LMFDB - Embedded newform 414.2.i.b.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			307.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.307
Dual form			414.2.i.b.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-1.59283 - 1.83823i) q^{5} +(1.56130 + 1.00339i) q^{7} +(0.415415 - 0.909632i) q^{8} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-1.59283 - 1.83823i) q^{5} +(1.56130 + 1.00339i) q^{7} +(0.415415 - 0.909632i) q^{8} +(2.04620 - 1.31501i) q^{10} +(0.790323 + 5.49682i) q^{11} +(0.966031 - 0.620830i) q^{13} +(-1.21537 + 1.40261i) q^{14} +(0.841254 + 0.540641i) q^{16} +(7.20366 - 2.11519i) q^{17} +(4.29408 + 1.26086i) q^{19} +(1.01042 + 2.21252i) q^{20} -5.55334 q^{22} +(2.45093 + 4.12225i) q^{23} +(-0.130388 + 0.906870i) q^{25} +(0.477031 + 1.04455i) q^{26} +(-1.21537 - 1.40261i) q^{28} +(2.81913 - 0.827771i) q^{29} +(-0.863019 + 1.88975i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.06847 + 7.43136i) q^{34} +(-0.642438 - 4.46825i) q^{35} +(-5.06718 + 5.84784i) q^{37} +(-1.85913 + 4.07093i) q^{38} +(-2.33380 + 0.685265i) q^{40} +(0.450833 + 0.520289i) q^{41} +(-3.55862 - 7.79229i) q^{43} +(0.790323 - 5.49682i) q^{44} +(-4.42909 + 1.83933i) q^{46} -7.09992 q^{47} +(-1.47703 - 3.23425i) q^{49} +(-0.879083 - 0.258122i) q^{50} +(-1.10181 + 0.323520i) q^{52} +(-4.53311 - 2.91326i) q^{53} +(8.84555 - 10.2083i) q^{55} +(1.56130 - 1.00339i) q^{56} +(0.418141 + 2.90824i) q^{58} +(3.39399 - 2.18119i) q^{59} +(-0.157543 + 0.344971i) q^{61} +(-1.74769 - 1.12317i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(-2.67995 - 0.786905i) q^{65} +(-0.420243 + 2.92285i) q^{67} -7.50778 q^{68} +4.51420 q^{70} +(-2.14473 + 14.9169i) q^{71} +(11.0242 + 3.23701i) q^{73} +(-5.06718 - 5.84784i) q^{74} +(-3.76492 - 2.41956i) q^{76} +(-4.28150 + 9.37518i) q^{77} +(8.86394 - 5.69651i) q^{79} +(-0.346156 - 2.40757i) q^{80} +(-0.579153 + 0.372199i) q^{82} +(6.84228 - 7.89641i) q^{83} +(-15.3624 - 9.87283i) q^{85} +(8.21942 - 2.41344i) q^{86} +(5.32839 + 1.56456i) q^{88} +(-4.47642 - 9.80199i) q^{89} +2.13120 q^{91} +(-1.19028 - 4.64578i) q^{92} +(1.01042 - 7.02765i) q^{94} +(-4.52201 - 9.90183i) q^{95} +(6.51094 + 7.51402i) q^{97} +(3.41153 - 1.00172i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−1.59283	−	1.83823i	−0.712337	−	0.822080i	0.278027	−	0.960573i	$-0.410320\pi$
$5$	−1.59283	−	1.83823i	−0.712337	−	0.822080i	−0.990363	+	0.138493i	$0.955774\pi$
$6$		0			0
$7$	1.56130	+	1.00339i	0.590116	+	0.379245i	0.801354	−	0.598190i	$-0.204113\pi$
$7$	1.56130	+	1.00339i	0.590116	+	0.379245i	−0.211238	+	0.977435i	$0.567750\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$		0			0
$10$	2.04620	−	1.31501i	0.647065	−	0.415844i
$11$	0.790323	+	5.49682i	0.238291	+	1.65735i	0.660479	+	0.750844i	$0.270353\pi$
$11$	0.790323	+	5.49682i	0.238291	+	1.65735i	−0.422188	+	0.906508i	$0.638738\pi$
$12$		0			0
$13$	0.966031	−	0.620830i	0.267929	−	0.172187i	−0.399777	−	0.916612i	$-0.630913\pi$
$13$	0.966031	−	0.620830i	0.267929	−	0.172187i	0.667706	+	0.744425i	$0.267276\pi$
$14$	−1.21537	+	1.40261i	−0.324821	+	0.374864i
$15$		0			0
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	7.20366	−	2.11519i	1.74714	−	0.513008i	0.757043	−	0.653365i	$-0.226643\pi$
$17$	7.20366	−	2.11519i	1.74714	−	0.513008i	0.990101	+	0.140357i	$0.0448250\pi$
$18$		0			0
$19$	4.29408	+	1.26086i	0.985130	+	0.289260i	0.734340	−	0.678781i	$-0.237492\pi$
$19$	4.29408	+	1.26086i	0.985130	+	0.289260i	0.250789	+	0.968042i	$0.419310\pi$
$20$	1.01042	+	2.21252i	0.225938	+	0.494734i
$21$		0			0
$22$	−5.55334			−1.18398
$23$	2.45093	+	4.12225i	0.511054	+	0.859548i
$23$	2.45093	+	4.12225i	0.511054	+	0.859548i
$24$		0			0
$25$	−0.130388	+	0.906870i	−0.0260776	+	0.181374i
$26$	0.477031	+	1.04455i	0.0935534	+	0.204853i
$27$		0			0
$28$	−1.21537	−	1.40261i	−0.229683	−	0.265069i
$29$	2.81913	−	0.827771i	0.523499	−	0.153713i	−0.00929715	−	0.999957i	$-0.502959\pi$
$29$	2.81913	−	0.827771i	0.523499	−	0.153713i	0.532796	+	0.846244i	$0.321141\pi$
$30$		0			0
$31$	−0.863019	+	1.88975i	−0.155003	+	0.339409i	−0.971163	−	0.238417i	$-0.923371\pi$
$31$	−0.863019	+	1.88975i	−0.155003	+	0.339409i	0.816160	+	0.577826i	$0.196099\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$		0			0
$34$	1.06847	+	7.43136i	0.183241	+	1.27447i
$35$	−0.642438	−	4.46825i	−0.108592	−	0.755273i
$36$		0			0
$37$	−5.06718	+	5.84784i	−0.833039	+	0.961379i	−0.999696	−	0.0246361i	$-0.992157\pi$
$37$	−5.06718	+	5.84784i	−0.833039	+	0.961379i	0.166657	+	0.986015i	$0.446703\pi$
$38$	−1.85913	+	4.07093i	−0.301591	+	0.660393i
$39$		0			0
$40$	−2.33380	+	0.685265i	−0.369006	+	0.108350i
$41$	0.450833	+	0.520289i	0.0704083	+	0.0812555i	0.789861	−	0.613286i	$-0.210153\pi$
$41$	0.450833	+	0.520289i	0.0704083	+	0.0812555i	−0.719453	+	0.694542i	$0.755607\pi$
$42$		0			0
$43$	−3.55862	−	7.79229i	−0.542684	−	1.18831i	−0.960115	−	0.279604i	$-0.909797\pi$
$43$	−3.55862	−	7.79229i	−0.542684	−	1.18831i	0.417431	−	0.908709i	$-0.362931\pi$
$44$	0.790323	−	5.49682i	0.119146	−	0.828676i
