LMFDB - Embedded newform 440.2.y.b.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
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} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 15x^10 - 22x^9 + 89x^8 - 118x^7 + 205x^6 - 68x^5 + 1061x^4 - 1490x^3 + 2760x^2 - 1600*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.2
Root			$0.421568 - 1.29745i$ of defining polynomial
Character	$\chi$	$=$	440.201
Dual form			440.2.y.b.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260543 + 0.801870i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.46997 - 4.52411i) q^{7} +(1.85194 - 1.34551i) q^{9} +O(q^{10})$	\(q+(0.260543 + 0.801870i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.46997 - 4.52411i) q^{7} +(1.85194 - 1.34551i) q^{9} +(0.231864 - 3.30851i) q^{11} +(-3.06058 + 2.22364i) q^{13} +(-0.260543 + 0.801870i) q^{15} +(-4.03055 - 2.92836i) q^{17} +(0.964489 + 2.96839i) q^{19} +4.01074 q^{21} +9.39001 q^{23} +(0.309017 + 0.951057i) q^{25} +(3.60777 + 2.62120i) q^{27} +(-0.805585 + 2.47934i) q^{29} +(2.98421 - 2.16816i) q^{31} +(2.71341 - 0.676086i) q^{33} +(3.84844 - 2.79605i) q^{35} +(-1.06536 + 3.27883i) q^{37} +(-2.58048 - 1.87483i) q^{39} +(2.88263 + 8.87181i) q^{41} -11.7051 q^{43} +2.28912 q^{45} +(-0.513451 - 1.58024i) q^{47} +(-12.6436 - 9.18613i) q^{49} +(1.29804 - 3.99494i) q^{51} +(1.56945 - 1.14027i) q^{53} +(2.13228 - 2.54035i) q^{55} +(-2.12897 + 1.54679i) q^{57} +(0.0321114 - 0.0988288i) q^{59} +(8.21258 + 5.96679i) q^{61} +(-3.36494 - 10.3562i) q^{63} -3.78308 q^{65} -4.99277 q^{67} +(2.44651 + 7.52957i) q^{69} +(5.03960 + 3.66149i) q^{71} +(-2.25783 + 6.94889i) q^{73} +(-0.682112 + 0.495583i) q^{75} +(-14.6272 - 5.91239i) q^{77} +(-8.53069 + 6.19791i) q^{79} +(0.960251 - 2.95535i) q^{81} +(-4.60338 - 3.34455i) q^{83} +(-1.53953 - 4.73819i) q^{85} -2.19800 q^{87} +13.6371 q^{89} +(5.56102 + 17.1151i) q^{91} +(2.51610 + 1.82805i) q^{93} +(-0.964489 + 2.96839i) q^{95} +(-11.0809 + 8.05072i) q^{97} +(-4.02224 - 6.43913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9}+O(q^{10}) $ 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9	$ 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37} - q^{39} + 7 q^{41} + 6 q^{43} - 20 q^{45} - 2 q^{47} - 19 q^{49} - 33 q^{51} + 3 q^{53} + 4 q^{55} - 25 q^{57} + 19 q^{59} + 22 q^{61} - 2 q^{63} + 12 q^{65} + 22 q^{67} + 21 q^{69} + 44 q^{71} + 17 q^{73} - q^{75} - 38 q^{77} - 43 q^{79} - 85 q^{81} - 15 q^{83} + 18 q^{85} + 50 q^{87} + 2 q^{89} + 59 q^{91} + 5 q^{93} - 3 q^{95} - 20 q^{97} - 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.260543	+	0.801870i	0.150425	+	0.462960i	0.997669	−	0.0682442i	$-0.0217397\pi$
$3$	0.260543	+	0.801870i	0.150425	+	0.462960i	−0.847244	+	0.531204i	$0.821740\pi$
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	1.46997	−	4.52411i	0.555597	−	1.70995i	−0.138764	−	0.990325i	$-0.544313\pi$
$7$	1.46997	−	4.52411i	0.555597	−	1.70995i	0.694361	−	0.719627i	$-0.255687\pi$
$8$		0			0
$9$	1.85194	−	1.34551i	0.617313	−	0.448504i
$10$		0			0
$11$	0.231864	−	3.30851i	0.0699096	−	0.997553i
$11$	0.231864	−	3.30851i	0.0699096	−	0.997553i
$12$		0			0
$13$	−3.06058	+	2.22364i	−0.848851	+	0.616726i	−0.924829	−	0.380383i	$-0.875792\pi$
$13$	−3.06058	+	2.22364i	−0.848851	+	0.616726i	0.0759779	+	0.997109i	$0.475792\pi$
$14$		0			0
$15$	−0.260543	+	0.801870i	−0.0672720	+	0.207042i
$16$		0			0
$17$	−4.03055	−	2.92836i	−0.977551	−	0.710233i	−0.0203914	−	0.999792i	$-0.506491\pi$
$17$	−4.03055	−	2.92836i	−0.977551	−	0.710233i	−0.957160	+	0.289559i	$0.906491\pi$
$18$		0			0
$19$	0.964489	+	2.96839i	0.221269	+	0.680996i	0.998649	+	0.0519645i	$0.0165483\pi$
$19$	0.964489	+	2.96839i	0.221269	+	0.680996i	−0.777380	+	0.629031i	$0.783452\pi$
$20$		0			0
$21$	4.01074			0.875215
$22$		0			0
$23$	9.39001			1.95795			0.978976	−	0.203975i	$-0.0653861\pi$
$23$	9.39001			1.95795			0.978976	+	0.203975i	$0.0653861\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	3.60777	+	2.62120i	0.694316	+	0.504450i
$28$		0			0
$29$	−0.805585	+	2.47934i	−0.149593	+	0.460401i	−0.997573	−	0.0696276i	$-0.977819\pi$
$29$	−0.805585	+	2.47934i	−0.149593	+	0.460401i	0.847980	+	0.530029i	$0.177819\pi$
$30$		0			0
$31$	2.98421	−	2.16816i	0.535980	−	0.389413i	−0.286610	−	0.958047i	$-0.592528\pi$
$31$	2.98421	−	2.16816i	0.535980	−	0.389413i	0.822590	+	0.568635i	$0.192528\pi$
$32$		0			0
$33$	2.71341	−	0.676086i	0.472343	−	0.117691i
$34$		0			0
$35$	3.84844	−	2.79605i	0.650504	−	0.472619i
$36$		0			0
$37$	−1.06536	+	3.27883i	−0.175143	+	0.539036i	−0.999640	−	0.0268308i	$-0.991458\pi$
$37$	−1.06536	+	3.27883i	−0.175143	+	0.539036i	0.824497	+	0.565867i	$0.191458\pi$
$38$		0			0
$39$	−2.58048	−	1.87483i	−0.413208	−	0.300213i
$40$		0			0
$41$	2.88263	+	8.87181i	0.450190	+	1.38554i	0.876690	+	0.481056i	$0.159747\pi$
$41$	2.88263	+	8.87181i	0.450190	+	1.38554i	−0.426499	+	0.904488i	$0.640253\pi$
$42$		0			0
$43$	−11.7051			−1.78500			−0.892502	−	0.451043i	$-0.851052\pi$
$43$	−11.7051			−1.78500			−0.892502	+	0.451043i	$0.851052\pi$
$44$		0			0
$45$	2.28912			0.341242
$46$		0			0
$47$	−0.513451	−	1.58024i	−0.0748945	−	0.230502i	0.906600	−	0.421990i	$-0.138668\pi$
$47$	−0.513451	−	1.58024i	−0.0748945	−	0.230502i	−0.981495	+	0.191489i	$0.938668\pi$
$48$		0			0
$49$	−12.6436	−	9.18613i	−1.80623	−	1.31230i
$50$		0			0
$51$	1.29804	−	3.99494i	0.181761	−	0.559404i
$52$		0			0
$53$	1.56945	−	1.14027i	0.215580	−	0.156628i	−0.474755	−	0.880118i	$-0.657463\pi$
$53$	1.56945	−	1.14027i	0.215580	−	0.156628i	0.690335	+	0.723490i	$0.257463\pi$
$54$		0			0
$55$	2.13228	−	2.54035i	0.287516	−	0.342541i
$56$		0			0
$57$	−2.12897	+	1.54679i	−0.281990	+	0.204877i
$58$		0			0
$59$	0.0321114	−	0.0988288i	0.00418055	−	0.0128664i	−0.948944	−	0.315443i	$-0.897847\pi$
$59$	0.0321114	−	0.0988288i	0.00418055	−	0.0128664i	0.953125	+	0.302577i	$0.0978468\pi$
$60$		0			0
$61$	8.21258	+	5.96679i	1.05151	+	0.763969i	0.972499	−	0.232905i	$-0.0748231\pi$
$61$	8.21258	+	5.96679i	1.05151	+	0.763969i	0.0790130	+	0.996874i	$0.474823\pi$
$62$		0			0
$63$	−3.36494	−	10.3562i	−0.423943	−	1.30476i
$64$		0			0
$65$	−3.78308			−0.469233
$66$		0			0
$67$	−4.99277			−0.609964			−0.304982	−	0.952358i	$-0.598650\pi$
$67$	−4.99277			−0.609964			−0.304982	+	0.952358i	$0.598650\pi$
$68$		0			0
$69$	2.44651	+	7.52957i	0.294525	+	0.906454i
$70$		0			0
$71$	5.03960	+	3.66149i	0.598091	+	0.434538i	0.845201	−	0.534449i	$-0.179481\pi$
$71$	5.03960	+	3.66149i	0.598091	+	0.434538i	−0.247110	+	0.968987i	$0.579481\pi$
$72$		0			0
$73$	−2.25783	+	6.94889i	−0.264259	+	0.813306i	0.727604	+	0.685998i	$0.240634\pi$
$73$	−2.25783	+	6.94889i	−0.264259	+	0.813306i	−0.991863	+	0.127309i	$0.959366\pi$
