LMFDB - Embedded newform 668.2.e.a.9.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.14
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.383878 + 2.88073i) q^{3} +(1.71454 + 0.758185i) q^{5} +(0.166885 - 0.358871i) q^{7} +(-5.25594 + 1.42611i) q^{9} +O(q^{10})$	\(q+(0.383878 + 2.88073i) q^{3} +(1.71454 + 0.758185i) q^{5} +(0.166885 - 0.358871i) q^{7} +(-5.25594 + 1.42611i) q^{9} +(0.801379 - 1.02750i) q^{11} +(-2.57893 + 5.03785i) q^{13} +(-1.52595 + 5.23019i) q^{15} +(1.81167 + 0.137408i) q^{17} +(-1.54588 + 2.32546i) q^{19} +(1.09788 + 0.342989i) q^{21} +(4.00572 + 1.59300i) q^{23} +(-0.999554 - 1.09891i) q^{25} +(-2.75135 - 6.55445i) q^{27} +(-3.15161 + 1.25333i) q^{29} +(4.27583 - 0.988100i) q^{31} +(3.26758 + 1.91412i) q^{33} +(0.558222 - 0.488770i) q^{35} +(-2.37739 - 0.645063i) q^{37} +(-15.5027 - 5.49529i) q^{39} +(-0.773470 + 0.377649i) q^{41} +(0.670758 - 7.06732i) q^{43} +(-10.0928 - 1.53985i) q^{45} +(-0.216966 - 11.4630i) q^{47} +(4.40984 + 5.23306i) q^{49} +(0.299625 + 5.27167i) q^{51} +(1.11755 + 6.49761i) q^{53} +(2.15303 - 1.15410i) q^{55} +(-7.29246 - 3.56057i) q^{57} +(1.61396 - 0.122412i) q^{59} +(-4.42349 + 4.50800i) q^{61} +(-0.365349 + 2.12420i) q^{63} +(-8.24131 + 6.68229i) q^{65} +(-1.47198 + 0.650924i) q^{67} +(-3.05129 + 12.1509i) q^{69} +(4.98792 - 0.568833i) q^{71} +(6.50564 - 4.87880i) q^{73} +(2.78197 - 3.30130i) q^{75} +(-0.235001 - 0.459066i) q^{77} +(4.64014 - 12.3433i) q^{79} +(3.72817 - 2.18394i) q^{81} +(-4.25916 + 5.90913i) q^{83} +(3.00200 + 1.60917i) q^{85} +(-4.82035 - 8.59782i) q^{87} +(1.27162 + 4.35847i) q^{89} +(1.37755 + 1.76625i) q^{91} +(4.48785 + 11.9382i) q^{93} +(-4.41361 + 2.81504i) q^{95} +(11.7440 + 2.71391i) q^{97} +(-2.74668 + 6.54333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.383878	+	2.88073i	0.221632	+	1.66319i	0.650261	+	0.759711i	$0.274659\pi$
$3$	0.383878	+	2.88073i	0.221632	+	1.66319i	−0.428629	+	0.903481i	$0.641003\pi$
$4$		0			0
$5$	1.71454	+	0.758185i	0.766766	+	0.339071i	0.750564	−	0.660798i	$-0.229782\pi$
$5$	1.71454	+	0.758185i	0.766766	+	0.339071i	0.0162026	+	0.999869i	$0.494842\pi$
$6$		0			0
$7$	0.166885	−	0.358871i	0.0630767	−	0.135641i	−0.872673	−	0.488304i	$-0.837616\pi$
$7$	0.166885	−	0.358871i	0.0630767	−	0.135641i	0.935750	+	0.352664i	$0.114724\pi$
$8$		0			0
$9$	−5.25594	+	1.42611i	−1.75198	+	0.475369i
$10$		0			0
$11$	0.801379	−	1.02750i	0.241625	−	0.309803i	−0.652351	−	0.757917i	$-0.726217\pi$
$11$	0.801379	−	1.02750i	0.241625	−	0.309803i	0.893976	+	0.448114i	$0.147904\pi$
$12$		0			0
$13$	−2.57893	+	5.03785i	−0.715267	+	1.39725i	0.193986	+	0.981004i	$0.437858\pi$
$13$	−2.57893	+	5.03785i	−0.715267	+	1.39725i	−0.909253	+	0.416244i	$0.863346\pi$
$14$		0			0
$15$	−1.52595	+	5.23019i	−0.393999	+	1.35043i
$16$		0			0
$17$	1.81167	+	0.137408i	0.439394	+	0.0333262i	0.293467	−	0.955969i	$-0.405191\pi$
$17$	1.81167	+	0.137408i	0.439394	+	0.0333262i	0.145927	+	0.989295i	$0.453384\pi$
$18$		0			0
$19$	−1.54588	+	2.32546i	−0.354649	+	0.533498i	−0.966229	−	0.257685i	$-0.917040\pi$
$19$	−1.54588	+	2.32546i	−0.354649	+	0.533498i	0.611580	+	0.791183i	$0.290534\pi$
$20$		0			0
$21$	1.09788	+	0.342989i	0.239576	+	0.0748463i
$22$		0			0
$23$	4.00572	+	1.59300i	0.835251	+	0.332163i	0.747733	−	0.664000i	$-0.231143\pi$
$23$	4.00572	+	1.59300i	0.835251	+	0.332163i	0.0875182	+	0.996163i	$0.472106\pi$
$24$		0			0
$25$	−0.999554	−	1.09891i	−0.199911	−	0.219783i
$26$		0			0
$27$	−2.75135	−	6.55445i	−0.529497	−	1.26140i
$28$		0			0
$29$	−3.15161	+	1.25333i	−0.585240	+	0.232738i	−0.643350	−	0.765572i	$-0.722456\pi$
$29$	−3.15161	+	1.25333i	−0.585240	+	0.232738i	0.0581109	+	0.998310i	$0.481492\pi$
$30$		0			0
$31$	4.27583	−	0.988100i	0.767962	−	0.177468i	0.177047	−	0.984202i	$-0.443345\pi$
$31$	4.27583	−	0.988100i	0.767962	−	0.177468i	0.590914	+	0.806734i	$0.298767\pi$
$32$		0			0
$33$	3.26758	+	1.91412i	0.568813	+	0.333206i
$34$		0			0
$35$	0.558222	−	0.488770i	0.0943568	−	0.0826171i
$36$		0			0
$37$	−2.37739	−	0.645063i	−0.390840	−	0.106048i	0.0610201	−	0.998137i	$-0.480565\pi$
$37$	−2.37739	−	0.645063i	−0.390840	−	0.106048i	−0.451860	+	0.892089i	$0.649239\pi$
$38$		0			0
$39$	−15.5027	−	5.49529i	−2.48242	−	0.879951i
$40$		0			0
$41$	−0.773470	+	0.377649i	−0.120796	+	0.0589789i	−0.498155	−	0.867088i	$-0.665989\pi$
$41$	−0.773470	+	0.377649i	−0.120796	+	0.0589789i	0.377359	+	0.926067i	$0.376832\pi$
$42$		0			0
$43$	0.670758	−	7.06732i	0.102290	−	1.07776i	−0.785923	−	0.618324i	$-0.787812\pi$
$43$	0.670758	−	7.06732i	0.102290	−	1.07776i	0.888213	−	0.459432i	$-0.151947\pi$
$44$		0			0
$45$	−10.0928	−	1.53985i	−1.50454	−	0.229547i
$46$		0			0
$47$	−0.216966	−	11.4630i	−0.0316478	−	1.67205i	−0.564187	−	0.825647i	$-0.690810\pi$
$47$	−0.216966	−	11.4630i	−0.0316478	−	1.67205i	0.532539	−	0.846405i	$-0.321238\pi$
$48$		0			0
$49$	4.40984	+	5.23306i	0.629977	+	0.747580i
$50$		0			0
$51$	0.299625	+	5.27167i	0.0419560	+	0.738182i
$52$		0			0
$53$	1.11755	+	6.49761i	0.153507	+	0.892516i	0.955458	+	0.295126i	$0.0953617\pi$
$53$	1.11755	+	6.49761i	0.153507	+	0.892516i	−0.801951	+	0.597390i	$0.796205\pi$
$54$		0			0
$55$	2.15303	−	1.15410i	0.290315	−	0.155618i
$56$		0			0
$57$	−7.29246	−	3.56057i	−0.965910	−	0.471609i
$58$		0			0
$59$	1.61396	−	0.122412i	0.210119	−	0.0159367i	0.0298518	−	0.999554i	$-0.490496\pi$
$59$	1.61396	−	0.122412i	0.210119	−	0.0159367i	0.180267	+	0.983618i	$0.442304\pi$
$60$		0			0
$61$	−4.42349	+	4.50800i	−0.566369	+	0.577191i	−0.936005	−	0.351986i	$-0.885506\pi$
$61$	−4.42349	+	4.50800i	−0.566369	+	0.577191i	0.369636	+	0.929177i	$0.379482\pi$
$62$		0			0
$63$	−0.365349	+	2.12420i	−0.0460297	+	0.267624i
$64$		0			0
$65$	−8.24131	+	6.68229i	−1.02221	+	0.828836i
$66$		0			0
$67$	−1.47198	+	0.650924i	−0.179831	+	0.0795230i	−0.492387	−	0.870377i	$-0.663875\pi$
$67$	−1.47198	+	0.650924i	−0.179831	+	0.0795230i	0.312555	+	0.949900i	$0.398815\pi$
$68$		0			0
$69$	−3.05129	+	12.1509i	−0.367332	+	1.46280i
$70$		0			0
$71$	4.98792	−	0.568833i	0.591957	−	0.0675081i	0.187815	−	0.982204i	$-0.439859\pi$
$71$	4.98792	−	0.568833i	0.591957	−	0.0675081i	0.404142	+	0.914696i	$0.367570\pi$
$72$		0			0
$73$	6.50564	−	4.87880i	0.761427	−	0.571020i	−0.146964	−	0.989142i	$-0.546950\pi$
$73$	6.50564	−	4.87880i	0.761427	−	0.571020i	0.908391	+	0.418122i	$0.137312\pi$
$74$		0			0
$75$	2.78197	−	3.30130i	0.321234	−	0.381201i
$76$		0			0
$77$	−0.235001	−	0.459066i	−0.0267809	−	0.0523154i
$78$		0			0
$79$	4.64014	−	12.3433i	0.522057	−	1.38873i	−0.366694	−	0.930342i	$-0.619510\pi$
$79$	4.64014	−	12.3433i	0.522057	−	1.38873i	0.888751	−	0.458391i	$-0.151574\pi$
$80$		0			0
$81$	3.72817	−	2.18394i	0.414242	−	0.242660i
$82$		0			0
$83$	−4.25916	+	5.90913i	−0.467503	+	0.648612i	−0.977344	−	0.211657i	$-0.932114\pi$
