LMFDB - Embedded newform 864.2.bn.a.35.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(35,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("864.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			35.38
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22979 - 0.698290i) q^{2} +(1.02478 - 1.71750i) q^{4} +(1.23783 + 0.949818i) q^{5} +(-0.182169 + 0.0488121i) q^{7} +(0.0609543 - 2.82777i) q^{8} +O(q^{10})$	\(q+(1.22979 - 0.698290i) q^{2} +(1.02478 - 1.71750i) q^{4} +(1.23783 + 0.949818i) q^{5} +(-0.182169 + 0.0488121i) q^{7} +(0.0609543 - 2.82777i) q^{8} +(2.18552 + 0.303717i) q^{10} +(-0.272333 + 2.06858i) q^{11} +(5.07750 - 0.668466i) q^{13} +(-0.189945 + 0.187236i) q^{14} +(-1.89964 - 3.52014i) q^{16} +6.30311 q^{17} +(-4.50721 - 1.86695i) q^{19} +(2.89982 - 1.15262i) q^{20} +(1.10955 + 2.73409i) q^{22} +(-1.21725 + 4.54282i) q^{23} +(-0.664034 - 2.47821i) q^{25} +(5.77750 - 4.36765i) q^{26} +(-0.102849 + 0.362898i) q^{28} +(-2.61679 - 3.41027i) q^{29} +(5.30049 - 3.06024i) q^{31} +(-4.79424 - 3.00254i) q^{32} +(7.75152 - 4.40140i) q^{34} +(-0.271856 - 0.112607i) q^{35} +(1.61800 + 3.90619i) q^{37} +(-6.84661 + 0.851381i) q^{38} +(2.76132 - 3.44239i) q^{40} +(-3.10492 - 0.831961i) q^{41} +(7.37655 + 0.971142i) q^{43} +(3.27371 + 2.58758i) q^{44} +(1.67525 + 6.43673i) q^{46} +(-1.00866 - 0.582347i) q^{47} +(-6.03137 + 3.48222i) q^{49} +(-2.54713 - 2.58400i) q^{50} +(4.05524 - 9.40567i) q^{52} +(-3.04502 - 7.35132i) q^{53} +(-2.30187 + 2.30187i) q^{55} +(0.126925 + 0.518108i) q^{56} +(-5.59947 - 2.36665i) q^{58} +(-5.58808 + 7.28252i) q^{59} +(-5.17233 + 3.96887i) q^{61} +(4.38157 - 7.46474i) q^{62} +(-7.99257 - 0.344730i) q^{64} +(6.91999 + 3.99526i) q^{65} +(2.18675 - 0.287891i) q^{67} +(6.45931 - 10.8256i) q^{68} +(-0.412959 + 0.0513517i) q^{70} +(-5.65361 + 5.65361i) q^{71} +(6.45325 + 6.45325i) q^{73} +(4.71745 + 3.67397i) q^{74} +(-7.82540 + 5.82794i) q^{76} +(-0.0513608 - 0.390124i) q^{77} +(-6.05908 + 10.4946i) q^{79} +(0.992060 - 6.16163i) q^{80} +(-4.39936 + 1.14499i) q^{82} +(-6.52915 - 8.50896i) q^{83} +(7.80215 + 5.98680i) q^{85} +(9.74977 - 3.95667i) q^{86} +(5.83286 + 0.896185i) q^{88} +(-1.53722 - 1.53722i) q^{89} +(-0.892335 + 0.369617i) q^{91} +(6.55491 + 6.74603i) q^{92} +(-1.64708 - 0.0118330i) q^{94} +(-3.80589 - 6.59199i) q^{95} +(4.59956 - 7.96668i) q^{97} +(-4.98575 + 8.49405i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.22979	−	0.698290i	0.869595	−	0.493766i
$2$	1.22979	−	0.698290i	0.869595	−	0.493766i
$3$		0			0
$3$		0			0
$4$	1.02478	−	1.71750i	0.512391	−	0.858752i
$5$	1.23783	+	0.949818i	0.553573	+	0.424771i	0.847297	−	0.531119i	$-0.178228\pi$
$5$	1.23783	+	0.949818i	0.553573	+	0.424771i	−0.293725	+	0.955890i	$0.594895\pi$
$6$		0			0
$7$	−0.182169	+	0.0488121i	−0.0688534	+	0.0184492i	−0.293081	−	0.956088i	$-0.594681\pi$
$7$	−0.182169	+	0.0488121i	−0.0688534	+	0.0184492i	0.224228	+	0.974537i	$0.428014\pi$
$8$	0.0609543	−	2.82777i	0.0215506	−	0.999768i
$9$		0			0
$10$	2.18552	+	0.303717i	0.691122	+	0.0960439i
$11$	−0.272333	+	2.06858i	−0.0821116	+	0.623700i	0.900067	+	0.435751i	$0.143517\pi$
$11$	−0.272333	+	2.06858i	−0.0821116	+	0.623700i	−0.982179	+	0.187949i	$0.939816\pi$
$12$		0			0
$13$	5.07750	−	0.668466i	1.40825	−	0.185399i	0.612233	−	0.790678i	$-0.290272\pi$
$13$	5.07750	−	0.668466i	1.40825	−	0.185399i	0.796014	+	0.605279i	$0.206938\pi$
$14$	−0.189945	+	0.187236i	−0.0507650	+	0.0500408i
$15$		0			0
$16$	−1.89964	−	3.52014i	−0.474911	−	0.880034i
$17$	6.30311			1.52873			0.764364	−	0.644785i	$-0.223053\pi$
$17$	6.30311			1.52873			0.764364	+	0.644785i	$0.223053\pi$
$18$		0			0
$19$	−4.50721	−	1.86695i	−1.03403	−	0.428307i	−0.199862	−	0.979824i	$-0.564049\pi$
$19$	−4.50721	−	1.86695i	−1.03403	−	0.428307i	−0.834164	+	0.551517i	$0.814049\pi$
$20$	2.89982	−	1.15262i	0.648419	−	0.257733i
$21$		0			0
$22$	1.10955	+	2.73409i	0.236558	+	0.582910i
$23$	−1.21725	+	4.54282i	−0.253813	+	0.947244i	0.714933	+	0.699193i	$0.246457\pi$
$23$	−1.21725	+	4.54282i	−0.253813	+	0.947244i	−0.968747	+	0.248052i	$0.920210\pi$
$24$		0			0
$25$	−0.664034	−	2.47821i	−0.132807	−	0.495642i
$26$	5.77750	−	4.36765i	1.13306	−	0.856566i
$27$		0			0
$28$	−0.102849	+	0.362898i	−0.0194366	+	0.0685813i
$29$	−2.61679	−	3.41027i	−0.485926	−	0.633271i	0.484465	−	0.874811i	$-0.339014\pi$
$29$	−2.61679	−	3.41027i	−0.485926	−	0.633271i	−0.970391	+	0.241540i	$0.922348\pi$
$30$		0			0
$31$	5.30049	−	3.06024i	0.951997	−	0.549635i	0.0582960	−	0.998299i	$-0.481433\pi$
$31$	5.30049	−	3.06024i	0.951997	−	0.549635i	0.893701	+	0.448664i	$0.148100\pi$
$32$	−4.79424	−	3.00254i	−0.847510	−	0.530779i
$33$		0			0
$34$	7.75152	−	4.40140i	1.32937	−	0.754833i
$35$	−0.271856	−	0.112607i	−0.0459521	−	0.0190340i
$36$		0			0
$37$	1.61800	+	3.90619i	0.265997	+	0.642173i	0.999288	−	0.0377422i	$-0.0120166\pi$
$37$	1.61800	+	3.90619i	0.265997	+	0.642173i	−0.733291	+	0.679915i	$0.762017\pi$
$38$	−6.84661	+	0.851381i	−1.11067	+	0.138112i
$39$		0			0
$40$	2.76132	−	3.44239i	0.436603	−	0.544290i
$41$	−3.10492	−	0.831961i	−0.484907	−	0.129930i	0.00807955	−	0.999967i	$-0.497428\pi$
$41$	−3.10492	−	0.831961i	−0.484907	−	0.129930i	−0.492987	+	0.870037i	$0.664095\pi$
$42$		0			0
$43$	7.37655	+	0.971142i	1.12491	+	0.148098i	0.669946	−	0.742410i	$-0.266317\pi$
$43$	7.37655	+	0.971142i	1.12491	+	0.148098i	0.454968	+	0.890508i	$0.349651\pi$
$44$	3.27371	+	2.58758i	0.493530	+	0.390092i
$45$		0			0
$46$	1.67525	+	6.43673i	0.247002	+	0.949043i
$47$	−1.00866	−	0.582347i	−0.147128	−	0.0849441i	0.424629	−	0.905367i	$-0.360405\pi$
$47$	−1.00866	−	0.582347i	−0.147128	−	0.0849441i	−0.571757	+	0.820423i	$0.693738\pi$
$48$		0			0
$49$	−6.03137	+	3.48222i	−0.861625	+	0.497459i
$50$	−2.54713	−	2.58400i	−0.360219	−	0.365432i
$51$		0			0
$52$	4.05524	−	9.40567i	0.562361	−	1.30433i
$53$	−3.04502	−	7.35132i	−0.418265	−	1.00978i	−0.982850	−	0.184407i	$-0.940964\pi$
$53$	−3.04502	−	7.35132i	−0.418265	−	1.00978i	0.564585	−	0.825375i	$-0.309036\pi$
$54$		0			0
$55$	−2.30187	+	2.30187i	−0.310385	+	0.310385i
$56$	0.126925	+	0.518108i	0.0169611	+	0.0692350i
$57$		0			0
$58$	−5.59947	−	2.36665i	−0.735246	−	0.310756i
$59$	−5.58808	+	7.28252i	−0.727506	+	0.948104i	−0.999901	−	0.0140816i	$-0.995518\pi$
$59$	−5.58808	+	7.28252i	−0.727506	+	0.948104i	0.272395	+	0.962185i	$0.412184\pi$
$60$		0			0
$61$	−5.17233	+	3.96887i	−0.662249	+	0.508161i	−0.884327	−	0.466868i	$-0.845382\pi$
$61$	−5.17233	+	3.96887i	−0.662249	+	0.508161i	0.222079	+	0.975029i	$0.428716\pi$
$62$	4.38157	−	7.46474i	0.556460	−	0.948023i
$63$		0			0
$64$	−7.99257	−	0.344730i	−0.999071	−	0.0430912i
$65$	6.91999	+	3.99526i	0.858319	+	0.495551i
$66$		0			0
$67$	2.18675	−	0.287891i	0.267154	−	0.0351714i	0.00424064	−	0.999991i	$-0.498650\pi$
$67$	2.18675	−	0.287891i	0.267154	−	0.0351714i	0.262913	+	0.964820i	$0.415317\pi$
$68$	6.45931	−	10.8256i	0.783307	−	1.31280i
$69$		0			0
$70$	−0.412959	+	0.0513517i	−0.0493580	+	0.00613771i
$71$	−5.65361	+	5.65361i	−0.670960	+	0.670960i	−0.957937	−	0.286977i	$-0.907350\pi$
$71$	−5.65361	+	5.65361i	−0.670960	+	0.670960i	0.286977	+	0.957937i	$0.407350\pi$
$72$		0			0
$73$	6.45325	+	6.45325i	0.755296	+	0.755296i	0.975462	−	0.220167i	$-0.0706601\pi$
$73$	6.45325	+	6.45325i	0.755296	+	0.755296i	−0.220167	+	0.975462i	$0.570660\pi$
$74$	4.71745	+	3.67397i	0.548392	+	0.427090i
$75$		0			0
$76$	−7.82540	+	5.82794i	−0.897635	+	0.668511i
$77$	−0.0513608	−	0.390124i	−0.00585311	−	0.0444588i
$78$		0			0
$79$	−6.05908	+	10.4946i	−0.681700	+	1.18074i	0.292762	+	0.956185i	$0.405426\pi$
$79$	−6.05908	+	10.4946i	−0.681700	+	1.18074i	−0.974462	+	0.224554i	$0.927908\pi$
$80$	0.992060	−	6.16163i	0.110916	−	0.688891i
