LMFDB - Embedded newform 400.2.y.d.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, degree $4$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.5
Character	$\chi$	$=$	400.289
Dual form			400.2.y.d.209.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.685617 + 0.222770i) q^{3} +(-2.21883 + 0.277142i) q^{5} +4.42421i q^{7} +(-2.00661 - 1.45789i) q^{9} +O(q^{10})$	\(q+(0.685617 + 0.222770i) q^{3} +(-2.21883 + 0.277142i) q^{5} +4.42421i q^{7} +(-2.00661 - 1.45789i) q^{9} +(-3.36456 + 2.44449i) q^{11} +(0.592198 - 0.815091i) q^{13} +(-1.58300 - 0.304276i) q^{15} +(-3.49650 + 1.13608i) q^{17} +(-0.865323 - 2.66319i) q^{19} +(-0.985584 + 3.03332i) q^{21} +(4.41940 + 6.08278i) q^{23} +(4.84638 - 1.22986i) q^{25} +(-2.32219 - 3.19622i) q^{27} +(-2.81461 + 8.66249i) q^{29} +(0.593581 + 1.82685i) q^{31} +(-2.85136 + 0.926462i) q^{33} +(-1.22613 - 9.81657i) q^{35} +(5.77680 - 7.95108i) q^{37} +(0.587599 - 0.426916i) q^{39} +(6.62927 + 4.81644i) q^{41} +2.12609i q^{43} +(4.85636 + 2.67868i) q^{45} +(-4.17988 - 1.35813i) q^{47} -12.5737 q^{49} -2.65035 q^{51} +(-0.585317 - 0.190181i) q^{53} +(6.78790 - 6.35637i) q^{55} -2.01870i q^{57} +(-2.72648 - 1.98090i) q^{59} +(5.75438 - 4.18080i) q^{61} +(6.45000 - 8.87766i) q^{63} +(-1.08809 + 1.97267i) q^{65} +(1.37620 - 0.447154i) q^{67} +(1.67495 + 5.15497i) q^{69} +(-1.05084 + 3.23416i) q^{71} +(0.838758 + 1.15445i) q^{73} +(3.59674 + 0.236419i) q^{75} +(-10.8150 - 14.8855i) q^{77} +(-4.38778 + 13.5042i) q^{79} +(1.41926 + 4.36802i) q^{81} +(-1.70127 + 0.552776i) q^{83} +(7.44328 - 3.48980i) q^{85} +(-3.85949 + 5.31213i) q^{87} +(9.97574 - 7.24780i) q^{89} +(3.60614 + 2.62001i) q^{91} +1.38475i q^{93} +(2.65808 + 5.66934i) q^{95} +(4.35975 + 1.41657i) q^{97} +10.3151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 32 * q + 2 * q^5 + 10 * q^9	$ 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53} + 28 q^{55} + 30 q^{59} + 14 q^{61} + 20 q^{63} - 26 q^{65} - 4 q^{69} - 12 q^{71} + 40 q^{73} - 16 q^{75} - 16 q^{79} - 52 q^{81} - 30 q^{83} + 60 q^{85} - 110 q^{87} + 24 q^{89} + 4 q^{91} - 68 q^{95} + 30 q^{97} - 92 q^{99}+O(q^{100}) $ 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.685617	+	0.222770i	0.395841	+	0.128617i	0.500172	−	0.865926i	$-0.333270\pi$
$3$	0.685617	+	0.222770i	0.395841	+	0.128617i	−0.104331	+	0.994543i	$0.533270\pi$
$4$		0			0
$5$	−2.21883	+	0.277142i	−0.992290	+	0.123942i
$5$	−2.21883	+	0.277142i	−0.992290	+	0.123942i
$6$		0			0
$7$			4.42421i			1.67220i	0.548580	+	0.836098i	$0.315169\pi$
$7$			4.42421i			1.67220i	−0.548580	+	0.836098i	$0.684831\pi$
$8$		0			0
$9$	−2.00661	−	1.45789i	−0.668869	−	0.485962i
$10$		0			0
$11$	−3.36456	+	2.44449i	−1.01445	+	0.737043i	−0.965138	−	0.261741i	$-0.915704\pi$
$11$	−3.36456	+	2.44449i	−1.01445	+	0.737043i	−0.0493141	+	0.998783i	$0.515704\pi$
$12$		0			0
$13$	0.592198	−	0.815091i	0.164246	−	0.226066i	−0.718959	−	0.695053i	$-0.755381\pi$
$13$	0.592198	−	0.815091i	0.164246	−	0.226066i	0.883205	+	0.468987i	$0.155381\pi$
$14$		0			0
$15$	−1.58300	−	0.304276i	−0.408730	−	0.0785637i
$16$		0			0
$17$	−3.49650	+	1.13608i	−0.848027	+	0.275541i	−0.700619	−	0.713535i	$-0.747093\pi$
$17$	−3.49650	+	1.13608i	−0.848027	+	0.275541i	−0.147407	+	0.989076i	$0.547093\pi$
$18$		0			0
$19$	−0.865323	−	2.66319i	−0.198519	−	0.610978i	−0.999917	−	0.0128475i	$-0.995910\pi$
$19$	−0.865323	−	2.66319i	−0.198519	−	0.610978i	0.801399	−	0.598131i	$-0.204090\pi$
$20$		0			0
$21$	−0.985584	+	3.03332i	−0.215072	+	0.661924i
$22$		0			0
$23$	4.41940	+	6.08278i	0.921508	+	1.26835i	0.963081	+	0.269212i	$0.0867632\pi$
$23$	4.41940	+	6.08278i	0.921508	+	1.26835i	−0.0415726	+	0.999135i	$0.513237\pi$
$24$		0			0
$25$	4.84638	−	1.22986i	0.969277	−	0.245972i
$26$		0			0
$27$	−2.32219	−	3.19622i	−0.446906	−	0.615114i
$28$		0			0
$29$	−2.81461	+	8.66249i	−0.522660	+	1.60858i	0.246236	+	0.969210i	$0.420806\pi$
$29$	−2.81461	+	8.66249i	−0.522660	+	1.60858i	−0.768896	+	0.639374i	$0.779194\pi$
$30$		0			0
$31$	0.593581	+	1.82685i	0.106610	+	0.328113i	0.990105	−	0.140328i	$-0.0448158\pi$
$31$	0.593581	+	1.82685i	0.106610	+	0.328113i	−0.883495	+	0.468441i	$0.844816\pi$
$32$		0			0
$33$	−2.85136	+	0.926462i	−0.496358	+	0.161276i
$34$		0			0
$35$	−1.22613	−	9.81657i	−0.207255	−	1.65930i
$36$		0			0
$37$	5.77680	−	7.95108i	0.949700	−	1.30715i	−0.00196066	−	0.999998i	$-0.500624\pi$
$37$	5.77680	−	7.95108i	0.949700	−	1.30715i	0.951661	−	0.307152i	$-0.0993759\pi$
$38$		0			0
$39$	0.587599	−	0.426916i	0.0940912	−	0.0683612i
$40$		0			0
$41$	6.62927	+	4.81644i	1.03532	+	0.752202i	0.969366	−	0.245621i	$-0.0789918\pi$
$41$	6.62927	+	4.81644i	1.03532	+	0.752202i	0.0659514	+	0.997823i	$0.478992\pi$
$42$		0			0
$43$			2.12609i			0.324225i	0.986772	+	0.162113i	$0.0518308\pi$
$43$			2.12609i			0.324225i	−0.986772	+	0.162113i	$0.948169\pi$
$44$		0			0
$45$	4.85636	+	2.67868i	0.723943	+	0.399314i
$46$		0			0
$47$	−4.17988	−	1.35813i	−0.609699	−	0.198103i	−0.0121375	−	0.999926i	$-0.503864\pi$
$47$	−4.17988	−	1.35813i	−0.609699	−	0.198103i	−0.597561	+	0.801823i	$0.703864\pi$
$48$		0			0
$49$	−12.5737			−1.79624
$50$		0			0
$51$	−2.65035			−0.371123
$52$		0			0
$53$	−0.585317	−	0.190181i	−0.0803994	−	0.0261234i	0.268541	−	0.963268i	$-0.413458\pi$
$53$	−0.585317	−	0.190181i	−0.0803994	−	0.0261234i	−0.348941	+	0.937145i	$0.613458\pi$
$54$		0			0
$55$	6.78790	−	6.35637i	0.915280	−	0.857093i
$56$		0			0
$57$		−	2.01870i		−	0.267383i
$58$		0			0
$59$	−2.72648	−	1.98090i	−0.354957	−	0.257891i	0.395989	−	0.918255i	$-0.370402\pi$
$59$	−2.72648	−	1.98090i	−0.354957	−	0.257891i	−0.750946	+	0.660364i	$0.770402\pi$
$60$		0			0
$61$	5.75438	−	4.18080i	0.736773	−	0.535297i	−0.154926	−	0.987926i	$-0.549514\pi$
$61$	5.75438	−	4.18080i	0.736773	−	0.535297i	0.891699	+	0.452629i	$0.149514\pi$
$62$		0			0
$63$	6.45000	−	8.87766i	0.812623	−	1.11848i
$64$		0			0
$65$	−1.08809	+	1.97267i	−0.134961	+	0.244679i
$66$		0			0
$67$	1.37620	−	0.447154i	0.168130	−	0.0546286i	−0.223743	−	0.974648i	$-0.571828\pi$
$67$	1.37620	−	0.447154i	0.168130	−	0.0546286i	0.391872	+	0.920020i	$0.371828\pi$
$68$		0			0
$69$	1.67495	+	5.15497i	0.201640	+	0.620585i
$70$		0			0
$71$	−1.05084	+	3.23416i	−0.124712	+	0.383824i	−0.993848	−	0.110748i	$-0.964675\pi$
$71$	−1.05084	+	3.23416i	−0.124712	+	0.383824i	0.869137	+	0.494572i	$0.164675\pi$
$72$		0			0
$73$	0.838758	+	1.15445i	0.0981692	+	0.135118i	0.855276	−	0.518173i	$-0.173388\pi$
$73$	0.838758	+	1.15445i	0.0981692	+	0.135118i	−0.757107	+	0.653291i	$0.773388\pi$
$74$		0			0
$75$	3.59674	+	0.236419i	0.415316	+	0.0272993i
$76$		0			0
$77$	−10.8150	−	14.8855i	−1.23248	−	1.69636i
$78$		0			0
$79$	−4.38778	+	13.5042i	−0.493663	+	1.51934i	0.325366	+	0.945588i	$0.394512\pi$
