920298i
$629$			11.3131i			0.451081i
$630$		0			0
$631$	−7.54155			−0.300225			−0.150112	−	0.988669i	$-0.547964\pi$
$631$	−7.54155			−0.300225			−0.150112	+	0.988669i	$0.547964\pi$
$632$	−3.88948	+	19.9848i	−0.154715	+	0.794954i
$633$	−30.5267			−1.21333
$634$	16.5366	+	33.4168i	0.656751	+	1.32715i
$635$		0			0
$636$	−20.0505	+	26.2798i	−0.795053	+	1.04206i
$637$			56.8220i			2.25137i
$638$	1.62654	−	0.804906i	0.0643953	−	0.0318665i
$639$	−1.01777			−0.0402625
$640$		0			0
$641$	−19.5415			−0.771843			−0.385921	−	0.922532i	$-0.626116\pi$
$641$	−19.5415			−0.771843			−0.385921	+	0.922532i	$0.626116\pi$
$642$	−20.0000	+	9.89718i	−0.789338	+	0.390611i
$643$		−	17.4075i		−	0.686484i	−0.939247	−	0.343242i	$-0.888475\pi$
$643$		−	17.4075i		−	0.686484i	0.939247	−	0.343242i	$-0.111525\pi$
$644$	−42.9751	+	56.3268i	−1.69346	+	2.21959i
$645$		0			0
$646$	−1.34552	−	2.71901i	−0.0529389	−	0.106978i
$647$	−43.0753			−1.69346			−0.846732	−	0.532020i	$-0.821433\pi$
$647$	−43.0753			−1.69346			−0.846732	+	0.532020i	$0.821433\pi$
$648$	4.65896	−	23.9386i	0.183021	−	0.940396i
$649$	4.60855			0.180901
$650$		0			0
$651$			67.7860i			2.65674i
$652$	22.8576	+	17.4395i	0.895174	+	0.682983i
$653$		−	6.98379i		−	0.273297i	−0.990620	−	0.136648i	$-0.956367\pi$
$653$		−	6.98379i		−	0.273297i	0.990620	−	0.136648i	$-0.0436331\pi$
$654$	−40.9506	+	20.2648i	−1.60130	+	0.792415i
$655$		0			0
$656$	2.98748	+	10.9087i	0.116642	+	0.425914i
$657$	1.58230			0.0617312
$658$	−27.8462	+	13.7799i	−1.08556	+	0.537197i
$659$		−	5.78732i		−	0.225442i	−0.993627	−	0.112721i	$-0.964043\pi$
$659$		−	5.78732i		−	0.225442i	0.993627	−	0.112721i	$-0.0359566\pi$
$660$		0			0
$661$		−	29.6124i		−	1.15179i	−0.817523	−	0.575895i	$-0.804654\pi$
$661$		−	29.6124i		−	1.15179i	0.817523	−	0.575895i	$-0.195346\pi$
$662$	−19.0923	−	38.5812i	−0.742042	−	1.49950i
$663$	18.5925			0.722073
$664$	−0.609817	−	0.118683i	−0.0236655	−	0.00460581i
$665$		0			0
$666$	−0.360121	−	0.727726i	−0.0139544	−	0.0281988i
$667$			14.3452i			0.555447i
$668$	−0.559096	+	0.732798i	−0.0216321	+	0.0283528i
$669$		−	11.5295i		−	0.445757i
$670$		0			0
$671$	−0.457689			−0.0176689
$672$	−31.5626	+	28.0664i	−1.21755	+	1.08269i
$673$	−39.5316			−1.52383			−0.761915	−	0.647677i	$-0.775741\pi$
$673$	−39.5316			−1.52383			−0.761915	+	0.647677i	$0.775741\pi$
$674$	37.4243	−	18.5197i	1.44153	−	0.713354i
$675$		0			0
$676$	−9.85406	+	12.9156i	−0.379002	+	0.496752i
$677$		−	13.4716i		−	0.517757i	−0.965910	−	0.258879i	$-0.916647\pi$
$677$		−	13.4716i		−	0.517757i	0.965910	−	0.258879i	$-0.0833530\pi$
$678$	7.07064	+	14.2882i	0.271546	+	0.548735i
$679$	−37.0437			−1.42161
$680$		0			0
$681$	44.1732			1.69272
$682$	−4.10089	−	8.28699i	−0.157031	−	0.317325i