$45$		0			0
$46$	−4.42909	+	1.83933i	−0.653034	+	0.271194i
$47$	−7.09992			−1.03563			−0.517815	−	0.855493i	$-0.673254\pi$
$47$	−7.09992			−1.03563			−0.517815	+	0.855493i	$0.673254\pi$
$48$		0			0
$49$	−1.47703	−	3.23425i	−0.211004	−	0.462035i
$50$	−0.879083	−	0.258122i	−0.124321	−	0.0365040i
$51$		0			0
$52$	−1.10181	+	0.323520i	−0.152793	+	0.0448641i
$53$	−4.53311	−	2.91326i	−0.622671	−	0.400166i	0.190919	−	0.981606i	$-0.438853\pi$
$53$	−4.53311	−	2.91326i	−0.622671	−	0.400166i	−0.813590	+	0.581439i	$0.802490\pi$
$54$		0			0
$55$	8.84555	−	10.2083i	1.19273	−	1.37649i
$56$	1.56130	−	1.00339i	0.208638	−	0.134083i
$57$		0			0
$58$	0.418141	+	2.90824i	0.0549047	+	0.381870i
$59$	3.39399	−	2.18119i	0.441860	−	0.283966i	−0.300734	−	0.953708i	$-0.597232\pi$
$59$	3.39399	−	2.18119i	0.441860	−	0.283966i	0.742594	+	0.669742i	$0.233595\pi$
$60$		0			0
$61$	−0.157543	+	0.344971i	−0.0201713	+	0.0441690i	−0.919450	−	0.393208i	$-0.871365\pi$
$61$	−0.157543	+	0.344971i	−0.0201713	+	0.0441690i	0.899278	+	0.437377i	$0.144092\pi$
$62$	−1.74769	−	1.12317i	−0.221957	−	0.142643i
$63$		0			0
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−2.67995	−	0.786905i	−0.332407	−	0.0976036i
$66$		0			0
$67$	−0.420243	+	2.92285i	−0.0513408	+	0.357083i	0.947915	+	0.318522i	$0.103187\pi$
$67$	−0.420243	+	2.92285i	−0.0513408	+	0.357083i	−0.999256	+	0.0385611i	$0.987723\pi$
$68$	−7.50778			−0.910452
$69$		0			0
$70$	4.51420			0.539550
$71$	−2.14473	+	14.9169i	−0.254532	+	1.77031i	0.315731	+	0.948849i	$0.397750\pi$
$71$	−2.14473	+	14.9169i	−0.254532	+	1.77031i	−0.570264	+	0.821462i	$0.693159\pi$
$72$		0			0
$73$	11.0242	+	3.23701i	1.29029	+	0.378863i	0.853685	−	0.520790i	$-0.174363\pi$
$73$	11.0242	+	3.23701i	1.29029	+	0.378863i	0.436605	+	0.899653i	$0.356181\pi$
$74$	−5.06718	−	5.84784i	−0.589048	−	0.679797i
$75$		0			0
$76$	−3.76492	−	2.41956i	−0.431866	−	0.277543i
$77$	−4.28150	+	9.37518i	−0.487923	+	1.06840i
$78$		0			0
$79$	8.86394	−	5.69651i	0.997272	−	0.640908i	0.0632029	−	0.998001i	$-0.479868\pi$
$79$	8.86394	−	5.69651i	0.997272	−	0.640908i	0.934069	+	0.357093i	$0.116232\pi$
$80$	−0.346156	−	2.40757i	−0.0387014	−	0.269174i
$81$		0			0
$82$	−0.579153	+	0.372199i	−0.0639568	+	0.0411025i
$83$	6.84228	−	7.89641i	0.751037	−	0.866743i	−0.243631	−	0.969868i	$-0.578339\pi$
$83$	6.84228	−	7.89641i	0.751037	−	0.866743i	0.994668	+	0.103125i	$0.0328841\pi$
$84$		0			0
$85$	−15.3624	−	9.87283i	−1.66629	−	1.07086i
$86$	8.21942	−	2.41344i	0.886323	−	0.260248i
$87$		0			0
$88$	5.32839	+	1.56456i	0.568009	+	0.166782i
$89$	−4.47642	−	9.80199i	−0.474499	−	1.03901i	−0.983939	−	0.178502i	$-0.942875\pi$
$89$	−4.47642	−	9.80199i	−0.474499	−	1.03901i	0.509440	−	0.860506i	$-0.329853\pi$
$90$		0			0
$91$	2.13120			0.223410
$92$	−1.19028	−	4.64578i	−0.124095	−	0.484356i
$93$		0			0
$94$	1.01042	−	7.02765i	0.104217	−	0.724847i
$95$	−4.52201	−	9.90183i	−0.463949	−	1.01591i
$96$		0			0
$97$	6.51094	+	7.51402i	0.661085	+	0.762933i	0.982954	−	0.183851i	$-0.0588564\pi$
$97$	6.51094	+	7.51402i	0.661085	+	0.762933i	−0.321869	+	0.946784i	$0.604311\pi$
$98$	3.41153	−	1.00172i	0.344616	−	0.101189i
$99$		0			0
$100$	0.380601	−	0.833401i	0.0380601	−	0.0833401i
$101$	−3.21670	+	3.71227i	−0.320074	+	0.369385i	−0.892871	−	0.450312i	$-0.851313\pi$
$101$	−3.21670	+	3.71227i	−0.320074	+	0.369385i	0.572797	+	0.819697i	$0.305858\pi$
$102$		0			0
$103$	1.11616	+	7.76307i	0.109979	+	0.764918i	0.967936	+	0.251197i	$0.0808243\pi$
$103$	1.11616	+	7.76307i	0.109979	+	0.764918i	−0.857957	+	0.513721i	$0.828267\pi$
$104$	−0.163423	−	1.13663i	−0.0160250	−	0.111456i
$105$		0			0
$106$	3.52873	−	4.07237i	0.342741	−	0.395544i
$107$	3.86497	−	8.46310i	0.373641	−	0.818159i	−0.625635	−	0.780116i	$-0.715160\pi$
$107$	3.86497	−	8.46310i	0.373641	−	0.818159i	0.999276	−	0.0380435i	$-0.0121125\pi$
$108$		0			0
$109$	−13.9016	+	4.08189i	−1.33153	+	0.390974i	−0.868642	−	0.495441i	$-0.835007\pi$
$109$	−13.9016	+	4.08189i	−1.33153	+	0.390974i	−0.462893	+	0.886414i	$0.653188\pi$
$110$	8.84555	+	10.2083i	0.843390	+	0.973324i
$111$		0			0
$112$	0.770978	+	1.68821i	0.0728506	+	0.159520i
$113$	2.09266	−	14.5548i	0.196861	−	1.36920i	−0.616461	−	0.787385i	$-0.711434\pi$
$113$	2.09266	−	14.5548i	0.196861	−	1.36920i	0.813322	−	0.581814i	$-0.197657\pi$
$114$		0			0
$115$	3.67371	−	11.0714i	0.342575	−	1.03242i
$116$	−2.93814			−0.272800
$117$		0			0
$118$	1.67597	+	3.66986i	0.154285	+	0.337838i
$119$	13.3694	+	3.92562i	1.22557	+	0.359861i
$120$		0			0
$121$	−19.0360	+	5.58946i	−1.73054	+	0.508133i
$122$	−0.319039	−	0.205034i	−0.0288844	−	0.0185629i
$123$		0			0
$124$	1.36046	−	1.57006i	0.122173	−	0.140996i
$125$	−8.35628	+	5.37026i	−0.747409	+	0.480330i
$126$		0			0
$127$	−0.987167	−	6.86590i	−0.0875969	−	0.609250i	−0.985579	−	0.169217i	$-0.945876\pi$
$127$	−0.987167	−	6.86590i	−0.0875969	−	0.609250i	0.897982	−	0.440033i	$-0.145033\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$		0			0
$130$	1.16029	−	2.54069i	0.101764	−	0.222833i
