LMFDB - Embedded newform 700.2.k.b.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(43,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("700.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.k (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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	700.43
Dual form			700.2.k.b.407.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.802007 - 1.16481i) q^{2} +(-1.75731 + 1.75731i) q^{3} +(-0.713568 + 1.86837i) q^{4} +(3.45630 + 0.637557i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.74859 - 0.667278i) q^{8} -3.17626i q^{9} +O(q^{10})$	\(q+(-0.802007 - 1.16481i) q^{2} +(-1.75731 + 1.75731i) q^{3} +(-0.713568 + 1.86837i) q^{4} +(3.45630 + 0.637557i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.74859 - 0.667278i) q^{8} -3.17626i q^{9} +5.34495i q^{11} +(-2.02935 - 4.53727i) q^{12} +(2.61810 + 2.61810i) q^{13} +(-0.256541 + 1.39075i) q^{14} +(-2.98164 - 2.66642i) q^{16} +(1.04271 - 1.04271i) q^{17} +(-3.69974 + 2.54738i) q^{18} +0.260506 q^{19} +2.48521 q^{21} +(6.22586 - 4.28669i) q^{22} +(1.06132 - 1.06132i) q^{23} +(-3.65750 + 6.00273i) q^{24} +(0.949856 - 5.14933i) q^{26} +(0.309743 + 0.309743i) q^{27} +(1.82571 - 0.816571i) q^{28} -1.36847i q^{29} -2.05153i q^{31} +(-0.714582 + 5.61154i) q^{32} +(-9.39273 - 9.39273i) q^{33} +(-2.05081 - 0.378297i) q^{34} +(5.93444 + 2.26648i) q^{36} +(-8.20890 + 8.20890i) q^{37} +(-0.208927 - 0.303440i) q^{38} -9.20162 q^{39} -9.70325 q^{41} +(-1.99316 - 2.89480i) q^{42} +(-6.86124 + 6.86124i) q^{43} +(-9.98637 - 3.81399i) q^{44} +(-2.08742 - 0.385049i) q^{46} +(0.976925 + 0.976925i) q^{47} +(9.92539 - 0.553932i) q^{48} +1.00000i q^{49} +3.66471i q^{51} +(-6.75979 + 3.02340i) q^{52} +(-1.81765 - 1.81765i) q^{53} +(0.112376 - 0.609208i) q^{54} +(-2.41538 - 1.47171i) q^{56} +(-0.457788 + 0.457788i) q^{57} +(-1.59400 + 1.09752i) q^{58} +4.53183 q^{59} -4.13667 q^{61} +(-2.38965 + 1.64535i) q^{62} +(-2.24596 + 2.24596i) q^{63} +(7.10948 - 3.66814i) q^{64} +(-3.40771 + 18.4738i) q^{66} +(-4.96620 - 4.96620i) q^{67} +(1.20412 + 2.69221i) q^{68} +3.73012i q^{69} +7.29096i q^{71} +(-2.11945 - 8.73023i) q^{72} +(-9.65689 - 9.65689i) q^{73} +(16.1454 + 2.97822i) q^{74} +(-0.185888 + 0.486722i) q^{76} +(3.77945 - 3.77945i) q^{77} +(7.37977 + 10.7181i) q^{78} -10.1963 q^{79} +8.44015 q^{81} +(7.78208 + 11.3025i) q^{82} +(5.83046 - 5.83046i) q^{83} +(-1.77337 + 4.64330i) q^{84} +(13.4948 + 2.48928i) q^{86} +(2.40482 + 2.40482i) q^{87} +(3.56657 + 14.6911i) q^{88} -7.63211i q^{89} -3.70256i q^{91} +(1.22561 + 2.74026i) q^{92} +(3.60518 + 3.60518i) q^{93} +(0.354432 - 1.92143i) q^{94} +(-8.60546 - 11.1169i) q^{96} +(-11.5761 + 11.5761i) q^{97} +(1.16481 - 0.802007i) q^{98} +16.9770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{6}+O(q^{10}) $ 36 * q - 8 * q^6	$ 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) $ 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.802007	−	1.16481i	−0.567105	−	0.823646i
$2$	−0.802007	−	1.16481i	−0.567105	−	0.823646i
$3$	−1.75731	+	1.75731i	−1.01458	+	1.01458i	−0.0146899	+	0.999892i	$0.504676\pi$
$3$	−1.75731	+	1.75731i	−1.01458	+	1.01458i	−0.999892	+	0.0146899i	$0.995324\pi$
$4$	−0.713568	+	1.86837i	−0.356784	+	0.934187i
$5$		0			0
$5$		0			0
$6$	3.45630	+	0.637557i	1.41103	+	0.260282i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	2.74859	−	0.667278i	0.971773	−	0.235918i
$9$		−	3.17626i		−	1.05875i
$10$		0			0
$11$			5.34495i			1.61156i	0.592212	+	0.805782i	$0.298255\pi$
$11$			5.34495i			1.61156i	−0.592212	+	0.805782i	$0.701745\pi$
$12$	−2.02935	−	4.53727i	−0.585822	−	1.30980i
$13$	2.61810	+	2.61810i	0.726131	+	0.726131i	0.969847	−	0.243716i	$-0.0783664\pi$
$13$	2.61810	+	2.61810i	0.726131	+	0.726131i	−0.243716	+	0.969847i	$0.578366\pi$
$14$	−0.256541	+	1.39075i	−0.0685634	+	0.371694i
$15$		0			0
$16$	−2.98164	−	2.66642i	−0.745410	−	0.666606i
$17$	1.04271	−	1.04271i	0.252893	−	0.252893i	−0.569262	−	0.822156i	$-0.692771\pi$
$17$	1.04271	−	1.04271i	0.252893	−	0.252893i	0.822156	+	0.569262i	$0.192771\pi$
$18$	−3.69974	+	2.54738i	−0.872038	+	0.600424i
$19$	0.260506			0.0597641			0.0298820	−	0.999553i	$-0.490487\pi$
$19$	0.260506			0.0597641			0.0298820	+	0.999553i	$0.490487\pi$
$20$		0			0
$21$	2.48521			0.542317
$22$	6.22586	−	4.28669i	1.32736	−	0.913926i
$23$	1.06132	−	1.06132i	0.221300	−	0.221300i	−0.587746	−	0.809046i	$-0.699985\pi$
$23$	1.06132	−	1.06132i	0.221300	−	0.221300i	0.809046	+	0.587746i	$0.199985\pi$
$24$	−3.65750	+	6.00273i	−0.746585	+	1.22530i
$25$		0			0
$26$	0.949856	−	5.14933i	0.186282	−	1.00987i
$27$	0.309743	+	0.309743i	0.0596101	+	0.0596101i
$28$	1.82571	−	0.816571i	0.345027	−	0.154317i
$29$		−	1.36847i		−	0.254118i	−0.991895	−	0.127059i	$-0.959446\pi$
$29$		−	1.36847i		−	0.254118i	0.991895	−	0.127059i	$-0.0405537\pi$
$30$		0			0
$31$		−	2.05153i		−	0.368466i	−0.982883	−	0.184233i	$-0.941020\pi$
$31$		−	2.05153i		−	0.368466i	0.982883	−	0.184233i	$-0.0589802\pi$
$32$	−0.714582	+	5.61154i	−0.126321	+	0.991989i
$33$	−9.39273	−	9.39273i	−1.63506	−	1.63506i
$34$	−2.05081	−	0.378297i	−0.351712	−	0.0648775i
$35$		0			0
$36$	5.93444	+	2.26648i	0.989073	+	0.377746i
$37$	−8.20890	+	8.20890i	−1.34954	+	1.34954i	−0.463370	+	0.886165i	$0.653360\pi$
$37$	−8.20890	+	8.20890i	−1.34954	+	1.34954i	−0.886165	+	0.463370i	$0.846640\pi$
$38$	−0.208927	−	0.303440i	−0.0338925	−	0.0492244i
$39$	−9.20162			−1.47344
$40$		0			0
$41$	−9.70325			−1.51539			−0.757697	−	0.652607i	$-0.773675\pi$
$41$	−9.70325			−1.51539			−0.757697	+	0.652607i	$0.773675\pi$
$42$	−1.99316	−	2.89480i	−0.307551	−	0.446677i
$43$	−6.86124	+	6.86124i	−1.04633	+	1.04633i	−0.0474554	+	0.998873i	$0.515111\pi$
$43$	−6.86124	+	6.86124i	−1.04633	+	1.04633i	−0.998873	+	0.0474554i	$0.984889\pi$
$44$	−9.98637	−	3.81399i	−1.50550	−	0.574981i
$45$		0			0
$46$	−2.08742	−	0.385049i	−0.307773	−	0.0567724i
$47$	0.976925	+	0.976925i	0.142499	+	0.142499i	0.774758	−	0.632258i	$-0.217872\pi$
$47$	0.976925	+	0.976925i	0.142499	+	0.142499i	−0.632258	+	0.774758i	$0.717872\pi$
$48$	9.92539	−	0.553932i	1.43261	−	0.0799532i
$49$			1.00000i			0.142857i
$50$		0			0
$51$			3.66471i			0.513162i
$52$	−6.75979	+	3.02340i	−0.937414	+	0.419270i
$53$	−1.81765	−	1.81765i	−0.249673	−	0.249673i	0.571163	−	0.820837i	$-0.306492\pi$
$53$	−1.81765	−	1.81765i	−0.249673	−	0.249673i	−0.820837	+	0.571163i	$0.806492\pi$
$54$	0.112376	−	0.609208i	0.0152924	−	0.0829028i
$55$		0			0
$56$	−2.41538	−	1.47171i	−0.322769	−	0.196665i
$57$	−0.457788	+	0.457788i	−0.0606356	+	0.0606356i
$58$	−1.59400	+	1.09752i	−0.209303	+	0.144111i
$59$	4.53183			0.589994			0.294997	−	0.955498i	$-0.404681\pi$
$59$	4.53183			0.589994			0.294997	+	0.955498i	$0.404681\pi$
$60$		0			0
$61$	−4.13667			−0.529647			−0.264823	−	0.964297i	$-0.585314\pi$
$61$	−4.13667			−0.529647			−0.264823	+	0.964297i	$0.585314\pi$
$62$	−2.38965	+	1.64535i	−0.303486	+	0.208959i
$63$	−2.24596	+	2.24596i	−0.282964	+	0.282964i
$64$	7.10948	−	3.66814i	0.888685	−	0.458518i
$65$		0			0
$66$	−3.40771	+	18.4738i	−0.419461	+	2.27397i
$67$	−4.96620	−	4.96620i	−0.606718	−	0.606718i	0.335369	−	0.942087i	$-0.391139\pi$
$67$	−4.96620	−	4.96620i	−0.606718	−	0.606718i	−0.942087	+	0.335369i	$0.891139\pi$
$68$	1.20412	+	2.69221i	0.146021	+	0.326478i
$69$			3.73012i			0.449053i
$70$		0			0
$71$			7.29096i			0.865278i	0.901567	+	0.432639i	$0.142417\pi$
$71$			7.29096i			0.865278i	−0.901567	+	0.432639i	$0.857583\pi$
$72$	−2.11945	−	8.73023i	−0.249779	−	1.02887i
$73$	−9.65689	−	9.65689i	−1.13025	−	1.13025i	−0.990135	−	0.140119i	$-0.955252\pi$
$73$	−9.65689	−	9.65689i	−1.13025	−	1.13025i	−0.140119	−	0.990135i	$-0.544748\pi$
$74$	16.1454	+	2.97822i	1.87687	+	0.346211i
$75$		0			0
$76$	−0.185888	+	0.486722i	−0.0213229	+	0.0558308i
$77$	3.77945	−	3.77945i	0.430709	−	0.430709i
$78$	7.37977	+	10.7181i	0.835594	+	1.21359i
$79$	−10.1963			−1.14717			−0.573584	−	0.819147i	$-0.694447\pi$
