LMFDB - Embedded newform 400.3.bg.a.113.2

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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.2
Root			$-3.40366i$ of defining polynomial
Character	$\chi$	$=$	400.113
Dual form			400.3.bg.a.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14941 - 2.25584i) q^{3} +(-4.68874 + 1.73657i) q^{5} +(6.58346 - 6.58346i) q^{7} +(1.52238 + 2.09537i) q^{9} +O(q^{10})$	\(q+(1.14941 - 2.25584i) q^{3} +(-4.68874 + 1.73657i) q^{5} +(6.58346 - 6.58346i) q^{7} +(1.52238 + 2.09537i) q^{9} +(3.81477 + 2.77159i) q^{11} +(17.5244 + 2.77559i) q^{13} +(-1.47185 + 12.5731i) q^{15} +(-7.44532 - 14.6123i) q^{17} +(-16.0908 - 5.22822i) q^{19} +(-7.28417 - 22.4184i) q^{21} +(-5.91002 - 37.3144i) q^{23} +(18.9686 - 16.2847i) q^{25} +(28.9823 - 4.59034i) q^{27} +(-1.46851 + 0.477149i) q^{29} +(9.29144 - 28.5961i) q^{31} +(10.6370 - 5.41983i) q^{33} +(-19.4355 + 42.3008i) q^{35} +(1.26903 - 8.01234i) q^{37} +(26.4040 - 36.3420i) q^{39} +(-30.0830 + 21.8566i) q^{41} +(25.9880 + 25.9880i) q^{43} +(-10.7768 - 7.18094i) q^{45} +(-41.1918 - 20.9883i) q^{47} -37.6840i q^{49} -41.5207 q^{51} +(37.0947 - 72.8025i) q^{53} +(-22.6996 - 6.37067i) q^{55} +(-30.2890 + 30.2890i) q^{57} +(-24.7807 - 34.1077i) q^{59} +(96.0793 + 69.8057i) q^{61} +(23.8173 + 3.77229i) q^{63} +(-86.9875 + 17.4184i) q^{65} +(39.7150 + 77.9450i) q^{67} +(-90.9685 - 29.5575i) q^{69} +(5.14879 + 15.8463i) q^{71} +(9.91177 + 62.5804i) q^{73} +(-14.9330 - 61.5081i) q^{75} +(43.3611 - 6.86772i) q^{77} +(19.2036 - 6.23964i) q^{79} +(15.7542 - 48.4864i) q^{81} +(-22.1438 + 11.2828i) q^{83} +(60.2844 + 55.5838i) q^{85} +(-0.611550 + 3.86118i) q^{87} +(-39.7082 + 54.6536i) q^{89} +(133.644 - 97.0982i) q^{91} +(-53.8287 - 53.8287i) q^{93} +(84.5249 - 3.42907i) q^{95} +(-26.2088 - 13.3540i) q^{97} +12.2128i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$1$

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
$3$	1.14941	−	2.25584i	0.383137	−	0.751948i	−0.616229	−	0.787567i	$-0.711340\pi$
$3$	1.14941	−	2.25584i	0.383137	−	0.751948i	0.999365	+	0.0356190i	$0.0113403\pi$
$4$		0			0
$5$	−4.68874	+	1.73657i	−0.937749	+	0.347314i
$5$	−4.68874	+	1.73657i	−0.937749	+	0.347314i
$6$		0			0
$7$	6.58346	−	6.58346i	0.940495	−	0.940495i	−0.0578317	−	0.998326i	$-0.518419\pi$
$7$	6.58346	−	6.58346i	0.940495	−	0.940495i	0.998326	+	0.0578317i	$0.0184187\pi$
$8$		0			0
$9$	1.52238	+	2.09537i	0.169153	+	0.232819i
$10$		0			0
$11$	3.81477	+	2.77159i	0.346797	+	0.251963i	0.747524	−	0.664235i	$-0.231242\pi$
$11$	3.81477	+	2.77159i	0.346797	+	0.251963i	−0.400727	+	0.916198i	$0.631242\pi$
$12$		0			0
$13$	17.5244	+	2.77559i	1.34803	+	0.213507i	0.788363	−	0.615210i	$-0.210929\pi$
$13$	17.5244	+	2.77559i	1.34803	+	0.213507i	0.559668	+	0.828717i	$0.310929\pi$
$14$		0			0
$15$	−1.47185	+	12.5731i	−0.0981235	+	0.838208i
$16$		0			0
$17$	−7.44532	−	14.6123i	−0.437960	−	0.859545i	−0.999485	−	0.0320852i	$-0.989785\pi$
$17$	−7.44532	−	14.6123i	−0.437960	−	0.859545i	0.561525	−	0.827460i	$-0.310215\pi$
$18$		0			0
$19$	−16.0908	−	5.22822i	−0.846885	−	0.275170i	−0.146744	−	0.989174i	$-0.546879\pi$
$19$	−16.0908	−	5.22822i	−0.846885	−	0.275170i	−0.700141	+	0.714005i	$0.746879\pi$
$20$		0			0
$21$	−7.28417	−	22.4184i	−0.346865	−	1.06754i
$22$		0			0
$23$	−5.91002	−	37.3144i	−0.256957	−	1.62237i	−0.691960	−	0.721936i	$-0.743253\pi$
$23$	−5.91002	−	37.3144i	−0.256957	−	1.62237i	0.435003	−	0.900429i	$-0.356747\pi$
$24$		0			0
$25$	18.9686	−	16.2847i	0.758745	−	0.651387i
$26$		0			0
$27$	28.9823	−	4.59034i	1.07342	−	0.170013i
$28$		0			0
$29$	−1.46851	+	0.477149i	−0.0506384	+	0.0164534i	−0.334227	−	0.942493i	$-0.608475\pi$
$29$	−1.46851	+	0.477149i	−0.0506384	+	0.0164534i	0.283588	+	0.958946i	$0.408475\pi$
$30$		0			0
$31$	9.29144	−	28.5961i	0.299724	−	0.922456i	−0.681870	−	0.731474i	$-0.738833\pi$
$31$	9.29144	−	28.5961i	0.299724	−	0.922456i	0.981594	−	0.190982i	$-0.0611671\pi$
$32$		0			0
$33$	10.6370	−	5.41983i	0.322334	−	0.164237i
$34$		0			0
$35$	−19.4355	+	42.3008i	−0.555300	+	1.20859i
$36$		0			0
$37$	1.26903	−	8.01234i	0.0342981	−	0.216550i	−0.964587	−	0.263766i	$-0.915035\pi$
$37$	1.26903	−	8.01234i	0.0342981	−	0.216550i	0.998885	+	0.0472168i	$0.0150352\pi$
$38$		0			0
$39$	26.4040	−	36.3420i	0.677027	−	0.931847i
$40$		0			0
$41$	−30.0830	+	21.8566i	−0.733733	+	0.533088i	−0.890742	−	0.454509i	$-0.849815\pi$
$41$	−30.0830	+	21.8566i	−0.733733	+	0.533088i	0.157009	+	0.987597i	$0.449815\pi$
$42$		0			0
$43$	25.9880	+	25.9880i	0.604371	+	0.604371i	0.941470	−	0.337098i	$-0.109445\pi$
$43$	25.9880	+	25.9880i	0.604371	+	0.604371i	−0.337098	+	0.941470i	$0.609445\pi$
$44$		0			0
$45$	−10.7768	−	7.18094i	−0.239484	−	0.159576i
$46$		0			0
$47$	−41.1918	−	20.9883i	−0.876421	−	0.446559i	−0.0429212	−	0.999078i	$-0.513666\pi$
$47$	−41.1918	−	20.9883i	−0.876421	−	0.446559i	−0.833500	+	0.552520i	$0.813666\pi$
$48$		0			0
$49$		−	37.6840i		−	0.769060i
$50$		0			0
$51$	−41.5207			−0.814132
$52$		0			0
$53$	37.0947	−	72.8025i	0.699900	−	1.37363i	−0.217656	−	0.976026i	$-0.569841\pi$
$53$	37.0947	−	72.8025i	0.699900	−	1.37363i	0.917556	−	0.397606i	$-0.130159\pi$
$54$		0			0
$55$	−22.6996	−	6.37067i	−0.412719	−	0.115830i
$56$		0			0
$57$	−30.2890	+	30.2890i	−0.531386	+	0.531386i
$58$		0			0
$59$	−24.7807	−	34.1077i	−0.420012	−	0.578097i	0.545612	−	0.838038i	$-0.316297\pi$
$59$	−24.7807	−	34.1077i	−0.420012	−	0.578097i	−0.965625	+	0.259940i	$0.916297\pi$
$60$		0			0
$61$	96.0793	+	69.8057i	1.57507	+	1.14436i	0.922087	+	0.386983i	$0.126483\pi$
$61$	96.0793	+	69.8057i	1.57507	+	1.14436i	0.652983	+	0.757372i	$0.273517\pi$
$62$		0			0
$63$	23.8173	+	3.77229i	0.378052	+	0.0598776i
$64$		0			0
$65$	−86.9875	+	17.4184i	−1.33827	+	0.267975i
$66$		0			0
$67$	39.7150	+	77.9450i	0.592761	+	1.16336i	0.971319	+	0.237781i	$0.0764199\pi$
$67$	39.7150	+	77.9450i	0.592761	+	1.16336i	−0.378558	+	0.925577i	$0.623580\pi$
$68$		0			0
$69$	−90.9685	−	29.5575i	−1.31838	−	0.428369i
$70$		0			0
$71$	5.14879	+	15.8463i	0.0725181	+	0.223188i	0.980746	−	0.195288i	$-0.0625643\pi$
$71$	5.14879	+	15.8463i	0.0725181	+	0.223188i	−0.908228	+	0.418476i	$0.862564\pi$
$72$		0			0
$73$	9.91177	+	62.5804i	0.135778	+	0.857266i	0.957721	+	0.287697i	$0.0928898\pi$
$73$	9.91177	+	62.5804i	0.135778	+	0.857266i	−0.821944	+	0.569569i	$0.807110\pi$
$74$		0			0
$75$	−14.9330	−	61.5081i	−0.199106	−	0.820108i
$76$		0			0
$77$	43.3611	−	6.86772i	0.563131	−	0.0891912i
$78$		0			0
$79$	19.2036	−	6.23964i	0.243084	−	0.0789827i	−0.184941	−	0.982750i	$-0.559209\pi$
$79$	19.2036	−	6.23964i	0.243084	−	0.0789827i	0.428025	+	0.903767i	$0.359209\pi$
$80$		0			0
$81$	15.7542	−	48.4864i	0.194496	−	0.598598i
$82$		0			0
