LMFDB - Embedded newform 1000.2.d.c.501.7

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

$q$-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	$0.162935\pi$
$3$			1.69676i			0.979626i	−0.871828	+	0.489813i	$0.837065\pi$
$4$	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	$-0.965374\pi$
$11$		−	0.720144i		−	0.217132i	0.994089	−	0.108566i	$-0.0346258\pi$
$12$	−2.69794	+	2.05842i	−0.778829	+	0.594216i
$13$		−	4.59595i		−	1.27469i	−0.770580	−	0.637343i	$-0.780033\pi$
$13$		−	4.59595i		−	1.27469i	0.770580	−	0.637343i	$-0.219967\pi$
$14$	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	$-0.967089\pi$
$19$		−	0.899742i		−	0.206415i	0.994660	−	0.103208i	$-0.0329106\pi$
$20$		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	$-0.947093\pi$
$29$		−	1.78194i		−	0.330899i	0.986218	−	0.165449i	$-0.0529075\pi$
$30$		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	$-0.872462\pi$
$37$		−	4.74502i		−	0.780076i	0.920799	−	0.390038i	$-0.127538\pi$
$38$	−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	$0.306994\pi$
$43$			10.7770i			1.64347i	−0.569868	+	0.821736i	$0.693006\pi$
$44$	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	$0.233275\pi$
$53$			9.74069i			1.33799i	−0.743268	+	0.668994i	$0.766725\pi$
$54$	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	$0.136768\pi$
$59$			6.39947i			0.833141i	−0.909103	+	0.416570i	$0.863232\pi$
$60$		0			0
$61$		−	0.635551i		−	0.0813740i	−0.999172	−	0.0406870i	$-0.987045\pi$
$61$		−	0.635551i		−	0.0813740i	0.999172	−	0.0406870i	$-0.0129547\pi$
$62$	−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	$-0.966174\pi$
$67$		−	1.73643i		−	0.212138i	0.994359	−	0.106069i	$-0.0338265\pi$
$68$	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	$-0.996163\pi$
$83$		−	0.219648i		−	0.0241095i	0.999927	−	0.0120548i	$-0.00383724\pi$
$84$	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	$-0.670082\pi$
$101$		−	17.2981i		−	1.72122i	0.509264	−	0.860610i	$-0.329918\pi$
$102$	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	$-0.851599\pi$
$107$		−	9.29949i		−	0.899015i	0.893276	−	0.449508i	$-0.148401\pi$
$108$	−8.42028	+	6.42434i	−0.810241	+	0.618182i
$109$		−	19.0410i		−	1.82379i	−0.410418	−	0.911897i	$-0.634617\pi$
$109$		−	19.0410i		−	1.82379i	0.410418	−	0.911897i	$-0.365383\pi$
$110$		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	$0.199903\pi$
$131$			13.4494i			1.17508i	−0.809196	+	0.587538i	$0.800097\pi$
$132$	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	$-0.866110\pi$
$139$		−	9.62833i		−	0.816665i	0.912833	−	0.408332i	$-0.133890\pi$
$140$		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	$0.176685\pi$
$149$			12.8658i			1.05401i	−0.849862	+	0.527005i	$0.823315\pi$
$150$		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	$-0.725882\pi$
$157$		−	19.0105i		−	1.51721i	0.651553	−	0.758603i	$-0.274118\pi$
$158$	−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	$-0.809653\pi$
$163$		−	14.3754i		−	1.12597i	0.826468	−	0.562984i	$-0.190347\pi$
$164$	−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	$0.0359476\pi$
$173$			2.96448i			0.225385i	−0.993630	+	0.112693i	$0.964052\pi$
$174$	−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	$-0.803272\pi$
$179$		−	15.5047i		−	1.15888i	0.815016	−	0.579438i	$-0.196728\pi$
$180$		0			0
$181$			6.57069i			0.488395i	0.969725	+	0.244198i	$0.0785246\pi$
$181$			6.57069i			0.488395i	−0.969725	+	0.244198i	$0.921475\pi$
$182$	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	$0.212282\pi$
$197$			17.3637i			1.23711i	−0.785740	+	0.618557i	$0.787718\pi$
$198$	−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	$0.212576\pi$
$211$			17.9912i			1.23856i	−0.785169	+	0.619281i	$0.787424\pi$
$212$	−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	$-0.667976\pi$
$227$		−	26.0338i		−	1.72792i	0.503557	−	0.863962i	$-0.332024\pi$
$228$	1.85205	+	2.42745i	0.122655	+	0.160762i
$229$			13.9303i			0.920539i	0.887779	+	0.460269i	$0.152247\pi$
$229$			13.9303i			0.920539i	−0.887779	+	0.460269i	$0.847753\pi$
$230$		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	$0.197727\pi$
$251$			18.4410i			1.16399i	−0.813193	+	0.581993i	$0.802273\pi$
$252$	−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	$0.0714301\pi$
$269$			7.29938i			0.445051i	−0.974927	+	0.222526i	$0.928570\pi$
$270$		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	$0.0416463\pi$
