LMFDB - Embedded newform 400.2.s.d.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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([2, 1, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.s (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:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Root			$0.482716 - 1.32928i$ of defining polynomial
Character	$\chi$	$=$	400.107
Dual form			400.2.s.d.243.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19301 - 0.759419i) q^{2} +1.39319 q^{3} +(0.846564 + 1.81200i) q^{4} +(-1.66209 - 1.05801i) q^{6} +(2.13436 + 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} -1.05903 q^{9} +O(q^{10})$	\(q+(-1.19301 - 0.759419i) q^{2} +1.39319 q^{3} +(0.846564 + 1.81200i) q^{4} +(-1.66209 - 1.05801i) q^{6} +(2.13436 + 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} -1.05903 q^{9} +(2.17074 - 2.17074i) q^{11} +(1.17942 + 2.52445i) q^{12} +1.54663i q^{13} +(-0.925449 - 4.16720i) q^{14} +(-2.56666 + 3.06794i) q^{16} +(3.86386 + 3.86386i) q^{17} +(1.26344 + 0.804250i) q^{18} +(0.0136865 - 0.0136865i) q^{19} +(2.97357 + 2.97357i) q^{21} +(-4.23822 + 0.941219i) q^{22} +(3.15240 - 3.15240i) q^{23} +(0.510047 - 3.90738i) q^{24} +(1.17454 - 1.84515i) q^{26} -5.65499 q^{27} +(-2.06058 + 5.67434i) q^{28} +(3.33787 + 3.33787i) q^{29} +8.92639i q^{31} +(5.39191 - 1.71093i) q^{32} +(3.02424 - 3.02424i) q^{33} +(-1.67535 - 7.54394i) q^{34} +(-0.896540 - 1.91896i) q^{36} -7.24737i q^{37} +(-0.0267220 + 0.00593441i) q^{38} +2.15475i q^{39} -10.3771i q^{41} +(-1.28932 - 5.80569i) q^{42} -2.02975i q^{43} +(5.77103 + 2.09570i) q^{44} +(-6.15484 + 1.36686i) q^{46} +(-3.34313 + 3.34313i) q^{47} +(-3.57583 + 4.27421i) q^{48} +2.11103i q^{49} +(5.38308 + 5.38308i) q^{51} +(-2.80249 + 1.30932i) q^{52} +7.30702 q^{53} +(6.74648 + 4.29451i) q^{54} +(6.76751 - 5.20472i) q^{56} +(0.0190679 - 0.0190679i) q^{57} +(-1.44728 - 6.51696i) q^{58} +(-3.52732 - 3.52732i) q^{59} +(1.41629 - 1.41629i) q^{61} +(6.77887 - 10.6493i) q^{62} +(-2.26036 - 2.26036i) q^{63} +(-7.73194 - 2.05356i) q^{64} +(-5.90462 + 1.31129i) q^{66} -0.748197i q^{67} +(-3.73030 + 10.2723i) q^{68} +(4.39187 - 4.39187i) q^{69} -0.269603 q^{71} +(-0.387713 + 2.97020i) q^{72} +(-0.811870 - 0.811870i) q^{73} +(-5.50380 + 8.64622i) q^{74} +(0.0363865 + 0.0132134i) q^{76} +9.26628 q^{77} +(1.63636 - 2.57064i) q^{78} -2.80567 q^{79} -4.70135 q^{81} +(-7.88056 + 12.3800i) q^{82} -12.8279 q^{83} +(-2.87077 + 7.90541i) q^{84} +(-1.54143 + 2.42152i) q^{86} +(4.65027 + 4.65027i) q^{87} +(-5.29341 - 6.88283i) q^{88} -13.3732 q^{89} +(-3.30108 + 3.30108i) q^{91} +(8.38083 + 3.04342i) q^{92} +12.4361i q^{93} +(6.52724 - 1.44956i) q^{94} +(7.51194 - 2.38364i) q^{96} +(-6.33466 - 6.33466i) q^{97} +(1.60315 - 2.51848i) q^{98} +(-2.29888 + 2.29888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} + 6 q^{17} + 24 q^{18} - 2 q^{19} - 16 q^{21} - 12 q^{22} + 2 q^{23} - 4 q^{24} - 16 q^{26} + 24 q^{27} - 40 q^{28} + 14 q^{29} - 20 q^{32} + 8 q^{33} + 28 q^{34} - 4 q^{36} - 24 q^{38} - 8 q^{42} - 44 q^{44} + 12 q^{46} - 38 q^{47} - 4 q^{48} + 8 q^{51} - 8 q^{52} - 12 q^{53} + 4 q^{54} + 20 q^{56} + 24 q^{57} - 20 q^{58} + 10 q^{59} + 14 q^{61} + 40 q^{62} + 6 q^{63} + 16 q^{64} + 4 q^{66} + 60 q^{68} - 32 q^{69} + 24 q^{71} + 68 q^{72} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 44 q^{77} + 36 q^{78} - 16 q^{79} + 2 q^{81} - 48 q^{82} - 40 q^{83} + 24 q^{84} - 36 q^{86} - 24 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{92} - 28 q^{94} - 40 q^{96} - 18 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 + 6 * q^17 + 24 * q^18 - 2 * q^19 - 16 * q^21 - 12 * q^22 + 2 * q^23 - 4 * q^24 - 16 * q^26 + 24 * q^27 - 40 * q^28 + 14 * q^29 - 20 * q^32 + 8 * q^33 + 28 * q^34 - 4 * q^36 - 24 * q^38 - 8 * q^42 - 44 * q^44 + 12 * q^46 - 38 * q^47 - 4 * q^48 + 8 * q^51 - 8 * q^52 - 12 * q^53 + 4 * q^54 + 20 * q^56 + 24 * q^57 - 20 * q^58 + 10 * q^59 + 14 * q^61 + 40 * q^62 + 6 * q^63 + 16 * q^64 + 4 * q^66 + 60 * q^68 - 32 * q^69 + 24 * q^71 + 68 * q^72 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 44 * q^77 + 36 * q^78 - 16 * q^79 + 2 * q^81 - 48 * q^82 - 40 * q^83 + 24 * q^84 - 36 * q^86 - 24 * q^87 + 8 * q^88 + 12 * q^89 + 8 * q^92 - 28 * q^94 - 40 * q^96 - 18 * q^97 + 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.19301	−	0.759419i	−0.843588	−	0.536991i
$2$	−1.19301	−	0.759419i	−0.843588	−	0.536991i
$3$	1.39319			0.804356			0.402178	−	0.915561i	$-0.368253\pi$
$3$	1.39319			0.804356			0.402178	+	0.915561i	$0.368253\pi$
$4$	0.846564	+	1.81200i	0.423282	+	0.905998i
$5$		0			0
$5$		0			0
$6$	−1.66209	−	1.05801i	−0.678546	−	0.431932i
$7$	2.13436	+	2.13436i	0.806714	+	0.806714i	0.984135	−	0.177421i	$-0.0567754\pi$
$7$	2.13436	+	2.13436i	0.806714	+	0.806714i	−0.177421	+	0.984135i	$0.556775\pi$
$8$	0.366101	−	2.80463i	0.129436	−	0.991588i
$9$	−1.05903			−0.353011
$10$		0			0
$11$	2.17074	−	2.17074i	0.654501	−	0.654501i	−0.299572	−	0.954074i	$-0.596844\pi$
$11$	2.17074	−	2.17074i	0.654501	−	0.654501i	0.954074	+	0.299572i	$0.0968440\pi$
$12$	1.17942	+	2.52445i	0.340470	+	0.728745i
$13$			1.54663i			0.428958i	0.976729	+	0.214479i	$0.0688054\pi$
$13$			1.54663i			0.428958i	−0.976729	+	0.214479i	$0.931195\pi$
$14$	−0.925449	−	4.16720i	−0.247337	−	1.11373i
$15$		0			0
$16$	−2.56666	+	3.06794i	−0.641664	+	0.766986i
$17$	3.86386	+	3.86386i	0.937125	+	0.937125i	0.998137	−	0.0610123i	$-0.0194329\pi$
$17$	3.86386	+	3.86386i	0.937125	+	0.937125i	−0.0610123	+	0.998137i	$0.519433\pi$
$18$	1.26344	+	0.804250i	0.297796	+	0.189564i
$19$	0.0136865	−	0.0136865i	0.00313991	−	0.00313991i	−0.705535	−	0.708675i	$-0.749293\pi$
$19$	0.0136865	−	0.0136865i	0.00313991	−	0.00313991i	0.708675	+	0.705535i	$0.249293\pi$
$20$		0			0
$21$	2.97357	+	2.97357i	0.648886	+	0.648886i
$22$	−4.23822	+	0.941219i	−0.903591	+	0.200669i
$23$	3.15240	−	3.15240i	0.657320	−	0.657320i	−0.297425	−	0.954745i	$-0.596128\pi$
$23$	3.15240	−	3.15240i	0.657320	−	0.657320i	0.954745	+	0.297425i	$0.0961279\pi$
$24$	0.510047	−	3.90738i	0.104113	−	0.797590i
$25$		0			0
$26$	1.17454	−	1.84515i	0.230347	−	0.361864i
$27$	−5.65499			−1.08830
$28$	−2.06058	+	5.67434i	−0.389413	+	1.07235i
$29$	3.33787	+	3.33787i	0.619826	+	0.619826i	0.945487	−	0.325660i	$-0.105587\pi$
$29$	3.33787	+	3.33787i	0.619826	+	0.619826i	−0.325660	+	0.945487i	$0.605587\pi$
$30$		0			0
$31$			8.92639i			1.60323i	0.597843	+	0.801613i	$0.296025\pi$
$31$			8.92639i			1.60323i	−0.597843	+	0.801613i	$0.703975\pi$
$32$	5.39191	−	1.71093i	0.953164	−	0.302452i
$33$	3.02424	−	3.02424i	0.526452	−	0.526452i
$34$	−1.67535	−	7.54394i	−0.287320	−	1.29377i
$35$		0			0
$36$	−0.896540	−	1.91896i	−0.149423	−	0.319827i
$37$		−	7.24737i		−	1.19146i	−0.803184	−	0.595730i	$-0.796863\pi$
$37$		−	7.24737i		−	1.19146i	0.803184	−	0.595730i	$-0.203137\pi$
$38$	−0.0267220	+	0.00593441i	−0.00433489	+	0.000962688i
$39$			2.15475i			0.345035i
$40$		0			0
$41$		−	10.3771i		−	1.62063i	−0.585996	−	0.810314i	$-0.699296\pi$
$41$		−	10.3771i		−	1.62063i	0.585996	−	0.810314i	$-0.300704\pi$
$42$	−1.28932	−	5.80569i	−0.198947	−	0.895838i
$43$		−	2.02975i		−	0.309534i	−0.987951	−	0.154767i	$-0.950537\pi$
$43$		−	2.02975i		−	0.309534i	0.987951	−	0.154767i	$-0.0494627\pi$
$44$	5.77103	+	2.09570i	0.870015	+	0.315938i
$45$		0			0
$46$	−6.15484	+	1.36686i	−0.907482	+	0.201533i
$47$	−3.34313	+	3.34313i	−0.487646	+	0.487646i	−0.907563	−	0.419917i	$-0.862059\pi$
$47$	−3.34313	+	3.34313i	−0.487646	+	0.487646i	0.419917	+	0.907563i	$0.362059\pi$
$48$	−3.57583	+	4.27421i	−0.516127	+	0.616930i
$49$			2.11103i			0.301575i
$50$		0			0
$51$	5.38308	+	5.38308i	0.753782	+	0.753782i
$52$	−2.80249	+	1.30932i	−0.388635	+	0.181570i
$53$	7.30702			1.00370			0.501848	−	0.864956i	$-0.332654\pi$
$53$	7.30702			1.00370			0.501848	+	0.864956i	$0.332654\pi$
$54$	6.74648	+	4.29451i	0.918080	+	0.584408i
$55$		0			0
$56$	6.76751	−	5.20472i	0.904346	−	0.695510i
$57$	0.0190679	−	0.0190679i	0.00252560	−	0.00252560i
$58$	−1.44728	−	6.51696i	−0.190037	−	0.855719i
$59$	−3.52732	−	3.52732i	−0.459218	−	0.459218i	0.439181	−	0.898399i	$-0.355269\pi$
$59$	−3.52732	−	3.52732i	−0.459218	−	0.459218i	−0.898399	+	0.439181i	$0.855269\pi$
$60$		0			0
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	−0.610601	−	0.791939i	$-0.709072\pi$