$79$	−10.1963			−1.14717			−0.573584	+	0.819147i	$0.694447\pi$
$80$		0			0
$81$	8.44015			0.937795
$82$	7.78208	+	11.3025i	0.859387	+	1.24815i
$83$	5.83046	−	5.83046i	0.639977	−	0.639977i	−0.310573	−	0.950550i	$-0.600521\pi$
$83$	5.83046	−	5.83046i	0.639977	−	0.639977i	0.950550	+	0.310573i	$0.100521\pi$
$84$	−1.77337	+	4.64330i	−0.193490	+	0.506625i
$85$		0			0
$86$	13.4948	+	2.48928i	1.45518	+	0.268426i
$87$	2.40482	+	2.40482i	0.257823	+	0.257823i
$88$	3.56657	+	14.6911i	0.380197	+	1.56607i
$89$		−	7.63211i		−	0.809002i	−0.914538	−	0.404501i	$-0.867445\pi$
$89$		−	7.63211i		−	0.809002i	0.914538	−	0.404501i	$-0.132555\pi$
$90$		0			0
$91$		−	3.70256i		−	0.388133i
$92$	1.22561	+	2.74026i	0.127779	+	0.285691i
$93$	3.60518	+	3.60518i	0.373839	+	0.373839i
$94$	0.354432	−	1.92143i	0.0365568	−	0.198181i
$95$		0			0
$96$	−8.60546	−	11.1169i	−0.878291	−	1.13462i
$97$	−11.5761	+	11.5761i	−1.17538	+	1.17538i	−0.194469	+	0.980909i	$0.562298\pi$
$97$	−11.5761	+	11.5761i	−1.17538	+	1.17538i	−0.980909	+	0.194469i	$0.937702\pi$
$98$	1.16481	−	0.802007i	0.117664	−	0.0810150i
$99$	16.9770			1.70625
$100$		0			0
$101$	2.83998			0.282589			0.141294	−	0.989968i	$-0.454874\pi$
$101$	2.83998			0.282589			0.141294	+	0.989968i	$0.454874\pi$
$102$	4.26870	−	2.93913i	0.422664	−	0.291017i
$103$	8.22332	−	8.22332i	0.810268	−	0.810268i	−0.174406	−	0.984674i	$-0.555801\pi$
$103$	8.22332	−	8.22332i	0.810268	−	0.810268i	0.984674	+	0.174406i	$0.0558006\pi$
$104$	8.94309	+	5.44909i	0.876942	+	0.534327i
$105$		0			0
$106$	−0.659449	+	3.57499i	−0.0640514	+	0.347233i
$107$	2.48983	+	2.48983i	0.240701	+	0.240701i	0.817140	−	0.576439i	$-0.195558\pi$
$107$	2.48983	+	2.48983i	0.240701	+	0.240701i	−0.576439	+	0.817140i	$0.695558\pi$
$108$	−0.799739	+	0.357693i	−0.0769549	+	0.0344190i
$109$			3.64777i			0.349393i	0.984622	+	0.174696i	$0.0558944\pi$
$109$			3.64777i			0.349393i	−0.984622	+	0.174696i	$0.944106\pi$
$110$		0			0
$111$		−	28.8511i		−	2.73843i
$112$	0.222892	+	3.99379i	0.0210613	+	0.377377i
$113$	8.10112	+	8.10112i	0.762089	+	0.762089i	0.976700	−	0.214611i	$-0.0688482\pi$
$113$	8.10112	+	8.10112i	0.762089	+	0.762089i	−0.214611	+	0.976700i	$0.568848\pi$
$114$	0.900387	+	0.166087i	0.0843289	+	0.0155555i
$115$		0			0
$116$	2.55681	+	0.976494i	0.237393	+	0.0906652i
$117$	8.31577	−	8.31577i	0.768794	−	0.768794i
$118$	−3.63456	−	5.27873i	−0.334589	−	0.485946i
$119$	−1.47461			−0.135177
$120$		0			0
$121$	−17.5685			−1.59714
$122$	3.31764	+	4.81844i	0.300365	+	0.436241i
$123$	17.0516	−	17.0516i	1.53749	−	1.53749i
$124$	3.83303	+	1.46391i	0.344216	+	0.131463i
$125$		0			0
$126$	4.41739	+	0.814840i	0.393532	+	0.0725917i
$127$	6.08151	+	6.08151i	0.539647	+	0.539647i	0.923425	−	0.383778i	$-0.125377\pi$
$127$	6.08151	+	6.08151i	0.539647	+	0.539647i	−0.383778	+	0.923425i	$0.625377\pi$
$128$	−9.97455	−	5.33932i	−0.881634	−	0.471934i
$129$		−	24.1146i		−	2.12317i
$130$		0			0
$131$		−	7.01462i		−	0.612870i	−0.951892	−	0.306435i	$-0.900864\pi$
$131$		−	7.01462i		−	0.612870i	0.951892	−	0.306435i	$-0.0991363\pi$
$132$	24.2515	−	10.8468i	2.11082	−	0.944091i
$133$	−0.184205	−	0.184205i	−0.0159726	−	0.0159726i
$134$	−1.80175	+	9.76762i	−0.155648	+	0.843794i
$135$		0			0
$136$	2.17020	−	3.56175i	0.186093	−	0.305417i
$137$	4.48720	−	4.48720i	0.383368	−	0.383368i	−0.488946	−	0.872314i	$-0.662619\pi$
$137$	4.48720	−	4.48720i	0.383368	−	0.383368i	0.872314	+	0.488946i	$0.162619\pi$
$138$	4.34488	−	2.99158i	0.369861	−	0.254660i
$139$	−3.41676			−0.289806			−0.144903	−	0.989446i	$-0.546287\pi$
$139$	−3.41676			−0.289806			−0.144903	+	0.989446i	$0.546287\pi$
$140$		0			0
$141$	−3.43352			−0.289154
$142$	8.49259	−	5.84740i	0.712682	−	0.490703i
$143$	−13.9936	+	13.9936i	−1.17021	+	1.17021i
$144$	−8.46926	+	9.47047i	−0.705771	+	0.789206i
$145$		0			0
$146$	−3.50355	+	18.9933i	−0.289956	+	1.57190i
$147$	−1.75731	−	1.75731i	−0.144940	−	0.144940i
$148$	−9.47968	−	21.1949i	−0.779225	−	1.74221i
$149$			13.3974i			1.09756i	0.835968	+	0.548778i	$0.184907\pi$
$149$			13.3974i			1.09756i	−0.835968	+	0.548778i	$0.815093\pi$
$150$		0			0
$151$			2.17365i			0.176889i	0.996081	+	0.0884446i	$0.0281896\pi$
$151$			2.17365i			0.176889i	−0.996081	+	0.0884446i	$0.971810\pi$
$152$	0.716023	−	0.173830i	0.0580771	−	0.0140994i
$153$	−3.31191	−	3.31191i	−0.267752	−	0.267752i
$154$	−7.43350	−	1.37120i	−0.599008	−	0.110494i
$155$		0			0
$156$	6.56599	−	17.1921i	0.525700	−	1.37647i
$157$	−3.34615	+	3.34615i	−0.267052	+	0.267052i	−0.827911	−	0.560859i	$-0.810471\pi$
$157$	−3.34615	+	3.34615i	−0.267052	+	0.267052i	0.560859	+	0.827911i	$0.310471\pi$
$158$	8.17747	+	11.8767i	0.650565	+	0.944860i
$159$	6.38834			0.506628
$160$		0			0
$161$	−1.50093			−0.118290
$162$	−6.76906	−	9.83118i	−0.531828	−	0.772410i
$163$	−8.52401	+	8.52401i	−0.667652	+	0.667652i	−0.957172	−	0.289520i	$-0.906504\pi$
$163$	−8.52401	+	8.52401i	−0.667652	+	0.667652i	0.289520	+	0.957172i	$0.406504\pi$
$164$	6.92393	−	18.1293i	0.540668	−	1.41566i
$165$		0			0
$166$	−11.4675	−	2.11531i	−0.890048	−	0.164180i
$167$	−3.96863	−	3.96863i	−0.307102	−	0.307102i	0.536682	−	0.843784i	$-0.319677\pi$
$167$	−3.96863	−	3.96863i	−0.307102	−	0.307102i	−0.843784	+	0.536682i	$0.819677\pi$
$168$	6.83082	−	1.65832i	0.527009	−	0.127942i
$169$			0.708922i			0.0545325i
$170$		0			0
$171$		−	0.827433i		−	0.0632754i
$172$	−7.92339	−	17.7153i	−0.604153	−	1.35078i
$173$	8.51471	+	8.51471i	0.647361	+	0.647361i	0.952355	−	0.304993i	$-0.0986542\pi$
$173$	8.51471	+	8.51471i	0.647361	+	0.647361i	−0.304993	+	0.952355i	$0.598654\pi$
$174$	0.872475	−	4.72984i	0.0661422	−	0.358568i
$175$		0			0
$176$	14.2519	−	15.9367i	1.07428	−	1.20128i
$177$	−7.96383	+	7.96383i	−0.598598	+	0.598598i
$178$	−8.88997	+	6.12101i	−0.666331	+	0.458789i
$179$	−1.47311			−0.110106			−0.0550528	−	0.998483i	$-0.517533\pi$
$179$	−1.47311			−0.110106			−0.0550528	+	0.998483i	$0.517533\pi$
$180$		0			0
$181$	9.31481			0.692364			0.346182	−	0.938167i	$-0.387478\pi$
$181$	9.31481			0.692364			0.346182	+	0.938167i	$0.387478\pi$
$182$	−4.31278	+	2.96948i	−0.319684	+	0.220112i
$183$	7.26941	−	7.26941i	0.537370	−	0.537370i
$184$	2.20893	−	3.62531i	0.162844	−	0.267262i
$185$		0			0
$186$	1.30797	−	7.09073i	0.0959050	−	0.519917i
$187$	5.57322	+	5.57322i	0.407554	+	0.407554i
$188$	−2.52236	+	1.12816i	−0.183962	+	0.0822794i
$189$		−	0.438043i		−	0.0318629i
$190$		0			0
$191$			21.5073i			1.55621i	0.628132	+	0.778107i	$0.283820\pi$
$191$			21.5073i			1.55621i	−0.628132	+	0.778107i	$0.716180\pi$
$192$	−6.04749	+	18.9396i	−0.436440	+	1.36685i
$193$	2.75964	+	2.75964i	0.198643	+	0.198643i	0.799418	−	0.600775i	$-0.205141\pi$
$193$	2.75964	+	2.75964i	0.198643	+	0.198643i	−0.600775	+	0.799418i	$0.705141\pi$
$194$	22.7681	+	4.19986i	1.63466	+	0.301532i
$195$		0			0
$196$	−1.86837	−	0.713568i	−0.133455	−	0.0509692i
$197$	10.8418	−	10.8418i	0.772443	−	0.772443i	−0.206090	−	0.978533i	$-0.566074\pi$
$197$	10.8418	−	10.8418i	0.772443	−	0.772443i	0.978533	+	0.206090i	$0.0660740\pi$
$198$	−13.6157	−	19.7750i	−0.967622	−	1.40534i
$199$	−20.6266			−1.46218			−0.731091	−	0.682280i	$-0.760989\pi$
$199$	−20.6266			−1.46218			−0.731091	+	0.682280i	$0.760989\pi$
$200$		0			0
$201$	17.4543			1.23113
$202$	−2.27769	−	3.30804i	−0.160257	−	0.232753i
$203$	−0.967652	+	0.967652i	−0.0679158	+	0.0679158i
$204$	−6.84705	−	2.61502i	−0.479389	−	0.183088i
$205$		0			0
$206$	−16.1738	−	2.98345i	−1.12688	−	0.207867i
$207$	−3.37102	−	3.37102i	−0.234302	−	0.234302i
$208$	−0.825269	−	14.7872i	−0.0572221	−	1.02531i
$209$			1.39239i			0.0963137i
$210$		0			0
$211$		−	1.55999i		−	0.107394i	−0.998557	−	0.0536969i	$-0.982900\pi$
$211$		−	1.55999i		−	0.107394i	0.998557	−	0.0536969i	$-0.0171005\pi$
$212$	4.69307	−	2.09903i	0.322321	−	0.144162i
$213$	−12.8125	−	12.8125i	−0.877895	−	0.877895i
$214$	0.903320	−	4.89705i	0.0617497	−	0.334755i
$215$		0			0
$216$	1.05804	+	0.644672i	0.0719906	+	0.0438644i
$217$	−1.45065	+	1.45065i	−0.0984768	+	0.0984768i
