LMFDB - Embedded newform 400.2.u.f.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, 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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 13x^10 - 24x^9 + 93x^8 - 6x^7 + 342x^6 + 786x^5 + 1473x^4 + 84x^3 + 688x^2 + 168*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.3
Root			$-0.861543 - 2.65156i$ of defining polynomial
Character	$\chi$	$=$	400.81
Dual form			400.2.u.f.321.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25555 - 1.63875i) q^{3} +(-2.20302 + 0.383000i) q^{5} +2.70809 q^{7} +(1.47494 - 4.53940i) q^{9} +O(q^{10})$	\(q+(2.25555 - 1.63875i) q^{3} +(-2.20302 + 0.383000i) q^{5} +2.70809 q^{7} +(1.47494 - 4.53940i) q^{9} +(-1.91120 - 5.88208i) q^{11} +(-0.0683725 + 0.210429i) q^{13} +(-4.34139 + 4.47409i) q^{15} +(2.51204 + 1.82510i) q^{17} +(2.68270 + 1.94909i) q^{19} +(6.10822 - 4.43788i) q^{21} +(-0.557161 - 1.71477i) q^{23} +(4.70662 - 1.68752i) q^{25} +(-1.52753 - 4.70124i) q^{27} +(-3.77603 + 2.74345i) q^{29} +(4.04356 + 2.93782i) q^{31} +(-13.9501 - 10.1353i) q^{33} +(-5.96598 + 1.03720i) q^{35} +(-2.00918 + 6.18361i) q^{37} +(0.190623 + 0.586678i) q^{39} +(-1.15044 + 3.54068i) q^{41} -11.1384 q^{43} +(-1.51074 + 10.5653i) q^{45} +(3.60959 - 2.62252i) q^{47} +0.333733 q^{49} +8.65692 q^{51} +(2.32993 - 1.69279i) q^{53} +(6.46327 + 12.2264i) q^{55} +9.24503 q^{57} +(1.06770 - 3.28603i) q^{59} +(1.57525 + 4.84813i) q^{61} +(3.99427 - 12.2931i) q^{63} +(0.0700319 - 0.489766i) q^{65} +(7.18245 + 5.21835i) q^{67} +(-4.06678 - 2.95469i) q^{69} +(-7.37333 + 5.35704i) q^{71} +(1.08812 + 3.34888i) q^{73} +(7.85060 - 11.5193i) q^{75} +(-5.17571 - 15.9292i) q^{77} +(-4.24945 + 3.08741i) q^{79} +(0.434757 + 0.315869i) q^{81} +(0.598743 + 0.435012i) q^{83} +(-6.23310 - 3.05863i) q^{85} +(-4.02119 + 12.3760i) q^{87} +(4.99625 + 15.3769i) q^{89} +(-0.185159 + 0.569860i) q^{91} +13.9348 q^{93} +(-6.65654 - 3.26642i) q^{95} +(8.09228 - 5.87939i) q^{97} -29.5201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	$ 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.25555	−	1.63875i	1.30224	−	0.946134i	0.302267	−	0.953223i	$-0.402257\pi$
$3$	2.25555	−	1.63875i	1.30224	−	0.946134i	0.999975	+	0.00708906i	$0.00225654\pi$
$4$		0			0
$5$	−2.20302	+	0.383000i	−0.985222	+	0.171283i
$5$	−2.20302	+	0.383000i	−0.985222	+	0.171283i
$6$		0			0
$7$	2.70809			1.02356			0.511780	−	0.859116i	$-0.328986\pi$
$7$	2.70809			1.02356			0.511780	+	0.859116i	$0.328986\pi$
$8$		0			0
$9$	1.47494	−	4.53940i	0.491647	−	1.51313i
$10$		0			0
$11$	−1.91120	−	5.88208i	−0.576250	−	1.77351i	−0.631883	−	0.775064i	$-0.717718\pi$
$11$	−1.91120	−	5.88208i	−0.576250	−	1.77351i	0.0556334	−	0.998451i	$-0.482282\pi$
$12$		0			0
$13$	−0.0683725	+	0.210429i	−0.0189631	+	0.0583625i	−0.960090	−	0.279690i	$-0.909768\pi$
$13$	−0.0683725	+	0.210429i	−0.0189631	+	0.0583625i	0.941127	+	0.338053i	$0.109768\pi$
$14$		0			0
$15$	−4.34139	+	4.47409i	−1.12094	+	1.15520i
$16$		0			0
$17$	2.51204	+	1.82510i	0.609259	+	0.442653i	0.849153	−	0.528146i	$-0.177113\pi$
$17$	2.51204	+	1.82510i	0.609259	+	0.442653i	−0.239894	+	0.970799i	$0.577113\pi$
$18$		0			0
$19$	2.68270	+	1.94909i	0.615452	+	0.447152i	0.851330	−	0.524630i	$-0.175796\pi$
$19$	2.68270	+	1.94909i	0.615452	+	0.447152i	−0.235878	+	0.971783i	$0.575796\pi$
$20$		0			0
$21$	6.10822	−	4.43788i	1.33292	−	0.968426i
$22$		0			0
$23$	−0.557161	−	1.71477i	−0.116176	−	0.357554i	0.876014	−	0.482285i	$-0.160193\pi$
$23$	−0.557161	−	1.71477i	−0.116176	−	0.357554i	−0.992191	+	0.124732i	$0.960193\pi$
$24$		0			0
$25$	4.70662	−	1.68752i	0.941324	−	0.337503i
$26$		0			0
$27$	−1.52753	−	4.70124i	−0.293973	−	0.904755i
$28$		0			0
$29$	−3.77603	+	2.74345i	−0.701191	+	0.509445i	−0.880320	−	0.474380i	$-0.842672\pi$
$29$	−3.77603	+	2.74345i	−0.701191	+	0.509445i	0.179129	+	0.983826i	$0.442672\pi$
$30$		0			0
$31$	4.04356	+	2.93782i	0.726245	+	0.527648i	0.888373	−	0.459122i	$-0.151836\pi$
$31$	4.04356	+	2.93782i	0.726245	+	0.527648i	−0.162128	+	0.986770i	$0.551836\pi$
$32$		0			0
$33$	−13.9501	−	10.1353i	−2.42840	−	1.76434i
$34$		0			0
$35$	−5.96598	+	1.03720i	−1.00843	+	0.175318i
$36$		0			0
$37$	−2.00918	+	6.18361i	−0.330306	+	1.01658i	0.638682	+	0.769471i	$0.279480\pi$
$37$	−2.00918	+	6.18361i	−0.330306	+	1.01658i	−0.968988	+	0.247108i	$0.920520\pi$
$38$		0			0
$39$	0.190623	+	0.586678i	0.0305242	+	0.0939437i
$40$		0			0
$41$	−1.15044	+	3.54068i	−0.179668	+	0.552962i	−0.999816	−	0.0191899i	$-0.993891\pi$
$41$	−1.15044	+	3.54068i	−0.179668	+	0.552962i	0.820148	+	0.572152i	$0.193891\pi$
$42$		0			0
$43$	−11.1384			−1.69859			−0.849295	−	0.527918i	$-0.822973\pi$
$43$	−11.1384			−1.69859			−0.849295	+	0.527918i	$0.822973\pi$
$44$		0			0
$45$	−1.51074	+	10.5653i	−0.225208	+	1.57498i
$46$		0			0
$47$	3.60959	−	2.62252i	0.526513	−	0.382534i	−0.292539	−	0.956254i	$-0.594500\pi$
$47$	3.60959	−	2.62252i	0.526513	−	0.382534i	0.819052	+	0.573719i	$0.194500\pi$
$48$		0			0
$49$	0.333733			0.0476761
$50$		0			0
$51$	8.65692			1.21221
$52$		0			0
$53$	2.32993	−	1.69279i	0.320040	−	0.232523i	−0.416153	−	0.909295i	$-0.636622\pi$
$53$	2.32993	−	1.69279i	0.320040	−	0.232523i	0.736193	+	0.676772i	$0.236622\pi$
$54$		0			0
$55$	6.46327	+	12.2264i	0.871507	+	1.64860i
$56$		0			0
$57$	9.24503			1.22453
$58$		0			0
$59$	1.06770	−	3.28603i	0.139002	−	0.427805i	−0.857189	−	0.515002i	$-0.827791\pi$
$59$	1.06770	−	3.28603i	0.139002	−	0.427805i	0.996191	+	0.0871975i	$0.0277911\pi$
$60$		0			0
$61$	1.57525	+	4.84813i	0.201691	+	0.620740i	0.999833	+	0.0182712i	$0.00581621\pi$
$61$	1.57525	+	4.84813i	0.201691	+	0.620740i	−0.798142	+	0.602469i	$0.794184\pi$
$62$		0			0
$63$	3.99427	−	12.2931i	0.503231	−	1.54879i
$64$		0			0
$65$	0.0700319	−	0.489766i	0.00868639	−	0.0607481i
$66$		0			0
$67$	7.18245	+	5.21835i	0.877476	+	0.637523i	0.932582	−	0.360957i	$-0.117550\pi$
$67$	7.18245	+	5.21835i	0.877476	+	0.637523i	−0.0551069	+	0.998480i	$0.517550\pi$
$68$		0			0
$69$	−4.06678	−	2.95469i	−0.489583	−	0.355703i
$70$		0			0
$71$	−7.37333	+	5.35704i	−0.875054	+	0.635764i	−0.931938	−	0.362617i	$-0.881883\pi$
$71$	−7.37333	+	5.35704i	−0.875054	+	0.635764i	0.0568844	+	0.998381i	$0.481883\pi$
$72$		0			0
$73$	1.08812	+	3.34888i	0.127355	+	0.391957i	0.994323	−	0.106406i	$-0.0339344\pi$
$73$	1.08812	+	3.34888i	0.127355	+	0.391957i	−0.866968	+	0.498364i	$0.833934\pi$
$74$		0			0
$75$	7.85060	−	11.5193i	0.906509	−	1.33013i
$76$		0			0
$77$	−5.17571	−	15.9292i	−0.589827	−	1.81530i
$78$		0			0
$79$	−4.24945	+	3.08741i	−0.478100	+	0.347360i	−0.800590	−	0.599213i	$-0.795480\pi$
$79$	−4.24945	+	3.08741i	−0.478100	+	0.347360i	0.322489	+	0.946573i	$0.395480\pi$
$80$		0			0
$81$	0.434757	+	0.315869i	0.0483063	+	0.0350966i
$82$		0			0
$83$	0.598743	+	0.435012i	0.0657205	+	0.0477488i	0.620160	−	0.784475i	$-0.287067\pi$