$61$	1.41629	−	1.41629i	0.181338	−	0.181338i	0.791939	+	0.610601i	$0.209072\pi$
$62$	6.77887	−	10.6493i	0.860918	−	1.35246i
$63$	−2.26036	−	2.26036i	−0.284779	−	0.284779i
$64$	−7.73194	−	2.05356i	−0.966492	−	0.256695i
$65$		0			0
$66$	−5.90462	+	1.31129i	−0.726809	+	0.161409i
$67$		−	0.748197i		−	0.0914068i	−0.998955	−	0.0457034i	$-0.985447\pi$
$67$		−	0.748197i		−	0.0914068i	0.998955	−	0.0457034i	$-0.0145529\pi$
$68$	−3.73030	+	10.2723i	−0.452365	+	1.24570i
$69$	4.39187	−	4.39187i	0.528719	−	0.528719i
$70$		0			0
$71$	−0.269603			−0.0319960			−0.0159980	−	0.999872i	$-0.505093\pi$
$71$	−0.269603			−0.0319960			−0.0159980	+	0.999872i	$0.505093\pi$
$72$	−0.387713	+	2.97020i	−0.0456925	+	0.350041i
$73$	−0.811870	−	0.811870i	−0.0950222	−	0.0950222i	0.657998	−	0.753020i	$-0.271404\pi$
$73$	−0.811870	−	0.811870i	−0.0950222	−	0.0950222i	−0.753020	+	0.657998i	$0.771404\pi$
$74$	−5.50380	+	8.64622i	−0.639803	+	1.00510i
$75$		0			0
$76$	0.0363865	+	0.0132134i	0.00417381	+	0.00151568i
$77$	9.26628			1.05599
$78$	1.63636	−	2.57064i	0.185281	−	0.291068i
$79$	−2.80567			−0.315662			−0.157831	−	0.987466i	$-0.550450\pi$
$79$	−2.80567			−0.315662			−0.157831	+	0.987466i	$0.550450\pi$
$80$		0			0
$81$	−4.70135			−0.522372
$82$	−7.88056	+	12.3800i	−0.870262	+	1.36714i
$83$	−12.8279			−1.40804			−0.704022	−	0.710178i	$-0.748614\pi$
$83$	−12.8279			−1.40804			−0.704022	+	0.710178i	$0.748614\pi$
$84$	−2.87077	+	7.90541i	−0.313227	+	0.862551i
$85$		0			0
$86$	−1.54143	+	2.42152i	−0.166217	+	0.261119i
$87$	4.65027	+	4.65027i	0.498561	+	0.498561i
$88$	−5.29341	−	6.88283i	−0.564279	−	0.733712i
$89$	−13.3732			−1.41755			−0.708777	−	0.705432i	$-0.750753\pi$
$89$	−13.3732			−1.41755			−0.708777	+	0.705432i	$0.750753\pi$
$90$		0			0
$91$	−3.30108	+	3.30108i	−0.346047	+	0.346047i
$92$	8.38083	+	3.04342i	0.873762	+	0.317299i
$93$			12.4361i			1.28957i
$94$	6.52724	−	1.44956i	0.673233	−	0.149511i
$95$		0			0
$96$	7.51194	−	2.38364i	0.766684	−	0.243279i
$97$	−6.33466	−	6.33466i	−0.643187	−	0.643187i	0.308151	−	0.951338i	$-0.400290\pi$
$97$	−6.33466	−	6.33466i	−0.643187	−	0.643187i	−0.951338	+	0.308151i	$0.900290\pi$
$98$	1.60315	−	2.51848i	0.161943	−	0.254405i
$99$	−2.29888	+	2.29888i	−0.231046	+	0.231046i
$100$		0			0
$101$	−3.78129	−	3.78129i	−0.376252	−	0.376252i	0.493496	−	0.869748i	$-0.335719\pi$
$101$	−3.78129	−	3.78129i	−0.376252	−	0.376252i	−0.869748	+	0.493496i	$0.835719\pi$
$102$	−2.33407	−	10.5101i	−0.231108	−	1.04066i
$103$	−10.7199	+	10.7199i	−1.05626	+	1.05626i	−0.0579430	+	0.998320i	$0.518454\pi$
$103$	−10.7199	+	10.7199i	−1.05626	+	1.05626i	−0.998320	+	0.0579430i	$0.981546\pi$
$104$	4.33774	+	0.566224i	0.425350	+	0.0555228i
$105$		0			0
$106$	−8.71737	−	5.54909i	−0.846706	−	0.538975i
$107$	−10.9109			−1.05479			−0.527397	−	0.849619i	$-0.676832\pi$
$107$	−10.9109			−1.05479			−0.527397	+	0.849619i	$0.676832\pi$
$108$	−4.78731	−	10.2468i	−0.460659	−	0.986000i
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	0.992870	−	0.119200i	$-0.0380329\pi$
$109$	9.12139	+	9.12139i	0.873670	+	0.873670i	−0.119200	+	0.992870i	$0.538033\pi$
$110$		0			0
$111$		−	10.0969i		−	0.958359i
$112$	−12.0263	+	1.06993i	−1.13638	+	0.101098i
$113$	−4.88810	+	4.88810i	−0.459834	+	0.459834i	−0.898601	−	0.438767i	$-0.855415\pi$
$113$	−4.88810	+	4.88810i	−0.459834	+	0.459834i	0.438767	+	0.898601i	$0.355415\pi$
$114$	−0.0372288	+	0.00826773i	−0.00348679	+	0.000774344i
$115$		0			0
$116$	−3.22248	+	8.87392i	−0.299200	+	0.823923i
$117$		−	1.63793i		−	0.151427i
$118$	1.52943	+	6.88685i	0.140795	+	0.633986i
$119$			16.4938i			1.51198i
$120$		0			0
$121$			1.57582i			0.143256i
$122$	−2.76522	+	0.614097i	−0.250351	+	0.0555978i
$123$		−	14.4572i		−	1.30356i
$124$	−16.1746	+	7.55676i	−1.45252	+	0.678617i
$125$		0			0
$126$	0.980081	+	4.41321i	0.0873125	+	0.393160i
$127$	−1.38586	+	1.38586i	−0.122975	+	0.122975i	−0.765916	−	0.642941i	$-0.777714\pi$
$127$	−1.38586	+	1.38586i	−0.122975	+	0.122975i	0.642941	+	0.765916i	$0.277714\pi$
$128$	7.66480	+	8.32171i	0.677479	+	0.735542i
$129$		−	2.82782i		−	0.248976i
$130$		0			0
$131$	−3.52096	−	3.52096i	−0.307627	−	0.307627i	0.536361	−	0.843989i	$-0.319798\pi$
$131$	−3.52096	−	3.52096i	−0.307627	−	0.307627i	−0.843989	+	0.536361i	$0.819798\pi$
$132$	8.04012	+	2.91969i	0.699802	+	0.254127i
$133$	0.0584241			0.00506601
$134$	−0.568195	+	0.892609i	−0.0490846	+	0.0771097i
$135$		0			0
$136$	12.2513	−	9.42216i	1.05054	−	0.807943i
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	−0.424732	−	0.905319i	$-0.639632\pi$
$137$	5.62512	−	5.62512i	0.480587	−	0.480587i	0.905319	+	0.424732i	$0.139632\pi$
$138$	−8.57484	+	1.90429i	−0.729939	+	0.162104i
$139$	−12.1022	−	12.1022i	−1.02650	−	1.02650i	−0.999639	−	0.0268584i	$-0.991450\pi$
$139$	−12.1022	−	12.1022i	−1.02650	−	1.02650i	−0.0268584	−	0.999639i	$-0.508550\pi$
$140$		0			0
$141$	−4.65760	+	4.65760i	−0.392241	+	0.392241i
$142$	0.321641	+	0.204742i	0.0269915	+	0.0171816i
$143$	3.35733	+	3.35733i	0.280754	+	0.280754i
$144$	2.71817	−	3.24905i	0.226514	−	0.270754i
$145$		0			0
$146$	0.352023	+	1.58512i	0.0291336	+	0.131186i
$147$			2.94105i			0.242574i
$148$	13.1322	−	6.13537i	1.07946	−	0.504324i
$149$	13.5590	−	13.5590i	1.11080	−	1.11080i	0.117757	−	0.993042i	$-0.462430\pi$
$149$	13.5590	−	13.5590i	1.11080	−	1.11080i	0.993042	−	0.117757i	$-0.0375702\pi$
$150$		0			0
$151$	−20.7185			−1.68605			−0.843025	−	0.537874i	$-0.819228\pi$
$151$	−20.7185			−1.68605			−0.843025	+	0.537874i	$0.819228\pi$
$152$	−0.0333751	−	0.0433964i	−0.00270707	−	0.00351991i
$153$	−4.09196	−	4.09196i	−0.330815	−	0.330815i
$154$	−11.0548	−	7.03699i	−0.890821	−	0.567057i
$155$		0			0
$156$	−3.90439	+	1.82413i	−0.312601	+	0.146047i
$157$	5.72312			0.456755			0.228377	−	0.973573i	$-0.426658\pi$
$157$	5.72312			0.456755			0.228377	+	0.973573i	$0.426658\pi$
$158$	3.34720	+	2.13068i	0.266289	+	0.169508i
$159$	10.1800			0.807329
$160$		0			0
$161$	13.4567			1.06054
$162$	5.60878	+	3.57030i	0.440667	+	0.280509i
$163$	17.9900			1.40909			0.704543	−	0.709662i	$-0.251152\pi$
$163$	17.9900			1.40909			0.704543	+	0.709662i	$0.251152\pi$
$164$	18.8032	−	8.78487i	1.46829	−	0.685983i
$165$		0			0
$166$	15.3039	+	9.74175i	1.18781	+	0.756106i
$167$	−2.39642	−	2.39642i	−0.185441	−	0.185441i	0.608281	−	0.793722i	$-0.291859\pi$
$167$	−2.39642	−	2.39642i	−0.185441	−	0.185441i	−0.793722	+	0.608281i	$0.791859\pi$
$168$	9.42839	−	7.25114i	0.727416	−	0.559438i
$169$	10.6079			0.815995
$170$		0			0
$171$	−0.0144945	+	0.0144945i	−0.00110842	+	0.00110842i
$172$	3.67790	−	1.71832i	0.280437	−	0.131020i
$173$		−	9.45205i		−	0.718626i	−0.933217	−	0.359313i	$-0.883011\pi$
$173$		−	9.45205i		−	0.718626i	0.933217	−	0.359313i	$-0.116989\pi$
$174$	−2.01633	−	9.07934i	−0.152858	−	0.688303i
$175$		0			0
$176$	1.08816	+	12.2312i	0.0820230	+	0.921963i
$177$	−4.91421	−	4.91421i	−0.369375	−	0.369375i
$178$	15.9544	+	10.1559i	1.19583	+	0.761213i
$179$	11.7991	−	11.7991i	0.881905	−	0.881905i	−0.111824	−	0.993728i	$-0.535669\pi$
$179$	11.7991	−	11.7991i	0.881905	−	0.881905i	0.993728	+	0.111824i	$0.0356691\pi$
$180$		0			0
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	0.795225	−	0.606314i	$-0.207352\pi$
$181$	2.54155	+	2.54155i	0.188912	+	0.188912i	−0.606314	+	0.795225i	$0.707352\pi$
$182$	6.44513	−	1.43133i	0.477745	−	0.106097i
$183$	1.97316	−	1.97316i	0.145860	−	0.145860i
$184$	−7.68722	−	9.99541i	−0.566709	−	0.736871i
$185$		0			0
$186$	9.44423	−	14.8365i	0.692484	−	1.08786i
$187$	16.7748			1.22670
$188$	−8.88791	−	3.22756i	−0.648217	−	0.235394i
$189$	−12.0698	−	12.0698i	−0.877949	−	0.877949i
$190$		0			0
$191$		−	5.46421i		−	0.395376i	−0.980265	−	0.197688i	$-0.936657\pi$
$191$		−	5.46421i		−	0.395376i	0.980265	−	0.197688i	$-0.0633433\pi$
$192$	−10.7720	−	2.86099i	−0.777404	−	0.206474i
$193$	−4.82485	+	4.82485i	−0.347300	+	0.347300i	−0.859103	−	0.511803i	$-0.828978\pi$
$193$	−4.82485	+	4.82485i	−0.347300	+	0.347300i	0.511803	+	0.859103i	$0.328978\pi$
$194$	2.74667	+	12.3680i	0.197200	+	0.887970i
$195$		0			0
$196$	−3.82517	+	1.78712i	−0.273226	+	0.127651i
$197$		−	2.94582i		−	0.209881i	−0.994478	−	0.104941i	$-0.966535\pi$
$197$		−	2.94582i		−	0.209881i	0.994478	−	0.104941i	$-0.0334653\pi$
$198$	4.48841	−	0.996782i	0.318977	−	0.0708382i
