LMFDB - Embedded newform 810.2.s.a.773.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			773.3
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.28326 - 1.83119i) q^{5} +(2.33095 + 1.63215i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.11878 + 1.93606i) q^{10} +(-0.754583 + 2.07320i) q^{11} +(-0.310645 - 3.55068i) q^{13} +(-2.17983 - 1.82909i) q^{14} +(0.939693 + 0.342020i) q^{16} +(1.90217 - 0.509686i) q^{17} +(3.47249 - 2.00484i) q^{19} +(-0.945782 - 2.02620i) q^{20} +(0.932403 - 1.99954i) q^{22} +(2.00124 + 2.85807i) q^{23} +(-1.70649 + 4.69978i) q^{25} +3.56425i q^{26} +(2.01212 + 2.01212i) q^{28} +(5.57992 - 4.68211i) q^{29} +(-1.26447 + 7.17115i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-1.93936 + 0.341961i) q^{34} +(-0.00244633 - 6.36288i) q^{35} +(-2.37558 - 8.86580i) q^{37} +(-3.63401 + 1.69457i) q^{38} +(0.765588 + 2.10092i) q^{40} +(3.83276 - 4.56771i) q^{41} +(-2.90599 - 6.23192i) q^{43} +(-1.10313 + 1.91067i) q^{44} +(-1.74453 - 3.02161i) q^{46} +(-0.930319 + 1.32863i) q^{47} +(0.375281 + 1.03108i) q^{49} +(2.10961 - 4.53316i) q^{50} +(0.310645 - 3.55068i) q^{52} +(9.27688 - 9.27688i) q^{53} +(4.76474 - 1.27867i) q^{55} +(-1.82909 - 2.17983i) q^{56} +(-5.96676 + 4.17797i) q^{58} +(-0.501506 + 0.182533i) q^{59} +(1.48752 + 8.43613i) q^{61} +(1.88466 - 7.03365i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-6.10332 + 5.12530i) q^{65} +(12.8796 - 1.12682i) q^{67} +(1.96178 - 0.171634i) q^{68} +(-0.552124 + 6.33888i) q^{70} +(10.9618 + 6.32882i) q^{71} +(4.15955 - 15.5236i) q^{73} +(1.59384 + 9.03911i) q^{74} +(3.76787 - 1.37139i) q^{76} +(-5.14267 + 3.60094i) q^{77} +(-0.411239 - 0.490096i) q^{79} +(-0.579567 - 2.15965i) q^{80} +(-4.21628 + 4.21628i) q^{82} +(0.521651 - 5.96250i) q^{83} +(-3.37431 - 2.82918i) q^{85} +(2.35178 + 6.46147i) q^{86} +(1.26545 - 1.80726i) q^{88} +(2.76440 + 4.78809i) q^{89} +(5.07115 - 8.78349i) q^{91} +(1.47454 + 3.16216i) q^{92} +(1.04258 - 1.24250i) q^{94} +(-8.12735 - 3.78604i) q^{95} +(-4.90756 + 2.28843i) q^{97} +(-0.283989 - 1.05986i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−1.28326	−	1.83119i	−0.573891	−	0.818931i
$5$	−1.28326	−	1.83119i	−0.573891	−	0.818931i
$6$		0			0
$7$	2.33095	+	1.63215i	0.881017	+	0.616895i	0.924089	−	0.382177i	$-0.124826\pi$
$7$	2.33095	+	1.63215i	0.881017	+	0.616895i	−0.0430721	+	0.999072i	$0.513715\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	1.11878	+	1.93606i	0.353789	+	0.612236i
$11$	−0.754583	+	2.07320i	−0.227515	+	0.625093i	−0.999950	−	0.0100010i	$-0.996817\pi$
$11$	−0.754583	+	2.07320i	−0.227515	+	0.625093i	0.772435	+	0.635094i	$0.219039\pi$
$12$		0			0
$13$	−0.310645	−	3.55068i	−0.0861573	−	0.984782i	−0.909078	−	0.416626i	$-0.863212\pi$
$13$	−0.310645	−	3.55068i	−0.0861573	−	0.984782i	0.822921	−	0.568156i	$-0.192343\pi$
$14$	−2.17983	−	1.82909i	−0.582584	−	0.488846i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	1.90217	−	0.509686i	0.461345	−	0.123617i	−0.0206580	−	0.999787i	$-0.506576\pi$
$17$	1.90217	−	0.509686i	0.461345	−	0.123617i	0.482003	+	0.876170i	$0.339909\pi$
$18$		0			0
$19$	3.47249	−	2.00484i	0.796644	−	0.459942i	−0.0456525	−	0.998957i	$-0.514537\pi$
$19$	3.47249	−	2.00484i	0.796644	−	0.459942i	0.842296	+	0.539015i	$0.181203\pi$
$20$	−0.945782	−	2.02620i	−0.211483	−	0.453073i
$21$		0			0
$22$	0.932403	−	1.99954i	0.198789	−	0.426304i
$23$	2.00124	+	2.85807i	0.417287	+	0.595948i	0.971678	−	0.236309i	$-0.0759376\pi$
$23$	2.00124	+	2.85807i	0.417287	+	0.595948i	−0.554391	+	0.832256i	$0.687049\pi$
$24$		0			0
$25$	−1.70649	+	4.69978i	−0.341297	+	0.939955i
$26$			3.56425i			0.699006i
$27$		0			0
$28$	2.01212	+	2.01212i	0.380255	+	0.380255i
$29$	5.57992	−	4.68211i	1.03616	−	0.869445i	0.0445931	−	0.999005i	$-0.485801\pi$
$29$	5.57992	−	4.68211i	1.03616	−	0.869445i	0.991572	+	0.129560i	$0.0413564\pi$
$30$		0			0
$31$	−1.26447	+	7.17115i	−0.227105	+	1.28798i	0.631515	+	0.775364i	$0.282433\pi$
$31$	−1.26447	+	7.17115i	−0.227105	+	1.28798i	−0.858620	+	0.512613i	$0.828678\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	−1.93936	+	0.341961i	−0.332597	+	0.0586459i
$35$	−0.00244633	−	6.36288i	−0.000413506	−	1.07552i
$36$		0			0
$37$	−2.37558	−	8.86580i	−0.390544	−	1.45753i	−0.829240	−	0.558893i	$-0.811226\pi$
$37$	−2.37558	−	8.86580i	−0.390544	−	1.45753i	0.438696	−	0.898636i	$-0.355441\pi$
$38$	−3.63401	+	1.69457i	−0.589514	+	0.274895i
$39$		0			0
$40$	0.765588	+	2.10092i	0.121050	+	0.332185i
$41$	3.83276	−	4.56771i	0.598577	−	0.713357i	−0.378653	−	0.925539i	$-0.623613\pi$
$41$	3.83276	−	4.56771i	0.598577	−	0.713357i	0.977230	+	0.212182i	$0.0680570\pi$
$42$		0			0
$43$	−2.90599	−	6.23192i	−0.443159	−	0.950358i	−0.993330	−	0.115306i	$-0.963215\pi$
$43$	−2.90599	−	6.23192i	−0.443159	−	0.950358i	0.550171	−	0.835052i	$-0.314563\pi$
$44$	−1.10313	+	1.91067i	−0.166303	+	0.288045i
$45$		0			0
$46$	−1.74453	−	3.02161i	−0.257216	−	0.445512i
$47$	−0.930319	+	1.32863i	−0.135701	+	0.193801i	−0.881251	−	0.472649i	$-0.843298\pi$
$47$	−0.930319	+	1.32863i	−0.135701	+	0.193801i	0.745550	+	0.666450i	$0.232187\pi$
$48$		0			0
$49$	0.375281	+	1.03108i	0.0536116	+	0.147297i
$50$	2.10961	−	4.53316i	0.298343	−	0.641086i
$51$		0			0
$52$	0.310645	−	3.55068i	0.0430786	−	0.492391i
$53$	9.27688	−	9.27688i	1.27428	−	1.27428i	0.330457	−	0.943821i	$-0.392797\pi$
$53$	9.27688	−	9.27688i	1.27428	−	1.27428i	0.943821	−	0.330457i	$-0.107203\pi$
$54$		0			0
$55$	4.76474	−	1.27867i	0.642478	−	0.172416i
$56$	−1.82909	−	2.17983i	−0.244423	−	0.291292i
$57$		0			0
$58$	−5.96676	+	4.17797i	−0.783474	+	0.548594i
$59$	−0.501506	+	0.182533i	−0.0652906	+	0.0237638i	−0.374459	−	0.927243i	$-0.622172\pi$
$59$	−0.501506	+	0.182533i	−0.0652906	+	0.0237638i	0.309168	+	0.951007i	$0.399949\pi$
$60$		0			0
$61$	1.48752	+	8.43613i	0.190457	+	1.08014i	0.918741	+	0.394860i	$0.129207\pi$
$61$	1.48752	+	8.43613i	0.190457	+	1.08014i	−0.728284	+	0.685275i	$0.759682\pi$
$62$	1.88466	−	7.03365i	0.239352	−	0.893275i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−6.10332	+	5.12530i	−0.757024	+	0.635715i
$66$		0			0
$67$	12.8796	−	1.12682i	1.57349	−	0.137663i	0.733282	−	0.679925i	$-0.237987\pi$
$67$	12.8796	−	1.12682i	1.57349	−	0.137663i	0.840210	+	0.542262i	$0.182432\pi$
$68$	1.96178	−	0.171634i	0.237901	−	0.0208136i
$69$		0			0
$70$	−0.552124	+	6.33888i	−0.0659915	+	0.757641i
$71$	10.9618	+	6.32882i	1.30093	+	0.751092i	0.980564	−	0.196202i	$-0.0628607\pi$
$71$	10.9618	+	6.32882i	1.30093	+	0.751092i	0.320366	+	0.947294i	$0.396194\pi$
$72$		0			0
$73$	4.15955	−	15.5236i	0.486838	−	1.81690i	−0.0847994	−	0.996398i	$-0.527025\pi$
$73$	4.15955	−	15.5236i	0.486838	−	1.81690i	0.571637	−	0.820506i	$-0.306308\pi$
$74$	1.59384	+	9.03911i	0.185280	+	1.05078i
$75$		0			0
$76$	3.76787	−	1.37139i	0.432204	−	0.157310i
$77$	−5.14267	+	3.60094i	−0.586062	+	0.410365i
$78$		0			0
$79$	−0.411239	−	0.490096i	−0.0462680	−	0.0551401i	0.742414	−	0.669941i	$-0.233681\pi$
$79$	−0.411239	−	0.490096i	−0.0462680	−	0.0551401i	−0.788682	+	0.614801i	$0.789236\pi$
$80$	−0.579567	−	2.15965i	−0.0647976	−	0.241457i
$81$		0			0
$82$	−4.21628	+	4.21628i	−0.465610	+	0.465610i
$83$	0.521651	−	5.96250i	0.0572586	−	0.654469i	−0.912286	−	0.409554i	$-0.865684\pi$
$83$	0.521651	−	5.96250i	0.0572586	−	0.654469i	0.969545	−	0.244915i	$-0.0787601\pi$
$84$		0			0
$85$	−3.37431	−	2.82918i	−0.365996	−	0.306867i
$86$	2.35178	+	6.46147i	0.253599	+	0.696759i
$87$		0			0
$88$	1.26545	−	1.80726i	0.134898	−	0.192654i
$89$	2.76440	+	4.78809i	0.293026	+	0.507536i	0.974524	−	0.224284i	$-0.0720043\pi$
