LMFDB - Embedded newform 400.3.bg.f.33.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.6
Character	$\chi$	$=$	400.33
Dual form			400.3.bg.f.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.61980 + 0.414935i) q^{3} +(-2.28576 + 4.44694i) q^{5} +(-4.29378 + 4.29378i) q^{7} +(-1.86835 - 0.607064i) q^{9} +O(q^{10})$	\(q+(2.61980 + 0.414935i) q^{3} +(-2.28576 + 4.44694i) q^{5} +(-4.29378 + 4.29378i) q^{7} +(-1.86835 - 0.607064i) q^{9} +(2.00916 + 6.18355i) q^{11} +(20.7906 - 10.5933i) q^{13} +(-7.83342 + 10.7016i) q^{15} +(-24.6968 + 3.91159i) q^{17} +(-18.5820 + 25.5759i) q^{19} +(-13.0305 + 9.46718i) q^{21} +(-13.7056 + 26.8987i) q^{23} +(-14.5506 - 20.3293i) q^{25} +(-25.9130 - 13.2033i) q^{27} +(-14.5201 - 19.9851i) q^{29} +(33.8512 + 24.5943i) q^{31} +(2.69781 + 17.0333i) q^{33} +(-9.27963 - 28.9087i) q^{35} +(29.0865 + 57.0855i) q^{37} +(58.8626 - 19.1256i) q^{39} +(5.34467 - 16.4492i) q^{41} +(-20.7467 - 20.7467i) q^{43} +(6.97019 - 6.92085i) q^{45} +(-0.378171 + 2.38768i) q^{47} +12.1269i q^{49} -66.3237 q^{51} +(23.2382 + 3.68057i) q^{53} +(-32.0903 - 5.19952i) q^{55} +(-59.2932 + 59.2932i) q^{57} +(41.9585 + 13.6331i) q^{59} +(-5.55656 - 17.1013i) q^{61} +(10.6289 - 5.41569i) q^{63} +(-0.414396 + 116.668i) q^{65} +(46.5510 - 7.37295i) q^{67} +(-47.0670 + 64.7821i) q^{69} +(48.8317 - 35.4783i) q^{71} +(38.4282 - 75.4196i) q^{73} +(-29.6842 - 59.2962i) q^{75} +(-35.1777 - 17.9239i) q^{77} +(14.7911 + 20.3582i) q^{79} +(-48.1043 - 34.9498i) q^{81} +(9.44942 + 59.6613i) q^{83} +(39.0565 - 118.766i) q^{85} +(-29.7471 - 58.3819i) q^{87} +(18.0838 - 5.87579i) q^{89} +(-43.7847 + 134.756i) q^{91} +(78.4781 + 78.4781i) q^{93} +(-71.2605 - 141.093i) q^{95} +(-14.5335 + 91.7608i) q^{97} -12.7727i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$	$1$

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
$3$	2.61980	+	0.414935i	0.873265	+	0.138312i	0.576951	−	0.816779i	$-0.304242\pi$
$3$	2.61980	+	0.414935i	0.873265	+	0.138312i	0.296314	+	0.955090i	$0.404242\pi$
$4$		0			0
$5$	−2.28576	+	4.44694i	−0.457152	+	0.889388i
$5$	−2.28576	+	4.44694i	−0.457152	+	0.889388i
$6$		0			0
$7$	−4.29378	+	4.29378i	−0.613397	+	0.613397i	−0.943830	−	0.330433i	$-0.892805\pi$
$7$	−4.29378	+	4.29378i	−0.613397	+	0.613397i	0.330433	+	0.943830i	$0.392805\pi$
$8$		0			0
$9$	−1.86835	−	0.607064i	−0.207595	−	0.0674516i
$10$		0			0
$11$	2.00916	+	6.18355i	0.182651	+	0.562141i	0.999900	−	0.0141435i	$-0.00450217\pi$
$11$	2.00916	+	6.18355i	0.182651	+	0.562141i	−0.817249	+	0.576284i	$0.804502\pi$
$12$		0			0
$13$	20.7906	−	10.5933i	1.59928	−	0.814871i	0.599379	−	0.800465i	$-0.295414\pi$
$13$	20.7906	−	10.5933i	1.59928	−	0.814871i	0.999896	−	0.0144060i	$-0.00458574\pi$
$14$		0			0
$15$	−7.83342	+	10.7016i	−0.522228	+	0.713442i
$16$		0			0
$17$	−24.6968	+	3.91159i	−1.45276	+	0.230094i	−0.832377	−	0.554209i	$-0.813021\pi$
$17$	−24.6968	+	3.91159i	−1.45276	+	0.230094i	−0.620378	+	0.784303i	$0.713021\pi$
$18$		0			0
$19$	−18.5820	+	25.5759i	−0.977998	+	1.34610i	−0.0400966	+	0.999196i	$0.512767\pi$
$19$	−18.5820	+	25.5759i	−0.977998	+	1.34610i	−0.937901	+	0.346903i	$0.887233\pi$
$20$		0			0
$21$	−13.0305	+	9.46718i	−0.620498	+	0.450818i
$22$		0			0
$23$	−13.7056	+	26.8987i	−0.595894	+	1.16951i	0.374329	+	0.927296i	$0.377873\pi$
$23$	−13.7056	+	26.8987i	−0.595894	+	1.16951i	−0.970223	+	0.242212i	$0.922127\pi$
$24$		0			0
$25$	−14.5506	−	20.3293i	−0.582023	−	0.813172i
$26$		0			0
$27$	−25.9130	−	13.2033i	−0.959740	−	0.489012i
$28$		0			0
$29$	−14.5201	−	19.9851i	−0.500692	−	0.689143i	0.481623	−	0.876378i	$-0.340047\pi$
$29$	−14.5201	−	19.9851i	−0.500692	−	0.689143i	−0.982315	+	0.187235i	$0.940047\pi$
$30$		0			0
$31$	33.8512	+	24.5943i	1.09197	+	0.793365i	0.979731	−	0.200316i	$-0.0641968\pi$
$31$	33.8512	+	24.5943i	1.09197	+	0.793365i	0.112242	+	0.993681i	$0.464197\pi$
$32$		0			0
$33$	2.69781	+	17.0333i	0.0817518	+	0.516160i
$34$		0			0
$35$	−9.27963	−	28.9087i	−0.265132	−	0.825964i
$36$		0			0
$37$	29.0865	+	57.0855i	0.786122	+	1.54285i	0.838925	+	0.544247i	$0.183184\pi$
$37$	29.0865	+	57.0855i	0.786122	+	1.54285i	−0.0528033	+	0.998605i	$0.516816\pi$
$38$		0			0
$39$	58.8626	−	19.1256i	1.50930	−	0.490400i
$40$		0			0
$41$	5.34467	−	16.4492i	0.130358	−	0.401200i	−0.864481	−	0.502665i	$-0.832353\pi$
$41$	5.34467	−	16.4492i	0.130358	−	0.401200i	0.994839	+	0.101465i	$0.0323529\pi$
$42$		0			0
$43$	−20.7467	−	20.7467i	−0.482481	−	0.482481i	0.423442	−	0.905923i	$-0.360822\pi$
$43$	−20.7467	−	20.7467i	−0.482481	−	0.482481i	−0.905923	+	0.423442i	$0.860822\pi$
$44$		0			0
$45$	6.97019	−	6.92085i	0.154893	−	0.153797i
$46$		0			0
$47$	−0.378171	+	2.38768i	−0.00804619	+	0.0508016i	−0.991385	−	0.130982i	$-0.958187\pi$
$47$	−0.378171	+	2.38768i	−0.00804619	+	0.0508016i	0.983339	+	0.181784i	$0.0581870\pi$
$48$		0			0
$49$			12.1269i			0.247488i
$50$		0			0
$51$	−66.3237			−1.30047
$52$		0			0
$53$	23.2382	+	3.68057i	0.438457	+	0.0694447i	0.371761	−	0.928329i	$-0.378754\pi$
$53$	23.2382	+	3.68057i	0.438457	+	0.0694447i	0.0666960	+	0.997773i	$0.478754\pi$
$54$		0			0
$55$	−32.0903	−	5.19952i	−0.583460	−	0.0945366i
$56$		0			0
$57$	−59.2932	+	59.2932i	−1.04023	+	1.04023i
$58$		0			0
$59$	41.9585	+	13.6331i	0.711161	+	0.231070i	0.642187	−	0.766548i	$-0.278027\pi$
$59$	41.9585	+	13.6331i	0.711161	+	0.231070i	0.0689741	+	0.997618i	$0.478027\pi$
$60$		0			0
$61$	−5.55656	−	17.1013i	−0.0910912	−	0.280350i	0.895124	−	0.445817i	$-0.147087\pi$
$61$	−5.55656	−	17.1013i	−0.0910912	−	0.280350i	−0.986215	+	0.165467i	$0.947087\pi$
$62$		0			0
$63$	10.6289	−	5.41569i	0.168713	−	0.0859634i
$64$		0			0
$65$	−0.414396	+	116.668i	−0.00637533	+	1.79490i
$66$		0			0
$67$	46.5510	−	7.37295i	0.694791	−	0.110044i	0.200957	−	0.979600i	$-0.435595\pi$
$67$	46.5510	−	7.37295i	0.694791	−	0.110044i	0.493834	+	0.869556i	$0.335595\pi$
$68$		0			0
$69$	−47.0670	+	64.7821i	−0.682130	+	0.938872i
$70$		0			0
$71$	48.8317	−	35.4783i	0.687770	−	0.499694i	−0.188156	−	0.982139i	$-0.560251\pi$
$71$	48.8317	−	35.4783i	0.687770	−	0.499694i	0.875926	+	0.482445i	$0.160251\pi$
$72$		0			0
$73$	38.4282	−	75.4196i	0.526414	−	1.03314i	−0.462772	−	0.886477i	$-0.653145\pi$
$73$	38.4282	−	75.4196i	0.526414	−	1.03314i	0.989186	−	0.146668i	$-0.0468548\pi$
$74$		0			0
$75$	−29.6842	−	59.2962i	−0.395790	−	0.790615i
$76$		0			0
$77$	−35.1777	−	17.9239i	−0.456853	−	0.232778i
$78$		0			0
$79$	14.7911	+	20.3582i	0.187229	+	0.257698i	0.892305	−	0.451433i	$-0.149087\pi$
$79$	14.7911	+	20.3582i	0.187229	+	0.257698i	−0.705076	+	0.709132i	$0.749087\pi$
$80$		0			0
$81$	−48.1043	−	34.9498i	−0.593881	−	0.431479i
$82$		0			0