$74$		0			0
$75$	−0.682112	+	0.495583i	−0.0787635	+	0.0572250i
$76$		0			0
$77$	−14.6272	−	5.91239i	−1.66693	−	0.673780i
$78$		0			0
$79$	−8.53069	+	6.19791i	−0.959778	+	0.697319i	−0.953099	−	0.302658i	$-0.902126\pi$
$79$	−8.53069	+	6.19791i	−0.959778	+	0.697319i	−0.00667849	+	0.999978i	$0.502126\pi$
$80$		0			0
$81$	0.960251	−	2.95535i	0.106695	−	0.328372i
$82$		0			0
$83$	−4.60338	−	3.34455i	−0.505287	−	0.367113i	0.305746	−	0.952113i	$-0.401094\pi$
$83$	−4.60338	−	3.34455i	−0.505287	−	0.367113i	−0.811033	+	0.585001i	$0.801094\pi$
$84$		0			0
$85$	−1.53953	−	4.73819i	−0.166986	−	0.513929i
$86$		0			0
$87$	−2.19800			−0.235650
$88$		0			0
$89$	13.6371			1.44553			0.722767	−	0.691091i	$-0.242870\pi$
$89$	13.6371			1.44553			0.722767	+	0.691091i	$0.242870\pi$
$90$		0			0
$91$	5.56102	+	17.1151i	0.582953	+	1.79415i
$92$		0			0
$93$	2.51610	+	1.82805i	0.260907	+	0.189560i
$94$		0			0
$95$	−0.964489	+	2.96839i	−0.0989545	+	0.304551i
$96$		0			0
$97$	−11.0809	+	8.05072i	−1.12509	+	0.817427i	−0.984973	−	0.172708i	$-0.944748\pi$
$97$	−11.0809	+	8.05072i	−1.12509	+	0.817427i	−0.140118	+	0.990135i	$0.544748\pi$
$98$		0			0
$99$	−4.02224	−	6.43913i	−0.404250	−	0.647157i
$100$		0			0
$101$	−3.91797	+	2.84657i	−0.389852	+	0.283244i	−0.765395	−	0.643561i	$-0.777456\pi$
$101$	−3.91797	+	2.84657i	−0.389852	+	0.283244i	0.375543	+	0.926805i	$0.377456\pi$
$102$		0			0
$103$	0.279529	−	0.860303i	0.0275428	−	0.0847682i	−0.936340	−	0.351094i	$-0.885810\pi$
$103$	0.279529	−	0.860303i	0.0275428	−	0.0847682i	0.963883	+	0.266326i	$0.0858097\pi$
$104$		0			0
$105$	3.24476	+	2.35745i	0.316656	+	0.230064i
$106$		0			0
$107$	−4.57082	−	14.0675i	−0.441878	−	1.35996i	−0.885872	−	0.463931i	$-0.846439\pi$
$107$	−4.57082	−	14.0675i	−0.441878	−	1.35996i	0.443994	−	0.896030i	$-0.353561\pi$
$108$		0			0
$109$	3.39429			0.325114			0.162557	−	0.986699i	$-0.448026\pi$
$109$	3.39429			0.325114			0.162557	+	0.986699i	$0.448026\pi$
$110$		0			0
$111$	−2.90677			−0.275898
$112$		0			0
$113$	−3.14440	−	9.67748i	−0.295801	−	0.910381i	−0.982951	−	0.183866i	$-0.941139\pi$
$113$	−3.14440	−	9.67748i	−0.295801	−	0.910381i	0.687151	−	0.726515i	$-0.258861\pi$
$114$		0			0
$115$	7.59668	+	5.51931i	0.708394	+	0.514678i
$116$		0			0
$117$	−2.67607	+	8.23608i	−0.247402	+	0.761426i
$118$		0			0
$119$	−19.1730	+	13.9300i	−1.75759	+	1.27696i
$120$		0			0
$121$	−10.8925	−	1.53425i	−0.990225	−	0.139477i
$122$		0			0
$123$	−6.36299	+	4.62298i	−0.573732	+	0.416840i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	8.86580	+	6.44138i	0.786712	+	0.571580i	0.906986	−	0.421161i	$-0.138377\pi$
$127$	8.86580	+	6.44138i	0.786712	+	0.571580i	−0.120274	+	0.992741i	$0.538377\pi$
$128$		0			0
$129$	−3.04968	−	9.38594i	−0.268509	−	0.826386i
$130$		0			0
$131$	12.9021			1.12726			0.563631	−	0.826027i	$-0.309404\pi$
$131$	12.9021			1.12726			0.563631	+	0.826027i	$0.309404\pi$
$132$		0			0
$133$	14.8471			1.28741
$134$		0			0
$135$	1.37805	+	4.24119i	0.118603	+	0.365023i
$136$		0			0
$137$	−15.2762	−	11.0988i	−1.30514	−	0.948236i	−0.305144	−	0.952306i	$-0.598705\pi$
$137$	−15.2762	−	11.0988i	−1.30514	−	0.948236i	−0.999992	+	0.00406991i	$0.998705\pi$
$138$		0			0
$139$	3.36495	−	10.3563i	0.285412	−	0.878406i	−0.700863	−	0.713295i	$-0.747202\pi$
$139$	3.36495	−	10.3563i	0.285412	−	0.878406i	0.986275	−	0.165111i	$-0.0527982\pi$
$140$		0			0
$141$	1.13337	−	0.823442i	0.0954471	−	0.0693463i
$142$		0			0
$143$	6.64729	+	10.6415i	0.555875	+	0.889889i
$144$		0			0
$145$	−2.10905	+	1.53231i	−0.175147	+	0.127252i
$146$		0			0
$147$	4.07187	−	12.5319i	0.335842	−	1.03362i
$148$		0			0
$149$	−1.37058	−	0.995782i	−0.112282	−	0.0815776i	0.530227	−	0.847856i	$-0.322107\pi$
$149$	−1.37058	−	0.995782i	−0.112282	−	0.0815776i	−0.642509	+	0.766278i	$0.722107\pi$
$150$		0			0
$151$	−1.07842	−	3.31904i	−0.0877606	−	0.270099i	0.897539	−	0.440935i	$-0.145353\pi$
$151$	−1.07842	−	3.31904i	−0.0877606	−	0.270099i	−0.985299	+	0.170836i	$0.945353\pi$
$152$		0			0
$153$	−11.4045			−0.921997
$154$		0			0
$155$	3.68869			0.296283
$156$		0			0
$157$	6.39675	+	19.6872i	0.510517	+	1.57121i	0.791294	+	0.611435i	$0.209408\pi$
$157$	6.39675	+	19.6872i	0.510517	+	1.57121i	−0.280778	+	0.959773i	$0.590592\pi$
$158$		0			0
$159$	1.32326	+	0.961403i	0.104941	+	0.0762442i
$160$		0			0
$161$	13.8030	−	42.4814i	1.08783	−	3.34800i
$162$		0			0
$163$	−13.2542	+	9.62977i	−1.03815	+	0.754262i	−0.969924	−	0.243408i	$-0.921735\pi$
$163$	−13.2542	+	9.62977i	−1.03815	+	0.754262i	−0.0682284	+	0.997670i	$0.521735\pi$
$164$		0			0
$165$	2.59259	+	1.04794i	0.201833	+	0.0815817i
$166$		0			0
$167$	−11.6508	+	8.46481i	−0.901567	+	0.655027i	−0.938868	−	0.344277i	$-0.888124\pi$
$167$	−11.6508	+	8.46481i	−0.901567	+	0.655027i	0.0373009	+	0.999304i	$0.488124\pi$
$168$		0			0
$169$	0.405336	−	1.24750i	0.0311797	−	0.0959612i
$170$		0			0
$171$	5.78018	+	4.19955i	0.442021	+	0.321147i
$172$		0			0
$173$	−2.51031	−	7.72595i	−0.190855	−	0.587393i	0.809144	−	0.587610i	$-0.199931\pi$
$173$	−2.51031	−	7.72595i	−0.190855	−	0.587393i	−1.00000		0.000216923i	$0.999931\pi$
$174$		0			0
$175$	4.75693			0.359590
$176$		0			0
$177$	0.0876143			0.00658549
$178$		0			0
$179$	0.925011	+	2.84689i	0.0691386	+	0.212787i	0.979656	−	0.200684i	$-0.0643164\pi$
$179$	0.925011	+	2.84689i	0.0691386	+	0.212787i	−0.910517	+	0.413471i	$0.864316\pi$
$180$		0			0
$181$	11.7521	+	8.53841i	0.873527	+	0.634655i	0.931531	−	0.363662i	$-0.118474\pi$
$181$	11.7521	+	8.53841i	0.873527	+	0.634655i	−0.0580038	+	0.998316i	$0.518474\pi$
$182$		0			0
$183$	−2.64486	+	8.14003i	−0.195513	+	0.601728i
$184$		0			0
$185$	−2.78914	+	2.02643i	−0.205062	+	0.148986i
$186$		0			0
$187$	−10.6231	+	12.6561i	−0.776835	+	0.925508i
$188$		0			0
$189$	17.1619	−	12.4689i	1.24835	−	0.906976i
$190$		0			0
$191$	−2.46207	+	7.57746i	−0.178149	+	0.548286i	−0.999763	−	0.0217578i	$-0.993074\pi$
$191$	−2.46207	+	7.57746i	−0.178149	+	0.548286i	0.821614	+	0.570044i	$0.193074\pi$
$192$		0			0
$193$	15.7728	+	11.4596i	1.13535	+	0.824879i	0.986464	−	0.163976i	$-0.0524320\pi$
$193$	15.7728	+	11.4596i	1.13535	+	0.824879i	0.148884	+	0.988855i	$0.452432\pi$
$194$		0			0
$195$	−0.985657	−	3.03354i	−0.0705843	−	0.217236i
$196$		0			0
$197$	17.9751			1.28067			0.640336	−	0.768095i	$-0.278795\pi$
$197$	17.9751			1.28067			0.640336	+	0.768095i	$0.278795\pi$
$198$		0			0
$199$	−7.17717			−0.508776			−0.254388	−	0.967102i	$-0.581874\pi$
$199$	−7.17717			−0.508776			−0.254388	+	0.967102i	$0.581874\pi$
$200$		0			0
$201$	−1.30083	−	4.00355i	−0.0917537	−	0.282389i
$202$		0			0
$203$	10.0326	+	7.28911i	0.704150	+	0.511595i
$204$		0			0