$81$		0			0
$82$	−4.39936	+	1.14499i	−0.485828	+	0.126444i
$83$	−6.52915	−	8.50896i	−0.716668	−	0.933980i	0.283016	−	0.959115i	$-0.408665\pi$
$83$	−6.52915	−	8.50896i	−0.716668	−	0.933980i	−0.999684	+	0.0251354i	$0.991998\pi$
$84$		0			0
$85$	7.80215	+	5.98680i	0.846262	+	0.649360i
$86$	9.74977	−	3.95667i	1.05134	−	0.426659i
$87$		0			0
$88$	5.83286	+	0.896185i	0.621785	+	0.0955337i
$89$	−1.53722	−	1.53722i	−0.162945	−	0.162945i	0.620925	−	0.783870i	$-0.286757\pi$
$89$	−1.53722	−	1.53722i	−0.162945	−	0.162945i	−0.783870	+	0.620925i	$0.786757\pi$
$90$		0			0
$91$	−0.892335	+	0.369617i	−0.0935421	+	0.0387464i
$92$	6.55491	+	6.74603i	0.683396	+	0.703322i
$93$		0			0
$94$	−1.64708	−	0.0118330i	−0.169884	−	0.00122048i
$95$	−3.80589	−	6.59199i	−0.390476	−	0.676324i
$96$		0			0
$97$	4.59956	−	7.96668i	0.467015	−	0.808893i	−0.532275	−	0.846571i	$-0.678663\pi$
$97$	4.59956	−	7.96668i	0.467015	−	0.808893i	0.999290	+	0.0376780i	$0.0119961\pi$
$98$	−4.98575	+	8.49405i	−0.503637	+	0.858029i
$99$		0			0
$100$	−4.93683	−	1.39914i	−0.493683	−	0.139914i
$101$	1.72259	−	13.0843i	0.171404	−	1.30194i	−0.662095	−	0.749420i	$-0.730333\pi$
$101$	1.72259	−	13.0843i	0.171404	−	1.30194i	0.833499	−	0.552521i	$-0.186334\pi$
$102$		0			0
$103$	1.25788	−	4.69448i	0.123943	−	0.462561i	−0.875857	−	0.482571i	$-0.839703\pi$
$103$	1.25788	−	4.69448i	0.123943	−	0.462561i	0.999800	+	0.0200099i	$0.00636978\pi$
$104$	−1.58077	−	14.3988i	−0.155008	−	1.41191i
$105$		0			0
$106$	−8.87810	−	6.91430i	−0.862317	−	0.671576i
$107$	−11.1138	+	4.60349i	−1.07441	+	0.445036i	−0.848545	−	0.529122i	$-0.822521\pi$
$107$	−11.1138	+	4.60349i	−1.07441	+	0.445036i	−0.225866	+	0.974158i	$0.572521\pi$
$108$		0			0
$109$	−2.59220	+	6.25812i	−0.248288	+	0.599419i	−0.998059	−	0.0622777i	$-0.980164\pi$
$109$	−2.59220	+	6.25812i	−0.248288	+	0.599419i	0.749771	+	0.661697i	$0.230164\pi$
$110$	−1.22345	+	4.43820i	−0.116652	+	0.423166i
$111$		0			0
$112$	0.517881	+	0.548535i	0.0489352	+	0.0518316i
$113$	2.82489	+	4.89284i	0.265743	+	0.460280i	0.967758	−	0.251882i	$-0.0810495\pi$
$113$	2.82489	+	4.89284i	0.265743	+	0.460280i	−0.702015	+	0.712162i	$0.747716\pi$
$114$		0			0
$115$	−5.82159	+	4.46707i	−0.542866	+	0.416556i
$116$	−8.53879	+	0.999567i	−0.792807	+	0.0928075i
$117$		0			0
$118$	−1.78687	+	12.8581i	−0.164494	+	1.18368i
$119$	−1.14823	+	0.307668i	−0.105258	+	0.0282039i
$120$		0			0
$121$	6.42033	+	1.72032i	0.583667	+	0.156393i
$122$	−3.58947	+	8.49267i	−0.324976	+	0.768890i
$123$		0			0
$124$	0.175874	−	12.2397i	0.0157940	−	1.09916i
$125$	4.51729	−	10.9057i	0.404039	−	0.975436i
$126$		0			0
$127$		−	12.7548i		−	1.13181i	−0.824471	−	0.565904i	$-0.808527\pi$
$127$		−	12.7548i		−	1.13181i	0.824471	−	0.565904i	$-0.191473\pi$
$128$	−10.0699	+	5.15718i	−0.890064	+	0.455835i
$129$		0			0
$130$	11.3000	+	0.0811817i	0.991076	+	0.00712010i
$131$	2.33731	+	17.7536i	0.204212	+	1.55114i	0.719724	+	0.694260i	$0.244268\pi$
$131$	2.33731	+	17.7536i	0.204212	+	1.55114i	−0.515512	+	0.856882i	$0.672398\pi$
$132$		0			0
$133$	0.912204	+	0.120094i	0.0790982	+	0.0104135i
$134$	2.48821	−	1.88103i	0.214949	−	0.162496i
$135$		0			0
$136$	0.384202	−	17.8237i	0.0329450	−	1.52837i
$137$	2.77292	+	10.3487i	0.236906	+	0.884146i	0.977280	+	0.211951i	$0.0679818\pi$
$137$	2.77292	+	10.3487i	0.236906	+	0.884146i	−0.740374	+	0.672195i	$0.765352\pi$
$138$		0			0
$139$	−11.6990	+	15.2464i	−0.992297	+	1.29319i	−0.0364452	+	0.999336i	$0.511603\pi$
$139$	−11.6990	+	15.2464i	−0.992297	+	1.29319i	−0.955851	+	0.293851i	$0.905063\pi$
$140$	−0.471996	+	0.351517i	−0.0398909	+	0.0297086i
$141$		0			0
$142$	−3.00491	+	10.9006i	−0.252167	+	0.914761i
$143$			10.6853i			0.893546i
$144$		0			0
$145$		−	6.70680i		−	0.556969i
$146$	12.4424	+	3.42992i	1.02974	+	0.283862i
$147$		0			0
$148$	8.36698	+	1.22408i	0.687762	+	0.100618i
$149$	−5.98683	+	7.80219i	−0.490460	+	0.639180i	−0.971365	−	0.237593i	$-0.923642\pi$
$149$	−5.98683	+	7.80219i	−0.490460	+	0.639180i	0.480905	+	0.876773i	$0.340308\pi$
$150$		0			0
$151$	−4.21015	−	15.7125i	−0.342617	−	1.27867i	−0.895371	−	0.445321i	$-0.853090\pi$
$151$	−4.21015	−	15.7125i	−0.342617	−	1.27867i	0.552754	−	0.833345i	$-0.313577\pi$
$152$	−5.55404	+	12.6316i	−0.450492	+	1.02456i
$153$		0			0
$154$	−0.335583	−	0.443907i	−0.0270420	−	0.0357711i
$155$	9.46776	+	1.24645i	0.760469	+	0.100118i
$156$		0			0
$157$	2.49337	+	18.9390i	0.198993	+	1.51150i	0.741217	+	0.671266i	$0.234249\pi$
$157$	2.49337	+	18.9390i	0.198993	+	1.51150i	−0.542224	+	0.840234i	$0.682418\pi$
$158$	−0.123118	+	17.1372i	−0.00979470	+	1.36336i
$159$		0			0
$160$	−3.08258	−	8.27028i	−0.243699	−	0.653823i
$161$		−	0.886979i		−	0.0699037i
$162$		0			0
$163$	−4.72964	+	11.4184i	−0.370454	+	0.894355i	0.623219	+	0.782047i	$0.285824\pi$
$163$	−4.72964	+	11.4184i	−0.370454	+	0.894355i	−0.993673	+	0.112308i	$0.964176\pi$
$164$	−4.61076	+	4.48013i	−0.360040	+	0.349840i
$165$		0			0
$166$	−13.9712	−	5.90502i	−1.08438	−	0.458318i
$167$	−6.37075	−	1.70704i	−0.492983	−	0.132095i	0.00375827	−	0.999993i	$-0.498804\pi$
$167$	−6.37075	−	1.70704i	−0.492983	−	0.132095i	−0.496742	+	0.867898i	$0.665470\pi$
$168$		0			0
$169$	12.7772	−	3.42363i	0.982859	−	0.263356i
$170$	13.7756	+	1.91436i	1.05654	+	0.146825i
$171$		0			0
$172$	9.22730	−	11.6741i	0.703575	−	0.890138i
$173$	−14.6813	+	11.2654i	−1.11620	+	0.856490i	−0.990762	−	0.135612i	$-0.956700\pi$
$173$	−14.6813	+	11.2654i	−1.11620	+	0.856490i	−0.125437	+	0.992102i	$0.540033\pi$
$174$		0			0
$175$	0.241933	+	0.419040i	0.0182884	+	0.0316765i
$176$	7.79901	−	2.97091i	0.587873	−	0.223941i
$177$		0			0
$178$	−2.96389	−	0.817037i	−0.222153	−	0.0612395i
$179$	0.357886	−	0.864013i	0.0267496	−	0.0645793i	−0.909940	−	0.414739i	$-0.863873\pi$
$179$	0.357886	−	0.864013i	0.0267496	−	0.0645793i	0.936690	+	0.350160i	$0.113873\pi$
$180$		0			0
$181$	−10.8036	+	4.47498i	−0.803022	+	0.332622i	−0.746166	−	0.665760i	$-0.768107\pi$
$181$	−10.8036	+	4.47498i	−0.803022	+	0.332622i	−0.0568556	+	0.998382i	$0.518107\pi$
$182$	−0.839288	+	1.07766i	−0.0622121	+	0.0798816i
$183$		0			0
$184$	12.7719	+	3.71900i	0.941555	+	0.274168i
$185$	−1.70737	+	6.37198i	−0.125528	+	0.468477i
$186$		0			0
$187$	−1.71655	+	13.0385i	−0.125526	+	0.953468i
$188$	−2.03384	+	1.13559i	−0.148333	+	0.0828215i
$189$		0			0
$190$	−9.28357	−	5.44917i	−0.673501	−	0.395324i
$191$	8.75611	−	15.1660i	0.633570	−	1.09738i	−0.353246	−	0.935530i	$-0.614922\pi$
$191$	8.75611	−	15.1660i	0.633570	−	1.09738i	0.986816	−	0.161845i	$-0.0517444\pi$
$192$		0			0
$193$	8.05348	+	13.9490i	0.579702	+	1.00407i	0.995513	+	0.0946224i	$0.0301644\pi$
$193$	8.05348	+	13.9490i	0.579702	+	1.00407i	−0.415811	+	0.909451i	$0.636502\pi$
$194$	0.0934608	−	13.0092i	0.00671010	−	0.934006i
$195$		0			0
$196$	−0.200126	+	13.9274i	−0.0142947	+	0.994816i
$197$	−18.5595	+	7.68761i	−1.32231	+	0.547720i	−0.928453	−	0.371451i	$-0.878860\pi$
$197$	−18.5595	+	7.68761i	−1.32231	+	0.547720i	−0.393860	+	0.919171i	$0.628860\pi$
$198$		0			0
$199$	−13.9295	−	13.9295i	−0.987439	−	0.987439i	0.0124834	−	0.999922i	$-0.496026\pi$
$199$	−13.9295	−	13.9295i	−0.987439	−	0.987439i	−0.999922	+	0.0124834i	$0.996026\pi$
$200$	−7.04829	+	1.72668i	−0.498389	+	0.122095i
$201$		0			0
$202$	−7.01824	−	17.2939i	−0.493802	−	1.21679i
$203$	0.643161	+	0.493515i	0.0451410	+	0.0346379i
$204$		0			0
$205$	−3.05314	−	3.97893i	−0.213241	−	0.277901i
$206$	−1.73117	−	6.65161i	−0.120617	−	0.463439i
$207$		0			0
$208$	−11.9985	−	16.6037i	−0.831949	−	1.15126i
$209$	5.08939	−	8.81509i	0.352041	−	0.609752i
$210$		0			0
$211$	−1.20877	−	9.18154i	−0.0832153	−	0.632083i	−0.981331	−	0.192325i	$-0.938397\pi$
$211$	−1.20877	−	9.18154i	−0.0832153	−	0.632083i	0.898116	−	0.439759i	$-0.144936\pi$
