LMFDB - Embedded newform 400.3.bg.c.337.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [400,3,Mod(17,400)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(400, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("400.17"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$400 = 2^{4} \cdot 5^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$ , degree $8$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			337.2
Character	$\chi$	$=$	400.337
Dual form			400.3.bg.c.273.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.210730 - 0.107372i) q^{3} +(-3.31432 + 3.74370i) q^{5} +(7.64532 + 7.64532i) q^{7} +(-5.25719 - 7.23590i) q^{9} +(-7.33868 - 5.33186i) q^{11} +(-2.12306 + 13.4044i) q^{13} +(1.10040 - 0.433046i) q^{15} +(0.704962 - 0.359196i) q^{17} +(-13.5696 - 4.40902i) q^{19} +(-0.790204 - 2.43200i) q^{21} +(-13.5597 + 2.14764i) q^{23} +(-3.03063 - 24.8156i) q^{25} +(0.663895 + 4.19167i) q^{27} +(-36.6306 + 11.9020i) q^{29} +(2.87530 - 8.84925i) q^{31} +(0.973987 + 1.91156i) q^{33} +(-53.9608 + 3.28280i) q^{35} +(9.13820 + 1.44735i) q^{37} +(1.88666 - 2.59677i) q^{39} +(-33.7351 + 24.5100i) q^{41} +(-49.4021 + 49.4021i) q^{43} +(44.5130 + 4.30070i) q^{45} +(-9.65116 + 18.9415i) q^{47} +67.9017i q^{49} -0.187125 q^{51} +(-56.8742 - 28.9788i) q^{53} +(44.2836 - 9.80236i) q^{55} +(2.38611 + 2.38611i) q^{57} +(45.6440 + 62.8235i) q^{59} +(11.4153 + 8.29369i) q^{61} +(15.1279 - 95.5136i) q^{63} +(-43.1458 - 52.3747i) q^{65} +(46.8978 - 23.8956i) q^{67} +(3.08803 + 1.00336i) q^{69} +(0.846117 + 2.60408i) q^{71} +(60.7976 - 9.62940i) q^{73} +(-2.02587 + 5.55481i) q^{75} +(-15.3427 - 96.8703i) q^{77} +(6.18905 - 2.01094i) q^{79} +(-24.5646 + 75.6022i) q^{81} +(-50.9593 - 100.013i) q^{83} +(-0.991742 + 3.82966i) q^{85} +(8.99712 + 1.42500i) q^{87} +(65.5853 - 90.2704i) q^{89} +(-118.713 + 86.2498i) q^{91} +(-1.55608 + 1.55608i) q^{93} +(61.4799 - 36.1875i) q^{95} +(-58.6053 + 115.019i) q^{97} +81.1325i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} + 10 q^{15} + 60 q^{17} - 90 q^{19} - 6 q^{21} - 10 q^{23} - 40 q^{25} + 100 q^{27} - 110 q^{29} + 6 q^{31} - 190 q^{33} + 120 q^{35}+ \cdots + 270 q^{97}+O(q^{100})$ 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 + 10 * q^15 + 60 * q^17 - 90 * q^19 - 6 * q^21 - 10 * q^23 - 40 * q^25 + 100 * q^27 - 110 * q^29 + 6 * q^31 - 190 * q^33 + 120 * q^35 + 50 * q^37 - 390 * q^39 - 86 * q^41 - 230 * q^43 + 310 * q^45 - 70 * q^47 + 16 * q^51 - 190 * q^53 + 250 * q^55 - 650 * q^57 + 260 * q^59 + 114 * q^61 + 20 * q^63 + 360 * q^65 - 270 * q^67 + 340 * q^69 + 66 * q^71 + 30 * q^73 + 90 * q^75 - 250 * q^77 + 210 * q^79 + 62 * q^81 + 600 * q^85 - 300 * q^87 - 10 * q^89 + 6 * q^91 + 520 * q^93 - 310 * q^95 + 270 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$ .

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{9}{20}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	−0.210730	−	0.107372i	−0.0702435	−	0.0357908i	0.418516	−	0.908209i	$-0.362550\pi$
$3$	−0.210730	−	0.107372i	−0.0702435	−	0.0357908i	−0.488759	+	0.872419i	$0.662550\pi$
$4$		0			0
$5$	−3.31432	+	3.74370i	−0.662863	+	0.748741i
$5$	−3.31432	+	3.74370i	−0.662863	+	0.748741i
$6$		0			0
$7$	7.64532	+	7.64532i	1.09219	+	1.09219i	0.995295	+	0.0968934i	$0.0308906\pi$
$7$	7.64532	+	7.64532i	1.09219	+	1.09219i	0.0968934	+	0.995295i	$0.469109\pi$
$8$		0			0
$9$	−5.25719	−	7.23590i	−0.584132	−	0.803989i
$10$		0			0
$11$	−7.33868	−	5.33186i	−0.667152	−	0.484715i	0.201918	−	0.979402i	$-0.435282\pi$
$11$	−7.33868	−	5.33186i	−0.667152	−	0.484715i	−0.869071	+	0.494688i	$0.835282\pi$
$12$		0			0
$13$	−2.12306	+	13.4044i	−0.163312	+	1.03111i	0.760799	+	0.648987i	$0.224807\pi$
$13$	−2.12306	+	13.4044i	−0.163312	+	1.03111i	−0.924111	+	0.382124i	$0.875193\pi$
$14$		0			0
$15$	1.10040	−	0.433046i	0.0733598	−	0.0288697i
$16$		0			0
$17$	0.704962	−	0.359196i	0.0414683	−	0.0211292i	−0.433133	−	0.901330i	$-0.642592\pi$
$17$	0.704962	−	0.359196i	0.0414683	−	0.0211292i	0.474602	+	0.880201i	$0.342592\pi$
$18$		0			0
$19$	−13.5696	−	4.40902i	−0.714187	−	0.232054i	−0.0706862	−	0.997499i	$-0.522519\pi$
$19$	−13.5696	−	4.40902i	−0.714187	−	0.232054i	−0.643501	+	0.765445i	$0.722519\pi$
$20$		0			0
$21$	−0.790204	−	2.43200i	−0.0376288	−	0.115809i
$22$		0			0
$23$	−13.5597	+	2.14764i	−0.589551	+	0.0933757i	−0.444080	−	0.895987i	$-0.646470\pi$
$23$	−13.5597	+	2.14764i	−0.589551	+	0.0933757i	−0.145470	+	0.989363i	$0.546470\pi$
$24$		0			0
$25$	−3.03063	−	24.8156i	−0.121225	−	0.992625i
$26$		0			0
$27$	0.663895	+	4.19167i	0.0245887	+	0.155247i
$28$		0			0
$29$	−36.6306	+	11.9020i	−1.26312	+	0.410413i	−0.862606	−	0.505876i	$-0.831169\pi$
$29$	−36.6306	+	11.9020i	−1.26312	+	0.410413i	−0.400517	+	0.916289i	$0.631169\pi$
$30$		0			0
$31$	2.87530	−	8.84925i	0.0927515	−	0.285460i	−0.893910	−	0.448247i	$-0.852048\pi$
$31$	2.87530	−	8.84925i	0.0927515	−	0.285460i	0.986661	+	0.162787i	$0.0520485\pi$
$32$		0			0
$33$	0.973987	+	1.91156i	0.0295148	+	0.0579260i
$34$		0			0
$35$	−53.9608	+	3.28280i	−1.54174	+	0.0937944i
$36$		0			0
$37$	9.13820	+	1.44735i	0.246978	+	0.0391175i	0.278696	−	0.960379i	$-0.410098\pi$
$37$	9.13820	+	1.44735i	0.246978	+	0.0391175i	−0.0317178	+	0.999497i	$0.510098\pi$
$38$		0			0
$39$	1.88666	−	2.59677i	0.0483759	−	0.0665838i
$40$		0			0
$41$	−33.7351	+	24.5100i	−0.822807	+	0.597805i	−0.917515	−	0.397701i	$-0.869808\pi$
$41$	−33.7351	+	24.5100i	−0.822807	+	0.597805i	0.0947079	+	0.995505i	$0.469808\pi$
$42$		0			0
$43$	−49.4021	+	49.4021i	−1.14889	+	1.14889i	−0.162113	+	0.986772i	$0.551831\pi$
$43$	−49.4021	+	49.4021i	−1.14889	+	1.14889i	−0.986772	+	0.162113i	$0.948169\pi$
$44$		0			0
$45$	44.5130	+	4.30070i	0.989179	+	0.0955711i
$46$		0			0
$47$	−9.65116	+	18.9415i	−0.205344	+	0.403010i	−0.970594	−	0.240723i	$-0.922615\pi$
$47$	−9.65116	+	18.9415i	−0.205344	+	0.403010i	0.765250	+	0.643733i	$0.222615\pi$
$48$		0			0
$49$			67.9017i			1.38575i
$50$		0			0
$51$	−0.187125			−0.00366911
$52$		0			0
$53$	−56.8742	−	28.9788i	−1.07310	−	0.546771i	−0.174102	−	0.984728i	$-0.555702\pi$
$53$	−56.8742	−	28.9788i	−1.07310	−	0.546771i	−0.898996	+	0.437957i	$0.855702\pi$
$54$		0			0
$55$	44.2836	−	9.80236i	0.805156	−	0.178225i
$56$		0			0
$57$	2.38611	+	2.38611i	0.0418616	+	0.0418616i
$58$		0			0
$59$	45.6440	+	62.8235i	0.773627	+	1.06481i	0.995957	+	0.0898343i	$0.0286338\pi$
$59$	45.6440	+	62.8235i	0.773627	+	1.06481i	−0.222330	+	0.974971i	$0.571366\pi$
$60$		0			0
$61$	11.4153	+	8.29369i	0.187136	+	0.135962i	0.677409	−	0.735607i	$-0.263103\pi$
$61$	11.4153	+	8.29369i	0.187136	+	0.135962i	−0.490273	+	0.871569i	$0.663103\pi$
$62$		0			0
$63$	15.1279	−	95.5136i	0.240125	−	1.51609i
$64$		0			0
$65$	−43.1458	−	52.3747i	−0.663781	−	0.805764i
