LMFDB - Embedded newform 400.2.q.e.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(149,400)]

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, 2]))

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

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

chi := DirichletCharacter("400.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ 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			349.4
Root			$-1.41313 - 0.0554252i$ of defining polynomial
Character	$\chi$	$=$	400.349
Dual form			400.2.q.e.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0554252 - 1.41313i) q^{2} +(0.488516 - 0.488516i) q^{3} +(-1.99386 + 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} -4.71540 q^{7} +(0.331870 + 2.80889i) q^{8} +2.52270i q^{9} +O(q^{10})$	\(q+(-0.0554252 - 1.41313i) q^{2} +(0.488516 - 0.488516i) q^{3} +(-1.99386 + 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} -4.71540 q^{7} +(0.331870 + 2.80889i) q^{8} +2.52270i q^{9} +(-3.91360 + 3.91360i) q^{11} +(-0.897506 + 1.05055i) q^{12} +(0.0878822 - 0.0878822i) q^{13} +(0.261352 + 6.66346i) q^{14} +(3.95092 - 0.624658i) q^{16} -4.67442i q^{17} +(3.56490 - 0.139821i) q^{18} +(-1.81249 - 1.81249i) q^{19} +(-2.30355 + 2.30355i) q^{21} +(5.74732 + 5.31350i) q^{22} -1.63007 q^{23} +(1.53431 + 1.21006i) q^{24} +(-0.129060 - 0.119318i) q^{26} +(2.69793 + 2.69793i) q^{27} +(9.40184 - 0.738648i) q^{28} +(-3.26362 - 3.26362i) q^{29} -2.12875 q^{31} +(-1.10170 - 5.54854i) q^{32} +3.82371i q^{33} +(-6.60555 + 0.259081i) q^{34} +(-0.395171 - 5.02991i) q^{36} +(-3.97797 - 3.97797i) q^{37} +(-2.46082 + 2.66173i) q^{38} -0.0858637i q^{39} +8.25504i q^{41} +(3.38288 + 3.12753i) q^{42} +(2.27336 + 2.27336i) q^{43} +(7.19010 - 8.41620i) q^{44} +(0.0903468 + 2.30349i) q^{46} +4.06129i q^{47} +(1.62493 - 2.23524i) q^{48} +15.2350 q^{49} +(-2.28353 - 2.28353i) q^{51} +(-0.161458 + 0.188991i) q^{52} +(-5.03938 - 5.03938i) q^{53} +(3.66298 - 3.96205i) q^{54} +(-1.56490 - 13.2450i) q^{56} -1.77086 q^{57} +(-4.43103 + 4.79280i) q^{58} +(5.16453 - 5.16453i) q^{59} +(7.12726 + 7.12726i) q^{61} +(0.117986 + 3.00819i) q^{62} -11.8956i q^{63} +(-7.77972 + 1.86437i) q^{64} +(5.40339 - 0.211930i) q^{66} +(-7.49920 + 7.49920i) q^{67} +(0.732228 + 9.32012i) q^{68} +(-0.796314 + 0.796314i) q^{69} -4.54072i q^{71} +(-7.08600 + 0.837210i) q^{72} -8.30557 q^{73} +(-5.40090 + 5.84186i) q^{74} +(3.89776 + 3.32992i) q^{76} +(18.4542 - 18.4542i) q^{77} +(-0.121336 + 0.00475901i) q^{78} -11.5317 q^{79} -4.93215 q^{81} +(11.6654 - 0.457537i) q^{82} +(1.16919 - 1.16919i) q^{83} +(4.23211 - 4.95379i) q^{84} +(3.08655 - 3.33855i) q^{86} -3.18866 q^{87} +(-12.2917 - 9.69406i) q^{88} +3.24572i q^{89} +(-0.414400 + 0.414400i) q^{91} +(3.25012 - 0.255343i) q^{92} +(-1.03993 + 1.03993i) q^{93} +(5.73912 - 0.225098i) q^{94} +(-3.24875 - 2.17235i) q^{96} +13.9581i q^{97} +(-0.844405 - 21.5290i) q^{98} +(-9.87285 - 9.87285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8	$ 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26} - 10 q^{27} + 10 q^{28} - 4 q^{31} - 2 q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 28 q^{38} - 10 q^{42} + 44 q^{44} - 10 q^{46} + 58 q^{48} - 4 q^{49} + 10 q^{51} + 16 q^{53} - 10 q^{54} + 6 q^{56} + 16 q^{57} - 4 q^{58} - 20 q^{59} + 4 q^{61} - 22 q^{62} - 38 q^{64} + 32 q^{66} - 50 q^{67} - 50 q^{68} + 54 q^{72} - 40 q^{73} - 10 q^{74} + 60 q^{76} + 8 q^{77} + 48 q^{78} - 12 q^{79} - 8 q^{81} + 12 q^{82} - 2 q^{83} - 34 q^{84} + 6 q^{86} + 64 q^{87} - 56 q^{88} - 50 q^{92} - 44 q^{93} - 32 q^{94} - 34 q^{96} + 30 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * 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 $

$2$	−0.0554252	−	1.41313i	−0.0391915	−	0.999232i
$2$	−0.0554252	−	1.41313i	−0.0391915	−	0.999232i
$3$	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
$7$	−4.71540			−1.78226			−0.891128	−	0.453753i	$-0.850085\pi$
$7$	−4.71540			−1.78226			−0.891128	+	0.453753i	$0.850085\pi$
$8$	0.331870	+	2.80889i	0.117334	+	0.993093i
$9$			2.52270i			0.840901i
$10$		0			0
$11$	−3.91360	+	3.91360i	−1.17999	+	1.17999i	−0.200249	+	0.979745i	$0.564175\pi$
$11$	−3.91360	+	3.91360i	−1.17999	+	1.17999i	−0.979745	+	0.200249i	$0.935825\pi$
$12$	−0.897506	+	1.05055i	−0.259088	+	0.303269i
$13$	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
$17$		−	4.67442i		−	1.13371i	−0.823816	−	0.566857i	$-0.808159\pi$
$17$		−	4.67442i		−	1.13371i	0.823816	−	0.566857i	$-0.191841\pi$
$18$	3.56490	−	0.139821i	0.840255	−	0.0329562i
$19$	−1.81249	−	1.81249i	−0.415813	−	0.415813i	0.467945	−	0.883758i	$-0.344995\pi$
$19$	−1.81249	−	1.81249i	−0.415813	−	0.415813i	−0.883758	+	0.467945i	$0.844995\pi$
$20$		0			0
$21$	−2.30355	+	2.30355i	−0.502676	+	0.502676i
$22$	5.74732	+	5.31350i	1.22533	+	1.13284i
$23$	−1.63007			−0.339893			−0.169946	−	0.985453i	$-0.554359\pi$
$23$	−1.63007			−0.339893			−0.169946	+	0.985453i	$0.554359\pi$
$24$	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
$28$	9.40184	−	0.738648i	1.77678	−	0.139591i
$29$	−3.26362	−	3.26362i	−0.606039	−	0.606039i	0.335869	−	0.941909i	$-0.390970\pi$
$29$	−3.26362	−	3.26362i	−0.606039	−	0.606039i	−0.941909	+	0.335869i	$0.890970\pi$
$30$		0			0
$31$	−2.12875			−0.382334			−0.191167	−	0.981557i	$-0.561227\pi$
$31$	−2.12875			−0.382334			−0.191167	+	0.981557i	$0.561227\pi$
$32$	−1.10170	−	5.54854i	−0.194755	−	0.980852i
$33$			3.82371i			0.665622i
$34$	−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	$0.903022\pi$
$38$	−2.46082	+	2.66173i	−0.399197	+	0.431790i
$39$		−	0.0858637i		−	0.0137492i
$40$		0			0
$41$			8.25504i			1.28922i	0.764511	+	0.644611i	$0.222980\pi$
$41$			8.25504i			1.28922i	−0.764511	+	0.644611i	$0.777020\pi$
$42$	3.38288	+	3.12753i	0.521990	+	0.482589i
$43$	2.27336	+	2.27336i	0.346685	+	0.346685i	0.858873	−	0.512188i	$-0.171165\pi$
$43$	2.27336	+	2.27336i	0.346685	+	0.346685i	−0.512188	+	0.858873i	$0.671165\pi$
$44$	7.19010	−	8.41620i	1.08395	−	1.26879i
$45$		0			0
$46$	0.0903468	+	2.30349i	0.0133209	+	0.339631i
$47$			4.06129i			0.592400i	0.955126	+	0.296200i	$0.0957195\pi$
$47$			4.06129i			0.592400i	−0.955126	+	0.296200i	$0.904281\pi$
$48$	1.62493	−	2.23524i	0.234539	−	0.322630i
$49$	15.2350			2.17643
$50$		0			0
$51$	−2.28353	−	2.28353i	−0.319758	−	0.319758i
$52$	−0.161458	+	0.188991i	−0.0223902	+	0.0262083i
$53$	−5.03938	−	5.03938i	−0.692211	−	0.692211i	0.270507	−	0.962718i	$-0.412809\pi$
$53$	−5.03938	−	5.03938i	−0.692211	−	0.692211i	−0.962718	+	0.270507i	$0.912809\pi$
