LMFDB - Embedded newform 1020.3.bc.a.701.14

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			701.14
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02913 + 2.20967i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-7.12660 - 7.12660i) q^{7} +(-0.765285 - 8.96740i) q^{9} +O(q^{10})$	\(q+(-2.02913 + 2.20967i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-7.12660 - 7.12660i) q^{7} +(-0.765285 - 8.96740i) q^{9} +(-1.92573 + 1.92573i) q^{11} +14.4519 q^{13} +(-6.70213 + 0.285463i) q^{15} +(15.6039 - 6.74664i) q^{17} -8.80173i q^{19} +(30.2082 - 1.28666i) q^{21} +(-26.2783 + 26.2783i) q^{23} +5.00000i q^{25} +(21.3679 + 16.5050i) q^{27} +(20.4067 + 20.4067i) q^{29} +(-38.5931 + 38.5931i) q^{31} +(-0.347677 - 8.16278i) q^{33} -22.5363i q^{35} +(-3.92278 + 3.92278i) q^{37} +(-29.3248 + 31.9340i) q^{39} +(-17.0154 + 17.0154i) q^{41} +23.9958i q^{43} +(12.9687 - 15.3887i) q^{45} -67.4512i q^{47} +52.5770i q^{49} +(-16.7545 + 48.1693i) q^{51} -94.2288 q^{53} -6.08969 q^{55} +(19.4489 + 17.8598i) q^{57} +88.6826 q^{59} +(-17.6026 - 17.6026i) q^{61} +(-58.4533 + 69.3610i) q^{63} +(22.8505 + 22.8505i) q^{65} -80.6140 q^{67} +(-4.74437 - 111.389i) q^{69} +(50.0090 + 50.0090i) q^{71} +(-23.0400 + 23.0400i) q^{73} +(-11.0484 - 10.1456i) q^{75} +27.4478 q^{77} +(-58.8042 - 58.8042i) q^{79} +(-79.8287 + 13.7252i) q^{81} +21.4676 q^{83} +(35.3394 + 14.0046i) q^{85} +(-86.4998 + 3.68428i) q^{87} -23.5953i q^{89} +(-102.993 - 102.993i) q^{91} +(-6.96772 - 163.588i) q^{93} +(13.9168 - 13.9168i) q^{95} +(-46.4595 + 46.4595i) q^{97} +(18.7425 + 15.7951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.02913	+	2.20967i	−0.676376	+	0.736557i
$3$	−2.02913	+	2.20967i	−0.676376	+	0.736557i
$4$		0			0
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$		0			0
$7$	−7.12660	−	7.12660i	−1.01809	−	1.01809i	−0.999833	−	0.0182528i	$-0.994190\pi$
$7$	−7.12660	−	7.12660i	−1.01809	−	1.01809i	−0.0182528	−	0.999833i	$-0.505810\pi$
$8$		0			0
$9$	−0.765285	−	8.96740i	−0.0850317	−	0.996378i
$10$		0			0
$11$	−1.92573	+	1.92573i	−0.175066	+	0.175066i	−0.789201	−	0.614135i	$-0.789505\pi$
$11$	−1.92573	+	1.92573i	−0.175066	+	0.175066i	0.614135	+	0.789201i	$0.289505\pi$
$12$		0			0
$13$	14.4519			1.11169			0.555844	−	0.831287i	$-0.312395\pi$
$13$	14.4519			1.11169			0.555844	+	0.831287i	$0.312395\pi$
$14$		0			0
$15$	−6.70213	+	0.285463i	−0.446808	+	0.0190309i
$16$		0			0
$17$	15.6039	−	6.74664i	0.917879	−	0.396861i
$17$	15.6039	−	6.74664i	0.917879	−	0.396861i
$18$		0			0
$19$		−	8.80173i		−	0.463249i	−0.972805	−	0.231625i	$-0.925596\pi$
$19$		−	8.80173i		−	0.463249i	0.972805	−	0.231625i	$-0.0744041\pi$
$20$		0			0
$21$	30.2082	−	1.28666i	1.43849	−	0.0612694i
$22$		0			0
$23$	−26.2783	+	26.2783i	−1.14254	+	1.14254i	−0.154552	+	0.987985i	$0.549393\pi$
$23$	−26.2783	+	26.2783i	−1.14254	+	1.14254i	−0.987985	+	0.154552i	$0.950607\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	21.3679	+	16.5050i	0.791402	+	0.611295i
$28$		0			0
$29$	20.4067	+	20.4067i	0.703678	+	0.703678i	0.965198	−	0.261520i	$-0.0842236\pi$
$29$	20.4067	+	20.4067i	0.703678	+	0.703678i	−0.261520	+	0.965198i	$0.584224\pi$
$30$		0			0
$31$	−38.5931	+	38.5931i	−1.24494	+	1.24494i	−0.287013	+	0.957927i	$0.592662\pi$
$31$	−38.5931	+	38.5931i	−1.24494	+	1.24494i	−0.957927	+	0.287013i	$0.907338\pi$
$32$		0			0
$33$	−0.347677	−	8.16278i	−0.0105357	−	0.247357i
$34$		0			0
$35$		−	22.5363i		−	0.643894i
$36$		0			0
$37$	−3.92278	+	3.92278i	−0.106021	+	0.106021i	−0.758127	−	0.652106i	$-0.773886\pi$
$37$	−3.92278	+	3.92278i	−0.106021	+	0.106021i	0.652106	+	0.758127i	$0.273886\pi$
$38$		0			0
$39$	−29.3248	+	31.9340i	−0.751919	+	0.818821i
$40$		0			0
$41$	−17.0154	+	17.0154i	−0.415011	+	0.415011i	−0.883480	−	0.468469i	$-0.844806\pi$
$41$	−17.0154	+	17.0154i	−0.415011	+	0.415011i	0.468469	+	0.883480i	$0.344806\pi$
$42$		0			0
$43$			23.9958i			0.558042i	0.960285	+	0.279021i	$0.0900099\pi$
$43$			23.9958i			0.558042i	−0.960285	+	0.279021i	$0.909990\pi$
$44$		0			0
$45$	12.9687	−	15.3887i	0.288193	−	0.341972i
$46$		0			0
$47$		−	67.4512i		−	1.43513i	−0.696491	−	0.717566i	$-0.745256\pi$
$47$		−	67.4512i		−	1.43513i	0.696491	−	0.717566i	$-0.254744\pi$
$48$		0			0
$49$			52.5770i			1.07300i
$50$		0			0
$51$	−16.7545	+	48.1693i	−0.328520	+	0.944497i
$52$		0			0
$53$	−94.2288			−1.77790			−0.888951	−	0.458002i	$-0.848565\pi$
$53$	−94.2288			−1.77790			−0.888951	+	0.458002i	$0.848565\pi$
$54$		0			0
$55$	−6.08969			−0.110722
$56$		0			0
$57$	19.4489	+	17.8598i	0.341209	+	0.313330i
$58$		0			0
$59$	88.6826			1.50310			0.751548	−	0.659679i	$-0.229308\pi$
$59$	88.6826			1.50310			0.751548	+	0.659679i	$0.229308\pi$
$60$		0			0
$61$	−17.6026	−	17.6026i	−0.288567	−	0.288567i	0.547946	−	0.836514i	$-0.315410\pi$
$61$	−17.6026	−	17.6026i	−0.288567	−	0.288567i	−0.836514	+	0.547946i	$0.815410\pi$
$62$		0			0
$63$	−58.4533	+	69.3610i	−0.927829	+	1.10097i
$64$		0			0
$65$	22.8505	+	22.8505i	0.351547	+	0.351547i
$66$		0			0
$67$	−80.6140			−1.20319			−0.601597	−	0.798800i	$-0.705469\pi$
$67$	−80.6140			−1.20319			−0.601597	+	0.798800i	$0.705469\pi$
$68$		0			0
$69$	−4.74437	−	111.389i	−0.0687590	−	1.61433i
$70$		0			0
$71$	50.0090	+	50.0090i	0.704353	+	0.704353i	0.965342	−	0.260989i	$-0.0840487\pi$
$71$	50.0090	+	50.0090i	0.704353	+	0.704353i	−0.260989	+	0.965342i	$0.584049\pi$
$72$		0			0
$73$	−23.0400	+	23.0400i	−0.315616	+	0.315616i	−0.847081	−	0.531465i	$-0.821642\pi$
$73$	−23.0400	+	23.0400i	−0.315616	+	0.315616i	0.531465	+	0.847081i	$0.321642\pi$
$74$		0			0
$75$	−11.0484	−	10.1456i	−0.147311	−	0.135275i
$76$		0			0
$77$	27.4478			0.356465
$78$		0			0
$79$	−58.8042	−	58.8042i	−0.744357	−	0.744357i	0.229056	−	0.973413i	$-0.426436\pi$
$79$	−58.8042	−	58.8042i	−0.744357	−	0.744357i	−0.973413	+	0.229056i	$0.926436\pi$
$80$		0			0
$81$	−79.8287	+	13.7252i	−0.985539	+	0.169447i
$82$		0			0
$83$	21.4676			0.258646			0.129323	−	0.991603i	$-0.458720\pi$
$83$	21.4676			0.258646			0.129323	+	0.991603i	$0.458720\pi$
$84$		0			0
$85$	35.3394	+	14.0046i	0.415757	+	0.164760i
$86$		0			0
$87$	−86.4998	+	3.68428i	−0.994250	+	0.0423481i
$88$		0			0
$89$		−	23.5953i		−	0.265116i	−0.991175	−	0.132558i	$-0.957681\pi$