$83$	−4.25916	+	5.90913i	−0.467503	+	0.648612i	0.509841	+	0.860269i	$0.329704\pi$
$84$		0			0
$85$	3.00200	+	1.60917i	0.325612	+	0.174539i
$86$		0			0
$87$	−4.82035	−	8.59782i	−0.516796	−	0.921783i
$88$		0			0
$89$	1.27162	+	4.35847i	0.134792	+	0.461997i	0.999165	−	0.0408534i	$-0.0130077\pi$
$89$	1.27162	+	4.35847i	0.134792	+	0.461997i	−0.864374	+	0.502850i	$0.832285\pi$
$90$		0			0
$91$	1.37755	+	1.76625i	0.144407	+	0.185153i
$92$		0			0
$93$	4.48785	+	11.9382i	0.465369	+	1.23793i
$94$		0			0
$95$	−4.41361	+	2.81504i	−0.452826	+	0.288817i
$96$		0			0
$97$	11.7440	+	2.71391i	1.19242	+	0.275556i	0.774290	−	0.632831i	$-0.218107\pi$
$97$	11.7440	+	2.71391i	1.19242	+	0.275556i	0.418130	+	0.908387i	$0.362685\pi$
$98$		0			0
$99$	−2.74668	+	6.54333i	−0.276051	+	0.657629i
$100$		0			0
$101$	0.0674593	+	0.710773i	0.00671245	+	0.0707246i	0.998254	−	0.0590632i	$-0.0188114\pi$
$101$	0.0674593	+	0.710773i	0.00671245	+	0.0707246i	−0.991542	+	0.129788i	$0.958570\pi$
$102$		0			0
$103$	13.3825	−	9.26609i	1.31862	−	0.913015i	0.319221	−	0.947680i	$-0.396579\pi$
$103$	13.3825	−	9.26609i	1.31862	−	0.913015i	0.999399	+	0.0346653i	$0.0110365\pi$
$104$		0			0
$105$	1.62230	+	1.42046i	0.158321	+	0.138623i
$106$		0			0
$107$	−0.458397	−	0.317395i	−0.0443149	−	0.0306837i	0.546898	−	0.837199i	$-0.315809\pi$
$107$	−0.458397	−	0.317395i	−0.0443149	−	0.0306837i	−0.591213	+	0.806516i	$0.701351\pi$
$108$		0			0
$109$	0.568727	+	0.362740i	0.0544742	+	0.0347442i	0.564699	−	0.825297i	$-0.308992\pi$
$109$	0.568727	+	0.362740i	0.0544742	+	0.0347442i	−0.510225	+	0.860041i	$0.670438\pi$
$110$		0			0
$111$	0.945625	−	7.09624i	0.0897548	−	0.673545i
$112$		0			0
$113$	6.59482	−	10.7847i	0.620388	−	1.01454i	−0.375749	−	0.926722i	$-0.622614\pi$
$113$	6.59482	−	10.7847i	0.620388	−	1.01454i	0.996137	−	0.0878135i	$-0.0279879\pi$
$114$		0			0
$115$	5.66019	+	5.76834i	0.527815	+	0.537900i
$116$		0			0
$117$	6.37020	−	30.1565i	0.588925	−	2.78797i
$118$		0			0
$119$	0.351652	−	0.627224i	0.0322359	−	0.0574975i
$120$		0			0
$121$	2.26555	+	9.02193i	0.205959	+	0.820175i
$122$		0			0
$123$	−1.38483	−	2.08319i	−0.124865	−	0.187835i
$124$		0			0
$125$	−3.84457	−	11.5345i	−0.343869	−	1.03168i
$126$		0			0
$127$	14.4757	+	1.65084i	1.28451	+	0.146488i	0.728707	−	0.684826i	$-0.240122\pi$
$127$	14.4757	+	1.65084i	1.28451	+	0.146488i	0.555803	+	0.831314i	$0.312411\pi$
$128$		0			0
$129$	20.6165	−	0.780720i	1.81519	−	0.0687386i
$130$		0			0
$131$	−1.05887	+	18.6300i	−0.0925142	+	1.62771i	0.532030	+	0.846725i	$0.321429\pi$
$131$	−1.05887	+	18.6300i	−0.0925142	+	1.62771i	−0.624544	+	0.780989i	$0.714715\pi$
$132$		0			0
$133$	0.576557	+	0.942857i	0.0499938	+	0.0817561i
$134$		0			0
$135$	0.252188	−	13.3239i	0.0217049	−	1.14674i
$136$		0			0
$137$	−12.3919	+	4.39259i	−1.05871	+	0.375284i	−0.805789	−	0.592203i	$-0.798258\pi$
$137$	−12.3919	+	4.39259i	−1.05871	+	0.375284i	−0.252920	+	0.967487i	$0.581391\pi$
$138$		0			0
$139$	5.46635	+	5.16448i	0.463650	+	0.438046i	0.882714	−	0.469911i	$-0.155714\pi$
$139$	5.46635	+	5.16448i	0.463650	+	0.438046i	−0.419064	+	0.907957i	$0.637642\pi$
$140$		0			0
$141$	32.9386	−	5.02543i	2.77393	−	0.423217i
$142$		0			0
$143$	3.10968	+	6.68708i	0.260045	+	0.559202i
$144$		0			0
$145$	−6.35383	−	0.240611i	−0.527657	−	0.0199816i
$146$		0			0
$147$	−13.3822	+	14.7124i	−1.10374	+	1.21346i
$148$		0			0
$149$	10.7628	+	8.72679i	0.881723	+	0.714926i	0.959399	−	0.282052i	$-0.0910152\pi$
$149$	10.7628	+	8.72679i	0.881723	+	0.714926i	−0.0776764	+	0.996979i	$0.524750\pi$
$150$		0			0
$151$	−12.9749	−	9.73033i	−1.05588	−	0.791843i	−0.0771590	−	0.997019i	$-0.524585\pi$
$151$	−12.9749	−	9.73033i	−1.05588	−	0.791843i	−0.978725	+	0.205176i	$0.934223\pi$
$152$		0			0
$153$	−9.71797	+	1.86143i	−0.785651	+	0.150487i
$154$		0			0
$155$	8.08025	+	1.54773i	0.649021	+	0.124317i
$156$		0			0
$157$	−5.04300	−	23.8735i	−0.402475	−	1.90531i	−0.424237	−	0.905551i	$-0.639458\pi$
$157$	−5.04300	−	23.8735i	−0.402475	−	1.90531i	0.0217614	−	0.999763i	$-0.493073\pi$
$158$		0			0
$159$	−18.2889	+	5.71365i	−1.45040	+	0.453122i
$160$		0			0
$161$	1.24018	−	1.17169i	0.0977396	−	0.0923421i
$162$		0			0
$163$	−3.21111	+	9.63402i	−0.251514	+	0.754594i	0.744680	+	0.667422i	$0.232602\pi$
$163$	−3.21111	+	9.63402i	−0.251514	+	0.754594i	−0.996193	+	0.0871722i	$0.972217\pi$
$164$		0			0
$165$	4.15114	+	5.75928i	0.323166	+	0.448359i
$166$		0			0
$167$	12.7409	−	2.16101i	0.985919	−	0.167224i
$167$	12.7409	−	2.16101i	0.985919	−	0.167224i
$168$		0			0
$169$	−11.1277	−	15.4385i	−0.855975	−	1.18758i
$170$		0			0
$171$	4.80869	−	14.4271i	0.367730	−	1.10327i
$172$		0			0
$173$	1.47843	−	1.39679i	0.112403	−	0.106196i	−0.628494	−	0.777814i	$-0.716328\pi$
$173$	1.47843	−	1.39679i	0.112403	−	0.106196i	0.740897	+	0.671619i	$0.234401\pi$
$174$		0			0
$175$	−0.561179	+	0.175319i	−0.0424212	+	0.0132529i
$176$		0			0
$177$	0.972199	+	4.60238i	0.0730750	+	0.345936i
$178$		0			0
$179$	−5.18039	−	0.992277i	−0.387201	−	0.0741663i	−0.00916653	−	0.999958i	$-0.502918\pi$
$179$	−5.18039	−	0.992277i	−0.387201	−	0.0741663i	−0.378034	+	0.925792i	$0.623400\pi$
$180$		0			0
$181$	9.49454	−	1.81863i	0.705724	−	0.135178i	0.177298	−	0.984157i	$-0.443264\pi$
$181$	9.49454	−	1.81863i	0.705724	−	0.135178i	0.528426	+	0.848980i	$0.322782\pi$
$182$		0			0
$183$	−14.6844	−	11.0124i	−1.08550	−	0.814056i
$184$		0			0
$185$	−3.58705	−	2.90848i	−0.263725	−	0.213836i
$186$		0			0
$187$	1.59302	−	1.75137i	0.116493	−	0.128073i
$188$		0			0
$189$	−2.81136	−	0.106462i	−0.204496	−	0.00774399i
$190$		0			0
$191$	−3.37204	−	7.25126i	−0.243992	−	0.524683i	0.745976	−	0.665973i	$-0.231983\pi$
$191$	−3.37204	−	7.25126i	−0.243992	−	0.524683i	−0.989968	+	0.141290i	$0.954875\pi$
$192$		0			0
$193$	8.85198	−	1.35054i	0.637180	−	0.0972142i	0.175813	−	0.984424i	$-0.443745\pi$
$193$	8.85198	−	1.35054i	0.637180	−	0.0972142i	0.461367	+	0.887209i	$0.347359\pi$
$194$		0			0
$195$	−22.4136	−	21.1758i	−1.60507	−	1.51643i
$196$		0			0
$197$	−1.92151	+	0.681125i	−0.136902	+	0.0485282i	−0.401673	−	0.915783i	$-0.631571\pi$
$197$	−1.92151	+	0.681125i	−0.136902	+	0.0485282i	0.264771	+	0.964311i	$0.414704\pi$
$198$		0			0
$199$	−0.206881	+	10.9302i	−0.0146654	+	0.774819i	0.914381	+	0.404855i	$0.132678\pi$
$199$	−0.206881	+	10.9302i	−0.0146654	+	0.774819i	−0.929046	+	0.369964i	$0.879370\pi$
$200$		0			0
$201$	−2.44020	−	3.99052i	−0.172118	−	0.281469i
$202$		0			0
$203$	−0.0761719	+	1.34019i	−0.00534622	+	0.0940626i
$204$		0			0
$205$	−1.61247	+	0.0610622i	−0.112620	+	0.00426477i
$206$		0			0
$207$	−23.3256	−	2.66010i	−1.62124	−	0.184890i
$208$		0			0
$209$	1.15057	+	3.45197i	0.0795869	+	0.238778i
$210$		0			0
$211$	−1.23615	−	1.85954i	−0.0851001	−	0.128016i	0.787768	−	0.615972i	$-0.211237\pi$
$211$	−1.23615	−	1.85954i	−0.0851001	−	0.128016i	−0.872868	+	0.487956i	$0.837743\pi$