$683$		−	41.8857i		−	1.60271i	−0.598187	−	0.801356i	$-0.704112\pi$
$683$		−	41.8857i		−	1.60271i	0.598187	−	0.801356i	$-0.295888\pi$
$684$	0.173105	+	0.132072i	0.00661883	+	0.00504991i
$685$		0			0
$686$	29.9151	−	14.8037i	1.14216	−	0.565209i
$687$	−23.6364			−0.901784
$688$	−41.5769	+	11.3863i	−1.58511	+	0.434099i
$689$	44.7677			1.70551
$690$		0			0
$691$			34.8109i			1.32427i	0.749386	+	0.662134i	$0.230349\pi$
$691$			34.8109i			1.32427i	−0.749386	+	0.662134i	$0.769651\pi$
$692$	−4.71369	−	3.59636i	−0.179188	−	0.136713i
$693$		−	0.383434i		−	0.0145655i
$694$	3.69987	+	7.47662i	0.140445	+	0.283809i
$695$		0			0
$696$	−1.63372	+	8.39435i	−0.0619260	+	0.318187i
$697$	−6.74156			−0.255355
$698$	−11.7563	−	23.7568i	−0.444981	−	0.899208i
$699$			21.3690i			0.808249i
$700$		0			0
$701$		−	42.3521i		−	1.59962i	−0.600257	−	0.799808i	$-0.704935\pi$
$701$		−	42.3521i		−	1.59962i	0.600257	−	0.799808i	$-0.295065\pi$
$702$	−30.8489	+	15.2658i	−1.16432	+	0.576172i
$703$	−4.26930			−0.161020
$704$	2.16065	−	5.34065i	0.0814324	−	0.201283i
$705$		0			0
$706$	31.8789	−	15.7755i	1.19978	−	0.593721i
$707$		−	76.1183i		−	2.86272i
$708$	−13.1728	+	17.2654i	−0.495065	+	0.648874i
$709$			12.6239i			0.474102i	0.971497	+	0.237051i	$0.0761809\pi$
$709$			12.6239i			0.474102i	−0.971497	+	0.237051i	$0.923819\pi$
$710$		0			0
$711$	0.870980			0.0326643
$712$	−0.742047	+	3.81277i	−0.0278094	+	0.142890i
$713$	73.0867			2.73712
$714$	−11.1657	−	22.5634i	−0.417866	−	0.844415i
$715$		0			0
$716$	24.6533	+	18.8095i	0.921338	+	0.702945i
$717$		−	15.7035i		−	0.586459i
$718$	−1.42597	+	0.705655i	−0.0532168	+	0.0263348i
$719$	−21.8304			−0.814136			−0.407068	−	0.913398i	$-0.633449\pi$
$719$	−21.8304			−0.814136			−0.407068	+	0.913398i	$0.633449\pi$
$720$		0			0
$721$	−41.3931			−1.54156
$722$	−23.0565	+	11.4097i	−0.858076	+	0.424626i
$723$			20.1844i			0.750666i
$724$	−10.4477	−	7.97122i	−0.388287	−	0.296248i
$725$		0			0
$726$	11.1550	+	22.5419i	0.414003	+	0.836608i
$727$	−32.2227			−1.19507			−0.597537	−	0.801841i	$-0.703854\pi$
$727$	−32.2227			−1.19507			−0.597537	+	0.801841i	$0.703854\pi$
$728$	56.1486	+	10.9277i	2.08100	+	0.405008i
$729$	−27.9994			−1.03701
$730$		0			0
$731$		−	25.6944i		−	0.950342i
$732$	1.30823	−	1.71468i	0.0483537	−	0.0633765i
$733$			22.6294i			0.835837i	0.908485	+	0.417918i	$0.137240\pi$
$733$			22.6294i			0.835837i	−0.908485	+	0.417918i	$0.862760\pi$
$734$	−8.69610	+	4.30334i	−0.320979	+	0.158839i
$735$		0			0
$736$	30.2612	+	34.0307i	1.11544	+	1.25439i
$737$	−1.25048			−0.0460619
$738$	0.433659	−	0.214600i	0.0159632	−	0.00789952i
$739$			26.3553i			0.969494i	0.874654	+	0.484747i	$0.161088\pi$
$739$			26.3553i			0.969494i	−0.874654	+	0.484747i	$0.838912\pi$
$740$		0			0
$741$			7.01639i			0.257754i