$89$		−	23.5953i		−	0.265116i	0.991175	−	0.132558i	$-0.0423191\pi$
$90$		0			0
$91$	−102.993	−	102.993i	−1.13179	−	1.13179i
$92$		0			0
$93$	−6.96772	−	163.588i	−0.0749217	−	1.75902i
$94$		0			0
$95$	13.9168	−	13.9168i	0.146492	−	0.146492i
$96$		0			0
$97$	−46.4595	+	46.4595i	−0.478964	+	0.478964i	−0.904800	−	0.425836i	$-0.859980\pi$
$97$	−46.4595	+	46.4595i	−0.478964	+	0.478964i	0.425836	+	0.904800i	$0.359980\pi$
$98$		0			0
$99$	18.7425	+	15.7951i	0.189318	+	0.159546i
$100$		0			0
$101$		−	45.9080i		−	0.454534i	−0.973832	−	0.227267i	$-0.927021\pi$
$101$		−	45.9080i		−	0.454534i	0.973832	−	0.227267i	$-0.0729790\pi$
$102$		0			0
$103$	−100.216			−0.972967			−0.486484	−	0.873690i	$-0.661721\pi$
$103$	−100.216			−0.972967			−0.486484	+	0.873690i	$0.661721\pi$
$104$		0			0
$105$	49.7978	+	45.7290i	0.474265	+	0.435514i
$106$		0			0
$107$	−62.0375	−	62.0375i	−0.579790	−	0.579790i	0.355055	−	0.934845i	$-0.384462\pi$
$107$	−62.0375	−	62.0375i	−0.579790	−	0.579790i	−0.934845	+	0.355055i	$0.884462\pi$
$108$		0			0
$109$	75.8302	+	75.8302i	0.695690	+	0.695690i	0.963478	−	0.267788i	$-0.0862926\pi$
$109$	75.8302	+	75.8302i	0.695690	+	0.695690i	−0.267788	+	0.963478i	$0.586293\pi$
$110$		0			0
$111$	−0.708230	−	16.6279i	−0.00638045	−	0.149800i
$112$		0			0
$113$	−98.2257	+	98.2257i	−0.869254	+	0.869254i	−0.992390	−	0.123136i	$-0.960705\pi$
$113$	−98.2257	+	98.2257i	−0.869254	+	0.869254i	0.123136	+	0.992390i	$0.460705\pi$
$114$		0			0
$115$	−83.0994			−0.722603
$116$		0			0
$117$	−11.0599	−	129.596i	−0.0945287	−	1.10766i
$118$		0			0
$119$	−159.284	−	63.1224i	−1.33852	−	0.530440i
$120$		0			0
$121$			113.583i			0.938704i
$122$		0			0
$123$	−3.07202	−	72.1250i	−0.0249757	−	0.586382i
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$		0			0
$127$			163.094i			1.28421i	0.766617	+	0.642104i	$0.221938\pi$
$127$			163.094i			1.28421i	−0.766617	+	0.642104i	$0.778062\pi$
$128$		0			0
$129$	−53.0228	−	48.6905i	−0.411030	−	0.377446i
$130$		0			0
$131$	172.895	+	172.895i	1.31981	+	1.31981i	0.913925	+	0.405884i	$0.133036\pi$
$131$	172.895	+	172.895i	1.31981	+	1.31981i	0.405884	+	0.913925i	$0.366964\pi$
$132$		0			0
$133$	−62.7265	+	62.7265i	−0.471628	+	0.471628i
$134$		0			0
$135$	7.68890	+	59.8822i	0.0569548	+	0.443572i
$136$		0			0
$137$		−	177.572i		−	1.29615i	−0.761577	−	0.648074i	$-0.775575\pi$
$137$		−	177.572i		−	1.29615i	0.761577	−	0.648074i	$-0.224425\pi$
$138$		0			0
$139$	−144.748	+	144.748i	−1.04135	+	1.04135i	−0.0422465	+	0.999107i	$0.513451\pi$
$139$	−144.748	+	144.748i	−1.04135	+	1.04135i	−0.999107	+	0.0422465i	$0.986549\pi$
$140$		0			0
$141$	149.045	+	136.867i	1.05706	+	0.970688i
$142$		0			0
$143$	−27.8305	+	27.8305i	−0.194619	+	0.194619i
$144$		0			0
$145$			64.5316i			0.445045i
$146$		0			0
$147$	−116.178	−	106.685i	−0.790325	−	0.725751i
$148$		0			0
$149$			176.683i			1.18579i	0.805279	+	0.592896i	$0.202015\pi$
$149$			176.683i			1.18579i	−0.805279	+	0.592896i	$0.797985\pi$
$150$		0			0
$151$			271.139i			1.79562i	0.440378	+	0.897812i	$0.354844\pi$
$151$			271.139i			1.79562i	−0.440378	+	0.897812i	$0.645156\pi$
$152$		0			0
$153$	−72.4413	−	134.764i	−0.473473	−	0.880808i
$154$		0			0
$155$	−122.042			−0.787369
$156$		0			0
$157$	−153.925			−0.980412			−0.490206	−	0.871607i	$-0.663079\pi$
$157$	−153.925			−0.980412			−0.490206	+	0.871607i	$0.663079\pi$
$158$		0			0
$159$	191.202	−	208.215i	1.20253	−	1.30953i
$160$		0			0
$161$	374.551			2.32640
$162$		0			0
$163$	−21.3679	−	21.3679i	−0.131091	−	0.131091i	0.638517	−	0.769608i	$-0.279548\pi$
$163$	−21.3679	−	21.3679i	−0.131091	−	0.131091i	−0.769608	+	0.638517i	$0.779548\pi$
$164$		0			0
$165$	12.3568	−	13.4562i	0.0748895	−	0.0815528i
$166$		0			0
$167$	21.9423	+	21.9423i	0.131391	+	0.131391i	0.769744	−	0.638353i	$-0.220384\pi$
$167$	21.9423	+	21.9423i	0.131391	+	0.131391i	−0.638353	+	0.769744i	$0.720384\pi$
$168$		0			0
$169$	39.8587			0.235850
$170$		0			0
$171$	−78.9287	+	6.73583i	−0.461571	+	0.0393908i
$172$		0			0
$173$	−158.225	−	158.225i	−0.914596	−	0.914596i	0.0820337	−	0.996630i	$-0.473858\pi$
$173$	−158.225	−	158.225i	−0.914596	−	0.914596i	−0.996630	+	0.0820337i	$0.973858\pi$
$174$		0			0
$175$	35.6330	−	35.6330i	0.203617	−	0.203617i
$176$		0			0
$177$	−179.948	+	195.959i	−1.01666	+	1.10712i
$178$		0			0
$179$	−308.059			−1.72100			−0.860499	−	0.509453i	$-0.829848\pi$
$179$	−308.059			−1.72100			−0.860499	+	0.509453i	$0.829848\pi$
$180$		0			0
$181$	204.994	+	204.994i	1.13257	+	1.13257i	0.989749	+	0.142816i	$0.0456159\pi$
$181$	204.994	+	204.994i	1.13257	+	1.13257i	0.142816	+	0.989749i	$0.454384\pi$
$182$		0			0
$183$	74.6139	−	3.17803i	0.407726	−	0.0173663i
$184$		0			0
$185$	−12.4049			−0.0670536
$186$		0			0
$187$	−17.0568	+	43.0412i	−0.0912126	+	0.230167i
$188$		0			0
$189$	−34.6559	−	269.905i	−0.183364	−	1.42807i
$190$		0			0
$191$			255.477i			1.33758i	0.743452	+	0.668789i	$0.233187\pi$
$191$			255.477i			1.33758i	−0.743452	+	0.668789i	$0.766813\pi$
$192$		0			0
$193$	151.165	+	151.165i	0.783239	+	0.783239i	0.980376	−	0.197137i	$-0.0631643\pi$
$193$	151.165	+	151.165i	0.783239	+	0.783239i	−0.197137	+	0.980376i	$0.563164\pi$
$194$		0			0
$195$	−96.8588	+	4.12550i	−0.496712	+	0.0211564i
$196$		0			0
$197$	30.9843	−	30.9843i	0.157281	−	0.157281i	−0.624080	−	0.781361i	$-0.714526\pi$
$197$	30.9843	−	30.9843i	0.157281	−	0.157281i	0.781361	+	0.624080i	$0.214526\pi$
$198$		0			0
$199$	27.6856	−	27.6856i	0.139124	−	0.139124i	−0.634115	−	0.773239i	$-0.718635\pi$
$199$	27.6856	−	27.6856i	0.139124	−	0.139124i	0.773239	+	0.634115i	$0.218635\pi$
$200$		0			0
$201$	163.576	−	178.130i	0.813811	−	0.886221i
$202$		0			0
$203$		−	290.861i		−	1.43281i
$204$		0			0
$205$	−53.8075			−0.262476
$206$		0			0
$207$	255.759	+	215.538i	1.23555	+	1.04125i
$208$		0			0
$209$	16.9498	+	16.9498i	0.0810993	+	0.0810993i
$210$		0			0
$211$	−213.398	−	213.398i	−1.01136	−	1.01136i	−0.999935	−	0.0114297i	$-0.996362\pi$
$211$	−213.398	−	213.398i	−1.01136	−	1.01136i	−0.0114297	−	0.999935i	$-0.503638\pi$
$212$		0			0
$213$	−211.978	+	9.02878i	−0.995203	+	0.0423886i
$214$		0			0
$215$	−37.9407	+	37.9407i	−0.176468	+	0.176468i
$216$		0			0