$218$	4.24896	−	2.92554i	0.287776	−	0.198142i
$219$	33.9403			2.29347
$220$		0			0
$221$	5.45982			0.367267
$222$	−33.6061	+	23.1388i	−2.25549	+	1.55298i
$223$	−1.29543	+	1.29543i	−0.0867482	+	0.0867482i	−0.749149	−	0.662401i	$-0.769537\pi$
$223$	−1.29543	+	1.29543i	−0.0867482	+	0.0867482i	0.662401	+	0.749149i	$0.269537\pi$
$224$	4.47324	−	3.46267i	0.298881	−	0.231359i
$225$		0			0
$226$	2.93911	−	15.9334i	0.195507	−	1.05988i
$227$	−4.13758	−	4.13758i	−0.274621	−	0.274621i	0.556336	−	0.830957i	$-0.312207\pi$
$227$	−4.13758	−	4.13758i	−0.274621	−	0.274621i	−0.830957	+	0.556336i	$0.812207\pi$
$228$	−0.528657	−	1.18198i	−0.0350111	−	0.0782787i
$229$		−	21.9435i		−	1.45007i	−0.688713	−	0.725035i	$-0.741824\pi$
$229$		−	21.9435i		−	1.45007i	0.688713	−	0.725035i	$-0.258176\pi$
$230$		0			0
$231$			13.2833i			0.873979i
$232$	−0.913147	−	3.76135i	−0.0599510	−	0.246945i
$233$	−4.58768	−	4.58768i	−0.300549	−	0.300549i	0.540680	−	0.841229i	$-0.318167\pi$
$233$	−4.58768	−	4.58768i	−0.300549	−	0.300549i	−0.841229	+	0.540680i	$0.818167\pi$
$234$	−16.3556	−	3.01699i	−1.06920	−	0.197227i
$235$		0			0
$236$	−3.23377	+	8.46716i	−0.210501	+	0.551165i
$237$	17.9180	−	17.9180i	1.16390	−	1.16390i
$238$	1.18265	+	1.71764i	0.0766597	+	0.111338i
$239$	8.09920			0.523894			0.261947	−	0.965082i	$-0.415635\pi$
$239$	8.09920			0.523894			0.261947	+	0.965082i	$0.415635\pi$
$240$		0			0
$241$	−3.33737			−0.214979			−0.107489	−	0.994206i	$-0.534281\pi$
$241$	−3.33737			−0.214979			−0.107489	+	0.994206i	$0.534281\pi$
$242$	14.0901	+	20.4640i	0.905746	+	1.31548i
$243$	−15.7612	+	15.7612i	−1.01108	+	1.01108i
$244$	2.95180	−	7.72885i	0.188969	−	0.494789i
$245$		0			0
$246$	−33.5374	−	6.18638i	−2.13827	−	0.394429i
$247$	0.682030	+	0.682030i	0.0433965	+	0.0433965i
$248$	−1.36894	−	5.63882i	−0.0869279	−	0.358066i
$249$			20.4918i			1.29862i
$250$		0			0
$251$		−	1.41618i		−	0.0893882i	−0.999001	−	0.0446941i	$-0.985769\pi$
$251$		−	1.41618i		−	0.0893882i	0.999001	−	0.0446941i	$-0.0142313\pi$
$252$	−2.59364	−	5.79893i	−0.163384	−	0.365298i
$253$	5.67269	+	5.67269i	0.356639	+	0.356639i
$254$	2.20639	−	11.9612i	0.138441	−	0.750514i
$255$		0			0
$256$	1.78036	+	15.9006i	0.111273	+	0.993790i
$257$	5.70231	−	5.70231i	0.355700	−	0.355700i	−0.506525	−	0.862225i	$-0.669070\pi$
$257$	5.70231	−	5.70231i	0.355700	−	0.355700i	0.862225	+	0.506525i	$0.169070\pi$
$258$	−28.0890	+	19.3401i	−1.74874	+	1.20406i
$259$	11.6091			0.721357
$260$		0			0
$261$	−4.34660			−0.269048
$262$	−8.17071	+	5.62578i	−0.504788	+	0.347562i
$263$	−12.7242	+	12.7242i	−0.784609	+	0.784609i	−0.980605	−	0.195996i	$-0.937206\pi$
$263$	−12.7242	+	12.7242i	−0.784609	+	0.784609i	0.195996	+	0.980605i	$0.437206\pi$
$264$	−32.0843	−	19.5492i	−1.97465	−	1.20317i
$265$		0			0
$266$	−0.0668303	+	0.362298i	−0.00409763	+	0.0222139i
$267$	13.4120	+	13.4120i	0.820799	+	0.820799i
$268$	12.8224	−	5.73500i	0.783256	−	0.350321i
$269$			11.2354i			0.685037i	0.939511	+	0.342518i	$0.111280\pi$
$269$			11.2354i			0.685037i	−0.939511	+	0.342518i	$0.888720\pi$
$270$		0			0
$271$			25.4140i			1.54379i	0.635749	+	0.771896i	$0.280692\pi$
$271$			25.4140i			1.54379i	−0.635749	+	0.771896i	$0.719308\pi$
$272$	−5.88927	+	0.328678i	−0.357090	+	0.0199290i
$273$	6.50653	+	6.50653i	0.393793	+	0.393793i
$274$	−8.82552	−	1.62797i	−0.533169	−	0.0983494i
$275$		0			0
$276$	−6.96925	−	2.66169i	−0.419500	−	0.160215i
$277$	9.43789	−	9.43789i	0.567068	−	0.567068i	−0.364238	−	0.931306i	$-0.618671\pi$
$277$	9.43789	−	9.43789i	0.567068	−	0.567068i	0.931306	+	0.364238i	$0.118671\pi$
$278$	2.74027	+	3.97988i	0.164350	+	0.238698i
$279$	−6.51620			−0.390115
$280$		0			0
$281$	12.5370			0.747894			0.373947	−	0.927450i	$-0.378004\pi$
$281$	12.5370			0.747894			0.373947	+	0.927450i	$0.378004\pi$
$282$	2.75371	+	3.99940i	0.163981	+	0.238161i
$283$	19.8441	−	19.8441i	1.17961	−	1.17961i	0.199769	−	0.979843i	$-0.435981\pi$
$283$	19.8441	−	19.8441i	1.17961	−	1.17961i	0.979843	−	0.199769i	$-0.0640192\pi$
$284$	−13.6222	−	5.20260i	−0.808331	−	0.308717i
$285$		0			0
$286$	27.5229	+	5.07694i	1.62747	+	0.300206i
$287$	6.86124	+	6.86124i	0.405006	+	0.405006i
$288$	17.8237	+	2.26970i	1.05027	+	0.133743i
$289$			14.8255i			0.872090i
$290$		0			0
$291$		−	40.6856i		−	2.38503i
$292$	24.9335	−	11.1518i	1.45912	−	0.652611i
$293$	12.6339	+	12.6339i	0.738078	+	0.738078i	0.972206	−	0.234128i	$-0.0752234\pi$
$293$	12.6339	+	12.6339i	0.738078	+	0.738078i	−0.234128	+	0.972206i	$0.575223\pi$
$294$	−0.637557	+	3.45630i	−0.0371831	+	0.201576i
$295$		0			0
$296$	−17.0853	+	28.0405i	−0.993062	+	1.62982i
$297$	−1.65556	+	1.65556i	−0.0960655	+	0.0960655i
$298$	15.6054	−	10.7448i	0.903997	−	0.622429i
$299$	5.55727			0.321385
$300$		0			0
$301$	9.70325			0.559286
$302$	2.53189	−	1.74328i	0.145694	−	0.100315i
$303$	−4.99072	+	4.99072i	−0.286709	+	0.286709i
$304$	−0.776734	−	0.694618i	−0.0445487	−	0.0398391i
$305$		0			0
$306$	−1.20157	+	6.51392i	−0.0686892	+	0.372376i
$307$	−9.69470	−	9.69470i	−0.553306	−	0.553306i	0.374087	−	0.927393i	$-0.377956\pi$
$307$	−9.69470	−	9.69470i	−0.553306	−	0.553306i	−0.927393	+	0.374087i	$0.877956\pi$
$308$	4.36453	+	9.75833i	0.248692	+	0.556032i
$309$			28.9018i			1.64417i
$310$		0			0
$311$			11.2026i			0.635241i	0.948218	+	0.317620i	$0.102884\pi$
$311$			11.2026i			0.635241i	−0.948218	+	0.317620i	$0.897116\pi$
$312$	−25.2915	+	6.14004i	−1.43185	+	0.347611i
$313$	−0.162815	−	0.162815i	−0.00920285	−	0.00920285i	0.702490	−	0.711693i	$-0.252071\pi$
$313$	−0.162815	−	0.162815i	−0.00920285	−	0.00920285i	−0.711693	+	0.702490i	$0.752071\pi$
$314$	6.58128	+	1.21400i	0.371403	+	0.0685098i
$315$		0			0
$316$	7.27572	−	19.0504i	0.409291	−	1.07167i
$317$	−10.1395	+	10.1395i	−0.569490	+	0.569490i	−0.931986	−	0.362495i	$-0.881925\pi$
$317$	−10.1395	+	10.1395i	−0.569490	+	0.569490i	0.362495	+	0.931986i	$0.381925\pi$
$318$	−5.12350	−	7.44121i	−0.287311	−	0.417282i
$319$	7.31439			0.409527
$320$		0			0
$321$	−8.75080			−0.488422
$322$	1.20375	+	1.74830i	0.0670826	+	0.0974287i
$323$	0.271631	−	0.271631i	0.0151139	−	0.0151139i
$324$	−6.02262	+	15.7694i	−0.334590	+	0.876075i
$325$		0			0
$326$	16.7652	+	3.09254i	0.928537	+	0.171280i
$327$	−6.41025	−	6.41025i	−0.354488	−	0.354488i
$328$	−26.6703	+	6.47476i	−1.47262	+	0.357509i
$329$		−	1.38158i		−	0.0761690i
$330$		0			0
$331$			16.7224i			0.919149i	0.888139	+	0.459574i	$0.151998\pi$
$331$			16.7224i			0.919149i	−0.888139	+	0.459574i	$0.848002\pi$
$332$	6.73305	+	15.0539i	0.369524	+	0.826191i
$333$	26.0736	+	26.0736i	1.42882	+	1.42882i
$334$	−1.43983	+	7.80558i	−0.0787842	+	0.427102i
$335$		0			0
$336$	−7.41000	−	6.62662i	−0.404249	−	0.361512i
$337$	−9.74524	+	9.74524i	−0.530857	+	0.530857i	−0.920827	−	0.389970i	$-0.872485\pi$
$337$	−9.74524	+	9.74524i	−0.530857	+	0.530857i	0.389970	+	0.920827i	$0.372485\pi$
$338$	0.825760	−	0.568561i	0.0449154	−	0.0309256i
$339$	−28.4723			−1.54640
$340$		0			0
$341$	10.9654			0.593807
$342$	−0.963803	+	0.663608i	−0.0521165	+	0.0358838i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−14.2804	+	23.4371i	−0.769946	+	1.26364i
$345$		0			0
$346$	3.08917	−	16.7469i	0.166075	−	0.900318i
$347$	−2.94912	−	2.94912i	−0.158317	−	0.158317i	0.623503	−	0.781821i	$-0.285709\pi$
$347$	−2.94912	−	2.94912i	−0.158317	−	0.158317i	−0.781821	+	0.623503i	$0.785709\pi$
$348$	−6.20909	+	2.77709i	−0.332842	+	0.148868i
$349$			30.1290i			1.61277i	0.591393	+	0.806383i	$0.298578\pi$
$349$			30.1290i			1.61277i	−0.591393	+	0.806383i	$0.701422\pi$
$350$		0			0
$351$			1.62188i			0.0865695i
$352$	−29.9934	−	3.81941i	−1.59865	−	0.203575i
$353$	3.87092	+	3.87092i	0.206028	+	0.206028i	0.802577	−	0.596549i	$-0.203462\pi$
$353$	3.87092	+	3.87092i	0.206028	+	0.206028i	−0.596549	+	0.802577i	$0.703462\pi$
$354$	15.6634	+	2.88930i	0.832500	+	0.153565i
$355$		0			0
$356$	14.2596	+	5.44603i	0.755759	+	0.288639i
$357$	2.59134	−	2.59134i	0.137148	−	0.137148i
$358$	1.18145	+	1.71590i	0.0624414	+	0.0906880i