$131$	−2.85424	−	1.83431i	−0.249376	−	0.160264i	0.409981	−	0.912094i	$-0.365535\pi$
$131$	−2.85424	−	1.83431i	−0.249376	−	0.160264i	−0.659357	+	0.751830i	$0.729172\pi$
$132$		0			0
$133$	5.43923	+	6.27720i	0.471641	+	0.544302i
$134$	−2.83329	−	0.831930i	−0.244759	−	0.0718678i
$135$		0			0
$136$	1.06847	−	7.43136i	0.0916204	−	0.637234i
$137$	−9.21973			−0.787695			−0.393847	−	0.919176i	$-0.628856\pi$
$137$	−9.21973			−0.787695			−0.393847	+	0.919176i	$0.628856\pi$
$138$		0			0
$139$	−13.4691			−1.14244			−0.571218	−	0.820798i	$-0.693529\pi$
$139$	−13.4691			−1.14244			−0.571218	+	0.820798i	$0.693529\pi$
$140$	−0.642438	+	4.46825i	−0.0542959	+	0.377636i
$141$		0			0
$142$	−14.4598	−	4.24579i	−1.21344	−	0.356299i
$143$	4.17607	+	4.81944i	0.349220	+	0.403022i
$144$		0			0
$145$	−6.01203	−	3.86370i	−0.499272	−	0.320863i
$146$	−4.77297	+	10.4514i	−0.395014	+	0.864960i
$147$		0			0
$148$	6.50945	−	4.18337i	0.535074	−	0.343871i
$149$	−1.58769	−	11.0426i	−0.130068	−	0.904646i	−0.945461	−	0.325737i	$-0.894388\pi$
$149$	−1.58769	−	11.0426i	−0.130068	−	0.904646i	0.815392	−	0.578909i	$-0.196521\pi$
$150$		0			0
$151$	12.8717	−	8.27212i	1.04748	−	0.673176i	0.100656	−	0.994921i	$-0.467906\pi$
$151$	12.8717	−	8.27212i	1.04748	−	0.673176i	0.946826	+	0.321746i	$0.104270\pi$
$152$	2.93074	−	3.38226i	0.237714	−	0.274337i
$153$		0			0
$154$	−8.67044	−	5.57215i	−0.698684	−	0.449017i
$155$	4.84843	−	1.42363i	0.389436	−	0.114349i
$156$		0			0
$157$	−2.71881	−	0.798314i	−0.216984	−	0.0637124i	0.171434	−	0.985196i	$-0.445160\pi$
$157$	−2.71881	−	0.798314i	−0.216984	−	0.0637124i	−0.388418	+	0.921483i	$0.626978\pi$
$158$	4.37706	+	9.58442i	0.348220	+	0.762496i
$159$		0			0
$160$	2.43232			0.192292
$161$	−0.309572	+	8.89530i	−0.0243977	+	0.701048i
$162$		0			0
$163$	−3.55284	+	24.7105i	−0.278280	+	1.93548i	0.0687756	+	0.997632i	$0.478091\pi$
$163$	−3.55284	+	24.7105i	−0.278280	+	1.93548i	−0.347055	+	0.937845i	$0.612818\pi$
$164$	−0.285989	−	0.626228i	−0.0223320	−	0.0489002i
$165$		0			0
$166$	6.84228	+	7.89641i	0.531064	+	0.612880i
$167$	8.32792	−	2.44530i	0.644434	−	0.189223i	0.0568457	−	0.998383i	$-0.481896\pi$
$167$	8.32792	−	2.44530i	0.644434	−	0.189223i	0.587588	+	0.809160i	$0.300077\pi$
$168$		0			0
$169$	−4.85261	+	10.6257i	−0.373278	+	0.817364i
$170$	11.9586	−	13.8010i	0.917185	−	1.05849i
$171$		0			0
$172$	1.21913	+	8.47922i	0.0929577	+	0.646535i
$173$	2.19552	+	15.2702i	0.166922	+	1.16097i	0.885199	+	0.465212i	$0.154022\pi$
$173$	2.19552	+	15.2702i	0.166922	+	1.16097i	−0.718277	+	0.695757i	$0.755069\pi$
$174$		0			0
$175$	−1.11352	+	1.28507i	−0.0841739	+	0.0971419i
$176$	−2.30694	+	5.05150i	−0.173892	+	0.380771i
$177$		0			0
$178$	10.3393	−	3.03589i	0.774962	−	0.227549i
$179$	−3.96185	−	4.57222i	−0.296123	−	0.341744i	0.588118	−	0.808775i	$-0.299869\pi$
$179$	−3.96185	−	4.57222i	−0.296123	−	0.341744i	−0.884241	+	0.467031i	$0.845324\pi$
$180$		0			0
$181$	−2.60376	−	5.70144i	−0.193536	−	0.423784i	0.787841	−	0.615879i	$-0.211199\pi$
$181$	−2.60376	−	5.70144i	−0.193536	−	0.423784i	−0.981376	+	0.192095i	$0.938472\pi$
$182$	−0.303301	+	2.10951i	−0.0224822	+	0.156367i
$183$		0			0
$184$	4.76788	−	0.517000i	0.351493	−	0.0381138i
$185$	18.8208			1.38373
$186$		0			0
$187$	17.3200	+	37.9255i	1.26656	+	2.77339i
$188$	6.81232	+	2.00028i	0.496840	+	0.145885i
$189$		0			0
$190$	10.4446	−	3.06681i	0.757730	−	0.222490i
$191$	−16.2287	−	10.4295i	−1.17427	−	0.754655i	−0.199942	−	0.979808i	$-0.564076\pi$
$191$	−16.2287	−	10.4295i	−1.17427	−	0.754655i	−0.974323	+	0.225153i	$0.927712\pi$
$192$		0			0
$193$	16.9481	−	19.5591i	1.21995	−	1.40790i	0.334995	−	0.942220i	$-0.391265\pi$
$193$	16.9481	−	19.5591i	1.21995	−	1.40790i	0.884955	−	0.465677i	$-0.154189\pi$
$194$	−8.36414	+	5.37531i	−0.600510	+	0.385925i
$195$		0			0
$196$	0.506008	+	3.51936i	0.0361434	+	0.251383i
$197$	−15.4650	+	9.93876i	−1.10184	+	0.708107i	−0.959499	−	0.281711i	$-0.909098\pi$
$197$	−15.4650	+	9.93876i	−1.10184	+	0.708107i	−0.142337	+	0.989818i	$0.545462\pi$
$198$		0			0
$199$	3.59651	−	7.87525i	0.254949	−	0.558262i	−0.738271	−	0.674504i	$-0.764358\pi$
$199$	3.59651	−	7.87525i	0.254949	−	0.558262i	0.993221	+	0.116242i	$0.0370849\pi$
$200$	0.770753	+	0.495333i	0.0545004	+	0.0350253i
$201$		0			0
$202$	−3.21670	−	3.71227i	−0.226326	−	0.261195i
$203$	5.23208	+	1.53628i	0.367220	+	0.107826i
$204$		0			0
$205$	0.238308	−	1.65747i	0.0166441	−	0.115762i
$206$	−7.84290			−0.546441
$207$		0			0
$208$	1.14832			0.0796219
$209$	−3.53698	+	24.6003i	−0.244658	+	1.70164i
$210$		0			0
$211$	−13.3232	−	3.91206i	−0.917209	−	0.269317i	−0.211137	−	0.977457i	$-0.567717\pi$
$211$	−13.3232	−	3.91206i	−0.917209	−	0.269317i	−0.706073	+	0.708140i	$0.749535\pi$
$212$	3.52873	+	4.07237i	0.242354	+	0.279692i
$213$		0			0
$214$	7.82692	+	5.03006i	0.535037	+	0.343847i
$215$	−8.65571	+	18.9534i	−0.590315	+	1.29261i
$216$		0			0
$217$	−3.24358	+	2.08452i	−0.220189	+	0.141507i
$218$	−2.06193	−	14.3410i	−0.139652	−	0.971298i
$219$		0			0
$220$	−11.3633	+	7.30272i	−0.766110	+	0.492349i