$217$	550.076			2.53491
$218$		0			0
$219$	−4.15970	−	97.6617i	−0.0189941	−	0.445944i
$220$		0			0
$221$	225.507	−	97.5021i	1.02039	−	0.441186i
$222$		0			0
$223$			80.0906i			0.359151i	0.983744	+	0.179575i	$0.0574724\pi$
$223$			80.0906i			0.359151i	−0.983744	+	0.179575i	$0.942528\pi$
$224$		0			0
$225$	44.8370	−	3.82643i	0.199276	−	0.0170063i
$226$		0			0
$227$	318.663	−	318.663i	1.40380	−	1.40380i	0.616258	−	0.787545i	$-0.288648\pi$
$227$	318.663	−	318.663i	1.40380	−	1.40380i	0.787545	−	0.616258i	$-0.211352\pi$
$228$		0			0
$229$			210.424i			0.918882i	0.888208	+	0.459441i	$0.151950\pi$
$229$			210.424i			0.918882i	−0.888208	+	0.459441i	$0.848050\pi$
$230$		0			0
$231$	−55.6951	+	60.6506i	−0.241104	+	0.262557i
$232$		0			0
$233$	44.8496	+	44.8496i	0.192487	+	0.192487i	0.796770	−	0.604283i	$-0.206540\pi$
$233$	44.8496	+	44.8496i	0.192487	+	0.192487i	−0.604283	+	0.796770i	$0.706540\pi$
$234$		0			0
$235$	106.650	−	106.650i	0.453829	−	0.453829i
$236$		0			0
$237$	249.259	−	10.6167i	1.05173	−	0.0447961i
$238$		0			0
$239$		−	260.966i		−	1.09191i	−0.837815	−	0.545955i	$-0.816167\pi$
$239$		−	260.966i		−	1.09191i	0.837815	−	0.545955i	$-0.183833\pi$
$240$		0			0
$241$	100.517	−	100.517i	0.417085	−	0.417085i	−0.467113	−	0.884198i	$-0.654706\pi$
$241$	100.517	−	100.517i	0.417085	−	0.417085i	0.884198	+	0.467113i	$0.154706\pi$
$242$		0			0
$243$	131.654	−	204.245i	0.541787	−	0.840516i
$244$		0			0
$245$	−83.1315	+	83.1315i	−0.339312	+	0.339312i
$246$		0			0
$247$		−	127.202i		−	0.514989i
$248$		0			0
$249$	−43.5606	+	47.4364i	−0.174942	+	0.190508i
$250$		0			0
$251$			156.051i			0.621716i	0.950456	+	0.310858i	$0.100616\pi$
$251$			156.051i			0.621716i	−0.950456	+	0.310858i	$0.899384\pi$
$252$		0			0
$253$		−	101.210i		−	0.400039i
$254$		0			0
$255$	−102.654	+	49.6712i	−0.402563	+	0.194789i
$256$		0			0
$257$	−265.279			−1.03221			−0.516106	−	0.856525i	$-0.672619\pi$
$257$	−265.279			−1.03221			−0.516106	+	0.856525i	$0.672619\pi$
$258$		0			0
$259$	55.9121			0.215877
$260$		0			0
$261$	167.378	−	198.612i	0.641295	−	0.760965i
$262$		0			0
$263$	110.361			0.419624			0.209812	−	0.977742i	$-0.432715\pi$
$263$	110.361			0.419624			0.209812	+	0.977742i	$0.432715\pi$
$264$		0			0
$265$	−148.989	−	148.989i	−0.562222	−	0.562222i
$266$		0			0
$267$	52.1379	+	47.8779i	0.195273	+	0.179318i
$268$		0			0
$269$	177.791	+	177.791i	0.660934	+	0.660934i	0.955600	−	0.294666i	$-0.0952085\pi$
$269$	177.791	+	177.791i	0.660934	+	0.660934i	−0.294666	+	0.955600i	$0.595208\pi$
$270$		0			0
$271$	98.4785			0.363389			0.181695	−	0.983355i	$-0.441842\pi$
$271$	98.4785			0.363389			0.181695	+	0.983355i	$0.441842\pi$
$272$		0			0
$273$	436.568	−	18.5947i	1.59915	−	0.0681125i
$274$		0			0
$275$	−9.62865	−	9.62865i	−0.0350133	−	0.0350133i
$276$		0			0
$277$	−238.488	+	238.488i	−0.860966	+	0.860966i	−0.991450	−	0.130484i	$-0.958347\pi$
$277$	−238.488	+	238.488i	−0.860966	+	0.860966i	0.130484	+	0.991450i	$0.458347\pi$
$278$		0			0
$279$	375.615	+	316.545i	1.34629	+	1.13457i
$280$		0			0
$281$	−48.7233			−0.173392			−0.0866962	−	0.996235i	$-0.527631\pi$
$281$	−48.7233			−0.173392			−0.0866962	+	0.996235i	$0.527631\pi$
$282$		0			0
$283$	−95.4838	−	95.4838i	−0.337399	−	0.337399i	0.517989	−	0.855387i	$-0.326681\pi$
$283$	−95.4838	−	95.4838i	−0.337399	−	0.337399i	−0.855387	+	0.517989i	$0.826681\pi$
$284$		0			0
$285$	2.51257	+	58.9903i	0.00881605	+	0.206984i
$286$		0			0
$287$	242.525			0.845033
$288$		0			0
$289$	197.966	−	210.548i	0.685002	−	0.728541i
$290$		0			0
$291$	−8.38794	−	196.933i	−0.0288245	−	0.676744i
$292$		0			0
$293$		−	7.56414i		−	0.0258162i	−0.999917	−	0.0129081i	$-0.995891\pi$
$293$		−	7.56414i		−	0.0258162i	0.999917	−	0.0129081i	$-0.00410888\pi$
$294$		0			0
$295$	140.220	+	140.220i	0.475321	+	0.475321i
$296$		0			0
$297$	−72.9329	+	9.36461i	−0.245565	+	0.0315307i
$298$		0			0
$299$	−379.773	+	379.773i	−1.27014	+	1.27014i
$300$		0			0
$301$	171.009	−	171.009i	0.568135	−	0.568135i
$302$		0			0
$303$	101.441	+	93.1531i	0.334790	+	0.307436i
$304$		0			0
$305$		−	55.6644i		−	0.182506i
$306$		0			0
$307$	194.222			0.632646			0.316323	−	0.948652i	$-0.397552\pi$
$307$	194.222			0.632646			0.316323	+	0.948652i	$0.397552\pi$
$308$		0			0
$309$	203.350	−	221.443i	0.658091	−	0.716646i
$310$		0			0
$311$	−291.103	−	291.103i	−0.936023	−	0.936023i	0.0620505	−	0.998073i	$-0.480236\pi$
$311$	−291.103	−	291.103i	−0.936023	−	0.936023i	−0.998073	+	0.0620505i	$0.980236\pi$
$312$		0			0
$313$	−29.2841	−	29.2841i	−0.0935595	−	0.0935595i	0.658778	−	0.752337i	$-0.271074\pi$
$313$	−29.2841	−	29.2841i	−0.0935595	−	0.0935595i	−0.752337	+	0.658778i	$0.771074\pi$
$314$		0			0
$315$	−202.092	+	17.2467i	−0.641562	+	0.0547514i
$316$		0			0
$317$	−11.0783	+	11.0783i	−0.0349472	+	0.0349472i	−0.724364	−	0.689417i	$-0.757867\pi$
$317$	−11.0783	+	11.0783i	−0.0349472	+	0.0349472i	0.689417	+	0.724364i	$0.257867\pi$
$318$		0			0
$319$	−78.5955			−0.246381
$320$		0			0
$321$	262.965	−	11.2004i	0.819204	−	0.0348923i
$322$		0			0
$323$	−59.3821	−	137.342i	−0.183846	−	0.425206i
$324$		0			0
$325$			72.2597i			0.222338i
$326$		0			0
$327$	−321.429	+	13.6906i	−0.982963	+	0.0418673i
$328$		0			0
$329$	−480.698	+	480.698i	−1.46109	+	1.46109i
$330$		0			0
$331$		−	4.89535i		−	0.0147896i	−0.999973	−	0.00739479i	$-0.997646\pi$
$331$		−	4.89535i		−	0.0147896i	0.999973	−	0.00739479i	$-0.00235385\pi$
$332$		0			0
$333$	38.1792	+	32.1751i	0.114652	+	0.0966219i
$334$		0			0
$335$	−127.462	−	127.462i	−0.380483	−	0.380483i
$336$		0			0
$337$	199.230	−	199.230i	0.591187	−	0.591187i	−0.346765	−	0.937952i	$-0.612720\pi$
$337$	199.230	−	199.230i	0.591187	−	0.591187i	0.937952	+	0.346765i	$0.112720\pi$
$338$		0			0
$339$	−17.7340	−	416.359i	−0.0523126	−	1.22820i
$340$		0			0
$341$		−	148.640i		−	0.435894i
$342$		0			0
$343$	25.4915	−	25.4915i	0.0743193	−	0.0743193i
$344$		0			0
$345$	168.619	−	183.622i	0.488751	−	0.532238i
$346$		0			0
$347$	−32.9992	+	32.9992i	−0.0950986	+	0.0950986i	−0.753056	−	0.657957i	$-0.771421\pi$
$347$	−32.9992	+	32.9992i	−0.0950986	+	0.0950986i	0.657957	+	0.753056i	$0.271421\pi$
$348$		0			0
$349$		−	142.114i		−	0.407204i	−0.979054	−	0.203602i	$-0.934735\pi$
