LMFDB - Embedded newform 1020.3.bc.a.701.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(701,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1020.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bc (of order $4$, degree $2$, 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:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			701.1
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99983 - 0.0319133i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-2.18976 - 2.18976i) q^{7} +(8.99796 + 0.191469i) q^{9} +O(q^{10})$	\(q+(-2.99983 - 0.0319133i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-2.18976 - 2.18976i) q^{7} +(8.99796 + 0.191469i) q^{9} +(2.26356 - 2.26356i) q^{11} -4.05188 q^{13} +(-4.69269 - 4.79361i) q^{15} +(-11.1590 - 12.8248i) q^{17} +11.8967i q^{19} +(6.49904 + 6.63880i) q^{21} +(-0.0371822 + 0.0371822i) q^{23} +5.00000i q^{25} +(-26.9863 - 0.861530i) q^{27} +(34.6140 + 34.6140i) q^{29} +(-9.04346 + 9.04346i) q^{31} +(-6.86253 + 6.71805i) q^{33} -6.92464i q^{35} +(36.4906 - 36.4906i) q^{37} +(12.1550 + 0.129309i) q^{39} +(-43.0142 + 43.0142i) q^{41} -76.4038i q^{43} +(13.9243 + 14.5298i) q^{45} +20.9618i q^{47} -39.4099i q^{49} +(33.0659 + 38.8284i) q^{51} +32.5614 q^{53} +7.15800 q^{55} +(0.379664 - 35.6881i) q^{57} -110.898 q^{59} +(-29.2924 - 29.2924i) q^{61} +(-19.2841 - 20.1227i) q^{63} +(-6.40659 - 6.40659i) q^{65} -32.0851 q^{67} +(0.112727 - 0.110354i) q^{69} +(-43.3816 - 43.3816i) q^{71} +(-49.8925 + 49.8925i) q^{73} +(0.159567 - 14.9992i) q^{75} -9.91332 q^{77} +(-50.0620 - 50.0620i) q^{79} +(80.9267 + 3.44567i) q^{81} -120.012 q^{83} +(2.63383 - 37.9218i) q^{85} +(-102.732 - 104.941i) q^{87} -31.9624i q^{89} +(8.87266 + 8.87266i) q^{91} +(27.4175 - 26.8402i) q^{93} +(-18.8104 + 18.8104i) q^{95} +(70.2744 - 70.2744i) q^{97} +(20.8008 - 19.9340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{3}+O(q^{10}) $ 96 * q - 8 * q^3	$ 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) $ 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.99983	−	0.0319133i	−0.999943	−	0.0106378i
$3$	−2.99983	−	0.0319133i	−0.999943	−	0.0106378i
$4$		0			0
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$		0			0
$7$	−2.18976	−	2.18976i	−0.312823	−	0.312823i	0.533179	−	0.846002i	$-0.320997\pi$
$7$	−2.18976	−	2.18976i	−0.312823	−	0.312823i	−0.846002	+	0.533179i	$0.820997\pi$
$8$		0			0
$9$	8.99796	+	0.191469i	0.999774	+	0.0212744i
$10$		0			0
$11$	2.26356	−	2.26356i	0.205778	−	0.205778i	−0.596692	−	0.802470i	$-0.703519\pi$
$11$	2.26356	−	2.26356i	0.205778	−	0.205778i	0.802470	+	0.596692i	$0.203519\pi$
$12$		0			0
$13$	−4.05188			−0.311683			−0.155842	−	0.987782i	$-0.549809\pi$
$13$	−4.05188			−0.311683			−0.155842	+	0.987782i	$0.549809\pi$
$14$		0			0
$15$	−4.69269	−	4.79361i	−0.312846	−	0.319574i
$16$		0			0
$17$	−11.1590	−	12.8248i	−0.656414	−	0.754401i
$17$	−11.1590	−	12.8248i	−0.656414	−	0.754401i
$18$		0			0
$19$			11.8967i			0.626143i	0.949730	+	0.313072i	$0.101358\pi$
$19$			11.8967i			0.626143i	−0.949730	+	0.313072i	$0.898642\pi$
$20$		0			0
$21$	6.49904	+	6.63880i	0.309478	+	0.316133i
$22$		0			0
$23$	−0.0371822	+	0.0371822i	−0.00161662	+	0.00161662i	−0.707915	−	0.706298i	$-0.750364\pi$
$23$	−0.0371822	+	0.0371822i	−0.00161662	+	0.00161662i	0.706298	+	0.707915i	$0.250364\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	−26.9863	−	0.861530i	−0.999491	−	0.0319085i
$28$		0			0
$29$	34.6140	+	34.6140i	1.19359	+	1.19359i	0.976053	+	0.217534i	$0.0698013\pi$
$29$	34.6140	+	34.6140i	1.19359	+	1.19359i	0.217534	+	0.976053i	$0.430199\pi$
$30$		0			0
$31$	−9.04346	+	9.04346i	−0.291725	+	0.291725i	−0.837761	−	0.546037i	$-0.816136\pi$
$31$	−9.04346	+	9.04346i	−0.291725	+	0.291725i	0.546037	+	0.837761i	$0.316136\pi$
$32$		0			0
$33$	−6.86253	+	6.71805i	−0.207955	+	0.203577i
$34$		0			0
$35$		−	6.92464i		−	0.197847i
$36$		0			0
$37$	36.4906	−	36.4906i	0.986232	−	0.986232i	−0.0136742	−	0.999907i	$-0.504353\pi$
$37$	36.4906	−	36.4906i	0.986232	−	0.986232i	0.999907	+	0.0136742i	$0.00435277\pi$
$38$		0			0
$39$	12.1550	+	0.129309i	0.311665	+	0.00331562i
$40$		0			0
$41$	−43.0142	+	43.0142i	−1.04913	+	1.04913i	−0.0503978	+	0.998729i	$0.516049\pi$
$41$	−43.0142	+	43.0142i	−1.04913	+	1.04913i	−0.998729	+	0.0503978i	$0.983951\pi$
$42$		0			0
$43$		−	76.4038i		−	1.77683i	−0.459038	−	0.888417i	$-0.651806\pi$
$43$		−	76.4038i		−	1.77683i	0.459038	−	0.888417i	$-0.348194\pi$
$44$		0			0
$45$	13.9243	+	14.5298i	0.309429	+	0.322884i
$46$		0			0
$47$			20.9618i			0.445997i	0.974819	+	0.222998i	$0.0715844\pi$
$47$			20.9618i			0.445997i	−0.974819	+	0.222998i	$0.928416\pi$
$48$		0			0
$49$		−	39.4099i		−	0.804283i
$50$		0			0
$51$	33.0659	+	38.8284i	0.648352	+	0.761341i
$52$		0			0
$53$	32.5614			0.614366			0.307183	−	0.951651i	$-0.400614\pi$
$53$	32.5614			0.614366			0.307183	+	0.951651i	$0.400614\pi$
$54$		0			0
$55$	7.15800			0.130145
$56$		0			0
$57$	0.379664	−	35.6881i	0.00666077	−	0.626108i
$58$		0			0
$59$	−110.898			−1.87963			−0.939814	−	0.341688i	$-0.889002\pi$
$59$	−110.898			−1.87963			−0.939814	+	0.341688i	$0.889002\pi$
$60$		0			0
$61$	−29.2924	−	29.2924i	−0.480203	−	0.480203i	0.424993	−	0.905196i	$-0.360276\pi$
$61$	−29.2924	−	29.2924i	−0.480203	−	0.480203i	−0.905196	+	0.424993i	$0.860276\pi$
$62$		0			0
$63$	−19.2841	−	20.1227i	−0.306098	−	0.319408i
$64$		0			0
$65$	−6.40659	−	6.40659i	−0.0985629	−	0.0985629i
$66$		0			0
$67$	−32.0851			−0.478882			−0.239441	−	0.970911i	$-0.576964\pi$
$67$	−32.0851			−0.478882			−0.239441	+	0.970911i	$0.576964\pi$
$68$		0			0
$69$	0.112727	−	0.110354i	0.00163372	−	0.00159933i
$70$		0			0
$71$	−43.3816	−	43.3816i	−0.611008	−	0.611008i	0.332200	−	0.943209i	$-0.392209\pi$
$71$	−43.3816	−	43.3816i	−0.611008	−	0.611008i	−0.943209	+	0.332200i	$0.892209\pi$
$72$		0			0
$73$	−49.8925	+	49.8925i	−0.683458	+	0.683458i	−0.960778	−	0.277319i	$-0.910554\pi$
$73$	−49.8925	+	49.8925i	−0.683458	+	0.683458i	0.277319	+	0.960778i	$0.410554\pi$
$74$		0			0
$75$	0.159567	−	14.9992i	0.00212756	−	0.199989i
$76$		0			0
$77$	−9.91332			−0.128744
$78$		0			0
$79$	−50.0620	−	50.0620i	−0.633696	−	0.633696i	0.315297	−	0.948993i	$-0.397896\pi$
$79$	−50.0620	−	50.0620i	−0.633696	−	0.633696i	−0.948993	+	0.315297i	$0.897896\pi$
$80$		0			0