$205$	−2.88263	+	8.87181i	−0.201331	+	0.619634i
$206$		0			0
$207$	17.3897	−	12.6344i	1.20867	−	0.878149i
$208$		0			0
$209$	10.0446	−	2.50276i	0.694798	−	0.173119i
$210$		0			0
$211$	3.58625	−	2.60556i	0.246888	−	0.179374i	−0.457459	−	0.889231i	$-0.651240\pi$
$211$	3.58625	−	2.60556i	0.246888	−	0.179374i	0.704346	+	0.709857i	$0.251240\pi$
$212$		0			0
$213$	−1.62300	+	4.99508i	−0.111206	+	0.342257i
$214$		0			0
$215$	−9.46959	−	6.88006i	−0.645821	−	0.469216i
$216$		0			0
$217$	−5.42227	−	16.6880i	−0.368088	−	1.13286i
$218$		0			0
$219$	−6.16037			−0.416280
$220$		0			0
$221$	18.8474			1.26781
$222$		0			0
$223$	−4.70031	−	14.4661i	−0.314756	−	0.968720i	−0.975855	−	0.218421i	$-0.929909\pi$
$223$	−4.70031	−	14.4661i	−0.314756	−	0.968720i	0.661098	−	0.750299i	$-0.270091\pi$
$224$		0			0
$225$	1.85194	+	1.34551i	0.123463	+	0.0897008i
$226$		0			0
$227$	1.32382	−	4.07431i	0.0878652	−	0.270421i	−0.897463	−	0.441089i	$-0.854592\pi$
$227$	1.32382	−	4.07431i	0.0878652	−	0.270421i	0.985329	+	0.170667i	$0.0545924\pi$
$228$		0			0
$229$	3.31418	−	2.40789i	0.219007	−	0.159118i	−0.472872	−	0.881131i	$-0.656783\pi$
$229$	3.31418	−	2.40789i	0.219007	−	0.159118i	0.691880	+	0.722013i	$0.256783\pi$
$230$		0			0
$231$	0.929945	−	13.2696i	0.0611859	−	0.873074i
$232$		0			0
$233$	13.9580	−	10.1411i	0.914421	−	0.664365i	−0.0277085	−	0.999616i	$-0.508821\pi$
$233$	13.9580	−	10.1411i	0.914421	−	0.664365i	0.942129	+	0.335251i	$0.108821\pi$
$234$		0			0
$235$	0.513451	−	1.58024i	0.0334938	−	0.103083i
$236$		0			0
$237$	−7.19253	−	5.22568i	−0.467205	−	0.339445i
$238$		0			0
$239$	−1.05259	−	3.23954i	−0.0680865	−	0.209549i	0.911224	−	0.411910i	$-0.135138\pi$
$239$	−1.05259	−	3.23954i	−0.0680865	−	0.209549i	−0.979311	+	0.202362i	$0.935138\pi$
$240$		0			0
$241$	−20.1839			−1.30016			−0.650080	−	0.759866i	$-0.725265\pi$
$241$	−20.1839			−1.30016			−0.650080	+	0.759866i	$0.725265\pi$
$242$		0			0
$243$	15.9983			1.02629
$244$		0			0
$245$	−4.82943	−	14.8635i	−0.308541	−	0.949592i
$246$		0			0
$247$	−9.55252	−	6.94031i	−0.607813	−	0.441602i
$248$		0			0
$249$	1.48252	−	4.56272i	0.0939507	−	0.289151i
$250$		0			0
$251$	−15.9353	+	11.5777i	−1.00583	+	0.730776i	−0.963330	−	0.268321i	$-0.913531\pi$
$251$	−15.9353	+	11.5777i	−1.00583	+	0.730776i	−0.0424968	+	0.999097i	$0.513531\pi$
$252$		0			0
$253$	2.17720	−	31.0669i	0.136880	−	1.95316i
$254$		0			0
$255$	3.39830	−	2.46901i	0.212810	−	0.154615i
$256$		0			0
$257$	−3.31063	+	10.1891i	−0.206512	+	0.635577i	0.793136	+	0.609044i	$0.208447\pi$
$257$	−3.31063	+	10.1891i	−0.206512	+	0.635577i	−0.999648	+	0.0265331i	$0.991553\pi$
$258$		0			0
$259$	13.2677	+	9.63957i	0.824417	+	0.598974i
$260$		0			0
$261$	1.84408	+	5.67550i	0.114146	+	0.351305i
$262$		0			0
$263$	8.86317			0.546527			0.273263	−	0.961939i	$-0.411897\pi$
$263$	8.86317			0.546527			0.273263	+	0.961939i	$0.411897\pi$
$264$		0			0
$265$	1.93994			0.119170
$266$		0			0
$267$	3.55307	+	10.9352i	0.217444	+	0.669225i
$268$		0			0
$269$	1.74328	+	1.26656i	0.106289	+	0.0772238i	0.639660	−	0.768658i	$-0.279075\pi$
$269$	1.74328	+	1.26656i	0.106289	+	0.0772238i	−0.533371	+	0.845881i	$0.679075\pi$
$270$		0			0
$271$	3.16904	−	9.75331i	0.192506	−	0.592472i	−0.807491	−	0.589880i	$-0.799175\pi$
$271$	3.16904	−	9.75331i	0.192506	−	0.592472i	0.999997	−	0.00259160i	$-0.000824934\pi$
$272$		0			0
$273$	−12.2752	+	8.91844i	−0.742927	+	0.539768i
$274$		0			0
$275$	3.21823	−	0.801870i	0.194067	−	0.0483546i
$276$		0			0
$277$	−11.9939	+	8.71410i	−0.720645	+	0.523579i	−0.886590	−	0.462556i	$-0.846933\pi$
$277$	−11.9939	+	8.71410i	−0.720645	+	0.523579i	0.165945	+	0.986135i	$0.446933\pi$
$278$		0			0
$279$	2.60930	−	8.03059i	0.156214	−	0.480779i
$280$		0			0
$281$	13.6295	+	9.90242i	0.813069	+	0.590729i	0.914719	−	0.404091i	$-0.132412\pi$
$281$	13.6295	+	9.90242i	0.813069	+	0.590729i	−0.101650	+	0.994820i	$0.532412\pi$
$282$		0			0
$283$	−1.51240	−	4.65468i	−0.0899028	−	0.276692i	0.895989	−	0.444076i	$-0.146468\pi$
$283$	−1.51240	−	4.65468i	−0.0899028	−	0.276692i	−0.985892	+	0.167384i	$0.946468\pi$
$284$		0			0
$285$	−2.63156			−0.155880
$286$		0			0
$287$	44.3744			2.61934
$288$		0			0
$289$	2.41671	+	7.43787i	0.142159	+	0.437522i
$290$		0			0
$291$	−9.34268	−	6.78786i	−0.547678	−	0.397911i
$292$		0			0
$293$	3.69507	−	11.3723i	0.215869	−	0.664375i	−0.783222	−	0.621742i	$-0.786425\pi$
$293$	3.69507	−	11.3723i	0.215869	−	0.664375i	0.999091	−	0.0426332i	$-0.0135747\pi$
$294$		0			0
$295$	0.0840688	−	0.0610796i	0.00489467	−	0.00355619i
$296$		0			0
$297$	9.50878	−	11.3286i	0.551755	−	0.657351i
$298$		0			0
$299$	−28.7388	+	20.8800i	−1.66201	+	1.20752i
$300$		0			0
$301$	−17.2061	+	52.9549i	−0.991743	+	3.05227i
$302$		0			0
$303$	−3.30338	−	2.40005i	−0.189774	−	0.137879i
$304$		0			0
$305$	3.13692	+	9.65446i	0.179620	+	0.552813i
$306$		0			0
$307$	16.8325			0.960680			0.480340	−	0.877082i	$-0.340513\pi$
$307$	16.8325			0.960680			0.480340	+	0.877082i	$0.340513\pi$
$308$		0			0
$309$	0.762681			0.0433874
$310$		0			0
$311$	7.60024	+	23.3911i	0.430970	+	1.32639i	0.897160	+	0.441705i	$0.145626\pi$
$311$	7.60024	+	23.3911i	0.430970	+	1.32639i	−0.466190	+	0.884684i	$0.654374\pi$
$312$		0			0
$313$	−5.83297	−	4.23790i	−0.329699	−	0.239540i	0.410604	−	0.911814i	$-0.365318\pi$
$313$	−5.83297	−	4.23790i	−0.329699	−	0.239540i	−0.740303	+	0.672274i	$0.765318\pi$
$314$		0			0
$315$	3.36494	−	10.3562i	0.189593	−	0.583508i
$316$		0			0
$317$	6.92439	−	5.03086i	0.388912	−	0.282561i	−0.376097	−	0.926580i	$-0.622734\pi$
$317$	6.92439	−	5.03086i	0.388912	−	0.282561i	0.765010	+	0.644019i	$0.222734\pi$
$318$		0			0
$319$	8.01612	+	3.24016i	0.448817	+	0.181414i
$320$		0			0
$321$	10.0894	−	7.33041i	0.563138	−	0.409144i
$322$		0			0
$323$	4.80511	−	14.7886i	0.267364	−	0.822861i
$324$		0			0
$325$	−3.06058	−	2.22364i	−0.169770	−	0.123345i
$326$		0			0
$327$	0.884359	+	2.72178i	0.0489052	+	0.150515i
$328$		0			0
$329$	−7.90393			−0.435758
$330$		0			0
$331$	−25.4094			−1.39662			−0.698312	−	0.715793i	$-0.746065\pi$
$331$	−25.4094			−1.39662			−0.698312	+	0.715793i	$0.746065\pi$
$332$		0			0
$333$	2.43873	+	7.50564i	0.133642	+	0.411306i
$334$		0			0
$335$	−4.03924	−	2.93468i	−0.220687	−	0.160339i
$336$		0			0
$337$	−5.85288	+	18.0133i	−0.318827	+	0.981248i	0.655324	+	0.755348i	$0.272532\pi$
$337$	−5.85288	+	18.0133i	−0.318827	+	0.981248i	−0.974150	+	0.225900i	$0.927468\pi$
$338$		0			0
$339$	6.94083	−	5.04281i	0.376974	−	0.273888i
$340$		0			0
$341$	−6.48144	−	10.3760i	−0.350990	−	0.561893i
$342$		0			0
$343$	−33.2057	+	24.1254i	−1.79294	+	1.30265i
$344$		0			0
$345$	−2.44651	+	7.52957i	−0.131715	+	0.405378i
$346$		0			0
