LMFDB - Embedded newform 400.2.l.g.101.1

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			101.1
Root			$-1.41313 - 0.0554252i$ of defining polynomial
Character	$\chi$	$=$	400.101
Dual form			400.2.l.g.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41313 - 0.0554252i) q^{2} +(0.488516 - 0.488516i) q^{3} +(1.99386 + 0.156646i) q^{4} +(-0.717411 + 0.663259i) q^{6} -4.71540i q^{7} +(-2.80889 - 0.331870i) q^{8} +2.52270i q^{9} +O(q^{10})$	\(q+(-1.41313 - 0.0554252i) q^{2} +(0.488516 - 0.488516i) q^{3} +(1.99386 + 0.156646i) q^{4} +(-0.717411 + 0.663259i) q^{6} -4.71540i q^{7} +(-2.80889 - 0.331870i) q^{8} +2.52270i q^{9} +(-3.91360 - 3.91360i) q^{11} +(1.05055 - 0.897506i) q^{12} +(0.0878822 - 0.0878822i) q^{13} +(-0.261352 + 6.66346i) q^{14} +(3.95092 + 0.624658i) q^{16} -4.67442 q^{17} +(0.139821 - 3.56490i) q^{18} +(1.81249 - 1.81249i) q^{19} +(-2.30355 - 2.30355i) q^{21} +(5.31350 + 5.74732i) q^{22} +1.63007i q^{23} +(-1.53431 + 1.21006i) q^{24} +(-0.129060 + 0.119318i) q^{26} +(2.69793 + 2.69793i) q^{27} +(0.738648 - 9.40184i) q^{28} +(3.26362 - 3.26362i) q^{29} -2.12875 q^{31} +(-5.54854 - 1.10170i) q^{32} -3.82371 q^{33} +(6.60555 + 0.259081i) q^{34} +(-0.395171 + 5.02991i) q^{36} +(-3.97797 - 3.97797i) q^{37} +(-2.66173 + 2.46082i) q^{38} -0.0858637i q^{39} -8.25504i q^{41} +(3.12753 + 3.38288i) q^{42} +(-2.27336 - 2.27336i) q^{43} +(-7.19010 - 8.41620i) q^{44} +(0.0903468 - 2.30349i) q^{46} +4.06129 q^{47} +(2.23524 - 1.62493i) q^{48} -15.2350 q^{49} +(-2.28353 + 2.28353i) q^{51} +(0.188991 - 0.161458i) q^{52} +(5.03938 + 5.03938i) q^{53} +(-3.66298 - 3.96205i) q^{54} +(-1.56490 + 13.2450i) q^{56} -1.77086i q^{57} +(-4.79280 + 4.43103i) q^{58} +(-5.16453 - 5.16453i) q^{59} +(7.12726 - 7.12726i) q^{61} +(3.00819 + 0.117986i) q^{62} +11.8956 q^{63} +(7.77972 + 1.86437i) q^{64} +(5.40339 + 0.211930i) q^{66} +(7.49920 - 7.49920i) q^{67} +(-9.32012 - 0.732228i) q^{68} +(0.796314 + 0.796314i) q^{69} +4.54072i q^{71} +(0.837210 - 7.08600i) q^{72} +8.30557i q^{73} +(5.40090 + 5.84186i) q^{74} +(3.89776 - 3.32992i) q^{76} +(-18.4542 + 18.4542i) q^{77} +(-0.00475901 + 0.121336i) q^{78} +11.5317 q^{79} -4.93215 q^{81} +(-0.457537 + 11.6654i) q^{82} +(1.16919 - 1.16919i) q^{83} +(-4.23211 - 4.95379i) q^{84} +(3.08655 + 3.33855i) q^{86} -3.18866i q^{87} +(9.69406 + 12.2917i) q^{88} +3.24572i q^{89} +(-0.414400 - 0.414400i) q^{91} +(-0.255343 + 3.25012i) q^{92} +(-1.03993 + 1.03993i) q^{93} +(-5.73912 - 0.225098i) q^{94} +(-3.24875 + 2.17235i) q^{96} +13.9581 q^{97} +(21.5290 + 0.844405i) q^{98} +(9.87285 - 9.87285i) 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41313	−	0.0554252i	−0.999232	−	0.0391915i
$2$	−1.41313	−	0.0554252i	−0.999232	−	0.0391915i
$3$	0.488516	−	0.488516i	0.282045	−	0.282045i	−0.551879	−	0.833924i	$-0.686089\pi$
$3$	0.488516	−	0.488516i	0.282045	−	0.282045i	0.833924	+	0.551879i	$0.186089\pi$
$4$	1.99386	+	0.156646i	0.996928	+	0.0783229i
$5$		0			0
$5$		0			0
$6$	−0.717411	+	0.663259i	−0.292882	+	0.270774i
$7$		−	4.71540i		−	1.78226i	−0.453753	−	0.891128i	$-0.649915\pi$
$7$		−	4.71540i		−	1.78226i	0.453753	−	0.891128i	$-0.350085\pi$
$8$	−2.80889	−	0.331870i	−0.993093	−	0.117334i
$9$			2.52270i			0.840901i
$10$		0			0
$11$	−3.91360	−	3.91360i	−1.17999	−	1.17999i	−0.979745	−	0.200249i	$-0.935825\pi$
$11$	−3.91360	−	3.91360i	−1.17999	−	1.17999i	−0.200249	−	0.979745i	$-0.564175\pi$
$12$	1.05055	−	0.897506i	0.303269	−	0.259088i
$13$	0.0878822	−	0.0878822i	0.0243741	−	0.0243741i	−0.694815	−	0.719189i	$-0.744514\pi$
$13$	0.0878822	−	0.0878822i	0.0243741	−	0.0243741i	0.719189	+	0.694815i	$0.244514\pi$
$14$	−0.261352	+	6.66346i	−0.0698493	+	1.78089i
$15$		0			0
$16$	3.95092	+	0.624658i	0.987731	+	0.156165i
$17$	−4.67442			−1.13371			−0.566857	−	0.823816i	$-0.691841\pi$
$17$	−4.67442			−1.13371			−0.566857	+	0.823816i	$0.691841\pi$
$18$	0.139821	−	3.56490i	0.0329562	−	0.840255i
$19$	1.81249	−	1.81249i	0.415813	−	0.415813i	−0.467945	−	0.883758i	$-0.655005\pi$
$19$	1.81249	−	1.81249i	0.415813	−	0.415813i	0.883758	+	0.467945i	$0.155005\pi$
$20$		0			0
$21$	−2.30355	−	2.30355i	−0.502676	−	0.502676i
$22$	5.31350	+	5.74732i	1.13284	+	1.22533i
$23$			1.63007i			0.339893i	0.985453	+	0.169946i	$0.0543594\pi$
$23$			1.63007i			0.339893i	−0.985453	+	0.169946i	$0.945641\pi$
$24$	−1.53431	+	1.21006i	−0.313190	+	0.247003i
$25$		0			0
$26$	−0.129060	+	0.119318i	−0.0253107	+	0.0234002i
$27$	2.69793	+	2.69793i	0.519217	+	0.519217i
$28$	0.738648	−	9.40184i	0.139591	−	1.77678i
$29$	3.26362	−	3.26362i	0.606039	−	0.606039i	−0.335869	−	0.941909i	$-0.609030\pi$
$29$	3.26362	−	3.26362i	0.606039	−	0.606039i	0.941909	+	0.335869i	$0.109030\pi$
$30$		0			0
$31$	−2.12875			−0.382334			−0.191167	−	0.981557i	$-0.561227\pi$
$31$	−2.12875			−0.382334			−0.191167	+	0.981557i	$0.561227\pi$
$32$	−5.54854	−	1.10170i	−0.980852	−	0.194755i
$33$	−3.82371			−0.665622
$34$	6.60555	+	0.259081i	1.13284	+	0.0444320i
$35$		0			0
$36$	−0.395171	+	5.02991i	−0.0658618	+	0.838318i
$37$	−3.97797	−	3.97797i	−0.653974	−	0.653974i	0.299973	−	0.953948i	$-0.403022\pi$
$37$	−3.97797	−	3.97797i	−0.653974	−	0.653974i	−0.953948	+	0.299973i	$0.903022\pi$
$38$	−2.66173	+	2.46082i	−0.431790	+	0.399197i
$39$		−	0.0858637i		−	0.0137492i
$40$		0			0
$41$		−	8.25504i		−	1.28922i	−0.764511	−	0.644611i	$-0.777020\pi$
$41$		−	8.25504i		−	1.28922i	0.764511	−	0.644611i	$-0.222980\pi$
$42$	3.12753	+	3.38288i	0.482589	+	0.521990i
$43$	−2.27336	−	2.27336i	−0.346685	−	0.346685i	0.512188	−	0.858873i	$-0.328835\pi$
$43$	−2.27336	−	2.27336i	−0.346685	−	0.346685i	−0.858873	+	0.512188i	$0.828835\pi$
$44$	−7.19010	−	8.41620i	−1.08395	−	1.26879i
$45$		0			0
$46$	0.0903468	−	2.30349i	0.0133209	−	0.339631i
$47$	4.06129			0.592400			0.296200	−	0.955126i	$-0.404281\pi$
$47$	4.06129			0.592400			0.296200	+	0.955126i	$0.404281\pi$
$48$	2.23524	−	1.62493i	0.322630	−	0.234539i
$49$	−15.2350			−2.17643
$50$		0			0
$51$	−2.28353	+	2.28353i	−0.319758	+	0.319758i
$52$	0.188991	−	0.161458i	0.0262083	−	0.0223902i
$53$	5.03938	+	5.03938i	0.692211	+	0.692211i	0.962718	−	0.270507i	$-0.0871912\pi$
$53$	5.03938	+	5.03938i	0.692211	+	0.692211i	−0.270507	+	0.962718i	$0.587191\pi$
$54$	−3.66298	−	3.96205i	−0.498469	−	0.539167i
$55$		0			0
$56$	−1.56490	+	13.2450i	−0.209119	+	1.76994i
$57$		−	1.77086i		−	0.234556i
$58$	−4.79280	+	4.43103i	−0.629325	+	0.581822i
$59$	−5.16453	−	5.16453i	−0.672365	−	0.672365i	0.285896	−	0.958261i	$-0.407709\pi$
$59$	−5.16453	−	5.16453i	−0.672365	−	0.672365i	−0.958261	+	0.285896i	$0.907709\pi$
$60$		0			0
$61$	7.12726	−	7.12726i	0.912552	−	0.912552i	−0.0839206	−	0.996472i	$-0.526744\pi$
$61$	7.12726	−	7.12726i	0.912552	−	0.912552i	0.996472	+	0.0839206i	$0.0267442\pi$
$62$	3.00819	+	0.117986i	0.382041	+	0.0149843i
$63$	11.8956			1.49870
$64$	7.77972	+	1.86437i	0.972466	+	0.233047i
$65$		0			0
$66$	5.40339	+	0.211930i	0.665111	+	0.0260868i
$67$	7.49920	−	7.49920i	0.916173	−	0.916173i	−0.0805758	−	0.996748i	$-0.525676\pi$
$67$	7.49920	−	7.49920i	0.916173	−	0.916173i	0.996748	+	0.0805758i	$0.0256759\pi$
$68$	−9.32012	−	0.732228i	−1.13023	−	0.0887957i
$69$	0.796314	+	0.796314i	0.0958649	+	0.0958649i
$70$		0			0
$71$			4.54072i			0.538884i	0.963017	+	0.269442i	$0.0868393\pi$
$71$			4.54072i			0.538884i	−0.963017	+	0.269442i	$0.913161\pi$
$72$	0.837210	−	7.08600i	0.0986662	−	0.835093i
$73$			8.30557i			0.972093i	0.873933	+	0.486047i	$0.161561\pi$
$73$			8.30557i			0.972093i	−0.873933	+	0.486047i	$0.838439\pi$
$74$	5.40090	+	5.84186i	0.627842	+	0.679102i
$75$		0			0
$76$	3.89776	−	3.32992i	0.447104	−	0.381968i
$77$	−18.4542	+	18.4542i	−2.10305	+	2.10305i
$78$	−0.00475901	+	0.121336i	−0.000538852	+	0.0137386i
$79$	11.5317			1.29742			0.648709	−	0.761037i	$-0.275309\pi$
$79$	11.5317			1.29742			0.648709	+	0.761037i	$0.275309\pi$
