LMFDB - Embedded newform 675.2.r.a.631.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			631.7
Character	$\chi$	$=$	675.631
Dual form			675.2.r.a.46.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.956880 + 1.06272i) q^{2} +(-0.00470356 - 0.0447514i) q^{4} +(2.07212 + 0.840433i) q^{5} +(1.92019 + 3.32586i) q^{7} +(-2.26178 - 1.64328i) q^{8} +O(q^{10})$	\(q+(-0.956880 + 1.06272i) q^{2} +(-0.00470356 - 0.0447514i) q^{4} +(2.07212 + 0.840433i) q^{5} +(1.92019 + 3.32586i) q^{7} +(-2.26178 - 1.64328i) q^{8} +(-2.87591 + 1.39789i) q^{10} +(-3.49787 + 3.88478i) q^{11} +(-2.25011 - 2.49900i) q^{13} +(-5.37185 - 1.14182i) q^{14} +(3.99864 - 0.849937i) q^{16} +(3.90998 + 2.84077i) q^{17} +(-1.90903 - 1.38699i) q^{19} +(0.0278642 - 0.0966831i) q^{20} +(-0.781401 - 7.43453i) q^{22} +(-4.56147 - 0.969570i) q^{23} +(3.58734 + 3.48295i) q^{25} +4.80884 q^{26} +(0.139805 - 0.101574i) q^{28} +(6.71254 + 2.98862i) q^{29} +(0.593962 - 0.264449i) q^{31} +(-0.127249 + 0.220402i) q^{32} +(-6.76033 + 1.43695i) q^{34} +(1.18369 + 8.50536i) q^{35} +(0.315262 - 0.970276i) q^{37} +(3.30069 - 0.701584i) q^{38} +(-3.30561 - 5.30596i) q^{40} +(2.50903 + 2.78656i) q^{41} +(-2.34851 - 4.06773i) q^{43} +(0.190302 + 0.138262i) q^{44} +(5.39516 - 3.91981i) q^{46} +(-10.9118 - 4.85827i) q^{47} +(-3.87423 + 6.71036i) q^{49} +(-7.13407 + 0.479583i) q^{50} +(-0.101250 + 0.112450i) q^{52} +(-2.92011 + 2.12158i) q^{53} +(-10.5129 + 5.10999i) q^{55} +(1.12228 - 10.6778i) q^{56} +(-9.59917 + 4.27383i) q^{58} +(5.20768 + 5.78372i) q^{59} +(-4.40843 + 4.89605i) q^{61} +(-0.287314 + 0.884263i) q^{62} +(2.41404 + 7.42965i) q^{64} +(-2.56225 - 7.06930i) q^{65} +(-0.930565 + 0.414314i) q^{67} +(0.108737 - 0.188339i) q^{68} +(-10.1715 - 6.88068i) q^{70} +(2.82082 - 2.04945i) q^{71} +(-1.38140 - 4.25150i) q^{73} +(0.729467 + 1.26347i) q^{74} +(-0.0530904 + 0.0919553i) q^{76} +(-19.6368 - 4.17393i) q^{77} +(1.49826 + 0.667070i) q^{79} +(8.99997 + 1.59942i) q^{80} -5.36219 q^{82} +(1.18152 - 11.2414i) q^{83} +(5.71446 + 9.17248i) q^{85} +(6.57011 + 1.39652i) q^{86} +(14.2952 - 3.03854i) q^{88} +(0.935178 + 2.87818i) q^{89} +(3.99070 - 12.2821i) q^{91} +(-0.0219345 + 0.208692i) q^{92} +(15.6043 - 6.94749i) q^{94} +(-2.79006 - 4.47841i) q^{95} +(14.8057 + 6.59193i) q^{97} +(-3.42408 - 10.5382i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.956880	+	1.06272i	−0.676616	+	0.751458i	−0.979472	−	0.201578i	$-0.935393\pi$
$2$	−0.956880	+	1.06272i	−0.676616	+	0.751458i	0.302856	+	0.953036i	$0.402060\pi$
$3$		0			0
$3$		0			0
$4$	−0.00470356	−	0.0447514i	−0.00235178	−	0.0223757i
$5$	2.07212	+	0.840433i	0.926679	+	0.375853i
$5$	2.07212	+	0.840433i	0.926679	+	0.375853i
$6$		0			0
$7$	1.92019	+	3.32586i	0.725762	+	1.25706i	0.958660	+	0.284556i	$0.0918460\pi$
$7$	1.92019	+	3.32586i	0.725762	+	1.25706i	−0.232897	+	0.972501i	$0.574821\pi$
$8$	−2.26178	−	1.64328i	−0.799662	−	0.580988i
$9$		0			0
$10$	−2.87591	+	1.39789i	−0.909444	+	0.442052i
$11$	−3.49787	+	3.88478i	−1.05465	+	1.17131i	−0.0698578	+	0.997557i	$0.522255\pi$
$11$	−3.49787	+	3.88478i	−1.05465	+	1.17131i	−0.984790	+	0.173748i	$0.944412\pi$
$12$		0			0
$13$	−2.25011	−	2.49900i	−0.624069	−	0.693099i	0.345360	−	0.938470i	$-0.387757\pi$
$13$	−2.25011	−	2.49900i	−0.624069	−	0.693099i	−0.969429	+	0.245371i	$0.921090\pi$
$14$	−5.37185	−	1.14182i	−1.43569	−	0.305165i
$15$		0			0
$16$	3.99864	−	0.849937i	0.999660	−	0.212484i
$17$	3.90998	+	2.84077i	0.948309	+	0.688987i	0.950406	−	0.311011i	$-0.100668\pi$
$17$	3.90998	+	2.84077i	0.948309	+	0.688987i	−0.00209712	+	0.999998i	$0.500668\pi$
$18$		0			0
$19$	−1.90903	−	1.38699i	−0.437961	−	0.318197i	0.346863	−	0.937916i	$-0.387247\pi$
$19$	−1.90903	−	1.38699i	−0.437961	−	0.318197i	−0.784824	+	0.619719i	$0.787247\pi$
$20$	0.0278642	−	0.0966831i	0.00623063	−	0.0216190i
$21$		0			0
$22$	−0.781401	−	7.43453i	−0.166595	−	1.58505i
$23$	−4.56147	−	0.969570i	−0.951132	−	0.202169i	−0.293882	−	0.955842i	$-0.594947\pi$
$23$	−4.56147	−	0.969570i	−0.951132	−	0.202169i	−0.657250	+	0.753672i	$0.728281\pi$
$24$		0			0
$25$	3.58734	+	3.48295i	0.717469	+	0.696591i
$26$	4.80884			0.943090
$27$		0			0
$28$	0.139805	−	0.101574i	0.0264207	−	0.0191957i
$29$	6.71254	+	2.98862i	1.24649	+	0.554972i	0.920626	−	0.390445i	$-0.127679\pi$
$29$	6.71254	+	2.98862i	1.24649	+	0.554972i	0.325862	+	0.945417i	$0.394346\pi$
$30$		0			0
$31$	0.593962	−	0.264449i	0.106679	−	0.0474964i	−0.352703	−	0.935735i	$-0.614738\pi$
$31$	0.593962	−	0.264449i	0.106679	−	0.0474964i	0.459382	+	0.888239i	$0.348071\pi$
$32$	−0.127249	+	0.220402i	−0.0224947	+	0.0389619i
$33$		0			0
$34$	−6.76033	+	1.43695i	−1.15939	+	0.246435i
$35$	1.18369	+	8.50536i	0.200080	+	1.43767i
$36$		0			0
$37$	0.315262	−	0.970276i	0.0518287	−	0.159512i	−0.921792	−	0.387685i	$-0.873275\pi$
$37$	0.315262	−	0.970276i	0.0518287	−	0.159512i	0.973621	+	0.228172i	$0.0732749\pi$
$38$	3.30069	−	0.701584i	0.535443	−	0.113812i
$39$		0			0
$40$	−3.30561	−	5.30596i	−0.522664	−	0.838945i
$41$	2.50903	+	2.78656i	0.391845	+	0.435188i	0.906498	−	0.422211i	$-0.138746\pi$
$41$	2.50903	+	2.78656i	0.391845	+	0.435188i	−0.514653	+	0.857399i	$0.672079\pi$
$42$		0			0
$43$	−2.34851	−	4.06773i	−0.358144	−	0.620324i	0.629507	−	0.776995i	$-0.283257\pi$
$43$	−2.34851	−	4.06773i	−0.358144	−	0.620324i	−0.987651	+	0.156671i	$0.949924\pi$
$44$	0.190302	+	0.138262i	0.0286890	+	0.0208438i
$45$		0			0
$46$	5.39516	−	3.91981i	0.795473	−	0.577945i
$47$	−10.9118	−	4.85827i	−1.59166	−	0.708651i	−0.596108	−	0.802904i	$-0.703287\pi$
$47$	−10.9118	−	4.85827i	−1.59166	−	0.708651i	−0.995548	+	0.0942531i	$0.969954\pi$
$48$		0			0
$49$	−3.87423	+	6.71036i	−0.553461	+	0.958623i
$50$	−7.13407	+	0.479583i	−1.00891	+	0.0678233i
$51$		0			0
$52$	−0.101250	+	0.112450i	−0.0140409	+	0.0155940i
$53$	−2.92011	+	2.12158i	−0.401108	+	0.291422i	−0.769992	−	0.638054i	$-0.779740\pi$
$53$	−2.92011	+	2.12158i	−0.401108	+	0.291422i	0.368884	+	0.929475i	$0.379740\pi$
$54$		0			0
$55$	−10.5129	+	5.10999i	−1.41756	+	0.689031i
$56$	1.12228	−	10.6778i	0.149971	−	1.42688i
$57$		0			0
$58$	−9.59917	+	4.27383i	−1.26043	+	0.561181i
$59$	5.20768	+	5.78372i	0.677982	+	0.752976i	0.979710	−	0.200418i	$-0.0642302\pi$
$59$	5.20768	+	5.78372i	0.677982	+	0.752976i	−0.301728	+	0.953394i	$0.597563\pi$
$60$		0			0
$61$	−4.40843	+	4.89605i	−0.564441	+	0.626875i	−0.956031	−	0.293264i	$-0.905258\pi$
$61$	−4.40843	+	4.89605i	−0.564441	+	0.626875i	0.391590	+	0.920140i	$0.371925\pi$
$62$	−0.287314	+	0.884263i	−0.0364890	+	0.112301i
$63$		0			0
$64$	2.41404	+	7.42965i	0.301755	+	0.928707i
$65$	−2.56225	−	7.06930i	−0.317808	−	0.876839i
$66$		0			0
$67$	−0.930565	+	0.414314i	−0.113687	+	0.0506165i	−0.462792	−	0.886467i	$-0.653152\pi$
$67$	−0.930565	+	0.414314i	−0.113687	+	0.0506165i	0.349105	+	0.937084i	$0.386486\pi$
$68$	0.108737	−	0.188339i	0.0131863	−	0.0228394i
$69$		0			0
$70$	−10.1715	−	6.88068i	−1.21573	−	0.822398i
$71$	2.82082	−	2.04945i	0.334770	−	0.243225i	−0.407682	−	0.913124i	$-0.633663\pi$
$71$	2.82082	−	2.04945i	0.334770	−	0.243225i	0.742452	+	0.669899i	$0.233663\pi$
$72$		0			0
$73$	−1.38140	−	4.25150i	−0.161680	−	0.497601i	0.837096	−	0.547056i	$-0.184252\pi$
$73$	−1.38140	−	4.25150i	−0.161680	−	0.497601i	−0.998776	+	0.0494551i	$0.984252\pi$
$74$	0.729467	+	1.26347i	0.0847988	+	0.146876i
$75$		0			0
$76$	−0.0530904	+	0.0919553i	−0.00608989	+	0.0105480i
$77$	−19.6368	−	4.17393i	−2.23782	−	0.475663i
$78$		0			0
$79$	1.49826	+	0.667070i	0.168568	+	0.0750513i	0.489286	−	0.872123i	$-0.337257\pi$
$79$	1.49826	+	0.667070i	0.168568	+	0.0750513i	−0.320718	+	0.947175i	$0.603924\pi$
$80$	8.99997	+	1.59942i	1.00623	+	0.178821i