$277$			4.34266i			0.260925i	−0.991453	+	0.130463i	$0.958354\pi$
$278$	−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	$0.264644\pi$
$283$			24.8597i			1.47776i	−0.673839	+	0.738879i	$0.735356\pi$
$284$	−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	$-0.788104\pi$
$293$		−	21.1433i		−	1.23521i	0.786490	−	0.617603i	$-0.211896\pi$
$294$	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	$-0.937698\pi$
$307$		−	6.81511i		−	0.388959i	0.980907	−	0.194479i	$-0.0623017\pi$
$308$	−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	$0.265354\pi$
$317$			26.3642i			1.48076i	−0.672189	+	0.740380i	$0.734646\pi$
$318$	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	$-0.684580\pi$
$331$		−	30.4387i		−	1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$332$	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	$0.0506106\pi$
$347$			5.89868i			0.316658i	−0.987386	+	0.158329i	$0.949389\pi$
$348$	3.66800	+	4.80759i	0.196625	+	0.257714i
$349$		−	18.7429i		−	1.00329i	−0.865075	−	0.501643i	$-0.832729\pi$
$349$		−	18.7429i		−	1.00329i	0.865075	−	0.501643i	$-0.167271\pi$
$350$		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	$-0.934513\pi$
$373$		−	7.89076i		−	0.408568i	0.978912	−	0.204284i	$-0.0654866\pi$
$374$	−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	$0.0357976\pi$
$379$			4.36955i			0.224449i	−0.993683	+	0.112224i	$0.964202\pi$
$380$		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	$-0.847678\pi$
$389$		−	18.1641i		−	0.920957i	0.887671	−	0.460478i	$-0.152322\pi$
$390$		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	$-0.841291\pi$
$397$		−	19.0559i		−	0.956389i	0.878254	−	0.478194i	$-0.158709\pi$
$398$	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	$-0.869679\pi$
$419$		−	16.2968i		−	0.796149i	0.917353	−	0.398074i	$-0.130321\pi$
$420$		0			0
$421$			13.3488i			0.650579i	0.945614	+	0.325290i	$0.105462\pi$
$421$			13.3488i			0.650579i	−0.945614	+	0.325290i	$0.894538\pi$
$422$	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	$0.0335369\pi$
$443$			4.42692i			0.210329i	−0.994455	+	0.105165i	$0.966463\pi$
$444$	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	$0.163131\pi$
$461$			21.0565i			0.980701i	−0.871525	+	0.490350i	$0.836869\pi$
$462$	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	$0.00685348\pi$
$467$			0.930499i			0.0430583i	−0.999768	+	0.0215292i	$0.993147\pi$
$468$	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	$-0.943875\pi$
$491$		−	7.77369i		−	0.350822i	0.984495	−	0.175411i	$-0.0561253\pi$
$492$	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	$-0.978404\pi$
$499$		−	3.02886i		−	0.135590i	0.997699	−	0.0677952i	$-0.0215964\pi$
$500$		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	$0.292239\pi$
$509$			35.8471i			1.58889i	−0.607334	+	0.794446i	$0.707761\pi$
$510$		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	$-0.827765\pi$
$523$		−	23.5586i		−	1.03015i	0.857146	−	0.515073i	$-0.172235\pi$
$524$	−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	$0.101273\pi$
$541$			14.5520i			0.625638i	−0.949813	+	0.312819i	$0.898727\pi$
$542$	−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	$0.0478624\pi$
$547$			7.00697i			0.299597i	−0.988717	+	0.149798i	$0.952138\pi$
$548$	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	$0.226907\pi$
$557$			30.8696i			1.30799i	−0.756501	+	0.653993i	$0.773093\pi$
$558$	−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	$-0.865003\pi$
$563$		−	19.5281i		−	0.823011i	0.911407	−	0.411505i	$-0.134997\pi$
$564$	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	$0.0240039\pi$
$571$			3.60054i			0.150678i	−0.997158	+	0.0753389i	$0.975996\pi$
$572$	−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	$0.0676236\pi$
$587$			10.2171i			0.421703i	−0.977518	+	0.210851i	$0.932376\pi$
$588$	−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	$0.129680\pi$
$613$			19.6201i			0.792448i	−0.918154	+	0.396224i	$0.870320\pi$
$614$	−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	$0.120024\pi$
$619$			18.3211i			0.736388i	−0.929749	+	0.368194i	$0.879976\pi$
$620$		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	$0.111525\pi$
$643$			17.4075i			0.686484i	−0.939247	+	0.343242i	$0.888475\pi$
$644$	−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	$0.0436331\pi$
$653$			6.98379i			0.273297i	−0.990620	+	0.136648i	$0.956367\pi$