$221$	5.64579	−	6.51558i	0.379777	−	0.438286i
$222$		0			0
$223$	3.18413	+	2.04631i	0.213225	+	0.137031i	0.642894	−	0.765955i	$-0.277733\pi$
$223$	3.18413	+	2.04631i	0.213225	+	0.137031i	−0.429669	+	0.902986i	$0.641370\pi$
$224$	−1.78074	+	0.522874i	−0.118981	+	0.0349360i
$225$		0			0
$226$	14.1088	+	4.14272i	0.938505	+	0.275570i
$227$	−4.08445	−	8.94371i	−0.271095	−	0.593615i	0.724299	−	0.689486i	$-0.242164\pi$
$227$	−4.08445	−	8.94371i	−0.271095	−	0.593615i	−0.995394	+	0.0958714i	$0.969436\pi$
$228$		0			0
$229$	−19.7726			−1.30661			−0.653307	−	0.757093i	$-0.726619\pi$
$229$	−19.7726			−1.30661			−0.653307	+	0.757093i	$0.726619\pi$
$230$	10.4359	+	5.21194i	0.688123	+	0.343665i
$231$		0			0
$232$	0.418141	−	2.90824i	0.0274523	−	0.190935i
$233$	6.94406	+	15.2054i	0.454921	+	0.996137i	0.988616	+	0.150460i	$0.0480756\pi$
$233$	6.94406	+	15.2054i	0.454921	+	0.996137i	−0.533695	+	0.845677i	$0.679197\pi$
$234$		0			0
$235$	11.3090	+	13.0513i	0.737717	+	0.851370i
$236$	−3.87102	+	1.13663i	−0.251982	+	0.0739886i
$237$		0			0
$238$	−5.78833	+	12.6747i	−0.375202	+	0.821577i
$239$	−5.60130	+	6.46424i	−0.362318	+	0.418137i	−0.907415	−	0.420236i	$-0.861947\pi$
$239$	−5.60130	+	6.46424i	−0.362318	+	0.418137i	0.545097	+	0.838373i	$0.316493\pi$
$240$		0			0
$241$	−3.00884	−	20.9269i	−0.193816	−	1.34802i	−0.821791	−	0.569789i	$-0.807025\pi$
$241$	−3.00884	−	20.9269i	−0.193816	−	1.34802i	0.627975	−	0.778234i	$-0.283884\pi$
$242$	−2.82347	−	19.6377i	−0.181500	−	1.26236i
$243$		0			0
$244$	0.248351	−	0.286612i	0.0158990	−	0.0183485i
$245$	−3.59262	+	7.86673i	−0.229524	+	0.502587i
$246$		0			0
$247$	4.93099	−	1.44787i	0.313751	−	0.0921258i
$248$	1.36046	+	1.57006i	0.0863896	+	0.0996989i
$249$		0			0
$250$	−4.12637	−	9.03549i	−0.260975	−	0.571455i
$251$	−1.65048	+	11.4793i	−0.104177	+	0.724569i	0.869050	+	0.494724i	$0.164731\pi$
$251$	−1.65048	+	11.4793i	−0.104177	+	0.724569i	−0.973227	+	0.229845i	$0.926178\pi$
$252$		0			0
$253$	−20.7222	+	16.7302i	−1.30280	+	1.05182i
$254$	6.93650			0.435235
$255$		0			0
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−8.10542	−	2.37997i	−0.505602	−	0.148458i	0.0189768	−	0.999820i	$-0.493959\pi$
$257$	−8.10542	−	2.37997i	−0.505602	−	0.148458i	−0.524579	+	0.851362i	$0.675777\pi$
$258$		0			0
$259$	−13.7790	+	4.04589i	−0.856188	+	0.251399i
$260$	2.34970	+	1.51006i	0.145722	+	0.0936499i
$261$		0			0
$262$	2.22184	−	2.56414i	0.137266	−	0.158413i
$263$	26.3237	−	16.9172i	1.62319	−	1.04316i	0.669307	−	0.742986i	$-0.266591\pi$
$263$	26.3237	−	16.9172i	1.62319	−	1.04316i	0.953884	−	0.300175i	$-0.0970452\pi$
$264$		0			0
$265$	1.86527	+	12.9732i	0.114582	+	0.796939i
$266$	−6.98739	+	4.49052i	−0.428424	+	0.275332i
$267$		0			0
$268$	1.22668	−	2.68606i	0.0749316	−	0.164077i
$269$	7.78907	+	5.00573i	0.474908	+	0.305205i	0.756111	−	0.654443i	$-0.227097\pi$
$269$	7.78907	+	5.00573i	0.474908	+	0.305205i	−0.281203	+	0.959648i	$0.590733\pi$
$270$		0			0
$271$	−10.7864	−	12.4482i	−0.655228	−	0.756173i	0.326762	−	0.945107i	$-0.394042\pi$
$271$	−10.7864	−	12.4482i	−0.655228	−	0.756173i	−0.981990	+	0.188933i	$0.939497\pi$
$272$	7.20366	+	2.11519i	0.436786	+	0.128252i
$273$		0			0
$274$	1.31210	−	9.12588i	0.0792671	−	0.551315i
$275$	−5.08795			−0.306815
$276$		0			0
$277$	29.2151			1.75537			0.877684	−	0.479240i	$-0.159088\pi$
$277$	29.2151			1.75537			0.877684	+	0.479240i	$0.159088\pi$
$278$	1.91686	−	13.3320i	0.114965	−	0.799602i
$279$		0			0
$280$	−4.33134	−	1.27180i	−0.258847	−	0.0760044i
$281$	7.87921	+	9.09310i	0.470034	+	0.542449i	0.940421	−	0.340012i	$-0.110431\pi$
$281$	7.87921	+	9.09310i	0.470034	+	0.542449i	−0.470387	+	0.882460i	$0.655886\pi$
$282$		0			0
$283$	−8.64671	−	5.55691i	−0.513994	−	0.330324i	0.257798	−	0.966199i	$-0.417003\pi$
$283$	−8.64671	−	5.55691i	−0.513994	−	0.330324i	−0.771792	+	0.635875i	$0.780639\pi$
$284$	6.26043	−	13.7084i	0.371488	−	0.813445i
$285$		0			0
$286$	−5.36470	+	3.44768i	−0.317221	+	0.203866i
$287$	0.181835	+	1.26469i	0.0107334	+	0.0746521i
$288$		0			0
$289$	33.1174	−	21.2833i	1.94808	−	1.25196i
$290$	4.67997	−	5.40098i	0.274817	−	0.317156i
$291$		0			0
$292$	−9.66571	−	6.21177i	−0.565643	−	0.363517i
$293$	−0.242114	+	0.0710912i	−0.0141445	+	0.00415319i	−0.288797	−	0.957390i	$-0.593255\pi$
$293$	−0.242114	+	0.0710912i	−0.0141445	+	0.00415319i	0.274653	+	0.961544i	$0.411437\pi$
$294$		0			0
$295$	−9.41558	−	2.76466i	−0.548196	−	0.160965i
$296$	3.21440	+	7.03855i	0.186833	+	0.409107i
$297$		0			0
$298$	11.1562			0.646259
$299$	4.92689	+	2.46061i	0.284929	+	0.142301i
$300$		0			0
$301$	2.26261	−	15.7368i	0.130414	−	0.907053i
$302$	6.35609	+	13.9179i	0.365752	+	0.800885i
$303$		0			0
$304$	2.93074	+	3.38226i	0.168090	+	0.193986i
$305$	0.885075	−	0.259881i	0.0506792	−	0.0148808i
$306$		0			0
$307$	−0.121406	+	0.265842i	−0.00692900	+	0.0151724i	−0.913065	−	0.407814i	$-0.866291\pi$
$307$	−0.121406	+	0.265842i	−0.00692900	+	0.0151724i	0.906136	+	0.422987i	$0.139018\pi$
$308$	6.74937	−	7.78919i	0.384581	−	0.443830i