$81$	80.9267	+	3.44567i	0.999095	+	0.0425391i
$82$		0			0
$83$	−120.012			−1.44593			−0.722965	−	0.690885i	$-0.757221\pi$
$83$	−120.012			−1.44593			−0.722965	+	0.690885i	$0.757221\pi$
$84$		0			0
$85$	2.63383	−	37.9218i	0.0309862	−	0.446139i
$86$		0			0
$87$	−102.732	−	104.941i	−1.18082	−	1.20622i
$88$		0			0
$89$		−	31.9624i		−	0.359128i	−0.983746	−	0.179564i	$-0.942531\pi$
$89$		−	31.9624i		−	0.359128i	0.983746	−	0.179564i	$-0.0574687\pi$
$90$		0			0
$91$	8.87266	+	8.87266i	0.0975018	+	0.0975018i
$92$		0			0
$93$	27.4175	−	26.8402i	0.294811	−	0.288605i
$94$		0			0
$95$	−18.8104	+	18.8104i	−0.198004	+	0.198004i
$96$		0			0
$97$	70.2744	−	70.2744i	0.724478	−	0.724478i	−0.245036	−	0.969514i	$-0.578800\pi$
$97$	70.2744	−	70.2744i	0.724478	−	0.724478i	0.969514	+	0.245036i	$0.0787997\pi$
$98$		0			0
$99$	20.8008	−	19.9340i	0.210109	−	0.201354i
$100$		0			0
$101$			52.8752i			0.523517i	0.965133	+	0.261759i	$0.0843024\pi$
$101$			52.8752i			0.523517i	−0.965133	+	0.261759i	$0.915698\pi$
$102$		0			0
$103$	−114.454			−1.11120			−0.555601	−	0.831449i	$-0.687512\pi$
$103$	−114.454			−1.11120			−0.555601	+	0.831449i	$0.687512\pi$
$104$		0			0
$105$	−0.220989	+	20.7728i	−0.00210465	+	0.197836i
$106$		0			0
$107$	−80.1008	−	80.1008i	−0.748606	−	0.748606i	0.225612	−	0.974217i	$-0.427562\pi$
$107$	−80.1008	−	80.1008i	−0.748606	−	0.748606i	−0.974217	+	0.225612i	$0.927562\pi$
$108$		0			0
$109$	−85.9591	−	85.9591i	−0.788615	−	0.788615i	0.192652	−	0.981267i	$-0.438291\pi$
$109$	−85.9591	−	85.9591i	−0.788615	−	0.788615i	−0.981267	+	0.192652i	$0.938291\pi$
$110$		0			0
$111$	−110.630	+	108.301i	−0.996668	+	0.975685i
$112$		0			0
$113$	47.0253	−	47.0253i	0.416153	−	0.416153i	−0.467722	−	0.883875i	$-0.654925\pi$
$113$	47.0253	−	47.0253i	0.416153	−	0.416153i	0.883875	+	0.467722i	$0.154925\pi$
$114$		0			0
$115$	−0.117581			−0.00102244
$116$		0			0
$117$	−36.4587	−	0.775811i	−0.311613	−	0.00663086i
$118$		0			0
$119$	−3.64766	+	52.5190i	−0.0306526	+	0.441336i
$120$		0			0
$121$			110.753i			0.915311i
$122$		0			0
$123$	130.408	−	127.663i	1.06023	−	1.03791i
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	168.170i		−	1.32418i	−0.749426	−	0.662088i	$-0.769670\pi$
$127$		−	168.170i		−	1.32418i	0.749426	−	0.662088i	$-0.230330\pi$
$128$		0			0
$129$	−2.43830	+	229.199i	−0.0189016	+	1.77673i
$130$		0			0
$131$	−67.1436	−	67.1436i	−0.512546	−	0.512546i	0.402760	−	0.915306i	$-0.368051\pi$
$131$	−67.1436	−	67.1436i	−0.512546	−	0.512546i	−0.915306	+	0.402760i	$0.868051\pi$
$132$		0			0
$133$	26.0510	−	26.0510i	0.195872	−	0.195872i
$134$		0			0
$135$	−41.3068	−	44.0312i	−0.305976	−	0.326157i
$136$		0			0
$137$			163.185i			1.19113i	0.803308	+	0.595564i	$0.203071\pi$
$137$			163.185i			1.19113i	−0.803308	+	0.595564i	$0.796929\pi$
$138$		0			0
$139$	160.879	−	160.879i	1.15740	−	1.15740i	0.172367	−	0.985033i	$-0.444858\pi$
$139$	160.879	−	160.879i	1.15740	−	1.15740i	0.985033	−	0.172367i	$-0.0551416\pi$
$140$		0			0
$141$	0.668963	−	62.8820i	0.00474441	−	0.445971i
$142$		0			0
$143$	−9.17167	+	9.17167i	−0.0641376	+	0.0641376i
$144$		0			0
$145$			109.459i			0.754891i
$146$		0			0
$147$	−1.25770	+	118.223i	−0.00855579	+	0.804237i
$148$		0			0
$149$		−	203.079i		−	1.36295i	−0.731843	−	0.681473i	$-0.761340\pi$
$149$		−	203.079i		−	1.36295i	0.731843	−	0.681473i	$-0.238660\pi$
$150$		0			0
$151$			83.3600i			0.552053i	0.961150	+	0.276027i	$0.0890178\pi$
$151$			83.3600i			0.552053i	−0.961150	+	0.276027i	$0.910982\pi$
$152$		0			0
$153$	−97.9530	−	117.534i	−0.640216	−	0.768195i
$154$		0			0
$155$	−28.5979			−0.184503
$156$		0			0
$157$	−293.578			−1.86992			−0.934961	−	0.354751i	$-0.884566\pi$
$157$	−293.578			−1.86992			−0.934961	+	0.354751i	$0.884566\pi$
$158$		0			0
$159$	−97.6786	−	1.03914i	−0.614331	−	0.00653549i
$160$		0			0
$161$	0.162841			0.00101143
$162$		0			0
$163$	−179.646	−	179.646i	−1.10213	−	1.10213i	−0.994154	−	0.107971i	$-0.965565\pi$
$163$	−179.646	−	179.646i	−1.10213	−	1.10213i	−0.107971	−	0.994154i	$-0.534435\pi$
$164$		0			0
$165$	−21.4728	−	0.228436i	−0.130138	−	0.00138446i
$166$		0			0
$167$	109.032	+	109.032i	0.652883	+	0.652883i	0.953686	−	0.300803i	$-0.0972547\pi$
$167$	109.032	+	109.032i	0.652883	+	0.652883i	−0.300803	+	0.953686i	$0.597255\pi$
$168$		0			0
$169$	−152.582			−0.902854
$170$		0			0
$171$	−2.27786	+	107.046i	−0.0133208	+	0.626001i
$172$		0			0
$173$	−69.2385	−	69.2385i	−0.400223	−	0.400223i	0.478089	−	0.878311i	$-0.341330\pi$
$173$	−69.2385	−	69.2385i	−0.400223	−	0.400223i	−0.878311	+	0.478089i	$0.841330\pi$
$174$		0			0
$175$	10.9488	−	10.9488i	0.0625647	−	0.0625647i
$176$		0			0
$177$	332.675	+	3.53913i	1.87952	+	0.0199951i
$178$		0			0
$179$	−116.820			−0.652625			−0.326313	−	0.945262i	$-0.605806\pi$
$179$	−116.820			−0.652625			−0.326313	+	0.945262i	$0.605806\pi$
$180$		0			0
$181$	107.530	+	107.530i	0.594089	+	0.594089i	0.938733	−	0.344644i	$-0.112000\pi$
$181$	107.530	+	107.530i	0.594089	+	0.594089i	−0.344644	+	0.938733i	$0.612000\pi$
$182$		0			0
$183$	86.9374	+	88.8070i	0.475068	+	0.485284i
$184$		0			0
$185$	115.393			0.623748
$186$		0			0
$187$	−54.2889	−	3.77059i	−0.290315	−	0.0201636i
$188$		0			0
$189$	57.2070	+	60.9801i	0.302682	+	0.322646i
$190$		0			0
$191$			132.320i			0.692776i	0.938091	+	0.346388i	$0.112592\pi$
$191$			132.320i			0.692776i	−0.938091	+	0.346388i	$0.887408\pi$
$192$		0			0
$193$	−162.586	−	162.586i	−0.842414	−	0.842414i	0.146758	−	0.989172i	$-0.453116\pi$
$193$	−162.586	−	162.586i	−0.842414	−	0.842414i	−0.989172	+	0.146758i	$0.953116\pi$
$194$		0			0
$195$	19.0142	+	19.4231i	0.0975088	+	0.0996058i
$196$		0			0
$197$	−64.0240	+	64.0240i	−0.324995	+	0.324995i	−0.850680	−	0.525685i	$-0.823809\pi$
$197$	−64.0240	+	64.0240i	−0.324995	+	0.324995i	0.525685	+	0.850680i	$0.323809\pi$
$198$		0			0
$199$	11.6305	−	11.6305i	0.0584446	−	0.0584446i	−0.677280	−	0.735725i	$-0.736842\pi$
$199$	11.6305	−	11.6305i	0.0584446	−	0.0584446i	0.735725	+	0.677280i	$0.236842\pi$
$200$		0			0
$201$	96.2498	+	1.02394i	0.478855	+	0.00509424i
$202$		0			0
$203$		−	151.593i		−	0.746764i
$204$		0			0
$205$	−136.023			−0.663526
$206$		0			0
$207$	−0.341683	+	0.327445i	−0.00165064	+	0.00158186i
$208$		0			0
$209$	26.9289	+	26.9289i	0.128847	+	0.128847i
$210$		0			0