$81$		0			0
$82$	−5.36219			−0.592154
$83$	1.18152	−	11.2414i	0.129688	−	1.23390i	−0.715185	−	0.698936i	$-0.753657\pi$
$83$	1.18152	−	11.2414i	0.129688	−	1.23390i	0.844873	−	0.534967i	$-0.179676\pi$
$84$		0			0
$85$	5.71446	+	9.17248i	0.619820	+	0.994895i
$86$	6.57011	+	1.39652i	0.708473	+	0.150591i
$87$		0			0
$88$	14.2952	−	3.03854i	1.52388	−	0.323910i
$89$	0.935178	+	2.87818i	0.0991286	+	0.305087i	0.988308	−	0.152473i	$-0.0487237\pi$
$89$	0.935178	+	2.87818i	0.0991286	+	0.305087i	−0.889179	+	0.457559i	$0.848724\pi$
$90$		0			0
$91$	3.99070	−	12.2821i	0.418339	−	1.28752i
$92$	−0.0219345	+	0.208692i	−0.00228682	+	0.0217577i
$93$		0			0
$94$	15.6043	−	6.94749i	1.60946	−	0.716579i
$95$	−2.79006	−	4.47841i	−0.286254	−	0.459475i
$96$		0			0
$97$	14.8057	+	6.59193i	1.50329	+	0.669309i	0.982820	−	0.184569i	$-0.0590888\pi$
$97$	14.8057	+	6.59193i	1.50329	+	0.669309i	0.520474	+	0.853878i	$0.325755\pi$
$98$	−3.42408	−	10.5382i	−0.345885	−	1.06452i
$99$		0			0
$100$	0.138994	−	0.176921i	0.0138994	−	0.0176921i
$101$	2.79104	+	4.83422i	0.277719	+	0.481023i	0.970817	−	0.239820i	$-0.0770884\pi$
$101$	2.79104	+	4.83422i	0.277719	+	0.481023i	−0.693099	+	0.720843i	$0.743755\pi$
$102$		0			0
$103$	−0.0651481	−	0.619843i	−0.00641923	−	0.0610749i	0.990843	−	0.135017i	$-0.0431088\pi$
$103$	−0.0651481	−	0.619843i	−0.00641923	−	0.0610749i	−0.997263	+	0.0739417i	$0.976442\pi$
$104$	0.982702	+	9.34978i	0.0963618	+	0.916822i
$105$		0			0
$106$	0.539538	−	5.13336i	0.0524046	−	0.498596i
$107$	−8.51791			−0.823458			−0.411729	−	0.911306i	$-0.635075\pi$
$107$	−8.51791			−0.823458			−0.411729	+	0.911306i	$0.635075\pi$
$108$		0			0
$109$	−3.14970	+	9.69377i	−0.301686	+	0.928495i	0.679207	+	0.733947i	$0.262324\pi$
$109$	−3.14970	+	9.69377i	−0.301686	+	0.928495i	−0.980893	+	0.194548i	$0.937676\pi$
$110$	4.62908	−	16.0619i	0.441365	−	1.53145i
$111$		0			0
$112$	10.5049	+	11.6669i	0.992620	+	1.10242i
$113$	4.24309	+	4.71243i	0.399156	+	0.443308i	0.908897	−	0.417020i	$-0.136926\pi$
$113$	4.24309	+	4.71243i	0.399156	+	0.443308i	−0.509741	+	0.860328i	$0.670259\pi$
$114$		0			0
$115$	−8.63704	−	5.84268i	−0.805408	−	0.544832i
$116$	0.102172	−	0.314453i	0.00948642	−	0.0291962i
$117$		0			0
$118$	−11.1296			−1.02456
$119$	−1.94010	+	18.4588i	−0.177849	+	1.69212i
$120$		0			0
$121$	−1.70660	−	16.2372i	−0.155145	−	1.47611i
$122$	−0.984813	−	9.36987i	−0.0891607	−	0.848308i
$123$		0			0
$124$	−0.0146282	−	0.0253368i	−0.00131365	−	0.00227531i
$125$	4.50621	+	10.2320i	0.403047	+	0.915179i
$126$		0			0
$127$	4.60449	+	14.1712i	0.408583	+	1.25749i	0.917867	+	0.396889i	$0.129910\pi$
$127$	4.60449	+	14.1712i	0.408583	+	1.25749i	−0.509284	+	0.860599i	$0.670090\pi$
$128$	−10.6706	−	4.75086i	−0.943157	−	0.419920i
$129$		0			0
$130$	9.96447	+	4.04151i	0.873942	+	0.354464i
$131$	12.3027	−	5.47750i	1.07489	−	0.478571i	0.208542	−	0.978014i	$-0.433128\pi$
$131$	12.3027	−	5.47750i	1.07489	−	0.478571i	0.866347	+	0.499442i	$0.166462\pi$
$132$		0			0
$133$	0.947245	−	9.01243i	0.0821365	−	0.781477i
$134$	0.450138	−	1.38538i	0.0388860	−	0.119679i
$135$		0			0
$136$	−4.17535	−	12.8504i	−0.358033	−	1.10191i
$137$	8.93278	−	1.89872i	0.763179	−	0.162219i	0.190151	−	0.981755i	$-0.439102\pi$
$137$	8.93278	−	1.89872i	0.763179	−	0.162219i	0.573028	+	0.819536i	$0.305769\pi$
$138$		0			0
$139$	−11.4759	−	2.43928i	−0.973376	−	0.206897i	−0.306339	−	0.951922i	$-0.599104\pi$
$139$	−11.4759	−	2.43928i	−0.973376	−	0.206897i	−0.667037	+	0.745025i	$0.732438\pi$
$140$	0.375059	−	0.0929771i	0.0316983	−	0.00785800i
$141$		0			0
$142$	−0.521193	+	4.95882i	−0.0437376	+	0.416135i
$143$	17.5787			1.47000
$144$		0			0
$145$	11.3974	+	11.8342i	0.946507	+	0.982778i
$146$	5.84000	+	2.60014i	0.483322	+	0.215189i
$147$		0			0
$148$	−0.0449040	−	0.00954465i	−0.00369109	−	0.000784565i
$149$	4.73317	−	8.19809i	0.387756	−	0.671614i	−0.604391	−	0.796688i	$-0.706584\pi$
$149$	4.73317	−	8.19809i	0.387756	−	0.671614i	0.992147	+	0.125074i	$0.0399169\pi$
$150$		0			0
$151$	7.67377	+	13.2914i	0.624482	+	1.08164i	0.988641	+	0.150298i	$0.0480234\pi$
$151$	7.67377	+	13.2914i	0.624482	+	1.08164i	−0.364158	+	0.931337i	$0.618643\pi$
$152$	2.03859	+	6.27414i	0.165352	+	0.508900i
$153$		0			0
$154$	23.2258	−	16.8745i	1.87159	−	1.35979i
$155$	1.45301	−	0.0487838i	0.116709	−	0.00391841i
$156$		0			0
$157$	10.9037	−	18.8858i	0.870210	−	1.50725i	0.00843010	−	0.999964i	$-0.497317\pi$
$157$	10.9037	−	18.8858i	0.870210	−	1.50725i	0.861780	−	0.507283i	$-0.169350\pi$
$158$	−2.14257	+	0.953934i	−0.170454	+	0.0758909i
$159$		0			0
$160$	−0.448909	+	0.349755i	−0.0354893	+	0.0276505i
$161$	−5.53422	−	17.0326i	−0.436157	−	1.34235i
$162$		0			0
$163$	−3.56614	+	10.9754i	−0.279321	+	0.859663i	0.708722	+	0.705488i	$0.249272\pi$
$163$	−3.56614	+	10.9754i	−0.279321	+	0.859663i	−0.988044	+	0.154175i	$0.950728\pi$
$164$	0.112901	−	0.125389i	0.00881609	−	0.00979126i
$165$		0			0
$166$	10.8159	+	12.0123i	0.839477	+	0.932334i
$167$	3.85690	−	1.71720i	0.298456	−	0.132881i	−0.252045	−	0.967715i	$-0.581103\pi$
$167$	3.85690	−	1.71720i	0.298456	−	0.132881i	0.550501	+	0.834834i	$0.314437\pi$
$168$		0			0
$169$	0.176859	−	1.68270i	0.0136045	−	0.129438i
$170$	−15.2159	−	2.70407i	−1.16700	−	0.207393i
$171$		0			0
$172$	−0.170990	+	0.124232i	−0.0130379	+	0.00947258i
$173$	6.60700	−	7.33782i	0.502321	−	0.557884i	−0.437647	−	0.899147i	$-0.644188\pi$
$173$	6.60700	−	7.33782i	0.502321	−	0.557884i	0.939968	+	0.341263i	$0.110855\pi$
$174$		0			0
$175$	−4.69545	+	18.6189i	−0.354943	+	1.40746i
$176$	−10.6849	+	18.5068i	−0.805405	+	1.39500i
$177$		0			0
$178$	−3.95356	−	1.76024i	−0.296332	−	0.131935i
$179$	2.85965	−	2.07766i	0.213740	−	0.155292i	−0.475764	−	0.879573i	$-0.657828\pi$
$179$	2.85965	−	2.07766i	0.213740	−	0.155292i	0.689504	+	0.724281i	$0.257828\pi$
$180$		0			0
$181$	12.3513	+	8.97372i	0.918062	+	0.667011i	0.943041	−	0.332677i	$-0.107952\pi$
$181$	12.3513	+	8.97372i	0.918062	+	0.667011i	−0.0249788	+	0.999688i	$0.507952\pi$
$182$	9.23386	+	15.9935i	0.684459	+	1.18552i
$183$		0			0
$184$	8.72379	+	9.68874i	0.643126	+	0.714264i
$185$	1.46871	−	1.74557i	0.107982	−	0.128337i
$186$		0			0
$187$	−24.7124	+	5.25277i	−1.80715	+	0.384121i
$188$	−0.166090	+	0.511171i	−0.0121133	+	0.0372810i
$189$		0			0
$190$	7.42906	+	1.32025i	0.538960	+	0.0957808i
$191$	18.1452	−	3.85689i	1.31294	−	0.279075i	0.502340	−	0.864670i	$-0.332473\pi$
$191$	18.1452	−	3.85689i	1.31294	−	0.279075i	0.810603	+	0.585596i	$0.199139\pi$
$192$		0			0
$193$	−5.82208	+	10.0841i	−0.419082	+	0.725872i	−0.995847	−	0.0910384i	$-0.970981\pi$
$193$	−5.82208	+	10.0841i	−0.419082	+	0.725872i	0.576765	+	0.816910i	$0.304315\pi$
$194$	−21.1727	+	9.42669i	−1.52011	+	0.676797i
$195$		0			0
$196$	0.318520	+	0.141814i	0.0227515	+	0.0101296i
$197$	−6.93084	+	5.03555i	−0.493802	+	0.358768i	−0.806645	−	0.591037i	$-0.798719\pi$
$197$	−6.93084	+	5.03555i	−0.493802	+	0.358768i	0.312843	+	0.949805i	$0.398719\pi$
$198$		0			0
$199$	17.3700			1.23133			0.615663	−	0.788010i	$-0.288888\pi$
$199$	17.3700			1.23133			0.615663	+	0.788010i	$0.288888\pi$
$200$	−2.39032	−	13.7727i	−0.169021	−	0.973878i
$201$		0			0
$202$	−7.80812	−	1.65967i	−0.549378	−	0.116774i
$203$	2.94961	+	28.0637i	0.207022	+	1.96968i
$204$		0			0
$205$	2.85709	+	7.88276i	0.199548	+	0.550556i
$206$	0.721060	+	0.523881i	0.0502386	+	0.0365005i
$207$		0			0
$208$	−11.1214	−	8.08016i	−0.771129	−	0.560258i
$209$	12.0657	−	2.56464i	0.834600	−	0.177400i
$210$		0			0
$211$	4.59169	+	0.975994i	0.316105	+	0.0671902i	0.363232	−	0.931699i	$-0.381673\pi$
$211$	4.59169	+	0.975994i	0.316105	+	0.0671902i	−0.0471270	+	0.998889i	$0.515007\pi$