$742$	−26.8852	−	54.3291i	−0.986987	−	1.99448i
$743$	−0.548881			−0.0201365			−0.0100682	−	0.999949i	$-0.503205\pi$
$743$	−0.548881			−0.0201365			−0.0100682	+	0.999949i	$0.503205\pi$
$744$	42.7681	+	8.32358i	1.56795	+	0.305157i
$745$		0			0
$746$	−4.94938	−	10.0016i	−0.181210	−	0.366184i
$747$			0.0265771i			0.000972404i
$748$	2.73007	+	2.08293i	0.0998211	+	0.0761596i
$749$		−	40.9214i		−	1.49524i
$750$		0			0
$751$	22.2625			0.812371			0.406185	−	0.913791i	$-0.366859\pi$
$751$	22.2625			0.812371			0.406185	+	0.913791i	$0.366859\pi$
$752$	5.27485	+	19.2610i	0.192354	+	0.702377i
$753$	−31.2900			−1.14027
$754$	10.3805	−	5.13689i	0.378037	−	0.187075i
$755$		0			0
$756$	37.0526	+	28.2696i	1.34759	+	1.02816i
$757$		−	8.81385i		−	0.320345i	−0.987089	−	0.160172i	$-0.948795\pi$
$757$		−	8.81385i		−	0.320345i	0.987089	−	0.160172i	$-0.0512050\pi$
$758$	2.74074	+	5.53844i	0.0995483	+	0.201165i
$759$	9.83675			0.357052
$760$		0			0
$761$	4.81932			0.174700			0.0873500	−	0.996178i	$-0.472160\pi$
$761$	4.81932			0.174700			0.0873500	+	0.996178i	$0.472160\pi$
$762$	2.52722	+	5.10695i	0.0915515	+	0.185005i
$763$		−	83.7879i		−	3.03332i
$764$	1.39101	−	1.82317i	0.0503249	−	0.0659600i
$765$		0			0
$766$	15.6418	−	7.74046i	0.565160	−	0.279674i
$767$	29.4116			1.06199
$768$	13.8323	+	23.3601i	0.499129	+	0.842934i
$769$	−28.5713			−1.03031			−0.515153	−	0.857098i	$-0.672265\pi$
$769$	−28.5713			−1.03031			−0.515153	+	0.857098i	$0.672265\pi$
$770$		0			0
$771$			6.85661i			0.246935i
$772$	18.9228	−	24.8019i	0.681048	−	0.892638i
$773$			9.95026i			0.357886i	0.983859	+	0.178943i	$0.0572678\pi$
$773$			9.95026i			0.357886i	−0.983859	+	0.178943i	$0.942732\pi$
$774$	0.817914	+	1.65282i	0.0293993	+	0.0594095i
$775$		0			0
$776$	−4.54867	+	23.3719i	−0.163288	+	0.839002i
$777$	−35.4283			−1.27098
$778$	−11.3932	−	23.0231i	−0.408466	−	0.825419i
$779$		−	2.54411i		−	0.0911523i
$780$		0			0
$781$		−	6.05746i		−	0.216753i
$782$	−24.3278	+	12.0388i	−0.869962	+	0.430508i
$783$	9.43645			0.337231
$784$	−13.0626	−	47.6977i	−0.466520	−	1.70349i
$785$		0			0
$786$	28.9250	−	14.3138i	1.03172	−	0.510555i
$787$			49.1601i			1.75237i	0.481975	+	0.876185i	$0.339919\pi$
$787$			49.1601i			1.75237i	−0.481975	+	0.876185i	$0.660081\pi$
$788$	−27.6093	−	21.0648i	−0.983539	−	0.750402i
$789$			41.0453i			1.46125i
$790$		0			0
$791$	−29.2347			−1.03947
$792$	−0.241919	−	0.0470827i	−0.00859623	−	0.00167301i
$793$	−2.92096			−0.103726
$794$	−11.9526	−	24.1535i	−0.424181	−	0.857176i
$795$		0			0
$796$	−10.9194	+	14.3119i	−0.387028	+	0.507272i
$797$			45.6344i			1.61645i	0.588871	+	0.808227i	$0.299573\pi$
$797$			45.6344i			1.61645i	−0.588871	+	0.808227i	$0.700427\pi$
$798$	8.51494	−	4.21369i	0.301425	−	0.149163i
$799$	−11.9032			−0.421107