$199$			2.14620i			0.152140i	0.997102	+	0.0760700i	$0.0242372\pi$
$199$			2.14620i			0.152140i	−0.997102	+	0.0760700i	$0.975763\pi$
$200$		0			0
$201$		−	1.04238i		−	0.0735236i
$202$	1.63955	+	7.38271i	0.115358	+	0.519446i
$203$			14.2485i			1.00005i
$204$	−5.19699	+	14.3112i	−0.363862	+	1.00199i
$205$		0			0
$206$	20.9299	−	4.64809i	1.45825	−	0.323848i
$207$	−3.33849	+	3.33849i	−0.232041	+	0.232041i
$208$	−4.74498	−	3.96967i	−0.329005	−	0.275247i
$209$		−	0.0594197i		−	0.00411014i
$210$		0			0
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	0.871708	−	0.490025i	$-0.163012\pi$
$211$	5.54427	+	5.54427i	0.381684	+	0.381684i	−0.490025	+	0.871708i	$0.663012\pi$
$212$	6.18586	+	13.2403i	0.424847	+	0.909346i
$213$	−0.375608			−0.0257362
$214$	13.0168	+	8.28593i	0.889812	+	0.566414i
$215$		0			0
$216$	−2.07030	+	15.8602i	−0.140866	+	1.07915i
$217$	−19.0522	+	19.0522i	−1.29335	+	1.29335i
$218$	−3.95498	−	17.8089i	−0.267865	−	1.20617i
$219$	−1.13109	−	1.13109i	−0.0764317	−	0.0764317i
$220$		0			0
$221$	−5.97597	+	5.97597i	−0.401988	+	0.401988i
$222$	−7.66781	+	12.0458i	−0.514630	+	0.808461i
$223$	−1.16163	−	1.16163i	−0.0777882	−	0.0777882i	0.667142	−	0.744930i	$-0.267517\pi$
$223$	−1.16163	−	1.16163i	−0.0777882	−	0.0777882i	−0.744930	+	0.667142i	$0.767517\pi$
$224$	15.1601	+	7.85656i	1.01292	+	0.524939i
$225$		0			0
$226$	9.54369	−	2.11945i	0.634837	−	0.140984i
$227$		−	12.8161i		−	0.850632i	−0.905045	−	0.425316i	$-0.860163\pi$
$227$		−	12.8161i		−	0.850632i	0.905045	−	0.425316i	$-0.139837\pi$
$228$	0.0506931	+	0.0184087i	0.00335723	+	0.00121915i
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	−0.674093	−	0.738647i	$-0.735465\pi$
$229$	0.976882	−	0.976882i	0.0645542	−	0.0645542i	0.738647	+	0.674093i	$0.235465\pi$
$230$		0			0
$231$	12.9097			0.849393
$232$	10.5835	−	8.13950i	0.694840	−	0.534384i
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	0.716990	−	0.697083i	$-0.245519\pi$
$233$	0.303870	+	0.303870i	0.0199072	+	0.0199072i	−0.697083	+	0.716990i	$0.745519\pi$
$234$	−1.24388	+	1.95408i	−0.0813149	+	0.127742i
$235$		0			0
$236$	3.40538	−	9.37758i	0.221671	−	0.610429i
$237$	−3.90881			−0.253905
$238$	12.5257	−	19.6773i	0.811921	−	1.27549i
$239$	−12.5096			−0.809178			−0.404589	−	0.914499i	$-0.632585\pi$
$239$	−12.5096			−0.809178			−0.404589	+	0.914499i	$0.632585\pi$
$240$		0			0
$241$	−19.5775			−1.26110			−0.630548	−	0.776150i	$-0.717170\pi$
$241$	−19.5775			−1.26110			−0.630548	+	0.776150i	$0.717170\pi$
$242$	1.19671	−	1.87997i	0.0769273	−	0.120849i
$243$	10.4151			0.668129
$244$	3.76530	+	1.36733i	0.241049	+	0.0875346i
$245$		0			0
$246$	−10.9791	+	17.2477i	−0.700001	+	1.09967i
$247$	0.0211680	+	0.0211680i	0.00134689	+	0.00134689i
$248$	25.0352	+	3.26796i	1.58974	+	0.207516i
$249$	−17.8716			−1.13257
$250$		0			0
$251$	5.17763	−	5.17763i	0.326809	−	0.326809i	−0.524563	−	0.851372i	$-0.675771\pi$
$251$	5.17763	−	5.17763i	0.326809	−	0.326809i	0.851372	+	0.524563i	$0.175771\pi$
$252$	2.18222	−	6.00931i	0.137467	−	0.378551i
$253$		−	13.6860i		−	0.860433i
$254$	2.70580	−	0.600902i	0.169777	−	0.0377040i
$255$		0			0
$256$	−2.82454	−	15.7487i	−0.176534	−	0.984295i
$257$	14.7989	+	14.7989i	0.923131	+	0.923131i	0.997249	−	0.0741183i	$-0.0236142\pi$
$257$	14.7989	+	14.7989i	0.923131	+	0.923131i	−0.0741183	+	0.997249i	$0.523614\pi$
$258$	−2.14750	+	3.37363i	−0.133698	+	0.210033i
$259$	15.4685	−	15.4685i	0.961168	−	0.961168i
$260$		0			0
$261$	−3.53491	−	3.53491i	−0.218805	−	0.218805i
$262$	1.52667	+	6.87443i	0.0943178	+	0.424704i
$263$	−11.7906	+	11.7906i	−0.727038	+	0.727038i	−0.970029	−	0.242991i	$-0.921871\pi$
$263$	−11.7906	+	11.7906i	−0.727038	+	0.727038i	0.242991	+	0.970029i	$0.421871\pi$
$264$	−7.37470	−	9.58906i	−0.453881	−	0.590166i
$265$		0			0
$266$	−0.0697008	−	0.0443684i	−0.00427363	−	0.00272040i
$267$	−18.6313			−1.14022
$268$	1.35573	−	0.633397i	0.0828144	−	0.0386909i
$269$	2.10121	+	2.10121i	0.128113	+	0.128113i	0.768256	−	0.640143i	$-0.221125\pi$
$269$	2.10121	+	2.10121i	0.128113	+	0.128113i	−0.640143	+	0.768256i	$0.721125\pi$
$270$		0			0
$271$			18.8596i			1.14564i	0.819683	+	0.572818i	$0.194150\pi$
$271$			18.8596i			1.14564i	−0.819683	+	0.572818i	$0.805850\pi$
$272$	−21.7713	+	1.93690i	−1.32008	+	0.117442i
$273$	−4.59901	+	4.59901i	−0.278345	+	0.278345i
$274$	−10.9827	+	2.43902i	−0.663488	+	0.147347i
$275$		0			0
$276$	11.6761	+	4.24005i	0.702816	+	0.255221i
$277$		−	9.91909i		−	0.595980i	−0.954569	−	0.297990i	$-0.903684\pi$
$277$		−	9.91909i		−	0.595980i	0.954569	−	0.297990i	$-0.0963162\pi$
$278$	5.24746	+	23.6288i	0.314722	+	1.41716i
$279$		−	9.45334i		−	0.565956i
$280$		0			0
$281$		−	9.31434i		−	0.555647i	−0.960632	−	0.277823i	$-0.910387\pi$
$281$		−	9.31434i		−	0.555647i	0.960632	−	0.277823i	$-0.0896130\pi$
$282$	9.09366	−	2.01951i	0.541519	−	0.120260i
$283$		−	3.42364i		−	0.203514i	−0.994809	−	0.101757i	$-0.967554\pi$
$283$		−	3.42364i		−	0.203514i	0.994809	−	0.101757i	$-0.0324465\pi$
$284$	−0.228237	−	0.488520i	−0.0135434	−	0.0289883i
$285$		0			0
$286$	−1.45572	−	6.55496i	−0.0860785	−	0.387603i
$287$	22.1485	−	22.1485i	1.30738	−	1.30738i
$288$	−5.71021	+	1.81193i	−0.336477	+	0.106769i
$289$			12.8589i			0.756405i
$290$		0			0
$291$	−8.82535	−	8.82535i	−0.517351	−	0.517351i
$292$	0.783805	−	2.15841i	0.0458687	−	0.126311i
$293$	−2.66471			−0.155674			−0.0778369	−	0.996966i	$-0.524801\pi$
$293$	−2.66471			−0.155674			−0.0778369	+	0.996966i	$0.524801\pi$
$294$	2.23349	−	3.50872i	0.130260	−	0.204633i
$295$		0			0
$296$	−20.3262	−	2.65327i	−1.18144	−	0.154218i
$297$	−12.2755	+	12.2755i	−0.712296	+	0.712296i
$298$	−26.4731	+	5.87912i	−1.53355	+	0.340568i
$299$	4.87559	+	4.87559i	0.281963	+	0.281963i
$300$		0			0
$301$	4.33223	−	4.33223i	0.249706	−	0.249706i
$302$	24.7175	+	15.7341i	1.42233	+	0.905393i
$303$	−5.26804	−	5.26804i	−0.302641	−	0.302641i
$304$	0.00686086	+	0.0771181i	0.000393497	+	0.00442303i
$305$		0			0
$306$	1.77425	+	7.98928i	0.101427	+	0.456717i
$307$		−	10.5554i		−	0.602430i	−0.953556	−	0.301215i	$-0.902608\pi$
$307$		−	10.5554i		−	0.602430i	0.953556	−	0.301215i	$-0.0973922\pi$
$308$	7.84450	+	16.7905i	0.446982	+	0.956725i
$309$	−14.9348	+	14.9348i	−0.849612	+	0.849612i
$310$		0			0
$311$	−20.4762			−1.16110			−0.580550	−	0.814225i	$-0.697162\pi$
$311$	−20.4762			−1.16110			−0.580550	+	0.814225i	$0.697162\pi$
$312$	6.04327	+	0.788855i	0.342133	+	0.0446601i
$313$	2.82393	+	2.82393i	0.159618	+	0.159618i	0.782397	−	0.622780i	$-0.213997\pi$
$313$	2.82393	+	2.82393i	0.159618	+	0.159618i	−0.622780	+	0.782397i	$0.713997\pi$
$314$	−6.82776	−	4.34625i	−0.385313	−	0.245273i
$315$		0			0
$316$	−2.37518	−	5.08385i	−0.133614	−	0.285989i
$317$	−20.2533			−1.13754			−0.568769	−	0.822497i	$-0.692580\pi$
$317$	−20.2533			−1.13754			−0.568769	+	0.822497i	$0.692580\pi$
$318$	−12.1449	−	7.73091i	−0.681053	−	0.433528i
$319$	14.4913			0.811354
$320$		0			0
$321$	−15.2009			−0.848430
$322$	−16.0541	−	10.2193i	−0.894658	−	0.569499i
$323$	0.105766			0.00588497
$324$	−3.98000	−	8.51883i	−0.221111	−	0.473268i
$325$		0			0
$326$	−21.4623	−	13.6620i	−1.18869	−	0.756666i
$327$	12.7078	+	12.7078i	0.702742	+	0.702742i
$328$	−29.1039	−	3.79907i	−1.60700	−	0.209768i
$329$	−14.2709			−0.786781
$330$		0			0
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.0741908	−	0.997244i	$-0.476363\pi$
$331$	19.4930	−	19.4930i	1.07143	−	1.07143i	0.997244	−	0.0741908i	$-0.0236374\pi$
$332$	−10.8596	−	23.2441i	−0.596000	−	1.27569i
$333$			7.67521i			0.420599i
$334$	1.03908	+	4.67885i	0.0568557	+	0.256016i
$335$		0			0
$336$	−16.7549	+	1.49061i	−0.914053	+	0.0813192i
$337$	5.89449	+	5.89449i	0.321093	+	0.321093i	0.849186	−	0.528093i	$-0.177093\pi$
$337$	5.89449	+	5.89449i	0.321093	+	0.321093i	−0.528093	+	0.849186i	$0.677093\pi$
$338$	−12.6554	−	8.05587i	−0.688364	−	0.438181i
$339$	−6.81003	+	6.81003i	−0.369870	+	0.369870i
$340$		0			0
$341$	19.3768	+	19.3768i	1.04931	+	1.04931i
$342$	0.0282995	−	0.00628473i	0.00153026	−	0.000339839i
$343$	10.4349	−	10.4349i	0.563429	−	0.563429i
$344$	−5.69271	−	0.743095i	−0.306930	−	0.0400650i
$345$		0			0
$346$	−7.17807	+	11.2764i	−0.385895	+	0.606225i
$347$	11.4626			0.615346			0.307673	−	0.951492i	$-0.400450\pi$
$347$	11.4626			0.615346			0.307673	+	0.951492i	$0.400450\pi$