$212$	0.108679	+	0.120700i	0.00746407	+	0.00828969i
$213$		0			0
$214$	8.15062	−	9.05218i	0.557165	−	0.618794i
$215$	−1.44772	−	10.4026i	−0.0987340	−	0.709450i
$216$		0			0
$217$	2.02004	+	1.46764i	0.137129	+	0.0996301i
$218$	−7.28791	−	12.6230i	−0.493599	−	0.854939i
$219$		0			0
$220$	0.278127	+	0.446431i	0.0187513	+	0.0300984i
$221$	−1.69881	−	16.1631i	−0.114274	−	1.08725i
$222$		0			0
$223$	10.5491	−	11.7160i	0.706422	−	0.784561i	−0.277963	−	0.960592i	$-0.589659\pi$
$223$	10.5491	−	11.7160i	0.706422	−	0.784561i	0.984385	+	0.176031i	$0.0563259\pi$
$224$	−0.977368			−0.0653032
$225$		0			0
$226$	−9.06813			−0.603203
$227$	−4.82528	+	5.35901i	−0.320265	+	0.355690i	−0.881683	−	0.471842i	$-0.843589\pi$
$227$	−4.82528	+	5.35901i	−0.320265	+	0.355690i	0.561418	+	0.827532i	$0.310256\pi$
$228$		0			0
$229$	−1.07910	−	10.2669i	−0.0713086	−	0.678456i	−0.970533	−	0.240968i	$-0.922535\pi$
$229$	−1.07910	−	10.2669i	−0.0713086	−	0.678456i	0.899224	−	0.437488i	$-0.144132\pi$
$230$	14.4738	−	3.58804i	0.954371	−	0.236589i
$231$		0			0
$232$	−10.2712	−	17.7902i	−0.674337	−	1.16799i
$233$	10.0148	+	7.27620i	0.656094	+	0.476680i	0.865341	−	0.501183i	$-0.167102\pi$
$233$	10.0148	+	7.27620i	0.656094	+	0.476680i	−0.209248	+	0.977863i	$0.567102\pi$
$234$		0			0
$235$	−18.5276	−	19.2376i	−1.20861	−	1.25492i
$236$	0.234334	−	0.260255i	0.0152539	−	0.0169411i
$237$		0			0
$238$	−17.7602	−	19.7247i	−1.15122	−	1.27856i
$239$	15.6686	+	3.33046i	1.01352	+	0.215430i	0.684592	−	0.728927i	$-0.259980\pi$
$239$	15.6686	+	3.33046i	1.01352	+	0.215430i	0.328925	+	0.944356i	$0.393314\pi$
$240$		0			0
$241$	2.86314	−	0.608580i	0.184431	−	0.0392021i	−0.114770	−	0.993392i	$-0.536613\pi$
$241$	2.86314	−	0.608580i	0.184431	−	0.0392021i	0.299201	+	0.954190i	$0.403280\pi$
$242$	18.8886	+	13.7234i	1.21421	+	0.882173i
$243$		0			0
$244$	0.239840	+	0.174254i	0.0153542	+	0.0111555i
$245$	−13.6675	+	10.6486i	−0.873183	+	0.680316i
$246$		0			0
$247$	0.829435	+	7.89155i	0.0527757	+	0.502127i
$248$	−1.77798	−	0.377921i	−0.112902	−	0.0239980i
$249$		0			0
$250$	−15.1857	−	5.00196i	−0.960427	−	0.316352i
$251$	4.72015			0.297933			0.148967	−	0.988842i	$-0.452405\pi$
$251$	4.72015			0.297933			0.148967	+	0.988842i	$0.452405\pi$
$252$		0			0
$253$	19.7220	−	14.3289i	1.23991	−	0.900849i
$254$	−19.4660	−	8.66681i	−1.22140	−	0.543804i
$255$		0			0
$256$	0.986086	−	0.439034i	0.0616304	−	0.0274396i
$257$	10.6050	−	18.3684i	0.661523	−	1.14579i	−0.318692	−	0.947858i	$-0.603244\pi$
$257$	10.6050	−	18.3684i	0.661523	−	1.14579i	0.980215	−	0.197934i	$-0.0634230\pi$
$258$		0			0
$259$	3.83236	−	0.814594i	0.238132	−	0.0506164i
$260$	−0.304309	+	0.147915i	−0.0188725	+	0.00917331i
$261$		0			0
$262$	−5.95111	+	18.3156i	−0.367661	+	1.13154i
$263$	−7.23524	+	1.53790i	−0.446144	+	0.0948309i	−0.425505	−	0.904956i	$-0.639904\pi$
$263$	−7.23524	+	1.53790i	−0.446144	+	0.0948309i	−0.0206393	+	0.999787i	$0.506570\pi$
$264$		0			0
$265$	−7.83385	+	1.94201i	−0.481230	+	0.119297i
$266$	8.67131	+	9.63047i	0.531672	+	0.590482i
$267$		0			0
$268$	0.0229181	+	0.0396953i	0.00139994	+	0.00242478i
$269$	−22.6424	−	16.4507i	−1.38053	−	1.00301i	−0.996830	−	0.0795565i	$-0.974650\pi$
$269$	−22.6424	−	16.4507i	−1.38053	−	1.00301i	−0.383700	−	0.923458i	$-0.625350\pi$
$270$		0			0
$271$	−16.6545	+	12.1002i	−1.01169	+	0.735034i	−0.964562	−	0.263855i	$-0.915006\pi$
$271$	−16.6545	+	12.1002i	−1.01169	+	0.735034i	−0.0471255	+	0.998889i	$0.515006\pi$
$272$	18.0491	+	8.03596i	1.09439	+	0.487252i
$273$		0			0
$274$	−6.52978	+	11.3099i	−0.394479	+	0.683257i
$275$	−26.0786	+	1.75312i	−1.57260	+	0.105717i
$276$		0			0
$277$	−1.82156	+	2.02305i	−0.109447	+	0.121553i	−0.795379	−	0.606112i	$-0.792728\pi$
$277$	−1.82156	+	2.02305i	−0.109447	+	0.121553i	0.685932	+	0.727666i	$0.259395\pi$
$278$	13.5734	−	9.86163i	0.814077	−	0.591461i
$279$		0			0
$280$	11.2995	−	21.1824i	0.675272	−	1.26589i
$281$	−2.51223	+	23.9023i	−0.149867	+	1.42589i	0.618452	+	0.785822i	$0.287760\pi$
$281$	−2.51223	+	23.9023i	−0.149867	+	1.42589i	−0.768319	+	0.640067i	$0.778907\pi$
$282$		0			0
$283$	7.03966	−	3.13426i	0.418464	−	0.186312i	−0.186693	−	0.982418i	$-0.559777\pi$
$283$	7.03966	−	3.13426i	0.418464	−	0.186312i	0.605157	+	0.796106i	$0.293110\pi$
$284$	−0.104983	−	0.116596i	−0.00622962	−	0.00691869i
$285$		0			0
$286$	−16.8207	+	18.6813i	−0.994628	+	1.10465i
$287$	−4.44991	+	13.6954i	−0.262670	+	0.808415i
$288$		0			0
$289$	1.96470	+	6.04671i	0.115570	+	0.355689i
$290$	−23.4825	+	0.788408i	−1.37894	+	0.0462969i
$291$		0			0
$292$	−0.183763	+	0.0818166i	−0.0107539	+	0.00478795i
$293$	13.7967	−	23.8965i	0.806010	−	1.39605i	−0.109597	−	0.993976i	$-0.534956\pi$
$293$	13.7967	−	23.8965i	0.806010	−	1.39605i	0.915607	−	0.402074i	$-0.131711\pi$
$294$		0			0
$295$	5.93010	+	16.3612i	0.345264	+	0.952589i
$296$	−2.30749	+	1.67649i	−0.134120	+	0.0974441i
$297$		0			0
$298$	4.18322	+	12.8746i	0.242327	+	0.745807i
$299$	7.84086	+	13.5808i	0.453449	+	0.785397i
$300$		0			0
$301$	9.01914	−	15.6216i	0.519855	−	0.900415i
$302$	−21.4679	−	4.56314i	−1.23534	−	0.262579i
$303$		0			0
$304$	−8.81236	−	3.92352i	−0.505423	−	0.225029i
$305$	−13.2496	+	6.44021i	−0.758669	+	0.368765i
$306$		0			0
$307$	−29.8034			−1.70097			−0.850485	−	0.526000i	$-0.823691\pi$
$307$	−29.8034			−1.70097			−0.850485	+	0.526000i	$0.823691\pi$
$308$	−0.0944262	+	0.898406i	−0.00538043	+	0.0511914i
$309$		0			0
$310$	−1.33851	+	1.59083i	−0.0760224	+	0.0903529i
$311$	−5.41338	−	1.15065i	−0.306964	−	0.0652473i	0.0518541	−	0.998655i	$-0.483487\pi$
$311$	−5.41338	−	1.15065i	−0.306964	−	0.0652473i	−0.358818	+	0.933407i	$0.616820\pi$
$312$		0			0
$313$	−5.60052	+	1.19043i	−0.316560	+	0.0672869i	−0.363452	−	0.931613i	$-0.618402\pi$
$313$	−5.60052	+	1.19043i	−0.316560	+	0.0672869i	0.0468916	+	0.998900i	$0.485068\pi$
$314$	9.63679	+	29.6590i	0.543836	+	1.67375i
$315$		0			0
$316$	0.0228051	−	0.0701870i	0.00128289	−	0.00394833i
$317$	1.21704	−	11.5794i	0.0683559	−	0.650363i	−0.905679	−	0.423964i	$-0.860638\pi$
$317$	1.21704	−	11.5794i	0.0683559	−	0.650363i	0.974035	−	0.226399i	$-0.0726952\pi$
$318$		0			0
$319$	−35.0897	+	15.6230i	−1.96465	+	0.874718i
$320$	−1.24195	+	17.4240i	−0.0694272	+	0.974029i
$321$		0			0
$322$	23.3965	+	10.4168i	1.30383	+	0.580504i
$323$	−3.52414	−	10.8462i	−0.196089	−	0.603498i
$324$		0			0
$325$	0.631986	−	16.8018i	0.0350563	−	0.931998i
$326$	−8.25148	−	14.2920i	−0.457007	−	0.791560i
$327$		0			0
$328$	−1.09578	−	10.4257i	−0.0605044	−	0.575661i
$329$	−4.79486	−	45.6201i	−0.264349	−	2.51511i
$330$		0			0
$331$	2.09180	−	19.9021i	0.114976	−	1.09392i	−0.773120	−	0.634260i	$-0.781305\pi$
$331$	2.09180	−	19.9021i	0.114976	−	1.09392i	0.888095	−	0.459659i	$-0.152028\pi$
$332$	−0.508625			−0.0279144
$333$		0			0
$334$	−1.86568	+	5.74198i	−0.102086	+	0.314187i
$335$	−2.27644	+	0.0764300i	−0.124375	+	0.00417582i
$336$		0			0
$337$	−2.65966	−	2.95385i	−0.144881	−	0.160907i	0.666337	−	0.745651i	$-0.267861\pi$
$337$	−2.65966	−	2.95385i	−0.144881	−	0.160907i	−0.811217	+	0.584745i	$0.801195\pi$
$338$	1.61901	+	1.79809i	0.0880625	+	0.0978033i
$339$		0			0
$340$	0.383603	−	0.298873i	0.0208038	−	0.0162087i
$341$	−1.05028	+	3.23242i	−0.0568757	+	0.175045i
$342$		0			0
$343$	−2.87436			−0.155201
$344$	−1.37262	+	13.0596i	−0.0740067	+	0.704126i
$345$		0			0
$346$	1.47596	+	14.0428i	0.0793481	+	0.754946i
$347$	3.83972	+	36.5325i	0.206127	+	1.96117i	0.268989	+	0.963143i	$0.413311\pi$
$347$	3.83972	+	36.5325i	0.206127	+	1.96117i	−0.0628621	+	0.998022i	$0.520023\pi$
$348$		0			0
$349$	5.56763	+	9.64341i	0.298028	+	0.516200i	0.975685	−	0.219179i	$-0.0703377\pi$
