LMFDB - Embedded newform 400.2.l.f.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(101,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("400.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.l (of order $4$, degree $2$, 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:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			301.1
Root			$1.35979 + 0.388551i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.f.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35979 - 0.388551i) q^{2} +(-1.03997 - 1.03997i) q^{3} +(1.69806 + 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} +1.49668i q^{7} +(-1.89842 - 2.09667i) q^{8} -0.836925i q^{9} +O(q^{10})$	\(q+(-1.35979 - 0.388551i) q^{2} +(-1.03997 - 1.03997i) q^{3} +(1.69806 + 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} +1.49668i q^{7} +(-1.89842 - 2.09667i) q^{8} -0.836925i q^{9} +(0.423260 - 0.423260i) q^{11} +(-0.666995 - 2.86486i) q^{12} +(-1.85704 - 1.85704i) q^{13} +(0.581538 - 2.03517i) q^{14} +(1.76679 + 3.58866i) q^{16} +6.50950 q^{17} +(-0.325188 + 1.13804i) q^{18} +(-1.75725 - 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +(-0.740003 + 0.411086i) q^{22} -7.19295i q^{23} +(-0.206172 + 4.15477i) q^{24} +(1.80363 + 3.24674i) q^{26} +(-3.99029 + 3.99029i) q^{27} +(-1.58154 + 2.54145i) q^{28} +(-6.57892 - 6.57892i) q^{29} -6.75252 q^{31} +(-1.00808 - 5.56631i) q^{32} -0.880355 q^{33} +(-8.85156 - 2.52928i) q^{34} +(0.884375 - 1.42115i) q^{36} +(1.95300 - 1.95300i) q^{37} +(1.70671 + 3.07227i) q^{38} +3.86254i q^{39} -7.70745i q^{41} +(-2.72130 + 1.51174i) q^{42} +(-6.13581 + 6.13581i) q^{43} +(1.16598 - 0.271462i) q^{44} +(-2.79483 + 9.78090i) q^{46} -6.65476 q^{47} +(1.89469 - 5.56950i) q^{48} +4.75994 q^{49} +(-6.76969 - 6.76969i) q^{51} +(-1.19103 - 5.11569i) q^{52} +(5.29390 - 5.29390i) q^{53} +(6.97638 - 3.87552i) q^{54} +(3.13804 - 2.84133i) q^{56} +3.65497i q^{57} +(6.38970 + 11.5022i) q^{58} +(5.91841 - 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} +(9.18201 + 2.62370i) q^{62} +1.25261 q^{63} +(-0.792016 + 7.96070i) q^{64} +(1.19710 + 0.342063i) q^{66} +(-6.35614 - 6.35614i) q^{67} +(11.0535 + 6.87857i) q^{68} +(-7.48045 + 7.48045i) q^{69} +4.08932i q^{71} +(-1.75475 + 1.58883i) q^{72} +2.43800i q^{73} +(-3.41451 + 1.89683i) q^{74} +(-1.12703 - 4.84079i) q^{76} +(0.633485 + 0.633485i) q^{77} +(1.50079 - 5.25224i) q^{78} +11.6722 q^{79} +5.78878 q^{81} +(-2.99474 + 10.4805i) q^{82} +(2.81439 + 2.81439i) q^{83} +(4.28778 - 0.998279i) q^{84} +(10.7275 - 5.95933i) q^{86} +13.6838i q^{87} +(-1.69096 - 0.0839103i) q^{88} +10.5543i q^{89} +(2.77940 - 2.77940i) q^{91} +(7.60076 - 12.2140i) q^{92} +(7.02242 + 7.02242i) q^{93} +(9.04907 + 2.58572i) q^{94} +(-4.74042 + 6.83717i) q^{96} +18.1512 q^{97} +(-6.47252 - 1.84948i) q^{98} +(-0.354237 - 0.354237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8	$ 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8} - 2 q^{11} - 8 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{16} + 8 q^{17} - 18 q^{18} - 14 q^{19} - 20 q^{21} - 2 q^{22} - 14 q^{24} - 16 q^{26} + 10 q^{27} - 26 q^{28} - 4 q^{31} + 16 q^{32} - 28 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} - 10 q^{38} - 10 q^{42} - 44 q^{44} - 10 q^{46} - 8 q^{47} + 28 q^{48} + 4 q^{49} + 10 q^{51} + 12 q^{52} + 16 q^{53} + 10 q^{54} + 6 q^{56} + 60 q^{58} + 20 q^{59} + 4 q^{61} + 18 q^{62} + 8 q^{63} + 38 q^{64} + 32 q^{66} - 50 q^{67} + 60 q^{68} + 14 q^{72} + 10 q^{74} + 60 q^{76} + 8 q^{77} - 4 q^{78} + 12 q^{79} - 8 q^{81} - 42 q^{82} + 2 q^{83} + 34 q^{84} + 6 q^{86} - 30 q^{88} + 2 q^{92} + 44 q^{93} + 32 q^{94} - 34 q^{96} - 64 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8 - 2 * q^11 - 8 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^16 + 8 * q^17 - 18 * q^18 - 14 * q^19 - 20 * q^21 - 2 * q^22 - 14 * q^24 - 16 * q^26 + 10 * q^27 - 26 * q^28 - 4 * q^31 + 16 * q^32 - 28 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 - 10 * q^38 - 10 * q^42 - 44 * q^44 - 10 * q^46 - 8 * q^47 + 28 * q^48 + 4 * q^49 + 10 * q^51 + 12 * q^52 + 16 * q^53 + 10 * q^54 + 6 * q^56 + 60 * q^58 + 20 * q^59 + 4 * q^61 + 18 * q^62 + 8 * q^63 + 38 * q^64 + 32 * q^66 - 50 * q^67 + 60 * q^68 + 14 * q^72 + 10 * q^74 + 60 * q^76 + 8 * q^77 - 4 * q^78 + 12 * q^79 - 8 * q^81 - 42 * q^82 + 2 * q^83 + 34 * q^84 + 6 * q^86 - 30 * q^88 + 2 * q^92 + 44 * q^93 + 32 * q^94 - 34 * q^96 - 64 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−1.35979	−	0.388551i	−0.961516	−	0.274747i
$2$	−1.35979	−	0.388551i	−0.961516	−	0.274747i
$3$	−1.03997	−	1.03997i	−0.600427	−	0.600427i	0.339999	−	0.940426i	$-0.389573\pi$
$3$	−1.03997	−	1.03997i	−0.600427	−	0.600427i	−0.940426	+	0.339999i	$0.889573\pi$
$4$	1.69806	+	1.05670i	0.849028	+	0.528348i
$5$		0			0
$5$		0			0
$6$	1.01006	+	1.81822i	0.412355	+	0.742286i
$7$			1.49668i			0.565693i	0.959165	+	0.282846i	$0.0912786\pi$
$7$			1.49668i			0.565693i	−0.959165	+	0.282846i	$0.908721\pi$
$8$	−1.89842	−	2.09667i	−0.671192	−	0.741283i
$9$		−	0.836925i		−	0.278975i
$10$		0			0
$11$	0.423260	−	0.423260i	0.127618	−	0.127618i	−0.640413	−	0.768031i	$-0.721237\pi$
$11$	0.423260	−	0.423260i	0.127618	−	0.127618i	0.768031	+	0.640413i	$0.221237\pi$
$12$	−0.666995	−	2.86486i	−0.192545	−	0.827014i
$13$	−1.85704	−	1.85704i	−0.515051	−	0.515051i	0.401019	−	0.916070i	$-0.368656\pi$
$13$	−1.85704	−	1.85704i	−0.515051	−	0.515051i	−0.916070	+	0.401019i	$0.868656\pi$
$14$	0.581538	−	2.03517i	0.155422	−	0.543923i
$15$		0			0
$16$	1.76679	+	3.58866i	0.441697	+	0.897164i
$17$	6.50950			1.57879			0.789393	−	0.613888i	$-0.210395\pi$
$17$	6.50950			1.57879			0.789393	+	0.613888i	$0.210395\pi$
$18$	−0.325188	+	1.13804i	−0.0766476	+	0.268239i
$19$	−1.75725	−	1.75725i	−0.403141	−	0.403141i	0.476198	−	0.879338i	$-0.342015\pi$
$19$	−1.75725	−	1.75725i	−0.403141	−	0.403141i	−0.879338	+	0.476198i	$0.842015\pi$
$20$		0			0
$21$	1.55650	−	1.55650i	0.339657	−	0.339657i
$22$	−0.740003	+	0.411086i	−0.157769	+	0.0876439i
$23$		−	7.19295i		−	1.49983i	−0.661532	−	0.749917i	$-0.730094\pi$
$23$		−	7.19295i		−	1.49983i	0.661532	−	0.749917i	$-0.269906\pi$
$24$	−0.206172	+	4.15477i	−0.0420846	+	0.848088i
$25$		0			0
$26$	1.80363	+	3.24674i	0.353721	+	0.636739i
$27$	−3.99029	+	3.99029i	−0.767931	+	0.767931i
$28$	−1.58154	+	2.54145i	−0.298883	+	0.480289i
$29$	−6.57892	−	6.57892i	−1.22167	−	1.22167i	−0.967036	−	0.254639i	$-0.918043\pi$
$29$	−6.57892	−	6.57892i	−1.22167	−	1.22167i	−0.254639	−	0.967036i	$-0.581957\pi$
$30$		0			0
$31$	−6.75252			−1.21279			−0.606394	−	0.795164i	$-0.707385\pi$
$31$	−6.75252			−1.21279			−0.606394	+	0.795164i	$0.707385\pi$
$32$	−1.00808	−	5.56631i	−0.178205	−	0.983993i
$33$	−0.880355			−0.153250
$34$	−8.85156	−	2.52928i	−1.51803	−	0.433767i
$35$		0			0
$36$	0.884375	−	1.42115i	0.147396	−	0.236858i
$37$	1.95300	−	1.95300i	0.321071	−	0.321071i	−0.528107	−	0.849178i	$-0.677098\pi$
$37$	1.95300	−	1.95300i	0.321071	−	0.321071i	0.849178	+	0.528107i	$0.177098\pi$
$38$	1.70671	+	3.07227i	0.276865	+	0.498388i
$39$			3.86254i			0.618501i
$40$		0			0
$41$		−	7.70745i		−	1.20370i	−0.798609	−	0.601851i	$-0.794430\pi$
$41$		−	7.70745i		−	1.20370i	0.798609	−	0.601851i	$-0.205570\pi$
$42$	−2.72130	+	1.51174i	−0.419906	+	0.233266i
$43$	−6.13581	+	6.13581i	−0.935702	+	0.935702i	−0.998054	−	0.0623522i	$-0.980140\pi$
$43$	−6.13581	+	6.13581i	−0.935702	+	0.935702i	0.0623522	+	0.998054i	$0.480140\pi$
$44$	1.16598	−	0.271462i	0.175778	−	0.0409244i
$45$		0			0
$46$	−2.79483	+	9.78090i	−0.412075	+	1.44211i
$47$	−6.65476			−0.970697			−0.485348	−	0.874321i	$-0.661307\pi$
$47$	−6.65476			−0.970697			−0.485348	+	0.874321i	$0.661307\pi$
$48$	1.89469	−	5.56950i	0.273475	−	0.803888i
$49$	4.75994			0.679992
$50$		0			0
$51$	−6.76969	−	6.76969i	−0.947946	−	0.947946i
$52$	−1.19103	−	5.11569i	−0.165167	−	0.709419i
$53$	5.29390	−	5.29390i	0.727173	−	0.727173i	−0.242882	−	0.970056i	$-0.578093\pi$
$53$	5.29390	−	5.29390i	0.727173	−	0.727173i	0.970056	+	0.242882i	$0.0780929\pi$
$54$	6.97638	−	3.87552i	0.949365	−	0.527391i
$55$		0			0
$56$	3.13804	−	2.84133i	0.419338	−	0.379688i
$57$			3.65497i			0.484113i