$211$	235.432	+	235.432i	1.11579	+	1.11579i	0.992352	+	0.123440i	$0.0393926\pi$
$211$	235.432	+	235.432i	1.11579	+	1.11579i	0.123440	+	0.992352i	$0.460607\pi$
$212$		0			0
$213$	128.753	+	131.522i	0.604474	+	0.617474i
$214$		0			0
$215$	120.805	−	120.805i	0.561884	−	0.561884i
$216$		0			0
$217$	39.6061			0.182517
$218$		0			0
$219$	151.261	−	148.077i	0.690690	−	0.676149i
$220$		0			0
$221$	45.2151	+	51.9646i	0.204593	+	0.235134i
$222$		0			0
$223$		−	202.839i		−	0.909590i	−0.890596	−	0.454795i	$-0.849712\pi$
$223$		−	202.839i		−	0.909590i	0.890596	−	0.454795i	$-0.150288\pi$
$224$		0			0
$225$	−0.957346	+	44.9898i	−0.00425487	+	0.199955i
$226$		0			0
$227$	40.2369	−	40.2369i	0.177255	−	0.177255i	−0.612903	−	0.790158i	$-0.709998\pi$
$227$	40.2369	−	40.2369i	0.177255	−	0.177255i	0.790158	+	0.612903i	$0.209998\pi$
$228$		0			0
$229$		−	58.1423i		−	0.253897i	−0.991909	−	0.126948i	$-0.959482\pi$
$229$		−	58.1423i		−	0.253897i	0.991909	−	0.126948i	$-0.0405182\pi$
$230$		0			0
$231$	29.7383	+	0.316367i	0.128737	+	0.00136955i
$232$		0			0
$233$	320.383	+	320.383i	1.37504	+	1.37504i	0.852803	+	0.522232i	$0.174901\pi$
$233$	320.383	+	320.383i	1.37504	+	1.37504i	0.522232	+	0.852803i	$0.325099\pi$
$234$		0			0
$235$	−33.1436	+	33.1436i	−0.141037	+	0.141037i
$236$		0			0
$237$	148.580	+	151.775i	0.626919	+	0.640401i
$238$		0			0
$239$		−	228.154i		−	0.954619i	−0.878735	−	0.477309i	$-0.841612\pi$
$239$		−	228.154i		−	0.954619i	0.878735	−	0.477309i	$-0.158388\pi$
$240$		0			0
$241$	69.8928	−	69.8928i	0.290011	−	0.290011i	−0.547073	−	0.837085i	$-0.684258\pi$
$241$	69.8928	−	69.8928i	0.290011	−	0.290011i	0.837085	+	0.547073i	$0.184258\pi$
$242$		0			0
$243$	−242.656	−	12.9191i	−0.998586	−	0.0531648i
$244$		0			0
$245$	62.3125	−	62.3125i	0.254337	−	0.254337i
$246$		0			0
$247$		−	48.2041i		−	0.195158i
$248$		0			0
$249$	360.016	+	3.82999i	1.44585	+	0.0153815i
$250$		0			0
$251$			296.478i			1.18119i	0.806968	+	0.590594i	$0.201107\pi$
$251$			296.478i			1.18119i	−0.806968	+	0.590594i	$0.798893\pi$
$252$		0			0
$253$			0.168328i			0.000665329i
$254$		0			0
$255$	−9.11124	+	113.675i	−0.0357304	+	0.445784i
$256$		0			0
$257$	155.098			0.603494			0.301747	−	0.953388i	$-0.402430\pi$
$257$	155.098			0.603494			0.301747	+	0.953388i	$0.402430\pi$
$258$		0			0
$259$	−159.812			−0.617033
$260$		0			0
$261$	304.828	+	318.083i	1.16792	+	1.21871i
$262$		0			0
$263$	362.898			1.37984			0.689919	−	0.723886i	$-0.257646\pi$
$263$	362.898			1.37984			0.689919	+	0.723886i	$0.257646\pi$
$264$		0			0
$265$	51.4841	+	51.4841i	0.194279	+	0.194279i
$266$		0			0
$267$	−1.02003	+	95.8817i	−0.00382032	+	0.359108i
$268$		0			0
$269$	154.130	+	154.130i	0.572975	+	0.572975i	0.932959	−	0.359983i	$-0.117218\pi$
$269$	154.130	+	154.130i	0.572975	+	0.572975i	−0.359983	+	0.932959i	$0.617218\pi$
$270$		0			0
$271$	−111.667			−0.412054			−0.206027	−	0.978546i	$-0.566053\pi$
$271$	−111.667			−0.412054			−0.206027	+	0.978546i	$0.566053\pi$
$272$		0			0
$273$	−26.3333	−	26.8996i	−0.0964591	−	0.0985335i
$274$		0			0
$275$	11.3178	+	11.3178i	0.0411556	+	0.0411556i
$276$		0			0
$277$	−20.5155	+	20.5155i	−0.0740633	+	0.0740633i	−0.743168	−	0.669105i	$-0.766678\pi$
$277$	−20.5155	+	20.5155i	−0.0740633	+	0.0740633i	0.669105	+	0.743168i	$0.266678\pi$
$278$		0			0
$279$	−83.1043	+	79.6412i	−0.297865	+	0.285452i
$280$		0			0
$281$	−66.1666			−0.235468			−0.117734	−	0.993045i	$-0.537563\pi$
$281$	−66.1666			−0.235468			−0.117734	+	0.993045i	$0.537563\pi$
$282$		0			0
$283$	161.400	+	161.400i	0.570317	+	0.570317i	0.932217	−	0.361900i	$-0.117872\pi$
$283$	161.400	+	161.400i	0.570317	+	0.570317i	−0.361900	+	0.932217i	$0.617872\pi$
$284$		0			0
$285$	57.0282	−	55.8276i	0.200099	−	0.195886i
$286$		0			0
$287$	188.382			0.656383
$288$		0			0
$289$	−39.9518	+	286.225i	−0.138241	+	0.990399i
$290$		0			0
$291$	−213.054	+	208.569i	−0.732144	+	0.716730i
$292$		0			0
$293$		−	246.594i		−	0.841619i	−0.907149	−	0.420809i	$-0.861746\pi$
$293$		−	246.594i		−	0.841619i	0.907149	−	0.420809i	$-0.138254\pi$
$294$		0			0
$295$	−175.345	−	175.345i	−0.594390	−	0.594390i
$296$		0			0
$297$	−63.0351	+	59.1348i	−0.212239	+	0.199107i
$298$		0			0
$299$	0.150658	−	0.150658i	0.000503873	−	0.000503873i
$300$		0			0
$301$	−167.306	+	167.306i	−0.555835	+	0.555835i
$302$		0			0
$303$	1.68743	−	158.617i	0.00556906	−	0.523487i
$304$		0			0
$305$		−	92.6306i		−	0.303707i
$306$		0			0
$307$	−93.4312			−0.304336			−0.152168	−	0.988355i	$-0.548625\pi$
$307$	−93.4312			−0.304336			−0.152168	+	0.988355i	$0.548625\pi$
$308$		0			0
$309$	343.342	+	3.65260i	1.11114	+	0.0118207i
$310$		0			0
$311$	205.615	+	205.615i	0.661143	+	0.661143i	0.955649	−	0.294506i	$-0.0951553\pi$
$311$	205.615	+	205.615i	0.661143	+	0.661143i	−0.294506	+	0.955649i	$0.595155\pi$
$312$		0			0
$313$	−15.2743	−	15.2743i	−0.0487998	−	0.0487998i	0.682286	−	0.731086i	$-0.260986\pi$
$313$	−15.2743	−	15.2743i	−0.0487998	−	0.0487998i	−0.731086	+	0.682286i	$0.760986\pi$
$314$		0			0
$315$	1.32586	−	62.3077i	0.00420907	−	0.197802i
$316$		0			0
$317$	64.8545	−	64.8545i	0.204588	−	0.204588i	−0.597374	−	0.801963i	$-0.703789\pi$
$317$	64.8545	−	64.8545i	0.204588	−	0.204588i	0.801963	+	0.597374i	$0.203789\pi$
$318$		0			0
$319$	156.702			0.491228
$320$		0			0
$321$	237.733	+	242.845i	0.740600	+	0.756527i
$322$		0			0
$323$	152.573	−	132.756i	0.472363	−	0.411009i
$324$		0			0
$325$		−	20.2594i		−	0.0623366i
$326$		0			0
$327$	255.119	+	260.606i	0.780182	+	0.796960i
$328$		0			0
$329$	45.9015	−	45.9015i	0.139518	−	0.139518i
$330$		0			0
$331$		−	301.229i		−	0.910058i	−0.890477	−	0.455029i	$-0.849629\pi$
$331$		−	301.229i		−	0.910058i	0.890477	−	0.455029i	$-0.150371\pi$
$332$		0			0
$333$	335.328	−	321.354i	1.00699	−	0.965028i
$334$		0			0
$335$	−50.7310	−	50.7310i	−0.151436	−	0.151436i
$336$		0			0
$337$	111.565	−	111.565i	0.331054	−	0.331054i	−0.521932	−	0.852987i	$-0.674789\pi$
$337$	111.565	−	111.565i	0.331054	−	0.331054i	0.852987	+	0.521932i	$0.174789\pi$
$338$		0			0
$339$	−142.569	+	139.567i	−0.420556	+	0.411703i
$340$		0			0
$341$			40.9408i			0.120061i
$342$		0			0
$343$	−193.597	+	193.597i	−0.564422	+	0.564422i
$344$		0			0
$345$	0.352722	+	0.00375239i	0.00102238	+	1.08765e-5i
$346$		0			0
$347$	−342.677	+	342.677i	−0.987543	+	0.987543i	−0.999923	−	0.0123807i	$-0.996059\pi$