$349$	5.56763	+	9.64341i	0.298028	+	0.516200i	−0.677657	+	0.735378i	$0.737004\pi$
$350$	−15.2938	−	22.8060i	−0.817486	−	1.21903i
$351$		0			0
$352$	−0.411112	−	1.26527i	−0.0219124	−	0.0674393i
$353$	2.71907	+	1.21061i	0.144722	+	0.0644343i	0.477820	−	0.878458i	$-0.341427\pi$
$353$	2.71907	+	1.21061i	0.144722	+	0.0644343i	−0.333098	+	0.942892i	$0.608094\pi$
$354$		0			0
$355$	7.56750	−	1.87598i	0.401641	−	0.0995668i
$356$	0.124404	−	0.0553882i	0.00659339	−	0.00293557i
$357$		0			0
$358$	−0.528368	+	5.02709i	−0.0279251	+	0.265690i
$359$	−0.714480	+	2.19894i	−0.0377088	+	0.116056i	−0.968139	−	0.250413i	$-0.919433\pi$
$359$	−0.714480	+	2.19894i	−0.0377088	+	0.116056i	0.930430	+	0.366469i	$0.119433\pi$
$360$		0			0
$361$	−4.15068	−	12.7745i	−0.218457	−	0.672341i
$362$	−21.3552	+	4.53920i	−1.12241	+	0.238575i
$363$		0			0
$364$	−0.568412	−	0.120820i	−0.0297929	−	0.00633267i
$365$	0.710688	−	9.97059i	0.0371991	−	0.521885i
$366$		0			0
$367$	1.77075	−	16.8476i	0.0924324	−	0.879435i	−0.845816	−	0.533474i	$-0.820886\pi$
$367$	1.77075	−	16.8476i	0.0924324	−	0.879435i	0.938249	−	0.345961i	$-0.112447\pi$
$368$	−19.0637			−0.993766
$369$		0			0
$370$	0.449676	+	3.23113i	0.0233775	+	0.167979i
$371$	−12.6632	−	5.63803i	−0.657442	−	0.292712i
$372$		0			0
$373$	24.6592	+	5.24148i	1.27681	+	0.271394i	0.795927	−	0.605393i	$-0.206984\pi$
$373$	24.6592	+	5.24148i	1.27681	+	0.271394i	0.480880	+	0.876787i	$0.340317\pi$
$374$	18.0645	−	31.2886i	0.934094	−	1.61790i
$375$		0			0
$376$	16.6967	+	28.9196i	0.861069	+	1.49141i
$377$	−7.63542	−	23.4994i	−0.393244	−	1.21028i
$378$		0			0
$379$	19.7932	−	14.3806i	1.01671	−	0.738681i	0.0511021	−	0.998693i	$-0.483727\pi$
$379$	19.7932	−	14.3806i	1.01671	−	0.738681i	0.965605	+	0.260012i	$0.0837266\pi$
$380$	−0.187292	+	0.145923i	−0.00960787	+	0.00748570i
$381$		0			0
$382$	−13.2640	+	22.9739i	−0.678645	+	1.17545i
$383$	0.00459473	−	0.00204571i	0.000234780	−	0.000104531i	−0.406619	−	0.913598i	$-0.633292\pi$
$383$	0.00459473	−	0.00204571i	0.000234780	−	0.000104531i	0.406854	+	0.913493i	$0.366626\pi$
$384$		0			0
$385$	−37.1818	−	25.1523i	−1.89496	−	1.28188i
$386$	−5.14561	−	15.8365i	−0.261904	−	0.806059i
$387$		0			0
$388$	0.225358	−	0.693582i	0.0114408	−	0.0352113i
$389$	−6.97691	+	7.74865i	−0.353744	+	0.392872i	−0.893584	−	0.448895i	$-0.851818\pi$
$389$	−6.97691	+	7.74865i	−0.353744	+	0.392872i	0.539841	+	0.841767i	$0.318484\pi$
$390$		0			0
$391$	−15.0809	−	16.7491i	−0.762675	−	0.847037i
$392$	19.7897	−	8.81094i	0.999531	−	0.445020i
$393$		0			0
$394$	1.28059	−	12.1840i	0.0645151	−	0.613820i
$395$	2.54395	+	2.64144i	0.128000	+	0.132905i
$396$		0			0
$397$	−4.80180	+	3.48871i	−0.240996	+	0.175094i	−0.701727	−	0.712446i	$-0.747587\pi$
$397$	−4.80180	+	3.48871i	−0.240996	+	0.175094i	0.460731	+	0.887540i	$0.347587\pi$
$398$	−16.6210	+	18.4595i	−0.833135	+	0.925290i
$399$		0			0
$400$	17.3048	+	10.8781i	0.865239	+	0.543903i
$401$	−9.95507	+	17.2427i	−0.497133	+	0.861059i	−0.999995	−	0.00330780i	$-0.998947\pi$
$401$	−9.95507	+	17.2427i	−0.497133	+	0.861059i	0.502862	+	0.864367i	$0.332280\pi$
$402$		0			0
$403$	−1.99734	−	0.889274i	−0.0994946	−	0.0442979i
$404$	0.203210	−	0.147641i	0.0101101	−	0.00734540i
$405$		0			0
$406$	−32.6463	−	23.7190i	−1.62021	−	1.17715i
$407$	2.66656	+	4.61862i	0.132177	+	0.228937i
$408$		0			0
$409$	−3.27138	−	3.63324i	−0.161759	−	0.179652i	0.656816	−	0.754051i	$-0.271903\pi$
$409$	−3.27138	−	3.63324i	−0.161759	−	0.179652i	−0.818576	+	0.574399i	$0.805236\pi$
$410$	−11.1111	−	4.50656i	−0.548737	−	0.222563i
$411$		0			0
$412$	−0.0274324	+	0.00583093i	−0.00135150	+	0.000287269i
$413$	−9.23611	+	28.4258i	−0.454479	+	1.39874i
$414$		0			0
$415$	11.8959	−	22.3005i	0.583946	−	1.09469i
$416$	0.837111	−	0.177933i	0.0410427	−	0.00872390i
$417$		0			0
$418$	−8.81990	+	15.2765i	−0.431395	+	0.747199i
$419$	−11.6448	+	5.18460i	−0.568886	+	0.253284i	−0.670961	−	0.741492i	$-0.734118\pi$
$419$	−11.6448	+	5.18460i	−0.568886	+	0.253284i	0.102075	+	0.994777i	$0.467452\pi$
$420$		0			0
$421$	−16.0386	−	7.14085i	−0.781674	−	0.348024i	−0.0232033	−	0.999731i	$-0.507387\pi$
$421$	−16.0386	−	7.14085i	−0.781674	−	0.348024i	−0.758471	+	0.651707i	$0.774053\pi$
$422$	−5.43091	+	3.94579i	−0.264372	+	0.192078i
$423$		0			0
$424$	10.0910			0.490063
$425$	4.13218	+	23.8091i	0.200440	+	1.15491i
$426$		0			0
$427$	−24.7486	−	5.26047i	−1.19767	−	0.254572i
$428$	0.0400645	+	0.381188i	0.00193659	+	0.0184254i
$429$		0			0
$430$	12.4404	+	8.41549i	0.599927	+	0.405831i
$431$	−23.8727	−	17.3445i	−1.14991	−	0.835456i	−0.161438	−	0.986883i	$-0.551613\pi$
$431$	−23.8727	−	17.3445i	−1.14991	−	0.835456i	−0.988469	+	0.151427i	$0.951613\pi$
$432$		0			0
$433$	15.9668	+	11.6006i	0.767316	+	0.557488i	0.901146	−	0.433517i	$-0.142727\pi$
$433$	15.9668	+	11.6006i	0.767316	+	0.557488i	−0.133830	+	0.991004i	$0.542727\pi$
$434$	−3.49263	+	0.742382i	−0.167652	+	0.0356355i
$435$		0			0
$436$	0.448624	+	0.0953580i	0.0214852	+	0.00456682i
$437$	7.36318	+	8.17764i	0.352229	+	0.391190i
$438$		0			0
$439$	8.21559	−	9.12433i	0.392109	−	0.435481i	−0.514476	−	0.857505i	$-0.672014\pi$
$439$	8.21559	−	9.12433i	0.392109	−	0.435481i	0.906585	+	0.422024i	$0.138680\pi$
$440$	32.1751	+	5.71796i	1.53389	+	0.272593i
$441$		0			0
$442$	18.8024	+	13.6608i	0.894341	+	0.649777i
$443$	11.4062	+	19.7562i	0.541926	+	0.938643i	0.998793	+	0.0491085i	$0.0156380\pi$
$443$	11.4062	+	19.7562i	0.541926	+	0.938643i	−0.456868	+	0.889535i	$0.651029\pi$
$444$		0			0
$445$	−0.481121	+	6.74988i	−0.0228073	+	0.319975i
$446$	2.35660	+	22.4216i	0.111588	+	1.06169i
$447$		0			0
$448$	−20.0746	+	22.2951i	−0.948435	+	1.05334i
$449$	4.10374			0.193668			0.0968338	−	0.995301i	$-0.469128\pi$
$449$	4.10374			0.193668			0.0968338	+	0.995301i	$0.469128\pi$
$450$		0			0
$451$	−19.6015			−0.922997
$452$	0.190930	−	0.212049i	0.00898058	−	0.00997395i
$453$		0			0
$454$	−1.07793	−	10.2559i	−0.0505900	−	0.481331i
$455$	18.5915	−	22.0961i	0.871583	−	1.03588i
$456$		0			0
$457$	9.06472	+	15.7006i	0.424030	+	0.734441i	0.996329	−	0.0856035i	$-0.0272818\pi$
$457$	9.06472	+	15.7006i	0.424030	+	0.734441i	−0.572299	+	0.820045i	$0.693948\pi$
$458$	11.9434	+	8.67742i	0.558080	+	0.405469i
$459$		0			0
$460$	−0.220843	+	0.414001i	−0.0102968	+	0.0193029i
$461$	−15.7461	+	17.4878i	−0.733370	+	0.814490i	−0.988308	−	0.152468i	$-0.951278\pi$
$461$	−15.7461	+	17.4878i	−0.733370	+	0.814490i	0.254939	+	0.966957i	$0.417945\pi$
$462$		0			0
$463$	−2.39487	−	2.65977i	−0.111299	−	0.123610i	0.684921	−	0.728617i	$-0.259837\pi$
$463$	−2.39487	−	2.65977i	−0.111299	−	0.123610i	−0.796220	+	0.605008i	$0.793170\pi$
$464$	29.3812	+	6.24516i	1.36399	+	0.289924i
$465$		0			0
$466$	−17.3156	+	3.68054i	−0.802129	+	0.170498i
$467$	−12.8399	−	9.32877i	−0.594162	−	0.431684i	0.249640	−	0.968339i	$-0.419688\pi$
$467$	−12.8399	−	9.32877i	−0.594162	−	0.431684i	−0.843802	+	0.536655i	$0.819688\pi$
$468$		0			0
$469$	−3.16481	−	2.29937i	−0.146137	−	0.106175i
$470$	38.1729	−	1.28163i	1.76078	−	0.0591171i
$471$		0			0
$472$	−2.27437	−	21.6392i	−0.104686	−	0.996026i
$473$	24.0170	+	5.10498i	1.10430	+	0.234727i
$474$		0			0
$475$	−2.01752	−	11.6247i	−0.0925700	−	0.533376i
$476$	0.835184			0.0382806
$477$		0			0
$478$	−18.5323	+	13.4645i	−0.847648	+	0.615852i
$479$	15.3830	+	6.84896i	0.702868	+	0.312937i	0.726870	−	0.686775i	$-0.240974\pi$
$479$	15.3830	+	6.84896i	0.702868	+	0.312937i	−0.0240023	+	0.999712i	$0.507641\pi$
$480$		0			0
$481$	−3.13410	+	1.39539i	−0.142903	+	0.0636244i
$482$	−2.09293	+	3.62506i	−0.0953304	+	0.165117i
$483$		0			0
$484$	−0.718609	+	0.152745i	−0.0326640	+	0.00694295i
$485$	25.1391	+	26.1025i	1.14151	+	1.18525i