$212$	−15.7464	−	2.30368i	−1.08147	−	0.158217i
$213$		0			0
$214$	−10.4531	+	13.4220i	−0.714560	+	0.917508i
$215$	8.20848	+	8.20848i	0.559814	+	0.559814i
$216$		0			0
$217$	−0.816209	+	0.816209i	−0.0554079	+	0.0554079i
$218$	1.18212	+	9.50630i	0.0800629	+	0.643848i
$219$		0			0
$220$	1.59456	+	6.31240i	0.107505	+	0.425582i
$221$	32.0041	−	4.21341i	2.15283	−	0.283425i
$222$		0			0
$223$	10.1056	+	5.83446i	0.676720	+	0.390705i	0.798618	−	0.601838i	$-0.205565\pi$
$223$	10.1056	+	5.83446i	0.676720	+	0.390705i	−0.121898	+	0.992543i	$0.538898\pi$
$224$	1.01992	+	0.312953i	0.0681465	+	0.0209100i
$225$		0			0
$226$	6.89065	+	4.04460i	0.458359	+	0.269043i
$227$	7.81290	−	5.99505i	0.518560	−	0.397905i	−0.316053	−	0.948742i	$-0.602358\pi$
$227$	7.81290	−	5.99505i	0.518560	−	0.397905i	0.834613	+	0.550836i	$0.185691\pi$
$228$		0			0
$229$	12.5307	−	16.3303i	0.828049	−	1.07913i	−0.167591	−	0.985857i	$-0.553599\pi$
$229$	12.5307	−	16.3303i	0.828049	−	1.07913i	0.995640	−	0.0932778i	$-0.0297345\pi$
$230$	−4.04005	+	9.55873i	−0.266393	+	0.630284i
$231$		0			0
$232$	−9.80296	+	7.19182i	−0.643596	+	0.472166i
$233$	−6.59241	+	6.59241i	−0.431883	+	0.431883i	−0.889269	−	0.457385i	$-0.848786\pi$
$233$	−6.59241	+	6.59241i	−0.431883	+	0.431883i	0.457385	+	0.889269i	$0.348786\pi$
$234$		0			0
$235$	−0.695416	−	1.67888i	−0.0453640	−	0.109518i
$236$	6.78120	+	17.0605i	0.441419	+	1.11055i
$237$		0			0
$238$	−1.19725	+	1.18017i	−0.0776059	+	0.0764988i
$239$	2.57351	−	1.48582i	0.166466	−	0.0961094i	−0.414452	−	0.910071i	$-0.636027\pi$
$239$	2.57351	−	1.48582i	0.166466	−	0.0961094i	0.580919	+	0.813962i	$0.302693\pi$
$240$		0			0
$241$	−12.7728	−	7.37437i	−0.822768	−	0.475025i	0.0286023	−	0.999591i	$-0.490894\pi$
$241$	−12.7728	−	7.37437i	−0.822768	−	0.475025i	−0.851370	+	0.524566i	$0.824228\pi$
$242$	9.09697	−	2.36761i	0.584775	−	0.152196i
$243$		0			0
$244$	1.51604	+	12.9507i	0.0970542	+	0.829085i
$245$	−10.7733	−	1.41833i	−0.688279	−	0.0906136i
$246$		0			0
$247$	−24.1334	−	6.46652i	−1.53557	−	0.411455i
$248$	−8.33057	−	15.1751i	−0.528992	−	0.963620i
$249$		0			0
$250$	−2.06001	−	16.5661i	−0.130286	−	1.04773i
$251$	2.22936	+	5.38215i	0.140716	+	0.339718i	0.978489	−	0.206301i	$-0.0661426\pi$
$251$	2.22936	+	5.38215i	0.140716	+	0.339718i	−0.837773	+	0.546019i	$0.816143\pi$
$252$		0			0
$253$	−9.06569	−	3.75513i	−0.569955	−	0.236083i
$254$	−8.90657	−	15.6858i	−0.558848	−	0.984215i
$255$		0			0
$256$	−8.78272	+	13.3740i	−0.548920	+	0.835875i
$257$	25.6176	−	14.7904i	1.59798	−	0.922597i	0.606110	−	0.795381i	$-0.292729\pi$
$257$	25.6176	−	14.7904i	1.59798	−	0.922597i	0.991875	−	0.127216i	$-0.0406041\pi$
$258$		0			0
$259$	−0.485418	−	0.632609i	−0.0301624	−	0.0393084i
$260$	13.9534	−	7.79084i	0.865351	−	0.483168i
$261$		0			0
$262$	15.2716	+	20.2012i	0.943482	+	1.24803i
$263$	−2.36165	−	8.81380i	−0.145626	−	0.543482i	−0.999727	−	0.0233752i	$-0.992559\pi$
$263$	−2.36165	−	8.81380i	−0.145626	−	0.543482i	0.854101	−	0.520107i	$-0.174108\pi$
$264$		0			0
$265$	3.21321	−	11.9919i	0.197386	−	0.736655i
$266$	1.20568	−	0.489292i	0.0739252	−	0.0300004i
$267$		0			0
$268$	1.74649	−	4.05077i	0.106684	−	0.247440i
$269$	−3.17330	−	1.31442i	−0.193479	−	0.0801417i	0.283840	−	0.958872i	$-0.408392\pi$
$269$	−3.17330	−	1.31442i	−0.193479	−	0.0801417i	−0.477319	+	0.878730i	$0.658392\pi$
$270$		0			0
$271$	5.08474			0.308876			0.154438	−	0.988002i	$-0.450643\pi$
$271$	5.08474			0.308876			0.154438	+	0.988002i	$0.450643\pi$
$272$	−11.9737	−	22.1878i	−0.726009	−	1.34533i
$273$		0			0
$274$	10.6365	+	10.7904i	0.642574	+	0.651873i
$275$	5.30721	−	0.698708i	0.320037	−	0.0421337i
$276$		0			0
$277$	1.87712	−	14.2581i	0.112785	−	0.856686i	−0.837747	−	0.546059i	$-0.816127\pi$
$277$	1.87712	−	14.2581i	0.112785	−	0.856686i	0.950532	−	0.310628i	$-0.100539\pi$
$278$	−3.74092	+	26.9193i	−0.224365	+	1.61451i
$279$		0			0
$280$	−0.334996	+	0.761883i	−0.0200199	+	0.0455312i
$281$	17.8709	−	4.78849i	1.06609	−	0.285657i	0.317203	−	0.948358i	$-0.397256\pi$
$281$	17.8709	−	4.78849i	1.06609	−	0.285657i	0.748885	+	0.662700i	$0.230590\pi$
$282$		0			0
$283$	−5.06226	−	3.88441i	−0.300920	−	0.230904i	0.447253	−	0.894407i	$-0.352402\pi$
$283$	−5.06226	−	3.88441i	−0.300920	−	0.230904i	−0.748174	+	0.663503i	$0.769069\pi$
$284$	3.91638	+	15.5038i	0.232394	+	0.919982i
$285$		0			0
$286$	7.46141	+	13.1407i	0.441202	+	0.777024i
$287$	0.606230			0.0357846
$288$		0			0
$289$	22.7292			1.33701
$290$	−4.68329	−	8.24797i	−0.275012	−	0.484338i
$291$		0			0
$292$	17.6967	−	4.47031i	1.03562	−	0.261605i
$293$	−3.71685	−	2.85204i	−0.217141	−	0.166618i	0.494464	−	0.869198i	$-0.335364\pi$
$293$	−3.71685	−	2.85204i	−0.217141	−	0.166618i	−0.711604	+	0.702580i	$0.752031\pi$
$294$		0			0
$295$	−13.8341	+	3.70685i	−0.805455	+	0.215821i
$296$	11.1444	−	4.33722i	0.647756	−	0.252096i
$297$		0			0
$298$	−1.91437	+	13.7756i	−0.110897	+	0.798000i
$299$	−3.14385	+	23.8799i	−0.181813	+	1.38101i
$300$		0			0
$301$	−1.39118	+	0.183153i	−0.0801865	+	0.0105567i
$302$	−16.1495	−	16.3832i	−0.929299	−	0.942748i
$303$		0			0
$304$	1.99018	+	19.4125i	0.114145	+	1.11339i
$305$	−10.1721			−0.582455
$306$		0			0
$307$	1.25336	+	0.519157i	0.0715328	+	0.0296299i	0.418163	−	0.908372i	$-0.362674\pi$
$307$	1.25336	+	0.519157i	0.0715328	+	0.0296299i	−0.346630	+	0.938002i	$0.612674\pi$
$308$	−0.722674	−	0.311580i	−0.0411782	−	0.0177539i
$309$		0			0
$310$	12.5138	−	5.07836i	0.710735	−	0.288432i
$311$	−3.21569	+	12.0011i	−0.182345	+	0.680520i	0.812839	+	0.582489i	$0.197921\pi$
$311$	−3.21569	+	12.0011i	−0.182345	+	0.680520i	−0.995183	+	0.0980311i	$0.968746\pi$
$312$		0			0
$313$	−5.69999	−	21.2727i	−0.322183	−	1.20240i	−0.917114	−	0.398625i	$-0.869487\pi$
$313$	−5.69999	−	21.2727i	−0.322183	−	1.20240i	0.594931	−	0.803776i	$-0.297179\pi$
$314$	16.2913	+	21.5500i	0.919370	+	1.21614i
$315$		0			0
$316$	11.8153	+	21.1612i	0.664665	+	1.19041i
$317$	−4.20063	−	5.47436i	−0.235931	−	0.307471i	0.660350	−	0.750958i	$-0.270408\pi$
$317$	−4.20063	−	5.47436i	−0.235931	−	0.307471i	−0.896281	+	0.443487i	$0.853741\pi$
$318$		0			0
$319$	7.76705	−	4.48431i	0.434871	−	0.251073i
$320$	−9.56598	−	8.01820i	−0.534755	−	0.448231i
$321$		0			0
$322$	−0.619368	−	1.09080i	−0.0345160	−	0.0607879i
$323$	−28.4095	−	11.7676i	−1.58074	−	0.654766i
$324$		0			0
$325$	−5.02824	−	12.1392i	−0.278916	−	0.673364i
$326$	2.15685	+	17.3449i	0.119457	+	0.960644i
$327$		0			0
$328$	−2.54185	+	8.72929i	−0.140350	+	0.481994i
$329$	0.212171	+	0.0568512i	0.0116974	+	0.00313431i
$330$		0			0
$331$	23.0090	+	3.02919i	1.26469	+	0.166499i	0.732875	−	0.680363i	$-0.238178\pi$
$331$	23.0090	+	3.02919i	1.26469	+	0.166499i	0.531812	+	0.846862i	$0.321511\pi$
$332$	−21.3051	+	2.49402i	−1.16927	+	0.136877i
$333$		0			0
$334$	−9.02671	+	2.34933i	−0.493920	+	0.128550i
$335$	2.98026	+	1.72065i	0.162829	+	0.0940092i
$336$		0			0
$337$	28.0526	−	16.1962i	1.52812	−	0.882261i	0.528680	−	0.848821i	$-0.322687\pi$
$337$	28.0526	−	16.1962i	1.52812	−	0.882261i	0.999441	−	0.0334395i	$-0.0106461\pi$
$338$	13.3226	−	13.1325i	0.724653	−	0.714315i
$339$		0			0
$340$	18.2779	−	7.26506i	0.991257	−	0.394003i
$341$	4.88685	+	11.7979i	0.264638	+	0.638892i
$342$		0			0
$343$	1.86226	−	1.86226i	0.100552	−	0.100552i
$344$	3.19580	−	20.8000i	0.172306	−	1.12146i
$345$		0			0
$346$	−10.1885	+	24.1059i	−0.547736	+	1.29594i
$347$	12.8019	−	16.6838i	0.687242	−	0.895631i	−0.311262	−	0.950324i	$-0.600752\pi$
$347$	12.8019	−	16.6838i	0.687242	−	0.895631i	0.998503	+	0.0546935i	$0.0174182\pi$
$348$		0			0
$349$	−12.1603	+	9.33096i	−0.650928	+	0.499475i	−0.880641	−	0.473784i	$-0.842888\pi$
$349$	−12.1603	+	9.33096i	−0.650928	+	0.499475i	0.229713	+	0.973258i	$0.426221\pi$