$89$	2.76440	+	4.78809i	0.293026	+	0.507536i	−0.681498	+	0.731820i	$0.738671\pi$
$90$		0			0
$91$	5.07115	−	8.78349i	0.531601	−	0.920760i
$92$	1.47454	+	3.16216i	0.153731	+	0.329678i
$93$		0			0
$94$	1.04258	−	1.24250i	0.107534	−	0.128154i
$95$	−8.12735	−	3.78604i	−0.833848	−	0.388440i
$96$		0			0
$97$	−4.90756	+	2.28843i	−0.498287	+	0.232355i	−0.655480	−	0.755213i	$-0.727533\pi$
$97$	−4.90756	+	2.28843i	−0.498287	+	0.232355i	0.157193	+	0.987568i	$0.449756\pi$
$98$	−0.283989	−	1.05986i	−0.0286872	−	0.107062i
$99$		0			0
$100$	−2.49667	+	4.33205i	−0.249667	+	0.433205i
$101$	−6.84891	+	1.20765i	−0.681492	+	0.120165i	−0.503669	−	0.863897i	$-0.668017\pi$
$101$	−6.84891	+	1.20765i	−0.681492	+	0.120165i	−0.177824	+	0.984062i	$0.556906\pi$
$102$		0			0
$103$	3.26681	+	1.52334i	0.321888	+	0.150099i	0.576845	−	0.816853i	$-0.304284\pi$
$103$	3.26681	+	1.52334i	0.321888	+	0.150099i	−0.254957	+	0.966952i	$0.582061\pi$
$104$	−0.618925	+	3.51010i	−0.0606906	+	0.344193i
$105$		0			0
$106$	−10.0501	+	8.43305i	−0.976154	+	0.819090i
$107$	5.47880	+	5.47880i	0.529656	+	0.529656i	0.920470	−	0.390814i	$-0.127806\pi$
$107$	5.47880	+	5.47880i	0.529656	+	0.529656i	−0.390814	+	0.920470i	$0.627806\pi$
$108$		0			0
$109$			1.65947i			0.158948i	0.996837	+	0.0794741i	$0.0253241\pi$
$109$			1.65947i			0.158948i	−0.996837	+	0.0794741i	$0.974676\pi$
$110$	−4.85805	+	0.858532i	−0.463197	+	0.0818578i
$111$		0			0
$112$	1.63215	+	2.33095i	0.154224	+	0.220254i
$113$	1.72136	−	3.69147i	0.161932	−	0.347264i	−0.808554	−	0.588422i	$-0.799749\pi$
$113$	1.72136	−	3.69147i	0.161932	−	0.347264i	0.970486	+	0.241158i	$0.0775272\pi$
$114$		0			0
$115$	2.66554	−	7.33228i	0.248563	−	0.683739i
$116$	6.30819	−	3.64203i	0.585700	−	0.338154i
$117$		0			0
$118$	0.515507	−	0.138130i	0.0474562	−	0.0127159i
$119$	5.26576	+	1.91658i	0.482711	+	0.175693i
$120$		0			0
$121$	4.69773	+	3.94186i	0.427066	+	0.358351i
$122$	−0.746600	−	8.53367i	−0.0675940	−	0.772603i
$123$		0			0
$124$	−2.49051	+	6.84263i	−0.223655	+	0.614486i
$125$	10.7960	−	2.90614i	0.965627	−	0.259933i
$126$		0			0
$127$	−20.7723	−	5.56593i	−1.84325	−	0.493896i	−0.844138	−	0.536126i	$-0.819887\pi$
$127$	−20.7723	−	5.56593i	−1.84325	−	0.493896i	−0.999108	+	0.0422296i	$0.986554\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	6.52680	−	4.57385i	0.572438	−	0.401154i
$131$	−8.94717	−	1.57763i	−0.781718	−	0.137838i	−0.231473	−	0.972841i	$-0.574355\pi$
$131$	−8.94717	−	1.57763i	−0.781718	−	0.137838i	−0.550245	+	0.835003i	$0.685466\pi$
$132$		0			0
$133$	11.3664	+	0.994432i	0.985593	+	0.0862282i
$134$	−12.9288			−1.11688
$135$		0			0
$136$	−1.96928			−0.168864
$137$	−12.7789	−	1.11801i	−1.09178	−	0.0955182i	−0.472984	−	0.881071i	$-0.656823\pi$
$137$	−12.7789	−	1.11801i	−1.09178	−	0.0955182i	−0.618794	+	0.785553i	$0.712379\pi$
$138$		0			0
$139$	3.77558	+	0.665737i	0.320241	+	0.0564671i	0.331458	−	0.943470i	$-0.392460\pi$
$139$	3.77558	+	0.665737i	0.320241	+	0.0564671i	−0.0112172	+	0.999937i	$0.503571\pi$
$140$	1.10249	−	6.26664i	0.0931777	−	0.529628i
$141$		0			0
$142$	−10.3685	−	7.26012i	−0.870107	−	0.609256i
$143$	7.59568	+	2.03526i	0.635183	+	0.170197i
$144$		0			0
$145$	−15.7343	−	4.20951i	−1.30666	−	0.349581i
$146$	−5.49669	+	15.1020i	−0.454909	+	1.24985i
$147$		0			0
$148$	−0.799964	−	9.14363i	−0.0657566	−	0.751601i
$149$	3.98138	+	3.34078i	0.326168	+	0.273687i	0.791136	−	0.611640i	$-0.209490\pi$
$149$	3.98138	+	3.34078i	0.326168	+	0.273687i	−0.464969	+	0.885327i	$0.653934\pi$
$150$		0			0
$151$	3.51053	+	1.27773i	0.285683	+	0.103980i	0.480887	−	0.876783i	$-0.340315\pi$
$151$	3.51053	+	1.27773i	0.285683	+	0.103980i	−0.195204	+	0.980763i	$0.562537\pi$
$152$	−3.87306	+	1.03778i	−0.314147	+	0.0841753i
$153$		0			0
$154$	5.43694	−	3.13902i	0.438121	−	0.252949i
$155$	14.7543	−	6.88697i	1.18510	−	0.553175i
$156$		0			0
$157$	−6.16617	+	13.2234i	−0.492114	+	1.05534i	0.490800	+	0.871272i	$0.336705\pi$
$157$	−6.16617	+	13.2234i	−0.492114	+	1.05534i	−0.982913	+	0.184069i	$0.941073\pi$
$158$	0.366960	+	0.524073i	0.0291937	+	0.0416930i
$159$		0			0
$160$	0.389136	+	2.20195i	0.0307639	+	0.174079i
$161$			9.92833i			0.782462i
$162$		0			0
$163$	−1.38626	−	1.38626i	−0.108581	−	0.108581i	0.650729	−	0.759310i	$-0.274463\pi$
$163$	−1.38626	−	1.38626i	−0.108581	−	0.108581i	−0.759310	+	0.650729i	$0.774463\pi$
$164$	4.56771	−	3.83276i	0.356678	−	0.299289i
$165$		0			0
$166$	−1.03933	+	5.89434i	−0.0806678	+	0.457490i
$167$	−11.6010	−	5.40961i	−0.897709	−	0.418609i	−0.0817061	−	0.996656i	$-0.526037\pi$
$167$	−11.6010	−	5.40961i	−0.897709	−	0.418609i	−0.816003	+	0.578048i	$0.803815\pi$
$168$		0			0
$169$	0.291651	−	0.0514260i	0.0224347	−	0.00395584i
$170$	3.11490	+	3.11250i	0.238902	+	0.238718i
$171$		0			0
$172$	−1.77968	−	6.64186i	−0.135699	−	0.506437i
$173$	−23.2620	+	10.8472i	−1.76857	+	0.824700i	−0.791693	+	0.610920i	$0.790800\pi$
$173$	−23.2620	+	10.8472i	−1.76857	+	0.824700i	−0.976882	+	0.213780i	$0.931422\pi$
$174$		0			0
$175$	−11.6485	+	8.16971i	−0.880542	+	0.617572i
$176$	−1.41815	+	1.69009i	−0.106897	+	0.127395i
$177$		0			0
$178$	−2.33658	−	5.01080i	−0.175134	−	0.375576i
$179$	−4.88174	+	8.45543i	−0.364879	+	0.631988i	−0.988757	−	0.149533i	$-0.952223\pi$
$179$	−4.88174	+	8.45543i	−0.364879	+	0.631988i	0.623878	+	0.781522i	$0.285556\pi$
$180$		0			0
$181$	9.25156	+	16.0242i	0.687663	+	1.19107i	0.972592	+	0.232518i	$0.0746966\pi$
$181$	9.25156	+	16.0242i	0.687663	+	1.19107i	−0.284929	+	0.958549i	$0.591970\pi$
$182$	−5.81738	+	8.30809i	−0.431213	+	0.615836i
$183$		0			0
$184$	−1.19333	−	3.27864i	−0.0879732	−	0.241704i
$185$	−13.1864	+	15.7273i	−0.969487	+	1.15629i
$186$		0			0
$187$	−0.378667	+	4.32819i	−0.0276909	+	0.316508i
$188$	−1.14690	+	1.14690i	−0.0836463	+	0.0836463i
$189$		0			0
$190$	7.76644	+	4.47998i	0.563437	+	0.325012i
$191$	−9.22039	−	10.9884i	−0.667164	−	0.795095i	0.321231	−	0.947001i	$-0.395903\pi$
$191$	−9.22039	−	10.9884i	−0.667164	−	0.795095i	−0.988395	+	0.151906i	$0.951459\pi$
$192$		0			0
$193$	3.45892	−	2.42196i	0.248979	−	0.174337i	−0.442425	−	0.896806i	$-0.645882\pi$
$193$	3.45892	−	2.42196i	0.248979	−	0.174337i	0.691403	+	0.722469i	$0.256993\pi$
$194$	5.08833	−	1.85200i	0.365321	−	0.132966i
$195$		0			0
$196$	0.190535	+	1.08058i	0.0136097	+	0.0771843i
$197$	−4.93329	+	18.4113i	−0.351482	+	1.31175i	0.533372	+	0.845881i	$0.320925\pi$
$197$	−4.93329	+	18.4113i	−0.351482	+	1.31175i	−0.884854	+	0.465868i	$0.845742\pi$
$198$		0			0
$199$	−5.80047	−	3.34890i	−0.411184	−	0.237397i	0.280114	−	0.959967i	$-0.409628\pi$
$199$	−5.80047	−	3.34890i	−0.411184	−	0.237397i	−0.691298	+	0.722569i	$0.742961\pi$
$200$	2.86473	−	4.09796i	0.202567	−	0.289770i
$201$		0			0
$202$	6.92810	−	0.606131i	0.487460	−	0.0426472i
$203$	20.6484	−	1.80650i	1.44923	−	0.126792i
$204$		0			0
$205$	−13.2828	−	1.15695i	−0.927708	−	0.0808046i
$206$	−3.12161	−	1.80226i	−0.217493	−	0.125570i
$207$		0			0
$208$	0.922495	−	3.44280i	0.0639635	−	0.238715i
$209$	1.53616	+	8.71198i	0.106258	+	0.602621i
$210$		0			0
$211$	10.6327	−	3.86999i	0.731986	−	0.266421i	0.0509809	−	0.998700i	$-0.483765\pi$
$211$	10.6327	−	3.86999i	0.731986	−	0.266421i	0.681005	+	0.732278i	$0.261543\pi$
$212$	10.7469	−	7.52503i	0.738097	−	0.516821i
$213$		0			0
$214$	−4.98045	−	5.93546i	−0.340456	−	0.405740i
$215$	−7.68266	+	13.3186i	−0.523953	+	0.908319i
$216$		0			0
$217$	−14.6518	+	14.6518i	−0.994629	+	0.994629i
$218$	0.144632	−	1.65315i	0.00979573	−	0.111966i
$219$		0			0