$83$	0.598743	+	0.435012i	0.0657205	+	0.0477488i	−0.554440	+	0.832224i	$0.687067\pi$
$84$		0			0
$85$	−6.23310	−	3.05863i	−0.676074	−	0.331756i
$86$		0			0
$87$	−4.02119	+	12.3760i	−0.431117	+	1.32684i
$88$		0			0
$89$	4.99625	+	15.3769i	0.529602	+	1.62995i	0.755033	+	0.655687i	$0.227621\pi$
$89$	4.99625	+	15.3769i	0.529602	+	1.62995i	−0.225431	+	0.974259i	$0.572379\pi$
$90$		0			0
$91$	−0.185159	+	0.569860i	−0.0194099	+	0.0597375i
$92$		0			0
$93$	13.9348			1.44497
$94$		0			0
$95$	−6.65654	−	3.26642i	−0.682947	−	0.335128i
$96$		0			0
$97$	8.09228	−	5.87939i	0.821647	−	0.596961i	−0.0955370	−	0.995426i	$-0.530457\pi$
$97$	8.09228	−	5.87939i	0.821647	−	0.596961i	0.917184	+	0.398465i	$0.130457\pi$
$98$		0			0
$99$	−29.5201			−2.96688
$100$		0			0
$101$	6.90049			0.686624			0.343312	−	0.939221i	$-0.388451\pi$
$101$	6.90049			0.686624			0.343312	+	0.939221i	$0.388451\pi$
$102$		0			0
$103$	−7.94303	+	5.77095i	−0.782650	+	0.568629i	−0.905773	−	0.423763i	$-0.860709\pi$
$103$	−7.94303	+	5.77095i	−0.782650	+	0.568629i	0.123123	+	0.992391i	$0.460709\pi$
$104$		0			0
$105$	−11.7568	+	12.1162i	−1.14735	+	1.18242i
$106$		0			0
$107$	4.56250			0.441073			0.220537	−	0.975379i	$-0.429219\pi$
$107$	4.56250			0.441073			0.220537	+	0.975379i	$0.429219\pi$
$108$		0			0
$109$	3.70250	−	11.3951i	0.354635	−	1.09145i	−0.601586	−	0.798808i	$-0.705464\pi$
$109$	3.70250	−	11.3951i	0.354635	−	1.09145i	0.956221	−	0.292646i	$-0.0945359\pi$
$110$		0			0
$111$	5.60161	+	17.2400i	0.531681	+	1.63635i
$112$		0			0
$113$	−1.80641	+	5.55956i	−0.169933	+	0.522999i	−0.999366	−	0.0356067i	$-0.988664\pi$
$113$	−1.80641	+	5.55956i	−0.169933	+	0.522999i	0.829433	+	0.558606i	$0.188664\pi$
$114$		0			0
$115$	1.88420	+	3.56428i	0.175702	+	0.332371i
$116$		0			0
$117$	0.854377	+	0.620741i	0.0789871	+	0.0573875i
$118$		0			0
$119$	6.80282	+	4.94254i	0.623614	+	0.453082i
$120$		0			0
$121$	−22.0470	+	16.0181i	−2.00427	+	1.45619i
$122$		0			0
$123$	3.20744	+	9.87147i	0.289205	+	0.890081i
$124$		0			0
$125$	−9.72248	+	5.52027i	−0.869605	+	0.493748i
$126$		0			0
$127$	−6.06630	−	18.6702i	−0.538297	−	1.65671i	−0.736415	−	0.676530i	$-0.763483\pi$
$127$	−6.06630	−	18.6702i	−0.538297	−	1.65671i	0.198118	−	0.980178i	$-0.436517\pi$
$128$		0			0
$129$	−25.1232	+	18.2531i	−2.21198	+	1.60709i
$130$		0			0
$131$	3.99325	+	2.90127i	0.348892	+	0.253485i	0.748404	−	0.663243i	$-0.230820\pi$
$131$	3.99325	+	2.90127i	0.348892	+	0.253485i	−0.399512	+	0.916728i	$0.630820\pi$
$132$		0			0
$133$	7.26497	+	5.27831i	0.629953	+	0.457688i
$134$		0			0
$135$	5.16575	+	9.77191i	0.444597	+	0.841032i
$136$		0			0
$137$	3.21276	−	9.88785i	0.274484	−	0.844776i	−0.714871	−	0.699256i	$-0.753515\pi$
$137$	3.21276	−	9.88785i	0.274484	−	0.844776i	0.989355	−	0.145520i	$-0.0464854\pi$
$138$		0			0
$139$	−4.49777	−	13.8427i	−0.381496	−	1.17412i	−0.938990	−	0.343944i	$-0.888237\pi$
$139$	−4.49777	−	13.8427i	−0.381496	−	1.17412i	0.557494	−	0.830181i	$-0.311763\pi$
$140$		0			0
$141$	3.84395	−	11.8305i	0.323719	−	0.996304i
$142$		0			0
$143$	1.36843			0.114434
$144$		0			0
$145$	7.26794	−	7.49010i	0.603570	−	0.622019i
$146$		0			0
$147$	0.752751	−	0.546906i	0.0620859	−	0.0451080i
$148$		0			0
$149$	−19.2003			−1.57295			−0.786477	−	0.617620i	$-0.788097\pi$
$149$	−19.2003			−1.57295			−0.786477	+	0.617620i	$0.788097\pi$
$150$		0			0
$151$	7.90466			0.643272			0.321636	−	0.946863i	$-0.395767\pi$
$151$	7.90466			0.643272			0.321636	+	0.946863i	$0.395767\pi$
$152$		0			0
$153$	11.9900	−	8.71124i	0.969334	−	0.704262i
$154$		0			0
$155$	−10.0332	−	4.92340i	−0.805890	−	0.395457i
$156$		0			0
$157$	−12.3625			−0.986634			−0.493317	−	0.869849i	$-0.664216\pi$
$157$	−12.3625			−0.986634			−0.493317	+	0.869849i	$0.664216\pi$
$158$		0			0
$159$	2.48120	−	7.63635i	0.196772	−	0.605602i
$160$		0			0
$161$	−1.50884	−	4.64374i	−0.118913	−	0.365978i
$162$		0			0
$163$	4.38241	−	13.4877i	0.343257	−	1.05643i	−0.619254	−	0.785191i	$-0.712565\pi$
$163$	4.38241	−	13.4877i	0.343257	−	1.05643i	0.962511	−	0.271244i	$-0.0874351\pi$
$164$		0			0
$165$	34.6142	+	16.9855i	2.69471	+	1.32232i
$166$		0			0
$167$	−8.49753	−	6.17381i	−0.657558	−	0.477744i	0.208279	−	0.978069i	$-0.433214\pi$
$167$	−8.49753	−	6.17381i	−0.657558	−	0.477744i	−0.865838	+	0.500325i	$0.833214\pi$
$168$		0			0
$169$	10.4776	+	7.61243i	0.805970	+	0.585572i
$170$		0			0
$171$	12.8045	−	9.30304i	0.979187	−	0.711421i
$172$		0			0
$173$	−7.12904	−	21.9409i	−0.542011	−	1.66814i	−0.727993	−	0.685584i	$-0.759547\pi$
$173$	−7.12904	−	21.9409i	−0.542011	−	1.66814i	0.185983	−	0.982553i	$-0.440453\pi$
$174$		0			0
$175$	12.7459	−	4.56994i	0.963502	−	0.345455i
$176$		0			0
$177$	−2.97675	−	9.16149i	−0.223746	−	0.688620i
$178$		0			0
$179$	−4.70983	+	3.42189i	−0.352029	+	0.255764i	−0.749720	−	0.661755i	$-0.769812\pi$
$179$	−4.70983	+	3.42189i	−0.352029	+	0.255764i	0.397691	+	0.917520i	$0.369812\pi$
$180$		0			0
$181$	5.90139	+	4.28761i	0.438647	+	0.318696i	0.785097	−	0.619373i	$-0.212613\pi$
$181$	5.90139	+	4.28761i	0.438647	+	0.318696i	−0.346450	+	0.938068i	$0.612613\pi$
$182$		0			0
$183$	11.4980	+	8.35375i	0.849953	+	0.617527i
$184$		0			0
$185$	2.05794	−	14.3921i	0.151303	−	1.05813i
$186$		0			0
$187$	5.93439	−	18.2642i	0.433966	−	1.33561i
$188$		0			0
$189$	−4.13667	−	12.7314i	−0.300899	−	0.926071i
$190$		0			0
$191$	0.213245	−	0.656301i	0.0154299	−	0.0474882i	−0.943045	−	0.332665i	$-0.892052\pi$
$191$	0.213245	−	0.656301i	0.0154299	−	0.0474882i	0.958475	+	0.285177i	$0.0920522\pi$
$192$		0			0
$193$	−1.54724			−0.111373			−0.0556864	−	0.998448i	$-0.517735\pi$
$193$	−1.54724			−0.111373			−0.0556864	+	0.998448i	$0.517735\pi$
$194$		0			0
$195$	−0.644646	−	1.21946i	−0.0461640	−	0.0873272i
$196$		0			0
$197$	−0.349257	+	0.253750i	−0.0248835	+	0.0180789i	−0.600157	−	0.799882i	$-0.704895\pi$
$197$	−0.349257	+	0.253750i	−0.0248835	+	0.0180789i	0.575274	+	0.817961i	$0.304895\pi$
$198$		0			0
$199$	1.78236			0.126348			0.0631739	−	0.998003i	$-0.479878\pi$
$199$	1.78236			0.126348			0.0631739	+	0.998003i	$0.479878\pi$
$200$		0			0
$201$	24.7520			1.74587
$202$		0			0
$203$	−10.2258	+	7.42949i	−0.717712	+	0.521448i
$204$		0			0
$205$	1.17836	−	8.24083i	0.0823002	−	0.575564i
$206$		0			0
$207$	−8.60580			−0.598144
$208$		0			0
$209$	6.33754	−	19.5050i	0.438377	−	1.34919i
$210$		0			0
$211$	5.96947	+	18.3721i	0.410955	+	1.26479i	0.915819	+	0.401591i	$0.131543\pi$
$211$	5.96947	+	18.3721i	0.410955	+	1.26479i	−0.504864	+	0.863199i	$0.668457\pi$
$212$		0			0
$213$	−7.85206	+	24.1661i	−0.538014	+	1.65584i
$214$		0			0
$215$	24.5382	−	4.26601i	1.67349	−	0.290939i
$216$		0			0
$217$	10.9503	+	7.95587i	0.743356	+	0.540080i
$218$		0			0
$219$	7.94230	+	5.77042i	0.536691	+	0.389929i
$220$		0			0
$221$	−0.555809	+	0.403819i	−0.0373878	+	0.0271638i
$222$		0			0