$800$		0			0
$801$	0.166168			0.00587127
$802$	21.1134	−	10.4482i	0.745541	−	0.368937i
$803$			9.41733i			0.332330i
$804$	3.57430	−	4.68478i	0.126056	−	0.165219i
$805$		0			0
$806$	−26.1718	−	52.8874i	−0.921862	−	1.86288i
$807$	−12.3853			−0.435984
$808$	−48.0252	−	9.34673i	−1.68952	−	0.328817i
$809$	−13.2646			−0.466360			−0.233180	−	0.972434i	$-0.574913\pi$
$809$	−13.2646			−0.466360			−0.233180	+	0.972434i	$0.574913\pi$
$810$		0			0
$811$			31.0646i			1.09083i	0.838167	+	0.545413i	$0.183627\pi$
$811$			31.0646i			1.09083i	−0.838167	+	0.545413i	$0.816373\pi$
$812$	−12.4680	−	9.51262i	−0.437542	−	0.333827i
$813$		−	13.2843i		−	0.465899i
$814$	4.33120	−	2.14333i	0.151808	−	0.0751237i
$815$		0			0
$816$	−15.6070	+	4.27415i	−0.546353	+	0.149625i
$817$	9.69649			0.339237
$818$	31.8127	−	15.7428i	1.11230	−	0.550433i
$819$		−	2.44707i		−	0.0855075i
$820$		0			0
$821$			16.9551i			0.591738i	0.955229	+	0.295869i	$0.0956092\pi$
$821$			16.9551i			0.591738i	−0.955229	+	0.295869i	$0.904391\pi$
$822$	19.5830	+	39.5729i	0.683036	+	1.38026i
$823$	35.5910			1.24063			0.620313	−	0.784354i	$-0.287006\pi$
$823$	35.5910			1.24063			0.620313	+	0.784354i	$0.287006\pi$
$824$	−5.08275	+	26.1161i	−0.177066	+	0.909797i
$825$		0			0
$826$	−17.6631	−	35.6933i	−0.614579	−	1.24193i
$827$		−	11.4594i		−	0.398481i	−0.979951	−	0.199240i	$-0.936153\pi$
$827$		−	11.4594i		−	0.398481i	0.979951	−	0.199240i	$-0.0638474\pi$
$828$	1.18169	−	1.54883i	0.0410667	−	0.0538254i
$829$			3.98218i			0.138307i	0.997606	+	0.0691534i	$0.0220298\pi$
$829$			3.98218i			0.138307i	−0.997606	+	0.0691534i	$0.977970\pi$
$830$		0			0
$831$	−7.36847			−0.255609
$832$	13.7892	−	34.0839i	0.478055	−	1.18165i
$833$	29.4770			1.02132
$834$	−20.7073	+	10.2472i	−0.717033	+	0.354830i
$835$		0			0
$836$	−0.786053	+	1.03027i	−0.0271862	+	0.0356325i
$837$		−	48.0774i		−	1.66180i
$838$	−10.2219	−	20.6563i	−0.353111	−	0.713559i
$839$	−54.2269			−1.87212			−0.936060	−	0.351840i	$-0.885556\pi$
$839$	−54.2269			−1.87212			−0.936060	+	0.351840i	$0.885556\pi$
$840$		0			0
$841$	25.8247			0.890506
$842$	8.37284	+	16.9197i	0.288547	+	0.583090i
$843$		−	16.6966i		−	0.575060i
$844$	−28.6069	−	21.8259i	−0.984690	−	0.751280i
$845$		0			0
$846$	0.765690	−	0.378908i	0.0263250	−	0.0130271i
$847$	−46.1223			−1.58478
$848$	−37.5790	+	10.2915i	−1.29047	+	0.353410i
$849$	−42.1810			−1.44765
$850$		0			0
$851$			38.1988i			1.30944i
$852$	22.6936	+	17.3144i	0.777471	+	0.593180i
$853$			28.9671i			0.991814i	0.868376	+	0.495907i	$0.165164\pi$
$853$			28.9671i			0.991814i	−0.868376	+	0.495907i	$0.834836\pi$
$854$	1.75418	+	3.54481i	0.0600268	+	0.121301i
$855$		0			0
$856$	−25.8185	−	5.02483i	−0.882458	−	0.171745i
$857$	49.1740			1.67975			0.839876	−	0.542779i	$-0.182628\pi$