$349$		−	142.114i		−	0.407204i	0.979054	−	0.203602i	$-0.0652648\pi$
$350$		0			0
$351$	308.807	+	238.529i	0.879793	+	0.679570i
$352$		0			0
$353$			251.688i			0.712998i	0.934296	+	0.356499i	$0.116030\pi$
$353$			251.688i			0.712998i	−0.934296	+	0.356499i	$0.883970\pi$
$354$		0			0
$355$			158.142i			0.445472i
$356$		0			0
$357$	462.687	−	223.881i	1.29604	−	0.627118i
$358$		0			0
$359$	608.063			1.69377			0.846884	−	0.531777i	$-0.178476\pi$
$359$	608.063			1.69377			0.846884	+	0.531777i	$0.178476\pi$
$360$		0			0
$361$	283.529			0.785400
$362$		0			0
$363$	−250.981	−	230.475i	−0.691408	−	0.634916i
$364$		0			0
$365$	−72.8588			−0.199613
$366$		0			0
$367$	−144.379	−	144.379i	−0.393404	−	0.393404i	0.482495	−	0.875899i	$-0.339731\pi$
$367$	−144.379	−	144.379i	−0.393404	−	0.393404i	−0.875899	+	0.482495i	$0.839731\pi$
$368$		0			0
$369$	165.606	+	139.563i	0.448797	+	0.378219i
$370$		0			0
$371$	671.531	+	671.531i	1.81006	+	1.81006i
$372$		0			0
$373$	194.808			0.522273			0.261136	−	0.965302i	$-0.415903\pi$
$373$	194.808			0.522273			0.261136	+	0.965302i	$0.415903\pi$
$374$		0			0
$375$	−1.42732	−	33.5106i	−0.00380618	−	0.0893617i
$376$		0			0
$377$	294.916	+	294.916i	0.782271	+	0.782271i
$378$		0			0
$379$	−5.41595	+	5.41595i	−0.0142901	+	0.0142901i	−0.714216	−	0.699926i	$-0.753216\pi$
$379$	−5.41595	+	5.41595i	−0.0142901	+	0.0142901i	0.699926	+	0.714216i	$0.253216\pi$
$380$		0			0
$381$	−360.385	−	330.939i	−0.945892	−	0.868607i
$382$		0			0
$383$	−634.562			−1.65682			−0.828410	−	0.560123i	$-0.810754\pi$
$383$	−634.562			−1.65682			−0.828410	+	0.560123i	$0.810754\pi$
$384$		0			0
$385$	43.3988	+	43.3988i	0.112724	+	0.112724i
$386$		0			0
$387$	215.180	−	18.3636i	0.556021	−	0.0474513i
$388$		0			0
$389$	251.247			0.645879			0.322940	−	0.946420i	$-0.395329\pi$
$389$	251.247			0.645879			0.322940	+	0.946420i	$0.395329\pi$
$390$		0			0
$391$	−232.755	+	587.336i	−0.595281	+	1.50214i
$392$		0			0
$393$	−732.866	+	31.2150i	−1.86480	+	0.0794274i
$394$		0			0
$395$		−	185.955i		−	0.470773i
$396$		0			0
$397$	−53.2426	−	53.2426i	−0.134112	−	0.134112i	0.636864	−	0.770976i	$-0.280231\pi$
$397$	−53.2426	−	53.2426i	−0.134112	−	0.134112i	−0.770976	+	0.636864i	$0.780231\pi$
$398$		0			0
$399$	−11.3248	−	265.885i	−0.0283830	−	0.666378i
$400$		0			0
$401$	206.592	−	206.592i	0.515192	−	0.515192i	−0.400921	−	0.916113i	$-0.631310\pi$
$401$	206.592	−	206.592i	0.515192	−	0.515192i	0.916113	+	0.400921i	$0.131310\pi$
$402$		0			0
$403$	−557.746	+	557.746i	−1.38398	+	1.38398i
$404$		0			0
$405$	−147.922	−	104.519i	−0.365239	−	0.258071i
$406$		0			0
$407$		−	15.1084i		−	0.0371214i
$408$		0			0
$409$	−444.763			−1.08744			−0.543720	−	0.839266i	$-0.682985\pi$
$409$	−444.763			−1.08744			−0.543720	+	0.839266i	$0.682985\pi$
$410$		0			0
$411$	392.376	+	360.317i	0.954687	+	0.876684i
$412$		0			0
$413$	−632.006	−	632.006i	−1.53028	−	1.53028i
$414$		0			0
$415$	33.9433	+	33.9433i	0.0817911	+	0.0817911i
$416$		0			0
$417$	−26.1333	−	613.558i	−0.0626697	−	1.47136i
$418$		0			0
$419$	−79.2500	+	79.2500i	−0.189141	+	0.189141i	−0.795325	−	0.606184i	$-0.792700\pi$
$419$	−79.2500	+	79.2500i	−0.189141	+	0.189141i	0.606184	+	0.795325i	$0.292700\pi$
$420$		0			0
$421$	−675.786			−1.60519			−0.802596	−	0.596523i	$-0.796549\pi$
$421$	−675.786			−1.60519			−0.802596	+	0.596523i	$0.796549\pi$
$422$		0			0
$423$	−604.862	+	51.6194i	−1.42993	+	0.122032i
$424$		0			0
$425$	33.7332	+	78.0197i	0.0793723	+	0.183576i
$426$		0			0
$427$			250.894i			0.587573i
$428$		0			0
$429$	−5.02461	−	117.968i	−0.0117124	−	0.274984i
$430$		0			0
$431$	−49.0841	+	49.0841i	−0.113884	+	0.113884i	−0.761752	−	0.647868i	$-0.775661\pi$
$431$	−49.0841	+	49.0841i	−0.113884	+	0.113884i	0.647868	+	0.761752i	$0.275661\pi$
$432$		0			0
$433$		−	649.869i		−	1.50085i	−0.660954	−	0.750427i	$-0.729848\pi$
$433$		−	649.869i		−	1.50085i	0.660954	−	0.750427i	$-0.270152\pi$
$434$		0			0
$435$	−142.593	−	130.943i	−0.327801	−	0.301018i
$436$		0			0
$437$	231.295	+	231.295i	0.529279	+	0.529279i
$438$		0			0
$439$	−248.118	+	248.118i	−0.565189	+	0.565189i	−0.930777	−	0.365588i	$-0.880868\pi$
$439$	−248.118	+	248.118i	−0.565189	+	0.565189i	0.365588	+	0.930777i	$0.380868\pi$
$440$		0			0
$441$	471.479	−	40.2364i	1.06911	−	0.0912389i
$442$		0			0
$443$		−	368.904i		−	0.832740i	−0.909195	−	0.416370i	$-0.863302\pi$
$443$		−	368.904i		−	0.832740i	0.909195	−	0.416370i	$-0.136698\pi$
$444$		0			0
$445$	37.3075	−	37.3075i	0.0838371	−	0.0838371i
$446$		0			0
$447$	−390.411	−	358.512i	−0.873403	−	0.802041i
$448$		0			0
$449$	−41.3853	+	41.3853i	−0.0921721	+	0.0921721i	−0.751689	−	0.659517i	$-0.770761\pi$
$449$	−41.3853	+	41.3853i	−0.0921721	+	0.0921721i	0.659517	+	0.751689i	$0.270761\pi$
$450$		0			0
$451$		−	65.5343i		−	0.145309i
$452$		0			0
$453$	−599.128	−	550.176i	−1.32258	−	1.21452i
$454$		0			0
$455$		−	325.693i		−	0.715810i
$456$		0			0
$457$		−	122.772i		−	0.268647i	−0.990938	−	0.134324i	$-0.957114\pi$
$457$		−	122.772i		−	0.268647i	0.990938	−	0.134324i	$-0.0428862\pi$
$458$		0			0
$459$	444.776	+	113.381i	0.969011	+	0.247018i
$460$		0			0
$461$	539.213			1.16966			0.584830	−	0.811156i	$-0.301161\pi$
$461$	539.213			1.16966			0.584830	+	0.811156i	$0.301161\pi$
$462$		0			0
$463$	922.385			1.99219			0.996096	−	0.0882752i	$-0.0281355\pi$
$463$	922.385			1.99219			0.996096	+	0.0882752i	$0.0281355\pi$
$464$		0			0
$465$	247.639	−	269.673i	0.532557	−	0.579942i
$466$		0			0
$467$	601.835			1.28873			0.644363	−	0.764720i	$-0.277123\pi$
$467$	601.835			1.28873			0.644363	+	0.764720i	$0.277123\pi$
$468$		0			0
$469$	574.504	+	574.504i	1.22496	+	1.22496i
$470$		0			0
$471$	312.333	−	340.123i	0.663127	−	0.722129i
$472$		0			0
$473$	−46.2094	−	46.2094i	−0.0976944	−	0.0976944i
$474$		0			0
$475$	44.0087			0.0926498
$476$		0			0
$477$	72.1119	+	844.988i	0.151178	+	1.77146i
$478$		0			0
$479$	281.746	+	281.746i	0.588196	+	0.588196i	0.937143	−	0.348947i	$-0.113461\pi$
$479$	281.746	+	281.746i	0.588196	+	0.588196i	−0.348947	+	0.937143i	$0.613461\pi$
$480$		0			0
$481$	−56.6917	+	56.6917i	−0.117862	+	0.117862i
$482$		0			0
$483$	−760.011	+	827.633i	−1.57352	+	1.71353i
$484$		0			0
$485$	−146.918			−0.302924
$486$		0			0