$359$	−23.3214			−1.23085			−0.615427	−	0.788194i	$-0.711016\pi$
$359$	−23.3214			−1.23085			−0.615427	+	0.788194i	$0.711016\pi$
$360$		0			0
$361$	−18.9321			−0.996428
$362$	−7.47055	−	10.8500i	−0.392643	−	0.570263i
$363$	30.8733	−	30.8733i	1.62043	−	1.62043i
$364$	6.91776	+	2.64203i	0.362589	+	0.138480i
$365$		0			0
$366$	−14.2976	−	2.63736i	−0.747347	−	0.137857i
$367$	−9.09160	−	9.09160i	−0.474578	−	0.474578i	0.428815	−	0.903392i	$-0.358931\pi$
$367$	−9.09160	−	9.09160i	−0.474578	−	0.474578i	−0.903392	+	0.428815i	$0.858931\pi$
$368$	−5.99438	+	0.334544i	−0.312479	+	0.0174393i
$369$			30.8201i			1.60443i
$370$		0			0
$371$			2.57054i			0.133456i
$372$	−9.30835	+	4.16328i	−0.482616	+	0.215856i
$373$	10.2814	+	10.2814i	0.532349	+	0.532349i	0.921271	−	0.388922i	$-0.127152\pi$
$373$	10.2814	+	10.2814i	0.532349	+	0.532349i	−0.388922	+	0.921271i	$0.627152\pi$
$374$	2.02198	−	10.9615i	0.104554	−	0.566806i
$375$		0			0
$376$	3.33705	+	2.03329i	0.172095	+	0.104859i
$377$	3.58278	−	3.58278i	0.184523	−	0.184523i
$378$	−0.510237	+	0.351314i	−0.0262438	+	0.0180696i
$379$	−18.3234			−0.941208			−0.470604	−	0.882344i	$-0.655964\pi$
$379$	−18.3234			−0.941208			−0.470604	+	0.882344i	$0.655964\pi$
$380$		0			0
$381$	−21.3742			−1.09503
$382$	25.0519	−	17.2490i	1.28177	−	0.882537i
$383$	−13.1272	+	13.1272i	−0.670767	+	0.670767i	−0.957893	−	0.287126i	$-0.907300\pi$
$383$	−13.1272	+	13.1272i	−0.670767	+	0.670767i	0.287126	+	0.957893i	$0.407300\pi$
$384$	26.9112	−	8.14552i	1.37331	−	0.415674i
$385$		0			0
$386$	1.00121	−	5.42771i	0.0509601	−	0.276263i
$387$	21.7931	+	21.7931i	1.10780	+	1.10780i
$388$	−13.3682	−	29.8889i	−0.678666	−	1.51738i
$389$		−	33.0621i		−	1.67632i	−0.545428	−	0.838158i	$-0.683633\pi$
$389$		−	33.0621i		−	1.67632i	0.545428	−	0.838158i	$-0.316367\pi$
$390$		0			0
$391$		−	2.21328i		−	0.111930i
$392$	0.667278	+	2.74859i	0.0337026	+	0.138825i
$393$	12.3268	+	12.3268i	0.621807	+	0.621807i
$394$	−21.3238	−	3.93343i	−1.07428	−	0.198163i
$395$		0			0
$396$	−12.1142	+	31.7193i	−0.608763	+	1.59396i
$397$	−21.0417	+	21.0417i	−1.05605	+	1.05605i	−0.0577223	+	0.998333i	$0.518384\pi$
$397$	−21.0417	+	21.0417i	−1.05605	+	1.05605i	−0.998333	+	0.0577223i	$0.981616\pi$
$398$	16.5427	+	24.0261i	0.829211	+	1.20432i
$399$	0.647411			0.0324111
$400$		0			0
$401$	34.2819			1.71196			0.855979	−	0.517011i	$-0.172955\pi$
$401$	34.2819			1.71196			0.855979	+	0.517011i	$0.172955\pi$
$402$	−13.9985	−	20.3309i	−0.698180	−	1.01402i
$403$	5.37113	−	5.37113i	0.267555	−	0.267555i
$404$	−2.02652	+	5.30615i	−0.100823	+	0.263991i
$405$		0			0
$406$	1.90319	+	0.351067i	0.0944540	+	0.0174232i
$407$	−43.8762	−	43.8762i	−2.17486	−	2.17486i
$408$	2.44538	+	10.0728i	0.121064	+	0.498677i
$409$		−	2.12348i		−	0.104999i	−0.998621	−	0.0524997i	$-0.983281\pi$
$409$		−	2.12348i		−	0.104999i	0.998621	−	0.0524997i	$-0.0167188\pi$
$410$		0			0
$411$			15.7708i			0.777916i
$412$	9.49633	+	21.2321i	0.467851	+	1.04603i
$413$	−3.20449	−	3.20449i	−0.157683	−	0.157683i
$414$	−1.22302	+	6.63017i	−0.0601079	+	0.325855i
$415$		0			0
$416$	−16.5624	+	12.8207i	−0.812040	+	0.628588i
$417$	6.00430	−	6.00430i	0.294032	−	0.294032i
$418$	1.62187	−	1.11671i	0.0793283	−	0.0546199i
$419$	−25.4554			−1.24358			−0.621789	−	0.783185i	$-0.713594\pi$
$419$	−25.4554			−1.24358			−0.621789	+	0.783185i	$0.713594\pi$
$420$		0			0
$421$	6.51083			0.317318			0.158659	−	0.987333i	$-0.449283\pi$
$421$	6.51083			0.317318			0.158659	+	0.987333i	$0.449283\pi$
$422$	−1.81709	+	1.25112i	−0.0884544	+	0.0609036i
$423$	3.10297	−	3.10297i	0.150871	−	0.150871i
$424$	−6.20885	−	3.78309i	−0.301528	−	0.183723i
$425$		0			0
$426$	−4.64840	+	25.1998i	−0.225216	+	1.22093i
$427$	2.92507	+	2.92507i	0.141554	+	0.141554i
$428$	−6.42860	+	2.87527i	−0.310738	+	0.138982i
$429$		−	49.1823i		−	2.37454i
$430$		0			0
$431$		−	21.2397i		−	1.02308i	−0.859259	−	0.511540i	$-0.829075\pi$
$431$		−	21.2397i		−	1.02308i	0.859259	−	0.511540i	$-0.170925\pi$
$432$	−0.0976361	−	1.74945i	−0.00469752	−	0.0841704i
$433$	10.3951	+	10.3951i	0.499557	+	0.499557i	0.911300	−	0.411743i	$-0.135080\pi$
$433$	10.3951	+	10.3951i	0.499557	+	0.499557i	−0.411743	+	0.911300i	$0.635080\pi$
$434$	2.85317	+	0.526302i	0.136957	+	0.0252633i
$435$		0			0
$436$	−6.81540	−	2.60293i	−0.326398	−	0.124658i
$437$	0.276479	−	0.276479i	0.0132258	−	0.0132258i
$438$	−27.2203	−	39.5340i	−1.30064	−	1.88901i
$439$	5.29498			0.252715			0.126358	−	0.991985i	$-0.459671\pi$
$439$	5.29498			0.252715			0.126358	+	0.991985i	$0.459671\pi$
$440$		0			0
$441$	3.17626			0.151250
$442$	−4.37882	−	6.35966i	−0.208279	−	0.302498i
$443$	−21.0751	+	21.0751i	−1.00131	+	1.00131i	−0.00130819	+	0.999999i	$0.500416\pi$
$443$	−21.0751	+	21.0751i	−1.00131	+	1.00131i	−0.999999	+	0.00130819i	$0.999584\pi$
$444$	53.9047	+	20.5873i	2.55820	+	0.977028i
$445$		0			0
$446$	2.54787	+	0.469985i	0.120645	+	0.0222545i
$447$	−23.5433	−	23.5433i	−1.11356	−	1.11356i
$448$	−7.62093	−	2.43339i	−0.360055	−	0.114967i
$449$		−	9.50768i		−	0.448695i	−0.974509	−	0.224347i	$-0.927975\pi$
$449$		−	9.50768i		−	0.448695i	0.974509	−	0.224347i	$-0.0720251\pi$
$450$		0			0
$451$		−	51.8635i		−	2.44215i
$452$	−20.9166	+	9.35522i	−0.983835	+	0.440032i
$453$	−3.81977	−	3.81977i	−0.179469	−	0.179469i
$454$	−1.50113	+	8.13787i	−0.0704514	+	0.381929i
$455$		0			0
$456$	−0.952800	+	1.56374i	−0.0446190	+	0.0732290i
$457$	18.9164	−	18.9164i	0.884870	−	0.884870i	−0.109155	−	0.994025i	$-0.534814\pi$
$457$	18.9164	−	18.9164i	0.884870	−	0.884870i	0.994025	+	0.109155i	$0.0348144\pi$
$458$	−25.5601	+	17.5989i	−1.19434	+	0.822341i
$459$	0.645942			0.0301500
$460$		0			0
$461$	4.58670			0.213624			0.106812	−	0.994279i	$-0.465936\pi$
$461$	4.58670			0.213624			0.106812	+	0.994279i	$0.465936\pi$
$462$	15.4726	−	10.6533i	0.719849	−	0.495638i
$463$	5.55531	−	5.55531i	0.258177	−	0.258177i	−0.566135	−	0.824312i	$-0.691562\pi$
$463$	5.55531	−	5.55531i	0.258177	−	0.258177i	0.824312	+	0.566135i	$0.191562\pi$
$464$	−3.64891	+	4.08027i	−0.169396	+	0.189422i
$465$		0			0
$466$	−1.66443	+	9.02313i	−0.0771030	+	0.417989i
$467$	24.5850	+	24.5850i	1.13766	+	1.13766i	0.988869	+	0.148791i	$0.0475380\pi$
$467$	24.5850	+	24.5850i	1.13766	+	1.13766i	0.148791	+	0.988869i	$0.452462\pi$
$468$	9.60310	+	21.4708i	0.443904	+	0.992490i
$469$			7.02327i			0.324305i
$470$		0			0
$471$		−	11.7604i		−	0.541893i
$472$	12.4561	−	3.02399i	0.573341	−	0.139190i
$473$	−36.6730	−	36.6730i	−1.68623	−	1.68623i
$474$	−35.2414	−	6.50069i	−1.61869	−	0.298587i
$475$		0			0
$476$	1.05223	−	2.75512i	0.0482291	−	0.126281i
$477$	−5.77333	+	5.77333i	−0.264343	+	0.264343i
$478$	−6.49562	−	9.43404i	−0.297103	−	0.431503i
$479$	29.7468			1.35917			0.679583	−	0.733599i	$-0.262161\pi$
$479$	29.7468			1.35917			0.679583	+	0.733599i	$0.262161\pi$
$480$		0			0
$481$	−42.9835			−1.95988
$482$	2.67660	+	3.88741i	0.121916	+	0.177066i
$483$	2.63759	−	2.63759i	0.120015	−	0.120015i
$484$	12.5364	−	32.8246i	0.569834	−	1.49203i
$485$		0			0
$486$	30.9994	+	5.71821i	1.40616	+	0.259383i
$487$	4.19081	+	4.19081i	0.189904	+	0.189904i	0.795654	−	0.605751i	$-0.207127\pi$
$487$	4.19081	+	4.19081i	0.189904	+	0.189904i	−0.605751	+	0.795654i	$0.707127\pi$
$488$	−11.3700	+	2.76031i	−0.514696	+	0.124953i
$489$		−	29.9586i		−	1.35477i
$490$		0			0
$491$			19.0115i			0.857977i	0.903310	+	0.428989i	$0.141130\pi$
$491$			19.0115i			0.857977i	−0.903310	+	0.428989i	$0.858870\pi$
$492$	19.6913	+	44.0262i	0.887752	+	1.98486i
$493$	−1.42691	−	1.42691i	−0.0642647	−	0.0642647i
$494$	0.247443	−	1.34143i	0.0111330	−	0.0603538i
$495$		0			0
$496$	−5.47026	+	6.11694i	−0.245622	+	0.274659i
$497$	5.15549	−	5.15549i	0.231255	−	0.231255i
$498$	23.8691	−	16.4346i	1.06960	−	0.736452i
$499$	33.1209			1.48270			0.741348	−	0.671121i	$-0.234187\pi$
$499$	33.1209			1.48270			0.741348	+	0.671121i	$0.234187\pi$
$500$		0			0
$501$	13.9482			0.623161
$502$	−1.64958	+	1.13578i	−0.0736242	+	0.0506925i