$79$	−4.38778	+	13.5042i	−0.493663	+	1.51934i	−0.819030	+	0.573751i	$0.805488\pi$
$80$		0			0
$81$	1.41926	+	4.36802i	0.157695	+	0.485336i
$82$		0			0
$83$	−1.70127	+	0.552776i	−0.186739	+	0.0606750i	−0.400894	−	0.916125i	$-0.631300\pi$
$83$	−1.70127	+	0.552776i	−0.186739	+	0.0606750i	0.214155	+	0.976800i	$0.431300\pi$
$84$		0			0
$85$	7.44328	−	3.48980i	0.807337	−	0.378522i
$86$		0			0
$87$	−3.85949	+	5.31213i	−0.413781	+	0.569521i
$88$		0			0
$89$	9.97574	−	7.24780i	1.05743	−	0.768265i	0.0838161	−	0.996481i	$-0.473289\pi$
$89$	9.97574	−	7.24780i	1.05743	−	0.768265i	0.973611	+	0.228216i	$0.0732892\pi$
$90$		0			0
$91$	3.60614	+	2.62001i	0.378026	+	0.274652i
$92$		0			0
$93$			1.38475i			0.143592i
$94$		0			0
$95$	2.65808	+	5.66934i	0.272714	+	0.581662i
$96$		0			0
$97$	4.35975	+	1.41657i	0.442665	+	0.143831i	0.521865	−	0.853028i	$-0.325237\pi$
$97$	4.35975	+	1.41657i	0.442665	+	0.143831i	−0.0791998	+	0.996859i	$0.525237\pi$
$98$		0			0
$99$	10.3151			1.03671
$100$		0			0
$101$	−5.03284			−0.500787			−0.250393	−	0.968144i	$-0.580560\pi$
$101$	−5.03284			−0.500787			−0.250393	+	0.968144i	$0.580560\pi$
$102$		0			0
$103$	10.7744	+	3.50080i	1.06163	+	0.344944i	0.787223	−	0.616669i	$-0.211518\pi$
$103$	10.7744	+	3.50080i	1.06163	+	0.344944i	0.274407	+	0.961614i	$0.411518\pi$
$104$		0			0
$105$	1.34618	−	7.00355i	0.131374	−	0.683476i
$106$		0			0
$107$		−	14.0443i		−	1.35771i	−0.734272	−	0.678855i	$-0.762476\pi$
$107$		−	14.0443i		−	1.35771i	0.734272	−	0.678855i	$-0.237524\pi$
$108$		0			0
$109$	−6.92174	−	5.02894i	−0.662982	−	0.481685i	0.204686	−	0.978828i	$-0.434383\pi$
$109$	−6.92174	−	5.02894i	−0.662982	−	0.481685i	−0.867669	+	0.497143i	$0.834383\pi$
$110$		0			0
$111$	5.73194	−	4.16449i	0.544051	−	0.395276i
$112$		0			0
$113$	7.52597	−	10.3586i	0.707983	−	0.974455i	−0.291855	−	0.956463i	$-0.594272\pi$
$113$	7.52597	−	10.3586i	0.707983	−	0.974455i	0.999838	−	0.0179927i	$-0.00572758\pi$
$114$		0			0
$115$	−11.4917	−	12.2718i	−1.07160	−	1.14435i
$116$		0			0
$117$	−2.37662	+	0.772210i	−0.219719	+	0.0713909i
$118$		0			0
$119$	−5.02627	−	15.4693i	−0.460758	−	1.41807i
$120$		0			0
$121$	1.94551	−	5.98766i	0.176865	−	0.544333i
$122$		0			0
$123$	3.47217	+	4.77904i	0.313075	+	0.430911i
$124$		0			0
$125$	−10.4124	+	4.07198i	−0.931317	+	0.364209i
$126$		0			0
$127$	2.61259	+	3.59592i	0.231830	+	0.319086i	0.909044	−	0.416699i	$-0.136813\pi$
$127$	2.61259	+	3.59592i	0.231830	+	0.319086i	−0.677215	+	0.735786i	$0.736813\pi$
$128$		0			0
$129$	−0.473629	+	1.45768i	−0.0417008	+	0.128342i
$130$		0			0
$131$	2.52014	+	7.75620i	0.220186	+	0.677662i	0.998745	+	0.0500906i	$0.0159510\pi$
$131$	2.52014	+	7.75620i	0.220186	+	0.677662i	−0.778559	+	0.627572i	$0.784049\pi$
$132$		0			0
$133$	11.7825	−	3.82838i	1.02168	−	0.331962i
$134$		0			0
$135$	6.03835	+	6.44829i	0.519699	+	0.554981i
$136$		0			0
$137$	−0.159116	+	0.219004i	−0.0135942	+	0.0187108i	−0.815760	−	0.578391i	$-0.803681\pi$
$137$	−0.159116	+	0.219004i	−0.0135942	+	0.0187108i	0.802166	+	0.597101i	$0.203681\pi$
$138$		0			0
$139$	−7.81604	+	5.67869i	−0.662948	+	0.481660i	−0.867657	−	0.497163i	$-0.834375\pi$
$139$	−7.81604	+	5.67869i	−0.662948	+	0.481660i	0.204709	+	0.978823i	$0.434375\pi$
$140$		0			0
$141$	−2.56325	−	1.86231i	−0.215864	−	0.156835i
$142$		0			0
$143$			4.19005i			0.350389i
$144$		0			0
$145$	3.84440	−	20.0006i	0.319260	−	1.66096i
$146$		0			0
$147$	−8.62072	−	2.80104i	−0.711025	−	0.231026i
$148$		0			0
$149$	−11.3569			−0.930397			−0.465198	−	0.885206i	$-0.654017\pi$
$149$	−11.3569			−0.930397			−0.465198	+	0.885206i	$0.654017\pi$
$150$		0			0
$151$	−10.8642			−0.884114			−0.442057	−	0.896987i	$-0.645751\pi$
$151$	−10.8642			−0.884114			−0.442057	+	0.896987i	$0.645751\pi$
$152$		0			0
$153$	8.67239	+	2.81783i	0.701121	+	0.227808i
$154$		0			0
$155$	−1.82335	−	3.88897i	−0.146455	−	0.312369i
$156$		0			0
$157$			21.5721i			1.72164i	0.508912	+	0.860819i	$0.330048\pi$
$157$			21.5721i			1.72164i	−0.508912	+	0.860819i	$0.669952\pi$
$158$		0			0
$159$	−0.358936	−	0.260782i	−0.0284655	−	0.0206814i
$160$		0			0
$161$	−26.9115	+	19.5524i	−2.12093	+	1.54094i
$162$		0			0
$163$	5.70694	−	7.85493i	0.447002	−	0.615245i	−0.524748	−	0.851257i	$-0.675841\pi$
$163$	5.70694	−	7.85493i	0.447002	−	0.615245i	0.971750	+	0.236012i	$0.0758405\pi$
$164$		0			0
$165$	6.06991	−	2.84589i	0.472542	−	0.221552i
$166$		0			0
$167$	−0.699115	+	0.227156i	−0.0540992	+	0.0175779i	−0.335942	−	0.941883i	$-0.609054\pi$
$167$	−0.699115	+	0.227156i	−0.0540992	+	0.0175779i	0.281842	+	0.959461i	$0.409054\pi$
$168$		0			0
$169$	3.70355	+	11.3983i	0.284888	+	0.876796i
$170$		0			0
$171$	−2.14626	+	6.60552i	−0.164129	+	0.505137i
$172$		0			0
$173$	8.15995	+	11.2312i	0.620389	+	0.853893i	0.997381	−	0.0723239i	$-0.0230415\pi$
$173$	8.15995	+	11.2312i	0.620389	+	0.853893i	−0.376992	+	0.926217i	$0.623042\pi$
$174$		0			0
$175$	5.44116	+	21.4414i	0.411313	+	1.62082i
$176$		0			0
$177$	−1.42803	−	1.96552i	−0.107337	−	0.147737i
$178$		0			0
$179$	−1.22860	+	3.78123i	−0.0918297	+	0.282623i	−0.986414	−	0.164276i	$-0.947471\pi$
$179$	−1.22860	+	3.78123i	−0.0918297	+	0.282623i	0.894585	+	0.446898i	$0.147471\pi$
$180$		0			0
$181$	4.32651	+	13.3156i	0.321587	+	0.989742i	0.972958	+	0.230983i	$0.0741941\pi$
$181$	4.32651	+	13.3156i	0.321587	+	0.989742i	−0.651371	+	0.758759i	$0.725806\pi$
$182$		0			0
$183$	4.87666	−	1.58452i	0.360493	−	0.117131i
$184$		0			0
$185$	−10.6141	+	19.2431i	−0.780367	+	1.41478i
$186$		0			0
$187$	8.98704	−	12.3696i	0.657197	−	0.904555i
$188$		0			0
$189$	14.1408	−	10.2739i	1.02859	−	0.747315i
$190$		0			0
$191$	6.65895	+	4.83801i	0.481825	+	0.350066i	0.802032	−	0.597281i	$-0.203752\pi$
$191$	6.65895	+	4.83801i	0.481825	+	0.350066i	−0.320207	+	0.947348i	$0.603752\pi$
$192$		0			0
$193$			18.3340i			1.31971i	0.751392	+	0.659856i	$0.229383\pi$
$193$			18.3340i			1.31971i	−0.751392	+	0.659856i	$0.770617\pi$
$194$		0			0
$195$	−1.18546	+	1.11010i	−0.0848929	+	0.0794960i
$196$		0			0
$197$	−4.25891	−	1.38380i	−0.303435	−	0.0985919i	0.153342	−	0.988173i	$-0.450996\pi$
$197$	−4.25891	−	1.38380i	−0.303435	−	0.0985919i	−0.456777	+	0.889581i	$0.650996\pi$
$198$		0			0
$199$	−15.8157			−1.12114			−0.560572	−	0.828106i	$-0.689419\pi$
$199$	−15.8157			−1.12114			−0.560572	+	0.828106i	$0.689419\pi$
$200$		0			0
$201$	1.04316			0.0735787
$202$		0			0
$203$	−38.3247	−	12.4525i	−2.68987	−	0.873991i
$204$		0			0
$205$	−16.0440	−	8.84961i	−1.12056	−	0.618083i
$206$		0			0
$207$		−	18.6487i		−	1.29618i
$208$		0			0
$209$	9.42159	+	6.84518i	0.651705	+	0.473491i
$210$		0			0
$211$	−8.90363	+	6.46887i	−0.612951	+	0.445335i	−0.850452	−	0.526052i	$-0.823672\pi$