$83$	−22.1438	+	11.2828i	−0.266793	+	0.135938i	−0.582270	−	0.812995i	$-0.697835\pi$
$83$	−22.1438	+	11.2828i	−0.266793	+	0.135938i	0.315477	+	0.948933i	$0.397835\pi$
$84$		0			0
$85$	60.2844	+	55.5838i	0.709229	+	0.653927i
$86$		0			0
$87$	−0.611550	+	3.86118i	−0.00702931	+	0.0443813i
$88$		0			0
$89$	−39.7082	+	54.6536i	−0.446159	+	0.614085i	−0.971567	−	0.236765i	$-0.923913\pi$
$89$	−39.7082	+	54.6536i	−0.446159	+	0.614085i	0.525408	+	0.850851i	$0.323913\pi$
$90$		0			0
$91$	133.644	−	97.0982i	1.46862	−	1.06701i
$92$		0			0
$93$	−53.8287	−	53.8287i	−0.578804	−	0.578804i
$94$		0			0
$95$	84.5249	−	3.42907i	0.889736	−	0.0360955i
$96$		0			0
$97$	−26.2088	−	13.3540i	−0.270194	−	0.137671i	0.313645	−	0.949540i	$-0.398450\pi$
$97$	−26.2088	−	13.3540i	−0.270194	−	0.137671i	−0.583839	+	0.811870i	$0.698450\pi$
$98$		0			0
$99$			12.2128i			0.123361i
$100$		0			0
$101$	140.710			1.39317			0.696586	−	0.717474i	$-0.254702\pi$
$101$	140.710			1.39317			0.696586	+	0.717474i	$0.254702\pi$
$102$		0			0
$103$	16.8755	−	33.1201i	0.163840	−	0.321554i	−0.794461	−	0.607316i	$-0.792246\pi$
$103$	16.8755	−	33.1201i	0.163840	−	0.321554i	0.958301	+	0.285761i	$0.0922464\pi$
$104$		0			0
$105$	73.0847	+	92.4645i	0.696045	+	0.880614i
$106$		0			0
$107$	−93.0390	+	93.0390i	−0.869523	+	0.869523i	−0.992420	−	0.122896i	$-0.960782\pi$
$107$	−93.0390	+	93.0390i	−0.869523	+	0.869523i	0.122896	+	0.992420i	$0.460782\pi$
$108$		0			0
$109$	−110.706	−	152.374i	−1.01565	−	1.39793i	−0.915206	−	0.402986i	$-0.867972\pi$
$109$	−110.706	−	152.374i	−1.01565	−	1.39793i	−0.100448	−	0.994942i	$-0.532028\pi$
$110$		0			0
$111$	−16.6160	−	12.0722i	−0.149693	−	0.108759i
$112$		0			0
$113$	158.222	+	25.0599i	1.40020	+	0.221769i	0.810445	−	0.585815i	$-0.199226\pi$
$113$	158.222	+	25.0599i	1.40020	+	0.221769i	0.589752	+	0.807585i	$0.299226\pi$
$114$		0			0
$115$	92.5097	+	164.694i	0.804432	+	1.43213i
$116$		0			0
$117$	20.8628	+	40.9456i	0.178315	+	0.349962i
$118$		0			0
$119$	−145.215	−	47.1833i	−1.22030	−	0.396498i
$120$		0			0
$121$	−30.5203	−	93.9318i	−0.252234	−	0.776296i
$122$		0			0
$123$	14.7274	+	92.9849i	0.119735	+	0.755975i
$124$		0			0
$125$	−60.6595	+	109.295i	−0.485276	+	0.874361i
$126$		0			0
$127$	−115.861	+	18.3506i	−0.912294	+	0.144493i	−0.594899	−	0.803800i	$-0.702808\pi$
$127$	−115.861	+	18.3506i	−0.912294	+	0.144493i	−0.317395	+	0.948293i	$0.602808\pi$
$128$		0			0
$129$	88.4957	−	28.7540i	0.686013	−	0.222899i
$130$		0			0
$131$	−54.0155	+	166.243i	−0.412332	+	1.26903i	0.502283	+	0.864703i	$0.332494\pi$
$131$	−54.0155	+	166.243i	−0.412332	+	1.26903i	−0.914615	+	0.404325i	$0.867506\pi$
$132$		0			0
$133$	−140.353	+	71.5135i	−1.05529	+	0.537695i
$134$		0			0
$135$	−127.919	+	71.8527i	−0.947548	+	0.532243i
$136$		0			0
$137$	−9.54211	+	60.2465i	−0.0696505	+	0.439756i	0.928078	+	0.372387i	$0.121460\pi$
$137$	−9.54211	+	60.2465i	−0.0696505	+	0.439756i	−0.997728	+	0.0673690i	$0.978540\pi$
$138$		0			0
$139$	−45.5691	+	62.7205i	−0.327835	+	0.451227i	−0.940839	−	0.338853i	$-0.889961\pi$
$139$	−45.5691	+	62.7205i	−0.327835	+	0.451227i	0.613004	+	0.790080i	$0.289961\pi$
$140$		0			0
$141$	−94.6925	+	68.7982i	−0.671578	+	0.487930i
$142$		0			0
$143$	59.1588	+	59.1588i	0.413698	+	0.413698i
$144$		0			0
$145$	6.05688	−	4.78741i	0.0417716	−	0.0330166i
$146$		0			0
$147$	−85.0092	−	43.3143i	−0.578294	−	0.294655i
$148$		0			0
$149$			146.792i			0.985181i	0.870261	+	0.492590i	$0.163950\pi$
$149$			146.792i			0.985181i	−0.870261	+	0.492590i	$0.836050\pi$
$150$		0			0
$151$	81.4983			0.539724			0.269862	−	0.962899i	$-0.413022\pi$
$151$	81.4983			0.539724			0.269862	+	0.962899i	$0.413022\pi$
$152$		0			0
$153$	19.2835	−	37.8460i	0.126036	−	0.247360i
$154$		0			0
$155$	6.09404	+	150.215i	0.0393164	+	0.969130i
$156$		0			0
$157$	−211.160	+	211.160i	−1.34497	+	1.34497i	−0.453938	+	0.891033i	$0.649981\pi$
$157$	−211.160	+	211.160i	−1.34497	+	1.34497i	−0.891033	+	0.453938i	$0.850019\pi$
$158$		0			0
$159$	−121.594	−	167.360i	−0.764742	−	1.05258i
$160$		0			0
$161$	−284.566	−	206.750i	−1.76749	−	1.28416i
$162$		0			0
$163$	84.8146	+	13.4333i	0.520335	+	0.0824129i	0.411077	−	0.911601i	$-0.365153\pi$
$163$	84.8146	+	13.4333i	0.520335	+	0.0824129i	0.109258	+	0.994013i	$0.465153\pi$
$164$		0			0
$165$	−40.4623	+	43.8842i	−0.245226	+	0.265965i
$166$		0			0
$167$	−17.8505	−	35.0337i	−0.106889	−	0.209782i	0.831366	−	0.555725i	$-0.187559\pi$
$167$	−17.8505	−	35.0337i	−0.106889	−	0.209782i	−0.938256	+	0.345943i	$0.887559\pi$
$168$		0			0
$169$	138.672	+	45.0574i	0.820546	+	0.266612i
$170$		0			0
$171$	−13.5412	−	41.6755i	−0.0791883	−	0.243717i
$172$		0			0
$173$	35.6189	+	224.889i	0.205889	+	1.29993i	0.846632	+	0.532179i	$0.178627\pi$
$173$	35.6189	+	224.889i	0.205889	+	1.29993i	−0.640742	+	0.767756i	$0.721373\pi$
$174$		0			0
$175$	17.6697	−	232.089i	0.100970	−	1.32622i
$176$		0			0
$177$	−105.425	+	16.6977i	−0.595622	+	0.0943372i
$178$		0			0
$179$	7.90838	−	2.56959i	0.0441809	−	0.0143552i	−0.286843	−	0.957978i	$-0.592606\pi$
$179$	7.90838	−	2.56959i	0.0441809	−	0.0143552i	0.331024	+	0.943622i	$0.392606\pi$
$180$		0			0
$181$	33.4318	−	102.892i	0.184706	−	0.568466i	−0.815237	−	0.579127i	$-0.803394\pi$
$181$	33.4318	−	102.892i	0.184706	−	0.568466i	0.999943	+	0.0106608i	$0.00339351\pi$
$182$		0			0
$183$	267.905	−	136.505i	1.46396	−	0.745927i
$184$		0			0
$185$	7.96385	+	39.7716i	0.0430478	+	0.214981i
$186$		0			0
$187$	12.0971	−	76.3778i	0.0646902	−	0.408438i
$188$		0			0
$189$	160.583	−	221.024i	0.849647	−	1.16944i
$190$		0			0
$191$	185.233	−	134.580i	0.969808	−	0.704607i	0.0144000	−	0.999896i	$-0.495416\pi$
$191$	185.233	−	134.580i	0.969808	−	0.704607i	0.955408	+	0.295290i	$0.0954162\pi$
$192$		0			0
$193$	176.707	+	176.707i	0.915582	+	0.915582i	0.996704	−	0.0811226i	$-0.0258505\pi$
$193$	176.707	+	176.707i	0.915582	+	0.915582i	−0.0811226	+	0.996704i	$0.525851\pi$
$194$		0			0
$195$	−60.6912	+	216.251i	−0.311237	+	1.10898i
$196$		0			0
$197$	−15.3892	−	7.84117i	−0.0781175	−	0.0398029i	0.414495	−	0.910051i	$-0.363958\pi$
$197$	−15.3892	−	7.84117i	−0.0781175	−	0.0398029i	−0.492613	+	0.870249i	$0.663958\pi$
$198$		0			0
$199$			266.747i			1.34044i	0.742164	+	0.670218i	$0.233800\pi$
$199$			266.747i			1.34044i	−0.742164	+	0.670218i	$0.766200\pi$
$200$		0			0
$201$	221.481			1.10189
$202$		0			0
$203$	−6.52661	+	12.8092i	−0.0321508	+	0.0630995i
$204$		0			0
$205$	103.096	−	154.721i	0.502908	−	0.754739i
$206$		0			0
$207$	69.1902	−	69.1902i	0.334252	−	0.334252i
$208$		0			0
$209$	−46.8923	−	64.5417i	−0.224365	−	0.308812i
$210$		0			0
$211$	−200.960	−	146.006i	−0.952419	−	0.691973i	−0.00104087	−	0.999999i	$-0.500331\pi$
$211$	−200.960	−	146.006i	−0.952419	−	0.691973i	−0.951378	+	0.308027i	$0.900331\pi$