$503$	22.3897	−	22.3897i	0.998307	−	0.998307i	−0.00169150	−	0.999999i	$-0.500538\pi$
$503$	22.3897	−	22.3897i	0.998307	−	0.998307i	0.999999	+	0.00169150i	$0.000538420\pi$
$504$	−4.67453	+	7.67188i	−0.208220	+	0.341733i
$505$		0			0
$506$	2.05807	−	11.1571i	0.0914923	−	0.495995i
$507$	−1.24579	−	1.24579i	−0.0553277	−	0.0553277i
$508$	−15.7021	+	7.02296i	−0.696668	+	0.311594i
$509$			11.2200i			0.497316i	0.968591	+	0.248658i	$0.0799895\pi$
$509$			11.2200i			0.497316i	−0.968591	+	0.248658i	$0.920011\pi$
$510$		0			0
$511$			13.6569i			0.604146i
$512$	17.0934	−	14.8262i	0.755427	−	0.655232i
$513$	0.0806898	+	0.0806898i	0.00356254	+	0.00356254i
$514$	−11.2154	−	2.06882i	−0.494690	−	0.0912516i
$515$		0			0
$516$	45.0551	+	17.2074i	1.98344	+	0.757514i
$517$	−5.22162	+	5.22162i	−0.229647	+	0.229647i
$518$	−9.31062	−	13.5225i	−0.409085	−	0.594142i
$519$	−29.9259			−1.31360
$520$		0			0
$521$	28.9477			1.26822			0.634111	−	0.773242i	$-0.281366\pi$
$521$	28.9477			1.26822			0.634111	+	0.773242i	$0.281366\pi$
$522$	3.48601	+	5.06297i	0.152578	+	0.221600i
$523$	−15.9070	+	15.9070i	−0.695566	+	0.695566i	−0.963451	−	0.267885i	$-0.913675\pi$
$523$	−15.9070	+	15.9070i	−0.695566	+	0.695566i	0.267885	+	0.963451i	$0.413675\pi$
$524$	13.1059	+	5.00541i	0.572535	+	0.218662i
$525$		0			0
$526$	25.0262	+	4.61639i	1.09120	+	0.201284i
$527$	−2.13915	−	2.13915i	−0.0931827	−	0.0931827i
$528$	2.96074	+	53.0507i	0.128850	+	2.30874i
$529$			20.7472i			0.902053i
$530$		0			0
$531$		−	14.3943i		−	0.624659i
$532$	0.475607	−	0.212721i	0.0206202	−	0.00922263i
$533$	−25.4041	−	25.4041i	−1.10037	−	1.10037i
$534$	4.86591	−	26.3789i	0.210568	−	1.14153i
$535$		0			0
$536$	−16.9639	−	10.3362i	−0.732728	−	0.446456i
$537$	2.58871	−	2.58871i	0.111711	−	0.111711i
$538$	13.0872	−	9.01090i	0.564227	−	0.388488i
$539$	−5.34495			−0.230223
$540$		0			0
$541$	−5.85289			−0.251635			−0.125818	−	0.992053i	$-0.540155\pi$
$541$	−5.85289			−0.251635			−0.125818	+	0.992053i	$0.540155\pi$
$542$	29.6025	−	20.3822i	1.27154	−	0.875492i
$543$	−16.3690	+	16.3690i	−0.702460	+	0.702460i
$544$	5.10609	+	6.59629i	0.218922	+	0.282813i
$545$		0			0
$546$	2.36059	−	12.7972i	0.101024	−	0.547668i
$547$	13.8207	+	13.8207i	0.590930	+	0.590930i	0.937883	−	0.346952i	$-0.112783\pi$
$547$	13.8207	+	13.8207i	0.590930	+	0.590930i	−0.346952	+	0.937883i	$0.612783\pi$
$548$	5.18185	+	11.5857i	0.221358	+	0.494917i
$549$			13.1391i			0.560765i
$550$		0			0
$551$		−	0.356493i		−	0.0151871i
$552$	2.48902	+	10.2526i	0.105940	+	0.436378i
$553$	7.20984	+	7.20984i	0.306594	+	0.306594i
$554$	−18.5626	−	3.42410i	−0.788650	−	0.145476i
$555$		0			0
$556$	2.43809	−	6.38379i	0.103398	−	0.270733i
$557$	−24.8411	+	24.8411i	−1.05255	+	1.05255i	−0.0540097	+	0.998540i	$0.517200\pi$
$557$	−24.8411	+	24.8411i	−1.05255	+	1.05255i	−0.998540	+	0.0540097i	$0.982800\pi$
$558$	5.22604	+	7.59014i	0.221236	+	0.321316i
$559$	−35.9268			−1.51954
$560$		0			0
$561$	−19.5877			−0.826994
$562$	−10.0548	−	14.6032i	−0.424134	−	0.615999i
$563$	20.9923	−	20.9923i	0.884719	−	0.884719i	−0.109290	−	0.994010i	$-0.534858\pi$
$563$	20.9923	−	20.9923i	0.884719	−	0.884719i	0.994010	+	0.109290i	$0.0348579\pi$
$564$	2.45005	−	6.41509i	0.103166	−	0.270124i
$565$		0			0
$566$	−39.0298	−	7.19952i	−1.64055	−	0.302619i
$567$	−5.96809	−	5.96809i	−0.250636	−	0.250636i
$568$	4.86509	+	20.0399i	0.204135	+	0.840854i
$569$		−	31.2222i		−	1.30890i	−0.756105	−	0.654451i	$-0.772900\pi$
$569$		−	31.2222i		−	1.30890i	0.756105	−	0.654451i	$-0.227100\pi$
$570$		0			0
$571$		−	24.0996i		−	1.00854i	−0.863546	−	0.504269i	$-0.831762\pi$
$571$		−	24.0996i		−	1.00854i	0.863546	−	0.504269i	$-0.168238\pi$
$572$	−16.1599	−	36.1308i	−0.675681	−	1.51070i
$573$	−37.7950	−	37.7950i	−1.57891	−	1.57891i
$574$	2.48928	−	13.4948i	0.103901	−	0.563262i
$575$		0			0
$576$	−11.6510	−	22.5816i	−0.485457	−	0.940898i
$577$	−2.33354	+	2.33354i	−0.0971465	+	0.0971465i	−0.754010	−	0.656863i	$-0.771883\pi$
$577$	−2.33354	+	2.33354i	−0.0971465	+	0.0971465i	0.656863	+	0.754010i	$0.271883\pi$
$578$	17.2689	−	11.8902i	0.718293	−	0.494566i
$579$	−9.69907			−0.403080
$580$		0			0
$581$	−8.24552			−0.342082
$582$	−47.3911	+	32.6302i	−1.96442	+	1.35256i
$583$	9.71526	−	9.71526i	0.402365	−	0.402365i
$584$	−32.9866	−	20.0990i	−1.36500	−	0.831702i
$585$		0			0
$586$	4.58361	−	24.8485i	0.189347	−	1.02648i
$587$	29.4634	+	29.4634i	1.21608	+	1.21608i	0.968992	+	0.247092i	$0.0794751\pi$
$587$	29.4634	+	29.4634i	1.21608	+	1.21608i	0.247092	+	0.968992i	$0.420525\pi$
$588$	4.53727	−	2.02935i	0.187114	−	0.0836889i
$589$		−	0.534436i		−	0.0220210i
$590$		0			0
$591$			38.1046i			1.56741i
$592$	46.3644	−	2.58758i	1.90557	−	0.106349i
$593$	−0.200346	−	0.200346i	−0.00822722	−	0.00822722i	0.702981	−	0.711208i	$-0.251852\pi$
$593$	−0.200346	−	0.200346i	−0.00822722	−	0.00822722i	−0.711208	+	0.702981i	$0.751852\pi$
$594$	3.25619	+	0.600644i	0.133603	+	0.0246447i
$595$		0			0
$596$	−25.0313	−	9.55994i	−1.02532	−	0.391591i
$597$	36.2473	−	36.2473i	1.48350	−	1.48350i
$598$	−4.45697	−	6.47317i	−0.182259	−	0.264707i
$599$	1.58439			0.0647364			0.0323682	−	0.999476i	$-0.489695\pi$
$599$	1.58439			0.0647364			0.0323682	+	0.999476i	$0.489695\pi$
$600$		0			0
$601$	13.2735			0.541438			0.270719	−	0.962658i	$-0.412738\pi$
$601$	13.2735			0.541438			0.270719	+	0.962658i	$0.412738\pi$
$602$	−7.78208	−	11.3025i	−0.317174	−	0.460654i
$603$	−15.7740	+	15.7740i	−0.642365	+	0.642365i
$604$	−4.06119	−	1.55105i	−0.165248	−	0.0631112i
$605$		0			0
$606$	9.81584	+	1.81065i	0.398741	+	0.0735526i
$607$	−24.2582	−	24.2582i	−0.984610	−	0.984610i	0.0152729	−	0.999883i	$-0.495138\pi$
$607$	−24.2582	−	24.2582i	−0.984610	−	0.984610i	−0.999883	+	0.0152729i	$0.995138\pi$
$608$	−0.186153	+	1.46184i	−0.00754948	+	0.0592853i
$609$		−	3.40092i		−	0.137812i
$610$		0			0
$611$			5.11538i			0.206946i
$612$	8.55115	−	3.82461i	0.345660	−	0.154601i
$613$	13.6697	+	13.6697i	0.552114	+	0.552114i	0.927050	−	0.374937i	$-0.122336\pi$
$613$	13.6697	+	13.6697i	0.552114	+	0.552114i	−0.374937	+	0.927050i	$0.622336\pi$
$614$	−3.51727	+	19.0677i	−0.141946	+	0.769511i
$615$		0			0
$616$	7.86622	−	12.9101i	0.316939	−	0.520163i
$617$	22.2105	−	22.2105i	0.894159	−	0.894159i	−0.100752	−	0.994912i	$-0.532125\pi$
$617$	22.2105	−	22.2105i	0.894159	−	0.894159i	0.994912	+	0.100752i	$0.0321249\pi$
$618$	33.6651	−	23.1795i	1.35421	−	0.932414i
$619$	34.2163			1.37527			0.687634	−	0.726058i	$-0.258649\pi$
$619$	34.2163			1.37527			0.687634	+	0.726058i	$0.258649\pi$
$620$		0			0
$621$	0.657471			0.0263834
$622$	13.0489	−	8.98456i	0.523213	−	0.360248i
$623$	−5.39672	+	5.39672i	−0.216215	+	0.216215i
$624$	27.4359	+	24.5354i	1.09832	+	0.982203i
$625$		0			0
$626$	−0.0590698	+	0.320227i	−0.00236090	+	0.0127989i
$627$	−2.44686	−	2.44686i	−0.0977181	−	0.0977181i
$628$	−3.86416	−	8.63958i	−0.154197	−	0.344757i
$629$			17.1189i			0.682577i
$630$		0			0
$631$			26.0102i			1.03545i	0.855548	+	0.517724i	$0.173221\pi$
$631$			26.0102i			1.03545i	−0.855548	+	0.517724i	$0.826779\pi$
$632$	−28.0253	+	6.80373i	−1.11479	+	0.270638i
$633$	2.74137	+	2.74137i	0.108960	+	0.108960i
$634$	19.9425	+	3.67864i	0.792019	+	0.146097i
$635$		0			0
$636$	−4.55852	+	11.9358i	−0.180757	+	0.473285i
$637$	−2.61810	+	2.61810i	−0.103733	+	0.103733i
$638$	−5.86619	−	8.51988i	−0.232245	−	0.337305i
$639$	23.1580			0.916116
$640$		0			0
$641$	−22.9451			−0.906276			−0.453138	−	0.891440i	$-0.649695\pi$
$641$	−22.9451			−0.906276			−0.453138	+	0.891440i	$0.649695\pi$
$642$	7.01821	+	10.1930i	0.276987	+	0.402287i
$643$	−17.9293	+	17.9293i	−0.707062	+	0.707062i	−0.965916	−	0.258855i	$-0.916655\pi$
$643$	−17.9293	+	17.9293i	−0.707062	+	0.707062i	0.258855	+	0.965916i	$0.416655\pi$
$644$	1.07101	−	2.80429i	0.0422039	−	0.110505i
$645$		0			0
$646$	−0.534248	−	0.0985486i	−0.0210197	−	0.00387734i
$647$	23.6097	+	23.6097i	0.928195	+	0.928195i	0.997589	−	0.0693944i	$-0.0221067\pi$