$309$		0			0
$310$	0.719134	+	5.00169i	0.0408441	+	0.284077i
$311$	−1.28912	−	8.96601i	−0.0730991	−	0.508416i	−0.993171	−	0.116666i	$-0.962779\pi$
$311$	−1.28912	−	8.96601i	−0.0730991	−	0.508416i	0.920072	−	0.391749i	$-0.128130\pi$
$312$		0			0
$313$	−3.74536	+	4.32238i	−0.211700	+	0.244315i	−0.851662	−	0.524092i	$-0.824405\pi$
$313$	−3.74536	+	4.32238i	−0.211700	+	0.244315i	0.639961	+	0.768407i	$0.278950\pi$
$314$	1.17711	−	2.57752i	0.0664284	−	0.145458i
$315$		0			0
$316$	−10.1098	+	2.96850i	−0.568720	+	0.166991i
$317$	−11.9911	−	13.8385i	−0.673487	−	0.777245i	0.311431	−	0.950269i	$-0.399192\pi$
$317$	−11.9911	−	13.8385i	−0.673487	−	0.777245i	−0.984918	+	0.173024i	$0.944646\pi$
$318$		0			0
$319$	6.77813	+	14.8420i	0.379502	+	0.830994i
$320$	−0.346156	+	2.40757i	−0.0193507	+	0.134587i
$321$		0			0
$322$	−8.76071	−	1.57236i	−0.488215	−	0.0876239i
$323$	33.6000			1.86956
$324$		0			0
$325$	0.437053	+	0.957013i	0.0242434	+	0.0530855i
$326$	−23.9534	−	7.03335i	−1.32665	−	0.389541i
$327$		0			0
$328$	0.660554	−	0.193956i	0.0364730	−	0.0107094i
$329$	−11.0851	−	7.12396i	−0.611142	−	0.392757i
$330$		0			0
$331$	0.756224	−	0.872729i	0.0415658	−	0.0479695i	−0.734586	−	0.678516i	$-0.762624\pi$
$331$	0.756224	−	0.872729i	0.0415658	−	0.0479695i	0.776152	+	0.630546i	$0.217169\pi$
$332$	−8.78979	+	5.64886i	−0.482402	+	0.310021i
$333$		0			0
$334$	1.23522	+	8.59116i	0.0675883	+	0.470087i
$335$	6.04224	−	3.88311i	0.330123	−	0.212157i
$336$		0			0
$337$	−6.90165	+	15.1125i	−0.375957	+	0.823230i	0.623196	+	0.782066i	$0.285834\pi$
$337$	−6.90165	+	15.1125i	−0.375957	+	0.823230i	−0.999152	+	0.0411644i	$0.986893\pi$
$338$	−9.82698	−	6.31542i	−0.534517	−	0.343513i
$339$		0			0
$340$	11.9586	+	13.8010i	0.648548	+	0.748464i
$341$	−11.0697	−	3.25035i	−0.599456	−	0.176016i
$342$		0			0
$343$	2.78799	−	19.3909i	0.150537	−	1.04701i
$344$	−8.56642			−0.461870
$345$		0			0
$346$	−15.4272			−0.829371
$347$	−0.0186228	+	0.129524i	−0.000999725	+	0.00695324i	−0.990315	−	0.138837i	$-0.955663\pi$
$347$	−0.0186228	+	0.129524i	−0.000999725	+	0.00695324i	0.989315	+	0.145791i	$0.0465726\pi$
$348$		0			0
$349$	−17.9308	−	5.26496i	−0.959815	−	0.281827i	−0.235947	−	0.971766i	$-0.575819\pi$
$349$	−17.9308	−	5.26496i	−0.959815	−	0.281827i	−0.723868	+	0.689939i	$0.757637\pi$
$350$	−1.11352	−	1.28507i	−0.0595200	−	0.0686897i
$351$		0			0
$352$	−4.67177	−	3.00236i	−0.249006	−	0.160027i
$353$	13.6597	−	29.9105i	0.727031	−	1.59198i	−0.0767505	−	0.997050i	$-0.524454\pi$
$353$	13.6597	−	29.9105i	0.727031	−	1.59198i	0.803781	−	0.594925i	$-0.202818\pi$
$354$		0			0
$355$	30.8368	−	19.8176i	1.63665	−	1.05181i
$356$	1.53355	+	10.6661i	0.0812781	+	0.565302i
$357$		0			0
$358$	5.08951	−	3.27083i	0.268989	−	0.172869i
$359$	4.29811	−	4.96028i	0.226845	−	0.261793i	−0.630905	−	0.775860i	$-0.717316\pi$
$359$	4.29811	−	4.96028i	0.226845	−	0.261793i	0.857750	+	0.514067i	$0.171862\pi$
$360$		0			0
$361$	0.865557	+	0.556260i	0.0455556	+	0.0292768i
$362$	6.01396	−	1.76586i	0.316087	−	0.0928114i
$363$		0			0
$364$	−2.04487	−	0.600428i	−0.107180	−	0.0314710i
$365$	−11.6094	−	25.4211i	−0.607664	−	1.33060i
$366$		0			0
$367$	−15.7482			−0.822052			−0.411026	−	0.911624i	$-0.634829\pi$
$367$	−15.7482			−0.822052			−0.411026	+	0.911624i	$0.634829\pi$
$368$	−0.166803	+	4.79293i	−0.00869518	+	0.249849i
$369$		0			0
$370$	−2.67848	+	18.6293i	−0.139248	+	0.968489i
$371$	−4.15443	−	9.09694i	−0.215687	−	0.472289i
$372$		0			0
$373$	−10.5690	−	12.1973i	−0.547243	−	0.631552i	0.412996	−	0.910733i	$-0.364482\pi$
$373$	−10.5690	−	12.1973i	−0.547243	−	0.631552i	−0.960238	+	0.279181i	$0.909937\pi$
$374$	−40.0044	+	11.7463i	−2.06858	+	0.607389i
$375$		0			0
$376$	−2.94941	+	6.45831i	−0.152104	+	0.333062i
$377$	2.20946	−	2.54985i	0.113793	−	0.131324i
$378$		0			0
$379$	−3.02940	−	21.0699i	−0.155610	−	1.08229i	−0.906605	−	0.421981i	$-0.861335\pi$
$379$	−3.02940	−	21.0699i	−0.155610	−	1.08229i	0.750995	−	0.660308i	$-0.229574\pi$
$380$	1.54917	+	10.7747i	0.0794709	+	0.552732i
$381$		0			0
$382$	12.6330	−	14.5792i	0.646359	−	0.745938i
$383$	−11.1739	+	24.4675i	−0.570961	+	1.25023i	0.375323	+	0.926894i	$0.377532\pi$
$383$	−11.1739	+	24.4675i	−0.570961	+	1.25023i	−0.946284	+	0.323336i	$0.895196\pi$
$384$		0			0
$385$	24.0534	−	7.06273i	1.22588	−	0.359950i
$386$	16.9481	+	19.5591i	0.862635	+	0.995534i
$387$		0			0
$388$	−4.13025	−	9.04399i	−0.209682	−	0.459139i
$389$	4.15477	−	28.8971i	0.210655	−	1.46514i	−0.560321	−	0.828275i	$-0.689322\pi$
$389$	4.15477	−	28.8971i	0.210655	−	1.46514i	0.770977	−	0.636864i	$-0.219769\pi$
$390$		0			0
$391$	26.3750	+	24.5111i	1.33384	+	1.23958i
$392$	−3.55555			−0.179583
$393$		0			0
$394$	−7.63669	−	16.7220i	−0.384731	−	0.842444i
$395$	−24.5903	−	7.22035i	−1.23727	−	0.363295i
$396$		0			0
$397$	2.07632	−	0.609661i	0.104207	−	0.0305980i	−0.229213	−	0.973376i	$-0.573615\pi$
$397$	2.07632	−	0.609661i	0.104207	−	0.0305980i	0.333421	+	0.942778i	$0.391797\pi$
$398$	7.28325	+	4.68066i	0.365076	+	0.234620i
$399$		0			0