$350$	0.590139	+	0.346394i	0.0315443	+	0.0185155i
$351$		0			0
$352$	7.51662	−	9.09957i	0.400637	−	0.485009i
$353$	29.1219	+	16.8135i	1.55000	+	0.894894i	0.998140	+	0.0609591i	$0.0194159\pi$
$353$	29.1219	+	16.8135i	1.55000	+	0.894894i	0.551862	+	0.833935i	$0.313917\pi$
$354$		0			0
$355$	−12.3681	+	1.62829i	−0.656430	+	0.0864206i
$356$	−4.21550	+	1.06487i	−0.223421	+	0.0564378i
$357$		0			0
$358$	−0.163206	−	1.31247i	−0.00862570	−	0.0693659i
$359$	22.4302	−	22.4302i	1.18382	−	1.18382i	0.205071	−	0.978747i	$-0.434257\pi$
$359$	22.4302	−	22.4302i	1.18382	−	1.18382i	0.978747	−	0.205071i	$-0.0657426\pi$
$360$		0			0
$361$	3.39444	+	3.39444i	0.178655	+	0.178655i
$362$	−10.1613	+	13.0473i	−0.534066	+	0.685751i
$363$		0			0
$364$	−0.279630	+	1.91137i	−0.0146566	+	0.100183i
$365$	1.85859	+	14.1174i	0.0972832	+	0.738939i
$366$		0			0
$367$	−6.04156	+	10.4643i	−0.315367	+	0.546231i	−0.979515	−	0.201369i	$-0.935461\pi$
$367$	−6.04156	+	10.4643i	−0.315367	+	0.546231i	0.664149	+	0.747601i	$0.268794\pi$
$368$	18.3037	−	4.34487i	0.954146	−	0.226492i
$369$		0			0
$370$	2.34978	+	9.02846i	0.122159	+	0.469367i
$371$	0.913542	+	1.19055i	0.0474287	+	0.0618103i
$372$		0			0
$373$	−19.4821	−	14.9492i	−1.00875	−	0.774039i	−0.0344728	−	0.999406i	$-0.510975\pi$
$373$	−19.4821	−	14.9492i	−1.00875	−	0.774039i	−0.974274	+	0.225367i	$0.927642\pi$
$374$	6.99364	+	17.2333i	0.361632	+	0.891111i
$375$		0			0
$376$	−1.70823	+	2.81675i	−0.0880951	+	0.145263i
$377$	−15.5664	−	15.5664i	−0.801712	−	0.801712i
$378$		0			0
$379$	12.0738	−	5.00114i	0.620191	−	0.256891i	−0.0503881	−	0.998730i	$-0.516046\pi$
$379$	12.0738	−	5.00114i	0.620191	−	0.256891i	0.670579	+	0.741838i	$0.266046\pi$
$380$	−15.2220	−	0.218727i	−0.780871	−	0.0112205i
$381$		0			0
$382$	0.177920	−	24.7654i	0.00910317	−	1.26711i
$383$	−12.5301	−	21.7028i	−0.640260	−	1.10896i	−0.985375	−	0.170403i	$-0.945493\pi$
$383$	−12.5301	−	21.7028i	−0.640260	−	1.10896i	0.345114	−	0.938561i	$-0.387840\pi$
$384$		0			0
$385$	0.306971	−	0.531689i	0.0156447	−	0.0270974i
$386$	19.6446	+	11.5308i	0.999883	+	0.586900i
$387$		0			0
$388$	−8.96925	−	16.0639i	−0.455345	−	0.815520i
$389$	3.54358	−	26.9161i	0.179666	−	1.36470i	−0.629444	−	0.777046i	$-0.716717\pi$
$389$	3.54358	−	26.9161i	0.179666	−	1.36470i	0.809110	−	0.587657i	$-0.199949\pi$
$390$		0			0
$391$	−7.67243	+	28.6339i	−0.388012	+	1.44808i
$392$	9.47927	+	17.2676i	0.478775	+	0.872145i
$393$		0			0
$394$	−17.4562	+	22.4141i	−0.879431	+	1.12921i
$395$	−17.4681	+	7.23552i	−0.878915	+	0.364058i
$396$		0			0
$397$	−10.7365	+	25.9202i	−0.538849	+	1.30090i	0.386678	+	0.922215i	$0.373623\pi$
$397$	−10.7365	+	25.9202i	−0.538849	+	1.30090i	−0.925527	+	0.378682i	$0.876377\pi$
$398$	−26.8573	−	7.40359i	−1.34624	−	0.371109i
$399$		0			0
$400$	−7.46221	+	7.04521i	−0.373111	+	0.352260i
$401$	−1.29812	−	2.24840i	−0.0648248	−	0.112280i	0.831791	−	0.555088i	$-0.187316\pi$
$401$	−1.29812	−	2.24840i	−0.0648248	−	0.112280i	−0.896616	+	0.442808i	$0.853982\pi$
$402$		0			0
$403$	24.8676	−	19.0816i	1.23874	−	0.950522i
$404$	−20.7071	−	16.3671i	−1.03022	−	0.814296i
$405$		0			0
$406$	1.13557	+	0.157808i	0.0563575	+	0.00783189i
$407$	−8.52089	+	2.28316i	−0.422365	+	0.113172i
$408$		0			0
$409$	−33.0964	−	8.86816i	−1.63651	−	0.438503i	−0.680721	−	0.732543i	$-0.738333\pi$
$409$	−33.0964	−	8.86816i	−1.63651	−	0.438503i	−0.955793	+	0.294041i	$0.905000\pi$
$410$	−6.53318	−	2.76128i	−0.322651	−	0.136370i
$411$		0			0
$412$	−6.77373	−	6.97124i	−0.333718	−	0.343448i
$413$	0.662500	−	1.59942i	0.0325995	−	0.0787021i
$414$		0			0
$415$		−	16.7341i		−	0.821446i
$416$	−26.3499	−	12.0406i	−1.29191	−	0.590340i
$417$		0			0
$418$	0.103414	−	14.3946i	0.00505814	−	0.704063i
$419$	1.72866	+	13.1305i	0.0844507	+	0.641467i	0.980358	+	0.197226i	$0.0631932\pi$
$419$	1.72866	+	13.1305i	0.0844507	+	0.641467i	−0.895907	+	0.444241i	$0.853473\pi$
$420$		0			0
$421$	16.0885	+	2.11809i	0.784105	+	0.103229i	0.511940	−	0.859021i	$-0.328927\pi$
$421$	16.0885	+	2.11809i	0.784105	+	0.103229i	0.272165	+	0.962251i	$0.412260\pi$
$422$	−7.89792	−	10.4473i	−0.384465	−	0.508568i
$423$		0			0
$424$	−20.9735	+	8.16252i	−1.01856	+	0.396407i
$425$	−4.18548	−	15.6204i	−0.203026	−	0.757702i
$426$		0			0
$427$	0.748510	−	0.975477i	0.0362229	−	0.0472066i
$428$	−3.48272	+	23.8056i	−0.168344	+	1.15069i
$429$		0			0
$430$	15.8266	+	4.36284i	0.763228	+	0.210395i
$431$		−	29.3391i		−	1.41321i	−0.707606	−	0.706607i	$-0.750225\pi$
$431$		−	29.3391i		−	1.41321i	0.707606	−	0.706607i	$-0.249775\pi$
$432$		0			0
$433$			28.9049i			1.38908i	0.719453	+	0.694541i	$0.244393\pi$
$433$			28.9049i			1.38908i	−0.719453	+	0.694541i	$0.755607\pi$
$434$	−0.433818	+	1.57372i	−0.0208239	+	0.0755409i
$435$		0			0
$436$	8.09191	+	10.8653i	0.387532	+	0.520355i
$437$	13.9676	−	18.2029i	0.668161	−	0.870765i
$438$		0			0
$439$	−5.28812	−	19.7355i	−0.252388	−	0.941925i	−0.969525	−	0.244993i	$-0.921214\pi$
$439$	−5.28812	−	19.7355i	−0.252388	−	0.941925i	0.717137	−	0.696932i	$-0.245452\pi$
$440$	6.36886	+	6.64948i	0.303624	+	0.317001i
$441$		0			0
$442$	36.4162	−	27.5297i	1.73214	−	1.30946i
$443$	−11.1272	−	1.46493i	−0.528671	−	0.0696009i	−0.138534	−	0.990358i	$-0.544239\pi$
$443$	−11.1272	−	1.46493i	−0.528671	−	0.0696009i	−0.390137	+	0.920757i	$0.627572\pi$
$444$		0			0
$445$	−0.442733	−	3.36289i	−0.0209875	−	0.159416i
$446$	16.5019	+	0.118553i	0.781389	+	0.00561367i
$447$		0			0
$448$	1.47283	−	0.327335i	0.0695845	−	0.0154651i
$449$			2.12286i			0.100184i	0.998745	+	0.0500920i	$0.0159515\pi$
$449$			2.12286i			0.100184i	−0.998745	+	0.0500920i	$0.984049\pi$
$450$		0			0
$451$	2.56655	−	6.19620i	0.120854	−	0.291768i
$452$	11.2984	+	0.162348i	0.531431	+	0.00763622i
$453$		0			0
$454$	5.42197	−	12.8283i	0.254466	−	0.602064i
$455$	−1.45563	−	0.390034i	−0.0682408	−	0.0182851i
$456$		0			0
$457$	7.06014	−	1.89176i	0.330260	−	0.0884928i	−0.0898791	−	0.995953i	$-0.528648\pi$
$457$	7.06014	−	1.89176i	0.330260	−	0.0884928i	0.420139	+	0.907460i	$0.361981\pi$
$458$	4.00685	−	28.8329i	0.187228	−	1.34727i
$459$		0			0
$460$	1.70634	+	14.5764i	0.0795585	+	0.679627i
$461$	−0.816306	+	0.626374i	−0.0380192	+	0.0291731i	−0.627596	−	0.778539i	$-0.715961\pi$
$461$	−0.816306	+	0.626374i	−0.0380192	+	0.0291731i	0.589577	+	0.807712i	$0.299294\pi$
$462$		0			0
$463$	−13.0471	−	22.5983i	−0.606352	−	1.05023i	−0.991836	−	0.127518i	$-0.959299\pi$
$463$	−13.0471	−	22.5983i	−0.606352	−	1.05023i	0.385485	−	0.922714i	$-0.374034\pi$
$464$	−7.03364	+	15.6898i	−0.326529	+	0.728379i
$465$		0			0
$466$	−3.50389	+	12.7107i	−0.162315	+	0.588813i
$467$	−4.77434	+	11.5263i	−0.220930	+	0.533372i	−0.995017	−	0.0997073i	$-0.968209\pi$
$467$	−4.77434	+	11.5263i	−0.220930	+	0.533372i	0.774087	+	0.633079i	$0.218209\pi$
$468$		0			0
$469$	−0.384305	+	0.159184i	−0.0177456	+	0.00735045i
$470$	−2.02757	−	1.57908i	−0.0935246	−	0.0728374i
$471$		0			0
$472$	20.2527	+	16.2457i	0.932205	+	0.747769i
$473$	−4.01776	+	14.9945i	−0.184737	+	0.689448i
$474$		0			0
$475$	−1.63375	+	12.4095i	−0.0749614	+	0.569389i
$476$	−0.648267	+	2.28739i	−0.0297133	+	0.104842i
$477$		0			0
$478$	2.12735	−	3.62430i	0.0973028	−	0.165772i
$479$	17.2030	−	29.7964i	0.786023	−	1.36143i	−0.142362	−	0.989815i	$-0.545470\pi$
$479$	17.2030	−	29.7964i	0.786023	−	1.36143i	0.928386	−	0.371618i	$-0.121197\pi$
$480$		0			0
$481$	10.8265	+	18.7521i	0.493647	+	0.855022i
$482$	−20.8573	−	0.149844i	−0.950026	−	0.00682519i
$483$		0			0
$484$	9.53411	−	9.26399i	0.433369	−	0.421091i
$485$	13.2603	−	5.49262i	0.602121	−	0.249407i
$486$		0			0
$487$	10.2955	+	10.2955i	0.466536	+	0.466536i	0.900790	−	0.434255i	$-0.142988\pi$