$487$	120.330	+	120.330i	0.247085	+	0.247085i	0.819773	−	0.572689i	$-0.194100\pi$
$487$	120.330	+	120.330i	0.247085	+	0.247085i	−0.572689	+	0.819773i	$0.694100\pi$
$488$		0			0
$489$	90.5741	−	3.85782i	0.185223	−	0.00788920i
$490$		0			0
$491$	−179.120			−0.364807			−0.182403	−	0.983224i	$-0.558388\pi$
$491$	−179.120			−0.364807			−0.182403	+	0.983224i	$0.558388\pi$
$492$		0			0
$493$	456.101	+	180.748i	0.925154	+	0.366629i
$494$		0			0
$495$	4.66035	+	54.6087i	0.00941485	+	0.110321i
$496$		0			0
$497$		−	712.789i		−	1.43418i
$498$		0			0
$499$	−294.438	−	294.438i	−0.590056	−	0.590056i	0.347591	−	0.937646i	$-0.387000\pi$
$499$	−294.438	−	294.438i	−0.590056	−	0.590056i	−0.937646	+	0.347591i	$0.887000\pi$
$500$		0			0
$501$	−93.0089	+	3.96152i	−0.185646	+	0.00790723i
$502$		0			0
$503$	−376.405	+	376.405i	−0.748320	+	0.748320i	−0.974164	−	0.225844i	$-0.927486\pi$
$503$	−376.405	+	376.405i	−0.748320	+	0.748320i	0.225844	+	0.974164i	$0.427486\pi$
$504$		0			0
$505$	72.5868	−	72.5868i	0.143736	−	0.143736i
$506$		0			0
$507$	−80.8784	+	88.0746i	−0.159523	+	0.173717i
$508$		0			0
$509$		−	775.516i		−	1.52361i	−0.647808	−	0.761804i	$-0.724314\pi$
$509$		−	775.516i		−	1.52361i	0.647808	−	0.761804i	$-0.275686\pi$
$510$		0			0
$511$	328.393			0.642648
$512$		0			0
$513$	145.272	−	188.074i	0.283182	−	0.366616i
$514$		0			0
$515$	−158.455	−	158.455i	−0.307679	−	0.307679i
$516$		0			0
$517$	129.893	+	129.893i	0.251243	+	0.251243i
$518$		0			0
$519$	670.684	−	28.5664i	1.29226	−	0.0550413i
$520$		0			0
$521$	93.7972	−	93.7972i	0.180033	−	0.180033i	−0.611337	−	0.791370i	$-0.709368\pi$
$521$	93.7972	−	93.7972i	0.180033	−	0.180033i	0.791370	+	0.611337i	$0.209368\pi$
$522$		0			0
$523$	196.732			0.376160			0.188080	−	0.982154i	$-0.439774\pi$
$523$	196.732			0.376160			0.188080	+	0.982154i	$0.439774\pi$
$524$		0			0
$525$	6.43329	+	151.041i	0.0122539	+	0.287697i
$526$		0			0
$527$	−341.831	+	862.579i	−0.648635	+	1.63677i
$528$		0			0
$529$		−	852.102i		−	1.61078i
$530$		0			0
$531$	−67.8675	−	795.253i	−0.127811	−	1.49765i
$532$		0			0
$533$	−245.906	+	245.906i	−0.461362	+	0.461362i
$534$		0			0
$535$		−	196.180i		−	0.366691i
$536$		0			0
$537$	625.090	−	680.708i	1.16404	−	1.26761i
$538$		0			0
$539$	−101.249	−	101.249i	−0.187846	−	0.187846i
$540$		0			0
$541$	47.8521	−	47.8521i	0.0884511	−	0.0884511i	−0.661497	−	0.749948i	$-0.730078\pi$
$541$	47.8521	−	47.8521i	0.0884511	−	0.0884511i	0.749948	+	0.661497i	$0.230078\pi$
$542$		0			0
$543$	−868.930	+	37.0103i	−1.60024	+	0.0681589i
$544$		0			0
$545$			239.796i			0.439993i
$546$		0			0
$547$	−497.936	+	497.936i	−0.910304	+	0.910304i	−0.996296	−	0.0859917i	$-0.972594\pi$
$547$	−497.936	+	497.936i	−0.910304	+	0.910304i	0.0859917	+	0.996296i	$0.472594\pi$
$548$		0			0
$549$	−144.379	+	171.321i	−0.262985	+	0.312060i
$550$		0			0
$551$	179.614	−	179.614i	0.325978	−	0.325978i
$552$		0			0
$553$			838.149i			1.51564i
$554$		0			0
$555$	25.1711	−	27.4108i	0.0453534	−	0.0493887i
$556$		0			0
$557$			846.792i			1.52027i	0.649763	+	0.760137i	$0.274868\pi$
$557$			846.792i			1.52027i	−0.649763	+	0.760137i	$0.725132\pi$
$558$		0			0
$559$			346.786i			0.620369i
$560$		0			0
$561$	−60.4965	−	125.026i	−0.107837	−	0.222862i
$562$		0			0
$563$	1044.84			1.85584			0.927921	−	0.372777i	$-0.121594\pi$
$563$	1044.84			1.85584			0.927921	+	0.372777i	$0.121594\pi$
$564$		0			0
$565$	−310.617			−0.549764
$566$		0			0
$567$	666.722	+	471.093i	1.17588	+	0.830852i
$568$		0			0
$569$	170.378			0.299434			0.149717	−	0.988729i	$-0.452164\pi$
$569$	170.378			0.299434			0.149717	+	0.988729i	$0.452164\pi$
$570$		0			0
$571$	312.578	+	312.578i	0.547422	+	0.547422i	0.925694	−	0.378273i	$-0.123482\pi$
$571$	312.578	+	312.578i	0.547422	+	0.547422i	−0.378273	+	0.925694i	$0.623482\pi$
$572$		0			0
$573$	−564.521	−	518.396i	−0.985202	−	0.904705i
$574$		0			0
$575$	−131.392	−	131.392i	−0.228507	−	0.228507i
$576$		0			0
$577$	−479.239			−0.830570			−0.415285	−	0.909691i	$-0.636318\pi$
$577$	−479.239			−0.830570			−0.415285	+	0.909691i	$0.636318\pi$
$578$		0			0
$579$	−640.758	+	27.2918i	−1.10666	+	0.0471361i
$580$		0			0
$581$	−152.991	−	152.991i	−0.263324	−	0.263324i
$582$		0			0
$583$	181.459	−	181.459i	0.311251	−	0.311251i
$584$		0			0
$585$	187.423	−	222.397i	0.320381	−	0.380166i
$586$		0			0
$587$	−809.409			−1.37889			−0.689445	−	0.724338i	$-0.742146\pi$
$587$	−809.409			−1.37889			−0.689445	+	0.724338i	$0.742146\pi$
$588$		0			0
$589$	339.686	+	339.686i	0.576717	+	0.576717i
$590$		0			0
$591$	5.59400	+	131.336i	0.00946531	+	0.222227i
$592$		0			0
$593$	−510.189			−0.860353			−0.430176	−	0.902745i	$-0.641549\pi$
$593$	−510.189			−0.860353			−0.430176	+	0.902745i	$0.641549\pi$
$594$		0			0
$595$	−152.044	−	351.655i	−0.255537	−	0.591017i
$596$		0			0
$597$	4.99844	+	117.354i	0.00837260	+	0.196572i
$598$		0			0
$599$		−	178.838i		−	0.298561i	−0.988795	−	0.149281i	$-0.952304\pi$
$599$		−	178.838i		−	0.298561i	0.988795	−	0.149281i	$-0.0476958\pi$
$600$		0			0
$601$	−362.122	−	362.122i	−0.602533	−	0.602533i	0.338451	−	0.940984i	$-0.390097\pi$
$601$	−362.122	−	362.122i	−0.602533	−	0.602533i	−0.940984	+	0.338451i	$0.890097\pi$
$602$		0			0
$603$	61.6927	+	722.898i	0.102310	+	1.19884i
$604$		0			0
$605$	−179.591	+	179.591i	−0.296844	+	0.296844i
$606$		0			0
$607$	516.300	−	516.300i	0.850577	−	0.850577i	−0.139627	−	0.990204i	$-0.544590\pi$
$607$	516.300	−	516.300i	0.850577	−	0.850577i	0.990204	+	0.139627i	$0.0445903\pi$
$608$		0			0
$609$	642.706	+	590.193i	1.05535	+	0.969118i
$610$		0			0
$611$		−	974.801i		−	1.59542i
$612$		0			0
$613$	−475.052			−0.774962			−0.387481	−	0.921878i	$-0.626655\pi$
$613$	−475.052			−0.774962			−0.387481	+	0.921878i	$0.626655\pi$
$614$		0			0
$615$	109.182	−	118.897i	0.177532	−	0.193328i
$616$		0			0
$617$	693.798	+	693.798i	1.12447	+	1.12447i	0.991061	+	0.133410i	$0.0425926\pi$
$617$	693.798	+	693.798i	1.12447	+	1.12447i	0.133410	+	0.991061i	$0.457407\pi$
$618$		0			0
$619$	285.924	+	285.924i	0.461913	+	0.461913i	0.899282	−	0.437369i	$-0.144090\pi$
$619$	285.924	+	285.924i	0.461913	+	0.461913i	−0.437369	+	0.899282i	$0.644090\pi$
$620$		0			0
$621$	−995.235	+	127.789i	−1.60263	+	0.205779i