$212$		0			0
$213$	3.55341	+	14.1505i	0.243476	+	0.969576i
$214$		0			0
$215$	6.50838	−	11.6087i	0.443868	−	0.791704i
$216$		0			0
$217$	0.358972	−	1.69937i	0.0243686	−	0.115361i
$218$		0			0
$219$	16.5519	+	16.8681i	1.11847	+	1.13984i
$220$		0			0
$221$	−5.36441	+	8.77254i	−0.360849	+	0.590105i
$222$		0			0
$223$	3.39419	−	25.4710i	0.227292	−	1.70566i	−0.391557	−	0.920154i	$-0.628064\pi$
$223$	3.39419	−	25.4710i	0.227292	−	1.70566i	0.618849	−	0.785510i	$-0.287599\pi$
$224$		0			0
$225$	6.82077	+	4.35035i	0.454718	+	0.290023i
$226$		0			0
$227$	9.90887	+	6.86092i	0.657675	+	0.455375i	0.850582	−	0.525842i	$-0.176250\pi$
$227$	9.90887	+	6.86092i	0.657675	+	0.455375i	−0.192907	+	0.981217i	$0.561792\pi$
$228$		0			0
$229$	−14.9392	−	13.0805i	−0.987212	−	0.864386i	0.00355048	−	0.999994i	$-0.498870\pi$
$229$	−14.9392	−	13.0805i	−0.987212	−	0.864386i	−0.990763	+	0.135608i	$0.956701\pi$
$230$		0			0
$231$	1.23223	−	0.853201i	0.0810751	−	0.0561365i
$232$		0			0
$233$	2.47671	+	26.0954i	0.162255	+	1.70957i	0.591437	+	0.806352i	$0.298561\pi$
$233$	2.47671	+	26.0954i	0.162255	+	1.70957i	−0.429182	+	0.903218i	$0.641198\pi$
$234$		0			0
$235$	8.31908	−	19.8183i	0.542677	−	1.29280i
$236$		0			0
$237$	37.3391	+	8.62867i	2.42543	+	0.560493i
$238$		0			0
$239$	−6.57038	+	4.19065i	−0.425003	+	0.271071i	−0.732884	−	0.680354i	$-0.761826\pi$
$239$	−6.57038	+	4.19065i	−0.425003	+	0.271071i	0.307881	+	0.951425i	$0.400380\pi$
$240$		0			0
$241$	−1.12391	−	2.98973i	−0.0723972	−	0.192585i	0.894880	−	0.446307i	$-0.147261\pi$
$241$	−1.12391	−	2.98973i	−0.0723972	−	0.192585i	−0.967277	+	0.253722i	$0.918345\pi$
$242$		0			0
$243$	−5.39264	−	6.91424i	−0.345938	−	0.443549i
$244$		0			0
$245$	3.59323	+	12.3158i	0.229563	+	0.786826i
$246$		0			0
$247$	−7.72861	−	13.7851i	−0.491760	−	0.877126i
$248$		0			0
$249$	−18.6576	−	10.0011i	−1.18238	−	0.633794i
$250$		0			0
$251$	14.0579	−	19.5039i	0.887329	−	1.23108i	−0.0847457	−	0.996403i	$-0.527008\pi$
$251$	14.0579	−	19.5039i	0.887329	−	1.23108i	0.972074	−	0.234673i	$-0.0754019\pi$
$252$		0			0
$253$	4.84690	−	2.83928i	0.304722	−	0.178504i
$254$		0			0
$255$	−3.48318	+	9.26568i	−0.218125	+	0.580239i
$256$		0			0
$257$	−8.91256	−	17.4104i	−0.555950	−	1.08603i	−0.983309	−	0.181946i	$-0.941760\pi$
$257$	−8.91256	−	17.4104i	−0.555950	−	1.08603i	0.427358	−	0.904082i	$-0.359444\pi$
$258$		0			0
$259$	−0.628245	+	0.745524i	−0.0390372	+	0.0463246i
$260$		0			0
$261$	14.7773	−	11.0820i	0.914691	−	0.685958i
$262$		0			0
$263$	−16.5313	+	1.88526i	−1.01936	+	0.116250i	−0.606944	−	0.794744i	$-0.707605\pi$
$263$	−16.5313	+	1.88526i	−1.01936	+	0.116250i	−0.412418	+	0.910995i	$0.635316\pi$
$264$		0			0
$265$	−3.01031	+	11.9877i	−0.184922	+	0.736401i
$266$		0			0
$267$	−12.0674	+	5.33632i	−0.738515	+	0.326577i
$268$		0			0
$269$	0.423121	−	0.343079i	0.0257982	−	0.0209179i	−0.616825	−	0.787101i	$-0.711581\pi$
$269$	0.423121	−	0.343079i	0.0257982	−	0.0209179i	0.642623	+	0.766183i	$0.277846\pi$
$270$		0			0
$271$	−2.35239	+	13.6772i	−0.142897	+	0.830828i	0.822251	+	0.569125i	$0.192718\pi$
$271$	−2.35239	+	13.6772i	−0.142897	+	0.830828i	−0.965148	+	0.261703i	$0.915716\pi$
$272$		0			0
$273$	−4.55927	+	4.64638i	−0.275940	+	0.281212i
$274$		0			0
$275$	−1.93015	+	0.146394i	−0.116393	+	0.00882792i
$276$		0			0
$277$	15.1869	+	7.41505i	0.912492	+	0.445527i	0.834237	−	0.551406i	$-0.185909\pi$
$277$	15.1869	+	7.41505i	0.912492	+	0.445527i	0.0782549	+	0.996933i	$0.475065\pi$
$278$		0			0
$279$	−21.0644	+	11.2912i	−1.26109	+	0.675986i
$280$		0			0
$281$	3.83616	+	22.3041i	0.228846	+	1.33055i	0.841526	+	0.540217i	$0.181658\pi$
$281$	3.83616	+	22.3041i	0.228846	+	1.33055i	−0.612680	+	0.790331i	$0.709908\pi$
$282$		0			0
$283$	−0.125038	−	2.19995i	−0.00743275	−	0.130773i	−0.999962	−	0.00876324i	$-0.997211\pi$
$283$	−0.125038	−	2.19995i	−0.00743275	−	0.130773i	0.992529	−	0.122010i	$-0.0389340\pi$
$284$		0			0
$285$	−9.80366	−	11.6338i	−0.580719	−	0.689126i
$286$		0			0
$287$	0.00644672	+	0.340600i	0.000380538	+	0.0201050i
$288$		0			0
$289$	−13.5423	−	2.06614i	−0.796604	−	0.121538i
$290$		0			0
$291$	−3.30979	+	34.8731i	−0.194024	+	2.04430i
$292$		0			0
$293$	−6.46933	+	3.15867i	−0.377943	+	0.184532i	−0.617909	−	0.786249i	$-0.712020\pi$
$293$	−6.46933	+	3.15867i	−0.377943	+	0.184532i	0.239967	+	0.970781i	$0.422863\pi$
$294$		0			0
$295$	2.86000	+	1.01380i	0.166516	+	0.0590255i
$296$		0			0
$297$	−8.93956	−	2.42560i	−0.518726	−	0.140747i
$298$		0			0
$299$	−18.3558	+	16.0720i	−1.06154	+	0.929467i
$300$		0			0
$301$	−2.42432	−	1.42015i	−0.139735	−	0.0818559i
$302$		0			0
$303$	−2.02165	+	0.467183i	−0.116141	+	0.0268389i
$304$		0			0
$305$	−11.0021	+	4.37534i	−0.629981	+	0.250531i
$306$		0			0
$307$	−8.10057	−	19.2978i	−0.462324	−	1.10138i	−0.970711	−	0.240252i	$-0.922770\pi$
$307$	−8.10057	−	19.2978i	−0.462324	−	1.10138i	0.508386	−	0.861129i	$-0.330242\pi$
$308$		0			0
$309$	31.8304	+	34.9944i	1.81077	+	1.99076i
$310$		0			0
$311$	14.1200	+	5.61526i	0.800674	+	0.318412i	0.733814	−	0.679350i	$-0.237738\pi$
$311$	14.1200	+	5.61526i	0.800674	+	0.318412i	0.0668594	+	0.997762i	$0.478702\pi$
$312$		0			0
$313$	0.308485	+	0.0963742i	0.0174366	+	0.00544739i	0.306904	−	0.951741i	$-0.400707\pi$
$313$	0.308485	+	0.0963742i	0.0174366	+	0.00544739i	−0.289467	+	0.957188i	$0.593478\pi$
$314$		0			0
$315$	−2.23694	+	3.36503i	−0.126038	+	0.189598i
$316$		0			0
$317$	−11.4027	−	0.864850i	−0.640440	−	0.0485748i	−0.248597	−	0.968607i	$-0.579970\pi$
$317$	−11.4027	−	0.864850i	−0.640440	−	0.0485748i	−0.391843	+	0.920032i	$0.628162\pi$
$318$		0			0
$319$	−1.23784	+	4.24267i	−0.0693055	+	0.237544i
$320$		0			0
$321$	0.738361	−	1.44236i	0.0412113	−	0.0805047i
$322$		0			0
$323$	−3.12016	+	4.00055i	−0.173610	+	0.222596i
$324$		0			0
$325$	8.11394	−	2.20158i	0.450081	−	0.122122i
$326$		0			0
$327$	−0.826633	+	1.77760i	−0.0457129	+	0.0983014i
$328$		0			0
$329$	−4.14995	−	1.83514i	−0.228794	−	0.101175i
$330$		0			0
$331$	−2.24687	−	16.8611i	−0.123499	−	0.926773i	−0.938006	−	0.346619i	$-0.887330\pi$
$331$	−2.24687	−	16.8611i	−0.123499	−	0.926773i	0.814507	−	0.580154i	$-0.197008\pi$
$332$		0			0
$333$	13.4153			0.735155
$334$		0			0
$335$	−3.01730			−0.164853
$336$		0			0
$337$	−2.49861	−	18.7503i	−0.136108	−	1.02139i	−0.917608	−	0.397487i	$-0.869883\pi$
$337$	−2.49861	−	18.7503i	−0.136108	−	1.02139i	0.781500	−	0.623905i	$-0.214455\pi$
$338$		0			0
$339$	33.5993	+	14.8579i	1.82486	+	0.806970i
$340$		0			0
$341$	2.41129	−	5.18525i	0.130579	−	0.280797i
$342$		0			0
$343$	5.28769	−	1.43472i	0.285509	−	0.0774678i
$344$		0			0
$345$	−14.4442	+	18.5198i	−0.777650	+	0.997074i
$346$		0			0
$347$	−15.8722	+	31.0058i	−0.852065	+	1.66448i	−0.110217	+	0.993907i	$0.535155\pi$
$347$	−15.8722	+	31.0058i	−0.852065	+	1.66448i	−0.741847	+	0.670569i	$0.766050\pi$