$220$	4.91439	−	0.431858i	0.331328	−	0.0291158i
$221$	−2.40063	−	6.59569i	−0.161484	−	0.443674i
$222$		0			0
$223$	−2.48741	+	3.55238i	−0.166569	+	0.237885i	−0.893755	−	0.448555i	$-0.851939\pi$
$223$	−2.48741	+	3.55238i	−0.166569	+	0.237885i	0.727186	+	0.686440i	$0.240828\pi$
$224$	−1.42278	−	2.46433i	−0.0950637	−	0.164655i
$225$		0			0
$226$	−2.03654	+	3.52739i	−0.135469	+	0.234639i
$227$	4.69767	+	10.0742i	0.311796	+	0.668648i	0.998288	−	0.0584891i	$-0.0186283\pi$
$227$	4.69767	+	10.0742i	0.311796	+	0.668648i	−0.686492	+	0.727137i	$0.740851\pi$
$228$		0			0
$229$	−6.44496	+	7.68081i	−0.425895	+	0.507562i	−0.935733	−	0.352708i	$-0.885261\pi$
$229$	−6.44496	+	7.68081i	−0.425895	+	0.507562i	0.509838	+	0.860270i	$0.329705\pi$
$230$	−3.29445	+	7.07206i	−0.217229	+	0.466318i
$231$		0			0
$232$	−6.60161	+	3.07838i	−0.433417	+	0.202105i
$233$	−3.74540	−	13.9780i	−0.245369	−	0.915730i	−0.973198	−	0.229971i	$-0.926137\pi$
$233$	−3.74540	−	13.9780i	−0.245369	−	0.915730i	0.727828	−	0.685759i	$-0.240530\pi$
$234$		0			0
$235$	3.62682	−	0.00139440i	0.236587	−	9.09606e-5i
$236$	−0.525584	+	0.0926746i	−0.0342126	+	0.00603260i
$237$		0			0
$238$	−5.07868	−	2.36823i	−0.329202	−	0.153509i
$239$	1.43765	−	8.15330i	0.0929936	−	0.527393i	−0.902350	−	0.431004i	$-0.858160\pi$
$239$	1.43765	−	8.15330i	0.0929936	−	0.527393i	0.995344	−	0.0963892i	$-0.0307293\pi$
$240$		0			0
$241$	−21.3477	+	17.9128i	−1.37512	+	1.15387i	−0.404145	+	0.914695i	$0.632431\pi$
$241$	−21.3477	+	17.9128i	−1.37512	+	1.15387i	−0.970978	+	0.239171i	$0.923124\pi$
$242$	−4.33629	−	4.33629i	−0.278748	−	0.278748i
$243$		0			0
$244$			8.56627i			0.548399i
$245$	1.40651	−	2.01035i	0.0898587	−	0.128437i
$246$		0			0
$247$	−8.19727	−	11.7069i	−0.521580	−	0.744893i
$248$	3.07741	−	6.59953i	0.195416	−	0.419071i
$249$		0			0
$250$	−11.0082	+	1.95414i	−0.696222	+	0.123591i
$251$	−21.5632	+	12.4495i	−1.36106	+	0.785808i	−0.989765	−	0.142707i	$-0.954419\pi$
$251$	−21.5632	+	12.4495i	−1.36106	+	0.785808i	−0.371294	+	0.928515i	$0.621086\pi$
$252$		0			0
$253$	−7.43544	+	1.99232i	−0.467462	+	0.125256i
$254$	20.2082	+	7.35518i	1.26797	+	0.461505i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.657637	−	7.51683i	−0.0410223	−	0.468887i	−0.988726	−	0.149736i	$-0.952158\pi$
$257$	−0.657637	−	7.51683i	−0.0410223	−	0.468887i	0.947704	−	0.319151i	$-0.103398\pi$
$258$		0			0
$259$	8.93295	−	24.5431i	0.555066	−	1.52503i
$260$	−6.90060	+	3.98760i	−0.427957	+	0.247301i
$261$		0			0
$262$	8.77563	+	2.35142i	0.542160	+	0.145271i
$263$	24.7399	+	17.3231i	1.52553	+	1.06819i	0.971892	+	0.235429i	$0.0756494\pi$
$263$	24.7399	+	17.3231i	1.52553	+	1.06819i	0.553637	+	0.832758i	$0.313239\pi$
$264$		0			0
$265$	−28.8924	−	5.08305i	−1.77484	−	0.312249i
$266$	−11.2365	−	1.98130i	−0.688953	−	0.121481i
$267$		0			0
$268$	12.8796	+	1.12682i	0.786746	+	0.0688313i
$269$	−1.42750			−0.0870360			−0.0435180	−	0.999053i	$-0.513857\pi$
$269$	−1.42750			−0.0870360			−0.0435180	+	0.999053i	$0.513857\pi$
$270$		0			0
$271$	20.7284			1.25916			0.629579	−	0.776936i	$-0.283227\pi$
$271$	20.7284			1.25916			0.629579	+	0.776936i	$0.283227\pi$
$272$	1.96178	+	0.171634i	0.118951	+	0.0104068i
$273$		0			0
$274$	12.6329	+	2.22752i	0.763179	+	0.134569i
$275$	−8.45589	−	7.08426i	−0.509909	−	0.427197i
$276$		0			0
$277$	13.2186	+	9.25578i	0.794230	+	0.556126i	0.898783	−	0.438394i	$-0.144452\pi$
$277$	13.2186	+	9.25578i	0.794230	+	0.556126i	−0.104553	+	0.994519i	$0.533341\pi$
$278$	−3.70319	−	0.992267i	−0.222103	−	0.0595122i
$279$		0			0
$280$	−1.64447	+	6.14670i	−0.0982760	+	0.367336i
$281$	−1.27929	+	3.51481i	−0.0763158	+	0.209676i	−0.971984	−	0.235047i	$-0.924476\pi$
$281$	−1.27929	+	3.51481i	−0.0763158	+	0.209676i	0.895668	+	0.444723i	$0.146698\pi$
$282$		0			0
$283$	2.00354	+	22.9006i	0.119098	+	1.36130i	0.786956	+	0.617009i	$0.211656\pi$
$283$	2.00354	+	22.9006i	0.119098	+	1.36130i	−0.667858	+	0.744289i	$0.732789\pi$
$284$	9.69631	+	8.13617i	0.575370	+	0.482793i
$285$		0			0
$286$	−7.38939	−	2.68952i	−0.436944	−	0.159035i
$287$	16.3892	−	4.39147i	0.967422	−	0.259220i
$288$		0			0
$289$	−11.3639	+	6.56098i	−0.668467	+	0.385940i
$290$	15.3075	+	5.56482i	0.898890	+	0.326778i
$291$		0			0
$292$	6.79200	−	14.5655i	0.397472	−	0.852381i
$293$	1.18414	+	1.69112i	0.0691779	+	0.0987963i	0.852250	−	0.523134i	$-0.175237\pi$
$293$	1.18414	+	1.69112i	0.0691779	+	0.0987963i	−0.783072	+	0.621931i	$0.786349\pi$
$294$		0			0
$295$	0.977816	+	0.684114i	0.0569306	+	0.0398306i
$296$			9.17855i			0.533493i
$297$		0			0
$298$	−3.67506	−	3.67506i	−0.212891	−	0.212891i
$299$	9.52641	−	7.99361i	0.550927	−	0.462282i
$300$		0			0
$301$	3.39770	−	19.2693i	0.195840	−	1.11066i
$302$	−3.38581	−	1.57883i	−0.194831	−	0.0908514i
$303$		0			0
$304$	3.94877	−	0.696275i	0.226477	−	0.0399341i
$305$	13.5393	−	13.5497i	0.775256	−	0.775852i
$306$		0			0
$307$	1.55353	+	5.79784i	0.0886644	+	0.330900i	0.995983	−	0.0895440i	$-0.0285410\pi$
$307$	1.55353	+	5.79784i	0.0886644	+	0.330900i	−0.907318	+	0.420444i	$0.861874\pi$
$308$	−5.68984	+	2.65321i	−0.324209	+	0.151181i
$309$		0			0
$310$	−15.2984	+	5.57484i	−0.868893	+	0.316630i
$311$	−9.13869	+	10.8911i	−0.518207	+	0.617575i	−0.960156	−	0.279465i	$-0.909843\pi$
$311$	−9.13869	+	10.8911i	−0.518207	+	0.617575i	0.441949	+	0.897040i	$0.354287\pi$
$312$		0			0
$313$	8.12676	+	17.4279i	0.459351	+	0.985082i	0.990463	+	0.137780i	$0.0439968\pi$
$313$	8.12676	+	17.4279i	0.459351	+	0.985082i	−0.531111	+	0.847302i	$0.678225\pi$
$314$	7.29519	−	12.6356i	0.411692	−	0.713071i
$315$		0			0
$316$	−0.319887	−	0.554061i	−0.0179951	−	0.0311684i
$317$	14.0550	−	20.0726i	0.789407	−	1.12739i	−0.199651	−	0.979867i	$-0.563981\pi$
$317$	14.0550	−	20.0726i	0.789407	−	1.12739i	0.989059	−	0.147524i	$-0.0471302\pi$
$318$		0			0
$319$	5.49643	+	15.1013i	0.307741	+	0.845512i
$320$	−0.195743	−	2.22748i	−0.0109423	−	0.124520i
$321$		0			0
$322$	0.865311	−	9.89055i	0.0482219	−	0.551179i
$323$	5.58344	−	5.58344i	0.310671	−	0.310671i
$324$		0			0
$325$	17.2175	+	4.59924i	0.955057	+	0.255120i
$326$	1.26017	+	1.50181i	0.0697942	+	0.0831775i
$327$		0			0
$328$	−4.88438	+	3.42008i	−0.269695	+	0.188842i
$329$	−4.33706	+	1.57856i	−0.239110	+	0.0870288i
$330$		0			0
$331$	−3.20550	−	18.1793i	−0.176190	−	0.999224i	−0.936761	−	0.349969i	$-0.886192\pi$
$331$	−3.20550	−	18.1793i	−0.176190	−	0.999224i	0.760571	−	0.649255i	$-0.224919\pi$
$332$	1.54910	−	5.78133i	0.0850180	−	0.317292i
$333$		0			0
$334$	11.0853	+	6.40012i	0.606562	+	0.350199i
$335$	−18.5913	−	22.1389i	−1.01575	−	1.20958i
$336$		0			0
$337$	1.34060	−	0.117287i	0.0730269	−	0.00638903i	−0.0505837	−	0.998720i	$-0.516108\pi$
$337$	1.34060	−	0.117287i	0.0730269	−	0.00638903i	0.123611	+	0.992331i	$0.460553\pi$
$338$	−0.295023	+	0.0258112i	−0.0160472	+	0.00140394i
$339$		0			0
$340$	−2.83177	−	3.37214i	−0.153574	−	0.182880i
$341$	−13.9131	−	8.03272i	−0.753435	−	0.434996i
$342$		0			0
$343$	4.34730	−	16.2243i	0.234732	−	0.876032i
$344$	1.19403	+	6.77169i	0.0643779	+	0.365105i
$345$		0			0
$346$	24.1188	−	8.77854i	1.29664	−	0.471937i
$347$	27.9462	−	19.5682i	1.50023	−	1.05047i	0.519648	−	0.854380i	$-0.326063\pi$
$347$	27.9462	−	19.5682i	1.50023	−	1.05047i	0.980585	−	0.196094i	$-0.0628258\pi$
$348$		0			0
$349$	−20.0335	−	23.8750i	−1.07237	−	1.27800i	−0.958681	−	0.284483i	$-0.908178\pi$
$349$	−20.0335	−	23.8750i	−1.07237	−	1.27800i	−0.113688	−	0.993517i	$-0.536266\pi$
$350$	12.3162	−	7.12339i	0.658328	−	0.380761i
$351$		0			0
$352$	1.56006	−	1.56006i	0.0831513	−	0.0831513i
