LMFDB - Embedded newform 400.2.l.g.301.6

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			301.6
Root			$1.35979 + 0.388551i$ of defining polynomial
Character	$\chi$	$=$	400.301
Dual form			400.2.l.g.101.6

$q$-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	0.940426	−	0.339999i	$-0.110427\pi$
$3$	1.03997	+	1.03997i	0.600427	+	0.600427i	−0.339999	+	0.940426i	$0.610427\pi$
$4$	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	$-0.908721\pi$
$7$		−	1.49668i		−	0.565693i	0.959165	−	0.282846i	$-0.0912786\pi$
$8$	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	0.916070	−	0.401019i	$-0.131344\pi$
$13$	1.85704	+	1.85704i	0.515051	+	0.515051i	−0.401019	+	0.916070i	$0.631344\pi$
$14$	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	$-0.789605\pi$
$17$	−6.50950			−1.57879			−0.789393	+	0.613888i	$0.789605\pi$
$18$	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	$0.269906\pi$
$23$			7.19295i			1.49983i	−0.661532	+	0.749917i	$0.730094\pi$
$24$	−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	−0.849178	−	0.528107i	$-0.822902\pi$
$37$	−1.95300	+	1.95300i	−0.321071	+	0.321071i	0.528107	+	0.849178i	$0.322902\pi$
$38$	−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	−0.0623522	−	0.998054i	$-0.519860\pi$
$43$	6.13581	−	6.13581i	0.935702	−	0.935702i	0.998054	+	0.0623522i	$0.0198602\pi$
$44$	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	$-0.338693\pi$
$47$	6.65476			0.970697			0.485348	+	0.874321i	$0.338693\pi$
$48$	−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	−0.970056	−	0.242882i	$-0.921907\pi$
$53$	−5.29390	+	5.29390i	−0.727173	+	0.727173i	0.242882	+	0.970056i	$0.421907\pi$
$54$	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	0.979238	−	0.202712i	$-0.0649756\pi$
$67$	6.35614	+	6.35614i	0.776526	+	0.776526i	−0.202712	+	0.979238i	$0.564976\pi$
$68$	−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	$-0.954430\pi$
$73$		−	2.43800i		−	0.285346i	0.989770	−	0.142673i	$-0.0455698\pi$
$74$	−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	0.535571	−	0.844490i	$-0.320096\pi$
$83$	−2.81439	−	2.81439i	−0.308919	−	0.308919i	−0.844490	+	0.535571i	$0.820096\pi$
$84$	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	$-0.873025\pi$
$97$	−18.1512			−1.84298			−0.921488	+	0.388407i	$0.873025\pi$
$98$	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	$0.0149860\pi$
$103$			0.955267i			0.0941253i	−0.998892	+	0.0470626i	$0.985014\pi$
$104$	−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	−0.963612	−	0.267305i	$-0.913867\pi$
$107$	−7.20266	+	7.20266i	−0.696308	+	0.696308i	0.267305	+	0.963612i	$0.413867\pi$
$108$	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	$-0.529199\pi$
$113$	−1.94751			−0.183206			−0.0916029	+	0.995796i	$0.529199\pi$
$114$	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	$-0.481376\pi$
$127$	1.31796			0.116950			0.0584750	+	0.998289i	$0.481376\pi$
$128$	−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	$0.0512884\pi$
$137$			3.75559i			0.320862i	−0.987047	+	0.160431i	$0.948712\pi$
$138$	−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	0.889470	−	0.456994i	$-0.151074\pi$
$157$	5.41891	+	5.41891i	0.432476	+	0.432476i	−0.456994	+	0.889470i	$0.651074\pi$
$158$	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	0.406608	−	0.913603i	$-0.366711\pi$
$163$	−6.47288	−	6.47288i	−0.506995	−	0.506995i	−0.913603	+	0.406608i	$0.866711\pi$
$164$	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	$0.104030\pi$
$167$			8.29734i			0.642068i	−0.947068	+	0.321034i	$0.895970\pi$
$168$	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	0.0881700	−	0.996105i	$-0.471898\pi$
$173$	−11.9420	−	11.9420i	−0.907935	−	0.907935i	−0.996105	+	0.0881700i	$0.971898\pi$