$347$	−342.677	+	342.677i	−0.987543	+	0.987543i	0.0123807	+	0.999923i	$0.496059\pi$
$348$		0			0
$349$			406.942i			1.16602i	0.812464	+	0.583011i	$0.198126\pi$
$349$			406.942i			1.16602i	−0.812464	+	0.583011i	$0.801874\pi$
$350$		0			0
$351$	109.345	+	3.49082i	0.311524	+	0.00994535i
$352$		0			0
$353$		−	606.185i		−	1.71724i	−0.512614	−	0.858619i	$-0.671323\pi$
$353$		−	606.185i		−	1.71724i	0.512614	−	0.858619i	$-0.328677\pi$
$354$		0			0
$355$		−	137.185i		−	0.386436i
$356$		0			0
$357$	12.6184	−	157.432i	0.0353457	−	0.440985i
$358$		0			0
$359$	−124.228			−0.346039			−0.173020	−	0.984918i	$-0.555352\pi$
$359$	−124.228			−0.346039			−0.173020	+	0.984918i	$0.555352\pi$
$360$		0			0
$361$	219.468			0.607945
$362$		0			0
$363$	3.53449	−	332.239i	0.00973688	−	0.915259i
$364$		0			0
$365$	−157.774			−0.432257
$366$		0			0
$367$	154.973	+	154.973i	0.422271	+	0.422271i	0.885985	−	0.463714i	$-0.153483\pi$
$367$	154.973	+	154.973i	0.422271	+	0.422271i	−0.463714	+	0.885985i	$0.653483\pi$
$368$		0			0
$369$	−395.276	+	378.804i	−1.07121	+	1.02657i
$370$		0			0
$371$	−71.3017	−	71.3017i	−0.192188	−	0.192188i
$372$		0			0
$373$	−710.992			−1.90614			−0.953072	−	0.302744i	$-0.902097\pi$
$373$	−710.992			−1.90614			−0.953072	+	0.302744i	$0.902097\pi$
$374$		0			0
$375$	23.9680	−	23.4634i	0.0639148	−	0.0625692i
$376$		0			0
$377$	−140.252	−	140.252i	−0.372021	−	0.372021i
$378$		0			0
$379$	−219.606	+	219.606i	−0.579435	+	0.579435i	−0.934748	−	0.355312i	$-0.884374\pi$
$379$	−219.606	+	219.606i	−0.579435	+	0.579435i	0.355312	+	0.934748i	$0.384374\pi$
$380$		0			0
$381$	−5.36688	+	504.483i	−0.0140863	+	1.32410i
$382$		0			0
$383$	−95.8461			−0.250251			−0.125126	−	0.992141i	$-0.539933\pi$
$383$	−95.8461			−0.250251			−0.125126	+	0.992141i	$0.539933\pi$
$384$		0			0
$385$	−15.6743	−	15.6743i	−0.0407126	−	0.0407126i
$386$		0			0
$387$	14.6290	−	687.479i	0.0378010	−	1.77643i
$388$		0			0
$389$	−395.217			−1.01598			−0.507991	−	0.861362i	$-0.669612\pi$
$389$	−395.217			−1.01598			−0.507991	+	0.861362i	$0.669612\pi$
$390$		0			0
$391$	0.891773	+	0.0619373i	0.00228075	+	0.000158407i
$392$		0			0
$393$	199.277	+	203.562i	0.507065	+	0.517970i
$394$		0			0
$395$		−	158.310i		−	0.400784i
$396$		0			0
$397$	219.428	+	219.428i	0.552715	+	0.552715i	0.927224	−	0.374508i	$-0.122188\pi$
$397$	219.428	+	219.428i	0.552715	+	0.552715i	−0.374508	+	0.927224i	$0.622188\pi$
$398$		0			0
$399$	−78.9800	+	77.3172i	−0.197945	+	0.193778i
$400$		0			0
$401$	−55.6727	+	55.6727i	−0.138835	+	0.138835i	−0.773108	−	0.634274i	$-0.781299\pi$
$401$	−55.6727	+	55.6727i	−0.138835	+	0.138835i	0.634274	+	0.773108i	$0.281299\pi$
$402$		0			0
$403$	36.6430	−	36.6430i	0.0909256	−	0.0909256i
$404$		0			0
$405$	122.508	+	133.404i	0.302489	+	0.329394i
$406$		0			0
$407$		−	165.197i		−	0.405890i
$408$		0			0
$409$	9.52262			0.0232827			0.0116413	−	0.999932i	$-0.496294\pi$
$409$	9.52262			0.0232827			0.0116413	+	0.999932i	$0.496294\pi$
$410$		0			0
$411$	5.20777	−	489.526i	0.0126710	−	1.19106i
$412$		0			0
$413$	242.840	+	242.840i	0.587991	+	0.587991i
$414$		0			0
$415$	−189.756	−	189.756i	−0.457243	−	0.457243i
$416$		0			0
$417$	−487.743	+	477.474i	−1.16965	+	1.14502i
$418$		0			0
$419$	−20.8675	+	20.8675i	−0.0498030	+	0.0498030i	−0.731570	−	0.681767i	$-0.761212\pi$
$419$	−20.8675	+	20.8675i	−0.0498030	+	0.0498030i	0.681767	+	0.731570i	$0.261212\pi$
$420$		0			0
$421$	−145.505			−0.345619			−0.172809	−	0.984955i	$-0.555284\pi$
$421$	−145.505			−0.345619			−0.172809	+	0.984955i	$0.555284\pi$
$422$		0			0
$423$	−4.01355	+	188.614i	−0.00948829	+	0.445896i
$424$		0			0
$425$	64.1241	−	55.7952i	0.150880	−	0.131283i
$426$		0			0
$427$			128.287i			0.300438i
$428$		0			0
$429$	27.8062	−	27.2208i	0.0648162	−	0.0634516i
$430$		0			0
$431$	−215.231	+	215.231i	−0.499375	+	0.499375i	−0.911243	−	0.411868i	$-0.864876\pi$
$431$	−215.231	+	215.231i	−0.499375	+	0.499375i	0.411868	+	0.911243i	$0.364876\pi$
$432$		0			0
$433$		−	201.324i		−	0.464951i	−0.972602	−	0.232476i	$-0.925317\pi$
$433$		−	201.324i		−	0.464951i	0.972602	−	0.232476i	$-0.0746826\pi$
$434$		0			0
$435$	3.49321	−	328.359i	0.00803036	−	0.754848i
$436$		0			0
$437$	−0.442346	−	0.442346i	−0.00101223	−	0.00101223i
$438$		0			0
$439$	535.991	−	535.991i	1.22094	−	1.22094i	0.253635	−	0.967300i	$-0.418374\pi$
$439$	535.991	−	535.991i	1.22094	−	1.22094i	0.967300	−	0.253635i	$-0.0816263\pi$
$440$		0			0
$441$	7.54578	−	354.609i	0.0171106	−	0.804101i
$442$		0			0
$443$			135.194i			0.305179i	0.988290	+	0.152590i	$0.0487613\pi$
$443$			135.194i			0.305179i	−0.988290	+	0.152590i	$0.951239\pi$
$444$		0			0
$445$	50.5370	−	50.5370i	0.113566	−	0.113566i
$446$		0			0
$447$	−6.48093	+	609.203i	−0.0144987	+	1.36287i
$448$		0			0
$449$	421.160	−	421.160i	0.937996	−	0.937996i	−0.0601912	−	0.998187i	$-0.519171\pi$
$449$	421.160	−	421.160i	0.937996	−	0.937996i	0.998187	+	0.0601912i	$0.0191710\pi$
$450$		0			0
$451$			194.730i			0.431775i
$452$		0			0
$453$	2.66030	−	250.066i	0.00587262	−	0.552022i
$454$		0			0
$455$			28.0578i			0.0616655i
$456$		0			0
$457$			439.579i			0.961879i	0.876754	+	0.480939i	$0.159704\pi$
$457$			439.579i			0.961879i	−0.876754	+	0.480939i	$0.840296\pi$
$458$		0			0
$459$	290.092	+	355.708i	0.632008	+	0.774962i
$460$		0			0
$461$	281.577			0.610796			0.305398	−	0.952225i	$-0.401210\pi$
$461$	281.577			0.610796			0.305398	+	0.952225i	$0.401210\pi$
$462$		0			0
$463$	−665.345			−1.43703			−0.718516	−	0.695511i	$-0.755178\pi$
$463$	−665.345			−1.43703			−0.718516	+	0.695511i	$0.755178\pi$
$464$		0			0
$465$	85.7890	+	0.912656i	0.184492	+	0.00196270i
$466$		0			0
$467$	−286.298			−0.613058			−0.306529	−	0.951861i	$-0.599168\pi$
$467$	−286.298			−0.613058			−0.306529	+	0.951861i	$0.599168\pi$
$468$		0			0
$469$	70.2587	+	70.2587i	0.149805	+	0.149805i
$470$		0			0
$471$	880.683	+	9.36905i	1.86982	+	0.0198918i
$472$		0			0
$473$	−172.945	−	172.945i	−0.365633	−	0.365633i
$474$		0			0
$475$	−59.4836			−0.125229
$476$		0			0
$477$	292.986	+	6.23450i	0.614227	+	0.0130702i
$478$		0			0
$479$	358.725	+	358.725i	0.748904	+	0.748904i	0.974273	−	0.225370i	$-0.0723590\pi$
$479$	358.725	+	358.725i	0.748904	+	0.748904i	−0.225370	+	0.974273i	$0.572359\pi$
$480$		0			0
$481$	−147.856	+	147.856i	−0.307392	+	0.307392i