$487$	10.2955	+	10.2955i	0.466536	+	0.466536i	−0.434255	+	0.900790i	$0.642988\pi$
$488$	10.9078	+	14.8681i	0.493771	+	0.673046i
$489$		0			0
$490$	−14.2393	+	5.77861i	−0.643266	+	0.261051i
$491$	30.7507	+	23.5959i	1.38776	+	1.06487i	0.989017	+	0.147804i	$0.0472205\pi$
$491$	30.7507	+	23.5959i	1.38776	+	1.06487i	0.398744	+	0.917062i	$0.369446\pi$
$492$		0			0
$493$	−16.4939	−	21.4953i	−0.742849	−	0.968100i
$494$	−34.1946	+	8.89962i	−1.53849	+	0.400413i
$495$		0			0
$496$	−20.8415	−	12.8451i	−0.935811	−	0.576762i
$497$	0.753949	−	1.30588i	0.0338192	−	0.0585766i
$498$		0			0
$499$	−4.08556	−	31.0329i	−0.182895	−	1.38922i	−0.798892	−	0.601475i	$-0.794580\pi$
$499$	−4.08556	−	31.0329i	−0.182895	−	1.38922i	0.615997	−	0.787748i	$-0.288753\pi$
$500$	−14.1014	−	18.9344i	−0.630632	−	0.846774i
$501$		0			0
$502$	6.49995	+	5.06219i	0.290107	+	0.225937i
$503$	12.1484	+	12.1484i	0.541668	+	0.541668i	0.924018	−	0.382349i	$-0.124885\pi$
$503$	12.1484	+	12.1484i	0.541668	+	0.541668i	−0.382349	+	0.924018i	$0.624885\pi$
$504$		0			0
$505$	14.5600	−	14.5600i	0.647911	−	0.647911i
$506$	−13.7711	+	1.71244i	−0.612200	+	0.0761275i
$507$		0			0
$508$	−21.9065	−	13.0709i	−0.971943	−	0.579929i
$509$	−32.3068	+	4.25327i	−1.43197	+	0.188523i	−0.806274	−	0.591542i	$-0.798519\pi$
$509$	−32.3068	+	4.25327i	−1.43197	+	0.188523i	−0.625699	+	0.780065i	$0.715186\pi$
$510$		0			0
$511$	−1.49058	−	0.860586i	−0.0659393	−	0.0380701i
$512$	−1.46200	+	22.5801i	−0.0646118	+	0.997910i
$513$		0			0
$514$	21.1764	−	36.0776i	0.934053	−	1.59132i
$515$	6.01594	−	4.61619i	0.265094	−	0.203414i
$516$		0			0
$517$	1.47932	−	1.92789i	0.0650605	−	0.0847885i
$518$	−1.03871	−	0.439016i	−0.0456382	−	0.0192892i
$519$		0			0
$520$	11.7195	−	19.3246i	0.513933	−	0.847440i
$521$	17.0885	−	17.0885i	0.748659	−	0.748659i	−0.225568	−	0.974227i	$-0.572424\pi$
$521$	17.0885	−	17.0885i	0.748659	−	0.748659i	0.974227	+	0.225568i	$0.0724239\pi$
$522$		0			0
$523$	9.11458	+	22.0046i	0.398553	+	0.962192i	0.988010	+	0.154392i	$0.0493419\pi$
$523$	9.11458	+	22.0046i	0.398553	+	0.962192i	−0.589457	+	0.807800i	$0.700658\pi$
$524$	32.8872	+	14.1793i	1.43668	+	0.619424i
$525$		0			0
$526$	−9.05893	−	9.19003i	−0.394988	−	0.400704i
$527$	33.4096	−	19.2890i	1.45534	−	0.840243i
$528$		0			0
$529$	0.763016	+	0.440528i	0.0331746	+	0.0191534i
$530$	−4.42222	−	16.9913i	−0.192089	−	0.738054i
$531$		0			0
$532$	1.14107	−	1.44364i	0.0494718	−	0.0625899i
$533$	−16.3214	−	2.14875i	−0.706958	−	0.0930727i
$534$		0			0
$535$	−18.1294	−	4.85777i	−0.783804	−	0.210020i
$536$	−0.680797	−	6.20116i	−0.0294059	−	0.267849i
$537$		0			0
$538$	−4.82035	+	0.599413i	−0.207820	+	0.0258425i
$539$	−5.56069	−	13.4247i	−0.239516	−	0.578243i
$540$		0			0
$541$	17.1432	+	7.10093i	0.737042	+	0.305293i	0.719442	−	0.694552i	$-0.244397\pi$
$541$	17.1432	+	7.10093i	0.737042	+	0.305293i	0.0175999	+	0.999845i	$0.494397\pi$
$542$	6.25318	−	3.55063i	0.268597	−	0.152512i
$543$		0			0
$544$	−30.2186	−	18.9253i	−1.29561	−	0.811417i
$545$	−9.15277	+	5.28435i	−0.392062	+	0.226357i
$546$		0			0
$547$	18.8407	+	24.5537i	0.805571	+	1.04984i	0.997654	+	0.0684617i	$0.0218091\pi$
$547$	18.8407	+	24.5537i	0.805571	+	1.04984i	−0.192083	+	0.981379i	$0.561524\pi$
$548$	20.6155	+	5.84263i	0.880651	+	0.249585i
$549$		0			0
$550$	6.03887	−	4.56524i	0.257498	−	0.194662i
$551$	5.42764	+	20.2562i	0.231225	+	0.862944i
$552$		0			0
$553$	0.591513	−	2.20755i	0.0251537	−	0.0938748i
$554$	−7.64783	−	18.8453i	−0.324925	−	0.800660i
$555$		0			0
$556$	14.1969	+	35.7174i	0.602082	+	1.51475i
$557$	−12.1460	−	5.03103i	−0.514641	−	0.213171i	0.110220	−	0.993907i	$-0.464844\pi$
$557$	−12.1460	−	5.03103i	−0.514641	−	0.213171i	−0.624861	+	0.780736i	$0.714844\pi$
$558$		0			0
$559$	38.1037			1.61161
$560$	0.120039	+	1.17088i	0.00507258	+	0.0494789i
$561$		0			0
$562$	18.6337	−	18.3679i	0.786017	−	0.774804i
$563$	−37.9720	+	4.99911i	−1.60033	+	0.210688i	−0.877235	−	0.480060i	$-0.840615\pi$
$563$	−37.9720	+	4.99911i	−1.60033	+	0.210688i	−0.723096	+	0.690748i	$0.757281\pi$
$564$		0			0
$565$	−1.15059	+	8.73962i	−0.0484058	+	0.367679i
$566$	−8.93798	−	1.24209i	−0.375691	−	0.0522091i
$567$		0			0
$568$	15.6425	+	16.3317i	0.656345	+	0.685264i
$569$	−19.4891	+	5.22209i	−0.817026	+	0.218921i	−0.643046	−	0.765828i	$-0.722329\pi$
$569$	−19.4891	+	5.22209i	−0.817026	+	0.218921i	−0.173980	+	0.984749i	$0.555663\pi$
$570$		0			0
$571$	18.5429	+	14.2285i	0.775998	+	0.595444i	0.918990	−	0.394280i	$-0.129006\pi$
$571$	18.5429	+	14.2285i	0.775998	+	0.595444i	−0.142993	+	0.989724i	$0.545673\pi$
$572$	18.3520	+	10.9501i	0.767335	+	0.457845i
$573$		0			0
$574$	0.745538	−	0.423324i	0.0311181	−	0.0176692i
$575$	12.0664			0.503202
$576$		0			0
$577$	−14.5094			−0.604036			−0.302018	−	0.953302i	$-0.597660\pi$
$577$	−14.5094			−0.604036			−0.302018	+	0.953302i	$0.597660\pi$
$578$	27.9522	−	15.8716i	1.16266	−	0.660170i
$579$		0			0
$580$	−11.5190	−	6.87301i	−0.478298	−	0.285386i
$581$	1.60475	+	1.23137i	0.0665763	+	0.0510858i
$582$		0			0
$583$	16.0361	−	4.29685i	0.664145	−	0.177957i
$584$	18.6417	−	17.8550i	0.771397	−	0.738843i
$585$		0			0
$586$	−6.56250	−	0.911979i	−0.271094	−	0.0376735i
$587$	−0.0604785	+	0.459380i	−0.00249622	+	0.0189606i	−0.992648	−	0.121040i	$-0.961377\pi$
$587$	−0.0604785	+	0.459380i	−0.00249622	+	0.0189606i	0.990151	+	0.140001i	$0.0447104\pi$
$588$		0			0
$589$	−29.6038	+	3.89741i	−1.21980	+	0.160590i
$590$	−14.4247	+	14.2189i	−0.593855	+	0.585383i
$591$		0			0
$592$	10.6767	−	13.1159i	0.438809	−	0.539061i
$593$	25.9623			1.06614			0.533072	−	0.846070i	$-0.321038\pi$
$593$	25.9623			1.06614			0.533072	+	0.846070i	$0.321038\pi$
$594$		0			0
$595$	−1.71354	−	0.709771i	−0.0702483	−	0.0290978i
$596$	7.26509	+	18.2780i	0.297590	+	0.748694i
$597$		0			0
$598$	12.8088	+	31.5627i	0.523791	+	1.29069i
$599$	2.67253	−	9.97403i	0.109197	−	0.407528i	−0.889591	−	0.456759i	$-0.849010\pi$
$599$	2.67253	−	9.97403i	0.109197	−	0.407528i	0.998787	+	0.0492307i	$0.0156769\pi$
$600$		0			0
$601$	6.80599	+	25.4003i	0.277622	+	1.03610i	0.954064	+	0.299604i	$0.0968544\pi$
$601$	6.80599	+	25.4003i	0.277622	+	1.03610i	−0.676442	+	0.736496i	$0.736479\pi$
$602$	−1.58297	+	1.19669i	−0.0645172	+	0.0487734i
$603$		0			0
$604$	−31.3008	−	8.87094i	−1.27361	−	0.360953i
$605$	6.31327	+	8.22761i	0.256671	+	0.334500i
$606$		0			0
$607$	−1.14113	+	0.658834i	−0.0463172	+	0.0267413i	−0.522980	−	0.852345i	$-0.675180\pi$
$607$	−1.14113	+	0.658834i	−0.0463172	+	0.0267413i	0.476663	+	0.879086i	$0.341846\pi$
$608$	16.0031	+	22.4837i	0.649011	+	0.911834i
$609$		0			0
$610$	−12.5096	+	7.10310i	−0.506500	+	0.287596i
$611$	−5.51073	−	2.28262i	−0.222940	−	0.0923449i
$612$		0			0
$613$	−8.44938	−	20.3986i	−0.341267	−	0.823892i	−0.997588	−	0.0694101i	$-0.977888\pi$
$613$	−8.44938	−	20.3986i	−0.341267	−	0.823892i	0.656321	−	0.754482i	$-0.272112\pi$
$614$	1.90389	−	0.236750i	0.0768348	−	0.00955446i
$615$		0			0
$616$	−1.10631	+	0.121457i	−0.0445746	+	0.00489364i
$617$	−24.5016	−	6.56520i	−0.986399	−	0.264305i	−0.270662	−	0.962674i	$-0.587243\pi$
$617$	−24.5016	−	6.56520i	−0.986399	−	0.264305i	−0.715737	+	0.698370i	$0.753909\pi$
$618$		0			0
$619$	−3.03125	−	0.399072i	−0.121836	−	0.0160400i	0.0693614	−	0.997592i	$-0.477904\pi$
$619$	−3.03125	−	0.399072i	−0.121836	−	0.0160400i	−0.191198	+	0.981552i	$0.561237\pi$
$620$	11.8432	−	14.9836i	0.475634	−	0.601755i
$621$		0			0
$622$	4.42562	+	17.0044i	0.177451	+	0.681813i
$623$	0.355069	+	0.204999i	0.0142255	+	0.00821311i
$624$		0			0
$625$	4.84054	−	2.79469i	0.193621	−	0.111787i
$626$	−21.8643	−	22.1807i	−0.873873	−	0.886520i
$627$		0			0
$628$	35.0830	+	15.1260i	1.39997	+	0.603594i
$629$	10.1984	+	24.6211i	0.406637	+	0.981708i
$630$		0			0