$347$	6.38484	+	4.63885i	0.342756	+	0.249027i	0.745824	−	0.666143i	$-0.232056\pi$
$347$	6.38484	+	4.63885i	0.342756	+	0.249027i	−0.403068	+	0.915170i	$0.632056\pi$
$348$		0			0
$349$	2.30483	+	7.09353i	0.123375	+	0.379708i	0.993601	−	0.112943i	$-0.0360278\pi$
$349$	2.30483	+	7.09353i	0.123375	+	0.379708i	−0.870227	+	0.492651i	$0.836028\pi$
$350$		0			0
$351$	−16.8705			−0.900478
$352$		0			0
$353$	−2.03405			−0.108262			−0.0541308	−	0.998534i	$-0.517239\pi$
$353$	−2.03405			−0.108262			−0.0541308	+	0.998534i	$0.517239\pi$
$354$		0			0
$355$	1.92496	+	5.92441i	0.102166	+	0.314435i
$356$		0			0
$357$	−16.1655	−	11.7449i	−0.855568	−	0.621606i
$358$		0			0
$359$	5.03775	−	15.5046i	0.265882	−	0.818301i	−0.725607	−	0.688110i	$-0.758441\pi$
$359$	5.03775	−	15.5046i	0.265882	−	0.818301i	0.991489	−	0.130191i	$-0.0415592\pi$
$360$		0			0
$361$	7.49021	−	5.44196i	0.394222	−	0.286419i
$362$		0			0
$363$	−1.60770	−	9.13409i	−0.0843822	−	0.479416i
$364$		0			0
$365$	−5.91108	+	4.29465i	−0.309400	+	0.224792i
$366$		0			0
$367$	−0.238220	+	0.733165i	−0.0124350	+	0.0382709i	−0.957081	−	0.289819i	$-0.906405\pi$
$367$	−0.238220	+	0.733165i	−0.0124350	+	0.0382709i	0.944647	+	0.328090i	$0.106405\pi$
$368$		0			0
$369$	17.2756	+	12.5514i	0.899330	+	0.653402i
$370$		0			0
$371$	−2.85166	−	8.77652i	−0.148051	−	0.455654i
$372$		0			0
$373$	−5.01958			−0.259904			−0.129952	−	0.991520i	$-0.541482\pi$
$373$	−5.01958			−0.259904			−0.129952	+	0.991520i	$0.541482\pi$
$374$		0			0
$375$	−0.843136			−0.0435394
$376$		0			0
$377$	−3.04759	−	9.37953i	−0.156959	−	0.483070i
$378$		0			0
$379$	−2.95681	−	2.14825i	−0.151881	−	0.110348i	0.509250	−	0.860619i	$-0.329923\pi$
$379$	−2.95681	−	2.14825i	−0.151881	−	0.110348i	−0.661130	+	0.750271i	$0.729923\pi$
$380$		0			0
$381$	−2.85522	+	8.78748i	−0.146278	+	0.450196i
$382$		0			0
$383$	−4.43460	+	3.22192i	−0.226597	+	0.164633i	−0.695291	−	0.718728i	$-0.744725\pi$
$383$	−4.43460	+	3.22192i	−0.226597	+	0.164633i	0.468694	+	0.883361i	$0.344725\pi$
$384$		0			0
$385$	−8.35846	−	13.3809i	−0.425986	−	0.681953i
$386$		0			0
$387$	−21.6770	+	15.7493i	−1.10191	+	0.800581i
$388$		0			0
$389$	0.259746	−	0.799417i	0.0131697	−	0.0405321i	−0.944256	−	0.329213i	$-0.893217\pi$
$389$	0.259746	−	0.799417i	0.0131697	−	0.0405321i	0.957425	+	0.288681i	$0.0932166\pi$
$390$		0			0
$391$	−37.8469	−	27.4974i	−1.91400	−	1.39060i
$392$		0			0
$393$	3.36156	+	10.3458i	0.169568	+	0.521877i
$394$		0			0
$395$	−10.5445			−0.530552
$396$		0			0
$397$	3.61935			0.181650			0.0908249	−	0.995867i	$-0.471050\pi$
$397$	3.61935			0.181650			0.0908249	+	0.995867i	$0.471050\pi$
$398$		0			0
$399$	3.86831	+	11.9054i	0.193658	+	0.596018i
$400$		0			0
$401$	−8.16132	−	5.92954i	−0.407557	−	0.296107i	0.365055	−	0.930986i	$-0.381050\pi$
$401$	−8.16132	−	5.92954i	−0.407557	−	0.296107i	−0.772612	+	0.634879i	$0.781050\pi$
$402$		0			0
$403$	−4.31221	+	13.2716i	−0.214807	+	0.661107i
$404$		0			0
$405$	2.51397	−	1.82651i	0.124920	−	0.0907598i
$406$		0			0
$407$	10.6010	+	4.28498i	0.525473	+	0.212399i
$408$		0			0
$409$	−10.0189	+	7.27916i	−0.495403	+	0.359931i	−0.807258	−	0.590198i	$-0.799050\pi$
$409$	−10.0189	+	7.27916i	−0.495403	+	0.359931i	0.311855	+	0.950130i	$0.399050\pi$
$410$		0			0
$411$	4.91970	−	15.1413i	0.242671	−	0.746864i
$412$		0			0
$413$	−0.399909	−	0.290551i	−0.0196783	−	0.0142971i
$414$		0			0
$415$	−1.75834	−	5.41160i	−0.0863133	−	0.265645i
$416$		0			0
$417$	9.18109			0.449600
$418$		0			0
$419$	−0.612942			−0.0299442			−0.0149721	−	0.999888i	$-0.504766\pi$
$419$	−0.612942			−0.0299442			−0.0149721	+	0.999888i	$0.504766\pi$
$420$		0			0
$421$	−10.3660	−	31.9031i	−0.505206	−	1.55486i	−0.800424	−	0.599434i	$-0.795392\pi$
$421$	−10.3660	−	31.9031i	−0.505206	−	1.55486i	0.295218	−	0.955430i	$-0.404608\pi$
$422$		0			0
$423$	−3.07711	−	2.23565i	−0.149614	−	0.108701i
$424$		0			0
$425$	1.53953	−	4.73819i	0.0746783	−	0.229836i
$426$		0			0
$427$	39.0666	−	28.3836i	1.89057	−	1.37358i
$428$		0			0
$429$	−6.80122	+	8.10285i	−0.328366	+	0.391209i
$430$		0			0
$431$	−7.05473	+	5.12556i	−0.339814	+	0.246890i	−0.744583	−	0.667529i	$-0.767352\pi$
$431$	−7.05473	+	5.12556i	−0.339814	+	0.246890i	0.404769	+	0.914419i	$0.367352\pi$
$432$		0			0
$433$	−3.51360	+	10.8138i	−0.168853	+	0.519676i	−0.999300	−	0.0374224i	$-0.988085\pi$
$433$	−3.51360	+	10.8138i	−0.168853	+	0.519676i	0.830447	+	0.557098i	$0.188085\pi$
$434$		0			0
$435$	−1.77822	−	1.29195i	−0.0852589	−	0.0619443i
$436$		0			0
$437$	9.05656	+	27.8732i	0.433234	+	1.33336i
$438$		0			0
$439$	24.3176			1.16061			0.580307	−	0.814398i	$-0.302933\pi$
$439$	24.3176			1.16061			0.580307	+	0.814398i	$0.302933\pi$
$440$		0			0
$441$	−35.7752			−1.70358
$442$		0			0
$443$	−0.0704295	−	0.216760i	−0.00334620	−	0.0102986i	0.949369	−	0.314162i	$-0.101723\pi$
$443$	−0.0704295	−	0.216760i	−0.00334620	−	0.0102986i	−0.952716	+	0.303863i	$0.901723\pi$
$444$		0			0
$445$	11.0327	+	8.01571i	0.522999	+	0.379981i
$446$		0			0
$447$	0.441393	−	1.35847i	0.0208772	−	0.0642534i
$448$		0			0
$449$	−32.6872	+	23.7486i	−1.54260	+	1.12077i	−0.593928	+	0.804518i	$0.702424\pi$
$449$	−32.6872	+	23.7486i	−1.54260	+	1.12077i	−0.948676	+	0.316249i	$0.897576\pi$
$450$		0			0
$451$	30.0208	−	7.48014i	1.41363	−	0.352226i
$452$		0			0
$453$	2.38046	−	1.72951i	0.111844	−	0.0812593i
$454$		0			0
$455$	−5.56102	+	17.1151i	−0.260705	+	0.802367i
$456$		0			0
$457$	−3.67858	−	2.67265i	−0.172077	−	0.125021i	0.498413	−	0.866939i	$-0.333916\pi$
$457$	−3.67858	−	2.67265i	−0.172077	−	0.125021i	−0.670490	+	0.741918i	$0.733916\pi$
$458$		0			0
$459$	−6.86547	−	21.1297i	−0.320453	−	0.986252i
$460$		0			0
$461$	−36.5792			−1.70366			−0.851832	−	0.523815i	$-0.824508\pi$
$461$	−36.5792			−1.70366			−0.851832	+	0.523815i	$0.824508\pi$
$462$		0			0
$463$	−5.18502			−0.240968			−0.120484	−	0.992715i	$-0.538445\pi$
$463$	−5.18502			−0.240968			−0.120484	+	0.992715i	$0.538445\pi$
$464$		0			0
$465$	0.961064	+	2.95785i	0.0445683	+	0.137167i
$466$		0			0
$467$	8.15502	+	5.92497i	0.377369	+	0.274175i	0.760260	−	0.649619i	$-0.225071\pi$
$467$	8.15502	+	5.92497i	0.377369	+	0.274175i	−0.382891	+	0.923794i	$0.625071\pi$
$468$		0			0
$469$	−7.33923	+	22.5878i	−0.338894	+	1.04301i
$470$		0			0
$471$	−14.1199	+	10.2587i	−0.650612	+	0.472697i
$472$		0			0
$473$	−2.71398	+	38.7263i	−0.124789	+	1.78064i
$474$		0			0
$475$	−2.52507	+	1.83457i	−0.115858	+	0.0841757i
$476$		0			0
$477$	1.37227	−	4.22342i	0.0628320	−	0.193377i
$478$		0			0
$479$	−2.07381	−	1.50671i	−0.0947548	−	0.0688434i	0.539399	−	0.842050i	$-0.318651\pi$
$479$	−2.07381	−	1.50671i	−0.0947548	−	0.0688434i	−0.634154	+	0.773207i	$0.718651\pi$
$480$		0			0