$54$	3.66298	−	3.96205i	0.498469	−	0.539167i
$55$		0			0
$56$	−1.56490	−	13.2450i	−0.209119	−	1.76994i
$57$	−1.77086			−0.234556
$58$	−4.43103	+	4.79280i	−0.581822	+	0.629325i
$59$	5.16453	−	5.16453i	0.672365	−	0.672365i	−0.285896	−	0.958261i	$-0.592291\pi$
$59$	5.16453	−	5.16453i	0.672365	−	0.672365i	0.958261	+	0.285896i	$0.0922911\pi$
$60$		0			0
$61$	7.12726	+	7.12726i	0.912552	+	0.912552i	0.996472	−	0.0839206i	$-0.0267442\pi$
$61$	7.12726	+	7.12726i	0.912552	+	0.912552i	−0.0839206	+	0.996472i	$0.526744\pi$
$62$	0.117986	+	3.00819i	0.0149843	+	0.382041i
$63$		−	11.8956i		−	1.49870i
$64$	−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	−0.996748	−	0.0805758i	$-0.974324\pi$
$67$	−7.49920	+	7.49920i	−0.916173	+	0.916173i	0.0805758	+	0.996748i	$0.474324\pi$
$68$	0.732228	+	9.32012i	0.0887957	+	1.13023i
$69$	−0.796314	+	0.796314i	−0.0958649	+	0.0958649i
$70$		0			0
$71$		−	4.54072i		−	0.538884i	−0.963017	−	0.269442i	$-0.913161\pi$
$71$		−	4.54072i		−	0.538884i	0.963017	−	0.269442i	$-0.0868393\pi$
$72$	−7.08600	+	0.837210i	−0.835093	+	0.0986662i
$73$	−8.30557			−0.972093			−0.486047	−	0.873933i	$-0.661561\pi$
$73$	−8.30557			−0.972093			−0.486047	+	0.873933i	$0.661561\pi$
$74$	−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
$78$	−0.121336	+	0.00475901i	−0.0137386	+	0.000538852i
$79$	−11.5317			−1.29742			−0.648709	−	0.761037i	$-0.724691\pi$
$79$	−11.5317			−1.29742			−0.648709	+	0.761037i	$0.724691\pi$
$80$		0			0
$81$	−4.93215			−0.548017
$82$	11.6654	−	0.457537i	1.28823	−	0.0505266i
$83$	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
$87$	−3.18866			−0.341861
$88$	−12.2917	−	9.69406i	−1.31030	−	1.03339i
$89$			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
$92$	3.25012	−	0.255343i	0.338848	−	0.0266214i
$93$	−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
$97$			13.9581i			1.41723i	0.705598	+	0.708613i	$0.250679\pi$
$97$			13.9581i			1.41723i	−0.705598	+	0.708613i	$0.749321\pi$
$98$	−0.844405	−	21.5290i	−0.0852978	−	2.17476i
$99$	−9.87285	−	9.87285i	−0.992258	−	0.992258i
$100$		0			0
$101$	13.4088	−	13.4088i	1.33422	−	1.33422i	0.432672	−	0.901552i	$-0.357571\pi$
$101$	13.4088	−	13.4088i	1.33422	−	1.33422i	0.901552	−	0.432672i	$-0.142429\pi$
$102$	−3.10035	+	3.35348i	−0.306981	+	0.332044i
$103$	−13.7638			−1.35618			−0.678092	−	0.734977i	$-0.737193\pi$
$103$	−13.7638			−1.35618			−0.678092	+	0.734977i	$0.737193\pi$
$104$	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	$0.742862\pi$
$108$	−5.80190	−	4.95666i	−0.558288	−	0.476955i
$109$	0.149698	+	0.149698i	0.0143385	+	0.0143385i	0.714240	−	0.699901i	$-0.246773\pi$
$109$	0.149698	+	0.149698i	0.0143385	+	0.0143385i	−0.699901	+	0.714240i	$0.746773\pi$
$110$		0			0
$111$	−3.88660			−0.368900
$112$	−18.6302	+	2.94551i	−1.76039	+	0.278325i
$113$			5.97999i			0.562550i	0.959627	+	0.281275i	$0.0907573\pi$
$113$			5.97999i			0.562550i	−0.959627	+	0.281275i	$0.909243\pi$
$114$	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
$118$	−7.58439	−	7.01189i	−0.698199	−	0.645497i
$119$			22.0418i			2.02057i
$120$		0			0
$121$		−	19.6325i		−	1.78477i
$122$	9.67669	−	10.4668i	0.876086	−	0.947615i
$123$	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
$127$			2.73076i			0.242315i	0.992633	+	0.121158i	$0.0386607\pi$
$127$			2.73076i			0.242315i	−0.992633	+	0.121158i	$0.961339\pi$
$128$	3.06579	+	10.8904i	0.270980	+	0.962585i
$129$	2.22115			0.195561
$130$		0			0
$131$	−0.813555	−	0.813555i	−0.0710806	−	0.0710806i	0.670673	−	0.741753i	$-0.266006\pi$
$131$	−0.813555	−	0.813555i	−0.0710806	−	0.0710806i	−0.741753	+	0.670673i	$0.766006\pi$
$132$	−0.598967	−	7.62392i	−0.0521334	−	0.663577i
$133$	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
$137$	−0.199812			−0.0170711			−0.00853557	−	0.999964i	$-0.502717\pi$
$137$	−0.199812			−0.0170711			−0.00853557	+	0.999964i	$0.502717\pi$
$138$	1.16943	+	1.08116i	0.0995484	+	0.0920342i
$139$	11.6301	−	11.6301i	0.986448	−	0.986448i	−0.0134610	−	0.999909i	$-0.504285\pi$
$139$	11.6301	−	11.6301i	0.986448	−	0.986448i	0.999909	+	0.0134610i	$0.00428488\pi$
$140$		0			0
$141$	1.98400	+	1.98400i	0.167083	+	0.167083i
$142$	−6.41661	+	0.251670i	−0.538470	+	0.0211197i
$143$			0.687871i			0.0575227i
$144$	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
$148$	8.55463	+	7.30837i	0.703186	+	0.600744i
$149$	1.13384	−	1.13384i	0.0928880	−	0.0928880i	−0.659136	−	0.752024i	$-0.729078\pi$
$149$	1.13384	−	1.13384i	0.0928880	−	0.0928880i	0.752024	+	0.659136i	$0.229078\pi$
$150$		0			0
$151$		−	7.12216i		−	0.579593i	−0.957088	−	0.289797i	$-0.906412\pi$
$151$		−	7.12216i		−	0.579593i	0.957088	−	0.289797i	$-0.0935877\pi$
$152$	4.48957	−	5.69259i	0.364152	−	0.461730i
$153$	11.7922			0.953341
$154$	−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	−0.886818	−	0.462120i	$-0.847089\pi$
$157$	−5.32145	+	5.32145i	−0.424698	+	0.424698i	0.462120	+	0.886818i	$0.347089\pi$
$158$	0.639147	+	16.2957i	0.0508478	+	1.29642i
$159$	−4.92363			−0.390469
$160$		0			0
$161$	7.68643			0.605775
$162$	0.273365	+	6.96976i	0.0214776	+	0.547596i
$163$	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
$167$	−9.86820			−0.763624			−0.381812	−	0.924240i	$-0.624700\pi$
$167$	−9.86820			−0.763624			−0.381812	+	0.924240i	$0.624700\pi$
$168$	−7.23490	−	5.70594i	−0.558184	−	0.440223i
$169$			12.9846i			0.998812i
$170$		0			0
$171$	4.57237	−	4.57237i	0.349658	−	0.349658i
$172$	−4.88887	−	4.17665i	−0.372773	−	0.318466i
$173$	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
$177$		−	5.04591i		−	0.379274i
$178$	4.58662	−	0.179895i	0.343782	−	0.0134837i
$179$	−0.419587	−	0.419587i	−0.0313614	−	0.0313614i	0.691252	−	0.722614i	$-0.257059\pi$
$179$	−0.419587	−	0.419587i	−0.0313614	−	0.0313614i	−0.722614	+	0.691252i	$0.757059\pi$
$180$		0			0
$181$	−14.2605	+	14.2605i	−1.05998	+	1.05998i	−0.0618956	+	0.998083i	$0.519715\pi$
$181$	−14.2605	+	14.2605i	−1.05998	+	1.05998i	−0.998083	+	0.0618956i	$0.980285\pi$
$182$	0.608568	+	0.562632i	0.0451101	+	0.0417050i
$183$	6.96356			0.514761
$184$	−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
$188$	−0.636183	−	8.09762i	−0.0463984	−	0.590580i
$189$	−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	$0.284285\pi$
$192$	−2.88974	+	4.71130i	−0.208549	+	0.340008i
$193$			16.8667i			1.21409i	0.794667	+	0.607045i	$0.207645\pi$
$193$			16.8667i			1.21409i	−0.794667	+	0.607045i	$0.792355\pi$
$194$	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	$0.692126\pi$