$482$		0			0
$483$	−0.488494	−	0.00519679i	−0.00101137	−	1.07594e-5i
$484$		0			0
$485$	222.227			0.458200
$486$		0			0
$487$	324.597	+	324.597i	0.666523	+	0.666523i	0.956909	−	0.290386i	$-0.0937838\pi$
$487$	324.597	+	324.597i	0.666523	+	0.666523i	−0.290386	+	0.956909i	$0.593784\pi$
$488$		0			0
$489$	533.176	+	544.642i	1.09034	+	1.11379i
$490$		0			0
$491$	−301.991			−0.615053			−0.307527	−	0.951539i	$-0.599501\pi$
$491$	−301.991			−0.615053			−0.307527	+	0.951539i	$0.599501\pi$
$492$		0			0
$493$	57.6593	−	830.177i	0.116956	−	1.68393i
$494$		0			0
$495$	64.4074	+	1.37054i	0.130116	+	0.00276876i
$496$		0			0
$497$			189.991i			0.382276i
$498$		0			0
$499$	−401.358	−	401.358i	−0.804324	−	0.804324i	0.179444	−	0.983768i	$-0.442570\pi$
$499$	−401.358	−	401.358i	−0.804324	−	0.804324i	−0.983768	+	0.179444i	$0.942570\pi$
$500$		0			0
$501$	−323.596	−	330.556i	−0.645901	−	0.659792i
$502$		0			0
$503$	−45.8020	+	45.8020i	−0.0910577	+	0.0910577i	−0.751168	−	0.660111i	$-0.770509\pi$
$503$	−45.8020	+	45.8020i	−0.0910577	+	0.0910577i	0.660111	+	0.751168i	$0.270509\pi$
$504$		0			0
$505$	−83.6031	+	83.6031i	−0.165551	+	0.165551i
$506$		0			0
$507$	457.721	+	4.86941i	0.902803	+	0.00960436i
$508$		0			0
$509$		−	825.317i		−	1.62145i	−0.585428	−	0.810724i	$-0.699074\pi$
$509$		−	825.317i		−	1.62145i	0.585428	−	0.810724i	$-0.300926\pi$
$510$		0			0
$511$	218.505			0.427604
$512$		0			0
$513$	10.2494	−	321.048i	0.0199793	−	0.625824i
$514$		0			0
$515$	−180.967	−	180.967i	−0.351393	−	0.351393i
$516$		0			0
$517$	47.4484	+	47.4484i	0.0917763	+	0.0917763i
$518$		0			0
$519$	205.494	+	209.913i	0.395942	+	0.404457i
$520$		0			0
$521$	−436.963	+	436.963i	−0.838700	+	0.838700i	−0.988688	−	0.149987i	$-0.952077\pi$
$521$	−436.963	+	436.963i	−0.838700	+	0.838700i	0.149987	+	0.988688i	$0.452077\pi$
$522$		0			0
$523$	−214.301			−0.409753			−0.204876	−	0.978788i	$-0.565679\pi$
$523$	−214.301			−0.409753			−0.204876	+	0.978788i	$0.565679\pi$
$524$		0			0
$525$	−33.1940	+	32.4952i	−0.0632267	+	0.0618956i
$526$		0			0
$527$	216.897	+	15.0644i	0.411569	+	0.0285852i
$528$		0			0
$529$			528.997i			0.999995i
$530$		0			0
$531$	−997.856	−	21.2336i	−1.87920	−	0.0399879i
$532$		0			0
$533$	174.288	−	174.288i	0.326995	−	0.326995i
$534$		0			0
$535$		−	253.301i		−	0.473460i
$536$		0			0
$537$	350.440	+	3.72811i	0.652588	+	0.00694248i
$538$		0			0
$539$	−89.2065	−	89.2065i	−0.165504	−	0.165504i
$540$		0			0
$541$	630.578	−	630.578i	1.16558	−	1.16558i	0.182345	−	0.983235i	$-0.441631\pi$
$541$	630.578	−	630.578i	1.16558	−	1.16558i	0.983235	−	0.182345i	$-0.0583687\pi$
$542$		0			0
$543$	−319.141	−	326.004i	−0.587736	−	0.600376i
$544$		0			0
$545$		−	271.826i		−	0.498764i
$546$		0			0
$547$	488.617	−	488.617i	0.893267	−	0.893267i	−0.101563	−	0.994829i	$-0.532384\pi$
$547$	488.617	−	488.617i	0.893267	−	0.893267i	0.994829	+	0.101563i	$0.0323842\pi$
$548$		0			0
$549$	−257.963	−	269.180i	−0.469878	−	0.490310i
$550$		0			0
$551$	−411.793	+	411.793i	−0.747356	+	0.747356i
$552$		0			0
$553$			219.248i			0.396470i
$554$		0			0
$555$	−346.161	−	3.68259i	−0.623713	−	0.00663530i
$556$		0			0
$557$			842.536i			1.51263i	0.654207	+	0.756316i	$0.273003\pi$
$557$			842.536i			1.51263i	−0.654207	+	0.756316i	$0.726997\pi$
$558$		0			0
$559$			309.579i			0.553809i
$560$		0			0
$561$	162.737	+	13.0437i	0.290084	+	0.0232507i
$562$		0			0
$563$	220.876			0.392319			0.196160	−	0.980572i	$-0.437153\pi$
$563$	220.876			0.392319			0.196160	+	0.980572i	$0.437153\pi$
$564$		0			0
$565$	148.707			0.263198
$566$		0			0
$567$	−169.665	−	184.756i	−0.299233	−	0.325848i
$568$		0			0
$569$	394.682			0.693642			0.346821	−	0.937931i	$-0.387261\pi$
$569$	394.682			0.693642			0.346821	+	0.937931i	$0.387261\pi$
$570$		0			0
$571$	420.727	+	420.727i	0.736825	+	0.736825i	0.971962	−	0.235137i	$-0.0755539\pi$
$571$	420.727	+	420.727i	0.736825	+	0.736825i	−0.235137	+	0.971962i	$0.575554\pi$
$572$		0			0
$573$	4.22278	−	396.938i	0.00736960	−	0.692736i
$574$		0			0
$575$	−0.185911	−	0.185911i	−0.000323324	−	0.000323324i
$576$		0			0
$577$	−621.807			−1.07765			−0.538827	−	0.842416i	$-0.681132\pi$
$577$	−621.807			−1.07765			−0.538827	+	0.842416i	$0.681132\pi$
$578$		0			0
$579$	482.542	+	492.919i	0.833405	+	0.851328i
$580$		0			0
$581$	262.798	+	262.798i	0.452321	+	0.452321i
$582$		0			0
$583$	73.7046	−	73.7046i	0.126423	−	0.126423i
$584$		0			0
$585$	−56.4196	−	58.8729i	−0.0964437	−	0.100637i
$586$		0			0
$587$	−494.744			−0.842834			−0.421417	−	0.906867i	$-0.638467\pi$
$587$	−494.744			−0.842834			−0.421417	+	0.906867i	$0.638467\pi$
$588$		0			0
$589$	−107.588	−	107.588i	−0.182661	−	0.182661i
$590$		0			0
$591$	194.104	−	190.018i	0.328434	−	0.321519i
$592$		0			0
$593$	802.717			1.35365			0.676827	−	0.736142i	$-0.263354\pi$
$593$	802.717			1.35365			0.676827	+	0.736142i	$0.263354\pi$
$594$		0			0
$595$	−88.8073	+	77.2723i	−0.149256	+	0.129869i
$596$		0			0
$597$	−35.2606	+	34.5183i	−0.0590630	+	0.0578196i
$598$		0			0
$599$			885.831i			1.47885i	0.673239	+	0.739425i	$0.264903\pi$
$599$			885.831i			1.47885i	−0.673239	+	0.739425i	$0.735097\pi$
$600$		0			0
$601$	−661.146	−	661.146i	−1.10008	−	1.10008i	−0.994401	−	0.105677i	$-0.966299\pi$
$601$	−661.146	−	661.146i	−1.10008	−	1.10008i	−0.105677	−	0.994401i	$-0.533701\pi$
$602$		0			0
$603$	−288.700	−	6.14330i	−0.478773	−	0.0101879i
$604$		0			0
$605$	−175.115	+	175.115i	−0.289447	+	0.289447i
$606$		0			0
$607$	−599.241	+	599.241i	−0.987217	+	0.987217i	−0.999919	−	0.0127023i	$-0.995957\pi$
$607$	−599.241	+	599.241i	−0.987217	+	0.987217i	0.0127023	+	0.999919i	$0.495957\pi$
$608$		0			0
$609$	−4.83784	+	454.753i	−0.00794391	+	0.746722i
$610$		0			0
$611$		−	84.9349i		−	0.139010i
$612$		0			0
$613$	−434.292			−0.708470			−0.354235	−	0.935156i	$-0.615259\pi$
$613$	−434.292			−0.708470			−0.354235	+	0.935156i	$0.615259\pi$
$614$		0			0
$615$	408.045	+	4.34094i	0.663489	+	0.00705845i
$616$		0			0
$617$	−68.8211	−	68.8211i	−0.111542	−	0.111542i	0.649133	−	0.760675i	$-0.275132\pi$
$617$	−68.8211	−	68.8211i	−0.111542	−	0.111542i	−0.760675	+	0.649133i	$0.775132\pi$
$618$		0			0
$619$	154.062	+	154.062i	0.248888	+	0.248888i	0.820514	−	0.571626i	$-0.193687\pi$
$619$	154.062	+	154.062i	0.248888	+	0.248888i	−0.571626	+	0.820514i	$0.693687\pi$