$66$		0			0
$67$	46.8978	−	23.8956i	0.699968	−	0.356651i	−0.0675175	−	0.997718i	$-0.521508\pi$
$67$	46.8978	−	23.8956i	0.699968	−	0.356651i	0.767485	+	0.641067i	$0.221508\pi$
$68$		0			0
$69$	3.08803	+	1.00336i	0.0447541	+	0.0145415i
$70$		0			0
$71$	0.846117	+	2.60408i	0.0119171	+	0.0366772i	0.956838	−	0.290621i	$-0.0938619\pi$
$71$	0.846117	+	2.60408i	0.0119171	+	0.0366772i	−0.944921	+	0.327298i	$0.893862\pi$
$72$		0			0
$73$	60.7976	−	9.62940i	0.832844	−	0.131910i	0.274571	−	0.961567i	$-0.411464\pi$
$73$	60.7976	−	9.62940i	0.832844	−	0.131910i	0.558273	+	0.829657i	$0.311464\pi$
$74$		0			0
$75$	−2.02587	+	5.55481i	−0.0270116	+	0.0740642i
$76$		0			0
$77$	−15.3427	−	96.8703i	−0.199256	−	1.25806i
$78$		0			0
$79$	6.18905	−	2.01094i	0.0783423	−	0.0254550i	−0.269584	−	0.962977i	$-0.586886\pi$
$79$	6.18905	−	2.01094i	0.0783423	−	0.0254550i	0.347926	+	0.937522i	$0.386886\pi$
$80$		0			0
$81$	−24.5646	+	75.6022i	−0.303267	+	0.933360i
$82$		0			0
$83$	−50.9593	−	100.013i	−0.613967	−	1.20498i	−0.963413	−	0.268021i	$-0.913630\pi$
$83$	−50.9593	−	100.013i	−0.613967	−	1.20498i	0.349446	−	0.936957i	$-0.386370\pi$
$84$		0			0
$85$	−0.991742	+	3.82966i	−0.0116676	+	0.0450548i
$86$		0			0
$87$	8.99712	+	1.42500i	0.103415	+	0.0163794i
$88$		0			0
$89$	65.5853	−	90.2704i	0.736914	−	1.01427i	−0.261877	−	0.965101i	$-0.584341\pi$
$89$	65.5853	−	90.2704i	0.736914	−	1.01427i	0.998790	−	0.0491732i	$-0.0156586\pi$
$90$		0			0
$91$	−118.713	+	86.2498i	−1.30454	+	0.947800i
$92$		0			0
$93$	−1.55608	+	1.55608i	−0.0167320	+	0.0167320i
$94$		0			0
$95$	61.4799	−	36.1875i	0.647156	−	0.380921i
$96$		0			0
$97$	−58.6053	+	115.019i	−0.604178	+	1.18577i	0.363029	+	0.931778i	$0.381743\pi$
$97$	−58.6053	+	115.019i	−0.604178	+	1.18577i	−0.967207	+	0.253989i	$0.918257\pi$
$98$		0			0
$99$			81.1325i			0.819521i
$100$		0			0
$101$	−32.5145			−0.321926			−0.160963	−	0.986960i	$-0.551460\pi$
$101$	−32.5145			−0.321926			−0.160963	+	0.986960i	$0.551460\pi$
$102$		0			0
$103$	46.2893	+	23.5856i	0.449411	+	0.228986i	0.664022	−	0.747713i	$-0.268848\pi$
$103$	46.2893	+	23.5856i	0.449411	+	0.228986i	−0.214611	+	0.976700i	$0.568848\pi$
$104$		0			0
$105$	11.7237	+	5.10212i	0.111654	+	0.0485916i
$106$		0			0
$107$	34.7993	+	34.7993i	0.325227	+	0.325227i	0.850768	−	0.525541i	$-0.176137\pi$
$107$	34.7993	+	34.7993i	0.325227	+	0.325227i	−0.525541	+	0.850768i	$0.676137\pi$
$108$		0			0
$109$	76.0086	+	104.617i	0.697326	+	0.959787i	0.999978	+	0.00668585i	$0.00212819\pi$
$109$	76.0086	+	104.617i	0.697326	+	0.959787i	−0.302651	+	0.953101i	$0.597872\pi$
$110$		0			0
$111$	−1.77029	−	1.28619i	−0.0159486	−	0.0115873i
$112$		0			0
$113$	11.9724	−	75.5905i	0.105950	−	0.668942i	−0.876357	−	0.481663i	$-0.840033\pi$
$113$	11.9724	−	75.5905i	0.105950	−	0.668942i	0.982307	−	0.187279i	$-0.0599670\pi$
$114$		0			0
$115$	36.9009	−	57.8813i	0.320877	−	0.503316i
$116$		0			0
$117$	108.155	−	55.1075i	0.924398	−	0.471004i
$118$		0			0
$119$	8.13582	+	2.64349i	0.0683682	+	0.0222142i
$120$		0			0
$121$	−11.9636	−	36.8202i	−0.0988729	−	0.304299i
$122$		0			0
$123$	9.74071	−	1.54278i	0.0791928	−	0.0125429i
$124$		0			0
$125$	102.947	+	70.9011i	0.823574	+	0.567208i
$126$		0			0
$127$	−9.58264	−	60.5024i	−0.0754539	−	0.476397i	−0.996262	−	0.0863815i	$-0.972470\pi$
$127$	−9.58264	−	60.5024i	−0.0754539	−	0.476397i	0.920808	−	0.390016i	$-0.127530\pi$
$128$		0			0
$129$	15.7149	−	5.10609i	0.121821	−	0.0395821i
$130$		0			0
$131$	1.09573	−	3.37230i	0.00836432	−	0.0257427i	−0.946787	−	0.321860i	$-0.895692\pi$
$131$	1.09573	−	3.37230i	0.00836432	−	0.0257427i	0.955152	+	0.296117i	$0.0956919\pi$
$132$		0			0
$133$	−70.0353	−	137.452i	−0.526581	−	1.03347i
$134$		0			0
$135$	−17.8927	−	11.4071i	−0.132539	−	0.0844969i
$136$		0			0
$137$	246.624	+	39.0615i	1.80018	+	0.285120i	0.964497	−	0.264094i	$-0.0850728\pi$
$137$	246.624	+	39.0615i	1.80018	+	0.285120i	0.835682	+	0.549214i	$0.185073\pi$
$138$		0			0
$139$	81.3839	−	112.015i	0.585496	−	0.805866i	−0.408789	−	0.912629i	$-0.634049\pi$
$139$	81.3839	−	112.015i	0.585496	−	0.805866i	0.994284	+	0.106763i	$0.0340487\pi$
$140$		0			0
$141$	4.06758	−	2.95527i	0.0288481	−	0.0209594i
$142$		0			0
$143$	87.0511	−	87.0511i	0.608749	−	0.608749i
$144$		0			0
$145$	76.8477	−	176.581i	0.529984	−	1.21780i
$146$		0			0
$147$	7.29078	−	14.3090i	0.0495971	−	0.0973399i
$148$		0			0
$149$			103.072i			0.691761i	0.938279	+	0.345880i	$0.112420\pi$
$149$			103.072i			0.691761i	−0.938279	+	0.345880i	$0.887580\pi$
$150$		0			0
$151$	47.0940			0.311880			0.155940	−	0.987766i	$-0.450159\pi$
$151$	47.0940			0.311880			0.155940	+	0.987766i	$0.450159\pi$
$152$		0			0
$153$	−6.30522	−	3.21267i	−0.0412106	−	0.0209978i
$154$		0			0
$155$	23.5993	+	40.0935i	0.152254	+	0.258667i
$156$		0			0
$157$	94.7590	+	94.7590i	0.603561	+	0.603561i	0.941256	−	0.337695i	$-0.109647\pi$
$157$	94.7590	+	94.7590i	0.603561	+	0.603561i	−0.337695	+	0.941256i	$0.609647\pi$
$158$		0			0
$159$	8.87359	+	12.2134i	0.0558087	+	0.0768141i
$160$		0			0
$161$	−120.087	−	87.2486i	−0.745884	−	0.541917i
$162$		0			0
$163$	−41.3763	+	261.240i	−0.253842	+	1.60270i	0.450459	+	0.892797i	$0.351260\pi$
$163$	−41.3763	+	261.240i	−0.253842	+	1.60270i	−0.704302	+	0.709901i	$0.748740\pi$
$164$		0			0
$165$	−10.3844	−	2.68919i	−0.0629358	−	0.0162981i
$166$		0			0
$167$	239.969	−	122.270i	1.43694	−	0.732158i	0.449969	−	0.893044i	$-0.351435\pi$
$167$	239.969	−	122.270i	1.43694	−	0.732158i	0.986973	+	0.160886i	$0.0514351\pi$
$168$		0			0
$169$	−14.4433	−	4.69292i	−0.0854634	−	0.0277687i
$170$		0			0
$171$	39.4345	+	121.367i	0.230611	+	0.709749i
$172$		0			0
$173$	−184.026	+	29.1468i	−1.06373	+	0.168479i	−0.663682	−	0.748014i	$-0.731007\pi$
$173$	−184.026	+	29.1468i	−1.06373	+	0.168479i	−0.400050	+	0.916493i	$0.631007\pi$
$174$		0			0
$175$	166.553	−	212.893i	0.951733	−	1.21653i
$176$		0			0
$177$	−2.87305	−	18.1397i	−0.0162319	−	0.102484i
$178$		0			0
$179$	−194.558	+	63.2157i	−1.08692	+	0.353161i	−0.797054	−	0.603908i	$-0.793609\pi$
$179$	−194.558	+	63.2157i	−1.08692	+	0.353161i	−0.289862	+	0.957068i	$0.593609\pi$
$180$		0			0
$181$	8.53397	−	26.2649i	0.0471490	−	0.145110i	−0.924710	−	0.380671i	$-0.875693\pi$
$181$	8.53397	−	26.2649i	0.0471490	−	0.145110i	0.971859	+	0.235562i	$0.0756929\pi$
$182$		0			0
$183$	−1.51503	−	2.97342i	−0.00827887	−	0.0162482i
$184$		0			0
$185$	−35.7053	+	29.4137i	−0.193002	+	0.158993i
$186$		0			0
$187$	−7.08867	−	1.12273i	−0.0379073	−	0.00600393i
$188$		0			0
$189$	−26.9710	+	37.1223i	−0.142703	+	0.196414i
$190$		0			0
$191$	−75.2465	+	54.6697i	−0.393960	+	0.286229i	−0.767076	−	0.641556i	$-0.778289\pi$
$191$	−75.2465	+	54.6697i	−0.393960	+	0.286229i	0.373116	+	0.927785i	$0.378289\pi$
$192$		0			0