$353$	0.833185	−	9.52334i	0.0443459	−	0.506876i	−0.941244	−	0.337726i	$-0.890342\pi$
$353$	0.833185	−	9.52334i	0.0443459	−	0.506876i	0.985590	−	0.169150i	$-0.0541023\pi$
$354$		0			0
$355$	−2.47764	−	28.1947i	−0.131499	−	1.49642i
$356$	1.89096	+	5.19538i	0.100221	+	0.275355i
$357$		0			0
$358$	5.60011	−	7.99778i	0.295975	−	0.422696i
$359$	−6.15484	−	10.6605i	−0.324840	−	0.562640i	0.656640	−	0.754204i	$-0.271977\pi$
$359$	−6.15484	−	10.6605i	−0.324840	−	0.562640i	−0.981480	+	0.191565i	$0.938644\pi$
$360$		0			0
$361$	−1.46121	+	2.53089i	−0.0769059	+	0.133205i
$362$	−7.81975	−	16.7695i	−0.410997	−	0.881386i
$363$		0			0
$364$	6.51934	−	7.76945i	0.341706	−	0.407230i
$365$	−33.7645	+	12.3040i	−1.76731	+	0.644019i
$366$		0			0
$367$	5.57694	−	2.60057i	0.291114	−	0.135749i	−0.271575	−	0.962417i	$-0.587545\pi$
$367$	5.57694	−	2.60057i	0.291114	−	0.135749i	0.562689	+	0.826669i	$0.309767\pi$
$368$	0.903033	+	3.37017i	0.0470739	+	0.175682i
$369$		0			0
$370$	14.5070	−	14.5181i	0.754182	−	0.754762i
$371$	36.7652	−	6.48270i	1.90876	−	0.336565i
$372$		0			0
$373$	−0.525752	−	0.245162i	−0.0272224	−	0.0126940i	0.408959	−	0.912553i	$-0.365892\pi$
$373$	−0.525752	−	0.245162i	−0.0272224	−	0.0126940i	−0.436182	+	0.899859i	$0.643670\pi$
$374$	0.754453	−	4.27872i	0.0390118	−	0.221247i
$375$		0			0
$376$	1.24250	−	1.04258i	0.0640768	−	0.0537668i
$377$	−18.3580	−	18.3580i	−0.945488	−	0.945488i
$378$		0			0
$379$		−	35.4469i		−	1.82079i	−0.413744	−	0.910393i	$-0.635779\pi$
$379$		−	35.4469i		−	1.82079i	0.413744	−	0.910393i	$-0.364221\pi$
$380$	−7.34644	−	5.13982i	−0.376864	−	0.263667i
$381$		0			0
$382$	8.22759	+	11.7502i	0.420960	+	0.601194i
$383$	−9.96747	+	21.3753i	−0.509314	+	1.09223i	0.468637	+	0.883391i	$0.344745\pi$
$383$	−9.96747	+	21.3753i	−0.509314	+	1.09223i	−0.977951	+	0.208836i	$0.933032\pi$
$384$		0			0
$385$	13.1934	+	4.79625i	0.672396	+	0.244440i
$386$	−3.65685	+	2.11128i	−0.186129	+	0.107461i
$387$		0			0
$388$	−5.23038	+	1.40148i	−0.265532	+	0.0711492i
$389$	−24.5522	−	8.93627i	−1.24485	−	0.453087i	−0.366189	−	0.930541i	$-0.619338\pi$
$389$	−24.5522	−	8.93627i	−1.24485	−	0.453087i	−0.878657	+	0.477454i	$0.841560\pi$
$390$		0			0
$391$	5.26342	+	4.41653i	0.266183	+	0.223354i
$392$	−0.0956316	−	1.09307i	−0.00483012	−	0.0552086i
$393$		0			0
$394$	6.51916	−	17.9113i	0.328431	−	0.902356i
$395$	−0.369730	+	1.38198i	−0.0186031	+	0.0695348i
$396$		0			0
$397$	13.4304	+	3.59866i	0.674052	+	0.180612i	0.579579	−	0.814916i	$-0.303217\pi$
$397$	13.4304	+	3.59866i	0.674052	+	0.180612i	0.0944725	+	0.995527i	$0.469884\pi$
$398$	5.48652	+	3.84170i	0.275014	+	0.192567i
$399$		0			0
$400$	−3.21099	+	3.83269i	−0.160550	+	0.191635i
$401$	19.7676	+	3.48557i	0.987148	+	0.174061i	0.643839	−	0.765161i	$-0.277341\pi$
$401$	19.7676	+	3.48557i	0.987148	+	0.174061i	0.343310	+	0.939222i	$0.388452\pi$
$402$		0			0
$403$	25.8553	+	2.26204i	1.28794	+	0.112680i
$404$	−6.95457			−0.346003
$405$		0			0
$406$	−20.7273			−1.02868
$407$	20.1732	+	1.76492i	0.999946	+	0.0874840i
$408$		0			0
$409$	35.7803	+	6.30902i	1.76922	+	0.311961i	0.960923	−	0.276814i	$-0.0892787\pi$
$409$	35.7803	+	6.30902i	1.76922	+	0.311961i	0.808296	+	0.588776i	$0.200390\pi$
$410$	13.1314	+	2.31021i	0.648513	+	0.114093i
$411$		0			0
$412$	2.95265	+	2.06747i	0.145467	+	0.101857i
$413$	−1.46691	−	0.393057i	−0.0721819	−	0.0193411i
$414$		0			0
$415$	−11.5879	+	6.69619i	−0.568825	+	0.328703i
$416$	−1.21904	+	3.34930i	−0.0597685	+	0.164213i
$417$		0			0
$418$	−0.771013	−	8.81272i	−0.0377115	−	0.431044i
$419$	−2.40069	−	2.01442i	−0.117281	−	0.0984108i	0.582261	−	0.813002i	$-0.302168\pi$
$419$	−2.40069	−	2.01442i	−0.117281	−	0.0984108i	−0.699542	+	0.714591i	$0.746613\pi$
$420$		0			0
$421$	19.4497	+	7.07911i	0.947920	+	0.345015i	0.769289	−	0.638901i	$-0.220611\pi$
$421$	19.4497	+	7.07911i	0.947920	+	0.345015i	0.178631	+	0.983916i	$0.442833\pi$
$422$	−10.9295	+	2.92856i	−0.532042	+	0.142560i
$423$		0			0
$424$	−11.3618	+	6.55975i	−0.551779	+	0.318569i
$425$	−0.850626	+	9.80957i	−0.0412614	+	0.475834i
$426$		0			0
$427$	−10.3017	+	22.0921i	−0.498534	+	1.06911i
$428$	4.44418	+	6.34695i	0.214818	+	0.306792i
$429$		0			0
$430$	8.81421	−	12.5983i	0.425059	−	0.607544i
$431$			8.49808i			0.409338i	0.978831	+	0.204669i	$0.0656118\pi$
$431$			8.49808i			0.409338i	−0.978831	+	0.204669i	$0.934388\pi$
$432$		0			0
$433$	3.46967	+	3.46967i	0.166742	+	0.166742i	0.785546	−	0.618804i	$-0.212382\pi$
$433$	3.46967	+	3.46967i	0.166742	+	0.166742i	−0.618804	+	0.785546i	$0.712382\pi$
$434$	15.8730	−	13.3191i	0.761930	−	0.639335i
$435$		0			0
$436$	−0.288164	+	1.63426i	−0.0138005	+	0.0782668i
$437$	12.6793	+	5.91243i	0.606531	+	0.282830i
$438$		0			0
$439$	−10.3029	+	1.81667i	−0.491729	+	0.0867050i	−0.414014	−	0.910271i	$-0.635873\pi$
$439$	−10.3029	+	1.81667i	−0.491729	+	0.0867050i	−0.0777148	+	0.996976i	$0.524762\pi$
$440$	−4.93333	+	0.00189671i	−0.235187	+	9.04223e-5i
$441$		0			0
$442$	1.81665	+	6.77982i	0.0864091	+	0.322483i
$443$	−20.5313	+	9.57392i	−0.975473	+	0.454871i	−0.843938	−	0.536441i	$-0.819768\pi$
$443$	−20.5313	+	9.57392i	−0.975473	+	0.454871i	−0.131535	+	0.991312i	$0.541991\pi$
$444$		0			0
$445$	5.22043	−	11.2065i	0.247472	−	0.531239i
$446$	2.78755	−	3.32207i	0.131994	−	0.157305i
$447$		0			0
$448$	1.20259	+	2.57896i	0.0568170	+	0.121844i
$449$	−9.37114	+	16.2313i	−0.442251	+	0.766002i	−0.997856	−	0.0654445i	$-0.979153\pi$
$449$	−9.37114	+	16.2313i	−0.442251	+	0.766002i	0.555605	+	0.831447i	$0.312487\pi$
$450$		0			0
$451$	6.57764	+	11.3928i	0.309729	+	0.536466i
$452$	2.33623	−	3.33648i	0.109887	−	0.156935i
$453$		0			0
$454$	−3.80177	−	10.4453i	−0.178426	−	0.490222i
$455$	−22.5918	+	1.98528i	−1.05912	+	0.0930714i
$456$		0			0
$457$	0.252711	−	2.88851i	0.0118213	−	0.135119i	−0.987991	−	0.154514i	$-0.950619\pi$
$457$	0.252711	−	2.88851i	0.0118213	−	0.135119i	0.999812	+	0.0193958i	$0.00617426\pi$
$458$	7.08986	−	7.08986i	0.331288	−	0.331288i
$459$		0			0
$460$	3.89828	−	6.75802i	0.181758	−	0.315094i
$461$	−22.9686	−	27.3729i	−1.06975	−	1.27488i	−0.959721	−	0.280954i	$-0.909349\pi$
$461$	−22.9686	−	27.3729i	−1.06975	−	1.27488i	−0.110032	−	0.993928i	$-0.535095\pi$
$462$		0			0
$463$	−29.2466	+	20.4787i	−1.35920	+	0.951724i	−0.359374	+	0.933193i	$0.617010\pi$
$463$	−29.2466	+	20.4787i	−1.35920	+	0.951724i	−0.999828	+	0.0185305i	$0.994101\pi$
$464$	6.84478	−	2.49130i	0.317761	−	0.115656i
$465$		0			0
$466$	2.51288	+	14.2513i	0.116407	+	0.660177i
$467$	3.00296	−	11.2072i	0.138960	−	0.518607i	−0.860990	−	0.508622i	$-0.830155\pi$
$467$	3.00296	−	11.2072i	0.138960	−	0.518607i	0.999950	−	0.00998457i	$-0.00317824\pi$
$468$		0			0
$469$	31.8608	+	18.3949i	1.47120	+	0.849395i
$470$	−3.61314	−	0.314709i	−0.166662	−	0.0145164i
$471$		0			0
$472$	0.531661	−	0.0465143i	0.0244717	−	0.00214099i
$473$	15.1128	−	1.32220i	0.694888	−	0.0607948i
$474$		0			0
$475$	3.49655	+	19.7412i	0.160433	+	0.905787i
$476$	4.85295	+	2.80185i	0.222435	+	0.128423i
$477$		0			0
$478$	−2.14278	+	7.99697i	−0.0980086	+	0.365773i
$479$	−4.10558	−	23.2839i	−0.187589	−	1.06387i	−0.922584	−	0.385796i	$-0.873927\pi$
$479$	−4.10558	−	23.2839i	−0.187589	−	1.06387i	0.734996	−	0.678072i	$-0.237184\pi$
$480$		0			0
$481$	−30.7417	+	11.1891i	−1.40170	+	0.510177i
$482$	22.8276	−	15.9841i	1.03977	−	0.728055i
$483$		0			0
$484$	3.94186	+	4.69773i	0.179175	+	0.213533i
$485$	10.4882	+	6.05000i	0.476246	+	0.274716i
$486$		0			0
$487$	−24.2950	+	24.2950i	−1.10091	+	1.10091i	−0.106612	+	0.994301i	$0.534000\pi$