$857$	49.1740			1.67975			0.839876	+	0.542779i	$0.182628\pi$
$858$	−3.52247	−	7.11813i	−0.120255	−	0.243009i
$859$		−	11.8879i		−	0.405610i	−0.979219	−	0.202805i	$-0.934994\pi$
$859$		−	11.8879i		−	0.405610i	0.979219	−	0.202805i	$-0.0650057\pi$
$860$		0			0
$861$		−	21.1121i		−	0.719498i
$862$	33.1441	−	16.4016i	1.12889	−	0.558641i
$863$	2.10569			0.0716784			0.0358392	−	0.999358i	$-0.488590\pi$
$863$	2.10569			0.0716784			0.0358392	+	0.999358i	$0.488590\pi$
$864$	22.3859	−	19.9062i	0.761583	−	0.677223i
$865$		0			0
$866$	−20.0557	+	9.92474i	−0.681521	+	0.337256i
$867$			19.1999i			0.652063i
$868$	−48.4655	+	63.5229i	−1.64503	+	2.15611i
$869$			5.18380i			0.175848i
$870$		0			0
$871$	−7.98052			−0.270409
$872$	−52.8641	−	10.2885i	−1.79021	−	0.348412i
$873$	1.01859			0.0344742
$874$	−4.54319	−	9.18078i	−0.153676	−	0.310545i
$875$		0			0
$876$	−35.2810	−	26.9180i	−1.19203	−	0.909476i
$877$		−	35.4248i		−	1.19621i	−0.801418	−	0.598105i	$-0.795921\pi$
$877$		−	35.4248i		−	1.19621i	0.801418	−	0.598105i	$-0.204079\pi$
$878$	−25.2492	+	12.4948i	−0.852120	+	0.421679i
$879$	35.8752			1.21004
$880$		0			0
$881$	35.4798			1.19534			0.597672	−	0.801741i	$-0.296093\pi$
$881$	35.4798			1.19534			0.597672	+	0.801741i	$0.296093\pi$
$882$	−1.89614	+	0.938323i	−0.0638465	+	0.0315950i
$883$			3.31152i			0.111442i	0.998446	+	0.0557208i	$0.0177457\pi$
$883$			3.31152i			0.111442i	−0.998446	+	0.0557208i	$0.982254\pi$
$884$	17.4232	+	13.2932i	0.586007	+	0.447100i
$885$		0			0
$886$	2.77673	+	5.61115i	0.0932859	+	0.188510i
$887$	9.76373			0.327834			0.163917	−	0.986474i	$-0.447587\pi$
$887$	9.76373			0.327834			0.163917	+	0.986474i	$0.447587\pi$
$888$	−4.35032	+	22.3527i	−0.145987	+	0.750109i
$889$	−10.4492			−0.350454
$890$		0			0
$891$		−	6.20935i		−	0.208021i
$892$	8.24336	−	10.8044i	0.276008	−	0.361759i
$893$		−	4.49202i		−	0.150320i
$894$	27.6700	−	13.6927i	0.925424	−	0.457954i
$895$		0			0
$896$	−49.6445	+	3.73478i	−1.65851	+	0.124770i
$897$	62.7779			2.09609
$898$	−8.98456	+	4.44608i	−0.299819	+	0.148368i
$899$			16.1779i			0.539562i
$900$		0			0
$901$		−	23.2237i		−	0.773694i
$902$	1.27723	+	2.58100i	0.0425271	+	0.0859379i
$903$	80.4655			2.67772
$904$	−3.58979	+	18.4450i	−0.119395	+	0.613471i
$905$		0			0
$906$	12.3347	+	24.9258i	0.409794	+	0.828103i
$907$		−	23.9575i		−	0.795495i	−0.917495	−	0.397747i	$-0.869792\pi$
$907$		−	23.9575i		−	0.795495i	0.917495	−	0.397747i	$-0.130208\pi$
$908$	41.3951	+	31.5829i	1.37375	+	1.04811i
$909$			2.09304i			0.0694216i
$910$		0			0
$911$	8.70638			0.288455			0.144228	−	0.989545i	$-0.453930\pi$
$911$	8.70638			0.288455			0.144228	+	0.989545i	$0.453930\pi$
$912$	−1.61297	−	5.88972i	−0.0534107	−	0.195028i
$913$	−0.158178			−0.00523494
$914$	−35.2233	+	17.4306i	−1.16508	+	0.576551i