$223$	−5.58844	−	17.1994i	−0.374229	−	1.15176i	−0.943997	−	0.329954i	$-0.892967\pi$
$223$	−5.58844	−	17.1994i	−0.374229	−	1.15176i	0.569768	−	0.821806i	$-0.307033\pi$
$224$		0			0
$225$	−0.718324	−	23.8542i	−0.0478883	−	1.59028i
$226$		0			0
$227$	1.31830	+	4.05730i	0.0874985	+	0.269293i	0.985226	−	0.171258i	$-0.0547832\pi$
$227$	1.31830	+	4.05730i	0.0874985	+	0.269293i	−0.897728	+	0.440551i	$0.854783\pi$
$228$		0			0
$229$	22.4488	−	16.3100i	1.48346	−	1.07780i	0.507037	−	0.861924i	$-0.330741\pi$
$229$	22.4488	−	16.3100i	1.48346	−	1.07780i	0.976422	−	0.215872i	$-0.0692594\pi$
$230$		0			0
$231$	−37.7781	−	27.4474i	−2.48561	−	1.80590i
$232$		0			0
$233$	−8.04210	−	5.84293i	−0.526855	−	0.382783i	0.292325	−	0.956319i	$-0.405571\pi$
$233$	−8.04210	−	5.84293i	−0.526855	−	0.382783i	−0.819180	+	0.573536i	$0.805571\pi$
$234$		0			0
$235$	−6.94759	+	7.15995i	−0.453211	+	0.467064i
$236$		0			0
$237$	−4.52535	+	13.9276i	−0.293953	+	0.904694i
$238$		0			0
$239$	2.35260	+	7.24055i	0.152177	+	0.468352i	0.997864	−	0.0653270i	$-0.0208091\pi$
$239$	2.35260	+	7.24055i	0.152177	+	0.468352i	−0.845687	+	0.533679i	$0.820809\pi$
$240$		0			0
$241$	−1.25097	+	3.85010i	−0.0805822	+	0.248007i	−0.983229	−	0.182376i	$-0.941621\pi$
$241$	−1.25097	+	3.85010i	−0.0805822	+	0.248007i	0.902647	+	0.430382i	$0.141621\pi$
$242$		0			0
$243$	16.3278			1.04743
$244$		0			0
$245$	−0.735221	+	0.127820i	−0.0469716	+	0.00816610i
$246$		0			0
$247$	−0.593568	+	0.431252i	−0.0377678	+	0.0274399i
$248$		0			0
$249$	2.06337			0.130761
$250$		0			0
$251$	−15.3929			−0.971591			−0.485795	−	0.874073i	$-0.661470\pi$
$251$	−15.3929			−0.971591			−0.485795	+	0.874073i	$0.661470\pi$
$252$		0			0
$253$	−9.02155	+	6.55454i	−0.567180	+	0.412080i
$254$		0			0
$255$	−19.0714	+	3.31560i	−1.19430	+	0.207631i
$256$		0			0
$257$	3.06508			0.191194			0.0955972	−	0.995420i	$-0.469524\pi$
$257$	3.06508			0.191194			0.0955972	+	0.995420i	$0.469524\pi$
$258$		0			0
$259$	−5.44102	+	16.7457i	−0.338089	+	1.04053i
$260$		0			0
$261$	6.88419	+	21.1874i	0.426121	+	1.31146i
$262$		0			0
$263$	3.26006	−	10.0334i	0.201024	−	0.618687i	−0.798830	−	0.601557i	$-0.794547\pi$
$263$	3.26006	−	10.0334i	0.201024	−	0.618687i	0.999853	−	0.0171300i	$-0.00545291\pi$
$264$		0			0
$265$	−4.48454	+	4.62162i	−0.275483	+	0.283904i
$266$		0			0
$267$	36.4682	+	26.4957i	2.23182	+	1.62151i
$268$		0			0
$269$	−0.543008	−	0.394519i	−0.0331078	−	0.0240542i	0.571108	−	0.820875i	$-0.306514\pi$
$269$	−0.543008	−	0.394519i	−0.0331078	−	0.0240542i	−0.604216	+	0.796821i	$0.706514\pi$
$270$		0			0
$271$	−14.9299	+	10.8472i	−0.906928	+	0.658922i	−0.940236	−	0.340523i	$-0.889396\pi$
$271$	−14.9299	+	10.8472i	−0.906928	+	0.658922i	0.0333080	+	0.999445i	$0.489396\pi$
$272$		0			0
$273$	0.516225	+	1.58878i	0.0312433	+	0.0961571i
$274$		0			0
$275$	−18.9214	−	24.4596i	−1.14100	−	1.47497i
$276$		0			0
$277$	−1.27109	−	3.91201i	−0.0763724	−	0.235050i	0.905581	−	0.424173i	$-0.139435\pi$
$277$	−1.27109	−	3.91201i	−0.0763724	−	0.235050i	−0.981953	+	0.189124i	$0.939435\pi$
$278$		0			0
$279$	19.3000	−	14.0222i	1.15546	−	0.839490i
$280$		0			0
$281$	−6.75134	−	4.90514i	−0.402751	−	0.292616i	0.367909	−	0.929862i	$-0.380074\pi$
$281$	−6.75134	−	4.90514i	−0.402751	−	0.292616i	−0.770661	+	0.637246i	$0.780074\pi$
$282$		0			0
$283$	0.272848	+	0.198236i	0.0162191	+	0.0117839i	0.595865	−	0.803084i	$-0.296809\pi$
$283$	0.272848	+	0.198236i	0.0162191	+	0.0117839i	−0.579646	+	0.814868i	$0.696809\pi$
$284$		0			0
$285$	−20.3670	+	3.54085i	−1.20644	+	0.209742i
$286$		0			0
$287$	−3.11549	+	9.58848i	−0.183901	+	0.565990i
$288$		0			0
$289$	−2.27395	−	6.99849i	−0.133762	−	0.411676i
$290$		0			0
$291$	8.61768	−	26.5225i	0.505177	−	1.55478i
$292$		0			0
$293$	−22.5665			−1.31835			−0.659174	−	0.751990i	$-0.729094\pi$
$293$	−22.5665			−1.31835			−0.659174	+	0.751990i	$0.729094\pi$
$294$		0			0
$295$	−1.09361	+	7.64813i	−0.0636724	+	0.445291i
$296$		0			0
$297$	−24.7337	+	17.9701i	−1.43519	+	1.04273i
$298$		0			0
$299$	0.398931			0.0230708
$300$		0			0
$301$	−30.1638			−1.73861
$302$		0			0
$303$	15.5644	−	11.3082i	0.894151	−	0.649639i
$304$		0			0
$305$	−5.32716	−	10.0772i	−0.305032	−	0.577020i
$306$		0			0
$307$	−0.775011			−0.0442322			−0.0221161	−	0.999755i	$-0.507040\pi$
$307$	−0.775011			−0.0442322			−0.0221161	+	0.999755i	$0.507040\pi$
$308$		0			0
$309$	−8.45874	+	26.0333i	−0.481201	+	1.48098i
$310$		0			0
$311$	−2.23153	−	6.86793i	−0.126538	−	0.389445i	0.867640	−	0.497193i	$-0.165636\pi$
$311$	−2.23153	−	6.86793i	−0.126538	−	0.389445i	−0.994178	+	0.107748i	$0.965636\pi$
$312$		0			0
$313$	7.54307	−	23.2152i	0.426360	−	1.31220i	−0.475326	−	0.879810i	$-0.657670\pi$
$313$	7.54307	−	23.2152i	0.426360	−	1.31220i	0.901686	−	0.432391i	$-0.142330\pi$
$314$		0			0
$315$	−4.09121	+	28.6118i	−0.230514	+	1.61209i
$316$		0			0
$317$	20.1580	+	14.6456i	1.13219	+	0.822581i	0.986011	−	0.166677i	$-0.0533038\pi$
$317$	20.1580	+	14.6456i	1.13219	+	0.822581i	0.146175	+	0.989259i	$0.453304\pi$
$318$		0			0
$319$	23.3540	+	16.9676i	1.30757	+	0.950005i
$320$		0			0
$321$	10.2909	−	7.47680i	0.574384	−	0.417314i
$322$		0			0
$323$	3.18174	+	9.79240i	0.177037	+	0.544863i
$324$		0			0
$325$	0.0332987	+	1.10579i	0.00184708	+	0.0613381i
$326$		0			0
$327$	−10.3226	−	31.7697i	−0.570842	−	1.75687i
$328$		0			0
$329$	9.77509	−	7.10202i	0.538918	−	0.391547i
$330$		0			0
$331$	4.24549	+	3.08453i	0.233353	+	0.169541i	0.698317	−	0.715789i	$-0.253933\pi$
$331$	4.24549	+	3.08453i	0.233353	+	0.169541i	−0.464964	+	0.885330i	$0.653933\pi$
$332$		0			0
$333$	25.1065	+	18.2409i	1.37583	+	0.999596i
$334$		0			0
$335$	−17.8217	−	8.74527i	−0.973705	−	0.477805i
$336$		0			0
$337$	−9.28987	+	28.5913i	−0.506051	+	1.55747i	0.292945	+	0.956129i	$0.405365\pi$
$337$	−9.28987	+	28.5913i	−0.506051	+	1.55747i	−0.798996	+	0.601336i	$0.794635\pi$
$338$		0			0
$339$	5.03630	+	15.5001i	0.273534	+	0.841851i
$340$		0			0
$341$	9.55242	−	29.3993i	0.517293	−	1.59206i
$342$		0			0
$343$	−18.0528			−0.974761
$344$		0			0
$345$	10.0909	+	4.95167i	0.543274	+	0.266589i
$346$		0			0
$347$	−12.7137	+	9.23702i	−0.682505	+	0.495869i	−0.874188	−	0.485588i	$-0.838606\pi$
$347$	−12.7137	+	9.23702i	−0.682505	+	0.495869i	0.191683	+	0.981457i	$0.438606\pi$
$348$		0			0
$349$	13.5808			0.726961			0.363481	−	0.931602i	$-0.381588\pi$
$349$	13.5808			0.726961			0.363481	+	0.931602i	$0.381588\pi$
$350$		0			0
$351$	1.09372			0.0583784
$352$		0			0
$353$	−25.1732	+	18.2894i	−1.33984	+	0.973448i	−0.340386	+	0.940286i	$0.610558\pi$
$353$	−25.1732	+	18.2894i	−1.33984	+	0.973448i	−0.999450	+	0.0331617i	$0.989442\pi$
$354$		0			0
$355$	14.1919	−	14.6257i	0.753227	−	0.776250i
$356$		0			0
$357$	23.4437			1.24077
$358$		0			0
$359$	8.22663	−	25.3190i	0.434185	−	1.33628i	−0.459734	−	0.888057i	$-0.652055\pi$