$212$		0			0
$213$	41.6650	+	6.59908i	0.195610	+	0.0309816i
$214$		0			0
$215$	−166.981	−	76.7209i	−0.776655	−	0.356842i
$216$		0			0
$217$	−127.092	−	249.431i	−0.585676	−	1.14945i
$218$		0			0
$219$	152.564	+	49.5712i	0.696641	+	0.226352i
$220$		0			0
$221$	−89.9171	−	276.736i	−0.406865	−	1.25220i
$222$		0			0
$223$	8.86348	+	55.9618i	0.0397466	+	0.250950i	0.999559	−	0.0296920i	$-0.00945265\pi$
$223$	8.86348	+	55.9618i	0.0397466	+	0.250950i	−0.959813	+	0.280642i	$0.909453\pi$
$224$		0			0
$225$	62.9998	+	14.9549i	0.279999	+	0.0664662i
$226$		0			0
$227$	−152.356	+	24.1307i	−0.671170	+	0.106303i	−0.482713	−	0.875779i	$-0.660349\pi$
$227$	−152.356	+	24.1307i	−0.671170	+	0.106303i	−0.188457	+	0.982081i	$0.560349\pi$
$228$		0			0
$229$	−80.9675	+	26.3079i	−0.353570	+	0.114882i	−0.480416	−	0.877041i	$-0.659514\pi$
$229$	−80.9675	+	26.3079i	−0.353570	+	0.114882i	0.126847	+	0.991922i	$0.459514\pi$
$230$		0			0
$231$	34.3472	−	105.710i	0.148689	−	0.457618i
$232$		0			0
$233$	49.0406	−	24.9874i	0.210475	−	0.107242i	−0.345575	−	0.938391i	$-0.612316\pi$
$233$	49.0406	−	24.9874i	0.210475	−	0.107242i	0.556050	+	0.831149i	$0.312316\pi$
$234$		0			0
$235$	229.585	+	26.8761i	0.976959	+	0.114366i
$236$		0			0
$237$	7.99719	−	50.4923i	0.0337434	−	0.213048i
$238$		0			0
$239$	8.97514	−	12.3532i	0.0375529	−	0.0516871i	−0.789828	−	0.613329i	$-0.789830\pi$
$239$	8.97514	−	12.3532i	0.0375529	−	0.0516871i	0.827381	+	0.561642i	$0.189830\pi$
$240$		0			0
$241$	191.342	−	139.018i	0.793950	−	0.576839i	−0.115183	−	0.993344i	$-0.536745\pi$
$241$	191.342	−	139.018i	0.793950	−	0.576839i	0.909133	+	0.416506i	$0.136745\pi$
$242$		0			0
$243$	95.4714	+	95.4714i	0.392886	+	0.392886i
$244$		0			0
$245$	65.4409	+	176.690i	0.267106	+	0.721185i
$246$		0			0
$247$	−267.471	−	136.283i	−1.08288	−	0.551753i
$248$		0			0
$249$			62.9216i			0.252697i
$250$		0			0
$251$	68.4984			0.272902			0.136451	−	0.990647i	$-0.456430\pi$
$251$	68.4984			0.272902			0.136451	+	0.990647i	$0.456430\pi$
$252$		0			0
$253$	80.8750	−	158.726i	0.319664	−	0.627376i
$254$		0			0
$255$	194.680	−	72.1037i	0.763451	−	0.282760i
$256$		0			0
$257$	8.28497	−	8.28497i	0.0322372	−	0.0322372i	−0.690804	−	0.723042i	$-0.742743\pi$
$257$	8.28497	−	8.28497i	0.0322372	−	0.0322372i	0.723042	+	0.690804i	$0.242743\pi$
$258$		0			0
$259$	−44.3943	−	61.1035i	−0.171407	−	0.235921i
$260$		0			0
$261$	−3.23543	−	2.35068i	−0.0123963	−	0.00900643i
$262$		0			0
$263$	−91.2822	−	14.4577i	−0.347081	−	0.0549722i	−0.0195395	−	0.999809i	$-0.506220\pi$
$263$	−91.2822	−	14.4577i	−0.347081	−	0.0549722i	−0.327541	+	0.944837i	$0.606220\pi$
$264$		0			0
$265$	−47.5008	+	405.770i	−0.179248	+	1.53121i
$266$		0			0
$267$	77.6491	+	152.395i	0.290820	+	0.570767i
$268$		0			0
$269$	−203.293	−	66.0538i	−0.755735	−	0.245553i	−0.0942877	−	0.995545i	$-0.530057\pi$
$269$	−203.293	−	66.0538i	−0.755735	−	0.245553i	−0.661447	+	0.749992i	$0.730057\pi$
$270$		0			0
$271$	−119.535	−	367.892i	−0.441090	−	1.35754i	−0.886715	−	0.462316i	$-0.847019\pi$
$271$	−119.535	−	367.892i	−0.441090	−	1.35754i	0.445625	−	0.895220i	$-0.352981\pi$
$272$		0			0
$273$	−65.4265	−	413.086i	−0.239657	−	1.51314i
$274$		0			0
$275$	117.496	−	9.54900i	0.427256	−	0.0347237i
$276$		0			0
$277$	35.9094	−	5.68749i	0.129637	−	0.0205324i	−0.0912789	−	0.995825i	$-0.529095\pi$
$277$	35.9094	−	5.68749i	0.129637	−	0.0205324i	0.220916	+	0.975293i	$0.429095\pi$
$278$		0			0
$279$	74.0645	−	24.0650i	0.265464	−	0.0862545i
$280$		0			0
$281$	−53.3063	+	164.060i	−0.189702	+	0.583843i	−0.999998	−	0.00217821i	$-0.999307\pi$
$281$	−53.3063	+	164.060i	−0.189702	+	0.583843i	0.810295	+	0.586022i	$0.199307\pi$
$282$		0			0
$283$	−290.318	+	147.924i	−1.02586	+	0.522701i	−0.884148	−	0.467207i	$-0.845260\pi$
$283$	−290.318	+	147.924i	−1.02586	+	0.522701i	−0.141710	+	0.989908i	$0.545260\pi$
$284$		0			0
$285$	89.4184	−	194.617i	0.313749	−	0.682865i
$286$		0			0
$287$	−54.1584	+	341.943i	−0.188705	+	1.19144i
$288$		0			0
$289$	11.7845	−	16.2200i	0.0407769	−	0.0561246i
$290$		0			0
$291$	−60.2493	+	43.7737i	−0.207042	+	0.150425i
$292$		0			0
$293$	68.8337	+	68.8337i	0.234927	+	0.234927i	0.814746	−	0.579818i	$-0.196877\pi$
$293$	68.8337	+	68.8337i	0.234927	+	0.234927i	−0.579818	+	0.814746i	$0.696877\pi$
$294$		0			0
$295$	175.421	+	116.889i	0.594648	+	0.396234i
$296$		0			0
$297$	123.283	+	62.8160i	0.415095	+	0.211502i
$298$		0			0
$299$		−	670.316i		−	2.24186i
$300$		0			0
$301$	342.182			1.13682
$302$		0			0
$303$	161.734	−	317.421i	0.533775	−	1.04759i
$304$		0			0
$305$	−571.714	−	160.452i	−1.87447	−	0.526073i
$306$		0			0
$307$	196.445	−	196.445i	0.639887	−	0.639887i	−0.310641	−	0.950527i	$-0.600544\pi$
$307$	196.445	−	196.445i	0.639887	−	0.639887i	0.950527	+	0.310641i	$0.100544\pi$
$308$		0			0
$309$	−55.3169	−	76.1372i	−0.179019	−	0.246399i
$310$		0			0
$311$	194.521	+	141.328i	0.625470	+	0.454431i	0.854828	−	0.518911i	$-0.173663\pi$
$311$	194.521	+	141.328i	0.625470	+	0.454431i	−0.229358	+	0.973342i	$0.573663\pi$
$312$		0			0
$313$	−203.623	−	32.2507i	−0.650552	−	0.103037i	−0.177568	−	0.984108i	$-0.556823\pi$
$313$	−203.623	−	32.2507i	−0.650552	−	0.103037i	−0.472984	+	0.881071i	$0.656823\pi$
$314$		0			0
$315$	−118.224	+	23.6731i	−0.375314	+	0.0751529i
$316$		0			0
$317$	−15.7136	−	30.8396i	−0.0495696	−	0.0972858i	0.864893	−	0.501956i	$-0.167386\pi$
$317$	−15.7136	−	30.8396i	−0.0495696	−	0.0972858i	−0.914463	+	0.404671i	$0.867386\pi$
$318$		0			0
$319$	−6.92450	−	2.24991i	−0.0217069	−	0.00705300i
$320$		0			0
$321$	102.942	+	316.822i	0.320690	+	0.986983i
$322$		0			0
$323$	43.4051	+	274.049i	0.134381	+	0.848449i
$324$		0			0
$325$	377.614	−	232.730i	1.16189	−	0.716093i
$326$		0			0
$327$	−470.979	+	74.5958i	−1.44030	+	0.228122i
$328$		0			0
$329$	−409.360	+	133.009i	−1.24426	+	0.404283i
$330$		0			0
$331$	−7.67891	+	23.6332i	−0.0231991	+	0.0713995i	−0.961986	−	0.273099i	$-0.911951\pi$
$331$	−7.67891	+	23.6332i	−0.0231991	+	0.0713995i	0.938787	+	0.344499i	$0.111951\pi$
$332$		0			0
$333$	18.7207	−	9.53870i	0.0562185	−	0.0286447i
$334$		0			0
$335$	−321.570	−	296.496i	−0.959912	−	0.885063i
$336$		0			0
$337$	39.5913	−	249.970i	0.117482	−	0.741750i	−0.856672	−	0.515862i	$-0.827472\pi$
$337$	39.5913	−	249.970i	0.117482	−	0.741750i	0.974153	−	0.225888i	$-0.0725284\pi$
$338$		0			0
$339$	238.394	−	328.121i	0.703226	−	0.967907i
$340$		0			0
$341$	114.702	−	83.3356i	0.336368	−	0.244386i
$342$		0			0
$343$	74.4988	+	74.4988i	0.217198	+	0.217198i
$344$		0			0
$345$	477.857	−	19.3860i	1.38509	−	0.0561914i
$346$		0			0
$347$	185.879	+	94.7100i	0.535674	+	0.272939i	0.700830	−	0.713328i	$-0.252813\pi$
$347$	185.879	+	94.7100i	0.535674	+	0.272939i	−0.165157	+	0.986267i	$0.552813\pi$
$348$		0			0