$915$		0			0
$916$	−22.1499	−	16.8995i	−0.731853	−	0.558375i
$917$			59.1825i			1.95438i
$918$	7.91932	+	16.0032i	0.261376	+	0.528184i
$919$	−28.2017			−0.930289			−0.465144	−	0.885235i	$-0.653998\pi$
$919$	−28.2017			−0.930289			−0.465144	+	0.885235i	$0.653998\pi$
$920$		0			0
$921$	11.5636			0.381034
$922$	13.2074	+	26.6893i	0.434964	+	0.878966i
$923$		−	38.6586i		−	1.27246i
$924$	−6.52298	+	8.54957i	−0.214590	+	0.281260i
$925$		0			0
$926$	38.1090	−	18.8586i	1.25234	−	0.619731i
$927$	1.13819			0.0373831
$928$	−7.53276	+	6.69836i	−0.247275	+	0.219885i
$929$	−12.8660			−0.422119			−0.211059	−	0.977473i	$-0.567691\pi$
$929$	−12.8660			−0.422119			−0.211059	+	0.977473i	$0.567691\pi$
$930$		0			0
$931$			11.1240i			0.364573i
$932$	−15.2784	+	20.0251i	−0.500459	+	0.655944i
$933$			5.48948i			0.179718i
$934$	0.583643	+	1.17941i	0.0190974	+	0.0385916i
$935$		0			0
$936$	−1.54392	−	0.300481i	−0.0504648	−	0.00982152i
$937$	−8.91407			−0.291210			−0.145605	−	0.989343i	$-0.546513\pi$
$937$	−8.91407			−0.291210			−0.145605	+	0.989343i	$0.546513\pi$
$938$	4.79269	+	9.68497i	0.156487	+	0.316226i
$939$		−	13.8830i		−	0.453053i
$940$		0			0
$941$		−	29.6233i		−	0.965691i	−0.875706	−	0.482845i	$-0.839603\pi$
$941$		−	29.6233i		−	0.965691i	0.875706	−	0.482845i	$-0.160397\pi$
$942$	−40.8852	+	20.2324i	−1.33211	+	0.659206i
$943$	−22.7630			−0.741265
$944$	−24.6888	+	6.76132i	−0.803552	+	0.220062i
$945$		0			0
$946$	−9.83709	+	4.86797i	−0.319831	+	0.158271i
$947$		−	0.0952553i		−	0.00309538i	−0.999999	−	0.00154769i	$-0.999507\pi$
$947$		−	0.0952553i		−	0.00309538i	0.999999	−	0.00154769i	$-0.000492645\pi$
$948$	−19.4205	−	14.8171i	−0.630750	−	0.481237i
$949$			60.1012i			1.95097i
$950$		0			0
$951$	−44.7337			−1.45059
$952$	5.66887	−	29.1277i	0.183729	−	0.944033i
$953$	−34.3248			−1.11189			−0.555945	−	0.831219i	$-0.687643\pi$
$953$	−34.3248			−1.11189			−0.555945	+	0.831219i	$0.687643\pi$
$954$	0.739266	+	1.49389i	0.0239346	+	0.0483666i
$955$		0			0
$956$	11.2277	−	14.7159i	0.363129	−	0.475947i
$957$			2.17738i			0.0703848i
$958$	15.6915	−	7.76507i	0.506969	−	0.250878i
$959$	−80.9690			−2.61463
$960$		0			0
$961$	51.4240			1.65884
$962$	27.6416	−	13.6787i	0.891201	−	0.441019i
$963$			1.12522i			0.0362598i
$964$	−14.4314	+	18.9150i	−0.464805	+	0.609212i
$965$		0			0
$966$	−37.7012	−	76.1859i	−1.21302	−	2.45124i
$967$	7.19999			0.231536			0.115768	−	0.993276i	$-0.463067\pi$
$967$	7.19999			0.231536			0.115768	+	0.993276i	$0.463067\pi$
$968$	−5.66345	+	29.0999i	−0.182030	+	0.935305i
$969$	3.63983			0.116928
$970$		0			0
$971$			53.7682i			1.72550i	0.505627	+	0.862752i	$0.331261\pi$
$971$			53.7682i			1.72550i	−0.505627	+	0.862752i	$0.668739\pi$
$972$	−1.99818	−	1.52453i	−0.0640916	−	0.0488994i