$198$	−13.4044	+	14.4988i	−0.952608	+	1.03038i
$199$			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
$202$	−19.6915	−	18.2051i	−1.38549	−	1.28091i
$203$	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
$207$		−	4.11218i		−	0.285816i
$208$	0.292320	−	0.402112i	0.0202687	−	0.0278815i
$209$	14.1867			0.981314
$210$		0			0
$211$	1.90906	+	1.90906i	0.131425	+	0.131425i	0.769759	−	0.638334i	$-0.220376\pi$
$211$	1.90906	+	1.90906i	0.131425	+	0.131425i	−0.638334	+	0.769759i	$0.720376\pi$
$212$	10.8372	+	9.25839i	0.744301	+	0.635869i
$213$	−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
$217$	10.0379			0.681418
$218$	0.203245	−	0.219839i	0.0137655	−	0.0148894i
$219$	−4.05740	+	4.05740i	−0.274174	+	0.274174i
$220$		0			0
$221$	−0.410798	−	0.410798i	−0.0276333	−	0.0276333i
$222$	0.215416	+	5.49226i	0.0144578	+	0.368617i
$223$			24.1071i			1.61433i	0.590326	+	0.807165i	$0.298999\pi$
$223$			24.1071i			1.61433i	−0.590326	+	0.807165i	$0.701001\pi$
$224$	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	−0.450035	−	0.893011i	$-0.648588\pi$
$227$	6.67411	−	6.67411i	0.442977	−	0.442977i	0.893011	+	0.450035i	$0.148588\pi$
$228$	3.53084	−	0.277397i	0.233835	−	0.0183711i
$229$	−16.0807	+	16.0807i	−1.06264	+	1.06264i	−0.0647388	+	0.997902i	$0.520621\pi$
$229$	−16.0807	+	16.0807i	−1.06264	+	1.06264i	−0.997902	+	0.0647388i	$0.979379\pi$
$230$		0			0
$231$		−	18.0303i		−	1.18631i
$232$	8.08406	−	10.2503i	0.530744	−	0.672962i
$233$	−16.4976			−1.08079			−0.540396	−	0.841411i	$-0.681726\pi$
$233$	−16.4976			−1.08079			−0.540396	+	0.841411i	$0.681726\pi$
$234$	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
$238$	31.1478	−	1.22167i	2.01901	−	0.0791891i
$239$	−5.25917			−0.340188			−0.170094	−	0.985428i	$-0.554407\pi$
$239$	−5.25917			−0.340188			−0.170094	+	0.985428i	$0.554407\pi$
$240$		0			0
$241$	−14.1126			−0.909075			−0.454538	−	0.890728i	$-0.650196\pi$
$241$	−14.1126			−0.909075			−0.454538	+	0.890728i	$0.650196\pi$
$242$	−27.7432	+	1.08813i	−1.78340	+	0.0699479i
$243$	−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
$247$	−0.318571			−0.0202702
$248$	−0.706468	−	5.97942i	−0.0448608	−	0.379693i
$249$		−	1.14234i		−	0.0723927i
$250$		0			0
$251$	−9.98825	+	9.98825i	−0.630453	+	0.630453i	−0.948182	−	0.317729i	$-0.897080\pi$
$251$	−9.98825	+	9.98825i	−0.630453	+	0.630453i	0.317729	+	0.948182i	$0.397080\pi$
$252$	1.86339	+	23.7181i	0.117383	+	1.49410i
$253$	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
$257$			8.44760i			0.526947i	0.964667	+	0.263474i	$0.0848682\pi$
$257$			8.44760i			0.526947i	−0.964667	+	0.263474i	$0.915132\pi$
$258$	−0.123108	−	3.13877i	−0.00766435	−	0.195411i
$259$	18.7577	+	18.7577i	1.16555	+	1.16555i
$260$		0			0
$261$	8.23315	−	8.23315i	0.509619	−	0.509619i
$262$	−1.10457	+	1.19475i	−0.0682403	+	0.0738118i
$263$	18.3064			1.12882			0.564410	−	0.825494i	$-0.309104\pi$
$263$	18.3064			1.12882			0.564410	+	0.825494i	$0.309104\pi$
$264$	−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
$268$	13.7776	−	16.1270i	0.841601	−	0.985115i
$269$	−13.5631	−	13.5631i	−0.826955	−	0.826955i	0.160140	−	0.987094i	$-0.448806\pi$
$269$	−13.5631	−	13.5631i	−0.826955	−	0.826955i	−0.987094	+	0.160140i	$0.948806\pi$
$270$		0			0
$271$	−2.24520			−0.136386			−0.0681930	−	0.997672i	$-0.521723\pi$
$271$	−2.24520			−0.136386			−0.0681930	+	0.997672i	$0.521723\pi$
$272$	−2.91991	−	18.4683i	−0.177046	−	1.11980i
$273$			0.404882i			0.0245046i
$274$	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	$0.850130\pi$
$278$	−17.0793	−	15.7901i	−1.02435	−	0.947030i
$279$		−	5.37020i		−	0.321506i
$280$		0			0
$281$		−	6.04084i		−	0.360367i	−0.983633	−	0.180183i	$-0.942331\pi$
$281$		−	6.04084i		−	0.360367i	0.983633	−	0.180183i	$-0.0576691\pi$
$282$	2.69369	−	2.91361i	0.160407	−	0.173503i
$283$	−15.1350	−	15.1350i	−0.899682	−	0.899682i	0.0957259	−	0.995408i	$-0.469483\pi$
$283$	−15.1350	−	15.1350i	−0.899682	−	0.899682i	−0.995408	+	0.0957259i	$0.969483\pi$
$284$	0.711284	+	9.05354i	0.0422070	+	0.537229i
$285$		0			0
$286$	0.972049	−	0.0381254i	0.0574785	−	0.00225440i
$287$		−	38.9259i		−	2.29772i
$288$	13.9973	−	2.77927i	0.824800	−	0.163770i
$289$	−4.85021			−0.285306
$290$		0			0
$291$	6.81873	+	6.81873i	0.399721	+	0.399721i
$292$	16.5601	−	1.30103i	0.969107	−	0.0761371i
$293$	−10.7777	−	10.7777i	−0.629637	−	0.629637i	0.318339	−	0.947977i	$-0.396875\pi$
$293$	−10.7777	−	10.7777i	−0.629637	−	0.629637i	−0.947977	+	0.318339i	$0.896875\pi$
$294$	−10.9298	−	10.1048i	−0.637438	−	0.589322i
$295$		0			0
$296$	9.85351	−	12.4939i	0.572724	−	0.726190i
$297$	−21.1172			−1.22534
$298$	−1.66511	−	1.53942i	−0.0964571	−	0.0891762i
$299$	−0.143254	+	0.143254i	−0.00828459	+	0.00828459i
$300$		0			0
$301$	−10.7198	−	10.7198i	−0.617881	−	0.617881i
$302$	−10.0645	+	0.394747i	−0.579148	+	0.0227152i
$303$		−	13.1008i		−	0.752621i
$304$	−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	−0.443098	−	0.896473i	$-0.646120\pi$
$307$	7.94378	−	7.94378i	0.453376	−	0.453376i	0.896473	+	0.443098i	$0.146120\pi$
$308$	−33.9042	+	39.6858i	−1.93187	+	2.26131i
$309$	−6.72382	+	6.72382i	−0.382505	+	0.382505i
$310$		0			0
$311$			31.1649i			1.76720i	0.468244	+	0.883599i	$0.344887\pi$
$311$			31.1649i			1.76720i	−0.468244	+	0.883599i	$0.655113\pi$
$312$	0.241182	−	0.0284956i	0.0136542	−	0.00161325i
$313$	5.35842			0.302876			0.151438	−	0.988467i	$-0.451610\pi$
$313$	5.35842			0.302876			0.151438	+	0.988467i	$0.451610\pi$
$314$	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	−0.911078	−	0.412235i	$-0.864748\pi$
$317$	−8.88165	+	8.88165i	−0.498843	+	0.498843i	0.412235	+	0.911078i	$0.364748\pi$
$318$	0.272893	+	6.95771i	0.0153031	+	0.390169i
$319$	25.5450			1.43025
$320$		0			0
$321$	0.320463			0.0178865
$322$	−0.426022	−	10.8619i	−0.0237413	−	0.605310i
$323$	−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
$327$	0.146260			0.00808817
$328$	−23.1875	+	2.73960i	−1.28032	+	0.151269i
$329$		−	19.1506i		−	1.05581i
$330$		0			0
$331$	6.07281	−	6.07281i	0.333792	−	0.333792i	−0.520233	−	0.854025i	$-0.674155\pi$
$331$	6.07281	−	6.07281i	0.333792	−	0.333792i	0.854025	+	0.520233i	$0.174155\pi$
$332$	−2.14805	+	2.51435i	−0.117890	+	0.137993i
$333$	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
$337$			22.0227i			1.19965i	0.800130	+	0.599827i	$0.204764\pi$
$337$			22.0227i			1.19965i	−0.800130	+	0.599827i	$0.795236\pi$
$338$	18.3488	−	0.719672i	0.998044	−	0.0391450i