$349$		−	198.448i		−	0.568620i	−0.958732	−	0.284310i	$-0.908235\pi$
$349$		−	198.448i		−	0.568620i	0.958732	−	0.284310i	$-0.0917645\pi$
$350$		0			0
$351$	520.638			1.48330
$352$		0			0
$353$	82.9237	−	162.747i	0.234911	−	0.461039i	−0.743215	−	0.669053i	$-0.766700\pi$
$353$	82.9237	−	162.747i	0.234911	−	0.461039i	0.978126	+	0.208014i	$0.0666999\pi$
$354$		0			0
$355$	−51.6597	−	65.3582i	−0.145520	−	0.184108i
$356$		0			0
$357$	−273.350	+	273.350i	−0.765687	+	0.765687i
$358$		0			0
$359$	114.552	+	157.667i	0.319086	+	0.439184i	0.938188	−	0.346127i	$-0.112503\pi$
$359$	114.552	+	157.667i	0.319086	+	0.439184i	−0.619102	+	0.785310i	$0.712503\pi$
$360$		0			0
$361$	−60.4750	−	43.9376i	−0.167521	−	0.121711i
$362$		0			0
$363$	−246.976	−	39.1172i	−0.680375	−	0.107761i
$364$		0			0
$365$	−155.149	−	276.211i	−0.425066	−	0.756743i
$366$		0			0
$367$	62.4163	+	122.499i	0.170072	+	0.333785i	0.960273	−	0.279063i	$-0.0900239\pi$
$367$	62.4163	+	122.499i	0.170072	+	0.333785i	−0.790201	+	0.612848i	$0.790024\pi$
$368$		0			0
$369$	−91.5954	−	29.7611i	−0.248226	−	0.0806535i
$370$		0			0
$371$	−235.081	−	723.504i	−0.633641	−	1.95015i
$372$		0			0
$373$	62.8520	+	396.832i	0.168504	+	1.06389i	0.916455	+	0.400139i	$0.131038\pi$
$373$	62.8520	+	396.832i	0.168504	+	1.06389i	−0.747951	+	0.663754i	$0.768962\pi$
$374$		0			0
$375$	176.830	+	262.463i	0.471547	+	0.699902i
$376$		0			0
$377$	−27.0592	+	4.28575i	−0.0717750	+	0.0113680i
$378$		0			0
$379$	−509.120	+	165.423i	−1.34332	+	0.436473i	−0.890442	−	0.455097i	$-0.849604\pi$
$379$	−509.120	+	165.423i	−1.34332	+	0.436473i	−0.452883	+	0.891570i	$0.649604\pi$
$380$		0			0
$381$	−91.7760	+	282.458i	−0.240882	+	0.741359i
$382$		0			0
$383$	−412.878	+	210.372i	−1.07801	+	0.549274i	−0.900505	−	0.434846i	$-0.856803\pi$
$383$	−412.878	+	210.372i	−1.07801	+	0.549274i	−0.177505	+	0.984120i	$0.556803\pi$
$384$		0			0
$385$	−191.383	+	107.501i	−0.497098	+	0.279222i
$386$		0			0
$387$	−14.8910	+	94.0178i	−0.0384779	+	0.242940i
$388$		0			0
$389$	−19.0616	+	26.2360i	−0.0490015	+	0.0674448i	−0.832815	−	0.553552i	$-0.813272\pi$
$389$	−19.0616	+	26.2360i	−0.0490015	+	0.0674448i	0.783813	+	0.620997i	$0.213272\pi$
$390$		0			0
$391$	−501.246	+	364.176i	−1.28196	+	0.931397i
$392$		0			0
$393$	312.932	+	312.932i	0.796264	+	0.796264i
$394$		0			0
$395$	−79.2053	+	62.6045i	−0.200520	+	0.158492i
$396$		0			0
$397$	−145.742	−	74.2593i	−0.367109	−	0.187051i	0.260698	−	0.965420i	$-0.416047\pi$
$397$	−145.742	−	74.2593i	−0.367109	−	0.187051i	−0.627807	+	0.778369i	$0.716047\pi$
$398$		0			0
$399$			398.813i			0.999532i
$400$		0			0
$401$	−461.933			−1.15195			−0.575977	−	0.817466i	$-0.695378\pi$
$401$	−461.933			−1.15195			−0.575977	+	0.817466i	$0.695378\pi$
$402$		0			0
$403$	242.198	−	475.341i	0.600988	−	1.17951i
$404$		0			0
$405$	10.3328	+	254.699i	0.0255131	+	0.628885i
$406$		0			0
$407$	27.0480	−	27.0480i	0.0664570	−	0.0664570i
$408$		0			0
$409$	152.579	+	210.007i	0.373054	+	0.513465i	0.953728	−	0.300672i	$-0.0972108\pi$
$409$	152.579	+	210.007i	0.373054	+	0.513465i	−0.580674	+	0.814136i	$0.697211\pi$
$410$		0			0
$411$	124.939	+	90.7735i	0.303988	+	0.220860i
$412$		0			0
$413$	−387.690	−	61.4041i	−0.938717	−	0.148678i
$414$		0			0
$415$	84.2331	−	91.3566i	0.202971	−	0.220136i
$416$		0			0
$417$	89.1101	+	174.888i	0.213693	+	0.419397i
$418$		0			0
$419$	374.972	+	121.836i	0.894922	+	0.290778i	0.720139	−	0.693829i	$-0.244078\pi$
$419$	374.972	+	121.836i	0.894922	+	0.290778i	0.174782	+	0.984607i	$0.444078\pi$
$420$		0			0
$421$	96.2390	+	296.193i	0.228596	+	0.703547i	0.997907	+	0.0646716i	$0.0206000\pi$
$421$	96.2390	+	296.193i	0.228596	+	0.703547i	−0.769310	+	0.638875i	$0.779400\pi$
$422$		0			0
$423$	−18.7312	−	118.264i	−0.0442818	−	0.279584i
$424$		0			0
$425$	−379.184	−	155.930i	−0.892197	−	0.366894i
$426$		0			0
$427$	1092.10	−	172.971i	2.55760	−	0.405085i
$428$		0			0
$429$	201.451	−	65.4553i	0.469582	−	0.152577i
$430$		0			0
$431$	−223.411	+	687.587i	−0.518354	+	1.59533i	0.258741	+	0.965947i	$0.416692\pi$
$431$	−223.411	+	687.587i	−0.518354	+	1.59533i	−0.777095	+	0.629383i	$0.783308\pi$
$432$		0			0
$433$	213.481	−	108.774i	0.493027	−	0.251210i	−0.189755	−	0.981831i	$-0.560770\pi$
$433$	213.481	−	108.774i	0.493027	−	0.251210i	0.682783	+	0.730621i	$0.260770\pi$
$434$		0			0
$435$	−3.83781	−	19.1661i	−0.00882255	−	0.0440599i
$436$		0			0
$437$	−99.9910	+	631.318i	−0.228812	+	1.44466i
$438$		0			0
$439$	−43.7867	+	60.2673i	−0.0997420	+	0.137283i	−0.855971	−	0.517024i	$-0.827040\pi$
$439$	−43.7867	+	60.2673i	−0.0997420	+	0.137283i	0.756229	+	0.654307i	$0.227040\pi$
$440$		0			0
$441$	78.9618	−	57.3691i	0.179052	−	0.130089i
$442$		0			0
$443$	−144.493	−	144.493i	−0.326170	−	0.326170i	0.524958	−	0.851128i	$-0.324081\pi$
$443$	−144.493	−	144.493i	−0.326170	−	0.326170i	−0.851128	+	0.524958i	$0.824081\pi$
$444$		0			0
$445$	91.2715	−	325.213i	0.205104	−	0.730815i
$446$		0			0
$447$	331.140	+	168.724i	0.740805	+	0.377459i
$448$		0			0
$449$		−	63.0893i		−	0.140511i	−0.997529	−	0.0702554i	$-0.977619\pi$
$449$		−	63.0893i		−	0.140511i	0.997529	−	0.0702554i	$-0.0223814\pi$
$450$		0			0
$451$	−175.338			−0.388775
$452$		0			0
$453$	93.6750	−	183.848i	0.206788	−	0.405845i
$454$		0			0
$455$	−458.006	+	687.352i	−1.00661	+	1.51066i
$456$		0			0
$457$	456.270	−	456.270i	0.998403	−	0.998403i	−0.00159596	−	0.999999i	$-0.500508\pi$
$457$	456.270	−	456.270i	0.998403	−	0.998403i	0.999999	+	0.00159596i	$0.000508011\pi$
$458$		0			0
$459$	−282.858	−	389.320i	−0.616247	−	0.848192i
$460$		0			0
$461$	−279.602	−	203.143i	−0.606512	−	0.440656i	0.241673	−	0.970358i	$-0.422304\pi$
$461$	−279.602	−	203.143i	−0.606512	−	0.440656i	−0.848184	+	0.529701i	$0.822304\pi$
$462$		0			0
$463$	704.232	+	111.539i	1.52102	+	0.240906i	0.860324	−	0.509748i	$-0.170261\pi$
$463$	704.232	+	111.539i	1.52102	+	0.240906i	0.660696	+	0.750654i	$0.270261\pi$
$464$		0			0
$465$	345.867	+	158.912i	0.743799	+	0.341745i
$466$		0			0
$467$	−45.3195	−	88.9445i	−0.0970438	−	0.190459i	0.837381	−	0.546620i	$-0.184086\pi$
$467$	−45.3195	−	88.9445i	−0.0970438	−	0.190459i	−0.934425	+	0.356160i	$0.884086\pi$
$468$		0			0
$469$	774.610	+	251.686i	1.65162	+	0.536644i
$470$		0			0
$471$	233.635	+	719.055i	0.496041	+	1.52666i
$472$		0			0
$473$	27.1101	+	171.166i	0.0573152	+	0.361874i
$474$		0			0
$475$	−390.361	+	162.862i	−0.821812	+	0.342867i
$476$		0			0
$477$	209.020	−	33.1055i	0.438197	−	0.0694037i
$478$		0			0
$479$	−828.170	+	269.089i	−1.72896	+	0.561772i	−0.993298	−	0.115581i	$-0.963127\pi$
$479$	−828.170	+	269.089i	−1.72896	+	0.561772i	−0.735658	+	0.677353i	$0.763127\pi$
$480$		0			0
$481$	44.4780	−	136.889i	0.0924698	−	0.284593i
$482$		0			0
$483$	−793.478	+	404.297i	−1.64281	+	0.837055i