$481$	−4.03033	−	12.4041i	−0.183767	−	0.565577i
$482$		0			0
$483$	37.6609			1.71363
$484$		0			0
$485$	−13.6967			−0.621935
$486$		0			0
$487$	0.745567	+	2.29462i	0.0337849	+	0.103979i	0.966527	−	0.256565i	$-0.0825909\pi$
$487$	0.745567	+	2.29462i	0.0337849	+	0.103979i	−0.932742	+	0.360545i	$0.882591\pi$
$488$		0			0
$489$	−11.1751	−	8.11921i	−0.505357	−	0.367163i
$490$		0			0
$491$	4.64533	−	14.2969i	0.209641	−	0.645208i	−0.789850	−	0.613300i	$-0.789842\pi$
$491$	4.64533	−	14.2969i	0.209641	−	0.645208i	0.999491	−	0.0319079i	$-0.0101583\pi$
$492$		0			0
$493$	10.5074	−	7.63404i	0.473227	−	0.343820i
$494$		0			0
$495$	0.530764	−	7.57358i	0.0238561	−	0.340407i
$496$		0			0
$497$	23.9730	−	17.4174i	1.07534	−	0.781278i
$498$		0			0
$499$	2.29614	−	7.06680i	0.102789	−	0.316353i	−0.886416	−	0.462890i	$-0.846813\pi$
$499$	2.29614	−	7.06680i	0.102789	−	0.316353i	0.989205	+	0.146536i	$0.0468126\pi$
$500$		0			0
$501$	−9.82323	−	7.13699i	−0.438869	−	0.318857i
$502$		0			0
$503$	4.69638	+	14.4540i	0.209401	+	0.644471i	0.999504	+	0.0314963i	$0.0100272\pi$
$503$	4.69638	+	14.4540i	0.209401	+	0.644471i	−0.790103	+	0.612975i	$0.789973\pi$
$504$		0			0
$505$	−4.84287			−0.215505
$506$		0			0
$507$	1.10594			0.0491164
$508$		0			0
$509$	−7.11646	−	21.9022i	−0.315431	−	0.970798i	−0.975576	−	0.219660i	$-0.929505\pi$
$509$	−7.11646	−	21.9022i	−0.315431	−	0.970798i	0.660145	−	0.751138i	$-0.270495\pi$
$510$		0			0
$511$	28.1186	+	20.4294i	1.24389	+	0.903741i
$512$		0			0
$513$	−4.30109	+	13.2374i	−0.189898	+	0.584445i
$514$		0			0
$515$	0.731817	−	0.531696i	0.0322477	−	0.0234293i
$516$		0			0
$517$	−5.34729	+	1.33236i	−0.235174	+	0.0585970i
$518$		0			0
$519$	5.54116	−	4.02589i	0.243230	−	0.176717i
$520$		0			0
$521$	0.341879	−	1.05220i	0.0149780	−	0.0460975i	−0.943288	−	0.331975i	$-0.892285\pi$
$521$	0.341879	−	1.05220i	0.0149780	−	0.0460975i	0.958266	+	0.285877i	$0.0922850\pi$
$522$		0			0
$523$	0.945974	+	0.687290i	0.0413645	+	0.0300531i	0.608275	−	0.793726i	$-0.291862\pi$
$523$	0.945974	+	0.687290i	0.0413645	+	0.0300531i	−0.566911	+	0.823779i	$0.691862\pi$
$524$		0			0
$525$	1.23939	+	3.81444i	0.0540913	+	0.166476i
$526$		0			0
$527$	−18.3772			−0.800522
$528$		0			0
$529$	65.1723			2.83358
$530$		0			0
$531$	−0.0735069	−	0.226231i	−0.00318993	−	0.00981759i
$532$		0			0
$533$	−28.5502	−	20.7429i	−1.23665	−	0.898476i
$534$		0			0
$535$	4.57082	−	14.0675i	0.197614	−	0.608193i
$536$		0			0
$537$	−2.04183	+	1.48348i	−0.0881115	+	0.0640168i
$538$		0			0
$539$	−33.3240	+	39.7016i	−1.43537	+	1.71007i
$540$		0			0
$541$	2.77596	−	2.01685i	0.119348	−	0.0867112i	−0.526510	−	0.850169i	$-0.676500\pi$
$541$	2.77596	−	2.01685i	0.119348	−	0.0867112i	0.645858	+	0.763458i	$0.276500\pi$
$542$		0			0
$543$	−3.78476	+	11.6483i	−0.162420	+	0.499876i
$544$		0			0
$545$	2.74604	+	1.99511i	0.117627	+	0.0854612i
$546$		0			0
$547$	−12.9614	−	39.8911i	−0.554190	−	1.70562i	−0.698072	−	0.716027i	$-0.745959\pi$
$547$	−12.9614	−	39.8911i	−0.554190	−	1.70562i	0.143882	−	0.989595i	$-0.454041\pi$
$548$		0			0
$549$	23.2376			0.991755
$550$		0			0
$551$	−8.13662			−0.346632
$552$		0			0
$553$	15.5001	+	47.7045i	0.659133	+	2.02860i
$554$		0			0
$555$	−2.35162	−	1.70856i	−0.0998209	−	0.0725241i
$556$		0			0
$557$	−10.0451	+	30.9156i	−0.425624	+	1.30994i	0.476771	+	0.879028i	$0.341807\pi$
$557$	−10.0451	+	30.9156i	−0.425624	+	1.30994i	−0.902395	+	0.430910i	$0.858193\pi$
$558$		0			0
$559$	35.8242	−	26.0278i	1.51520	−	1.10086i
$560$		0			0
$561$	−12.9163	−	5.22085i	−0.545328	−	0.220424i
$562$		0			0
$563$	30.1426	−	21.8999i	1.27036	−	0.922969i	0.271141	−	0.962540i	$-0.412599\pi$
$563$	30.1426	−	21.8999i	1.27036	−	0.922969i	0.999217	+	0.0395706i	$0.0125990\pi$
$564$		0			0
$565$	3.14440	−	9.67748i	0.132286	−	0.407135i
$566$		0			0
$567$	−11.9588	−	8.68856i	−0.502222	−	0.364885i
$568$		0			0
$569$	−11.5993	−	35.6989i	−0.486267	−	1.49658i	−0.830138	−	0.557559i	$-0.811738\pi$
$569$	−11.5993	−	35.6989i	−0.486267	−	1.49658i	0.343871	−	0.939017i	$-0.388262\pi$
$570$		0			0
$571$	−21.6905			−0.907718			−0.453859	−	0.891073i	$-0.649953\pi$
$571$	−21.6905			−0.907718			−0.453859	+	0.891073i	$0.649953\pi$
$572$		0			0
$573$	−6.71762			−0.280632
$574$		0			0
$575$	2.90167	+	8.93043i	0.121008	+	0.372425i
$576$		0			0
$577$	21.7873	+	15.8294i	0.907019	+	0.658988i	0.940259	−	0.340460i	$-0.110583\pi$
$577$	21.7873	+	15.8294i	0.907019	+	0.658988i	−0.0332403	+	0.999447i	$0.510583\pi$
$578$		0			0
$579$	−5.07961	+	15.6334i	−0.211101	+	0.649703i
$580$		0			0
$581$	−21.8980	+	15.9098i	−0.908481	+	0.660050i
$582$		0			0
$583$	−3.40870	−	5.45692i	−0.141174	−	0.226003i
$584$		0			0
$585$	−7.00603	+	5.09018i	−0.289664	+	0.210453i
$586$		0			0
$587$	−4.78226	+	14.7183i	−0.197385	+	0.607488i	0.802556	+	0.596577i	$0.203473\pi$
$587$	−4.78226	+	14.7183i	−0.197385	+	0.607488i	−0.999940	+	0.0109109i	$0.996527\pi$
$588$		0			0
$589$	9.31418	+	6.76715i	0.383784	+	0.278836i
$590$		0			0
$591$	4.68329	+	14.4137i	0.192645	+	0.592900i
$592$		0			0
$593$	24.7646			1.01696			0.508481	−	0.861073i	$-0.330207\pi$
$593$	24.7646			1.01696			0.508481	+	0.861073i	$0.330207\pi$
$594$		0			0
$595$	−23.6992			−0.971571
$596$		0			0
$597$	−1.86996	−	5.75516i	−0.0765326	−	0.235543i
$598$		0			0
$599$	−10.4687	−	7.60597i	−0.427740	−	0.310772i	0.353004	−	0.935622i	$-0.385160\pi$
$599$	−10.4687	−	7.60597i	−0.427740	−	0.310772i	−0.780745	+	0.624850i	$0.785160\pi$
$600$		0			0
$601$	−5.80697	+	17.8720i	−0.236871	+	0.729015i	0.759996	+	0.649927i	$0.225201\pi$
$601$	−5.80697	+	17.8720i	−0.236871	+	0.729015i	−0.996868	+	0.0790874i	$0.974799\pi$
$602$		0			0
$603$	−9.24630	+	6.71783i	−0.376539	+	0.273571i
$604$		0			0
$605$	−7.91039	−	7.64367i	−0.321603	−	0.310759i
$606$		0			0
$607$	11.6066	−	8.43268i	0.471097	−	0.342272i	−0.326772	−	0.945103i	$-0.605961\pi$
$607$	11.6066	−	8.43268i	0.471097	−	0.342272i	0.797869	+	0.602831i	$0.205961\pi$
$608$		0			0
$609$	−3.23099	+	9.94397i	−0.130926	+	0.402950i
$610$		0			0
$611$	5.08534	+	3.69471i	0.205731	+	0.149472i
$612$		0			0
$613$	−12.1838	−	37.4979i	−0.492099	−	1.51453i	−0.821429	−	0.570310i	$-0.806823\pi$
$613$	−12.1838	−	37.4979i	−0.492099	−	1.51453i	0.329330	−	0.944215i	$-0.393177\pi$
$614$		0			0
$615$	−7.86509			−0.317151
$616$		0			0
$617$	32.9316			1.32578			0.662888	−	0.748718i	$-0.269330\pi$
$617$	32.9316			1.32578			0.662888	+	0.748718i	$0.269330\pi$
$618$		0			0
$619$	−12.7342	−	39.1919i	−0.511832	−	1.57526i	−0.788973	−	0.614428i	$-0.789387\pi$
$619$	−12.7342	−	39.1919i	−0.511832	−	1.57526i	0.277141	−	0.960829i	$-0.410613\pi$
$620$		0			0
$621$	33.8770	+	24.6131i	1.35944	+	0.987689i
$622$		0			0