$400$	−0.599980	+	0.692414i	−0.0299990	+	0.0346207i
$401$	5.73614	−	3.68639i	0.286449	−	0.184090i	−0.389523	−	0.921017i	$-0.627360\pi$
$401$	5.73614	−	3.68639i	0.286449	−	0.184090i	0.675972	+	0.736927i	$0.263724\pi$
$402$		0			0
$403$	0.339510	+	2.36134i	0.0169122	+	0.117627i
$404$	4.13227	−	2.65565i	0.205588	−	0.132123i
$405$		0			0
$406$	−2.26524	+	4.96019i	−0.112422	+	0.246170i
$407$	−36.1492	−	23.2317i	−1.79185	−	1.15155i
$408$		0			0
$409$	8.43702	+	9.73684i	0.417184	+	0.481456i	0.924977	−	0.380023i	$-0.124084\pi$
$409$	8.43702	+	9.73684i	0.417184	+	0.481456i	−0.507793	+	0.861479i	$0.669539\pi$
$410$	1.60668	+	0.471764i	0.0793483	+	0.0232988i
$411$		0			0
$412$	1.11616	−	7.76307i	0.0549893	−	0.382459i
$413$	7.48762			0.368441
$414$		0			0
$415$	−25.4140			−1.24752
$416$	−0.163423	+	1.13663i	−0.00801249	+	0.0557281i
$417$		0			0
$418$	−23.8465	−	7.00196i	−1.16637	−	0.342477i
$419$	4.88423	+	5.63670i	0.238610	+	0.275371i	0.862407	−	0.506216i	$-0.168956\pi$
$419$	4.88423	+	5.63670i	0.238610	+	0.275371i	−0.623797	+	0.781587i	$0.714411\pi$
$420$		0			0
$421$	0.720254	+	0.462879i	0.0351030	+	0.0225594i	0.558075	−	0.829791i	$-0.311540\pi$
$421$	0.720254	+	0.462879i	0.0351030	+	0.0225594i	−0.522972	+	0.852350i	$0.675177\pi$
$422$	5.76833	−	12.6309i	0.280798	−	0.614862i
$423$		0			0
$424$	−4.53311	+	2.91326i	−0.220147	+	0.141480i
$425$	0.978926	+	6.80858i	0.0474849	+	0.330264i
$426$		0			0
$427$	−0.592111	+	0.380527i	−0.0286543	+	0.0184150i
$428$	−6.09274	+	7.03140i	−0.294504	+	0.339876i
$429$		0			0
$430$	−17.5286	−	11.2650i	−0.845304	−	0.543244i
$431$	−25.9406	+	7.61686i	−1.24952	+	0.366891i	−0.838583	−	0.544774i	$-0.816615\pi$
$431$	−25.9406	+	7.61686i	−1.24952	+	0.366891i	−0.410934	+	0.911665i	$0.634797\pi$
$432$		0			0
$433$	20.9024	+	6.13751i	1.00451	+	0.294950i	0.742304	−	0.670063i	$-0.233733\pi$
$433$	20.9024	+	6.13751i	1.00451	+	0.294950i	0.262203	+	0.965013i	$0.415551\pi$
$434$	−1.60170	−	3.50723i	−0.0768839	−	0.168352i
$435$		0			0
$436$	14.4885			0.693874
$437$	5.32693	+	20.7915i	0.254822	+	0.994594i
$438$		0			0
$439$	−2.15413	+	14.9823i	−0.102811	+	0.715067i	0.871588	+	0.490240i	$0.163091\pi$
$439$	−2.15413	+	14.9823i	−0.102811	+	0.715067i	−0.974399	+	0.224827i	$0.927818\pi$
$440$	−5.61123	−	12.2869i	−0.267505	−	0.585754i
$441$		0			0
$442$	5.64579	+	6.51558i	0.268543	+	0.309915i
$443$	−14.6455	+	4.30031i	−0.695829	+	0.204314i	−0.610474	−	0.792037i	$-0.709021\pi$
$443$	−14.6455	+	4.30031i	−0.695829	+	0.204314i	−0.0853558	+	0.996351i	$0.527203\pi$
$444$		0			0
$445$	−10.8881	+	23.8416i	−0.516145	+	1.13020i
$446$	−2.47863	+	2.86050i	−0.117367	+	0.135448i
$447$		0			0
$448$	−0.264125	−	1.83703i	−0.0124787	−	0.0867916i
$449$	4.03517	+	28.0652i	0.190432	+	1.32448i	0.830868	+	0.556470i	$0.187844\pi$
$449$	4.03517	+	28.0652i	0.190432	+	1.32448i	−0.640436	+	0.768011i	$0.721247\pi$
$450$		0			0
$451$	−2.50363	+	2.88934i	−0.117891	+	0.136054i
$452$	−6.10845	+	13.3756i	−0.287317	+	0.629137i
$453$		0			0
$454$	9.43395	−	2.77006i	0.442757	−	0.130005i
$455$	−3.39464	−	3.91763i	−0.159143	−	0.183661i
$456$		0			0
$457$	−8.21817	−	17.9953i	−0.384430	−	0.841784i	−0.998615	−	0.0526214i	$-0.983242\pi$
$457$	−8.21817	−	17.9953i	−0.384430	−	0.841784i	0.614185	−	0.789162i	$-0.289485\pi$
$458$	2.81394	−	19.5714i	0.131487	−	0.914511i
$459$		0			0
$460$	−6.64408	+	9.58795i	−0.309782	+	0.447040i
$461$	−10.9505			−0.510014			−0.255007	−	0.966939i	$-0.582078\pi$
$461$	−10.9505			−0.510014			−0.255007	+	0.966939i	$0.582078\pi$
$462$		0			0
$463$	−3.99367	−	8.74491i	−0.185601	−	0.406410i	0.793844	−	0.608122i	$-0.208077\pi$
$463$	−3.99367	−	8.74491i	−0.185601	−	0.406410i	−0.979445	+	0.201712i	$0.935350\pi$
$464$	2.81913	+	0.827771i	0.130875	+	0.0384283i
$465$		0			0
$466$	−16.0388	+	4.70943i	−0.742985	+	0.218160i
$467$	13.3427	+	8.57486i	0.617428	+	0.396797i	0.811636	−	0.584163i	$-0.198577\pi$
$467$	13.3427	+	8.57486i	0.617428	+	0.396797i	−0.194208	+	0.980960i	$0.562214\pi$
$468$		0			0
$469$	−3.58888	+	4.14179i	−0.165719	+	0.191250i
$470$	−14.5279	+	9.33648i	−0.670120	+	0.430660i
$471$		0			0
$472$	−0.574161	−	3.99338i	−0.0264279	−	0.183810i
$473$	40.0203	−	25.7195i	1.84014	−	1.18258i
$474$		0			0
$475$	−1.70333	+	3.72977i	−0.0781541	+	0.171134i
$476$	−11.7219	−	7.53321i	−0.537272	−	0.345284i
$477$		0			0
$478$	−5.60130	−	6.46424i	−0.256197	−	0.295667i
$479$	27.1063	+	7.95912i	1.23852	+	0.363662i	0.834458	−	0.551071i	$-0.185781\pi$
$479$	27.1063	+	7.95912i	1.23852	+	0.363662i	0.404059	+	0.914733i	$0.367599\pi$
$480$		0			0
$481$	−1.26454	+	8.79505i	−0.0576579	+	0.401020i
$482$	21.1421			0.962998
$483$		0			0
$484$	19.8396			0.901800
$485$	3.44164	−	23.9372i	0.156277	−	1.08693i
$486$		0			0
$487$	1.94021	+	0.569697i	0.0879192	+	0.0258154i	0.325396	−	0.945578i	$-0.394502\pi$
$487$	1.94021	+	0.569697i	0.0879192	+	0.0258154i	−0.237477	+	0.971393i	$0.576320\pi$
$488$	0.248351	+	0.286612i	0.0112423	+	0.0129743i
$489$		0			0
$490$	−7.27538	−	4.67560i	−0.328668	−	0.211222i