$487$	−24.2950	+	24.2950i	−1.10091	+	1.10091i	−0.994301	+	0.106612i	$0.966000\pi$
$488$	0.746600	−	8.53367i	0.0337970	−	0.386301i
$489$		0			0
$490$	−1.57637	+	1.88011i	−0.0712132	+	0.0849349i
$491$	10.3444	+	28.4210i	0.466836	+	1.28262i	0.920253	+	0.391323i	$0.127983\pi$
$491$	10.3444	+	28.4210i	0.466836	+	1.28262i	−0.453417	+	0.891299i	$0.649795\pi$
$492$		0			0
$493$	8.22757	−	11.7502i	0.370551	−	0.529202i
$494$	7.14575	+	12.3768i	0.321503	+	0.556859i
$495$		0			0
$496$	−3.64089	+	6.30620i	−0.163481	+	0.283157i
$497$	15.2219	+	32.6435i	0.682796	+	1.46426i
$498$		0			0
$499$	5.75122	−	6.85404i	0.257460	−	0.306829i	−0.621795	−	0.783180i	$-0.713596\pi$
$499$	5.75122	−	6.85404i	0.257460	−	0.306829i	0.879255	+	0.476351i	$0.158041\pi$
$500$	11.1367	−	0.987277i	0.498047	−	0.0441524i
$501$		0			0
$502$	22.5662	−	10.5228i	1.00718	−	0.469656i
$503$	−2.50671	−	9.35515i	−0.111768	−	0.417126i	0.887256	−	0.461277i	$-0.152608\pi$
$503$	−2.50671	−	9.35515i	−0.111768	−	0.417126i	−0.999025	+	0.0441510i	$0.985942\pi$
$504$		0			0
$505$	11.0004	+	10.9919i	0.489510	+	0.489134i
$506$	7.58079	−	1.33670i	0.337007	−	0.0594235i
$507$		0			0
$508$	−19.4902	−	9.08845i	−0.864739	−	0.403235i
$509$	−2.24538	+	12.7342i	−0.0995246	+	0.564432i	0.893742	+	0.448581i	$0.148071\pi$
$509$	−2.24538	+	12.7342i	−0.0995246	+	0.564432i	−0.993267	+	0.115851i	$0.963041\pi$
$510$		0			0
$511$	35.0326	−	29.3958i	1.54975	−	1.30040i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			7.54554i			0.332820i
$515$	−1.40265	−	7.93698i	−0.0618081	−	0.349745i
$516$		0			0
$517$	−2.05252	−	2.93130i	−0.0902697	−	0.128919i
$518$	−11.0380	+	23.6711i	−0.484983	+	1.04005i
$519$		0			0
$520$	7.22188	−	3.37100i	0.316701	−	0.147828i
$521$	6.31624	−	3.64668i	0.276719	−	0.159764i	−0.355218	−	0.934784i	$-0.615593\pi$
$521$	6.31624	−	3.64668i	0.276719	−	0.159764i	0.631937	+	0.775019i	$0.282260\pi$
$522$		0			0
$523$	−17.1061	+	4.58356i	−0.747996	+	0.200425i	−0.612629	−	0.790371i	$-0.709888\pi$
$523$	−17.1061	+	4.58356i	−0.747996	+	0.200425i	−0.135367	+	0.990796i	$0.543221\pi$
$524$	−8.53729	−	3.10732i	−0.372953	−	0.135744i
$525$		0			0
$526$	−23.1360	−	19.4134i	−1.00878	−	0.846464i
$527$	1.24980	+	14.2853i	0.0544421	+	0.622275i
$528$		0			0
$529$	3.70288	−	10.1736i	0.160995	−	0.442330i
$530$	28.3394	+	7.58184i	1.23098	+	0.329334i
$531$		0			0
$532$	11.0210	+	2.95308i	0.477823	+	0.128032i
$533$	−17.4091	−	12.1900i	−0.754073	−	0.528007i
$534$		0			0
$535$	3.00198	−	17.0634i	0.129787	−	0.737717i
$536$	−12.7324	−	2.24506i	−0.549954	−	0.0969718i
$537$		0			0
$538$	1.42207	+	0.124415i	0.0613096	+	0.00536389i
$539$	−2.42081			−0.104272
$540$		0			0
$541$	−4.99006			−0.214539			−0.107270	−	0.994230i	$-0.534211\pi$
$541$	−4.99006			−0.214539			−0.107270	+	0.994230i	$0.534211\pi$
$542$	−20.6495	−	1.80660i	−0.886971	−	0.0775999i
$543$		0			0
$544$	−1.93936	−	0.341961i	−0.0831493	−	0.0146615i
$545$	3.03880	−	2.12953i	0.130168	−	0.0912190i
$546$		0			0
$547$	−6.99531	−	4.89817i	−0.299098	−	0.209431i	0.414388	−	0.910100i	$-0.363996\pi$
$547$	−6.99531	−	4.89817i	−0.299098	−	0.209431i	−0.713486	+	0.700670i	$0.752885\pi$
$548$	−12.3907	−	3.32007i	−0.529303	−	0.141826i
$549$		0			0
$550$	7.80628	+	7.79428i	0.332861	+	0.332349i
$551$	9.98932	−	27.4454i	0.425559	−	1.16921i
$552$		0			0
$553$	−0.158669	−	1.81359i	−0.00674729	−	0.0771218i
$554$	−12.3616	−	10.3726i	−0.525195	−	0.440691i
$555$		0			0
$556$	3.60262	+	1.31125i	0.152785	+	0.0556092i
$557$	−44.2783	+	11.8643i	−1.87613	+	0.502708i	−0.876354	+	0.481668i	$0.840031\pi$
$557$	−44.2783	+	11.8643i	−1.87613	+	0.502708i	−0.999779	+	0.0210397i	$0.993302\pi$
$558$		0			0
$559$	−21.2248	+	12.2542i	−0.897714	+	0.518296i
$560$	2.17393	−	5.97999i	0.0918655	−	0.252701i
$561$		0			0
$562$	1.58075	−	3.38994i	0.0666801	−	0.142996i
$563$	−5.68723	−	8.12221i	−0.239688	−	0.342310i	0.681228	−	0.732072i	$-0.261446\pi$
$563$	−5.68723	−	8.12221i	−0.239688	−	0.342310i	−0.920916	+	0.389761i	$0.872557\pi$
$564$		0			0
$565$	−8.96872	+	1.58498i	−0.377317	+	0.0666807i
$566$		−	22.9880i		−	0.966260i
$567$		0			0
$568$	−8.95030	−	8.95030i	−0.375546	−	0.375546i
$569$	−7.99794	+	6.71107i	−0.335291	+	0.281343i	−0.794852	−	0.606804i	$-0.792451\pi$
$569$	−7.99794	+	6.71107i	−0.335291	+	0.281343i	0.459561	+	0.888146i	$0.348007\pi$
$570$		0			0
$571$	2.59341	−	14.7080i	0.108531	−	0.615509i	−0.881220	−	0.472706i	$-0.843277\pi$
$571$	2.59341	−	14.7080i	0.108531	−	0.615509i	0.989751	−	0.142803i	$-0.0456116\pi$
$572$	7.12687	+	3.32331i	0.297989	+	0.138955i
$573$		0			0
$574$	−16.7096	+	2.94634i	−0.697443	+	0.122978i
$575$	−16.8474	+	4.52812i	−0.702583	+	0.188836i
$576$		0			0
$577$	−7.61321	−	28.4129i	−0.316942	−	1.18284i	−0.922168	−	0.386790i	$-0.873584\pi$
$577$	−7.61321	−	28.4129i	−0.316942	−	1.18284i	0.605226	−	0.796054i	$-0.293083\pi$
$578$	11.8925	−	5.54558i	0.494664	−	0.230666i
$579$		0			0
$580$	−14.7643	−	6.87779i	−0.613054	−	0.285585i
$581$	10.9476	−	13.0469i	0.454184	−	0.541276i
$582$		0			0
$583$	12.2327	+	26.2330i	0.506625	+	1.08646i
$584$	−8.03563	+	13.9181i	−0.332517	+	0.575936i
$585$		0			0
$586$	−1.03224	−	1.78789i	−0.0426414	−	0.0738570i
$587$	−11.2483	+	16.0642i	−0.464265	+	0.663039i	−0.981202	−	0.192984i	$-0.938183\pi$
$587$	−11.2483	+	16.0642i	−0.464265	+	0.663039i	0.516937	+	0.856024i	$0.327072\pi$
$588$		0			0
$589$	9.98618	+	27.4368i	0.411473	+	1.13051i
$590$	−0.914470	−	0.766733i	−0.0376481	−	0.0315659i
$591$		0			0
$592$	0.799964	−	9.14363i	0.0328783	−	0.375801i
$593$	22.9430	−	22.9430i	0.942156	−	0.942156i	−0.0562600	−	0.998416i	$-0.517918\pi$
$593$	22.9430	−	22.9430i	0.942156	−	0.942156i	0.998416	+	0.0562600i	$0.0179176\pi$
$594$		0			0
$595$	−3.24772	−	12.1021i	−0.133144	−	0.496136i
$596$	3.34078	+	3.98138i	0.136844	+	0.163084i
$597$		0			0
$598$	−10.1868	+	7.13291i	−0.416571	+	0.291686i
$599$	30.8648	−	11.2339i	1.26110	−	0.459004i	0.376964	−	0.926228i	$-0.376968\pi$
$599$	30.8648	−	11.2339i	1.26110	−	0.459004i	0.884139	+	0.467224i	$0.154746\pi$
$600$		0			0
$601$	0.493528	+	2.79894i	0.0201314	+	0.114171i	0.993218	−	0.116271i	$-0.0370940\pi$
$601$	0.493528	+	2.79894i	0.0201314	+	0.114171i	−0.973086	+	0.230442i	$0.925983\pi$
$602$	−5.06420	+	18.8998i	−0.206401	+	0.770300i
$603$		0			0
$604$	3.23532	+	1.86791i	0.131643	+	0.0760043i
$605$	1.18988	−	13.6608i	0.0483754	−	0.555392i
$606$		0			0
$607$	14.4866	−	1.26741i	0.587993	−	0.0514427i	0.210723	−	0.977546i	$-0.432418\pi$
$607$	14.4866	−	1.26741i	0.587993	−	0.0514427i	0.377270	+	0.926103i	$0.376863\pi$
$608$	−3.99443	+	0.349467i	−0.161995	+	0.0141728i
$609$		0			0
$610$	−14.6687	+	12.3181i	−0.593917	+	0.498745i
$611$	5.00656	+	2.89054i	0.202544	+	0.116939i
$612$		0			0
$613$	−0.461340	+	1.72174i	−0.0186333	+	0.0695406i	−0.974616	−	0.223881i	$-0.928127\pi$
$613$	−0.461340	+	1.72174i	−0.0186333	+	0.0695406i	0.955983	+	0.293422i	$0.0947940\pi$
$614$	−1.04230	−	5.91117i	−0.0420638	−	0.238556i
$615$		0			0
$616$	5.89943	−	2.14722i	0.237695	−	0.0865138i
$617$	9.23889	−	6.46914i	0.371944	−	0.260438i	−0.372627	−	0.927981i	$-0.621543\pi$
$617$	9.23889	−	6.46914i	0.371944	−	0.260438i	0.744571	+	0.667543i	$0.232654\pi$
$618$		0			0
$619$	12.3371	+	14.7028i	0.495871	+	0.590956i	0.954700	−	0.297569i	$-0.0961757\pi$
$619$	12.3371	+	14.7028i	0.495871	+	0.590956i	−0.458830	+	0.888524i	$0.651731\pi$
$620$	15.7261	−	4.22028i	0.631576	−	0.169490i
$621$		0			0
$622$	10.0531	−	10.0531i	0.403094	−	0.403094i
$623$	−1.37119	+	15.6727i	−0.0549354	+	0.627915i
$624$		0			0
$625$	−19.1758	−	16.0402i	−0.767032	−	0.641609i