$211$	−8.90363	+	6.46887i	−0.612951	+	0.445335i	0.237501	+	0.971387i	$0.423672\pi$
$212$		0			0
$213$	−1.44095	+	1.98330i	−0.0987321	+	0.135893i
$214$		0			0
$215$	−0.589228	−	4.71742i	−0.0401850	−	0.321726i
$216$		0			0
$217$	−8.08239	+	2.62613i	−0.548669	+	0.178273i
$218$		0			0
$219$	0.317889	+	0.978361i	0.0214809	+	0.0661115i
$220$		0			0
$221$	−1.14461	+	3.52276i	−0.0769950	+	0.236966i
$222$		0			0
$223$	−6.43657	−	8.85918i	−0.431024	−	0.593254i	0.537164	−	0.843478i	$-0.319496\pi$
$223$	−6.43657	−	8.85918i	−0.431024	−	0.593254i	−0.968188	+	0.250224i	$0.919496\pi$
$224$		0			0
$225$	−11.5178	−	4.59763i	−0.767852	−	0.306509i
$226$		0			0
$227$	9.47239	+	13.0376i	0.628705	+	0.865338i	0.997950	−	0.0639942i	$-0.0203839\pi$
$227$	9.47239	+	13.0376i	0.628705	+	0.865338i	−0.369246	+	0.929332i	$0.620384\pi$
$228$		0			0
$229$	3.59538	−	11.0654i	0.237589	−	0.731225i	−0.759178	−	0.650883i	$-0.774399\pi$
$229$	3.59538	−	11.0654i	0.237589	−	0.731225i	0.996767	−	0.0803416i	$-0.0256011\pi$
$230$		0			0
$231$	−4.09887	−	12.6150i	−0.269686	−	0.830007i
$232$		0			0
$233$	−1.19209	+	0.387335i	−0.0780966	+	0.0253751i	−0.347805	−	0.937567i	$-0.613073\pi$
$233$	−1.19209	+	0.387335i	−0.0780966	+	0.0253751i	0.269708	+	0.962942i	$0.413073\pi$
$234$		0			0
$235$	9.65083	+	1.85503i	0.629551	+	0.121009i
$236$		0			0
$237$	−6.01666	+	8.28123i	−0.390824	+	0.537924i
$238$		0			0
$239$	−24.6435	+	17.9046i	−1.59406	+	1.15815i	−0.696212	+	0.717837i	$0.745132\pi$
$239$	−24.6435	+	17.9046i	−1.59406	+	1.15815i	−0.897844	+	0.440313i	$0.854868\pi$
$240$		0			0
$241$	−7.63923	−	5.55022i	−0.492086	−	0.357521i	0.313900	−	0.949456i	$-0.398364\pi$
$241$	−7.63923	−	5.55022i	−0.492086	−	0.357521i	−0.805986	+	0.591935i	$0.798364\pi$
$242$		0			0
$243$			15.1632i			0.972720i
$244$		0			0
$245$	27.8988	−	3.48469i	1.78239	−	0.222629i
$246$		0			0
$247$	−2.68319	−	0.871820i	−0.170727	−	0.0554726i
$248$		0			0
$249$	−1.28956			−0.0817226
$250$		0			0
$251$	28.8744			1.82254			0.911268	−	0.411814i	$-0.135105\pi$
$251$	28.8744			1.82254			0.911268	+	0.411814i	$0.135105\pi$
$252$		0			0
$253$	−29.7386	−	9.66267i	−1.86965	−	0.607487i
$254$		0			0
$255$	5.88066	−	0.734522i	0.368261	−	0.0459975i
$256$		0			0
$257$		−	9.55064i		−	0.595753i	−0.954604	−	0.297876i	$-0.903722\pi$
$257$		−	9.55064i		−	0.595753i	0.954604	−	0.297876i	$-0.0962783\pi$
$258$		0			0
$259$	35.1773	+	25.5578i	2.18581	+	1.58808i
$260$		0			0
$261$	18.2767	−	13.2788i	1.13130	−	0.821939i
$262$		0			0
$263$	−0.221496	+	0.304863i	−0.0136580	+	0.0187986i	−0.815791	−	0.578346i	$-0.803698\pi$
$263$	−0.221496	+	0.304863i	−0.0136580	+	0.0187986i	0.802133	+	0.597145i	$0.203698\pi$
$264$		0			0
$265$	1.35142	+	0.259763i	0.0830173	+	0.0159571i
$266$		0			0
$267$	8.45413	−	2.74691i	0.517384	−	0.168108i
$268$		0			0
$269$	0.798313	+	2.45696i	0.0486740	+	0.149803i	0.972439	−	0.233156i	$-0.0749051\pi$
$269$	0.798313	+	2.45696i	0.0486740	+	0.149803i	−0.923765	+	0.382959i	$0.874905\pi$
$270$		0			0
$271$	9.84426	−	30.2975i	0.597996	−	1.84044i	0.0587871	−	0.998271i	$-0.481277\pi$
$271$	9.84426	−	30.2975i	0.597996	−	1.84044i	0.539209	−	0.842172i	$-0.318723\pi$
$272$		0			0
$273$	1.88877	+	2.59967i	0.114313	+	0.157339i
$274$		0			0
$275$	−13.2996	+	15.9849i	−0.801994	+	0.963925i
$276$		0			0
$277$	12.0904	+	16.6410i	0.726440	+	0.999859i	0.999285	+	0.0378009i	$0.0120353\pi$
$277$	12.0904	+	16.6410i	0.726440	+	0.999859i	−0.272845	+	0.962058i	$0.587965\pi$
$278$		0			0
$279$	1.47226	−	4.53115i	0.0881419	−	0.271273i
$280$		0			0
$281$	−8.05965	−	24.8051i	−0.480798	−	1.47975i	−0.837975	−	0.545709i	$-0.816261\pi$
$281$	−8.05965	−	24.8051i	−0.480798	−	1.47975i	0.357177	−	0.934037i	$-0.383739\pi$
$282$		0			0
$283$	−14.4464	+	4.69390i	−0.858747	+	0.279024i	−0.705105	−	0.709103i	$-0.749100\pi$
$283$	−14.4464	+	4.69390i	−0.858747	+	0.279024i	−0.153642	+	0.988127i	$0.549100\pi$
$284$		0			0
$285$	0.559465	+	4.47914i	0.0331399	+	0.265321i
$286$		0			0
$287$	−21.3090	+	29.3293i	−1.25783	+	1.73125i
$288$		0			0
$289$	−2.81844	+	2.04771i	−0.165790	+	0.120454i
$290$		0			0
$291$	2.67354	+	1.94244i	0.156726	+	0.113868i
$292$		0			0
$293$		−	0.578055i		−	0.0337703i	−0.999857	−	0.0168852i	$-0.994625\pi$
$293$		−	0.578055i		−	0.0337703i	0.999857	−	0.0168852i	$-0.00537497\pi$
$294$		0			0
$295$	6.59857	+	3.63966i	0.384184	+	0.211909i
$296$		0			0
$297$	15.6263	+	5.07729i	0.906730	+	0.294615i
$298$		0			0
$299$	7.57518			0.438084
$300$		0			0
$301$	−9.40627			−0.542168
$302$		0			0
$303$	−3.45060	−	1.12117i	−0.198232	−	0.0644095i
$304$		0			0
$305$	−11.6093	+	10.8713i	−0.664747	+	0.622487i
$306$		0			0
$307$		−	13.0649i		−	0.745655i	−0.927901	−	0.372827i	$-0.878388\pi$
$307$		−	13.0649i		−	0.745655i	0.927901	−	0.372827i	$-0.121612\pi$
$308$		0			0
$309$	6.60721	+	4.80042i	0.375871	+	0.273086i
$310$		0			0
$311$	9.93631	−	7.21915i	0.563436	−	0.409361i	−0.269279	−	0.963062i	$-0.586785\pi$
$311$	9.93631	−	7.21915i	0.563436	−	0.409361i	0.832715	+	0.553702i	$0.186785\pi$
$312$		0			0
$313$	18.4933	−	25.4538i	1.04530	−	1.43873i	0.152489	−	0.988305i	$-0.451271\pi$
$313$	18.4933	−	25.4538i	1.04530	−	1.43873i	0.892812	−	0.450429i	$-0.148729\pi$
$314$		0			0
$315$	−11.8511	+	21.4856i	−0.667731	+	1.21057i
$316$		0			0
$317$	−6.37755	+	2.07219i	−0.358199	+	0.116386i	−0.482588	−	0.875848i	$-0.660303\pi$
$317$	−6.37755	+	2.07219i	−0.358199	+	0.116386i	0.124389	+	0.992234i	$0.460303\pi$
$318$		0			0
$319$	−11.7055	−	36.0257i	−0.655381	−	2.01705i
$320$		0			0
$321$	3.12865	−	9.62898i	0.174624	−	0.537437i
$322$		0			0
$323$	6.05121	+	8.32878i	0.336698	+	0.463426i
$324$		0			0
$325$	1.86757	−	4.67857i	0.103594	−	0.259520i
$326$		0			0
$327$	−3.62536	−	4.98988i	−0.200483	−	0.275941i
$328$		0			0
$329$	6.00864	−	18.4927i	0.331267	−	1.01954i
$330$		0			0
$331$	7.48497	+	23.0364i	0.411411	+	1.26619i	0.915422	+	0.402495i	$0.131857\pi$
$331$	7.48497	+	23.0364i	0.411411	+	1.26619i	−0.504011	+	0.863697i	$0.668143\pi$
$332$		0			0
$333$	−23.1835	+	7.53279i	−1.27045	+	0.412794i
$334$		0			0
$335$	−2.92962	+	1.37356i	−0.160062	+	0.0750456i
$336$		0			0
$337$	3.08580	−	4.24724i	0.168094	−	0.231362i	−0.716657	−	0.697426i	$-0.754328\pi$
$337$	3.08580	−	4.24724i	0.168094	−	0.231362i	0.884751	+	0.466064i	$0.154328\pi$
$338$		0			0
$339$	7.46752	−	5.42547i	0.405580	−	0.294671i
$340$		0			0
$341$	−6.46287	−	4.69555i	−0.349984	−	0.254278i
$342$		0			0
$343$		−	24.6591i		−	1.33147i
$344$		0			0
$345$	−5.14508	−	10.9738i	−0.277002	−	0.590808i
$346$		0			0
$347$	4.89695	+	1.59112i	0.262882	+	0.0854156i	0.437493	−	0.899222i	$-0.355867\pi$
$347$	4.89695	+	1.59112i	0.262882	+	0.0854156i	−0.174610	+	0.984638i	$0.555867\pi$
$348$		0			0
$349$	−13.1711			−0.705032			−0.352516	−	0.935806i	$-0.614674\pi$