$339$	2.92132	+	2.92132i	0.158664	+	0.158664i
$340$		0			0
$341$	8.33106	−	8.33106i	0.451152	−	0.451152i
$342$	−6.71477	−	6.20792i	−0.363093	−	0.335686i
$343$	−38.8315			−2.09670
$344$	−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	$0.899080\pi$
$348$	6.35773	−	0.499490i	0.340810	−	0.0267755i
$349$	8.65696	+	8.65696i	0.463396	+	0.463396i	0.899767	−	0.436371i	$-0.143736\pi$
$349$	8.65696	+	8.65696i	0.463396	+	0.463396i	−0.436371	+	0.899767i	$0.643736\pi$
$350$		0			0
$351$	0.474200			0.0253109
$352$	26.0263	+	17.4031i	1.38721	+	0.927589i
$353$		−	26.6153i		−	1.41659i	−0.705916	−	0.708296i	$-0.749464\pi$
$353$		−	26.6153i		−	1.41659i	0.705916	−	0.708296i	$-0.250536\pi$
$354$	−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
$358$	−0.569674	+	0.616185i	−0.0301082	+	0.0325664i
$359$		−	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
$362$	20.9424	+	19.3616i	1.10071	+	1.01762i
$363$	−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
$367$			15.6741i			0.818182i	0.912494	+	0.409091i	$0.134154\pi$
$367$			15.6741i			0.818182i	−0.912494	+	0.409091i	$0.865846\pi$
$368$	−6.44027	+	1.01823i	−0.335722	+	0.0530792i
$369$	−20.8250			−1.08411
$370$		0			0
$371$	23.7627	+	23.7627i	1.23370	+	1.23370i
$372$	1.91057	−	2.23637i	0.0990582	−	0.115950i
$373$	5.44481	+	5.44481i	0.281922	+	0.281922i	0.833875	−	0.551953i	$-0.186117\pi$
$373$	5.44481	+	5.44481i	0.281922	+	0.281922i	−0.551953	+	0.833875i	$0.686117\pi$
$374$	24.8375	−	26.8654i	1.28432	−	1.38918i
$375$		0			0
$376$	−11.4077	+	1.34782i	−0.588308	+	0.0695085i
$377$	−0.573629			−0.0295434
$378$	−17.2724	+	18.6827i	−0.888399	+	0.960933i
$379$	17.4103	−	17.4103i	0.894309	−	0.894309i	−0.100616	−	0.994925i	$-0.532081\pi$
$379$	17.4103	−	17.4103i	0.894309	−	0.894309i	0.994925	+	0.100616i	$0.0320814\pi$
$380$		0			0
$381$	1.33402	+	1.33402i	0.0683438	+	0.0683438i
$382$	−0.960543	−	24.4901i	−0.0491457	−	1.25302i
$383$		−	9.04928i		−	0.462396i	−0.972907	−	0.231198i	$-0.925735\pi$
$383$		−	9.04928i		−	0.462396i	0.972907	−	0.231198i	$-0.0742646\pi$
$384$	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
$388$	−2.18647	−	27.8303i	−0.111001	−	1.41287i
$389$	15.3617	−	15.3617i	0.778871	−	0.778871i	−0.200768	−	0.979639i	$-0.564344\pi$
$389$	15.3617	−	15.3617i	0.778871	−	0.778871i	0.979639	+	0.200768i	$0.0643437\pi$
$390$		0			0
$391$			7.61962i			0.385341i
$392$	5.05605	+	42.7935i	0.255369	+	2.16140i
$393$	−0.794869			−0.0400959
$394$	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	−0.903220	−	0.429179i	$-0.858803\pi$
$397$	−9.44519	+	9.44519i	−0.474041	+	0.474041i	0.429179	+	0.903220i	$0.358803\pi$
$398$	9.39024	−	0.368301i	0.470690	−	0.0184613i
$399$	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	$0.681099\pi$
$402$	10.3539	−	0.406098i	0.516406	−	0.0202543i
$403$	−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
$407$	31.1363			1.54337
$408$	5.65635	−	7.17202i	0.280031	−	0.355068i
$409$		−	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
$412$	27.4430	−	2.15604i	1.35202	−	0.106220i
$413$	−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
$417$		−	11.3629i		−	0.556445i
$418$	−0.786300	−	20.0476i	−0.0384592	−	0.980560i
$419$	−27.1191	−	27.1191i	−1.32485	−	1.32485i	−0.909794	−	0.415060i	$-0.863761\pi$
$419$	−27.1191	−	27.1191i	−1.32485	−	1.32485i	−0.415060	−	0.909794i	$-0.636239\pi$
$420$		0			0
$421$	−26.9594	+	26.9594i	−1.31392	+	1.31392i	−0.395421	+	0.918500i	$0.629401\pi$
$421$	−26.9594	+	26.9594i	−1.31392	+	1.31392i	−0.918500	+	0.395421i	$0.870599\pi$
$422$	2.59193	−	2.80355i	0.126173	−	0.136475i
$423$	−10.2454			−0.498150
$424$	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
$428$	−0.705357	−	0.602598i	−0.0340947	−	0.0291277i
$429$	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	$0.681434\pi$
$432$	12.3446	+	8.97403i	0.593930	+	0.431763i
$433$		−	16.8061i		−	0.807649i	−0.914837	−	0.403824i	$-0.867681\pi$
$433$		−	16.8061i		−	0.807649i	0.914837	−	0.403824i	$-0.132319\pi$
$434$	−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
$438$	5.95851	+	5.50874i	0.284708	+	0.263218i
$439$			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
$442$	−0.557742	+	0.603279i	−0.0265291	+	0.0286951i
$443$	12.5397	+	12.5397i	0.595781	+	0.595781i	0.939187	−	0.343406i	$-0.111581\pi$
$443$	12.5397	+	12.5397i	0.595781	+	0.595781i	−0.343406	+	0.939187i	$0.611581\pi$
$444$	7.74933	−	0.608820i	0.367767	−	0.0288933i
$445$		0			0
$446$	34.0664	−	1.33614i	1.61309	−	0.0632681i
$447$		−	1.10780i		−	0.0523972i
$448$	36.6845	−	8.79127i	1.73318	−	0.415349i
$449$	−18.0707			−0.852811			−0.426406	−	0.904532i	$-0.640220\pi$
$449$	−18.0707			−0.852811			−0.426406	+	0.904532i	$0.640220\pi$
$450$		0			0
$451$	−32.3069	−	32.3069i	−1.52127	−	1.52127i
$452$	−0.936740	−	11.9232i	−0.0440605	−	0.560822i
$453$	−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
$457$	−18.6637			−0.873052			−0.436526	−	0.899692i	$-0.643791\pi$
$457$	−18.6637			−0.873052			−0.436526	+	0.899692i	$0.643791\pi$
$458$	23.6153	+	21.8328i	1.10347	+	1.02018i
$459$	12.6113	−	12.6113i	0.588643	−	0.588643i
$460$		0			0
$461$	−0.831229	−	0.831229i	−0.0387142	−	0.0387142i	0.687485	−	0.726199i	$-0.258715\pi$
$461$	−0.831229	−	0.831229i	−0.0387142	−	0.0387142i	−0.726199	+	0.687485i	$0.758715\pi$
$462$	−25.4791	+	0.999335i	−1.18540	+	0.0464933i
$463$			7.82533i			0.363674i	0.983329	+	0.181837i	$0.0582043\pi$
$463$			7.82533i			0.363674i	−0.983329	+	0.181837i	$0.941796\pi$
$464$	−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	−0.475034	−	0.879967i	$-0.657564\pi$
$467$	8.75068	−	8.75068i	0.404933	−	0.404933i	0.879967	+	0.475034i	$0.157564\pi$
$468$	−0.476768	−	0.407311i	−0.0220386	−	0.0188280i
$469$	35.3617	−	35.3617i	1.63285	−	1.63285i
$470$		0			0
$471$			5.19922i			0.239568i
$472$	16.2206	+	12.7926i	0.746612	+	0.588829i
$473$	−17.7941			−0.818172
$474$	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
$478$	0.291491	+	7.43188i	0.0133325	+	0.339926i
$479$	−2.10417			−0.0961421			−0.0480710	−	0.998844i	$-0.515307\pi$
$479$	−2.10417			−0.0961421			−0.0480710	+	0.998844i	$0.515307\pi$
$480$		0			0
$481$	−0.699186			−0.0318801
$482$	0.782196	+	19.9430i	0.0356281	+	0.908377i
$483$	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
$487$	−4.87183			−0.220764			−0.110382	−	0.993889i	$-0.535207\pi$
$487$	−4.87183			−0.220764			−0.110382	+	0.993889i	$0.535207\pi$
$488$	−17.6544	+	22.3850i	−0.799175	+	1.01332i
$489$		−	12.0185i		−	0.543494i
$490$		0			0