$626$	−6.57689	−	18.0699i	−0.262865	−	0.722217i
$627$		0			0
$628$	−8.36870	+	11.9517i	−0.333948	+	0.476927i
$629$	−9.03755	−	15.6535i	−0.360351	−	0.624146i
$630$		0			0
$631$	1.62237	−	2.81002i	0.0645854	−	0.111865i	−0.831925	−	0.554889i	$-0.812761\pi$
$631$	1.62237	−	2.81002i	0.0645854	−	0.111865i	0.896510	+	0.443024i	$0.146094\pi$
$632$	0.270380	+	0.579833i	0.0107552	+	0.0230645i
$633$		0			0
$634$	−15.7510	+	18.7713i	−0.625550	+	0.745502i
$635$	16.4640	+	45.1805i	0.653356	+	1.79293i
$636$		0			0
$637$	3.54445	−	1.65280i	0.140436	−	0.0654865i
$638$	−4.15935	−	15.5229i	−0.164670	−	0.614558i
$639$		0			0
$640$	0.000859699		2.23607i	3.39826e−5		0.0883883i
$641$	33.0518	−	5.82793i	1.30547	−	0.230189i	0.522708	−	0.852512i	$-0.324922\pi$
$641$	33.0518	−	5.82793i	1.30547	−	0.230189i	0.782761	+	0.622323i	$0.213811\pi$
$642$		0			0
$643$	−18.7697	−	8.75244i	−0.740203	−	0.345162i	0.0156729	−	0.999877i	$-0.495011\pi$
$643$	−18.7697	−	8.75244i	−0.740203	−	0.345162i	−0.755876	+	0.654715i	$0.772789\pi$
$644$	−1.72404	+	9.77750i	−0.0679366	+	0.385287i
$645$		0			0
$646$	−6.04882	+	5.07556i	−0.237988	+	0.199695i
$647$	11.1061	+	11.1061i	0.436624	+	0.436624i	0.890874	−	0.454250i	$-0.150093\pi$
$647$	11.1061	+	11.1061i	0.436624	+	0.436624i	−0.454250	+	0.890874i	$0.650093\pi$
$648$		0			0
$649$		−	1.17746i		−	0.0462193i
$650$	−16.7512	−	6.08234i	−0.657035	−	0.238569i
$651$		0			0
$652$	−1.12448	−	1.60593i	−0.0440381	−	0.0628929i
$653$	−4.40318	+	9.44265i	−0.172310	+	0.369520i	−0.973430	−	0.228983i	$-0.926460\pi$
$653$	−4.40318	+	9.44265i	−0.172310	+	0.369520i	0.801120	+	0.598503i	$0.204238\pi$
$654$		0			0
$655$	8.59262	+	18.4085i	0.335741	+	0.719278i
$656$	5.16387	−	2.98136i	0.201615	−	0.116403i
$657$		0			0
$658$	4.45814	−	1.19455i	0.173796	−	0.0465686i
$659$	21.1581	+	7.70092i	0.824202	+	0.299985i	0.719477	−	0.694516i	$-0.244381\pi$
$659$	21.1581	+	7.70092i	0.824202	+	0.299985i	0.104725	+	0.994501i	$0.466604\pi$
$660$		0			0
$661$	−26.2606	−	22.0352i	−1.02142	−	0.857072i	−0.0316132	−	0.999500i	$-0.510064\pi$
$661$	−26.2606	−	22.0352i	−1.02142	−	0.857072i	−0.989805	+	0.142429i	$0.954509\pi$
$662$	1.60887	+	18.3895i	0.0625306	+	0.714728i
$663$		0			0
$664$	−2.04708	+	5.62432i	−0.0794422	+	0.218266i
$665$	−12.7651	−	22.0901i	−0.495008	−	0.856618i
$666$		0			0
$667$	24.5485	+	6.57776i	0.950522	+	0.254692i
$668$	−10.4853	−	7.34192i	−0.405690	−	0.284067i
$669$		0			0
$670$	16.5910	+	23.6750i	0.640966	+	0.914645i
$671$	−18.6122	−	3.28184i	−0.718518	−	0.126694i
$672$		0			0
$673$	−13.0169	−	1.13884i	−0.501767	−	0.0438989i	−0.166537	−	0.986035i	$-0.553258\pi$
$673$	−13.0169	−	1.13884i	−0.501767	−	0.0438989i	−0.335230	+	0.942136i	$0.608814\pi$
$674$	−1.34572			−0.0518351
$675$		0			0
$676$	0.296150			0.0113904
$677$	5.44425	+	0.476310i	0.209240	+	0.0183061i	0.191294	−	0.981533i	$-0.438732\pi$
$677$	5.44425	+	0.476310i	0.209240	+	0.0183061i	0.0179460	+	0.999839i	$0.494287\pi$
$678$		0			0
$679$	−15.1743	−	2.67565i	−0.582338	−	0.102682i
$680$	2.52709	+	3.60611i	0.0969096	+	0.138288i
$681$		0			0
$682$	13.1600	+	9.21476i	0.503924	+	0.352851i
$683$	30.1560	+	8.08027i	1.15389	+	0.309183i	0.784522	−	0.620102i	$-0.212909\pi$
$683$	30.1560	+	8.08027i	1.15389	+	0.309183i	0.369365	+	0.929284i	$0.379575\pi$
$684$		0			0
$685$	14.3514	+	24.8353i	0.548339	+	0.948909i
$686$	−5.74480	+	15.7837i	−0.219337	+	0.602625i
$687$		0			0
$688$	−0.599297	−	6.84999i	−0.0228480	−	0.261153i
$689$	−35.8211	−	30.0575i	−1.36467	−	1.14510i
$690$		0			0
$691$	−26.1554	−	9.51978i	−0.994998	−	0.362150i	−0.207344	−	0.978268i	$-0.566482\pi$
$691$	−26.1554	−	9.51978i	−0.994998	−	0.362150i	−0.787654	+	0.616118i	$0.788704\pi$
$692$	−24.7922	+	6.64304i	−0.942457	+	0.252531i
$693$		0			0
$694$	−29.5454	+	17.0580i	−1.12153	+	0.647514i
$695$	−3.62597	−	7.76811i	−0.137541	−	0.294661i
$696$		0			0
$697$	4.96249	−	10.6421i	0.187968	−	0.403098i
$698$	17.8764	+	25.5302i	0.676633	+	0.966332i
$699$		0			0
$700$	−12.8902	+	6.02286i	−0.487203	+	0.227643i
$701$		−	3.18583i		−	0.120327i	−0.998189	−	0.0601636i	$-0.980838\pi$
$701$		−	3.18583i		−	0.120327i	0.998189	−	0.0601636i	$-0.0191623\pi$
$702$		0			0
$703$	−26.0237	−	26.0237i	−0.981504	−	0.981504i
$704$	−1.69009	+	1.41815i	−0.0636976	+	0.0534486i
$705$		0			0
$706$	−1.66003	+	9.41449i	−0.0624760	+	0.354319i
$707$	−17.9355	−	8.36348i	−0.674536	−	0.314541i
$708$		0			0
$709$	−38.5450	+	6.79652i	−1.44759	+	0.255249i	−0.841546	−	0.540185i	$-0.818354\pi$
$709$	−38.5450	+	6.79652i	−1.44759	+	0.255249i	−0.606040	+	0.795434i	$0.707243\pi$
$710$	0.0108818	+	28.3033i	0.000408385	+	1.06220i
$711$		0			0
$712$	−1.43096	−	5.34042i	−0.0536275	−	0.200141i
$713$	−23.0261	+	10.7373i	−0.862335	+	0.402113i
$714$		0			0
$715$	−6.02030	−	16.5209i	−0.225146	−	0.617846i
$716$	−6.27585	+	7.47927i	−0.234539	+	0.279513i
$717$		0			0
$718$	5.20230	+	11.1564i	0.194148	+	0.416352i
$719$	−15.4208	+	26.7095i	−0.575097	+	0.996097i	0.420934	+	0.907091i	$0.361702\pi$
$719$	−15.4208	+	26.7095i	−0.575097	+	0.996097i	−0.996031	+	0.0890060i	$0.971631\pi$
$720$		0			0
$721$	5.12846	+	8.88275i	0.190994	+	0.330811i
$722$	1.67623	−	2.39391i	0.0623830	−	0.0890921i
$723$		0			0
$724$	6.32844	+	17.3872i	0.235195	+	0.646192i
$725$	12.4828	+	34.2143i	0.463599	+	1.27069i
$726$		0			0
$727$	2.04871	−	23.4169i	0.0759825	−	0.868484i	−0.858579	−	0.512682i	$-0.828652\pi$
$727$	2.04871	−	23.4169i	0.0759825	−	0.868484i	0.934561	−	0.355802i	$-0.115792\pi$
$728$	−7.17169	+	7.17169i	−0.265800	+	0.265800i
$729$		0			0
$730$	34.7083	−	9.31437i	1.28461	−	0.344740i
$731$	−8.70402	−	10.3730i	−0.321930	−	0.383661i
$732$		0			0
$733$	5.70626	−	3.99557i	0.210766	−	0.147580i	−0.463427	−	0.886135i	$-0.653381\pi$
$733$	5.70626	−	3.99557i	0.210766	−	0.147580i	0.674193	+	0.738555i	$0.264492\pi$
$734$	−5.78238	+	2.10461i	−0.213431	+	0.0776827i
$735$		0			0
$736$	−0.605868	−	3.43605i	−0.0223326	−	0.126654i
$737$	−7.38260	+	27.5522i	−0.271941	+	1.01490i
$738$		0			0
$739$	35.6918	+	20.6067i	1.31294	+	0.758028i	0.982583	−	0.185826i	$-0.0594961\pi$
$739$	35.6918	+	20.6067i	1.31294	+	0.758028i	0.330361	+	0.943855i	$0.392829\pi$
$740$	−15.7171	+	13.1985i	−0.577773	+	0.485188i
$741$		0			0
$742$	−37.1903	+	3.25373i	−1.36530	+	0.119448i
$743$	−7.10086	+	0.621245i	−0.260505	+	0.0227913i	−0.216660	−	0.976247i	$-0.569516\pi$
$743$	−7.10086	+	0.621245i	−0.260505	+	0.0227913i	−0.0438452	+	0.999038i	$0.513961\pi$
$744$		0			0
$745$	1.00844	−	11.5777i	0.0369462	−	0.424175i
$746$	0.502384	+	0.290051i	0.0183936	+	0.0106195i
$747$		0			0
$748$	−1.12450	+	4.19668i	−0.0411157	+	0.153446i
$749$	3.82860	+	21.7131i	0.139894	+	0.793378i
$750$		0			0
$751$	−25.2143	+	9.17724i	−0.920081	+	0.334882i	−0.758271	−	0.651940i	$-0.773956\pi$
$751$	−25.2143	+	9.17724i	−0.920081	+	0.334882i	−0.161810	+	0.986822i	$0.551733\pi$
$752$	−1.32863	+	0.930319i	−0.0484503	+	0.0339253i
$753$		0			0
$754$	16.6882	+	19.8882i	0.607748	+	0.724286i
$755$	−2.16516	−	8.06809i	−0.0787984	−	0.293628i
$756$		0			0
$757$	2.62217	−	2.62217i	0.0953042	−	0.0953042i	−0.657847	−	0.753151i	$-0.728533\pi$
$757$	2.62217	−	2.62217i	0.0953042	−	0.0953042i	0.753151	+	0.657847i	$0.228533\pi$
$758$	−3.08940	+	35.3120i	−0.112212	+	1.28259i
$759$		0			0
$760$	6.87051	+	5.76055i	0.249220	+	0.208957i
$761$	7.85627	+	21.5849i	0.284789	+	0.782452i	0.996774	+	0.0802575i	$0.0255743\pi$
$761$	7.85627	+	21.5849i	0.284789	+	0.782452i	−0.711985	+	0.702195i	$0.752204\pi$
$762$		0			0
$763$	−2.70850	+	3.86814i	−0.0980544	+	0.140036i
$764$	−7.17219	−	12.4226i	−0.259481	−	0.449434i