$193$	−172.622	+	172.622i	−0.894415	+	0.894415i	−0.994935	−	0.100520i	$-0.967949\pi$
$193$	−172.622	+	172.622i	−0.894415	+	0.894415i	0.100520	+	0.994935i	$0.467949\pi$
$194$		0			0
$195$	3.46853	+	15.6696i	0.0177873	+	0.0803569i
$196$		0			0
$197$	−19.6944	+	38.6524i	−0.0999715	+	0.196205i	−0.935575	−	0.353128i	$-0.885118\pi$
$197$	−19.6944	+	38.6524i	−0.0999715	+	0.196205i	0.835604	+	0.549333i	$0.185118\pi$
$198$		0			0
$199$			331.210i			1.66437i	0.554496	+	0.832186i	$0.312911\pi$
$199$			331.210i			1.66437i	−0.554496	+	0.832186i	$0.687089\pi$
$200$		0			0
$201$	−12.4485			−0.0619330
$202$		0			0
$203$	−371.047	−	189.058i	−1.82782	−	0.931319i
$204$		0			0
$205$	20.0507	−	207.528i	0.0978081	−	1.01233i
$206$		0			0
$207$	86.8259	+	86.8259i	0.419449	+	0.419449i
$208$		0			0
$209$	76.0744	+	104.707i	0.363992	+	0.500992i
$210$		0			0
$211$	−203.359	−	147.749i	−0.963785	−	0.700231i	−0.00975810	−	0.999952i	$-0.503106\pi$
$211$	−203.359	−	147.749i	−0.963785	−	0.700231i	−0.954027	+	0.299722i	$0.903106\pi$
$212$		0			0
$213$	0.101304	−	0.639609i	0.000475606	−	0.00300286i
$214$		0			0
$215$	−21.2126	−	348.681i	−0.0986634	−	1.62177i
$216$		0			0
$217$	89.6379	−	45.6728i	0.413078	−	0.210474i
$218$		0			0
$219$	−13.8458	−	4.49879i	−0.0632230	−	0.0205424i
$220$		0			0
$221$	3.31815	+	10.2122i	0.0150143	+	0.0462091i
$222$		0			0
$223$	74.7975	−	11.8468i	0.335415	−	0.0531245i	0.0135446	−	0.999908i	$-0.495688\pi$
$223$	74.7975	−	11.8468i	0.335415	−	0.0531245i	0.321870	+	0.946784i	$0.395688\pi$
$224$		0			0
$225$	−163.631	+	152.390i	−0.727248	+	0.677288i
$226$		0			0
$227$	53.6868	+	338.965i	0.236506	+	1.49324i	0.764850	+	0.644208i	$0.222813\pi$
$227$	53.6868	+	338.965i	0.236506	+	1.49324i	−0.528345	+	0.849030i	$0.677187\pi$
$228$		0			0
$229$	22.2341	−	7.22430i	0.0970921	−	0.0315471i	−0.260068	−	0.965590i	$-0.583745\pi$
$229$	22.2341	−	7.22430i	0.0970921	−	0.0315471i	0.357160	+	0.934043i	$0.383745\pi$
$230$		0			0
$231$	−7.16802	+	22.0609i	−0.0310304	+	0.0955017i
$232$		0			0
$233$	−86.9078	−	170.566i	−0.372995	−	0.732044i	0.625858	−	0.779937i	$-0.284749\pi$
$233$	−86.9078	−	170.566i	−0.372995	−	0.732044i	−0.998852	+	0.0478936i	$0.984749\pi$
$234$		0			0
$235$	−38.9242	−	98.9090i	−0.165635	−	0.420890i
$236$		0			0
$237$	−1.52014	−	0.240767i	−0.00641409	−	0.00101589i
$238$		0			0
$239$	−32.3070	+	44.4668i	−0.135176	+	0.186054i	−0.871239	−	0.490860i	$-0.836683\pi$
$239$	−32.3070	+	44.4668i	−0.135176	+	0.186054i	0.736063	+	0.676913i	$0.236683\pi$
$240$		0			0
$241$	−27.3775	+	19.8909i	−0.113600	+	0.0825349i	−0.643135	−	0.765753i	$-0.722366\pi$
$241$	−27.3775	+	19.8909i	−0.113600	+	0.0825349i	0.529535	+	0.848288i	$0.322366\pi$
$242$		0			0
$243$	40.3022	−	40.3022i	0.165853	−	0.165853i
$244$		0			0
$245$	−254.204	−	225.048i	−1.03757	−	0.918562i
$246$		0			0
$247$	87.9094	−	172.532i	0.355908	−	0.698510i
$248$		0			0
$249$			26.5474i			0.106616i
$250$		0			0
$251$	−221.852			−0.883872			−0.441936	−	0.897046i	$-0.645708\pi$
$251$	−221.852			−0.883872			−0.441936	+	0.897046i	$0.645708\pi$
$252$		0			0
$253$	110.961	+	56.5374i	0.438581	+	0.223468i
$254$		0			0
$255$	0.620190	−	0.700539i	0.00243212	−	0.00274721i
$256$		0			0
$257$	−20.3380	−	20.3380i	−0.0791363	−	0.0791363i	0.666431	−	0.745567i	$-0.267821\pi$
$257$	−20.3380	−	20.3380i	−0.0791363	−	0.0791363i	−0.745567	+	0.666431i	$0.767821\pi$
$258$		0			0
$259$	58.7990	+	80.9299i	0.227023	+	0.312471i
$260$		0			0
$261$	278.695	+	202.484i	1.06780	+	0.775801i
$262$		0			0
$263$	0.847808	−	5.35285i	0.00322361	−	0.0203530i	−0.986024	−	0.166603i	$-0.946720\pi$
$263$	0.847808	−	5.35285i	0.00322361	−	0.0203530i	0.989248	+	0.146250i	$0.0467203\pi$
$264$		0			0
$265$	296.987	−	116.875i	1.12071	−	0.441038i
$266$		0			0
$267$	−23.5134	+	11.9807i	−0.0880651	+	0.0448714i
$268$		0			0
$269$	−59.0391	−	19.1830i	−0.219476	−	0.0713122i	0.197215	−	0.980360i	$-0.436810\pi$
$269$	−59.0391	−	19.1830i	−0.219476	−	0.0713122i	−0.416691	+	0.909048i	$0.636810\pi$
$270$		0			0
$271$	99.9539	+	307.626i	0.368833	+	1.13515i	0.947546	+	0.319621i	$0.103556\pi$
$271$	99.9539	+	307.626i	0.368833	+	1.13515i	−0.578712	+	0.815532i	$0.696444\pi$
$272$		0			0
$273$	34.2772	−	5.42898i	0.125558	−	0.0198864i
$274$		0			0
$275$	−110.073	+	198.273i	−0.400264	+	0.720992i
$276$		0			0
$277$	11.4134	+	72.0614i	0.0412036	+	0.260150i	0.999688	−	0.0249971i	$-0.00795767\pi$
$277$	11.4134	+	72.0614i	0.0412036	+	0.260150i	−0.958484	+	0.285147i	$0.907958\pi$
$278$		0			0
$279$	−79.1483	+	25.7168i	−0.283686	+	0.0921750i
$280$		0			0
$281$	−84.2374	+	259.256i	−0.299777	+	0.922619i	0.681798	+	0.731541i	$0.261199\pi$
$281$	−84.2374	+	259.256i	−0.299777	+	0.922619i	−0.981575	+	0.191079i	$0.938801\pi$
$282$		0			0
$283$	−89.6096	−	175.869i	−0.316642	−	0.621445i	0.676750	−	0.736212i	$-0.263388\pi$
$283$	−89.6096	−	175.869i	−0.316642	−	0.621445i	−0.993392	+	0.114768i	$0.963388\pi$
$284$		0			0
$285$	−16.8412	+	1.02457i	−0.0590920	+	0.00359497i
$286$		0			0
$287$	−445.302	−	70.5289i	−1.55158	−	0.245745i
$288$		0			0
$289$	−169.502	+	233.299i	−0.586512	+	0.807265i
$290$		0			0
$291$	24.6998	−	17.9455i	0.0848792	−	0.0616683i
$292$		0			0
$293$	237.228	−	237.228i	0.809652	−	0.809652i	−0.174929	−	0.984581i	$-0.555970\pi$
$293$	237.228	−	237.228i	0.809652	−	0.809652i	0.984581	+	0.174929i	$0.0559695\pi$
$294$		0			0
$295$	−386.471	−	37.3396i	−1.31007	−	0.126575i
$296$		0			0
$297$	17.4773	−	34.3011i	0.0588461	−	0.115492i
$298$		0			0
$299$		−	186.319i		−	0.623142i
$300$		0			0
$301$	−755.389			−2.50960
$302$		0			0
$303$	6.85180	+	3.49117i	0.0226132	+	0.0115220i
$304$		0			0
$305$	−68.8829	+	15.2475i	−0.225846	+	0.0499919i
$306$		0			0
$307$	79.0993	+	79.0993i	0.257653	+	0.257653i	0.824099	−	0.566446i	$-0.191682\pi$
$307$	79.0993	+	79.0993i	0.257653	+	0.257653i	−0.566446	+	0.824099i	$0.691682\pi$
$308$		0			0
$309$	−7.22212	−	9.94040i	−0.0233726	−	0.0321696i
$310$		0			0
$311$	91.8901	+	66.7620i	0.295466	+	0.214669i	0.725635	−	0.688080i	$-0.241546\pi$
$311$	91.8901	+	66.7620i	0.295466	+	0.214669i	−0.430169	+	0.902748i	$0.641546\pi$
$312$		0			0
$313$	−16.0776	+	101.510i	−0.0513662	+	0.324314i	0.948603	+	0.316469i	$0.102497\pi$
$313$	−16.0776	+	101.510i	−0.0513662	+	0.324314i	−0.999969	+	0.00784510i	$0.997503\pi$
$314$		0			0
$315$	307.436	+	373.197i	0.975988	+	1.18475i
$316$		0			0
$317$	−363.850	+	185.391i	−1.14779	+	0.584829i	−0.921172	−	0.389155i	$-0.872767\pi$
$317$	−363.850	+	185.391i	−1.14779	+	0.584829i	−0.226618	+	0.973984i	$0.572767\pi$
$318$		0			0
$319$	332.280	+	107.964i	1.04163	+	0.338446i
$320$		0			0
$321$	−3.59678	−	11.0698i	−0.0112049	−	0.0344852i
$322$		0			0
$323$	−11.1497	+	1.76594i	−0.0345193	+	0.00546731i
$324$		0			0
$325$	339.074	+	12.0611i	1.04330	+	0.0371111i
$326$		0			0