$58$	6.38970	+	11.5022i	0.839009	+	1.51031i
$59$	5.91841	−	5.91841i	0.770511	−	0.770511i	−0.207685	−	0.978196i	$-0.566593\pi$
$59$	5.91841	−	5.91841i	0.770511	−	0.770511i	0.978196	+	0.207685i	$0.0665929\pi$
$60$		0			0
$61$	−1.43686	−	1.43686i	−0.183971	−	0.183971i	0.609113	−	0.793084i	$-0.291526\pi$
$61$	−1.43686	−	1.43686i	−0.183971	−	0.183971i	−0.793084	+	0.609113i	$0.791526\pi$
$62$	9.18201	+	2.62370i	1.16612	+	0.333210i
$63$	1.25261			0.157814
$64$	−0.792016	+	7.96070i	−0.0990020	+	0.995087i
$65$		0			0
$66$	1.19710	+	0.342063i	0.147353	+	0.0421051i
$67$	−6.35614	−	6.35614i	−0.776526	−	0.776526i	0.202712	−	0.979238i	$-0.435024\pi$
$67$	−6.35614	−	6.35614i	−0.776526	−	0.776526i	−0.979238	+	0.202712i	$0.935024\pi$
$68$	11.0535	+	6.87857i	1.34043	+	0.834149i
$69$	−7.48045	+	7.48045i	−0.900540	+	0.900540i
$70$		0			0
$71$			4.08932i			0.485313i	0.970112	+	0.242657i	$0.0780188\pi$
$71$			4.08932i			0.485313i	−0.970112	+	0.242657i	$0.921981\pi$
$72$	−1.75475	+	1.58883i	−0.206799	+	0.187246i
$73$			2.43800i			0.285346i	0.989770	+	0.142673i	$0.0455698\pi$
$73$			2.43800i			0.285346i	−0.989770	+	0.142673i	$0.954430\pi$
$74$	−3.41451	+	1.89683i	−0.396929	+	0.220502i
$75$		0			0
$76$	−1.12703	−	4.84079i	−0.129279	−	0.555276i
$77$	0.633485	+	0.633485i	0.0721924	+	0.0721924i
$78$	1.50079	−	5.25224i	0.169931	−	0.594699i
$79$	11.6722			1.31323			0.656615	−	0.754226i	$-0.271988\pi$
$79$	11.6722			1.31323			0.656615	+	0.754226i	$0.271988\pi$
$80$		0			0
$81$	5.78878			0.643198
$82$	−2.99474	+	10.4805i	−0.330714	+	1.15738i
$83$	2.81439	+	2.81439i	0.308919	+	0.308919i	0.844490	−	0.535571i	$-0.179904\pi$
$83$	2.81439	+	2.81439i	0.308919	+	0.308919i	−0.535571	+	0.844490i	$0.679904\pi$
$84$	4.28778	−	0.998279i	0.467835	−	0.108921i
$85$		0			0
$86$	10.7275	−	5.95933i	1.15677	−	0.642611i
$87$			13.6838i			1.46705i
$88$	−1.69096	−	0.0839103i	−0.180257	−	0.00894487i
$89$			10.5543i			1.11876i	0.828912	+	0.559379i	$0.188960\pi$
$89$			10.5543i			1.11876i	−0.828912	+	0.559379i	$0.811040\pi$
$90$		0			0
$91$	2.77940	−	2.77940i	0.291360	−	0.291360i
$92$	7.60076	−	12.2140i	0.792434	−	1.27340i
$93$	7.02242	+	7.02242i	0.728191	+	0.728191i
$94$	9.04907	+	2.58572i	0.933341	+	0.266696i
$95$		0			0
$96$	−4.74042	+	6.83717i	−0.483817	+	0.697815i
$97$	18.1512			1.84298			0.921488	−	0.388407i	$-0.126975\pi$
$97$	18.1512			1.84298			0.921488	+	0.388407i	$0.126975\pi$
$98$	−6.47252	−	1.84948i	−0.653823	−	0.186826i
$99$	−0.354237	−	0.354237i	−0.0356021	−	0.0356021i
$100$		0			0
$101$	−1.04036	+	1.04036i	−0.103520	+	0.103520i	−0.756970	−	0.653450i	$-0.773321\pi$
$101$	−1.04036	+	1.04036i	−0.103520	+	0.103520i	0.653450	+	0.756970i	$0.273321\pi$
$102$	6.57498	+	11.8357i	0.651020	+	1.17191i
$103$		−	0.955267i		−	0.0941253i	−0.998892	−	0.0470626i	$-0.985014\pi$
$103$		−	0.955267i		−	0.0941253i	0.998892	−	0.0470626i	$-0.0149860\pi$
$104$	−0.368154	+	7.41904i	−0.0361005	+	0.727497i
$105$		0			0
$106$	−9.25555	+	5.14164i	−0.898978	+	0.499400i
$107$	7.20266	−	7.20266i	0.696308	−	0.696308i	−0.267305	−	0.963612i	$-0.586133\pi$
$107$	7.20266	−	7.20266i	0.696308	−	0.696308i	0.963612	+	0.267305i	$0.0861330\pi$
$108$	−10.9922	+	2.55921i	−1.05773	+	0.246260i
$109$	−5.67807	−	5.67807i	−0.543861	−	0.543861i	0.380798	−	0.924658i	$-0.375649\pi$
$109$	−5.67807	−	5.67807i	−0.543861	−	0.543861i	−0.924658	+	0.380798i	$0.875649\pi$
$110$		0			0
$111$	−4.06212			−0.385560
$112$	−5.37108	+	2.64432i	−0.507519	+	0.249865i
$113$	1.94751			0.183206			0.0916029	−	0.995796i	$-0.470801\pi$
$113$	1.94751			0.183206			0.0916029	+	0.995796i	$0.470801\pi$
$114$	1.42014	−	4.97000i	0.133009	−	0.465483i
$115$		0			0
$116$	−4.21946	−	18.1233i	−0.391767	−	1.68271i
$117$	−1.55420	+	1.55420i	−0.143686	+	0.143686i
$118$	−10.3474	+	5.74818i	−0.952555	+	0.529163i
$119$			9.74266i			0.893108i
$120$		0			0
$121$			10.6417i			0.967427i
$122$	1.39553	+	2.51212i	0.126346	+	0.227437i
$123$	−8.01552	+	8.01552i	−0.722735	+	0.722735i
$124$	−11.4662	−	7.13536i	−1.02969	−	0.640774i
$125$		0			0
$126$	−1.70329	−	0.486703i	−0.151741	−	0.0433590i
$127$	−1.31796			−0.116950			−0.0584750	−	0.998289i	$-0.518624\pi$
$127$	−1.31796			−0.116950			−0.0584750	+	0.998289i	$0.518624\pi$
$128$	4.17011	−	10.5171i	0.368589	−	0.929592i
$129$	12.7621			1.12364
$130$		0			0
$131$	1.03026	+	1.03026i	0.0900139	+	0.0900139i	0.750680	−	0.660666i	$-0.229726\pi$
$131$	1.03026	+	1.03026i	0.0900139	+	0.0900139i	−0.660666	+	0.750680i	$0.729726\pi$
$132$	−1.49489	−	0.930268i	−0.130114	−	0.0809694i
$133$	2.63004	−	2.63004i	0.228054	−	0.228054i
$134$	6.17333	+	11.1127i	0.533294	+	0.959991i
$135$		0			0
$136$	−12.3578	−	13.6483i	−1.05967	−	1.17033i
$137$		−	3.75559i		−	0.320862i	−0.987047	−	0.160431i	$-0.948712\pi$
$137$		−	3.75559i		−	0.320862i	0.987047	−	0.160431i	$-0.0512884\pi$
$138$	13.0784	−	7.26530i	1.11331	−	0.618463i
$139$	12.9485	−	12.9485i	1.09828	−	1.09828i	0.103669	−	0.994612i	$-0.466942\pi$
$139$	12.9485	−	12.9485i	1.09828	−	1.09828i	0.994612	−	0.103669i	$-0.0330584\pi$
$140$		0			0
$141$	6.92075	+	6.92075i	0.582832	+	0.582832i
$142$	1.58891	−	5.56062i	0.133338	−	0.466637i
$143$	−1.57202			−0.131459
$144$	3.00344	−	1.47867i	0.250286	−	0.123222i
$145$		0			0
$146$	0.947288	−	3.31517i	0.0783982	−	0.274365i
$147$	−4.95020	−	4.95020i	−0.408285	−	0.408285i
$148$	5.38003	−	1.25258i	0.442236	−	0.102961i
$149$	−15.8472	+	15.8472i	−1.29825	+	1.29825i	−0.368709	+	0.929545i	$0.620200\pi$
$149$	−15.8472	+	15.8472i	−1.29825	+	1.29825i	−0.929545	+	0.368709i	$0.879800\pi$
$150$		0			0
$151$			11.5316i			0.938424i	0.883085	+	0.469212i	$0.155462\pi$
$151$			11.5316i			0.938424i	−0.883085	+	0.469212i	$0.844538\pi$
$152$	−0.348371	+	7.02036i	−0.0282566	+	0.569427i
$153$		−	5.44797i		−	0.440442i
$154$	−0.615265	−	1.10755i	−0.0495795	−	0.0892488i
$155$		0			0
$156$	−4.08153	+	6.55880i	−0.326784	+	0.525125i
$157$	−5.41891	−	5.41891i	−0.432476	−	0.432476i	0.456994	−	0.889470i	$-0.348926\pi$
$157$	−5.41891	−	5.41891i	−0.432476	−	0.432476i	−0.889470	+	0.456994i	$0.848926\pi$
$158$	−15.8718	−	4.53526i	−1.26269	−	0.360806i
$159$	−11.0110			−0.873229
$160$		0			0
$161$	10.7656			0.848445
$162$	−7.87153	−	2.24924i	−0.618446	−	0.176717i
$163$	6.47288	+	6.47288i	0.506995	+	0.506995i	0.913603	−	0.406608i	$-0.133289\pi$
$163$	6.47288	+	6.47288i	0.506995	+	0.506995i	−0.406608	+	0.913603i	$0.633289\pi$
$164$	8.14443	−	13.0877i	0.635973	−	1.02198i
$165$		0			0
$166$	−2.73344	−	4.92051i	−0.212156	−	0.381906i
$167$		−	8.29734i		−	0.642068i	−0.947068	−	0.321034i	$-0.895970\pi$
$167$		−	8.29734i		−	0.642068i	0.947068	−	0.321034i	$-0.104030\pi$
$168$	−6.21837	−	0.308573i	−0.479757	−	0.0238069i
$169$		−	6.10279i		−	0.469445i
$170$		0			0
$171$	−1.47069	+	1.47069i	−0.112466	+	0.112466i
$172$	−16.9026	+	3.93526i	−1.28881	+	0.300061i
$173$	11.9420	+	11.9420i	0.907935	+	0.907935i	0.996105	−	0.0881700i	$-0.0281019\pi$
$173$	11.9420	+	11.9420i	0.907935	+	0.907935i	−0.0881700	+	0.996105i	$0.528102\pi$
$174$	5.31684	−	18.6070i	0.403069	−	1.41060i
$175$		0			0
$176$	2.26675	+	0.771125i	0.170862	+	0.0581257i
$177$	−12.3099			−0.925271
$178$	4.10090	−	14.3517i	0.307376	−	1.07570i
$179$	−10.8703	−	10.8703i	−0.812481	−	0.812481i	0.172524	−	0.985005i	$-0.444808\pi$
$179$	−10.8703	−	10.8703i	−0.812481	−	0.812481i	−0.985005	+	0.172524i	$0.944808\pi$
$180$		0			0
$181$	−4.09403	+	4.09403i	−0.304307	+	0.304307i	−0.842696	−	0.538389i	$-0.819033\pi$
$181$	−4.09403	+	4.09403i	−0.304307	+	0.304307i	0.538389	+	0.842696i	$0.319033\pi$
$182$	−4.85934	+	2.69946i	−0.360198	+	0.200097i
$183$			2.98858i			0.220922i
$184$	−15.0812	+	13.6552i	−1.11180	+	1.00668i
$185$		0			0
$186$	−6.82044	−	12.2776i	−0.500099	−	0.900236i
$187$	2.75521	−	2.75521i	0.201481	−	0.201481i
$188$	−11.3002	−	7.03206i	−0.824148	−	0.512866i
$189$	−5.97219	−	5.97219i	−0.434413	−	0.434413i
$190$		0			0
$191$	19.2542			1.39319			0.696594	−	0.717466i	$-0.254698\pi$
$191$	19.2542			1.39319			0.696594	+	0.717466i	$0.254698\pi$
$192$	9.10256	−	7.45521i	0.656921	−	0.538034i
$193$	−24.8152			−1.78624			−0.893119	−	0.449820i	$-0.851488\pi$
$193$	−24.8152			−1.78624			−0.893119	+	0.449820i	$0.851488\pi$
$194$	−24.6818	−	7.05267i	−1.77205	−	0.506352i