$486$		0			0
$487$	−3.07445	+	9.46219i	−0.139317	+	0.428773i	−0.996236	−	0.0866771i	$-0.972375\pi$
$487$	−3.07445	+	9.46219i	−0.139317	+	0.428773i	0.856920	+	0.515450i	$0.172375\pi$
$488$	18.0165	−	3.82953i	0.815569	−	0.173355i
$489$		0			0
$490$	1.76159	−	24.7142i	0.0795804	−	1.11647i
$491$	−7.86619	−	8.73629i	−0.354996	−	0.394263i	0.539024	−	0.842291i	$-0.318793\pi$
$491$	−7.86619	−	8.73629i	−0.354996	−	0.394263i	−0.894020	+	0.448027i	$0.852127\pi$
$492$		0			0
$493$	17.7559	+	30.7542i	0.799688	+	1.38510i
$494$	−9.18019	−	6.66980i	−0.413036	−	0.300089i
$495$		0			0
$496$	2.15027	−	1.56227i	0.0965502	−	0.0701478i
$497$	12.2327	+	5.44634i	0.548710	+	0.244302i
$498$		0			0
$499$	12.7440	−	22.0733i	0.570501	−	0.988137i	−0.426013	−	0.904717i	$-0.640082\pi$
$499$	12.7440	−	22.0733i	0.570501	−	0.988137i	0.996514	−	0.0834204i	$-0.0265844\pi$
$500$	0.436701	−	0.249786i	0.0195299	−	0.0111708i
$501$		0			0
$502$	−4.51661	+	5.01621i	−0.201586	+	0.223884i
$503$	3.86329	−	2.80684i	0.172256	−	0.125151i	−0.498317	−	0.866995i	$-0.666048\pi$
$503$	3.86329	−	2.80684i	0.172256	−	0.125151i	0.670573	+	0.741844i	$0.266048\pi$
$504$		0			0
$505$	1.72052	+	12.3628i	0.0765621	+	0.550135i
$506$	−3.64397	+	34.6700i	−0.161994	+	1.54127i
$507$		0			0
$508$	0.612521	−	0.272712i	0.0271762	−	0.0120996i
$509$	0.140363	+	0.155889i	0.00622150	+	0.00690968i	0.746248	−	0.665669i	$-0.231854\pi$
$509$	0.140363	+	0.155889i	0.00622150	+	0.00690968i	−0.740026	+	0.672578i	$0.765187\pi$
$510$		0			0
$511$	11.4874	−	12.7580i	0.508171	−	0.564381i
$512$	6.74190	−	20.7494i	0.297953	−	0.917005i
$513$		0			0
$514$	9.37282	+	28.8466i	0.413417	+	1.27237i
$515$	0.385942	−	1.33914i	0.0170066	−	0.0590095i
$516$		0			0
$517$	57.0415	−	25.3965i	2.50868	−	1.11694i
$518$	−2.80142	+	4.85221i	−0.123088	+	0.213194i
$519$		0			0
$520$	−5.82160	+	20.1997i	−0.255294	+	0.885818i
$521$	10.5015	−	7.62978i	0.460079	−	0.334267i	−0.333484	−	0.942756i	$-0.608224\pi$
$521$	10.5015	−	7.62978i	0.460079	−	0.334267i	0.793562	+	0.608489i	$0.208224\pi$
$522$		0			0
$523$	11.1175	+	34.2162i	0.486136	+	1.49617i	0.830329	+	0.557273i	$0.188152\pi$
$523$	11.1175	+	34.2162i	0.486136	+	1.49617i	−0.344194	+	0.938899i	$0.611848\pi$
$524$	−0.302992	−	0.524797i	−0.0132363	−	0.0229259i
$525$		0			0
$526$	5.28890	−	9.16064i	0.230607	−	0.399423i
$527$	3.07362	+	0.653317i	0.133889	+	0.0284590i
$528$		0			0
$529$	−1.14461	−	0.509612i	−0.0497655	−	0.0221570i
$530$	5.43223	−	10.1835i	0.235961	−	0.442342i
$531$		0			0
$532$	−0.407774			−0.0176792
$533$	1.31802	−	12.5402i	0.0570900	−	0.543175i
$534$		0			0
$535$	−17.6501	−	7.15874i	−0.763081	−	0.309499i
$536$	2.78557	+	0.592092i	0.120318	+	0.0255745i
$537$		0			0
$538$	39.1485	−	8.32127i	1.68781	−	0.358756i
$539$	−12.5167	−	38.5225i	−0.539133	−	1.65928i
$540$		0			0
$541$	5.95413	−	18.3249i	0.255988	−	0.787850i	−0.737646	−	0.675188i	$-0.764062\pi$
$541$	5.95413	−	18.3249i	0.255988	−	0.787850i	0.993633	−	0.112661i	$-0.0359376\pi$
$542$	3.07719	−	29.2775i	0.132177	−	1.25758i
$543$		0			0
$544$	−1.12365	+	0.500282i	−0.0481762	+	0.0214494i
$545$	−14.6735	+	17.4395i	−0.628544	+	0.747027i
$546$		0			0
$547$	39.9472	+	17.7856i	1.70802	+	0.760459i	0.998440	+	0.0558322i	$0.0177812\pi$
$547$	39.9472	+	17.7856i	1.70802	+	0.760459i	0.709578	+	0.704627i	$0.248885\pi$
$548$	−0.126986	−	0.390823i	−0.00542458	−	0.0166951i
$549$		0			0
$550$	23.0910	−	29.3918i	0.984603	−	1.25327i
$551$	−8.66924	−	15.0156i	−0.369322	−	0.639685i
$552$		0			0
$553$	0.658364	+	6.26392i	0.0279965	+	0.266369i
$554$	−0.406925	−	3.87163i	−0.0172886	−	0.164490i
$555$		0			0
$556$	−0.0551836	+	0.525037i	−0.00234031	+	0.0222665i
$557$	−42.9035			−1.81788			−0.908939	−	0.416929i	$-0.863106\pi$
$557$	−42.9035			−1.81788			−0.908939	+	0.416929i	$0.863106\pi$
$558$		0			0
$559$	−4.88088	+	15.0218i	−0.206439	+	0.635354i
$560$	11.9622	+	33.0038i	0.505494	+	1.39467i
$561$		0			0
$562$	−22.9976	−	25.5414i	−0.970094	−	1.07740i
$563$	−10.6413	−	11.8183i	−0.448476	−	0.498083i	0.475935	−	0.879480i	$-0.342110\pi$
$563$	−10.6413	−	11.8183i	−0.448476	−	0.498083i	−0.924411	+	0.381397i	$0.875443\pi$
$564$		0			0
$565$	4.83170	+	13.3307i	0.203271	+	0.560828i
$566$	−3.40526	+	10.4803i	−0.143134	+	0.440520i
$567$		0			0
$568$	−9.74791			−0.409013
$569$	2.46904	−	23.4914i	0.103508	−	0.984810i	−0.812313	−	0.583222i	$-0.801792\pi$
$569$	2.46904	−	23.4914i	0.103508	−	0.984810i	0.915820	−	0.401588i	$-0.131542\pi$
$570$		0			0
$571$	0.122040	+	1.16113i	0.00510720	+	0.0485917i	0.996779	−	0.0802014i	$-0.0255563\pi$
$571$	0.122040	+	1.16113i	0.00510720	+	0.0485917i	−0.991671	+	0.128793i	$0.958890\pi$
$572$	−0.0826824	−	0.786670i	−0.00345712	−	0.0328923i
$573$		0			0
$574$	−10.2964	−	17.8339i	−0.429763	−	0.744372i
$575$	−12.9866	−	19.3656i	−0.541578	−	0.807600i
$576$		0			0
$577$	−10.2147	−	31.4377i	−0.425244	−	1.30877i	−0.902760	−	0.430144i	$-0.858463\pi$
$577$	−10.2147	−	31.4377i	−0.425244	−	1.30877i	0.477516	−	0.878623i	$-0.341537\pi$
$578$	−8.30596	−	3.69805i	−0.345482	−	0.153819i
$579$		0			0
$580$	0.475989	−	0.565714i	0.0197643	−	0.0234900i
$581$	39.6560	−	17.6560i	1.64521	−	0.732494i
$582$		0			0
$583$	1.97228	−	18.7650i	0.0816835	−	0.777167i
$584$	−3.86200	+	11.8860i	−0.159811	+	0.491847i
$585$		0			0
$586$	12.1936	+	37.5281i	0.503714	+	1.55027i
$587$	3.60347	−	0.765941i	0.148731	−	0.0316138i	−0.132944	−	0.991123i	$-0.542443\pi$
$587$	3.60347	−	0.765941i	0.148731	−	0.0316138i	0.281675	+	0.959510i	$0.409110\pi$
$588$		0			0
$589$	−1.50068	−	0.318979i	−0.0618343	−	0.0131433i
$590$	−23.0619	−	9.35369i	−0.949442	−	0.385085i
$591$		0			0
$592$	0.435945	−	4.14774i	0.0179172	−	0.170471i
$593$	−18.3600			−0.753956			−0.376978	−	0.926222i	$-0.623037\pi$
$593$	−18.3600			−0.753956			−0.376978	+	0.926222i	$0.623037\pi$
$594$		0			0
$595$	−19.5335	+	36.6184i	−0.800797	+	1.50121i
$596$	−0.389138	−	0.173256i	−0.0159397	−	0.00709682i
$597$		0			0
$598$	−21.9354	−	4.66250i	−0.897004	−	0.190664i
$599$	−21.7553	+	37.6813i	−0.888897	+	1.53961i	−0.0477161	+	0.998861i	$0.515194\pi$
$599$	−21.7553	+	37.6813i	−0.888897	+	1.53961i	−0.841181	+	0.540754i	$0.818139\pi$
$600$		0			0
$601$	4.47712	+	7.75460i	0.182626	+	0.316317i	0.942774	−	0.333433i	$-0.108207\pi$
$601$	4.47712	+	7.75460i	0.182626	+	0.316317i	−0.760148	+	0.649750i	$0.774874\pi$
$602$	7.97120	+	24.5328i	0.324882	+	0.999884i
$603$		0			0
$604$	0.558712	−	0.405928i	0.0227337	−	0.0165170i
$605$	10.1100	−	35.0796i	0.411030	−	1.42619i
$606$		0			0
$607$	2.21210	−	3.83147i	0.0897864	−	0.155515i	−0.817634	−	0.575738i	$-0.804715\pi$
$607$	2.21210	−	3.83147i	0.0897864	−	0.155515i	0.907421	+	0.420223i	$0.138048\pi$
$608$	0.548617	−	0.244260i	0.0222494	−	0.00990605i
$609$		0			0
$610$	5.83410	−	20.2431i	0.236216	−	0.819621i
$611$	12.4121	+	38.2004i	0.502138	+	1.54542i
$612$		0			0
$613$	−6.60377	+	20.3243i	−0.266724	+	0.820891i	0.724568	+	0.689204i	$0.242040\pi$
$613$	−6.60377	+	20.3243i	−0.266724	+	0.820891i	−0.991291	+	0.131687i	$0.957960\pi$
$614$	28.5183	−	31.6727i	1.15090	−	1.27821i
$615$		0			0
$616$	37.5553	+	41.7093i	1.51314	+	1.68052i
$617$	29.4288	−	13.1026i	1.18476	−	0.527489i	0.282745	−	0.959195i	$-0.408755\pi$
$617$	29.4288	−	13.1026i	1.18476	−	0.527489i	0.902014	+	0.431706i	$0.142088\pi$
$618$		0			0
$619$	4.20729	−	40.0297i	0.169105	−	1.60893i	−0.500178	−	0.865922i	$-0.666732\pi$
$619$	4.20729	−	40.0297i	0.169105	−	1.60893i	0.669284	−	0.743007i	$-0.266601\pi$
$620$	−0.00901746	−	0.0647948i	−0.000362150	−	0.00260222i
$621$		0			0
$622$	6.40277	−	4.65188i	0.256728	−	0.186524i
$623$	−7.77671	+	8.63691i	−0.311567	+	0.346031i
$624$		0			0