$491$	14.3582	−	14.3582i	0.647975	−	0.647975i	−0.304528	−	0.952503i	$-0.598499\pi$
$491$	14.3582	−	14.3582i	0.647975	−	0.647975i	0.952503	+	0.304528i	$0.0984987\pi$
$492$	−8.67237	−	7.40895i	−0.390981	−	0.334021i
$493$	−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
$497$			21.4113i			0.960429i
$498$	−1.61427	+	0.0633143i	−0.0723370	+	0.00283718i
$499$	25.1060	+	25.1060i	1.12390	+	1.12390i	0.991150	+	0.132748i	$0.0423801\pi$
$499$	25.1060	+	25.1060i	1.12390	+	1.12390i	0.132748	+	0.991150i	$0.457620\pi$
$500$		0			0
$501$	−4.82077	+	4.82077i	−0.215376	+	0.215376i
$502$	14.6683	+	13.5611i	0.654677	+	0.605260i
$503$	18.8868			0.842120			0.421060	−	0.907033i	$-0.361658\pi$
$503$	18.8868			0.842120			0.421060	+	0.907033i	$0.361658\pi$
$504$	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
$508$	−0.427761	−	5.44473i	−0.0189788	−	0.241571i
$509$	22.9756	+	22.9756i	1.01837	+	1.01837i	0.999828	+	0.0185459i	$0.00590369\pi$
$509$	22.9756	+	22.9756i	1.01837	+	1.01837i	0.0185459	+	0.999828i	$0.494096\pi$
$510$		0			0
$511$	39.1641			1.73252
$512$	−7.81868	−	21.2337i	−0.345540	−	0.938404i
$513$		−	9.77993i		−	0.431794i
$514$	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
$518$	25.4674	−	27.5467i	1.11897	−	1.21033i
$519$		−	13.1009i		−	0.575066i
$520$		0			0
$521$		−	20.2089i		−	0.885367i	−0.896678	−	0.442683i	$-0.854027\pi$
$521$		−	20.2089i		−	0.885367i	0.896678	−	0.442683i	$-0.145973\pi$
$522$	−12.0908	−	11.1782i	−0.529201	−	0.489255i
$523$	−3.93445	−	3.93445i	−0.172042	−	0.172042i	0.615834	−	0.787876i	$-0.288819\pi$
$523$	−3.93445	−	3.93445i	−0.172042	−	0.172042i	−0.787876	+	0.615834i	$0.788819\pi$
$524$	1.74955	+	1.49467i	0.0764295	+	0.0652951i
$525$		0			0
$526$	−1.01464	−	25.8693i	−0.0442402	−	1.12795i
$527$			9.95066i			0.433458i
$528$	2.38851	+	15.1072i	0.103947	+	0.657456i
$529$	−20.3429			−0.884473
$530$		0			0
$531$	13.0286	+	13.0286i	0.565393	+	0.565393i
$532$	−18.3795	−	15.7019i	−0.796853	−	0.680765i
$533$	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
$537$	−0.409950			−0.0176906
$538$	−18.4146	+	19.9181i	−0.793910	+	0.858729i
$539$	−59.6238	+	59.6238i	−2.56818	+	2.56818i
$540$		0			0
$541$	−3.17895	−	3.17895i	−0.136674	−	0.136674i	0.635460	−	0.772134i	$-0.280811\pi$
$541$	−3.17895	−	3.17895i	−0.136674	−	0.136674i	−0.772134	+	0.635460i	$0.780811\pi$
$542$	0.124440	+	3.17275i	0.00534518	+	0.136281i
$543$			13.9330i			0.597923i
$544$	−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	−0.734951	−	0.678120i	$-0.762795\pi$
$547$	−1.32918	+	1.32918i	−0.0568317	+	0.0568317i	0.678120	+	0.734951i	$0.262795\pi$
$548$	0.398397	−	0.0312998i	0.0170187	−	0.00133706i
$549$	−17.9800	+	17.9800i	−0.767366	+	0.767366i
$550$		0			0
$551$			11.8306i			0.503998i
$552$	−2.50103	−	1.97249i	−0.106451	−	0.0839545i
$553$	54.3766			2.31233
$554$	−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	$0.518160\pi$
$557$	−24.9082	+	24.9082i	−1.05539	+	1.05539i	−0.998373	+	0.0570196i	$0.981840\pi$
$558$	−7.58878	+	0.297645i	−0.321259	+	0.0126003i
$559$	0.399576			0.0169003
$560$		0			0
$561$	17.8736			0.754625
$562$	−8.53648	+	0.334815i	−0.360090	+	0.0141233i
$563$	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
$567$	23.2571			0.976706
$568$	12.7544	−	1.50693i	0.535162	−	0.0632293i
$569$		−	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	−0.994582	−	0.103953i	$-0.966851\pi$
$571$	−21.2821	+	21.2821i	−0.890629	+	0.890629i	0.103953	+	0.994582i	$0.466851\pi$
$572$	−0.107752	−	1.37152i	−0.00450534	−	0.0573460i
$573$	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
$577$		−	36.3491i		−	1.51323i	−0.653860	−	0.756615i	$-0.726852\pi$
$577$		−	36.3491i		−	1.51323i	0.653860	−	0.756615i	$-0.273148\pi$
$578$	0.268824	+	6.85396i	0.0111816	+	0.285087i
$579$	8.23964	+	8.23964i	0.342428	+	0.342428i
$580$		0			0
$581$	−5.51321	+	5.51321i	−0.228726	+	0.228726i
$582$	9.25780	−	10.0137i	0.383748	−	0.415080i
$583$	39.4442			1.63361
$584$	−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	$0.811321\pi$
$588$	−13.6735	+	16.0052i	−0.563887	+	0.660044i
$589$	3.85833	+	3.85833i	0.158980	+	0.158980i
$590$		0			0
$591$	3.50665			0.144244
$592$	−18.2015	−	13.2318i	−0.748078	−	0.543823i
$593$			1.40974i			0.0578911i	0.999581	+	0.0289455i	$0.00921494\pi$
$593$			1.40974i			0.0578911i	−0.999581	+	0.0289455i	$0.990785\pi$
$594$	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
$598$	0.210376	+	0.194496i	0.00860291	+	0.00795354i
$599$		−	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	$0.136690\pi$
$601$			20.4138i			0.832695i	−0.909206	+	0.416347i	$0.863310\pi$
$602$	−14.5543	+	15.7426i	−0.593190	+	0.641622i
$603$	−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
$607$			0.758240i			0.0307760i	0.999882	+	0.0153880i	$0.00489835\pi$
$607$			0.758240i			0.0307760i	−0.999882	+	0.0153880i	$0.995102\pi$
$608$	−8.05983	+	12.0535i	−0.326869	+	0.488833i
$609$	15.0358			0.609283
$610$		0			0
$611$	0.356915	+	0.356915i	0.0144392	+	0.0144392i
$612$	−23.5119	+	1.84719i	−0.950413	+	0.0746684i
$613$	−12.0341	−	12.0341i	−0.486052	−	0.486052i	0.421006	−	0.907058i	$-0.361677\pi$
$613$	−12.0341	−	12.0341i	−0.486052	−	0.486052i	−0.907058	+	0.421006i	$0.861677\pi$
$614$	−11.6659	−	10.7853i	−0.470796	−	0.435259i
$615$		0			0
$616$	57.9602	+	45.7114i	2.33528	+	1.84176i
$617$	32.6899			1.31605			0.658023	−	0.752998i	$-0.271393\pi$
$617$	32.6899			1.31605			0.658023	+	0.752998i	$0.271393\pi$
$618$	9.87428	+	9.12894i	0.397202	+	0.367220i
$619$	−26.3836	+	26.3836i	−1.06045	+	1.06045i	−0.0623934	+	0.998052i	$0.519873\pi$
$619$	−26.3836	+	26.3836i	−1.06045	+	1.06045i	−0.998052	+	0.0623934i	$0.980127\pi$
$620$		0			0
$621$	−4.39781	−	4.39781i	−0.176478	−	0.176478i
$622$	44.0399	−	1.72732i	1.76584	−	0.0692592i
$623$		−	15.3049i		−	0.613178i
$624$	−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
$628$	9.77662	−	11.4438i	0.390130	−	0.456657i
$629$	−18.5947	+	18.5947i	−0.741420	+	0.741420i
$630$		0			0
$631$			6.08765i			0.242345i	0.992631	+	0.121173i	$0.0386655\pi$
$631$			6.08765i			0.242345i	−0.992631	+	0.121173i	$0.961335\pi$
$632$	−3.82703	−	32.3913i	−0.152231	−	1.28846i
$633$	1.86521			0.0741354
$634$	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
$638$	−1.41584	−	36.0983i	−0.0560535	−	1.42915i
$639$	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	$0.429213\pi$
$642$	−0.0177617	−	0.452855i	−0.000700999	−	0.0178728i
$643$	−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