$83$	9.44942	+	59.6613i	0.113848	+	0.718810i	0.976900	+	0.213695i	$0.0685500\pi$
$83$	9.44942	+	59.6613i	0.113848	+	0.718810i	−0.863052	+	0.505115i	$0.831450\pi$
$84$		0			0
$85$	39.0565	−	118.766i	0.459488	−	1.39725i
$86$		0			0
$87$	−29.7471	−	58.3819i	−0.341920	−	0.671056i
$88$		0			0
$89$	18.0838	−	5.87579i	0.203189	−	0.0660201i	−0.205654	−	0.978625i	$-0.565932\pi$
$89$	18.0838	−	5.87579i	0.203189	−	0.0660201i	0.408843	+	0.912605i	$0.365932\pi$
$90$		0			0
$91$	−43.7847	+	134.756i	−0.481151	+	1.48083i
$92$		0			0
$93$	78.4781	+	78.4781i	0.843851	+	0.843851i
$94$		0			0
$95$	−71.2605	−	141.093i	−0.750110	−	1.48519i
$96$		0			0
$97$	−14.5335	+	91.7608i	−0.149830	+	0.945988i	0.792152	+	0.610324i	$0.208961\pi$
$97$	−14.5335	+	91.7608i	−0.149830	+	0.945988i	−0.941982	+	0.335664i	$0.891039\pi$
$98$		0			0
$99$		−	12.7727i		−	0.129017i
$100$		0			0
$101$	−60.1977			−0.596017			−0.298008	−	0.954563i	$-0.596322\pi$
$101$	−60.1977			−0.596017			−0.298008	+	0.954563i	$0.596322\pi$
$102$		0			0
$103$	54.4044	+	8.61681i	0.528198	+	0.0836584i	0.414838	−	0.909895i	$-0.363838\pi$
$103$	54.4044	+	8.61681i	0.528198	+	0.0836584i	0.113361	+	0.993554i	$0.463838\pi$
$104$		0			0
$105$	−12.3155	−	79.5854i	−0.117290	−	0.757957i
$106$		0			0
$107$	−73.1357	+	73.1357i	−0.683511	+	0.683511i	−0.960790	−	0.277278i	$-0.910568\pi$
$107$	−73.1357	+	73.1357i	−0.683511	+	0.683511i	0.277278	+	0.960790i	$0.410568\pi$
$108$		0			0
$109$	5.21258	+	1.69367i	0.0478218	+	0.0155382i	0.332830	−	0.942987i	$-0.391996\pi$
$109$	5.21258	+	1.69367i	0.0478218	+	0.0155382i	−0.285008	+	0.958525i	$0.591996\pi$
$110$		0			0
$111$	52.5140	+	161.621i	0.473099	+	1.45605i
$112$		0			0
$113$	99.1775	−	50.5335i	0.877677	−	0.447199i	0.0437299	−	0.999043i	$-0.486076\pi$
$113$	99.1775	−	50.5335i	0.877677	−	0.447199i	0.833947	+	0.551845i	$0.186076\pi$
$114$		0			0
$115$	−88.2893	−	122.432i	−0.767733	−	1.06462i
$116$		0			0
$117$	−45.2750	+	7.17085i	−0.386965	+	0.0612893i
$118$		0			0
$119$	89.2473	−	122.838i	0.749977	−	1.03225i
$120$		0			0
$121$	63.6915	−	46.2746i	0.526376	−	0.382435i
$122$		0			0
$123$	20.8273	−	40.8759i	0.169328	−	0.332324i
$124$		0			0
$125$	123.662	−	18.2377i	0.989299	−	0.145901i
$126$		0			0
$127$	198.188	+	100.982i	1.56054	+	0.795134i	0.999467	−	0.0326336i	$-0.0103894\pi$
$127$	198.188	+	100.982i	1.56054	+	0.795134i	0.561071	+	0.827768i	$0.310389\pi$
$128$		0			0
$129$	−45.7435	−	62.9606i	−0.354601	−	0.488066i
$130$		0			0
$131$	−100.733	−	73.1867i	−0.768953	−	0.558677i	0.132690	−	0.991158i	$-0.457639\pi$
$131$	−100.733	−	73.1867i	−0.768953	−	0.558677i	−0.901643	+	0.432480i	$0.857639\pi$
$132$		0			0
$133$	−30.0303	−	189.604i	−0.225792	−	1.42559i
$134$		0			0
$135$	117.945	−	85.0538i	0.873669	−	0.630028i
$136$		0			0
$137$	17.3367	+	34.0251i	0.126545	+	0.248359i	0.945583	−	0.325380i	$-0.105492\pi$
$137$	17.3367	+	34.0251i	0.126545	+	0.248359i	−0.819038	+	0.573739i	$0.805492\pi$
$138$		0			0
$139$	189.537	−	61.5842i	1.36357	−	0.443052i	0.466339	−	0.884606i	$-0.345573\pi$
$139$	189.537	−	61.5842i	1.36357	−	0.443052i	0.897234	+	0.441555i	$0.145573\pi$
$140$		0			0
$141$	−1.98146	+	6.09831i	−0.0140529	+	0.0432504i
$142$		0			0
$143$	107.276	+	107.276i	0.750181	+	0.750181i
$144$		0			0
$145$	122.062	−	18.8886i	0.841808	−	0.130266i
$146$		0			0
$147$	−5.03188	+	31.7700i	−0.0342305	+	0.216123i
$148$		0			0
$149$		−	56.6606i		−	0.380273i	−0.981758	−	0.190136i	$-0.939107\pi$
$149$		−	56.6606i		−	0.380273i	0.981758	−	0.190136i	$-0.0608930\pi$
$150$		0			0
$151$	−186.781			−1.23696			−0.618480	−	0.785800i	$-0.712251\pi$
$151$	−186.781			−1.23696			−0.618480	+	0.785800i	$0.712251\pi$
$152$		0			0
$153$	48.5170	+	7.68434i	0.317104	+	0.0502244i
$154$		0			0
$155$	−186.745	+	94.3175i	−1.20481	+	0.608500i
$156$		0			0
$157$	145.046	−	145.046i	0.923862	−	0.923862i	−0.0734375	−	0.997300i	$-0.523397\pi$
$157$	145.046	−	145.046i	0.923862	−	0.923862i	0.997300	+	0.0734375i	$0.0233969\pi$
$158$		0			0
$159$	59.3521	+	19.2847i	0.373284	+	0.121287i
$160$		0			0
$161$	−56.6484	−	174.346i	−0.351853	−	1.08289i
$162$		0			0
$163$	−120.622	+	61.4601i	−0.740014	+	0.377056i	−0.783002	−	0.622019i	$-0.786312\pi$
$163$	−120.622	+	61.4601i	−0.740014	+	0.377056i	0.0429874	+	0.999076i	$0.486312\pi$
$164$		0			0
$165$	−81.9126	−	26.9371i	−0.496440	−	0.163255i
$166$		0			0
$167$	15.6481	−	2.47842i	0.0937012	−	0.0148408i	−0.109408	−	0.993997i	$-0.534895\pi$
$167$	15.6481	−	2.47842i	0.0937012	−	0.0148408i	0.203109	+	0.979156i	$0.434895\pi$
$168$		0			0
$169$	220.694	−	303.759i	1.30588	−	1.79739i
$170$		0			0
$171$	50.2438	−	36.5043i	0.293824	−	0.213475i
$172$		0			0
$173$	−124.502	+	244.348i	−0.719663	+	1.41242i	0.183455	+	0.983028i	$0.441272\pi$
$173$	−124.502	+	244.348i	−0.719663	+	1.41242i	−0.903119	+	0.429391i	$0.858728\pi$
$174$		0			0
$175$	149.767	+	24.8125i	0.855809	+	0.141786i
$176$		0			0
$177$	104.266	+	53.1261i	0.589072	+	0.300147i
$178$		0			0
$179$	−51.7857	−	71.2769i	−0.289306	−	0.398195i	0.639483	−	0.768805i	$-0.279149\pi$
$179$	−51.7857	−	71.2769i	−0.289306	−	0.398195i	−0.928788	+	0.370610i	$0.879149\pi$
$180$		0			0
$181$	−175.412	−	127.445i	−0.969129	−	0.704114i	−0.0138763	−	0.999904i	$-0.504417\pi$
$181$	−175.412	−	127.445i	−0.969129	−	0.704114i	−0.955253	+	0.295790i	$0.904417\pi$
$182$		0			0
$183$	−7.46111	−	47.1076i	−0.0407711	−	0.257419i
$184$		0			0
$185$	−320.341	−	1.13782i	−1.73157	−	0.00615040i
$186$		0			0
$187$	−73.8073	−	144.855i	−0.394692	−	0.774626i
$188$		0			0
$189$	167.957	−	54.5724i	0.888660	−	0.288743i
$190$		0			0
$191$	12.5841	−	38.7299i	0.0658854	−	0.202774i	−0.912694	−	0.408643i	$-0.866002\pi$
$191$	12.5841	−	38.7299i	0.0658854	−	0.202774i	0.978580	+	0.205869i	$0.0660020\pi$
$192$		0			0
$193$	213.799	+	213.799i	1.10777	+	1.10777i	0.993444	+	0.114324i	$0.0364702\pi$
$193$	213.799	+	213.799i	1.10777	+	1.10777i	0.114324	+	0.993444i	$0.463530\pi$
$194$		0			0
$195$	−49.4954	+	305.475i	−0.253822	+	1.56654i
$196$		0			0
$197$	−52.8963	+	333.974i	−0.268509	+	1.69530i	0.372715	+	0.927946i	$0.378427\pi$
$197$	−52.8963	+	333.974i	−0.268509	+	1.69530i	−0.641224	+	0.767353i	$0.721573\pi$
$198$		0			0
$199$		−	57.3193i		−	0.288037i	−0.989575	−	0.144018i	$-0.953998\pi$
$199$		−	57.3193i		−	0.288037i	0.989575	−	0.144018i	$-0.0460025\pi$
$200$		0			0
$201$	125.013			0.621957
$202$		0			0
$203$	148.158	+	23.4659i	0.729841	+	0.115595i
$204$		0			0
$205$	60.9320	+	61.3664i	0.297229	+	0.299348i
$206$		0			0
$207$	41.9361	−	41.9361i	0.202590	−	0.202590i
$208$		0			0
$209$	−195.484	−	63.5165i	−0.935328	−	0.303907i
$210$		0			0
$211$	−82.7510	−	254.681i	−0.392185	−	1.20702i	−0.931132	−	0.364681i	$-0.881178\pi$