$349$	−13.1711			−0.705032			−0.352516	+	0.935806i	$0.614674\pi$
$350$		0			0
$351$	−3.98041			−0.212459
$352$		0			0
$353$	−4.00520	−	1.30137i	−0.213175	−	0.0692648i	0.200483	−	0.979697i	$-0.435749\pi$
$353$	−4.00520	−	1.30137i	−0.213175	−	0.0692648i	−0.413658	+	0.910432i	$0.635749\pi$
$354$		0			0
$355$	1.43531	−	7.46726i	0.0761786	−	0.396321i
$356$		0			0
$357$		−	11.7257i		−	0.620590i
$358$		0			0
$359$	6.33780	+	4.60468i	0.334496	+	0.243026i	0.742336	−	0.670028i	$-0.233718\pi$
$359$	6.33780	+	4.60468i	0.334496	+	0.243026i	−0.407840	+	0.913053i	$0.633718\pi$
$360$		0			0
$361$	9.02752	−	6.55888i	0.475132	−	0.345204i
$362$		0			0
$363$	2.66775	−	3.67184i	0.140020	−	0.192722i
$364$		0			0
$365$	−2.18100	−	2.32907i	−0.114159	−	0.121909i
$366$		0			0
$367$	25.2462	−	8.20297i	1.31784	−	0.428192i	0.436087	−	0.899905i	$-0.356364\pi$
$367$	25.2462	−	8.20297i	1.31784	−	0.428192i	0.881752	+	0.471713i	$0.156364\pi$
$368$		0			0
$369$	−6.28051	−	19.3294i	−0.326950	−	1.00625i
$370$		0			0
$371$	0.841401	−	2.58957i	0.0436834	−	0.134444i
$372$		0			0
$373$	10.4207	+	14.3429i	0.539565	+	0.742648i	0.988550	−	0.150891i	$-0.0482144\pi$
$373$	10.4207	+	14.3429i	0.539565	+	0.742648i	−0.448985	+	0.893539i	$0.648214\pi$
$374$		0			0
$375$	−8.04606	+	0.472234i	−0.415497	+	0.0243861i
$376$		0			0
$377$	5.39391	+	7.42408i	0.277800	+	0.382359i
$378$		0			0
$379$	−1.22379	+	3.76645i	−0.0628621	+	0.193470i	−0.977555	−	0.210680i	$-0.932432\pi$
$379$	−1.22379	+	3.76645i	−0.0628621	+	0.193470i	0.914693	+	0.404149i	$0.132432\pi$
$380$		0			0
$381$	0.990171	+	3.04743i	0.0507280	+	0.156125i
$382$		0			0
$383$	2.31295	−	0.751522i	0.118186	−	0.0384010i	−0.249327	−	0.968419i	$-0.580209\pi$
$383$	2.31295	−	0.751522i	0.118186	−	0.0384010i	0.367513	+	0.930018i	$0.380209\pi$
$384$		0			0
$385$	28.1219	+	30.0311i	1.43323	+	1.53053i
$386$		0			0
$387$	3.09959	−	4.26622i	0.157561	−	0.216864i
$388$		0			0
$389$	18.9367	−	13.7583i	0.960131	−	0.697576i	0.00694945	−	0.999976i	$-0.497788\pi$
$389$	18.9367	−	13.7583i	0.960131	−	0.697576i	0.953181	+	0.302400i	$0.0977879\pi$
$390$		0			0
$391$	−22.3630	−	16.2477i	−1.13094	−	0.821679i
$392$		0			0
$393$			5.87919i			0.296566i
$394$		0			0
$395$	5.99314	−	31.1795i	0.301548	−	1.56881i
$396$		0			0
$397$	21.6876	+	7.04674i	1.08847	+	0.353666i	0.797656	−	0.603113i	$-0.206073\pi$
$397$	21.6876	+	7.04674i	1.08847	+	0.353666i	0.290816	+	0.956779i	$0.406073\pi$
$398$		0			0
$399$	8.93115			0.447117
$400$		0			0
$401$	9.91722			0.495243			0.247621	−	0.968857i	$-0.420351\pi$
$401$	9.91722			0.495243			0.247621	+	0.968857i	$0.420351\pi$
$402$		0			0
$403$	1.84057	+	0.598038i	0.0916853	+	0.0297904i
$404$		0			0
$405$	−4.35965	−	9.29856i	−0.216633	−	0.462049i
$406$		0			0
$407$			40.8732i			2.02601i
$408$		0			0
$409$	17.1610	+	12.4682i	0.848555	+	0.616511i	0.924747	−	0.380582i	$-0.124276\pi$
$409$	17.1610	+	12.4682i	0.848555	+	0.616511i	−0.0761926	+	0.997093i	$0.524276\pi$
$410$		0			0
$411$	−0.157880	+	0.114707i	−0.00778765	+	0.00565806i
$412$		0			0
$413$	8.76393	−	12.0625i	0.431245	−	0.593558i
$414$		0			0
$415$	3.62163	−	1.69801i	0.177779	−	0.0833519i
$416$		0			0
$417$	−6.62385	+	2.15222i	−0.324371	+	0.105395i
$418$		0			0
$419$	−10.8049	−	33.2539i	−0.527852	−	1.62456i	−0.758607	−	0.651549i	$-0.774120\pi$
$419$	−10.8049	−	33.2539i	−0.527852	−	1.62456i	0.230755	−	0.973012i	$-0.425880\pi$
$420$		0			0
$421$	−2.85113	+	8.77488i	−0.138956	+	0.427661i	−0.996184	−	0.0872744i	$-0.972184\pi$
$421$	−2.85113	+	8.77488i	−0.138956	+	0.427661i	0.857229	+	0.514936i	$0.172184\pi$
$422$		0			0
$423$	6.40739	+	8.81902i	0.311538	+	0.428795i
$424$		0			0
$425$	−15.5482	+	9.80610i	−0.754197	+	0.475666i
$426$		0			0
$427$	18.4968	+	25.4586i	0.895122	+	1.23203i
$428$		0			0
$429$	−0.933418	+	2.87277i	−0.0450659	+	0.138698i
$430$		0			0
$431$	−11.7308	−	36.1037i	−0.565053	−	1.73905i	−0.667795	−	0.744345i	$-0.732762\pi$
$431$	−11.7308	−	36.1037i	−0.565053	−	1.73905i	0.102742	−	0.994708i	$-0.467238\pi$
$432$		0			0
$433$	−29.1617	+	9.47523i	−1.40142	+	0.455350i	−0.909651	−	0.415373i	$-0.863651\pi$
$433$	−29.1617	+	9.47523i	−1.40142	+	0.455350i	−0.491773	+	0.870723i	$0.663651\pi$
$434$		0			0
$435$	7.09133	−	12.8563i	0.340003	−	0.616414i
$436$		0			0
$437$	12.3754	−	17.0333i	0.591996	−	0.814812i
$438$		0			0
$439$	25.4505	−	18.4908i	1.21468	−	0.882520i	0.219036	−	0.975717i	$-0.429709\pi$
$439$	25.4505	−	18.4908i	1.21468	−	0.882520i	0.995648	+	0.0931969i	$0.0297086\pi$
$440$		0			0
$441$	25.2304	+	18.3310i	1.20145	+	0.872904i
$442$		0			0
$443$			25.4445i			1.20890i	0.796641	+	0.604452i	$0.206608\pi$
$443$			25.4445i			1.20890i	−0.796641	+	0.604452i	$0.793392\pi$
$444$		0			0
$445$	−20.1258	+	18.8463i	−0.954053	+	0.893401i
$446$		0			0
$447$	−7.78651	−	2.52999i	−0.368289	−	0.119664i
$448$		0			0
$449$	−12.6494			−0.596963			−0.298481	−	0.954415i	$-0.596480\pi$
$449$	−12.6494			−0.596963			−0.298481	+	0.954415i	$0.596480\pi$
$450$		0			0
$451$	−34.0783			−1.60469
$452$		0			0
$453$	−7.44866	−	2.42022i	−0.349969	−	0.113712i
$454$		0			0
$455$	−8.72751	−	4.81394i	−0.409152	−	0.225681i
$456$		0			0
$457$			22.5919i			1.05680i	0.848994	+	0.528402i	$0.177209\pi$
$457$			22.5919i			1.05680i	−0.848994	+	0.528402i	$0.822791\pi$
$458$		0			0
$459$	11.7507	+	8.53741i	0.548477	+	0.398492i
$460$		0			0
$461$	7.60565	−	5.52583i	0.354230	−	0.257363i	−0.396411	−	0.918073i	$-0.629745\pi$
$461$	7.60565	−	5.52583i	0.354230	−	0.257363i	0.750642	+	0.660710i	$0.229745\pi$
$462$		0			0
$463$	22.4539	−	30.9051i	1.04352	−	1.43628i	0.149225	−	0.988803i	$-0.452322\pi$
$463$	22.4539	−	30.9051i	1.04352	−	1.43628i	0.894295	−	0.447478i	$-0.147678\pi$
$464$		0			0
$465$	−0.383773	−	3.07253i	−0.0177971	−	0.142485i
$466$		0			0
$467$	19.7604	−	6.42055i	0.914404	−	0.297108i	0.186235	−	0.982505i	$-0.440372\pi$
$467$	19.7604	−	6.42055i	0.914404	−	0.297108i	0.728169	+	0.685397i	$0.240372\pi$
$468$		0			0
$469$	1.97831	+	6.08860i	0.0913497	+	0.281146i
$470$		0			0
$471$	−4.80561	+	14.7902i	−0.221431	+	0.681495i
$472$		0			0
$473$	−5.19721	−	7.15335i	−0.238968	−	0.328911i
$474$		0			0
$475$	−7.46904	−	11.8426i	−0.342703	−	0.543377i
$476$		0			0
$477$	0.897239	+	1.23494i	0.0410817	+	0.0565442i
$478$		0			0
$479$	0.768102	−	2.36397i	0.0350955	−	0.108013i	−0.931974	−	0.362525i	$-0.881915\pi$
$479$	0.768102	−	2.36397i	0.0350955	−	0.108013i	0.967070	+	0.254512i	$0.0819148\pi$
$480$		0			0
$481$	−3.05985	−	9.41724i	−0.139517	−	0.429389i
$482$		0			0
$483$	−22.8067	+	7.41034i	−1.03774	+	0.337182i
$484$		0			0
$485$	−10.0661	−	1.93485i	−0.457078	−	0.0878570i
$486$		0			0
$487$	−16.5501	+	22.7793i	−0.749958	+	1.03223i	0.248025	+	0.968754i	$0.420218\pi$