$622$		0			0
$623$	−168.155	+	168.155i	−0.269911	+	0.269911i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−71.8466	+	3.06016i	−0.114588	+	0.00488064i
$628$		0			0
$629$	−34.7452	+	87.6763i	−0.0552388	+	0.139390i
$630$		0			0
$631$		−	341.848i		−	0.541756i	−0.962614	−	0.270878i	$-0.912686\pi$
$631$		−	341.848i		−	0.541756i	0.962614	−	0.270878i	$-0.0873140\pi$
$632$		0			0
$633$	904.550	−	38.5275i	1.42899	−	0.0608649i
$634$		0			0
$635$	−257.875	+	257.875i	−0.406102	+	0.406102i
$636$		0			0
$637$			759.839i			1.19284i
$638$		0			0
$639$	410.180	−	486.722i	0.641909	−	0.761694i
$640$		0			0
$641$	51.1057	+	51.1057i	0.0797281	+	0.0797281i	0.745846	−	0.666118i	$-0.232045\pi$
$641$	51.1057	+	51.1057i	0.0797281	+	0.0797281i	−0.666118	+	0.745846i	$0.732045\pi$
$642$		0			0
$643$	−307.178	+	307.178i	−0.477727	+	0.477727i	−0.904404	−	0.426677i	$-0.859684\pi$
$643$	−307.178	+	307.178i	−0.477727	+	0.477727i	0.426677	+	0.904404i	$0.359684\pi$
$644$		0			0
$645$	−6.84993	−	160.823i	−0.0106200	−	0.249338i
$646$		0			0
$647$			513.453i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$647$			513.453i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$648$		0			0
$649$	−170.779	+	170.779i	−0.263141	+	0.263141i
$650$		0			0
$651$	−1116.17	+	1215.49i	−1.71455	+	1.86711i
$652$		0			0
$653$	514.508	−	514.508i	0.787915	−	0.787915i	−0.193237	−	0.981152i	$-0.561899\pi$
$653$	514.508	−	514.508i	0.787915	−	0.787915i	0.981152	+	0.193237i	$0.0618987\pi$
$654$		0			0
$655$			546.742i			0.834720i
$656$		0			0
$657$	224.241	+	188.977i	0.341310	+	0.287635i
$658$		0			0
$659$		−	315.764i		−	0.479156i	−0.970877	−	0.239578i	$-0.922991\pi$
$659$		−	315.764i		−	0.479156i	0.970877	−	0.239578i	$-0.0770091\pi$
$660$		0			0
$661$			365.392i			0.552787i	0.961045	+	0.276393i	$0.0891392\pi$
$661$			365.392i			0.552787i	−0.961045	+	0.276393i	$0.910861\pi$
$662$		0			0
$663$	−242.135	+	696.141i	−0.365212	+	1.04999i
$664$		0			0
$665$	−198.358			−0.298283
$666$		0			0
$667$	−1072.51			−1.60796
$668$		0			0
$669$	−176.974	−	162.514i	−0.264535	−	0.242921i
$670$		0			0
$671$	67.7958			0.101037
$672$		0			0
$673$	−930.039	−	930.039i	−1.38193	−	1.38193i	−0.841188	−	0.540743i	$-0.818143\pi$
$673$	−930.039	−	930.039i	−1.38193	−	1.38193i	−0.540743	−	0.841188i	$-0.681857\pi$
$674$		0			0
$675$	−82.5249	+	106.839i	−0.122259	+	0.158280i
$676$		0			0
$677$	649.114	+	649.114i	0.958810	+	0.958810i	0.999185	−	0.0403748i	$-0.0128552\pi$
$677$	649.114	+	649.114i	0.958810	+	0.958810i	−0.0403748	+	0.999185i	$0.512855\pi$
$678$		0			0
$679$	662.197			0.975254
$680$		0			0
$681$	57.5324	+	1350.75i	0.0844822	+	1.98348i
$682$		0			0
$683$	236.907	+	236.907i	0.346863	+	0.346863i	0.858940	−	0.512077i	$-0.171124\pi$
$683$	236.907	+	236.907i	0.346863	+	0.346863i	−0.512077	+	0.858940i	$0.671124\pi$
$684$		0			0
$685$	280.767	−	280.767i	0.409878	−	0.409878i
$686$		0			0
$687$	−464.967	−	426.977i	−0.676808	−	0.621509i
$688$		0			0
$689$	−1361.79			−1.97647
$690$		0			0
$691$	−499.054	−	499.054i	−0.722220	−	0.722220i	0.246837	−	0.969057i	$-0.420609\pi$
$691$	−499.054	−	499.054i	−0.722220	−	0.722220i	−0.969057	+	0.246837i	$0.920609\pi$
$692$		0			0
$693$	−21.0054	−	246.136i	−0.0303108	−	0.355174i
$694$		0			0
$695$	−457.734			−0.658610
$696$		0			0
$697$	−150.711	+	380.305i	−0.216228	+	0.545631i
$698$		0			0
$699$	−190.108	+	8.09728i	−0.271972	+	0.0115841i
$700$		0			0
$701$		−	568.709i		−	0.811283i	−0.914032	−	0.405641i	$-0.867048\pi$
$701$		−	568.709i		−	0.811283i	0.914032	−	0.405641i	$-0.132952\pi$
$702$		0			0
$703$	34.5272	+	34.5272i	0.0491141	+	0.0491141i
$704$		0			0
$705$	19.2549	+	452.067i	0.0273119	+	0.641229i
$706$		0			0
$707$	−327.168	+	327.168i	−0.462755	+	0.462755i
$708$		0			0
$709$	−767.681	+	767.681i	−1.08277	+	1.08277i	−0.0865160	+	0.996250i	$0.527573\pi$
$709$	−767.681	+	767.681i	−1.08277	+	1.08277i	−0.996250	+	0.0865160i	$0.972427\pi$
$710$		0			0
$711$	−482.319	+	572.323i	−0.678367	+	0.804955i
$712$		0			0
$713$		−	2028.33i		−	2.84478i
$714$		0			0
$715$	−88.0079			−0.123088
$716$		0			0
$717$	576.650	+	529.534i	0.804254	+	0.738541i
$718$		0			0
$719$	−129.102	−	129.102i	−0.179558	−	0.179558i	0.611605	−	0.791163i	$-0.290524\pi$
$719$	−129.102	−	129.102i	−0.179558	−	0.179558i	−0.791163	+	0.611605i	$0.790524\pi$
$720$		0			0
$721$	714.197	+	714.197i	0.990565	+	0.990565i
$722$		0			0
$723$	18.1477	+	426.073i	0.0251006	+	0.589313i
$724$		0			0
$725$	−102.033	+	102.033i	−0.140736	+	0.140736i
$726$		0			0
$727$	−743.210			−1.02230			−0.511149	−	0.859492i	$-0.670780\pi$
$727$	−743.210			−1.02230			−0.511149	+	0.859492i	$0.670780\pi$
$728$		0			0
$729$	184.171	+	705.352i	0.252636	+	0.967561i
$730$		0			0
$731$	161.891	+	374.429i	0.221465	+	0.512215i
$732$		0			0
$733$			728.809i			0.994283i	0.867669	+	0.497141i	$0.165617\pi$
$733$			728.809i			0.994283i	−0.867669	+	0.497141i	$0.834383\pi$
$734$		0			0
$735$	−15.0088	−	352.377i	−0.0204201	−	0.479425i
$736$		0			0
$737$	155.241	−	155.241i	0.210639	−	0.210639i
$738$		0			0
$739$		−	598.907i		−	0.810429i	−0.914222	−	0.405215i	$-0.867197\pi$
$739$		−	598.907i		−	0.810429i	0.914222	−	0.405215i	$-0.132803\pi$
$740$		0			0
$741$	281.075	+	258.109i	0.379318	+	0.348326i
$742$		0			0
$743$	−265.612	−	265.612i	−0.357485	−	0.357485i	0.505400	−	0.862885i	$-0.331345\pi$
$743$	−265.612	−	265.612i	−0.357485	−	0.357485i	−0.862885	+	0.505400i	$0.831345\pi$
$744$		0			0
$745$	−279.360	+	279.360i	−0.374980	+	0.374980i
$746$		0			0
$747$	−16.4289	−	192.509i	−0.0219931	−	0.257710i
$748$		0			0
$749$			884.234i			1.18055i
$750$		0			0
$751$	963.718	−	963.718i	1.28325	−	1.28325i	0.344436	−	0.938810i	$-0.388070\pi$
$751$	963.718	−	963.718i	1.28325	−	1.28325i	0.938810	−	0.344436i	$-0.111930\pi$
$752$		0			0
$753$	−344.821	−	316.647i	−0.457929	−	0.420514i
$754$		0			0
$755$	−428.709	+	428.709i	−0.567826	+	0.567826i
$756$		0			0
$757$		−	798.550i		−	1.05489i	−0.849590	−	0.527444i	$-0.823151\pi$
$757$		−	798.550i		−	1.05489i	0.849590	−	0.527444i	$-0.176849\pi$
$758$		0			0
$759$	223.641	+	205.368i	0.294652	+	0.270577i
$760$		0			0
$761$		−	729.339i		−	0.958395i	−0.877707	−	0.479198i	$-0.840928\pi$