$211$	−82.7510	−	254.681i	−0.392185	−	1.20702i	0.538948	−	0.842339i	$-0.318822\pi$
$212$		0			0
$213$	142.650	−	72.6839i	0.669719	−	0.341239i
$214$		0			0
$215$	139.681	−	44.8373i	0.649680	−	0.208546i
$216$		0			0
$217$	−250.952	+	39.7469i	−1.15646	+	0.183165i
$218$		0			0
$219$	131.968	−	181.639i	0.602595	−	0.829400i
$220$		0			0
$221$	−472.025	+	342.946i	−2.13586	+	1.55179i
$222$		0			0
$223$	−62.3797	+	122.427i	−0.279730	+	0.549000i	−0.987534	−	0.157409i	$-0.949686\pi$
$223$	−62.3797	+	122.427i	−0.279730	+	0.549000i	0.707804	+	0.706409i	$0.249686\pi$
$224$		0			0
$225$	14.8444	+	46.8154i	0.0659752	+	0.208069i
$226$		0			0
$227$	−206.386	−	105.159i	−0.909191	−	0.463256i	−0.0641396	−	0.997941i	$-0.520430\pi$
$227$	−206.386	−	105.159i	−0.909191	−	0.463256i	−0.845051	+	0.534685i	$0.820430\pi$
$228$		0			0
$229$	54.9834	+	75.6781i	0.240102	+	0.330472i	0.912014	−	0.410159i	$-0.134527\pi$
$229$	54.9834	+	75.6781i	0.240102	+	0.330472i	−0.671912	+	0.740631i	$0.734527\pi$
$230$		0			0
$231$	−84.7210	−	61.5534i	−0.366758	−	0.266465i
$232$		0			0
$233$	30.7615	+	194.221i	0.132024	+	0.833565i	0.961456	+	0.274958i	$0.0886639\pi$
$233$	30.7615	+	194.221i	0.132024	+	0.833565i	−0.829433	+	0.558607i	$0.811336\pi$
$234$		0			0
$235$	−9.75345	−	7.13937i	−0.0415041	−	0.0303803i
$236$		0			0
$237$	30.3023	+	59.4716i	0.127858	+	0.250935i
$238$		0			0
$239$	−189.259	+	61.4938i	−0.791877	+	0.257296i	−0.676903	−	0.736072i	$-0.736678\pi$
$239$	−189.259	+	61.4938i	−0.791877	+	0.257296i	−0.114974	+	0.993369i	$0.536678\pi$
$240$		0			0
$241$	−91.9444	+	282.976i	−0.381512	+	1.17417i	0.557467	+	0.830199i	$0.311773\pi$
$241$	−91.9444	+	282.976i	−0.381512	+	1.17417i	−0.938979	+	0.343974i	$0.888227\pi$
$242$		0			0
$243$	73.5603	+	73.5603i	0.302717	+	0.302717i
$244$		0			0
$245$	−53.9277	−	27.7192i	−0.220113	−	0.113140i
$246$		0			0
$247$	−115.396	+	728.582i	−0.467190	+	2.94972i
$248$		0			0
$249$			160.221i			0.643459i
$250$		0			0
$251$	−300.129			−1.19573			−0.597867	−	0.801595i	$-0.703985\pi$
$251$	−300.129			−1.19573			−0.597867	+	0.801595i	$0.703985\pi$
$252$		0			0
$253$	−193.866	−	30.7053i	−0.766269	−	0.121365i
$254$		0			0
$255$	151.600	−	294.938i	0.594511	−	1.15662i
$256$		0			0
$257$	45.9173	−	45.9173i	0.178667	−	0.178667i	−0.612108	−	0.790774i	$-0.709678\pi$
$257$	45.9173	−	45.9173i	0.178667	−	0.178667i	0.790774	+	0.612108i	$0.209678\pi$
$258$		0			0
$259$	−370.004	−	120.221i	−1.42859	−	0.464176i
$260$		0			0
$261$	14.9963	+	46.1539i	0.0574571	+	0.176835i
$262$		0			0
$263$	59.4193	−	30.2756i	0.225929	−	0.115116i	−0.337363	−	0.941375i	$-0.609535\pi$
$263$	59.4193	−	30.2756i	0.225929	−	0.115116i	0.563291	+	0.826258i	$0.309535\pi$
$264$		0			0
$265$	−69.4843	+	94.9260i	−0.262205	+	0.358211i
$266$		0			0
$267$	49.8140	−	7.88976i	0.186569	−	0.0295497i
$268$		0			0
$269$	41.5205	−	57.1481i	0.154351	−	0.212446i	−0.724838	−	0.688920i	$-0.758085\pi$
$269$	41.5205	−	57.1481i	0.154351	−	0.212446i	0.879189	+	0.476473i	$0.158085\pi$
$270$		0			0
$271$	351.677	−	255.508i	1.29770	−	0.942835i	0.297771	−	0.954637i	$-0.403757\pi$
$271$	351.677	−	255.508i	1.29770	−	0.942835i	0.999930	+	0.0118019i	$0.00375676\pi$
$272$		0			0
$273$	−170.622	+	334.864i	−0.624988	+	1.22661i
$274$		0			0
$275$	96.4728	−	130.819i	0.350810	−	0.475705i
$276$		0			0
$277$	55.9099	+	28.4875i	0.201841	+	0.102843i	0.551989	−	0.833851i	$-0.313869\pi$
$277$	55.9099	+	28.4875i	0.201841	+	0.102843i	−0.350148	+	0.936694i	$0.613869\pi$
$278$		0			0
$279$	−48.3156	−	66.5007i	−0.173174	−	0.238354i
$280$		0			0
$281$	163.182	+	118.558i	0.580717	+	0.421916i	0.838983	−	0.544158i	$-0.183151\pi$
$281$	163.182	+	118.558i	0.580717	+	0.421916i	−0.258265	+	0.966074i	$0.583151\pi$
$282$		0			0
$283$	57.2013	+	361.155i	0.202125	+	1.27617i	0.854971	+	0.518675i	$0.173575\pi$
$283$	57.2013	+	361.155i	0.202125	+	1.27617i	−0.652847	+	0.757490i	$0.726425\pi$
$284$		0			0
$285$	−128.143	−	399.204i	−0.449626	−	1.40072i
$286$		0			0
$287$	47.6804	+	93.5781i	0.166134	+	0.326056i
$288$		0			0
$289$	319.778	−	103.902i	1.10650	−	0.359523i
$290$		0			0
$291$	−76.1495	+	234.364i	−0.261682	+	0.805375i
$292$		0			0
$293$	−81.2115	−	81.2115i	−0.277172	−	0.277172i	0.554807	−	0.831979i	$-0.312792\pi$
$293$	−81.2115	−	81.2115i	−0.277172	−	0.277172i	−0.831979	+	0.554807i	$0.812792\pi$
$294$		0			0
$295$	−156.533	+	155.425i	−0.530620	+	0.526864i
$296$		0			0
$297$	29.5801	−	186.762i	0.0995964	−	0.628827i
$298$		0			0
$299$			704.427i			2.35594i
$300$		0			0
$301$	178.163			0.591905
$302$		0			0
$303$	−157.706	−	24.9781i	−0.520481	−	0.0824360i
$304$		0			0
$305$	88.7496	+	14.3799i	0.290982	+	0.0471472i
$306$		0			0
$307$	139.708	−	139.708i	0.455074	−	0.455074i	−0.441960	−	0.897035i	$-0.645717\pi$
$307$	139.708	−	139.708i	0.455074	−	0.455074i	0.897035	+	0.441960i	$0.145717\pi$
$308$		0			0
$309$	138.953	+	45.1486i	0.449686	+	0.146112i
$310$		0			0
$311$	110.133	+	338.955i	0.354126	+	1.08989i	0.956515	+	0.291685i	$0.0942158\pi$
$311$	110.133	+	338.955i	0.354126	+	1.08989i	−0.602388	+	0.798203i	$0.705784\pi$
$312$		0			0
$313$	−90.0605	+	45.8881i	−0.287733	+	0.146607i	−0.591900	−	0.806011i	$-0.701622\pi$
$313$	−90.0605	+	45.8881i	−0.287733	+	0.146607i	0.304167	+	0.952619i	$0.401622\pi$
$314$		0			0
$315$	−0.211854	+	59.6451i	−0.000672553	+	0.189349i
$316$		0			0
$317$	346.283	−	54.8458i	1.09237	−	0.173015i	0.415848	−	0.909434i	$-0.363485\pi$
$317$	346.283	−	54.8458i	1.09237	−	0.173015i	0.676526	+	0.736419i	$0.263485\pi$
$318$		0			0
$319$	94.4060	−	129.939i	0.295944	−	0.407332i
$320$		0			0
$321$	−221.947	+	161.254i	−0.691424	+	0.502349i
$322$		0			0
$323$	358.873	−	704.328i	1.11106	−	2.18058i
$324$		0			0
$325$	−517.870	−	268.519i	−1.59345	−	0.826212i
$326$		0			0
$327$	12.9531	+	6.59994i	0.0396120	+	0.0201833i
$328$		0			0
$329$	−8.62838	−	11.8759i	−0.0262261	−	0.0360971i
$330$		0			0
$331$	−228.642	−	166.118i	−0.690763	−	0.501868i	0.186148	−	0.982522i	$-0.440400\pi$
$331$	−228.642	−	166.118i	−0.690763	−	0.501868i	−0.876911	+	0.480653i	$0.840400\pi$
$332$		0			0
$333$	−19.6893	−	124.313i	−0.0591270	−	0.373313i
$334$		0			0
$335$	−73.6174	+	223.862i	−0.219753	+	0.668246i
$336$		0			0
$337$	−81.6745	−	160.295i	−0.242358	−	0.475654i	0.737501	−	0.675346i	$-0.236006\pi$
$337$	−81.6745	−	160.295i	−0.242358	−	0.475654i	−0.979859	+	0.199692i	$0.936006\pi$
$338$		0			0
$339$	280.793	−	91.2351i	0.828297	−	0.269130i
$340$		0			0
$341$	−84.0678	+	258.734i	−0.246533	+	0.758751i
$342$		0			0
$343$	−262.465	−	262.465i	−0.765206	−	0.765206i
$344$		0			0
$345$	−180.499	−	357.381i	−0.523184	−	1.03589i
$346$		0			0
$347$	−56.0117	+	353.644i	−0.161417	+	1.01915i	0.765379	+	0.643580i	$0.222552\pi$