$195$		0			0
$196$	8.08265	+	5.02981i	0.577332	+	0.359272i
$197$	−2.81324	+	2.81324i	−0.200435	+	0.200435i	−0.800186	−	0.599751i	$-0.795266\pi$
$197$	−2.81324	+	2.81324i	−0.200435	+	0.200435i	0.599751	+	0.800186i	$0.295266\pi$
$198$	0.344048	+	0.619327i	0.0244505	+	0.0440136i
$199$			21.2194i			1.50420i	0.659048	+	0.752101i	$0.270959\pi$
$199$			21.2194i			1.50420i	−0.659048	+	0.752101i	$0.729041\pi$
$200$		0			0
$201$			13.2204i			0.932495i
$202$	1.81891	−	1.01044i	0.127978	−	0.0710944i
$203$	9.84655	−	9.84655i	0.691092	−	0.691092i
$204$	−4.34181	−	18.6488i	−0.303987	−	1.30568i
$205$		0			0
$206$	−0.371170	+	1.29896i	−0.0258607	+	0.0905030i
$207$	−6.01996			−0.418416
$208$	3.38329	−	9.94529i	0.234589	−	0.689582i
$209$	−1.48755			−0.102896
$210$		0			0
$211$	15.5715	+	15.5715i	1.07199	+	1.07199i	0.997200	+	0.0747872i	$0.0238278\pi$
$211$	15.5715	+	15.5715i	1.07199	+	1.07199i	0.0747872	+	0.997200i	$0.476172\pi$
$212$	14.5834	−	3.39530i	1.00159	−	0.233190i
$213$	4.25277	−	4.25277i	0.291395	−	0.291395i
$214$	−12.5927	+	6.99550i	−0.860820	+	0.478203i
$215$		0			0
$216$	15.9415	+	0.791065i	1.08468	+	0.0538251i
$217$		−	10.1064i		−	0.686065i
$218$	5.51476	+	9.92721i	0.373507	+	0.672355i
$219$	2.53545	−	2.53545i	0.171330	−	0.171330i
$220$		0			0
$221$	−12.0884	−	12.0884i	−0.813155	−	0.813155i
$222$	5.52363	+	1.57834i	0.370722	+	0.105931i
$223$	−7.88779			−0.528205			−0.264103	−	0.964495i	$-0.585076\pi$
$223$	−7.88779			−0.528205			−0.264103	+	0.964495i	$0.585076\pi$
$224$	8.33099	−	1.50878i	0.556638	−	0.100809i
$225$		0			0
$226$	−2.64820	−	0.756705i	−0.176155	−	0.0503353i
$227$	−5.98838	−	5.98838i	−0.397463	−	0.397463i	0.479874	−	0.877337i	$-0.340682\pi$
$227$	−5.98838	−	5.98838i	−0.397463	−	0.397463i	−0.877337	+	0.479874i	$0.840682\pi$
$228$	−3.86220	+	6.20635i	−0.255780	+	0.411026i
$229$	19.4584	−	19.4584i	1.28585	−	1.28585i	0.348563	−	0.937286i	$-0.386670\pi$
$229$	19.4584	−	19.4584i	1.28585	−	1.28585i	0.937286	−	0.348563i	$-0.113330\pi$
$230$		0			0
$231$		−	1.31761i		−	0.0866925i
$232$	−1.30426	+	26.2833i	−0.0856286	+	1.72559i
$233$		−	2.68717i		−	0.176042i	−0.996119	−	0.0880212i	$-0.971946\pi$
$233$		−	2.68717i		−	0.176042i	0.996119	−	0.0880212i	$-0.0280543\pi$
$234$	2.71728	−	1.50950i	0.177634	−	0.0986793i
$235$		0			0
$236$	16.3037	−	3.79583i	1.06128	−	0.247087i
$237$	−12.1388	−	12.1388i	−0.788499	−	0.788499i
$238$	3.78552	−	13.2480i	0.245379	−	0.858738i
$239$	−12.6359			−0.817346			−0.408673	−	0.912681i	$-0.634008\pi$
$239$	−12.6359			−0.817346			−0.408673	+	0.912681i	$0.634008\pi$
$240$		0			0
$241$	7.53314			0.485252			0.242626	−	0.970120i	$-0.421991\pi$
$241$	7.53314			0.485252			0.242626	+	0.970120i	$0.421991\pi$
$242$	4.13485	−	14.4705i	0.265798	−	0.930197i
$243$	5.95070	+	5.95070i	0.381738	+	0.381738i
$244$	−0.921544	−	3.95819i	−0.0589958	−	0.253397i
$245$		0			0
$246$	14.0139	−	7.78498i	0.893491	−	0.496352i
$247$			6.52658i			0.415276i
$248$	12.8191	+	14.1578i	0.814014	+	0.899020i
$249$		−	5.85376i		−	0.370967i
$250$		0			0
$251$	−9.95683	+	9.95683i	−0.628470	+	0.628470i	−0.947683	−	0.319213i	$-0.896581\pi$
$251$	−9.95683	+	9.95683i	−0.628470	+	0.628470i	0.319213	+	0.947683i	$0.396581\pi$
$252$	2.12700	+	1.32363i	0.133989	+	0.0833807i
$253$	−3.04449	−	3.04449i	−0.191405	−	0.191405i
$254$	1.79215	+	0.512094i	0.112449	+	0.0321317i
$255$		0			0
$256$	−9.75692	+	12.6808i	−0.609808	+	0.792549i
$257$	4.51630			0.281719			0.140860	−	0.990030i	$-0.455013\pi$
$257$	4.51630			0.281719			0.140860	+	0.990030i	$0.455013\pi$
$258$	−17.3538	−	4.95874i	−1.08040	−	0.308717i
$259$	2.92302	+	2.92302i	0.181628	+	0.181628i
$260$		0			0
$261$	−5.50606	+	5.50606i	−0.340817	+	0.340817i
$262$	−1.00062	−	1.80124i	−0.0618188	−	0.111281i
$263$		−	20.2127i		−	1.24637i	−0.782075	−	0.623185i	$-0.785838\pi$
$263$		−	20.2127i		−	1.24637i	0.782075	−	0.623185i	$-0.214162\pi$
$264$	1.67128	+	1.84581i	0.102860	+	0.113602i
$265$		0			0
$266$	−4.59821	+	2.55440i	−0.281935	+	0.156620i
$267$	10.9762	−	10.9762i	0.671732	−	0.671732i
$268$	−4.07657	−	17.5096i	−0.249016	−	1.06957i
$269$	16.9430	+	16.9430i	1.03304	+	1.03304i	0.999435	+	0.0335999i	$0.0106972\pi$
$269$	16.9430	+	16.9430i	1.03304	+	1.03304i	0.0335999	+	0.999435i	$0.489303\pi$
$270$		0			0
$271$	−3.64054			−0.221147			−0.110573	−	0.993868i	$-0.535269\pi$
$271$	−3.64054			−0.221147			−0.110573	+	0.993868i	$0.535269\pi$
$272$	11.5009	+	23.3604i	0.697345	+	1.41643i
$273$	−5.78099			−0.349881
$274$	−1.45924	+	5.10681i	−0.0881559	+	0.308514i
$275$		0			0
$276$	−20.6068	+	4.79766i	−1.24038	+	0.288785i
$277$	−16.0090	+	16.0090i	−0.961888	+	0.961888i	−0.999300	−	0.0374115i	$-0.988089\pi$
$277$	−16.0090	+	16.0090i	−0.961888	+	0.961888i	0.0374115	+	0.999300i	$0.488089\pi$
$278$	−22.6385	+	12.5761i	−1.35777	+	0.754266i
$279$			5.65135i			0.338338i
$280$		0			0
$281$		−	5.51857i		−	0.329210i	−0.986360	−	0.164605i	$-0.947365\pi$
$281$		−	5.51857i		−	0.329210i	0.986360	−	0.164605i	$-0.0526350\pi$
$282$	−6.72170	−	12.0998i	−0.400271	−	0.720535i
$283$	2.36694	−	2.36694i	0.140700	−	0.140700i	−0.633249	−	0.773949i	$-0.718279\pi$
$283$	2.36694	−	2.36694i	0.140700	−	0.140700i	0.773949	+	0.633249i	$0.218279\pi$
$284$	−4.32117	+	6.94389i	−0.256414	+	0.412044i
$285$		0			0
$286$	2.13762	+	0.610812i	0.126400	+	0.0361180i
$287$	11.5356			0.680925
$288$	−4.65858	+	0.843689i	−0.274509	+	0.0497148i
$289$	25.3736			1.49257
$290$		0			0
$291$	−18.8767	−	18.8767i	−1.10657	−	1.10657i
$292$	−2.57623	+	4.13986i	−0.150762	+	0.242267i
$293$	−19.1812	+	19.1812i	−1.12058	+	1.12058i	−0.128922	+	0.991655i	$0.541152\pi$
$293$	−19.1812	+	19.1812i	−1.12058	+	1.12058i	−0.991655	+	0.128922i	$0.958848\pi$
$294$	4.80782	+	8.65463i	0.280398	+	0.504749i
$295$		0			0
$296$	−7.80240	−	0.387177i	−0.453505	−	0.0225042i
$297$			3.37786i			0.196003i
$298$	27.7063	−	15.3914i	1.60498	−	0.891601i
$299$	−13.3576	+	13.3576i	−0.772491	+	0.772491i
$300$		0			0
$301$	−9.18335	−	9.18335i	−0.529320	−	0.529320i
$302$	4.48060	−	15.6805i	0.257829	−	0.902311i
$303$	2.16390			0.124313
$304$	3.20148	−	9.41086i	0.183618	−	0.539750i
$305$		0			0
$306$	−2.11681	+	7.40809i	−0.121010	+	0.423492i
$307$	19.9292	+	19.9292i	1.13742	+	1.13742i	0.988911	+	0.148507i	$0.0474469\pi$
$307$	19.9292	+	19.9292i	1.13742	+	1.13742i	0.148507	+	0.988911i	$0.452553\pi$
$308$	0.406292	+	1.74510i	0.0231506	+	0.0994360i
$309$	−0.993449	+	0.993449i	−0.0565153	+	0.0565153i
$310$		0			0
$311$			5.73314i			0.325096i	0.986701	+	0.162548i	$0.0519713\pi$
$311$			5.73314i			0.325096i	−0.986701	+	0.162548i	$0.948029\pi$
$312$	8.09845	−	7.33271i	0.458484	−	0.415133i
$313$		−	0.212621i		−	0.0120180i	−0.999982	−	0.00600902i	$-0.998087\pi$
$313$		−	0.212621i		−	0.0120180i	0.999982	−	0.00600902i	$-0.00191274\pi$
$314$	5.26306	+	9.47411i	0.297011	+	0.534655i
$315$		0			0
$316$	19.8201	+	12.3340i	1.11497	+	0.693842i
$317$	−3.21582	−	3.21582i	−0.180618	−	0.180618i	0.611007	−	0.791625i	$-0.290765\pi$
$317$	−3.21582	−	3.21582i	−0.180618	−	0.180618i	−0.791625	+	0.611007i	$0.790765\pi$
$318$	14.9726	+	4.27834i	0.839624	+	0.239917i
$319$	−5.56919			−0.311815
$320$		0			0
$321$	−14.9811			−0.836164
$322$	−14.6389	−	4.18297i	−0.815793	−	0.233108i
$323$	−11.4388	−	11.4388i	−0.636473	−	0.636473i
$324$	9.82968	+	6.11698i	0.546093	+	0.339832i
$325$		0			0
$326$	−6.28671	−	11.3168i	−0.348188	−	0.626779i
$327$			11.8101i			0.653097i
$328$	−16.1599	+	14.6320i	−0.892284	+	0.807915i
$329$		−	9.96006i		−	0.549116i
$330$		0			0
$331$	22.0295	−	22.0295i	1.21085	−	1.21085i	0.240106	−	0.970747i	$-0.422818\pi$
$331$	22.0295	−	22.0295i	1.21085	−	1.21085i	0.970747	−	0.240106i	$-0.0771824\pi$
$332$	1.80504	+	7.75295i	0.0990643	+	0.425498i
$333$	−1.63451	−	1.63451i	−0.0895708	−	0.0895708i
$334$	−3.22394	+	11.2826i	−0.176406	+	0.617359i
$335$		0			0
$336$	8.33577	+	2.83575i	0.454754	+	0.154703i
$337$	−11.2122			−0.610767			−0.305384	−	0.952229i	$-0.598785\pi$
$337$	−11.2122			−0.610767			−0.305384	+	0.952229i	$0.598785\pi$
$338$	−2.37125	+	8.29851i	−0.128979	+	0.451379i
$339$	−2.02535	−	2.02535i	−0.110002	−	0.110002i
$340$		0			0
$341$	−2.85807	+	2.85807i	−0.154773	+	0.154773i