$327$	−4.78435	−	30.2072i	−0.0146310	−	0.0923767i
$328$		0			0
$329$	−218.600	+	71.0273i	−0.664437	+	0.215889i
$330$		0			0
$331$	37.2677	−	114.698i	0.112591	−	0.346520i	−0.878846	−	0.477106i	$-0.841686\pi$
$331$	37.2677	−	114.698i	0.112591	−	0.346520i	0.991437	+	0.130586i	$0.0416858\pi$
$332$		0			0
$333$	−37.5684	−	73.7321i	−0.112818	−	0.221418i
$334$		0			0
$335$	−65.9760	+	254.769i	−0.196943	+	0.760505i
$336$		0			0
$337$	−38.2752	−	6.06219i	−0.113576	−	0.0179887i	0.0993876	−	0.995049i	$-0.468312\pi$
$337$	−38.2752	−	6.06219i	−0.113576	−	0.0179887i	−0.212964	+	0.977060i	$0.568312\pi$
$338$		0			0
$339$	−10.6393	+	14.6437i	−0.0313843	+	0.0431968i
$340$		0			0
$341$	−68.2838	+	49.6111i	−0.200246	+	0.145487i
$342$		0			0
$343$	−144.510	+	144.510i	−0.421311	+	0.421311i
$344$		0			0
$345$	−13.9910	+	8.23522i	−0.0405536	+	0.0238702i
$346$		0			0
$347$	106.794	−	209.594i	0.307762	−	0.604018i	−0.684381	−	0.729125i	$-0.739927\pi$
$347$	106.794	−	209.594i	0.307762	−	0.604018i	0.992143	+	0.125107i	$0.0399274\pi$
$348$		0			0
$349$		−	16.9114i		−	0.0484568i	−0.999706	−	0.0242284i	$-0.992287\pi$
$349$		−	16.9114i		−	0.0484568i	0.999706	−	0.0242284i	$-0.00771289\pi$
$350$		0			0
$351$	−57.5965			−0.164093
$352$		0			0
$353$	−449.055	−	228.805i	−1.27211	−	0.648173i	−0.318132	−	0.948046i	$-0.603056\pi$
$353$	−449.055	−	228.805i	−1.27211	−	0.648173i	−0.953979	+	0.299873i	$0.903056\pi$
$354$		0			0
$355$	−12.5532	−	5.46313i	−0.0353611	−	0.0153891i
$356$		0			0
$357$	−1.43063	−	1.43063i	−0.00400736	−	0.00400736i
$358$		0			0
$359$	−198.037	−	272.575i	−0.551636	−	0.759262i	0.438597	−	0.898684i	$-0.355475\pi$
$359$	−198.037	−	272.575i	−0.551636	−	0.759262i	−0.990233	+	0.139422i	$0.955475\pi$
$360$		0			0
$361$	−127.362	−	92.5336i	−0.352802	−	0.256326i
$362$		0			0
$363$	−1.43238	+	9.04370i	−0.00394596	+	0.0249138i
$364$		0			0
$365$	−165.453	+	259.523i	−0.453296	+	0.711022i
$366$		0			0
$367$	−416.928	+	212.435i	−1.13604	+	0.578843i	−0.917797	−	0.397050i	$-0.870034\pi$
$367$	−416.928	+	212.435i	−1.13604	+	0.578843i	−0.218247	+	0.975894i	$0.570034\pi$
$368$		0			0
$369$	354.704	+	115.250i	0.961256	+	0.312331i
$370$		0			0
$371$	−213.269	−	656.374i	−0.574848	−	1.76920i
$372$		0			0
$373$	474.868	−	75.2117i	1.27310	−	0.201640i	0.516940	−	0.856022i	$-0.327071\pi$
$373$	474.868	−	75.2117i	1.27310	−	0.201640i	0.756164	+	0.654382i	$0.227071\pi$
$374$		0			0
$375$	−14.0812	−	25.9947i	−0.0375498	−	0.0693191i
$376$		0			0
$377$	−81.7709	−	516.281i	−0.216899	−	1.36945i
$378$		0			0
$379$	597.265	−	194.063i	1.57590	−	0.512040i	0.614901	−	0.788604i	$-0.289196\pi$
$379$	597.265	−	194.063i	1.57590	−	0.512040i	0.960995	+	0.276564i	$0.0891958\pi$
$380$		0			0
$381$	−4.47694	+	13.7786i	−0.0117505	+	0.0361643i
$382$		0			0
$383$	−175.227	−	343.902i	−0.457511	−	0.897916i	−0.998385	−	0.0568121i	$-0.981906\pi$
$383$	−175.227	−	343.902i	−0.457511	−	0.897916i	0.540874	−	0.841104i	$-0.318094\pi$
$384$		0			0
$385$	413.504	+	263.620i	1.07404	+	0.684727i
$386$		0			0
$387$	617.184	+	97.7524i	1.59479	+	0.252590i
$388$		0			0
$389$	230.009	−	316.581i	0.591284	−	0.813833i	−0.403592	−	0.914939i	$-0.632238\pi$
$389$	230.009	−	316.581i	0.591284	−	0.813833i	0.994876	+	0.101107i	$0.0322383\pi$
$390$		0			0
$391$	−8.78762	+	6.38458i	−0.0224747	+	0.0163289i
$392$		0			0
$393$	−0.592995	+	0.592995i	−0.00150889	+	0.00150889i
$394$		0			0
$395$	−12.9841	+	29.8348i	−0.0328711	+	0.0755313i
$396$		0			0
$397$	155.364	−	304.919i	0.391345	−	0.768058i	−0.608326	−	0.793687i	$-0.708159\pi$
$397$	155.364	−	304.919i	0.391345	−	0.768058i	0.999672	+	0.0256288i	$0.00815880\pi$
$398$		0			0
$399$			36.4852i			0.0914415i
$400$		0			0
$401$	665.647			1.65997			0.829983	−	0.557788i	$-0.188350\pi$
$401$	665.647			1.65997			0.829983	+	0.557788i	$0.188350\pi$
$402$		0			0
$403$	112.515	+	57.3292i	0.279193	+	0.142256i
$404$		0			0
$405$	−201.617	−	342.532i	−0.497820	−	0.845759i
$406$		0			0
$407$	−59.3452	−	59.3452i	−0.145811	−	0.145811i
$408$		0			0
$409$	−369.812	−	509.003i	−0.904187	−	1.24451i	−0.969113	−	0.246616i	$-0.920681\pi$
$409$	−369.812	−	509.003i	−0.904187	−	1.24451i	0.0649265	−	0.997890i	$-0.479319\pi$
$410$		0			0
$411$	−47.7771	−	34.7121i	−0.116246	−	0.0844577i
$412$		0			0
$413$	−131.343	+	829.269i	−0.318022	+	2.00791i
$414$		0			0
$415$	543.315	+	140.699i	1.30919	+	0.339033i
$416$		0			0
$417$	−29.1774	+	14.8666i	−0.0699699	+	0.0356514i
$418$		0			0
$419$	111.166	+	36.1200i	0.265312	+	0.0862052i	0.438652	−	0.898657i	$-0.355456\pi$
$419$	111.166	+	36.1200i	0.265312	+	0.0862052i	−0.173340	+	0.984862i	$0.555456\pi$
$420$		0			0
$421$	1.06048	+	3.26382i	0.00251896	+	0.00775255i	0.952308	−	0.305138i	$-0.0987026\pi$
$421$	1.06048	+	3.26382i	0.00251896	+	0.00775255i	−0.949789	+	0.312891i	$0.898703\pi$
$422$		0			0
$423$	187.796	−	29.7440i	0.443963	−	0.0703169i
$424$		0			0
$425$	−11.0501	−	16.4055i	−0.0260003	−	0.0386011i
$426$		0			0
$427$	23.8656	+	150.681i	0.0558913	+	0.352884i
$428$		0			0
$429$	−27.6912	+	8.99742i	−0.0645482	+	0.0209730i
$430$		0			0
$431$	−144.037	+	443.300i	−0.334193	+	1.02854i	0.632926	+	0.774212i	$0.281854\pi$
$431$	−144.037	+	443.300i	−0.334193	+	1.02854i	−0.967118	+	0.254327i	$0.918146\pi$
$432$		0			0
$433$	90.0802	+	176.792i	0.208037	+	0.408296i	0.971323	−	0.237765i	$-0.0764149\pi$
$433$	90.0802	+	176.792i	0.208037	+	0.408296i	−0.763285	+	0.646062i	$0.776415\pi$
$434$		0			0
$435$	−35.1541	+	28.9596i	−0.0808140	+	0.0665739i
$436$		0			0
$437$	193.468	+	30.6423i	0.442718	+	0.0701196i
$438$		0			0
$439$	−288.145	+	396.598i	−0.656367	+	0.903412i	−0.999354	−	0.0359283i	$-0.988561\pi$
$439$	−288.145	+	396.598i	−0.656367	+	0.903412i	0.342987	+	0.939340i	$0.388561\pi$
$440$		0			0
$441$	491.330	−	356.972i	1.11413	−	0.809461i
$442$		0			0
$443$	−241.629	+	241.629i	−0.545437	+	0.545437i	−0.925118	−	0.379681i	$-0.876034\pi$
$443$	−241.629	+	241.629i	−0.545437	+	0.545437i	0.379681	+	0.925118i	$0.376034\pi$
$444$		0			0
$445$	120.575	+	544.717i	0.270956	+	1.22408i
$446$		0			0
$447$	11.0671	−	21.7205i	0.0247587	−	0.0485917i
$448$		0			0
$449$			344.192i			0.766575i	0.923629	+	0.383288i	$0.125208\pi$
$449$			344.192i			0.766575i	−0.923629	+	0.383288i	$0.874792\pi$
$450$		0			0
$451$	378.255			0.838703
$452$		0			0
$453$	−9.92413	−	5.05660i	−0.0219076	−	0.0111625i
$454$		0			0
$455$	70.5576	−	730.284i	0.155072	−	1.60502i
$456$		0			0
$457$	−145.902	−	145.902i	−0.319260	−	0.319260i	0.529223	−	0.848483i	$-0.322484\pi$
$457$	−145.902	−	145.902i	−0.319260	−	0.319260i	−0.848483	+	0.529223i	$0.822484\pi$
$458$		0			0
$459$	1.97365	+	2.71650i	0.00429989	+	0.00591829i
$460$		0			0
$461$	270.507	+	196.534i	0.586782	+	0.426322i	0.841163	−	0.540782i	$-0.181872\pi$