$174$	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	$-0.148512\pi$
$193$	24.8152			1.78624			0.893119	+	0.449820i	$0.148512\pi$
$194$	−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	−0.599751	−	0.800186i	$-0.704734\pi$
$197$	2.81324	−	2.81324i	0.200435	−	0.200435i	0.800186	+	0.599751i	$0.204734\pi$
$198$	−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	$-0.414924\pi$
$223$	7.88779			0.528205			0.264103	+	0.964495i	$0.414924\pi$
$224$	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	0.877337	−	0.479874i	$-0.159318\pi$
$227$	5.98838	+	5.98838i	0.397463	+	0.397463i	−0.479874	+	0.877337i	$0.659318\pi$
$228$	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	$0.0280543\pi$
$233$			2.68717i			0.176042i	−0.996119	+	0.0880212i	$0.971946\pi$
$234$	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	$-0.544987\pi$
$257$	−4.51630			−0.281719			−0.140860	+	0.990030i	$0.544987\pi$
$258$	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	$0.214162\pi$
$263$			20.2127i			1.24637i	−0.782075	+	0.623185i	$0.785838\pi$
$264$	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	−0.0374115	−	0.999300i	$-0.511911\pi$
$277$	16.0090	−	16.0090i	0.961888	−	0.961888i	0.999300	+	0.0374115i	$0.0119112\pi$
$278$	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	−0.773949	−	0.633249i	$-0.781721\pi$
$283$	−2.36694	+	2.36694i	−0.140700	+	0.140700i	0.633249	+	0.773949i	$0.281721\pi$
$284$	−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	$-0.458848\pi$
$293$	19.1812	−	19.1812i	1.12058	−	1.12058i	0.991655	−	0.128922i	$-0.0411517\pi$
$294$	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	$-0.952553\pi$
$307$	−19.9292	−	19.9292i	−1.13742	−	1.13742i	−0.148507	−	0.988911i	$-0.547447\pi$
$308$	−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	$0.00191274\pi$
$313$			0.212621i			0.0120180i	−0.999982	+	0.00600902i	$0.998087\pi$
$314$	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	0.791625	−	0.611007i	$-0.209235\pi$
$317$	3.21582	+	3.21582i	0.180618	+	0.180618i	−0.611007	+	0.791625i	$0.709235\pi$
$318$	−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	$-0.401215\pi$
$337$	11.2122			0.610767			0.305384	+	0.952229i	$0.401215\pi$
$338$	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	−0.739518	−	0.673137i	$-0.764946\pi$
$347$	−1.23653	+	1.23653i	−0.0663803	+	0.0663803i	0.673137	+	0.739518i	$0.264946\pi$
$348$	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	$-0.506343\pi$
$353$	−0.748709			−0.0398497			−0.0199249	+	0.999801i	$0.506343\pi$
$354$	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	$-0.680790\pi$
$367$	−20.6101			−1.07584			−0.537920	+	0.842996i	$0.680790\pi$
$368$	−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	−0.829660	−	0.558269i	$-0.811466\pi$
$373$	−5.24143	+	5.24143i	−0.271391	+	0.271391i	0.558269	+	0.829660i	$0.311466\pi$
$374$	−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	$-0.771836\pi$
$383$	−29.5087			−1.50782			−0.753912	+	0.656975i	$0.771836\pi$
$384$	−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	$-0.965289\pi$
$397$	−21.9750	−	21.9750i	−1.10289	−	1.10289i	−0.108832	−	0.994060i	$-0.534711\pi$
$398$	−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	$-0.594467\pi$
$433$	−12.1705			−0.584877			−0.292439	+	0.956284i	$0.594467\pi$
$434$	−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	−0.615778	−	0.787920i	$-0.711158\pi$
$443$	3.62318	−	3.62318i	0.172142	−	0.172142i	0.787920	+	0.615778i	$0.211158\pi$
$444$	−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	$0.108586\pi$
$457$			14.3039i			0.669108i	−0.942377	+	0.334554i	$0.891414\pi$
$458$	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	$-0.351554\pi$
$463$	19.3500			0.899271			0.449636	+	0.893212i	$0.351554\pi$
$464$	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	0.187410	−	0.982282i	$-0.439991\pi$