$348$		0			0
$349$	−1.18645	+	4.06653i	−0.0635090	+	0.217677i	−0.985541	−	0.169437i	$-0.945805\pi$
$349$	−1.18645	+	4.06653i	−0.0635090	+	0.217677i	0.922032	+	0.387114i	$0.126528\pi$
$350$		0			0
$351$	40.1159	+	3.04263i	2.14123	+	0.162403i
$352$		0			0
$353$	−13.0129	+	19.5753i	−0.692606	+	1.04189i	0.303423	+	0.952856i	$0.401871\pi$
$353$	−13.0129	+	19.5753i	−0.692606	+	1.04189i	−0.996029	+	0.0890299i	$0.971623\pi$
$354$		0			0
$355$	8.98328	+	2.80648i	0.476783	+	0.148952i
$356$		0			0
$357$	1.94185	+	0.772238i	0.102774	+	0.0408712i
$358$		0			0
$359$	3.14740	+	3.46027i	0.166114	+	0.182626i	0.817158	−	0.576414i	$-0.195548\pi$
$359$	3.14740	+	3.46027i	0.166114	+	0.182626i	−0.651044	+	0.759040i	$0.725669\pi$
$360$		0			0
$361$	4.33592	+	10.3293i	0.228206	+	0.543650i
$362$		0			0
$363$	−25.1201	+	9.98976i	−1.31846	+	0.524326i
$364$		0			0
$365$	14.8532	−	3.43242i	0.777453	−	0.179661i
$366$		0			0
$367$	17.1688	+	10.0573i	0.896202	+	0.524988i	0.880050	−	0.474881i	$-0.157509\pi$
$367$	17.1688	+	10.0573i	0.896202	+	0.524988i	0.0161522	+	0.999870i	$0.494858\pi$
$368$		0			0
$369$	3.52674	−	3.08795i	0.183595	−	0.160752i
$370$		0			0
$371$	2.51831	+	0.683300i	0.130744	+	0.0354751i
$372$		0			0
$373$	−8.29123	−	2.93902i	−0.429304	−	0.152177i	0.110673	−	0.993857i	$-0.464699\pi$
$373$	−8.29123	−	2.93902i	−0.429304	−	0.152177i	−0.539977	+	0.841680i	$0.681567\pi$
$374$		0			0
$375$	31.7520	−	15.5030i	1.63967	−	0.800573i
$376$		0			0
$377$	1.81369	−	19.1096i	0.0934097	−	0.984195i
$378$		0			0
$379$	−4.29788	−	0.655726i	−0.220767	−	0.0336824i	0.0394975	−	0.999220i	$-0.487424\pi$
$379$	−4.29788	−	0.655726i	−0.220767	−	0.0336824i	−0.260265	+	0.965537i	$0.583810\pi$
$380$		0			0
$381$	0.801283	+	42.3343i	0.0410510	+	2.16885i
$382$		0			0
$383$	−18.9548	−	22.4933i	−0.968547	−	1.14935i	−0.988753	−	0.149557i	$-0.952215\pi$
$383$	−18.9548	−	22.4933i	−0.968547	−	1.14935i	0.0202061	−	0.999796i	$-0.493568\pi$
$384$		0			0
$385$	−0.0548625	−	0.965262i	−0.00279605	−	0.0491943i
$386$		0			0
$387$	6.55331	+	38.1020i	0.333123	+	1.93683i
$388$		0			0
$389$	20.1792	−	10.8167i	1.02312	−	0.548428i	0.126847	−	0.991922i	$-0.459514\pi$
$389$	20.1792	−	10.8167i	1.02312	−	0.548428i	0.896277	+	0.443494i	$0.146261\pi$
$390$		0			0
$391$	7.03814	+	3.43640i	0.355934	+	0.173786i
$392$		0			0
$393$	−54.0747	+	4.10134i	−2.72771	+	0.206885i
$394$		0			0
$395$	17.3142	−	17.6451i	0.871174	−	0.887819i
$396$		0			0
$397$	5.75801	−	33.4780i	0.288986	−	1.68021i	−0.370764	−	0.928727i	$-0.620904\pi$
$397$	5.75801	−	33.4780i	0.288986	−	1.68021i	0.659750	−	0.751485i	$-0.270662\pi$
$398$		0			0
$399$	−2.49479	+	2.02285i	−0.124896	+	0.101269i
$400$		0			0
$401$	−29.6422	+	13.1080i	−1.48026	+	0.654584i	−0.977709	−	0.209964i	$-0.932665\pi$
$401$	−29.6422	+	13.1080i	−1.48026	+	0.654584i	−0.502551	+	0.864548i	$0.667605\pi$
$402$		0			0
$403$	−6.04918	+	24.0892i	−0.301331	+	1.19997i
$404$		0			0
$405$	8.04794	−	0.917804i	0.399905	−	0.0456060i
$406$		0			0
$407$	−2.56799	+	1.92582i	−0.127290	+	0.0954594i
$408$		0			0
$409$	3.22974	−	3.83266i	0.159700	−	0.189513i	−0.678947	−	0.734187i	$-0.737564\pi$
$409$	3.22974	−	3.83266i	0.159700	−	0.189513i	0.838648	+	0.544674i	$0.183347\pi$
$410$		0			0
$411$	−17.4109	−	34.0114i	−0.858814	−	1.67766i
$412$		0			0
$413$	0.225415	−	0.599631i	0.0110920	−	0.0295059i
$414$		0			0
$415$	−11.7827	+	6.90222i	−0.578391	+	0.338817i
$416$		0			0
$417$	−12.7791	+	17.7296i	−0.625794	+	0.868224i
$418$		0			0
$419$	20.0135	+	10.7279i	0.977725	+	0.524093i	0.881966	−	0.471312i	$-0.156219\pi$
$419$	20.0135	+	10.7279i	0.977725	+	0.524093i	0.0957581	+	0.995405i	$0.469472\pi$
$420$		0			0
$421$	−14.4393	−	25.7547i	−0.703730	−	1.25521i	−0.957637	−	0.287979i	$-0.907017\pi$
$421$	−14.4393	−	25.7547i	−0.703730	−	1.25521i	0.253907	−	0.967229i	$-0.418284\pi$
$422$		0			0
$423$	17.4879	+	59.9395i	0.850289	+	2.91436i
$424$		0			0
$425$	−1.65986	−	2.12821i	−0.0805151	−	0.103233i
$426$		0			0
$427$	0.879578	+	2.33978i	0.0425658	+	0.113230i
$428$		0			0
$429$	−18.0699	+	11.5252i	−0.872425	+	0.556441i
$430$		0			0
$431$	−10.0971	−	2.33333i	−0.486359	−	0.112393i	−0.0251493	−	0.999684i	$-0.508006\pi$
$431$	−10.0971	−	2.33333i	−0.486359	−	0.112393i	−0.461210	+	0.887291i	$0.652584\pi$
$432$		0			0
$433$	−3.43645	+	8.18655i	−0.165145	+	0.393420i	−0.983404	−	0.181430i	$-0.941928\pi$
$433$	−3.43645	+	8.18655i	−0.165145	+	0.393420i	0.818259	+	0.574850i	$0.194940\pi$
$434$		0			0
$435$	−1.74596	−	18.3960i	−0.0837125	−	0.882022i
$436$		0			0
$437$	−9.89682	+	6.85257i	−0.473429	+	0.327803i
$438$		0			0
$439$	5.35208	+	4.68619i	0.255441	+	0.223660i	0.776912	−	0.629610i	$-0.216785\pi$
$439$	5.35208	+	4.68619i	0.255441	+	0.223660i	−0.521471	+	0.853269i	$0.674616\pi$
$440$		0			0
$441$	−30.6408	−	21.2157i	−1.45908	−	1.01027i
$442$		0			0
$443$	−32.6764	−	20.8413i	−1.55250	−	0.990202i	−0.986115	−	0.166064i	$-0.946894\pi$
$443$	−32.6764	−	20.8413i	−1.55250	−	0.990202i	−0.566389	−	0.824138i	$-0.691660\pi$
$444$		0			0
$445$	−1.12428	+	8.43690i	−0.0532959	+	0.399947i
$446$		0			0
$447$	−21.0079	+	34.3548i	−0.993641	+	1.62492i
$448$		0			0
$449$	−16.3239	−	16.6358i	−0.770371	−	0.785090i	0.210944	−	0.977498i	$-0.432346\pi$
$449$	−16.3239	−	16.6358i	−0.770371	−	0.785090i	−0.981315	+	0.192408i	$0.938370\pi$
$450$		0			0
$451$	−0.231809	+	1.09738i	−0.0109154	+	0.0516736i
$452$		0			0
$453$	23.0497	−	41.1125i	1.08297	−	1.93164i
$454$		0			0
$455$	1.02273	+	4.07274i	0.0479463	+	0.190933i
$456$		0			0
$457$	−19.5314	−	29.3810i	−0.913640	−	1.37439i	−0.927236	−	0.374478i	$-0.877822\pi$
$457$	−19.5314	−	29.3810i	−0.913640	−	1.37439i	0.0135957	−	0.999908i	$-0.495672\pi$
$458$		0			0
$459$	−4.08389	−	12.2525i	−0.190620	−	0.571899i
$460$		0			0
$461$	−36.3775	−	4.14857i	−1.69427	−	0.193218i	−0.787930	−	0.615765i	$-0.788847\pi$
$461$	−36.3775	−	4.14857i	−1.69427	−	0.193218i	−0.906341	+	0.422547i	$0.861136\pi$
$462$		0			0
$463$	26.5761	−	1.00640i	1.23510	−	0.0467714i	0.587798	−	0.809008i	$-0.299995\pi$
$463$	26.5761	−	1.00640i	1.23510	−	0.0467714i	0.647299	+	0.762236i	$0.275898\pi$
$464$		0			0
$465$	−1.35676	+	23.8712i	−0.0629184	+	1.10700i
$466$		0			0
$467$	−11.3701	−	18.5939i	−0.526148	−	0.860421i	0.473646	−	0.880715i	$-0.342937\pi$
$467$	−11.3701	−	18.5939i	−0.526148	−	0.860421i	−0.999794	+	0.0202938i	$0.993540\pi$
$468$		0			0
$469$	−0.0120546	+	0.636882i	−0.000556630	+	0.0294085i
$470$		0			0
$471$	66.8373	−	23.6921i	3.07970	−	1.09167i
$472$		0			0
$473$	−6.72413	−	6.35281i	−0.309176	−	0.292102i
$474$		0			0
$475$	4.10067	−	0.625638i	0.188152	−	0.0287062i
$476$		0			0
$477$	−15.1401	−	32.5573i	−0.693216	−	1.49070i
$478$		0			0
$479$	7.09128	+	0.268537i	0.324009	+	0.0122698i	0.199345	−	0.979929i	$-0.436118\pi$