$487$	−16.5501	+	22.7793i	−0.749958	+	1.03223i	−0.997983	+	0.0634753i	$0.979782\pi$
$488$		0			0
$489$	5.66262	−	4.11413i	0.256072	−	0.186047i
$490$		0			0
$491$	−8.64255	−	6.27918i	−0.390033	−	0.283375i	0.375436	−	0.926848i	$-0.377493\pi$
$491$	−8.64255	−	6.27918i	−0.390033	−	0.283375i	−0.765469	+	0.643473i	$0.777493\pi$
$492$		0			0
$493$		−	33.4861i		−	1.50814i
$494$		0			0
$495$	−22.8875	+	2.85876i	−1.02872	+	0.128492i
$496$		0			0
$497$	−14.3086	−	4.64915i	−0.641828	−	0.208543i
$498$		0			0
$499$	14.0624			0.629522			0.314761	−	0.949171i	$-0.398076\pi$
$499$	14.0624			0.629522			0.314761	+	0.949171i	$0.398076\pi$
$500$		0			0
$501$	−0.529929			−0.0236755
$502$		0			0
$503$	−14.1866	−	4.60949i	−0.632548	−	0.205527i	−0.0248443	−	0.999691i	$-0.507909\pi$
$503$	−14.1866	−	4.60949i	−0.632548	−	0.205527i	−0.607703	+	0.794164i	$0.707909\pi$
$504$		0			0
$505$	11.1670	−	1.39481i	0.496925	−	0.0620683i
$506$		0			0
$507$			8.63993i			0.383713i
$508$		0			0
$509$	17.6546	+	12.8268i	0.782525	+	0.568537i	0.905736	−	0.423843i	$-0.139319\pi$
$509$	17.6546	+	12.8268i	0.782525	+	0.568537i	−0.123211	+	0.992380i	$0.539319\pi$
$510$		0			0
$511$	−5.10754	+	3.71084i	−0.225944	+	0.164158i
$512$		0			0
$513$	−6.50271	+	8.95021i	−0.287102	+	0.395162i
$514$		0			0
$515$	−24.8767	−	4.78165i	−1.09620	−	0.210705i
$516$		0			0
$517$	17.3834	−	5.64821i	0.764521	−	0.248408i
$518$		0			0
$519$	3.09262	+	9.51810i	0.135751	+	0.417798i
$520$		0			0
$521$	3.86780	−	11.9039i	0.169451	−	0.521517i	−0.829885	−	0.557934i	$-0.811594\pi$
$521$	3.86780	−	11.9039i	0.169451	−	0.521517i	0.999337	+	0.0364165i	$0.0115943\pi$
$522$		0			0
$523$	−1.54902	−	2.13205i	−0.0677341	−	0.0932279i	0.773806	−	0.633423i	$-0.218351\pi$
$523$	−1.54902	−	2.13205i	−0.0677341	−	0.0932279i	−0.841540	+	0.540195i	$0.818351\pi$
$524$		0			0
$525$	−1.04597	+	15.9127i	−0.0456498	+	0.694489i
$526$		0			0
$527$	−4.15091	−	5.71324i	−0.180817	−	0.248873i
$528$		0			0
$529$	−10.3617	+	31.8902i	−0.450511	+	1.38653i
$530$		0			0
$531$	2.58304	+	7.94978i	0.112094	+	0.344991i
$532$		0			0
$533$	7.85168	−	2.55117i	0.340094	−	0.110503i
$534$		0			0
$535$	3.89225	+	31.1618i	0.168277	+	1.34724i
$536$		0			0
$537$	−1.68469	+	2.31878i	−0.0726999	+	0.100063i
$538$		0			0
$539$	42.3048	−	30.7363i	1.82220	−	1.32390i
$540$		0			0
$541$	−18.9703	−	13.7827i	−0.815597	−	0.592566i	0.0998509	−	0.995002i	$-0.468163\pi$
$541$	−18.9703	−	13.7827i	−0.815597	−	0.592566i	−0.915448	+	0.402436i	$0.868163\pi$
$542$		0			0
$543$			10.0932i			0.433142i
$544$		0			0
$545$	16.7519	+	9.24004i	0.717571	+	0.395800i
$546$		0			0
$547$	−7.51883	−	2.44302i	−0.321482	−	0.104456i	0.143830	−	0.989602i	$-0.454058\pi$
$547$	−7.51883	−	2.44302i	−0.321482	−	0.104456i	−0.465312	+	0.885146i	$0.654058\pi$
$548$		0			0
$549$	−17.6419			−0.752939
$550$		0			0
$551$	25.5054			1.08657
$552$		0			0
$553$	−59.7454	−	19.4125i	−2.54063	−	0.825502i
$554$		0			0
$555$	−11.5640	+	10.8289i	−0.490865	+	0.459659i
$556$		0			0
$557$			3.55358i			0.150570i	0.997162	+	0.0752850i	$0.0239867\pi$
$557$			3.55358i			0.150570i	−0.997162	+	0.0752850i	$0.976013\pi$
$558$		0			0
$559$	1.73296	+	1.25907i	0.0732962	+	0.0532528i
$560$		0			0
$561$	8.91724	−	6.47876i	0.376486	−	0.273533i
$562$		0			0
$563$	−10.8021	+	14.8678i	−0.455252	+	0.626601i	−0.973516	−	0.228620i	$-0.926579\pi$
$563$	−10.8021	+	14.8678i	−0.455252	+	0.626601i	0.518263	+	0.855221i	$0.326579\pi$
$564$		0			0
$565$	−13.8280	+	25.0697i	−0.581749	+	1.05469i
$566$		0			0
$567$	−19.3251	+	6.27910i	−0.811577	+	0.263697i
$568$		0			0
$569$	2.89396	+	8.90670i	0.121321	+	0.373388i	0.993213	−	0.116310i	$-0.0371068\pi$
$569$	2.89396	+	8.90670i	0.121321	+	0.373388i	−0.871892	+	0.489699i	$0.837107\pi$
$570$		0			0
$571$	−1.38008	+	4.24746i	−0.0577546	+	0.177750i	−0.975772	−	0.218790i	$-0.929789\pi$
$571$	−1.38008	+	4.24746i	−0.0577546	+	0.177750i	0.918017	+	0.396540i	$0.129789\pi$
$572$		0			0
$573$	3.48772	+	4.80044i	0.145702	+	0.200541i
$574$		0			0
$575$	28.8991	+	24.0443i	1.20517	+	1.00271i
$576$		0			0
$577$	−10.6670	−	14.6818i	−0.444072	−	0.611213i	0.527039	−	0.849841i	$-0.323302\pi$
$577$	−10.6670	−	14.6818i	−0.444072	−	0.611213i	−0.971111	+	0.238628i	$0.923302\pi$
$578$		0			0
$579$	−4.08428	+	12.5701i	−0.169737	+	0.522396i
$580$		0			0
$581$	−2.44560	−	7.52678i	−0.101461	−	0.312263i
$582$		0			0
$583$	2.43423	−	0.790929i	0.100815	−	0.0327569i
$584$		0			0
$585$	5.05930	−	2.37206i	0.209176	−	0.0980727i
$586$		0			0
$587$	14.1386	−	19.4602i	0.583564	−	0.803207i	−0.410516	−	0.911853i	$-0.634652\pi$
$587$	14.1386	−	19.4602i	0.583564	−	0.803207i	0.994080	+	0.108646i	$0.0346515\pi$
$588$		0			0
$589$	4.35162	−	3.16164i	0.179306	−	0.130273i
$590$		0			0
$591$	−2.61171	−	1.89752i	−0.107431	−	0.0780535i
$592$		0			0
$593$		−	8.48986i		−	0.348637i	−0.984689	−	0.174318i	$-0.944228\pi$
$593$		−	8.48986i		−	0.348637i	0.984689	−	0.174318i	$-0.0557722\pi$
$594$		0			0
$595$	15.4396	+	32.9307i	0.632963	+	1.35003i
$596$		0			0
$597$	−10.8435	−	3.52326i	−0.443794	−	0.144198i
$598$		0			0
$599$	−40.0858			−1.63786			−0.818930	−	0.573893i	$-0.805433\pi$
$599$	−40.0858			−1.63786			−0.818930	+	0.573893i	$0.805433\pi$
$600$		0			0
$601$	11.4877			0.468593			0.234296	−	0.972165i	$-0.424721\pi$
$601$	11.4877			0.468593			0.234296	+	0.972165i	$0.424721\pi$
$602$		0			0
$603$	−3.41339	−	1.10908i	−0.139004	−	0.0451652i
$604$		0			0
$605$	−2.65732	+	13.8248i	−0.108035	+	0.562057i
$606$		0			0
$607$			14.8012i			0.600762i	0.953819	+	0.300381i	$0.0971139\pi$
$607$			14.8012i			0.600762i	−0.953819	+	0.300381i	$0.902886\pi$
$608$		0			0
$609$	−23.5020	−	17.0752i	−0.952350	−	0.691923i
$610$		0			0
$611$	−3.58232	+	2.60271i	−0.144925	+	0.105294i
$612$		0			0
$613$	8.50243	−	11.7026i	0.343410	−	0.472663i	−0.602023	−	0.798478i	$-0.705639\pi$
$613$	8.50243	−	11.7026i	0.343410	−	0.472663i	0.945434	+	0.325815i	$0.105639\pi$
$614$		0			0
$615$	−9.02863	−	9.64157i	−0.364069	−	0.388786i
$616$		0			0
$617$	45.1347	−	14.6652i	1.81706	−	0.590397i	0.817153	−	0.576421i	$-0.195551\pi$
$617$	45.1347	−	14.6652i	1.81706	−	0.590397i	0.999902	−	0.0139758i	$-0.00444877\pi$
$618$		0			0
$619$	12.7328	+	39.1874i	0.511773	+	1.57507i	0.789078	+	0.614293i	$0.210559\pi$
$619$	12.7328	+	39.1874i	0.511773	+	1.57507i	−0.277306	+	0.960782i	$0.589441\pi$
$620$		0			0
$621$	9.17923	−	28.2508i	0.368350	−	1.13366i
$622$		0			0
$623$	32.0658	+	44.1348i	1.28469	+	1.76822i
$624$		0			0
$625$	21.9749	−	11.9207i	0.878996	−	0.476830i
$626$		0			0
$627$	4.93469	+	6.79202i	0.197073	+	0.271247i
$628$		0			0
$629$	−11.1655	+	34.3639i	−0.445198	+	1.37018i
$630$		0			0
$631$	−7.23887	−	22.2790i	−0.288175	−	0.886912i	−0.985429	−	0.170087i	$-0.945595\pi$