$80$		0			0
$81$	−4.93215			−0.548017
$82$	−0.457537	+	11.6654i	−0.0505266	+	1.28823i
$83$	1.16919	−	1.16919i	0.128335	−	0.128335i	−0.640022	−	0.768357i	$-0.721075\pi$
$83$	1.16919	−	1.16919i	0.128335	−	0.128335i	0.768357	+	0.640022i	$0.221075\pi$
$84$	−4.23211	−	4.95379i	−0.461761	−	0.540503i
$85$		0			0
$86$	3.08655	+	3.33855i	0.332831	+	0.360006i
$87$		−	3.18866i		−	0.341861i
$88$	9.69406	+	12.2917i	1.03339	+	1.31030i
$89$			3.24572i			0.344046i	0.985093	+	0.172023i	$0.0550304\pi$
$89$			3.24572i			0.344046i	−0.985093	+	0.172023i	$0.944970\pi$
$90$		0			0
$91$	−0.414400	−	0.414400i	−0.0434409	−	0.0434409i
$92$	−0.255343	+	3.25012i	−0.0266214	+	0.338848i
$93$	−1.03993	+	1.03993i	−0.107835	+	0.107835i
$94$	−5.73912	−	0.225098i	−0.591945	−	0.0232171i
$95$		0			0
$96$	−3.24875	+	2.17235i	−0.331574	+	0.221714i
$97$	13.9581			1.41723			0.708613	−	0.705598i	$-0.249321\pi$
$97$	13.9581			1.41723			0.708613	+	0.705598i	$0.249321\pi$
$98$	21.5290	+	0.844405i	2.17476	+	0.0852978i
$99$	9.87285	−	9.87285i	0.992258	−	0.992258i
$100$		0			0
$101$	13.4088	+	13.4088i	1.33422	+	1.33422i	0.901552	+	0.432672i	$0.142429\pi$
$101$	13.4088	+	13.4088i	1.33422	+	1.33422i	0.432672	+	0.901552i	$0.357571\pi$
$102$	3.35348	−	3.10035i	0.332044	−	0.306981i
$103$			13.7638i			1.35618i	0.734977	+	0.678092i	$0.237193\pi$
$103$			13.7638i			1.35618i	−0.734977	+	0.678092i	$0.762807\pi$
$104$	−0.276017	+	0.217686i	−0.0270657	+	0.0213459i
$105$		0			0
$106$	−6.84197	−	7.40059i	−0.664551	−	0.718808i
$107$	0.327996	+	0.327996i	0.0317086	+	0.0317086i	0.722783	−	0.691075i	$-0.242862\pi$
$107$	0.327996	+	0.327996i	0.0317086	+	0.0317086i	−0.691075	+	0.722783i	$0.742862\pi$
$108$	4.95666	+	5.80190i	0.476955	+	0.558288i
$109$	−0.149698	+	0.149698i	−0.0143385	+	0.0143385i	−0.714240	−	0.699901i	$-0.753227\pi$
$109$	−0.149698	+	0.149698i	−0.0143385	+	0.0143385i	0.699901	+	0.714240i	$0.253227\pi$
$110$		0			0
$111$	−3.88660			−0.368900
$112$	2.94551	−	18.6302i	0.278325	−	1.76039i
$113$	−5.97999			−0.562550			−0.281275	−	0.959627i	$-0.590757\pi$
$113$	−5.97999			−0.562550			−0.281275	+	0.959627i	$0.590757\pi$
$114$	−0.0981502	+	2.50245i	−0.00919261	+	0.234376i
$115$		0			0
$116$	7.01843	−	5.99596i	0.651644	−	0.556711i
$117$	0.221701	+	0.221701i	0.0204962	+	0.0204962i
$118$	7.01189	+	7.58439i	0.645497	+	0.698199i
$119$			22.0418i			2.02057i
$120$		0			0
$121$			19.6325i			1.78477i
$122$	−10.4668	+	9.67669i	−0.947615	+	0.876086i
$123$	−4.03272	−	4.03272i	−0.363618	−	0.363618i
$124$	−4.24442	−	0.333459i	−0.381160	−	0.0299455i
$125$		0			0
$126$	−16.8100	−	0.659314i	−1.49755	−	0.0587364i
$127$	2.73076			0.242315			0.121158	−	0.992633i	$-0.461339\pi$
$127$	2.73076			0.242315			0.121158	+	0.992633i	$0.461339\pi$
$128$	−10.8904	−	3.06579i	−0.962585	−	0.270980i
$129$	−2.22115			−0.195561
$130$		0			0
$131$	−0.813555	+	0.813555i	−0.0710806	+	0.0710806i	−0.741753	−	0.670673i	$-0.766006\pi$
$131$	−0.813555	+	0.813555i	−0.0710806	+	0.0710806i	0.670673	+	0.741753i	$0.266006\pi$
$132$	−7.62392	−	0.598967i	−0.663577	−	0.0521334i
$133$	−8.54661	−	8.54661i	−0.741085	−	0.741085i
$134$	−11.0130	+	10.1817i	−0.951375	+	0.879563i
$135$		0			0
$136$	13.1299	+	1.55130i	1.12588	+	0.133023i
$137$		−	0.199812i		−	0.0170711i	−0.999964	−	0.00853557i	$-0.997283\pi$
$137$		−	0.199812i		−	0.0170711i	0.999964	−	0.00853557i	$-0.00271699\pi$
$138$	−1.08116	−	1.16943i	−0.0920342	−	0.0995484i
$139$	−11.6301	−	11.6301i	−0.986448	−	0.986448i	0.0134610	−	0.999909i	$-0.495715\pi$
$139$	−11.6301	−	11.6301i	−0.986448	−	0.986448i	−0.999909	+	0.0134610i	$0.995715\pi$
$140$		0			0
$141$	1.98400	−	1.98400i	0.167083	−	0.167083i
$142$	0.251670	−	6.41661i	0.0211197	−	0.538470i
$143$	−0.687871			−0.0575227
$144$	−1.57583	+	9.96701i	−0.131319	+	0.830585i
$145$		0			0
$146$	0.460338	−	11.7368i	0.0380978	−	0.971346i
$147$	−7.44256	+	7.44256i	−0.613852	+	0.613852i
$148$	−7.30837	−	8.55463i	−0.600744	−	0.703186i
$149$	−1.13384	−	1.13384i	−0.0928880	−	0.0928880i	0.659136	−	0.752024i	$-0.270922\pi$
$149$	−1.13384	−	1.13384i	−0.0928880	−	0.0928880i	−0.752024	+	0.659136i	$0.770922\pi$
$150$		0			0
$151$			7.12216i			0.579593i	0.957088	+	0.289797i	$0.0935877\pi$
$151$			7.12216i			0.579593i	−0.957088	+	0.289797i	$0.906412\pi$
$152$	−5.69259	+	4.48957i	−0.461730	+	0.364152i
$153$		−	11.7922i		−	0.953341i
$154$	27.1009	−	25.0553i	2.18386	−	2.01901i
$155$		0			0
$156$	0.0134502	−	0.171200i	0.00107688	−	0.0137070i
$157$	5.32145	−	5.32145i	0.424698	−	0.424698i	−0.462120	−	0.886818i	$-0.652911\pi$
$157$	5.32145	−	5.32145i	0.424698	−	0.424698i	0.886818	+	0.462120i	$0.152911\pi$
$158$	−16.2957	−	0.639147i	−1.29642	−	0.0508478i
$159$	4.92363			0.390469
$160$		0			0
$161$	7.68643			0.605775
$162$	6.96976	+	0.273365i	0.547596	+	0.0214776i
$163$	12.3010	−	12.3010i	0.963488	−	0.963488i	−0.0358685	−	0.999357i	$-0.511420\pi$
$163$	12.3010	−	12.3010i	0.963488	−	0.963488i	0.999357	+	0.0358685i	$0.0114197\pi$
$164$	1.29312	−	16.4594i	0.100975	−	1.28526i
$165$		0			0
$166$	−1.71702	+	1.58741i	−0.133266	+	0.123207i
$167$		−	9.86820i		−	0.763624i	−0.924240	−	0.381812i	$-0.875300\pi$
$167$		−	9.86820i		−	0.763624i	0.924240	−	0.381812i	$-0.124700\pi$
$168$	5.70594	+	7.23490i	0.440223	+	0.558184i
$169$			12.9846i			0.998812i
$170$		0			0
$171$	4.57237	+	4.57237i	0.349658	+	0.349658i
$172$	−4.17665	−	4.88887i	−0.318466	−	0.372773i
$173$	13.4089	−	13.4089i	1.01946	−	1.01946i	0.0196525	−	0.999807i	$-0.493744\pi$
$173$	13.4089	−	13.4089i	1.01946	−	1.01946i	0.999807	−	0.0196525i	$-0.00625599\pi$
$174$	−0.176732	+	4.50599i	−0.0133980	+	0.341598i
$175$		0			0
$176$	−13.0177	−	17.9070i	−0.981243	−	1.34979i
$177$	−5.04591			−0.379274
$178$	0.179895	−	4.58662i	0.0134837	−	0.343782i
$179$	0.419587	−	0.419587i	0.0313614	−	0.0313614i	−0.691252	−	0.722614i	$-0.742941\pi$
$179$	0.419587	−	0.419587i	0.0313614	−	0.0313614i	0.722614	+	0.691252i	$0.242941\pi$
$180$		0			0
$181$	−14.2605	−	14.2605i	−1.05998	−	1.05998i	−0.998083	−	0.0618956i	$-0.980285\pi$
$181$	−14.2605	−	14.2605i	−1.05998	−	1.05998i	−0.0618956	−	0.998083i	$-0.519715\pi$
$182$	0.562632	+	0.608568i	0.0417050	+	0.0451101i
$183$		−	6.96356i		−	0.514761i
$184$	0.540971	−	4.57868i	0.0398809	−	0.337545i
$185$		0			0
$186$	1.52719	−	1.41191i	0.111979	−	0.103526i
$187$	18.2938	+	18.2938i	1.33777	+	1.33777i
$188$	8.09762	+	0.636183i	0.590580	+	0.0463984i
$189$	12.7218	−	12.7218i	0.925377	−	0.925377i
$190$		0			0
$191$	17.3304			1.25399			0.626993	−	0.779025i	$-0.284285\pi$
$191$	17.3304			1.25399			0.626993	+	0.779025i	$0.284285\pi$
$192$	4.71130	−	2.88974i	0.340008	−	0.208549i
$193$	−16.8667			−1.21409			−0.607045	−	0.794667i	$-0.707645\pi$
$193$	−16.8667			−1.21409			−0.607045	+	0.794667i	$0.707645\pi$
$194$	−19.7245	−	0.773628i	−1.41614	−	0.0555432i
$195$		0			0
$196$	−30.3765	−	2.38650i	−2.16975	−	0.170464i
$197$	3.58908	+	3.58908i	0.255712	+	0.255712i	0.823307	−	0.567596i	$-0.192126\pi$
$197$	3.58908	+	3.58908i	0.255712	+	0.255712i	−0.567596	+	0.823307i	$0.692126\pi$
$198$	−14.4988	+	13.4044i	−1.03038	+	0.952608i
$199$			6.64501i			0.471052i	0.971868	+	0.235526i	$0.0756813\pi$
$199$			6.64501i			0.471052i	−0.971868	+	0.235526i	$0.924319\pi$
$200$		0			0
$201$		−	7.32695i		−	0.516803i
$202$	−18.2051	−	19.6915i	−1.28091	−	1.38549i
$203$	−15.3893	−	15.3893i	−1.08012	−	1.08012i
$204$	−4.91073	+	4.19532i	−0.343820	+	0.293731i
$205$		0			0
$206$	0.762860	−	19.4500i	0.0531510	−	1.35514i
$207$	−4.11218			−0.285816
$208$	0.402112	−	0.292320i	0.0278815	−	0.0202687i
$209$	−14.1867			−0.981314
$210$		0			0
$211$	1.90906	−	1.90906i	0.131425	−	0.131425i	−0.638334	−	0.769759i	$-0.720376\pi$
$211$	1.90906	−	1.90906i	0.131425	−	0.131425i	0.769759	+	0.638334i	$0.220376\pi$
$212$	9.25839	+	10.8372i	0.635869	+	0.744301i