$479$	7.09128	+	0.268537i	0.324009	+	0.0122698i	0.124664	+	0.992199i	$0.460215\pi$
$480$		0			0
$481$	9.38085	−	10.3133i	0.427730	−	0.470248i
$482$		0			0
$483$	3.85140	+	3.12283i	0.175245	+	0.142094i
$484$		0			0
$485$	18.0779	+	13.5572i	0.820875	+	0.615602i
$486$		0			0
$487$	−21.1134	+	4.04416i	−0.956738	+	0.183258i	−0.642671	−	0.766143i	$-0.722174\pi$
$487$	−21.1134	+	4.04416i	−0.956738	+	0.183258i	−0.314067	+	0.949401i	$0.601692\pi$
$488$		0			0
$489$	−28.9857	−	5.55206i	−1.31078	−	0.251073i
$490$		0			0
$491$	2.92914	+	13.8665i	0.132190	+	0.625787i	0.993124	+	0.117070i	$0.0373501\pi$
$491$	2.92914	+	13.8665i	0.132190	+	0.625787i	−0.860933	+	0.508718i	$0.830120\pi$
$492$		0			0
$493$	−5.88189	+	1.83757i	−0.264907	+	0.0827599i
$494$		0			0
$495$	−9.67034	+	9.13631i	−0.434649	+	0.410647i
$496$		0			0
$497$	0.628272	−	1.88495i	0.0281819	−	0.0845516i
$498$		0			0
$499$	−4.42564	−	6.14011i	−0.198119	−	0.274869i	0.700450	−	0.713701i	$-0.252983\pi$
$499$	−4.42564	−	6.14011i	−0.198119	−	0.274869i	−0.898569	+	0.438832i	$0.855392\pi$
$500$		0			0
$501$	11.1162	+	35.8735i	0.496637	+	1.60271i
$502$		0			0
$503$	−24.0729	−	33.3987i	−1.07336	−	1.48917i	−0.858697	−	0.512484i	$-0.828725\pi$
$503$	−24.0729	−	33.3987i	−1.07336	−	1.48917i	−0.214662	−	0.976688i	$-0.568865\pi$
$504$		0			0
$505$	−0.423236	+	1.26980i	−0.0188337	+	0.0565052i
$506$		0			0
$507$	40.2025	−	37.9824i	1.78545	−	1.68686i
$508$		0			0
$509$	5.40387	−	1.68823i	0.239522	−	0.0748295i	−0.176080	−	0.984376i	$-0.556342\pi$
$509$	5.40387	−	1.68823i	0.239522	−	0.0748295i	0.415603	+	0.909546i	$0.363571\pi$
$510$		0			0
$511$	−0.665165	−	3.14888i	−0.0294252	−	0.139298i
$512$		0			0
$513$	19.4954	+	3.73424i	0.860742	+	0.164871i
$514$		0			0
$515$	29.9703	−	5.74066i	1.32065	−	0.252964i
$516$		0			0
$517$	−11.9521	−	8.96329i	−0.525653	−	0.394205i
$518$		0			0
$519$	4.59130	+	3.72276i	0.201536	+	0.163411i
$520$		0			0
$521$	12.7435	−	14.0102i	0.558301	−	0.613798i	−0.393944	−	0.919135i	$-0.628889\pi$
$521$	12.7435	−	14.0102i	0.558301	−	0.613798i	0.952245	+	0.305337i	$0.0987690\pi$
$522$		0			0
$523$	23.8192	+	0.901999i	1.04154	+	0.0394416i	0.553066	−	0.833137i	$-0.313458\pi$
$523$	23.8192	+	0.901999i	1.04154	+	0.0394416i	0.488473	+	0.872579i	$0.337554\pi$
$524$		0			0
$525$	−0.720471	−	1.54931i	−0.0314439	−	0.0676172i
$526$		0			0
$527$	7.88215	−	1.20258i	0.343352	−	0.0523851i
$528$		0			0
$529$	−3.21036	−	3.03307i	−0.139581	−	0.131873i
$530$		0			0
$531$	−8.30828	+	2.94507i	−0.360549	+	0.127805i
$532$		0			0
$533$	0.0921876	−	4.87056i	0.00399309	−	0.210967i
$534$		0			0
$535$	−0.545297	−	0.891736i	−0.0235752	−	0.0385531i
$536$		0			0
$537$	0.869844	−	15.3042i	0.0375366	−	0.660426i
$538$		0			0
$539$	8.91092	−	0.337444i	0.383820	−	0.0145347i
$540$		0			0
$541$	−43.1445	−	4.92028i	−1.85492	−	0.211540i	−0.886825	−	0.462105i	$-0.847094\pi$
$541$	−43.1445	−	4.92028i	−1.85492	−	0.211540i	−0.968100	+	0.250566i	$0.919383\pi$
$542$		0			0
$543$	8.88374	+	26.6531i	0.381238	+	1.14379i
$544$		0			0
$545$	0.700083	+	1.05313i	0.0299882	+	0.0451112i
$546$		0			0
$547$	−8.84681	−	35.2300i	−0.378262	−	1.50633i	−0.800217	−	0.599710i	$-0.795283\pi$
$547$	−8.84681	−	35.2300i	−0.378262	−	1.50633i	0.421955	−	0.906617i	$-0.361344\pi$
$548$		0			0
$549$	16.8207	−	30.0022i	0.717889	−	1.28046i
$550$		0			0
$551$	1.95743	−	9.26646i	0.0833893	−	0.394764i
$552$		0			0
$553$	−3.65529	−	3.72513i	−0.155439	−	0.158409i
$554$		0			0
$555$	7.00157	−	11.4498i	0.297200	−	0.486018i
$556$		0			0
$557$	−1.11200	+	8.34473i	−0.0471168	+	0.353578i	0.951787	+	0.306761i	$0.0992451\pi$
$557$	−1.11200	+	8.34473i	−0.0471168	+	0.353578i	−0.998903	+	0.0468169i	$0.985092\pi$
$558$		0			0
$559$	33.8743	+	21.6053i	1.43273	+	0.913808i
$560$		0			0
$561$	5.65675	+	3.91675i	0.238828	+	0.165365i
$562$		0			0
$563$	−35.5314	−	31.1107i	−1.49747	−	1.31116i	−0.813321	−	0.581816i	$-0.802342\pi$
$563$	−35.5314	−	31.1107i	−1.49747	−	1.31116i	−0.684149	−	0.729342i	$-0.739826\pi$
$564$		0			0
$565$	19.4838	−	13.4906i	0.819692	−	0.567556i
$566$		0			0
$567$	−0.161574	−	1.70240i	−0.00678549	−	0.0714941i
$568$		0			0
$569$	8.01388	−	19.0912i	0.335959	−	0.800346i	−0.662715	−	0.748872i	$-0.730596\pi$
$569$	8.01388	−	19.0912i	0.335959	−	0.800346i	0.998674	−	0.0514742i	$-0.0163920\pi$
$570$		0			0
$571$	36.2476	+	8.37644i	1.51691	+	0.350543i	0.899790	−	0.436323i	$-0.143720\pi$
$571$	36.2476	+	8.37644i	1.51691	+	0.350543i	0.617124	+	0.786866i	$0.288298\pi$
$572$		0			0
$573$	19.5945	−	12.4976i	0.818571	−	0.522093i
$574$		0			0
$575$	−2.25337	−	5.99423i	−0.0939720	−	0.249977i
$576$		0			0
$577$	4.72977	+	6.06434i	0.196903	+	0.252462i	0.876810	−	0.480836i	$-0.159667\pi$
$577$	4.72977	+	6.06434i	0.196903	+	0.252462i	−0.679907	+	0.733298i	$0.737980\pi$
$578$		0			0
$579$	7.28864	+	24.9817i	0.302906	+	1.03821i
$580$		0			0
$581$	1.40983	+	2.51464i	0.0584895	+	0.104325i
$582$		0			0
$583$	7.57187	+	4.05877i	0.313595	+	0.168097i
$584$		0			0
$585$	33.7861	−	46.8747i	1.39689	−	1.93803i
$586$		0			0
$587$	3.22186	−	1.88734i	0.132980	−	0.0778988i	−0.437460	−	0.899238i	$-0.644122\pi$
$587$	3.22186	−	1.88734i	0.132980	−	0.0778988i	0.570440	+	0.821339i	$0.306773\pi$
$588$		0			0
$589$	−4.31213	+	11.4708i	−0.177678	+	0.472645i
$590$		0			0
$591$	−2.69977	−	5.27389i	−0.111054	−	0.216939i
$592$		0			0
$593$	−11.0112	+	13.0667i	−0.452176	+	0.536587i	−0.942168	−	0.335140i	$-0.891216\pi$
$593$	−11.0112	+	13.0667i	−0.452176	+	0.536587i	0.489992	+	0.871727i	$0.337000\pi$
$594$		0			0
$595$	1.07847	−	0.808784i	0.0442131	−	0.0331569i
$596$		0			0
$597$	−31.5663	+	3.59989i	−1.29192	+	0.147334i
$598$		0			0
$599$	−8.55400	+	34.0640i	−0.349507	+	1.39182i	0.500815	+	0.865554i	$0.333034\pi$
$599$	−8.55400	+	34.0640i	−0.349507	+	1.39182i	−0.850322	+	0.526263i	$0.823593\pi$
$600$		0			0
$601$	11.7425	−	5.19264i	0.478987	−	0.211812i	−0.150824	−	0.988561i	$-0.548193\pi$
$601$	11.7425	−	5.19264i	0.478987	−	0.211812i	0.629811	+	0.776748i	$0.283132\pi$
$602$		0			0
$603$	6.80837	−	5.52043i	0.277258	−	0.224809i
$604$		0			0
$605$	−2.95592	+	17.1862i	−0.120175	+	0.698717i
$606$		0			0
$607$	−20.3394	+	20.7280i	−0.825550	+	0.841323i	−0.989408	−	0.145161i	$-0.953630\pi$
$607$	−20.3394	+	20.7280i	−0.825550	+	0.841323i	0.163858	+	0.986484i	$0.447606\pi$
$608$		0			0
$609$	−3.88995	+	0.295037i	−0.157629	+	0.0119555i
$610$		0			0
$611$	58.3085	+	28.4693i	2.35891	+	1.15174i
$612$		0			0
$613$	0.472662	−	0.253362i	0.0190906	−	0.0102332i	−0.462867	−	0.886428i	$-0.653179\pi$
$613$	0.472662	−	0.253362i	0.0190906	−	0.0102332i	0.481957	+	0.876195i	$0.339926\pi$
$614$		0			0
$615$	−0.794898	−	4.62167i	−0.0320534	−	0.186364i
$616$		0			0
$617$	2.55417	+	44.9387i	0.102827	+	1.80916i	0.473920	+	0.880568i	$0.342838\pi$
$617$	2.55417	+	44.9387i	0.102827	+	1.80916i	−0.371093	+	0.928596i	$0.621017\pi$