$467$	−17.1773	−	17.1773i	−0.794871	−	0.794871i	−0.982282	+	0.187410i	$0.939991\pi$
$468$	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	$0.255192\pi$
$487$			31.7138i			1.43709i	−0.695480	+	0.718546i	$0.744808\pi$
$488$	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	$0.0602377\pi$
$503$			8.43795i			0.376230i	−0.982147	+	0.188115i	$0.939762\pi$
$504$	−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	−0.448220	−	0.893923i	$-0.647942\pi$
$523$	10.1929	−	10.1929i	0.445703	−	0.445703i	0.893923	+	0.448220i	$0.147942\pi$
$524$	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	0.993716	−	0.111935i	$-0.0357048\pi$
$547$	20.6231	+	20.6231i	0.881781	+	0.881781i	−0.111935	+	0.993716i	$0.535705\pi$
$548$	−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	0.679356	−	0.733809i	$-0.262259\pi$
$557$	−1.28512	−	1.28512i	−0.0544523	−	0.0544523i	−0.733809	+	0.679356i	$0.762259\pi$
$558$	−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	0.997283	−	0.0736677i	$-0.0234704\pi$
$563$	21.9152	+	21.9152i	0.923615	+	0.923615i	−0.0736677	+	0.997283i	$0.523470\pi$
$564$	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	$-0.516153\pi$
$577$	−2.43681			−0.101446			−0.0507230	+	0.998713i	$0.516153\pi$
$578$	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	−0.698470	−	0.715639i	$-0.746135\pi$
$587$	0.415982	−	0.415982i	0.0171694	−	0.0171694i	0.715639	+	0.698470i	$0.246135\pi$
$588$	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	$-0.602021\pi$
$593$	−15.3439			−0.630098			−0.315049	+	0.949075i	$0.602021\pi$
$594$	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	$-0.750588\pi$
$607$	−34.9068			−1.41682			−0.708412	+	0.705800i	$0.750588\pi$
$608$	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	−0.710165	−	0.704035i	$-0.751380\pi$
$613$	−0.151779	+	0.151779i	−0.00613031	+	0.00613031i	0.704035	+	0.710165i	$0.251380\pi$
$614$	−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	$-0.998153\pi$
$617$		−	0.288199i		−	0.0116025i	0.999983	−	0.00580123i	$-0.00184660\pi$
$618$	−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	0.583422	−	0.812169i	$-0.301713\pi$
$643$	−5.80043	−	5.80043i	−0.228747	−	0.228747i	−0.812169	+	0.583422i	$0.801713\pi$
$644$	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	$0.364292\pi$
$647$			46.3186i			1.82097i	−0.413541	+	0.910485i	$0.635708\pi$
$648$	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	0.615236	−	0.788343i	$-0.289061\pi$
$653$	−4.42354	−	4.42354i	−0.173106	−	0.173106i	−0.788343	+	0.615236i	$0.789061\pi$
$654$	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	$-0.616436\pi$
$673$	−18.5586			−0.715382			−0.357691	+	0.933840i	$0.616436\pi$
$674$	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	−0.757414	−	0.652935i	$-0.773537\pi$
$677$	−2.71844	+	2.71844i	−0.104478	+	0.104478i	0.652935	+	0.757414i	$0.273537\pi$
$678$	−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	−0.906596	−	0.421999i	$-0.861329\pi$
$683$	−12.6646	+	12.6646i	−0.484598	+	0.484598i	0.421999	+	0.906596i	$0.361329\pi$
$684$	−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	$-0.975570\pi$
$727$		−	4.13463i		−	0.153345i	0.997056	−	0.0766724i	$-0.0244296\pi$
$728$	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	0.251817	−	0.967775i	$-0.418972\pi$
$733$	−19.3838	−	19.3838i	−0.715957	−	0.715957i	−0.967775	+	0.251817i	$0.918972\pi$
$734$	−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	$-0.939215\pi$
$743$		−	10.3473i		−	0.379604i	0.981822	−	0.189802i	$-0.0607846\pi$
$744$	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	$0.535836\pi$
$757$	−30.4305	+	30.4305i	−1.10601	+	1.10601i	−0.993669	+	0.112345i	$0.964164\pi$
$758$	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	−0.115527	−	0.993304i	$-0.536856\pi$