$213$	2.21821	+	2.21821i	0.151989	+	0.151989i
$214$	−0.445321	−	0.481680i	−0.0304415	−	0.0329270i
$215$		0			0
$216$	−6.68282	−	8.47355i	−0.454709	−	0.576552i
$217$			10.0379i			0.681418i
$218$	0.219839	−	0.203245i	0.0148894	−	0.0137655i
$219$	4.05740	+	4.05740i	0.274174	+	0.274174i
$220$		0			0
$221$	−0.410798	+	0.410798i	−0.0276333	+	0.0276333i
$222$	5.49226	+	0.215416i	0.368617	+	0.0144578i
$223$	−24.1071			−1.61433			−0.807165	−	0.590326i	$-0.798999\pi$
$223$	−24.1071			−1.61433			−0.807165	+	0.590326i	$0.798999\pi$
$224$	−5.19497	+	26.1636i	−0.347103	+	1.74813i
$225$		0			0
$226$	8.45048	+	0.331442i	0.562118	+	0.0220472i
$227$	−6.67411	+	6.67411i	−0.442977	+	0.442977i	−0.893011	−	0.450035i	$-0.851412\pi$
$227$	−6.67411	+	6.67411i	−0.442977	+	0.442977i	0.450035	+	0.893011i	$0.351412\pi$
$228$	0.277397	−	3.53084i	0.0183711	−	0.233835i
$229$	16.0807	+	16.0807i	1.06264	+	1.06264i	0.997902	+	0.0647388i	$0.0206214\pi$
$229$	16.0807	+	16.0807i	1.06264	+	1.06264i	0.0647388	+	0.997902i	$0.479379\pi$
$230$		0			0
$231$			18.0303i			1.18631i
$232$	−10.2503	+	8.08406i	−0.672962	+	0.530744i
$233$			16.4976i			1.08079i	0.841411	+	0.540396i	$0.181726\pi$
$233$			16.4976i			1.08079i	−0.841411	+	0.540396i	$0.818274\pi$
$234$	−0.301004	−	0.325579i	−0.0196772	−	0.0212838i
$235$		0			0
$236$	−9.48833	−	11.1063i	−0.617638	−	0.722961i
$237$	5.63342	−	5.63342i	0.365930	−	0.365930i
$238$	1.22167	−	31.1478i	0.0791891	−	2.01901i
$239$	5.25917			0.340188			0.170094	−	0.985428i	$-0.445593\pi$
$239$	5.25917			0.340188			0.170094	+	0.985428i	$0.445593\pi$
$240$		0			0
$241$	−14.1126			−0.909075			−0.454538	−	0.890728i	$-0.650196\pi$
$241$	−14.1126			−0.909075			−0.454538	+	0.890728i	$0.650196\pi$
$242$	1.08813	−	27.7432i	0.0699479	−	1.78340i
$243$	−10.5032	+	10.5032i	−0.673782	+	0.673782i
$244$	15.3272	−	13.0943i	0.981222	−	0.838275i
$245$		0			0
$246$	5.47523	+	5.92226i	0.349088	+	0.377589i
$247$		−	0.318571i		−	0.0202702i
$248$	5.97942	+	0.706468i	0.379693	+	0.0448608i
$249$		−	1.14234i		−	0.0723927i
$250$		0			0
$251$	−9.98825	−	9.98825i	−0.630453	−	0.630453i	0.317729	−	0.948182i	$-0.397080\pi$
$251$	−9.98825	−	9.98825i	−0.630453	−	0.630453i	−0.948182	+	0.317729i	$0.897080\pi$
$252$	23.7181	+	1.86339i	1.49410	+	0.117383i
$253$	6.37943	−	6.37943i	0.401071	−	0.401071i
$254$	−3.85890	−	0.151353i	−0.242129	−	0.00949671i
$255$		0			0
$256$	15.2196	+	4.93595i	0.951225	+	0.308497i
$257$	8.44760			0.526947			0.263474	−	0.964667i	$-0.415132\pi$
$257$	8.44760			0.526947			0.263474	+	0.964667i	$0.415132\pi$
$258$	3.13877	+	0.123108i	0.195411	+	0.00766435i
$259$	−18.7577	+	18.7577i	−1.16555	+	1.16555i
$260$		0			0
$261$	8.23315	+	8.23315i	0.509619	+	0.509619i
$262$	1.19475	−	1.10457i	0.0738118	−	0.0682403i
$263$		−	18.3064i		−	1.12882i	−0.825494	−	0.564410i	$-0.809104\pi$
$263$		−	18.3064i		−	1.12882i	0.825494	−	0.564410i	$-0.190896\pi$
$264$	10.7404	+	1.26897i	0.661024	+	0.0781000i
$265$		0			0
$266$	11.6037	+	12.5511i	0.711472	+	0.769560i
$267$	1.58559	+	1.58559i	0.0970364	+	0.0970364i
$268$	16.1270	−	13.7776i	0.985115	−	0.841601i
$269$	13.5631	−	13.5631i	0.826955	−	0.826955i	−0.160140	−	0.987094i	$-0.551194\pi$
$269$	13.5631	−	13.5631i	0.826955	−	0.826955i	0.987094	+	0.160140i	$0.0511945\pi$
$270$		0			0
$271$	−2.24520			−0.136386			−0.0681930	−	0.997672i	$-0.521723\pi$
$271$	−2.24520			−0.136386			−0.0681930	+	0.997672i	$0.521723\pi$
$272$	−18.4683	−	2.91991i	−1.11980	−	0.177046i
$273$	−0.404882			−0.0245046
$274$	−0.0110746	+	0.282360i	−0.000669044	+	0.0170580i
$275$		0			0
$276$	1.46300	+	1.71247i	0.0880620	+	0.103079i
$277$	−7.28255	−	7.28255i	−0.437566	−	0.437566i	0.453626	−	0.891192i	$-0.350130\pi$
$277$	−7.28255	−	7.28255i	−0.437566	−	0.437566i	−0.891192	+	0.453626i	$0.850130\pi$
$278$	15.7901	+	17.0793i	0.947030	+	1.02435i
$279$		−	5.37020i		−	0.321506i
$280$		0			0
$281$			6.04084i			0.360367i	0.983633	+	0.180183i	$0.0576691\pi$
$281$			6.04084i			0.360367i	−0.983633	+	0.180183i	$0.942331\pi$
$282$	−2.91361	+	2.69369i	−0.173503	+	0.160407i
$283$	15.1350	+	15.1350i	0.899682	+	0.899682i	0.995408	−	0.0957259i	$-0.0305172\pi$
$283$	15.1350	+	15.1350i	0.899682	+	0.899682i	−0.0957259	+	0.995408i	$0.530517\pi$
$284$	−0.711284	+	9.05354i	−0.0422070	+	0.537229i
$285$		0			0
$286$	0.972049	+	0.0381254i	0.0574785	+	0.00225440i
$287$	−38.9259			−2.29772
$288$	2.77927	−	13.9973i	0.163770	−	0.824800i
$289$	4.85021			0.285306
$290$		0			0
$291$	6.81873	−	6.81873i	0.399721	−	0.399721i
$292$	−1.30103	+	16.5601i	−0.0761371	+	0.969107i
$293$	10.7777	+	10.7777i	0.629637	+	0.629637i	0.947977	−	0.318339i	$-0.103125\pi$
$293$	10.7777	+	10.7777i	0.629637	+	0.629637i	−0.318339	+	0.947977i	$0.603125\pi$
$294$	10.9298	−	10.1048i	0.637438	−	0.589322i
$295$		0			0
$296$	9.85351	+	12.4939i	0.572724	+	0.726190i
$297$		−	21.1172i		−	1.22534i
$298$	1.53942	+	1.66511i	0.0891762	+	0.0964571i
$299$	0.143254	+	0.143254i	0.00828459	+	0.00828459i
$300$		0			0
$301$	−10.7198	+	10.7198i	−0.617881	+	0.617881i
$302$	0.394747	−	10.0645i	0.0227152	−	0.579148i
$303$	13.1008			0.752621
$304$	8.29319	−	6.02882i	0.475647	−	0.345776i
$305$		0			0
$306$	−0.653584	+	16.6639i	−0.0373629	+	0.952609i
$307$	−7.94378	+	7.94378i	−0.453376	+	0.453376i	−0.896473	−	0.443098i	$-0.853880\pi$
$307$	−7.94378	+	7.94378i	−0.453376	+	0.453376i	0.443098	+	0.896473i	$0.353880\pi$
$308$	−39.6858	+	33.9042i	−2.26131	+	1.93187i
$309$	6.72382	+	6.72382i	0.382505	+	0.382505i
$310$		0			0
$311$		−	31.1649i		−	1.76720i	−0.468244	−	0.883599i	$-0.655113\pi$
$311$		−	31.1649i		−	1.76720i	0.468244	−	0.883599i	$-0.344887\pi$
$312$	−0.0284956	+	0.241182i	−0.00161325	+	0.0136542i
$313$		−	5.35842i		−	0.302876i	−0.988467	−	0.151438i	$-0.951610\pi$
$313$		−	5.35842i		−	0.302876i	0.988467	−	0.151438i	$-0.0483903\pi$
$314$	−7.81482	+	7.22494i	−0.441016	+	0.407727i
$315$		0			0
$316$	22.9925	+	1.80639i	1.29343	+	0.101617i
$317$	8.88165	−	8.88165i	0.498843	−	0.498843i	−0.412235	−	0.911078i	$-0.635252\pi$
$317$	8.88165	−	8.88165i	0.498843	−	0.498843i	0.911078	+	0.412235i	$0.135252\pi$
$318$	−6.95771	−	0.272893i	−0.390169	−	0.0153031i
$319$	−25.5450			−1.43025
$320$		0			0
$321$	0.320463			0.0178865
$322$	−10.8619	−	0.426022i	−0.605310	−	0.0237413i
$323$	−8.47233	+	8.47233i	−0.471413	+	0.471413i
$324$	−9.83400	−	0.772600i	−0.546333	−	0.0429222i
$325$		0			0
$326$	−18.0646	+	16.7011i	−1.00051	+	0.924987i
$327$			0.146260i			0.00808817i
$328$	−2.73960	+	23.1875i	−0.151269	+	1.28032i
$329$		−	19.1506i		−	1.05581i
$330$		0			0
$331$	6.07281	+	6.07281i	0.333792	+	0.333792i	0.854025	−	0.520233i	$-0.174155\pi$
$331$	6.07281	+	6.07281i	0.333792	+	0.333792i	−0.520233	+	0.854025i	$0.674155\pi$
$332$	2.51435	−	2.14805i	0.137993	−	0.117890i
$333$	10.0352	−	10.0352i	0.549928	−	0.549928i
$334$	−0.546947	+	13.9450i	−0.0299276	+	0.763038i
$335$		0			0
$336$	−7.66222	−	10.5401i	−0.418008	−	0.575009i
$337$	22.0227			1.19965			0.599827	−	0.800130i	$-0.295236\pi$
$337$	22.0227			1.19965			0.599827	+	0.800130i	$0.295236\pi$
$338$	0.719672	−	18.3488i	0.0391450	−	0.998044i
$339$	−2.92132	+	2.92132i	−0.158664	+	0.158664i
$340$		0			0
$341$	8.33106	+	8.33106i	0.451152	+	0.451152i
$342$	−6.20792	−	6.71477i	−0.335686	−	0.363093i
$343$			38.8315i			2.09670i
$344$	5.63117	+	7.14009i	0.303612	+	0.384968i
$345$		0			0
$346$	−19.6917	+	18.2053i	−1.05863	+	0.978722i
$347$	−11.8920	−	11.8920i	−0.638395	−	0.638395i	0.311765	−	0.950159i	$-0.399080\pi$
$347$	−11.8920	−	11.8920i	−0.638395	−	0.638395i	−0.950159	+	0.311765i	$0.899080\pi$
$348$	0.499490	−	6.35773i	0.0267755	−	0.340810i
$349$	−8.65696	+	8.65696i	−0.463396	+	0.463396i	−0.899767	−	0.436371i	$-0.856264\pi$
$349$	−8.65696	+	8.65696i	−0.463396	+	0.463396i	0.436371	+	0.899767i	$0.356264\pi$
$350$		0			0
$351$	0.474200			0.0253109