$347$	−56.0117	+	353.644i	−0.161417	+	1.01915i	−0.926796	+	0.375566i	$0.877448\pi$
$348$		0			0
$349$			196.202i			0.562185i	0.959681	+	0.281092i	$0.0906967\pi$
$349$			196.202i			0.562185i	−0.959681	+	0.281092i	$0.909303\pi$
$350$		0			0
$351$	−678.613			−1.93337
$352$		0			0
$353$	−39.7960	−	6.30307i	−0.112737	−	0.0178557i	0.0998112	−	0.995006i	$-0.468176\pi$
$353$	−39.7960	−	6.30307i	−0.112737	−	0.0178557i	−0.212548	+	0.977151i	$0.568176\pi$
$354$		0			0
$355$	46.1523	+	298.247i	0.130007	+	0.840131i
$356$		0			0
$357$	284.779	−	284.779i	0.797701	−	0.797701i
$358$		0			0
$359$	−447.739	−	145.479i	−1.24718	−	0.405234i	−0.390272	−	0.920699i	$-0.627619\pi$
$359$	−447.739	−	145.479i	−1.24718	−	0.405234i	−0.856911	+	0.515465i	$0.827619\pi$
$360$		0			0
$361$	−197.281	−	607.168i	−0.546484	−	1.68191i
$362$		0			0
$363$	186.060	−	94.8021i	0.512561	−	0.261163i
$364$		0			0
$365$	247.549	+	343.279i	0.678216	+	0.940491i
$366$		0			0
$367$	−102.728	+	16.2705i	−0.279912	+	0.0443337i	−0.294812	−	0.955555i	$-0.595257\pi$
$367$	−102.728	+	16.2705i	−0.279912	+	0.0443337i	0.0148999	+	0.999889i	$0.495257\pi$
$368$		0			0
$369$	−19.9715	+	27.4884i	−0.0541232	+	0.0744942i
$370$		0			0
$371$	−115.583	+	83.9762i	−0.311545	+	0.226351i
$372$		0			0
$373$	70.9951	−	139.336i	0.190335	−	0.373554i	−0.776042	−	0.630681i	$-0.782776\pi$
$373$	70.9951	−	139.336i	0.190335	−	0.373554i	0.966378	+	0.257127i	$0.0827757\pi$
$374$		0			0
$375$	331.538	+	3.53290i	0.884100	+	0.00942107i
$376$		0			0
$377$	−513.590	−	261.687i	−1.36231	−	0.694130i
$378$		0			0
$379$	4.17993	+	5.75319i	0.0110289	+	0.0151799i	0.814496	−	0.580169i	$-0.197014\pi$
$379$	4.17993	+	5.75319i	0.0110289	+	0.0151799i	−0.803467	+	0.595349i	$0.797014\pi$
$380$		0			0
$381$	477.312	+	346.787i	1.25279	+	0.910203i
$382$		0			0
$383$	65.3879	+	412.843i	0.170726	+	1.07792i	0.913041	+	0.407868i	$0.133728\pi$
$383$	65.3879	+	412.843i	0.170726	+	1.07792i	−0.742315	+	0.670051i	$0.766272\pi$
$384$		0			0
$385$	160.114	−	115.463i	0.415881	−	0.299904i
$386$		0			0
$387$	26.1675	+	51.3567i	0.0676163	+	0.132705i
$388$		0			0
$389$	293.251	−	95.2829i	0.753858	−	0.244943i	0.0932175	−	0.995646i	$-0.470285\pi$
$389$	293.251	−	95.2829i	0.753858	−	0.244943i	0.660640	+	0.750702i	$0.270285\pi$
$390$		0			0
$391$	233.267	−	717.923i	0.596592	−	1.83612i
$392$		0			0
$393$	−233.532	−	233.532i	−0.594229	−	0.594229i
$394$		0			0
$395$	−124.341	+	19.2411i	−0.314786	+	0.0487117i
$396$		0			0
$397$	−80.9873	+	511.334i	−0.203998	+	1.28799i	0.646864	+	0.762606i	$0.276080\pi$
$397$	−80.9873	+	511.334i	−0.203998	+	1.28799i	−0.850862	+	0.525389i	$0.823920\pi$
$398$		0			0
$399$		−	509.184i		−	1.27615i
$400$		0			0
$401$	17.7636			0.0442982			0.0221491	−	0.999755i	$-0.492949\pi$
$401$	17.7636			0.0442982			0.0221491	+	0.999755i	$0.492949\pi$
$402$		0			0
$403$	964.321	+	152.733i	2.39286	+	0.378991i
$404$		0			0
$405$	265.375	−	134.030i	0.655247	−	0.330939i
$406$		0			0
$407$	−294.552	+	294.552i	−0.723714	+	0.723714i
$408$		0			0
$409$	−302.262	−	98.2109i	−0.739027	−	0.240124i	−0.0847739	−	0.996400i	$-0.527017\pi$
$409$	−302.262	−	98.2109i	−0.739027	−	0.240124i	−0.654253	+	0.756276i	$0.727017\pi$
$410$		0			0
$411$	31.3003	+	96.3324i	0.0761565	+	0.234386i
$412$		0			0
$413$	−238.698	+	121.623i	−0.577962	+	0.294486i
$414$		0			0
$415$	−286.909	−	94.3504i	−0.691348	−	0.227350i
$416$		0			0
$417$	522.101	−	82.6926i	1.25204	−	0.198304i
$418$		0			0
$419$	−354.384	+	487.768i	−0.845786	+	1.16413i	0.138989	+	0.990294i	$0.455615\pi$
$419$	−354.384	+	487.768i	−0.845786	+	1.16413i	−0.984775	+	0.173831i	$0.944385\pi$
$420$		0			0
$421$	560.379	−	407.139i	1.33107	−	0.967077i	0.331345	−	0.943510i	$-0.392498\pi$
$421$	560.379	−	407.139i	1.33107	−	0.967077i	0.999722	−	0.0235668i	$-0.00750225\pi$
$422$		0			0
$423$	2.15603	−	4.23145i	0.00509700	−	0.0100034i
$424$		0			0
$425$	438.873	+	445.153i	1.03264	+	1.04742i
$426$		0			0
$427$	97.2880	+	49.5707i	0.227841	+	0.116091i
$428$		0			0
$429$	236.528	+	325.553i	0.551348	+	0.758865i
$430$		0			0
$431$	614.616	+	446.545i	1.42602	+	1.03607i	0.990740	+	0.135773i	$0.0433519\pi$
$431$	614.616	+	446.545i	1.42602	+	1.03607i	0.435284	+	0.900293i	$0.356648\pi$
$432$		0			0
$433$	13.3387	+	84.2171i	0.0308053	+	0.194497i	0.998292	−	0.0584260i	$-0.0186082\pi$
$433$	13.3387	+	84.2171i	0.0308053	+	0.194497i	−0.967486	+	0.252923i	$0.918608\pi$
$434$		0			0
$435$	327.616	+	1.16366i	0.753139	+	0.00267509i
$436$		0			0
$437$	−433.281	−	850.362i	−0.991490	−	1.94591i
$438$		0			0
$439$	22.4719	−	7.30157i	0.0511889	−	0.0166323i	−0.283311	−	0.959028i	$-0.591433\pi$
$439$	22.4719	−	7.30157i	0.0511889	−	0.0166323i	0.334500	+	0.942396i	$0.391433\pi$
$440$		0			0
$441$	7.36182	−	22.6573i	0.0166935	−	0.0513772i
$442$		0			0
$443$	−464.801	−	464.801i	−1.04921	−	1.04921i	−0.998725	−	0.0504868i	$-0.983923\pi$
$443$	−464.801	−	464.801i	−1.04921	−	1.04921i	−0.0504868	−	0.998725i	$-0.516077\pi$
$444$		0			0
$445$	−15.2060	+	93.8484i	−0.0341708	+	0.210895i
$446$		0			0
$447$	23.5105	−	148.439i	0.0525961	−	0.332079i
$448$		0			0
$449$			159.668i			0.355608i	0.984066	+	0.177804i	$0.0568993\pi$
$449$			159.668i			0.355608i	−0.984066	+	0.177804i	$0.943101\pi$
$450$		0			0
$451$	112.453			0.249341
$452$		0			0
$453$	−489.328	−	77.5019i	−1.08019	−	0.171086i
$454$		0			0
$455$	−499.169	−	502.727i	−1.09707	−	1.10490i
$456$		0			0
$457$	−72.0602	+	72.0602i	−0.157681	+	0.157681i	−0.781538	−	0.623857i	$-0.785565\pi$
$457$	−72.0602	+	72.0602i	−0.157681	+	0.157681i	0.623857	+	0.781538i	$0.285565\pi$
$458$		0			0
$459$	691.615	+	224.719i	1.50679	+	0.489584i
$460$		0			0
$461$	−194.362	−	598.184i	−0.421609	−	1.29758i	−0.906204	−	0.422840i	$-0.861033\pi$
$461$	−194.362	−	598.184i	−0.421609	−	1.29758i	0.484595	−	0.874738i	$-0.338967\pi$
$462$		0			0
$463$	−365.100	+	186.028i	−0.788553	+	0.401788i	−0.801399	−	0.598130i	$-0.795911\pi$
$463$	−365.100	+	186.028i	−0.788553	+	0.401788i	0.0128466	+	0.999917i	$0.495911\pi$
$464$		0			0
$465$	−528.370	+	169.605i	−1.13628	+	0.364743i
$466$		0			0
$467$	−130.293	+	20.6364i	−0.279000	+	0.0441892i	−0.294366	−	0.955693i	$-0.595109\pi$
$467$	−130.293	+	20.6364i	−0.279000	+	0.0441892i	0.0153664	+	0.999882i	$0.495109\pi$
$468$		0			0
$469$	−168.222	+	231.538i	−0.358682	+	0.493684i
$470$		0			0
$471$	440.177	−	319.807i	0.934558	−	0.678996i
$472$		0			0
$473$	86.6047	−	169.971i	0.183097	−	0.359347i
$474$		0			0
$475$	790.318	+	5.61436i	1.66383	+	0.0118197i
$476$		0			0
$477$	−41.1828	−	20.9837i	−0.0863371	−	0.0439910i
$478$		0			0
$479$	−220.857	−	303.983i	−0.461079	−	0.634620i	0.513653	−	0.857998i	$-0.328292\pi$