$623$	20.0462	−	61.6959i	0.803135	−	2.47180i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	4.62394	+	7.40238i	0.184662	+	0.295622i
$628$		0			0
$629$	13.8956	−	10.0957i	0.554053	−	0.402543i
$630$		0			0
$631$	2.40842	−	7.41235i	0.0958776	−	0.295081i	−0.891604	−	0.452816i	$-0.850419\pi$
$631$	2.40842	−	7.41235i	0.0958776	−	0.295081i	0.987481	+	0.157735i	$0.0504193\pi$
$632$		0			0
$633$	3.02370	+	2.19684i	0.120181	+	0.0873167i
$634$		0			0
$635$	3.38643	+	10.4224i	0.134386	+	0.413599i
$636$		0			0
$637$	59.1234			2.34255
$638$		0			0
$639$	14.2596			0.564101
$640$		0			0
$641$	−5.24398	−	16.1393i	−0.207125	−	0.637464i	−0.999619	−	0.0275853i	$-0.991218\pi$
$641$	−5.24398	−	16.1393i	−0.207125	−	0.637464i	0.792495	−	0.609879i	$-0.208782\pi$
$642$		0			0
$643$	−0.280367	−	0.203699i	−0.0110566	−	0.00803310i	0.582243	−	0.813015i	$-0.302175\pi$
$643$	−0.280367	−	0.203699i	−0.0110566	−	0.00803310i	−0.593300	+	0.804982i	$0.702175\pi$
$644$		0			0
$645$	3.04968	−	9.38594i	0.120081	−	0.369571i
$646$		0			0
$647$	−6.65994	+	4.83873i	−0.261829	+	0.190230i	−0.710953	−	0.703239i	$-0.751736\pi$
$647$	−6.65994	+	4.83873i	−0.261829	+	0.190230i	0.449124	+	0.893469i	$0.351736\pi$
$648$		0			0
$649$	−0.319531	−	0.129156i	−0.0125427	−	0.00506981i
$650$		0			0
$651$	11.9689	−	8.69592i	0.469098	−	0.340820i
$652$		0			0
$653$	10.1807	−	31.3330i	0.398403	−	1.22616i	−0.527877	−	0.849321i	$-0.677012\pi$
$653$	10.1807	−	31.3330i	0.398403	−	1.22616i	0.926280	−	0.376836i	$-0.122988\pi$
$654$		0			0
$655$	10.4380	+	7.58366i	0.407847	+	0.296318i
$656$		0			0
$657$	5.16845	+	15.9069i	0.201640	+	0.620586i
$658$		0			0
$659$	18.7687			0.731127			0.365563	−	0.930786i	$-0.380876\pi$
$659$	18.7687			0.731127			0.365563	+	0.930786i	$0.380876\pi$
$660$		0			0
$661$	8.66066			0.336860			0.168430	−	0.985714i	$-0.446130\pi$
$661$	8.66066			0.336860			0.168430	+	0.985714i	$0.446130\pi$
$662$		0			0
$663$	4.91057	+	15.1132i	0.190711	+	0.586948i
$664$		0			0
$665$	12.0116	+	8.72691i	0.465788	+	0.338415i
$666$		0			0
$667$	−7.56445	+	23.2810i	−0.292897	+	0.901444i
$668$		0			0
$669$	10.3753	−	7.53808i	0.401132	−	0.291439i
$670$		0			0
$671$	21.6454	−	25.7879i	0.835610	−	0.995531i
$672$		0			0
$673$	9.47261	−	6.88225i	0.365142	−	0.265291i	−0.390052	−	0.920793i	$-0.627543\pi$
$673$	9.47261	−	6.88225i	0.365142	−	0.265291i	0.755194	+	0.655502i	$0.227543\pi$
$674$		0			0
$675$	−1.37805	+	4.24119i	−0.0530410	+	0.163243i
$676$		0			0
$677$	25.1379	+	18.2637i	0.966127	+	0.701932i	0.954566	−	0.298001i	$-0.0963198\pi$
$677$	25.1379	+	18.2637i	0.966127	+	0.701932i	0.0115613	+	0.999933i	$0.496320\pi$
$678$		0			0
$679$	20.1338	+	61.9654i	0.772663	+	2.37801i
$680$		0			0
$681$	3.61198			0.138411
$682$		0			0
$683$	−31.0210			−1.18698			−0.593492	−	0.804840i	$-0.702251\pi$
$683$	−31.0210			−1.18698			−0.593492	+	0.804840i	$0.702251\pi$
$684$		0			0
$685$	−5.83500	−	17.9583i	−0.222944	−	0.686150i
$686$		0			0
$687$	2.79431	+	2.03018i	0.106609	+	0.0774563i
$688$		0			0
$689$	−2.26786	+	6.97977i	−0.0863987	+	0.265908i
$690$		0			0
$691$	−33.9401	+	24.6589i	−1.29114	+	0.938069i	−0.999828	−	0.0185582i	$-0.994092\pi$
$691$	−33.9401	+	24.6589i	−1.29114	+	0.938069i	−0.291314	+	0.956628i	$0.594092\pi$
$692$		0			0
$693$	−35.0439	+	8.73172i	−1.33121	+	0.331690i
$694$		0			0
$695$	8.80956	−	6.40052i	0.334166	−	0.242786i
$696$		0			0
$697$	14.3613	−	44.1996i	0.543974	−	1.67418i
$698$		0			0
$699$	11.7685	+	8.55033i	0.445126	+	0.323403i
$700$		0			0
$701$	−3.02060	−	9.29646i	−0.114087	−	0.351122i	0.877669	−	0.479268i	$-0.159098\pi$
$701$	−3.02060	−	9.29646i	−0.114087	−	0.351122i	−0.991755	+	0.128145i	$0.959098\pi$
$702$		0			0
$703$	−10.7604			−0.405835
$704$		0			0
$705$	1.40092			0.0527618
$706$		0			0
$707$	7.11889	+	21.9097i	0.267733	+	0.823999i
$708$		0			0
$709$	−14.2652	−	10.3643i	−0.535742	−	0.389240i	0.286759	−	0.958003i	$-0.407422\pi$
$709$	−14.2652	−	10.3643i	−0.535742	−	0.389240i	−0.822501	+	0.568763i	$0.807422\pi$
$710$		0			0
$711$	−7.45895	+	22.9563i	−0.279732	+	0.860928i
$712$		0			0
$713$	28.0218	−	20.3590i	1.04942	−	0.762451i
$714$		0			0
$715$	−0.877159	+	12.5164i	−0.0328039	+	0.468085i
$716$		0			0
$717$	2.32345	−	1.68808i	0.0867707	−	0.0630426i
$718$		0			0
$719$	15.8862	−	48.8927i	0.592455	−	1.82339i	0.0254492	−	0.999676i	$-0.491898\pi$
$719$	15.8862	−	48.8927i	0.592455	−	1.82339i	0.567006	−	0.823714i	$-0.308102\pi$
$720$		0			0
$721$	−3.48120	−	2.52924i	−0.129647	−	0.0941939i
$722$		0			0
$723$	−5.25879	−	16.1849i	−0.195576	−	0.601922i
$724$		0			0
$725$	−2.60693			−0.0968189
$726$		0			0
$727$	−17.3527			−0.643577			−0.321788	−	0.946812i	$-0.604284\pi$
$727$	−17.3527			−0.643577			−0.321788	+	0.946812i	$0.604284\pi$
$728$		0			0
$729$	1.28751	+	3.96255i	0.0476856	+	0.146761i
$730$		0			0
$731$	47.1778	+	34.2767i	1.74493	+	1.26777i
$732$		0			0
$733$	13.2425	−	40.7562i	0.489123	−	1.50537i	−0.336796	−	0.941578i	$-0.609343\pi$
$733$	13.2425	−	40.7562i	0.489123	−	1.50537i	0.825919	−	0.563788i	$-0.190657\pi$
$734$		0			0
$735$	10.6603	−	7.74516i	0.393211	−	0.285684i
$736$		0			0
$737$	−1.15764	+	16.5186i	−0.0426423	+	0.608472i
$738$		0			0
$739$	19.8915	−	14.4520i	0.731722	−	0.531627i	−0.158386	−	0.987377i	$-0.550629\pi$
$739$	19.8915	−	14.4520i	0.731722	−	0.531627i	0.890108	+	0.455750i	$0.150629\pi$
$740$		0			0
$741$	3.07638	−	9.46814i	0.113014	−	0.347821i
$742$		0			0
$743$	3.79451	+	2.75687i	0.139207	+	0.101140i	0.655209	−	0.755447i	$-0.272580\pi$
$743$	3.79451	+	2.75687i	0.139207	+	0.101140i	−0.516002	+	0.856587i	$0.672580\pi$
$744$		0			0
$745$	−0.523513	−	1.61121i	−0.0191800	−	0.0590301i
$746$		0			0
$747$	−13.0253			−0.476571
$748$		0			0
$749$	−70.3621			−2.57097
$750$		0			0
$751$	−14.9231	−	45.9286i	−0.544552	−	1.67596i	−0.722053	−	0.691838i	$-0.756801\pi$
$751$	−14.9231	−	45.9286i	−0.544552	−	1.67596i	0.177501	−	0.984121i	$-0.443199\pi$
$752$		0			0
$753$	−13.4356	−	9.76155i	−0.489621	−	0.355731i
$754$		0			0
$755$	1.07842	−	3.31904i	0.0392478	−	0.120792i
$756$		0			0
$757$	−31.4094	+	22.8203i	−1.14159	+	0.829417i	−0.987341	−	0.158614i	$-0.949297\pi$
$757$	−31.4094	+	22.8203i	−1.14159	+	0.829417i	−0.154254	+	0.988031i	$0.549297\pi$
$758$		0			0
$759$	25.4789	−	6.34845i	0.924826	−	0.230434i
$760$		0			0
$761$	22.5616	−	16.3919i	0.817857	−	0.594208i	−0.0982411	−	0.995163i	$-0.531322\pi$
$761$	22.5616	−	16.3919i	0.817857	−	0.594208i	0.916098	+	0.400955i	$0.131322\pi$
$762$		0			0
$763$	4.98951	−	15.3561i	0.180632	−	0.555929i
$764$		0			0
$765$	−9.22641	−	6.70338i	−0.333582	−	0.242361i
$766$		0			0
$767$	0.121480	+	0.373877i	0.00438639	+	0.0134999i
$768$		0			0