$342$	2.57126	−	1.42839i	0.139038	−	0.0772383i
$343$			17.6009i			0.950359i
$344$	24.5131	+	1.21641i	1.32166	+	0.0655844i
$345$		0			0
$346$	−11.5986	−	20.8787i	−0.623542	−	1.12245i
$347$	1.23653	−	1.23653i	0.0663803	−	0.0663803i	−0.673137	−	0.739518i	$-0.735054\pi$
$347$	1.23653	−	1.23653i	0.0663803	−	0.0663803i	0.739518	+	0.673137i	$0.235054\pi$
$348$	−14.4596	+	23.2358i	−0.775115	+	1.24557i
$349$	−5.61778	−	5.61778i	−0.300713	−	0.300713i	0.540580	−	0.841293i	$-0.318205\pi$
$349$	−5.61778	−	5.61778i	−0.300713	−	0.300713i	−0.841293	+	0.540580i	$0.818205\pi$
$350$		0			0
$351$	14.8203			0.791047
$352$	−2.78268	−	1.92931i	−0.148317	−	0.102833i
$353$	0.748709			0.0398497			0.0199249	−	0.999801i	$-0.493657\pi$
$353$	0.748709			0.0398497			0.0199249	+	0.999801i	$0.493657\pi$
$354$	16.7389	+	4.78304i	0.889663	+	0.254216i
$355$		0			0
$356$	−11.1527	+	17.9219i	−0.591093	+	0.949856i
$357$	10.1321	−	10.1321i	0.536246	−	0.536246i
$358$	10.5576	+	19.0049i	0.557987	+	1.00444i
$359$			2.69883i			0.142439i	0.997461	+	0.0712195i	$0.0226891\pi$
$359$			2.69883i			0.142439i	−0.997461	+	0.0712195i	$0.977311\pi$
$360$		0			0
$361$		−	12.8241i		−	0.674955i
$362$	7.15776	−	3.97628i	0.376204	−	0.208989i
$363$	11.0671	−	11.0671i	0.580870	−	0.580870i
$364$	7.65656	−	1.78260i	0.401313	−	0.0934335i
$365$		0			0
$366$	1.16122	−	4.06384i	0.0606978	−	0.212420i
$367$	20.6101			1.07584			0.537920	−	0.842996i	$-0.319210\pi$
$367$	20.6101			1.07584			0.537920	+	0.842996i	$0.319210\pi$
$368$	25.8130	−	12.7084i	1.34560	−	0.662472i
$369$	−6.45056			−0.335802
$370$		0			0
$371$	7.92329	+	7.92329i	0.411357	+	0.411357i
$372$	4.50390	+	19.3450i	0.233516	+	1.00299i
$373$	5.24143	−	5.24143i	0.271391	−	0.271391i	−0.558269	−	0.829660i	$-0.688534\pi$
$373$	5.24143	−	5.24143i	0.271391	−	0.271391i	0.829660	+	0.558269i	$0.188534\pi$
$374$	−4.81705	+	2.67597i	−0.249084	+	0.138371i
$375$		0			0
$376$	12.6335	+	13.9528i	0.651524	+	0.719561i
$377$			24.4347i			1.25845i
$378$	5.80042	+	10.4414i	0.298341	+	0.537049i
$379$	5.41344	−	5.41344i	0.278070	−	0.278070i	−0.554268	−	0.832338i	$-0.687002\pi$
$379$	5.41344	−	5.41344i	0.278070	−	0.278070i	0.832338	+	0.554268i	$0.187002\pi$
$380$		0			0
$381$	1.37064	+	1.37064i	0.0702199	+	0.0702199i
$382$	−26.1817	−	7.48125i	−1.33957	−	0.382774i
$383$	29.5087			1.50782			0.753912	−	0.656975i	$-0.228164\pi$
$383$	29.5087			1.50782			0.753912	+	0.656975i	$0.228164\pi$
$384$	−15.2743	+	6.60071i	−0.779463	+	0.336841i
$385$		0			0
$386$	33.7435	+	9.64199i	1.71750	+	0.490764i
$387$	5.13521	+	5.13521i	0.261037	+	0.261037i
$388$	30.8218	+	19.1803i	1.56474	+	0.973732i
$389$	1.37884	−	1.37884i	0.0699099	−	0.0699099i	−0.671287	−	0.741197i	$-0.734258\pi$
$389$	1.37884	−	1.37884i	0.0699099	−	0.0699099i	0.741197	+	0.671287i	$0.234258\pi$
$390$		0			0
$391$		−	46.8225i		−	2.36792i
$392$	−9.03636	−	9.98001i	−0.456405	−	0.504067i
$393$		−	2.14287i		−	0.108094i
$394$	4.91850	−	2.73232i	0.247790	−	0.137652i
$395$		0			0
$396$	−0.227193	−	0.975834i	−0.0114169	−	0.0490375i
$397$	21.9750	+	21.9750i	1.10289	+	1.10289i	0.994060	+	0.108832i	$0.0347111\pi$
$397$	21.9750	+	21.9750i	1.10289	+	1.10289i	0.108832	+	0.994060i	$0.465289\pi$
$398$	8.24482	−	28.8539i	0.413275	−	1.44632i
$399$	−5.47033			−0.273859
$400$		0			0
$401$	−31.4584			−1.57096			−0.785479	−	0.618889i	$-0.787583\pi$
$401$	−31.4584			−1.57096			−0.785479	+	0.618889i	$0.787583\pi$
$402$	5.13680	−	17.9770i	0.256200	−	0.896609i
$403$	12.5397	+	12.5397i	0.624648	+	0.624648i
$404$	−2.86595	+	0.667248i	−0.142586	+	0.0331968i
$405$		0			0
$406$	−17.2151	+	9.56335i	−0.854372	+	0.474621i
$407$		−	1.65325i		−	0.0819487i
$408$	−1.34207	+	27.0455i	−0.0664426	+	1.33895i
$409$			12.8017i			0.633003i	0.948592	+	0.316502i	$0.102508\pi$
$409$			12.8017i			0.633003i	−0.948592	+	0.316502i	$0.897492\pi$
$410$		0			0
$411$	−3.90570	+	3.90570i	−0.192654	+	0.192654i
$412$	1.00943	−	1.62210i	0.0497309	−	0.0799150i
$413$	8.85797	+	8.85797i	0.435872	+	0.435872i
$414$	8.18588	+	2.33906i	0.402314	+	0.114959i
$415$		0			0
$416$	−8.46482	+	12.2089i	−0.415022	+	0.598592i
$417$	−26.9322			−1.31888
$418$	2.02275	+	0.577988i	0.0989360	+	0.0282703i
$419$	−11.4979	−	11.4979i	−0.561709	−	0.561709i	0.368084	−	0.929793i	$-0.380014\pi$
$419$	−11.4979	−	11.4979i	−0.561709	−	0.561709i	−0.929793	+	0.368084i	$0.880014\pi$
$420$		0			0
$421$	12.5714	−	12.5714i	0.612690	−	0.612690i	−0.330956	−	0.943646i	$-0.607371\pi$
$421$	12.5714	−	12.5714i	0.612690	−	0.612690i	0.943646	+	0.330956i	$0.107371\pi$
$422$	−15.1236	−	27.2243i	−0.736208	−	1.32526i
$423$			5.56953i			0.270800i
$424$	−21.1496	−	1.04950i	−1.02711	−	0.0509684i
$425$		0			0
$426$	−7.43529	+	4.13045i	−0.360241	+	0.200121i
$427$	2.15052	−	2.15052i	0.104071	−	0.104071i
$428$	19.8415	−	4.61950i	0.959077	−	0.223292i
$429$	1.63486	+	1.63486i	0.0789316	+	0.0789316i
$430$		0			0
$431$	−15.2579			−0.734946			−0.367473	−	0.930034i	$-0.619777\pi$
$431$	−15.2579			−0.734946			−0.367473	+	0.930034i	$0.619777\pi$
$432$	−21.3698	−	7.26978i	−1.02815	−	0.349768i
$433$	12.1705			0.584877			0.292439	−	0.956284i	$-0.405533\pi$
$433$	12.1705			0.584877			0.292439	+	0.956284i	$0.405533\pi$
$434$	−3.92684	+	13.7425i	−0.188495	+	0.659663i
$435$		0			0
$436$	−3.64169	−	15.6417i	−0.174405	−	0.749101i
$437$	−12.6398	+	12.6398i	−0.604644	+	0.604644i
$438$	−4.43283	+	2.46252i	−0.211809	+	0.117664i
$439$		−	39.7535i		−	1.89733i	−0.316283	−	0.948665i	$-0.602435\pi$
$439$		−	39.7535i		−	1.89733i	0.316283	−	0.948665i	$-0.397565\pi$
$440$		0			0
$441$		−	3.98371i		−	0.189701i
$442$	11.7407	+	21.1347i	0.558450	+	1.00527i
$443$	−3.62318	+	3.62318i	−0.172142	+	0.172142i	−0.787920	−	0.615778i	$-0.788842\pi$
$443$	−3.62318	+	3.62318i	−0.172142	+	0.172142i	0.615778	+	0.787920i	$0.288842\pi$
$444$	−6.89771	−	4.29243i	−0.327351	−	0.203710i
$445$		0			0
$446$	10.7257	+	3.06481i	0.507878	+	0.145123i
$447$	32.9612			1.55901
$448$	−11.9146	−	1.18540i	−0.562913	−	0.0560047i
$449$	−5.38425			−0.254098			−0.127049	−	0.991896i	$-0.540551\pi$
$449$	−5.38425			−0.254098			−0.127049	+	0.991896i	$0.540551\pi$
$450$		0			0
$451$	−3.26225	−	3.26225i	−0.153614	−	0.153614i
$452$	3.30697	+	2.05792i	0.155547	+	0.0967964i
$453$	11.9925	−	11.9925i	0.563455	−	0.563455i
$454$	5.81615	+	10.4697i	0.272965	+	0.491369i
$455$		0			0
$456$	7.66326	−	6.93867i	0.358865	−	0.324933i
$457$		−	14.3039i		−	0.669108i	−0.942377	−	0.334554i	$-0.891414\pi$
$457$		−	14.3039i		−	0.669108i	0.942377	−	0.334554i	$-0.108586\pi$
$458$	−34.0199	+	18.8988i	−1.58965	+	0.883081i
$459$	−25.9748	+	25.9748i	−1.21240	+	1.21240i
$460$		0			0
$461$	−4.50363	−	4.50363i	−0.209755	−	0.209755i	0.594408	−	0.804163i	$-0.297386\pi$
$461$	−4.50363	−	4.50363i	−0.209755	−	0.209755i	−0.804163	+	0.594408i	$0.797386\pi$
$462$	−0.511960	+	1.79167i	−0.0238185	+	0.0833563i
$463$	−19.3500			−0.899271			−0.449636	−	0.893212i	$-0.648446\pi$
$463$	−19.3500			−0.899271			−0.449636	+	0.893212i	$0.648446\pi$
$464$	11.9859	−	35.2330i	0.556433	−	1.63565i
$465$		0			0
$466$	−1.04410	+	3.65399i	−0.0483672	+	0.169268i
$467$	17.1773	+	17.1773i	0.794871	+	0.794871i	0.982282	−	0.187410i	$-0.0600094\pi$
$467$	17.1773	+	17.1773i	0.794871	+	0.794871i	−0.187410	+	0.982282i	$0.560009\pi$
$468$	−4.28145	+	0.996805i	−0.197910	+	0.0460773i
$469$	9.51312	−	9.51312i	0.439275	−	0.439275i
$470$		0			0
$471$			11.2710i			0.519341i
$472$	−23.6445	−	1.17331i	−1.08833	−	0.0540060i
$473$			5.19408i			0.238824i
$474$	11.7897	+	21.2227i	0.541517	+	0.974792i
$475$		0			0
$476$	−10.2950	+	16.5436i	−0.471872	+	0.758273i
$477$	−4.43060	−	4.43060i	−0.202863	−	0.202863i
$478$	17.1821	+	4.90968i	0.785892	+	0.224564i
$479$	5.54474			0.253346			0.126673	−	0.991945i	$-0.459570\pi$
$479$	5.54474			0.253346			0.126673	+	0.991945i	$0.459570\pi$
$480$		0			0
$481$	−7.25361			−0.330736
$482$	−10.2435	−	2.92701i	−0.466578	−	0.133322i
$483$	−11.1959	−	11.1959i	−0.509429	−	0.509429i
$484$	−11.2450	+	18.0702i	−0.511138	+	0.821373i
$485$		0			0
$486$	−5.77955	−	10.4039i	−0.262166	−	0.471928i
$487$		−	31.7138i		−	1.43709i	−0.695480	−	0.718546i	$-0.744808\pi$
$487$		−	31.7138i		−	1.43709i	0.695480	−	0.718546i	$-0.255192\pi$