$625$	0.738068	+	24.9891i	0.0295227	+	0.999564i
$626$	4.09393	−	7.09089i	0.163626	−	0.283409i
$627$		0			0
$628$	−0.896449	−	0.399125i	−0.0357722	−	0.0159268i
$629$	3.98900	−	2.89817i	0.159052	−	0.115558i
$630$		0			0
$631$	−0.646758	−	0.469897i	−0.0257470	−	0.0187063i	0.574837	−	0.818268i	$-0.305065\pi$
$631$	−0.646758	−	0.469897i	−0.0257470	−	0.0187063i	−0.600584	+	0.799561i	$0.705065\pi$
$632$	−2.29257	−	3.97084i	−0.0911934	−	0.157952i
$633$		0			0
$634$	11.1411	+	12.3735i	0.442470	+	0.491413i
$635$	−2.36887	+	33.2341i	−0.0940059	+	1.31885i
$636$		0			0
$637$	25.4867	−	5.41736i	1.00982	−	0.214644i
$638$	16.9738	−	52.2399i	0.671999	−	2.06820i
$639$		0			0
$640$	−18.1180	−	18.8123i	−0.716175	−	0.743620i
$641$	−28.1541	+	5.98433i	−1.11202	+	0.236367i	−0.727065	−	0.686569i	$-0.759116\pi$
$641$	−28.1541	+	5.98433i	−1.11202	+	0.236367i	−0.384954	+	0.922936i	$0.625783\pi$
$642$		0			0
$643$	24.5329	−	42.4923i	0.967484	−	1.67573i	0.264695	−	0.964332i	$-0.414729\pi$
$643$	24.5329	−	42.4923i	0.967484	−	1.67573i	0.702789	−	0.711399i	$-0.251938\pi$
$644$	−0.736200	+	0.327777i	−0.0290103	+	0.0129162i
$645$		0			0
$646$	14.8987	+	6.63332i	0.586180	+	0.260984i
$647$	11.9156	−	8.65721i	0.468452	−	0.340350i	−0.328386	−	0.944544i	$-0.606505\pi$
$647$	11.9156	−	8.65721i	0.468452	−	0.340350i	0.796838	+	0.604194i	$0.206505\pi$
$648$		0			0
$649$	−40.6843			−1.59700
$650$	17.2509	+	16.7490i	0.676638	+	0.656948i
$651$		0			0
$652$	0.507939	+	0.107966i	0.0198924	+	0.00422827i
$653$	−2.79240	−	26.5679i	−0.109275	−	1.03968i	−0.902481	−	0.430730i	$-0.858256\pi$
$653$	−2.79240	−	26.5679i	−0.109275	−	1.03968i	0.793206	−	0.608954i	$-0.208410\pi$
$654$		0			0
$655$	30.0960	−	1.01045i	1.17595	−	0.0394817i
$656$	12.4011	+	9.00994i	0.484182	+	0.351779i
$657$		0			0
$658$	53.0696	+	38.5573i	2.06887	+	1.50312i
$659$	−5.26842	+	1.11984i	−0.205228	+	0.0436226i	−0.309379	−	0.950939i	$-0.600121\pi$
$659$	−5.26842	+	1.11984i	−0.205228	+	0.0436226i	0.104150	+	0.994562i	$0.466788\pi$
$660$		0			0
$661$	23.7568	+	5.04966i	0.924032	+	0.196409i	0.645273	−	0.763952i	$-0.276744\pi$
$661$	23.7568	+	5.04966i	0.924032	+	0.196409i	0.278759	+	0.960361i	$0.410077\pi$
$662$	19.1488	+	21.2669i	0.744240	+	0.826563i
$663$		0			0
$664$	−21.1451	+	23.4840i	−0.820590	+	0.911357i
$665$	9.53715	−	17.8787i	0.369835	−	0.693307i
$666$		0			0
$667$	−27.7214	−	20.1408i	−1.07338	−	0.779854i
$668$	−0.0949884	−	0.164525i	−0.00367521	−	0.00636565i
$669$		0			0
$670$	2.09706	−	2.49236i	0.0810164	−	0.0962883i
$671$	−3.59998	−	34.2515i	−0.138976	−	1.32227i
$672$		0			0
$673$	22.8188	−	25.3428i	0.879599	−	0.976893i	−0.120276	−	0.992741i	$-0.538378\pi$
$673$	22.8188	−	25.3428i	0.879599	−	0.976893i	0.999874	+	0.0158471i	$0.00504451\pi$
$674$	5.68410			0.218943
$675$		0			0
$676$	−0.0761349			−0.00292826
$677$	−3.34059	+	3.71010i	−0.128389	+	0.142591i	−0.803912	−	0.594749i	$-0.797252\pi$
$677$	−3.34059	+	3.71010i	−0.128389	+	0.142591i	0.675522	+	0.737339i	$0.263918\pi$
$678$		0			0
$679$	6.50590	+	61.8995i	0.249673	+	2.37548i
$680$	2.14809	−	30.1367i	0.0823756	−	1.15569i
$681$		0			0
$682$	−2.43018	−	4.20919i	−0.0930563	−	0.161178i
$683$	−6.26357	−	4.55075i	−0.239669	−	0.174130i	0.461467	−	0.887157i	$-0.347323\pi$
$683$	−6.26357	−	4.55075i	−0.239669	−	0.174130i	−0.701136	+	0.713028i	$0.747323\pi$
$684$		0			0
$685$	20.1055	+	3.57303i	0.768192	+	0.136519i
$686$	2.75042	−	3.05465i	0.105012	−	0.116627i
$687$		0			0
$688$	−12.8481	−	14.2693i	−0.489831	−	0.544013i
$689$	11.8724	+	2.52356i	0.452303	+	0.0961400i
$690$		0			0
$691$	−31.3939	+	6.67298i	−1.19428	+	0.253852i	−0.761813	−	0.647797i	$-0.775690\pi$
$691$	−31.3939	+	6.67298i	−1.19428	+	0.253852i	−0.432468	+	0.901649i	$0.642357\pi$
$692$	−0.359454	−	0.261158i	−0.0136644	−	0.00992775i
$693$		0			0
$694$	−42.4980	−	30.8766i	−1.61320	−	1.17206i
$695$	−21.7294	−	14.6992i	−0.824244	−	0.557574i
$696$		0			0
$697$	1.89429	+	18.0230i	0.0717514	+	0.682669i
$698$	−15.5758	−	3.31074i	−0.589553	−	0.125313i
$699$		0			0
$700$	0.855307	+	0.122553i	0.0323276	+	0.00463205i
$701$	2.23365			0.0843639			0.0421819	−	0.999110i	$-0.486569\pi$
$701$	2.23365			0.0843639			0.0421819	+	0.999110i	$0.486569\pi$
$702$		0			0
$703$	−1.94761	+	1.41502i	−0.0734553	+	0.0533684i
$704$	−37.3066	−	16.6100i	−1.40604	−	0.626011i
$705$		0			0
$706$	−3.88837	+	1.73121i	−0.146341	+	0.0651551i
$707$	−10.7186	+	18.5652i	−0.403115	+	0.698216i
$708$		0			0
$709$	−40.0642	+	8.51592i	−1.50464	+	0.319822i	−0.885197	−	0.465216i	$-0.845976\pi$
$709$	−40.0642	+	8.51592i	−1.50464	+	0.319822i	−0.619447	+	0.785038i	$0.712643\pi$
$710$	−5.24754	+	9.83724i	−0.196936	+	0.369185i
$711$		0			0
$712$	2.61449	−	8.04659i	0.0979823	−	0.301559i
$713$	−2.96574	+	0.630388i	−0.111068	+	0.0236082i
$714$		0			0
$715$	36.4251	+	14.7737i	1.36222	+	0.552506i
$716$	−0.106429	−	0.118201i	−0.00397742	−	0.00441738i
$717$		0			0
$718$	−1.65319	−	2.86342i	−0.0616967	−	0.106862i
$719$	−11.5919	−	8.42199i	−0.432304	−	0.314087i	0.350265	−	0.936650i	$-0.386091\pi$
$719$	−11.5919	−	8.42199i	−0.432304	−	0.314087i	−0.782570	+	0.622563i	$0.786091\pi$
$720$		0			0
$721$	1.93641	−	1.40689i	0.0721158	−	0.0523952i
$722$	17.5474	+	7.81262i	0.653048	+	0.290756i
$723$		0			0
$724$	0.343491	−	0.594944i	0.0127657	−	0.0221109i
$725$	13.6710	+	34.1007i	0.507728	+	1.26647i
$726$		0			0
$727$	−22.8565	+	25.3847i	−0.847700	+	0.941466i	−0.998893	−	0.0470382i	$-0.985022\pi$
$727$	−22.8565	+	25.3847i	−0.847700	+	0.941466i	0.151193	+	0.988504i	$0.451688\pi$
$728$	−29.2091	+	21.2217i	−1.08256	+	0.786527i
$729$		0			0
$730$	9.91593	+	10.2959i	0.367005	+	0.381069i
$731$	2.37287	−	22.5763i	0.0877636	−	0.835015i
$732$		0			0
$733$	−40.6252	+	18.0875i	−1.50053	+	0.668078i	−0.982326	−	0.187180i	$-0.940065\pi$
$733$	−40.6252	+	18.0875i	−1.50053	+	0.668078i	−0.518202	+	0.855258i	$0.673398\pi$
$734$	16.2099	+	18.0029i	0.598318	+	0.664499i
$735$		0			0
$736$	0.794139	−	0.881980i	0.0292723	−	0.0325102i
$737$	1.64548	−	5.06426i	0.0606119	−	0.186544i
$738$		0			0
$739$	−6.83528	−	21.0368i	−0.251440	−	0.773852i	−0.994510	−	0.104639i	$-0.966631\pi$
$739$	−6.83528	−	21.0368i	−0.251440	−	0.773852i	0.743071	−	0.669213i	$-0.233369\pi$
$740$	−0.0850248	−	0.0575165i	−0.00312557	−	0.00211435i
$741$		0			0
$742$	18.1089	−	8.06258i	0.664797	−	0.295987i
$743$	−5.42519	+	9.39670i	−0.199031	+	0.344732i	−0.948214	−	0.317631i	$-0.897113\pi$
$743$	−5.42519	+	9.39670i	−0.199031	+	0.344732i	0.749184	+	0.662362i	$0.230446\pi$
$744$		0			0
$745$	16.6976	−	13.0095i	0.611754	−	0.476631i
$746$	−29.1662	+	21.1905i	−1.06785	+	0.775838i
$747$		0			0
$748$	0.351305	+	1.08120i	0.0128450	+	0.0395328i
$749$	−16.3560	−	28.3294i	−0.597635	−	1.03513i
$750$		0			0
$751$	7.68498	−	13.3108i	0.280429	−	0.485717i	−0.691062	−	0.722796i	$-0.742857\pi$
$751$	7.68498	−	13.3108i	0.280429	−	0.485717i	0.971490	+	0.237079i	$0.0761900\pi$
$752$	−47.7618	−	10.1521i	−1.74169	−	0.370208i
$753$		0			0
$754$	32.2795	+	14.3718i	1.17555	+	0.523389i
$755$	4.73045	+	33.9905i	0.172159	+	1.23704i
$756$		0			0
$757$	−32.9738			−1.19845			−0.599226	−	0.800580i	$-0.704525\pi$
$757$	−32.9738			−1.19845			−0.599226	+	0.800580i	$0.704525\pi$
$758$	−3.65712	+	34.7952i	−0.132833	+	1.26382i
$759$		0			0
$760$	−1.04879	+	14.7141i	−0.0380438	+	0.533735i
$761$	−31.3838	−	6.67084i	−1.13766	−	0.241818i	−0.399691	−	0.916650i	$-0.630883\pi$
$761$	−31.3838	−	6.67084i	−1.13766	−	0.241818i	−0.737971	+	0.674832i	$0.764216\pi$
$762$		0			0
$763$	−38.2881	+	8.13839i	−1.38612	+	0.294630i
$764$	−0.257948	−	0.793883i	−0.00933224	−	0.0287217i
$765$		0			0
$766$	−0.00222259	+	0.00684042i	−8.03054e−5	+	0.000247155i