$631$	−7.23887	−	22.2790i	−0.288175	−	0.886912i	0.697254	−	0.716824i	$-0.254405\pi$
$632$		0			0
$633$	−7.54555	+	2.45170i	−0.299909	+	0.0974463i
$634$		0			0
$635$	−6.79347	−	7.25467i	−0.269590	−	0.287893i
$636$		0			0
$637$	−7.44611	+	10.2487i	−0.295026	+	0.406068i
$638$		0			0
$639$	6.82366	−	4.95768i	0.269940	−	0.196123i
$640$		0			0
$641$	6.75647	+	4.90886i	0.266864	+	0.193888i	0.713168	−	0.700993i	$-0.247260\pi$
$641$	6.75647	+	4.90886i	0.266864	+	0.193888i	−0.446303	+	0.894882i	$0.647260\pi$
$642$		0			0
$643$		−	20.2024i		−	0.796704i	−0.917233	−	0.398352i	$-0.869582\pi$
$643$		−	20.2024i		−	0.796704i	0.917233	−	0.398352i	$-0.130418\pi$
$644$		0			0
$645$	0.646917	−	3.36561i	0.0254723	−	0.132521i
$646$		0			0
$647$	34.6329	+	11.2529i	1.36156	+	0.442397i	0.896563	−	0.442916i	$-0.146056\pi$
$647$	34.6329	+	11.2529i	1.36156	+	0.442397i	0.464995	+	0.885313i	$0.346056\pi$
$648$		0			0
$649$	14.0157			0.550164
$650$		0			0
$651$	−6.12645			−0.240114
$652$		0			0
$653$	−5.31609	−	1.72730i	−0.208035	−	0.0675946i	0.203146	−	0.979148i	$-0.434883\pi$
$653$	−5.31609	−	1.72730i	−0.208035	−	0.0675946i	−0.411181	+	0.911554i	$0.634883\pi$
$654$		0			0
$655$	−7.74132	−	16.5112i	−0.302479	−	0.645147i
$656$		0			0
$657$		−	3.53934i		−	0.138083i
$658$		0			0
$659$	−8.23648	−	5.98415i	−0.320848	−	0.233110i	0.415689	−	0.909507i	$-0.363540\pi$
$659$	−8.23648	−	5.98415i	−0.320848	−	0.233110i	−0.736537	+	0.676397i	$0.763540\pi$
$660$		0			0
$661$	−26.3960	+	19.1778i	−1.02668	+	0.745929i	−0.967642	−	0.252326i	$-0.918804\pi$
$661$	−26.3960	+	19.1778i	−1.02668	+	0.745929i	−0.0590415	+	0.998256i	$0.518804\pi$
$662$		0			0
$663$	−1.56953	+	2.16027i	−0.0609555	+	0.0838981i
$664$		0			0
$665$	−25.0824	+	11.7599i	−0.972653	+	0.456031i
$666$		0			0
$667$	−65.1309	+	21.1623i	−2.52188	+	0.819408i
$668$		0			0
$669$	−2.43946	−	7.50787i	−0.0943148	−	0.290271i
$670$		0			0
$671$	−9.14100	+	28.1331i	−0.352885	+	1.08607i
$672$		0			0
$673$	9.00594	+	12.3956i	0.347153	+	0.477816i	0.946514	−	0.322664i	$-0.104578\pi$
$673$	9.00594	+	12.3956i	0.347153	+	0.477816i	−0.599360	+	0.800479i	$0.704578\pi$
$674$		0			0
$675$	−15.1851	−	12.6342i	−0.584477	−	0.486289i
$676$		0			0
$677$	−25.6909	−	35.3605i	−0.987382	−	1.35901i	−0.932756	−	0.360507i	$-0.882604\pi$
$677$	−25.6909	−	35.3605i	−0.987382	−	1.35901i	−0.0546254	−	0.998507i	$-0.517396\pi$
$678$		0			0
$679$	−6.26720	+	19.2884i	−0.240513	+	0.740223i
$680$		0			0
$681$	3.59003	+	11.0490i	0.137570	+	0.423398i
$682$		0			0
$683$	2.51922	−	0.818543i	0.0963952	−	0.0313207i	−0.260422	−	0.965495i	$-0.583862\pi$
$683$	2.51922	−	0.818543i	0.0963952	−	0.0313207i	0.356818	+	0.934174i	$0.383862\pi$
$684$		0			0
$685$	0.292355	−	0.530030i	0.0111703	−	0.0202514i
$686$		0			0
$687$	4.93010	−	6.78570i	0.188095	−	0.258891i
$688$		0			0
$689$	−0.501638	+	0.364462i	−0.0191109	+	0.0138849i
$690$		0			0
$691$	−2.06952	−	1.50359i	−0.0787282	−	0.0571994i	0.547725	−	0.836658i	$-0.315494\pi$
$691$	−2.06952	−	1.50359i	−0.0787282	−	0.0571994i	−0.626453	+	0.779459i	$0.715494\pi$
$692$		0			0
$693$			45.6364i			1.73358i
$694$		0			0
$695$	15.7686	−	14.7662i	0.598139	−	0.560113i
$696$		0			0
$697$	−28.6511	−	9.30932i	−1.08524	−	0.352616i
$698$		0			0
$699$	−0.903606			−0.0341775
$700$		0			0
$701$	26.4567			0.999257			0.499628	−	0.866240i	$-0.333470\pi$
$701$	26.4567			0.999257			0.499628	+	0.866240i	$0.333470\pi$
$702$		0			0
$703$	−26.1741	−	8.50447i	−0.987173	−	0.320752i
$704$		0			0
$705$	6.20353	+	3.42176i	0.233638	+	0.128871i
$706$		0			0
$707$		−	22.2664i		−	0.837414i
$708$		0			0
$709$	−32.9190	−	23.9171i	−1.23630	−	0.898224i	−0.238953	−	0.971031i	$-0.576804\pi$
$709$	−32.9190	−	23.9171i	−1.23630	−	0.898224i	−0.997346	+	0.0728072i	$0.976804\pi$
$710$		0			0
$711$	28.4921	−	20.7007i	1.06854	−	0.776338i
$712$		0			0
$713$	−8.48908	+	11.6842i	−0.317919	+	0.437577i
$714$		0			0
$715$	−1.16124	−	9.29699i	−0.0434278	−	0.347688i
$716$		0			0
$717$	−20.8846	+	6.78582i	−0.779950	+	0.253421i
$718$		0			0
$719$	2.82852	+	8.70530i	0.105486	+	0.324653i	0.989844	−	0.142156i	$-0.0454036\pi$
$719$	2.82852	+	8.70530i	0.105486	+	0.324653i	−0.884358	+	0.466809i	$0.845404\pi$
$720$		0			0
$721$	−15.4883	+	47.6681i	−0.576815	+	1.77525i
$722$		0			0
$723$	−4.00116	−	5.50712i	−0.148805	−	0.204812i
$724$		0			0
$725$	−2.98705	+	45.4433i	−0.110936	+	1.68772i
$726$		0			0
$727$	−17.1114	−	23.5518i	−0.634627	−	0.873489i	0.363688	−	0.931521i	$-0.381518\pi$
$727$	−17.1114	−	23.5518i	−0.634627	−	0.873489i	−0.998315	+	0.0580316i	$0.981518\pi$
$728$		0			0
$729$	0.879858	−	2.70792i	0.0325873	−	0.100293i
$730$		0			0
$731$	−2.41541	−	7.43388i	−0.0893373	−	0.274952i
$732$		0			0
$733$	15.0623	−	4.89403i	0.556338	−	0.180765i	−0.0173349	−	0.999850i	$-0.505518\pi$
$733$	15.0623	−	4.89403i	0.556338	−	0.180765i	0.573673	+	0.819085i	$0.305518\pi$
$734$		0			0
$735$	19.9042	+	3.82586i	0.734176	+	0.141119i
$736$		0			0
$737$	−3.53724	+	4.86859i	−0.130296	+	0.179337i
$738$		0			0
$739$	−24.8299	+	18.0400i	−0.913381	+	0.663610i	−0.941868	−	0.335984i	$-0.890931\pi$
$739$	−24.8299	+	18.0400i	−0.913381	+	0.663610i	0.0284865	+	0.999594i	$0.490931\pi$
$740$		0			0
$741$	−1.64542	−	1.19547i	−0.0604461	−	0.0439167i
$742$		0			0
$743$			5.11321i			0.187586i	0.995592	+	0.0937928i	$0.0298991\pi$
$743$			5.11321i			0.187586i	−0.995592	+	0.0937928i	$0.970101\pi$
$744$		0			0
$745$	25.1991	−	3.14748i	0.923223	−	0.115315i
$746$		0			0
$747$	4.21966	+	1.37105i	0.154389	+	0.0501642i
$748$		0			0
$749$	62.1348			2.27036
$750$		0			0
$751$	−47.0313			−1.71620			−0.858098	−	0.513485i	$-0.828354\pi$
$751$	−47.0313			−1.71620			−0.858098	+	0.513485i	$0.828354\pi$
$752$		0			0
$753$	19.7968	+	6.43236i	0.721434	+	0.234408i
$754$		0			0
$755$	24.1057	−	3.01092i	0.877297	−	0.109579i
$756$		0			0
$757$			1.80945i			0.0657655i	0.999459	+	0.0328828i	$0.0104688\pi$
$757$			1.80945i			0.0657655i	−0.999459	+	0.0328828i	$0.989531\pi$
$758$		0			0
$759$	−18.2368	−	13.2498i	−0.661952	−	0.480936i
$760$		0			0
$761$	13.0268	−	9.46453i	0.472222	−	0.343089i	−0.326085	−	0.945341i	$-0.605730\pi$
$761$	13.0268	−	9.46453i	0.472222	−	0.343089i	0.798306	+	0.602251i	$0.205730\pi$
$762$		0			0
$763$	22.2491	−	30.6233i	0.805471	−	1.10864i
$764$		0			0
$765$	−20.0235	−	3.84879i	−0.723950	−	0.139153i
$766$		0			0
$767$	−3.22923	+	1.04924i	−0.116601	+	0.0378859i
$768$		0			0
$769$	−9.89913	−	30.4664i	−0.356972	−	1.09865i	−0.954857	−	0.297065i	$-0.903992\pi$
$769$	−9.89913	−	30.4664i	−0.356972	−	1.09865i	0.597885	−	0.801582i	$-0.296008\pi$
$770$		0			0
$771$	2.12760	−	6.54808i	0.0766237	−	0.235823i
$772$		0			0
$773$	9.22690	+	12.6997i	0.331869	+	0.456778i	0.942044	−	0.335488i	$-0.108901\pi$