$359$	8.22663	−	25.3190i	0.434185	−	1.33628i	0.893919	−	0.448228i	$-0.147945\pi$
$360$		0			0
$361$	−2.47343	−	7.61243i	−0.130180	−	0.400654i
$362$		0			0
$363$	−23.4784	+	72.2592i	−1.23230	+	3.79262i
$364$		0			0
$365$	−3.67977	−	6.96092i	−0.192608	−	0.364351i
$366$		0			0
$367$	−20.3126	−	14.7579i	−1.06031	−	0.770358i	−0.0861618	−	0.996281i	$-0.527460\pi$
$367$	−20.3126	−	14.7579i	−1.06031	−	0.770358i	−0.974145	+	0.225923i	$0.927460\pi$
$368$		0			0
$369$	14.3758	+	10.4446i	0.748373	+	0.543725i
$370$		0			0
$371$	6.30964	−	4.58422i	0.327580	−	0.238001i
$372$		0			0
$373$	−0.896671	−	2.75967i	−0.0464279	−	0.142890i	0.925155	−	0.379589i	$-0.123935\pi$
$373$	−0.896671	−	2.75967i	−0.0464279	−	0.142890i	−0.971583	+	0.236699i	$0.923935\pi$
$374$		0			0
$375$	−12.8832	+	28.3840i	−0.665284	+	1.46574i
$376$		0			0
$377$	−0.319124	−	0.982163i	−0.0164357	−	0.0505839i
$378$		0			0
$379$	−3.22416	+	2.34249i	−0.165614	+	0.120326i	−0.667505	−	0.744605i	$-0.732638\pi$
$379$	−3.22416	+	2.34249i	−0.165614	+	0.120326i	0.501891	+	0.864931i	$0.332638\pi$
$380$		0			0
$381$	−44.2786	−	32.1703i	−2.26846	−	1.64813i
$382$		0			0
$383$	−0.00459892	−	0.00334131i	−0.000234994	−	0.000170733i	0.587668	−	0.809102i	$-0.300046\pi$
$383$	−0.00459892	−	0.00334131i	−0.000234994	−	0.000170733i	−0.587903	+	0.808932i	$0.700046\pi$
$384$		0			0
$385$	17.5031	+	33.1101i	0.892040	+	1.68745i
$386$		0			0
$387$	−16.4285	+	50.5617i	−0.835107	+	2.57020i
$388$		0			0
$389$	8.00519	+	24.6374i	0.405879	+	1.24917i	0.920159	+	0.391545i	$0.128059\pi$
$389$	8.00519	+	24.6374i	0.405879	+	1.24917i	−0.514280	+	0.857623i	$0.671941\pi$
$390$		0			0
$391$	1.73002	−	5.32444i	0.0874906	−	0.269268i
$392$		0			0
$393$	13.7614			0.694173
$394$		0			0
$395$	8.17916	−	8.42917i	0.411538	−	0.424117i
$396$		0			0
$397$	−9.16678	+	6.66006i	−0.460068	+	0.334259i	−0.793558	−	0.608495i	$-0.791774\pi$
$397$	−9.16678	+	6.66006i	−0.460068	+	0.334259i	0.333490	+	0.942754i	$0.391774\pi$
$398$		0			0
$399$	25.0363			1.25338
$400$		0			0
$401$	6.06828			0.303035			0.151518	−	0.988455i	$-0.451584\pi$
$401$	6.06828			0.303035			0.151518	+	0.988455i	$0.451584\pi$
$402$		0			0
$403$	−0.894671	+	0.650016i	−0.0445667	+	0.0323796i
$404$		0			0
$405$	−1.07876	−	0.529356i	−0.0536039	−	0.0263039i
$406$		0			0
$407$	40.2124			1.99326
$408$		0			0
$409$	0.847821	−	2.60932i	0.0419220	−	0.129023i	−0.927905	−	0.372817i	$-0.878392\pi$
$409$	0.847821	−	2.60932i	0.0419220	−	0.129023i	0.969827	+	0.243794i	$0.0783920\pi$
$410$		0			0
$411$	−8.95721	−	27.5675i	−0.441827	−	1.35980i
$412$		0			0
$413$	2.89141	−	8.89885i	0.142277	−	0.437884i
$414$		0			0
$415$	−1.48565	−	0.729023i	−0.0729278	−	0.0357863i
$416$		0			0
$417$	−32.8298	−	23.8522i	−1.60768	−	1.16805i
$418$		0			0
$419$	−16.1307	−	11.7196i	−0.788036	−	0.572541i	0.119344	−	0.992853i	$-0.461921\pi$
$419$	−16.1307	−	11.7196i	−0.788036	−	0.572541i	−0.907380	+	0.420312i	$0.861921\pi$
$420$		0			0
$421$	16.8329	−	12.2298i	0.820383	−	0.596043i	−0.0964392	−	0.995339i	$-0.530745\pi$
$421$	16.8329	−	12.2298i	0.820383	−	0.596043i	0.916822	+	0.399296i	$0.130745\pi$
$422$		0			0
$423$	−6.58075	−	20.2535i	−0.319967	−	0.984757i
$424$		0			0
$425$	14.9031	+	4.35097i	0.722907	+	0.211053i
$426$		0			0
$427$	4.26592	+	13.1292i	0.206443	+	0.635365i
$428$		0			0
$429$	3.08657	−	2.24253i	0.149021	−	0.108270i
$430$		0			0
$431$	22.9738	+	16.6915i	1.10661	+	0.803999i	0.982126	−	0.188222i	$-0.0602726\pi$
$431$	22.9738	+	16.6915i	1.10661	+	0.803999i	0.124484	+	0.992222i	$0.460273\pi$
$432$		0			0
$433$	0.856621	+	0.622371i	0.0411666	+	0.0299093i	0.608178	−	0.793800i	$-0.291901\pi$
$433$	0.856621	+	0.622371i	0.0411666	+	0.0299093i	−0.567012	+	0.823710i	$0.691901\pi$
$434$		0			0
$435$	4.11879	−	28.8046i	0.197481	−	1.38108i
$436$		0			0
$437$	1.84754	−	5.68615i	0.0883800	−	0.272006i
$438$		0			0
$439$	−1.86423	−	5.73752i	−0.0889750	−	0.273837i	0.896662	−	0.442716i	$-0.145985\pi$
$439$	−1.86423	−	5.73752i	−0.0889750	−	0.273837i	−0.985637	+	0.168879i	$0.945985\pi$
$440$		0			0
$441$	0.492237	−	1.51495i	0.0234398	−	0.0721404i
$442$		0			0
$443$	−4.65442			−0.221138			−0.110569	−	0.993868i	$-0.535267\pi$
$443$	−4.65442			−0.221138			−0.110569	+	0.993868i	$0.535267\pi$
$444$		0			0
$445$	−16.8962	−	31.9621i	−0.800957	−	1.51515i
$446$		0			0
$447$	−43.3073	+	31.4646i	−2.04837	+	1.48823i
$448$		0			0
$449$	2.06662			0.0975300			0.0487650	−	0.998810i	$-0.484471\pi$
$449$	2.06662			0.0975300			0.0487650	+	0.998810i	$0.484471\pi$
$450$		0			0
$451$	23.0253			1.08422
$452$		0			0
$453$	17.8294	−	12.9538i	0.837696	−	0.608622i
$454$		0			0
$455$	0.189652	−	1.32633i	0.00889105	−	0.0621793i
$456$		0			0
$457$	13.1891			0.616962			0.308481	−	0.951231i	$-0.400179\pi$
$457$	13.1891			0.616962			0.308481	+	0.951231i	$0.400179\pi$
$458$		0			0
$459$	4.74305	−	14.5976i	0.221387	−	0.681358i
$460$		0			0
$461$	12.8573	+	39.5708i	0.598825	+	1.84299i	0.534681	+	0.845054i	$0.320432\pi$
$461$	12.8573	+	39.5708i	0.598825	+	1.84299i	0.0641445	+	0.997941i	$0.479568\pi$
$462$		0			0
$463$	4.50402	−	13.8619i	0.209320	−	0.644219i	−0.790189	−	0.612864i	$-0.790018\pi$
$463$	4.50402	−	13.8619i	0.209320	−	0.644219i	0.999508	−	0.0313558i	$-0.00998250\pi$
$464$		0			0
$465$	−30.6987	+	5.33703i	−1.42362	+	0.247499i
$466$		0			0
$467$	−23.8991	−	17.3637i	−1.10592	−	0.803495i	−0.123901	−	0.992295i	$-0.539540\pi$
$467$	−23.8991	−	17.3637i	−1.10592	−	0.803495i	−0.982016	+	0.188799i	$0.939540\pi$
$468$		0			0
$469$	19.4507	+	14.1318i	0.898149	+	0.652544i
$470$		0			0
$471$	−27.8842	+	20.2591i	−1.28484	+	0.933489i
$472$		0			0
$473$	21.2878	+	65.5170i	0.978813	+	3.01248i
$474$		0			0
$475$	15.9156	+	4.64655i	0.730256	+	0.213198i
$476$		0			0
$477$	−4.24776	−	13.0732i	−0.194491	−	0.598583i
$478$		0			0
$479$	−16.1865	+	11.7602i	−0.739581	+	0.537337i	−0.892580	−	0.450889i	$-0.851107\pi$
$479$	−16.1865	+	11.7602i	−0.739581	+	0.537337i	0.152999	+	0.988226i	$0.451107\pi$
$480$		0			0
$481$	−1.16384	−	0.845577i	−0.0530664	−	0.0385550i
$482$		0			0
$483$	−11.0132	−	8.00156i	−0.501118	−	0.364083i
$484$		0			0
$485$	−15.5757	+	16.0518i	−0.707255	+	0.728873i
$486$		0			0
$487$	−4.89158	+	15.0547i	−0.221659	+	0.682195i	0.776955	+	0.629556i	$0.216763\pi$
$487$	−4.89158	+	15.0547i	−0.221659	+	0.682195i	−0.998614	+	0.0526389i	$0.983237\pi$
$488$		0			0
$489$	−12.2182	−	37.6038i	−0.552526	−	1.70050i
$490$		0			0
$491$	−1.59500	+	4.90889i	−0.0719811	+	0.221535i	−0.980575	−	0.196146i	$-0.937157\pi$
$491$	−1.59500	+	4.90889i	−0.0719811	+	0.221535i	0.908593	+	0.417682i	$0.137157\pi$
$492$		0			0
$493$	−14.4926			−0.652715
$494$		0			0
$495$	65.0334	−	11.3062i	2.92303	−	0.508175i
$496$		0			0
$497$	−19.9676	+	14.5073i	−0.895671	+	0.650743i
$498$		0			0
$499$	35.9077			1.60745			0.803724	−	0.595002i	$-0.202849\pi$