$491$	−7.65343	+	16.7587i	−0.345394	+	0.756308i	0.654606	+	0.755971i	$0.272835\pi$
$491$	−7.65343	+	16.7587i	−0.345394	+	0.756308i	−1.00000		0.000337539i	$0.999893\pi$
$492$		0			0
$493$	18.5572	−	11.9260i	0.835772	−	0.537118i
$494$	0.731379	+	5.08685i	0.0329063	+	0.228868i
$495$		0			0
$496$	−1.74769	+	1.12317i	−0.0784738	+	0.0504320i
$497$	−18.3160	+	21.1378i	−0.821584	+	0.948159i
$498$		0			0
$499$	−10.6246	−	6.82800i	−0.475621	−	0.305663i	0.280779	−	0.959772i	$-0.409407\pi$
$499$	−10.6246	−	6.82800i	−0.475621	−	0.305663i	−0.756400	+	0.654109i	$0.773044\pi$
$500$	9.53077	−	2.79849i	0.426229	−	0.125152i
$501$		0			0
$502$	−11.1276	−	3.26736i	−0.496649	−	0.145829i
$503$	0.161210	+	0.353000i	0.00718798	+	0.0157395i	0.913192	−	0.407530i	$-0.133610\pi$
$503$	0.161210	+	0.353000i	0.00718798	+	0.0157395i	−0.906004	+	0.423269i	$0.860882\pi$
$504$		0			0
$505$	11.9477			0.531664
$506$	−13.6109	−	22.8923i	−0.605076	−	1.01769i
$507$		0			0
$508$	−0.987167	+	6.86590i	−0.0437985	+	0.304625i
$509$	−13.9512	−	30.5489i	−0.618376	−	1.35405i	−0.916695	−	0.399588i	$-0.869153\pi$
$509$	−13.9512	−	30.5489i	−0.618376	−	1.35405i	0.298319	−	0.954466i	$-0.403574\pi$
$510$		0			0
$511$	13.9642	+	16.1155i	0.617739	+	0.712909i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$		0			0
$514$	3.50926	−	7.68422i	0.154787	−	0.338936i
$515$	12.4924	−	14.4170i	0.550482	−	0.635290i
$516$		0			0
$517$	−5.61123	−	39.0269i	−0.246782	−	1.71640i
$518$	−2.04375	−	14.2146i	−0.0897971	−	0.624553i
$519$		0			0
$520$	−1.82909	+	2.11088i	−0.0802108	+	0.0925681i
$521$	−0.362903	+	0.794646i	−0.0158991	+	0.0348141i	−0.917415	−	0.397932i	$-0.869728\pi$
$521$	−0.362903	+	0.794646i	−0.0158991	+	0.0348141i	0.901516	+	0.432746i	$0.142455\pi$
$522$		0			0
$523$	19.4906	−	5.72296i	0.852265	−	0.250248i	0.173710	−	0.984797i	$-0.444425\pi$
$523$	19.4906	−	5.72296i	0.852265	−	0.250248i	0.678555	+	0.734549i	$0.262606\pi$
$524$	2.22184	+	2.56414i	0.0970615	+	0.112015i
$525$		0			0
$526$	12.9988	+	28.4634i	0.566774	+	1.24106i
$527$	−2.21973	+	15.4386i	−0.0966929	+	0.672514i
$528$		0			0
$529$	−10.9859	+	20.2067i	−0.477647	+	0.878552i
$530$	−13.1066			−0.569316
$531$		0			0
$532$	−3.45041	−	7.55534i	−0.149594	−	0.327565i
$533$	0.758529	+	0.222724i	0.0328556	+	0.00964726i
$534$		0			0
$535$	−21.7134	+	6.37562i	−0.938750	+	0.275642i
$536$	2.48414	+	1.59646i	0.107299	+	0.0689567i
$537$		0			0
$538$	−6.06328	+	6.99740i	−0.261407	+	0.301679i
$539$	16.6107	−	10.6751i	0.715475	−	0.459808i
$540$		0			0
$541$	0.948836	+	6.59930i	0.0407936	+	0.283726i	0.999999	+	0.00101737i	$0.000323839\pi$
$541$	0.948836	+	6.59930i	0.0407936	+	0.283726i	−0.959206	+	0.282709i	$0.908767\pi$
$542$	13.8565	−	8.90506i	0.595189	−	0.382505i
$543$		0			0
$544$	−3.11884	+	6.82931i	−0.133719	+	0.292804i
$545$	29.6464	+	19.0526i	1.26991	+	0.816123i
$546$		0			0
$547$	8.89250	+	10.2625i	0.380216	+	0.438793i	0.913311	−	0.407263i	$-0.133517\pi$
$547$	8.89250	+	10.2625i	0.380216	+	0.438793i	−0.533095	+	0.846055i	$0.678971\pi$
$548$	8.84626	+	2.59750i	0.377894	+	0.110960i
$549$		0			0
$550$	0.724090	−	5.03616i	0.0308753	−	0.214743i
$551$	13.1493			0.560178
$552$		0			0
$553$	19.5551			0.831567
$554$	−4.15775	+	28.9178i	−0.176646	+	1.22860i
$555$		0			0
$556$	12.9235	+	3.79469i	0.548080	+	0.160931i
$557$	10.5821	+	12.2124i	0.448377	+	0.517454i	0.934271	−	0.356563i	$-0.116052\pi$
$557$	10.5821	+	12.2124i	0.448377	+	0.517454i	−0.485895	+	0.874017i	$0.661506\pi$
$558$		0			0
$559$	−8.27542	−	5.31829i	−0.350013	−	0.224940i
$560$	1.87527	−	4.10626i	0.0792445	−	0.173521i
$561$		0			0
$562$	−10.1219	+	6.50493i	−0.426965	+	0.274394i
$563$	−0.467924	−	3.25448i	−0.0197206	−	0.137160i	0.977582	−	0.210553i	$-0.0675264\pi$
$563$	−0.467924	−	3.25448i	−0.0197206	−	0.137160i	−0.997303	+	0.0733928i	$0.976617\pi$
$564$		0			0
$565$	−30.0883	+	19.3366i	−1.26582	+	0.813495i
$566$	6.73090	−	7.76787i	0.282921	−	0.326508i
$567$		0			0
$568$	12.6779	+	8.14762i	0.531954	+	0.341866i
$569$	−25.1220	+	7.37647i	−1.05317	+	0.309238i	−0.762096	−	0.647464i	$-0.775830\pi$
$569$	−25.1220	+	7.37647i	−1.05317	+	0.309238i	−0.291071	+	0.956701i	$0.594012\pi$
$570$		0			0
$571$	−12.5762	−	3.69271i	−0.526299	−	0.154535i	0.00778034	−	0.999970i	$-0.497523\pi$
$571$	−12.5762	−	3.69271i	−0.526299	−	0.154535i	−0.534079	+	0.845434i	$0.679342\pi$
$572$	−2.64911	−	5.80075i	−0.110765	−	0.242542i
$573$		0			0
$574$	−1.27769			−0.0533298
$575$	−4.05792	+	1.68518i	−0.169227	+	0.0702769i
$576$		0			0
$577$	−5.40643	+	37.6025i	−0.225073	+	1.56541i	0.493365	+	0.869823i	$0.335767\pi$
$577$	−5.40643	+	37.6025i	−0.225073	+	1.56541i	−0.718437	+	0.695592i	$0.755142\pi$
$578$	16.3535	+	35.8092i	0.680217	+	1.48947i
$579$		0			0
$580$	4.67997	+	5.40098i	0.194325	+	0.224263i
$581$	18.6060	−	5.46322i	0.771907	−	0.226652i
$582$		0			0
$583$	12.4310	−	27.2201i	0.514840	−	1.12734i
$584$	7.52412	−	8.68330i	0.311350	−	0.359317i
$585$		0			0
$586$	−0.0359111	−	0.249767i	−0.00148347	−	0.0103178i
$587$	3.73817	+	25.9995i	0.154291	+	1.07312i	0.908922	+	0.416966i	$0.136907\pi$