$352$	17.4031	+	26.0263i	0.927589	+	1.38721i
$353$	26.6153			1.41659			0.708296	−	0.705916i	$-0.249464\pi$
$353$	26.6153			1.41659			0.708296	+	0.705916i	$0.249464\pi$
$354$	7.13051	+	0.279671i	0.378983	+	0.0148643i
$355$		0			0
$356$	−0.508429	+	6.47151i	−0.0269467	+	0.342989i
$357$	10.7678	+	10.7678i	0.569890	+	0.569890i
$358$	−0.616185	+	0.569674i	−0.0325664	+	0.0301082i
$359$		−	4.85032i		−	0.255990i	−0.991775	−	0.127995i	$-0.959146\pi$
$359$		−	4.85032i		−	0.255990i	0.991775	−	0.127995i	$-0.0408542\pi$
$360$		0			0
$361$			12.4298i			0.654199i
$362$	19.3616	+	20.9424i	1.01762	+	1.10071i
$363$	9.59078	+	9.59078i	0.503385	+	0.503385i
$364$	−0.761340	−	0.891168i	−0.0399051	−	0.0467099i
$365$		0			0
$366$	−0.385957	+	9.84039i	−0.0201743	+	0.514365i
$367$	15.6741			0.818182			0.409091	−	0.912494i	$-0.365846\pi$
$367$	15.6741			0.818182			0.409091	+	0.912494i	$0.365846\pi$
$368$	−1.01823	+	6.44027i	−0.0530792	+	0.335722i
$369$	20.8250			1.08411
$370$		0			0
$371$	23.7627	−	23.7627i	1.23370	−	1.23370i
$372$	−2.23637	+	1.91057i	−0.115950	+	0.0990582i
$373$	−5.44481	−	5.44481i	−0.281922	−	0.281922i	0.551953	−	0.833875i	$-0.313883\pi$
$373$	−5.44481	−	5.44481i	−0.281922	−	0.281922i	−0.833875	+	0.551953i	$0.813883\pi$
$374$	−24.8375	−	26.8654i	−1.28432	−	1.38918i
$375$		0			0
$376$	−11.4077	−	1.34782i	−0.588308	−	0.0695085i
$377$		−	0.573629i		−	0.0295434i
$378$	−18.6827	+	17.2724i	−0.960933	+	0.888399i
$379$	−17.4103	−	17.4103i	−0.894309	−	0.894309i	0.100616	−	0.994925i	$-0.467919\pi$
$379$	−17.4103	−	17.4103i	−0.894309	−	0.894309i	−0.994925	+	0.100616i	$0.967919\pi$
$380$		0			0
$381$	1.33402	−	1.33402i	0.0683438	−	0.0683438i
$382$	−24.4901	−	0.960543i	−1.25302	−	0.0491457i
$383$	9.04928			0.462396			0.231198	−	0.972907i	$-0.425735\pi$
$383$	9.04928			0.462396			0.231198	+	0.972907i	$0.425735\pi$
$384$	−6.81782	+	3.82245i	−0.347921	+	0.195064i
$385$		0			0
$386$	23.8348	+	0.934839i	1.21316	+	0.0475821i
$387$	5.73503	−	5.73503i	0.291528	−	0.291528i
$388$	27.8303	+	2.18647i	1.41287	+	0.111001i
$389$	−15.3617	−	15.3617i	−0.778871	−	0.778871i	0.200768	−	0.979639i	$-0.435656\pi$
$389$	−15.3617	−	15.3617i	−0.778871	−	0.778871i	−0.979639	+	0.200768i	$0.935656\pi$
$390$		0			0
$391$		−	7.61962i		−	0.385341i
$392$	42.7935	+	5.05605i	2.16140	+	0.255369i
$393$			0.794869i			0.0400959i
$394$	−4.87291	−	5.27076i	−0.245493	−	0.265537i
$395$		0			0
$396$	21.2316	−	18.1385i	1.06693	−	0.911494i
$397$	9.44519	−	9.44519i	0.474041	−	0.474041i	−0.429179	−	0.903220i	$-0.641197\pi$
$397$	9.44519	−	9.44519i	0.474041	−	0.474041i	0.903220	+	0.429179i	$0.141197\pi$
$398$	0.368301	−	9.39024i	0.0184613	−	0.470690i
$399$	−8.35031			−0.418038
$400$		0			0
$401$	−21.5765			−1.07748			−0.538739	−	0.842473i	$-0.681099\pi$
$401$	−21.5765			−1.07748			−0.538739	+	0.842473i	$0.681099\pi$
$402$	−0.406098	+	10.3539i	−0.0202543	+	0.516406i
$403$	−0.187079	+	0.187079i	−0.00931907	+	0.00931907i
$404$	24.6347	+	28.8356i	1.22562	+	1.43462i
$405$		0			0
$406$	20.8941	+	22.6000i	1.03696	+	1.12162i
$407$			31.1363i			1.54337i
$408$	7.17202	−	5.65635i	0.355068	−	0.280031i
$409$		−	4.17336i		−	0.206359i	−0.994663	−	0.103180i	$-0.967098\pi$
$409$		−	4.17336i		−	0.206359i	0.994663	−	0.103180i	$-0.0329017\pi$
$410$		0			0
$411$	−0.0976116	−	0.0976116i	−0.00481482	−	0.00481482i
$412$	−2.15604	+	27.4430i	−0.106220	+	1.35202i
$413$	−24.3529	+	24.3529i	−1.19833	+	1.19833i
$414$	5.81103	+	0.227918i	0.285597	+	0.0112016i
$415$		0			0
$416$	−0.584438	+	0.390798i	−0.0286544	+	0.0191604i
$417$	−11.3629			−0.556445
$418$	20.0476	+	0.786300i	0.980560	+	0.0384592i
$419$	27.1191	−	27.1191i	1.32485	−	1.32485i	0.415060	−	0.909794i	$-0.363761\pi$
$419$	27.1191	−	27.1191i	1.32485	−	1.32485i	0.909794	−	0.415060i	$-0.136239\pi$
$420$		0			0
$421$	−26.9594	−	26.9594i	−1.31392	−	1.31392i	−0.918500	−	0.395421i	$-0.870599\pi$
$421$	−26.9594	−	26.9594i	−1.31392	−	1.31392i	−0.395421	−	0.918500i	$-0.629401\pi$
$422$	−2.80355	+	2.59193i	−0.136475	+	0.126173i
$423$			10.2454i			0.498150i
$424$	−12.4826	−	15.8275i	−0.606210	−	0.768650i
$425$		0			0
$426$	−3.01167	−	3.25756i	−0.145916	−	0.157829i
$427$	−33.6079	−	33.6079i	−1.62640	−	1.62640i
$428$	0.602598	+	0.705357i	0.0291277	+	0.0340947i
$429$	−0.336036	+	0.336036i	−0.0162240	+	0.0162240i
$430$		0			0
$431$	−22.4059			−1.07925			−0.539626	−	0.841905i	$-0.681434\pi$
$431$	−22.4059			−1.07925			−0.539626	+	0.841905i	$0.681434\pi$
$432$	8.97403	+	12.3446i	0.431763	+	0.593930i
$433$	16.8061			0.807649			0.403824	−	0.914837i	$-0.367681\pi$
$433$	16.8061			0.807649			0.403824	+	0.914837i	$0.367681\pi$
$434$	0.556353	−	14.1848i	0.0267058	−	0.680894i
$435$		0			0
$436$	−0.321925	+	0.275026i	−0.0154174	+	0.0131714i
$437$	2.95448	+	2.95448i	0.141332	+	0.141332i
$438$	−5.50874	−	5.95851i	−0.263218	−	0.284708i
$439$			9.08322i			0.433519i	0.976225	+	0.216759i	$0.0695487\pi$
$439$			9.08322i			0.433519i	−0.976225	+	0.216759i	$0.930451\pi$
$440$		0			0
$441$		−	38.4335i		−	1.83017i
$442$	0.603279	−	0.557742i	0.0286951	−	0.0265291i
$443$	−12.5397	−	12.5397i	−0.595781	−	0.595781i	0.343406	−	0.939187i	$-0.388419\pi$
$443$	−12.5397	−	12.5397i	−0.595781	−	0.595781i	−0.939187	+	0.343406i	$0.888419\pi$
$444$	−7.74933	−	0.608820i	−0.367767	−	0.0288933i
$445$		0			0
$446$	34.0664	+	1.33614i	1.61309	+	0.0632681i
$447$	−1.10780			−0.0523972
$448$	8.79127	−	36.6845i	0.415349	−	1.73318i
$449$	18.0707			0.852811			0.426406	−	0.904532i	$-0.359780\pi$
$449$	18.0707			0.852811			0.426406	+	0.904532i	$0.359780\pi$
$450$		0			0
$451$	−32.3069	+	32.3069i	−1.52127	+	1.52127i
$452$	−11.9232	−	0.936740i	−0.560822	−	0.0440605i
$453$	3.47929	+	3.47929i	0.163471	+	0.163471i
$454$	9.80129	−	9.06146i	0.459997	−	0.425275i
$455$		0			0
$456$	−0.587695	+	4.97415i	−0.0275213	+	0.232936i
$457$		−	18.6637i		−	0.873052i	−0.899692	−	0.436526i	$-0.856209\pi$
$457$		−	18.6637i		−	0.873052i	0.899692	−	0.436526i	$-0.143791\pi$
$458$	−21.8328	−	23.6153i	−1.02018	−	1.10347i
$459$	−12.6113	−	12.6113i	−0.588643	−	0.588643i
$460$		0			0
$461$	−0.831229	+	0.831229i	−0.0387142	+	0.0387142i	−0.726199	−	0.687485i	$-0.758715\pi$
$461$	−0.831229	+	0.831229i	−0.0387142	+	0.0387142i	0.687485	+	0.726199i	$0.258715\pi$
$462$	0.999335	−	25.4791i	0.0464933	−	1.18540i
$463$	−7.82533			−0.363674			−0.181837	−	0.983329i	$-0.558204\pi$
$463$	−7.82533			−0.363674			−0.181837	+	0.983329i	$0.558204\pi$
$464$	14.9330	−	10.8557i	0.693246	−	0.503962i
$465$		0			0
$466$	0.914382	−	23.3132i	0.0423579	−	1.07996i
$467$	−8.75068	+	8.75068i	−0.404933	+	0.404933i	−0.879967	−	0.475034i	$-0.842436\pi$
$467$	−8.75068	+	8.75068i	−0.404933	+	0.404933i	0.475034	+	0.879967i	$0.342436\pi$
$468$	0.407311	+	0.476768i	0.0188280	+	0.0220386i
$469$	−35.3617	−	35.3617i	−1.63285	−	1.63285i
$470$		0			0
$471$		−	5.19922i		−	0.239568i
$472$	12.7926	+	16.2206i	0.588829	+	0.746612i
$473$			17.7941i			0.818172i
$474$	−8.27297	+	7.64850i	−0.379990	+	0.351307i
$475$		0			0
$476$	−3.45275	+	43.9481i	−0.158257	+	2.01436i
$477$	−12.7129	+	12.7129i	−0.582082	+	0.582082i
$478$	−7.43188	−	0.291491i	−0.339926	−	0.0133325i
$479$	2.10417			0.0961421			0.0480710	−	0.998844i	$-0.484693\pi$
$479$	2.10417			0.0961421			0.0480710	+	0.998844i	$0.484693\pi$
$480$		0			0
$481$	−0.699186			−0.0318801
$482$	19.9430	+	0.782196i	0.908377	+	0.0356281i
$483$	3.75494	−	3.75494i	0.170856	−	0.170856i
$484$	−3.07534	+	39.1443i	−0.139788	+	1.77929i
$485$		0			0
$486$	15.4245	−	14.2602i	0.699671	−	0.646858i
$487$		−	4.87183i		−	0.220764i	−0.993889	−	0.110382i	$-0.964793\pi$
$487$		−	4.87183i		−	0.220764i	0.993889	−	0.110382i	$-0.0352074\pi$
$488$	−22.3850	+	17.6544i	−1.01332	+	0.799175i
$489$		−	12.0185i		−	0.543494i
$490$		0			0
$491$	14.3582	+	14.3582i	0.647975	+	0.647975i	0.952503	−	0.304528i	$-0.0984987\pi$