$647$	−36.9848			−1.45402			−0.727011	−	0.686625i	$-0.759091\pi$
$647$	−36.9848			−1.45402			−0.727011	+	0.686625i	$0.759091\pi$
$648$	−1.63683	−	13.8539i	−0.0643009	−	0.544231i
$649$			40.4238i			1.58677i
$650$		0			0
$651$	4.90368	−	4.90368i	0.192190	−	0.192190i
$652$	−22.5995	+	26.4533i	−0.885065	+	1.03599i
$653$	−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
$657$		−	20.9525i		−	0.817435i
$658$	−27.0622	+	1.06143i	−1.05500	+	0.0413787i
$659$	15.5421	+	15.5421i	0.605434	+	0.605434i	0.941749	−	0.336316i	$-0.109181\pi$
$659$	15.5421	+	15.5421i	0.605434	+	0.605434i	−0.336316	+	0.941749i	$0.609181\pi$
$660$		0			0
$661$	29.6677	−	29.6677i	1.15394	−	1.15394i	0.168185	−	0.985755i	$-0.446209\pi$
$661$	29.6677	−	29.6677i	1.15394	−	1.15394i	0.985755	−	0.168185i	$-0.0537906\pi$
$662$	−8.91825	−	8.24507i	−0.346617	−	0.320454i
$663$	−0.401363			−0.0155877
$664$	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
$668$	19.6758	−	1.54581i	0.761278	−	0.0598092i
$669$	11.7767	+	11.7767i	0.455313	+	0.455313i
$670$		0			0
$671$	−55.7864			−2.15361
$672$	15.3192	+	10.2435i	0.590949	+	0.395152i
$673$			29.2198i			1.12634i	0.826340	+	0.563171i	$0.190419\pi$
$673$			29.2198i			1.12634i	−0.826340	+	0.563171i	$0.809581\pi$
$674$	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	$0.594601\pi$
$678$	3.96628	−	4.29011i	0.152324	−	0.164761i
$679$		−	65.8179i		−	2.52586i
$680$		0			0
$681$		−	6.52082i		−	0.249878i
$682$	−12.2346	−	11.3111i	−0.468487	−	0.433124i
$683$	−1.10407	−	1.10407i	−0.0422459	−	0.0422459i	0.685668	−	0.727914i	$-0.259510\pi$
$683$	−1.10407	−	1.10407i	−0.0422459	−	0.0422459i	−0.727914	+	0.685668i	$0.759510\pi$
$684$	−8.40041	+	9.83289i	−0.321198	+	0.375970i
$685$		0			0
$686$	2.15224	+	54.8738i	0.0821731	+	2.09509i
$687$			15.7113i			0.599425i
$688$	10.4020	+	7.56181i	0.396571	+	0.288291i
$689$	−0.885743			−0.0337441
$690$		0			0
$691$	−28.4233	−	28.4233i	−1.08127	−	1.08127i	−0.996391	−	0.0848830i	$-0.972948\pi$
$691$	−28.4233	−	28.4233i	−1.08127	−	1.08127i	−0.0848830	−	0.996391i	$-0.527052\pi$
$692$	−24.6350	+	28.8359i	−0.936481	+	1.09617i
$693$	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
$697$	38.5875			1.46161
$698$	11.7536	−	12.7132i	0.444879	−	0.481201i
$699$	−8.05933	+	8.05933i	−0.304832	+	0.304832i
$700$		0			0
$701$	−23.7991	−	23.7991i	−0.898880	−	0.898880i	0.0964573	−	0.995337i	$-0.469249\pi$
$701$	−23.7991	−	23.7991i	−0.898880	−	0.898880i	−0.995337	+	0.0964573i	$0.969249\pi$
$702$	−0.0262826	−	0.670105i	−0.000991974	−	0.0252915i
$703$			14.4200i			0.543862i
$704$	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
$708$	0.790421	+	10.0608i	0.0297058	+	0.378109i
$709$	−1.49921	+	1.49921i	−0.0563039	+	0.0563039i	−0.734698	−	0.678394i	$-0.762676\pi$
$709$	−1.49921	+	1.49921i	−0.0563039	+	0.0563039i	0.678394	+	0.734698i	$0.262676\pi$
$710$		0			0
$711$		−	29.0911i		−	1.09100i
$712$	−9.11688	+	1.07716i	−0.341670	+	0.0403682i
$713$	3.47000			0.129953
$714$	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
$718$	−6.85412	+	0.268830i	−0.255794	+	0.0100327i
$719$	−7.37612			−0.275083			−0.137541	−	0.990496i	$-0.543920\pi$
$719$	−7.37612			−0.275083			−0.137541	+	0.990496i	$0.543920\pi$
$720$		0			0
$721$	64.9017			2.41707
$722$	−17.5649	+	0.688923i	−0.653696	+	0.0256391i
$723$	−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
$727$	30.1470			1.11809			0.559045	−	0.829137i	$-0.311168\pi$
$727$	30.1470			1.11809			0.559045	+	0.829137i	$0.311168\pi$
$728$	−1.30153	−	1.02648i	−0.0482380	−	0.0380438i
$729$		−	4.53447i		−	0.167943i
$730$		0			0
$731$	10.6267	−	10.6267i	0.393041	−	0.393041i
$732$	−13.8843	+	1.09081i	−0.513180	+	0.0403176i
$733$	−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
$737$		−	58.6977i		−	2.16216i
$738$	1.15423	+	29.4284i	0.0424879	+	1.08328i
$739$	−31.0001	−	31.0001i	−1.14036	−	1.14036i	−0.988385	−	0.151973i	$-0.951437\pi$
$739$	−31.0001	−	31.0001i	−1.14036	−	1.14036i	−0.151973	−	0.988385i	$-0.548563\pi$
$740$		0			0
$741$	−0.155627	+	0.155627i	−0.00571710	+	0.00571710i
$742$	32.2626	−	34.8968i	1.18440	−	1.28110i
$743$	38.5395			1.41388			0.706938	−	0.707276i	$-0.250076\pi$
$743$	38.5395			1.41388			0.706938	+	0.707276i	$0.250076\pi$
$744$	−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
$748$	−39.3408	−	33.6096i	−1.43844	−	1.22889i
$749$	−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	$0.336357\pi$
$752$	2.53692	+	16.0458i	0.0925118	+	0.585132i
$753$			9.75884i			0.355632i
$754$	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	$0.605449\pi$
$758$	−25.5680	−	23.6380i	−0.928671	−	0.858573i
$759$		−	6.23290i		−	0.226240i
$760$		0			0
$761$			6.89608i			0.249983i	0.992158	+	0.124991i	$0.0398903\pi$
$761$			6.89608i			0.249983i	−0.992158	+	0.124991i	$0.960110\pi$
$762$	1.81120	−	1.95907i	0.0656128	−	0.0709698i
$763$	−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
$767$		−	0.907741i		−	0.0327766i
$768$	5.02373	−	9.84631i	0.181278	−	0.355298i
$769$	−11.8443			−0.427117			−0.213558	−	0.976930i	$-0.568505\pi$
$769$	−11.8443			−0.427117			−0.213558	+	0.976930i	$0.568505\pi$
$770$		0			0
$771$	4.12679	+	4.12679i	0.148623	+	0.148623i
$772$	−2.64209	−	33.6297i	−0.0950910	−	1.21036i
$773$	3.58865	+	3.58865i	0.129075	+	0.129075i	0.768693	−	0.639618i	$-0.220907\pi$
$773$	3.58865	+	3.58865i	0.129075	+	0.129075i	−0.639618	+	0.768693i	$0.720907\pi$
$774$	8.42219	+	7.78646i	0.302729	+	0.279878i
$775$		0			0
$776$	−39.2066	+	4.63226i	−1.40744	+	0.166288i
$777$	18.3269			0.657474
$778$	−22.5595	−	20.8567i	−0.808798	−	0.747748i
$779$	14.9622	−	14.9622i	0.536075	−	0.536075i
$780$		0			0
$781$	17.7705	+	17.7705i	0.635880	+	0.635880i
$782$	10.7675	−	0.422319i	0.385045	−	0.0151021i
$783$		−	17.6100i		−	0.629332i
$784$	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	−0.181977	−	0.983303i	$-0.558250\pi$
$787$	22.4800	−	22.4800i	0.801326	−	0.801326i	0.983303	+	0.181977i	$0.0582497\pi$
$788$	−7.71833	−	6.59390i	−0.274954	−	0.234898i
$789$	8.94296	−	8.94296i	0.318378	−	0.318378i
$790$		0			0
$791$		−	28.1981i		−	1.00261i
$792$	24.4552	−	31.0082i	0.868979	−	1.10183i
$793$	1.25272			0.0444853
$794$	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	−0.536552	−	0.843867i	$-0.680273\pi$
$797$	8.67589	−	8.67589i	0.307316	−	0.307316i	0.843867	+	0.536552i	$0.180273\pi$
$798$	−0.462818	−	11.8001i	−0.0163836	−	0.417717i
$799$	18.9842			0.671612
$800$		0			0
$801$	−8.18800			−0.289309
$802$	1.19588	+	30.4903i	0.0422280	+	1.07665i