$654$	−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	$0.0359566\pi$
$659$			5.78732i			0.225442i	−0.993627	+	0.112721i	$0.964043\pi$
$660$		0			0
$661$			29.6124i			1.15179i	0.817523	+	0.575895i	$0.195346\pi$
$661$			29.6124i			1.15179i	−0.817523	+	0.575895i	$0.804654\pi$
$662$	−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	$0.0833530\pi$
$677$			13.4716i			0.517757i	−0.965910	+	0.258879i	$0.916647\pi$
$678$	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	$0.295888\pi$
$683$			41.8857i			1.60271i	−0.598187	+	0.801356i	$0.704112\pi$
$684$	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	$-0.769651\pi$
$691$		−	34.8109i		−	1.32427i	0.749386	−	0.662134i	$-0.230349\pi$
$692$	−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	$0.295065\pi$
$701$			42.3521i			1.59962i	−0.600257	+	0.799808i	$0.704935\pi$
$702$	−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	$-0.923819\pi$
$709$		−	12.6239i		−	0.474102i	0.971497	−	0.237051i	$-0.0761809\pi$
$710$		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	$-0.862760\pi$
$733$		−	22.6294i		−	0.835837i	0.908485	−	0.417918i	$-0.137240\pi$
$734$	−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	$-0.838912\pi$
$739$		−	26.3553i		−	0.969494i	0.874654	−	0.484747i	$-0.161088\pi$
$740$		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	$0.0512050\pi$
$757$			8.81385i			0.320345i	−0.987089	+	0.160172i	$0.948795\pi$
$758$	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	$-0.942732\pi$
$773$		−	9.95026i		−	0.357886i	0.983859	−	0.178943i	$-0.0572678\pi$
$774$	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	$-0.660081\pi$
$787$		−	49.1601i		−	1.75237i	0.481975	−	0.876185i	$-0.339919\pi$
$788$	−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	$-0.700427\pi$
$797$		−	45.6344i		−	1.61645i	0.588871	−	0.808227i	$-0.299573\pi$
$798$	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	$-0.816373\pi$
$811$		−	31.0646i		−	1.09083i	0.838167	−	0.545413i	$-0.183627\pi$
$812$	−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	$-0.904391\pi$
$821$		−	16.9551i		−	0.591738i	0.955229	−	0.295869i	$-0.0956092\pi$
$822$	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	$0.0638474\pi$
$827$			11.4594i			0.398481i	−0.979951	+	0.199240i	$0.936153\pi$
$828$	1.18169	+	1.54883i	0.0410667	+	0.0538254i
$829$		−	3.98218i		−	0.138307i	−0.997606	−	0.0691534i	$-0.977970\pi$
$829$		−	3.98218i		−	0.138307i	0.997606	−	0.0691534i	$-0.0220298\pi$
$830$		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	$-0.834836\pi$
$853$		−	28.9671i		−	0.991814i	0.868376	−	0.495907i	$-0.165164\pi$
$854$	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	$0.0650057\pi$
$859$			11.8879i			0.405610i	−0.979219	+	0.202805i	$0.934994\pi$
$860$		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	$0.204079\pi$
$877$			35.4248i			1.19621i	−0.801418	+	0.598105i	$0.795921\pi$
$878$	−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	$-0.982254\pi$
$883$		−	3.31152i		−	0.111442i	0.998446	−	0.0557208i	$-0.0177457\pi$
$884$	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	$0.130208\pi$
$907$			23.9575i			0.795495i	−0.917495	+	0.397747i	$0.869792\pi$
$908$	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	$0.160397\pi$
$941$			29.6233i			0.965691i	−0.875706	+	0.482845i	$0.839603\pi$
$942$	−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	$0.000492645\pi$
$947$			0.0952553i			0.00309538i	−0.999999	+	0.00154769i	$0.999507\pi$
$948$	−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	$-0.668739\pi$
$971$		−	53.7682i		−	1.72550i	0.505627	−	0.862752i	$-0.331261\pi$
$972$	−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	$-0.937457\pi$
$997$		−	12.3284i		−	0.390444i	0.980759	−	0.195222i	$-0.0625427\pi$
$998$	−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.501.7	✓	40
4.3	odd	2		4000.2.d.c.2001.1		40
5.2	odd	4		1000.2.f.d.749.13		20
5.3	odd	4		1000.2.f.c.749.8		20
5.4	even	2	inner	1000.2.d.c.501.34	yes	40
8.3	odd	2		4000.2.d.c.2001.2		40
8.5	even	2	inner	1000.2.d.c.501.8	yes	40
20.3	even	4		4000.2.f.c.3249.15		20
20.7	even	4		4000.2.f.d.3249.6		20
20.19	odd	2		4000.2.d.c.2001.40		40
40.3	even	4		4000.2.f.d.3249.5		20
40.13	odd	4		1000.2.f.d.749.14		20
40.19	odd	2		4000.2.d.c.2001.39		40
40.27	even	4		4000.2.f.c.3249.16		20
40.29	even	2	inner	1000.2.d.c.501.33	yes	40
40.37	odd	4		1000.2.f.c.749.7		20

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