$499$	35.9077			1.60745			0.803724	+	0.595002i	$0.202849\pi$
$500$		0			0
$501$	−29.2839			−1.30831
$502$		0			0
$503$	6.48332	−	4.71041i	0.289077	−	0.210027i	−0.433790	−	0.901014i	$-0.642824\pi$
$503$	6.48332	−	4.71041i	0.289077	−	0.210027i	0.722867	+	0.690987i	$0.242824\pi$
$504$		0			0
$505$	−15.2019	+	2.64289i	−0.676477	+	0.117607i
$506$		0			0
$507$	36.1077			1.60360
$508$		0			0
$509$	−0.562705	+	1.73183i	−0.0249415	+	0.0767619i	−0.962752	−	0.270384i	$-0.912849\pi$
$509$	−0.562705	+	1.73183i	−0.0249415	+	0.0767619i	0.937811	+	0.347146i	$0.112849\pi$
$510$		0			0
$511$	2.94672	+	9.06907i	0.130355	+	0.401192i
$512$		0			0
$513$	5.06527	−	15.5893i	0.223637	−	0.688284i
$514$		0			0
$515$	15.2884	−	15.7557i	0.673688	−	0.694280i
$516$		0			0
$517$	−22.3246	−	16.2197i	−0.981833	−	0.713344i
$518$		0			0
$519$	−52.0356	−	37.8061i	−2.28411	−	1.65950i
$520$		0			0
$521$	−24.8215	+	18.0339i	−1.08745	+	0.790079i	−0.978967	−	0.204019i	$-0.934600\pi$
$521$	−24.8215	+	18.0339i	−1.08745	+	0.790079i	−0.108484	+	0.994098i	$0.534600\pi$
$522$		0			0
$523$	3.64258	+	11.2107i	0.159279	+	0.490210i	0.998569	−	0.0534734i	$-0.0170292\pi$
$523$	3.64258	+	11.2107i	0.159279	+	0.490210i	−0.839290	+	0.543683i	$0.817029\pi$
$524$		0			0
$525$	21.2601	−	31.1952i	0.927867	−	1.36147i
$526$		0			0
$527$	4.79576	+	14.7598i	0.208907	+	0.642949i
$528$		0			0
$529$	15.9774	−	11.6083i	0.694669	−	0.504707i
$530$		0			0
$531$	−13.3418	−	9.69341i	−0.578986	−	0.420658i
$532$		0			0
$533$	−0.666404	−	0.484171i	−0.0288652	−	0.0209718i
$534$		0			0
$535$	−10.0513	+	1.74744i	−0.434555	+	0.0755483i
$536$		0			0
$537$	−5.01562	+	15.4365i	−0.216440	+	0.666134i
$538$		0			0
$539$	−0.637832	−	1.96304i	−0.0274734	−	0.0845543i
$540$		0			0
$541$	−8.62453	+	26.5436i	−0.370798	+	1.14120i	0.575473	+	0.817821i	$0.304818\pi$
$541$	−8.62453	+	26.5436i	−0.370798	+	1.14120i	−0.946270	+	0.323377i	$0.895182\pi$
$542$		0			0
$543$	20.3372			0.872754
$544$		0			0
$545$	−3.79236	+	26.5218i	−0.162447	+	1.13607i
$546$		0			0
$547$	−14.3474	+	10.4240i	−0.613451	+	0.445698i	−0.850628	−	0.525768i	$-0.823778\pi$
$547$	−14.3474	+	10.4240i	−0.613451	+	0.445698i	0.237177	+	0.971466i	$0.423778\pi$
$548$		0			0
$549$	24.3311			1.03842
$550$		0			0
$551$	−15.4772			−0.659350
$552$		0			0
$553$	−11.5079	+	8.36096i	−0.489365	+	0.355544i
$554$		0			0
$555$	−18.9434	−	35.8346i	−0.804102	−	1.52110i
$556$		0			0
$557$	32.3697			1.37155			0.685775	−	0.727814i	$-0.259464\pi$
$557$	32.3697			1.37155			0.685775	+	0.727814i	$0.259464\pi$
$558$		0			0
$559$	0.761561	−	2.34384i	0.0322106	−	0.0991340i
$560$		0			0
$561$	−16.5452	−	50.9207i	−0.698537	−	2.14988i
$562$		0			0
$563$	−12.4896	+	38.4390i	−0.526374	+	1.62001i	0.235209	+	0.971945i	$0.424423\pi$
$563$	−12.4896	+	38.4390i	−0.526374	+	1.62001i	−0.761583	+	0.648068i	$0.775577\pi$
$564$		0			0
$565$	1.85025	−	12.9397i	0.0778407	−	0.544377i
$566$		0			0
$567$	1.17736	+	0.855402i	0.0494444	+	0.0359235i
$568$		0			0
$569$	−18.4838	−	13.4293i	−0.774882	−	0.562985i	0.128556	−	0.991702i	$-0.458966\pi$
$569$	−18.4838	−	13.4293i	−0.774882	−	0.562985i	−0.903439	+	0.428717i	$0.858966\pi$
$570$		0			0
$571$	−25.0776	+	18.2199i	−1.04946	+	0.762480i	−0.972110	−	0.234523i	$-0.924647\pi$
$571$	−25.0776	+	18.2199i	−1.04946	+	0.762480i	−0.0773536	+	0.997004i	$0.524647\pi$
$572$		0			0
$573$	−0.594530	−	1.82977i	−0.0248368	−	0.0764399i
$574$		0			0
$575$	−5.51604	−	7.13054i	−0.230035	−	0.297364i
$576$		0			0
$577$	−13.2010	−	40.6284i	−0.549564	−	1.69138i	−0.709884	−	0.704318i	$-0.751253\pi$
$577$	−13.2010	−	40.6284i	−0.549564	−	1.69138i	0.160321	−	0.987065i	$-0.448747\pi$
$578$		0			0
$579$	−3.48988	+	2.53554i	−0.145034	+	0.105374i
$580$		0			0
$581$	1.62145	+	1.17805i	0.0672689	+	0.0488737i
$582$		0			0
$583$	−14.4101	−	10.4696i	−0.596806	−	0.433605i
$584$		0			0
$585$	−2.11996	−	1.04028i	−0.0876494	−	0.0430103i
$586$		0			0
$587$	6.70607	−	20.6392i	0.276789	−	0.851869i	−0.711951	−	0.702229i	$-0.752188\pi$
$587$	6.70607	−	20.6392i	0.276789	−	0.851869i	0.988740	−	0.149640i	$-0.0478116\pi$
$588$		0			0
$589$	5.12156	+	15.7625i	0.211030	+	0.649485i
$590$		0			0
$591$	−0.371933	+	1.14469i	−0.0152993	+	0.0470863i
$592$		0			0
$593$	36.6696			1.50584			0.752920	−	0.658113i	$-0.228645\pi$
$593$	36.6696			1.50584			0.752920	+	0.658113i	$0.228645\pi$
$594$		0			0
$595$	−16.8798	−	8.28305i	−0.692003	−	0.339572i
$596$		0			0
$597$	4.02019	−	2.92084i	0.164535	−	0.119542i
$598$		0			0
$599$	37.2180			1.52069			0.760343	−	0.649521i	$-0.225031\pi$
$599$	37.2180			1.52069			0.760343	+	0.649521i	$0.225031\pi$
$600$		0			0
$601$	24.3070			0.991505			0.495752	−	0.868464i	$-0.334892\pi$
$601$	24.3070			0.991505			0.495752	+	0.868464i	$0.334892\pi$
$602$		0			0
$603$	34.2819	−	24.9073i	1.39607	−	1.01430i
$604$		0			0
$605$	42.4351	−	43.7322i	1.72523	−	1.77797i
$606$		0			0
$607$	−30.4134			−1.23444			−0.617222	−	0.786789i	$-0.711742\pi$
$607$	−30.4134			−1.23444			−0.617222	+	0.786789i	$0.711742\pi$
$608$		0			0
$609$	−10.8897	+	33.5152i	−0.441275	+	1.35810i
$610$		0			0
$611$	0.305058	+	0.938871i	0.0123413	+	0.0379827i
$612$		0			0
$613$	7.48825	−	23.0465i	0.302447	−	0.930837i	−0.678170	−	0.734905i	$-0.737227\pi$
$613$	7.48825	−	23.0465i	0.302447	−	0.930837i	0.980617	−	0.195932i	$-0.0627733\pi$
$614$		0			0
$615$	−10.8468	−	20.5186i	−0.437386	−	0.827391i
$616$		0			0
$617$	16.7300	+	12.1551i	0.673525	+	0.489345i	0.871203	−	0.490922i	$-0.163340\pi$
$617$	16.7300	+	12.1551i	0.673525	+	0.489345i	−0.197678	+	0.980267i	$0.563340\pi$
$618$		0			0
$619$	−15.5455	−	11.2945i	−0.624827	−	0.453963i	0.229777	−	0.973243i	$-0.426200\pi$
$619$	−15.5455	−	11.2945i	−0.624827	−	0.453963i	−0.854604	+	0.519280i	$0.826200\pi$
$620$		0			0
$621$	−7.21046	+	5.23870i	−0.289346	+	0.210222i
$622$		0			0
$623$	13.5303	+	41.6419i	0.542079	+	1.66835i
$624$		0			0
$625$	19.3046	−	15.8850i	0.772183	−	0.635400i
$626$		0			0
$627$	−17.6691	−	54.3800i	−0.705638	−	2.17173i
$628$		0			0
$629$	−16.3329	+	11.8665i	−0.651234	+	0.473149i
$630$		0			0
$631$	−5.43088	−	3.94576i	−0.216200	−	0.157078i	0.474415	−	0.880302i	$-0.342660\pi$
$631$	−5.43088	−	3.94576i	−0.216200	−	0.157078i	−0.690614	+	0.723223i	$0.742660\pi$
$632$		0			0
$633$	43.5718	+	31.6568i	1.73182	+	1.25824i
$634$		0			0
$635$	20.5149	+	38.8074i	0.814108	+	1.54002i
$636$		0			0
$637$	−0.0228182	+	0.0702271i	−0.000904088	+	0.00278250i
$638$		0			0
$639$	13.4425	+	41.3719i	0.531779	+	1.63665i
$640$		0			0
$641$	5.89451	−	18.1414i	0.232819	−	0.716544i	−0.764584	−	0.644524i	$-0.777056\pi$
$641$	5.89451	−	18.1414i	0.232819	−	0.716544i	0.997403	−	0.0720196i	$-0.0229444\pi$
$642$		0			0
$643$	41.2632			1.62726			0.813631	−	0.581381i	$-0.197488\pi$
$643$	41.2632			1.62726			0.813631	+	0.581381i	$0.197488\pi$
$644$		0			0
$645$	48.3561	−	49.8342i	1.90402	−	1.96222i
$646$		0			0