$767$	2.73566	−	26.0280i	0.0987788	−	0.939818i
$768$		0			0
$769$	−38.7820	+	17.2669i	−1.39852	+	0.622659i	−0.960999	−	0.276552i	$-0.910808\pi$
$769$	−38.7820	+	17.2669i	−1.39852	+	0.622659i	−0.437516	+	0.899211i	$0.644142\pi$
$770$	62.3085	−	15.4463i	2.24544	−	0.556645i
$771$		0			0
$772$	0.478663	+	0.213114i	0.0172275	+	0.00767016i
$773$	−0.355723	−	1.09480i	−0.0127945	−	0.0393773i	0.944455	−	0.328639i	$-0.106590\pi$
$773$	−0.355723	−	1.09480i	−0.0127945	−	0.0393773i	−0.957250	+	0.289262i	$0.906590\pi$
$774$		0			0
$775$	3.05181	+	1.12007i	0.109624	+	0.0402342i
$776$	−22.6549	−	39.2395i	−0.813265	−	1.40862i
$777$		0			0
$778$	−1.55860	−	14.8290i	−0.0558783	−	0.531647i
$779$	−0.924877	−	8.79962i	−0.0331372	−	0.315279i
$780$		0			0
$781$	−1.90522	+	18.1270i	−0.0681742	+	0.648634i
$782$	32.2302			1.15255
$783$		0			0
$784$	−9.78826	+	30.1252i	−0.349581	+	1.07590i
$785$	38.4660	−	29.9697i	1.37291	−	1.06966i
$786$		0			0
$787$	6.85895	+	7.61763i	0.244495	+	0.271539i	0.852885	−	0.522099i	$-0.174851\pi$
$787$	6.85895	+	7.61763i	0.244495	+	0.271539i	−0.608390	+	0.793638i	$0.708184\pi$
$788$	0.257947	+	0.286479i	0.00918899	+	0.0102054i
$789$		0			0
$790$	−5.24137	+	0.175975i	−0.186480	+	0.00626093i
$791$	−7.52535	+	23.1607i	−0.267571	+	0.823498i
$792$		0			0
$793$	22.1547			0.786737
$794$	0.887213	−	8.44126i	0.0314860	−	0.299569i
$795$		0			0
$796$	−0.0817007	−	0.777330i	−0.00289580	−	0.0275517i
$797$	−5.05457	−	48.0910i	−0.179042	−	1.70347i	−0.602961	−	0.797770i	$-0.706013\pi$
$797$	−5.05457	−	48.0910i	−0.179042	−	1.70347i	0.423919	−	0.905700i	$-0.360654\pi$
$798$		0			0
$799$	−28.8639	−	49.9937i	−1.02113	−	1.76865i
$800$	−1.22414	+	0.347455i	−0.0432798	+	0.0122844i
$801$		0			0
$802$	−8.79839	−	27.0787i	−0.310682	−	0.956181i
$803$	21.3481	+	9.50479i	0.753358	+	0.335417i
$804$		0			0
$805$	2.84719	−	39.9446i	0.100350	−	1.40786i
$806$	2.85627	−	1.27169i	0.100608	−	0.0447934i
$807$		0			0
$808$	1.63126	−	15.5204i	0.0573876	−	0.546007i
$809$	4.53484	−	13.9568i	0.159436	−	0.490695i	−0.839147	−	0.543905i	$-0.816945\pi$
$809$	4.53484	−	13.9568i	0.159436	−	0.490695i	0.998583	+	0.0532099i	$0.0169452\pi$
$810$		0			0
$811$	8.81534	+	27.1308i	0.309549	+	0.952692i	0.977941	+	0.208883i	$0.0669829\pi$
$811$	8.81534	+	27.1308i	0.309549	+	0.952692i	−0.668392	+	0.743809i	$0.733017\pi$
$812$	1.24201	−	0.263998i	0.0435862	−	0.00926452i
$813$		0			0
$814$	−7.45990	−	1.58565i	−0.261469	−	0.0555770i
$815$	−16.6136	+	19.7453i	−0.581948	+	0.691648i
$816$		0			0
$817$	−1.15854	+	11.0228i	−0.0405321	+	0.385638i
$818$	6.99144			0.244450
$819$		0			0
$820$	0.339326	−	0.164936i	0.0118498	−	0.00575980i
$821$	48.9692	+	21.8025i	1.70904	+	0.760912i	0.998351	+	0.0574003i	$0.0182811\pi$
$821$	48.9692	+	21.8025i	1.70904	+	0.760912i	0.710684	+	0.703511i	$0.248386\pi$
$822$		0			0
$823$	1.99694	+	0.424463i	0.0696090	+	0.0147958i	0.242585	−	0.970130i	$-0.422005\pi$
$823$	1.99694	+	0.424463i	0.0696090	+	0.0147958i	−0.172976	+	0.984926i	$0.555338\pi$
$824$	−0.871226	+	1.50901i	−0.0303506	+	0.0525688i
$825$		0			0
$826$	−21.3709	−	37.0155i	−0.743589	−	1.28793i
$827$	−13.2520	−	40.7853i	−0.460816	−	1.41824i	−0.864170	−	0.503201i	$-0.832156\pi$
$827$	−13.2520	−	40.7853i	−0.460816	−	1.41824i	0.403354	−	0.915044i	$-0.367844\pi$
$828$		0			0
$829$	30.3646	−	22.0611i	1.05460	−	0.766215i	0.0815222	−	0.996672i	$-0.474022\pi$
$829$	30.3646	−	22.0611i	1.05460	−	0.766215i	0.973083	+	0.230456i	$0.0740219\pi$
$830$	12.3163	+	33.9809i	0.427505	+	1.17949i
$831$		0			0
$832$	13.1349	−	22.7503i	0.455370	−	0.788723i
$833$	−34.2107	+	15.2316i	−1.18533	+	0.527744i
$834$		0			0
$835$	9.43515	−	0.316779i	0.326517	−	0.0109626i
$836$	−0.171523	−	0.527892i	−0.00593223	−	0.0182575i
$837$		0			0
$838$	5.63288	−	17.3362i	0.194585	−	0.598870i
$839$	0.521107	−	0.578748i	0.0179906	−	0.0199806i	−0.734082	−	0.679060i	$-0.762387\pi$
$839$	0.521107	−	0.578748i	0.0179906	−	0.0199806i	0.752073	+	0.659080i	$0.229054\pi$
$840$		0			0
$841$	16.7216	+	18.5713i	0.576608	+	0.640388i
$842$	22.9358	−	10.2117i	0.790419	−	0.351917i
$843$		0			0
$844$	0.0220798	−	0.210075i	0.000760017	−	0.00723108i
$845$	1.78067	−	3.33811i	0.0612568	−	0.114834i
$846$		0			0
$847$	50.7256	−	36.8543i	1.74295	−	1.26633i
$848$	−9.87324	+	10.9653i	−0.339049	+	0.376552i
$849$		0			0
$850$	−29.2564	−	18.3911i	−1.00349	−	0.630808i
$851$	−2.37881	+	4.12022i	−0.0815445	+	0.141239i
$852$		0			0
$853$	−1.93565	−	0.861806i	−0.0662753	−	0.0295077i	0.373331	−	0.927698i	$-0.378215\pi$
$853$	−1.93565	−	0.861806i	−0.0662753	−	0.0295077i	−0.439607	+	0.898190i	$0.644882\pi$
$854$	29.2718	−	21.2672i	1.00166	−	0.727750i
$855$		0			0
$856$	19.2657	+	13.9973i	0.658488	+	0.478419i
$857$	−2.95942	−	5.12586i	−0.101092	−	0.175096i	0.811043	−	0.584987i	$-0.198900\pi$
$857$	−2.95942	−	5.12586i	−0.101092	−	0.175096i	−0.912135	+	0.409890i	$0.865567\pi$
$858$		0			0
$859$	20.6752	+	22.9621i	0.705428	+	0.783457i	0.984230	−	0.176891i	$-0.0566041\pi$
$859$	20.6752	+	22.9621i	0.705428	+	0.783457i	−0.278802	+	0.960349i	$0.589937\pi$
$860$	−0.458720	+	0.113717i	−0.0156422	+	0.00387771i
$861$		0			0
$862$	41.2757	−	8.77342i	1.40586	−	0.298824i
$863$	−9.30552	+	28.6394i	−0.316764	+	0.974898i	0.658259	+	0.752792i	$0.271293\pi$
$863$	−9.30552	+	28.6394i	−0.316764	+	0.974898i	−0.975022	+	0.222106i	$0.928707\pi$
$864$		0			0
$865$	19.8574	−	9.65208i	0.675173	−	0.328180i
$866$	−27.6065	+	5.86794i	−0.938107	+	0.199401i
$867$		0			0
$868$	0.0561777	−	0.0973026i	0.00190679	−	0.00330266i
$869$	−7.83216	+	3.48710i	−0.265688	+	0.118292i
$870$		0			0
$871$	3.12925	+	1.39323i	0.106031	+	0.0472078i
$872$	23.0535	−	16.7494i	0.780692	−	0.567206i
$873$		0			0
$874$	−15.7362			−0.532286
$875$	−25.3775	+	34.6344i	−0.857916	+	1.17086i
$876$		0			0
$877$	−41.4649	−	8.81364i	−1.40017	−	0.297615i	−0.554883	−	0.831928i	$-0.687237\pi$
$877$	−41.4649	−	8.81364i	−1.40017	−	0.297615i	−0.845287	+	0.534313i	$0.820570\pi$
$878$	1.83531	+	17.4618i	0.0619386	+	0.589306i
$879$		0			0
$880$	−37.6941	+	29.3683i	−1.27067	+	0.990006i
$881$	−0.943118	−	0.685215i	−0.0317744	−	0.0230855i	0.571785	−	0.820404i	$-0.306251\pi$
$881$	−0.943118	−	0.685215i	−0.0317744	−	0.0230855i	−0.603559	+	0.797318i	$0.706251\pi$
$882$		0			0
$883$	−13.1391	−	9.54614i	−0.442167	−	0.321253i	0.344328	−	0.938849i	$-0.388107\pi$
$883$	−13.1391	−	9.54614i	−0.442167	−	0.321253i	−0.786495	+	0.617596i	$0.788107\pi$
$884$	−0.715330	+	0.152048i	−0.0240592	+	0.00511393i
$885$		0			0
$886$	−31.9097	−	6.78261i	−1.07203	−	0.227866i
$887$	19.4632	+	21.6161i	0.653511	+	0.725798i	0.975268	−	0.221025i	$-0.0709401\pi$
$887$	19.4632	+	21.6161i	0.653511	+	0.725798i	−0.321757	+	0.946822i	$0.604273\pi$
$888$		0			0
$889$	−38.2898	+	42.5252i	−1.28420	+	1.42625i
$890$	−6.71288	−	6.97013i	−0.225016	−	0.233639i
$891$		0			0
$892$	−0.573925	−	0.416981i	−0.0192164	−	0.0139615i
$893$	14.0926	+	24.4092i	0.471592	+	0.816822i
$894$		0			0
$895$	7.67167	−	1.90181i	0.256436	−	0.0635704i
$896$	−4.68885	−	44.6114i	−0.156644	−	1.49036i
$897$		0			0
$898$	−3.92679	+	4.36114i	−0.131039	+	0.145533i
$899$	4.77733			0.159333
$900$		0			0
$901$	−17.4445			−0.581160
$902$	18.7562	−	20.8309i	0.624514	−	0.693593i
$903$		0			0
$904$	−1.85310	−	17.6311i	−0.0616333	−	0.586401i
$905$	18.0515	+	28.9750i	0.600051	+	0.963162i
$906$		0			0
$907$	−2.44109	−	4.22810i	−0.0810552	−	0.140392i	0.822648	−	0.568551i	$-0.192496\pi$
$907$	−2.44109	−	4.22810i	−0.0810552	−	0.140392i	−0.903703	+	0.428159i	$0.859162\pi$
$908$	0.262519	+	0.190731i	0.00871200	+	0.00632964i
$909$		0			0
$910$	5.69216	+	40.9009i	0.188693	+	1.35585i