$491$	14.3582	+	14.3582i	0.647975	+	0.647975i	−0.304528	+	0.952503i	$0.598499\pi$
$492$	−7.40895	−	8.67237i	−0.334021	−	0.390981i
$493$	−15.2555	+	15.2555i	−0.687075	+	0.687075i
$494$	−0.0176569	+	0.450181i	−0.000794419	+	0.0202546i
$495$		0			0
$496$	−8.41052	−	1.32974i	−0.377644	−	0.0597071i
$497$	21.4113			0.960429
$498$	−0.0633143	+	1.61427i	−0.00283718	+	0.0723370i
$499$	−25.1060	+	25.1060i	−1.12390	+	1.12390i	−0.132748	+	0.991150i	$0.542380\pi$
$499$	−25.1060	+	25.1060i	−1.12390	+	1.12390i	−0.991150	+	0.132748i	$0.957620\pi$
$500$		0			0
$501$	−4.82077	−	4.82077i	−0.215376	−	0.215376i
$502$	13.5611	+	14.6683i	0.605260	+	0.654677i
$503$		−	18.8868i		−	0.842120i	−0.907033	−	0.421060i	$-0.861658\pi$
$503$		−	18.8868i		−	0.842120i	0.907033	−	0.421060i	$-0.138342\pi$
$504$	−33.4133	−	3.94778i	−1.48835	−	0.175848i
$505$		0			0
$506$	−9.36852	+	8.66136i	−0.416482	+	0.385044i
$507$	6.34316	+	6.34316i	0.281710	+	0.281710i
$508$	5.44473	+	0.427761i	0.241571	+	0.0189788i
$509$	−22.9756	+	22.9756i	−1.01837	+	1.01837i	−0.0185459	+	0.999828i	$0.505904\pi$
$509$	−22.9756	+	22.9756i	−1.01837	+	1.01837i	−0.999828	+	0.0185459i	$0.994096\pi$
$510$		0			0
$511$	39.1641			1.73252
$512$	−21.2337	−	7.81868i	−0.938404	−	0.345540i
$513$	9.77993			0.431794
$514$	−11.9375	−	0.468210i	−0.526542	−	0.0206519i
$515$		0			0
$516$	−4.42865	−	0.347933i	−0.194961	−	0.0153169i
$517$	−15.8942	−	15.8942i	−0.699028	−	0.699028i
$518$	27.5467	−	25.4674i	1.21033	−	1.11897i
$519$		−	13.1009i		−	0.575066i
$520$		0			0
$521$			20.2089i			0.885367i	0.896678	+	0.442683i	$0.145973\pi$
$521$			20.2089i			0.885367i	−0.896678	+	0.442683i	$0.854027\pi$
$522$	−11.1782	−	12.0908i	−0.489255	−	0.529201i
$523$	3.93445	+	3.93445i	0.172042	+	0.172042i	0.787876	−	0.615834i	$-0.211181\pi$
$523$	3.93445	+	3.93445i	0.172042	+	0.172042i	−0.615834	+	0.787876i	$0.711181\pi$
$524$	−1.74955	+	1.49467i	−0.0764295	+	0.0652951i
$525$		0			0
$526$	−1.01464	+	25.8693i	−0.0442402	+	1.12795i
$527$	9.95066			0.433458
$528$	−15.1072	−	2.38851i	−0.657456	−	0.103947i
$529$	20.3429			0.884473
$530$		0			0
$531$	13.0286	−	13.0286i	0.565393	−	0.565393i
$532$	−15.7019	−	18.3795i	−0.680765	−	0.796853i
$533$	−0.725471	−	0.725471i	−0.0314237	−	0.0314237i
$534$	−2.15276	−	2.32852i	−0.0931589	−	0.100765i
$535$		0			0
$536$	−23.5532	+	18.5757i	−1.01734	+	0.802346i
$537$		−	0.409950i		−	0.0176906i
$538$	−19.9181	+	18.4146i	−0.858729	+	0.793910i
$539$	59.6238	+	59.6238i	2.56818	+	2.56818i
$540$		0			0
$541$	−3.17895	+	3.17895i	−0.136674	+	0.136674i	−0.772134	−	0.635460i	$-0.780811\pi$
$541$	−3.17895	+	3.17895i	−0.136674	+	0.136674i	0.635460	+	0.772134i	$0.280811\pi$
$542$	3.17275	+	0.124440i	0.136281	+	0.00534518i
$543$	−13.9330			−0.597923
$544$	25.9362	+	5.14982i	1.11201	+	0.220797i
$545$		0			0
$546$	0.572150	+	0.0224407i	0.0244857	+	0.000960372i
$547$	1.32918	−	1.32918i	0.0568317	−	0.0568317i	−0.678120	−	0.734951i	$-0.737205\pi$
$547$	1.32918	−	1.32918i	0.0568317	−	0.0568317i	0.734951	+	0.678120i	$0.237205\pi$
$548$	0.0312998	−	0.398397i	0.00133706	−	0.0170187i
$549$	17.9800	+	17.9800i	0.767366	+	0.767366i
$550$		0			0
$551$		−	11.8306i		−	0.503998i
$552$	−1.97249	−	2.50103i	−0.0839545	−	0.106451i
$553$		−	54.3766i		−	2.31233i
$554$	9.88754	+	10.6948i	0.420081	+	0.454379i
$555$		0			0
$556$	−21.3669	−	25.0105i	−0.906157	−	1.06068i
$557$	24.9082	−	24.9082i	1.05539	−	1.05539i	0.0570196	−	0.998373i	$-0.481840\pi$
$557$	24.9082	−	24.9082i	1.05539	−	1.05539i	0.998373	−	0.0570196i	$-0.0181598\pi$
$558$	−0.297645	+	7.58878i	−0.0126003	+	0.321259i
$559$	−0.399576			−0.0169003
$560$		0			0
$561$	17.8736			0.754625
$562$	0.334815	−	8.53648i	0.0141233	−	0.360090i
$563$	3.80804	−	3.80804i	0.160490	−	0.160490i	−0.622294	−	0.782784i	$-0.713799\pi$
$563$	3.80804	−	3.80804i	0.160490	−	0.160490i	0.782784	+	0.622294i	$0.213799\pi$
$564$	4.26660	−	3.64503i	0.179656	−	0.153484i
$565$		0			0
$566$	−20.5488	−	22.2265i	−0.863731	−	0.934251i
$567$			23.2571i			0.976706i
$568$	1.50693	−	12.7544i	0.0632293	−	0.535162i
$569$		−	8.43971i		−	0.353811i	−0.984228	−	0.176905i	$-0.943391\pi$
$569$		−	8.43971i		−	0.353811i	0.984228	−	0.176905i	$-0.0566087\pi$
$570$		0			0
$571$	−21.2821	−	21.2821i	−0.890629	−	0.890629i	0.103953	−	0.994582i	$-0.466851\pi$
$571$	−21.2821	−	21.2821i	−0.890629	−	0.890629i	−0.994582	+	0.103953i	$0.966851\pi$
$572$	−1.37152	−	0.107752i	−0.0573460	−	0.00450534i
$573$	8.46619	−	8.46619i	0.353680	−	0.353680i
$574$	55.0072	+	2.15747i	2.29596	+	0.0900512i
$575$		0			0
$576$	−4.70326	+	19.6259i	−0.195969	+	0.817748i
$577$	−36.3491			−1.51323			−0.756615	−	0.653860i	$-0.773148\pi$
$577$	−36.3491			−1.51323			−0.756615	+	0.653860i	$0.773148\pi$
$578$	−6.85396	−	0.268824i	−0.285087	−	0.0111816i
$579$	−8.23964	+	8.23964i	−0.342428	+	0.342428i
$580$		0			0
$581$	−5.51321	−	5.51321i	−0.228726	−	0.228726i
$582$	−10.0137	+	9.25780i	−0.415080	+	0.383748i
$583$		−	39.4442i		−	1.63361i
$584$	2.75637	−	23.3294i	0.114059	−	0.965379i
$585$		0			0
$586$	−14.6328	−	15.8275i	−0.604477	−	0.653830i
$587$	−6.55994	−	6.55994i	−0.270758	−	0.270758i	0.558647	−	0.829405i	$-0.311321\pi$
$587$	−6.55994	−	6.55994i	−0.270758	−	0.270758i	−0.829405	+	0.558647i	$0.811321\pi$
$588$	−16.0052	+	13.6735i	−0.660044	+	0.563887i
$589$	−3.85833	+	3.85833i	−0.158980	+	0.158980i
$590$		0			0
$591$	3.50665			0.144244
$592$	−13.2318	−	18.2015i	−0.543823	−	0.748078i
$593$	−1.40974			−0.0578911			−0.0289455	−	0.999581i	$-0.509215\pi$
$593$	−1.40974			−0.0578911			−0.0289455	+	0.999581i	$0.509215\pi$
$594$	−1.17043	+	29.8413i	−0.0480231	+	1.22440i
$595$		0			0
$596$	−2.08311	−	2.43833i	−0.0853274	−	0.0998779i
$597$	3.24619	+	3.24619i	0.132858	+	0.132858i
$598$	−0.194496	−	0.210376i	−0.00795354	−	0.00860291i
$599$		−	23.3593i		−	0.954435i	−0.878785	−	0.477218i	$-0.841645\pi$
$599$		−	23.3593i		−	0.954435i	0.878785	−	0.477218i	$-0.158355\pi$
$600$		0			0
$601$		−	20.4138i		−	0.832695i	−0.909206	−	0.416347i	$-0.863310\pi$
$601$		−	20.4138i		−	0.832695i	0.909206	−	0.416347i	$-0.136690\pi$
$602$	15.7426	−	14.5543i	0.641622	−	0.593190i
$603$	18.9183	+	18.9183i	0.770411	+	0.770411i
$604$	−1.11566	+	14.2006i	−0.0453954	+	0.577813i
$605$		0			0
$606$	−18.5131	−	0.726115i	−0.752043	−	0.0294964i
$607$	0.758240			0.0307760			0.0153880	−	0.999882i	$-0.495102\pi$
$607$	0.758240			0.0307760			0.0153880	+	0.999882i	$0.495102\pi$
$608$	−12.0535	+	8.05983i	−0.488833	+	0.326869i
$609$	−15.0358			−0.609283
$610$		0			0
$611$	0.356915	−	0.356915i	0.0144392	−	0.0144392i
$612$	1.84719	−	23.5119i	0.0746684	−	0.950413i
$613$	12.0341	+	12.0341i	0.486052	+	0.486052i	0.907058	−	0.421006i	$-0.138323\pi$
$613$	12.0341	+	12.0341i	0.486052	+	0.486052i	−0.421006	+	0.907058i	$0.638323\pi$
$614$	11.6659	−	10.7853i	0.470796	−	0.435259i
$615$		0			0
$616$	57.9602	−	45.7114i	2.33528	−	1.84176i
$617$			32.6899i			1.31605i	0.752998	+	0.658023i	$0.228607\pi$
$617$			32.6899i			1.31605i	−0.752998	+	0.658023i	$0.771393\pi$
$618$	−9.12894	−	9.87428i	−0.367220	−	0.397202i
$619$	26.3836	+	26.3836i	1.06045	+	1.06045i	0.998052	+	0.0623934i	$0.0198733\pi$
$619$	26.3836	+	26.3836i	1.06045	+	1.06045i	0.0623934	+	0.998052i	$0.480127\pi$
$620$		0			0
$621$	−4.39781	+	4.39781i	−0.176478	+	0.176478i
$622$	−1.72732	+	44.0399i	−0.0692592	+	1.76584i
$623$	15.3049			0.613178
$624$	0.0536355	−	0.339241i	0.00214714	−	0.0135805i
$625$		0			0
$626$	−0.296991	+	7.57213i	−0.0118702	+	0.302643i
$627$	−6.93042	+	6.93042i	−0.276774	+	0.276774i
$628$	11.4438	−	9.77662i	0.456657	−	0.390130i
$629$	18.5947	+	18.5947i	0.741420	+	0.741420i
$630$		0			0
$631$		−	6.08765i		−	0.242345i	−0.992631	−	0.121173i	$-0.961335\pi$
$631$		−	6.08765i		−	0.242345i	0.992631	−	0.121173i	$-0.0386655\pi$
$632$	−32.3913	−	3.82703i	−1.28846	−	0.152231i
$633$		−	1.86521i		−	0.0741354i