$479$	−220.857	−	303.983i	−0.461079	−	0.634620i	−0.974732	+	0.223378i	$0.928292\pi$
$480$		0			0
$481$	1209.45	+	878.718i	2.51445	+	1.82686i
$482$		0			0
$483$	−76.0650	−	480.256i	−0.157484	−	0.994318i
$484$		0			0
$485$	−374.835	−	274.373i	−0.772856	−	0.565717i
$486$		0			0
$487$	28.1416	+	55.2310i	0.0577857	+	0.113411i	0.918093	−	0.396365i	$-0.129728\pi$
$487$	28.1416	+	55.2310i	0.0577857	+	0.113411i	−0.860307	+	0.509776i	$0.829728\pi$
$488$		0			0
$489$	−341.508	+	110.963i	−0.698380	+	0.226917i
$490$		0			0
$491$	161.487	−	497.005i	0.328893	−	1.01223i	−0.640759	−	0.767742i	$-0.721380\pi$
$491$	161.487	−	497.005i	0.328893	−	1.01223i	0.969652	−	0.244487i	$-0.0786197\pi$
$492$		0			0
$493$	436.773	+	436.773i	0.885950	+	0.885950i
$494$		0			0
$495$	56.7996	+	29.1954i	0.114747	+	0.0589807i
$496$		0			0
$497$	−57.3365	+	362.008i	−0.115365	+	0.728387i
$498$		0			0
$499$		−	106.338i		−	0.213103i	−0.994307	−	0.106551i	$-0.966019\pi$
$499$		−	106.338i		−	0.213103i	0.994307	−	0.106551i	$-0.0339809\pi$
$500$		0			0
$501$	42.0232			0.0838787
$502$		0			0
$503$	122.892	+	19.4641i	0.244318	+	0.0386961i	0.277392	−	0.960757i	$-0.410530\pi$
$503$	122.892	+	19.4641i	0.244318	+	0.0386961i	−0.0330746	+	0.999453i	$0.510530\pi$
$504$		0			0
$505$	137.598	−	267.696i	0.272470	−	0.530090i
$506$		0			0
$507$	704.213	−	704.213i	1.38898	−	1.38898i
$508$		0			0
$509$	397.384	+	129.118i	0.780716	+	0.253670i	0.672146	−	0.740419i	$-0.265373\pi$
$509$	397.384	+	129.118i	0.780716	+	0.253670i	0.108570	+	0.994089i	$0.465373\pi$
$510$		0			0
$511$	158.833	+	488.837i	0.310828	+	0.956629i
$512$		0			0
$513$	819.200	−	417.403i	1.59688	−	0.813652i
$514$		0			0
$515$	−162.674	+	222.237i	−0.315872	+	0.431529i
$516$		0			0
$517$	−15.5241	+	2.45878i	−0.0300273	+	0.00475586i
$518$		0			0
$519$	−427.558	+	588.483i	−0.823811	+	1.13388i
$520$		0			0
$521$	−617.533	+	448.664i	−1.18528	+	0.861159i	−0.992758	−	0.120133i	$-0.961668\pi$
$521$	−617.533	+	448.664i	−1.18528	+	0.861159i	−0.192525	+	0.981292i	$0.561668\pi$
$522$		0			0
$523$	103.022	−	202.192i	0.196983	−	0.386601i	−0.771295	−	0.636478i	$-0.780390\pi$
$523$	103.022	−	202.192i	0.196983	−	0.386601i	0.968277	+	0.249878i	$0.0803904\pi$
$524$		0			0
$525$	382.062	+	127.147i	0.727737	+	0.242185i
$526$		0			0
$527$	−932.220	−	474.990i	−1.76892	−	0.901309i
$528$		0			0
$529$	−224.759	−	309.354i	−0.424875	−	0.584790i
$530$		0			0
$531$	−70.1170	−	50.9430i	−0.132047	−	0.0959379i
$532$		0			0
$533$	−63.1331	−	398.606i	−0.118449	−	0.747854i
$534$		0			0
$535$	−158.059	−	492.401i	−0.295438	−	0.920376i
$536$		0			0
$537$	−106.093	−	208.219i	−0.197566	−	0.387744i
$538$		0			0
$539$	−74.9873	+	24.3649i	−0.139123	+	0.0452038i
$540$		0			0
$541$	−74.4947	+	229.271i	−0.137698	+	0.423791i	−0.996000	−	0.0893539i	$-0.971520\pi$
$541$	−74.4947	+	229.271i	−0.137698	+	0.423791i	0.858302	+	0.513145i	$0.171520\pi$
$542$		0			0
$543$	−406.663	−	406.663i	−0.748920	−	0.748920i
$544$		0			0
$545$	−19.4464	+	19.3087i	−0.0356814	+	0.0354288i
$546$		0			0
$547$	122.821	−	775.461i	0.224536	−	1.41766i	−0.575546	−	0.817770i	$-0.695210\pi$
$547$	122.821	−	775.461i	0.224536	−	1.41766i	0.800081	−	0.599892i	$-0.204790\pi$
$548$		0			0
$549$			35.3245i			0.0643434i
$550$		0			0
$551$	780.949			1.41733
$552$		0			0
$553$	−150.923	−	23.9039i	−0.272917	−	0.0432258i
$554$		0			0
$555$	−838.755	−	135.901i	−1.51127	−	0.244867i
$556$		0			0
$557$	−372.519	+	372.519i	−0.668795	+	0.668795i	−0.957437	−	0.288642i	$-0.906796\pi$
$557$	−372.519	+	372.519i	−0.668795	+	0.668795i	0.288642	+	0.957437i	$0.406796\pi$
$558$		0			0
$559$	−651.112	−	211.559i	−1.16478	−	0.378460i
$560$		0			0
$561$	−133.255	−	410.116i	−0.237531	−	0.731044i
$562$		0			0
$563$	−306.429	+	156.133i	−0.544278	+	0.277324i	−0.704436	−	0.709768i	$-0.748800\pi$
$563$	−306.429	+	156.133i	−0.544278	+	0.277324i	0.160157	+	0.987091i	$0.448800\pi$
$564$		0			0
$565$	−1.97680	+	556.544i	−0.00349876	+	0.985034i
$566$		0			0
$567$	356.616	−	56.4825i	0.628953	−	0.0996163i
$568$		0			0
$569$	−68.9614	+	94.9173i	−0.121198	+	0.166814i	−0.865305	−	0.501246i	$-0.832875\pi$
$569$	−68.9614	+	94.9173i	−0.121198	+	0.166814i	0.744107	+	0.668060i	$0.232875\pi$
$570$		0			0
$571$	548.667	−	398.630i	0.960888	−	0.698126i	0.00753145	−	0.999972i	$-0.497603\pi$
$571$	548.667	−	398.630i	0.960888	−	0.698126i	0.953357	+	0.301845i	$0.0976026\pi$
$572$		0			0
$573$	49.0382	−	96.2428i	0.0855814	−	0.167963i
$574$		0			0
$575$	746.256	−	112.767i	1.29784	−	0.196117i
$576$		0			0
$577$	−273.507	−	139.359i	−0.474015	−	0.241523i	0.200627	−	0.979668i	$-0.435702\pi$
$577$	−273.507	−	139.359i	−0.474015	−	0.241523i	−0.674642	+	0.738145i	$0.735702\pi$
$578$		0			0
$579$	471.397	+	648.823i	0.814158	+	1.12059i
$580$		0			0
$581$	−296.746	−	215.599i	−0.510750	−	0.371082i
$582$		0			0
$583$	23.9302	+	151.089i	0.0410467	+	0.259158i
$584$		0			0
$585$	71.5994	−	217.726i	0.122392	−	0.372181i
$586$		0			0
$587$	−268.579	−	527.117i	−0.457546	−	0.897984i	−0.998382	−	0.0568564i	$-0.981892\pi$
$587$	−268.579	−	527.117i	−0.457546	−	0.897984i	0.540837	−	0.841128i	$-0.318108\pi$
$588$		0			0
$589$	−1258.04	+	408.763i	−2.13590	+	0.693994i
$590$		0			0
$591$	−277.155	+	852.995i	−0.468959	+	1.44331i
$592$		0			0
$593$	32.0160	+	32.0160i	0.0539899	+	0.0539899i	0.733586	−	0.679596i	$-0.237845\pi$
$593$	32.0160	+	32.0160i	0.0539899	+	0.0539899i	−0.679596	+	0.733586i	$0.737845\pi$
$594$		0			0
$595$	342.257	+	677.656i	0.575222	+	1.13892i
$596$		0			0
$597$	23.7838	−	150.165i	0.0398388	−	0.251533i
$598$		0			0
$599$			551.494i			0.920691i	0.887740	+	0.460345i	$0.152274\pi$
$599$			551.494i			0.920691i	−0.887740	+	0.460345i	$0.847726\pi$
$600$		0			0
$601$	584.341			0.972281			0.486140	−	0.873881i	$-0.338404\pi$
$601$	584.341			0.972281			0.486140	+	0.873881i	$0.338404\pi$
$602$		0			0
$603$	−91.4495	−	14.4842i	−0.151658	−	0.0240202i
$604$		0			0
$605$	60.1968	+	389.005i	0.0994988	+	0.642984i
$606$		0			0
$607$	291.296	−	291.296i	0.479895	−	0.479895i	−0.425203	−	0.905098i	$-0.639797\pi$
$607$	291.296	−	291.296i	0.479895	−	0.479895i	0.905098	+	0.425203i	$0.139797\pi$
$608$		0			0
$609$	378.406	+	122.952i	0.621357	+	0.201891i
$610$		0			0
$611$	17.4311	+	53.6473i	0.0285287	+	0.0878024i
$612$		0			0
$613$	114.523	−	58.3525i	0.186824	−	0.0951917i	−0.358077	−	0.933692i	$-0.616567\pi$
$613$	114.523	−	58.3525i	0.186824	−	0.0951917i	0.544901	+	0.838501i	$0.316567\pi$
$614$		0			0
$615$	134.166	+	186.050i	0.218157	+	0.302521i
$616$		0			0
$617$	1131.72	−	179.247i	1.83424	−	0.290514i	0.859048	−	0.511895i	$-0.171056\pi$
$617$	1131.72	−	179.247i	1.83424	−	0.290514i	0.975188	+	0.221380i	$0.0710562\pi$
$618$		0			0