$484$		0			0
$485$	146.077	+	17.1002i	0.301189	+	0.0352582i
$486$		0			0
$487$	77.6661	−	490.364i	0.159479	−	1.00691i	−0.770003	−	0.638040i	$-0.779745\pi$
$487$	77.6661	−	490.364i	0.159479	−	1.00691i	0.929482	−	0.368868i	$-0.120255\pi$
$488$		0			0
$489$	127.790	−	175.888i	0.261330	−	0.359689i
$490$		0			0
$491$	−135.584	+	98.5073i	−0.276138	+	0.200626i	−0.717231	−	0.696835i	$-0.754591\pi$
$491$	−135.584	+	98.5073i	−0.276138	+	0.200626i	0.441093	+	0.897461i	$0.354591\pi$
$492$		0			0
$493$	17.9058	+	17.9058i	0.0363200	+	0.0363200i
$494$		0			0
$495$	−21.2083	−	57.2625i	−0.0428451	−	0.115682i
$496$		0			0
$497$	138.221	+	70.4269i	0.278110	+	0.141704i
$498$		0			0
$499$			199.265i			0.399328i	0.979864	+	0.199664i	$0.0639851\pi$
$499$			199.265i			0.399328i	−0.979864	+	0.199664i	$0.936015\pi$
$500$		0			0
$501$	−99.5481			−0.198699
$502$		0			0
$503$	361.401	−	709.290i	0.718492	−	1.41012i	−0.185532	−	0.982638i	$-0.559401\pi$
$503$	361.401	−	709.290i	0.718492	−	1.41012i	0.904024	−	0.427481i	$-0.140599\pi$
$504$		0			0
$505$	−659.754	+	244.354i	−1.30644	+	0.483868i
$506$		0			0
$507$	261.034	−	261.034i	0.514860	−	0.514860i
$508$		0			0
$509$	99.1120	+	136.416i	0.194719	+	0.268008i	0.895201	−	0.445662i	$-0.147032\pi$
$509$	99.1120	+	136.416i	0.194719	+	0.268008i	−0.700482	+	0.713670i	$0.747032\pi$
$510$		0			0
$511$	477.250	+	346.742i	0.933952	+	0.678556i
$512$		0			0
$513$	−490.348	−	77.6635i	−0.955844	−	0.151391i
$514$		0			0
$515$	−21.6096	+	184.597i	−0.0419604	+	0.358441i
$516$		0			0
$517$	−98.9663	−	194.232i	−0.191424	−	0.375691i
$518$		0			0
$519$	548.255	+	178.139i	1.05637	+	0.343235i
$520$		0			0
$521$	279.151	+	859.137i	0.535798	+	1.64902i	0.741919	+	0.670490i	$0.233916\pi$
$521$	279.151	+	859.137i	0.535798	+	1.64902i	−0.206121	+	0.978526i	$0.566084\pi$
$522$		0			0
$523$	−0.893732	−	5.64280i	−0.00170886	−	0.0107893i	0.986819	−	0.161827i	$-0.0517386\pi$
$523$	−0.893732	−	5.64280i	−0.00170886	−	0.0107893i	−0.988528	+	0.151037i	$0.951739\pi$
$524$		0			0
$525$	−503.247	−	306.625i	−0.958565	−	0.584048i
$526$		0			0
$527$	−487.032	+	77.1383i	−0.924159	+	0.146372i
$528$		0			0
$529$	−854.327	+	277.588i	−1.61499	+	0.524740i
$530$		0			0
$531$	33.7428	−	103.850i	0.0635457	−	0.195574i
$532$		0			0
$533$	−587.853	+	299.526i	−1.10291	+	0.561962i
$534$		0			0
$535$	274.667	−	597.805i	0.513396	−	1.11739i
$536$		0			0
$537$	3.29338	−	20.7936i	0.00613293	−	0.0387218i
$538$		0			0
$539$	104.445	−	143.756i	0.193775	−	0.266708i
$540$		0			0
$541$	−568.079	+	412.734i	−1.05005	+	0.762909i	−0.972223	−	0.234058i	$-0.924799\pi$
$541$	−568.079	+	412.734i	−1.05005	+	0.762909i	−0.0778309	+	0.996967i	$0.524799\pi$
$542$		0			0
$543$	−193.682	−	193.682i	−0.356690	−	0.356690i
$544$		0			0
$545$	783.682	+	522.194i	1.43795	+	0.958154i
$546$		0			0
$547$	−102.294	−	52.1216i	−0.187010	−	0.0952862i	0.357979	−	0.933730i	$-0.383466\pi$
$547$	−102.294	−	52.1216i	−0.187010	−	0.0952862i	−0.544989	+	0.838443i	$0.683466\pi$
$548$		0			0
$549$			307.592i			0.560277i
$550$		0			0
$551$	26.1242			0.0474124
$552$		0			0
$553$	85.3479	−	167.505i	0.154336	−	0.302902i
$554$		0			0
$555$	98.8722	+	27.7486i	0.178148	+	0.0499975i
$556$		0			0
$557$	719.095	−	719.095i	1.29101	−	1.29101i	0.356853	−	0.934160i	$-0.383850\pi$
$557$	719.095	−	719.095i	1.29101	−	1.29101i	0.934160	−	0.356853i	$-0.116150\pi$
$558$		0			0
$559$	383.292	+	527.556i	0.685674	+	0.943749i
$560$		0			0
$561$	−158.392	−	115.079i	−0.282339	−	0.205131i
$562$		0			0
$563$	−370.346	−	58.6570i	−0.657808	−	0.104187i	−0.181398	−	0.983410i	$-0.558062\pi$
$563$	−370.346	−	58.6570i	−0.657808	−	0.104187i	−0.476410	+	0.879223i	$0.658062\pi$
$564$		0			0
$565$	−785.382	+	157.265i	−1.39006	+	0.278345i
$566$		0			0
$567$	−215.491	−	422.926i	−0.380055	−	0.745900i
$568$		0			0
$569$	648.640	+	210.756i	1.13997	+	0.370397i	0.817355	−	0.576135i	$-0.195440\pi$
$569$	648.640	+	210.756i	1.13997	+	0.370397i	0.322610	+	0.946532i	$0.395440\pi$
$570$		0			0
$571$	42.9687	+	132.244i	0.0752517	+	0.231601i	0.981606	−	0.190917i	$-0.0611462\pi$
$571$	42.9687	+	132.244i	0.0752517	+	0.231601i	−0.906354	+	0.422518i	$0.861146\pi$
$572$		0			0
$573$	−90.6822	−	572.545i	−0.158259	−	0.999206i
$574$		0			0
$575$	−719.758	−	611.560i	−1.25175	−	1.06358i
$576$		0			0
$577$	−69.5115	+	11.0095i	−0.120471	+	0.0190807i	−0.216379	−	0.976310i	$-0.569425\pi$
$577$	−69.5115	+	11.0095i	−0.120471	+	0.0190807i	0.0959080	+	0.995390i	$0.469425\pi$
$578$		0			0
$579$	601.733	−	195.515i	1.03926	−	0.337677i
$580$		0			0
$581$	−71.5028	+	220.063i	−0.123068	+	0.378766i
$582$		0			0
$583$	343.287	−	174.913i	0.588828	−	0.300023i
$584$		0			0
$585$	−168.925	−	155.754i	−0.288761	−	0.266245i
$586$		0			0
$587$	34.3351	−	216.783i	0.0584924	−	0.369307i	−0.941028	−	0.338330i	$-0.890138\pi$
$587$	34.3351	−	216.783i	0.0584924	−	0.369307i	0.999520	−	0.0309770i	$-0.00986188\pi$
$588$		0			0
$589$	−299.014	+	411.557i	−0.507664	+	0.698739i
$590$		0			0
$591$	−35.3769	+	25.7028i	−0.0598594	+	0.0434904i
$592$		0			0
$593$	−597.816	−	597.816i	−1.00812	−	1.00812i	−0.999967	−	0.00815551i	$-0.997404\pi$
$593$	−597.816	−	597.816i	−1.00812	−	1.00812i	−0.00815551	−	0.999967i	$-0.502596\pi$
$594$		0			0
$595$	762.814	−	30.9464i	1.28204	−	0.0520108i
$596$		0			0
$597$	601.740	+	306.602i	1.00794	+	0.513571i
$598$		0			0
$599$			658.191i			1.09882i	0.835554	+	0.549408i	$0.185147\pi$
$599$			658.191i			1.09882i	−0.835554	+	0.549408i	$0.814853\pi$
$600$		0			0
$601$	−350.388			−0.583009			−0.291504	−	0.956570i	$-0.594156\pi$
$601$	−350.388			−0.583009			−0.291504	+	0.956570i	$0.594156\pi$
$602$		0			0
$603$	−102.863	+	201.879i	−0.170585	+	0.334791i
$604$		0			0
$605$	306.221	+	387.422i	0.506151	+	0.640366i
$606$		0			0
$607$	−814.998	+	814.998i	−1.34266	+	1.34266i	−0.449268	+	0.893397i	$0.648315\pi$
$607$	−814.998	+	814.998i	−1.34266	+	1.34266i	−0.893397	+	0.449268i	$0.851685\pi$
$608$		0			0
$609$	21.3938	+	29.4460i	0.0351294	+	0.0483514i
$610$		0			0
$611$	−663.607	−	482.139i	−1.08610	−	0.789097i
$612$		0			0
$613$	633.098	+	100.273i	1.03279	+	0.163577i	0.649744	−	0.760153i	$-0.274876\pi$
$613$	633.098	+	100.273i	1.03279	+	0.163577i	0.383043	+	0.923731i	$0.374876\pi$
$614$		0			0
$615$	−230.528	−	410.407i	−0.374842	−	0.667329i
$616$		0			0
$617$	177.567	+	348.494i	0.287790	+	0.564820i	0.988962	−	0.148173i	$-0.0473391\pi$
$617$	177.567	+	348.494i	0.287790	+	0.564820i	−0.701171	+	0.712993i	$0.747339\pi$
$618$		0			0
$619$	−506.694	−	164.635i	−0.818569	−	0.265969i	−0.130346	−	0.991469i	$-0.541609\pi$
$619$	−506.694	−	164.635i	−0.818569	−	0.265969i	−0.688223	+	0.725499i	$0.741609\pi$
$620$		0			0
$621$	−342.572	−	1054.33i	−0.551645	−	1.69779i
$622$		0			0