$488$	−0.284854	+	5.74037i	−0.0128947	+	0.259855i
$489$		−	13.4632i		−	0.608827i
$490$		0			0
$491$	7.39419	−	7.39419i	0.333695	−	0.333695i	−0.520293	−	0.853988i	$-0.674177\pi$
$491$	7.39419	−	7.39419i	0.333695	−	0.333695i	0.853988	+	0.520293i	$0.174177\pi$
$492$	−22.0808	+	5.14083i	−0.995477	+	0.231767i
$493$	−42.8255	−	42.8255i	−1.92876	−	1.92876i
$494$	2.53591	−	8.87477i	0.114096	−	0.399295i
$495$		0			0
$496$	−11.9303	−	24.2325i	−0.535685	−	1.08807i
$497$	−6.12041			−0.274538
$498$	−2.27449	+	7.95988i	−0.101922	+	0.356691i
$499$	14.0103	+	14.0103i	0.627189	+	0.627189i	0.947360	−	0.320171i	$-0.103740\pi$
$499$	14.0103	+	14.0103i	0.627189	+	0.627189i	−0.320171	+	0.947360i	$0.603740\pi$
$500$		0			0
$501$	−8.62899	+	8.62899i	−0.385515	+	0.385515i
$502$	17.4079	−	9.67046i	0.776954	−	0.431614i
$503$		−	8.43795i		−	0.376230i	−0.982147	−	0.188115i	$-0.939762\pi$
$503$		−	8.43795i		−	0.376230i	0.982147	−	0.188115i	$-0.0602377\pi$
$504$	−2.37798	−	2.62631i	−0.105924	−	0.116985i
$505$		0			0
$506$	2.95692	+	5.32280i	0.131451	+	0.236627i
$507$	−6.34671	+	6.34671i	−0.281868	+	0.281868i
$508$	−2.23797	−	1.39268i	−0.0992937	−	0.0617902i
$509$	2.09367	+	2.09367i	0.0928004	+	0.0928004i	0.751983	−	0.659183i	$-0.229098\pi$
$509$	2.09367	+	2.09367i	0.0928004	+	0.0928004i	−0.659183	+	0.751983i	$0.729098\pi$
$510$		0			0
$511$	−3.64891			−0.161418
$512$	18.1945	−	13.4521i	0.804091	−	0.594506i
$513$	14.0239			0.619169
$514$	−6.14122	−	1.75481i	−0.270878	−	0.0774016i
$515$		0			0
$516$	21.6708	+	13.4857i	0.954003	+	0.593674i
$517$	−2.81669	+	2.81669i	−0.123878	+	0.123878i
$518$	−2.83895	−	5.11043i	−0.124736	−	0.224540i
$519$		−	24.8387i		−	1.09030i
$520$		0			0
$521$		−	28.2558i		−	1.23791i	−0.785428	−	0.618954i	$-0.787557\pi$
$521$		−	28.2558i		−	1.23791i	0.785428	−	0.618954i	$-0.212443\pi$
$522$	9.62647	−	5.34770i	0.421339	−	0.234062i
$523$	−10.1929	+	10.1929i	−0.445703	+	0.445703i	−0.893923	−	0.448220i	$-0.852058\pi$
$523$	−10.1929	+	10.1929i	−0.445703	+	0.445703i	0.448220	+	0.893923i	$0.352058\pi$
$524$	0.660765	+	2.83810i	0.0288657	+	0.123983i
$525$		0			0
$526$	−7.85368	+	27.4851i	−0.342437	+	1.19841i
$527$	−43.9555			−1.91473
$528$	−1.55540	−	3.15929i	−0.0676901	−	0.137491i
$529$	−28.7385			−1.24950
$530$		0			0
$531$	−4.95326	−	4.95326i	−0.214953	−	0.214953i
$532$	7.24512	−	1.68681i	0.314116	−	0.0731323i
$533$	−14.3131	+	14.3131i	−0.619967	+	0.619967i
$534$	−19.1901	+	10.6605i	−0.830438	+	0.461325i
$535$		0			0
$536$	−1.26009	+	25.3933i	−0.0544276	+	1.09682i
$537$			22.6095i			0.975671i
$538$	−16.4557	−	29.6222i	−0.709457	−	1.27710i
$539$	2.01469	−	2.01469i	0.0867790	−	0.0867790i
$540$		0			0
$541$	3.86053	+	3.86053i	0.165977	+	0.165977i	0.785209	−	0.619231i	$-0.212556\pi$
$541$	3.86053	+	3.86053i	0.165977	+	0.165977i	−0.619231	+	0.785209i	$0.712556\pi$
$542$	4.95036	+	1.41453i	0.212636	+	0.0607595i
$543$	8.51534			0.365428
$544$	−6.56211	−	36.2339i	−0.281348	−	1.55352i
$545$		0			0
$546$	7.86093	+	2.24621i	0.336417	+	0.0961289i
$547$	−20.6231	−	20.6231i	−0.881781	−	0.881781i	0.111935	−	0.993716i	$-0.464295\pi$
$547$	−20.6231	−	20.6231i	−0.881781	−	0.881781i	−0.993716	+	0.111935i	$0.964295\pi$
$548$	3.96852	−	6.37720i	0.169527	−	0.272421i
$549$	−1.20254	+	1.20254i	−0.0513233	+	0.0513233i
$550$		0			0
$551$			23.1216i			0.985014i
$552$	29.8850	+	1.48298i	1.27199	+	0.0631199i
$553$			17.4696i			0.742884i
$554$	27.9892	−	15.5486i	1.18915	−	0.660595i
$555$		0			0
$556$	35.6700	−	8.30468i	1.51275	−	0.352197i
$557$	1.28512	+	1.28512i	0.0544523	+	0.0544523i	0.733809	−	0.679356i	$-0.237741\pi$
$557$	1.28512	+	1.28512i	0.0544523	+	0.0544523i	−0.679356	+	0.733809i	$0.737741\pi$
$558$	2.19584	−	7.68465i	0.0929573	−	0.325317i
$559$	22.7889			0.963868
$560$		0			0
$561$	−5.73068			−0.241949
$562$	−2.14425	+	7.50409i	−0.0904496	+	0.316541i
$563$	−21.9152	−	21.9152i	−0.923615	−	0.923615i	0.0736677	−	0.997283i	$-0.476530\pi$
$563$	−21.9152	−	21.9152i	−0.923615	−	0.923615i	−0.997283	+	0.0736677i	$0.976530\pi$
$564$	4.43869	+	19.0650i	0.186903	+	0.802779i
$565$		0			0
$566$	−4.13822	+	2.29886i	−0.173942	+	0.0966284i
$567$			8.66397i			0.363852i
$568$	8.57394	−	7.76324i	0.359754	−	0.325738i
$569$			35.6668i			1.49523i	0.664132	+	0.747615i	$0.268801\pi$
$569$			35.6668i			1.49523i	−0.664132	+	0.747615i	$0.731199\pi$
$570$		0			0
$571$	5.60524	−	5.60524i	0.234572	−	0.234572i	−0.580026	−	0.814598i	$-0.696958\pi$
$571$	5.60524	−	5.60524i	0.234572	−	0.234572i	0.814598	+	0.580026i	$0.196958\pi$
$572$	−2.66938	−	1.66115i	−0.111613	−	0.0694562i
$573$	−20.0238	−	20.0238i	−0.836507	−	0.836507i
$574$	−15.6860	−	4.48217i	−0.654720	−	0.187082i
$575$		0			0
$576$	6.66251	+	0.662858i	0.277604	+	0.0276191i
$577$	2.43681			0.101446			0.0507230	−	0.998713i	$-0.483847\pi$
$577$	2.43681			0.101446			0.0507230	+	0.998713i	$0.483847\pi$
$578$	−34.5028	−	9.85896i	−1.43513	−	0.410079i
$579$	25.8071	+	25.8071i	1.07251	+	1.07251i
$580$		0			0
$581$	−4.21225	+	4.21225i	−0.174753	+	0.174753i
$582$	18.3338	+	33.0029i	0.759960	+	1.36802i
$583$		−	4.48139i		−	0.185600i
$584$	5.11167	−	4.62835i	0.211523	−	0.191522i
$585$		0			0
$586$	33.5353	−	18.6295i	1.38533	−	0.769578i
$587$	−0.415982	+	0.415982i	−0.0171694	+	0.0171694i	−0.715639	−	0.698470i	$-0.753865\pi$
$587$	−0.415982	+	0.415982i	−0.0171694	+	0.0171694i	0.698470	+	0.715639i	$0.253865\pi$
$588$	−3.17486	−	13.6366i	−0.130929	−	0.562363i
$589$	11.8659	+	11.8659i	0.488924	+	0.488924i
$590$		0			0
$591$	5.85136			0.240693
$592$	10.4592	+	3.55811i	0.429870	+	0.146237i
$593$	15.3439			0.630098			0.315049	−	0.949075i	$-0.397979\pi$
$593$	15.3439			0.630098			0.315049	+	0.949075i	$0.397979\pi$
$594$	1.31247	−	4.59318i	0.0538513	−	0.188460i
$595$		0			0
$596$	−43.6551	+	10.1638i	−1.78818	+	0.416324i
$597$	22.0675	−	22.0675i	0.903163	−	0.903163i
$598$	23.3537	−	12.9734i	0.955002	−	0.530523i
$599$		−	43.3487i		−	1.77118i	−0.464468	−	0.885590i	$-0.653754\pi$
$599$		−	43.3487i		−	1.77118i	0.464468	−	0.885590i	$-0.346246\pi$
$600$		0			0
$601$			38.7291i			1.57979i	0.613239	+	0.789897i	$0.289866\pi$
$601$			38.7291i			1.57979i	−0.613239	+	0.789897i	$0.710134\pi$
$602$	8.91923	+	16.0556i	0.363520	+	0.654379i
$603$	−5.31961	+	5.31961i	−0.216631	+	0.216631i
$604$	−12.1853	+	19.5812i	−0.495815	+	0.796748i
$605$		0			0
$606$	−2.94244	−	0.840784i	−0.119529	−	0.0341545i
$607$	34.9068			1.41682			0.708412	−	0.705800i	$-0.249412\pi$
$607$	34.9068			1.41682			0.708412	+	0.705800i	$0.249412\pi$
$608$	−8.00994	+	11.5528i	−0.324846	+	0.468530i
$609$	−20.4802			−0.829901
$610$		0			0
$611$	12.3582	+	12.3582i	0.499958	+	0.499958i
$612$	5.75684	−	9.25095i	0.232707	−	0.373947i
$613$	0.151779	−	0.151779i	0.00613031	−	0.00613031i	−0.704035	−	0.710165i	$-0.748620\pi$
$613$	0.151779	−	0.151779i	0.00613031	−	0.00613031i	0.710165	+	0.704035i	$0.248620\pi$
$614$	−19.3560	−	34.8430i	−0.781144	−	1.40615i
$615$		0			0
$616$	0.125587	−	2.53083i	0.00506004	−	0.101970i
$617$			0.288199i			0.0116025i	0.999983	+	0.00580123i	$0.00184660\pi$
$617$			0.288199i			0.0116025i	−0.999983	+	0.00580123i	$0.998153\pi$
$618$	1.73689	−	0.964876i	0.0698679	−	0.0388130i
$619$	−11.5307	+	11.5307i	−0.463460	+	0.463460i	−0.899788	−	0.436328i	$-0.856279\pi$
$619$	−11.5307	+	11.5307i	−0.463460	+	0.463460i	0.436328	+	0.899788i	$0.356279\pi$
$620$		0			0
$621$	28.7019	+	28.7019i	1.15177	+	1.15177i
$622$	2.22762	−	7.79586i	0.0893193	−	0.312585i
$623$	−15.7965			−0.632873
$624$	−13.8613	+	6.82428i	−0.554897	+	0.273190i
$625$		0			0
$626$	−0.0826141	+	0.289120i	−0.00330192	+	0.0115555i
$627$	1.54700	+	1.54700i	0.0617814	+	0.0617814i
$628$	−3.47547	−	14.9278i	−0.138686	−	0.595682i
$629$	12.7131	−	12.7131i	0.506903	−	0.506903i
$630$		0			0
$631$		−	14.2062i		−	0.565541i	−0.959188	−	0.282771i	$-0.908746\pi$
$631$		−	14.2062i		−	0.565541i	0.959188	−	0.282771i	$-0.0912536\pi$
$632$	−22.1588	−	24.4728i	−0.881430	−	0.973475i
$633$		−	32.3878i		−	1.28730i
$634$	3.12332	+	5.62234i	0.124043	+	0.223292i
$635$		0			0
$636$	−18.6973	−	11.6353i	−0.741396	−	0.461369i
$637$	−8.83942	−	8.83942i	−0.350230	−	0.350230i
$638$	7.57292	+	2.16391i	0.299815	+	0.0856702i
$639$	3.42245			0.135390