$634$	−13.0432	+	12.0586i	−0.518010	+	0.478909i
$635$		0			0
$636$	9.81701	+	0.771266i	0.389270	+	0.0305827i
$637$	−1.33889	+	1.33889i	−0.0530487	+	0.0530487i
$638$	36.0983	+	1.41584i	1.42915	+	0.0560535i
$639$	−11.4549			−0.453149
$640$		0			0
$641$	11.1680			0.441111			0.220555	−	0.975374i	$-0.429213\pi$
$641$	11.1680			0.441111			0.220555	+	0.975374i	$0.429213\pi$
$642$	−0.452855	−	0.0177617i	−0.0178728	−	0.000700999i
$643$	−21.9585	+	21.9585i	−0.865957	+	0.865957i	−0.992022	−	0.126065i	$-0.959765\pi$
$643$	−21.9585	+	21.9585i	−0.865957	+	0.865957i	0.126065	+	0.992022i	$0.459765\pi$
$644$	15.3256	+	1.20405i	0.603914	+	0.0474460i
$645$		0			0
$646$	12.4421	−	11.5029i	0.489526	−	0.452575i
$647$		−	36.9848i		−	1.45402i	−0.686625	−	0.727011i	$-0.740909\pi$
$647$		−	36.9848i		−	1.45402i	0.686625	−	0.727011i	$-0.259091\pi$
$648$	13.8539	+	1.63683i	0.544231	+	0.0643009i
$649$			40.4238i			1.58677i
$650$		0			0
$651$	4.90368	+	4.90368i	0.192190	+	0.192190i
$652$	26.4533	−	22.5995i	1.03599	−	0.885065i
$653$	−18.4157	+	18.4157i	−0.720663	+	0.720663i	−0.968740	−	0.248077i	$-0.920201\pi$
$653$	−18.4157	+	18.4157i	−0.720663	+	0.720663i	0.248077	+	0.968740i	$0.420201\pi$
$654$	0.00810646	−	0.206683i	0.000316988	−	0.00808196i
$655$		0			0
$656$	5.15658	−	32.6150i	0.201331	−	1.27340i
$657$	−20.9525			−0.817435
$658$	−1.06143	+	27.0622i	−0.0413787	+	1.05500i
$659$	−15.5421	+	15.5421i	−0.605434	+	0.605434i	−0.941749	−	0.336316i	$-0.890819\pi$
$659$	−15.5421	+	15.5421i	−0.605434	+	0.605434i	0.336316	+	0.941749i	$0.390819\pi$
$660$		0			0
$661$	29.6677	+	29.6677i	1.15394	+	1.15394i	0.985755	+	0.168185i	$0.0537906\pi$
$661$	29.6677	+	29.6677i	1.15394	+	1.15394i	0.168185	+	0.985755i	$0.446209\pi$
$662$	−8.24507	−	8.91825i	−0.320454	−	0.346617i
$663$			0.401363i			0.0155877i
$664$	−3.67215	+	2.89611i	−0.142507	+	0.112391i
$665$		0			0
$666$	−14.7373	+	13.6249i	−0.571058	+	0.527953i
$667$	5.31992	+	5.31992i	0.205988	+	0.205988i
$668$	1.54581	−	19.6758i	0.0598092	−	0.761278i
$669$	−11.7767	+	11.7767i	−0.455313	+	0.455313i
$670$		0			0
$671$	−55.7864			−2.15361
$672$	10.2435	+	15.3192i	0.395152	+	0.590949i
$673$	−29.2198			−1.12634			−0.563171	−	0.826340i	$-0.690419\pi$
$673$	−29.2198			−1.12634			−0.563171	+	0.826340i	$0.690419\pi$
$674$	−31.1209	−	1.22061i	−1.19873	−	0.0470163i
$675$		0			0
$676$	−2.03397	+	25.8893i	−0.0782298	+	0.995743i
$677$	17.2591	+	17.2591i	0.663320	+	0.663320i	0.956161	−	0.292841i	$-0.0946006\pi$
$677$	17.2591	+	17.2591i	0.663320	+	0.663320i	−0.292841	+	0.956161i	$0.594601\pi$
$678$	4.29011	−	3.96628i	0.164761	−	0.152324i
$679$		−	65.8179i		−	2.52586i
$680$		0			0
$681$			6.52082i			0.249878i
$682$	−11.3111	−	12.2346i	−0.433124	−	0.468487i
$683$	1.10407	+	1.10407i	0.0422459	+	0.0422459i	0.727914	−	0.685668i	$-0.240490\pi$
$683$	1.10407	+	1.10407i	0.0422459	+	0.0422459i	−0.685668	+	0.727914i	$0.740490\pi$
$684$	8.40041	+	9.83289i	0.321198	+	0.375970i
$685$		0			0
$686$	2.15224	−	54.8738i	0.0821731	−	2.09509i
$687$	15.7113			0.599425
$688$	−7.56181	−	10.4020i	−0.288291	−	0.396571i
$689$	0.885743			0.0337441
$690$		0			0
$691$	−28.4233	+	28.4233i	−1.08127	+	1.08127i	−0.0848830	+	0.996391i	$0.527052\pi$
$691$	−28.4233	+	28.4233i	−1.08127	+	1.08127i	−0.996391	+	0.0848830i	$0.972948\pi$
$692$	28.8359	−	24.6350i	1.09617	−	0.936481i
$693$	−46.5545	−	46.5545i	−1.76846	−	1.76846i
$694$	16.1458	+	17.4640i	0.612885	+	0.662924i
$695$		0			0
$696$	−1.05822	+	8.95660i	−0.0401118	+	0.339499i
$697$			38.5875i			1.46161i
$698$	12.7132	−	11.7536i	0.481201	−	0.444879i
$699$	8.05933	+	8.05933i	0.304832	+	0.304832i
$700$		0			0
$701$	−23.7991	+	23.7991i	−0.898880	+	0.898880i	−0.995337	−	0.0964573i	$-0.969249\pi$
$701$	−23.7991	+	23.7991i	−0.898880	+	0.898880i	0.0964573	+	0.995337i	$0.469249\pi$
$702$	−0.670105	−	0.0262826i	−0.0252915	−	0.000991974i
$703$	−14.4200			−0.543862
$704$	−23.1503	−	37.7431i	−0.872510	−	1.42250i
$705$		0			0
$706$	−37.6109	−	1.47516i	−1.41550	−	0.0555184i
$707$	63.2278	−	63.2278i	2.37793	−	2.37793i
$708$	−10.0608	−	0.790421i	−0.378109	−	0.0297058i
$709$	1.49921	+	1.49921i	0.0563039	+	0.0563039i	0.734698	−	0.678394i	$-0.237324\pi$
$709$	1.49921	+	1.49921i	0.0563039	+	0.0563039i	−0.678394	+	0.734698i	$0.737324\pi$
$710$		0			0
$711$			29.0911i			1.09100i
$712$	1.07716	−	9.11688i	0.0403682	−	0.341670i
$713$		−	3.47000i		−	0.129953i
$714$	−14.6194	−	15.8130i	−0.547118	−	0.591787i
$715$		0			0
$716$	0.902323	−	0.770870i	0.0337214	−	0.0288088i
$717$	2.56919	−	2.56919i	0.0959482	−	0.0959482i
$718$	−0.268830	+	6.85412i	−0.0100327	+	0.255794i
$719$	7.37612			0.275083			0.137541	−	0.990496i	$-0.456080\pi$
$719$	7.37612			0.275083			0.137541	+	0.990496i	$0.456080\pi$
$720$		0			0
$721$	64.9017			2.41707
$722$	0.688923	−	17.5649i	0.0256391	−	0.653696i
$723$	−6.89425	+	6.89425i	−0.256400	+	0.256400i
$724$	−26.1996	−	30.6673i	−0.973702	−	1.13974i
$725$		0			0
$726$	−13.0214	−	14.0846i	−0.483270	−	0.522727i
$727$			30.1470i			1.11809i	0.829137	+	0.559045i	$0.188832\pi$
$727$			30.1470i			1.11809i	−0.829137	+	0.559045i	$0.811168\pi$
$728$	1.02648	+	1.30153i	0.0380438	+	0.0482380i
$729$		−	4.53447i		−	0.167943i
$730$		0			0
$731$	10.6267	+	10.6267i	0.393041	+	0.393041i
$732$	1.09081	−	13.8843i	0.0403176	−	0.513180i
$733$	−1.43297	+	1.43297i	−0.0529279	+	0.0529279i	−0.733075	−	0.680147i	$-0.761916\pi$
$733$	−1.43297	+	1.43297i	−0.0529279	+	0.0529279i	0.680147	+	0.733075i	$0.261916\pi$
$734$	−22.1495	−	0.868740i	−0.817553	−	0.0320658i
$735$		0			0
$736$	1.79585	−	9.04449i	0.0661959	−	0.333384i
$737$	−58.6977			−2.16216
$738$	−29.4284	−	1.15423i	−1.08328	−	0.0424879i
$739$	31.0001	−	31.0001i	1.14036	−	1.14036i	0.151973	−	0.988385i	$-0.451437\pi$
$739$	31.0001	−	31.0001i	1.14036	−	1.14036i	0.988385	−	0.151973i	$-0.0485626\pi$
$740$		0			0
$741$	−0.155627	−	0.155627i	−0.00571710	−	0.00571710i
$742$	−34.8968	+	32.2626i	−1.28110	+	1.18440i
$743$		−	38.5395i		−	1.41388i	−0.707276	−	0.706938i	$-0.750076\pi$
$743$		−	38.5395i		−	1.41388i	0.707276	−	0.706938i	$-0.249924\pi$
$744$	3.26616	−	2.57592i	0.119743	−	0.0944378i
$745$		0			0
$746$	7.39243	+	7.99599i	0.270656	+	0.292754i
$747$	2.94952	+	2.94952i	0.107917	+	0.107917i
$748$	33.6096	+	39.3408i	1.22889	+	1.43844i
$749$	1.54664	−	1.54664i	0.0565128	−	0.0565128i
$750$		0			0
$751$	26.9523			0.983503			0.491751	−	0.870736i	$-0.336357\pi$
$751$	26.9523			0.983503			0.491751	+	0.870736i	$0.336357\pi$
$752$	16.0458	+	2.53692i	0.585132	+	0.0925118i
$753$	−9.75884			−0.355632
$754$	−0.0317935	+	0.810610i	−0.00115785	+	0.0295207i
$755$		0			0
$756$	27.3583	−	23.3727i	0.995012	−	0.850056i
$757$	17.0688	+	17.0688i	0.620377	+	0.620377i	0.945628	−	0.325251i	$-0.105449\pi$
$757$	17.0688	+	17.0688i	0.620377	+	0.620377i	−0.325251	+	0.945628i	$0.605449\pi$
$758$	23.6380	+	25.5680i	0.858573	+	0.928671i
$759$		−	6.23290i		−	0.226240i
$760$		0			0
$761$		−	6.89608i		−	0.249983i	−0.992158	−	0.124991i	$-0.960110\pi$
$761$		−	6.89608i		−	0.249983i	0.992158	−	0.124991i	$-0.0398903\pi$
$762$	−1.95907	+	1.81120i	−0.0709698	+	0.0656128i
$763$	0.705886	+	0.705886i	0.0255548	+	0.0255548i
$764$	34.5544	+	2.71474i	1.25013	+	0.0982158i
$765$		0			0
$766$	−12.7878	−	0.501558i	−0.462041	−	0.0181220i
$767$	−0.907741			−0.0327766
$768$	9.84631	−	5.02373i	0.355298	−	0.181278i
$769$	11.8443			0.427117			0.213558	−	0.976930i	$-0.431495\pi$
$769$	11.8443			0.427117			0.213558	+	0.976930i	$0.431495\pi$
$770$		0			0
$771$	4.12679	−	4.12679i	0.148623	−	0.148623i
$772$	−33.6297	−	2.64209i	−1.21036	−	0.0950910i
$773$	−3.58865	−	3.58865i	−0.129075	−	0.129075i	0.639618	−	0.768693i	$-0.279093\pi$
$773$	−3.58865	−	3.58865i	−0.129075	−	0.129075i	−0.768693	+	0.639618i	$0.779093\pi$
$774$	−8.42219	+	7.78646i	−0.302729	+	0.279878i
$775$		0			0