$803$	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
$807$	−13.2515			−0.466476
$808$	42.1138	+	33.2138i	1.48156	+	1.16846i
$809$		−	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	−0.386370	−	0.922344i	$-0.626271\pi$
$811$	15.2635	−	15.2635i	0.535974	−	0.535974i	0.922344	+	0.386370i	$0.126271\pi$
$812$	−33.0947	−	28.2734i	−1.16140	−	0.992201i
$813$	−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
$817$		−	8.24089i		−	0.288312i
$818$	−5.89749	+	0.231309i	−0.206201	+	0.00808754i
$819$	−1.04541	−	1.04541i	−0.0365295	−	0.0365295i
$820$		0			0
$821$	25.2883	−	25.2883i	0.882567	−	0.882567i	−0.111228	−	0.993795i	$-0.535478\pi$
$821$	25.2883	−	25.2883i	0.882567	−	0.882567i	0.993795	+	0.111228i	$0.0354782\pi$
$822$	0.143348	+	0.132527i	0.00499983	+	0.00462242i
$823$	7.12228			0.248267			0.124133	−	0.992266i	$-0.460385\pi$
$823$	7.12228			0.248267			0.124133	+	0.992266i	$0.460385\pi$
$824$	−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	$0.459660\pi$
$828$	0.644155	+	8.19909i	0.0223859	+	0.284938i
$829$	34.9802	+	34.9802i	1.21491	+	1.21491i	0.969391	+	0.245522i	$0.0789594\pi$
$829$	34.9802	+	34.9802i	1.21491	+	1.21491i	0.245522	+	0.969391i	$0.421041\pi$
$830$		0			0
$831$	−7.11529			−0.246827
$832$	−0.519854	+	0.847545i	−0.0180227	+	0.0293833i
$833$		−	71.2149i		−	2.46745i
$834$	−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
$838$	−36.8196	+	39.8258i	−1.27191	+	1.37576i
$839$			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
$842$	39.5913	+	36.6028i	1.36441	+	1.26142i
$843$	−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
$847$			92.5750i			3.18092i
$848$	−23.0581	−	16.7623i	−0.791818	−	0.575620i
$849$	−14.7874			−0.507501
$850$		0			0
$851$	6.48436	+	6.48436i	0.222281	+	0.222281i
$852$	4.77027	+	4.07532i	0.163427	+	0.139618i
$853$	−28.9107	−	28.9107i	−0.989884	−	0.989884i	0.0100656	−	0.999949i	$-0.496796\pi$
$853$	−28.9107	−	28.9107i	−0.989884	−	0.989884i	−0.999949	+	0.0100656i	$0.996796\pi$
$854$	−45.6295	+	49.3550i	−1.56141	+	1.68889i
$855$		0			0
$856$	−0.812454	+	1.03016i	−0.0277691	+	0.0352101i
$857$	−34.1485			−1.16649			−0.583245	−	0.812296i	$-0.698217\pi$
$857$	−34.1485			−1.16649			−0.583245	+	0.812296i	$0.698217\pi$
$858$	0.456237	−	0.493486i	0.0155757	−	0.0168473i
$859$	−20.4589	+	20.4589i	−0.698047	+	0.698047i	−0.963989	−	0.265942i	$-0.914317\pi$
$859$	−20.4589	+	20.4589i	−0.698047	+	0.698047i	0.265942	+	0.963989i	$0.414317\pi$
$860$		0			0
$861$	−19.0159	−	19.0159i	−0.648060	−	0.648060i
$862$	1.24185	+	31.6623i	0.0422976	+	1.07842i
$863$			35.3591i			1.20364i	0.798633	+	0.601818i	$0.205557\pi$
$863$			35.3591i			1.20364i	−0.798633	+	0.601818i	$0.794443\pi$
$864$	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
$868$	−20.0141	+	1.57240i	−0.679324	+	0.0533706i
$869$	45.1304	−	45.1304i	1.53094	−	1.53094i
$870$		0			0
$871$			1.31809i			0.0446618i
$872$	−0.370804	+	0.470165i	−0.0125570	+	0.0159218i
$873$	−35.2120			−1.19175
$874$	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	−0.651845	−	0.758353i	$-0.726005\pi$
$877$	3.15415	−	3.15415i	0.106508	−	0.106508i	0.758353	+	0.651845i	$0.226005\pi$
$878$	12.8358	−	0.503440i	0.433186	−	0.0169903i
$879$	−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	$0.388871\pi$
$882$	54.3114	−	2.13018i	1.82876	−	0.0717270i
$883$	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
$887$	34.8129			1.16890			0.584452	−	0.811429i	$-0.301310\pi$
$887$	34.8129			1.16890			0.584452	+	0.811429i	$0.301310\pi$
$888$	−1.28985	−	10.9170i	−0.0432845	−	0.366352i
$889$		−	12.8766i		−	0.431868i
$890$		0			0
$891$	19.3024	−	19.3024i	0.646656	−	0.646656i
$892$	−3.77627	−	48.0661i	−0.126439	−	1.60937i
$893$	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
$897$			0.139964i			0.00467325i
$898$	1.00157	+	25.5363i	0.0334230	+	0.852156i
$899$	6.94743	+	6.94743i	0.231710	+	0.231710i
$900$		0			0
$901$	−23.5562	+	23.5562i	−0.784770	+	0.784770i
$902$	−43.8631	+	47.4444i	−1.46048	+	1.57973i
$903$	−10.4736			−0.348540
$904$	−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	$0.851238\pi$
$908$	−12.2618	+	14.3527i	−0.406921	+	0.476311i
$909$	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	$0.784163\pi$
$912$	−6.99653	+	1.10618i	−0.231678	+	0.0366293i
$913$			9.15148i			0.302870i
$914$	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
$918$	−18.5203	−	17.1223i	−0.611261	−	0.565121i
$919$			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
$922$	−1.12856	+	1.22070i	−0.0371672	+	0.0402017i
$923$	−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
$927$		−	34.7219i		−	1.14042i
$928$	−14.5128	+	21.7039i	−0.476406	+	0.712464i
$929$	−30.3384			−0.995369			−0.497685	−	0.867358i	$-0.665816\pi$
$929$	−30.3384			−0.995369			−0.497685	+	0.867358i	$0.665816\pi$
$930$		0			0
$931$	−27.6133	−	27.6133i	−0.904990	−	0.904990i
$932$	32.8938	−	2.58427i	1.07747	−	0.0846507i
$933$	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
$937$	14.5267			0.474565			0.237283	−	0.971441i	$-0.423743\pi$
$937$	14.5267			0.474565			0.237283	+	0.971441i	$0.423743\pi$
$938$	−51.9306	−	48.0107i	−1.69559	−	1.56760i
$939$	2.61767	−	2.61767i	0.0854245	−	0.0854245i
$940$		0			0
$941$	37.2863	+	37.2863i	1.21550	+	1.21550i	0.969192	+	0.246307i	$0.0792172\pi$
$941$	37.2863	+	37.2863i	1.21550	+	1.21550i	0.246307	+	0.969192i	$0.420783\pi$
$942$	7.34716	−	0.288168i	0.239384	−	0.00938902i
$943$		−	13.4563i		−	0.438197i
$944$	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	−0.916527	−	0.399973i	$-0.869019\pi$
$947$	−15.8961	+	15.8961i	−0.516553	+	0.516553i	0.399973	+	0.916527i	$0.369019\pi$
$948$	10.3498	−	12.1147i	0.336145	−	0.393466i
$949$	−0.729912	+	0.729912i	−0.0236939	+	0.0236939i
$950$		0			0
$951$			8.67765i			0.281392i
$952$	−61.9129	+	7.31501i	−2.00661	+	0.237081i
$953$	−33.2248			−1.07626			−0.538129	−	0.842862i	$-0.680869\pi$
$953$	−33.2248			−1.07626			−0.538129	+	0.842862i	$0.680869\pi$
$954$	−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
$958$	0.116624	+	2.97346i	0.00376796	+	0.0960682i
$959$	0.942197			0.0304251
$960$		0			0
$961$	−26.4684			−0.853820
$962$	0.0387525	+	0.988038i	0.00124943	+	0.0318556i
$963$	−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
$967$	−1.79116			−0.0576000			−0.0288000	−	0.999585i	$-0.509169\pi$
$967$	−1.79116			−0.0576000			−0.0288000	+	0.999585i	$0.509169\pi$
$968$	55.1455	−	6.51543i	1.77244	−	0.209414i
$969$			8.27774i			0.265919i
$970$		0			0