$640$		0			0
$641$	19.7372			0.779572			0.389786	−	0.920905i	$-0.372549\pi$
$641$	19.7372			0.779572			0.389786	+	0.920905i	$0.372549\pi$
$642$	20.3712	+	5.82093i	0.803985	+	0.229734i
$643$	5.80043	+	5.80043i	0.228747	+	0.228747i	0.812169	−	0.583422i	$-0.198287\pi$
$643$	5.80043	+	5.80043i	0.228747	+	0.228747i	−0.583422	+	0.812169i	$0.698287\pi$
$644$	18.2805	+	11.3759i	0.720353	+	0.448274i
$645$		0			0
$646$	11.1098	+	19.9990i	0.437110	+	0.786849i
$647$		−	46.3186i		−	1.82097i	−0.413541	−	0.910485i	$-0.635708\pi$
$647$		−	46.3186i		−	1.82097i	0.413541	−	0.910485i	$-0.364292\pi$
$648$	−10.9895	−	12.1371i	−0.431710	−	0.476792i
$649$		−	5.01005i		−	0.196662i
$650$		0			0
$651$	−10.5103	+	10.5103i	−0.411932	+	0.411932i
$652$	4.15144	+	17.8312i	0.162583	+	0.698322i
$653$	4.42354	+	4.42354i	0.173106	+	0.173106i	0.788343	−	0.615236i	$-0.210939\pi$
$653$	4.42354	+	4.42354i	0.173106	+	0.173106i	−0.615236	+	0.788343i	$0.710939\pi$
$654$	4.58881	−	16.0592i	0.179437	−	0.627964i
$655$		0			0
$656$	27.6594	−	13.6174i	1.07992	−	0.531671i
$657$	2.04042			0.0796045
$658$	−3.86999	+	13.5436i	−0.150868	+	0.527984i
$659$	−15.2461	−	15.2461i	−0.593905	−	0.593905i	0.344779	−	0.938684i	$-0.387954\pi$
$659$	−15.2461	−	15.2461i	−0.593905	−	0.593905i	−0.938684	+	0.344779i	$0.887954\pi$
$660$		0			0
$661$	19.1271	−	19.1271i	0.743958	−	0.743958i	−0.229379	−	0.973337i	$-0.573670\pi$
$661$	19.1271	−	19.1271i	0.743958	−	0.743958i	0.973337	+	0.229379i	$0.0736696\pi$
$662$	−38.5151	+	21.3959i	−1.49693	+	0.831577i
$663$			25.1432i			0.976481i
$664$	0.557946	−	11.2437i	0.0216525	−	0.436341i
$665$		0			0
$666$	1.58750	+	2.85769i	0.0615145	+	0.110733i
$667$	−47.3218	+	47.3218i	−1.83231	+	1.83231i
$668$	8.76777	−	14.0894i	0.339235	−	0.545133i
$669$	8.20306	+	8.20306i	0.317149	+	0.317149i
$670$		0			0
$671$	−1.21633			−0.0469559
$672$	−10.2331	−	7.09490i	−0.394749	−	0.273692i
$673$	18.5586			0.715382			0.357691	−	0.933840i	$-0.383564\pi$
$673$	18.5586			0.715382			0.357691	+	0.933840i	$0.383564\pi$
$674$	15.2462	+	4.35651i	0.587263	+	0.167807i
$675$		0			0
$676$	6.44879	−	10.3629i	0.248030	−	0.398572i
$677$	2.71844	−	2.71844i	0.104478	−	0.104478i	−0.652935	−	0.757414i	$-0.726463\pi$
$677$	2.71844	−	2.71844i	0.104478	−	0.104478i	0.757414	+	0.652935i	$0.226463\pi$
$678$	1.96709	+	3.54100i	0.0755458	+	0.135991i
$679$			27.1666i			1.04256i
$680$		0			0
$681$			12.4555i			0.477295i
$682$	4.99688	−	2.77587i	0.191340	−	0.106293i
$683$	12.6646	−	12.6646i	0.484598	−	0.484598i	−0.421999	−	0.906596i	$-0.638671\pi$
$683$	12.6646	−	12.6646i	0.484598	−	0.484598i	0.906596	+	0.421999i	$0.138671\pi$
$684$	−4.05138	+	0.943239i	−0.154908	+	0.0360657i
$685$		0			0
$686$	6.83885	−	23.9335i	0.261108	−	0.913786i
$687$	−40.4723			−1.54412
$688$	−32.8600	−	11.1786i	−1.25278	−	0.426182i
$689$	−19.6620			−0.749063
$690$		0			0
$691$	26.8892	+	26.8892i	1.02291	+	1.02291i	0.999731	+	0.0231826i	$0.00737991\pi$
$691$	26.8892	+	26.8892i	1.02291	+	1.02291i	0.0231826	+	0.999731i	$0.492620\pi$
$692$	7.65914	+	32.8973i	0.291157	+	1.25057i
$693$	0.530180	−	0.530180i	0.0201399	−	0.0201399i
$694$	−2.16187	+	1.20096i	−0.0820636	+	0.0455880i
$695$		0			0
$696$	28.6903	−	25.9775i	1.08750	−	0.984675i
$697$		−	50.1717i		−	1.90039i
$698$	5.45621	+	9.82180i	0.206521	+	0.371761i
$699$	−2.79458	+	2.79458i	−0.105701	+	0.105701i
$700$		0			0
$701$	25.3725	+	25.3725i	0.958305	+	0.958305i	0.999165	−	0.0408602i	$-0.0130098\pi$
$701$	25.3725	+	25.3725i	0.958305	+	0.958305i	−0.0408602	+	0.999165i	$0.513010\pi$
$702$	−20.1524	−	5.75843i	−0.760605	−	0.217338i
$703$	−6.86382			−0.258874
$704$	3.03422	+	3.70467i	0.114356	+	0.139625i
$705$		0			0
$706$	−1.01809	−	0.290912i	−0.0383162	−	0.0109486i
$707$	−1.55709	−	1.55709i	−0.0585606	−	0.0585606i
$708$	−20.9029	−	13.0079i	−0.785581	−	0.488865i
$709$	16.1117	−	16.1117i	0.605089	−	0.605089i	−0.336570	−	0.941659i	$-0.609267\pi$
$709$	16.1117	−	16.1117i	0.605089	−	0.605089i	0.941659	+	0.336570i	$0.109267\pi$
$710$		0			0
$711$		−	9.76879i		−	0.366358i
$712$	22.1289	−	20.0365i	0.829316	−	0.750901i
$713$			48.5705i			1.81898i
$714$	−17.7143	+	9.84066i	−0.662941	+	0.368277i
$715$		0			0
$716$	−6.97175	−	29.9449i	−0.260546	−	1.11909i
$717$	13.1409	+	13.1409i	0.490757	+	0.490757i
$718$	1.04864	−	3.66985i	0.0391347	−	0.136958i
$719$	29.1676			1.08777			0.543884	−	0.839160i	$-0.316953\pi$
$719$	29.1676			1.08777			0.543884	+	0.839160i	$0.316953\pi$
$720$		0			0
$721$	1.42973			0.0532460
$722$	−4.98284	+	17.4381i	−0.185442	+	0.648980i
$723$	−7.83424	−	7.83424i	−0.291358	−	0.291358i
$724$	−11.2780	+	2.62575i	−0.419145	+	0.0975852i
$725$		0			0
$726$	−19.3490	+	10.7487i	−0.718108	+	0.398923i
$727$			4.13463i			0.153345i	0.997056	+	0.0766724i	$0.0244296\pi$
$727$			4.13463i			0.153345i	−0.997056	+	0.0766724i	$0.975570\pi$
$728$	−11.1039	−	0.551010i	−0.411540	−	0.0204218i
$729$		−	29.7434i		−	1.10161i
$730$		0			0
$731$	−39.9411	+	39.9411i	−1.47727	+	1.47727i
$732$	−3.15802	+	5.07478i	−0.116724	+	0.187569i
$733$	19.3838	+	19.3838i	0.715957	+	0.715957i	0.967775	−	0.251817i	$-0.0810282\pi$
$733$	19.3838	+	19.3838i	0.715957	+	0.715957i	−0.251817	+	0.967775i	$0.581028\pi$
$734$	−28.0255	−	8.00809i	−1.03444	−	0.295584i
$735$		0			0
$736$	−40.0382	+	7.25108i	−1.47583	+	0.267278i
$737$	−5.38060			−0.198197
$738$	8.77140	+	2.50637i	0.322880	+	0.0922608i
$739$	23.9820	+	23.9820i	0.882194	+	0.882194i	0.993757	−	0.111564i	$-0.0355859\pi$
$739$	23.9820	+	23.9820i	0.882194	+	0.882194i	−0.111564	+	0.993757i	$0.535586\pi$
$740$		0			0
$741$	6.78744	−	6.78744i	0.249343	−	0.249343i
$742$	−7.69540	−	13.8526i	−0.282507	−	0.508545i
$743$			10.3473i			0.379604i	0.981822	+	0.189802i	$0.0607846\pi$
$743$			10.3473i			0.379604i	−0.981822	+	0.189802i	$0.939215\pi$
$744$	1.39218	−	28.0551i	0.0510397	−	1.02855i
$745$		0			0
$746$	−9.16380	+	5.09068i	−0.335511	+	0.186383i
$747$	2.35543	−	2.35543i	0.0861808	−	0.0861808i
$748$	7.58993	−	1.76708i	0.277515	−	0.0646109i
$749$	10.7801	+	10.7801i	0.393896	+	0.393896i
$750$		0			0
$751$	−37.0217			−1.35094			−0.675470	−	0.737387i	$-0.736059\pi$
$751$	−37.0217			−1.35094			−0.675470	+	0.737387i	$0.736059\pi$
$752$	−11.7575	−	23.8817i	−0.428754	−	0.870874i
$753$	20.7096			0.754700
$754$	9.49412	−	33.2260i	0.345756	−	1.21002i
$755$		0			0
$756$	−3.83032	−	16.4519i	−0.139308	−	0.598350i
$757$	30.4305	−	30.4305i	1.10601	−	1.10601i	0.112345	−	0.993669i	$-0.464164\pi$
$757$	30.4305	−	30.4305i	1.10601	−	1.10601i	0.993669	−	0.112345i	$-0.0358361\pi$
$758$	−9.46454	+	5.25774i	−0.343768	+	0.190970i
$759$			6.33235i			0.229850i
$760$		0			0
$761$		−	43.1054i		−	1.56257i	−0.624174	−	0.781285i	$-0.714564\pi$
$761$		−	43.1054i		−	1.56257i	0.624174	−	0.781285i	$-0.285436\pi$
$762$	−1.33122	−	2.39634i	−0.0482249	−	0.0868103i
$763$	8.49827	−	8.49827i	0.307658	−	0.307658i
$764$	32.6948	+	20.3459i	1.18285	+	0.736088i
$765$		0			0
$766$	−40.1256	−	11.4656i	−1.44980	−	0.414271i
$767$	−21.9815			−0.793705
$768$	23.3345	−	3.04073i	0.842013	−	0.109723i
$769$	−31.2507			−1.12693			−0.563465	−	0.826140i	$-0.690532\pi$
$769$	−31.2507			−1.12693			−0.563465	+	0.826140i	$0.690532\pi$
$770$		0			0
$771$	−4.69682	−	4.69682i	−0.169152	−	0.169152i
$772$	−42.1376	−	26.2221i	−1.51657	−	0.943756i
$773$	−24.4047	+	24.4047i	−0.877778	+	0.877778i	−0.993304	−	0.115527i	$-0.963144\pi$
$773$	−24.4047	+	24.4047i	−0.877778	+	0.877778i	0.115527	+	0.993304i	$0.463144\pi$
$774$	−4.98751	−	8.97810i	−0.179272	−	0.322711i
$775$		0			0
$776$	−34.4586	−	38.0570i	−1.23699	−	1.36617i
$777$		−	6.07970i		−	0.218108i
$778$	−2.41068	+	1.33918i	−0.0864271	+	0.0480120i
$779$	−13.5439	+	13.5439i	−0.485261	+	0.485261i
$780$		0			0
$781$	1.73085	+	1.73085i	0.0619345	+	0.0619345i
$782$	−18.1929	+	63.6688i	−0.650579	+	2.27679i
$783$	52.5036			1.87632
$784$	8.40981	+	17.0818i	0.300350	+	0.610065i
$785$		0			0
$786$	−0.832616	+	2.91386i	−0.0296984	+	0.103934i
$787$	17.2122	+	17.2122i	0.613549	+	0.613549i	0.943869	−	0.330320i	$-0.107157\pi$
$787$	17.2122	+	17.2122i	0.613549	+	0.613549i	−0.330320	+	0.943869i	$0.607157\pi$
$788$	−7.74977	+	1.80430i	−0.276074	+	0.0642754i
$789$	−21.0206	+	21.0206i	−0.748354	+	0.748354i