$623$	98.3927	+	621.227i	0.157934	+	0.997154i
$624$		0			0
$625$	94.6181	−	617.796i	0.151389	−	0.988474i
$626$		0			0
$627$	−199.495	+	31.5968i	−0.318173	+	0.0503937i
$628$		0			0
$629$	−126.527	+	41.1110i	−0.201155	+	0.0653593i
$630$		0			0
$631$	69.5221	−	213.967i	0.110178	−	0.339092i	−0.880733	−	0.473613i	$-0.842950\pi$
$631$	69.5221	−	213.967i	0.110178	−	0.339092i	0.990911	+	0.134521i	$0.0429496\pi$
$632$		0			0
$633$	−560.353	+	285.514i	−0.885234	+	0.451049i
$634$		0			0
$635$	511.377	−	287.243i	0.805318	−	0.452351i
$636$		0			0
$637$	104.595	−	660.389i	0.164200	−	1.03672i
$638$		0			0
$639$	−25.3656	+	34.9127i	−0.0396957	+	0.0546364i
$640$		0			0
$641$	635.805	−	461.939i	0.991896	−	0.720654i	0.0315601	−	0.999502i	$-0.489952\pi$
$641$	635.805	−	461.939i	0.991896	−	0.720654i	0.960335	+	0.278848i	$0.0899524\pi$
$642$		0			0
$643$	408.621	+	408.621i	0.635491	+	0.635491i	0.949440	−	0.313949i	$-0.101652\pi$
$643$	408.621	+	408.621i	0.635491	+	0.635491i	−0.313949	+	0.949440i	$0.601652\pi$
$644$		0			0
$645$	−365.000	+	288.499i	−0.565892	+	0.447286i
$646$		0			0
$647$	730.065	+	371.987i	1.12839	+	0.574941i	0.915573	−	0.402152i	$-0.131738\pi$
$647$	730.065	+	371.987i	1.12839	+	0.574941i	0.212812	+	0.977093i	$0.431738\pi$
$648$		0			0
$649$		−	198.795i		−	0.306310i
$650$		0			0
$651$	−708.759			−1.08872
$652$		0			0
$653$	247.278	−	485.310i	0.378679	−	0.743200i	−0.620479	−	0.784223i	$-0.713062\pi$
$653$	247.278	−	485.310i	0.378679	−	0.743200i	0.999158	+	0.0410232i	$0.0130617\pi$
$654$		0			0
$655$	−35.4275	−	873.271i	−0.0540878	−	1.33324i
$656$		0			0
$657$	−116.040	+	116.040i	−0.176621	+	0.176621i
$658$		0			0
$659$	223.989	+	308.295i	0.339893	+	0.467822i	0.944410	−	0.328770i	$-0.106634\pi$
$659$	223.989	+	308.295i	0.339893	+	0.467822i	−0.604517	+	0.796592i	$0.706634\pi$
$660$		0			0
$661$	807.083	+	586.380i	1.22100	+	0.887110i	0.996183	−	0.0872901i	$-0.0278207\pi$
$661$	807.083	+	586.380i	1.22100	+	0.887110i	0.224820	+	0.974400i	$0.427821\pi$
$662$		0			0
$663$	−727.626	−	115.245i	−1.09748	−	0.173823i
$664$		0			0
$665$	533.891	−	579.042i	0.802844	−	0.870740i
$666$		0			0
$667$	26.4835	+	51.9767i	0.0397053	+	0.0779261i
$668$		0			0
$669$	136.429	+	44.3285i	0.203930	+	0.0662608i
$670$		0			0
$671$	173.047	+	532.585i	0.257895	+	0.793719i
$672$		0			0
$673$	51.8013	+	327.061i	0.0769708	+	0.485974i	0.995818	+	0.0913606i	$0.0291216\pi$
$673$	51.8013	+	327.061i	0.0769708	+	0.485974i	−0.918847	+	0.394614i	$0.870878\pi$
$674$		0			0
$675$	475.002	−	559.040i	0.703706	−	0.828207i
$676$		0			0
$677$	−95.1245	+	15.0662i	−0.140509	+	0.0222544i	−0.226293	−	0.974059i	$-0.572661\pi$
$677$	−95.1245	+	15.0662i	−0.140509	+	0.0222544i	0.0857838	+	0.996314i	$0.472661\pi$
$678$		0			0
$679$	−260.460	+	84.6287i	−0.383594	+	0.124637i
$680$		0			0
$681$	−120.684	+	371.427i	−0.177216	+	0.545414i
$682$		0			0
$683$	53.9401	−	27.4839i	0.0789753	−	0.0402399i	−0.414057	−	0.910251i	$-0.635889\pi$
$683$	53.9401	−	27.4839i	0.0789753	−	0.0402399i	0.493032	+	0.870011i	$0.335889\pi$
$684$		0			0
$685$	−59.8819	−	299.051i	−0.0874189	−	0.436571i
$686$		0			0
$687$	−33.7183	+	212.889i	−0.0490804	+	0.309882i
$688$		0			0
$689$	852.133	−	1172.86i	1.23677	−	1.70226i
$690$		0			0
$691$	−816.866	+	593.488i	−1.18215	+	0.858883i	−0.992413	−	0.122952i	$-0.960764\pi$
$691$	−816.866	+	593.488i	−1.18215	+	0.858883i	−0.189738	+	0.981835i	$0.560764\pi$
$692$		0			0
$693$	80.4023	+	80.4023i	0.116021	+	0.116021i
$694$		0			0
$695$	104.743	−	373.214i	0.150710	−	0.536999i
$696$		0			0
$697$	543.352	+	276.852i	0.779559	+	0.397205i
$698$		0			0
$699$		−	139.349i		−	0.199354i
$700$		0			0
$701$	290.914			0.414998			0.207499	−	0.978235i	$-0.433468\pi$
$701$	290.914			0.414998			0.207499	+	0.978235i	$0.433468\pi$
$702$		0			0
$703$	−62.3100	+	122.290i	−0.0886345	+	0.173955i
$704$		0			0
$705$	324.516	−	487.017i	0.460307	−	0.690805i
$706$		0			0
$707$	926.361	−	926.361i	1.31027	−	1.31027i
$708$		0			0
$709$	−710.682	−	978.170i	−1.00237	−	1.37965i	−0.923858	−	0.382735i	$-0.874982\pi$
$709$	−710.682	−	978.170i	−1.00237	−	1.37965i	−0.0785145	−	0.996913i	$-0.525018\pi$
$710$		0			0
$711$	42.3095	+	30.7396i	0.0595070	+	0.0432343i
$712$		0			0
$713$	−1121.96	−	177.701i	−1.57358	−	0.249230i
$714$		0			0
$715$	−380.114	−	174.647i	−0.531628	−	0.244261i
$716$		0			0
$717$	−17.5508	−	34.4455i	−0.0244782	−	0.0480411i
$718$		0			0
$719$	746.586	+	242.581i	1.03837	+	0.337386i	0.778093	−	0.628149i	$-0.216187\pi$
$719$	746.586	+	242.581i	1.03837	+	0.337386i	0.260274	+	0.965535i	$0.416187\pi$
$720$		0			0
$721$	−106.946	−	329.144i	−0.148329	−	0.456511i
$722$		0			0
$723$	−93.6728	−	591.427i	−0.129561	−	0.818017i
$724$		0			0
$725$	−20.0855	+	32.9651i	−0.0277041	+	0.0454691i
$726$		0			0
$727$	554.000	−	87.7449i	0.762035	−	0.120695i	0.236692	−	0.971585i	$-0.423937\pi$
$727$	554.000	−	87.7449i	0.762035	−	0.120695i	0.525344	+	0.850890i	$0.323937\pi$
$728$		0			0
$729$	761.482	−	247.421i	1.04456	−	0.339397i
$730$		0			0
$731$	186.254	−	573.232i	0.254794	−	0.784175i
$732$		0			0
$733$	−821.470	+	418.560i	−1.12070	+	0.571023i	−0.913322	−	0.407238i	$-0.866492\pi$
$733$	−821.470	+	418.560i	−1.12070	+	0.571023i	−0.207374	+	0.978262i	$0.566492\pi$
$734$		0			0
$735$	473.805	+	55.4652i	0.644632	+	0.0754629i
$736$		0			0
$737$	−64.5284	+	407.416i	−0.0875554	+	0.552803i
$738$		0			0
$739$	767.079	−	1055.79i	1.03800	−	1.42868i	0.139225	−	0.990261i	$-0.455539\pi$
$739$	767.079	−	1055.79i	1.03800	−	1.42868i	0.898771	−	0.438418i	$-0.144461\pi$
$740$		0			0
$741$	−614.867	+	446.727i	−0.829780	+	0.602871i
$742$		0			0
$743$	519.059	+	519.059i	0.698599	+	0.698599i	0.964108	−	0.265510i	$-0.0855402\pi$
$743$	519.059	+	519.059i	0.698599	+	0.698599i	−0.265510	+	0.964108i	$0.585540\pi$
$744$		0			0
$745$	−254.915	−	688.270i	−0.342167	−	0.923852i
$746$		0			0
$747$	−57.3528	−	29.2227i	−0.0767776	−	0.0391201i
$748$		0			0
$749$			1225.04i			1.63556i
$750$		0			0
$751$	404.740			0.538934			0.269467	−	0.963010i	$-0.413152\pi$
$751$	404.740			0.538934			0.269467	+	0.963010i	$0.413152\pi$
$752$		0			0
$753$	78.7327	−	154.522i	0.104559	−	0.205208i
$754$		0			0
$755$	−382.125	+	141.528i	−0.506126	+	0.187454i
$756$		0			0
$757$	167.278	−	167.278i	0.220975	−	0.220975i	−0.587934	−	0.808909i	$-0.700059\pi$
$757$	167.278	−	167.278i	0.220975	−	0.220975i	0.808909	+	0.587934i	$0.200059\pi$
$758$		0			0
$759$	−265.103	−	364.883i	−0.349279	−	0.480742i
$760$		0			0
$761$	278.142	+	202.082i	0.365496	+	0.265548i	0.755341	−	0.655332i	$-0.227471\pi$
$761$	278.142	+	202.082i	0.365496	+	0.265548i	−0.389845	+	0.920881i	$0.627471\pi$
$762$		0			0
$763$	−1731.98	−	274.319i	−2.26996	−	0.359526i
$764$		0			0
$765$	−24.6931	+	210.938i	−0.0322786	+	0.275735i