$647$	26.0095	−	18.8970i	1.02254	−	0.742917i	0.0557361	−	0.998446i	$-0.482249\pi$
$647$	26.0095	−	18.8970i	1.02254	−	0.742917i	0.966802	+	0.255528i	$0.0822494\pi$
$648$		0			0
$649$	−21.3693			−0.838818
$650$		0			0
$651$	37.7367			1.47902
$652$		0			0
$653$	24.0456	−	17.4701i	0.940976	−	0.683659i	−0.00767929	−	0.999971i	$-0.502444\pi$
$653$	24.0456	−	17.4701i	0.940976	−	0.683659i	0.948655	+	0.316311i	$0.102444\pi$
$654$		0			0
$655$	−9.90841	−	4.86214i	−0.387154	−	0.189980i
$656$		0			0
$657$	16.8069			0.655698
$658$		0			0
$659$	−15.1405	+	46.5976i	−0.589789	+	1.81518i	−0.0106678	+	0.999943i	$0.503396\pi$
$659$	−15.1405	+	46.5976i	−0.589789	+	1.81518i	−0.579121	+	0.815241i	$0.696604\pi$
$660$		0			0
$661$	6.05603	+	18.6386i	0.235552	+	0.724956i	0.997048	+	0.0767853i	$0.0244656\pi$
$661$	6.05603	+	18.6386i	0.235552	+	0.724956i	−0.761495	+	0.648171i	$0.775534\pi$
$662$		0			0
$663$	−0.591896	+	1.82167i	−0.0229873	+	0.0707477i
$664$		0			0
$665$	−18.0265	−	8.84576i	−0.699037	−	0.343024i
$666$		0			0
$667$	6.80823	+	4.94647i	0.263616	+	0.191528i
$668$		0			0
$669$	−40.7906	−	29.6361i	−1.57706	−	1.14580i
$670$		0			0
$671$	25.5065	−	18.5316i	0.984667	−	0.715403i
$672$		0			0
$673$	−6.95009	−	21.3902i	−0.267906	−	0.824531i	−0.991010	−	0.133791i	$-0.957285\pi$
$673$	−6.95009	−	21.3902i	−0.267906	−	0.824531i	0.723103	−	0.690740i	$-0.242715\pi$
$674$		0			0
$675$	−15.1229	−	19.5493i	−0.582081	−	0.752451i
$676$		0			0
$677$	0.0323639	+	0.0996058i	0.00124385	+	0.00382816i	0.951677	−	0.307102i	$-0.0993594\pi$
$677$	0.0323639	+	0.0996058i	0.00124385	+	0.00382816i	−0.950433	+	0.310930i	$0.899359\pi$
$678$		0			0
$679$	21.9146	−	15.9219i	0.841005	−	0.611026i
$680$		0			0
$681$	9.62240	+	6.99108i	0.368731	+	0.267899i
$682$		0			0
$683$	−29.4255	−	21.3789i	−1.12594	−	0.818041i	−0.140838	−	0.990033i	$-0.544980\pi$
$683$	−29.4255	−	21.3789i	−1.12594	−	0.818041i	−0.985098	+	0.171992i	$0.944980\pi$
$684$		0			0
$685$	−3.29073	+	23.0137i	−0.125732	+	0.879307i
$686$		0			0
$687$	23.9063	−	73.5761i	0.912083	−	2.80710i
$688$		0			0
$689$	0.196909	+	0.606024i	0.00750165	+	0.0230877i
$690$		0			0
$691$	1.53638	−	4.72848i	0.0584465	−	0.179880i	−0.917571	−	0.397572i	$-0.869853\pi$
$691$	1.53638	−	4.72848i	0.0584465	−	0.179880i	0.976017	+	0.217692i	$0.0698529\pi$
$692$		0			0
$693$	−79.9429			−3.03678
$694$		0			0
$695$	15.2105	+	28.7732i	0.576966	+	1.09143i
$696$		0			0
$697$	−9.35207	+	6.79467i	−0.354235	+	0.257367i
$698$		0			0
$699$	−27.7145			−1.04826
$700$		0			0
$701$	8.80733			0.332648			0.166324	−	0.986071i	$-0.446810\pi$
$701$	8.80733			0.332648			0.166324	+	0.986071i	$0.446810\pi$
$702$		0			0
$703$	−17.4424	+	12.6727i	−0.657853	+	0.477959i
$704$		0			0
$705$	−3.93724	+	27.5350i	−0.148285	+	1.03703i
$706$		0			0
$707$	18.6871			0.702801
$708$		0			0
$709$	−10.9565	+	33.7206i	−0.411480	+	1.26641i	0.503882	+	0.863773i	$0.331905\pi$
$709$	−10.9565	+	33.7206i	−0.411480	+	1.26641i	−0.915362	+	0.402633i	$0.868095\pi$
$710$		0			0
$711$	7.74729	+	23.8437i	0.290546	+	0.894209i
$712$		0			0
$713$	2.78476	−	8.57060i	0.104290	−	0.320972i
$714$		0			0
$715$	−3.01469	+	0.524110i	−0.112743	+	0.0196006i
$716$		0			0
$717$	17.1719	+	12.4761i	0.641295	+	0.465928i
$718$		0			0
$719$	0.880663	+	0.639839i	0.0328432	+	0.0238620i	0.604086	−	0.796919i	$-0.293538\pi$
$719$	0.880663	+	0.639839i	0.0328432	+	0.0238620i	−0.571243	+	0.820781i	$0.693538\pi$
$720$		0			0
$721$	−21.5104	+	15.6282i	−0.801090	+	0.582026i
$722$		0			0
$723$	3.48773	+	10.7341i	0.129710	+	0.399206i
$724$		0			0
$725$	−13.1427	+	19.2845i	−0.488109	+	0.716208i
$726$		0			0
$727$	−2.92535	−	9.00331i	−0.108495	−	0.333914i	0.882040	−	0.471175i	$-0.156170\pi$
$727$	−2.92535	−	9.00331i	−0.108495	−	0.333914i	−0.990535	+	0.137261i	$0.956170\pi$
$728$		0			0
$729$	35.5239	−	25.8096i	1.31570	−	0.955911i
$730$		0			0
$731$	−27.9801	−	20.3287i	−1.03488	−	0.751886i
$732$		0			0
$733$	−25.2568	−	18.3501i	−0.932880	−	0.677777i	0.0138164	−	0.999905i	$-0.495602\pi$
$733$	−25.2568	−	18.3501i	−0.932880	−	0.677777i	−0.946696	+	0.322128i	$0.895602\pi$
$734$		0			0
$735$	−1.44886	+	1.49315i	−0.0534421	+	0.0550757i
$736$		0			0
$737$	16.9677	−	52.2211i	0.625012	−	1.92359i
$738$		0			0
$739$	−7.98543	−	24.5766i	−0.293749	−	0.904066i	−0.983639	−	0.180152i	$-0.942341\pi$
$739$	−7.98543	−	24.5766i	−0.293749	−	0.904066i	0.689890	−	0.723914i	$-0.257659\pi$
$740$		0			0
$741$	−0.632106	+	1.94542i	−0.0232210	+	0.0714669i
$742$		0			0
$743$	28.7892			1.05617			0.528086	−	0.849191i	$-0.322910\pi$
$743$	28.7892			1.05617			0.528086	+	0.849191i	$0.322910\pi$
$744$		0			0
$745$	42.2988	−	7.35373i	1.54971	−	0.269420i
$746$		0			0
$747$	2.85781	−	2.07632i	0.104562	−	0.0759685i
$748$		0			0
$749$	12.3556			0.451465
$750$		0			0
$751$	−51.1434			−1.86625			−0.933125	−	0.359551i	$-0.882930\pi$
$751$	−51.1434			−1.86625			−0.933125	+	0.359551i	$0.882930\pi$
$752$		0			0
$753$	−34.7194	+	25.2251i	−1.26525	+	0.919255i
$754$		0			0
$755$	−17.4142	+	3.02749i	−0.633766	+	0.110182i
$756$		0			0
$757$	−39.1759			−1.42387			−0.711937	−	0.702243i	$-0.752182\pi$
$757$	−39.1759			−1.42387			−0.711937	+	0.702243i	$0.752182\pi$
$758$		0			0
$759$	−9.60728	+	29.5682i	−0.348722	+	1.07326i
$760$		0			0
$761$	−5.88506	−	18.1123i	−0.213333	−	0.656572i	−0.999268	−	0.0382622i	$-0.987818\pi$
$761$	−5.88506	−	18.1123i	−0.213333	−	0.656572i	0.785935	−	0.618310i	$-0.212182\pi$
$762$		0			0
$763$	10.0267	−	30.8590i	0.362991	−	1.11717i
$764$		0			0
$765$	−23.0778	+	23.7832i	−0.834381	+	0.859885i
$766$		0			0
$767$	0.618475	+	0.449348i	0.0223318	+	0.0162250i
$768$		0			0
$769$	−32.8071	−	23.8358i	−1.18305	−	0.859539i	−0.190542	−	0.981679i	$-0.561024\pi$
$769$	−32.8071	−	23.8358i	−1.18305	−	0.859539i	−0.992513	+	0.122140i	$0.961024\pi$
$770$		0			0
$771$	6.91344	−	5.02290i	0.248981	−	0.180896i
$772$		0			0
$773$	9.30015	+	28.6229i	0.334503	+	1.02950i	0.966966	+	0.254905i	$0.0820441\pi$
$773$	9.30015	+	28.6229i	0.334503	+	1.02950i	−0.632463	+	0.774591i	$0.717956\pi$
$774$		0			0
$775$	23.9891	+	7.00363i	0.861715	+	0.251578i
$776$		0			0
$777$	15.1696	+	46.6873i	0.544208	+	1.67490i
$778$		0			0
$779$	−9.98740	+	7.25627i	−0.357836	+	0.259983i
$780$		0			0
$781$	45.6025	+	33.1322i	1.63179	+	1.18556i
$782$		0			0
$783$	18.6656	+	13.5614i	0.667054	+	0.484643i
$784$		0			0
$785$	27.2349	−	4.73484i	0.972054	−	0.168994i
$786$		0			0
$787$	−4.41827	+	13.5980i	−0.157494	+	0.484717i	−0.998405	−	0.0564563i	$-0.982020\pi$
$787$	−4.41827	+	13.5980i	−0.157494	+	0.484717i	0.840911	+	0.541174i	$0.182020\pi$
$788$		0			0
$789$	−9.08908	−	27.9733i	−0.323580	−	0.995876i
$790$		0			0
$791$	−4.89192	+	15.0558i	−0.173937	+	0.535322i
$792$		0			0
$793$	−1.12789			−0.0400526
$794$		0			0
$795$	−2.54142	+	17.7733i	−0.0901348	+	0.630356i
$796$		0			0