$631$	23.0221	−	23.0221i	0.916494	−	0.916494i	−0.0802781	−	0.996773i	$-0.525581\pi$
$631$	23.0221	−	23.0221i	0.916494	−	0.916494i	0.996773	+	0.0802781i	$0.0255808\pi$
$632$	29.3071	+	17.7734i	1.16577	+	0.706987i
$633$		0			0
$634$	−8.98859	−	3.79908i	−0.356983	−	0.150881i
$635$	12.1148	−	15.7883i	0.480760	−	0.626538i
$636$		0			0
$637$	−28.2966	+	21.7127i	−1.12115	+	0.860290i
$638$	6.42052	−	10.9384i	0.254191	−	0.433056i
$639$		0			0
$640$	−17.3632	−	3.18090i	−0.686341	−	0.125736i
$641$	8.36589	+	4.83005i	0.330433	+	0.190776i	0.656033	−	0.754732i	$-0.272233\pi$
$641$	8.36589	+	4.83005i	0.330433	+	0.190776i	−0.325600	+	0.945507i	$0.605566\pi$
$642$		0			0
$643$	2.79706	−	0.368240i	0.110305	−	0.0145220i	−0.0751714	−	0.997171i	$-0.523950\pi$
$643$	2.79706	−	0.368240i	0.110305	−	0.0145220i	0.185477	+	0.982649i	$0.440617\pi$
$644$	−1.52339	−	0.908960i	−0.0600300	−	0.0358180i
$645$		0			0
$646$	−43.1549	+	5.36634i	−1.69791	+	0.211136i
$647$	11.1956	−	11.1956i	0.440143	−	0.440143i	−0.451917	−	0.892060i	$-0.649260\pi$
$647$	11.1956	−	11.1956i	0.440143	−	0.440143i	0.892060	+	0.451917i	$0.149260\pi$
$648$		0			0
$649$	−13.5426	−	13.5426i	−0.531595	−	0.531595i
$650$	−14.6604	−	11.4176i	−0.575028	−	0.447835i
$651$		0			0
$652$	14.7642	+	19.8245i	0.578212	+	0.776388i
$653$	1.35804	+	10.3154i	0.0531443	+	0.403671i	0.997255	+	0.0740426i	$0.0235901\pi$
$653$	1.35804	+	10.3154i	0.0531443	+	0.403671i	−0.944111	+	0.329628i	$0.893077\pi$
$654$		0			0
$655$	−13.9695	+	24.1959i	−0.545835	+	0.945414i
$656$	2.96962	+	12.5102i	0.115944	+	0.488440i
$657$		0			0
$658$	0.300626	−	0.0782420i	0.0117196	−	0.00305019i
$659$	−4.41166	−	5.74939i	−0.171854	−	0.223964i	0.699484	−	0.714649i	$-0.253413\pi$
$659$	−4.41166	−	5.74939i	−0.171854	−	0.223964i	−0.871337	+	0.490684i	$0.836747\pi$
$660$		0			0
$661$	25.7411	+	19.7519i	1.00121	+	0.768258i	0.972873	−	0.231340i	$-0.0743110\pi$
$661$	25.7411	+	19.7519i	1.00121	+	0.768258i	0.0283408	+	0.999598i	$0.490978\pi$
$662$	30.4115	−	12.3417i	1.18198	−	0.479672i
$663$		0			0
$664$	−24.4594	+	17.9443i	−0.949207	+	0.696374i
$665$	1.01508	+	1.01508i	0.0393632	+	0.0393632i
$666$		0			0
$667$	18.6775	−	7.73649i	0.723197	−	0.299558i
$668$	−9.46048	+	9.19245i	−0.366037	+	0.355667i
$669$		0			0
$670$	4.86661	+	0.0349628i	0.188014	+	0.00135073i
$671$	−6.80131	−	11.7802i	−0.262562	−	0.454770i
$672$		0			0
$673$	−3.04125	+	5.26761i	−0.117232	+	0.203051i	−0.918670	−	0.395027i	$-0.870735\pi$
$673$	−3.04125	+	5.26761i	−0.117232	+	0.203051i	0.801438	+	0.598078i	$0.204069\pi$
$674$	23.1892	−	39.5067i	0.893216	−	1.52174i
$675$		0			0
$676$	7.21372	−	25.4533i	0.277451	−	0.978974i
$677$	4.94663	−	37.5734i	0.190114	−	1.44406i	−0.584379	−	0.811481i	$-0.698662\pi$
$677$	4.94663	−	37.5734i	0.190114	−	1.44406i	0.774494	−	0.632582i	$-0.218005\pi$
$678$		0			0
$679$	−0.449028	+	1.67580i	−0.0172321	+	0.0643112i
$680$	17.4049	−	21.6978i	0.667447	−	0.832072i
$681$		0			0
$682$	14.2482	+	11.0965i	0.545590	+	0.424908i
$683$	5.74522	−	2.37975i	0.219835	−	0.0910585i	−0.270048	−	0.962847i	$-0.587040\pi$
$683$	5.74522	−	2.37975i	0.219835	−	0.0910585i	0.489883	+	0.871788i	$0.337040\pi$
$684$		0			0
$685$	−6.39696	+	15.4436i	−0.244415	+	0.590070i
$686$	0.989795	−	3.59058i	0.0377905	−	0.137089i
$687$		0			0
$688$	−10.5943	−	27.8113i	−0.403902	−	1.06030i
$689$	−20.3752	−	35.2909i	−0.776234	−	1.34448i
$690$		0			0
$691$	−4.60125	+	3.53066i	−0.175040	+	0.134313i	−0.692566	−	0.721355i	$-0.743520\pi$
$691$	−4.60125	+	3.53066i	−0.175040	+	0.134313i	0.517526	+	0.855667i	$0.326853\pi$
$692$	4.30317	+	36.7598i	0.163582	+	1.39740i
$693$		0			0
$694$	4.09358	−	29.4570i	0.155390	−	1.11817i
$695$	−28.9627	+	7.76053i	−1.09862	+	0.294374i
$696$		0			0
$697$	−19.5706	−	5.24394i	−0.741291	−	0.198628i
$698$	−8.43899	+	19.9666i	−0.319420	+	0.755746i
$699$		0			0
$700$	0.967633	+	0.0139041i	0.0365731	+	0.000525525i
$701$	−18.7779	+	45.3339i	−0.709232	+	1.71224i	−0.00732108	+	0.999973i	$0.502330\pi$
$701$	−18.7779	+	45.3339i	−0.709232	+	1.71224i	−0.701911	+	0.712265i	$0.747670\pi$
$702$		0			0
$703$		−	20.6267i		−	0.777952i
$704$	2.88974	−	16.4394i	0.108911	−	0.619582i
$705$		0			0
$706$	47.5546	+	0.341643i	1.78974	+	0.0128579i
$707$	0.324872	+	2.46765i	0.0122181	+	0.0928054i
$708$		0			0
$709$	26.9957	+	3.55406i	1.01385	+	0.133475i	0.619098	−	0.785314i	$-0.287498\pi$
$709$	26.9957	+	3.55406i	1.01385	+	0.133475i	0.394749	+	0.918789i	$0.370832\pi$
$710$	−14.0732	+	10.6390i	−0.528157	+	0.399273i
$711$		0			0
$712$	−4.44060	+	4.25320i	−0.166419	+	0.159395i
$713$	7.45013	+	27.8043i	0.279010	+	1.04128i
$714$		0			0
$715$	−10.1490	+	13.2265i	−0.379553	+	0.494643i
$716$	−1.11719	−	1.50010i	−0.0417514	−	0.0560612i
$717$		0			0
$718$	11.9217	−	43.2472i	0.444914	−	1.61397i
$719$			26.2968i			0.980706i	0.871524	+	0.490353i	$0.163132\pi$
$719$			26.2968i			0.980706i	−0.871524	+	0.490353i	$0.836868\pi$
$720$		0			0
$721$			0.916589i			0.0341356i
$722$	6.54476	+	1.80416i	0.243571	+	0.0671437i
$723$		0			0
$724$	−3.38549	+	23.1410i	−0.125821	+	0.860029i
$725$	−6.71373	+	8.74950i	−0.249341	+	0.324948i
$726$		0			0
$727$	9.44639	+	35.2544i	0.350347	+	1.30751i	0.886239	+	0.463228i	$0.153309\pi$
$727$	9.44639	+	35.2544i	0.350347	+	1.30751i	−0.535892	+	0.844287i	$0.680025\pi$
$728$	0.990801	+	2.54585i	0.0367215	+	0.0943554i
$729$		0			0
$730$	12.1437	+	16.0637i	0.449460	+	0.594543i
$731$	46.4952	+	6.12121i	1.71969	+	0.226401i
$732$		0			0
$733$	−6.28704	−	47.7548i	−0.232217	−	1.76386i	−0.569053	−	0.822301i	$-0.692690\pi$
$733$	−6.28704	−	47.7548i	−0.232217	−	1.76386i	0.336836	−	0.941563i	$-0.390643\pi$
$734$	−0.122761	+	17.0877i	−0.00453121	+	0.630717i
$735$		0			0
$736$	19.4758	−	18.1246i	0.717887	−	0.668081i
$737$			4.60186i			0.169512i
$738$		0			0
$739$	7.66115	−	18.4956i	0.281820	−	0.680373i	−0.718058	−	0.695983i	$-0.754969\pi$
$739$	7.66115	−	18.4956i	0.281820	−	0.680373i	0.999878	+	0.0156097i	$0.00496892\pi$
$740$	9.19422	+	9.46230i	0.337986	+	0.347841i
$741$		0			0
$742$	1.95482	+	0.826214i	0.0717636	+	0.0303313i
$743$	0.965648	+	0.258745i	0.0354262	+	0.00949242i	0.276489	−	0.961017i	$-0.410829\pi$
$743$	0.965648	+	0.258745i	0.0354262	+	0.00949242i	−0.241062	+	0.970510i	$0.577496\pi$
$744$		0			0
$745$	−14.8213	+	3.97136i	−0.543011	+	0.145499i
$746$	−34.3979	−	4.78021i	−1.25939	−	0.175016i
$747$		0			0
$748$	20.6345	+	16.3098i	0.754474	+	0.596344i
$749$	1.79989	−	1.38110i	0.0657664	−	0.0504643i
$750$		0			0
$751$	17.0984	+	29.6154i	0.623931	+	1.08068i	0.988746	+	0.149601i	$0.0477988\pi$
$751$	17.0984	+	29.6154i	0.623931	+	1.08068i	−0.364815	+	0.931080i	$0.618868\pi$
$752$	−0.133858	+	4.65686i	−0.00488130	+	0.169818i
$753$		0			0
$754$	−30.0134	−	8.27360i	−1.09302	−	0.301307i
$755$	9.71257	−	23.4482i	0.353477	−	0.853368i
$756$		0			0
$757$	−41.7298	+	17.2851i	−1.51670	+	0.628236i	−0.976926	−	0.213576i	$-0.931489\pi$
$757$	−41.7298	+	17.2851i	−1.51670	+	0.628236i	−0.539770	+	0.841813i	$0.681489\pi$
$758$	11.3561	−	14.5814i	0.412471	−	0.529620i
$759$		0			0
$760$	−18.8726	+	10.3604i	−0.684582	+	0.375810i
$761$	−6.80932	+	25.4127i	−0.246838	+	0.921210i	0.725613	+	0.688103i	$0.241556\pi$
$761$	−6.80932	+	25.4127i	−0.246838	+	0.921210i	−0.972451	+	0.233108i	$0.925111\pi$
$762$		0			0
$763$	0.166747	−	1.26657i	0.00603664	−	0.0458528i
$764$	−17.0746	−	30.5805i	−0.617738	−	1.10636i
$765$		0			0
$766$	−30.5644	−	17.9403i	−1.10434	−	0.648211i
$767$	−23.5054	+	40.7125i	−0.848730	+	1.47004i
$768$		0			0
$769$	23.8544	+	41.3170i	0.860211	+	1.48993i	0.871725	+	0.489995i	$0.163001\pi$
$769$	23.8544	+	41.3170i	0.860211	+	1.48993i	−0.0115146	+	0.999934i	$0.503665\pi$
$770$	0.00623750	−	0.868223i	0.000224784	−	0.0312886i
$771$		0			0