$348$	−4.48952	+	12.3630i	−0.240663	+	0.662728i
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	0.715563	−	0.698548i	$-0.246170\pi$
$349$	0.317872	+	0.317872i	0.0170153	+	0.0170153i	−0.698548	+	0.715563i	$0.746170\pi$
$350$		0			0
$351$		−	8.74618i		−	0.466837i
$352$	7.99044	−	15.4184i	0.425892	−	0.821803i
$353$	18.4551	−	18.4551i	0.982266	−	0.982266i	−0.0175800	−	0.999845i	$-0.505596\pi$
$353$	18.4551	−	18.4551i	0.982266	−	0.982266i	0.999845	+	0.0175800i	$0.00559616\pi$
$354$	2.13077	+	9.59466i	0.113249	+	0.509951i
$355$		0			0
$356$	−11.3213	−	24.2321i	−0.600026	−	1.28430i
$357$			22.9789i			1.21617i
$358$	−23.0369	+	5.11602i	−1.21754	+	0.270390i
$359$			15.5802i			0.822292i	0.911569	+	0.411146i	$0.134871\pi$
$359$			15.5802i			0.822292i	−0.911569	+	0.411146i	$0.865129\pi$
$360$		0			0
$361$			18.9996i			0.999980i
$362$	−1.10200	−	4.96220i	−0.0579199	−	0.260808i
$363$			2.19541i			0.115229i
$364$	−8.77611	−	3.18696i	−0.459993	−	0.167042i
$365$		0			0
$366$	−3.85246	+	0.855552i	−0.201372	+	0.0447204i
$367$	5.37489	−	5.37489i	0.280567	−	0.280567i	−0.552768	−	0.833335i	$-0.686428\pi$
$367$	5.37489	−	5.37489i	0.280567	−	0.280567i	0.833335	+	0.552768i	$0.186428\pi$
$368$	1.58025	+	17.7625i	0.0823762	+	0.925933i
$369$			10.9897i			0.572100i
$370$		0			0
$371$	15.5958	+	15.5958i	0.809696	+	0.809696i
$372$	−22.5342	+	10.5280i	−1.16834	+	0.545850i
$373$	−3.24424			−0.167980			−0.0839902	−	0.996467i	$-0.526766\pi$
$373$	−3.24424			−0.167980			−0.0839902	+	0.996467i	$0.526766\pi$
$374$	−20.0126	−	12.7391i	−1.03483	−	0.658726i
$375$		0			0
$376$	8.15233	+	10.6002i	0.420424	+	0.546662i
$377$	−5.16245	+	5.16245i	−0.265880	+	0.265880i
$378$	5.23340	+	23.5655i	0.269177	+	1.21208i
$379$	25.7690	+	25.7690i	1.32367	+	1.32367i	0.910785	+	0.412882i	$0.135478\pi$
$379$	25.7690	+	25.7690i	1.32367	+	1.32367i	0.412882	+	0.910785i	$0.364522\pi$
$380$		0			0
$381$	−1.93076	+	1.93076i	−0.0989160	+	0.0989160i
$382$	−4.14962	+	6.51888i	−0.212313	+	0.333535i
$383$	0.418091	+	0.418091i	0.0213634	+	0.0213634i	0.717708	−	0.696344i	$-0.245191\pi$
$383$	0.418091	+	0.418091i	0.0213634	+	0.0213634i	−0.696344	+	0.717708i	$0.745191\pi$
$384$	10.6785	+	11.5937i	0.544934	+	0.591638i
$385$		0			0
$386$	9.42019	−	2.09203i	0.479475	−	0.106481i
$387$			2.14957i			0.109269i
$388$	6.11568	−	16.8411i	0.310476	−	0.854976i
$389$	−13.3626	+	13.3626i	−0.677508	+	0.677508i	−0.959436	−	0.281927i	$-0.909026\pi$
$389$	−13.3626	+	13.3626i	−0.677508	+	0.677508i	0.281927	+	0.959436i	$0.409026\pi$
$390$		0			0
$391$	24.3609			1.23198
$392$	5.92066	+	0.772850i	0.299038	+	0.0390348i
$393$	−4.90535	−	4.90535i	−0.247442	−	0.247442i
$394$	−2.23712	+	3.51441i	−0.112704	+	0.177053i
$395$		0			0
$396$	−6.11171	−	2.21941i	−0.307125	−	0.111530i
$397$	13.8391			0.694564			0.347282	−	0.937761i	$-0.387105\pi$
$397$	13.8391			0.694564			0.347282	+	0.937761i	$0.387105\pi$
$398$	1.62986	−	2.56044i	0.0816977	−	0.128343i
$399$	0.0813957			0.00407488
$400$		0			0
$401$	20.3112			1.01430			0.507148	−	0.861859i	$-0.330700\pi$
$401$	20.3112			1.01430			0.507148	+	0.861859i	$0.330700\pi$
$402$	−0.791602	+	1.24357i	−0.0394815	+	0.0620237i
$403$	−13.8058			−0.687718
$404$	3.65057	−	10.0528i	0.181623	−	0.500144i
$405$		0			0
$406$	10.8206	−	16.9986i	0.537015	−	0.843626i
$407$	−15.7321	−	15.7321i	−0.779813	−	0.779813i
$408$	17.0683	−	13.1268i	0.845008	−	0.649874i
$409$	18.2875			0.904259			0.452130	−	0.891952i	$-0.350664\pi$
$409$	18.2875			0.904259			0.452130	+	0.891952i	$0.350664\pi$
$410$		0			0
$411$	7.83684	−	7.83684i	0.386563	−	0.386563i
$412$	−28.4995	−	10.3493i	−1.40407	−	0.509875i
$413$		−	15.0572i		−	0.740915i
$414$	6.51818	−	1.44755i	0.320351	−	0.0711433i
$415$		0			0
$416$	2.64618	+	8.33930i	0.129740	+	0.408868i
$417$	−16.8607	−	16.8607i	−0.825670	−	0.825670i
$418$	−0.0451245	+	0.0708885i	−0.00220711	+	0.00346727i
$419$	−17.3188	+	17.3188i	−0.846079	+	0.846079i	−0.989641	−	0.143563i	$-0.954144\pi$
$419$	−17.3188	+	17.3188i	−0.846079	+	0.846079i	0.143563	+	0.989641i	$0.454144\pi$
$420$		0			0
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	0.930074	−	0.367372i	$-0.119742\pi$
$421$	11.5457	+	11.5457i	0.562703	+	0.562703i	−0.367372	+	0.930074i	$0.619742\pi$
$422$	−2.40397	−	10.8248i	−0.117023	−	0.526944i
$423$	3.54048	−	3.54048i	0.172144	−	0.172144i
$424$	2.67511	−	20.4935i	0.129915	−	0.995252i
$425$		0			0
$426$	0.448105	+	0.285244i	0.0217108	+	0.0138201i
$427$	6.04577			0.292576
$428$	−9.23676	−	19.7705i	−0.446475	−	0.955641i
$429$	4.67738	+	4.67738i	0.225826	+	0.225826i
$430$		0			0
$431$		−	15.9479i		−	0.768185i	−0.923295	−	0.384093i	$-0.874514\pi$
$431$		−	15.9479i		−	0.768185i	0.923295	−	0.384093i	$-0.125486\pi$
$432$	14.5144	−	17.3492i	0.698325	−	0.834713i
$433$	−3.52109	+	3.52109i	−0.169213	+	0.169213i	−0.786633	−	0.617420i	$-0.788178\pi$
$433$	−3.52109	+	3.52109i	−0.169213	+	0.169213i	0.617420	+	0.786633i	$0.288178\pi$
$434$	37.1981	−	8.26092i	1.78557	−	0.396537i
$435$		0			0
$436$	−8.80607	+	24.2498i	−0.421734	+	1.16135i
$437$		−	0.0862907i		−	0.00412784i
$438$	0.490433	+	2.20837i	0.0234338	+	0.105520i
$439$		−	6.45840i		−	0.308242i	−0.988052	−	0.154121i	$-0.950745\pi$
$439$		−	6.45840i		−	0.308242i	0.988052	−	0.154121i	$-0.0492546\pi$
$440$		0			0
$441$		−	2.23565i		−	0.106459i
$442$	11.6677	−	2.59115i	0.554975	−	0.123248i
$443$			27.0992i			1.28752i	0.765226	+	0.643761i	$0.222627\pi$
$443$			27.0992i			1.28752i	−0.765226	+	0.643761i	$0.777373\pi$
$444$	18.2956	−	8.54771i	0.868271	−	0.405656i
$445$		0			0
$446$	0.503675	+	2.26800i	0.0238497	+	0.107393i
$447$	18.8903	−	18.8903i	0.893478	−	0.893478i
$448$	−12.1197	−	20.8858i	−0.572604	−	0.986763i
$449$		−	41.0879i		−	1.93906i	−0.244976	−	0.969529i	$-0.578780\pi$
$449$		−	41.0879i		−	1.93906i	0.244976	−	0.969529i	$-0.421220\pi$
$450$		0			0
$451$	−22.5259	−	22.5259i	−1.06070	−	1.06070i
$452$	−12.9953	−	4.71913i	−0.611248	−	0.221969i
$453$	−28.8648			−1.35619
$454$	−9.73276	+	15.2897i	−0.456781	+	0.717583i
$455$		0			0
$456$	−0.0464977	−	0.0604592i	−0.00217745	−	0.00283126i
$457$	18.2449	−	18.2449i	0.853462	−	0.853462i	−0.137096	−	0.990558i	$-0.543777\pi$
$457$	18.2449	−	18.2449i	0.853462	−	0.853462i	0.990558	+	0.137096i	$0.0437769\pi$
$458$	−1.90730	+	0.423571i	−0.0891221	+	0.0197922i
$459$	−21.8501	−	21.8501i	−1.01988	−	1.01988i
$460$		0			0
$461$	6.68802	−	6.68802i	0.311492	−	0.311492i	−0.533995	−	0.845488i	$-0.679310\pi$
$461$	6.68802	−	6.68802i	0.311492	−	0.311492i	0.845488	+	0.533995i	$0.179310\pi$
$462$	−15.4014	−	9.80384i	−0.716538	−	0.456116i
$463$	28.6926	+	28.6926i	1.33346	+	1.33346i	0.902254	+	0.431205i	$0.141911\pi$
$463$	28.6926	+	28.6926i	1.33346	+	1.33346i	0.431205	+	0.902254i	$0.358089\pi$
$464$	−18.8075	+	1.67322i	−0.873118	+	0.0776775i
$465$		0			0
$466$	−0.131756	−	0.593286i	−0.00610349	−	0.0274834i
$467$			32.4161i			1.50004i	0.661417	+	0.750018i	$0.269955\pi$
$467$			32.4161i			1.50004i	−0.661417	+	0.750018i	$0.730045\pi$
$468$	2.96793	−	1.38662i	0.137193	−	0.0640964i
$469$	1.59693	−	1.59693i	0.0737392	−	0.0737392i
$470$		0			0
$471$	7.97337			0.367394
$472$	−11.1842	+	8.60148i	−0.514794	+	0.395915i
$473$	−4.40605	−	4.40605i	−0.202591	−	0.202591i
$474$	4.66327	+	2.96843i	0.214191	+	0.136344i
$475$		0			0
$476$	−29.8867	+	13.9631i	−1.36985	+	0.639996i
$477$	−7.73837			−0.354316
$478$	14.9241	+	9.50003i	0.682613	+	0.434521i
$479$	−7.33117			−0.334970			−0.167485	−	0.985875i	$-0.553565\pi$
$479$	−7.33117			−0.334970			−0.167485	+	0.985875i	$0.553565\pi$
$480$		0			0
$481$	11.2090			0.511087
$482$	23.3562	+	14.8675i	1.06385	+	0.677197i
$483$	18.7477			0.853051
$484$	−2.85538	+	1.33403i	−0.129790	+	0.0606378i
$485$		0			0
$486$	−12.4254	−	7.90943i	−0.563626	−	0.358779i
$487$	11.7773	+	11.7773i	0.533681	+	0.533681i	0.921666	−	0.387985i	$-0.126829\pi$
$487$	11.7773	+	11.7773i	0.533681	+	0.533681i	−0.387985	+	0.921666i	$0.626829\pi$
$488$	−3.45368	−	4.49069i	−0.156341	−	0.203284i
$489$	25.0634			1.13341
$490$		0			0
$491$	−27.3556	+	27.3556i	−1.23454	+	1.23454i	−0.272343	+	0.962200i	$0.587798\pi$
$491$	−27.3556	+	27.3556i	−1.23454	+	1.23454i	−0.962200	+	0.272343i	$0.912202\pi$
$492$	26.1964	−	12.2390i	1.18103	−	0.551775i
$493$			25.7941i			1.16171i
$494$	−0.00917834	−	0.0413292i	−0.000412953	−	0.00185949i
$495$		0			0