$647$	23.6097	+	23.6097i	0.928195	+	0.928195i	−0.0693944	+	0.997589i	$0.522107\pi$
$648$	23.1985	−	5.63192i	0.911323	−	0.221243i
$649$			24.2224i			0.950814i
$650$		0			0
$651$		−	5.09849i		−	0.199826i
$652$	−9.84357	−	22.0085i	−0.385504	−	0.861919i
$653$	−24.5549	−	24.5549i	−0.960909	−	0.960909i	0.0383555	−	0.999264i	$-0.487788\pi$
$653$	−24.5549	−	24.5549i	−0.960909	−	0.960909i	−0.999264	+	0.0383555i	$0.987788\pi$
$654$	−2.32566	+	12.6078i	−0.0909406	+	0.493004i
$655$		0			0
$656$	28.9316	+	25.8730i	1.12959	+	1.01017i
$657$	−30.6728	+	30.6728i	−1.19666	+	1.19666i
$658$	−1.60928	+	1.10804i	−0.0627363	+	0.0431958i
$659$	48.2178			1.87830			0.939149	−	0.343511i	$-0.111616\pi$
$659$	48.2178			1.87830			0.939149	+	0.343511i	$0.111616\pi$
$660$		0			0
$661$	−23.0915			−0.898156			−0.449078	−	0.893493i	$-0.648248\pi$
$661$	−23.0915			−0.898156			−0.449078	+	0.893493i	$0.648248\pi$
$662$	19.4785	−	13.4115i	0.757053	−	0.521254i
$663$	−9.59459	+	9.59459i	−0.372623	+	0.372623i
$664$	12.1350	−	19.9161i	0.470930	−	0.772894i
$665$		0			0
$666$	9.45959	−	51.2820i	0.366552	−	1.98714i
$667$	−1.45237	−	1.45237i	−0.0562362	−	0.0562362i
$668$	10.2468	−	4.58300i	0.396460	−	0.177322i
$669$		−	4.55293i		−	0.176026i
$670$		0			0
$671$		−	22.1103i		−	0.853560i
$672$	−1.77588	+	13.9458i	−0.0685062	+	0.537973i
$673$	15.6001	+	15.6001i	0.601340	+	0.601340i	0.940668	−	0.339328i	$-0.110200\pi$
$673$	15.6001	+	15.6001i	0.601340	+	0.601340i	−0.339328	+	0.940668i	$0.610200\pi$
$674$	19.1671	+	3.53561i	0.738290	+	0.136186i
$675$		0			0
$676$	−1.32453	−	0.505864i	−0.0509435	−	0.0194563i
$677$	−12.3716	+	12.3716i	−0.475481	+	0.475481i	−0.903683	−	0.428202i	$-0.859147\pi$
$677$	−12.3716	+	12.3716i	−0.475481	+	0.475481i	0.428202	+	0.903683i	$0.359147\pi$
$678$	22.8350	+	33.1649i	0.876973	+	1.27369i
$679$	16.3711			0.628266
$680$		0			0
$681$	14.5420			0.557251
$682$	−8.79430	−	12.7726i	−0.336751	−	0.489087i
$683$	9.61470	−	9.61470i	0.367896	−	0.367896i	−0.498813	−	0.866710i	$-0.666231\pi$
$683$	9.61470	−	9.61470i	0.367896	−	0.367896i	0.866710	+	0.498813i	$0.166231\pi$
$684$	1.54595	+	0.590430i	0.0591111	+	0.0225757i
$685$		0			0
$686$	−1.39075	−	0.256541i	−0.0530991	−	0.00979477i
$687$	38.5615	+	38.5615i	1.47121	+	1.47121i
$688$	38.7527	−	2.16277i	1.47743	−	0.0824550i
$689$		−	9.51759i		−	0.362591i
$690$		0			0
$691$		−	14.1180i		−	0.537074i	−0.963269	−	0.268537i	$-0.913460\pi$
$691$		−	14.1180i		−	0.537074i	0.963269	−	0.268537i	$-0.0865402\pi$
$692$	−21.9845	+	9.83283i	−0.835725	+	0.373788i
$693$	−12.0045	−	12.0045i	−0.456014	−	0.456014i
$694$	−1.06995	+	5.80039i	−0.0406148	+	0.220180i
$695$		0			0
$696$	8.21453	+	5.00517i	0.311371	+	0.189720i
$697$	−10.1176	+	10.1176i	−0.383233	+	0.383233i
$698$	35.0946	−	24.1637i	1.32835	−	0.914608i
$699$	16.1239			0.609863
$700$		0			0
$701$	10.5837			0.399740			0.199870	−	0.979822i	$-0.435948\pi$
$701$	10.5837			0.399740			0.199870	+	0.979822i	$0.435948\pi$
$702$	1.88918	−	1.30076i	0.0713026	−	0.0490940i
$703$	−2.13846	+	2.13846i	−0.0806537	+	0.0806537i
$704$	19.6061	+	37.9999i	0.738931	+	1.43217i
$705$		0			0
$706$	1.40438	−	7.61339i	0.0528546	−	0.286534i
$707$	−2.00817	−	2.00817i	−0.0755250	−	0.0755250i
$708$	−9.19667	−	20.5621i	−0.345632	−	0.772772i
$709$		−	15.7607i		−	0.591905i	−0.955203	−	0.295952i	$-0.904363\pi$
$709$		−	15.7607i		−	0.591905i	0.955203	−	0.295952i	$-0.0956370\pi$
$710$		0			0
$711$			32.3859i			1.21457i
$712$	−5.09274	−	20.9775i	−0.190858	−	0.786166i
$713$	−2.17733	−	2.17733i	−0.0815415	−	0.0815415i
$714$	−5.09670	−	0.940148i	−0.190739	−	0.0351841i
$715$		0			0
$716$	1.05117	−	2.75232i	0.0392839	−	0.102859i
$717$	−14.2328	+	14.2328i	−0.531533	+	0.531533i
$718$	18.7039	+	27.1650i	0.698023	+	1.01379i
$719$	10.4085			0.388171			0.194085	−	0.980985i	$-0.437826\pi$
$719$	10.4085			0.388171			0.194085	+	0.980985i	$0.437826\pi$
$720$		0			0
$721$	−11.6295			−0.433106
$722$	15.1837	+	22.0524i	0.565079	+	0.820704i
$723$	5.86479	−	5.86479i	0.218114	−	0.218114i
$724$	−6.64675	+	17.4035i	−0.247025	+	0.646798i
$725$		0			0
$726$	−60.7222	−	11.2009i	−2.25361	−	0.415706i
$727$	−11.4932	−	11.4932i	−0.426259	−	0.426259i	0.461093	−	0.887352i	$-0.347458\pi$
$727$	−11.4932	−	11.4932i	−0.426259	−	0.426259i	−0.887352	+	0.461093i	$0.847458\pi$
$728$	−2.47063	−	10.1768i	−0.0915677	−	0.377177i
$729$		−	30.0740i		−	1.11385i
$730$		0			0
$731$			14.3085i			0.529219i
$732$	8.39475	+	18.7692i	0.310279	+	0.693729i
$733$	14.2256	+	14.2256i	0.525434	+	0.525434i	0.919208	−	0.393773i	$-0.128830\pi$
$733$	14.2256	+	14.2256i	0.525434	+	0.525434i	−0.393773	+	0.919208i	$0.628830\pi$
$734$	−3.29846	+	17.8815i	−0.121749	+	0.660019i
$735$		0			0
$736$	5.19722	+	6.71401i	0.191572	+	0.247482i
$737$	26.5441	−	26.5441i	0.977765	−	0.977765i
$738$	35.8995	−	24.7179i	1.32148	−	0.909879i
$739$	27.6363			1.01662			0.508308	−	0.861175i	$-0.330271\pi$
$739$	27.6363			1.01662			0.508308	+	0.861175i	$0.330271\pi$
$740$		0			0
$741$	−2.39707			−0.0880587
$742$	2.99420	−	2.06160i	0.109920	−	0.0756836i
$743$	−22.3607	+	22.3607i	−0.820334	+	0.820334i	−0.986156	−	0.165822i	$-0.946972\pi$
$743$	−22.3607	+	22.3607i	−0.820334	+	0.820334i	0.165822	+	0.986156i	$0.446972\pi$
$744$	12.3148	+	7.50349i	0.451482	+	0.275091i
$745$		0			0
$746$	3.73011	−	20.2216i	0.136569	−	0.740364i
$747$	−18.5191	−	18.5191i	−0.677577	−	0.677577i
$748$	−14.3897	+	6.43598i	−0.526140	+	0.235323i
$749$		−	3.52116i		−	0.128660i
$750$		0			0
$751$		−	23.4739i		−	0.856574i	−0.903643	−	0.428287i	$-0.859117\pi$
$751$		−	23.4739i		−	0.856574i	0.903643	−	0.428287i	$-0.140883\pi$
$752$	−0.307943	−	5.51774i	−0.0112295	−	0.201211i
$753$	2.48866	+	2.48866i	0.0906917	+	0.0906917i
$754$	−7.04669	−	1.29985i	−0.256625	−	0.0473376i
$755$		0			0
$756$	0.818428	+	0.312574i	0.0297659	+	0.0113682i
$757$	−1.19863	+	1.19863i	−0.0435649	+	0.0435649i	−0.728554	−	0.684989i	$-0.759807\pi$
$757$	−1.19863	+	1.19863i	−0.0435649	+	0.0435649i	0.684989	+	0.728554i	$0.259807\pi$
$758$	14.6955	+	21.3433i	0.533764	+	0.775222i
$759$	−19.9373			−0.723678
$760$		0			0
$761$	29.5482			1.07112			0.535560	−	0.844497i	$-0.320100\pi$
$761$	29.5482			1.07112			0.535560	+	0.844497i	$0.320100\pi$
$762$	17.1422	+	24.8969i	0.620998	+	0.901918i
$763$	2.57936	−	2.57936i	0.0933792	−	0.0933792i
$764$	−40.1837	−	15.3469i	−1.45379	−	0.555233i
$765$		0			0
$766$	25.8187	+	4.76258i	0.932869	+	0.172079i
$767$	11.8648	+	11.8648i	0.428413	+	0.428413i
$768$	−31.0710	−	24.8137i	−1.12118	−	0.895386i
$769$		−	39.8461i		−	1.43689i	−0.695584	−	0.718444i	$-0.744854\pi$
$769$		−	39.8461i		−	1.43689i	0.695584	−	0.718444i	$-0.255146\pi$
$770$		0			0
$771$			20.0414i			0.721774i
$772$	−7.12523	+	3.18685i	−0.256443	+	0.114697i
$773$	12.3176	+	12.3176i	0.443033	+	0.443033i	0.893030	−	0.449997i	$-0.148575\pi$
$773$	12.3176	+	12.3176i	0.443033	+	0.443033i	−0.449997	+	0.893030i	$0.648575\pi$
$774$	7.90660	−	42.8630i	0.284197	−	1.54068i
$775$		0			0
$776$	−24.0935	+	39.5425i	−0.864907	+	1.41949i
$777$	−20.4008	+	20.4008i	−0.731876	+	0.731876i
$778$	−38.5111	+	26.5161i	−1.38069	+	0.950646i
$779$	−2.52775			−0.0905661
$780$		0			0
$781$	−38.9699			−1.39445
$782$	−2.57805	+	1.77507i	−0.0921910	+	0.0634763i
$783$	0.423873	−	0.423873i	0.0151480	−	0.0151480i
$784$	2.66642	−	2.98164i	0.0952294	−	0.106487i
$785$		0			0
$786$	4.47222	−	24.2447i	0.159519	−	0.864779i
$787$	27.2484	+	27.2484i	0.971301	+	0.971301i	0.999600	−	0.0282988i	$-0.00900899\pi$
$787$	27.2484	+	27.2484i	0.971301	+	0.971301i	−0.0282988	+	0.999600i	$0.509009\pi$
$788$	12.5201	+	27.9928i	0.446011	+	0.997202i
$789$		−	44.7207i		−	1.59210i
$790$		0			0
$791$		−	11.4567i		−	0.407354i
$792$	46.6627	−	11.3283i	1.65809	−	0.402535i
$793$	−10.8302	−	10.8302i	−0.384593	−	0.384593i
$794$	41.3853	+	7.63402i	1.46871	+	0.270921i
$795$		0			0
$796$	14.7185	−	38.5382i	0.521684	−	1.36595i
$797$	4.70746	−	4.70746i	0.166747	−	0.166747i	−0.618801	−	0.785548i	$-0.712381\pi$
$797$	4.70746	−	4.70746i	0.166747	−	0.166747i	0.785548	+	0.618801i	$0.212381\pi$