$765$		0			0
$766$	11.7925	−	20.4252i	0.426081	−	0.737994i
$767$	0.803908	+	1.72399i	0.0290274	+	0.0622496i
$768$		0			0
$769$	23.2860	−	27.7511i	0.839714	−	1.00073i	−0.160193	−	0.987086i	$-0.551212\pi$
$769$	23.2860	−	27.7511i	0.839714	−	1.00073i	0.999907	−	0.0136460i	$-0.00434379\pi$
$770$	−12.7251	−	5.92788i	−0.458582	−	0.213626i
$771$		0			0
$772$	3.82694	−	1.78453i	0.137735	−	0.0642268i
$773$	−7.78565	−	29.0565i	−0.280030	−	1.04509i	−0.952395	−	0.304868i	$-0.901388\pi$
$773$	−7.78565	−	29.0565i	−0.280030	−	1.04509i	0.672364	−	0.740220i	$-0.265279\pi$
$774$		0			0
$775$	−31.5450	−	18.1802i	−1.13313	−	0.653052i
$776$	5.33263	−	0.940286i	0.191430	−	0.0337543i
$777$		0			0
$778$	23.6799	+	11.0421i	0.848966	+	0.395879i
$779$	4.15169	−	23.5454i	0.148750	−	0.843602i
$780$		0			0
$781$	−21.3925	+	17.9504i	−0.765484	+	0.642318i
$782$	−4.85847	−	4.85847i	−0.173738	−	0.173738i
$783$		0			0
$784$			1.09725i			0.0391875i
$785$	32.1273	−	5.67764i	1.14667	−	0.202644i
$786$		0			0
$787$	10.6829	+	15.2568i	0.380806	+	0.543847i	0.963104	−	0.269128i	$-0.0867354\pi$
$787$	10.6829	+	15.2568i	0.380806	+	0.543847i	−0.582299	+	0.812975i	$0.697847\pi$
$788$	−8.05542	+	17.2749i	−0.286963	+	0.615393i
$789$		0			0
$790$	0.488770	−	1.34449i	0.0173897	−	0.0478349i
$791$	10.0374	−	5.79512i	0.356890	−	0.206051i
$792$		0			0
$793$	29.4919	−	7.90234i	1.04729	−	0.280620i
$794$	−13.0656	−	4.75550i	−0.463682	−	0.168766i
$795$		0			0
$796$	−5.13081	−	4.30526i	−0.181857	−	0.152596i
$797$	4.49988	+	51.4339i	0.159394	+	1.82188i	0.482922	+	0.875663i	$0.339575\pi$
$797$	4.49988	+	51.4339i	0.159394	+	1.82188i	−0.323528	+	0.946219i	$0.604869\pi$
$798$		0			0
$799$	−1.09244	+	3.00146i	−0.0386479	+	0.106184i
$800$	3.53281	−	3.53825i	0.124904	−	0.125096i
$801$		0			0
$802$	−19.3886	−	5.19516i	−0.684636	−	0.183448i
$803$	29.0449	+	20.3374i	1.02497	+	0.717693i
$804$		0			0
$805$	18.1806	−	12.7406i	0.640783	−	0.449048i
$806$	−25.5597	−	4.50687i	−0.900303	−	0.158748i
$807$		0			0
$808$	6.92810	+	0.606131i	0.243730	+	0.0213236i
$809$	−10.9999			−0.386737			−0.193369	−	0.981126i	$-0.561941\pi$
$809$	−10.9999			−0.386737			−0.193369	+	0.981126i	$0.561941\pi$
$810$		0			0
$811$	−44.2162			−1.55264			−0.776320	−	0.630339i	$-0.782916\pi$
$811$	−44.2162			−1.55264			−0.776320	+	0.630339i	$0.782916\pi$
$812$	20.6484	+	1.80650i	0.724617	+	0.0633958i
$813$		0			0
$814$	−19.9426	−	3.51641i	−0.698987	−	0.123250i
$815$	−0.759570	+	4.31744i	−0.0266066	+	0.151233i
$816$		0			0
$817$	−22.5850	−	15.8142i	−0.790150	−	0.553269i
$818$	−35.0942	−	9.40347i	−1.22704	−	0.328785i
$819$		0			0
$820$	−12.8801	−	3.44590i	−0.449791	−	0.120336i
$821$	12.1883	−	33.4872i	0.425376	−	1.16871i	−0.523213	−	0.852202i	$-0.675267\pi$
$821$	12.1883	−	33.4872i	0.425376	−	1.16871i	0.948589	−	0.316509i	$-0.102511\pi$
$822$		0			0
$823$	4.60547	+	52.6407i	0.160536	+	1.83494i	0.468408	+	0.883513i	$0.344828\pi$
$823$	4.60547	+	52.6407i	0.160536	+	1.83494i	−0.307871	+	0.951428i	$0.599617\pi$
$824$	−2.76123	−	2.31694i	−0.0961919	−	0.0807146i
$825$		0			0
$826$	1.42707	+	0.519411i	0.0496541	+	0.0180726i
$827$	2.08759	−	0.559368i	0.0725926	−	0.0194511i	−0.222340	−	0.974969i	$-0.571369\pi$
$827$	2.08759	−	0.559368i	0.0725926	−	0.0194511i	0.294933	+	0.955518i	$0.404703\pi$
$828$		0			0
$829$	−11.6419	+	6.72145i	−0.404340	+	0.233446i	−0.688355	−	0.725374i	$-0.741667\pi$
$829$	−11.6419	+	6.72145i	−0.404340	+	0.233446i	0.284015	+	0.958820i	$0.408333\pi$
$830$	12.1274	−	5.66076i	0.420947	−	0.196488i
$831$		0			0
$832$	1.50632	−	3.23030i	0.0522221	−	0.111991i
$833$	1.23938	+	1.77001i	0.0429418	+	0.0613273i
$834$		0			0
$835$	4.98103	+	28.1855i	0.172376	+	0.975398i
$836$			8.84638i			0.305958i
$837$		0			0
$838$	2.21599	+	2.21599i	0.0765500	+	0.0765500i
$839$	−15.9939	+	13.4205i	−0.552171	+	0.463326i	−0.875675	−	0.482900i	$-0.839583\pi$
$839$	−15.9939	+	13.4205i	−0.552171	+	0.463326i	0.323504	+	0.946227i	$0.395139\pi$
$840$		0			0
$841$	4.17756	−	23.6921i	0.144054	−	0.816970i
$842$	−18.7587	−	8.74732i	−0.646467	−	0.301453i
$843$		0			0
$844$	11.1432	−	1.96485i	0.383565	−	0.0676328i
$845$	−0.468435	−	0.468075i	−0.0161146	−	0.0161023i
$846$		0			0
$847$	4.51647	+	16.8557i	0.155188	+	0.579168i
$848$	11.8903	−	5.54454i	0.408315	−	0.190400i
$849$		0			0
$850$	1.70235	−	9.69810i	0.0583901	−	0.332642i
$851$	20.5849	−	24.5322i	0.705642	−	0.840952i
$852$		0			0
$853$	5.95414	+	12.7687i	0.203866	+	0.437192i	0.981484	−	0.191545i	$-0.0613499\pi$
$853$	5.95414	+	12.7687i	0.203866	+	0.437192i	−0.777618	+	0.628737i	$0.783572\pi$
$854$	12.1879	−	21.1101i	0.417063	−	0.722374i
$855$		0			0
$856$	−3.87410	−	6.71014i	−0.132414	−	0.229348i
$857$	−24.9721	+	35.6638i	−0.853029	+	1.21825i	0.121185	+	0.992630i	$0.461330\pi$
$857$	−24.9721	+	35.6638i	−0.853029	+	1.21825i	−0.974215	+	0.225622i	$0.927558\pi$
$858$		0			0
$859$	−7.49726	−	20.5986i	−0.255803	−	0.702814i	−0.999415	−	0.0342019i	$-0.989111\pi$
$859$	−7.49726	−	20.5986i	−0.255803	−	0.702814i	0.743612	−	0.668612i	$-0.233111\pi$
$860$	−9.87869	+	11.7822i	−0.336860	+	0.401768i
$861$		0			0
$862$	0.740656	−	8.46574i	0.0252269	−	0.288344i
$863$	−23.8174	+	23.8174i	−0.810752	+	0.810752i	−0.984747	−	0.173994i	$-0.944333\pi$
$863$	−23.8174	+	23.8174i	−0.810752	+	0.810752i	0.173994	+	0.984747i	$0.444333\pi$
$864$		0			0
$865$	49.7145	+	28.6772i	1.69034	+	0.975053i
$866$	−3.15406	−	3.75887i	−0.107179	−	0.127732i
$867$		0			0
$868$	−16.9735	+	11.8849i	−0.576117	+	0.403401i
$869$	1.32638	−	0.482763i	0.0449944	−	0.0163766i
$870$		0			0
$871$	−8.00194	−	45.3813i	−0.271136	−	1.53769i
$872$	0.429502	−	1.60292i	0.0145448	−	0.0542819i
$873$		0			0
$874$	−12.1157	−	6.99500i	−0.409820	−	0.236610i
$875$	29.9083	+	10.8467i	1.01108	+	0.366685i
$876$		0			0
$877$	−12.2383	+	1.07072i	−0.413259	+	0.0361555i	−0.291890	−	0.956452i	$-0.594284\pi$
$877$	−12.2383	+	1.07072i	−0.413259	+	0.0361555i	−0.121369	+	0.992607i	$0.538729\pi$
$878$	10.4220	−	0.911806i	0.351725	−	0.0307719i
$879$		0			0
$880$	4.91472	+	0.428079i	0.165675	+	0.0144305i
$881$	14.6934	+	8.48321i	0.495032	+	0.285807i	0.726660	−	0.686998i	$-0.241072\pi$
$881$	14.6934	+	8.48321i	0.495032	+	0.285807i	−0.231628	+	0.972804i	$0.574405\pi$
$882$		0			0
$883$	7.44399	−	27.7814i	0.250510	−	0.934917i	−0.720023	−	0.693950i	$-0.755869\pi$
$883$	7.44399	−	27.7814i	0.250510	−	0.934917i	0.970533	−	0.240967i	$-0.0774645\pi$
$884$	−1.21883	−	6.91235i	−0.0409938	−	0.232487i
$885$		0			0
$886$	21.2876	−	7.74806i	0.715172	−	0.260301i
$887$	8.47972	−	5.93756i	0.284721	−	0.199364i	−0.422488	−	0.906369i	$-0.638843\pi$
$887$	8.47972	−	5.93756i	0.284721	−	0.199364i	0.707209	+	0.707005i	$0.249954\pi$
$888$		0			0
$889$	−39.3349	−	46.8775i	−1.31925	−	1.57222i
$890$	−6.17728	+	10.7089i	−0.207063	+	0.358962i
$891$		0			0
$892$	−3.06648	+	3.06648i	−0.102673	+	0.102673i
$893$	−0.566822	+	6.47881i	−0.0189680	+	0.216805i
$894$		0			0
$895$	21.7480	−	1.91113i	0.726956	−	0.0638820i
$896$	−0.973241	−	2.67396i	−0.0325137	−	0.0893307i
$897$		0			0
$898$	10.7501	−	15.3528i	0.358737	−	0.512329i
$899$	26.5205	+	45.9348i	0.884507	+	1.53201i
$900$		0			0
$901$	12.9180	−	22.3745i	0.430359	−	0.745404i
$902$	−5.55966	−	11.9227i	−0.185116	−	0.396983i
$903$		0			0
$904$	−2.61813	+	3.12016i	−0.0870777	+	0.103775i
$905$	17.4711	−	37.5045i	0.580759	−	1.24669i
$906$		0			0
$907$	28.3676	−	13.2280i	0.941930	−	0.439229i	0.109890	−	0.993944i	$-0.464950\pi$
$907$	28.3676	−	13.2280i	0.941930	−	0.439229i	0.832041	+	0.554714i	$0.187173\pi$
$908$	2.87694	+	10.7369i	0.0954746	+	0.356316i