$496$	−27.3856	−	22.9110i	−1.22965	−	1.02873i
$497$	−0.575432	−	0.575432i	−0.0258117	−	0.0258117i
$498$	21.3211	+	13.5721i	0.955422	+	0.608179i
$499$	−12.1629	+	12.1629i	−0.544488	+	0.544488i	−0.924841	−	0.380353i	$-0.875802\pi$
$499$	−12.1629	+	12.1629i	−0.544488	+	0.544488i	0.380353	+	0.924841i	$0.375802\pi$
$500$		0			0
$501$	−3.33866	−	3.33866i	−0.149160	−	0.149160i
$502$	−10.1090	+	2.24499i	−0.451185	+	0.100199i
$503$	13.2748	−	13.2748i	0.591892	−	0.591892i	−0.346250	−	0.938142i	$-0.612545\pi$
$503$	13.2748	−	13.2748i	0.591892	−	0.591892i	0.938142	+	0.346250i	$0.112545\pi$
$504$	−7.16701	+	5.51197i	−0.319244	+	0.245522i
$505$		0			0
$506$	−10.3934	+	16.3276i	−0.462045	+	0.725851i
$507$	14.7788			0.656350
$508$	−3.68440	−	1.33795i	−0.163469	−	0.0593621i
$509$	−9.29995	−	9.29995i	−0.412213	−	0.412213i	0.470296	−	0.882509i	$-0.344147\pi$
$509$	−9.29995	−	9.29995i	−0.412213	−	0.412213i	−0.882509	+	0.470296i	$0.844147\pi$
$510$		0			0
$511$		−	3.46565i		−	0.153312i
$512$	−8.59016	+	20.9334i	−0.379635	+	0.925136i
$513$	−0.0773972	+	0.0773972i	−0.00341717	+	0.00341717i
$514$	−6.41673	−	28.8939i	−0.283030	−	1.27446i
$515$		0			0
$516$	5.12400	−	2.39393i	0.225572	−	0.105387i
$517$			14.5141i			0.638329i
$518$	−30.2013	+	6.70708i	−1.32697	+	0.294692i
$519$		−	13.1685i		−	0.578031i
$520$		0			0
$521$			33.5279i			1.46888i	0.678671	+	0.734442i	$0.262556\pi$
$521$			33.5279i			1.46888i	−0.678671	+	0.734442i	$0.737444\pi$
$522$	1.53272	+	6.90168i	0.0670852	+	0.302078i
$523$		−	25.9463i		−	1.13455i	−0.823528	−	0.567276i	$-0.807997\pi$
$523$		−	25.9463i		−	1.13455i	0.823528	−	0.567276i	$-0.192003\pi$
$524$	3.39924	−	9.36067i	0.148497	−	0.408923i
$525$		0			0
$526$	23.0203	−	5.11233i	1.00373	−	0.222908i
$527$	−34.4903	+	34.4903i	−1.50242	+	1.50242i
$528$	1.51601	+	17.0404i	0.0659757	+	0.741587i
$529$			3.12481i			0.135861i
$530$		0			0
$531$	3.73554	+	3.73554i	0.162109	+	0.162109i
$532$	0.0494598	+	0.105864i	0.00214435	+	0.00458980i
$533$	16.0495			0.695182
$534$	22.2274	+	14.1490i	0.961875	+	0.612287i
$535$		0			0
$536$	−2.09842	−	0.273916i	−0.0906379	−	0.0118314i
$537$	16.4383	−	16.4383i	0.709365	−	0.709365i
$538$	−0.911073	−	4.10247i	−0.0392792	−	0.176870i
$539$	4.58248	+	4.58248i	0.197381	+	0.197381i
$540$		0			0
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	−0.604428	−	0.796660i	$-0.706598\pi$
$541$	4.47122	−	4.47122i	0.192233	−	0.192233i	0.796660	+	0.604428i	$0.206598\pi$
$542$	14.3223	−	22.4997i	0.615196	−	0.966445i
$543$	3.54085	+	3.54085i	0.151952	+	0.151952i
$544$	27.4444	+	14.2228i	1.17667	+	0.609798i
$545$		0			0
$546$	8.97927	−	1.99411i	0.384277	−	0.0853399i
$547$		−	15.5964i		−	0.666853i	−0.942776	−	0.333426i	$-0.891795\pi$
$547$		−	15.5964i		−	0.666853i	0.942776	−	0.333426i	$-0.108205\pi$
$548$	14.9547	+	5.43067i	0.638835	+	0.231987i
$549$	−1.49990	+	1.49990i	−0.0640142	+	0.0640142i
$550$		0			0
$551$	0.0913677			0.00389239
$552$	−10.7097	−	13.9255i	−0.455836	−	0.592707i
$553$	−5.98831	−	5.98831i	−0.254649	−	0.254649i
$554$	−7.53275	+	11.8336i	−0.320036	+	0.502762i
$555$		0			0
$556$	11.6839	−	32.1745i	0.495506	−	1.36450i
$557$	−15.5348			−0.658231			−0.329116	−	0.944290i	$-0.606751\pi$
$557$	−15.5348			−0.658231			−0.329116	+	0.944290i	$0.606751\pi$
$558$	−7.17905	+	11.2780i	−0.303913	+	0.477434i
$559$	3.13928			0.132777
$560$		0			0
$561$	23.3705			0.986703
$562$	−7.07349	+	11.1121i	−0.298377	+	0.468737i
$563$	−24.3087			−1.02449			−0.512245	−	0.858839i	$-0.671186\pi$
$563$	−24.3087			−1.02449			−0.512245	+	0.858839i	$0.671186\pi$
$564$	−12.3825	−	4.49659i	−0.521398	−	0.189341i
$565$		0			0
$566$	−2.59998	+	4.08445i	−0.109285	+	0.171682i
$567$	−10.0344	−	10.0344i	−0.421405	−	0.421405i
$568$	−0.0987022	+	0.756139i	−0.00414145	+	0.0317269i
$569$	−0.187259			−0.00785029			−0.00392515	−	0.999992i	$-0.501249\pi$
$569$	−0.187259			−0.00785029			−0.00392515	+	0.999992i	$0.501249\pi$
$570$		0			0
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	−0.870974	−	0.491328i	$-0.836511\pi$
$571$	−9.07187	+	9.07187i	−0.379646	+	0.379646i	0.491328	+	0.870974i	$0.336511\pi$
$572$	−3.24127	+	8.92566i	−0.135524	+	0.373200i
$573$		−	7.61266i		−	0.318023i
$574$	−43.2434	+	9.60346i	−1.80495	+	0.400841i
$575$		0			0
$576$	8.18838	+	2.17479i	0.341182	+	0.0906162i
$577$	1.53648	+	1.53648i	0.0639645	+	0.0639645i	0.738365	−	0.674401i	$-0.235598\pi$
$577$	1.53648	+	1.53648i	0.0639645	+	0.0639645i	−0.674401	+	0.738365i	$0.735598\pi$
$578$	9.76529	−	15.3408i	0.406183	−	0.638095i
$579$	−6.72191	+	6.72191i	−0.279353	+	0.279353i
$580$		0			0
$581$	−27.3794	−	27.3794i	−1.13589	−	1.13589i
$582$	3.82663	+	17.2309i	0.158619	+	0.714244i
$583$	15.8616	−	15.8616i	0.656920	−	0.656920i
$584$	−2.57423	+	1.97977i	−0.106522	+	0.0819235i
$585$		0			0
$586$	3.17903	+	2.02363i	0.131325	+	0.0835954i
$587$	3.06150			0.126362			0.0631808	−	0.998002i	$-0.479876\pi$
$587$	3.06150			0.126362			0.0631808	+	0.998002i	$0.479876\pi$
$588$	−5.32917	+	2.48979i	−0.219771	+	0.102677i
$589$	0.122171	+	0.122171i	0.00503398	+	0.00503398i
$590$		0			0
$591$		−	4.10408i		−	0.168819i
$592$	22.2345	+	18.6015i	0.913833	+	0.764518i
$593$	20.8213	−	20.8213i	0.855029	−	0.855029i	−0.135718	−	0.990747i	$-0.543334\pi$
$593$	20.8213	−	20.8213i	0.855029	−	0.855029i	0.990747	+	0.135718i	$0.0433342\pi$
$594$	23.9671	−	5.32258i	0.983380	−	0.218388i
$595$		0			0
$596$	36.0475	+	13.0903i	1.47656	+	0.536200i
$597$			2.99005i			0.122375i
$598$	−2.11403	−	9.51927i	−0.0864492	−	0.389272i
$599$		−	27.8866i		−	1.13942i	−0.821847	−	0.569709i	$-0.807056\pi$
$599$		−	27.8866i		−	1.13942i	0.821847	−	0.569709i	$-0.192944\pi$
$600$		0			0
$601$			4.70260i			0.191823i	0.995390	+	0.0959115i	$0.0305766\pi$
$601$			4.70260i			0.191823i	−0.995390	+	0.0959115i	$0.969423\pi$
$602$	−8.45839	+	1.87843i	−0.344738	+	0.0765592i
$603$			0.792365i			0.0322676i
$604$	−17.5396	−	37.5419i	−0.713675	−	1.52756i
$605$		0			0
$606$	2.28419	+	10.2855i	0.0927889	+	0.417819i
$607$	−28.8294	+	28.8294i	−1.17015	+	1.17015i	−0.187975	+	0.982174i	$0.560193\pi$
$607$	−28.8294	+	28.8294i	−1.17015	+	1.17015i	−0.982174	+	0.187975i	$0.939807\pi$
$608$	0.0503799	−	0.0972133i	0.00204317	−	0.00394252i
$609$			19.8507i			0.804393i
$610$		0			0
$611$	−5.17059	−	5.17059i	−0.209180	−	0.209180i
$612$	3.95050	−	10.8787i	0.159690	−	0.439746i
$613$	38.7980			1.56704			0.783518	−	0.621369i	$-0.213423\pi$
$613$	38.7980			1.56704			0.783518	+	0.621369i	$0.213423\pi$
$614$	−8.01599	+	12.5928i	−0.323499	+	0.508203i
$615$		0			0
$616$	3.39240	−	25.9885i	0.136684	−	1.04711i
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	−0.834907	−	0.550391i	$-0.814479\pi$
$617$	−7.06723	+	7.06723i	−0.284516	+	0.284516i	0.550391	+	0.834907i	$0.314479\pi$
$618$	29.1592	−	6.47565i	1.17296	−	0.260489i
$619$	28.1001	+	28.1001i	1.12944	+	1.12944i	0.990268	+	0.139172i	$0.0444440\pi$
$619$	28.1001	+	28.1001i	1.12944	+	1.12944i	0.139172	+	0.990268i	$0.455556\pi$
$620$		0			0
$621$	−17.8268	+	17.8268i	−0.715363	+	0.715363i
$622$	24.4284	+	15.5500i	0.979490	+	0.623500i
$623$	−28.5432	−	28.5432i	−1.14356	−	1.14356i
$624$	−6.61064	−	5.53049i	−0.264637	−	0.221397i
$625$		0			0
$626$	−1.22444	−	5.51353i	−0.0489384	−	0.220365i
$627$		−	0.0827827i		−	0.00330602i
$628$	4.84499	+	10.3703i	0.193336	+	0.413819i
$629$	28.0029	−	28.0029i	1.11655	−	1.11655i
$630$		0			0
$631$	38.2613			1.52316			0.761580	−	0.648071i	$-0.224424\pi$
$631$	38.2613			1.52316			0.761580	+	0.648071i	$0.224424\pi$
$632$	−1.02716	+	7.86886i	−0.0408582	+	0.313007i
$633$	7.72420	+	7.72420i	0.307010	+	0.307010i
$634$	24.1625	+	15.3807i	0.959614	+	0.610847i
$635$		0			0
$636$	8.61805	+	18.4462i	0.341728	+	0.731438i
$637$	−3.26498			−0.129363
$638$	−17.2883	−	11.0049i	−0.684449	−	0.435690i
$639$	0.285519			0.0112950
$640$		0			0
$641$	7.15922			0.282772			0.141386	−	0.989955i	$-0.454844\pi$
$641$	7.15922			0.282772			0.141386	+	0.989955i	$0.454844\pi$
$642$	18.1349	+	11.5438i	0.715726	+	0.455599i
$643$	−8.74864			−0.345013			−0.172506	−	0.985008i	$-0.555187\pi$
$643$	−8.74864			−0.345013			−0.172506	+	0.985008i	$0.555187\pi$
$644$	11.3920	+	24.3835i	0.448907	+	0.960845i
$645$		0			0
$646$	−0.126180	−	0.0803206i	−0.00496449	−	0.00316017i
$647$	−8.84125	−	8.84125i	−0.347585	−	0.347585i	0.511624	−	0.859209i	$-0.329044\pi$