$798$	−0.519228	−	0.754111i	−0.0183805	−	0.0266952i
$799$	2.03729			0.0720742
$800$		0			0
$801$	−24.2416			−0.856534
$802$	−27.4944	−	39.9320i	−0.970860	−	1.41005i
$803$	51.6156	−	51.6156i	1.82148	−	1.82148i
$804$	−12.4548	+	32.6111i	−0.439248	+	1.15011i
$805$		0			0
$806$	−10.5640	−	1.94866i	−0.372102	−	0.0686387i
$807$	−19.7441	−	19.7441i	−0.695026	−	0.695026i
$808$	7.80594	−	1.89506i	0.274612	−	0.0666678i
$809$			7.66689i			0.269553i	0.990876	+	0.134777i	$0.0430317\pi$
$809$			7.66689i			0.269553i	−0.990876	+	0.134777i	$0.956968\pi$
$810$		0			0
$811$		−	6.37079i		−	0.223709i	−0.993725	−	0.111854i	$-0.964321\pi$
$811$		−	6.37079i		−	0.223709i	0.993725	−	0.111854i	$-0.0356790\pi$
$812$	−1.11745	−	2.49842i	−0.0392148	−	0.0876774i
$813$	−44.6603	−	44.6603i	−1.56630	−	1.56630i
$814$	−15.9184	+	86.2965i	−0.557941	+	3.02469i
$815$		0			0
$816$	9.77168	−	10.9269i	0.342077	−	0.382516i
$817$	−1.78739	+	1.78739i	−0.0625329	+	0.0625329i
$818$	−2.47345	+	1.70305i	−0.0864822	+	0.0595456i
$819$	−11.7603			−0.410937
$820$		0			0
$821$	1.86339			0.0650326			0.0325163	−	0.999471i	$-0.489648\pi$
$821$	1.86339			0.0650326			0.0325163	+	0.999471i	$0.489648\pi$
$822$	18.3700	−	12.6483i	0.640727	−	0.441160i
$823$	33.4215	−	33.4215i	1.16500	−	1.16500i	0.181635	−	0.983366i	$-0.441861\pi$
$823$	33.4215	−	33.4215i	1.16500	−	1.16500i	0.983366	−	0.181635i	$-0.0581390\pi$
$824$	17.1153	−	28.0898i	0.596239	−	0.978553i
$825$		0			0
$826$	−1.16260	+	6.30265i	−0.0404520	+	0.219297i
$827$	−10.7786	−	10.7786i	−0.374809	−	0.374809i	0.494416	−	0.869225i	$-0.335382\pi$
$827$	−10.7786	−	10.7786i	−0.374809	−	0.374809i	−0.869225	+	0.494416i	$0.835382\pi$
$828$	8.70377	−	3.89287i	0.302477	−	0.135286i
$829$			24.0077i			0.833823i	0.908947	+	0.416911i	$0.136887\pi$
$829$			24.0077i			0.833823i	−0.908947	+	0.416911i	$0.863113\pi$
$830$		0			0
$831$			33.1705i			1.15067i
$832$	28.2169	+	9.00978i	0.978246	+	0.312358i
$833$	1.04271	+	1.04271i	0.0361276	+	0.0361276i
$834$	−11.8094	−	2.17838i	−0.408925	−	0.0754312i
$835$		0			0
$836$	−2.60151	−	0.993566i	−0.0899750	−	0.0343632i
$837$	0.635448	−	0.635448i	0.0219643	−	0.0219643i
$838$	20.4154	+	29.6507i	0.705239	+	1.02427i
$839$	−21.1523			−0.730259			−0.365130	−	0.930957i	$-0.618975\pi$
$839$	−21.1523			−0.730259			−0.365130	+	0.930957i	$0.618975\pi$
$840$		0			0
$841$	27.1273			0.935424
$842$	−5.22173	−	7.58388i	−0.179953	−	0.261358i
$843$	−22.0313	+	22.0313i	−0.758799	+	0.758799i
$844$	2.91464	+	1.11316i	0.100326	+	0.0383164i
$845$		0			0
$846$	−6.10298	−	1.12577i	−0.209825	−	0.0387047i
$847$	12.4228	+	12.4228i	0.426854	+	0.426854i
$848$	0.572953	+	10.2662i	0.0196753	+	0.352543i
$849$			69.7445i			2.39363i
$850$		0			0
$851$			17.4245i			0.597303i
$852$	33.0810	−	14.7959i	1.13334	−	0.506899i
$853$	−11.2132	−	11.2132i	−0.383931	−	0.383931i	0.488585	−	0.872516i	$-0.337513\pi$
$853$	−11.2132	−	11.2132i	−0.383931	−	0.383931i	−0.872516	+	0.488585i	$0.837513\pi$
$854$	1.06122	−	5.75308i	0.0363144	−	0.196866i
$855$		0			0
$856$	8.50494	+	5.18212i	0.290693	+	0.177121i
$857$	−20.0075	+	20.0075i	−0.683443	+	0.683443i	−0.960774	−	0.277331i	$-0.910550\pi$
$857$	−20.0075	+	20.0075i	−0.683443	+	0.683443i	0.277331	+	0.960774i	$0.410550\pi$
$858$	−57.2880	+	39.4445i	−1.95578	+	1.34661i
$859$	−27.9568			−0.953872			−0.476936	−	0.878938i	$-0.658253\pi$
$859$	−27.9568			−0.953872			−0.476936	+	0.878938i	$0.658253\pi$
$860$		0			0
$861$	−24.1146			−0.821824
$862$	−24.7402	+	17.0344i	−0.842656	+	0.580194i
$863$	−14.2838	+	14.2838i	−0.486228	+	0.486228i	−0.907114	−	0.420886i	$-0.861719\pi$
$863$	−14.2838	+	14.2838i	−0.486228	+	0.486228i	0.420886	+	0.907114i	$0.361719\pi$
$864$	−1.95947	+	1.51680i	−0.0666626	+	0.0516026i
$865$		0			0
$866$	3.77138	−	20.4453i	0.128157	−	0.694759i
$867$	−26.0530	−	26.0530i	−0.884807	−	0.884807i
$868$	−1.67522	−	3.74550i	−0.0568608	−	0.127131i
$869$		−	54.4985i		−	1.84874i
$870$		0			0
$871$		−	26.0041i		−	0.881114i
$872$	2.43408	+	10.0262i	0.0824282	+	0.339531i
$873$	36.7688	+	36.7688i	1.24443	+	1.24443i
$874$	−0.543783	−	0.100307i	−0.0183937	−	0.00339295i
$875$		0			0
$876$	−24.2187	+	63.4131i	−0.818274	+	2.14253i
$877$	−37.2749	+	37.2749i	−1.25868	+	1.25868i	−0.306964	+	0.951721i	$0.599313\pi$
$877$	−37.2749	+	37.2749i	−1.25868	+	1.25868i	−0.951721	+	0.306964i	$0.900687\pi$
$878$	−4.24661	−	6.16764i	−0.143316	−	0.208148i
$879$	−44.4032			−1.49768
$880$		0			0
$881$	−39.2472			−1.32227			−0.661136	−	0.750266i	$-0.729925\pi$
$881$	−39.2472			−1.32227			−0.661136	+	0.750266i	$0.729925\pi$
$882$	−2.54738	−	3.69974i	−0.0857749	−	0.124577i
$883$	−15.5015	+	15.5015i	−0.521668	+	0.521668i	−0.918075	−	0.396407i	$-0.870257\pi$
$883$	−15.5015	+	15.5015i	−0.521668	+	0.521668i	0.396407	+	0.918075i	$0.370257\pi$
$884$	−3.89596	+	10.2010i	−0.131035	+	0.343096i
$885$		0			0
$886$	41.4509	+	7.64611i	1.39257	+	0.256876i
$887$	24.4485	+	24.4485i	0.820900	+	0.820900i	0.986237	−	0.165337i	$-0.0528713\pi$
$887$	24.4485	+	24.4485i	0.820900	+	0.820900i	−0.165337	+	0.986237i	$0.552871\pi$
$888$	−19.2517	−	79.2999i	−0.646045	−	2.66113i
$889$		−	8.60056i		−	0.288453i
$890$		0			0
$891$			45.1122i			1.51132i
$892$	−1.49597	−	3.34472i	−0.0500887	−	0.111989i
$893$	0.254494	+	0.254494i	0.00851633	+	0.00851633i
$894$	−8.54159	+	46.3054i	−0.285674	+	1.54868i
$895$		0			0
$896$	3.27760	+	10.8285i	0.109497	+	0.361756i
$897$	−9.76583	+	9.76583i	−0.326072	+	0.326072i
$898$	−11.0746	+	7.62523i	−0.369566	+	0.254457i
$899$	−2.80745			−0.0936338
$900$		0			0
$901$	−3.79055			−0.126282
$902$	−60.4111	+	41.5949i	−2.01147	+	1.38496i
$903$	−17.0516	+	17.0516i	−0.567442	+	0.567442i
$904$	27.6723	+	16.8610i	0.920368	+	0.560787i
$905$		0			0
$906$	−1.38583	+	7.51280i	−0.0460410	+	0.249596i
$907$	31.6739	+	31.6739i	1.05172	+	1.05172i	0.998588	+	0.0531277i	$0.0169190\pi$
$907$	31.6739	+	31.6739i	1.05172	+	1.05172i	0.0531277	+	0.998588i	$0.483081\pi$
$908$	10.6830	−	4.77810i	0.354528	−	0.158567i
$909$		−	9.02052i		−	0.299192i
$910$		0			0
$911$		−	0.963995i		−	0.0319386i	−0.999872	−	0.0159693i	$-0.994917\pi$
$911$		−	0.963995i		−	0.0319386i	0.999872	−	0.0159693i	$-0.00508340\pi$
$912$	2.58562	−	0.144302i	0.0856184	−	0.00477833i
$913$	31.1636	+	31.1636i	1.03136	+	1.03136i
$914$	−37.2050	−	6.86292i	−1.23063	−	0.227005i
$915$		0			0
$916$	40.9987	+	15.6582i	1.35464	+	0.517362i
$917$	−4.96009	+	4.96009i	−0.163796	+	0.163796i
$918$	−0.518050	−	0.752400i	−0.0170982	−	0.0248329i
$919$	−39.6973			−1.30949			−0.654747	−	0.755848i	$-0.727225\pi$
$919$	−39.6973			−1.30949			−0.654747	+	0.755848i	$0.727225\pi$
$920$		0			0
$921$	34.0732			1.12275
$922$	−3.67857	−	5.34264i	−0.121147	−	0.175950i
$923$	−19.0885	+	19.0885i	−0.628305	+	0.628305i
$924$	−24.8182	−	9.47856i	−0.816459	−	0.311822i
$925$		0			0
$926$	−10.9263	−	2.01549i	−0.359060	−	0.0662330i
$927$	−26.1194	−	26.1194i	−0.857873	−	0.857873i
$928$	7.67920	+	0.977881i	0.252082	+	0.0321005i
$929$		−	15.4584i		−	0.507175i	−0.967313	−	0.253587i	$-0.918389\pi$
$929$		−	15.4584i		−	0.507175i	0.967313	−	0.253587i	$-0.0816105\pi$
$930$		0			0
$931$			0.260506i			0.00853772i
$932$	11.8451	−	5.29788i	0.388000	−	0.173538i
$933$	−19.6864	−	19.6864i	−0.644504	−	0.644504i
$934$	8.91953	−	48.3543i	0.291856	−	1.58220i
$935$		0			0
$936$	17.3077	−	28.4056i	0.565720	−	0.928465i
$937$	34.3456	−	34.3456i	1.12202	−	1.12202i	0.130585	−	0.991437i	$-0.458314\pi$
$937$	34.3456	−	34.3456i	1.12202	−	1.12202i	0.991437	−	0.130585i	$-0.0416856\pi$
$938$	8.18078	−	5.63272i	0.267112	−	0.183915i
$939$	0.572232			0.0186741
$940$		0			0
$941$	−19.0362			−0.620562			−0.310281	−	0.950645i	$-0.600423\pi$
$941$	−19.0362			−0.620562			−0.310281	+	0.950645i	$0.600423\pi$
$942$	−13.6987	+	9.43197i	−0.446328	+	0.307310i
$943$	−10.2982	+	10.2982i	−0.335356	+	0.335356i
$944$	−13.5123	−	12.0838i	−0.439788	−	0.393294i
$945$		0			0
$946$	−13.3051	+	72.1291i	−0.432586	+	2.34512i