$772$	32.2106	+	0.462839i	1.15928	+	0.0166580i
$773$	0.388763	−	0.161031i	0.0139828	−	0.00579188i	−0.375681	−	0.926749i	$-0.622591\pi$
$773$	0.388763	−	0.161031i	0.0139828	−	0.00579188i	0.389664	+	0.920957i	$0.372591\pi$
$774$		0			0
$775$	−11.1036	−	11.1036i	−0.398854	−	0.398854i
$776$	−22.2476	−	13.4921i	−0.798641	−	0.484339i
$777$		0			0
$778$	−14.4374	−	35.5757i	−0.517606	−	1.27545i
$779$	12.4413	+	9.54655i	0.445756	+	0.342041i
$780$		0			0
$781$	−10.1553	−	13.2346i	−0.363384	−	0.473571i
$782$	10.5593	+	40.5714i	0.377599	+	1.45083i
$783$		0			0
$784$	23.7153	+	14.6163i	0.846976	+	0.522011i
$785$	−14.9023	+	25.8115i	−0.531885	+	0.921252i
$786$		0			0
$787$	−0.0898985	−	0.682847i	−0.00320453	−	0.0243409i	0.989768	−	0.142687i	$-0.0455742\pi$
$787$	−0.0898985	−	0.682847i	−0.00320453	−	0.0243409i	−0.992972	+	0.118346i	$0.962241\pi$
$788$	−5.81598	+	39.7542i	−0.207186	+	1.41619i
$789$		0			0
$790$	−16.4296	+	21.0960i	−0.584540	+	0.750561i
$791$	−0.753437	−	0.753437i	−0.0267891	−	0.0267891i
$792$		0			0
$793$	−23.6095	+	23.6095i	−0.838396	+	0.838396i
$794$	4.89614	+	39.3737i	0.173758	+	1.39732i
$795$		0			0
$796$	−38.1988	+	9.64930i	−1.35392	+	0.342010i
$797$	30.0056	−	3.95031i	1.06285	−	0.139927i	0.421234	−	0.906952i	$-0.361597\pi$
$797$	30.0056	−	3.95031i	1.06285	−	0.139927i	0.641618	+	0.767025i	$0.278264\pi$
$798$		0			0
$799$	−6.35766	−	3.67060i	−0.224918	−	0.129856i
$800$	−4.25738	+	13.8749i	−0.150521	+	0.490553i
$801$		0			0
$802$	−3.16645	−	1.85861i	−0.111811	−	0.0656298i
$803$	−15.1065	+	11.5916i	−0.533096	+	0.409059i
$804$		0			0
$805$	0.842468	−	1.09793i	0.0296931	−	0.0386968i
$806$	17.2575	−	40.8312i	0.607871	−	1.43822i
$807$		0			0
$808$	−36.8945	−	5.66862i	−1.29794	−	0.199422i
$809$	1.16653	−	1.16653i	0.0410129	−	0.0410129i	−0.686303	−	0.727316i	$-0.740768\pi$
$809$	1.16653	−	1.16653i	0.0410129	−	0.0410129i	0.727316	+	0.686303i	$0.240768\pi$
$810$		0			0
$811$	−13.7394	−	33.1698i	−0.482455	−	1.16475i	−0.958440	−	0.285296i	$-0.907908\pi$
$811$	−13.7394	−	33.1698i	−0.482455	−	1.16475i	0.475984	−	0.879454i	$-0.342092\pi$
$812$	1.50671	−	0.598886i	0.0528753	−	0.0210168i
$813$		0			0
$814$	−8.88462	+	8.75787i	−0.311406	+	0.306963i
$815$	−16.6998	+	9.64166i	−0.584970	+	0.337732i
$816$		0			0
$817$	−31.4346	−	18.1488i	−1.09976	−	0.634946i
$818$	−46.8943	+	12.2049i	−1.63962	+	0.426734i
$819$		0			0
$820$	−9.96264	+	1.16624i	−0.347910	+	0.0407270i
$821$	3.64028	+	0.479253i	0.127047	+	0.0167260i	0.193781	−	0.981045i	$-0.437925\pi$
$821$	3.64028	+	0.479253i	0.127047	+	0.0167260i	−0.0667346	+	0.997771i	$0.521258\pi$
$822$		0			0
$823$	16.3712	+	4.38665i	0.570664	+	0.152909i	0.532601	−	0.846366i	$-0.321215\pi$
$823$	16.3712	+	4.38665i	0.570664	+	0.152909i	0.0380627	+	0.999275i	$0.487881\pi$
$824$	−13.1982	−	3.84315i	−0.459782	−	0.133882i
$825$		0			0
$826$	−0.302118	−	2.42957i	−0.0105120	−	0.0845355i
$827$	−8.45934	−	20.4226i	−0.294160	−	0.710165i	−0.999998	−	0.00179202i	$-0.999430\pi$
$827$	−8.45934	−	20.4226i	−0.294160	−	0.710165i	0.705838	−	0.708373i	$-0.250570\pi$
$828$		0			0
$829$	10.1087	+	4.18714i	0.351088	+	0.145425i	0.551256	−	0.834336i	$-0.314149\pi$
$829$	10.1087	+	4.18714i	0.351088	+	0.145425i	−0.200168	+	0.979762i	$0.564149\pi$
$830$	−11.6853	−	20.5795i	−0.405602	−	0.714325i
$831$		0			0
$832$	−40.8127	+	3.59240i	−1.41493	+	0.124544i
$833$	−38.0164	+	21.9488i	−1.31719	+	0.760480i
$834$		0			0
$835$	−6.26451	−	8.16407i	−0.216792	−	0.282529i
$836$	−9.92443	−	17.7746i	−0.343244	−	0.614748i
$837$		0			0
$838$	11.2948	+	14.9407i	0.390172	+	0.516117i
$839$	11.5040	+	42.9334i	0.397161	+	1.48222i	0.818069	+	0.575121i	$0.195045\pi$
$839$	11.5040	+	42.9334i	0.397161	+	1.48222i	−0.420908	+	0.907103i	$0.638288\pi$
$840$		0			0
$841$	2.72341	−	10.1639i	0.0939108	−	0.350480i
$842$	21.2646	−	8.62962i	0.732825	−	0.297396i
$843$		0			0
$844$	−17.0081	−	7.33301i	−0.585442	−	0.252413i
$845$	19.0677	+	7.89812i	0.655950	+	0.271704i
$846$		0			0
$847$	−1.25356			−0.0430728
$848$	−20.0932	+	24.6838i	−0.690004	+	0.847644i
$849$		0			0
$850$	−16.0549	−	16.2872i	−0.550677	−	0.558647i
$851$	−19.7146	+	2.59548i	−0.675808	+	0.0889719i
$852$		0			0
$853$	−1.79355	+	13.6233i	−0.0614099	+	0.466454i	0.932917	+	0.360090i	$0.117254\pi$
$853$	−1.79355	+	13.6233i	−0.0614099	+	0.466454i	−0.994327	+	0.106364i	$0.966079\pi$
$854$	0.239346	−	1.72231i	0.00819026	−	0.0589363i
$855$		0			0
$856$	12.3402	+	31.7079i	0.421778	+	1.08375i
$857$	−40.3548	+	10.8130i	−1.37849	+	0.369366i	−0.870574	−	0.492038i	$-0.836252\pi$
$857$	−40.3548	+	10.8130i	−1.37849	+	0.369366i	−0.507920	+	0.861404i	$0.669585\pi$
$858$		0			0
$859$	−23.9669	−	18.3904i	−0.817739	−	0.627473i	0.112820	−	0.993615i	$-0.464012\pi$
$859$	−23.9669	−	18.3904i	−0.817739	−	0.627473i	−0.930559	+	0.366142i	$0.880678\pi$
$860$	22.5100	−	5.68620i	0.767585	−	0.193898i
$861$		0			0
$862$	−20.4872	−	36.0810i	−0.697796	−	1.22892i
$863$	33.9351			1.15516			0.577582	−	0.816333i	$-0.303996\pi$
$863$	33.9351			1.15516			0.577582	+	0.816333i	$0.303996\pi$
$864$		0			0
$865$	−28.8729			−0.981710
$866$	20.1840	+	35.5471i	0.685881	+	1.20794i
$867$		0			0
$868$	0.565406	+	2.23828i	0.0191911	+	0.0759722i
$869$	−20.0589	−	15.3917i	−0.680451	−	0.522129i
$870$		0			0
$871$	10.9108	−	2.92353i	0.369697	−	0.0990601i
$872$	17.5385	+	7.71160i	0.593929	+	0.261148i
$873$		0			0
$874$	4.46634	−	32.1393i	0.151076	−	1.08713i
$875$	−0.290581	+	2.20718i	−0.00982342	+	0.0746163i
$876$		0			0
$877$	20.7199	−	2.72782i	0.699661	−	0.0921121i	0.227699	−	0.973731i	$-0.426880\pi$
$877$	20.7199	−	2.72782i	0.699661	−	0.0921121i	0.471961	+	0.881619i	$0.343546\pi$
$878$	−20.2844	−	20.5780i	−0.684566	−	0.694473i
$879$		0			0
$880$	12.4756	+	3.73017i	0.420554	+	0.125744i
$881$	−18.0274			−0.607358			−0.303679	−	0.952774i	$-0.598215\pi$
$881$	−18.0274			−0.607358			−0.303679	+	0.952774i	$0.598215\pi$
$882$		0			0
$883$	36.9716	+	15.3141i	1.24419	+	0.515361i	0.905022	−	0.425364i	$-0.139854\pi$
$883$	36.9716	+	15.3141i	1.24419	+	0.515361i	0.339170	+	0.940725i	$0.389854\pi$
$884$	25.5606	−	59.2849i	0.859697	−	1.99397i
$885$		0			0
$886$	−14.7072	+	5.96848i	−0.494096	+	0.200515i
$887$	4.29592	−	16.0326i	0.144243	−	0.538322i	−0.855545	−	0.517729i	$-0.826778\pi$
$887$	4.29592	−	16.0326i	0.144243	−	0.538322i	0.999788	−	0.0205937i	$-0.00655563\pi$
$888$		0			0
$889$	0.622590	+	2.32354i	0.0208810	+	0.0779289i
$890$	−2.89274	−	3.82650i	−0.0969649	−	0.128265i
$891$		0			0
$892$	20.3767	−	11.3773i	0.682264	−	0.380941i
$893$	3.45901	+	4.50787i	0.115751	+	0.150850i
$894$		0			0
$895$	1.26366	−	0.729572i	0.0422393	−	0.0243869i
$896$	1.58270	−	1.43101i	0.0528742	−	0.0478068i
$897$		0			0
$898$	1.48237	+	2.61068i	0.0494674	+	0.0871196i
$899$	−24.3065	−	10.0681i	−0.810668	−	0.335790i
$900$		0			0
$901$	−19.1931	−	46.3362i	−0.639414	−	1.54368i
$902$	−1.17042	−	9.41224i	−0.0389707	−	0.313393i
$903$		0			0
$904$	14.0080	−	7.68989i	0.465900	−	0.255762i
$905$	−17.6233	−	4.72216i	−0.585819	−	0.156970i
$906$		0			0
$907$	−40.0113	−	5.26758i	−1.32855	−	0.174907i	−0.567379	−	0.823457i	$-0.692043\pi$
$907$	−40.0113	−	5.26758i	−1.32855	−	0.174907i	−0.761173	+	0.648549i	$0.775376\pi$
$908$	−2.29000	−	19.5623i	−0.0759963	−	0.649198i
$909$		0			0
$910$	−2.06247	+	0.536788i	−0.0683704	+	0.0177943i
$911$	−12.5379	−	7.23877i	−0.415400	−	0.239831i	0.277707	−	0.960666i	$-0.410425\pi$
$911$	−12.5379	−	7.23877i	−0.415400	−	0.239831i	−0.693107	+	0.720834i	$0.743759\pi$
$912$		0			0
$913$	19.3796	−	11.1888i	0.641370	−	0.370295i
$914$	7.36152	−	7.25650i	0.243497	−	0.240024i
$915$		0			0
$916$	−15.2061	−	38.2564i	−0.502424	−	1.26403i
$917$	−1.29238	−	3.12008i	−0.0426781	−	0.103034i
$918$		0			0