$647$	−8.84125	−	8.84125i	−0.347585	−	0.347585i	−0.859209	+	0.511624i	$0.829044\pi$
$648$	−1.72117	+	13.1856i	−0.0676140	+	0.517978i
$649$	−15.3137			−0.601117
$650$		0			0
$651$	−26.5432	+	26.5432i	−1.04031	+	1.04031i
$652$	15.2297	+	32.5978i	0.596441	+	1.27663i
$653$		−	20.7854i		−	0.813396i	−0.913563	−	0.406698i	$-0.866680\pi$
$653$		−	20.7854i		−	0.813396i	0.913563	−	0.406698i	$-0.133320\pi$
$654$	−5.51003	−	24.8111i	−0.215459	−	0.970191i
$655$		0			0
$656$	31.8363	+	26.6344i	1.24300	+	1.03990i
$657$	0.859797	+	0.859797i	0.0335439	+	0.0335439i
$658$	17.0254	+	10.8376i	0.663719	+	0.422494i
$659$	−13.3330	+	13.3330i	−0.519382	+	0.519382i	−0.917384	−	0.398003i	$-0.869703\pi$
$659$	−13.3330	+	13.3330i	−0.519382	+	0.519382i	0.398003	+	0.917384i	$0.369703\pi$
$660$		0			0
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.977194	−	0.212350i	$-0.931888\pi$
$661$	−30.5831	−	30.5831i	−1.18954	−	1.18954i	−0.212350	−	0.977194i	$-0.568112\pi$
$662$	−38.0589	+	8.45208i	−1.47920	+	0.328499i
$663$	−8.32564	+	8.32564i	−0.323341	+	0.323341i
$664$	−4.69631	+	35.9775i	−0.182252	+	1.39620i
$665$		0			0
$666$	5.82870	−	9.15663i	0.225858	−	0.354812i
$667$	21.0446			0.814848
$668$	2.31358	−	6.37103i	0.0895151	−	0.246503i
$669$	−1.61836	−	1.61836i	−0.0625695	−	0.0625695i
$670$		0			0
$671$		−	6.14880i		−	0.237372i
$672$	21.1208	+	10.9457i	0.814752	+	0.422238i
$673$	−29.9888	+	29.9888i	−1.15598	+	1.15598i	−0.170652	+	0.985331i	$0.554587\pi$
$673$	−29.9888	+	29.9888i	−1.15598	+	1.15598i	−0.985331	+	0.170652i	$0.945413\pi$
$674$	−2.55582	−	11.5086i	−0.0984464	−	0.443295i
$675$		0			0
$676$	8.98030	+	19.2215i	0.345396	+	0.739289i
$677$			33.4274i			1.28472i	0.766403	+	0.642360i	$0.222044\pi$
$677$			33.4274i			1.28472i	−0.766403	+	0.642360i	$0.777956\pi$
$678$	13.2961	−	2.95279i	0.510635	−	0.113401i
$679$		−	27.0409i		−	1.03774i
$680$		0			0
$681$		−	17.8551i		−	0.684211i
$682$	−8.40169	−	37.8320i	−0.321717	−	1.44866i
$683$		−	4.07583i		−	0.155957i	−0.996955	−	0.0779787i	$-0.975153\pi$
$683$		−	4.07583i		−	0.155957i	0.996955	−	0.0779787i	$-0.0248466\pi$
$684$	−0.0385345	−	0.0139934i	−0.00147340	−	0.000535052i
$685$		0			0
$686$	−20.3734	+	4.52450i	−0.777858	+	0.172746i
$687$	1.36098	−	1.36098i	0.0519246	−	0.0519246i
$688$	6.22716	+	5.20968i	0.237408	+	0.198617i
$689$			11.3013i			0.430544i
$690$		0			0
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	0.522044	−	0.852919i	$-0.325170\pi$
$691$	−8.69768	−	8.69768i	−0.330875	−	0.330875i	−0.852919	+	0.522044i	$0.825170\pi$
$692$	17.1271	−	8.00177i	0.651074	−	0.304182i
$693$	−9.81330			−0.372776
$694$	−13.6751	−	8.70494i	−0.519098	−	0.330435i
$695$		0			0
$696$	14.7448	−	11.3398i	0.558899	−	0.429835i
$697$	40.0956	−	40.0956i	1.51873	−	1.51873i
$698$	−0.137828	−	0.620624i	−0.00521685	−	0.0234910i
$699$	0.423347	+	0.423347i	0.0160125	+	0.0160125i
$700$		0			0
$701$	11.8325	−	11.8325i	0.446908	−	0.446908i	−0.447418	−	0.894325i	$-0.647656\pi$
$701$	11.8325	−	11.8325i	0.446908	−	0.446908i	0.894325	+	0.447418i	$0.147656\pi$
$702$	−6.64202	+	10.4343i	−0.250687	+	0.393818i
$703$	−0.0991914	−	0.0991914i	−0.00374108	−	0.00374108i
$704$	−21.2417	+	12.3263i	−0.800578	+	0.464563i
$705$		0			0
$706$	−36.0323	+	8.00203i	−1.35609	+	0.301160i
$707$		−	16.1413i		−	0.607056i
$708$	4.74433	−	13.0647i	0.178303	−	0.491002i
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.247563	+	0.968872i	$0.579630\pi$
$709$	−32.3901	+	32.3901i	−1.21643	+	1.21643i	−0.968872	+	0.247563i	$0.920370\pi$
$710$		0			0
$711$	2.97129			0.111432
$712$	−4.89594	+	37.5069i	−0.183483	+	1.40563i
$713$	28.1395	+	28.1395i	1.05383	+	1.05383i
$714$	17.4506	−	27.4142i	0.653074	−	1.02595i
$715$		0			0
$716$	31.3686	+	11.3912i	1.17230	+	0.425709i
$717$	−17.4282			−0.650868
$718$	11.8319	−	18.5874i	0.441563	−	0.693676i
$719$	4.16893			0.155475			0.0777374	−	0.996974i	$-0.475230\pi$
$719$	4.16893			0.155475			0.0777374	+	0.996974i	$0.475230\pi$
$720$		0			0
$721$	−45.7603			−1.70420
$722$	14.4287	−	22.6668i	0.536980	−	0.843572i
$723$	−27.2751			−1.01437
$724$	−2.45369	+	6.75686i	−0.0911906	+	0.251117i
$725$		0			0
$726$	1.66724	−	2.61915i	0.0618769	−	0.0972059i
$727$	−28.6014	−	28.6014i	−1.06077	−	1.06077i	−0.998030	−	0.0627368i	$-0.980017\pi$
$727$	−28.6014	−	28.6014i	−1.06077	−	1.06077i	−0.0627368	−	0.998030i	$-0.519983\pi$
$728$	8.04978	+	10.4668i	0.298345	+	0.387927i
$729$	28.6142			1.05979
$730$		0			0
$731$	7.84269	−	7.84269i	0.290072	−	0.290072i
$732$	5.24577	+	1.90495i	0.193889	+	0.0704090i
$733$			18.7069i			0.690956i	0.938427	+	0.345478i	$0.112283\pi$
$733$			18.7069i			0.690956i	−0.938427	+	0.345478i	$0.887717\pi$
$734$	−10.4941	+	2.33052i	−0.387345	+	0.0860212i
$735$		0			0
$736$	11.6039	−	22.3910i	0.427726	−	0.825342i
$737$	−1.62414	−	1.62414i	−0.0598259	−	0.0598259i
$738$	8.34577	−	13.1108i	0.307212	−	0.482616i
$739$	34.6914	−	34.6914i	1.27614	−	1.27614i	0.333337	−	0.942808i	$-0.391825\pi$
$739$	34.6914	−	34.6914i	1.27614	−	1.27614i	0.942808	−	0.333337i	$-0.108175\pi$
$740$		0			0
$741$	0.0294910	+	0.0294910i	0.00108338	+	0.00108338i
$742$	−6.76227	−	30.4498i	−0.248251	−	1.11785i
$743$	−24.7660	+	24.7660i	−0.908577	+	0.908577i	−0.996157	−	0.0875803i	$-0.972087\pi$
$743$	−24.7660	+	24.7660i	−0.908577	+	0.908577i	0.0875803	+	0.996157i	$0.472087\pi$
$744$	34.8788	+	4.55288i	1.27872	+	0.166917i
$745$		0			0
$746$	3.87042	+	2.46374i	0.141706	+	0.0902039i
$747$	13.5852			0.497055
$748$	14.2010	+	30.3960i	0.519240	+	1.11139i
$749$	−23.2878	−	23.2878i	−0.850917	−	0.850917i
$750$		0			0
$751$			45.2370i			1.65072i	0.564606	+	0.825361i	$0.309028\pi$
$751$			45.2370i			1.65072i	−0.564606	+	0.825361i	$0.690972\pi$
$752$	−1.67586	−	18.8372i	−0.0611124	−	0.686922i
$753$	7.21340	−	7.21340i	0.262871	−	0.262871i
$754$	10.0793	−	2.23841i	0.367068	−	0.0815181i
$755$		0			0
$756$	11.6526	−	32.0883i	0.423800	−	1.16704i
$757$		−	6.44058i		−	0.234087i	−0.993127	−	0.117044i	$-0.962658\pi$
$757$		−	6.44058i		−	0.234087i	0.993127	−	0.117044i	$-0.0373417\pi$
$758$	−11.1733	−	50.3123i	−0.405833	−	1.82743i
$759$		−	19.0672i		−	0.692095i
$760$		0			0
$761$		−	9.50571i		−	0.344582i	−0.985046	−	0.172291i	$-0.944883\pi$
$761$		−	9.50571i		−	0.344582i	0.985046	−	0.172291i	$-0.0551169\pi$
$762$	3.76969	−	0.837169i	0.136561	−	0.0303274i
$763$			38.9367i			1.40960i
$764$	9.90112	−	4.62580i	0.358210	−	0.167356i
$765$		0			0
$766$	−0.181282	−	0.816294i	−0.00654998	−	0.0294939i
$767$	5.45546	−	5.45546i	0.196985	−	0.196985i
$768$	−3.93511	−	21.9409i	−0.141996	−	0.791724i
$769$		−	46.8513i		−	1.68950i	−0.535159	−	0.844751i	$-0.679748\pi$
$769$		−	46.8513i		−	1.68950i	0.535159	−	0.844751i	$-0.320252\pi$
$770$		0			0
$771$	20.6176	+	20.6176i	0.742526	+	0.742526i
$772$	−12.8271	−	4.65806i	−0.461659	−	0.167647i
$773$	−10.9964			−0.395513			−0.197756	−	0.980251i	$-0.563365\pi$
$773$	−10.9964			−0.395513			−0.197756	+	0.980251i	$0.563365\pi$
$774$	1.63243	−	2.56447i	0.0586764	−	0.0921780i
$775$		0			0
$776$	−20.0855	+	15.4473i	−0.721028	+	0.554524i
$777$	21.5506	−	21.5506i	0.773122	−	0.773122i
$778$	26.0895	−	5.79393i	0.935354	−	0.207723i
$779$	−0.142026	−	0.142026i	−0.00508862	−	0.00508862i
$780$		0			0
$781$	−0.585238	+	0.585238i	−0.0209414	+	0.0209414i
$782$	−29.0628	−	18.5001i	−1.03928	−	0.661562i
$783$	−18.8756	−	18.8756i	−0.674559	−	0.674559i
$784$	−6.47651	−	5.41828i	−0.231304	−	0.193510i
$785$		0			0
$786$	2.12693	+	9.57736i	0.0758651	+	0.341613i
$787$			25.5190i			0.909653i	0.890580	+	0.454826i	$0.150299\pi$
$787$			25.5190i			0.909653i	−0.890580	+	0.454826i	$0.849701\pi$
$788$	5.33782	−	2.49383i	0.190152	−	0.0888390i
$789$	−16.4265	+	16.4265i	−0.584797	+	0.584797i
$790$		0			0
$791$	−20.8660			−0.741909
$792$	5.60589	+	7.28914i	0.199197	+	0.259008i
$793$	2.19048	+	2.19048i	0.0777864	+	0.0777864i
$794$	−16.5102	−	10.5097i	−0.585926	−	0.372974i
$795$		0			0
$796$	−3.88890	+	1.81690i	−0.137838	+	0.0643981i
$797$	13.3808			0.473972			0.236986	−	0.971513i	$-0.423840\pi$
$797$	13.3808			0.473972			0.236986	+	0.971513i	$0.423840\pi$
$798$	−0.0971061	−	0.0618134i	−0.00343752	−	0.00218817i
$799$	−25.8348			−0.913969
$800$		0			0
$801$	14.1626			0.500412
$802$	−24.2316	−	15.4248i	−0.855648	−	0.544667i
$803$	−3.52471			−0.124384
$804$	1.88878	−	0.882440i	0.0666123	−	0.0311213i
$805$		0			0