$797$	−39.2055	+	28.4844i	−1.38873	+	1.00897i	−0.392725	+	0.919656i	$0.628468\pi$
$797$	−39.2055	+	28.4844i	−1.38873	+	1.00897i	−0.996003	+	0.0893148i	$0.971532\pi$
$798$		0			0
$799$	13.8538			0.490113
$800$		0			0
$801$	77.1711			2.72671
$802$		0			0
$803$	17.6188	−	12.8008i	0.621754	−	0.451731i
$804$		0			0
$805$	5.10256	+	9.65237i	0.179842	+	0.340201i
$806$		0			0
$807$	−1.87130			−0.0658729
$808$		0			0
$809$	−5.23619	+	16.1153i	−0.184095	+	0.566585i	−0.999932	−	0.0116969i	$-0.996277\pi$
$809$	−5.23619	+	16.1153i	−0.184095	+	0.566585i	0.815837	+	0.578282i	$0.196277\pi$
$810$		0			0
$811$	4.40687	+	13.5629i	0.154746	+	0.476259i	0.998135	−	0.0610441i	$-0.0194430\pi$
$811$	4.40687	+	13.5629i	0.154746	+	0.476259i	−0.843389	+	0.537303i	$0.819443\pi$
$812$		0			0
$813$	−15.8993	+	48.9329i	−0.557611	+	1.71615i
$814$		0			0
$815$	−4.48877	+	31.3921i	−0.157235	+	1.09962i
$816$		0			0
$817$	−29.8809	−	21.7098i	−1.04540	−	0.759529i
$818$		0			0
$819$	2.31373	+	1.68102i	0.0808481	+	0.0587396i
$820$		0			0
$821$	−37.0734	+	26.9354i	−1.29387	+	0.940051i	−0.999876	−	0.0157566i	$-0.994984\pi$
$821$	−37.0734	+	26.9354i	−1.29387	+	0.940051i	−0.293993	+	0.955808i	$0.594984\pi$
$822$		0			0
$823$	−4.23127	−	13.0225i	−0.147493	−	0.453936i	0.849830	−	0.527056i	$-0.176704\pi$
$823$	−4.23127	−	13.0225i	−0.147493	−	0.453936i	−0.997323	+	0.0731202i	$0.976704\pi$
$824$		0			0
$825$	−82.7614	−	24.1622i	−2.88138	−	0.841220i
$826$		0			0
$827$	11.6526	+	35.8630i	0.405201	+	1.24708i	0.920728	+	0.390206i	$0.127596\pi$
$827$	11.6526	+	35.8630i	0.405201	+	1.24708i	−0.515527	+	0.856873i	$0.672404\pi$
$828$		0			0
$829$	0.233422	−	0.169591i	0.00810707	−	0.00589013i	−0.583724	−	0.811952i	$-0.698405\pi$
$829$	0.233422	−	0.169591i	0.00810707	−	0.00589013i	0.591831	+	0.806062i	$0.298405\pi$
$830$		0			0
$831$	−9.27782	−	6.74073i	−0.321844	−	0.233833i
$832$		0			0
$833$	0.838351	+	0.609097i	0.0290471	+	0.0211040i
$834$		0			0
$835$	21.0848	+	10.3465i	0.729670	+	0.358056i
$836$		0			0
$837$	7.63476	−	23.4974i	0.263896	−	0.812188i
$838$		0			0
$839$	9.73467	+	29.9602i	0.336078	+	1.03434i	0.966189	+	0.257836i	$0.0830096\pi$
$839$	9.73467	+	29.9602i	0.336078	+	1.03434i	−0.630110	+	0.776505i	$0.716990\pi$
$840$		0			0
$841$	−2.22959	+	6.86196i	−0.0768823	+	0.236619i
$842$		0			0
$843$	−23.2663			−0.801334
$844$		0			0
$845$	−25.9980	−	12.7574i	−0.894358	−	0.438869i
$846$		0			0
$847$	−59.7052	+	43.3784i	−2.05150	+	1.49050i
$848$		0			0
$849$	0.940282			0.0322704
$850$		0			0
$851$	11.7229			0.401855
$852$		0			0
$853$	19.3025	−	14.0241i	0.660905	−	0.480175i	−0.206064	−	0.978539i	$-0.566065\pi$
$853$	19.3025	−	14.0241i	0.660905	−	0.480175i	0.866968	+	0.498363i	$0.166065\pi$
$854$		0			0
$855$	−24.6456	+	25.3990i	−0.842863	+	0.868626i
$856$		0			0
$857$	−20.4806			−0.699606			−0.349803	−	0.936823i	$-0.613751\pi$
$857$	−20.4806			−0.699606			−0.349803	+	0.936823i	$0.613751\pi$
$858$		0			0
$859$	4.48753	−	13.8112i	0.153113	−	0.471232i	−0.844852	−	0.535000i	$-0.820312\pi$
$859$	4.48753	−	13.8112i	0.153113	−	0.471232i	0.997965	+	0.0637677i	$0.0203117\pi$
$860$		0			0
$861$	8.68601	+	26.7328i	0.296019	+	0.911052i
$862$		0			0
$863$	10.7636	−	33.1270i	0.366397	−	1.12766i	−0.582704	−	0.812684i	$-0.698005\pi$
$863$	10.7636	−	33.1270i	0.366397	−	1.12766i	0.949101	−	0.314971i	$-0.101995\pi$
$864$		0			0
$865$	24.1088	+	45.6059i	0.819724	+	1.55065i
$866$		0			0
$867$	−16.5978	−	12.0590i	−0.563691	−	0.409545i
$868$		0			0
$869$	26.2819	+	19.0950i	0.891554	+	0.647752i
$870$		0			0
$871$	−1.58917	+	1.15460i	−0.0538471	+	0.0391222i
$872$		0			0
$873$	−14.7533	−	45.4059i	−0.499323	−	1.53676i
$874$		0			0
$875$	−26.3293	+	14.9494i	−0.890093	+	0.505381i
$876$		0			0
$877$	16.8588	+	51.8861i	0.569282	+	1.75207i	0.654872	+	0.755740i	$0.272723\pi$
$877$	16.8588	+	51.8861i	0.569282	+	1.75207i	−0.0855896	+	0.996330i	$0.527277\pi$
$878$		0			0
$879$	−50.8998	+	36.9809i	−1.71681	+	1.24733i
$880$		0			0
$881$	−0.341311	−	0.247977i	−0.0114991	−	0.00835457i	0.582021	−	0.813174i	$-0.302262\pi$
$881$	−0.341311	−	0.247977i	−0.0114991	−	0.00835457i	−0.593520	+	0.804819i	$0.702262\pi$
$882$		0			0
$883$	−38.9094	−	28.2693i	−1.30940	−	0.951338i	−1.00000		0.000407592i	$-0.999870\pi$
$883$	−38.9094	−	28.2693i	−1.30940	−	0.951338i	−0.309405	−	0.950930i	$-0.600130\pi$
$884$		0			0
$885$	10.0667	+	19.0429i	0.338388	+	0.640119i
$886$		0			0
$887$	−8.03221	+	24.7206i	−0.269695	+	0.830036i	0.720879	+	0.693061i	$0.243738\pi$
$887$	−8.03221	+	24.7206i	−0.269695	+	0.830036i	−0.990574	+	0.136976i	$0.956262\pi$
$888$		0			0
$889$	−16.4281	−	50.5604i	−0.550980	−	1.69574i
$890$		0			0
$891$	1.02706	−	3.16097i	0.0344078	−	0.105896i
$892$		0			0
$893$	14.7950			0.495095
$894$		0			0
$895$	9.06528	−	9.34237i	0.303019	−	0.312281i
$896$		0			0
$897$	0.899809	−	0.653749i	0.0300437	−	0.0218280i
$898$		0			0
$899$	−23.3284			−0.778045
$900$		0			0
$901$	8.94239			0.297914
$902$		0			0
$903$	−68.0358	+	49.4309i	−2.26409	+	1.64496i
$904$		0			0
$905$	−14.6431	−	7.18548i	−0.486752	−	0.238853i
$906$		0			0
$907$	26.3462			0.874810			0.437405	−	0.899265i	$-0.355898\pi$
$907$	26.3462			0.874810			0.437405	+	0.899265i	$0.355898\pi$
$908$		0			0
$909$	10.1778	−	31.3241i	0.337577	−	1.03895i
$910$		0			0
$911$	−5.15123	−	15.8539i	−0.170668	−	0.525262i	0.828741	−	0.559632i	$-0.189058\pi$
$911$	−5.15123	−	15.8539i	−0.170668	−	0.525262i	−0.999409	+	0.0343701i	$0.989058\pi$
$912$		0			0
$913$	1.41446	−	4.35325i	0.0468117	−	0.144072i
$914$		0			0
$915$	−28.5298	−	13.9998i	−0.943164	−	0.462819i
$916$		0			0
$917$	10.8141	+	7.85688i	0.357112	+	0.259457i
$918$		0			0
$919$	−9.43609	−	6.85572i	−0.311268	−	0.226149i	0.421173	−	0.906981i	$-0.361619\pi$
$919$	−9.43609	−	6.85572i	−0.311268	−	0.226149i	−0.732440	+	0.680831i	$0.761619\pi$
$920$		0			0
$921$	−1.74808	+	1.27005i	−0.0576011	+	0.0418496i
$922$		0			0
$923$	−0.623143	−	1.91784i	−0.0205110	−	0.0631264i
$924$		0			0
$925$	0.978505	+	32.4944i	0.0321731	+	1.06841i
$926$		0			0
$927$	14.4812	+	44.5685i	0.475624	+	1.46382i
$928$		0			0
$929$	−5.57900	+	4.05338i	−0.183041	+	0.132987i	−0.675533	−	0.737330i	$-0.736086\pi$
$929$	−5.57900	+	4.05338i	−0.183041	+	0.132987i	0.492492	+	0.870317i	$0.336086\pi$
$930$		0			0
$931$	0.895304	+	0.650476i	0.0293424	+	0.0213185i
$932$		0			0
$933$	−16.2882	−	11.8340i	−0.533250	−	0.387429i
$934$		0			0
$935$	−6.07842	+	42.5093i	−0.198786	+	1.39020i
$936$		0			0
$937$	−4.38520	+	13.4963i	−0.143258	+	0.440903i	−0.996783	−	0.0801490i	$-0.974460\pi$
$937$	−4.38520	+	13.4963i	−0.143258	+	0.440903i	0.853525	+	0.521052i	$0.174460\pi$
$938$		0			0
$939$	−21.0302	−	64.7243i	−0.686294	−	2.11220i
$940$		0			0
$941$	16.1342	−	49.6559i	0.525959	−	1.61874i	−0.236452	−	0.971643i	$-0.575985\pi$
$941$	16.1342	−	49.6559i	0.525959	−	1.61874i	0.762411	−	0.647093i	$-0.224015\pi$