$461$	270.507	+	196.534i	0.586782	+	0.426322i	−0.254381	+	0.967104i	$0.581872\pi$
$462$		0			0
$463$	4.34214	−	27.4152i	0.00937827	−	0.0592120i	−0.982555	−	0.185970i	$-0.940457\pi$
$463$	4.34214	−	27.4152i	0.00937827	−	0.0592120i	0.991934	+	0.126758i	$0.0404572\pi$
$464$		0			0
$465$	−0.668161	−	10.9828i	−0.00143690	−	0.0236190i
$466$		0			0
$467$	365.168	−	186.062i	0.781943	−	0.398420i	−0.0169777	−	0.999856i	$-0.505404\pi$
$467$	365.168	−	186.062i	0.781943	−	0.398420i	0.798921	+	0.601436i	$0.205404\pi$
$468$		0			0
$469$	541.238	+	175.859i	1.15403	+	0.374966i
$470$		0			0
$471$	−9.79409	−	30.1431i	−0.0207943	−	0.0639981i
$472$		0			0
$473$	625.951	−	99.1408i	1.32336	−	0.209600i
$474$		0			0
$475$	−68.2883	+	350.099i	−0.143765	+	0.737051i
$476$		0			0
$477$	89.3103	+	563.883i	0.187233	+	1.18215i
$478$		0			0
$479$	−579.516	+	188.296i	−1.20985	+	0.393103i	−0.843374	−	0.537326i	$-0.819434\pi$
$479$	−579.516	+	188.296i	−1.20985	+	0.393103i	−0.366472	+	0.930429i	$0.619434\pi$
$480$		0			0
$481$	−38.8018	+	119.420i	−0.0806691	+	0.248274i
$482$		0			0
$483$	15.9380	+	31.2800i	0.0329978	+	0.0647619i
$484$		0			0
$485$	−236.362	−	600.611i	−0.487344	−	1.23837i
$486$		0			0
$487$	−229.164	−	36.2960i	−0.470563	−	0.0745298i	−0.0833503	−	0.996520i	$-0.526562\pi$
$487$	−229.164	−	36.2960i	−0.470563	−	0.0745298i	−0.387213	+	0.921990i	$0.626562\pi$
$488$		0			0
$489$	36.7692	−	50.6085i	0.0751927	−	0.103494i
$490$		0			0
$491$	288.845	−	209.858i	0.588279	−	0.427409i	−0.253421	−	0.967356i	$-0.581556\pi$
$491$	288.845	−	209.858i	0.588279	−	0.427409i	0.841699	+	0.539947i	$0.181556\pi$
$492$		0			0
$493$	−21.5480	+	21.5480i	−0.0437079	+	0.0437079i
$494$		0			0
$495$	−303.736	−	268.899i	−0.613608	−	0.543230i
$496$		0			0
$497$	−13.4402	+	26.3779i	−0.0270426	+	0.0530742i
$498$		0			0
$499$		−	752.086i		−	1.50719i	−0.657341	−	0.753593i	$-0.728319\pi$
$499$		−	752.086i		−	1.50719i	0.657341	−	0.753593i	$-0.271681\pi$
$500$		0			0
$501$	−63.6973			−0.127140
$502$		0			0
$503$	728.768	+	371.326i	1.44884	+	0.738222i	0.988740	−	0.149644i	$-0.0478127\pi$
$503$	728.768	+	371.326i	1.44884	+	0.738222i	0.460102	+	0.887866i	$0.347813\pi$
$504$		0			0
$505$	107.763	−	121.725i	0.213393	−	0.241039i
$506$		0			0
$507$	2.53975	+	2.53975i	0.00500938	+	0.00500938i
$508$		0			0
$509$	−529.260	−	728.463i	−1.03980	−	1.43117i	−0.897327	−	0.441367i	$-0.854494\pi$
$509$	−529.260	−	728.463i	−1.03980	−	1.43117i	−0.142476	−	0.989798i	$-0.545506\pi$
$510$		0			0
$511$	538.437	+	391.197i	1.05369	+	0.765552i
$512$		0			0
$513$	9.47238	−	59.8062i	0.0184647	−	0.116581i
$514$		0			0
$515$	−241.715	+	95.1234i	−0.469349	+	0.184706i
$516$		0			0
$517$	171.820	−	87.5466i	0.332340	−	0.169336i
$518$		0			0
$519$	41.9094	+	13.6172i	0.0807503	+	0.0262374i
$520$		0			0
$521$	−145.536	−	447.915i	−0.279340	−	0.859721i	−0.988038	−	0.154209i	$-0.950717\pi$
$521$	−145.536	−	447.915i	−0.279340	−	0.859721i	0.708698	−	0.705512i	$-0.249283\pi$
$522$		0			0
$523$	582.366	−	92.2377i	1.11351	−	0.176363i	0.427543	−	0.903995i	$-0.359379\pi$
$523$	582.366	−	92.2377i	1.11351	−	0.176363i	0.685967	+	0.727632i	$0.259379\pi$
$524$		0			0
$525$	−57.9567	+	26.9799i	−0.110394	+	0.0513902i
$526$		0			0
$527$	−1.15164	−	7.27118i	−0.00218528	−	0.0137973i
$528$		0			0
$529$	−323.857	+	105.227i	−0.612205	+	0.198918i
$530$		0			0
$531$	214.626	−	660.550i	0.404192	−	1.24397i
$532$		0			0
$533$	−256.921	−	504.236i	−0.482029	−	0.946035i
$534$		0			0
$535$	−245.614	+	14.9424i	−0.459092	+	0.0279297i
$536$		0			0
$537$	47.7869	+	7.56870i	0.0889887	+	0.0140944i
$538$		0			0
$539$	362.043	−	498.309i	0.671693	−	0.924506i
$540$		0			0
$541$	4.98311	−	3.62044i	0.00921092	−	0.00669212i	−0.583170	−	0.812350i	$-0.698188\pi$
$541$	4.98311	−	3.62044i	0.00921092	−	0.00669212i	0.592381	+	0.805658i	$0.298188\pi$
$542$		0			0
$543$	−4.61849	+	4.61849i	−0.00850551	+	0.00850551i
$544$		0			0
$545$	−643.571	−	62.1796i	−1.18086	−	0.114091i
$546$		0			0
$547$	137.666	−	270.185i	0.251675	−	0.493940i	−0.730257	−	0.683172i	$-0.760600\pi$
$547$	137.666	−	270.185i	0.251675	−	0.493940i	0.981932	+	0.189232i	$0.0605998\pi$
$548$		0			0
$549$		−	126.201i		−	0.229875i
$550$		0			0
$551$	549.537			0.997344
$552$		0			0
$553$	62.6915	+	31.9429i	0.113366	+	0.0577630i
$554$		0			0
$555$	10.6824	−	2.36460i	0.0192476	−	0.00426054i
$556$		0			0
$557$	39.2190	+	39.2190i	0.0704112	+	0.0704112i	0.741435	−	0.671024i	$-0.234145\pi$
$557$	39.2190	+	39.2190i	0.0704112	+	0.0704112i	−0.671024	+	0.741435i	$0.734145\pi$
$558$		0			0
$559$	−557.324	−	767.091i	−0.997002	−	1.37226i
$560$		0			0
$561$	1.37325	+	0.997722i	0.00244786	+	0.00177847i
$562$		0			0
$563$	−93.1829	+	588.334i	−0.165511	+	1.04500i	0.755411	+	0.655251i	$0.227437\pi$
$563$	−93.1829	+	588.334i	−0.165511	+	1.04500i	−0.920922	+	0.389746i	$0.872563\pi$
$564$		0			0
$565$	243.308	+	295.352i	0.430634	+	0.522746i
$566$		0			0
$567$	−765.807	+	390.198i	−1.35063	+	0.688180i
$568$		0			0
$569$	258.923	+	84.1291i	0.455049	+	0.147854i	0.527568	−	0.849513i	$-0.323104\pi$
$569$	258.923	+	84.1291i	0.455049	+	0.147854i	−0.0725195	+	0.997367i	$0.523104\pi$
$570$		0			0
$571$	69.9094	+	215.159i	0.122433	+	0.376811i	0.993425	−	0.114487i	$-0.0365225\pi$
$571$	69.9094	+	215.159i	0.122433	+	0.376811i	−0.870991	+	0.491298i	$0.836523\pi$
$572$		0			0
$573$	21.7267	−	3.44118i	0.0379175	−	0.00600555i
$574$		0			0
$575$	94.3893	+	329.983i	0.164155	+	0.573884i
$576$		0			0
$577$	140.082	+	884.446i	0.242777	+	1.53284i	0.744391	+	0.667744i	$0.232740\pi$
$577$	140.082	+	884.446i	0.242777	+	1.53284i	−0.501614	+	0.865092i	$0.667260\pi$
$578$		0			0
$579$	54.9116	−	17.8419i	0.0948387	−	0.0308150i
$580$		0			0
$581$	375.033	−	1154.23i	0.645495	−	1.98663i
$582$		0			0
$583$	262.870	+	515.912i	0.450892	+	0.884926i
$584$		0			0
$585$	−152.152	+	587.542i	−0.260089	+	1.00435i
$586$		0			0
$587$	−346.752	−	54.9201i	−0.590718	−	0.0935606i	−0.146083	−	0.989272i	$-0.546667\pi$
$587$	−346.752	−	54.9201i	−0.590718	−	0.0935606i	−0.444635	+	0.895712i	$0.646667\pi$
$588$		0			0
$589$	−78.0330	+	107.403i	−0.132484	+	0.182348i
$590$		0			0
$591$	8.30041	−	6.03060i	0.0140447	−	0.0102041i
$592$		0			0
$593$	−355.629	+	355.629i	−0.599711	+	0.599711i	−0.940236	−	0.340525i	$-0.889395\pi$
$593$	−355.629	+	355.629i	−0.599711	+	0.599711i	0.340525	+	0.940236i	$0.389395\pi$
$594$		0			0
$595$	−36.8611	+	21.6967i	−0.0619514	+	0.0364651i
$596$		0			0
$597$	35.5629	−	69.7960i	0.0595693	−	0.116911i
$598$		0			0
$599$			1001.80i			1.67245i	0.548390	+	0.836223i	$0.315241\pi$
$599$			1001.80i			1.67245i	−0.548390	+	0.836223i	$0.684759\pi$
$600$		0			0
$601$	796.655			1.32555			0.662775	−	0.748819i	$-0.269379\pi$
$601$	796.655			1.32555			0.662775	+	0.748819i	$0.269379\pi$
$602$		0			0