$766$		0			0
$767$	−339.598	−	666.499i	−0.442762	−	0.868969i
$768$		0			0
$769$	162.525	+	52.8077i	0.211346	+	0.0686706i	0.412777	−	0.910832i	$-0.364559\pi$
$769$	162.525	+	52.8077i	0.211346	+	0.0686706i	−0.201430	+	0.979503i	$0.564559\pi$
$770$		0			0
$771$	−9.16678	−	28.2124i	−0.0118895	−	0.0365920i
$772$		0			0
$773$	−83.1560	−	525.026i	−0.107576	−	0.679206i	−0.981256	−	0.192706i	$-0.938273\pi$
$773$	−83.1560	−	525.026i	−0.107576	−	0.679206i	0.873681	−	0.486500i	$-0.161727\pi$
$774$		0			0
$775$	−289.433	−	693.738i	−0.373462	−	0.895145i
$776$		0			0
$777$	−188.867	+	29.9136i	−0.243073	+	0.0384989i
$778$		0			0
$779$	598.332	−	194.410i	0.768077	−	0.249563i
$780$		0			0
$781$	−24.2782	+	74.7205i	−0.0310860	+	0.0956729i
$782$		0			0
$783$	−40.3706	+	20.5698i	−0.0515588	+	0.0262705i
$784$		0			0
$785$	623.382	−	1356.77i	0.794117	−	1.72837i
$786$		0			0
$787$	−59.2289	+	373.957i	−0.0752591	+	0.475167i	0.921058	+	0.389425i	$0.127326\pi$
$787$	−59.2289	+	373.957i	−0.0752591	+	0.475167i	−0.996317	+	0.0857424i	$0.972674\pi$
$788$		0			0
$789$	−137.535	+	189.301i	−0.174316	+	0.239925i
$790$		0			0
$791$	1206.63	−	876.669i	1.52545	−	1.10830i
$792$		0			0
$793$	1489.98	+	1489.98i	1.87892	+	1.87892i
$794$		0			0
$795$	860.756	+	573.551i	1.08271	+	0.721447i
$796$		0			0
$797$	−848.786	−	432.478i	−1.06498	−	0.542633i	−0.168490	−	0.985703i	$-0.553889\pi$
$797$	−848.786	−	432.478i	−1.06498	−	0.542633i	−0.896487	+	0.443071i	$0.853889\pi$
$798$		0			0
$799$			758.170i			0.948898i
$800$		0			0
$801$	−174.970			−0.218440
$802$		0			0
$803$	−135.636	+	266.201i	−0.168912	+	0.331509i
$804$		0			0
$805$	1693.29	+	475.226i	2.10347	+	0.590342i
$806$		0			0
$807$	−382.674	+	382.674i	−0.474193	+	0.474193i
$808$		0			0
$809$	427.150	+	587.922i	0.527998	+	0.726727i	0.986824	−	0.161799i	$-0.0517297\pi$
$809$	427.150	+	587.922i	0.527998	+	0.726727i	−0.458826	+	0.888526i	$0.651730\pi$
$810$		0			0
$811$	121.097	+	87.9821i	0.149318	+	0.108486i	0.659936	−	0.751322i	$-0.270583\pi$
$811$	121.097	+	87.9821i	0.149318	+	0.108486i	−0.510618	+	0.859808i	$0.670583\pi$
$812$		0			0
$813$	−967.303	−	153.206i	−1.18979	−	0.188445i
$814$		0			0
$815$	−421.002	+	84.3013i	−0.516567	+	0.103437i
$816$		0			0
$817$	−282.297	−	554.039i	−0.345529	−	0.678138i
$818$		0			0
$819$	406.913	+	132.214i	0.496842	+	0.161434i
$820$		0			0
$821$	−197.621	−	608.214i	−0.240707	−	0.740821i	−0.996313	−	0.0857943i	$-0.972657\pi$
$821$	−197.621	−	608.214i	−0.240707	−	0.740821i	0.755605	−	0.655027i	$-0.227343\pi$
$822$		0			0
$823$	−194.429	−	1227.58i	−0.236245	−	1.49159i	−0.765670	−	0.643234i	$-0.777592\pi$
$823$	−194.429	−	1227.58i	−0.236245	−	1.49159i	0.529425	−	0.848357i	$-0.322408\pi$
$824$		0			0
$825$	113.510	−	276.027i	0.137587	−	0.334579i
$826$		0			0
$827$	1115.18	−	176.628i	1.34847	−	0.213576i	0.559918	−	0.828548i	$-0.310832\pi$
$827$	1115.18	−	176.628i	1.34847	−	0.213576i	0.788549	+	0.614971i	$0.210832\pi$
$828$		0			0
$829$	655.807	−	213.085i	0.791082	−	0.257038i	0.114517	−	0.993421i	$-0.463468\pi$
$829$	655.807	−	213.085i	0.791082	−	0.257038i	0.676565	+	0.736383i	$0.263468\pi$
$830$		0			0
$831$	28.4445	−	87.5433i	0.0342293	−	0.105347i
$832$		0			0
$833$	−550.648	+	280.569i	−0.661042	+	0.336818i
$834$		0			0
$835$	144.535	+	133.265i	0.173096	+	0.159599i
$836$		0			0
$837$	138.021	−	871.432i	0.164900	−	1.04114i
$838$		0			0
$839$	−896.187	+	1233.50i	−1.06816	+	1.47020i	−0.196238	+	0.980556i	$0.562872\pi$
$839$	−896.187	+	1233.50i	−1.06816	+	1.47020i	−0.871924	+	0.489642i	$0.837128\pi$
$840$		0			0
$841$	−678.454	+	492.926i	−0.806723	+	0.586119i
$842$		0			0
$843$	308.823	+	308.823i	0.366338	+	0.366338i
$844$		0			0
$845$	−728.444	+	29.5521i	−0.862064	+	0.0349728i
$846$		0			0
$847$	−819.326	−	417.467i	−0.967327	−	0.492878i
$848$		0			0
$849$			824.938i			0.971658i
$850$		0			0
$851$	−306.476			−0.360136
$852$		0			0
$853$	405.910	−	796.644i	0.475862	−	0.933932i	−0.520907	−	0.853613i	$-0.674406\pi$
$853$	405.910	−	796.644i	0.475862	−	0.933932i	0.996769	−	0.0803183i	$-0.0255937\pi$
$854$		0			0
$855$	135.864	+	171.891i	0.158905	+	0.201042i
$856$		0			0
$857$	−302.090	+	302.090i	−0.352497	+	0.352497i	−0.861038	−	0.508541i	$-0.830185\pi$
$857$	−302.090	+	302.090i	−0.352497	+	0.352497i	0.508541	+	0.861038i	$0.330185\pi$
$858$		0			0
$859$	−623.184	−	857.740i	−0.725477	−	0.998533i	−0.999324	−	0.0367598i	$-0.988296\pi$
$859$	−623.184	−	857.740i	−0.725477	−	0.998533i	0.273847	−	0.961773i	$-0.411704\pi$
$860$		0			0
$861$	709.120	+	515.206i	0.823600	+	0.598380i
$862$		0			0
$863$	−1102.02	−	174.542i	−1.27696	−	0.202251i	−0.519126	−	0.854698i	$-0.673742\pi$
$863$	−1102.02	−	174.542i	−1.27696	−	0.202251i	−0.757834	+	0.652447i	$0.773742\pi$
$864$		0			0
$865$	−557.543	−	992.591i	−0.644559	−	1.14750i
$866$		0			0
$867$	−23.0446	−	45.2275i	−0.0265796	−	0.0521655i
$868$		0			0
$869$	90.5512	+	29.4219i	0.104202	+	0.0338571i
$870$		0			0
$871$	479.637	+	1476.17i	0.550674	+	1.69480i
$872$		0			0
$873$	−11.9179	−	75.2470i	−0.0136517	−	0.0861935i
$874$		0			0
$875$	320.191	+	1118.89i	0.365932	+	1.27873i
$876$		0			0
$877$	512.451	−	81.1642i	0.584322	−	0.0925476i	0.142727	−	0.989762i	$-0.454413\pi$
$877$	512.451	−	81.1642i	0.584322	−	0.0925476i	0.441595	+	0.897214i	$0.354413\pi$
$878$		0			0
$879$	234.396	−	76.1600i	0.266663	−	0.0866439i
$880$		0			0
$881$	116.262	−	357.816i	0.131965	−	0.406148i	−0.863140	−	0.504964i	$-0.831506\pi$
$881$	116.262	−	357.816i	0.131965	−	0.406148i	0.995106	+	0.0988164i	$0.0315056\pi$
$882$		0			0
$883$	−364.916	+	185.934i	−0.413268	+	0.210571i	−0.648247	−	0.761430i	$-0.724498\pi$
$883$	−364.916	+	185.934i	−0.413268	+	0.210571i	0.234979	+	0.972000i	$0.424498\pi$
$884$		0			0
$885$	465.314	−	261.369i	0.525779	−	0.295333i
$886$		0			0
$887$	159.924	−	1009.72i	0.180298	−	1.13835i	−0.717047	−	0.697025i	$-0.754507\pi$
$887$	159.924	−	1009.72i	0.180298	−	1.13835i	0.897345	−	0.441330i	$-0.145493\pi$
$888$		0			0
$889$	−641.958	+	883.579i	−0.722113	+	0.993903i
$890$		0			0
$891$	194.483	−	141.300i	0.218275	−	0.158586i
$892$		0			0
$893$	553.078	+	553.078i	0.619349	+	0.619349i
$894$		0			0
$895$	−32.6181	+	25.7816i	−0.0364448	+	0.0288063i
$896$		0			0
$897$	−1512.13	−	770.469i	−1.68576	−	0.858939i
$898$		0			0
$899$			46.4272i			0.0516431i
$900$		0			0
$901$	−1339.99			−1.48723
$902$		0			0
$903$	393.307	−	771.909i	0.435556	−	0.854827i
$904$		0			0
$905$	21.9271	+	540.493i	0.0242288	+	0.597230i
$906$		0			0
$907$	−113.458	+	113.458i	−0.125092	+	0.125092i	−0.766881	−	0.641789i	$-0.778192\pi$
$907$	−113.458	+	113.458i	−0.125092	+	0.125092i	0.641789	+	0.766881i	$0.278192\pi$
$908$		0			0
$909$	214.214	+	294.840i	0.235659	+	0.324356i
$910$		0			0