$790$		0			0
$791$			2.91480i			0.103638i
$792$	−0.0702266	+	1.41521i	−0.00249539	+	0.0502871i
$793$			5.33662i			0.189509i
$794$	−21.3429	−	38.4197i	−0.757432	−	1.36347i
$795$		0			0
$796$	−22.4224	+	36.0317i	−0.794742	+	1.27711i
$797$	20.3220	+	20.3220i	0.719841	+	0.719841i	0.968573	−	0.248731i	$-0.0800136\pi$
$797$	20.3220	+	20.3220i	0.719841	+	0.719841i	−0.248731	+	0.968573i	$0.580014\pi$
$798$	7.43850	+	2.12551i	0.263320	+	0.0752421i
$799$	−43.3192			−1.53252
$800$		0			0
$801$	8.83319			0.312105
$802$	42.7768	+	12.2232i	1.51050	+	0.431616i
$803$	1.03191	+	1.03191i	0.0364153	+	0.0364153i
$804$	−13.9699	+	22.4490i	−0.492682	+	0.791714i
$805$		0			0
$806$	−12.1791	−	21.9237i	−0.428989	−	0.772229i
$807$		−	35.2405i		−	1.24052i
$808$	4.15634	+	0.206250i	0.146220	+	0.00725584i
$809$			2.80407i			0.0985859i	0.998784	+	0.0492930i	$0.0156968\pi$
$809$			2.80407i			0.0985859i	−0.998784	+	0.0492930i	$0.984303\pi$
$810$		0			0
$811$	−7.29902	+	7.29902i	−0.256303	+	0.256303i	−0.823549	−	0.567246i	$-0.808009\pi$
$811$	−7.29902	+	7.29902i	−0.256303	+	0.256303i	0.567246	+	0.823549i	$0.308009\pi$
$812$	27.1248	−	6.31518i	0.951894	−	0.221619i
$813$	3.78605	+	3.78605i	0.132782	+	0.132782i
$814$	−0.642373	+	2.24808i	−0.0225152	+	0.0787950i
$815$		0			0
$816$	12.3335	−	36.2547i	0.431759	−	1.26917i
$817$	21.5643			0.754439
$818$	4.97411	−	17.4076i	0.173916	−	0.608643i
$819$	−2.32615	−	2.32615i	−0.0812823	−	0.0812823i
$820$		0			0
$821$	−10.0517	+	10.0517i	−0.350806	+	0.350806i	−0.860409	−	0.509603i	$-0.829792\pi$
$821$	−10.0517	+	10.0517i	−0.350806	+	0.350806i	0.509603	+	0.860409i	$0.329792\pi$
$822$	6.82850	−	3.79337i	0.238171	−	0.132309i
$823$			34.2064i			1.19236i	0.802851	+	0.596179i	$0.203315\pi$
$823$			34.2064i			1.19236i	−0.802851	+	0.596179i	$0.796685\pi$
$824$	−2.00288	+	1.81350i	−0.0697735	+	0.0631761i
$825$		0			0
$826$	−8.60320	−	15.4868i	−0.299344	−	0.538853i
$827$	−31.3455	+	31.3455i	−1.08999	+	1.08999i	−0.0944595	+	0.995529i	$0.530112\pi$
$827$	−31.3455	+	31.3455i	−1.08999	+	1.08999i	−0.995529	+	0.0944595i	$0.969888\pi$
$828$	−10.2222	−	6.36126i	−0.355247	−	0.221069i
$829$	−3.87895	−	3.87895i	−0.134722	−	0.134722i	0.636530	−	0.771252i	$-0.280369\pi$
$829$	−3.87895	−	3.87895i	−0.134722	−	0.134722i	−0.771252	+	0.636530i	$0.780369\pi$
$830$		0			0
$831$	33.2978			1.15509
$832$	16.2542	−	13.3125i	0.563512	−	0.461530i
$833$	30.9849			1.07356
$834$	36.6221	+	10.4645i	1.26812	+	0.362357i
$835$		0			0
$836$	−2.52594	−	1.57189i	−0.0873614	−	0.0543648i
$837$	26.9445	−	26.9445i	0.931338	−	0.931338i
$838$	11.1672	+	20.1022i	0.385765	+	0.694421i
$839$		−	32.9463i		−	1.13743i	−0.822533	−	0.568717i	$-0.807440\pi$
$839$		−	32.9463i		−	1.13743i	0.822533	−	0.568717i	$-0.192560\pi$
$840$		0			0
$841$			57.5644i			1.98498i
$842$	−21.9790	+	12.2098i	−0.757447	+	0.420777i
$843$	−5.73915	+	5.73915i	−0.197667	+	0.197667i
$844$	9.98694	+	42.8956i	0.343765	+	1.47653i
$845$		0			0
$846$	2.16405	−	7.57340i	0.0744016	−	0.260379i
$847$	−15.9272			−0.547267
$848$	28.3512	+	9.64480i	0.973584	+	0.331204i
$849$	−4.92309			−0.168960
$850$		0			0
$851$	−14.0478	−	14.0478i	−0.481553	−	0.481553i
$852$	11.7153	−	2.72756i	0.401361	−	0.0934446i
$853$	−1.87566	+	1.87566i	−0.0642212	+	0.0642212i	−0.738488	−	0.674267i	$-0.764460\pi$
$853$	−1.87566	+	1.87566i	−0.0642212	+	0.0642212i	0.674267	+	0.738488i	$0.264460\pi$
$854$	−3.75984	+	2.08867i	−0.128659	+	0.0714728i
$855$		0			0
$856$	−28.7752	−	1.42791i	−0.983517	−	0.0488050i
$857$			23.1714i			0.791521i	0.918354	+	0.395760i	$0.129519\pi$
$857$			23.1714i			0.791521i	−0.918354	+	0.395760i	$0.870481\pi$
$858$	−1.58784	−	2.85829i	−0.0542078	−	0.0975803i
$859$	−10.5073	+	10.5073i	−0.358506	+	0.358506i	−0.863262	−	0.504756i	$-0.831582\pi$
$859$	−10.5073	+	10.5073i	−0.358506	+	0.358506i	0.504756	+	0.863262i	$0.331582\pi$
$860$		0			0
$861$	−11.9967	−	11.9967i	−0.408846	−	0.408846i
$862$	20.7475	+	5.92847i	0.706663	+	0.201924i
$863$	−25.2777			−0.860463			−0.430231	−	0.902719i	$-0.641568\pi$
$863$	−25.2777			−0.860463			−0.430231	+	0.902719i	$0.641568\pi$
$864$	26.2337	+	18.1886i	0.892488	+	0.618790i
$865$		0			0
$866$	−16.5493	−	4.72887i	−0.562369	−	0.160693i
$867$	−26.3878	−	26.3878i	−0.896177	−	0.896177i
$868$	10.6794	−	17.1612i	0.362481	−	0.582489i
$869$	4.94039	−	4.94039i	0.167591	−	0.167591i
$870$		0			0
$871$			23.6073i			0.799901i
$872$	−1.12566	+	22.6844i	−0.0381198	+	0.768190i
$873$		−	15.1912i		−	0.514144i
$874$	22.0987	−	12.2763i	0.747500	−	0.415251i
$875$		0			0
$876$	6.98453	−	1.62613i	0.235985	−	0.0549420i
$877$	16.7350	+	16.7350i	0.565101	+	0.565101i	0.930752	−	0.365651i	$-0.119154\pi$
$877$	16.7350	+	16.7350i	0.565101	+	0.565101i	−0.365651	+	0.930752i	$0.619154\pi$
$878$	−15.4463	+	54.0564i	−0.521286	+	1.82431i
$879$	39.8957			1.34565
$880$		0			0
$881$	9.38791			0.316287			0.158143	−	0.987416i	$-0.449449\pi$
$881$	9.38791			0.316287			0.158143	+	0.987416i	$0.449449\pi$
$882$	−1.54788	+	5.41701i	−0.0521197	+	0.182400i
$883$	21.5593	+	21.5593i	0.725527	+	0.725527i	0.969725	−	0.244198i	$-0.0785248\pi$
$883$	21.5593	+	21.5593i	0.725527	+	0.725527i	−0.244198	+	0.969725i	$0.578525\pi$
$884$	−7.75303	−	33.3006i	−0.260763	−	1.12002i
$885$		0			0
$886$	6.33455	−	3.51897i	0.212813	−	0.118222i
$887$			48.2072i			1.61864i	0.587368	+	0.809320i	$0.300164\pi$
$887$			48.2072i			1.61864i	−0.587368	+	0.809320i	$0.699836\pi$
$888$	7.71161	+	8.51691i	0.258785	+	0.285809i
$889$		−	1.97256i		−	0.0661577i
$890$		0			0
$891$	2.45016	−	2.45016i	0.0820834	−	0.0820834i
$892$	−13.3939	−	8.33500i	−0.448461	−	0.279076i
$893$	11.6941	+	11.6941i	0.391327	+	0.391327i
$894$	−44.8204	−	12.8071i	−1.49902	−	0.428335i
$895$		0			0
$896$	15.7408	+	6.24133i	0.525863	+	0.208508i
$897$	27.7830			0.927648
$898$	7.32144	+	2.09206i	0.244320	+	0.0698128i
$899$	44.4243	+	44.4243i	1.48163	+	1.48163i
$900$		0			0
$901$	34.4607	−	34.4607i	1.14805	−	1.14805i
$902$	3.16843	+	5.70353i	0.105497	+	0.189907i
$903$			19.1008i			0.635636i
$904$	−3.69718	−	4.08327i	−0.122966	−	0.135807i
$905$		0			0
$906$	−20.9669	+	11.6475i	−0.696579	+	0.386964i
$907$	31.8381	−	31.8381i	1.05717	−	1.05717i	0.0589044	−	0.998264i	$-0.481239\pi$
$907$	31.8381	−	31.8381i	1.05717	−	1.05717i	0.998264	−	0.0589044i	$-0.0187607\pi$
$908$	−3.84071	−	16.4965i	−0.127458	−	0.547456i
$909$	0.870707	+	0.870707i	0.0288795	+	0.0288795i
$910$		0			0
$911$	14.8669			0.492561			0.246281	−	0.969199i	$-0.420791\pi$
$911$	14.8669			0.492561			0.246281	+	0.969199i	$0.420791\pi$
$912$	−13.1165	+	6.45756i	−0.434329	+	0.213831i
$913$	2.38244			0.0788472
$914$	−5.55780	+	19.4503i	−0.183836	+	0.643358i
$915$		0			0
$916$	53.6031	−	12.4798i	1.77110	−	0.412346i
$917$	−1.54197	+	1.54197i	−0.0509202	+	0.0509202i
$918$	45.4128	−	25.2277i	1.49885	−	0.832638i
$919$		−	5.27591i		−	0.174036i	−0.996207	−	0.0870181i	$-0.972266\pi$
$919$		−	5.27591i		−	0.174036i	0.996207	−	0.0870181i	$-0.0277338\pi$
$920$		0			0
$921$		−	41.4515i		−	1.36587i
$922$	4.37410	+	7.87389i	0.144053	+	0.259313i
$923$	7.59404	−	7.59404i	0.249961	−	0.249961i
$924$	1.39231	−	2.23738i	0.0458038	−	0.0736043i
$925$		0			0
$926$	26.3119	+	7.51847i	0.864664	+	0.247072i
$927$	−0.799487			−0.0262586
$928$	−29.9882	+	43.2524i	−0.984411	+	1.41983i
$929$	−9.13997			−0.299873			−0.149936	−	0.988696i	$-0.547907\pi$
$929$	−9.13997			−0.299873			−0.149936	+	0.988696i	$0.547907\pi$
$930$		0			0
$931$	−8.36441	−	8.36441i	−0.274133	−	0.274133i
$932$	2.83952	−	4.56297i	0.0930116	−	0.149465i
$933$	5.96229	−	5.96229i	0.195197	−	0.195197i
$934$	−16.6833	−	30.0318i	−0.545893	−	0.982671i
$935$		0			0
$936$	6.20918	+	0.308117i	0.202953	+	0.0100711i
$937$		−	19.0036i		−	0.620819i	−0.950603	−	0.310410i	$-0.899534\pi$
$937$		−	19.0036i		−	0.620819i	0.950603	−	0.310410i	$-0.100466\pi$
$938$	−16.6322	+	9.23951i	−0.543060	+	0.301681i
$939$	−0.221119	+	0.221119i	−0.00721596	+	0.00721596i
$940$		0			0
$941$	1.48322	+	1.48322i	0.0483517	+	0.0483517i	0.730869	−	0.682518i	$-0.239115\pi$
$941$	1.48322	+	1.48322i	0.0483517	+	0.0483517i	−0.682518	+	0.730869i	$0.739115\pi$
$942$	4.37937	−	15.3262i	0.142687	−	0.499355i
$943$	−55.4393			−1.80535