$761$		−	729.339i		−	0.958395i	0.877707	−	0.479198i	$-0.159072\pi$
$762$		0			0
$763$		−	1080.82i		−	1.41655i
$764$		0			0
$765$	98.5403	−	327.620i	0.128811	−	0.428261i
$766$		0			0
$767$	1281.64			1.67097
$768$		0			0
$769$	−10.5784			−0.0137560			−0.00687801	−	0.999976i	$-0.502189\pi$
$769$	−10.5784			−0.0137560			−0.00687801	+	0.999976i	$0.502189\pi$
$770$		0			0
$771$	538.284	−	586.178i	0.698164	−	0.760283i
$772$		0			0
$773$	−608.979			−0.787813			−0.393906	−	0.919151i	$-0.628877\pi$
$773$	−608.979			−0.787813			−0.393906	+	0.919151i	$0.628877\pi$
$774$		0			0
$775$	−192.966	−	192.966i	−0.248988	−	0.248988i
$776$		0			0
$777$	−113.453	+	123.547i	−0.146014	+	0.159006i
$778$		0			0
$779$	149.765	+	149.765i	0.192253	+	0.192253i
$780$		0			0
$781$	−192.608			−0.246617
$782$		0			0
$783$	99.2354	+	772.859i	0.126737	+	0.987048i
$784$		0			0
$785$	−243.376	−	243.376i	−0.310034	−	0.310034i
$786$		0			0
$787$	787.269	−	787.269i	1.00034	−	1.00034i	0.000341613	−	1.00000i	$-0.499891\pi$
$787$	787.269	−	787.269i	1.00034	−	1.00034i	1.00000		0.000341613i	$-0.000108739\pi$
$788$		0			0
$789$	−223.937	+	243.862i	−0.283824	+	0.309077i
$790$		0			0
$791$	1400.03			1.76995
$792$		0			0
$793$	−254.392	−	254.392i	−0.320797	−	0.320797i
$794$		0			0
$795$	631.533	−	26.8989i	0.794382	−	0.0338351i
$796$		0			0
$797$	904.365			1.13471			0.567356	−	0.823473i	$-0.307966\pi$
$797$	904.365			1.13471			0.567356	+	0.823473i	$0.307966\pi$
$798$		0			0
$799$	−455.069	−	1052.50i	−0.569548	−	1.31728i
$800$		0			0
$801$	−211.589	+	18.0572i	−0.264156	+	0.0225433i
$802$		0			0
$803$		−	88.7375i		−	0.110507i
$804$		0			0
$805$	592.216	+	592.216i	0.735673	+	0.735673i
$806$		0			0
$807$	−753.621	+	32.0990i	−0.933855	+	0.0397757i
$808$		0			0
$809$	118.629	−	118.629i	0.146637	−	0.146637i	−0.629977	−	0.776614i	$-0.716936\pi$
$809$	118.629	−	118.629i	0.146637	−	0.146637i	0.776614	+	0.629977i	$0.216936\pi$
$810$		0			0
$811$	−366.015	+	366.015i	−0.451313	+	0.451313i	−0.895790	−	0.444477i	$-0.853389\pi$
$811$	−366.015	+	366.015i	−0.451313	+	0.451313i	0.444477	+	0.895790i	$0.353389\pi$
$812$		0			0
$813$	−199.825	+	217.605i	−0.245788	+	0.267657i
$814$		0			0
$815$		−	67.5712i		−	0.0829094i
$816$		0			0
$817$	211.205			0.258512
$818$		0			0
$819$	−844.763	+	1002.40i	−1.03146	+	1.22393i
$820$		0			0
$821$	−118.563	−	118.563i	−0.144412	−	0.144412i	0.631204	−	0.775617i	$-0.282561\pi$
$821$	−118.563	−	118.563i	−0.144412	−	0.144412i	−0.775617	+	0.631204i	$0.782561\pi$
$822$		0			0
$823$	−920.549	−	920.549i	−1.11853	−	1.11853i	−0.991958	−	0.126571i	$-0.959603\pi$
$823$	−920.549	−	920.549i	−1.11853	−	1.11853i	−0.126571	−	0.991958i	$-0.540397\pi$
$824$		0			0
$825$	40.8139	−	1.73838i	0.0494714	−	0.00210713i
$826$		0			0
$827$	−744.264	+	744.264i	−0.899956	+	0.899956i	−0.995432	−	0.0954753i	$-0.969563\pi$
$827$	−744.264	+	744.264i	−0.899956	+	0.899956i	0.0954753	+	0.995432i	$0.469563\pi$
$828$		0			0
$829$	−1147.62			−1.38434			−0.692170	−	0.721734i	$-0.743345\pi$
$829$	−1147.62			−1.38434			−0.692170	+	0.721734i	$0.743345\pi$
$830$		0			0
$831$	−43.0573	−	1010.90i	−0.0518138	−	1.21649i
$832$		0			0
$833$	354.718	+	820.407i	0.425832	+	0.984883i
$834$		0			0
$835$			69.3876i			0.0830989i
$836$		0			0
$837$	−1461.63	+	187.674i	−1.74627	+	0.224222i
$838$		0			0
$839$	528.074	−	528.074i	0.629409	−	0.629409i	−0.318510	−	0.947919i	$-0.603183\pi$
$839$	528.074	−	528.074i	0.629409	−	0.629409i	0.947919	+	0.318510i	$0.103183\pi$
$840$		0			0
$841$		−	8.13526i		−	0.00967331i
$842$		0			0
$843$	98.8657	−	107.662i	0.117278	−	0.127713i
$844$		0			0
$845$	63.0222	+	63.0222i	0.0745824	+	0.0745824i
$846$		0			0
$847$	809.462	−	809.462i	0.955681	−	0.955681i
$848$		0			0
$849$	404.737	−	17.2389i	0.476722	−	0.0203050i
$850$		0			0
$851$		−	206.168i		−	0.242266i
$852$		0			0
$853$	−960.058	+	960.058i	−1.12551	+	1.12551i	−0.134609	+	0.990899i	$0.542978\pi$
$853$	−960.058	+	960.058i	−1.12551	+	1.12551i	−0.990899	+	0.134609i	$0.957022\pi$
$854$		0			0
$855$	−135.448	−	114.147i	−0.158418	−	0.133505i
$856$		0			0
$857$	−186.684	+	186.684i	−0.217835	+	0.217835i	−0.807585	−	0.589751i	$-0.799226\pi$
$857$	−186.684	+	186.684i	−0.217835	+	0.217835i	0.589751	+	0.807585i	$0.299226\pi$
$858$		0			0
$859$		−	78.7013i		−	0.0916197i	−0.998950	−	0.0458098i	$-0.985413\pi$
$859$		−	78.7013i		−	0.0916197i	0.998950	−	0.0458098i	$-0.0145868\pi$
$860$		0			0
$861$	−492.113	+	535.899i	−0.571560	+	0.622415i
$862$		0			0
$863$		−	1426.01i		−	1.65239i	−0.563384	−	0.826195i	$-0.690501\pi$
$863$		−	1426.01i		−	1.65239i	0.563384	−	0.826195i	$-0.309499\pi$
$864$		0			0
$865$		−	500.352i		−	0.578441i
$866$		0			0
$867$	63.5449	+	864.668i	0.0732929	+	0.997310i
$868$		0			0
$869$	226.482			0.260624
$870$		0			0
$871$	−1165.03			−1.33758
$872$		0			0
$873$	452.176	+	381.067i	0.517957	+	0.436502i
$874$		0			0
$875$	112.681			0.128779
$876$		0			0
$877$	−510.471	−	510.471i	−0.582064	−	0.582064i	0.353406	−	0.935470i	$-0.385024\pi$
$877$	−510.471	−	510.471i	−0.582064	−	0.582064i	−0.935470	+	0.353406i	$0.885024\pi$
$878$		0			0
$879$	16.7142	+	15.3486i	0.0190151	+	0.0174614i
$880$		0			0
$881$	881.501	+	881.501i	1.00057	+	1.00057i	1.00000		0.000568793i	$0.000181053\pi$
$881$	881.501	+	881.501i	1.00057	+	1.00057i	0.000568793		1.00000i	$0.499819\pi$
$882$		0			0
$883$	−432.082			−0.489334			−0.244667	−	0.969607i	$-0.578679\pi$
$883$	−432.082			−0.489334			−0.244667	+	0.969607i	$0.578679\pi$
$884$		0			0
$885$	−594.362	+	25.3157i	−0.671596	+	0.0286053i
$886$		0			0
$887$	−1012.18	−	1012.18i	−1.14113	−	1.14113i	−0.988243	−	0.152888i	$-0.951142\pi$
$887$	−1012.18	−	1012.18i	−1.14113	−	1.14113i	−0.152888	−	0.988243i	$-0.548858\pi$
$888$		0			0
$889$	1162.31	−	1162.31i	1.30743	−	1.30743i
$890$		0			0
$891$	127.297	−	180.160i	0.142870	−	0.202199i
$892$		0			0
$893$	−593.688			−0.664824
$894$		0			0
$895$	−487.083	−	487.083i	−0.544227	−	0.544227i
$896$		0			0
$897$	−68.5654	−	1609.78i	−0.0764385	−	1.79463i
$898$		0			0
$899$	−1575.12			−1.75207
$900$		0			0
$901$	−1470.34	+	635.728i	−1.63190	+	0.705581i
$902$		0			0
$903$	30.8744	+	724.871i	0.0341909	+	0.802736i
$904$		0			0
$905$			648.249i			0.716297i
$906$		0			0