$769$	−38.2240			−1.37839			−0.689197	−	0.724574i	$-0.742036\pi$
$769$	−38.2240			−1.37839			−0.689197	+	0.724574i	$0.742036\pi$
$770$		0			0
$771$	−9.03288			−0.325311
$772$		0			0
$773$	2.59445	+	7.98490i	0.0933159	+	0.287197i	0.986811	−	0.161876i	$-0.0517544\pi$
$773$	2.59445	+	7.98490i	0.0933159	+	0.287197i	−0.893495	+	0.449073i	$0.851754\pi$
$774$		0			0
$775$	2.98421	+	2.16816i	0.107196	+	0.0778825i
$776$		0			0
$777$	−4.27287	+	13.1505i	−0.153288	+	0.471773i
$778$		0			0
$779$	−23.5547	+	17.1135i	−0.843936	+	0.613156i
$780$		0			0
$781$	13.2826	−	15.8246i	0.475287	−	0.566249i
$782$		0			0
$783$	−9.40520	+	6.83328i	−0.336114	+	0.244201i
$784$		0			0
$785$	−6.39675	+	19.6872i	−0.228310	+	0.702666i
$786$		0			0
$787$	−28.6593	−	20.8222i	−1.02159	−	0.742231i	−0.0549842	−	0.998487i	$-0.517511\pi$
$787$	−28.6593	−	20.8222i	−1.02159	−	0.742231i	−0.966609	+	0.256256i	$0.917511\pi$
$788$		0			0
$789$	2.30924	+	7.10712i	0.0822112	+	0.253020i
$790$		0			0
$791$	−48.4042			−1.72105
$792$		0			0
$793$	−38.4032			−1.36374
$794$		0			0
$795$	0.505440	+	1.55558i	0.0179261	+	0.0551709i
$796$		0			0
$797$	−43.1931	−	31.3816i	−1.52998	−	1.11159i	−0.956250	−	0.292550i	$-0.905496\pi$
$797$	−43.1931	−	31.3816i	−1.52998	−	1.11159i	−0.573729	−	0.819045i	$-0.694504\pi$
$798$		0			0
$799$	−2.55803	+	7.87280i	−0.0904966	+	0.278520i
$800$		0			0
$801$	25.2551	−	18.3489i	0.892347	−	0.648328i
$802$		0			0
$803$	22.4670	+	9.08126i	0.792842	+	0.320471i
$804$		0			0
$805$	36.1369	−	26.2550i	1.27366	−	0.925366i
$806$		0			0
$807$	−0.561421	+	1.72788i	−0.0197630	+	0.0608241i
$808$		0			0
$809$	3.10733	+	2.25760i	0.109248	+	0.0793731i	0.641068	−	0.767484i	$-0.278492\pi$
$809$	3.10733	+	2.25760i	0.109248	+	0.0793731i	−0.531820	+	0.846857i	$0.678492\pi$
$810$		0			0
$811$	7.33142	+	22.5638i	0.257441	+	0.792322i	0.993339	+	0.115229i	$0.0367603\pi$
$811$	7.33142	+	22.5638i	0.257441	+	0.792322i	−0.735898	+	0.677093i	$0.763240\pi$
$812$		0			0
$813$	8.64657			0.303248
$814$		0			0
$815$	−16.3831			−0.573877
$816$		0			0
$817$	−11.2894	−	34.7452i	−0.394966	−	1.21558i
$818$		0			0
$819$	33.3272	+	24.2136i	1.16455	+	0.846092i
$820$		0			0
$821$	0.0470633	−	0.144846i	0.00164252	−	0.00505516i	−0.950232	−	0.311543i	$-0.899154\pi$
$821$	0.0470633	−	0.144846i	0.00164252	−	0.00505516i	0.951874	+	0.306488i	$0.0991540\pi$
$822$		0			0
$823$	40.5913	−	29.4913i	1.41492	−	1.02800i	0.422341	−	0.906437i	$-0.361208\pi$
$823$	40.5913	−	29.4913i	1.41492	−	1.02800i	0.992583	−	0.121566i	$-0.0387916\pi$
$824$		0			0
$825$	1.48148	+	2.37168i	0.0515787	+	0.0825713i
$826$		0			0
$827$	−17.9610	+	13.0494i	−0.624566	+	0.453773i	−0.854513	−	0.519430i	$-0.826144\pi$
$827$	−17.9610	+	13.0494i	−0.624566	+	0.453773i	0.229948	+	0.973203i	$0.426144\pi$
$828$		0			0
$829$	2.52957	−	7.78523i	0.0878558	−	0.270392i	−0.897470	−	0.441075i	$-0.854597\pi$
$829$	2.52957	−	7.78523i	0.0878558	−	0.270392i	0.985326	+	0.170683i	$0.0545973\pi$
$830$		0			0
$831$	−10.1125	−	7.34717i	−0.350799	−	0.254871i
$832$		0			0
$833$	24.0604	+	74.0502i	0.833643	+	2.56569i
$834$		0			0
$835$	−14.4012			−0.498374
$836$		0			0
$837$	16.4495			0.568579
$838$		0			0
$839$	2.45790	+	7.56463i	0.0848561	+	0.261160i	0.984478	−	0.175510i	$-0.0561576\pi$
$839$	2.45790	+	7.56463i	0.0848561	+	0.261160i	−0.899622	+	0.436670i	$0.856158\pi$
$840$		0			0
$841$	17.9634	+	13.0511i	0.619426	+	0.450039i
$842$		0			0
$843$	−4.38938	+	13.5091i	−0.151178	+	0.465279i
$844$		0			0
$845$	1.06118	−	0.770995i	0.0365058	−	0.0265230i
$846$		0			0
$847$	−22.9527	+	47.0235i	−0.788665	+	1.61574i
$848$		0			0
$849$	3.33841	−	2.42549i	0.114574	−	0.0832428i
$850$		0			0
$851$	−10.0037	+	30.7882i	−0.342923	+	1.05541i
$852$		0			0
$853$	4.75049	+	3.45143i	0.162654	+	0.118175i	0.666135	−	0.745832i	$-0.267948\pi$
$853$	4.75049	+	3.45143i	0.162654	+	0.118175i	−0.503481	+	0.864006i	$0.667948\pi$
$854$		0			0
$855$	2.20783	+	6.79501i	0.0755063	+	0.232384i
$856$		0			0
$857$	30.9089			1.05583			0.527914	−	0.849298i	$-0.322974\pi$
$857$	30.9089			1.05583			0.527914	+	0.849298i	$0.322974\pi$
$858$		0			0
$859$	−10.9133			−0.372358			−0.186179	−	0.982516i	$-0.559610\pi$
$859$	−10.9133			−0.372358			−0.186179	+	0.982516i	$0.559610\pi$
$860$		0			0
$861$	11.5615	+	35.5825i	0.394014	+	1.21265i
$862$		0			0
$863$	9.97830	+	7.24966i	0.339665	+	0.246781i	0.744521	−	0.667599i	$-0.232678\pi$
$863$	9.97830	+	7.24966i	0.339665	+	0.246781i	−0.404855	+	0.914381i	$0.632678\pi$
$864$		0			0
$865$	2.51031	−	7.72595i	0.0853532	−	0.262690i
$866$		0			0
$867$	−5.33455	+	3.87577i	−0.181171	+	0.131628i
$868$		0			0
$869$	18.5279	+	29.6609i	0.628515	+	1.00618i
$870$		0			0
$871$	15.2808	−	11.1021i	0.517769	−	0.376181i
$872$		0			0
$873$	−9.68874	+	29.8189i	−0.327914	+	1.00922i
$874$		0			0
$875$	3.84844	+	2.79605i	0.130101	+	0.0945238i
$876$		0			0
$877$	−14.0157	−	43.1359i	−0.473276	−	1.45659i	−0.848269	−	0.529566i	$-0.822355\pi$
$877$	−14.0157	−	43.1359i	−0.473276	−	1.45659i	0.374992	−	0.927028i	$-0.377645\pi$
$878$		0			0
$879$	10.0818			0.340051
$880$		0			0
$881$	−24.4098			−0.822388			−0.411194	−	0.911548i	$-0.634888\pi$
$881$	−24.4098			−0.822388			−0.411194	+	0.911548i	$0.634888\pi$
$882$		0			0
$883$	10.8135	+	33.2805i	0.363903	+	1.11998i	0.950665	+	0.310218i	$0.100402\pi$
$883$	10.8135	+	33.2805i	0.363903	+	1.11998i	−0.586763	+	0.809759i	$0.699598\pi$
$884$		0			0
$885$	0.0708815	+	0.0514984i	0.00238265	+	0.00173110i
$886$		0			0
$887$	−13.8444	+	42.6087i	−0.464849	+	1.43066i	0.394322	+	0.918972i	$0.370979\pi$
$887$	−13.8444	+	42.6087i	−0.464849	+	1.43066i	−0.859172	+	0.511687i	$0.829021\pi$
$888$		0			0
$889$	42.1740	−	30.6412i	1.41447	−	1.02767i
$890$		0			0
$891$	−9.55516	−	3.86224i	−0.320110	−	0.129390i
$892$		0			0
$893$	4.19555	−	3.04825i	0.140399	−	0.102006i
$894$		0			0
$895$	−0.925011	+	2.84689i	−0.0309197	+	0.0951611i
$896$		0			0
$897$	−24.2308	−	17.6047i	−0.809041	−	0.587803i
$898$		0			0
$899$	2.97155	+	9.14550i	0.0991069	+	0.305020i
$900$		0			0
$901$	−9.66486			−0.321983
$902$		0			0
$903$	−46.9459			−1.56226
$904$		0			0
$905$	4.48891	+	13.8154i	0.149216	+	0.459240i
$906$		0			0
$907$	−5.61236	−	4.07762i	−0.186355	−	0.135395i	0.490696	−	0.871331i	$-0.336743\pi$
$907$	−5.61236	−	4.07762i	−0.186355	−	0.135395i	−0.677051	+	0.735936i	$0.736743\pi$
$908$		0			0
$909$	−3.42574	+	10.5433i	−0.113625	+	0.349701i
$910$		0			0
$911$	21.6373	−	15.7204i	0.716875	−	0.520840i	−0.168510	−	0.985700i	$-0.553895\pi$
$911$	21.6373	−	15.7204i	0.716875	−	0.520840i	0.885384	+	0.464860i	$0.153895\pi$
$912$		0			0
$913$	−12.1328	+	14.4549i	−0.401539	+	0.478386i
$914$		0			0
$915$	−6.92432	+	5.03081i	−0.228911	+	0.166314i
$916$		0			0