$619$	432.649	−	595.490i	0.698948	−	0.962019i	−0.301017	−	0.953619i	$-0.597326\pi$
$619$	432.649	−	595.490i	0.698948	−	0.962019i	0.999965	−	0.00840040i	$-0.00267396\pi$
$620$		0			0
$621$	710.304	−	516.066i	1.14381	−	0.831024i
$622$		0			0
$623$	−52.4186	+	102.877i	−0.0841390	+	0.165132i
$624$		0			0
$625$	−201.561	+	591.606i	−0.322498	+	0.946570i
$626$		0			0
$627$	−485.772	−	247.513i	−0.774756	−	0.394758i
$628$		0			0
$629$	−941.640	−	1296.06i	−1.49704	−	2.06050i
$630$		0			0
$631$	27.3799	+	19.8927i	0.0433913	+	0.0315256i	0.609270	−	0.792963i	$-0.291463\pi$
$631$	27.3799	+	19.8927i	0.0433913	+	0.0315256i	−0.565878	+	0.824489i	$0.691463\pi$
$632$		0			0
$633$	−111.114	−	701.549i	−0.175536	−	1.10829i
$634$		0			0
$635$	−902.073	+	650.511i	−1.42059	+	1.02443i
$636$		0			0
$637$	128.464	+	252.126i	0.201671	+	0.395801i
$638$		0			0
$639$	−112.772	+	36.6420i	−0.176483	+	0.0573427i
$640$		0			0
$641$	149.035	−	458.683i	0.232504	−	0.715573i	−0.764939	−	0.644103i	$-0.777231\pi$
$641$	149.035	−	458.683i	0.232504	−	0.715573i	0.997443	−	0.0714705i	$-0.0227692\pi$
$642$		0			0
$643$	568.656	+	568.656i	0.884380	+	0.884380i	0.993976	−	0.109597i	$-0.0349559\pi$
$643$	568.656	+	568.656i	0.884380	+	0.884380i	−0.109597	+	0.993976i	$0.534956\pi$
$644$		0			0
$645$	384.541	−	59.5059i	0.596187	−	0.0922573i
$646$		0			0
$647$	−100.194	+	632.597i	−0.154859	+	0.977739i	0.780787	+	0.624798i	$0.214819\pi$
$647$	−100.194	+	632.597i	−0.154859	+	0.977739i	−0.935645	+	0.352942i	$0.885181\pi$
$648$		0			0
$649$			286.843i			0.441977i
$650$		0			0
$651$	−673.935			−1.03523
$652$		0			0
$653$	201.766	+	31.9565i	0.308983	+	0.0489380i	0.309000	−	0.951062i	$-0.400006\pi$
$653$	201.766	+	31.9565i	0.308983	+	0.0489380i	−1.76546e−5		1.00000i	$0.500006\pi$
$654$		0			0
$655$	555.708	−	280.666i	0.848410	−	0.428497i
$656$		0			0
$657$	−117.582	+	117.582i	−0.178968	+	0.178968i
$658$		0			0
$659$	1240.28	+	402.990i	1.88206	+	0.611518i	0.985784	+	0.168016i	$0.0537360\pi$
$659$	1240.28	+	402.990i	1.88206	+	0.611518i	0.896274	+	0.443502i	$0.146264\pi$
$660$		0			0
$661$	−236.020	−	726.394i	−0.357065	−	1.09893i	−0.954803	−	0.297240i	$-0.903934\pi$
$661$	−236.020	−	726.394i	−0.357065	−	1.09893i	0.597738	−	0.801691i	$-0.296066\pi$
$662$		0			0
$663$	−1378.91	+	702.589i	−2.07980	+	1.05971i
$664$		0			0
$665$	911.800	+	299.846i	1.37113	+	0.450897i
$666$		0			0
$667$	736.580	−	116.663i	1.10432	−	0.174907i
$668$		0			0
$669$	−214.221	+	294.850i	−0.320211	+	0.440733i
$670$		0			0
$671$	94.5829	−	68.7185i	0.140958	−	0.102412i
$672$		0			0
$673$	43.5522	−	85.4761i	0.0647136	−	0.127008i	−0.856384	−	0.516340i	$-0.827294\pi$
$673$	43.5522	−	85.4761i	0.0647136	−	0.127008i	0.921097	+	0.389332i	$0.127294\pi$
$674$		0			0
$675$	108.635	+	718.909i	0.160940	+	1.06505i
$676$		0			0
$677$	637.601	+	324.874i	0.941804	+	0.479873i	0.856308	−	0.516465i	$-0.172752\pi$
$677$	637.601	+	324.874i	0.941804	+	0.479873i	0.0854961	+	0.996339i	$0.472752\pi$
$678$		0			0
$679$	−331.597	−	456.404i	−0.488361	−	0.672171i
$680$		0			0
$681$	−497.056	−	361.132i	−0.729891	−	0.530297i
$682$		0			0
$683$	−28.9430	−	182.739i	−0.0423763	−	0.267553i	0.957399	−	0.288770i	$-0.0932461\pi$
$683$	−28.9430	−	182.739i	−0.0423763	−	0.267553i	−0.999775	+	0.0212163i	$0.993246\pi$
$684$		0			0
$685$	−190.935	−	0.678186i	−0.278738	−	0.000990053i
$686$		0			0
$687$	112.644	+	221.076i	0.163965	+	0.321799i
$688$		0			0
$689$	522.125	−	169.649i	0.757801	−	0.246225i
$690$		0			0
$691$	−223.255	+	687.107i	−0.323089	+	0.994366i	0.649207	+	0.760612i	$0.275101\pi$
$691$	−223.255	+	687.107i	−0.323089	+	0.994366i	−0.972296	+	0.233754i	$0.924899\pi$
$692$		0			0
$693$	54.8433	+	54.8433i	0.0791389	+	0.0791389i
$694$		0			0
$695$	−159.374	+	983.625i	−0.229316	+	1.41529i
$696$		0			0
$697$	−67.6539	+	427.150i	−0.0970644	+	0.612840i
$698$		0			0
$699$			521.582i			0.746183i
$700$		0			0
$701$	−78.7859			−0.112391			−0.0561954	−	0.998420i	$-0.517897\pi$
$701$	−78.7859			−0.112391			−0.0561954	+	0.998420i	$0.517897\pi$
$702$		0			0
$703$	−2000.50	−	316.847i	−2.84566	−	0.450708i
$704$		0			0
$705$	−22.5897	−	22.7507i	−0.0320421	−	0.0322705i
$706$		0			0
$707$	258.476	−	258.476i	0.365595	−	0.365595i
$708$		0			0
$709$	−919.344	−	298.713i	−1.29668	−	0.421316i	−0.422253	−	0.906478i	$-0.638761\pi$
$709$	−919.344	−	298.713i	−1.29668	−	0.421316i	−0.874424	+	0.485162i	$0.838761\pi$
$710$		0			0
$711$	−15.2762	−	47.0154i	−0.0214856	−	0.0661257i
$712$		0			0
$713$	−1125.50	+	573.473i	−1.57855	+	0.804310i
$714$		0			0
$715$	−722.257	+	231.842i	−1.01015	+	0.324255i
$716$		0			0
$717$	−521.335	+	82.5713i	−0.727105	+	0.115162i
$718$		0			0
$719$	−140.139	+	192.884i	−0.194908	+	0.268268i	−0.895274	−	0.445516i	$-0.853020\pi$
$719$	−140.139	+	192.884i	−0.194908	+	0.268268i	0.700366	+	0.713784i	$0.253020\pi$
$720$		0			0
$721$	−270.599	+	196.602i	−0.375311	+	0.272680i
$722$		0			0
$723$	−358.292	+	703.188i	−0.495563	+	0.972597i
$724$		0			0
$725$	−195.009	+	585.978i	−0.268978	+	0.808246i
$726$		0			0
$727$	630.875	+	321.447i	0.867779	+	0.442156i	0.830414	−	0.557146i	$-0.188104\pi$
$727$	630.875	+	321.447i	0.867779	+	0.442156i	0.0373646	+	0.999302i	$0.488104\pi$
$728$		0			0
$729$	476.739	+	656.175i	0.653963	+	0.900102i
$730$		0			0
$731$	593.530	+	431.225i	0.811942	+	0.589911i
$732$		0			0
$733$	−87.7744	−	554.186i	−0.119747	−	0.756052i	−0.972356	−	0.233503i	$-0.924981\pi$
$733$	−87.7744	−	554.186i	−0.119747	−	0.756052i	0.852609	−	0.522549i	$-0.175019\pi$
$734$		0			0
$735$	−129.778	−	94.9952i	−0.176568	−	0.129245i
$736$		0			0
$737$	139.119	+	273.037i	0.188764	+	0.370471i
$738$		0			0
$739$	−1097.44	+	356.580i	−1.48504	+	0.482517i	−0.935613	−	0.353028i	$-0.885152\pi$
$739$	−1097.44	+	356.580i	−1.48504	+	0.482517i	−0.549422	+	0.835545i	$0.685152\pi$
$740$		0			0
$741$	−604.628	+	1860.85i	−0.815962	+	2.51127i
$742$		0			0
$743$	−812.004	−	812.004i	−1.09287	−	1.09287i	−0.995221	−	0.0976508i	$-0.968867\pi$
$743$	−812.004	−	812.004i	−1.09287	−	1.09287i	−0.0976508	−	0.995221i	$-0.531133\pi$
$744$		0			0
$745$	251.966	+	129.513i	0.338210	+	0.173843i
$746$		0			0
$747$	18.5634	−	117.205i	0.0248506	−	0.156900i
$748$		0			0
$749$		−	628.057i		−	0.838528i
$750$		0			0
$751$	87.3907			0.116366			0.0581829	−	0.998306i	$-0.481469\pi$
$751$	87.3907			0.116366			0.0581829	+	0.998306i	$0.481469\pi$
$752$		0			0
$753$	−786.277	−	124.534i	−1.04419	−	0.165384i
$754$		0			0
$755$	426.937	−	830.604i	0.565479	−	1.10014i
$756$		0			0
$757$	−47.4566	+	47.4566i	−0.0626903	+	0.0626903i	−0.737757	−	0.675067i	$-0.764115\pi$
$757$	−47.4566	+	47.4566i	−0.0626903	+	0.0626903i	0.675067	+	0.737757i	$0.264115\pi$
$758$		0			0