$942$		0			0
$943$	6.71243			0.218587
$944$		0			0
$945$	13.9893	+	26.4632i	0.455072	+	0.860847i
$946$		0			0
$947$	37.3041	−	27.1030i	1.21222	−	0.880729i	0.216789	−	0.976218i	$-0.430442\pi$
$947$	37.3041	−	27.1030i	1.21222	−	0.880729i	0.995430	+	0.0954891i	$0.0304415\pi$
$948$		0			0
$949$	−0.779100			−0.0252906
$950$		0			0
$951$	69.4680			2.25265
$952$		0			0
$953$	8.85255	−	6.43175i	0.286762	−	0.208345i	−0.435099	−	0.900382i	$-0.643287\pi$
$953$	8.85255	−	6.43175i	0.286762	−	0.208345i	0.721862	+	0.692038i	$0.243287\pi$
$954$		0			0
$955$	−0.218420	+	1.52752i	−0.00706792	+	0.0494293i
$956$		0			0
$957$	80.4817			2.60161
$958$		0			0
$959$	8.70043	−	26.7772i	0.280951	−	0.864680i
$960$		0			0
$961$	−1.85992	−	5.72424i	−0.0599974	−	0.184653i
$962$		0			0
$963$	6.72942	−	20.7110i	0.216852	−	0.667403i
$964$		0			0
$965$	3.40860	−	0.592593i	0.109727	−	0.0190762i
$966$		0			0
$967$	30.5553	+	22.1997i	0.982592	+	0.713895i	0.958286	−	0.285809i	$-0.0922624\pi$
$967$	30.5553	+	22.1997i	0.982592	+	0.713895i	0.0243059	+	0.999705i	$0.492262\pi$
$968$		0			0
$969$	23.2239	+	16.8731i	0.746059	+	0.542043i
$970$		0			0
$971$	4.91458	−	3.57065i	0.157716	−	0.114588i	−0.506128	−	0.862458i	$-0.668924\pi$
$971$	4.91458	−	3.57065i	0.157716	−	0.114588i	0.663844	+	0.747871i	$0.268924\pi$
$972$		0			0
$973$	−12.1804	−	37.4873i	−0.390485	−	1.20179i
$974$		0			0
$975$	1.88722	+	2.43959i	0.0604395	+	0.0781295i
$976$		0			0
$977$	−1.17670	−	3.62152i	−0.0376461	−	0.115863i	0.930467	−	0.366375i	$-0.119401\pi$
$977$	−1.17670	−	3.62152i	−0.0376461	−	0.115863i	−0.968114	+	0.250512i	$0.919401\pi$
$978$		0			0
$979$	80.8992	−	58.7767i	2.58555	−	1.87851i
$980$		0			0
$981$	−46.2661	−	33.6143i	−1.47716	−	1.07322i
$982$		0			0
$983$	43.8645	+	31.8694i	1.39906	+	1.01648i	0.994802	+	0.101832i	$0.0324705\pi$
$983$	43.8645	+	31.8694i	1.39906	+	1.01648i	0.404259	+	0.914645i	$0.367530\pi$
$984$		0			0
$985$	0.672235	−	0.692782i	0.0214192	−	0.0220739i
$986$		0			0
$987$	10.4097	−	32.0379i	0.331346	−	1.01978i
$988$		0			0
$989$	6.20589	+	19.0998i	0.197336	+	0.607337i
$990$		0			0
$991$	0.742481	−	2.28512i	0.0235857	−	0.0725892i	−0.938571	−	0.345087i	$-0.887850\pi$
$991$	0.742481	−	2.28512i	0.0235857	−	0.0725892i	0.962157	+	0.272497i	$0.0878496\pi$
$992$		0			0
$993$	14.6307			0.464291
$994$		0			0
$995$	−3.92657	+	0.682642i	−0.124481	+	0.0216412i
$996$		0			0
$997$	38.4271	−	27.9189i	1.21700	−	0.884201i	0.221151	−	0.975240i	$-0.429019\pi$
$997$	38.4271	−	27.9189i	1.21700	−	0.884201i	0.995847	+	0.0910386i	$0.0290187\pi$
$998$		0			0
$999$	32.1397			1.01686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.f.81.3		12
4.3	odd	2		100.2.g.a.81.1	yes	12
12.11	even	2		900.2.n.c.181.3		12
20.3	even	4		500.2.i.b.349.1		24
20.7	even	4		500.2.i.b.349.6		24
20.19	odd	2		500.2.g.a.401.3		12
25.11	even	5		10000.2.a.bc.1.2		6
25.14	even	10		10000.2.a.bd.1.5		6
25.21	even	5	inner	400.2.u.f.321.3		12
100.3	even	20		500.2.i.b.149.6		24
100.11	odd	10		2500.2.a.d.1.5		6
100.23	even	20		2500.2.c.c.1249.11		12
100.27	even	20		2500.2.c.c.1249.2		12
100.39	odd	10		2500.2.a.c.1.2		6
100.47	even	20		500.2.i.b.149.1		24
100.71	odd	10		100.2.g.a.21.1	✓	12
100.79	odd	10		500.2.g.a.101.3		12
300.71	even	10		900.2.n.c.721.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.21.1	✓	12	100.71	odd	10
100.2.g.a.81.1	yes	12	4.3	odd	2
400.2.u.f.81.3		12	1.1	even	1	trivial
400.2.u.f.321.3		12	25.21	even	5	inner
500.2.g.a.101.3		12	100.79	odd	10
500.2.g.a.401.3		12	20.19	odd	2
500.2.i.b.149.1		24	100.47	even	20
500.2.i.b.149.6		24	100.3	even	20
500.2.i.b.349.1		24	20.3	even	4
500.2.i.b.349.6		24	20.7	even	4
900.2.n.c.181.3		12	12.11	even	2
900.2.n.c.721.3		12	300.71	even	10
2500.2.a.c.1.2		6	100.39	odd	10
2500.2.a.d.1.5		6	100.11	odd	10
2500.2.c.c.1249.2		12	100.27	even	20
2500.2.c.c.1249.11		12	100.23	even	20
10000.2.a.bc.1.2		6	25.11	even	5
10000.2.a.bd.1.5		6	25.14	even	10

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.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.25555 - 1.63875i) q^{3} +(-2.20302 + 0.383000i) q^{5} +2.70809 q^{7} +(1.47494 - 4.53940i) q^{9} +O(q^{10})\)	\(q+(2.25555 - 1.63875i) q^{3} +(-2.20302 + 0.383000i) q^{5} +2.70809 q^{7} +(1.47494 - 4.53940i) q^{9} +(-1.91120 - 5.88208i) q^{11} +(-0.0683725 + 0.210429i) q^{13} +(-4.34139 + 4.47409i) q^{15} +(2.51204 + 1.82510i) q^{17} +(2.68270 + 1.94909i) q^{19} +(6.10822 - 4.43788i) q^{21} +(-0.557161 - 1.71477i) q^{23} +(4.70662 - 1.68752i) q^{25} +(-1.52753 - 4.70124i) q^{27} +(-3.77603 + 2.74345i) q^{29} +(4.04356 + 2.93782i) q^{31} +(-13.9501 - 10.1353i) q^{33} +(-5.96598 + 1.03720i) q^{35} +(-2.00918 + 6.18361i) q^{37} +(0.190623 + 0.586678i) q^{39} +(-1.15044 + 3.54068i) q^{41} -11.1384 q^{43} +(-1.51074 + 10.5653i) q^{45} +(3.60959 - 2.62252i) q^{47} +0.333733 q^{49} +8.65692 q^{51} +(2.32993 - 1.69279i) q^{53} +(6.46327 + 12.2264i) q^{55} +9.24503 q^{57} +(1.06770 - 3.28603i) q^{59} +(1.57525 + 4.84813i) q^{61} +(3.99427 - 12.2931i) q^{63} +(0.0700319 - 0.489766i) q^{65} +(7.18245 + 5.21835i) q^{67} +(-4.06678 - 2.95469i) q^{69} +(-7.37333 + 5.35704i) q^{71} +(1.08812 + 3.34888i) q^{73} +(7.85060 - 11.5193i) q^{75} +(-5.17571 - 15.9292i) q^{77} +(-4.24945 + 3.08741i) q^{79} +(0.434757 + 0.315869i) q^{81} +(0.598743 + 0.435012i) q^{83} +(-6.23310 - 3.05863i) q^{85} +(-4.02119 + 12.3760i) q^{87} +(4.99625 + 15.3769i) q^{89} +(-0.185159 + 0.569860i) q^{91} +13.9348 q^{93} +(-6.65654 - 3.26642i) q^{95} +(8.09228 - 5.87939i) q^{97} -29.5201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9	\( 12 q - 2 q^{3} - 4 q^{5} + 2 q^{7} - 3 q^{9} + 5 q^{11} - 2 q^{13} - 18 q^{15} + q^{17} + 8 q^{19} + 2 q^{21} + 6 q^{23} - 26 q^{25} + 34 q^{27} - 18 q^{29} - 12 q^{31} - 35 q^{33} + 3 q^{35} + 13 q^{37} - 22 q^{39} - 23 q^{41} - 50 q^{43} + 71 q^{45} - q^{47} + 34 q^{49} - 14 q^{51} + 21 q^{53} - 5 q^{55} + 72 q^{57} - 9 q^{59} - 26 q^{61} + 32 q^{63} - 18 q^{65} + 37 q^{67} - 44 q^{69} - 21 q^{71} + 18 q^{73} + 73 q^{75} - 60 q^{77} + 24 q^{79} + 18 q^{81} + 46 q^{83} - 16 q^{85} - 57 q^{87} - 2 q^{89} + 32 q^{91} + 22 q^{93} - 6 q^{95} - 7 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^5 + 2 * q^7 - 3 * q^9 + 5 * q^11 - 2 * q^13 - 18 * q^15 + q^17 + 8 * q^19 + 2 * q^21 + 6 * q^23 - 26 * q^25 + 34 * q^27 - 18 * q^29 - 12 * q^31 - 35 * q^33 + 3 * q^35 + 13 * q^37 - 22 * q^39 - 23 * q^41 - 50 * q^43 + 71 * q^45 - q^47 + 34 * q^49 - 14 * q^51 + 21 * q^53 - 5 * q^55 + 72 * q^57 - 9 * q^59 - 26 * q^61 + 32 * q^63 - 18 * q^65 + 37 * q^67 - 44 * q^69 - 21 * q^71 + 18 * q^73 + 73 * q^75 - 60 * q^77 + 24 * q^79 + 18 * q^81 + 46 * q^83 - 16 * q^85 - 57 * q^87 - 2 * q^89 + 32 * q^91 + 22 * q^93 - 6 * q^95 - 7 * q^97 - 40 * q^99

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