$919$	−29.1031	+	29.1031i	−0.960023	+	0.960023i	−0.999231	−	0.0392080i	$-0.987517\pi$
$919$	−29.1031	+	29.1031i	−0.960023	+	0.960023i	0.0392080	+	0.999231i	$0.487517\pi$
$920$	12.2770	+	16.7344i	0.404760	+	0.551717i
$921$		0			0
$922$	−0.566497	+	1.34033i	−0.0186566	+	0.0441414i
$923$	−24.9270	+	32.4855i	−0.820482	+	1.06927i
$924$		0			0
$925$	8.60595	−	6.60357i	0.282962	−	0.217124i
$926$	−31.8254	−	18.6806i	−1.04585	−	0.613881i
$927$		0			0
$928$	2.30607	+	24.2067i	0.0757005	+	0.794623i
$929$	29.1277	+	16.8169i	0.955650	+	0.551745i	0.894831	−	0.446404i	$-0.147296\pi$
$929$	29.1277	+	16.8169i	0.955650	+	0.551745i	0.0608185	+	0.998149i	$0.480629\pi$
$930$		0			0
$931$	33.6858	−	4.43482i	1.10401	−	0.145345i
$932$	4.56671	+	18.0783i	0.149588	+	0.592174i
$933$		0			0
$934$	2.17723	+	17.5088i	0.0712412	+	0.572905i
$935$	−14.5090	+	14.5090i	−0.474494	+	0.474494i
$936$		0			0
$937$	−17.3037	−	17.3037i	−0.565288	−	0.565288i	0.365517	−	0.930805i	$-0.380892\pi$
$937$	−17.3037	−	17.3037i	−0.565288	−	0.565288i	−0.930805	+	0.365517i	$0.880892\pi$
$938$	−0.361459	+	0.464120i	−0.0118020	+	0.0151541i
$939$		0			0
$940$	−3.59614	−	0.526110i	−0.117293	−	0.0171598i
$941$	2.65581	+	20.1729i	0.0865770	+	0.657618i	0.978621	+	0.205670i	$0.0659373\pi$
$941$	2.65581	+	20.1729i	0.0865770	+	0.657618i	−0.892044	+	0.451948i	$0.850729\pi$
$942$		0			0
$943$	7.55890	−	13.0924i	0.246152	−	0.426347i
$944$	36.2508	+	5.83660i	1.17986	+	0.189965i
$945$		0			0
$946$	5.52949	+	21.2457i	0.179779	+	0.690757i
$947$	−5.84508	−	7.61746i	−0.189940	−	0.247534i	0.688670	−	0.725075i	$-0.258195\pi$
$947$	−5.84508	−	7.61746i	−0.189940	−	0.247534i	−0.878610	+	0.477541i	$0.841528\pi$
$948$		0			0
$949$	37.0802	+	28.4526i	1.20367	+	0.923611i
$950$	6.65629	+	16.4020i	0.215958	+	0.532151i
$951$		0			0
$952$	0.800024	+	3.26569i	0.0259289	+	0.105842i
$953$	8.74554	+	8.74554i	0.283296	+	0.283296i	0.834422	−	0.551126i	$-0.185802\pi$
$953$	8.74554	+	8.74554i	0.283296	+	0.283296i	−0.551126	+	0.834422i	$0.685802\pi$
$954$		0			0
$955$	25.2435	−	10.4562i	0.816861	−	0.338355i
$956$	0.0853909	−	5.94265i	0.00276174	−	0.192199i
$957$		0			0
$958$	0.349556	−	48.6561i	0.0112936	−	1.57201i
$959$	−1.01028	−	1.74986i	−0.0326236	−	0.0565058i
$960$		0			0
$961$	3.23015	−	5.59478i	0.104198	−	0.180477i
$962$	26.4088	+	15.5011i	0.851454	+	0.499777i
$963$		0			0
$964$	−25.7548	+	14.3802i	−0.829508	+	0.463155i
$965$	−3.28023	+	24.9158i	−0.105594	+	0.802069i
$966$		0			0
$967$	−9.00995	+	33.6256i	−0.289740	+	1.08133i	0.655565	+	0.755139i	$0.272431\pi$
$967$	−9.00995	+	33.6256i	−0.289740	+	1.08133i	−0.945305	+	0.326187i	$0.894236\pi$
$968$	5.25603	−	18.0504i	0.168935	−	0.580161i
$969$		0			0
$970$	12.4720	−	16.0144i	0.400453	−	0.514190i
$971$	33.5566	−	13.8996i	1.07688	−	0.446060i	0.227468	−	0.973785i	$-0.426955\pi$
$971$	33.5566	−	13.8996i	1.07688	−	0.446060i	0.849415	+	0.527726i	$0.176955\pi$
$972$		0			0
$973$	1.38699	−	3.34848i	0.0444648	−	0.107347i
$974$	19.8507	+	5.47211i	0.636056	+	0.175338i
$975$		0			0
$976$	23.7965	+	10.6679i	0.761708	+	0.341470i
$977$	0.540538	+	0.936239i	0.0172933	+	0.0299530i	0.874543	−	0.484949i	$-0.161162\pi$
$977$	0.540538	+	0.936239i	0.0172933	+	0.0299530i	−0.857249	+	0.514902i	$0.827828\pi$
$978$		0			0
$979$	3.59849	−	2.76122i	0.115008	−	0.0882490i
$980$	−13.4762	+	17.0497i	−0.430483	+	0.544631i
$981$		0			0
$982$	54.2938	+	7.54511i	1.73258	+	0.240774i
$983$	−32.7423	+	8.77327i	−1.04432	+	0.279824i	−0.739901	−	0.672715i	$-0.765128\pi$
$983$	−32.7423	+	8.77327i	−1.04432	+	0.279824i	−0.304416	+	0.952539i	$0.598461\pi$
$984$		0			0
$985$	−30.2753	−	8.11224i	−0.964652	−	0.258478i
$986$	−35.2941	−	14.9172i	−1.12399	−	0.475061i
$987$		0			0
$988$	−35.8377	+	34.8224i	−1.14015	+	1.10785i
$989$	−13.3908	+	32.3283i	−0.425803	+	1.02798i
$990$		0			0
$991$			47.7127i			1.51564i	0.652461	+	0.757822i	$0.273736\pi$
$991$			47.7127i			1.51564i	−0.652461	+	0.757822i	$0.726264\pi$
$992$	−34.6003	−	1.24339i	−1.09856	−	0.0394778i
$993$		0			0
$994$	0.0153199	−	2.13243i	0.000485916	−	0.0676367i
$995$	−4.01183	−	30.4729i	−0.127184	−	0.966055i
$996$		0			0
$997$	−18.4893	−	2.43417i	−0.585563	−	0.0770909i	−0.168077	−	0.985774i	$-0.553756\pi$
$997$	−18.4893	−	2.43417i	−0.585563	−	0.0770909i	−0.417487	+	0.908683i	$0.637089\pi$
$998$	−26.6944	−	35.3111i	−0.844995	−	1.11775i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.38		368
3.2	odd	2		288.2.bf.a.227.9	yes	368
9.4	even	3		288.2.bf.a.131.25	yes	368
9.5	odd	6	inner	864.2.bn.a.611.22		368
32.11	odd	8	inner	864.2.bn.a.683.22		368
96.11	even	8		288.2.bf.a.11.25	✓	368
288.139	odd	24		288.2.bf.a.203.9	yes	368
288.203	even	24	inner	864.2.bn.a.395.38		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.25	✓	368	96.11	even	8
288.2.bf.a.131.25	yes	368	9.4	even	3
288.2.bf.a.203.9	yes	368	288.139	odd	24
288.2.bf.a.227.9	yes	368	3.2	odd	2
864.2.bn.a.35.38		368	1.1	even	1	trivial
864.2.bn.a.395.38		368	288.203	even	24	inner
864.2.bn.a.611.22		368	9.5	odd	6	inner
864.2.bn.a.683.22		368	32.11	odd	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22979 - 0.698290i) q^{2} +(1.02478 - 1.71750i) q^{4} +(1.23783 + 0.949818i) q^{5} +(-0.182169 + 0.0488121i) q^{7} +(0.0609543 - 2.82777i) q^{8} +O(q^{10})\)	\(q+(1.22979 - 0.698290i) q^{2} +(1.02478 - 1.71750i) q^{4} +(1.23783 + 0.949818i) q^{5} +(-0.182169 + 0.0488121i) q^{7} +(0.0609543 - 2.82777i) q^{8} +(2.18552 + 0.303717i) q^{10} +(-0.272333 + 2.06858i) q^{11} +(5.07750 - 0.668466i) q^{13} +(-0.189945 + 0.187236i) q^{14} +(-1.89964 - 3.52014i) q^{16} +6.30311 q^{17} +(-4.50721 - 1.86695i) q^{19} +(2.89982 - 1.15262i) q^{20} +(1.10955 + 2.73409i) q^{22} +(-1.21725 + 4.54282i) q^{23} +(-0.664034 - 2.47821i) q^{25} +(5.77750 - 4.36765i) q^{26} +(-0.102849 + 0.362898i) q^{28} +(-2.61679 - 3.41027i) q^{29} +(5.30049 - 3.06024i) q^{31} +(-4.79424 - 3.00254i) q^{32} +(7.75152 - 4.40140i) q^{34} +(-0.271856 - 0.112607i) q^{35} +(1.61800 + 3.90619i) q^{37} +(-6.84661 + 0.851381i) q^{38} +(2.76132 - 3.44239i) q^{40} +(-3.10492 - 0.831961i) q^{41} +(7.37655 + 0.971142i) q^{43} +(3.27371 + 2.58758i) q^{44} +(1.67525 + 6.43673i) q^{46} +(-1.00866 - 0.582347i) q^{47} +(-6.03137 + 3.48222i) q^{49} +(-2.54713 - 2.58400i) q^{50} +(4.05524 - 9.40567i) q^{52} +(-3.04502 - 7.35132i) q^{53} +(-2.30187 + 2.30187i) q^{55} +(0.126925 + 0.518108i) q^{56} +(-5.59947 - 2.36665i) q^{58} +(-5.58808 + 7.28252i) q^{59} +(-5.17233 + 3.96887i) q^{61} +(4.38157 - 7.46474i) q^{62} +(-7.99257 - 0.344730i) q^{64} +(6.91999 + 3.99526i) q^{65} +(2.18675 - 0.287891i) q^{67} +(6.45931 - 10.8256i) q^{68} +(-0.412959 + 0.0513517i) q^{70} +(-5.65361 + 5.65361i) q^{71} +(6.45325 + 6.45325i) q^{73} +(4.71745 + 3.67397i) q^{74} +(-7.82540 + 5.82794i) q^{76} +(-0.0513608 - 0.390124i) q^{77} +(-6.05908 + 10.4946i) q^{79} +(0.992060 - 6.16163i) q^{80} +(-4.39936 + 1.14499i) q^{82} +(-6.52915 - 8.50896i) q^{83} +(7.80215 + 5.98680i) q^{85} +(9.74977 - 3.95667i) q^{86} +(5.83286 + 0.896185i) q^{88} +(-1.53722 - 1.53722i) q^{89} +(-0.892335 + 0.369617i) q^{91} +(6.55491 + 6.74603i) q^{92} +(-1.64708 - 0.0118330i) q^{94} +(-3.80589 - 6.59199i) q^{95} +(4.59956 - 7.96668i) q^{97} +(-4.98575 + 8.49405i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34} - 16 q^{37} + 12 q^{38} - 4 q^{40} + 12 q^{41} - 4 q^{43} - 16 q^{46} + 24 q^{47} + 168 q^{50} - 4 q^{52} - 16 q^{55} + 12 q^{56} + 32 q^{58} + 12 q^{59} - 4 q^{61} - 16 q^{64} + 24 q^{65} - 4 q^{67} + 60 q^{68} - 4 q^{70} - 16 q^{73} + 12 q^{74} - 28 q^{76} + 12 q^{77} - 8 q^{79} - 16 q^{82} + 132 q^{83} - 24 q^{85} + 12 q^{86} - 4 q^{88} - 16 q^{91} - 216 q^{92} - 20 q^{94} - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more