$806$	16.4706	+	10.4844i	0.580150	+	0.369298i
$807$	2.92738	+	2.92738i	0.103049	+	0.103049i
$808$	−11.9895	+	9.22079i	−0.421788	+	0.324386i
$809$	52.7958			1.85620			0.928102	−	0.372327i	$-0.121440\pi$
$809$	52.7958			1.85620			0.928102	+	0.372327i	$0.121440\pi$
$810$		0			0
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	−0.678929	−	0.734204i	$-0.737556\pi$
$811$	1.57411	−	1.57411i	0.0552745	−	0.0552745i	0.734204	+	0.678929i	$0.237556\pi$
$812$	−25.8181	+	12.0622i	−0.906039	+	0.423301i
$813$			26.2749i			0.921500i
$814$	6.82137	+	30.7159i	0.239089	+	1.07659i
$815$		0			0
$816$	−30.3315	+	2.69846i	−1.06182	+	0.0944650i
$817$	−0.0277803	−	0.0277803i	−0.000971909	−	0.000971909i
$818$	−21.8173	−	13.8879i	−0.762822	−	0.485579i
$819$	3.49595	−	3.49595i	0.122158	−	0.122158i
$820$		0			0
$821$	−25.7715	−	25.7715i	−0.899431	−	0.899431i	0.0959548	−	0.995386i	$-0.469410\pi$
$821$	−25.7715	−	25.7715i	−0.899431	−	0.899431i	−0.995386	+	0.0959548i	$0.969410\pi$
$822$	−15.3009	+	3.39801i	−0.533681	+	0.118519i
$823$	17.5565	−	17.5565i	0.611982	−	0.611982i	−0.331480	−	0.943462i	$-0.607548\pi$
$823$	17.5565	−	17.5565i	0.611982	−	0.611982i	0.943462	+	0.331480i	$0.107548\pi$
$824$	26.1408	+	33.9900i	0.910658	+	1.18410i
$825$		0			0
$826$	−11.4347	+	17.9634i	−0.397864	+	0.625027i
$827$	−14.8548			−0.516551			−0.258276	−	0.966071i	$-0.583154\pi$
$827$	−14.8548			−0.516551			−0.258276	+	0.966071i	$0.583154\pi$
$828$	−8.87558	−	3.22308i	−0.308448	−	0.112010i
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	0.855387	−	0.517990i	$-0.173320\pi$
$829$	9.71444	+	9.71444i	0.337397	+	0.337397i	−0.517990	+	0.855387i	$0.673320\pi$
$830$		0			0
$831$		−	13.8191i		−	0.479380i
$832$	3.17610	−	11.9585i	0.110112	−	0.414585i
$833$	−8.15672	+	8.15672i	−0.282614	+	0.282614i
$834$	7.31069	+	32.9193i	0.253148	+	1.13990i
$835$		0			0
$836$	0.107668	−	0.0503026i	0.00372378	−	0.00173975i
$837$		−	50.4786i		−	1.74480i
$838$	33.8138	−	7.50934i	1.16808	−	0.259406i
$839$		−	4.54484i		−	0.156905i	−0.996918	−	0.0784527i	$-0.975002\pi$
$839$		−	4.54484i		−	0.156905i	0.996918	−	0.0784527i	$-0.0249979\pi$
$840$		0			0
$841$		−	6.71729i		−	0.231631i
$842$	−5.00615	−	22.5422i	−0.172523	−	0.776855i
$843$		−	12.9766i		−	0.446938i
$844$	−5.35262	+	14.7398i	−0.184245	+	0.507364i
$845$		0			0
$846$	−6.91256	+	1.53513i	−0.237659	+	0.0527790i
$847$	−3.36337	+	3.36337i	−0.115567	+	0.115567i
$848$	−18.7546	+	22.4175i	−0.644036	+	0.769820i
$849$		−	4.76977i		−	0.163698i
$850$		0			0
$851$	−22.8466	−	22.8466i	−0.783171	−	0.783171i
$852$	−0.317976	−	0.680600i	−0.0108937	−	0.0233170i
$853$	−37.3745			−1.27968			−0.639839	−	0.768509i	$-0.720999\pi$
$853$	−37.3745			−1.27968			−0.639839	+	0.768509i	$0.720999\pi$
$854$	−7.21269	−	4.59128i	−0.246813	−	0.157110i
$855$		0			0
$856$	−3.99449	+	30.6010i	−0.136529	+	1.04592i
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	−0.929893	−	0.367831i	$-0.880101\pi$
$857$	−16.4541	+	16.4541i	−0.562062	+	0.562062i	0.367831	+	0.929893i	$0.380101\pi$
$858$	−2.02809	−	9.13228i	−0.0692378	−	0.311771i
$859$	−15.7662	−	15.7662i	−0.537935	−	0.537935i	0.384987	−	0.922922i	$-0.374206\pi$
$859$	−15.7662	−	15.7662i	−0.537935	−	0.537935i	−0.922922	+	0.384987i	$0.874206\pi$
$860$		0			0
$861$	30.8570	−	30.8570i	1.05160	−	1.05160i
$862$	−12.1112	+	19.0261i	−0.412508	+	0.648032i
$863$	22.6395	+	22.6395i	0.770659	+	0.770659i	0.978222	−	0.207563i	$-0.0665532\pi$
$863$	22.6395	+	22.6395i	0.770659	+	0.770659i	−0.207563	+	0.978222i	$0.566553\pi$
$864$	−30.4912	+	9.67528i	−1.03733	+	0.329160i
$865$		0			0
$866$	6.87470	−	1.52673i	0.233612	−	0.0518803i
$867$			17.9148i			0.608419i
$868$	−50.6513	−	18.3936i	−1.71922	−	0.624318i
$869$	−6.09036	+	6.09036i	−0.206601	+	0.206601i
$870$		0			0
$871$	1.15719			0.0392097
$872$	28.9215	−	22.2428i	0.979406	−	0.753236i
$873$	6.70861	+	6.70861i	0.227052	+	0.227052i
$874$	−0.0655308	+	0.102946i	−0.00221661	+	0.00348220i
$875$		0			0
$876$	1.09199	−	3.00706i	0.0368948	−	0.101599i
$877$	30.0542			1.01486			0.507429	−	0.861694i	$-0.330596\pi$
$877$	30.0542			1.01486			0.507429	+	0.861694i	$0.330596\pi$
$878$	−4.90463	+	7.70496i	−0.165523	+	0.260030i
$879$	−3.71243			−0.125217
$880$		0			0
$881$	−3.86747			−0.130298			−0.0651492	−	0.997876i	$-0.520752\pi$
$881$	−3.86747			−0.130298			−0.0651492	+	0.997876i	$0.520752\pi$
$882$	−1.69779	+	2.66716i	−0.0571677	+	0.0898078i
$883$	0.485919			0.0163525			0.00817624	−	0.999967i	$-0.497397\pi$
$883$	0.485919			0.0163525			0.00817624	+	0.999967i	$0.497397\pi$
$884$	−15.8875	−	5.76939i	−0.534354	−	0.194046i
$885$		0			0
$886$	20.5797	−	32.3297i	0.691388	−	1.08614i
$887$	−12.9762	−	12.9762i	−0.435699	−	0.435699i	0.454863	−	0.890561i	$-0.349688\pi$
$887$	−12.9762	−	12.9762i	−0.435699	−	0.435699i	−0.890561	+	0.454863i	$0.849688\pi$
$888$	−28.3182	−	3.69650i	−0.950297	−	0.124047i
$889$	−5.91587			−0.198412
$890$		0			0
$891$	−10.2054	+	10.2054i	−0.341893	+	0.341893i
$892$	1.12147	−	3.08825i	0.0375496	−	0.103402i
$893$			0.0915117i			0.00306232i
$894$	−36.8820	+	8.19071i	−1.23352	+	0.273938i
$895$		0			0
$896$	−1.40209	+	34.1210i	−0.0468406	+	1.13990i
$897$	6.79261	+	6.79261i	0.226799	+	0.226799i
$898$	−31.2030	+	49.0184i	−1.04126	+	1.63577i
$899$	−29.7951	+	29.7951i	−0.993722	+	0.993722i
$900$		0			0
$901$	28.2333	+	28.2333i	0.940588	+	0.940588i
$902$	9.76711	+	43.9803i	0.325209	+	1.46438i
$903$	6.03560	−	6.03560i	0.200852	−	0.200852i
$904$	11.9198	+	15.4989i	0.396446	+	0.515485i
$905$		0			0
$906$	34.4361	+	21.9205i	1.14406	+	0.728259i
$907$	−54.3645			−1.80514			−0.902571	−	0.430540i	$-0.858323\pi$
$907$	−54.3645			−1.80514			−0.902571	+	0.430540i	$0.858323\pi$
$908$	23.2226	−	10.8496i	0.770670	−	0.360057i
$909$	4.00451	+	4.00451i	0.132821	+	0.132821i
$910$		0			0
$911$			40.0402i			1.32659i	0.748358	+	0.663295i	$0.230843\pi$
$911$			40.0402i			1.32659i	−0.748358	+	0.663295i	$0.769157\pi$
$912$	0.00955845	+	0.107440i	0.000316512	+	0.00355769i
$913$	−27.8460	+	27.8460i	−0.921567	+	0.921567i
$914$	−35.6220	+	7.91090i	−1.17827	+	0.261669i
$915$		0			0
$916$	2.59710	+	0.943112i	0.0858106	+	0.0311613i
$917$		−	15.0300i		−	0.496335i
$918$	9.47409	+	42.6609i	0.312691	+	1.40802i
$919$			8.81475i			0.290772i	0.989375	+	0.145386i	$0.0464423\pi$
$919$			8.81475i			0.290772i	−0.989375	+	0.145386i	$0.953558\pi$
$920$		0			0
$921$		−	14.7057i		−	0.484568i
$922$	−13.0579	+	2.89989i	−0.430040	+	0.0955028i
$923$		−	0.416977i		−	0.0137250i
$924$	10.9289	+	23.3922i	0.359533	+	0.769548i
$925$		0			0
$926$	−12.4410	−	56.0204i	−0.408835	−	1.84095i
$927$	11.3527	−	11.3527i	0.372872	−	0.372872i
$928$	23.7083	+	12.2866i	0.778264	+	0.403329i
$929$			47.9673i			1.57376i	0.617109	+	0.786878i	$0.288304\pi$
$929$			47.9673i			1.57376i	−0.617109	+	0.786878i	$0.711696\pi$
$930$		0			0
$931$	0.0288926	+	0.0288926i	0.000946918	+	0.000946918i
$932$	−0.293365	+	0.807856i	−0.00960951	+	0.0264622i
$933$	−28.5272			−0.933938
$934$	24.6174	−	38.6728i	0.805506	−	1.26541i
$935$		0			0
$936$	−4.59380	−	0.599650i	−0.150153	−	0.0196002i
$937$	−13.8299	+	13.8299i	−0.451803	+	0.451803i	−0.895953	−	0.444150i	$-0.853506\pi$
$937$	−13.8299	+	13.8299i	−0.451803	+	0.451803i	0.444150	+	0.895953i	$0.353506\pi$
$938$	−3.11789	+	0.692418i	−0.101803	+	0.0226083i
$939$	3.93426	+	3.93426i	0.128390	+	0.128390i
$940$		0			0
$941$	−5.19108	+	5.19108i	−0.169224	+	0.169224i	−0.786638	−	0.617414i	$-0.788180\pi$
$941$	−5.19108	+	5.19108i	−0.169224	+	0.169224i	0.617414	+	0.786638i	$0.288180\pi$
$942$	−9.51234	−	6.05513i	−0.309929	−	0.197287i
$943$	−32.7127	−	32.7127i	−1.06527	−	1.06527i
$944$	19.8750	−	1.76819i	0.646877	−	0.0575498i
$945$		0			0
$946$	1.91044	+	8.60253i	0.0621138	+	0.279692i
$947$			24.1342i			0.784255i	0.919911	+	0.392128i	$0.128261\pi$
$947$			24.1342i			0.784255i	−0.919911	+	0.392128i	$0.871739\pi$
$948$	−3.30906	−	7.08275i	−0.107473	−	0.230037i
$949$	1.25566	−	1.25566i	0.0407606	−	0.0407606i
$950$		0			0
$951$	−28.2166			−0.914986
$952$	46.2590	+	6.03840i	1.49926	+	0.195706i
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	0.232430	−	0.972613i	$-0.425332\pi$
$953$	−22.8500	−	22.8500i	−0.740183	−	0.740183i	−0.972613	+	0.232430i	$0.925332\pi$
$954$	9.23198	+	5.87667i	0.298896	+	0.190264i
$955$		0			0
$956$	−10.5902	−	22.6673i	−0.342511	−	0.733114i