$907$	−18.5371	−	18.5371i	−0.0204378	−	0.0204378i	0.696814	−	0.717252i	$-0.254600\pi$
$907$	−18.5371	−	18.5371i	−0.0204378	−	0.0204378i	−0.717252	+	0.696814i	$0.754600\pi$
$908$		0			0
$909$	−411.675	+	35.1327i	−0.452888	+	0.0386498i
$910$		0			0
$911$	207.264	−	207.264i	0.227513	−	0.227513i	−0.584140	−	0.811653i	$-0.698568\pi$
$911$	207.264	−	207.264i	0.227513	−	0.227513i	0.811653	+	0.584140i	$0.198568\pi$
$912$		0			0
$913$	−41.3409	+	41.3409i	−0.0452803	+	0.0452803i
$914$		0			0
$915$	123.000	+	112.950i	0.134426	+	0.123443i
$916$		0			0
$917$		−	2464.31i		−	2.68736i
$918$		0			0
$919$	162.842			0.177195			0.0885975	−	0.996068i	$-0.471761\pi$
$919$	162.842			0.177195			0.0885975	+	0.996068i	$0.471761\pi$
$920$		0			0
$921$	−394.102	+	429.167i	−0.427906	+	0.465980i
$922$		0			0
$923$	722.728	+	722.728i	0.783020	+	0.783020i
$924$		0			0
$925$	−19.6139	−	19.6139i	−0.0212042	−	0.0212042i
$926$		0			0
$927$	76.6935	+	898.674i	0.0827330	+	0.969443i
$928$		0			0
$929$	−909.550	+	909.550i	−0.979063	+	0.979063i	−0.999785	−	0.0207219i	$-0.993404\pi$
$929$	−909.550	+	909.550i	−0.979063	+	0.979063i	0.0207219	+	0.999785i	$0.493404\pi$
$930$		0			0
$931$	462.768			0.497066
$932$		0			0
$933$	1233.93	−	52.5566i	1.32254	−	0.0563308i
$934$		0			0
$935$	−95.0232	+	41.0850i	−0.101629	+	0.0439411i
$936$		0			0
$937$			1307.32i			1.39521i	0.716481	+	0.697607i	$0.245752\pi$
$937$			1307.32i			1.39521i	−0.716481	+	0.697607i	$0.754248\pi$
$938$		0			0
$939$	124.129	−	5.28704i	0.132193	−	0.00563050i
$940$		0			0
$941$	−484.473	+	484.473i	−0.514849	+	0.514849i	−0.916008	−	0.401159i	$-0.868607\pi$
$941$	−484.473	+	484.473i	−0.514849	+	0.514849i	0.401159	+	0.916008i	$0.368607\pi$
$942$		0			0
$943$		−	894.275i		−	0.948329i
$944$		0			0
$945$	371.961	−	481.553i	0.393610	−	0.509580i
$946$		0			0
$947$	−473.011	−	473.011i	−0.499484	−	0.499484i	0.411793	−	0.911277i	$-0.364903\pi$
$947$	−473.011	−	473.011i	−0.499484	−	0.499484i	−0.911277	+	0.411793i	$0.864903\pi$
$948$		0			0
$949$	−332.972	+	332.972i	−0.350866	+	0.350866i
$950$		0			0
$951$	−2.00010	−	46.9585i	−0.00210316	−	0.0493781i
$952$		0			0
$953$			399.658i			0.419369i	0.977769	+	0.209684i	$0.0672436\pi$
$953$			399.658i			0.419369i	−0.977769	+	0.209684i	$0.932756\pi$
$954$		0			0
$955$	−403.945	+	403.945i	−0.422979	+	0.422979i
$956$		0			0
$957$	159.480	−	173.670i	0.166646	−	0.181473i
$958$		0			0
$959$	−1265.49	+	1265.49i	−1.31959	+	1.31959i
$960$		0			0
$961$		−	2017.86i		−	2.09975i
$962$		0			0
$963$	−508.839	+	603.792i	−0.528390	+	0.626991i
$964$		0			0
$965$			478.026i			0.495364i
$966$		0			0
$967$			1030.78i			1.06596i	0.846129	+	0.532979i	$0.178927\pi$
$967$			1030.78i			1.06596i	−0.846129	+	0.532979i	$0.821073\pi$
$968$		0			0
$969$	423.974	+	147.469i	0.437537	+	0.152187i
$970$		0			0
$971$	1510.93			1.55605			0.778027	−	0.628231i	$-0.216221\pi$
$971$	1510.93			1.55605			0.778027	+	0.628231i	$0.216221\pi$
$972$		0			0
$973$	2063.13			2.12038
$974$		0			0
$975$	−159.670	−	146.624i	−0.163764	−	0.150384i
$976$		0			0
$977$	−126.277			−0.129249			−0.0646247	−	0.997910i	$-0.520585\pi$
$977$	−126.277			−0.129249			−0.0646247	+	0.997910i	$0.520585\pi$
$978$		0			0
$979$	45.4382	+	45.4382i	0.0464129	+	0.0464129i
$980$		0			0
$981$	621.969	−	738.032i	0.634015	−	0.752326i
$982$		0			0
$983$	792.388	+	792.388i	0.806091	+	0.806091i	0.984040	−	0.177949i	$-0.0569461\pi$
$983$	792.388	+	792.388i	0.806091	+	0.806091i	−0.177949	+	0.984040i	$0.556946\pi$
$984$		0			0
$985$	97.9809			0.0994730
$986$		0			0
$987$	−86.7866	−	2037.58i	−0.0879297	−	2.06442i
$988$		0			0
$989$	−630.570	−	630.570i	−0.637583	−	0.637583i
$990$		0			0
$991$	−522.747	+	522.747i	−0.527495	+	0.527495i	−0.919825	−	0.392330i	$-0.871669\pi$
$991$	−522.747	+	522.747i	−0.527495	+	0.527495i	0.392330	+	0.919825i	$0.371669\pi$
$992$		0			0
$993$	10.8171	+	9.93328i	0.0108934	+	0.0100033i
$994$		0			0
$995$	87.5496			0.0879895
$996$		0			0
$997$	486.319	+	486.319i	0.487782	+	0.487782i	0.907606	−	0.419823i	$-0.137908\pi$
$997$	486.319	+	486.319i	0.487782	+	0.487782i	−0.419823	+	0.907606i	$0.637908\pi$
$998$		0			0
$999$	−148.567	+	19.0760i	−0.148715	+	0.0190951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.14	yes	96
3.2	odd	2	inner	1020.3.bc.a.701.13	✓	96
17.13	even	4	inner	1020.3.bc.a.761.13	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.13	✓	96	3.2	odd	2	inner
1020.3.bc.a.701.14	yes	96	1.1	even	1	trivial
1020.3.bc.a.761.13	yes	96	17.13	even	4	inner
1020.3.bc.a.761.14	yes	96	51.47	odd	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)

\(f(q)\)	\(=\)	\(q+(-2.02913 + 2.20967i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-7.12660 - 7.12660i) q^{7} +(-0.765285 - 8.96740i) q^{9} +O(q^{10})\)	\(q+(-2.02913 + 2.20967i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-7.12660 - 7.12660i) q^{7} +(-0.765285 - 8.96740i) q^{9} +(-1.92573 + 1.92573i) q^{11} +14.4519 q^{13} +(-6.70213 + 0.285463i) q^{15} +(15.6039 - 6.74664i) q^{17} -8.80173i q^{19} +(30.2082 - 1.28666i) q^{21} +(-26.2783 + 26.2783i) q^{23} +5.00000i q^{25} +(21.3679 + 16.5050i) q^{27} +(20.4067 + 20.4067i) q^{29} +(-38.5931 + 38.5931i) q^{31} +(-0.347677 - 8.16278i) q^{33} -22.5363i q^{35} +(-3.92278 + 3.92278i) q^{37} +(-29.3248 + 31.9340i) q^{39} +(-17.0154 + 17.0154i) q^{41} +23.9958i q^{43} +(12.9687 - 15.3887i) q^{45} -67.4512i q^{47} +52.5770i q^{49} +(-16.7545 + 48.1693i) q^{51} -94.2288 q^{53} -6.08969 q^{55} +(19.4489 + 17.8598i) q^{57} +88.6826 q^{59} +(-17.6026 - 17.6026i) q^{61} +(-58.4533 + 69.3610i) q^{63} +(22.8505 + 22.8505i) q^{65} -80.6140 q^{67} +(-4.74437 - 111.389i) q^{69} +(50.0090 + 50.0090i) q^{71} +(-23.0400 + 23.0400i) q^{73} +(-11.0484 - 10.1456i) q^{75} +27.4478 q^{77} +(-58.8042 - 58.8042i) q^{79} +(-79.8287 + 13.7252i) q^{81} +21.4676 q^{83} +(35.3394 + 14.0046i) q^{85} +(-86.4998 + 3.68428i) q^{87} -23.5953i q^{89} +(-102.993 - 102.993i) q^{91} +(-6.96772 - 163.588i) q^{93} +(13.9168 - 13.9168i) q^{95} +(-46.4595 + 46.4595i) q^{97} +(18.7425 + 15.7951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 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

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