$618$		0			0
$619$	−6.42678	−	7.62652i	−0.258314	−	0.306536i	0.620017	−	0.784589i	$-0.287126\pi$
$619$	−6.42678	−	7.62652i	−0.258314	−	0.306536i	−0.878331	+	0.478053i	$0.841343\pi$
$620$		0			0
$621$	−0.579905	−	30.6382i	−0.0232708	−	1.22947i
$622$		0			0
$623$	1.77634	+	0.271016i	0.0711677	+	0.0108580i
$624$		0			0
$625$	1.45184	−	15.2970i	0.0580734	−	0.611881i
$626$		0			0
$627$	−9.50251	+	4.63963i	−0.379494	+	0.185289i
$628$		0			0
$629$	−4.21839	−	1.49531i	−0.168198	−	0.0596219i
$630$		0			0
$631$	24.0964	+	6.53813i	0.959261	+	0.260279i	0.706868	−	0.707346i	$-0.250108\pi$
$631$	24.0964	+	6.53813i	0.959261	+	0.260279i	0.252393	+	0.967625i	$0.418782\pi$
$632$		0			0
$633$	4.88230	−	4.27486i	0.194054	−	0.169910i
$634$		0			0
$635$	23.5675	+	13.8057i	0.935249	+	0.547862i
$636$		0			0
$637$	−37.7360	+	8.72041i	−1.49516	+	0.345515i
$638$		0			0
$639$	−25.4050	+	10.1031i	−1.00501	+	0.399671i
$640$		0			0
$641$	2.87029	+	6.83781i	0.113370	+	0.270077i	0.968801	−	0.247838i	$-0.0797202\pi$
$641$	2.87029	+	6.83781i	0.113370	+	0.270077i	−0.855432	+	0.517916i	$0.826708\pi$
$642$		0			0
$643$	14.6929	+	16.1534i	0.579431	+	0.637029i	0.957392	−	0.288793i	$-0.0932539\pi$
$643$	14.6929	+	16.1534i	0.579431	+	0.637029i	−0.377960	+	0.925822i	$0.623374\pi$
$644$		0			0
$645$	35.9399	+	14.2926i	1.41513	+	0.562770i
$646$		0			0
$647$	−17.0944	−	5.34048i	−0.672050	−	0.209956i	−0.0569164	−	0.998379i	$-0.518127\pi$
$647$	−17.0944	−	5.34048i	−0.672050	−	0.209956i	−0.615134	+	0.788423i	$0.710898\pi$
$648$		0			0
$649$	1.16761	−	1.75644i	0.0458328	−	0.0689461i
$650$		0			0
$651$	5.03324	+	0.381751i	0.197268	+	0.0149620i
$652$		0			0
$653$	10.7510	−	36.8491i	0.420721	−	1.44202i	−0.423439	−	0.905924i	$-0.639177\pi$
$653$	10.7510	−	36.8491i	0.420721	−	1.44202i	0.844160	−	0.536091i	$-0.180100\pi$
$654$		0			0
$655$	−15.9405	+	31.1392i	−0.622847	+	1.21671i
$656$		0			0
$657$	−27.2355	+	34.9204i	−1.06256	+	1.36237i
$658$		0			0
$659$	−10.7406	+	2.91427i	−0.418393	+	0.113524i	−0.464835	−	0.885397i	$-0.653886\pi$
$659$	−10.7406	+	2.91427i	−0.418393	+	0.113524i	0.0464421	+	0.998921i	$0.485212\pi$
$660$		0			0
$661$	9.99716	−	21.4980i	0.388844	−	0.836174i	−0.610191	−	0.792255i	$-0.708907\pi$
$661$	9.99716	−	21.4980i	0.388844	−	0.836174i	0.999035	−	0.0439191i	$-0.0139844\pi$
$662$		0			0
$663$	−27.3306	−	12.0858i	−1.06143	−	0.469375i
$664$		0			0
$665$	0.273671	+	2.05370i	0.0106125	+	0.0796392i
$666$		0			0
$667$	−14.6210			−0.566129
$668$		0			0
$669$	74.6780			2.88722
$670$		0			0
$671$	1.08708	+	8.15775i	0.0419662	+	0.314926i
$672$		0			0
$673$	28.2613	+	12.4974i	1.08939	+	0.481739i	0.869575	−	0.493802i	$-0.164393\pi$
$673$	28.2613	+	12.4974i	1.08939	+	0.481739i	0.219819	+	0.975541i	$0.429453\pi$
$674$		0			0
$675$	−4.45265	+	9.57502i	−0.171383	+	0.368543i
$676$		0			0
$677$	31.0180	−	8.41620i	1.19212	−	0.323461i	0.390107	−	0.920769i	$-0.372438\pi$
$677$	31.0180	−	8.41620i	1.19212	−	0.323461i	0.802012	+	0.597308i	$0.203763\pi$
$678$		0			0
$679$	2.93384	−	3.76166i	0.112590	−	0.144359i
$680$		0			0
$681$	−15.9607	+	31.1786i	−0.611614	+	1.19477i
$682$		0			0
$683$	7.76539	−	26.6158i	0.297134	−	1.01843i	−0.665224	−	0.746643i	$-0.731664\pi$
$683$	7.76539	−	26.6158i	0.297134	−	1.01843i	0.962359	−	0.271782i	$-0.0876129\pi$
$684$		0			0
$685$	−24.5768	−	1.86405i	−0.939030	−	0.0712217i
$686$		0			0
$687$	31.9466	−	48.0572i	1.21884	−	1.83350i
$688$		0			0
$689$	−35.6161	−	11.1269i	−1.35686	−	0.423900i
$690$		0			0
$691$	−1.39970	−	0.556633i	−0.0532471	−	0.0211753i	0.342757	−	0.939424i	$-0.388639\pi$
$691$	−1.39970	−	0.556633i	−0.0532471	−	0.0211753i	−0.396004	+	0.918249i	$0.629603\pi$
$692$		0			0
$693$	1.88983	+	2.07769i	0.0717887	+	0.0789248i
$694$		0			0
$695$	5.45665	+	12.9992i	0.206983	+	0.493089i
$696$		0			0
$697$	−1.45316	+	0.577894i	−0.0550424	+	0.0218893i
$698$		0			0
$699$	−74.2232	+	17.1522i	−2.80738	+	0.648757i
$700$		0			0
$701$	12.1187	+	7.09904i	0.457717	+	0.268127i	0.716208	−	0.697886i	$-0.245876\pi$
$701$	12.1187	+	7.09904i	0.457717	+	0.268127i	−0.258492	+	0.966014i	$0.583225\pi$
$702$		0			0
$703$	5.17522	−	4.53133i	0.195187	−	0.170902i
$704$		0			0
$705$	60.2848	+	16.3572i	2.27046	+	0.616049i
$706$		0			0
$707$	0.266334	+	0.0944083i	0.0100165	+	0.00355059i
$708$		0			0
$709$	−32.5531	+	15.8942i	−1.22256	+	0.596918i	−0.932873	−	0.360205i	$-0.882707\pi$
$709$	−32.5531	+	15.8942i	−1.22256	+	0.596918i	−0.289684	+	0.957122i	$0.593550\pi$
$710$		0			0
$711$	−6.78539	+	71.4931i	−0.254472	+	2.68120i
$712$		0			0
$713$	18.7018	+	2.85333i	0.700389	+	0.106858i
$714$		0			0
$715$	0.261635	+	13.8230i	0.00978459	+	0.516950i
$716$		0			0
$717$	−14.5944	−	17.3188i	−0.545037	−	0.646783i
$718$		0			0
$719$	−1.76946	−	31.1323i	−0.0659897	−	1.16104i	−0.845262	−	0.534352i	$-0.820556\pi$
$719$	−1.76946	−	31.1323i	−0.0659897	−	1.16104i	0.779272	−	0.626685i	$-0.215589\pi$
$720$		0			0
$721$	−1.09198	−	6.34898i	−0.0406676	−	0.236448i
$722$		0			0
$723$	8.18115	−	4.38537i	0.304260	−	0.163094i
$724$		0			0
$725$	4.52751	+	2.21057i	0.168148	+	0.0820986i
$726$		0			0
$727$	−17.9299	+	1.35991i	−0.664982	+	0.0504362i	−0.403792	−	0.914851i	$-0.632308\pi$
$727$	−17.9299	+	1.35991i	−0.664982	+	0.0504362i	−0.261191	+	0.965287i	$0.584115\pi$
$728$		0			0
$729$	26.9265	−	27.4410i	0.997278	−	1.01633i
$730$		0			0
$731$	2.18629	−	12.7115i	0.0808630	−	0.470151i
$732$		0			0
$733$	−7.50865	+	6.08823i	−0.277338	+	0.224874i	−0.758362	−	0.651834i	$-0.774000\pi$
$733$	−7.50865	+	6.08823i	−0.277338	+	0.224874i	0.481024	+	0.876708i	$0.340265\pi$
$734$		0			0
$735$	−34.0991	+	15.0789i	−1.25776	+	0.556193i
$736$		0			0
$737$	−0.510794	+	2.03410i	−0.0188153	+	0.0749270i
$738$		0			0
$739$	2.69664	−	0.307530i	0.0991974	−	0.0113127i	−0.0635677	−	0.997978i	$-0.520248\pi$
$739$	2.69664	−	0.307530i	0.0991974	−	0.0113127i	0.162765	+	0.986665i	$0.447959\pi$
$740$		0			0
$741$	36.7444	−	27.5559i	1.34984	−	1.01229i
$742$		0			0
$743$	29.5445	−	35.0597i	1.08388	−	1.28622i	0.128221	−	0.991746i	$-0.459073\pi$
$743$	29.5445	−	35.0597i	1.08388	−	1.28622i	0.955660	−	0.294472i	$-0.0951436\pi$
$744$		0			0
$745$	11.8367	+	23.1226i	0.433665	+	0.847148i
$746$		0			0
$747$	13.9588	−	37.1321i	0.510726	−	1.35859i
$748$		0			0
$749$	−0.190404	+	0.111537i	−0.00695719	+	0.00407547i
$750$		0			0
$751$	8.49386	−	11.7843i	0.309945	−	0.430016i	−0.627252	−	0.778816i	$-0.715820\pi$
$751$	8.49386	−	11.7843i	0.309945	−	0.430016i	0.937197	+	0.348800i	$0.113411\pi$
$752$		0			0
$753$	61.5821	+	33.0100i	2.24417	+	1.20295i
$754$		0			0
$755$	−14.8687	−	26.5204i	−0.541126	−	0.965178i
$756$		0			0
$757$	13.4806	+	46.2046i	0.489961	+	1.67934i	0.710289	+	0.703910i	$0.248564\pi$
$757$	13.4806	+	46.2046i	0.489961	+	1.67934i	−0.220329	+	0.975426i	$0.570713\pi$
$758$		0			0