$911$	34.1968	−	37.9794i	1.13299	−	1.25831i	0.170989	−	0.985273i	$-0.445304\pi$
$911$	34.1968	−	37.9794i	1.13299	−	1.25831i	0.962002	−	0.273042i	$-0.0880297\pi$
$912$		0			0
$913$	39.5375	+	43.9109i	1.30850	+	1.45324i
$914$	−25.3592	−	5.39026i	−0.838807	−	0.178294i
$915$		0			0
$916$	−0.454382	+	0.0965820i	−0.0150132	+	0.00319116i
$917$	41.8408	+	30.3991i	1.38170	+	1.00387i
$918$		0			0
$919$	−14.6917	−	10.6741i	−0.484634	−	0.352107i	0.318483	−	0.947928i	$-0.396827\pi$
$919$	−14.6917	−	10.6741i	−0.484634	−	0.352107i	−0.803117	+	0.595822i	$0.796827\pi$
$920$	9.93397	+	27.4080i	0.327513	+	0.903614i
$921$		0			0
$922$	−3.51758	−	33.4675i	−0.115845	−	1.10219i
$923$	−11.4687	−	2.43776i	−0.377498	−	0.0802397i
$924$		0			0
$925$	4.51038	−	2.38267i	0.148300	−	0.0783418i
$926$	5.11819			0.168194
$927$		0			0
$928$	−1.51286	+	1.09916i	−0.0496622	+	0.0360817i
$929$	−22.5716	−	10.0495i	−0.740551	−	0.329715i	0.00155345	−	0.999999i	$-0.499506\pi$
$929$	−22.5716	−	10.0495i	−0.740551	−	0.329715i	−0.742104	+	0.670284i	$0.766172\pi$
$930$		0			0
$931$	16.7032	−	7.43675i	0.547425	−	0.243729i
$932$	0.278515	−	0.482401i	0.00912305	−	0.0158016i
$933$		0			0
$934$	22.2002	−	4.71879i	0.726412	−	0.154404i
$935$	−55.6215	−	9.88472i	−1.81902	−	0.323265i
$936$		0			0
$937$	−0.780220	+	2.40127i	−0.0254887	+	0.0784461i	−0.962992	−	0.269531i	$-0.913131\pi$
$937$	−0.780220	+	2.40127i	−0.0254887	+	0.0784461i	0.937503	+	0.347977i	$0.113131\pi$
$938$	5.47193	−	1.16309i	0.178665	−	0.0379764i
$939$		0			0
$940$	−0.773762	+	0.919619i	−0.0252373	+	0.0299947i
$941$	−2.79133	−	3.10008i	−0.0909947	−	0.101060i	0.695928	−	0.718112i	$-0.254993\pi$
$941$	−2.79133	−	3.10008i	−0.0909947	−	0.101060i	−0.786922	+	0.617052i	$0.788327\pi$
$942$		0			0
$943$	−8.74311	−	15.1435i	−0.284715	−	0.493140i
$944$	25.7394	+	18.7008i	0.837747	+	0.608659i
$945$		0			0
$946$	−28.4066	+	20.6386i	−0.923577	+	0.671018i
$947$	−50.0397	−	22.2791i	−1.62607	−	0.723974i	−0.627564	−	0.778565i	$-0.715948\pi$
$947$	−50.0397	−	22.2791i	−1.62607	−	0.723974i	−0.998509	+	0.0545912i	$0.982614\pi$
$948$		0			0
$949$	−7.51623	+	13.0185i	−0.243987	+	0.422598i
$950$	14.2843	+	8.97934i	0.463444	+	0.291328i
$951$		0			0
$952$	34.7212	−	38.5618i	1.12532	−	1.24980i
$953$	6.88510	−	5.00232i	0.223030	−	0.162041i	−0.470659	−	0.882315i	$-0.655984\pi$
$953$	6.88510	−	5.00232i	0.223030	−	0.162041i	0.693690	+	0.720274i	$0.255984\pi$
$954$		0			0
$955$	40.8405	+	7.25793i	1.32157	+	0.234861i
$956$	0.0753446	−	0.716856i	0.00243682	−	0.0231848i
$957$		0			0
$958$	−21.9982	+	9.79425i	−0.710731	+	0.316438i
$959$	23.4675	+	26.0633i	0.757805	+	0.841627i
$960$		0			0
$961$	−20.4602	+	22.7233i	−0.660006	+	0.733011i
$962$	1.51604	−	4.66590i	0.0488792	−	0.150435i
$963$		0			0
$964$	−0.0407017	−	0.125267i	−0.00131091	−	0.00403458i
$965$	−20.5391	+	16.0024i	−0.661176	+	0.515137i
$966$		0			0
$967$	−43.5021	+	19.3684i	−1.39893	+	0.622845i	−0.961097	−	0.276211i	$-0.910921\pi$
$967$	−43.5021	+	19.3684i	−1.39893	+	0.622845i	−0.437835	+	0.899056i	$0.644254\pi$
$968$	−22.8223	+	39.5294i	−0.733537	+	1.27052i
$969$		0			0
$970$	−51.7948	+	1.73897i	−1.66303	+	0.0558351i
$971$	−4.89465	+	3.55617i	−0.157077	+	0.114123i	−0.663547	−	0.748134i	$-0.730950\pi$
$971$	−4.89465	+	3.55617i	−0.157077	+	0.114123i	0.506471	+	0.862257i	$0.330950\pi$
$972$		0			0
$973$	−13.9232	−	42.8512i	−0.446358	−	1.37375i
$974$	−7.11380	−	12.3215i	−0.227941	−	0.394805i
$975$		0			0
$976$	−13.4664	+	23.3244i	−0.431048	+	0.746597i
$977$	−7.13278	−	1.51612i	−0.228198	−	0.0485049i	0.0923934	−	0.995723i	$-0.470548\pi$
$977$	−7.13278	−	1.51612i	−0.228198	−	0.0485049i	−0.320591	+	0.947218i	$0.603882\pi$
$978$		0			0
$979$	−14.4522	−	6.43455i	−0.461895	−	0.205649i
$980$	0.540826	+	0.561552i	0.0172761	+	0.0179381i
$981$		0			0
$982$	16.8113			0.536469
$983$	−2.52668	+	24.0397i	−0.0805885	+	0.766748i	0.877365	+	0.479824i	$0.159299\pi$
$983$	−2.52668	+	24.0397i	−0.0805885	+	0.766748i	−0.957953	+	0.286924i	$0.907367\pi$
$984$		0			0
$985$	−18.5936	+	4.60934i	−0.592440	+	0.146866i
$986$	−49.6735	−	10.5584i	−1.58193	−	0.336249i
$987$		0			0
$988$	0.349256	−	0.0742367i	0.0111113	−	0.00236178i
$989$	6.76869	+	20.8319i	0.215232	+	0.662415i
$990$		0			0
$991$	15.5428	−	47.8359i	0.493734	−	1.51956i	−0.325186	−	0.945650i	$-0.605427\pi$
$991$	15.5428	−	47.8359i	0.493734	−	1.51956i	0.818920	−	0.573907i	$-0.194573\pi$
$992$	−0.0172961	+	0.164561i	−0.000549152	+	0.00522483i
$993$		0			0
$994$	−17.4931	+	7.78845i	−0.554849	+	0.247035i
$995$	35.9926	+	14.5983i	1.14104	+	0.462798i
$996$		0			0
$997$	−35.4434	−	15.7804i	−1.12250	−	0.499771i	−0.240328	−	0.970692i	$-0.577255\pi$
$997$	−35.4434	−	15.7804i	−1.12250	−	0.499771i	−0.882176	+	0.470921i	$0.843922\pi$
$998$	11.2633	+	34.6649i	0.356534	+	1.09730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.631.7		224
3.2	odd	2		225.2.q.a.31.22	✓	224
9.2	odd	6		225.2.q.a.106.7	yes	224
9.7	even	3	inner	675.2.r.a.181.22		224
25.21	even	5	inner	675.2.r.a.496.22		224
75.71	odd	10		225.2.q.a.121.7	yes	224
225.146	odd	30		225.2.q.a.196.22	yes	224
225.196	even	15	inner	675.2.r.a.46.7		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.22	✓	224	3.2	odd	2
225.2.q.a.106.7	yes	224	9.2	odd	6
225.2.q.a.121.7	yes	224	75.71	odd	10
225.2.q.a.196.22	yes	224	225.146	odd	30
675.2.r.a.46.7		224	225.196	even	15	inner
675.2.r.a.181.22		224	9.7	even	3	inner
675.2.r.a.496.22		224	25.21	even	5	inner
675.2.r.a.631.7		224	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.956880 + 1.06272i) q^{2} +(-0.00470356 - 0.0447514i) q^{4} +(2.07212 + 0.840433i) q^{5} +(1.92019 + 3.32586i) q^{7} +(-2.26178 - 1.64328i) q^{8} +O(q^{10})\)	\(q+(-0.956880 + 1.06272i) q^{2} +(-0.00470356 - 0.0447514i) q^{4} +(2.07212 + 0.840433i) q^{5} +(1.92019 + 3.32586i) q^{7} +(-2.26178 - 1.64328i) q^{8} +(-2.87591 + 1.39789i) q^{10} +(-3.49787 + 3.88478i) q^{11} +(-2.25011 - 2.49900i) q^{13} +(-5.37185 - 1.14182i) q^{14} +(3.99864 - 0.849937i) q^{16} +(3.90998 + 2.84077i) q^{17} +(-1.90903 - 1.38699i) q^{19} +(0.0278642 - 0.0966831i) q^{20} +(-0.781401 - 7.43453i) q^{22} +(-4.56147 - 0.969570i) q^{23} +(3.58734 + 3.48295i) q^{25} +4.80884 q^{26} +(0.139805 - 0.101574i) q^{28} +(6.71254 + 2.98862i) q^{29} +(0.593962 - 0.264449i) q^{31} +(-0.127249 + 0.220402i) q^{32} +(-6.76033 + 1.43695i) q^{34} +(1.18369 + 8.50536i) q^{35} +(0.315262 - 0.970276i) q^{37} +(3.30069 - 0.701584i) q^{38} +(-3.30561 - 5.30596i) q^{40} +(2.50903 + 2.78656i) q^{41} +(-2.34851 - 4.06773i) q^{43} +(0.190302 + 0.138262i) q^{44} +(5.39516 - 3.91981i) q^{46} +(-10.9118 - 4.85827i) q^{47} +(-3.87423 + 6.71036i) q^{49} +(-7.13407 + 0.479583i) q^{50} +(-0.101250 + 0.112450i) q^{52} +(-2.92011 + 2.12158i) q^{53} +(-10.5129 + 5.10999i) q^{55} +(1.12228 - 10.6778i) q^{56} +(-9.59917 + 4.27383i) q^{58} +(5.20768 + 5.78372i) q^{59} +(-4.40843 + 4.89605i) q^{61} +(-0.287314 + 0.884263i) q^{62} +(2.41404 + 7.42965i) q^{64} +(-2.56225 - 7.06930i) q^{65} +(-0.930565 + 0.414314i) q^{67} +(0.108737 - 0.188339i) q^{68} +(-10.1715 - 6.88068i) q^{70} +(2.82082 - 2.04945i) q^{71} +(-1.38140 - 4.25150i) q^{73} +(0.729467 + 1.26347i) q^{74} +(-0.0530904 + 0.0919553i) q^{76} +(-19.6368 - 4.17393i) q^{77} +(1.49826 + 0.667070i) q^{79} +(8.99997 + 1.59942i) q^{80} -5.36219 q^{82} +(1.18152 - 11.2414i) q^{83} +(5.71446 + 9.17248i) q^{85} +(6.57011 + 1.39652i) q^{86} +(14.2952 - 3.03854i) q^{88} +(0.935178 + 2.87818i) q^{89} +(3.99070 - 12.2821i) q^{91} +(-0.0219345 + 0.208692i) q^{92} +(15.6043 - 6.94749i) q^{94} +(-2.79006 - 4.47841i) q^{95} +(14.8057 + 6.59193i) q^{97} +(-3.42408 - 10.5382i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more