$776$	−39.2066	−	4.63226i	−1.40744	−	0.166288i
$777$			18.3269i			0.657474i
$778$	20.8567	+	22.5595i	0.747748	+	0.808798i
$779$	−14.9622	−	14.9622i	−0.536075	−	0.536075i
$780$		0			0
$781$	17.7705	−	17.7705i	0.635880	−	0.635880i
$782$	−0.422319	+	10.7675i	−0.0151021	+	0.385045i
$783$	17.6100			0.629332
$784$	−60.1925	−	9.51668i	−2.14973	−	0.339882i
$785$		0			0
$786$	0.0440558	−	1.12325i	0.00157142	−	0.0400650i
$787$	−22.4800	+	22.4800i	−0.801326	+	0.801326i	−0.983303	−	0.181977i	$-0.941750\pi$
$787$	−22.4800	+	22.4800i	−0.801326	+	0.801326i	0.181977	+	0.983303i	$0.441750\pi$
$788$	6.59390	+	7.71833i	0.234898	+	0.274954i
$789$	−8.94296	−	8.94296i	−0.318378	−	0.318378i
$790$		0			0
$791$			28.1981i			1.00261i
$792$	−31.0082	+	24.4552i	−1.10183	+	0.868979i
$793$		−	1.25272i		−	0.0444853i
$794$	−13.8708	+	12.8238i	−0.492255	+	0.455098i
$795$		0			0
$796$	−1.04091	+	13.2492i	−0.0368941	+	0.469605i
$797$	−8.67589	+	8.67589i	−0.307316	+	0.307316i	−0.843867	−	0.536552i	$-0.819727\pi$
$797$	−8.67589	+	8.67589i	−0.307316	+	0.307316i	0.536552	+	0.843867i	$0.319727\pi$
$798$	11.8001	+	0.462818i	0.417717	+	0.0163836i
$799$	−18.9842			−0.671612
$800$		0			0
$801$	−8.18800			−0.289309
$802$	30.4903	+	1.19588i	1.07665	+	0.0422280i
$803$	32.5046	−	32.5046i	1.14706	−	1.14706i
$804$	1.14774	−	14.6089i	0.0404775	−	0.515216i
$805$		0			0
$806$	0.274735	−	0.253998i	0.00967714	−	0.00894668i
$807$		−	13.2515i		−	0.466476i
$808$	−33.2138	−	42.1138i	−1.16846	−	1.48156i
$809$		−	27.9066i		−	0.981143i	−0.871401	−	0.490571i	$-0.836788\pi$
$809$		−	27.9066i		−	0.981143i	0.871401	−	0.490571i	$-0.163212\pi$
$810$		0			0
$811$	15.2635	+	15.2635i	0.535974	+	0.535974i	0.922344	−	0.386370i	$-0.126271\pi$
$811$	15.2635	+	15.2635i	0.535974	+	0.535974i	−0.386370	+	0.922344i	$0.626271\pi$
$812$	−28.2734	−	33.0947i	−0.992201	−	1.16140i
$813$	−1.09681	+	1.09681i	−0.0384670	+	0.0384670i
$814$	1.72574	−	43.9996i	0.0604871	−	1.54219i
$815$		0			0
$816$	−10.4485	+	7.59562i	−0.365770	+	0.265900i
$817$	−8.24089			−0.288312
$818$	−0.231309	+	5.89749i	−0.00808754	+	0.206201i
$819$	1.04541	−	1.04541i	0.0365295	−	0.0365295i
$820$		0			0
$821$	25.2883	+	25.2883i	0.882567	+	0.882567i	0.993795	−	0.111228i	$-0.0354782\pi$
$821$	25.2883	+	25.2883i	0.882567	+	0.882567i	−0.111228	+	0.993795i	$0.535478\pi$
$822$	0.132527	+	0.143348i	0.00462242	+	0.00499983i
$823$		−	7.12228i		−	0.248267i	−0.992266	−	0.124133i	$-0.960385\pi$
$823$		−	7.12228i		−	0.248267i	0.992266	−	0.124133i	$-0.0396151\pi$
$824$	4.56778	−	38.6609i	0.159126	−	1.34682i
$825$		0			0
$826$	35.7634	−	33.0639i	1.24437	−	1.15044i
$827$	32.1618	+	32.1618i	1.11837	+	1.11837i	0.991980	+	0.126394i	$0.0403403\pi$
$827$	32.1618	+	32.1618i	1.11837	+	1.11837i	0.126394	+	0.991980i	$0.459660\pi$
$828$	−8.19909	−	0.644155i	−0.284938	−	0.0223859i
$829$	−34.9802	+	34.9802i	−1.21491	+	1.21491i	−0.245522	+	0.969391i	$0.578959\pi$
$829$	−34.9802	+	34.9802i	−1.21491	+	1.21491i	−0.969391	+	0.245522i	$0.921041\pi$
$830$		0			0
$831$	−7.11529			−0.246827
$832$	0.847545	−	0.519854i	0.0293833	−	0.0180227i
$833$	71.2149			2.46745
$834$	16.0573	+	0.629793i	0.556018	+	0.0218079i
$835$		0			0
$836$	−28.2862	−	2.22228i	−0.978299	−	0.0768593i
$837$	−5.74321	−	5.74321i	−0.198514	−	0.198514i
$838$	−39.8258	+	36.8196i	−1.37576	+	1.27191i
$839$			11.1147i			0.383721i	0.981422	+	0.191861i	$0.0614521\pi$
$839$			11.1147i			0.383721i	−0.981422	+	0.191861i	$0.938548\pi$
$840$		0			0
$841$			7.69754i			0.265432i
$842$	36.6028	+	39.5913i	1.26142	+	1.36441i
$843$	2.95105	+	2.95105i	0.101640	+	0.101640i
$844$	4.10543	−	3.50734i	0.141315	−	0.120728i
$845$		0			0
$846$	0.567855	−	14.4781i	0.0195233	−	0.497767i
$847$	92.5750			3.18092
$848$	16.7623	+	23.0581i	0.575620	+	0.791818i
$849$	14.7874			0.507501
$850$		0			0
$851$	6.48436	−	6.48436i	0.222281	−	0.222281i
$852$	4.07532	+	4.77027i	0.139618	+	0.163427i
$853$	28.9107	+	28.9107i	0.989884	+	0.989884i	0.999949	−	0.0100656i	$-0.00320402\pi$
$853$	28.9107	+	28.9107i	0.989884	+	0.989884i	−0.0100656	+	0.999949i	$0.503204\pi$
$854$	45.6295	+	49.3550i	1.56141	+	1.68889i
$855$		0			0
$856$	−0.812454	−	1.03016i	−0.0277691	−	0.0352101i
$857$		−	34.1485i		−	1.16649i	−0.812296	−	0.583245i	$-0.801783\pi$
$857$		−	34.1485i		−	1.16649i	0.812296	−	0.583245i	$-0.198217\pi$
$858$	0.493486	−	0.456237i	0.0168473	−	0.0155757i
$859$	20.4589	+	20.4589i	0.698047	+	0.698047i	0.963989	−	0.265942i	$-0.0856829\pi$
$859$	20.4589	+	20.4589i	0.698047	+	0.698047i	−0.265942	+	0.963989i	$0.585683\pi$
$860$		0			0
$861$	−19.0159	+	19.0159i	−0.648060	+	0.648060i
$862$	31.6623	+	1.24185i	1.07842	+	0.0422976i
$863$	−35.3591			−1.20364			−0.601818	−	0.798633i	$-0.705557\pi$
$863$	−35.3591			−1.20364			−0.601818	+	0.798633i	$0.705557\pi$
$864$	−11.9972	−	17.9419i	−0.408154	−	0.610395i
$865$		0			0
$866$	−23.7491	−	0.931480i	−0.807028	−	0.0316530i
$867$	2.36940	−	2.36940i	0.0804692	−	0.0804692i
$868$	−1.57240	+	20.0141i	−0.0533706	+	0.679324i
$869$	−45.1304	−	45.1304i	−1.53094	−	1.53094i
$870$		0			0
$871$		−	1.31809i		−	0.0446618i
$872$	0.470165	−	0.370804i	0.0159218	−	0.0125570i
$873$			35.2120i			1.19175i
$874$	−4.01130	−	4.33880i	−0.135684	−	0.146762i
$875$		0			0
$876$	7.45430	+	8.72545i	0.251857	+	0.294806i
$877$	−3.15415	+	3.15415i	−0.106508	+	0.106508i	−0.758353	−	0.651845i	$-0.773995\pi$
$877$	−3.15415	+	3.15415i	−0.106508	+	0.106508i	0.651845	+	0.758353i	$0.273995\pi$
$878$	0.503440	−	12.8358i	0.0169903	−	0.433186i
$879$	10.5301			0.355172
$880$		0			0
$881$	20.3066			0.684146			0.342073	−	0.939673i	$-0.388871\pi$
$881$	20.3066			0.684146			0.342073	+	0.939673i	$0.388871\pi$
$882$	−2.13018	+	54.3114i	−0.0717270	+	1.82876i
$883$	0.523303	−	0.523303i	0.0176105	−	0.0176105i	−0.698247	−	0.715857i	$-0.746036\pi$
$883$	0.523303	−	0.523303i	0.0176105	−	0.0176105i	0.715857	+	0.698247i	$0.246036\pi$
$884$	−0.883423	+	0.754723i	−0.0297127	+	0.0253841i
$885$		0			0
$886$	17.0252	+	18.4153i	0.571973	+	0.618673i
$887$			34.8129i			1.16890i	0.811429	+	0.584452i	$0.198690\pi$
$887$			34.8129i			1.16890i	−0.811429	+	0.584452i	$0.801310\pi$
$888$	10.9170	+	1.28985i	0.366352	+	0.0432845i
$889$		−	12.8766i		−	0.431868i
$890$		0			0
$891$	19.3024	+	19.3024i	0.646656	+	0.646656i
$892$	−48.0661	−	3.77627i	−1.60937	−	0.126439i
$893$	7.36103	−	7.36103i	0.246328	−	0.246328i
$894$	1.56546	+	0.0614001i	0.0523569	+	0.00205353i
$895$		0			0
$896$	−14.4564	+	51.3527i	−0.482956	+	1.71557i
$897$	0.139964			0.00467325
$898$	−25.5363	−	1.00157i	−0.852156	−	0.0334230i
$899$	−6.94743	+	6.94743i	−0.231710	+	0.231710i
$900$		0			0
$901$	−23.5562	−	23.5562i	−0.784770	−	0.784770i
$902$	47.4444	−	43.8631i	1.57973	−	1.46048i
$903$			10.4736i			0.348540i
$904$	16.7971	+	1.98458i	0.558664	+	0.0660061i
$905$		0			0
$906$	−4.72384	−	5.10952i	−0.156939	−	0.169752i
$907$	−13.3188	−	13.3188i	−0.442244	−	0.442244i	0.450521	−	0.892766i	$-0.351238\pi$
$907$	−13.3188	−	13.3188i	−0.442244	−	0.442244i	−0.892766	+	0.450521i	$0.851238\pi$
$908$	−14.3527	+	12.2618i	−0.476311	+	0.406921i
$909$	−33.8264	+	33.8264i	−1.12195	+	1.12195i
$910$		0			0
$911$	−47.0117			−1.55757			−0.778783	−	0.627294i	$-0.784163\pi$
$911$	−47.0117			−1.55757			−0.778783	+	0.627294i	$0.784163\pi$
$912$	1.10618	−	6.99653i	0.0366293	−	0.231678i
$913$	−9.15148			−0.302870
$914$	−1.03444	+	26.3742i	−0.0342163	+	0.872382i
$915$		0			0
$916$	29.5436	+	34.5815i	0.976148	+	1.14261i
$917$	3.83624	+	3.83624i	0.126684	+	0.126684i
$918$	17.1223	+	18.5203i	0.565121	+	0.611261i
$919$			31.3426i			1.03390i	0.856016	+	0.516949i	$0.172932\pi$
$919$			31.3426i			1.03390i	−0.856016	+	0.516949i	$0.827068\pi$
$920$		0			0
$921$			7.76133i			0.255745i
$922$	1.22070	−	1.12856i	0.0402017	−	0.0371672i
$923$	0.399048	+	0.399048i	0.0131348	+	0.0131348i
$924$	−2.82437	+	35.9499i	−0.0929151	+	1.18266i