$917$	18.9657	−	58.3705i	0.626303	−	1.92756i
$918$		0			0
$919$	−44.5982	−	32.4025i	−1.47116	−	1.06886i	−0.980276	−	0.197632i	$-0.936675\pi$
$919$	−44.5982	−	32.4025i	−1.47116	−	1.06886i	−0.490881	−	0.871227i	$-0.663325\pi$
$920$		0			0
$921$	4.38559	+	13.4975i	0.144510	+	0.444757i
$922$		0			0
$923$	−23.5659			−0.775681
$924$		0			0
$925$	−3.44757			−0.113355
$926$		0			0
$927$	−0.639877	−	1.96934i	−0.0210163	−	0.0646815i
$928$		0			0
$929$	−11.0730	−	8.04499i	−0.363293	−	0.263948i	0.391131	−	0.920335i	$-0.372084\pi$
$929$	−11.0730	−	8.04499i	−0.363293	−	0.263948i	−0.754424	+	0.656387i	$0.772084\pi$
$930$		0			0
$931$	15.0734	−	46.3911i	0.494011	−	1.52041i
$932$		0			0
$933$	−16.7765	+	12.1888i	−0.549237	+	0.399044i
$934$		0			0
$935$	−16.0333	+	3.99494i	−0.524346	+	0.130649i
$936$		0			0
$937$	−15.2988	+	11.1152i	−0.499790	+	0.363119i	−0.808937	−	0.587896i	$-0.799957\pi$
$937$	−15.2988	+	11.1152i	−0.499790	+	0.363119i	0.309147	+	0.951014i	$0.399957\pi$
$938$		0			0
$939$	1.87850	−	5.78144i	0.0613027	−	0.188670i
$940$		0			0
$941$	8.89866	+	6.46526i	0.290088	+	0.210761i	0.723306	−	0.690528i	$-0.242622\pi$
$941$	8.89866	+	6.46526i	0.290088	+	0.210761i	−0.433218	+	0.901289i	$0.642622\pi$
$942$		0			0
$943$	27.0679	+	83.3064i	0.881451	+	2.71283i
$944$		0			0
$945$	21.2133			0.690068
$946$		0			0
$947$	−11.9776			−0.389219			−0.194610	−	0.980881i	$-0.562344\pi$
$947$	−11.9776			−0.389219			−0.194610	+	0.980881i	$0.562344\pi$
$948$		0			0
$949$	−8.54156	−	26.2882i	−0.277271	−	0.853352i
$950$		0			0
$951$	5.83820	+	4.24170i	0.189317	+	0.137547i
$952$		0			0
$953$	−8.11980	+	24.9902i	−0.263026	+	0.809511i	0.729115	+	0.684391i	$0.239932\pi$
$953$	−8.11980	+	24.9902i	−0.263026	+	0.809511i	−0.992142	+	0.125120i	$0.960068\pi$
$954$		0			0
$955$	−6.44577	+	4.68313i	−0.208580	+	0.151542i
$956$		0			0
$957$	−0.509636	+	7.27209i	−0.0164742	+	0.235073i
$958$		0			0
$959$	−72.6679	+	52.7963i	−2.34657	+	1.70488i
$960$		0			0
$961$	−5.37491	+	16.5423i	−0.173384	+	0.533621i
$962$		0			0
$963$	−27.3929	−	19.9021i	−0.882724	−	0.641337i
$964$		0			0
$965$	6.02466	+	18.5420i	0.193941	+	0.596888i
$966$		0			0
$967$	−11.2656			−0.362277			−0.181138	−	0.983458i	$-0.557978\pi$
$967$	−11.2656			−0.362277			−0.181138	+	0.983458i	$0.557978\pi$
$968$		0			0
$969$	13.1105			0.421170
$970$		0			0
$971$	−17.6151	−	54.2138i	−0.565296	−	1.73980i	−0.667069	−	0.744996i	$-0.732452\pi$
$971$	−17.6151	−	54.2138i	−0.565296	−	1.73980i	0.101773	−	0.994808i	$-0.467548\pi$
$972$		0			0
$973$	−41.9065	−	30.4468i	−1.34346	−	0.976080i
$974$		0			0
$975$	0.985657	−	3.03354i	0.0315663	−	0.0971510i
$976$		0			0
$977$	28.3013	−	20.5621i	0.905437	−	0.657839i	−0.0344195	−	0.999407i	$-0.510958\pi$
$977$	28.3013	−	20.5621i	0.905437	−	0.657839i	0.939857	+	0.341569i	$0.110958\pi$
$978$		0			0
$979$	3.16196	−	45.1186i	0.101057	−	1.44200i
$980$		0			0
$981$	6.28601	−	4.56705i	0.200697	−	0.145815i
$982$		0			0
$983$	5.55084	−	17.0837i	0.177044	−	0.544886i	−0.822677	−	0.568509i	$-0.807520\pi$
$983$	5.55084	−	17.0837i	0.177044	−	0.544886i	0.999721	+	0.0236234i	$0.00752026\pi$
$984$		0			0
$985$	14.5421	+	10.5655i	0.463351	+	0.336644i
$986$		0			0
$987$	−2.05932	−	6.33793i	−0.0655488	−	0.201739i
$988$		0			0
$989$	−109.911			−3.49495
$990$		0			0
$991$	47.2159			1.49986			0.749931	−	0.661516i	$-0.230087\pi$
$991$	47.2159			1.49986			0.749931	+	0.661516i	$0.230087\pi$
$992$		0			0
$993$	−6.62024	−	20.3750i	−0.210087	−	0.646581i
$994$		0			0
$995$	−5.80645	−	4.21863i	−0.184077	−	0.133740i
$996$		0			0
$997$	−6.23192	+	19.1799i	−0.197367	+	0.607433i	0.802574	+	0.596553i	$0.203463\pi$
$997$	−6.23192	+	19.1799i	−0.197367	+	0.607433i	−0.999941	+	0.0108803i	$0.996537\pi$
$998$		0			0
$999$	−12.4380	+	9.03675i	−0.393522	+	0.285910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.b.201.2	yes	12
4.3	odd	2		880.2.bo.j.641.2		12
11.2	odd	10		4840.2.a.be.1.4		6
11.4	even	5	inner	440.2.y.b.81.2	✓	12
11.9	even	5		4840.2.a.bf.1.4		6
44.15	odd	10		880.2.bo.j.81.2		12
44.31	odd	10		9680.2.a.cx.1.3		6
44.35	even	10		9680.2.a.cy.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.b.81.2	✓	12	11.4	even	5	inner
440.2.y.b.201.2	yes	12	1.1	even	1	trivial
880.2.bo.j.81.2		12	44.15	odd	10
880.2.bo.j.641.2		12	4.3	odd	2
4840.2.a.be.1.4		6	11.2	odd	10
4840.2.a.bf.1.4		6	11.9	even	5
9680.2.a.cx.1.3		6	44.31	odd	10
9680.2.a.cy.1.3		6	44.35	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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.260543 + 0.801870i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.46997 - 4.52411i) q^{7} +(1.85194 - 1.34551i) q^{9} +O(q^{10})\)	\(q+(0.260543 + 0.801870i) q^{3} +(0.809017 + 0.587785i) q^{5} +(1.46997 - 4.52411i) q^{7} +(1.85194 - 1.34551i) q^{9} +(0.231864 - 3.30851i) q^{11} +(-3.06058 + 2.22364i) q^{13} +(-0.260543 + 0.801870i) q^{15} +(-4.03055 - 2.92836i) q^{17} +(0.964489 + 2.96839i) q^{19} +4.01074 q^{21} +9.39001 q^{23} +(0.309017 + 0.951057i) q^{25} +(3.60777 + 2.62120i) q^{27} +(-0.805585 + 2.47934i) q^{29} +(2.98421 - 2.16816i) q^{31} +(2.71341 - 0.676086i) q^{33} +(3.84844 - 2.79605i) q^{35} +(-1.06536 + 3.27883i) q^{37} +(-2.58048 - 1.87483i) q^{39} +(2.88263 + 8.87181i) q^{41} -11.7051 q^{43} +2.28912 q^{45} +(-0.513451 - 1.58024i) q^{47} +(-12.6436 - 9.18613i) q^{49} +(1.29804 - 3.99494i) q^{51} +(1.56945 - 1.14027i) q^{53} +(2.13228 - 2.54035i) q^{55} +(-2.12897 + 1.54679i) q^{57} +(0.0321114 - 0.0988288i) q^{59} +(8.21258 + 5.96679i) q^{61} +(-3.36494 - 10.3562i) q^{63} -3.78308 q^{65} -4.99277 q^{67} +(2.44651 + 7.52957i) q^{69} +(5.03960 + 3.66149i) q^{71} +(-2.25783 + 6.94889i) q^{73} +(-0.682112 + 0.495583i) q^{75} +(-14.6272 - 5.91239i) q^{77} +(-8.53069 + 6.19791i) q^{79} +(0.960251 - 2.95535i) q^{81} +(-4.60338 - 3.34455i) q^{83} +(-1.53953 - 4.73819i) q^{85} -2.19800 q^{87} +13.6371 q^{89} +(5.56102 + 17.1151i) q^{91} +(2.51610 + 1.82805i) q^{93} +(-0.964489 + 2.96839i) q^{95} +(-11.0809 + 8.05072i) q^{97} +(-4.02224 - 6.43913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9}+O(q^{10}) \) 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9	\( 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37} - q^{39} + 7 q^{41} + 6 q^{43} - 20 q^{45} - 2 q^{47} - 19 q^{49} - 33 q^{51} + 3 q^{53} + 4 q^{55} - 25 q^{57} + 19 q^{59} + 22 q^{61} - 2 q^{63} + 12 q^{65} + 22 q^{67} + 21 q^{69} + 44 q^{71} + 17 q^{73} - q^{75} - 38 q^{77} - 43 q^{79} - 85 q^{81} - 15 q^{83} + 18 q^{85} + 50 q^{87} + 2 q^{89} + 59 q^{91} + 5 q^{93} - 3 q^{95} - 20 q^{97} - 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Introduction

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