$947$	4.00114	+	4.00114i	0.130020	+	0.130020i	0.769122	−	0.639102i	$-0.220694\pi$
$947$	4.00114	+	4.00114i	0.130020	+	0.130020i	−0.639102	+	0.769122i	$0.720694\pi$
$948$	20.6917	+	46.2631i	0.672037	+	1.50256i
$949$		−	50.5655i		−	1.64142i
$950$		0			0
$951$		−	35.6364i		−	1.15559i
$952$	−4.05309	+	0.983974i	−0.131362	+	0.0318908i
$953$	10.9748	+	10.9748i	0.355509	+	0.355509i	0.862154	−	0.506646i	$-0.169115\pi$
$953$	10.9748	+	10.9748i	0.355509	+	0.355509i	−0.506646	+	0.862154i	$0.669115\pi$
$954$	11.3551	+	2.09458i	0.367635	+	0.0678146i
$955$		0			0
$956$	−5.77933	+	15.1323i	−0.186917	+	0.489415i
$957$	−12.8536	+	12.8536i	−0.415499	+	0.415499i
$958$	−23.8572	−	34.6494i	−0.770790	−	1.11947i
$959$	−6.34587			−0.204919
$960$		0			0
$961$	26.7912			0.864233
$962$	34.4731	+	50.0676i	1.11146	+	1.61425i
$963$	7.90836	−	7.90836i	0.254843	−	0.254843i
$964$	2.38144	−	6.23546i	0.0767011	−	0.200831i
$965$		0			0
$966$	−5.18766	−	0.956927i	−0.166910	−	0.0307886i
$967$	5.51012	+	5.51012i	0.177194	+	0.177194i	0.790131	−	0.612938i	$-0.210012\pi$
$967$	5.51012	+	5.51012i	0.177194	+	0.177194i	−0.612938	+	0.790131i	$0.710012\pi$
$968$	−48.2887	+	11.7231i	−1.55206	+	0.376794i
$969$			0.954678i			0.0306687i
$970$		0			0
$971$		−	48.6007i		−	1.55967i	−0.625984	−	0.779836i	$-0.715302\pi$
$971$		−	48.6007i		−	1.55967i	0.625984	−	0.779836i	$-0.284698\pi$
$972$	−18.2011	−	40.6944i	−0.583800	−	1.30527i
$973$	2.41602	+	2.41602i	0.0774539	+	0.0774539i
$974$	1.52044	−	8.24255i	0.0487180	−	0.264108i
$975$		0			0
$976$	12.3341	+	11.0301i	0.394804	+	0.353066i
$977$	−16.0958	+	16.0958i	−0.514949	+	0.514949i	−0.916039	−	0.401090i	$-0.868632\pi$
$977$	−16.0958	+	16.0958i	−0.514949	+	0.514949i	0.401090	+	0.916039i	$0.368632\pi$
$978$	−34.8961	+	24.0270i	−1.11585	+	0.768299i
$979$	40.7933			1.30376
$980$		0			0
$981$	11.5863			0.369921
$982$	22.1448	−	15.2474i	0.706669	−	0.486563i
$983$	−10.0369	+	10.0369i	−0.320127	+	0.320127i	−0.848816	−	0.528689i	$-0.822684\pi$
$983$	−10.0369	+	10.0369i	−0.320127	+	0.320127i	0.528689	+	0.848816i	$0.322684\pi$
$984$	35.4897	−	58.2460i	1.13137	−	1.85681i
$985$		0			0
$986$	−0.517687	+	2.80647i	−0.0164865	+	0.0893762i
$987$	2.42786	+	2.42786i	0.0772797	+	0.0772797i
$988$	−1.76096	+	0.787612i	−0.0560237	+	0.0250573i
$989$			14.5639i			0.463104i
$990$		0			0
$991$			35.6319i			1.13188i	0.824445	+	0.565942i	$0.191487\pi$
$991$			35.6319i			1.13188i	−0.824445	+	0.565942i	$0.808513\pi$
$992$	11.5123	+	1.46599i	0.365515	+	0.0465452i
$993$	−29.3865	−	29.3865i	−0.932552	−	0.932552i
$994$	−10.1399	−	1.87043i	−0.321618	−	0.0593264i
$995$		0			0
$996$	−38.2864	−	14.6223i	−1.21315	−	0.463326i
$997$	10.8489	−	10.8489i	0.343587	−	0.343587i	−0.514127	−	0.857714i	$-0.671884\pi$
$997$	10.8489	−	10.8489i	0.343587	−	0.343587i	0.857714	+	0.514127i	$0.171884\pi$
$998$	−26.5632	−	38.5796i	−0.840844	−	1.22122i
$999$	−5.08530			−0.160892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.k.b.43.6		36
4.3	odd	2	inner	700.2.k.b.43.15		36
5.2	odd	4	inner	700.2.k.b.407.15		36
5.3	odd	4		140.2.k.a.127.4	yes	36
5.4	even	2		140.2.k.a.43.13	yes	36
20.3	even	4		140.2.k.a.127.13	yes	36
20.7	even	4	inner	700.2.k.b.407.6		36
20.19	odd	2		140.2.k.a.43.4	✓	36
35.3	even	12		980.2.x.l.667.9		72
35.4	even	6		980.2.x.k.863.1		72
35.9	even	6		980.2.x.k.263.13		72
35.13	even	4		980.2.k.l.687.4		36
35.18	odd	12		980.2.x.k.667.9		72
35.19	odd	6		980.2.x.l.263.13		72
35.23	odd	12		980.2.x.k.67.15		72
35.24	odd	6		980.2.x.l.863.1		72
35.33	even	12		980.2.x.l.67.15		72
35.34	odd	2		980.2.k.l.883.13		36
140.3	odd	12		980.2.x.l.667.13		72
140.19	even	6		980.2.x.l.263.9		72
140.23	even	12		980.2.x.k.67.1		72
140.39	odd	6		980.2.x.k.863.15		72
140.59	even	6		980.2.x.l.863.15		72
140.79	odd	6		980.2.x.k.263.9		72
140.83	odd	4		980.2.k.l.687.13		36
140.103	odd	12		980.2.x.l.67.1		72
140.123	even	12		980.2.x.k.667.13		72
140.139	even	2		980.2.k.l.883.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.4	✓	36	20.19	odd	2
140.2.k.a.43.13	yes	36	5.4	even	2
140.2.k.a.127.4	yes	36	5.3	odd	4
140.2.k.a.127.13	yes	36	20.3	even	4
700.2.k.b.43.6		36	1.1	even	1	trivial
700.2.k.b.43.15		36	4.3	odd	2	inner
700.2.k.b.407.6		36	20.7	even	4	inner
700.2.k.b.407.15		36	5.2	odd	4	inner
980.2.k.l.687.4		36	35.13	even	4
980.2.k.l.687.13		36	140.83	odd	4
980.2.k.l.883.4		36	140.139	even	2
980.2.k.l.883.13		36	35.34	odd	2
980.2.x.k.67.1		72	140.23	even	12
980.2.x.k.67.15		72	35.23	odd	12
980.2.x.k.263.9		72	140.79	odd	6
980.2.x.k.263.13		72	35.9	even	6
980.2.x.k.667.9		72	35.18	odd	12
980.2.x.k.667.13		72	140.123	even	12
980.2.x.k.863.1		72	35.4	even	6
980.2.x.k.863.15		72	140.39	odd	6
980.2.x.l.67.1		72	140.103	odd	12
980.2.x.l.67.15		72	35.33	even	12
980.2.x.l.263.9		72	140.19	even	6
980.2.x.l.263.13		72	35.19	odd	6
980.2.x.l.667.9		72	35.3	even	12
980.2.x.l.667.13		72	140.3	odd	12
980.2.x.l.863.1		72	35.24	odd	6
980.2.x.l.863.15		72	140.59	even	6

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.802007 - 1.16481i) q^{2} +(-1.75731 + 1.75731i) q^{3} +(-0.713568 + 1.86837i) q^{4} +(3.45630 + 0.637557i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.74859 - 0.667278i) q^{8} -3.17626i q^{9} +O(q^{10})\)	\(q+(-0.802007 - 1.16481i) q^{2} +(-1.75731 + 1.75731i) q^{3} +(-0.713568 + 1.86837i) q^{4} +(3.45630 + 0.637557i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.74859 - 0.667278i) q^{8} -3.17626i q^{9} +5.34495i q^{11} +(-2.02935 - 4.53727i) q^{12} +(2.61810 + 2.61810i) q^{13} +(-0.256541 + 1.39075i) q^{14} +(-2.98164 - 2.66642i) q^{16} +(1.04271 - 1.04271i) q^{17} +(-3.69974 + 2.54738i) q^{18} +0.260506 q^{19} +2.48521 q^{21} +(6.22586 - 4.28669i) q^{22} +(1.06132 - 1.06132i) q^{23} +(-3.65750 + 6.00273i) q^{24} +(0.949856 - 5.14933i) q^{26} +(0.309743 + 0.309743i) q^{27} +(1.82571 - 0.816571i) q^{28} -1.36847i q^{29} -2.05153i q^{31} +(-0.714582 + 5.61154i) q^{32} +(-9.39273 - 9.39273i) q^{33} +(-2.05081 - 0.378297i) q^{34} +(5.93444 + 2.26648i) q^{36} +(-8.20890 + 8.20890i) q^{37} +(-0.208927 - 0.303440i) q^{38} -9.20162 q^{39} -9.70325 q^{41} +(-1.99316 - 2.89480i) q^{42} +(-6.86124 + 6.86124i) q^{43} +(-9.98637 - 3.81399i) q^{44} +(-2.08742 - 0.385049i) q^{46} +(0.976925 + 0.976925i) q^{47} +(9.92539 - 0.553932i) q^{48} +1.00000i q^{49} +3.66471i q^{51} +(-6.75979 + 3.02340i) q^{52} +(-1.81765 - 1.81765i) q^{53} +(0.112376 - 0.609208i) q^{54} +(-2.41538 - 1.47171i) q^{56} +(-0.457788 + 0.457788i) q^{57} +(-1.59400 + 1.09752i) q^{58} +4.53183 q^{59} -4.13667 q^{61} +(-2.38965 + 1.64535i) q^{62} +(-2.24596 + 2.24596i) q^{63} +(7.10948 - 3.66814i) q^{64} +(-3.40771 + 18.4738i) q^{66} +(-4.96620 - 4.96620i) q^{67} +(1.20412 + 2.69221i) q^{68} +3.73012i q^{69} +7.29096i q^{71} +(-2.11945 - 8.73023i) q^{72} +(-9.65689 - 9.65689i) q^{73} +(16.1454 + 2.97822i) q^{74} +(-0.185888 + 0.486722i) q^{76} +(3.77945 - 3.77945i) q^{77} +(7.37977 + 10.7181i) q^{78} -10.1963 q^{79} +8.44015 q^{81} +(7.78208 + 11.3025i) q^{82} +(5.83046 - 5.83046i) q^{83} +(-1.77337 + 4.64330i) q^{84} +(13.4948 + 2.48928i) q^{86} +(2.40482 + 2.40482i) q^{87} +(3.56657 + 14.6911i) q^{88} -7.63211i q^{89} -3.70256i q^{91} +(1.22561 + 2.74026i) q^{92} +(3.60518 + 3.60518i) q^{93} +(0.354432 - 1.92143i) q^{94} +(-8.60546 - 11.1169i) q^{96} +(-11.5761 + 11.5761i) q^{97} +(1.16481 - 0.802007i) q^{98} +16.9770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{6}+O(q^{10}) \) 36 * q - 8 * q^6	\( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) 36 * q - 8 * q^6 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 - 28 * q^18 - 4 * q^22 - 32 * q^26 - 20 * q^37 + 20 * q^42 + 16 * q^46 + 24 * q^48 - 16 * q^52 + 44 * q^53 - 24 * q^56 + 16 * q^57 + 4 * q^58 - 64 * q^61 - 40 * q^62 + 32 * q^66 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 8 * q^76 + 76 * q^78 - 36 * q^81 - 56 * q^82 + 56 * q^86 + 40 * q^88 + 56 * q^92 - 32 * q^93 + 120 * q^96 - 20 * q^97

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