$773$	24.4047	−	24.4047i	0.877778	−	0.877778i	0.993304	+	0.115527i	$0.0368556\pi$
$774$	−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	0.330320	−	0.943869i	$-0.392843\pi$
$787$	−17.2122	−	17.2122i	−0.613549	−	0.613549i	−0.943869	+	0.330320i	$0.892843\pi$
$788$	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	0.248731	−	0.968573i	$-0.419986\pi$
$797$	−20.3220	−	20.3220i	−0.719841	−	0.719841i	−0.968573	+	0.248731i	$0.919986\pi$
$798$	−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	$-0.796685\pi$
$823$		−	34.2064i		−	1.19236i	0.802851	−	0.596179i	$-0.203315\pi$
$824$	−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	$-0.469888\pi$
$827$	31.3455	−	31.3455i	1.08999	−	1.08999i	0.995529	−	0.0944595i	$-0.0301123\pi$
$828$	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	−0.674267	−	0.738488i	$-0.735540\pi$
$853$	1.87566	−	1.87566i	0.0642212	−	0.0642212i	0.738488	+	0.674267i	$0.235540\pi$
$854$	−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	$-0.870481\pi$
$857$		−	23.1714i		−	0.791521i	0.918354	−	0.395760i	$-0.129519\pi$
$858$	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	$-0.358432\pi$
$863$	25.2777			0.860463			0.430231	+	0.902719i	$0.358432\pi$
$864$	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	0.365651	−	0.930752i	$-0.380846\pi$
$877$	−16.7350	−	16.7350i	−0.565101	−	0.565101i	−0.930752	+	0.365651i	$0.880846\pi$
$878$	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	0.244198	−	0.969725i	$-0.421475\pi$
$883$	−21.5593	−	21.5593i	−0.725527	−	0.725527i	−0.969725	+	0.244198i	$0.921475\pi$
$884$	−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	$-0.699836\pi$
$887$		−	48.2072i		−	1.61864i	0.587368	−	0.809320i	$-0.300164\pi$
$888$	−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	$0.518761\pi$
$907$	−31.8381	+	31.8381i	−1.05717	+	1.05717i	−0.998264	+	0.0589044i	$0.981239\pi$
$908$	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	$0.100466\pi$
$937$			19.0036i			0.620819i	−0.950603	+	0.310410i	$0.899534\pi$
$938$	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	0.639552	−	0.768748i	$-0.279120\pi$
$947$	−3.97577	−	3.97577i	−0.129195	−	0.129195i	−0.768748	+	0.639552i	$0.779120\pi$
$948$	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	$-0.913368\pi$
$953$		−	16.5970i		−	0.537628i	0.963192	−	0.268814i	$-0.0866317\pi$
$954$	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	$-0.955190\pi$
$967$		−	8.72635i		−	0.280621i	0.990108	−	0.140310i	$-0.0448100\pi$
$968$	−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	$-0.367918\pi$
$977$	25.2020			0.806284			0.403142	+	0.915137i	$0.367918\pi$
$978$	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	$0.0203268\pi$
$983$			4.00157i			0.127630i	−0.997962	+	0.0638151i	$0.979673\pi$
$984$	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	−0.274733	−	0.961521i	$-0.588590\pi$
$997$	21.6855	−	21.6855i	0.686787	−	0.686787i	0.961521	+	0.274733i	$0.0885895\pi$
$998$	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.g.301.6	yes	12
4.3	odd	2		1600.2.l.f.401.2		12
5.2	odd	4		400.2.q.e.349.3		12
5.3	odd	4		400.2.q.f.349.4		12
5.4	even	2		400.2.l.f.301.1	yes	12
16.5	even	4	inner	400.2.l.g.101.6	yes	12
16.11	odd	4		1600.2.l.f.1201.2		12
20.3	even	4		1600.2.q.f.849.5		12
20.7	even	4		1600.2.q.e.849.2		12
20.19	odd	2		1600.2.l.g.401.5		12
80.27	even	4		1600.2.q.f.49.5		12
80.37	odd	4		400.2.q.f.149.4		12
80.43	even	4		1600.2.q.e.49.2		12
80.53	odd	4		400.2.q.e.149.3		12
80.59	odd	4		1600.2.l.g.1201.5		12
80.69	even	4		400.2.l.f.101.1	✓	12

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

L-functions

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Database

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