$759$	−495.148	−	160.883i	−0.652369	−	0.211968i
$760$		0			0
$761$	−419.443	−	1290.91i	−0.551173	−	1.69634i	−0.705842	−	0.708370i	$-0.749431\pi$
$761$	−419.443	−	1290.91i	−0.551173	−	1.69634i	0.154669	−	0.987966i	$-0.450569\pi$
$762$		0			0
$763$	−29.6539	+	15.1094i	−0.0388649	+	0.0198026i
$764$		0			0
$765$	−145.070	+	198.188i	−0.189634	+	0.259069i
$766$		0			0
$767$	1016.76	−	161.039i	1.32563	−	0.209960i
$768$		0			0
$769$	−594.851	+	818.742i	−0.773538	+	1.06468i	0.222428	+	0.974949i	$0.428602\pi$
$769$	−594.851	+	818.742i	−0.773538	+	1.06468i	−0.995966	+	0.0897344i	$0.971398\pi$
$770$		0			0
$771$	139.347	−	101.241i	0.180735	−	0.131312i
$772$		0			0
$773$	−515.595	+	1011.91i	−0.667005	+	1.30907i	0.271044	+	0.962567i	$0.412631\pi$
$773$	−515.595	+	1011.91i	−0.667005	+	1.30907i	−0.938049	+	0.346504i	$0.887369\pi$
$774$		0			0
$775$	7.43094	−	1046.03i	0.00958830	−	1.34972i
$776$		0			0
$777$	−919.450	−	468.483i	−1.18333	−	0.602938i
$778$		0			0
$779$	321.388	+	442.353i	0.412565	+	0.567847i
$780$		0			0
$781$	317.492	+	230.672i	0.406520	+	0.295354i
$782$		0			0
$783$	112.388	+	709.588i	0.143535	+	0.906242i
$784$		0			0
$785$	313.471	+	976.554i	0.399327	+	1.24402i
$786$		0			0
$787$	−488.546	−	958.825i	−0.620770	−	1.21833i	−0.960624	−	0.277852i	$-0.910378\pi$
$787$	−488.546	−	958.825i	−0.620770	−	1.21833i	0.339854	−	0.940478i	$-0.389622\pi$
$788$		0			0
$789$	168.229	−	54.6608i	0.213218	−	0.0692786i
$790$		0			0
$791$	−208.867	+	642.826i	−0.264054	+	0.812675i
$792$		0			0
$793$	−296.684	−	296.684i	−0.374129	−	0.374129i
$794$		0			0
$795$	−221.423	+	219.855i	−0.278519	+	0.276548i
$796$		0			0
$797$	86.7153	−	547.499i	0.108802	−	0.686950i	−0.871641	−	0.490145i	$-0.836944\pi$
$797$	86.7153	−	547.499i	0.108802	−	0.686950i	0.980443	−	0.196804i	$-0.0630563\pi$
$798$		0			0
$799$		−	60.4473i		−	0.0756537i
$800$		0			0
$801$	−37.3540			−0.0466341
$802$		0			0
$803$	543.569	+	86.0928i	0.676922	+	0.107214i
$804$		0			0
$805$	904.790	+	146.601i	1.12396	+	0.182113i
$806$		0			0
$807$	132.488	−	132.488i	0.164173	−	0.164173i
$808$		0			0
$809$	−1085.80	−	352.798i	−1.34215	−	0.436091i	−0.452106	−	0.891964i	$-0.649327\pi$
$809$	−1085.80	−	352.798i	−1.34215	−	0.436091i	−0.890045	+	0.455873i	$0.849327\pi$
$810$		0			0
$811$	210.237	+	647.042i	0.259231	+	0.797832i	0.992966	+	0.118396i	$0.0377753\pi$
$811$	210.237	+	647.042i	0.259231	+	0.797832i	−0.733735	+	0.679436i	$0.762225\pi$
$812$		0			0
$813$	1027.34	−	523.457i	1.26364	−	0.643858i
$814$		0			0
$815$	2.40423	−	676.884i	0.00294998	−	0.830532i
$816$		0			0
$817$	916.128	−	145.100i	1.12133	−	0.177601i
$818$		0			0
$819$	163.611	−	225.191i	0.199769	−	0.274958i
$820$		0			0
$821$	788.327	−	572.753i	0.960204	−	0.697629i	0.00700562	−	0.999975i	$-0.497770\pi$
$821$	788.327	−	572.753i	0.960204	−	0.697629i	0.953198	+	0.302347i	$0.0977700\pi$
$822$		0			0
$823$	−62.4185	+	122.503i	−0.0758426	+	0.148850i	−0.925814	−	0.377979i	$-0.876619\pi$
$823$	−62.4185	+	122.503i	−0.0758426	+	0.148850i	0.849971	+	0.526829i	$0.176619\pi$
$824$		0			0
$825$	307.020	−	302.689i	0.372146	−	0.366896i
$826$		0			0
$827$	−1425.36	−	726.259i	−1.72354	−	0.878185i	−0.977115	−	0.212710i	$-0.931771\pi$
$827$	−1425.36	−	726.259i	−1.72354	−	0.878185i	−0.746420	−	0.665475i	$-0.768229\pi$
$828$		0			0
$829$	884.218	+	1217.02i	1.06661	+	1.46806i	0.873464	+	0.486889i	$0.161868\pi$
$829$	884.218	+	1217.02i	1.06661	+	1.46806i	0.193143	+	0.981171i	$0.438132\pi$
$830$		0			0
$831$	134.652	+	97.8305i	0.162036	+	0.117726i
$832$		0			0
$833$	−47.4356	−	299.496i	−0.0569455	−	0.359540i
$834$		0			0
$835$	−24.7465	+	75.2513i	−0.0296365	+	0.0901213i
$836$		0			0
$837$	−552.458	−	1084.26i	−0.660045	−	1.29541i
$838$		0			0
$839$	1420.30	−	461.482i	1.69284	−	0.550038i	0.705510	−	0.708700i	$-0.250718\pi$
$839$	1420.30	−	461.482i	1.69284	−	0.550038i	0.987333	+	0.158662i	$0.0507180\pi$
$840$		0			0
$841$	71.3093	−	219.467i	0.0847910	−	0.260960i
$842$		0			0
$843$	378.308	+	378.308i	0.448764	+	0.448764i
$844$		0			0
$845$	846.345	+	1675.73i	1.00159	+	1.98312i
$846$		0			0
$847$	−74.7844	+	472.170i	−0.0882933	+	0.557462i
$848$		0			0
$849$			969.886i			1.14239i
$850$		0			0
$851$	−1934.17			−2.27282
$852$		0			0
$853$	454.267	+	71.9488i	0.532552	+	0.0843479i	0.416918	−	0.908944i	$-0.363110\pi$
$853$	454.267	+	71.9488i	0.532552	+	0.0843479i	0.115634	+	0.993292i	$0.463110\pi$
$854$		0			0
$855$	47.4870	+	306.872i	0.0555403	+	0.358914i
$856$		0			0
$857$	767.610	−	767.610i	0.895694	−	0.895694i	−0.0993576	−	0.995052i	$-0.531679\pi$
$857$	767.610	−	767.610i	0.895694	−	0.895694i	0.995052	+	0.0993576i	$0.0316788\pi$
$858$		0			0
$859$	−194.360	−	63.1515i	−0.226263	−	0.0735174i	0.193691	−	0.981063i	$-0.437954\pi$
$859$	−194.360	−	63.1515i	−0.226263	−	0.0735174i	−0.419955	+	0.907545i	$0.637954\pi$
$860$		0			0
$861$	86.0842	+	264.940i	0.0999816	+	0.307712i
$862$		0			0
$863$	1121.38	−	571.371i	1.29940	−	0.662075i	0.339019	−	0.940780i	$-0.389905\pi$
$863$	1121.38	−	571.371i	1.29940	−	0.662075i	0.960377	+	0.278704i	$0.0899050\pi$
$864$		0			0
$865$	−802.022	−	1112.17i	−0.927193	−	1.28575i
$866$		0			0
$867$	880.865	−	139.515i	1.01599	−	0.160917i
$868$		0			0
$869$	−96.1682	+	132.364i	−0.110665	+	0.152318i
$870$		0			0
$871$	889.718	−	646.418i	1.02149	−	0.742156i
$872$		0			0
$873$	82.8584	−	162.619i	0.0949123	−	0.186276i
$874$		0			0
$875$	−452.671	+	609.288i	−0.517338	+	0.696329i
$876$		0			0
$877$	−1304.15	−	664.495i	−1.48705	−	0.757691i	−0.493360	−	0.869825i	$-0.664231\pi$
$877$	−1304.15	−	664.495i	−1.48705	−	0.757691i	−0.993693	+	0.112134i	$0.964231\pi$
$878$		0			0
$879$	−179.060	−	246.455i	−0.203709	−	0.280381i
$880$		0			0
$881$	557.810	+	405.273i	0.633156	+	0.460015i	0.857492	−	0.514497i	$-0.172021\pi$
$881$	557.810	+	405.273i	0.633156	+	0.460015i	−0.224336	+	0.974512i	$0.572021\pi$
$882$		0			0
$883$	−49.3239	−	311.419i	−0.0558594	−	0.352682i	−0.999749	−	0.0224202i	$-0.992863\pi$
$883$	−49.3239	−	311.419i	−0.0558594	−	0.352682i	0.943889	−	0.330262i	$-0.107137\pi$
$884$		0			0
$885$	−474.575	+	342.230i	−0.536243	+	0.386701i
$886$		0			0
$887$	160.233	+	314.476i	0.180647	+	0.354539i	0.963518	−	0.267645i	$-0.0862455\pi$
$887$	160.233	+	314.476i	0.180647	+	0.354539i	−0.782871	+	0.622184i	$0.786246\pi$
$888$		0			0
$889$	−1284.57	+	417.383i	−1.44496	+	0.469497i
$890$		0			0
$891$	119.465	−	367.675i	0.134080	−	0.412654i
$892$		0			0
$893$	−54.0398	−	54.0398i	−0.0605149	−	0.0605149i
$894$		0			0
$895$	435.334	−	67.3660i	0.486407	−	0.0752693i
$896$		0			0
$897$	−292.291	+	1845.45i	−0.325854	+	2.05736i
$898$		0			0
$899$		−	1033.63i		−	1.14976i
$900$		0			0
$901$	−588.307			−0.652949
$902$		0			0