$759$	10.0398	+	12.8727i	0.364423	+	0.467249i
$760$		0			0
$761$	−3.74036	−	9.94979i	−0.135588	−	0.360680i	0.850714	−	0.525628i	$-0.176170\pi$
$761$	−3.74036	−	9.94979i	−0.135588	−	0.360680i	−0.986302	+	0.164949i	$0.947254\pi$
$762$		0			0
$763$	0.225089	−	0.143564i	0.00814877	−	0.00519736i
$764$		0			0
$765$	−18.0732	−	4.17652i	−0.653437	−	0.151003i
$766$		0			0
$767$	−3.54559	+	8.44656i	−0.128024	+	0.304987i
$768$		0			0
$769$	−2.02694	−	21.3565i	−0.0730933	−	0.770135i	−0.954586	−	0.297937i	$-0.903702\pi$
$769$	−2.02694	−	21.3565i	−0.0730933	−	0.770135i	0.881492	−	0.472198i	$-0.156539\pi$
$770$		0			0
$771$	46.7332	−	32.3582i	1.68306	−	1.16535i
$772$		0			0
$773$	21.7696	+	19.0611i	0.782999	+	0.685580i	0.954039	−	0.299684i	$-0.0968812\pi$
$773$	21.7696	+	19.0611i	0.782999	+	0.685580i	−0.171039	+	0.985264i	$0.554713\pi$
$774$		0			0
$775$	−5.35976	−	3.71111i	−0.192528	−	0.133307i
$776$		0			0
$777$	−2.38882	−	1.52361i	−0.0856986	−	0.0546594i
$778$		0			0
$779$	0.317482	−	2.38248i	0.0113750	−	0.0853611i
$780$		0			0
$781$	3.41274	−	5.58093i	0.122117	−	0.199701i
$782$		0			0
$783$	16.8861	+	17.2087i	0.603459	+	0.614989i
$784$		0			0
$785$	9.45411	−	44.7557i	0.337432	−	1.59740i
$786$		0			0
$787$	−6.16674	+	10.9993i	−0.219821	+	0.392083i	−0.959859	−	0.280481i	$-0.909506\pi$
$787$	−6.16674	+	10.9993i	−0.219821	+	0.392083i	0.740039	+	0.672564i	$0.234807\pi$
$788$		0			0
$789$	−11.7769	−	46.8985i	−0.419270	−	1.66963i
$790$		0			0
$791$	−2.76972	−	4.16649i	−0.0984800	−	0.148143i
$792$		0			0
$793$	−11.3028	−	33.9107i	−0.401373	−	1.20420i
$794$		0			0
$795$	−35.6891	−	4.07005i	−1.26576	−	0.144350i
$796$		0			0
$797$	−1.46132	+	0.0553380i	−0.0517625	+	0.00196017i	−0.0637100	−	0.997968i	$-0.520293\pi$
$797$	−1.46132	+	0.0553380i	−0.0517625	+	0.00196017i	0.0119476	+	0.999929i	$0.496197\pi$
$798$		0			0
$799$	1.18203	−	20.7970i	0.0418174	−	0.735744i
$800$		0			0
$801$	−12.8992	−	21.0944i	−0.455771	−	0.745333i
$802$		0			0
$803$	0.200524	−	10.5943i	0.00707633	−	0.373865i
$804$		0			0
$805$	3.01469	−	1.06863i	0.106254	−	0.0376642i
$806$		0			0
$807$	1.15075	+	1.08720i	0.0405082	+	0.0382712i
$808$		0			0
$809$	−35.0080	+	5.34116i	−1.23082	+	0.187785i	−0.733443	−	0.679751i	$-0.762088\pi$
$809$	−35.0080	+	5.34116i	−1.23082	+	0.187785i	−0.497374	+	0.867536i	$0.665702\pi$
$810$		0			0
$811$	14.4718	+	31.1202i	0.508172	+	1.09278i	0.977728	+	0.209874i	$0.0673055\pi$
$811$	14.4718	+	31.1202i	0.508172	+	1.09278i	−0.469556	+	0.882903i	$0.655586\pi$
$812$		0			0
$813$	−40.3033	−	1.52623i	−1.41350	−	0.0535272i
$814$		0			0
$815$	−12.8099	+	14.0833i	−0.448713	+	0.493317i
$816$		0			0
$817$	15.3979	+	12.4851i	0.538704	+	0.436797i
$818$		0			0
$819$	−9.75919	−	7.31875i	−0.341014	−	0.255738i
$820$		0			0
$821$	36.7457	−	7.03845i	1.28243	−	0.245644i	0.498719	−	0.866764i	$-0.333804\pi$
$821$	36.7457	−	7.03845i	1.28243	−	0.245644i	0.783716	+	0.621120i	$0.213322\pi$
$822$		0			0
$823$	−21.8644	−	4.18801i	−0.762144	−	0.145985i	−0.207685	−	0.978196i	$-0.566593\pi$
$823$	−21.8644	−	4.18801i	−0.762144	−	0.145985i	−0.554459	+	0.832211i	$0.687075\pi$
$824$		0			0
$825$	−1.16267	−	5.50406i	−0.0404789	−	0.191627i
$826$		0			0
$827$	−27.9996	+	8.74739i	−0.973641	+	0.304176i	−0.743318	−	0.668938i	$-0.766749\pi$
$827$	−27.9996	+	8.74739i	−0.973641	+	0.304176i	−0.230322	+	0.973114i	$0.573978\pi$
$828$		0			0
$829$	−24.2050	+	22.8684i	−0.840675	+	0.794251i	−0.980622	−	0.195908i	$-0.937235\pi$
$829$	−24.2050	+	22.8684i	−0.840675	+	0.794251i	0.139947	+	0.990159i	$0.455307\pi$
$830$		0			0
$831$	−15.5308	+	46.5958i	−0.538759	+	1.61639i
$832$		0			0
$833$	7.27010	+	10.0865i	0.251894	+	0.349477i
$834$		0			0
$835$	23.4832	+	5.95480i	0.812670	+	0.206074i
$836$		0			0
$837$	−18.2407	−	25.3071i	−0.630492	−	0.874742i
$838$		0			0
$839$	2.87526	−	8.62638i	0.0992649	−	0.297816i	−0.887298	−	0.461196i	$-0.847421\pi$
$839$	2.87526	−	8.62638i	0.0992649	−	0.297816i	0.986563	+	0.163380i	$0.0522398\pi$
$840$		0			0
$841$	−12.7181	+	12.0157i	−0.438554	+	0.414336i
$842$		0			0
$843$	−62.7794	+	19.6130i	−2.16224	+	0.675507i
$844$		0			0
$845$	−7.37364	−	34.9068i	−0.253661	−	1.20083i
$846$		0			0
$847$	3.61580	+	0.692587i	0.124240	+	0.0237976i
$848$		0			0
$849$	6.28946	−	1.20471i	0.215854	−	0.0413457i
$850$		0			0
$851$	−8.49556	−	6.37111i	−0.291224	−	0.218399i
$852$		0			0
$853$	−38.8101	−	31.4684i	−1.32883	−	1.07746i	−0.990657	−	0.136374i	$-0.956455\pi$
$853$	−38.8101	−	31.4684i	−1.32883	−	1.07746i	−0.338176	−	0.941083i	$-0.609810\pi$
$854$		0			0
$855$	19.1831	−	21.0900i	0.656048	−	0.721261i
$856$		0			0
$857$	−12.3678	−	0.468352i	−0.422477	−	0.0159986i	−0.174252	−	0.984701i	$-0.555751\pi$
$857$	−12.3678	−	0.468352i	−0.422477	−	0.0159986i	−0.248225	+	0.968703i	$0.579847\pi$
$858$		0			0
$859$	5.76531	+	12.3978i	0.196710	+	0.423006i	0.980095	−	0.198531i	$-0.0636169\pi$
$859$	5.76531	+	12.3978i	0.196710	+	0.423006i	−0.783385	+	0.621537i	$0.786509\pi$
$860$		0			0
$861$	−0.978703	+	0.149320i	−0.0333541	+	0.00508882i
$862$		0			0
$863$	−10.2040	−	9.64051i	−0.347348	−	0.328167i	0.493187	−	0.869923i	$-0.335832\pi$
$863$	−10.2040	−	9.64051i	−0.347348	−	0.328167i	−0.840536	+	0.541756i	$0.817760\pi$
$864$		0			0
$865$	3.59385	−	1.27392i	0.122195	−	0.0433147i
$866$		0			0
$867$	0.753406	−	39.8048i	0.0255870	−	1.35184i
$868$		0			0
$869$	−8.96424	−	14.6594i	−0.304091	−	0.497287i
$870$		0			0
$871$	0.516893	−	9.09432i	0.0175142	−	0.308149i
$872$		0			0
$873$	−65.5960	+	2.48403i	−2.22009	+	0.0840716i
$874$		0			0
$875$	−4.78101	−	0.545236i	−0.161628	−	0.0184324i
$876$		0			0
$877$	−3.16160	−	9.48546i	−0.106760	−	0.320301i	0.881695	−	0.471820i	$-0.156403\pi$
$877$	−3.16160	−	9.48546i	−0.106760	−	0.320301i	−0.988454	+	0.151519i	$0.951584\pi$
$878$		0			0
$879$	−11.5827	−	17.4239i	−0.390676	−	0.587693i
$880$		0			0
$881$	13.3870	+	53.3102i	0.451020	+	1.79607i	0.591868	+	0.806035i	$0.298391\pi$
$881$	13.3870	+	53.3102i	0.451020	+	1.79607i	−0.140847	+	0.990031i	$0.544983\pi$
$882$		0			0
$883$	−11.6703	+	20.8157i	−0.392736	+	0.700503i	−0.995223	−	0.0976254i	$-0.968875\pi$
$883$	−11.6703	+	20.8157i	−0.392736	+	0.700503i	0.602487	+	0.798129i	$0.294177\pi$
$884$		0			0
$885$	−1.82258	+	8.62808i	−0.0612654	+	0.290030i
$886$		0			0
$887$	30.1158	+	30.6912i	1.01119	+	1.03051i	0.999532	+	0.0305780i	$0.00973481\pi$
$887$	30.1158	+	30.6912i	1.01119	+	1.03051i	0.0116573	+	0.999932i	$0.496289\pi$
$888$		0			0
$889$	3.00822	−	4.91941i	0.100892	−	0.164992i
$890$		0			0
$891$	0.743690	−	5.58086i	0.0249145	−	0.186966i
$892$		0			0
$893$	26.9922	+	17.2159i	0.903260	+	0.576108i
$894$		0			0
$895$	−8.12966	−	5.62899i	−0.271745	−	0.188157i
$896$		0			0
$897$	−53.3455	−	46.7084i	−1.78115	−	1.55955i
$898$		0			0
$899$	−12.2373	+	8.47315i	−0.408138	+	0.282595i
$900$		0			0