$957$	20.1890			0.652618
$958$	8.74618	+	5.56743i	0.282576	+	0.179876i
$959$	24.0121			0.775392
$960$		0			0
$961$	−48.6804			−1.57034
$962$	−13.3725	−	8.51235i	−0.431147	−	0.274449i
$963$	11.5550			0.372354
$964$	−16.5736	−	35.4743i	−0.533799	−	1.14255i
$965$		0			0
$966$	−22.3663	−	14.2374i	−0.719624	−	0.458080i
$967$	21.4211	+	21.4211i	0.688855	+	0.688855i	0.961979	−	0.273124i	$-0.0880569\pi$
$967$	21.4211	+	21.4211i	0.688855	+	0.688855i	−0.273124	+	0.961979i	$0.588057\pi$
$968$	4.41959	+	0.576910i	0.142051	+	0.0185426i
$969$	0.147351			0.00473361
$970$		0			0
$971$	−11.7978	+	11.7978i	−0.378609	+	0.378609i	−0.870600	−	0.491991i	$-0.836269\pi$
$971$	−11.7978	+	11.7978i	−0.378609	+	0.378609i	0.491991	+	0.870600i	$0.336269\pi$
$972$	8.81706	+	18.8721i	0.282807	+	0.605324i
$973$		−	51.6611i		−	1.65618i
$974$	−5.10658	−	22.9944i	−0.163625	−	0.736788i
$975$		0			0
$976$	0.709967	+	7.98025i	0.0227255	+	0.255442i
$977$	−2.15703	−	2.15703i	−0.0690096	−	0.0690096i	0.671760	−	0.740769i	$-0.265539\pi$
$977$	−2.15703	−	2.15703i	−0.0690096	−	0.0690096i	−0.740769	+	0.671760i	$0.765539\pi$
$978$	−29.9010	−	19.0336i	−0.956129	−	0.608629i
$979$	−29.0296	+	29.0296i	−0.927791	+	0.927791i
$980$		0			0
$981$	−9.65985	−	9.65985i	−0.308415	−	0.308415i
$982$	53.4101	−	11.8613i	1.70438	−	0.378508i
$983$	−19.9712	+	19.9712i	−0.636983	+	0.636983i	−0.949810	−	0.312827i	$-0.898724\pi$
$983$	−19.9712	+	19.9712i	−0.636983	+	0.636983i	0.312827	+	0.949810i	$0.398724\pi$
$984$	−40.5472	−	5.29280i	−1.29260	−	0.168728i
$985$		0			0
$986$	19.5886	−	30.7728i	0.623827	−	0.980004i
$987$	−19.8820			−0.632852
$988$	−0.0204363	+	0.0562765i	−0.000650164	+	0.00179039i
$989$	−6.39858	−	6.39858i	−0.203463	−	0.203463i
$990$		0			0
$991$		−	19.2270i		−	0.610767i	−0.952230	−	0.305383i	$-0.901215\pi$
$991$		−	19.2270i		−	0.610767i	0.952230	−	0.305383i	$-0.0987846\pi$
$992$	15.2724	+	48.1303i	0.484900	+	1.52814i
$993$	27.1574	−	27.1574i	0.861815	−	0.861815i
$994$	0.249504	+	1.12349i	0.00791379	+	0.0356350i
$995$		0			0
$996$	−15.1295	−	32.3833i	−0.479396	−	1.02611i
$997$			2.01694i			0.0638771i	0.999490	+	0.0319385i	$0.0101681\pi$
$997$			2.01694i			0.0638771i	−0.999490	+	0.0319385i	$0.989832\pi$
$998$	23.7473	−	5.27379i	0.751709	−	0.166939i
$999$			40.9838i			1.29667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.s.d.107.2		18
4.3	odd	2		1600.2.s.d.207.3		18
5.2	odd	4		80.2.j.b.43.8	✓	18
5.3	odd	4		400.2.j.d.43.2		18
5.4	even	2		80.2.s.b.27.8	yes	18
15.2	even	4		720.2.bd.g.523.2		18
15.14	odd	2		720.2.z.g.667.2		18
16.3	odd	4		400.2.j.d.307.2		18
16.13	even	4		1600.2.j.d.1007.7		18
20.3	even	4		1600.2.j.d.143.3		18
20.7	even	4		320.2.j.b.143.7		18
20.19	odd	2		320.2.s.b.207.7		18
40.19	odd	2		640.2.s.c.287.3		18
40.27	even	4		640.2.j.c.543.3		18
40.29	even	2		640.2.s.d.287.7		18
40.37	odd	4		640.2.j.d.543.7		18
80.3	even	4	inner	400.2.s.d.243.2		18
80.13	odd	4		1600.2.s.d.943.3		18
80.19	odd	4		80.2.j.b.67.8	yes	18
80.27	even	4		640.2.s.d.223.7		18
80.29	even	4		320.2.j.b.47.3		18
80.37	odd	4		640.2.s.c.223.3		18
80.59	odd	4		640.2.j.d.607.3		18
80.67	even	4		80.2.s.b.3.8	yes	18
80.69	even	4		640.2.j.c.607.7		18
80.77	odd	4		320.2.s.b.303.7		18
240.179	even	4		720.2.bd.g.307.2		18
240.227	odd	4		720.2.z.g.163.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.8	✓	18	5.2	odd	4
80.2.j.b.67.8	yes	18	80.19	odd	4
80.2.s.b.3.8	yes	18	80.67	even	4
80.2.s.b.27.8	yes	18	5.4	even	2
320.2.j.b.47.3		18	80.29	even	4
320.2.j.b.143.7		18	20.7	even	4
320.2.s.b.207.7		18	20.19	odd	2
320.2.s.b.303.7		18	80.77	odd	4
400.2.j.d.43.2		18	5.3	odd	4
400.2.j.d.307.2		18	16.3	odd	4
400.2.s.d.107.2		18	1.1	even	1	trivial
400.2.s.d.243.2		18	80.3	even	4	inner
640.2.j.c.543.3		18	40.27	even	4
640.2.j.c.607.7		18	80.69	even	4
640.2.j.d.543.7		18	40.37	odd	4
640.2.j.d.607.3		18	80.59	odd	4
640.2.s.c.223.3		18	80.37	odd	4
640.2.s.c.287.3		18	40.19	odd	2
640.2.s.d.223.7		18	80.27	even	4
640.2.s.d.287.7		18	40.29	even	2
720.2.z.g.163.2		18	240.227	odd	4
720.2.z.g.667.2		18	15.14	odd	2
720.2.bd.g.307.2		18	240.179	even	4
720.2.bd.g.523.2		18	15.2	even	4
1600.2.j.d.143.3		18	20.3	even	4
1600.2.j.d.1007.7		18	16.13	even	4
1600.2.s.d.207.3		18	4.3	odd	2
1600.2.s.d.943.3		18	80.13	odd	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19301 - 0.759419i) q^{2} +1.39319 q^{3} +(0.846564 + 1.81200i) q^{4} +(-1.66209 - 1.05801i) q^{6} +(2.13436 + 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} -1.05903 q^{9} +O(q^{10})\)	\(q+(-1.19301 - 0.759419i) q^{2} +1.39319 q^{3} +(0.846564 + 1.81200i) q^{4} +(-1.66209 - 1.05801i) q^{6} +(2.13436 + 2.13436i) q^{7} +(0.366101 - 2.80463i) q^{8} -1.05903 q^{9} +(2.17074 - 2.17074i) q^{11} +(1.17942 + 2.52445i) q^{12} +1.54663i q^{13} +(-0.925449 - 4.16720i) q^{14} +(-2.56666 + 3.06794i) q^{16} +(3.86386 + 3.86386i) q^{17} +(1.26344 + 0.804250i) q^{18} +(0.0136865 - 0.0136865i) q^{19} +(2.97357 + 2.97357i) q^{21} +(-4.23822 + 0.941219i) q^{22} +(3.15240 - 3.15240i) q^{23} +(0.510047 - 3.90738i) q^{24} +(1.17454 - 1.84515i) q^{26} -5.65499 q^{27} +(-2.06058 + 5.67434i) q^{28} +(3.33787 + 3.33787i) q^{29} +8.92639i q^{31} +(5.39191 - 1.71093i) q^{32} +(3.02424 - 3.02424i) q^{33} +(-1.67535 - 7.54394i) q^{34} +(-0.896540 - 1.91896i) q^{36} -7.24737i q^{37} +(-0.0267220 + 0.00593441i) q^{38} +2.15475i q^{39} -10.3771i q^{41} +(-1.28932 - 5.80569i) q^{42} -2.02975i q^{43} +(5.77103 + 2.09570i) q^{44} +(-6.15484 + 1.36686i) q^{46} +(-3.34313 + 3.34313i) q^{47} +(-3.57583 + 4.27421i) q^{48} +2.11103i q^{49} +(5.38308 + 5.38308i) q^{51} +(-2.80249 + 1.30932i) q^{52} +7.30702 q^{53} +(6.74648 + 4.29451i) q^{54} +(6.76751 - 5.20472i) q^{56} +(0.0190679 - 0.0190679i) q^{57} +(-1.44728 - 6.51696i) q^{58} +(-3.52732 - 3.52732i) q^{59} +(1.41629 - 1.41629i) q^{61} +(6.77887 - 10.6493i) q^{62} +(-2.26036 - 2.26036i) q^{63} +(-7.73194 - 2.05356i) q^{64} +(-5.90462 + 1.31129i) q^{66} -0.748197i q^{67} +(-3.73030 + 10.2723i) q^{68} +(4.39187 - 4.39187i) q^{69} -0.269603 q^{71} +(-0.387713 + 2.97020i) q^{72} +(-0.811870 - 0.811870i) q^{73} +(-5.50380 + 8.64622i) q^{74} +(0.0363865 + 0.0132134i) q^{76} +9.26628 q^{77} +(1.63636 - 2.57064i) q^{78} -2.80567 q^{79} -4.70135 q^{81} +(-7.88056 + 12.3800i) q^{82} -12.8279 q^{83} +(-2.87077 + 7.90541i) q^{84} +(-1.54143 + 2.42152i) q^{86} +(4.65027 + 4.65027i) q^{87} +(-5.29341 - 6.88283i) q^{88} -13.3732 q^{89} +(-3.30108 + 3.30108i) q^{91} +(8.38083 + 3.04342i) q^{92} +12.4361i q^{93} +(6.52724 - 1.44956i) q^{94} +(7.51194 - 2.38364i) q^{96} +(-6.33466 - 6.33466i) q^{97} +(1.60315 - 2.51848i) q^{98} +(-2.29888 + 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} + 6 q^{17} + 24 q^{18} - 2 q^{19} - 16 q^{21} - 12 q^{22} + 2 q^{23} - 4 q^{24} - 16 q^{26} + 24 q^{27} - 40 q^{28} + 14 q^{29} - 20 q^{32} + 8 q^{33} + 28 q^{34} - 4 q^{36} - 24 q^{38} - 8 q^{42} - 44 q^{44} + 12 q^{46} - 38 q^{47} - 4 q^{48} + 8 q^{51} - 8 q^{52} - 12 q^{53} + 4 q^{54} + 20 q^{56} + 24 q^{57} - 20 q^{58} + 10 q^{59} + 14 q^{61} + 40 q^{62} + 6 q^{63} + 16 q^{64} + 4 q^{66} + 60 q^{68} - 32 q^{69} + 24 q^{71} + 68 q^{72} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 44 q^{77} + 36 q^{78} - 16 q^{79} + 2 q^{81} - 48 q^{82} - 40 q^{83} + 24 q^{84} - 36 q^{86} - 24 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{92} - 28 q^{94} - 40 q^{96} - 18 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 + 6 * q^17 + 24 * q^18 - 2 * q^19 - 16 * q^21 - 12 * q^22 + 2 * q^23 - 4 * q^24 - 16 * q^26 + 24 * q^27 - 40 * q^28 + 14 * q^29 - 20 * q^32 + 8 * q^33 + 28 * q^34 - 4 * q^36 - 24 * q^38 - 8 * q^42 - 44 * q^44 + 12 * q^46 - 38 * q^47 - 4 * q^48 + 8 * q^51 - 8 * q^52 - 12 * q^53 + 4 * q^54 + 20 * q^56 + 24 * q^57 - 20 * q^58 + 10 * q^59 + 14 * q^61 + 40 * q^62 + 6 * q^63 + 16 * q^64 + 4 * q^66 + 60 * q^68 - 32 * q^69 + 24 * q^71 + 68 * q^72 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 44 * q^77 + 36 * q^78 - 16 * q^79 + 2 * q^81 - 48 * q^82 - 40 * q^83 + 24 * q^84 - 36 * q^86 - 24 * q^87 + 8 * q^88 + 12 * q^89 + 8 * q^92 - 28 * q^94 - 40 * q^96 - 18 * q^97 + 56 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

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Database

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