$909$		0			0
$910$	22.6789	−	0.00871933i	0.751797	−	0.000289043i
$911$	−45.1582	+	7.96262i	−1.49616	+	0.263813i	−0.861015	−	0.508580i	$-0.830171\pi$
$911$	−45.1582	+	7.96262i	−1.49616	+	0.263813i	−0.635144	+	0.772393i	$0.719059\pi$
$912$		0			0
$913$	11.9678	+	5.58068i	0.396077	+	0.184694i
$914$	−0.503500	+	2.85549i	−0.0166543	+	0.0944512i
$915$		0			0
$916$	−7.68081	+	6.44496i	−0.253781	+	0.212948i
$917$	−18.2805	−	18.2805i	−0.603675	−	0.603675i
$918$		0			0
$919$		−	13.2353i		−	0.436591i	−0.975883	−	0.218295i	$-0.929950\pi$
$919$		−	13.2353i		−	0.436591i	0.975883	−	0.218295i	$-0.0700496\pi$
$920$	−4.47245	+	6.39255i	−0.147452	+	0.210756i
$921$		0			0
$922$	20.4955	+	29.2706i	0.674982	+	0.963974i
$923$	19.0664	−	40.8880i	0.627578	−	1.34584i
$924$		0			0
$925$	45.7212	+	3.96466i	1.50330	+	0.130357i
$926$	30.9201	−	17.8517i	1.01610	−	0.586644i
$927$		0			0
$928$	−7.03587	+	1.88525i	−0.230964	+	0.0618865i
$929$	47.0429	+	17.1222i	1.54343	+	0.561762i	0.966864	−	0.255291i	$-0.0821711\pi$
$929$	47.0429	+	17.1222i	1.54343	+	0.561762i	0.576564	+	0.817052i	$0.304393\pi$
$930$		0			0
$931$	3.37031	+	2.82802i	0.110457	+	0.0926847i
$932$	−1.26124	−	14.4160i	−0.0413133	−	0.472213i
$933$		0			0
$934$	−3.96830	+	10.9028i	−0.129847	+	0.356751i
$935$	8.41165	−	4.86078i	0.275090	−	0.158965i
$936$		0			0
$937$	−32.7445	−	8.77387i	−1.06972	−	0.286630i	−0.319340	−	0.947640i	$-0.603461\pi$
$937$	−32.7445	−	8.77387i	−1.06972	−	0.286630i	−0.750377	+	0.661010i	$0.770128\pi$
$938$	−30.1364	−	21.1017i	−0.983987	−	0.688995i
$939$		0			0
$940$	3.57196	+	0.628417i	0.116504	+	0.0204967i
$941$	29.5834	+	5.21636i	0.964393	+	0.170048i	0.633605	−	0.773657i	$-0.281574\pi$
$941$	29.5834	+	5.21636i	0.964393	+	0.170048i	0.330788	+	0.943705i	$0.392686\pi$
$942$		0			0
$943$	20.7251	+	1.81321i	0.674902	+	0.0590463i
$944$	−0.533692			−0.0173702
$945$		0			0
$946$	−15.1705			−0.493237
$947$	−4.89240	−	0.428029i	−0.158982	−	0.0139091i	0.00738703	−	0.999973i	$-0.497649\pi$
$947$	−4.89240	−	0.428029i	−0.158982	−	0.0139091i	−0.166369	+	0.986064i	$0.553204\pi$
$948$		0			0
$949$	−56.4117	−	9.94690i	−1.83120	−	0.322890i
$950$	−1.76269	−	19.9708i	−0.0571893	−	0.647938i
$951$		0			0
$952$	−4.59029	−	3.21415i	−0.148772	−	0.104171i
$953$	−2.19037	−	0.586908i	−0.0709530	−	0.0190118i	0.223168	−	0.974780i	$-0.428360\pi$
$953$	−2.19037	−	0.586908i	−0.0709530	−	0.0190118i	−0.294121	+	0.955768i	$0.595027\pi$
$954$		0			0
$955$	−8.28971	+	30.9853i	−0.268249	+	1.00266i
$956$	2.83161	−	7.77979i	0.0915808	−	0.251616i
$957$		0			0
$958$	2.06063	+	23.5531i	0.0665759	+	0.760966i
$959$	−27.9623	−	23.4632i	−0.902950	−	0.757665i
$960$		0			0
$961$	−20.6960	−	7.53274i	−0.667614	−	0.242991i
$962$	31.5999	−	8.46717i	1.01882	−	0.272992i
$963$		0			0
$964$	−24.1339	+	13.9337i	−0.777299	+	0.448774i
$965$	−8.87377	−	3.22592i	−0.285657	−	0.103846i
$966$		0			0
$967$	−6.38350	+	13.6895i	−0.205279	+	0.440223i	−0.981812	−	0.189853i	$-0.939199\pi$
$967$	−6.38350	+	13.6895i	−0.205279	+	0.440223i	0.776533	+	0.630077i	$0.216977\pi$
$968$	−3.51743	−	5.02341i	−0.113054	−	0.161458i
$969$		0			0
$970$	−9.92102	−	6.94109i	−0.318545	−	0.222865i
$971$		−	1.09847i		−	0.0352515i	−0.999845	−	0.0176258i	$-0.994389\pi$
$971$		−	1.09847i		−	0.0352515i	0.999845	−	0.0176258i	$-0.00561074\pi$
$972$		0			0
$973$	7.71412	+	7.71412i	0.247303	+	0.247303i
$974$	26.3200	−	22.0851i	0.843348	−	0.707653i
$975$		0			0
$976$	−1.48752	+	8.43613i	−0.0476143	+	0.270034i
$977$	13.4583	+	6.27573i	0.430571	+	0.200778i	0.625807	−	0.779978i	$-0.284770\pi$
$977$	13.4583	+	6.27573i	0.430571	+	0.200778i	−0.195237	+	0.980756i	$0.562547\pi$
$978$		0			0
$979$	−12.0126	+	2.11815i	−0.383926	+	0.0676964i
$980$	1.73424	−	1.73557i	0.0553981	−	0.0554408i
$981$		0			0
$982$	−7.82798	−	29.2144i	−0.249801	−	0.932270i
$983$	−29.9762	+	13.9781i	−0.956092	+	0.445833i	−0.837093	−	0.547061i	$-0.815747\pi$
$983$	−29.9762	+	13.9781i	−0.956092	+	0.445833i	−0.119000	+	0.992894i	$0.537969\pi$
$984$		0			0
$985$	40.0452	−	14.5927i	1.27595	−	0.464962i
$986$	−9.22036	+	10.9884i	−0.293636	+	0.349942i
$987$		0			0
$988$	−6.03985	−	12.9525i	−0.192153	−	0.412074i
$989$	11.9956	−	20.7771i	0.381439	−	0.660672i
$990$		0			0
$991$	21.5317	+	37.2940i	0.683977	+	1.18468i	0.973757	+	0.227589i	$0.0730843\pi$
$991$	21.5317	+	37.2940i	0.683977	+	1.18468i	−0.289781	+	0.957093i	$0.593582\pi$
$992$	4.17665	−	5.96488i	0.132609	−	0.189385i
$993$		0			0
$994$	−12.3189	−	33.8460i	−0.390733	−	1.07353i
$995$	1.31105	+	14.9192i	0.0415629	+	0.472972i
$996$		0			0
$997$	−0.765510	+	8.74982i	−0.0242439	+	0.277109i	0.974390	+	0.224863i	$0.0721936\pi$
$997$	−0.765510	+	8.74982i	−0.0242439	+	0.277109i	−0.998634	+	0.0522461i	$0.983362\pi$
$998$	−6.32670	+	6.32670i	−0.200268	+	0.200268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.3		216
3.2	odd	2		270.2.r.a.113.12	✓	216
5.2	odd	4	inner	810.2.s.a.287.14		216
15.2	even	4		270.2.r.a.167.2	yes	216
27.11	odd	18	inner	810.2.s.a.683.14		216
27.16	even	9		270.2.r.a.173.2	yes	216
135.92	even	36	inner	810.2.s.a.197.3		216
135.97	odd	36		270.2.r.a.227.12	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.12	✓	216	3.2	odd	2
270.2.r.a.167.2	yes	216	15.2	even	4
270.2.r.a.173.2	yes	216	27.16	even	9
270.2.r.a.227.12	yes	216	135.97	odd	36
810.2.s.a.197.3		216	135.92	even	36	inner
810.2.s.a.287.14		216	5.2	odd	4	inner
810.2.s.a.683.14		216	27.11	odd	18	inner
810.2.s.a.773.3		216	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-1.28326 - 1.83119i) q^{5} +(2.33095 + 1.63215i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.11878 + 1.93606i) q^{10} +(-0.754583 + 2.07320i) q^{11} +(-0.310645 - 3.55068i) q^{13} +(-2.17983 - 1.82909i) q^{14} +(0.939693 + 0.342020i) q^{16} +(1.90217 - 0.509686i) q^{17} +(3.47249 - 2.00484i) q^{19} +(-0.945782 - 2.02620i) q^{20} +(0.932403 - 1.99954i) q^{22} +(2.00124 + 2.85807i) q^{23} +(-1.70649 + 4.69978i) q^{25} +3.56425i q^{26} +(2.01212 + 2.01212i) q^{28} +(5.57992 - 4.68211i) q^{29} +(-1.26447 + 7.17115i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-1.93936 + 0.341961i) q^{34} +(-0.00244633 - 6.36288i) q^{35} +(-2.37558 - 8.86580i) q^{37} +(-3.63401 + 1.69457i) q^{38} +(0.765588 + 2.10092i) q^{40} +(3.83276 - 4.56771i) q^{41} +(-2.90599 - 6.23192i) q^{43} +(-1.10313 + 1.91067i) q^{44} +(-1.74453 - 3.02161i) q^{46} +(-0.930319 + 1.32863i) q^{47} +(0.375281 + 1.03108i) q^{49} +(2.10961 - 4.53316i) q^{50} +(0.310645 - 3.55068i) q^{52} +(9.27688 - 9.27688i) q^{53} +(4.76474 - 1.27867i) q^{55} +(-1.82909 - 2.17983i) q^{56} +(-5.96676 + 4.17797i) q^{58} +(-0.501506 + 0.182533i) q^{59} +(1.48752 + 8.43613i) q^{61} +(1.88466 - 7.03365i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-6.10332 + 5.12530i) q^{65} +(12.8796 - 1.12682i) q^{67} +(1.96178 - 0.171634i) q^{68} +(-0.552124 + 6.33888i) q^{70} +(10.9618 + 6.32882i) q^{71} +(4.15955 - 15.5236i) q^{73} +(1.59384 + 9.03911i) q^{74} +(3.76787 - 1.37139i) q^{76} +(-5.14267 + 3.60094i) q^{77} +(-0.411239 - 0.490096i) q^{79} +(-0.579567 - 2.15965i) q^{80} +(-4.21628 + 4.21628i) q^{82} +(0.521651 - 5.96250i) q^{83} +(-3.37431 - 2.82918i) q^{85} +(2.35178 + 6.46147i) q^{86} +(1.26545 - 1.80726i) q^{88} +(2.76440 + 4.78809i) q^{89} +(5.07115 - 8.78349i) q^{91} +(1.47454 + 3.16216i) q^{92} +(1.04258 - 1.24250i) q^{94} +(-8.12735 - 3.78604i) q^{95} +(-4.90756 + 2.28843i) q^{97} +(-0.283989 - 1.05986i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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