$911$	−1420.57	−	1032.11i	−1.55936	−	1.13294i	−0.936535	−	0.350573i	$-0.885987\pi$
$911$	−1420.57	−	1032.11i	−1.55936	−	1.13294i	−0.622820	−	0.782365i	$-0.714013\pi$
$912$		0			0
$913$	−115.745	−	18.3322i	−0.126774	−	0.0200791i
$914$		0			0
$915$	−1019.09	+	1105.27i	−1.11376	+	1.20795i
$916$		0			0
$917$	738.843	+	1450.06i	0.805718	+	1.58131i
$918$		0			0
$919$	−416.300	−	135.264i	−0.452993	−	0.147186i	0.0736296	−	0.997286i	$-0.476542\pi$
$919$	−416.300	−	135.264i	−0.452993	−	0.147186i	−0.526622	+	0.850099i	$0.676542\pi$
$920$		0			0
$921$	−217.354	−	668.946i	−0.235998	−	0.726326i
$922$		0			0
$923$	46.2464	+	291.989i	0.0501045	+	0.316347i
$924$		0			0
$925$	−106.407	−	172.649i	−0.115034	−	0.186647i
$926$		0			0
$927$	95.0898	−	15.0607i	0.102578	−	0.0162468i
$928$		0			0
$929$	−1302.45	+	423.191i	−1.40199	+	0.455534i	−0.909833	−	0.414974i	$-0.863791\pi$
$929$	−1302.45	+	423.191i	−1.40199	+	0.455534i	−0.492155	+	0.870507i	$0.663791\pi$
$930$		0			0
$931$	−197.020	+	606.366i	−0.211622	+	0.651306i
$932$		0			0
$933$	542.399	−	276.366i	0.581349	−	0.296212i
$934$		0			0
$935$	75.9156	+	379.124i	0.0811932	+	0.405480i
$936$		0			0
$937$	−197.372	+	1246.16i	−0.210642	+	1.32994i	0.624981	+	0.780640i	$0.285107\pi$
$937$	−197.372	+	1246.16i	−0.210642	+	1.32994i	−0.835623	+	0.549303i	$0.814893\pi$
$938$		0			0
$939$	−306.799	+	422.272i	−0.326729	+	0.449704i
$940$		0			0
$941$	37.6478	−	27.3527i	0.0400083	−	0.0290677i	−0.567601	−	0.823303i	$-0.692129\pi$
$941$	37.6478	−	27.3527i	0.0400083	−	0.0290677i	0.607610	+	0.794236i	$0.292129\pi$
$942$		0			0
$943$	993.358	+	993.358i	1.05340	+	1.05340i
$944$		0			0
$945$	−369.110	+	1315.19i	−0.390593	+	1.39174i
$946$		0			0
$947$	1144.07	+	582.931i	1.20809	+	0.615555i	0.937784	−	0.347218i	$-0.112874\pi$
$947$	1144.07	+	582.931i	1.20809	+	0.615555i	0.270310	+	0.962773i	$0.412874\pi$
$948$		0			0
$949$			1124.20i			1.18461i
$950$		0			0
$951$	−87.6306			−0.0921458
$952$		0			0
$953$	−210.075	+	412.296i	−0.220436	+	0.432630i	−0.974568	−	0.224093i	$-0.928058\pi$
$953$	−210.075	+	412.296i	−0.220436	+	0.432630i	0.754132	+	0.656723i	$0.228058\pi$
$954$		0			0
$955$	−634.804	+	952.681i	−0.664716	+	0.997572i
$956$		0			0
$957$	−13.0345	+	13.0345i	−0.0136202	+	0.0136202i
$958$		0			0
$959$	333.811	+	459.451i	0.348082	+	0.479094i
$960$		0			0
$961$	46.0580	+	33.4631i	0.0479272	+	0.0348211i
$962$		0			0
$963$	−336.591	−	53.3108i	−0.349524	−	0.0553591i
$964$		0			0
$965$	−1135.40	−	521.670i	−1.17658	−	0.540591i
$966$		0			0
$967$	331.668	+	650.934i	0.342986	+	0.673148i	0.996484	−	0.0837799i	$-0.0266993\pi$
$967$	331.668	+	650.934i	0.342986	+	0.673148i	−0.653498	+	0.756928i	$0.726699\pi$
$968$		0			0
$969$	668.103	+	217.080i	0.689476	+	0.224024i
$970$		0			0
$971$	−48.6355	−	149.685i	−0.0500880	−	0.154155i	0.922884	−	0.385078i	$-0.125825\pi$
$971$	−48.6355	−	149.685i	−0.0500880	−	0.154155i	−0.972972	+	0.230923i	$0.925825\pi$
$972$		0			0
$973$	112.916	+	712.921i	0.116049	+	0.732704i
$974$		0			0
$975$	−90.9702	−	1119.34i	−0.0933027	−	1.14804i
$976$		0			0
$977$	82.4828	−	13.0640i	0.0844245	−	0.0133715i	−0.114079	−	0.993472i	$-0.536392\pi$
$977$	82.4828	−	13.0640i	0.0844245	−	0.0133715i	0.198504	+	0.980100i	$0.436392\pi$
$978$		0			0
$979$	−302.955	+	98.4361i	−0.309454	+	0.100548i
$980$		0			0
$981$	150.744	−	463.941i	0.153663	−	0.472927i
$982$		0			0
$983$	150.200	−	76.5307i	0.152798	−	0.0778543i	−0.375920	−	0.926652i	$-0.622673\pi$
$983$	150.200	−	76.5307i	0.152798	−	0.0778543i	0.528717	+	0.848798i	$0.322673\pi$
$984$		0			0
$985$	85.7725	+	10.0408i	0.0870787	+	0.0101937i
$986$		0			0
$987$	−170.475	+	1076.33i	−0.172720	+	1.09051i
$988$		0			0
$989$	816.136	−	1123.31i	0.825213	−	1.13581i
$990$		0			0
$991$	−269.381	+	195.717i	−0.271827	+	0.197494i	−0.715345	−	0.698772i	$-0.753730\pi$
$991$	−269.381	+	195.717i	−0.271827	+	0.197494i	0.443517	+	0.896266i	$0.353730\pi$
$992$		0			0
$993$	44.4867	+	44.4867i	0.0448003	+	0.0448003i
$994$		0			0
$995$	−463.225	−	1250.71i	−0.465553	−	1.25699i
$996$		0			0
$997$	−817.923	−	416.752i	−0.820384	−	0.418006i	−0.00717202	−	0.999974i	$-0.502283\pi$
$997$	−817.923	−	416.752i	−0.820384	−	0.418006i	−0.813212	+	0.581968i	$0.802283\pi$
$998$		0			0
$999$		−	238.041i		−	0.238279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.a.113.2		16
4.3	odd	2		50.3.f.a.13.1	✓	16
20.3	even	4		250.3.f.c.207.1		16
20.7	even	4		250.3.f.a.207.2		16
20.19	odd	2		250.3.f.b.43.2		16
25.2	odd	20	inner	400.3.bg.a.177.2		16
100.11	odd	10		250.3.f.a.93.2		16
100.23	even	20		250.3.f.b.157.2		16
100.27	even	20		50.3.f.a.27.1	yes	16
100.39	odd	10		250.3.f.c.93.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.13.1	✓	16	4.3	odd	2
50.3.f.a.27.1	yes	16	100.27	even	20
250.3.f.a.93.2		16	100.11	odd	10
250.3.f.a.207.2		16	20.7	even	4
250.3.f.b.43.2		16	20.19	odd	2
250.3.f.b.157.2		16	100.23	even	20
250.3.f.c.93.1		16	100.39	odd	10
250.3.f.c.207.1		16	20.3	even	4
400.3.bg.a.113.2		16	1.1	even	1	trivial
400.3.bg.a.177.2		16	25.2	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)

\(f(q)\)	\(=\)	\(q+(1.14941 - 2.25584i) q^{3} +(-4.68874 + 1.73657i) q^{5} +(6.58346 - 6.58346i) q^{7} +(1.52238 + 2.09537i) q^{9} +O(q^{10})\)	\(q+(1.14941 - 2.25584i) q^{3} +(-4.68874 + 1.73657i) q^{5} +(6.58346 - 6.58346i) q^{7} +(1.52238 + 2.09537i) q^{9} +(3.81477 + 2.77159i) q^{11} +(17.5244 + 2.77559i) q^{13} +(-1.47185 + 12.5731i) q^{15} +(-7.44532 - 14.6123i) q^{17} +(-16.0908 - 5.22822i) q^{19} +(-7.28417 - 22.4184i) q^{21} +(-5.91002 - 37.3144i) q^{23} +(18.9686 - 16.2847i) q^{25} +(28.9823 - 4.59034i) q^{27} +(-1.46851 + 0.477149i) q^{29} +(9.29144 - 28.5961i) q^{31} +(10.6370 - 5.41983i) q^{33} +(-19.4355 + 42.3008i) q^{35} +(1.26903 - 8.01234i) q^{37} +(26.4040 - 36.3420i) q^{39} +(-30.0830 + 21.8566i) q^{41} +(25.9880 + 25.9880i) q^{43} +(-10.7768 - 7.18094i) q^{45} +(-41.1918 - 20.9883i) q^{47} -37.6840i q^{49} -41.5207 q^{51} +(37.0947 - 72.8025i) q^{53} +(-22.6996 - 6.37067i) q^{55} +(-30.2890 + 30.2890i) q^{57} +(-24.7807 - 34.1077i) q^{59} +(96.0793 + 69.8057i) q^{61} +(23.8173 + 3.77229i) q^{63} +(-86.9875 + 17.4184i) q^{65} +(39.7150 + 77.9450i) q^{67} +(-90.9685 - 29.5575i) q^{69} +(5.14879 + 15.8463i) q^{71} +(9.91177 + 62.5804i) q^{73} +(-14.9330 - 61.5081i) q^{75} +(43.3611 - 6.86772i) q^{77} +(19.2036 - 6.23964i) q^{79} +(15.7542 - 48.4864i) q^{81} +(-22.1438 + 11.2828i) q^{83} +(60.2844 + 55.5838i) q^{85} +(-0.611550 + 3.86118i) q^{87} +(-39.7082 + 54.6536i) q^{89} +(133.644 - 97.0982i) q^{91} +(-53.8287 - 53.8287i) q^{93} +(84.5249 - 3.42907i) q^{95} +(-26.2088 - 13.3540i) q^{97} +12.2128i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Introduction

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