$773$	9.22690	+	12.6997i	0.331869	+	0.456778i	−0.610176	+	0.792266i	$0.708901\pi$
$774$		0			0
$775$	5.12349	+	8.12362i	0.184041	+	0.291809i
$776$		0			0
$777$	18.4246	+	25.3593i	0.660979	+	0.909760i
$778$		0			0
$779$	7.09065	−	21.8228i	0.254049	−	0.781883i
$780$		0			0
$781$	−4.37026	−	13.4503i	−0.156380	−	0.481289i
$782$		0			0
$783$	34.2233	−	11.1198i	1.22304	−	0.397390i
$784$		0			0
$785$	−5.97852	−	47.8646i	−0.213382	−	1.70836i
$786$		0			0
$787$	27.5069	−	37.8600i	0.980515	−	1.34956i	0.0439630	−	0.999033i	$-0.486002\pi$
$787$	27.5069	−	37.8600i	0.980515	−	1.34956i	0.936552	−	0.350530i	$-0.113998\pi$
$788$		0			0
$789$	−0.219776	+	0.159676i	−0.00782422	+	0.00568463i
$790$		0			0
$791$	45.8287	+	33.2965i	1.62948	+	1.18389i
$792$		0			0
$793$		−	7.16621i		−	0.254480i
$794$		0			0
$795$	0.868691	+	0.479155i	0.0308093	+	0.0169939i
$796$		0			0
$797$	31.9512	+	10.3816i	1.13177	+	0.367734i	0.814248	−	0.580517i	$-0.197149\pi$
$797$	31.9512	+	10.3816i	1.13177	+	0.367734i	0.317522	+	0.948251i	$0.397149\pi$
$798$		0			0
$799$	16.1579			0.571626
$800$		0			0
$801$	−30.5839			−1.08063
$802$		0			0
$803$	−5.64410	−	1.83388i	−0.199176	−	0.0647162i
$804$		0			0
$805$	54.2932	−	50.8416i	1.91358	−	1.79193i
$806$		0			0
$807$			1.86237i			0.0655586i
$808$		0			0
$809$	30.0875	+	21.8598i	1.05782	+	0.768551i	0.973684	−	0.227904i	$-0.0731871\pi$
$809$	30.0875	+	21.8598i	1.05782	+	0.768551i	0.0841356	+	0.996454i	$0.473187\pi$
$810$		0			0
$811$	−15.5454	+	11.2944i	−0.545872	+	0.396599i	−0.826261	−	0.563287i	$-0.809536\pi$
$811$	−15.5454	+	11.2944i	−0.545872	+	0.396599i	0.280389	+	0.959886i	$0.409536\pi$
$812$		0			0
$813$	13.4988	−	18.5795i	0.473423	−	0.651610i
$814$		0			0
$815$	−10.4858	+	19.0104i	−0.367301	+	0.665904i
$816$		0			0
$817$	5.66218	−	1.83975i	0.198095	−	0.0643649i
$818$		0			0
$819$	−3.41642	−	10.5147i	−0.119380	−	0.367412i
$820$		0			0
$821$	−6.26477	+	19.2810i	−0.218642	+	0.672911i	0.780233	+	0.625489i	$0.215100\pi$
$821$	−6.26477	+	19.2810i	−0.218642	+	0.672911i	−0.998875	+	0.0474217i	$0.984900\pi$
$822$		0			0
$823$	−7.80203	−	10.7386i	−0.271962	−	0.374323i	0.651089	−	0.759001i	$-0.274312\pi$
$823$	−7.80203	−	10.7386i	−0.271962	−	0.374323i	−0.923051	+	0.384678i	$0.874312\pi$
$824$		0			0
$825$	−12.6794	+	7.99676i	−0.441439	+	0.278412i
$826$		0			0
$827$	−15.1959	−	20.9153i	−0.528412	−	0.727296i	0.458476	−	0.888707i	$-0.348396\pi$
$827$	−15.1959	−	20.9153i	−0.528412	−	0.727296i	−0.986887	+	0.161411i	$0.948396\pi$
$828$		0			0
$829$	−7.77981	+	23.9438i	−0.270204	+	0.831602i	0.720245	+	0.693720i	$0.244029\pi$
$829$	−7.77981	+	23.9438i	−0.270204	+	0.831602i	−0.990449	+	0.137882i	$0.955971\pi$
$830$		0			0
$831$	4.58224	+	14.1027i	0.158956	+	0.489217i
$832$		0			0
$833$	43.9639	−	14.2847i	1.52326	−	0.494937i
$834$		0			0
$835$	1.48826	−	0.697775i	0.0515034	−	0.0241475i
$836$		0			0
$837$	4.46063	−	6.13953i	0.154182	−	0.212213i
$838$		0			0
$839$	12.7306	−	9.24933i	0.439509	−	0.319322i	−0.345931	−	0.938260i	$-0.612437\pi$
$839$	12.7306	−	9.24933i	0.439509	−	0.319322i	0.785440	+	0.618938i	$0.212437\pi$
$840$		0			0
$841$	−43.6552	−	31.7173i	−1.50535	−	1.09370i
$842$		0			0
$843$		−	18.8022i		−	0.647583i
$844$		0			0
$845$	−11.3765	−	24.2645i	−0.391363	−	0.834726i
$846$		0			0
$847$	26.4907	+	8.60735i	0.910232	+	0.295752i
$848$		0			0
$849$	−10.9503			−0.375814
$850$		0			0
$851$	73.8947			2.53308
$852$		0			0
$853$	36.0322	+	11.7076i	1.23372	+	0.400859i	0.852060	−	0.523444i	$-0.175353\pi$
$853$	36.0322	+	11.7076i	1.23372	+	0.400859i	0.381658	+	0.924304i	$0.375353\pi$
$854$		0			0
$855$	2.93152	−	15.2513i	0.100256	−	0.521585i
$856$		0			0
$857$			13.2868i			0.453868i	0.973910	+	0.226934i	$0.0728701\pi$
$857$			13.2868i			0.453868i	−0.973910	+	0.226934i	$0.927130\pi$
$858$		0			0
$859$	−42.6905	−	31.0164i	−1.45658	−	1.05827i	−0.984237	−	0.176852i	$-0.943409\pi$
$859$	−42.6905	−	31.0164i	−1.45658	−	1.05827i	−0.472342	−	0.881415i	$-0.656591\pi$
$860$		0			0
$861$	−21.1435	+	15.3616i	−0.720568	+	0.523523i
$862$		0			0
$863$	6.51626	−	8.96887i	0.221816	−	0.305304i	−0.683577	−	0.729879i	$-0.739576\pi$
$863$	6.51626	−	8.96887i	0.221816	−	0.305304i	0.905393	+	0.424575i	$0.139576\pi$
$864$		0			0
$865$	−21.2181	−	22.6586i	−0.721439	−	0.770417i
$866$		0			0
$867$	−2.38854	+	0.776083i	−0.0811190	+	0.0263572i
$868$		0			0
$869$	−18.2480	−	56.1615i	−0.619020	−	1.90515i
$870$		0			0
$871$	0.450512	−	1.38653i	0.0152650	−	0.0469809i
$872$		0			0
$873$	−6.68310	−	9.19850i	−0.226189	−	0.311322i
$874$		0			0
$875$	−18.0153	−	46.0669i	−0.609029	−	1.55734i
$876$		0			0
$877$	27.9060	+	38.4092i	0.942317	+	1.29699i	0.954857	+	0.297067i	$0.0960084\pi$
$877$	27.9060	+	38.4092i	0.942317	+	1.29699i	−0.0125397	+	0.999921i	$0.503992\pi$
$878$		0			0
$879$	0.128773	−	0.396324i	0.00434342	−	0.0133677i
$880$		0			0
$881$	12.2335	+	37.6507i	0.412156	+	1.26848i	0.914770	+	0.403974i	$0.132371\pi$
$881$	12.2335	+	37.6507i	0.412156	+	1.26848i	−0.502615	+	0.864511i	$0.667629\pi$
$882$		0			0
$883$	2.64538	−	0.859537i	0.0890242	−	0.0289257i	−0.264166	−	0.964477i	$-0.585097\pi$
$883$	2.64538	−	0.859537i	0.0890242	−	0.0289257i	0.353190	+	0.935551i	$0.385097\pi$
$884$		0			0
$885$	3.71328	+	3.96538i	0.124821	+	0.133295i
$886$		0			0
$887$	12.8916	−	17.7438i	0.432858	−	0.595778i	−0.535748	−	0.844378i	$-0.679970\pi$
$887$	12.8916	−	17.7438i	0.432858	−	0.595778i	0.968606	+	0.248600i	$0.0799704\pi$
$888$		0			0
$889$	−15.9091	+	11.5587i	−0.533575	+	0.387665i
$890$		0			0
$891$	−15.4528	−	11.2271i	−0.517688	−	0.376122i
$892$		0			0
$893$			12.3071i			0.411840i
$894$		0			0
$895$	1.67811	−	8.73040i	0.0560929	−	0.291825i
$896$		0			0
$897$	5.19367	+	1.68753i	0.173412	+	0.0563449i
$898$		0			0
$899$	−17.4958			−0.583518
$900$		0			0
$901$	2.26262			0.0753789
$902$		0			0
$903$	−6.44910	−	2.09544i	−0.214612	−	0.0697318i
$904$		0			0
$905$	−13.2901	−	28.3460i	−0.441777	−	0.942253i
$906$		0			0
$907$			16.5488i			0.549494i	0.961517	+	0.274747i	$0.0885941\pi$
$907$			16.5488i			0.549494i	−0.961517	+	0.274747i	$0.911406\pi$
$908$		0			0
$909$	10.0989	+	7.33731i	0.334961	+	0.243363i
$910$		0			0
$911$	−7.91637	+	5.75158i	−0.262281	+	0.190558i	−0.711152	−	0.703038i	$-0.751826\pi$
$911$	−7.91637	+	5.75158i	−0.262281	+	0.190558i	0.448871	+	0.893597i	$0.351826\pi$
$912$		0			0
$913$	4.37276	−	6.01859i	0.144717	−	0.199186i
$914$		0			0
$915$	−10.3813	+	4.86731i	−0.343196	+	0.160908i
$916$		0			0
$917$	−34.3151	+	11.1496i	−1.13318	+	0.368194i
$918$		0			0
$919$	14.4638	+	44.5150i	0.477117	+	1.46842i	0.843081	+	0.537786i	$0.180739\pi$
$919$	14.4638	+	44.5150i	0.477117	+	1.46842i	−0.365964	+	0.930629i	$0.619261\pi$
$920$		0			0
$921$	2.91048	−	8.95753i	0.0959035	−	0.295161i