$973$		−	42.3685i		−	1.35827i
$974$	38.1014	−	18.8548i	1.22085	−	0.604146i
$975$		0			0
$976$	2.45192	−	0.671487i	0.0784841	−	0.0214938i
$977$	−10.4880			−0.335541			−0.167770	−	0.985826i	$-0.553657\pi$
$977$	−10.4880			−0.335541			−0.167770	+	0.985826i	$0.553657\pi$
$978$	−30.9165	+	15.2993i	−0.988602	+	0.489218i
$979$			0.988982i			0.0316080i
$980$		0			0
$981$			2.30393i			0.0735587i
$982$	−4.87594	−	9.85320i	−0.155598	−	0.314428i
$983$	22.0512			0.703324			0.351662	−	0.936127i	$-0.385617\pi$
$983$	22.0512			0.703324			0.351662	+	0.936127i	$0.385617\pi$
$984$	−13.3202	−	2.59240i	−0.424633	−	0.0826426i
$985$		0			0
$986$	−2.66482	−	5.38501i	−0.0848651	−	0.171494i
$987$		−	37.2766i		−	1.18653i
$988$	−5.01657	+	6.57514i	−0.159598	+	0.209183i
$989$		−	86.7577i		−	2.75873i
$990$		0			0
$991$	4.31045			0.136926			0.0684630	−	0.997654i	$-0.478190\pi$
$991$	4.31045			0.136926			0.0684630	+	0.997654i	$0.478190\pi$
$992$	34.1272	+	38.3784i	1.08354	+	1.21851i
$993$	51.6472			1.63897
$994$	−46.9152	+	23.2164i	−1.48806	+	0.736379i
$995$		0			0
$996$	0.452129	−	0.592599i	0.0143263	−	0.0187772i
$997$			12.3284i			0.390444i	0.980759	+	0.195222i	$0.0625427\pi$
$997$			12.3284i			0.390444i	−0.980759	+	0.195222i	$0.937457\pi$
$998$	−1.89981	−	3.83910i	−0.0601375	−	0.121525i
$999$	25.1277			0.795005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.d.c.501.8	yes	40
4.3	odd	2		4000.2.d.c.2001.2		40
5.2	odd	4		1000.2.f.c.749.7		20
5.3	odd	4		1000.2.f.d.749.14		20
5.4	even	2	inner	1000.2.d.c.501.33	yes	40
8.3	odd	2		4000.2.d.c.2001.1		40
8.5	even	2	inner	1000.2.d.c.501.7	✓	40
20.3	even	4		4000.2.f.d.3249.5		20
20.7	even	4		4000.2.f.c.3249.16		20
20.19	odd	2		4000.2.d.c.2001.39		40
40.3	even	4		4000.2.f.c.3249.15		20
40.13	odd	4		1000.2.f.c.749.8		20
40.19	odd	2		4000.2.d.c.2001.40		40
40.27	even	4		4000.2.f.d.3249.6		20
40.29	even	2	inner	1000.2.d.c.501.34	yes	40
40.37	odd	4		1000.2.f.d.749.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.c.501.7	✓	40	8.5	even	2	inner
1000.2.d.c.501.8	yes	40	1.1	even	1	trivial
1000.2.d.c.501.33	yes	40	5.4	even	2	inner
1000.2.d.c.501.34	yes	40	40.29	even	2	inner
1000.2.f.c.749.7		20	5.2	odd	4
1000.2.f.c.749.8		20	40.13	odd	4
1000.2.f.d.749.13		20	40.37	odd	4
1000.2.f.d.749.14		20	5.3	odd	4
4000.2.d.c.2001.1		40	8.3	odd	2
4000.2.d.c.2001.2		40	4.3	odd	2
4000.2.d.c.2001.39		40	20.19	odd	2
4000.2.d.c.2001.40		40	40.19	odd	2
4000.2.f.c.3249.15		20	40.3	even	4
4000.2.f.c.3249.16		20	20.7	even	4
4000.2.f.d.3249.5		20	20.3	even	4
4000.2.f.d.3249.6		20	40.27	even	4