$925$		0			0
$926$	11.0582	+	0.433721i	0.363395	+	0.0142529i
$927$	−34.7219			−1.14042
$928$	−21.7039	+	14.5128i	−0.712464	+	0.476406i
$929$	30.3384			0.995369			0.497685	−	0.867358i	$-0.334184\pi$
$929$	30.3384			0.995369			0.497685	+	0.867358i	$0.334184\pi$
$930$		0			0
$931$	−27.6133	+	27.6133i	−0.904990	+	0.904990i
$932$	−2.58427	+	32.8938i	−0.0846507	+	1.07747i
$933$	−15.2245	−	15.2245i	−0.498429	−	0.498429i
$934$	12.8508	−	11.8808i	0.420492	−	0.388752i
$935$		0			0
$936$	−0.549157	−	0.696309i	−0.0179498	−	0.0227596i
$937$			14.5267i			0.474565i	0.971441	+	0.237283i	$0.0762567\pi$
$937$			14.5267i			0.474565i	−0.971441	+	0.237283i	$0.923743\pi$
$938$	48.0107	+	51.9306i	1.56760	+	1.69559i
$939$	−2.61767	−	2.61767i	−0.0854245	−	0.0854245i
$940$		0			0
$941$	37.2863	−	37.2863i	1.21550	−	1.21550i	0.246307	−	0.969192i	$-0.420783\pi$
$941$	37.2863	−	37.2863i	1.21550	−	1.21550i	0.969192	−	0.246307i	$-0.0792172\pi$
$942$	−0.288168	+	7.34716i	−0.00938902	+	0.239384i
$943$	13.4563			0.438197
$944$	−17.1786	−	23.6307i	−0.559116	−	0.769115i
$945$		0			0
$946$	0.986239	−	25.1453i	0.0320654	−	0.817543i
$947$	15.8961	−	15.8961i	0.516553	−	0.516553i	−0.399973	−	0.916527i	$-0.630981\pi$
$947$	15.8961	−	15.8961i	0.516553	−	0.516553i	0.916527	+	0.399973i	$0.130981\pi$
$948$	12.1147	−	10.3498i	0.393466	−	0.336145i
$949$	0.729912	+	0.729912i	0.0236939	+	0.0236939i
$950$		0			0
$951$		−	8.67765i		−	0.281392i
$952$	7.31501	−	61.9129i	0.237081	−	2.00661i
$953$			33.2248i			1.07626i	0.842862	+	0.538129i	$0.180869\pi$
$953$			33.2248i			1.07626i	−0.842862	+	0.538129i	$0.819131\pi$
$954$	18.6695	−	17.2603i	0.604447	−	0.558822i
$955$		0			0
$956$	10.4860	+	0.823827i	0.339143	+	0.0266445i
$957$	−12.4791	+	12.4791i	−0.403393	+	0.403393i
$958$	−2.97346	−	0.116624i	−0.0960682	−	0.00376796i
$959$	−0.942197			−0.0304251
$960$		0			0
$961$	−26.4684			−0.853820
$962$	0.988038	+	0.0387525i	0.0318556	+	0.00124943i
$963$	−0.827438	+	0.827438i	−0.0266638	+	0.0266638i
$964$	−28.1386	−	2.21069i	−0.906283	−	0.0712014i
$965$		0			0
$966$	−5.51433	+	5.09809i	−0.177421	+	0.164028i
$967$		−	1.79116i		−	0.0576000i	−0.999585	−	0.0288000i	$-0.990831\pi$
$967$		−	1.79116i		−	0.0576000i	0.999585	−	0.0288000i	$-0.00916859\pi$
$968$	6.51543	−	55.1455i	0.209414	−	1.77244i
$969$			8.27774i			0.265919i
$970$		0			0
$971$	5.31278	+	5.31278i	0.170495	+	0.170495i	0.787197	−	0.616702i	$-0.211531\pi$
$971$	5.31278	+	5.31278i	0.170495	+	0.170495i	−0.616702	+	0.787197i	$0.711531\pi$
$972$	−22.5872	+	19.2966i	−0.724485	+	0.618940i
$973$	−54.8404	+	54.8404i	−1.75810	+	1.75810i
$974$	−0.270022	+	6.88451i	−0.00865207	+	0.220594i
$975$		0			0
$976$	32.6114	−	23.7072i	1.04386	−	0.758848i
$977$	6.81676			0.218088			0.109044	−	0.994037i	$-0.465221\pi$
$977$	6.81676			0.218088			0.109044	+	0.994037i	$0.465221\pi$
$978$	−0.666126	+	16.9836i	−0.0213003	+	0.543076i
$979$	12.7025	−	12.7025i	0.405972	−	0.405972i
$980$		0			0
$981$	−0.377643	−	0.377643i	−0.0120572	−	0.0120572i
$982$	−19.4941	−	21.0857i	−0.622082	−	0.672873i
$983$			5.49468i			0.175253i	0.996153	+	0.0876265i	$0.0279282\pi$
$983$			5.49468i			0.175253i	−0.996153	+	0.0876265i	$0.972072\pi$
$984$	9.98913	+	12.6658i	0.318442	+	0.403771i
$985$		0			0
$986$	22.4036	−	20.7125i	0.713475	−	0.659620i
$987$	−9.35538	−	9.35538i	−0.297785	−	0.297785i
$988$	0.0499028	−	0.635184i	0.00158762	−	0.0202079i
$989$	3.70574	−	3.70574i	0.117836	−	0.117836i
$990$		0			0
$991$	48.7524			1.54867			0.774335	−	0.632775i	$-0.218084\pi$
$991$	48.7524			1.54867			0.774335	+	0.632775i	$0.218084\pi$
$992$	11.8114	+	2.34525i	0.375013	+	0.0744616i
$993$	5.93333			0.188289
$994$	−30.2569	−	1.18673i	−0.959691	−	0.0376407i
$995$		0			0
$996$	0.178942	−	2.27766i	0.00567000	−	0.0721703i
$997$	−42.5246	−	42.5246i	−1.34677	−	1.34677i	−0.889149	−	0.457618i	$-0.848703\pi$
$997$	−42.5246	−	42.5246i	−1.34677	−	1.34677i	−0.457618	−	0.889149i	$-0.651297\pi$
$998$	36.8694	−	34.0864i	1.16708	−	1.07899i
$999$		−	21.4646i		−	0.679109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.l.g.101.1	yes	12
4.3	odd	2		1600.2.l.f.1201.3		12
5.2	odd	4		400.2.q.f.149.3		12
5.3	odd	4		400.2.q.e.149.4		12
5.4	even	2		400.2.l.f.101.6	✓	12
16.3	odd	4		1600.2.l.f.401.3		12
16.13	even	4	inner	400.2.l.g.301.1	yes	12
20.3	even	4		1600.2.q.e.49.3		12
20.7	even	4		1600.2.q.f.49.4		12
20.19	odd	2		1600.2.l.g.1201.4		12
80.3	even	4		1600.2.q.f.849.4		12
80.13	odd	4		400.2.q.f.349.3		12
80.19	odd	4		1600.2.l.g.401.4		12
80.29	even	4		400.2.l.f.301.6	yes	12
80.67	even	4		1600.2.q.e.849.3		12
80.77	odd	4		400.2.q.e.349.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.6	✓	12	5.4	even	2
400.2.l.f.301.6	yes	12	80.29	even	4
400.2.l.g.101.1	yes	12	1.1	even	1	trivial
400.2.l.g.301.1	yes	12	16.13	even	4	inner
400.2.q.e.149.4		12	5.3	odd	4
400.2.q.e.349.4		12	80.77	odd	4
400.2.q.f.149.3		12	5.2	odd	4
400.2.q.f.349.3		12	80.13	odd	4
1600.2.l.f.401.3		12	16.3	odd	4
1600.2.l.f.1201.3		12	4.3	odd	2
1600.2.l.g.401.4		12	80.19	odd	4
1600.2.l.g.1201.4		12	20.19	odd	2
1600.2.q.e.49.3		12	20.3	even	4
1600.2.q.e.849.3		12	80.67	even	4
1600.2.q.f.49.4		12	20.7	even	4
1600.2.q.f.849.4		12	80.3	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)

\(f(q)\)	\(=\)	\(q+(-1.41313 - 0.0554252i) q^{2} +(0.488516 - 0.488516i) q^{3} +(1.99386 + 0.156646i) q^{4} +(-0.717411 + 0.663259i) q^{6} -4.71540i q^{7} +(-2.80889 - 0.331870i) q^{8} +2.52270i q^{9} +O(q^{10})\)	\(q+(-1.41313 - 0.0554252i) q^{2} +(0.488516 - 0.488516i) q^{3} +(1.99386 + 0.156646i) q^{4} +(-0.717411 + 0.663259i) q^{6} -4.71540i q^{7} +(-2.80889 - 0.331870i) q^{8} +2.52270i q^{9} +(-3.91360 - 3.91360i) q^{11} +(1.05055 - 0.897506i) q^{12} +(0.0878822 - 0.0878822i) q^{13} +(-0.261352 + 6.66346i) q^{14} +(3.95092 + 0.624658i) q^{16} -4.67442 q^{17} +(0.139821 - 3.56490i) q^{18} +(1.81249 - 1.81249i) q^{19} +(-2.30355 - 2.30355i) q^{21} +(5.31350 + 5.74732i) q^{22} +1.63007i q^{23} +(-1.53431 + 1.21006i) q^{24} +(-0.129060 + 0.119318i) q^{26} +(2.69793 + 2.69793i) q^{27} +(0.738648 - 9.40184i) q^{28} +(3.26362 - 3.26362i) q^{29} -2.12875 q^{31} +(-5.54854 - 1.10170i) q^{32} -3.82371 q^{33} +(6.60555 + 0.259081i) q^{34} +(-0.395171 + 5.02991i) q^{36} +(-3.97797 - 3.97797i) q^{37} +(-2.66173 + 2.46082i) q^{38} -0.0858637i q^{39} -8.25504i q^{41} +(3.12753 + 3.38288i) q^{42} +(-2.27336 - 2.27336i) q^{43} +(-7.19010 - 8.41620i) q^{44} +(0.0903468 - 2.30349i) q^{46} +4.06129 q^{47} +(2.23524 - 1.62493i) q^{48} -15.2350 q^{49} +(-2.28353 + 2.28353i) q^{51} +(0.188991 - 0.161458i) q^{52} +(5.03938 + 5.03938i) q^{53} +(-3.66298 - 3.96205i) q^{54} +(-1.56490 + 13.2450i) q^{56} -1.77086i q^{57} +(-4.79280 + 4.43103i) q^{58} +(-5.16453 - 5.16453i) q^{59} +(7.12726 - 7.12726i) q^{61} +(3.00819 + 0.117986i) q^{62} +11.8956 q^{63} +(7.77972 + 1.86437i) q^{64} +(5.40339 + 0.211930i) q^{66} +(7.49920 - 7.49920i) q^{67} +(-9.32012 - 0.732228i) q^{68} +(0.796314 + 0.796314i) q^{69} +4.54072i q^{71} +(0.837210 - 7.08600i) q^{72} +8.30557i q^{73} +(5.40090 + 5.84186i) q^{74} +(3.89776 - 3.32992i) q^{76} +(-18.4542 + 18.4542i) q^{77} +(-0.00475901 + 0.121336i) q^{78} +11.5317 q^{79} -4.93215 q^{81} +(-0.457537 + 11.6654i) q^{82} +(1.16919 - 1.16919i) q^{83} +(-4.23211 - 4.95379i) q^{84} +(3.08655 + 3.33855i) q^{86} -3.18866i q^{87} +(9.69406 + 12.2917i) q^{88} +3.24572i q^{89} +(-0.414400 - 0.414400i) q^{91} +(-0.255343 + 3.25012i) q^{92} +(-1.03993 + 1.03993i) q^{93} +(-5.73912 - 0.225098i) q^{94} +(-3.24875 + 2.17235i) q^{96} +13.9581 q^{97} +(21.5290 + 0.844405i) q^{98} +(9.87285 - 9.87285i) 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

Modular forms

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Database

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