$620$		0			0
$621$	1.03544	−	0.971375i	0.00166738	−	0.00156421i
$622$		0			0
$623$	−69.9901	+	69.9901i	−0.112344	+	0.112344i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−79.9228	−	81.6416i	−0.127469	−	0.130210i
$628$		0			0
$629$	−875.185	−	60.7852i	−1.39139	−	0.0966379i
$630$		0			0
$631$		−	892.800i		−	1.41490i	−0.706765	−	0.707449i	$-0.749846\pi$
$631$		−	892.800i		−	1.41490i	0.706765	−	0.707449i	$-0.250154\pi$
$632$		0			0
$633$	−698.743	−	713.770i	−1.10386	−	1.12760i
$634$		0			0
$635$	265.901	−	265.901i	0.418741	−	0.418741i
$636$		0			0
$637$			159.684i			0.250681i
$638$		0			0
$639$	−382.040	−	398.652i	−0.597871	−	0.623869i
$640$		0			0
$641$	142.048	+	142.048i	0.221603	+	0.221603i	0.809173	−	0.587570i	$-0.199915\pi$
$641$	142.048	+	142.048i	0.221603	+	0.221603i	−0.587570	+	0.809173i	$0.699915\pi$
$642$		0			0
$643$	303.047	−	303.047i	0.471301	−	0.471301i	−0.431034	−	0.902336i	$-0.641851\pi$
$643$	303.047	−	303.047i	0.471301	−	0.471301i	0.902336	+	0.431034i	$0.141851\pi$
$644$		0			0
$645$	−366.250	+	358.539i	−0.567830	+	0.555875i
$646$		0			0
$647$		−	341.928i		−	0.528482i	−0.964457	−	0.264241i	$-0.914879\pi$
$647$		−	341.928i		−	0.528482i	0.964457	−	0.264241i	$-0.0851214\pi$
$648$		0			0
$649$	−251.024	+	251.024i	−0.386786	+	0.386786i
$650$		0			0
$651$	−118.812	−	1.26396i	−0.182506	−	0.00194157i
$652$		0			0
$653$	−143.887	+	143.887i	−0.220348	+	0.220348i	−0.808645	−	0.588297i	$-0.799799\pi$
$653$	−143.887	+	143.887i	−0.220348	+	0.220348i	0.588297	+	0.808645i	$0.299799\pi$
$654$		0			0
$655$		−	212.327i		−	0.324163i
$656$		0			0
$657$	−458.483	+	439.378i	−0.697844	+	0.668764i
$658$		0			0
$659$		−	780.173i		−	1.18387i	−0.805984	−	0.591937i	$-0.798363\pi$
$659$		−	780.173i		−	1.18387i	0.805984	−	0.591937i	$-0.201637\pi$
$660$		0			0
$661$		−	817.904i		−	1.23737i	−0.785638	−	0.618687i	$-0.787665\pi$
$661$		−	817.904i		−	1.23737i	0.785638	−	0.618687i	$-0.212335\pi$
$662$		0			0
$663$	−133.979	−	157.328i	−0.202080	−	0.237297i
$664$		0			0
$665$	82.3805			0.123880
$666$		0			0
$667$	−2.57405			−0.00385915
$668$		0			0
$669$	−6.47326	+	608.481i	−0.00967602	+	0.909539i
$670$		0			0
$671$	−132.610			−0.197630
$672$		0			0
$673$	−713.672	−	713.672i	−1.06043	−	1.06043i	−0.998052	−	0.0623819i	$-0.980130\pi$
$673$	−713.672	−	713.672i	−1.06043	−	1.06043i	−0.0623819	−	0.998052i	$-0.519870\pi$
$674$		0			0
$675$	4.30765	−	134.931i	0.00638171	−	0.199898i
$676$		0			0
$677$	173.208	+	173.208i	0.255846	+	0.255846i	0.823362	−	0.567516i	$-0.192096\pi$
$677$	173.208	+	173.208i	0.255846	+	0.255846i	−0.567516	+	0.823362i	$0.692096\pi$
$678$		0			0
$679$	−307.769			−0.453268
$680$		0			0
$681$	−121.988	+	119.420i	−0.179130	+	0.175359i
$682$		0			0
$683$	95.1406	+	95.1406i	0.139298	+	0.139298i	0.773317	−	0.634019i	$-0.218596\pi$
$683$	95.1406	+	95.1406i	0.139298	+	0.139298i	−0.634019	+	0.773317i	$0.718596\pi$
$684$		0			0
$685$	−258.017	+	258.017i	−0.376668	+	0.376668i
$686$		0			0
$687$	−1.85552	+	174.417i	−0.00270090	+	0.253882i
$688$		0			0
$689$	−131.935			−0.191487
$690$		0			0
$691$	956.322	+	956.322i	1.38397	+	1.38397i	0.837442	+	0.546526i	$0.184050\pi$
$691$	956.322	+	956.322i	1.38397	+	1.38397i	0.546526	+	0.837442i	$0.315950\pi$
$692$		0			0
$693$	−89.1997	−	1.89810i	−0.128715	−	0.00273895i
$694$		0			0
$695$	508.743			0.732004
$696$		0			0
$697$	1031.65	+	71.6521i	1.48012	+	0.102801i
$698$		0			0
$699$	−950.871	−	971.320i	−1.36033	−	1.38958i
$700$		0			0
$701$			23.9132i			0.0341130i	0.999855	+	0.0170565i	$0.00542952\pi$
$701$			23.9132i			0.0341130i	−0.999855	+	0.0170565i	$0.994570\pi$
$702$		0			0
$703$	434.118	+	434.118i	0.617523	+	0.617523i
$704$		0			0
$705$	100.483	−	98.3674i	0.142529	−	0.139528i
$706$		0			0
$707$	115.784	−	115.784i	0.163768	−	0.163768i
$708$		0			0
$709$	644.433	−	644.433i	0.908933	−	0.908933i	−0.0872536	−	0.996186i	$-0.527809\pi$
$709$	644.433	−	644.433i	0.908933	−	0.908933i	0.996186	+	0.0872536i	$0.0278090\pi$
$710$		0			0
$711$	−440.870	−	460.041i	−0.620071	−	0.647034i
$712$		0			0
$713$		−	0.672512i		−	0.000943215i
$714$		0			0
$715$	−29.0034			−0.0405641
$716$		0			0
$717$	−7.28115	+	684.423i	−0.0101550	+	0.954565i
$718$		0			0
$719$	−822.344	−	822.344i	−1.14373	−	1.14373i	−0.987762	−	0.155971i	$-0.950149\pi$
$719$	−822.344	−	822.344i	−1.14373	−	1.14373i	−0.155971	−	0.987762i	$-0.549851\pi$
$720$		0			0
$721$	250.627	+	250.627i	0.347610	+	0.347610i
$722$		0			0
$723$	−211.897	+	207.436i	−0.293080	+	0.286910i
$724$		0			0
$725$	−173.070	+	173.070i	−0.238717	+	0.238717i
$726$		0			0
$727$	35.2596			0.0485001			0.0242501	−	0.999706i	$-0.492280\pi$
$727$	35.2596			0.0485001			0.0242501	+	0.999706i	$0.492280\pi$
$728$		0			0
$729$	727.516	+	46.4989i	0.997964	+	0.0637846i
$730$		0			0
$731$	−979.865	+	852.593i	−1.34044	+	1.16634i
$732$		0			0
$733$		−	745.483i		−	1.01703i	−0.861053	−	0.508515i	$-0.830195\pi$
$733$		−	745.483i		−	1.01703i	0.861053	−	0.508515i	$-0.169805\pi$
$734$		0			0
$735$	−188.915	+	184.938i	−0.257028	+	0.251617i
$736$		0			0
$737$	−72.6264	+	72.6264i	−0.0985433	+	0.0985433i
$738$		0			0
$739$		−	695.309i		−	0.940878i	−0.882432	−	0.470439i	$-0.844095\pi$
$739$		−	695.309i		−	0.940878i	0.882432	−	0.470439i	$-0.155905\pi$
$740$		0			0
$741$	−1.53835	+	144.604i	−0.00207605	+	0.195147i
$742$		0			0
$743$	725.850	+	725.850i	0.976918	+	0.976918i	0.999740	−	0.0228212i	$-0.00726485\pi$
$743$	725.850	+	725.850i	0.976918	+	0.976918i	−0.0228212	+	0.999740i	$0.507265\pi$
$744$		0			0
$745$	321.096	−	321.096i	0.431001	−	0.431001i
$746$		0			0
$747$	−1079.86	−	22.9786i	−1.44560	−	0.0307612i
$748$		0			0
$749$			350.804i			0.468363i
$750$		0			0
$751$	22.5628	−	22.5628i	0.0300436	−	0.0300436i	−0.691925	−	0.721969i	$-0.743237\pi$
$751$	22.5628	−	22.5628i	0.0300436	−	0.0300436i	0.721969	+	0.691925i	$0.243237\pi$
$752$		0			0
$753$	9.46162	−	889.385i	0.0125652	−	1.18112i
$754$		0			0
$755$	−131.804	+	131.804i	−0.174574	+	0.174574i
$756$		0			0
$757$			608.147i			0.803364i	0.915779	+	0.401682i	$0.131574\pi$
$757$			608.147i			0.803364i	−0.915779	+	0.401682i	$0.868426\pi$
$758$		0			0
$759$	0.00537192	−	0.504956i	7.07763e−6	−	0.000665291i
$760$		0			0
$761$			76.2172i			0.100154i	0.998745	+	0.0500770i	$0.0159467\pi$
$761$			76.2172i			0.100154i	−0.998745	+	0.0500770i	$0.984053\pi$