$903$	466.751	+	73.9261i	0.516890	+	0.0818673i
$904$		0			0
$905$	967.690	−	488.741i	1.06927	−	0.540045i
$906$		0			0
$907$	300.706	−	300.706i	0.331539	−	0.331539i	−0.521631	−	0.853171i	$-0.674676\pi$
$907$	300.706	−	300.706i	0.331539	−	0.331539i	0.853171	+	0.521631i	$0.174676\pi$
$908$		0			0
$909$	112.470	+	36.5439i	0.123730	+	0.0402023i
$910$		0			0
$911$	−257.153	−	791.436i	−0.282276	−	0.868755i	−0.987202	−	0.159475i	$-0.949020\pi$
$911$	−257.153	−	791.436i	−0.282276	−	0.868755i	0.704926	−	0.709281i	$-0.250980\pi$
$912$		0			0
$913$	−349.933	+	178.300i	−0.383278	+	0.195290i
$914$		0			0
$915$	226.539	+	74.4977i	0.247584	+	0.0814182i
$916$		0			0
$917$	746.772	−	118.277i	0.814365	−	0.128983i
$918$		0			0
$919$	157.460	−	216.725i	0.171338	−	0.235826i	−0.714709	−	0.699422i	$-0.753441\pi$
$919$	157.460	−	216.725i	0.171338	−	0.235826i	0.886047	+	0.463595i	$0.153441\pi$
$920$		0			0
$921$	423.976	−	308.036i	0.460343	−	0.334458i
$922$		0			0
$923$	639.406	−	1254.90i	0.692747	−	1.35959i
$924$		0			0
$925$	737.283	−	1421.94i	0.797062	−	1.53723i
$926$		0			0
$927$	−96.4157	−	49.1262i	−0.104008	−	0.0529949i
$928$		0			0
$929$	251.062	+	345.558i	0.270250	+	0.371967i	0.922474	−	0.386059i	$-0.126164\pi$
$929$	251.062	+	345.558i	0.270250	+	0.371967i	−0.652224	+	0.758026i	$0.726164\pi$
$930$		0			0
$931$	−310.156	−	225.342i	−0.333143	−	0.242043i
$932$		0			0
$933$	147.882	+	933.691i	0.158502	+	1.00074i
$934$		0			0
$935$	812.868	+	2.88724i	0.869378	+	0.00308796i
$936$		0			0
$937$	137.253	+	269.375i	0.146482	+	0.287487i	0.952576	−	0.304300i	$-0.0984227\pi$
$937$	137.253	+	269.375i	0.146482	+	0.287487i	−0.806094	+	0.591787i	$0.798423\pi$
$938$		0			0
$939$	−254.981	+	82.8482i	−0.271545	+	0.0882303i
$940$		0			0
$941$	475.125	−	1462.28i	0.504915	−	1.55397i	−0.295998	−	0.955188i	$-0.595652\pi$
$941$	475.125	−	1462.28i	0.504915	−	1.55397i	0.800913	−	0.598780i	$-0.204348\pi$
$942$		0			0
$943$	369.210	+	369.210i	0.391528	+	0.391528i
$944$		0			0
$945$	−141.229	+	871.633i	−0.149448	+	0.922363i
$946$		0			0
$947$	−37.7964	+	238.637i	−0.0399118	+	0.251993i	−0.999575	−	0.0291599i	$-0.990717\pi$
$947$	−37.7964	+	238.637i	−0.0399118	+	0.251993i	0.959663	+	0.281153i	$0.0907168\pi$
$948$		0			0
$949$		−	1975.10i		−	2.08124i
$950$		0			0
$951$	929.947			0.977862
$952$		0			0
$953$	499.042	+	79.0406i	0.523654	+	0.0829387i	0.412665	−	0.910883i	$-0.364598\pi$
$953$	499.042	+	79.0406i	0.523654	+	0.0829387i	0.110989	+	0.993822i	$0.464598\pi$
$954$		0			0
$955$	143.465	+	144.488i	0.150225	+	0.151296i
$956$		0			0
$957$	301.241	−	301.241i	0.314776	−	0.314776i
$958$		0			0
$959$	−220.536	−	71.6566i	−0.229965	−	0.0747201i
$960$		0			0
$961$	244.056	+	751.128i	0.253961	+	0.781611i
$962$		0			0
$963$	181.041	−	92.2452i	0.187997	−	0.0957894i
$964$		0			0
$965$	−1439.45	+	462.058i	−1.49165	+	0.478817i
$966$		0			0
$967$	−213.699	+	33.8466i	−0.220992	+	0.0350017i	−0.265948	−	0.963987i	$-0.585685\pi$
$967$	−213.699	+	33.8466i	−0.220992	+	0.0350017i	0.0449564	+	0.998989i	$0.485685\pi$
$968$		0			0
$969$	1232.42	−	1696.29i	1.27185	−	1.75055i
$970$		0			0
$971$	612.906	−	445.302i	0.631211	−	0.458601i	−0.225609	−	0.974218i	$-0.572437\pi$
$971$	612.906	−	445.302i	0.631211	−	0.458601i	0.856819	+	0.515617i	$0.172437\pi$
$972$		0			0
$973$	−549.400	+	1078.26i	−0.564645	+	1.10818i
$974$		0			0
$975$	−1245.30	−	918.347i	−1.27723	−	0.941894i
$976$		0			0
$977$	464.406	+	236.626i	0.475338	+	0.242197i	0.675211	−	0.737625i	$-0.264053\pi$
$977$	464.406	+	236.626i	0.475338	+	0.242197i	−0.199872	+	0.979822i	$0.564053\pi$
$978$		0			0
$979$	72.6665	+	100.017i	0.0742252	+	0.102162i
$980$		0			0
$981$	−8.71076	−	6.32874i	−0.00887947	−	0.00645131i
$982$		0			0
$983$	−7.09610	−	44.8030i	−0.00721882	−	0.0455778i	0.983816	−	0.179182i	$-0.0573450\pi$
$983$	−7.09610	−	44.8030i	−0.00721882	−	0.0455778i	−0.991035	+	0.133604i	$0.957345\pi$
$984$		0			0
$985$	−1364.25	−	998.612i	−1.38503	−	1.01382i
$986$		0			0
$987$	−17.6768	−	34.6928i	−0.0179097	−	0.0351497i
$988$		0			0
$989$	842.403	−	273.713i	0.851773	−	0.276758i
$990$		0			0
$991$	181.745	−	559.353i	0.183395	−	0.564433i	−0.816522	−	0.577315i	$-0.804101\pi$
$991$	181.745	−	559.353i	0.183395	−	0.564433i	0.999917	+	0.0128820i	$0.00410059\pi$
$992$		0			0
$993$	−530.068	−	530.068i	−0.533805	−	0.533805i
$994$		0			0
$995$	254.896	+	131.018i	0.256177	+	0.131677i
$996$		0			0
$997$	−187.374	+	1183.04i	−0.187938	+	1.18660i	0.695668	+	0.718364i	$0.255109\pi$
$997$	−187.374	+	1183.04i	−0.187938	+	1.18660i	−0.883606	+	0.468232i	$0.844891\pi$
$998$		0			0
$999$		−	1863.29i		−	1.86516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.33.6		64
4.3	odd	2		200.3.u.b.33.3	✓	64
25.22	odd	20	inner	400.3.bg.f.97.6		64
100.47	even	20		200.3.u.b.97.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.33.3	✓	64	4.3	odd	2
200.3.u.b.97.3	yes	64	100.47	even	20
400.3.bg.f.33.6		64	1.1	even	1	trivial
400.3.bg.f.97.6		64	25.22	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.61980 + 0.414935i) q^{3} +(-2.28576 + 4.44694i) q^{5} +(-4.29378 + 4.29378i) q^{7} +(-1.86835 - 0.607064i) q^{9} +O(q^{10})\)	\(q+(2.61980 + 0.414935i) q^{3} +(-2.28576 + 4.44694i) q^{5} +(-4.29378 + 4.29378i) q^{7} +(-1.86835 - 0.607064i) q^{9} +(2.00916 + 6.18355i) q^{11} +(20.7906 - 10.5933i) q^{13} +(-7.83342 + 10.7016i) q^{15} +(-24.6968 + 3.91159i) q^{17} +(-18.5820 + 25.5759i) q^{19} +(-13.0305 + 9.46718i) q^{21} +(-13.7056 + 26.8987i) q^{23} +(-14.5506 - 20.3293i) q^{25} +(-25.9130 - 13.2033i) q^{27} +(-14.5201 - 19.9851i) q^{29} +(33.8512 + 24.5943i) q^{31} +(2.69781 + 17.0333i) q^{33} +(-9.27963 - 28.9087i) q^{35} +(29.0865 + 57.0855i) q^{37} +(58.8626 - 19.1256i) q^{39} +(5.34467 - 16.4492i) q^{41} +(-20.7467 - 20.7467i) q^{43} +(6.97019 - 6.92085i) q^{45} +(-0.378171 + 2.38768i) q^{47} +12.1269i q^{49} -66.3237 q^{51} +(23.2382 + 3.68057i) q^{53} +(-32.0903 - 5.19952i) q^{55} +(-59.2932 + 59.2932i) q^{57} +(41.9585 + 13.6331i) q^{59} +(-5.55656 - 17.1013i) q^{61} +(10.6289 - 5.41569i) q^{63} +(-0.414396 + 116.668i) q^{65} +(46.5510 - 7.37295i) q^{67} +(-47.0670 + 64.7821i) q^{69} +(48.8317 - 35.4783i) q^{71} +(38.4282 - 75.4196i) q^{73} +(-29.6842 - 59.2962i) q^{75} +(-35.1777 - 17.9239i) q^{77} +(14.7911 + 20.3582i) q^{79} +(-48.1043 - 34.9498i) q^{81} +(9.44942 + 59.6613i) q^{83} +(39.0565 - 118.766i) q^{85} +(-29.7471 - 58.3819i) q^{87} +(18.0838 - 5.87579i) q^{89} +(-43.7847 + 134.756i) q^{91} +(78.4781 + 78.4781i) q^{93} +(-71.2605 - 141.093i) q^{95} +(-14.5335 + 91.7608i) q^{97} -12.7727i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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