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26751 + 0.627237i) q^{2} -1.69676i q^{3} +(1.21315 - 1.59005i) q^{4} +(1.06427 + 2.15066i) q^{6} -4.40040 q^{7} +(-0.540334 + 2.77634i) q^{8} +0.120998 q^{9} +O(q^{10})\)	\(q+(-1.26751 + 0.627237i) q^{2} -1.69676i q^{3} +(1.21315 - 1.59005i) q^{4} +(1.06427 + 2.15066i) q^{6} -4.40040 q^{7} +(-0.540334 + 2.77634i) q^{8} +0.120998 q^{9} +0.720144i q^{11} +(-2.69794 - 2.05842i) q^{12} +4.59595i q^{13} +(5.57753 - 2.76009i) q^{14} +(-1.05654 - 3.85794i) q^{16} +2.38420 q^{17} +(-0.153366 + 0.0758946i) q^{18} +0.899742i q^{19} +7.46643i q^{21} +(-0.451701 - 0.912788i) q^{22} +8.05029 q^{23} +(4.71078 + 0.916818i) q^{24} +(-2.88275 - 5.82539i) q^{26} -5.29559i q^{27} +(-5.33833 + 6.99687i) q^{28} +1.78194i q^{29} +9.07877 q^{31} +(3.75902 + 4.22727i) q^{32} +1.22191 q^{33} +(-3.02199 + 1.49546i) q^{34} +(0.146789 - 0.192394i) q^{36} +4.74502i q^{37} +(-0.564351 - 1.14043i) q^{38} +7.79823 q^{39} -2.82760 q^{41} +(-4.68322 - 9.46375i) q^{42} -10.7770i q^{43} +(1.14507 + 0.873642i) q^{44} +(-10.2038 + 5.04943i) q^{46} -4.99256 q^{47} +(-6.54601 + 1.79270i) q^{48} +12.3635 q^{49} -4.04541i q^{51} +(7.30780 + 5.57556i) q^{52} -9.74069i q^{53} +(3.32159 + 6.71220i) q^{54} +(2.37768 - 12.2170i) q^{56} +1.52665 q^{57} +(-1.11770 - 2.25863i) q^{58} -6.39947i q^{59} +0.635551i q^{61} +(-11.5074 + 5.69454i) q^{62} -0.532441 q^{63} +(-7.41608 - 3.00030i) q^{64} +(-1.54878 + 0.766429i) q^{66} +1.73643i q^{67} +(2.89238 - 3.79100i) q^{68} -13.6594i q^{69} -8.41146 q^{71} +(-0.0653795 + 0.335932i) q^{72} +13.0770 q^{73} +(-2.97625 - 6.01435i) q^{74} +(1.43064 + 1.09152i) q^{76} -3.16892i q^{77} +(-9.88431 + 4.89133i) q^{78} +7.19828 q^{79} -8.62236 q^{81} +(3.58401 - 1.77358i) q^{82} +0.219648i q^{83} +(11.8720 + 9.05788i) q^{84} +(6.75971 + 13.6599i) q^{86} +3.02354 q^{87} +(-1.99936 - 0.389118i) q^{88} +1.37331 q^{89} -20.2240i q^{91} +(9.76619 - 12.8004i) q^{92} -15.4045i q^{93} +(6.32811 - 3.13152i) q^{94} +(7.17267 - 6.37816i) q^{96} +8.41826 q^{97} +(-15.6708 + 7.75484i) q^{98} +0.0871363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9	\( 40 q + 6 q^{4} - 2 q^{6} - 24 q^{9} + 12 q^{14} + 18 q^{16} - 6 q^{24} + 20 q^{26} + 48 q^{31} - 6 q^{34} - 40 q^{36} + 8 q^{39} + 44 q^{41} + 8 q^{44} - 30 q^{46} + 12 q^{49} - 2 q^{54} + 50 q^{56} + 72 q^{64} + 42 q^{66} + 96 q^{71} + 6 q^{74} - 2 q^{76} + 96 q^{79} - 56 q^{81} + 116 q^{84} + 46 q^{86} - 44 q^{89} - 14 q^{94} + 12 q^{96}+O(q^{100}) \) 40 * q + 6 * q^4 - 2 * q^6 - 24 * q^9 + 12 * q^14 + 18 * q^16 - 6 * q^24 + 20 * q^26 + 48 * q^31 - 6 * q^34 - 40 * q^36 + 8 * q^39 + 44 * q^41 + 8 * q^44 - 30 * q^46 + 12 * q^49 - 2 * q^54 + 50 * q^56 + 72 * q^64 + 42 * q^66 + 96 * q^71 + 6 * q^74 - 2 * q^76 + 96 * q^79 - 56 * q^81 + 116 * q^84 + 46 * q^86 - 44 * q^89 - 14 * q^94 + 12 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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