$603$	−419.457	−	213.724i	−0.695617	−	0.354435i
$604$		0			0
$605$	177.495	+	77.2456i	0.293380	+	0.127679i
$606$		0			0
$607$	−728.906	−	728.906i	−1.20083	−	1.20083i	−0.973913	−	0.226920i	$-0.927134\pi$
$607$	−728.906	−	728.906i	−1.20083	−	1.20083i	−0.226920	−	0.973913i	$-0.572866\pi$
$608$		0			0
$609$	57.8912	+	79.6804i	0.0950595	+	0.130838i
$610$		0			0
$611$	−233.410	−	169.582i	−0.382013	−	0.277549i
$612$		0			0
$613$	−19.5383	+	123.360i	−0.0318732	+	0.201240i	−0.998486	−	0.0550007i	$-0.982484\pi$
$613$	−19.5383	+	123.360i	−0.0318732	+	0.201240i	0.966613	+	0.256240i	$0.0824839\pi$
$614$		0			0
$615$	−26.5081	+	41.5796i	−0.0431026	+	0.0676091i
$616$		0			0
$617$	−639.236	+	325.707i	−1.03604	+	0.527888i	−0.887399	−	0.461003i	$-0.847490\pi$
$617$	−639.236	+	325.707i	−1.03604	+	0.527888i	−0.148640	+	0.988891i	$0.547490\pi$
$618$		0			0
$619$	196.553	+	63.8639i	0.317533	+	0.103173i	0.463447	−	0.886125i	$-0.346612\pi$
$619$	196.553	+	63.8639i	0.317533	+	0.103173i	−0.145914	+	0.989297i	$0.546612\pi$
$620$		0			0
$621$	−18.0044	−	55.4118i	−0.0289926	−	0.0892300i
$622$		0			0
$623$	1191.57	−	188.726i	1.91263	−	0.302930i
$624$		0			0
$625$	−606.631	+	150.414i	−0.970609	+	0.240662i
$626$		0			0
$627$	−4.78849	−	30.2333i	−0.00763714	−	0.0482190i
$628$		0			0
$629$	6.96196	−	2.26208i	0.0110683	−	0.00359631i
$630$		0			0
$631$	−68.8404	+	211.869i	−0.109097	+	0.335767i	−0.990670	−	0.136281i	$-0.956485\pi$
$631$	−68.8404	+	211.869i	−0.109097	+	0.335767i	0.881573	+	0.472048i	$0.156485\pi$
$632$		0			0
$633$	26.9897	+	52.9703i	0.0426377	+	0.0836813i
$634$		0			0
$635$	258.263	+	164.650i	0.406713	+	0.259291i
$636$		0			0
$637$	−910.185	−	144.159i	−1.42886	−	0.226310i
$638$		0			0
$639$	14.3947	−	19.8126i	0.0225269	−	0.0310056i
$640$		0			0
$641$	−709.800	+	515.700i	−1.10733	+	0.804524i	−0.982241	−	0.187622i	$-0.939922\pi$
$641$	−709.800	+	515.700i	−1.10733	+	0.804524i	−0.125090	+	0.992145i	$0.539922\pi$
$642$		0			0
$643$	−430.122	+	430.122i	−0.668929	+	0.668929i	−0.957468	−	0.288539i	$-0.906831\pi$
$643$	−430.122	+	430.122i	−0.668929	+	0.668929i	0.288539	+	0.957468i	$0.406831\pi$
$644$		0			0
$645$	−32.9686	+	75.7553i	−0.0511141	+	0.117450i
$646$		0			0
$647$	−400.518	+	786.060i	−0.619038	+	1.21493i	0.342308	+	0.939588i	$0.388791\pi$
$647$	−400.518	+	786.060i	−0.619038	+	1.21493i	−0.961346	+	0.275343i	$0.911209\pi$
$648$		0			0
$649$		−	704.409i		−	1.08538i
$650$		0			0
$651$	−23.7934			−0.0365490
$652$		0			0
$653$	868.933	+	442.744i	1.33068	+	0.678015i	0.967302	−	0.253627i	$-0.0816237\pi$
$653$	868.933	+	442.744i	1.33068	+	0.678015i	0.363377	+	0.931642i	$0.381624\pi$
$654$		0			0
$655$	8.99330	+	15.2789i	0.0137302	+	0.0233266i
$656$		0			0
$657$	−389.302	−	389.302i	−0.592545	−	0.592545i
$658$		0			0
$659$	−337.348	−	464.320i	−0.511909	−	0.704582i	0.472331	−	0.881421i	$-0.343413\pi$
$659$	−337.348	−	464.320i	−0.511909	−	0.704582i	−0.984240	+	0.176839i	$0.943413\pi$
$660$		0			0
$661$	83.1335	+	60.4000i	0.125769	+	0.0913767i	0.648892	−	0.760881i	$-0.275233\pi$
$661$	83.1335	+	60.4000i	0.125769	+	0.0913767i	−0.523122	+	0.852258i	$0.675233\pi$
$662$		0			0
$663$	0.397276	−	2.50830i	0.000599210	−	0.00378326i
$664$		0			0
$665$	746.698	+	193.368i	1.12285	+	0.290779i
$666$		0			0
$667$	471.137	−	240.056i	0.706353	−	0.359905i
$668$		0			0
$669$	−17.0341	−	5.53472i	−0.0254621	−	0.00827313i
$670$		0			0
$671$	−39.5523	−	121.729i	−0.0589453	−	0.181415i
$672$		0			0
$673$	742.996	−	117.679i	1.10401	−	0.174857i	0.422280	−	0.906465i	$-0.361230\pi$
$673$	742.996	−	117.679i	1.10401	−	0.174857i	0.681726	+	0.731608i	$0.261230\pi$
$674$		0			0
$675$	102.007	−	29.1784i	0.151121	−	0.0432272i
$676$		0			0
$677$	−104.837	−	661.912i	−0.154855	−	0.977714i	−0.935651	−	0.352928i	$-0.885186\pi$
$677$	−104.837	−	661.912i	−0.154855	−	0.977714i	0.780796	−	0.624786i	$-0.214814\pi$
$678$		0			0
$679$	−1327.42	+	431.304i	−1.95496	+	0.635204i
$680$		0			0
$681$	25.0821	−	77.1947i	0.0368313	−	0.113355i
$682$		0			0
$683$	−477.148	−	936.456i	−0.698607	−	1.37109i	−0.918442	−	0.395556i	$-0.870552\pi$
$683$	−477.148	−	936.456i	−0.698607	−	1.37109i	0.219835	−	0.975537i	$-0.429448\pi$
$684$		0			0
$685$	−963.626	+	793.827i	−1.40675	+	1.15887i
$686$		0			0
$687$	−5.46109	−	0.864952i	−0.00794919	−	0.00125903i
$688$		0			0
$689$	509.193	−	700.843i	0.739031	−	1.01719i
$690$		0			0
$691$	−281.760	+	204.711i	−0.407757	+	0.296253i	−0.772693	−	0.634780i	$-0.781091\pi$
$691$	−281.760	+	204.711i	−0.407757	+	0.296253i	0.364936	+	0.931033i	$0.381091\pi$
$692$		0			0
$693$	−620.284	+	620.284i	−0.895071	+	0.895071i
$694$		0			0
$695$	149.620	+	675.931i	0.215281	+	0.972563i
$696$		0			0
$697$	−14.9781	+	29.3961i	−0.0214893	+	0.0421752i
$698$		0			0
$699$			45.2750i			0.0647711i
$700$		0			0
$701$	685.412			0.977764			0.488882	−	0.872350i	$-0.337405\pi$
$701$	685.412			0.977764			0.488882	+	0.872350i	$0.337405\pi$
$702$		0			0
$703$	−117.620	−	59.9304i	−0.167312	−	0.0852495i
$704$		0			0
$705$	−2.41759	+	25.0225i	−0.00342921	+	0.0354930i
$706$		0			0
$707$	−248.584	−	248.584i	−0.351604	−	0.351604i
$708$		0			0
$709$	−142.144	−	195.644i	−0.200485	−	0.275944i	0.696922	−	0.717146i	$-0.254552\pi$
$709$	−142.144	−	195.644i	−0.200485	−	0.275944i	−0.897408	+	0.441202i	$0.854552\pi$
$710$		0			0
$711$	−47.0880	−	34.2114i	−0.0662278	−	0.0481173i
$712$		0			0
$713$	−19.9831	+	126.168i	−0.0280267	+	0.176954i
$714$		0			0
$715$	37.3787	+	614.408i	0.0522778	+	0.859312i
$716$		0			0
$717$	11.5826	−	5.90162i	0.0161542	−	0.00823099i
$718$		0			0
$719$	126.747	+	41.1825i	0.176282	+	0.0572774i	0.395828	−	0.918325i	$-0.370458\pi$
$719$	126.747	+	41.1825i	0.176282	+	0.0572774i	−0.219546	+	0.975602i	$0.570458\pi$
$720$		0			0
$721$	173.577	+	534.216i	0.240745	+	0.740937i
$722$		0			0
$723$	7.90500	−	1.25203i	0.0109336	−	0.00173171i
$724$		0			0
$725$	406.369	+	872.940i	0.560509	+	1.20405i
$726$		0			0
$727$	−202.138	−	1276.25i	−0.278044	−	1.75550i	−0.591881	−	0.806025i	$-0.701615\pi$
$727$	−202.138	−	1276.25i	−0.278044	−	1.75550i	0.313837	−	0.949477i	$-0.398385\pi$
$728$		0			0
$729$	667.599	−	216.916i	0.915774	−	0.297553i
$730$		0			0
$731$	−17.0815	+	52.5716i	−0.0233674	+	0.0719173i
$732$		0			0
$733$	−379.282	−	744.383i	−0.517438	−	1.01553i	−0.990885	−	0.134707i	$-0.956991\pi$
$733$	−379.282	−	744.383i	−0.517438	−	1.01553i	0.473448	−	0.880822i	$-0.343009\pi$
$734$		0			0
$735$	29.4046	+	74.7189i	0.0400062	+	0.101658i
$736$		0			0
$737$	−471.576	−	74.6903i	−0.639859	−	0.101344i
$738$		0			0
$739$	651.261	−	896.383i	0.881273	−	1.21297i	−0.0947939	−	0.995497i	$-0.530219\pi$
$739$	651.261	−	896.383i	0.881273	−	1.21297i	0.976067	−	0.217471i	$-0.0697808\pi$
$740$		0			0
$741$	−37.0504	+	26.9187i	−0.0500005	+	0.0363275i
$742$		0			0