$901$	1.13181	+	11.9251i	0.0377059	+	0.397282i
$902$		0			0
$903$	3.16042	−	7.52897i	0.105172	−	0.250549i
$904$		0			0
$905$	17.6576	+	4.08050i	0.586960	+	0.135640i
$906$		0			0
$907$	8.56267	−	5.46135i	0.284319	−	0.181341i	−0.387884	−	0.921708i	$-0.626794\pi$
$907$	8.56267	−	5.46135i	0.284319	−	0.181341i	0.672203	+	0.740367i	$0.265348\pi$
$908$		0			0
$909$	−1.36820	−	3.63958i	−0.0453804	−	0.120717i
$910$		0			0
$911$	10.8423	+	13.9016i	0.359221	+	0.460580i	0.933761	−	0.357896i	$-0.116506\pi$
$911$	10.8423	+	13.9016i	0.359221	+	0.460580i	−0.574540	+	0.818476i	$0.694819\pi$
$912$		0			0
$913$	2.65843	+	9.11173i	0.0879811	+	0.301554i
$914$		0			0
$915$	−16.8277	−	30.0146i	−0.556306	−	0.992254i
$916$		0			0
$917$	6.50908	+	3.48908i	0.214949	+	0.115220i
$918$		0			0
$919$	−3.44258	+	4.77622i	−0.113560	+	0.157553i	−0.864182	−	0.503179i	$-0.832164\pi$
$919$	−3.44258	+	4.77622i	−0.113560	+	0.157553i	0.750622	+	0.660732i	$0.229754\pi$
$920$		0			0
$921$	52.4820	−	30.7436i	1.72934	−	1.01304i
$922$		0			0
$923$	−9.99782	+	26.5954i	−0.329082	+	0.875397i
$924$		0			0
$925$	1.66746	+	3.25732i	0.0548257	+	0.107100i
$926$		0			0
$927$	−57.1233	+	67.7869i	−1.87618	+	2.22642i
$928$		0			0
$929$	−0.603036	+	0.452237i	−0.0197850	+	0.0148374i	−0.609813	−	0.792546i	$-0.708755\pi$
$929$	−0.603036	+	0.452237i	−0.0197850	+	0.0148374i	0.590028	+	0.807383i	$0.299117\pi$
$930$		0			0
$931$	−18.9864	+	2.16524i	−0.622253	+	0.0709630i
$932$		0			0
$933$	−10.7557	+	42.8316i	−0.352125	+	1.40224i
$934$		0			0
$935$	4.05916	−	1.79499i	0.132749	−	0.0587026i
$936$		0			0
$937$	−34.3108	+	27.8202i	−1.12088	+	0.908845i	−0.996517	−	0.0833914i	$-0.973425\pi$
$937$	−34.3108	+	27.8202i	−1.12088	+	0.908845i	−0.124367	+	0.992236i	$0.539690\pi$
$938$		0			0
$939$	−0.159207	+	0.925658i	−0.00519554	+	0.0302077i
$940$		0			0
$941$	9.83262	−	10.0205i	0.320534	−	0.326659i	−0.534561	−	0.845130i	$-0.679523\pi$
$941$	9.83262	−	10.0205i	0.320534	−	0.326659i	0.855095	+	0.518472i	$0.173499\pi$
$942$		0			0
$943$	−3.69990	+	0.280623i	−0.120485	+	0.00913833i
$944$		0			0
$945$	−4.73948	−	2.31407i	−0.154175	−	0.0752766i
$946$		0			0
$947$	−5.76156	+	3.08839i	−0.187226	+	0.100359i	−0.563380	−	0.826198i	$-0.690499\pi$
$947$	−5.76156	+	3.08839i	−0.187226	+	0.100359i	0.376154	+	0.926557i	$0.377246\pi$
$948$		0			0
$949$	7.80104	+	45.3565i	0.253232	+	1.47233i
$950$		0			0
$951$	−1.88586	−	33.1802i	−0.0611531	−	1.07594i
$952$		0			0
$953$	6.43918	+	7.64123i	0.208586	+	0.247524i	0.858902	−	0.512139i	$-0.171147\pi$
$953$	6.43918	+	7.64123i	0.208586	+	0.247524i	−0.650317	+	0.759663i	$0.725364\pi$
$954$		0			0
$955$	−0.283709	−	14.9892i	−0.00918060	−	0.485040i
$956$		0			0
$957$	−12.6972	−	1.93720i	−0.410442	−	0.0626209i
$958$		0			0
$959$	−0.491646	+	5.18014i	−0.0158761	+	0.167276i
$960$		0			0
$961$	−10.5505	+	5.15132i	−0.340339	+	0.166172i
$962$		0			0
$963$	2.86195	+	1.01448i	0.0922249	+	0.0326913i
$964$		0			0
$965$	16.2011	+	4.39588i	0.521530	+	0.141508i
$966$		0			0
$967$	−31.9633	+	27.9865i	−1.02787	+	0.899984i	−0.995040	−	0.0994769i	$-0.968283\pi$
$967$	−31.9633	+	27.9865i	−1.02787	+	0.899984i	−0.0328292	+	0.999461i	$0.510452\pi$
$968$		0			0
$969$	−12.7223	−	7.45261i	−0.408698	−	0.239412i
$970$		0			0
$971$	−48.6204	+	11.2357i	−1.56030	+	0.360570i	−0.915031	−	0.403383i	$-0.867834\pi$
$971$	−48.6204	+	11.2357i	−1.56030	+	0.360570i	−0.645272	+	0.763953i	$0.723256\pi$
$972$		0			0
$973$	2.76564	−	1.09984i	0.0886623	−	0.0352592i
$974$		0			0
$975$	9.45693	+	22.5290i	0.302864	+	0.721504i
$976$		0			0
$977$	19.5796	+	21.5259i	0.626408	+	0.688675i	0.967936	−	0.251197i	$-0.0808241\pi$
$977$	19.5796	+	21.5259i	0.626408	+	0.688675i	−0.341528	+	0.939871i	$0.610945\pi$
$978$		0			0
$979$	5.49737	+	2.18620i	0.175697	+	0.0698712i
$980$		0			0
$981$	−3.50650	−	1.09547i	−0.111954	−	0.0349757i
$982$		0			0
$983$	−15.2012	+	22.8672i	−0.484844	+	0.729350i	−0.991113	−	0.133026i	$-0.957531\pi$
$983$	−15.2012	+	22.8672i	−0.484844	+	0.729350i	0.506268	+	0.862376i	$0.331025\pi$
$984$		0			0
$985$	−3.81093	−	0.289044i	−0.121426	−	0.00920970i
$986$		0			0
$987$	3.69348	−	12.6594i	0.117565	−	0.402952i
$988$		0			0
$989$	13.9451	−	27.2412i	0.443428	−	0.866220i
$990$		0			0
$991$	28.4452	−	36.4713i	0.903590	−	1.15855i	−0.0831976	−	0.996533i	$-0.526513\pi$
$991$	28.4452	−	36.4713i	0.903590	−	1.15855i	0.986788	−	0.162017i	$-0.0518000\pi$
$992$		0			0
$993$	47.7099	−	12.9453i	1.51403	−	0.410806i
$994$		0			0
$995$	−8.64179	+	18.5834i	−0.273963	+	0.589133i
$996$		0			0
$997$	26.6157	+	11.7697i	0.842928	+	0.372750i	0.780390	−	0.625293i	$-0.215020\pi$
$997$	26.6157	+	11.7697i	0.842928	+	0.372750i	0.0625379	+	0.998043i	$0.480081\pi$
$998$		0			0
$999$	2.31298	+	17.3572i	0.0731794	+	0.549159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.14	✓	1148
167.130	even	83	inner	668.2.e.a.297.14	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.14	✓	1148	1.1	even	1	trivial
668.2.e.a.297.14	yes	1148	167.130	even	83	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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(0.383878 + 2.88073i) q^{3} +(1.71454 + 0.758185i) q^{5} +(0.166885 - 0.358871i) q^{7} +(-5.25594 + 1.42611i) q^{9} +O(q^{10})\)	\(q+(0.383878 + 2.88073i) q^{3} +(1.71454 + 0.758185i) q^{5} +(0.166885 - 0.358871i) q^{7} +(-5.25594 + 1.42611i) q^{9} +(0.801379 - 1.02750i) q^{11} +(-2.57893 + 5.03785i) q^{13} +(-1.52595 + 5.23019i) q^{15} +(1.81167 + 0.137408i) q^{17} +(-1.54588 + 2.32546i) q^{19} +(1.09788 + 0.342989i) q^{21} +(4.00572 + 1.59300i) q^{23} +(-0.999554 - 1.09891i) q^{25} +(-2.75135 - 6.55445i) q^{27} +(-3.15161 + 1.25333i) q^{29} +(4.27583 - 0.988100i) q^{31} +(3.26758 + 1.91412i) q^{33} +(0.558222 - 0.488770i) q^{35} +(-2.37739 - 0.645063i) q^{37} +(-15.5027 - 5.49529i) q^{39} +(-0.773470 + 0.377649i) q^{41} +(0.670758 - 7.06732i) q^{43} +(-10.0928 - 1.53985i) q^{45} +(-0.216966 - 11.4630i) q^{47} +(4.40984 + 5.23306i) q^{49} +(0.299625 + 5.27167i) q^{51} +(1.11755 + 6.49761i) q^{53} +(2.15303 - 1.15410i) q^{55} +(-7.29246 - 3.56057i) q^{57} +(1.61396 - 0.122412i) q^{59} +(-4.42349 + 4.50800i) q^{61} +(-0.365349 + 2.12420i) q^{63} +(-8.24131 + 6.68229i) q^{65} +(-1.47198 + 0.650924i) q^{67} +(-3.05129 + 12.1509i) q^{69} +(4.98792 - 0.568833i) q^{71} +(6.50564 - 4.87880i) q^{73} +(2.78197 - 3.30130i) q^{75} +(-0.235001 - 0.459066i) q^{77} +(4.64014 - 12.3433i) q^{79} +(3.72817 - 2.18394i) q^{81} +(-4.25916 + 5.90913i) q^{83} +(3.00200 + 1.60917i) q^{85} +(-4.82035 - 8.59782i) q^{87} +(1.27162 + 4.35847i) q^{89} +(1.37755 + 1.76625i) q^{91} +(4.48785 + 11.9382i) q^{93} +(-4.41361 + 2.81504i) q^{95} +(11.7440 + 2.71391i) q^{97} +(-2.74668 + 6.54333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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