$971$	5.31278	−	5.31278i	0.170495	−	0.170495i	−0.616702	−	0.787197i	$-0.711531\pi$
$971$	5.31278	−	5.31278i	0.170495	−	0.170495i	0.787197	+	0.616702i	$0.211531\pi$
$972$	19.2966	−	22.5872i	0.618940	−	0.724485i
$973$	−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
$977$			6.81676i			0.218088i	0.994037	+	0.109044i	$0.0347789\pi$
$977$			6.81676i			0.218088i	−0.994037	+	0.109044i	$0.965221\pi$
$978$	−16.9836	+	0.666126i	−0.543076	+	0.0213003i
$979$	−12.7025	−	12.7025i	−0.405972	−	0.405972i
$980$		0			0
$981$	−0.377643	+	0.377643i	−0.0120572	+	0.0120572i
$982$	−21.0857	−	19.4941i	−0.672873	−	0.622082i
$983$	−5.49468			−0.175253			−0.0876265	−	0.996153i	$-0.527928\pi$
$983$	−5.49468			−0.175253			−0.0876265	+	0.996153i	$0.527928\pi$
$984$	−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
$988$	0.635184	−	0.0499028i	0.0202079	−	0.00158762i
$989$	−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	$0.218084\pi$
$992$	2.34525	+	11.8114i	0.0744616	+	0.375013i
$993$		−	5.93333i		−	0.188289i
$994$	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	$-0.651297\pi$
$998$	34.0864	−	36.8694i	1.07899	−	1.16708i
$999$		−	21.4646i		−	0.679109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.q.e.349.4		12
4.3	odd	2		1600.2.q.e.849.3		12
5.2	odd	4		400.2.l.f.301.6	yes	12
5.3	odd	4		400.2.l.g.301.1	yes	12
5.4	even	2		400.2.q.f.349.3		12
16.5	even	4		400.2.q.f.149.3		12
16.11	odd	4		1600.2.q.f.49.4		12
20.3	even	4		1600.2.l.f.401.3		12
20.7	even	4		1600.2.l.g.401.4		12
20.19	odd	2		1600.2.q.f.849.4		12
80.27	even	4		1600.2.l.g.1201.4		12
80.37	odd	4		400.2.l.f.101.6	✓	12
80.43	even	4		1600.2.l.f.1201.3		12
80.53	odd	4		400.2.l.g.101.1	yes	12
80.59	odd	4		1600.2.q.e.49.3		12
80.69	even	4	inner	400.2.q.e.149.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.6	✓	12	80.37	odd	4
400.2.l.f.301.6	yes	12	5.2	odd	4
400.2.l.g.101.1	yes	12	80.53	odd	4
400.2.l.g.301.1	yes	12	5.3	odd	4
400.2.q.e.149.4		12	80.69	even	4	inner
400.2.q.e.349.4		12	1.1	even	1	trivial
400.2.q.f.149.3		12	16.5	even	4
400.2.q.f.349.3		12	5.4	even	2
1600.2.l.f.401.3		12	20.3	even	4
1600.2.l.f.1201.3		12	80.43	even	4
1600.2.l.g.401.4		12	20.7	even	4
1600.2.l.g.1201.4		12	80.27	even	4
1600.2.q.e.49.3		12	80.59	odd	4
1600.2.q.e.849.3		12	4.3	odd	2
1600.2.q.f.49.4		12	16.11	odd	4
1600.2.q.f.849.4		12	20.19	odd	2

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.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0554252 - 1.41313i) q^{2} +(0.488516 - 0.488516i) q^{3} +(-1.99386 + 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} -4.71540 q^{7} +(0.331870 + 2.80889i) q^{8} +2.52270i q^{9} +O(q^{10})\)	\(q+(-0.0554252 - 1.41313i) q^{2} +(0.488516 - 0.488516i) q^{3} +(-1.99386 + 0.156646i) q^{4} +(-0.717411 - 0.663259i) q^{6} -4.71540 q^{7} +(0.331870 + 2.80889i) q^{8} +2.52270i q^{9} +(-3.91360 + 3.91360i) q^{11} +(-0.897506 + 1.05055i) q^{12} +(0.0878822 - 0.0878822i) q^{13} +(0.261352 + 6.66346i) q^{14} +(3.95092 - 0.624658i) q^{16} -4.67442i q^{17} +(3.56490 - 0.139821i) q^{18} +(-1.81249 - 1.81249i) q^{19} +(-2.30355 + 2.30355i) q^{21} +(5.74732 + 5.31350i) q^{22} -1.63007 q^{23} +(1.53431 + 1.21006i) q^{24} +(-0.129060 - 0.119318i) q^{26} +(2.69793 + 2.69793i) q^{27} +(9.40184 - 0.738648i) q^{28} +(-3.26362 - 3.26362i) q^{29} -2.12875 q^{31} +(-1.10170 - 5.54854i) q^{32} +3.82371i q^{33} +(-6.60555 + 0.259081i) q^{34} +(-0.395171 - 5.02991i) q^{36} +(-3.97797 - 3.97797i) q^{37} +(-2.46082 + 2.66173i) q^{38} -0.0858637i q^{39} +8.25504i q^{41} +(3.38288 + 3.12753i) q^{42} +(2.27336 + 2.27336i) q^{43} +(7.19010 - 8.41620i) q^{44} +(0.0903468 + 2.30349i) q^{46} +4.06129i q^{47} +(1.62493 - 2.23524i) q^{48} +15.2350 q^{49} +(-2.28353 - 2.28353i) q^{51} +(-0.161458 + 0.188991i) q^{52} +(-5.03938 - 5.03938i) q^{53} +(3.66298 - 3.96205i) q^{54} +(-1.56490 - 13.2450i) q^{56} -1.77086 q^{57} +(-4.43103 + 4.79280i) q^{58} +(5.16453 - 5.16453i) q^{59} +(7.12726 + 7.12726i) q^{61} +(0.117986 + 3.00819i) q^{62} -11.8956i q^{63} +(-7.77972 + 1.86437i) q^{64} +(5.40339 - 0.211930i) q^{66} +(-7.49920 + 7.49920i) q^{67} +(0.732228 + 9.32012i) q^{68} +(-0.796314 + 0.796314i) q^{69} -4.54072i q^{71} +(-7.08600 + 0.837210i) q^{72} -8.30557 q^{73} +(-5.40090 + 5.84186i) q^{74} +(3.89776 + 3.32992i) q^{76} +(18.4542 - 18.4542i) q^{77} +(-0.121336 + 0.00475901i) q^{78} -11.5317 q^{79} -4.93215 q^{81} +(11.6654 - 0.457537i) q^{82} +(1.16919 - 1.16919i) q^{83} +(4.23211 - 4.95379i) q^{84} +(3.08655 - 3.33855i) q^{86} -3.18866 q^{87} +(-12.2917 - 9.69406i) q^{88} +3.24572i q^{89} +(-0.414400 + 0.414400i) q^{91} +(3.25012 - 0.255343i) q^{92} +(-1.03993 + 1.03993i) q^{93} +(5.73912 - 0.225098i) q^{94} +(-3.24875 - 2.17235i) q^{96} +13.9581i q^{97} +(-0.844405 - 21.5290i) q^{98} +(-9.87285 - 9.87285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8	\( 12 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 6 q^{6} - 12 q^{7} - 2 q^{8} - 2 q^{11} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 2 q^{16} + 18 q^{18} + 14 q^{19} - 20 q^{21} + 20 q^{22} - 12 q^{23} + 14 q^{24} - 16 q^{26} - 10 q^{27} + 10 q^{28} - 4 q^{31} - 2 q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 28 q^{38} - 10 q^{42} + 44 q^{44} - 10 q^{46} + 58 q^{48} - 4 q^{49} + 10 q^{51} + 16 q^{53} - 10 q^{54} + 6 q^{56} + 16 q^{57} - 4 q^{58} - 20 q^{59} + 4 q^{61} - 22 q^{62} - 38 q^{64} + 32 q^{66} - 50 q^{67} - 50 q^{68} + 54 q^{72} - 40 q^{73} - 10 q^{74} + 60 q^{76} + 8 q^{77} + 48 q^{78} - 12 q^{79} - 8 q^{81} + 12 q^{82} - 2 q^{83} - 34 q^{84} + 6 q^{86} + 64 q^{87} - 56 q^{88} - 50 q^{92} - 44 q^{93} - 32 q^{94} - 34 q^{96} + 30 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 6 * q^6 - 12 * q^7 - 2 * q^8 - 2 * q^11 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 2 * q^16 + 18 * q^18 + 14 * q^19 - 20 * q^21 + 20 * q^22 - 12 * q^23 + 14 * q^24 - 16 * q^26 - 10 * q^27 + 10 * q^28 - 4 * q^31 - 2 * q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 28 * q^38 - 10 * q^42 + 44 * q^44 - 10 * q^46 + 58 * q^48 - 4 * q^49 + 10 * q^51 + 16 * q^53 - 10 * q^54 + 6 * q^56 + 16 * q^57 - 4 * q^58 - 20 * q^59 + 4 * q^61 - 22 * q^62 - 38 * q^64 + 32 * q^66 - 50 * q^67 - 50 * q^68 + 54 * q^72 - 40 * q^73 - 10 * q^74 + 60 * q^76 + 8 * q^77 + 48 * q^78 - 12 * q^79 - 8 * q^81 + 12 * q^82 - 2 * q^83 - 34 * q^84 + 6 * q^86 + 64 * q^87 - 56 * q^88 - 50 * q^92 - 44 * q^93 - 32 * q^94 - 34 * q^96 + 30 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more