$922$		0			0
$923$	2.01383	+	2.77179i	0.0662859	+	0.0912347i
$924$		0			0
$925$	18.2179	−	45.6387i	0.599000	−	1.50059i
$926$		0			0
$927$	−16.5162	−	22.7325i	−0.542462	−	0.746634i
$928$		0			0
$929$	9.88979	−	30.4376i	0.324473	−	0.998626i	−0.647204	−	0.762316i	$-0.724062\pi$
$929$	9.88979	−	30.4376i	0.324473	−	0.998626i	0.971678	−	0.236310i	$-0.0759380\pi$
$930$		0			0
$931$	10.8803	+	33.4861i	0.356587	+	1.09746i
$932$		0			0
$933$	8.42071	−	2.73606i	0.275682	−	0.0895744i
$934$		0			0
$935$	−16.5126	+	29.9367i	−0.540018	+	0.979034i
$936$		0			0
$937$	−5.53290	+	7.61538i	−0.180752	+	0.248784i	−0.889773	−	0.456404i	$-0.849137\pi$
$937$	−5.53290	+	7.61538i	−0.180752	+	0.248784i	0.709021	+	0.705188i	$0.249137\pi$
$938$		0			0
$939$	18.3496	−	13.3318i	0.598818	−	0.435067i
$940$		0			0
$941$	21.7709	+	15.8175i	0.709710	+	0.515635i	0.883080	−	0.469222i	$-0.155466\pi$
$941$	21.7709	+	15.8175i	0.709710	+	0.515635i	−0.173370	+	0.984857i	$0.555466\pi$
$942$		0			0
$943$			61.6102i			2.00630i
$944$		0			0
$945$	−28.5286	+	26.7150i	−0.928036	+	0.869038i
$946$		0			0
$947$	−26.2616	−	8.53292i	−0.853388	−	0.277283i	−0.150523	−	0.988606i	$-0.548096\pi$
$947$	−26.2616	−	8.53292i	−0.853388	−	0.277283i	−0.702864	+	0.711324i	$0.748096\pi$
$948$		0			0
$949$	1.43769			0.0466695
$950$		0			0
$951$	−4.83418			−0.156759
$952$		0			0
$953$	6.90375	+	2.24316i	0.223634	+	0.0726632i	0.418691	−	0.908129i	$-0.362489\pi$
$953$	6.90375	+	2.24316i	0.223634	+	0.0726632i	−0.195057	+	0.980792i	$0.562489\pi$
$954$		0			0
$955$	−16.1159	−	8.88924i	−0.521498	−	0.287649i
$956$		0			0
$957$		−	27.3075i		−	0.882726i
$958$		0			0
$959$	−0.968921	−	0.703962i	−0.0312881	−	0.0227321i
$960$		0			0
$961$	22.0945	−	16.0526i	0.712725	−	0.517825i
$962$		0			0
$963$	−20.4749	+	28.1813i	−0.659795	+	0.908130i
$964$		0			0
$965$	−5.08113	−	40.6800i	−0.163567	−	1.30954i
$966$		0			0
$967$	40.0152	−	13.0017i	1.28680	−	0.418108i	0.415832	−	0.909442i	$-0.363491\pi$
$967$	40.0152	−	13.0017i	1.28680	−	0.418108i	0.870971	+	0.491334i	$0.163491\pi$
$968$		0			0
$969$	2.29341	+	7.05838i	0.0736749	+	0.226748i
$970$		0			0
$971$	12.4166	−	38.2144i	0.398468	−	1.22636i	−0.527759	−	0.849394i	$-0.676968\pi$
$971$	12.4166	−	38.2144i	0.398468	−	1.22636i	0.926227	−	0.376965i	$-0.123032\pi$
$972$		0			0
$973$	−25.1237	−	34.5798i	−0.805429	−	1.10858i
$974$		0			0
$975$	2.32269	−	2.79166i	0.0743855	−	0.0894048i
$976$		0			0
$977$	−22.0223	−	30.3111i	−0.704555	−	0.969737i	−0.999897	−	0.0143451i	$-0.995434\pi$
$977$	−22.0223	−	30.3111i	−0.704555	−	0.969737i	0.295342	−	0.955392i	$-0.404566\pi$
$978$		0			0
$979$	−15.8468	+	48.7713i	−0.506465	+	1.55874i
$980$		0			0
$981$	6.55760	+	20.1822i	0.209368	+	0.644368i
$982$		0			0
$983$	−19.2974	+	6.27011i	−0.615492	+	0.199985i	−0.600138	−	0.799897i	$-0.704888\pi$
$983$	−19.2974	+	6.27011i	−0.615492	+	0.199985i	−0.0153540	+	0.999882i	$0.504888\pi$
$984$		0			0
$985$	9.83329	+	1.89010i	0.313315	+	0.0602236i
$986$		0			0
$987$	8.23925	−	11.3404i	0.262258	−	0.360968i
$988$		0			0
$989$	−12.9325	+	9.39603i	−0.411231	+	0.298776i
$990$		0			0
$991$	13.9232	+	10.1158i	0.442285	+	0.321339i	0.786542	−	0.617537i	$-0.211869\pi$
$991$	13.9232	+	10.1158i	0.442285	+	0.321339i	−0.344258	+	0.938875i	$0.611869\pi$
$992$		0			0
$993$			17.4615i			0.554125i
$994$		0			0
$995$	35.0922	−	4.38318i	1.11250	−	0.138956i
$996$		0			0
$997$	−4.61385	−	1.49913i	−0.146122	−	0.0474780i	0.235043	−	0.971985i	$-0.424477\pi$
$997$	−4.61385	−	1.49913i	−0.146122	−	0.0474780i	−0.381165	+	0.924507i	$0.624477\pi$
$998$		0			0
$999$	−38.8283			−1.22847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.d.289.5		32
4.3	odd	2		200.2.q.a.89.4	yes	32
20.3	even	4		1000.2.m.d.801.5		32
20.7	even	4		1000.2.m.e.801.4		32
20.19	odd	2		1000.2.q.c.449.5		32
25.3	odd	20		10000.2.a.bq.1.7		16
25.9	even	10	inner	400.2.y.d.209.5		32
25.22	odd	20		10000.2.a.br.1.10		16
100.3	even	20		5000.2.a.r.1.10		16
100.47	even	20		5000.2.a.q.1.7		16
100.59	odd	10		200.2.q.a.9.4	✓	32
100.63	even	20		1000.2.m.d.201.5		32
100.87	even	20		1000.2.m.e.201.4		32
100.91	odd	10		1000.2.q.c.49.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.9.4	✓	32	100.59	odd	10
200.2.q.a.89.4	yes	32	4.3	odd	2
400.2.y.d.209.5		32	25.9	even	10	inner
400.2.y.d.289.5		32	1.1	even	1	trivial
1000.2.m.d.201.5		32	100.63	even	20
1000.2.m.d.801.5		32	20.3	even	4
1000.2.m.e.201.4		32	100.87	even	20
1000.2.m.e.801.4		32	20.7	even	4
1000.2.q.c.49.5		32	100.91	odd	10
1000.2.q.c.449.5		32	20.19	odd	2
5000.2.a.q.1.7		16	100.47	even	20
5000.2.a.r.1.10		16	100.3	even	20
10000.2.a.bq.1.7		16	25.3	odd	20
10000.2.a.br.1.10		16	25.22	odd	20

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.685617 + 0.222770i) q^{3} +(-2.21883 + 0.277142i) q^{5} +4.42421i q^{7} +(-2.00661 - 1.45789i) q^{9} +O(q^{10})\)	\(q+(0.685617 + 0.222770i) q^{3} +(-2.21883 + 0.277142i) q^{5} +4.42421i q^{7} +(-2.00661 - 1.45789i) q^{9} +(-3.36456 + 2.44449i) q^{11} +(0.592198 - 0.815091i) q^{13} +(-1.58300 - 0.304276i) q^{15} +(-3.49650 + 1.13608i) q^{17} +(-0.865323 - 2.66319i) q^{19} +(-0.985584 + 3.03332i) q^{21} +(4.41940 + 6.08278i) q^{23} +(4.84638 - 1.22986i) q^{25} +(-2.32219 - 3.19622i) q^{27} +(-2.81461 + 8.66249i) q^{29} +(0.593581 + 1.82685i) q^{31} +(-2.85136 + 0.926462i) q^{33} +(-1.22613 - 9.81657i) q^{35} +(5.77680 - 7.95108i) q^{37} +(0.587599 - 0.426916i) q^{39} +(6.62927 + 4.81644i) q^{41} +2.12609i q^{43} +(4.85636 + 2.67868i) q^{45} +(-4.17988 - 1.35813i) q^{47} -12.5737 q^{49} -2.65035 q^{51} +(-0.585317 - 0.190181i) q^{53} +(6.78790 - 6.35637i) q^{55} -2.01870i q^{57} +(-2.72648 - 1.98090i) q^{59} +(5.75438 - 4.18080i) q^{61} +(6.45000 - 8.87766i) q^{63} +(-1.08809 + 1.97267i) q^{65} +(1.37620 - 0.447154i) q^{67} +(1.67495 + 5.15497i) q^{69} +(-1.05084 + 3.23416i) q^{71} +(0.838758 + 1.15445i) q^{73} +(3.59674 + 0.236419i) q^{75} +(-10.8150 - 14.8855i) q^{77} +(-4.38778 + 13.5042i) q^{79} +(1.41926 + 4.36802i) q^{81} +(-1.70127 + 0.552776i) q^{83} +(7.44328 - 3.48980i) q^{85} +(-3.85949 + 5.31213i) q^{87} +(9.97574 - 7.24780i) q^{89} +(3.60614 + 2.62001i) q^{91} +1.38475i q^{93} +(2.65808 + 5.66934i) q^{95} +(4.35975 + 1.41657i) q^{97} +10.3151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 32 * q + 2 * q^5 + 10 * q^9	\( 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53} + 28 q^{55} + 30 q^{59} + 14 q^{61} + 20 q^{63} - 26 q^{65} - 4 q^{69} - 12 q^{71} + 40 q^{73} - 16 q^{75} - 16 q^{79} - 52 q^{81} - 30 q^{83} + 60 q^{85} - 110 q^{87} + 24 q^{89} + 4 q^{91} - 68 q^{95} + 30 q^{97} - 92 q^{99}+O(q^{100}) \) 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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