$762$		0			0
$763$			376.460i			0.493395i
$764$		0			0
$765$	30.9599	−	340.715i	0.0404705	−	0.445379i
$766$		0			0
$767$	449.345			0.585848
$768$		0			0
$769$	94.3861			0.122739			0.0613694	−	0.998115i	$-0.480453\pi$
$769$	94.3861			0.122739			0.0613694	+	0.998115i	$0.480453\pi$
$770$		0			0
$771$	−465.268	−	4.94970i	−0.603460	−	0.00641984i
$772$		0			0
$773$	−1055.14			−1.36500			−0.682498	−	0.730887i	$-0.739106\pi$
$773$	−1055.14			−1.36500			−0.682498	+	0.730887i	$0.739106\pi$
$774$		0			0
$775$	−45.2173	−	45.2173i	−0.0583449	−	0.0583449i
$776$		0			0
$777$	479.408	+	5.10012i	0.616998	+	0.00656386i
$778$		0			0
$779$	−511.728	−	511.728i	−0.656904	−	0.656904i
$780$		0			0
$781$	−196.394			−0.251464
$782$		0			0
$783$	−904.281	−	963.924i	−1.15489	−	1.23106i
$784$		0			0
$785$	−464.187	−	464.187i	−0.591321	−	0.591321i
$786$		0			0
$787$	42.9959	−	42.9959i	0.0546327	−	0.0546327i	−0.679263	−	0.733895i	$-0.737700\pi$
$787$	42.9959	−	42.9959i	0.0546327	−	0.0546327i	0.733895	+	0.679263i	$0.237700\pi$
$788$		0			0
$789$	−1088.63	−	11.5813i	−1.37976	−	0.0146784i
$790$		0			0
$791$	−205.949			−0.260365
$792$		0			0
$793$	118.689	+	118.689i	0.149671	+	0.149671i
$794$		0			0
$795$	−152.800	−	156.086i	−0.192202	−	0.196335i
$796$		0			0
$797$	135.515			0.170031			0.0850155	−	0.996380i	$-0.472906\pi$
$797$	135.515			0.170031			0.0850155	+	0.996380i	$0.472906\pi$
$798$		0			0
$799$	268.832	−	233.914i	0.336460	−	0.292758i
$800$		0			0
$801$	6.11981	−	287.596i	0.00764022	−	0.359047i
$802$		0			0
$803$			225.869i			0.281281i
$804$		0			0
$805$	0.257474	+	0.257474i	0.000319843	+	0.000319843i
$806$		0			0
$807$	−457.446	−	467.284i	−0.566848	−	0.579038i
$808$		0			0
$809$	617.313	−	617.313i	0.763057	−	0.763057i	−0.213817	−	0.976874i	$-0.568590\pi$
$809$	617.313	−	617.313i	0.763057	−	0.763057i	0.976874	+	0.213817i	$0.0685896\pi$
$810$		0			0
$811$	228.449	−	228.449i	0.281688	−	0.281688i	−0.552094	−	0.833782i	$-0.686171\pi$
$811$	228.449	−	228.449i	0.281688	−	0.281688i	0.833782	+	0.552094i	$0.186171\pi$
$812$		0			0
$813$	334.981	+	3.56366i	0.412031	+	0.00438334i
$814$		0			0
$815$		−	568.092i		−	0.697045i
$816$		0			0
$817$	908.955			1.11255
$818$		0			0
$819$	78.1371	+	81.5347i	0.0954054	+	0.0995540i
$820$		0			0
$821$	−325.309	−	325.309i	−0.396235	−	0.396235i	0.480668	−	0.876903i	$-0.340394\pi$
$821$	−325.309	−	325.309i	−0.396235	−	0.396235i	−0.876903	+	0.480668i	$0.840394\pi$
$822$		0			0
$823$	562.258	+	562.258i	0.683181	+	0.683181i	0.960716	−	0.277534i	$-0.0895173\pi$
$823$	562.258	+	562.258i	0.683181	+	0.683181i	−0.277534	+	0.960716i	$0.589517\pi$
$824$		0			0
$825$	−33.5903	−	34.3126i	−0.0407155	−	0.0415911i
$826$		0			0
$827$	180.350	−	180.350i	0.218078	−	0.218078i	−0.589610	−	0.807688i	$-0.700719\pi$
$827$	180.350	−	180.350i	0.218078	−	0.218078i	0.807688	+	0.589610i	$0.200719\pi$
$828$		0			0
$829$	−661.248			−0.797645			−0.398823	−	0.917028i	$-0.630581\pi$
$829$	−661.248			−0.797645			−0.398823	+	0.917028i	$0.630581\pi$
$830$		0			0
$831$	62.1978	−	60.8884i	0.0748469	−	0.0732712i
$832$		0			0
$833$	−505.424	+	439.776i	−0.606752	+	0.527943i
$834$		0			0
$835$			344.788i			0.412920i
$836$		0			0
$837$	251.840	−	236.258i	0.300885	−	0.282268i
$838$		0			0
$839$	−446.791	+	446.791i	−0.532528	+	0.532528i	−0.921324	−	0.388796i	$-0.872891\pi$
$839$	−446.791	+	446.791i	−0.532528	+	0.532528i	0.388796	+	0.921324i	$0.372891\pi$
$840$		0			0
$841$			1555.26i			1.84930i
$842$		0			0
$843$	198.489	+	2.11160i	0.235455	+	0.00250486i
$844$		0			0
$845$	−241.254	−	241.254i	−0.285507	−	0.285507i
$846$		0			0
$847$	242.522	−	242.522i	0.286331	−	0.286331i
$848$		0			0
$849$	−479.021	−	489.323i	−0.564218	−	0.576352i
$850$		0			0
$851$			2.71360i			0.00318872i
$852$		0			0
$853$	600.280	−	600.280i	0.703728	−	0.703728i	−0.261480	−	0.965209i	$-0.584211\pi$
$853$	600.280	−	600.280i	0.703728	−	0.703728i	0.965209	+	0.261480i	$0.0842107\pi$
$854$		0			0
$855$	−172.857	+	165.653i	−0.202171	+	0.193747i
$856$		0			0
$857$	−738.207	+	738.207i	−0.861385	+	0.861385i	−0.991499	−	0.130114i	$-0.958466\pi$
$857$	−738.207	+	738.207i	−0.861385	+	0.861385i	0.130114	+	0.991499i	$0.458466\pi$
$858$		0			0
$859$			358.359i			0.417182i	0.978003	+	0.208591i	$0.0668877\pi$
$859$			358.359i			0.417182i	−0.978003	+	0.208591i	$0.933112\pi$
$860$		0			0
$861$	−565.114	−	6.01190i	−0.656346	−	0.00698246i
$862$		0			0
$863$		−	265.123i		−	0.307211i	−0.988132	−	0.153605i	$-0.950912\pi$
$863$		−	265.123i		−	0.307211i	0.988132	−	0.153605i	$-0.0490885\pi$
$864$		0			0
$865$		−	218.951i		−	0.253123i
$866$		0			0
$867$	128.983	−	857.352i	0.148769	−	0.988872i
$868$		0			0
$869$	−226.636			−0.260801
$870$		0			0
$871$	130.005			0.149259
$872$		0			0
$873$	645.782	−	618.871i	0.739727	−	0.708901i
$874$		0			0
$875$	34.6232			0.0395694
$876$		0			0
$877$	63.3843	+	63.3843i	0.0722740	+	0.0722740i	0.742320	−	0.670046i	$-0.233726\pi$
$877$	63.3843	+	63.3843i	0.0722740	+	0.0722740i	−0.670046	+	0.742320i	$0.733726\pi$
$878$		0			0
$879$	−7.86965	+	739.741i	−0.00895296	+	0.841571i
$880$		0			0
$881$	652.871	+	652.871i	0.741057	+	0.741057i	0.972782	−	0.231724i	$-0.0744367\pi$
$881$	652.871	+	652.871i	0.741057	+	0.741057i	−0.231724	+	0.972782i	$0.574437\pi$
$882$		0			0
$883$	88.3227			0.100026			0.0500128	−	0.998749i	$-0.484074\pi$
$883$	88.3227			0.100026			0.0500128	+	0.998749i	$0.484074\pi$
$884$		0			0
$885$	520.410	+	531.602i	0.588034	+	0.600680i
$886$		0			0
$887$	−1030.25	−	1030.25i	−1.16150	−	1.16150i	−0.984147	−	0.177355i	$-0.943246\pi$
$887$	−1030.25	−	1030.25i	−1.16150	−	1.16150i	−0.177355	−	0.984147i	$-0.556754\pi$
$888$		0			0
$889$	−368.253	+	368.253i	−0.414233	+	0.414233i
$890$		0			0
$891$	190.982	−	175.383i	0.214345	−	0.196838i
$892$		0			0
$893$	−249.377			−0.279258
$894$		0			0
$895$	−184.708	−	184.708i	−0.206378	−	0.206378i
$896$		0			0
$897$	−0.456756	+	0.447140i	−0.000509204	+	0.000498484i
$898$		0			0
$899$	−626.061			−0.696397
$900$		0			0
$901$	−363.354	−	417.594i	−0.403278	−	0.463478i
$902$		0			0
$903$	507.230	−	496.551i	0.561717	−	0.549891i
$904$		0			0
$905$			340.040i			0.375735i
$906$		0			0
$907$	−678.783	−	678.783i	−0.748383	−	0.748383i	0.225793	−	0.974175i	$-0.427503\pi$