$743$	333.821	−	333.821i	0.449289	−	0.449289i	−0.445829	−	0.895118i	$-0.647091\pi$
$743$	333.821	−	333.821i	0.449289	−	0.449289i	0.895118	+	0.445829i	$0.147091\pi$
$744$		0			0
$745$	−385.872	−	341.614i	−0.517950	−	0.458543i
$746$		0			0
$747$	−455.783	+	894.524i	−0.610151	+	1.19749i
$748$		0			0
$749$			532.104i			0.710419i
$750$		0			0
$751$	−698.285			−0.929807			−0.464904	−	0.885361i	$-0.653911\pi$
$751$	−698.285			−0.929807			−0.464904	+	0.885361i	$0.653911\pi$
$752$		0			0
$753$	46.7510	+	23.8208i	0.0620863	+	0.0316345i
$754$		0			0
$755$	−156.084	+	176.306i	−0.206734	+	0.233518i
$756$		0			0
$757$	−465.289	−	465.289i	−0.614648	−	0.614648i	0.329505	−	0.944154i	$-0.393118\pi$
$757$	−465.289	−	465.289i	−0.614648	−	0.614648i	−0.944154	+	0.329505i	$0.893118\pi$
$758$		0			0
$759$	−17.3123	−	23.8283i	−0.0228093	−	0.0313944i
$760$		0			0
$761$	−1146.83	−	833.219i	−1.50700	−	1.09490i	−0.967486	−	0.252924i	$-0.918608\pi$
$761$	−1146.83	−	833.219i	−1.50700	−	1.09490i	−0.539515	−	0.841976i	$-0.681392\pi$
$762$		0			0
$763$	−218.719	+	1380.94i	−0.286657	+	1.80988i
$764$		0			0
$765$	32.9248	−	12.9571i	0.0430389	−	0.0169373i
$766$		0			0
$767$	−939.020	+	478.454i	−1.22428	+	0.623800i
$768$		0			0
$769$	−805.374	−	261.682i	−1.04730	−	0.340288i	−0.265692	−	0.964058i	$-0.585600\pi$
$769$	−805.374	−	261.682i	−1.04730	−	0.340288i	−0.781608	+	0.623770i	$0.785600\pi$
$770$		0			0
$771$	2.10210	+	6.46959i	0.00272645	+	0.00839116i
$772$		0			0
$773$	−319.914	+	50.6693i	−0.413860	+	0.0655489i	−0.359893	−	0.932994i	$-0.617187\pi$
$773$	−319.914	+	50.6693i	−0.413860	+	0.0655489i	−0.0539672	+	0.998543i	$0.517187\pi$
$774$		0			0
$775$	−228.314	−	44.5335i	−0.294598	−	0.0574626i
$776$		0			0
$777$	−3.70109	−	23.3678i	−0.00476331	−	0.0300744i
$778$		0			0
$779$	565.836	−	183.851i	0.726361	−	0.236009i
$780$		0			0
$781$	7.67522	−	23.6219i	0.00982742	−	0.0302457i
$782$		0			0
$783$	−74.2081	−	145.642i	−0.0947740	−	0.186005i
$784$		0			0
$785$	−668.811	+	40.6884i	−0.851989	+	0.0518323i
$786$		0			0
$787$	813.494	+	128.845i	1.03366	+	0.163716i	0.650140	−	0.759815i	$-0.274710\pi$
$787$	813.494	+	128.845i	1.03366	+	0.163716i	0.383524	+	0.923531i	$0.374710\pi$
$788$		0			0
$789$	−0.753408	+	1.03698i	−0.000954890	+	0.00131429i
$790$		0			0
$791$	669.446	−	486.381i	0.846328	−	0.614893i
$792$		0			0
$793$	−135.408	+	135.408i	−0.170754	+	0.170754i
$794$		0			0
$795$	−75.1334	−	7.25914i	−0.0945074	−	0.00913099i
$796$		0			0
$797$	−393.451	+	772.191i	−0.493665	+	0.968872i	0.500974	+	0.865462i	$0.332975\pi$
$797$	−393.451	+	772.191i	−0.493665	+	0.968872i	−0.994639	+	0.103410i	$0.967025\pi$
$798$		0			0
$799$			16.8197i			0.0210509i
$800$		0			0
$801$	−997.982			−1.24592
$802$		0			0
$803$	−497.517	−	253.497i	−0.619573	−	0.315688i
$804$		0			0
$805$	724.640	−	160.402i	0.900174	−	0.199257i
$806$		0			0
$807$	10.3816	+	10.3816i	0.0128645	+	0.0128645i
$808$		0			0
$809$	72.5617	+	99.8726i	0.0896931	+	0.123452i	0.851505	−	0.524346i	$-0.175690\pi$
$809$	72.5617	+	99.8726i	0.0896931	+	0.123452i	−0.761812	+	0.647798i	$0.775690\pi$
$810$		0			0
$811$	−378.763	−	275.188i	−0.467033	−	0.339319i	0.329251	−	0.944242i	$-0.393204\pi$
$811$	−378.763	−	275.188i	−0.467033	−	0.339319i	−0.796284	+	0.604923i	$0.793204\pi$
$812$		0			0
$813$	11.9673	−	75.5585i	0.0147199	−	0.0929379i
$814$		0			0
$815$	−840.870	−	1020.73i	−1.03174	−	1.25243i
$816$		0			0
$817$	888.179	−	452.550i	1.08712	−	0.553916i
$818$		0			0
$819$	1248.19	+	405.562i	1.52404	+	0.495191i
$820$		0			0
$821$	285.639	+	879.107i	0.347916	+	1.07078i	0.960004	+	0.279986i	$0.0903298\pi$
$821$	285.639	+	879.107i	0.347916	+	1.07078i	−0.612088	+	0.790790i	$0.709670\pi$
$822$		0			0
$823$	757.643	−	119.999i	0.920587	−	0.145807i	0.321885	−	0.946779i	$-0.395684\pi$
$823$	757.643	−	119.999i	0.920587	−	0.145807i	0.598702	+	0.800972i	$0.295684\pi$
$824$		0			0
$825$	44.4847	−	29.9633i	0.0539208	−	0.0363192i
$826$		0			0
$827$	36.5445	+	230.733i	0.0441892	+	0.279000i	0.999882	−	0.0153664i	$-0.00489148\pi$
$827$	36.5445	+	230.733i	0.0441892	+	0.279000i	−0.955693	+	0.294366i	$0.904891\pi$
$828$		0			0
$829$	−1244.32	+	404.304i	−1.50099	+	0.487701i	−0.940306	−	0.340330i	$-0.889461\pi$
$829$	−1244.32	+	404.304i	−1.50099	+	0.487701i	−0.560682	+	0.828031i	$0.689461\pi$
$830$		0			0
$831$	5.33226	−	16.4110i	0.00641668	−	0.0197485i
$832$		0			0
$833$	24.3900	+	47.8681i	0.0292797	+	0.0574647i
$834$		0			0
$835$	−337.590	+	1303.62i	−0.404299	+	1.56122i
$836$		0			0
$837$	39.0020	+	6.17731i	0.0465974	+	0.00738030i
$838$		0			0
$839$	614.547	−	845.852i	0.732476	−	1.00817i	−0.266541	−	0.963824i	$-0.585881\pi$
$839$	614.547	−	845.852i	0.732476	−	1.00817i	0.999016	−	0.0443428i	$-0.0141194\pi$
$840$		0			0
$841$	519.757	−	377.626i	0.618023	−	0.449020i
$842$		0			0
$843$	45.5884	−	45.5884i	0.0540787	−	0.0540787i
$844$		0			0
$845$	65.4386	−	38.5177i	0.0774421	−	0.0455830i
$846$		0			0
$847$	190.037	−	372.968i	0.224364	−	0.440340i
$848$		0			0
$849$			46.6825i			0.0549853i
$850$		0			0
$851$	−127.019			−0.149259
$852$		0			0
$853$	32.3156	+	16.4656i	0.0378846	+	0.0193032i	0.472830	−	0.881154i	$-0.343232\pi$
$853$	32.3156	+	16.4656i	0.0378846	+	0.0193032i	−0.434946	+	0.900457i	$0.643232\pi$
$854$		0			0
$855$	−585.061	−	254.617i	−0.684281	−	0.297798i
$856$		0			0
$857$	687.485	+	687.485i	0.802199	+	0.802199i	0.983439	−	0.181240i	$-0.0580110\pi$
$857$	687.485	+	687.485i	0.802199	+	0.802199i	−0.181240	+	0.983439i	$0.558011\pi$
$858$		0			0
$859$	−884.589	−	1217.53i	−1.02979	−	1.41738i	−0.905106	−	0.425187i	$-0.860208\pi$
$859$	−884.589	−	1217.53i	−1.02979	−	1.41738i	−0.124684	−	0.992197i	$-0.539792\pi$
$860$		0			0
$861$	86.2658	+	62.6758i	0.100193	+	0.0727942i
$862$		0			0
$863$	−205.361	+	1296.60i	−0.237962	+	1.50243i	0.522269	+	0.852781i	$0.325086\pi$
$863$	−205.361	+	1296.60i	−0.237962	+	1.50243i	−0.760231	+	0.649653i	$0.774914\pi$
$864$		0			0
$865$	500.802	−	785.540i	0.578962	−	0.908138i
$866$		0			0
$867$	60.7692	−	30.9634i	0.0700913	−	0.0357133i
$868$		0			0
$869$	−56.1415	−	18.2415i	−0.0646047	−	0.0209913i
$870$		0			0
$871$	220.741	+	679.371i	0.253434	+	0.779990i
$872$		0			0
$873$	1140.37	−	180.617i	1.30626	−	0.206892i
$874$		0			0
$875$	245.000	+	1329.12i	0.280000	+	1.51900i
$876$		0			0
$877$	−58.9645	−	372.287i	−0.0672343	−	0.424501i	−0.998230	−	0.0594706i	$-0.981059\pi$
$877$	−58.9645	−	372.287i	−0.0672343	−	0.424501i	0.930996	−	0.365030i	$-0.118941\pi$
$878$		0			0
$879$	−75.4629	+	24.5194i	−0.0858509	+	0.0278947i
$880$		0			0
$881$	−297.148	+	914.528i	−0.337285	+	1.03806i	0.628300	+	0.777971i	$0.283751\pi$
$881$	−297.148	+	914.528i	−0.337285	+	1.03806i	−0.965585	+	0.260086i	$0.916249\pi$
$882$		0			0