$944$	31.6957	+	10.7826i	1.03161	+	0.350943i
$945$		0			0
$946$	2.01817	−	7.06286i	0.0656163	−	0.229633i
$947$	3.97577	+	3.97577i	0.129195	+	0.129195i	0.768748	−	0.639552i	$-0.220880\pi$
$947$	3.97577	+	3.97577i	0.129195	+	0.129195i	−0.639552	+	0.768748i	$0.720880\pi$
$948$	−7.78533	−	33.4393i	−0.252856	−	1.08606i
$949$	4.52747	−	4.52747i	0.146968	−	0.146968i
$950$		0			0
$951$			6.68870i			0.216896i
$952$	20.4271	−	18.4956i	0.662046	−	0.599447i
$953$			16.5970i			0.537628i	0.963192	+	0.268814i	$0.0866317\pi$
$953$			16.5970i			0.537628i	−0.963192	+	0.268814i	$0.913368\pi$
$954$	4.30317	+	7.74620i	0.139320	+	0.250792i
$955$		0			0
$956$	−21.4564	−	13.3523i	−0.693950	−	0.431843i
$957$	5.79179	+	5.79179i	0.187222	+	0.187222i
$958$	−7.53968	−	2.15442i	−0.243596	−	0.0696060i
$959$	5.62092			0.181509
$960$		0			0
$961$	14.5965			0.470855
$962$	9.86338	+	2.81840i	0.318008	+	0.0908688i
$963$	−6.02809	−	6.02809i	−0.194252	−	0.194252i
$964$	12.7917	+	7.96024i	0.411993	+	0.256382i
$965$		0			0
$966$	10.8738	+	19.5742i	0.349860	+	0.629789i
$967$			8.72635i			0.280621i	0.990108	+	0.140310i	$0.0448100\pi$
$967$			8.72635i			0.280621i	−0.990108	+	0.140310i	$0.955190\pi$
$968$	22.3121	−	20.2024i	0.717138	−	0.649330i
$969$			23.7921i			0.764311i
$970$		0			0
$971$	−14.5421	+	14.5421i	−0.466677	+	0.466677i	−0.900836	−	0.434159i	$-0.857045\pi$
$971$	−14.5421	+	14.5421i	−0.466677	+	0.466677i	0.434159	+	0.900836i	$0.357045\pi$
$972$	3.81654	+	16.3927i	0.122416	+	0.525796i
$973$	19.3799	+	19.3799i	0.621289	+	0.621289i
$974$	−12.3225	+	43.1242i	−0.394837	+	1.38179i
$975$		0			0
$976$	2.61777	−	7.69502i	0.0837928	−	0.246312i
$977$	−25.2020			−0.806284			−0.403142	−	0.915137i	$-0.632082\pi$
$977$	−25.2020			−0.806284			−0.403142	+	0.915137i	$0.632082\pi$
$978$	−5.23114	+	18.3071i	−0.167273	+	0.585397i
$979$	4.46723	+	4.46723i	0.142773	+	0.142773i
$980$		0			0
$981$	−4.75212	+	4.75212i	−0.151724	+	0.151724i
$982$	−12.9276	+	7.18152i	−0.412535	+	0.229171i
$983$		−	4.00157i		−	0.127630i	−0.997962	−	0.0638151i	$-0.979673\pi$
$983$		−	4.00157i		−	0.127630i	0.997962	−	0.0638151i	$-0.0203268\pi$
$984$	32.0227	+	1.58906i	1.02085	+	0.0506573i
$985$		0			0
$986$	41.5938	+	74.8736i	1.32462	+	2.38446i
$987$	−10.3582	+	10.3582i	−0.329704	+	0.329704i
$988$	−6.89661	+	11.0825i	−0.219410	+	0.352581i
$989$	44.1346	+	44.1346i	1.40340	+	1.40340i
$990$		0			0
$991$	−62.3391			−1.98027			−0.990134	−	0.140127i	$-0.955249\pi$
$991$	−62.3391			−1.98027			−0.990134	+	0.140127i	$0.955249\pi$
$992$	6.80709	+	37.5866i	0.216125	+	1.19338i
$993$	−45.8201			−1.45406
$994$	8.32247	+	2.37809i	0.263973	+	0.0754285i
$995$		0			0
$996$	6.18565	−	9.94001i	0.196000	−	0.314961i
$997$	−21.6855	+	21.6855i	−0.686787	+	0.686787i	−0.961521	−	0.274733i	$-0.911410\pi$
$997$	−21.6855	+	21.6855i	−0.686787	+	0.686787i	0.274733	+	0.961521i	$0.411410\pi$
$998$	−13.6074	−	24.4949i	−0.430734	−	0.775371i
$999$			15.5861i			0.493121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.f.301.1	yes	12
4.3	odd	2		1600.2.l.g.401.5		12
5.2	odd	4		400.2.q.f.349.4		12
5.3	odd	4		400.2.q.e.349.3		12
5.4	even	2		400.2.l.g.301.6	yes	12
16.5	even	4	inner	400.2.l.f.101.1	✓	12
16.11	odd	4		1600.2.l.g.1201.5		12
20.3	even	4		1600.2.q.e.849.2		12
20.7	even	4		1600.2.q.f.849.5		12
20.19	odd	2		1600.2.l.f.401.2		12
80.27	even	4		1600.2.q.e.49.2		12
80.37	odd	4		400.2.q.e.149.3		12
80.43	even	4		1600.2.q.f.49.5		12
80.53	odd	4		400.2.q.f.149.4		12
80.59	odd	4		1600.2.l.f.1201.2		12
80.69	even	4		400.2.l.g.101.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.1	✓	12	16.5	even	4	inner
400.2.l.f.301.1	yes	12	1.1	even	1	trivial
400.2.l.g.101.6	yes	12	80.69	even	4
400.2.l.g.301.6	yes	12	5.4	even	2
400.2.q.e.149.3		12	80.37	odd	4
400.2.q.e.349.3		12	5.3	odd	4
400.2.q.f.149.4		12	80.53	odd	4
400.2.q.f.349.4		12	5.2	odd	4
1600.2.l.f.401.2		12	20.19	odd	2
1600.2.l.f.1201.2		12	80.59	odd	4
1600.2.l.g.401.5		12	4.3	odd	2
1600.2.l.g.1201.5		12	16.11	odd	4
1600.2.q.e.49.2		12	80.27	even	4
1600.2.q.e.849.2		12	20.3	even	4
1600.2.q.f.49.5		12	80.43	even	4
1600.2.q.f.849.5		12	20.7	even	4

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35979 - 0.388551i) q^{2} +(-1.03997 - 1.03997i) q^{3} +(1.69806 + 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} +1.49668i q^{7} +(-1.89842 - 2.09667i) q^{8} -0.836925i q^{9} +O(q^{10})\)	\(q+(-1.35979 - 0.388551i) q^{2} +(-1.03997 - 1.03997i) q^{3} +(1.69806 + 1.05670i) q^{4} +(1.01006 + 1.81822i) q^{6} +1.49668i q^{7} +(-1.89842 - 2.09667i) q^{8} -0.836925i q^{9} +(0.423260 - 0.423260i) q^{11} +(-0.666995 - 2.86486i) q^{12} +(-1.85704 - 1.85704i) q^{13} +(0.581538 - 2.03517i) q^{14} +(1.76679 + 3.58866i) q^{16} +6.50950 q^{17} +(-0.325188 + 1.13804i) q^{18} +(-1.75725 - 1.75725i) q^{19} +(1.55650 - 1.55650i) q^{21} +(-0.740003 + 0.411086i) q^{22} -7.19295i q^{23} +(-0.206172 + 4.15477i) q^{24} +(1.80363 + 3.24674i) q^{26} +(-3.99029 + 3.99029i) q^{27} +(-1.58154 + 2.54145i) q^{28} +(-6.57892 - 6.57892i) q^{29} -6.75252 q^{31} +(-1.00808 - 5.56631i) q^{32} -0.880355 q^{33} +(-8.85156 - 2.52928i) q^{34} +(0.884375 - 1.42115i) q^{36} +(1.95300 - 1.95300i) q^{37} +(1.70671 + 3.07227i) q^{38} +3.86254i q^{39} -7.70745i q^{41} +(-2.72130 + 1.51174i) q^{42} +(-6.13581 + 6.13581i) q^{43} +(1.16598 - 0.271462i) q^{44} +(-2.79483 + 9.78090i) q^{46} -6.65476 q^{47} +(1.89469 - 5.56950i) q^{48} +4.75994 q^{49} +(-6.76969 - 6.76969i) q^{51} +(-1.19103 - 5.11569i) q^{52} +(5.29390 - 5.29390i) q^{53} +(6.97638 - 3.87552i) q^{54} +(3.13804 - 2.84133i) q^{56} +3.65497i q^{57} +(6.38970 + 11.5022i) q^{58} +(5.91841 - 5.91841i) q^{59} +(-1.43686 - 1.43686i) q^{61} +(9.18201 + 2.62370i) q^{62} +1.25261 q^{63} +(-0.792016 + 7.96070i) q^{64} +(1.19710 + 0.342063i) q^{66} +(-6.35614 - 6.35614i) q^{67} +(11.0535 + 6.87857i) q^{68} +(-7.48045 + 7.48045i) q^{69} +4.08932i q^{71} +(-1.75475 + 1.58883i) q^{72} +2.43800i q^{73} +(-3.41451 + 1.89683i) q^{74} +(-1.12703 - 4.84079i) q^{76} +(0.633485 + 0.633485i) q^{77} +(1.50079 - 5.25224i) q^{78} +11.6722 q^{79} +5.78878 q^{81} +(-2.99474 + 10.4805i) q^{82} +(2.81439 + 2.81439i) q^{83} +(4.28778 - 0.998279i) q^{84} +(10.7275 - 5.95933i) q^{86} +13.6838i q^{87} +(-1.69096 - 0.0839103i) q^{88} +10.5543i q^{89} +(2.77940 - 2.77940i) q^{91} +(7.60076 - 12.2140i) q^{92} +(7.02242 + 7.02242i) q^{93} +(9.04907 + 2.58572i) q^{94} +(-4.74042 + 6.83717i) q^{96} +18.1512 q^{97} +(-6.47252 - 1.84948i) q^{98} +(-0.354237 - 0.354237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8	\( 12 q - 4 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} + 8 q^{8} - 2 q^{11} - 8 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{16} + 8 q^{17} - 18 q^{18} - 14 q^{19} - 20 q^{21} - 2 q^{22} - 14 q^{24} - 16 q^{26} + 10 q^{27} - 26 q^{28} - 4 q^{31} + 16 q^{32} - 28 q^{33} - 6 q^{34} + 2 q^{36} - 8 q^{37} - 10 q^{38} - 10 q^{42} - 44 q^{44} - 10 q^{46} - 8 q^{47} + 28 q^{48} + 4 q^{49} + 10 q^{51} + 12 q^{52} + 16 q^{53} + 10 q^{54} + 6 q^{56} + 60 q^{58} + 20 q^{59} + 4 q^{61} + 18 q^{62} + 8 q^{63} + 38 q^{64} + 32 q^{66} - 50 q^{67} + 60 q^{68} + 14 q^{72} + 10 q^{74} + 60 q^{76} + 8 q^{77} - 4 q^{78} + 12 q^{79} - 8 q^{81} - 42 q^{82} + 2 q^{83} + 34 q^{84} + 6 q^{86} - 30 q^{88} + 2 q^{92} + 44 q^{93} + 32 q^{94} - 34 q^{96} - 64 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 + 8 * q^8 - 2 * q^11 - 8 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^16 + 8 * q^17 - 18 * q^18 - 14 * q^19 - 20 * q^21 - 2 * q^22 - 14 * q^24 - 16 * q^26 + 10 * q^27 - 26 * q^28 - 4 * q^31 + 16 * q^32 - 28 * q^33 - 6 * q^34 + 2 * q^36 - 8 * q^37 - 10 * q^38 - 10 * q^42 - 44 * q^44 - 10 * q^46 - 8 * q^47 + 28 * q^48 + 4 * q^49 + 10 * q^51 + 12 * q^52 + 16 * q^53 + 10 * q^54 + 6 * q^56 + 60 * q^58 + 20 * q^59 + 4 * q^61 + 18 * q^62 + 8 * q^63 + 38 * q^64 + 32 * q^66 - 50 * q^67 + 60 * q^68 + 14 * q^72 + 10 * q^74 + 60 * q^76 + 8 * q^77 - 4 * q^78 + 12 * q^79 - 8 * q^81 - 42 * q^82 + 2 * q^83 + 34 * q^84 + 6 * q^86 - 30 * q^88 + 2 * q^92 + 44 * q^93 + 32 * q^94 - 34 * q^96 - 64 * q^98 + 12 * q^99

Introduction

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