$907$	−678.783	−	678.783i	−0.748383	−	0.748383i	−0.974175	+	0.225793i	$0.927503\pi$
$908$		0			0
$909$	−10.1240	+	475.769i	−0.0111375	+	0.523399i
$910$		0			0
$911$	432.761	−	432.761i	0.475039	−	0.475039i	−0.428502	−	0.903541i	$-0.640958\pi$
$911$	432.761	−	432.761i	0.475039	−	0.475039i	0.903541	+	0.428502i	$0.140958\pi$
$912$		0			0
$913$	−271.654	+	271.654i	−0.297541	+	0.297541i
$914$		0			0
$915$	−2.95615	+	277.876i	−0.00323077	+	0.303690i
$916$		0			0
$917$			294.057i			0.320673i
$918$		0			0
$919$	1594.67			1.73523			0.867613	−	0.497240i	$-0.165653\pi$
$919$	1594.67			1.73523			0.867613	+	0.497240i	$0.165653\pi$
$920$		0			0
$921$	280.278	+	2.98170i	0.304319	+	0.00323746i
$922$		0			0
$923$	175.777	+	175.777i	0.190441	+	0.190441i
$924$		0			0
$925$	182.453	+	182.453i	0.197246	+	0.197246i
$926$		0			0
$927$	−1029.85	−	21.9144i	−1.11095	−	0.0236401i
$928$		0			0
$929$	975.448	−	975.448i	1.05000	−	1.05000i	0.0513152	−	0.998683i	$-0.483659\pi$
$929$	975.448	−	975.448i	1.05000	−	1.05000i	0.998683	−	0.0513152i	$-0.0163413\pi$
$930$		0			0
$931$	468.848			0.503596
$932$		0			0
$933$	−610.250	−	623.373i	−0.654072	−	0.668139i
$934$		0			0
$935$	−79.8764	−	91.8000i	−0.0854293	−	0.0981819i
$936$		0			0
$937$		−	314.163i		−	0.335286i	−0.985848	−	0.167643i	$-0.946384\pi$
$937$		−	314.163i		−	0.335286i	0.985848	−	0.167643i	$-0.0536155\pi$
$938$		0			0
$939$	45.3330	+	46.3079i	0.0482779	+	0.0493162i
$940$		0			0
$941$	283.433	−	283.433i	0.301204	−	0.301204i	−0.540281	−	0.841485i	$-0.681682\pi$
$941$	283.433	−	283.433i	0.301204	−	0.301204i	0.841485	+	0.540281i	$0.181682\pi$
$942$		0			0
$943$		−	3.19873i		−	0.00339208i
$944$		0			0
$945$	−5.96579	+	186.870i	−0.00631300	+	0.197746i
$946$		0			0
$947$	−771.348	−	771.348i	−0.814517	−	0.814517i	0.170790	−	0.985307i	$-0.445368\pi$
$947$	−771.348	−	771.348i	−0.814517	−	0.814517i	−0.985307	+	0.170790i	$0.945368\pi$
$948$		0			0
$949$	202.158	−	202.158i	0.213022	−	0.213022i
$950$		0			0
$951$	−196.622	+	192.483i	−0.206753	+	0.202400i
$952$		0			0
$953$			207.503i			0.217737i	0.994056	+	0.108868i	$0.0347227\pi$
$953$			207.503i			0.217737i	−0.994056	+	0.108868i	$0.965277\pi$
$954$		0			0
$955$	−209.217	+	209.217i	−0.219075	+	0.219075i
$956$		0			0
$957$	−470.079	−	5.00088i	−0.491200	−	0.00522558i
$958$		0			0
$959$	357.336	−	357.336i	0.372613	−	0.372613i
$960$		0			0
$961$			797.432i			0.829794i
$962$		0			0
$963$	−705.407	−	736.081i	−0.732510	−	0.764362i
$964$		0			0
$965$		−	514.142i		−	0.532790i
$966$		0			0
$967$			27.9139i			0.0288665i	0.999896	+	0.0144332i	$0.00459440\pi$
$967$			27.9139i			0.0288665i	−0.999896	+	0.0144332i	$0.995406\pi$
$968$		0			0
$969$	−461.930	+	393.376i	−0.476708	+	0.405961i
$970$		0			0
$971$	948.844			0.977182			0.488591	−	0.872513i	$-0.337511\pi$
$971$	948.844			0.977182			0.488591	+	0.872513i	$0.337511\pi$
$972$		0			0
$973$	−704.572			−0.724124
$974$		0			0
$975$	−0.646545	+	60.7748i	−0.000663123	+	0.0623331i
$976$		0			0
$977$	75.3864			0.0771611			0.0385805	−	0.999255i	$-0.487716\pi$
$977$	75.3864			0.0771611			0.0385805	+	0.999255i	$0.487716\pi$
$978$		0			0
$979$	−72.3487	−	72.3487i	−0.0739006	−	0.0739006i
$980$		0			0
$981$	−756.998	−	789.915i	−0.771660	−	0.805214i
$982$		0			0
$983$	998.920	+	998.920i	1.01620	+	1.01620i	0.999867	+	0.0163292i	$0.00519796\pi$
$983$	998.920	+	998.920i	1.01620	+	1.01620i	0.0163292	+	0.999867i	$0.494802\pi$
$984$		0			0
$985$	−202.462			−0.205545
$986$		0			0
$987$	−139.162	+	136.232i	−0.140994	+	0.138026i
$988$		0			0
$989$	2.84086	+	2.84086i	0.00287246	+	0.00287246i
$990$		0			0
$991$	−278.252	+	278.252i	−0.280779	+	0.280779i	−0.833420	−	0.552640i	$-0.813620\pi$
$991$	−278.252	+	278.252i	−0.280779	+	0.280779i	0.552640	+	0.833420i	$0.313620\pi$
$992$		0			0
$993$	−9.61323	+	903.636i	−0.00968099	+	0.910006i
$994$		0			0
$995$	36.7788			0.0369636
$996$		0			0
$997$	−461.875	−	461.875i	−0.463265	−	0.463265i	0.436459	−	0.899724i	$-0.356232\pi$
$997$	−461.875	−	461.875i	−0.463265	−	0.463265i	−0.899724	+	0.436459i	$0.856232\pi$
$998$		0			0
$999$	−1016.18	+	953.307i	−1.01720	+	0.954261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.1	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.26	yes	96
17.13	even	4	inner	1020.3.bc.a.761.26	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.1	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.26	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.1	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.26	yes	96	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99983 - 0.0319133i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-2.18976 - 2.18976i) q^{7} +(8.99796 + 0.191469i) q^{9} +O(q^{10})\)	\(q+(-2.99983 - 0.0319133i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-2.18976 - 2.18976i) q^{7} +(8.99796 + 0.191469i) q^{9} +(2.26356 - 2.26356i) q^{11} -4.05188 q^{13} +(-4.69269 - 4.79361i) q^{15} +(-11.1590 - 12.8248i) q^{17} +11.8967i q^{19} +(6.49904 + 6.63880i) q^{21} +(-0.0371822 + 0.0371822i) q^{23} +5.00000i q^{25} +(-26.9863 - 0.861530i) q^{27} +(34.6140 + 34.6140i) q^{29} +(-9.04346 + 9.04346i) q^{31} +(-6.86253 + 6.71805i) q^{33} -6.92464i q^{35} +(36.4906 - 36.4906i) q^{37} +(12.1550 + 0.129309i) q^{39} +(-43.0142 + 43.0142i) q^{41} -76.4038i q^{43} +(13.9243 + 14.5298i) q^{45} +20.9618i q^{47} -39.4099i q^{49} +(33.0659 + 38.8284i) q^{51} +32.5614 q^{53} +7.15800 q^{55} +(0.379664 - 35.6881i) q^{57} -110.898 q^{59} +(-29.2924 - 29.2924i) q^{61} +(-19.2841 - 20.1227i) q^{63} +(-6.40659 - 6.40659i) q^{65} -32.0851 q^{67} +(0.112727 - 0.110354i) q^{69} +(-43.3816 - 43.3816i) q^{71} +(-49.8925 + 49.8925i) q^{73} +(0.159567 - 14.9992i) q^{75} -9.91332 q^{77} +(-50.0620 - 50.0620i) q^{79} +(80.9267 + 3.44567i) q^{81} -120.012 q^{83} +(2.63383 - 37.9218i) q^{85} +(-102.732 - 104.941i) q^{87} -31.9624i q^{89} +(8.87266 + 8.87266i) q^{91} +(27.4175 - 26.8402i) q^{93} +(-18.8104 + 18.8104i) q^{95} +(70.2744 - 70.2744i) q^{97} +(20.8008 - 19.9340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 96 * q - 8 * q^3	\( 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) \) 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Introduction

L-functions

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Database

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