$883$	−16.1759	−	31.7470i	−0.0183192	−	0.0359535i	0.881666	−	0.471875i	$-0.156423\pi$
$883$	−16.1759	−	31.7470i	−0.0183192	−	0.0359535i	−0.899985	+	0.435921i	$0.856423\pi$
$884$		0			0
$885$	77.4320	+	49.3650i	0.0874938	+	0.0557796i
$886$		0			0
$887$	296.686	+	46.9904i	0.334482	+	0.0529768i	0.321417	−	0.946938i	$-0.395841\pi$
$887$	296.686	+	46.9904i	0.334482	+	0.0529768i	0.0130655	+	0.999915i	$0.495841\pi$
$888$		0			0
$889$	389.298	−	535.823i	0.437905	−	0.602725i
$890$		0			0
$891$	583.372	−	423.845i	0.654739	−	0.475696i
$892$		0			0
$893$	214.475	−	214.475i	0.240174	−	0.240174i
$894$		0			0
$895$	408.166	−	937.884i	0.456051	−	1.04792i
$896$		0			0
$897$	−20.0056	+	39.2632i	−0.0223028	+	0.0437717i
$898$		0			0
$899$			358.375i			0.398637i
$900$		0			0
$901$	−50.5032			−0.0560524
$902$		0			0
$903$	159.183	+	81.1080i	0.176283	+	0.0898206i
$904$		0			0
$905$	70.0436	+	118.999i	0.0773962	+	0.131490i
$906$		0			0
$907$	505.478	+	505.478i	0.557307	+	0.557307i	0.928540	−	0.371233i	$-0.121065\pi$
$907$	505.478	+	505.478i	0.557307	+	0.557307i	−0.371233	+	0.928540i	$0.621065\pi$
$908$		0			0
$909$	170.935	+	235.272i	0.188047	+	0.258825i
$910$		0			0
$911$	1112.30	+	808.135i	1.22097	+	0.887086i	0.996180	−	0.0873220i	$-0.0278309\pi$
$911$	1112.30	+	808.135i	1.22097	+	0.887086i	0.224788	+	0.974408i	$0.427831\pi$
$912$		0			0
$913$	−159.283	+	1005.67i	−0.174461	+	1.10150i
$914$		0			0
$915$	16.1529	+	4.18302i	0.0176534	+	0.00457160i
$916$		0			0
$917$	34.1594	−	17.4051i	0.0372513	−	0.0189805i
$918$		0			0
$919$	−1241.96	−	403.536i	−1.35142	−	0.439104i	−0.458252	−	0.888822i	$-0.651524\pi$
$919$	−1241.96	−	403.536i	−1.35142	−	0.439104i	−0.893170	+	0.449718i	$0.851524\pi$
$920$		0			0
$921$	−8.17554	−	25.1617i	−0.00887681	−	0.0273200i
$922$		0			0
$923$	−36.7026	+	5.81312i	−0.0397645	+	0.00629808i
$924$		0			0
$925$	8.22240	−	231.157i	0.00888909	−	0.249899i
$926$		0			0
$927$	−72.6888	−	458.939i	−0.0784129	−	0.495080i
$928$		0			0
$929$	−430.474	+	139.870i	−0.463374	+	0.150559i	−0.531394	−	0.847125i	$-0.678332\pi$
$929$	−430.474	+	139.870i	−0.463374	+	0.150559i	0.0680204	+	0.997684i	$0.478332\pi$
$930$		0			0
$931$	299.380	−	921.397i	0.321568	−	0.989685i
$932$		0			0
$933$	−12.1956	−	23.9353i	−0.0130714	−	0.0256541i
$934$		0			0
$935$	27.6973	−	22.8168i	0.0296227	−	0.0244030i
$936$		0			0
$937$	−517.916	−	82.0298i	−0.552738	−	0.0875451i	−0.126184	−	0.992007i	$-0.540273\pi$
$937$	−517.916	−	82.0298i	−0.552738	−	0.0875451i	−0.426555	+	0.904462i	$0.640273\pi$
$938$		0			0
$939$	14.2874	−	19.6650i	0.0152156	−	0.0209425i
$940$		0			0
$941$	983.490	−	714.547i	1.04515	−	0.759349i	0.0738692	−	0.997268i	$-0.476465\pi$
$941$	983.490	−	714.547i	1.04515	−	0.759349i	0.971285	+	0.237919i	$0.0764653\pi$
$942$		0			0
$943$	404.798	−	404.798i	0.429266	−	0.429266i
$944$		0			0
$945$	−49.5847	−	224.006i	−0.0524706	−	0.237044i
$946$		0			0
$947$	−561.219	+	1101.45i	−0.592628	+	1.16310i	0.378736	+	0.925505i	$0.376359\pi$
$947$	−561.219	+	1101.45i	−0.592628	+	1.16310i	−0.971365	+	0.237594i	$0.923641\pi$
$948$		0			0
$949$			835.402i			0.880297i
$950$		0			0
$951$	96.5800			0.101556
$952$		0			0
$953$	90.7422	+	46.2355i	0.0952174	+	0.0485157i	0.500951	−	0.865476i	$-0.332984\pi$
$953$	90.7422	+	46.2355i	0.0952174	+	0.0485157i	−0.405733	+	0.913992i	$0.632984\pi$
$954$		0			0
$955$	44.7232	−	462.893i	0.0468306	−	0.484705i
$956$		0			0
$957$	−58.4290	−	58.4290i	−0.0610544	−	0.0610544i
$958$		0			0
$959$	1586.89	+	2184.16i	1.65473	+	2.27754i
$960$		0			0
$961$	707.423	+	513.973i	0.736133	+	0.534832i
$962$		0			0
$963$	68.8578	−	434.751i	0.0715034	−	0.451455i
$964$		0			0
$965$	−74.1218	−	1218.37i	−0.0768102	−	1.26256i
$966$		0			0
$967$	421.887	−	214.962i	0.436284	−	0.222298i	−0.222032	−	0.975039i	$-0.571269\pi$
$967$	421.887	−	214.962i	0.436284	−	0.222298i	0.658316	+	0.752741i	$0.271269\pi$
$968$		0			0
$969$	2.53920	+	0.825036i	0.00262043	+	0.000851430i
$970$		0			0
$971$	−520.392	−	1601.60i	−0.535934	−	1.64943i	−0.741623	−	0.670817i	$-0.765944\pi$
$971$	−520.392	−	1601.60i	−0.535934	−	1.64943i	0.205690	−	0.978617i	$-0.434056\pi$
$972$		0			0
$973$	1478.60	−	234.187i	1.51963	−	0.240686i
$974$		0			0
$975$	−70.1582	−	38.9489i	−0.0719571	−	0.0399475i
$976$		0			0
$977$	17.9443	+	113.296i	0.0183667	+	0.115963i	0.995168	−	0.0981833i	$-0.0313032\pi$
$977$	17.9443	+	113.296i	0.0183667	+	0.115963i	−0.976802	+	0.214146i	$0.931303\pi$
$978$		0			0
$979$	−962.619	+	312.774i	−0.983267	+	0.319483i
$980$		0			0
$981$	357.405	−	1099.98i	0.364328	−	1.12128i
$982$		0			0
$983$	−583.651	−	1145.48i	−0.593744	−	1.16529i	−0.970978	−	0.239170i	$-0.923125\pi$
$983$	−583.651	−	1145.48i	−0.593744	−	1.16529i	0.377233	−	0.926118i	$-0.376875\pi$
$984$		0			0
$985$	−79.4297	−	201.836i	−0.0806393	−	0.204910i
$986$		0			0
$987$	53.6920	+	8.50397i	0.0543992	+	0.00861598i
$988$		0			0
$989$	563.778	−	775.973i	0.570048	−	0.784604i
$990$		0			0
$991$	392.287	−	285.013i	0.395850	−	0.287602i	−0.371999	−	0.928233i	$-0.621327\pi$
$991$	392.287	−	285.013i	0.395850	−	0.287602i	0.767848	+	0.640631i	$0.221327\pi$
$992$		0			0
$993$	−20.1689	+	20.1689i	−0.0203110	+	0.0203110i
$994$		0			0
$995$	−1239.95	−	1097.73i	−1.24618	−	1.10325i
$996$		0			0
$997$	589.304	−	1156.57i	0.591077	−	1.16005i	−0.380820	−	0.924649i	$-0.624358\pi$
$997$	589.304	−	1156.57i	0.591077	−	1.16005i	0.971897	−	0.235405i	$-0.0756417\pi$
$998$		0			0
$999$			39.2652i			0.0393045i

Display

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a_n

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a_n

instead) (See

a_n

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a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.c.337.2		32
4.3	odd	2		25.3.f.a.12.3	✓	32
12.11	even	2		225.3.r.a.37.2		32
20.3	even	4		125.3.f.a.43.3		32
20.7	even	4		125.3.f.b.43.2		32
20.19	odd	2		125.3.f.c.82.2		32
25.23	odd	20	inner	400.3.bg.c.273.2		32
100.11	odd	10		125.3.f.a.32.3		32
100.23	even	20		25.3.f.a.23.3	yes	32
100.27	even	20		125.3.f.c.93.2		32
100.39	odd	10		125.3.f.b.32.2		32
300.23	odd	20		225.3.r.a.73.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.12.3	✓	32	4.3	odd	2
25.3.f.a.23.3	yes	32	100.23	even	20
125.3.f.a.32.3		32	100.11	odd	10
125.3.f.a.43.3		32	20.3	even	4
125.3.f.b.32.2		32	100.39	odd	10
125.3.f.b.43.2		32	20.7	even	4
125.3.f.c.82.2		32	20.19	odd	2
125.3.f.c.93.2		32	100.27	even	20
225.3.r.a.37.2		32	12.11	even	2
225.3.r.a.73.2		32	300.23	odd	20
400.3.bg.c.273.2		32	25.23	odd	20	inner
400.3.bg.c.337.2		32	1.1	even	1	trivial

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

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	400.3.bg.c.337.2

Level	$400$
Weight	$3$
Character	400.337
Analytic conductor	$10.899$
Analytic rank	$0$
Dimension	$32$
Inner twists	$2$