$587$	3.73817	+	25.9995i	0.154291	+	1.07312i	−0.754631	+	0.656149i	$0.772184\pi$
$588$		0			0
$589$	−6.08858	+	7.02659i	−0.250875	+	0.289526i
$590$	4.07650	−	8.92629i	0.167827	−	0.367489i
$591$		0			0
$592$	−7.42436	+	2.17999i	−0.305140	+	0.0895970i
$593$	−1.09857	−	1.26782i	−0.0451130	−	0.0520632i	0.732745	−	0.680504i	$-0.238239\pi$
$593$	−1.09857	−	1.26782i	−0.0451130	−	0.0520632i	−0.777858	+	0.628441i	$0.783694\pi$
$594$		0			0
$595$	−14.0791	−	30.8289i	−0.577186	−	1.26386i
$596$	−1.58769	+	11.0426i	−0.0650342	+	0.452323i
$597$		0			0
$598$	−3.13673	+	4.52656i	−0.128271	+	0.185105i
$599$	−10.8835			−0.444689			−0.222344	−	0.974968i	$-0.571371\pi$
$599$	−10.8835			−0.444689			−0.222344	+	0.974968i	$0.571371\pi$
$600$		0			0
$601$	−11.4599	−	25.0936i	−0.467458	−	1.02359i	−0.985724	−	0.168370i	$-0.946150\pi$
$601$	−11.4599	−	25.0936i	−0.467458	−	1.02359i	0.518266	−	0.855220i	$-0.326578\pi$
$602$	15.2546	+	4.47915i	0.621731	+	0.182557i
$603$		0			0
$604$	−14.6808	+	4.31067i	−0.597353	+	0.175399i
$605$	40.5958	+	26.0893i	1.65045	+	1.06068i
$606$		0			0
$607$	24.2330	−	27.9663i	0.983586	−	1.13512i	−0.00723963	−	0.999974i	$-0.502304\pi$
$607$	24.2330	−	27.9663i	0.983586	−	1.13512i	0.990826	−	0.135145i	$-0.0431501\pi$
$608$	−3.76492	+	2.41956i	−0.152688	+	0.0981263i
$609$		0			0
$610$	0.131277	+	0.913051i	0.00531525	+	0.0369683i
$611$	−6.85874	+	4.40784i	−0.277475	+	0.178322i
$612$		0			0
$613$	4.26350	−	9.33575i	0.172201	−	0.377068i	−0.803779	−	0.594928i	$-0.797181\pi$
$613$	4.26350	−	9.33575i	0.172201	−	0.377068i	0.975980	+	0.217861i	$0.0699078\pi$
$614$	−0.245858	−	0.158003i	−0.00992203	−	0.00637650i
$615$		0			0
$616$	6.74937	+	7.78919i	0.271940	+	0.313835i
$617$	−6.74760	−	1.98128i	−0.271648	−	0.0797631i	0.143071	−	0.989712i	$-0.454302\pi$
$617$	−6.74760	−	1.98128i	−0.271648	−	0.0797631i	−0.414720	+	0.909949i	$0.636120\pi$
$618$		0			0
$619$	5.21995	−	36.3055i	0.209808	−	1.45924i	−0.563975	−	0.825792i	$-0.690729\pi$
$619$	5.21995	−	36.3055i	0.209808	−	1.45924i	0.773782	−	0.633451i	$-0.218362\pi$
$620$	−5.05312			−0.202938
$621$		0			0
$622$	9.05821			0.363201
$623$	2.84615	−	19.7954i	0.114029	−	0.793087i
$624$		0			0
$625$	27.5773	+	8.09743i	1.10309	+	0.323897i
$626$	−3.74536	−	4.32238i	−0.149695	−	0.172757i
$627$		0			0
$628$	2.38377	+	1.53195i	0.0951226	+	0.0611316i
$629$	−24.1330	+	52.8439i	−0.962245	+	2.10702i
$630$		0			0
$631$	−15.3141	+	9.84180i	−0.609646	+	0.391796i	−0.808724	−	0.588188i	$-0.799842\pi$
$631$	−15.3141	+	9.84180i	−0.609646	+	0.391796i	0.199078	+	0.979984i	$0.436205\pi$
$632$	−1.49951	−	10.4293i	−0.0596474	−	0.414857i
$633$		0			0
$634$	15.4041	−	9.89962i	0.611775	−	0.393164i
$635$	−11.0487	+	12.7509i	−0.438454	+	0.506003i
$636$		0			0
$637$	−3.43477	−	2.20740i	−0.136091	−	0.0874602i
$638$	−15.6556	+	4.59689i	−0.619811	+	0.181993i
$639$		0			0
$640$	−2.33380	−	0.685265i	−0.0922514	−	0.0270875i
$641$	−2.11700	−	4.63559i	−0.0836166	−	0.183095i	0.863205	−	0.504853i	$-0.168453\pi$
$641$	−2.11700	−	4.63559i	−0.0836166	−	0.183095i	−0.946822	+	0.321758i	$0.895726\pi$
$642$		0			0
$643$	−5.24644			−0.206899			−0.103450	−	0.994635i	$-0.532988\pi$
$643$	−5.24644			−0.206899			−0.103450	+	0.994635i	$0.532988\pi$
$644$	2.80313	−	8.44776i	0.110459	−	0.332889i
$645$		0			0
$646$	−4.78178	+	33.2580i	−0.188137	+	1.30852i
$647$	16.7895	+	36.7638i	0.660062	+	1.44533i	0.882465	+	0.470379i	$0.155883\pi$
$647$	16.7895	+	36.7638i	0.660062	+	1.44533i	−0.222403	+	0.974955i	$0.571390\pi$
$648$		0			0
$649$	14.6719	+	16.9323i	0.575924	+	0.664651i
$650$	−1.00947	+	0.296407i	−0.0395947	+	0.0116261i
$651$		0			0
$652$	10.3707	−	22.7086i	0.406147	−	0.889338i
$653$	9.73558	−	11.2355i	0.380982	−	0.439677i	−0.532577	−	0.846381i	$-0.678777\pi$
$653$	9.73558	−	11.2355i	0.380982	−	0.439677i	0.913560	+	0.406704i	$0.133322\pi$
$654$		0			0
$655$	1.17445	+	8.16849i	0.0458896	+	0.319169i
$656$	0.0979753	+	0.681433i	0.00382529	+	0.0266055i
$657$		0			0
$658$	8.62903	−	9.95843i	0.336395	−	0.388220i
$659$	10.7801	−	23.6051i	0.419932	−	0.919523i	−0.574922	−	0.818208i	$-0.694968\pi$
$659$	10.7801	−	23.6051i	0.419932	−	0.919523i	0.994854	−	0.101315i	$-0.0323050\pi$
$660$		0			0
$661$	46.2443	−	13.5786i	1.79870	−	0.528145i	0.801169	−	0.598438i	$-0.204212\pi$
$661$	46.2443	−	13.5786i	1.79870	−	0.528145i	0.997526	+	0.0702937i	$0.0223936\pi$
$662$	0.756224	+	0.872729i	0.0293915	+	0.0339196i
$663$		0			0
$664$	−4.34044	−	9.50424i	−0.168442	−	0.368836i
$665$	2.87514	−	19.9971i	0.111493	−	0.775453i
$666$		0			0
$667$	10.3218	+	9.59234i	0.399660	+	0.371417i
$668$	−8.67950			−0.335820
$669$		0			0
$670$	2.98369	+	6.53337i	0.115270	+	0.252406i
$671$	−2.02075	−	0.593346i	−0.0780103	−	0.0229059i
$672$		0			0
$673$	14.9182	−	4.38039i	0.575056	−	0.168852i	0.0187425	−	0.999824i	$-0.494034\pi$
$673$	14.9182	−	4.38039i	0.575056	−	0.168852i	0.556313	+	0.830973i	$0.312216\pi$
$674$	−13.9765	−	8.98213i	−0.538354	−	0.345979i
$675$		0			0
$676$	7.64966	−	8.82818i	0.294218	−	0.339545i
$677$	1.76046	−	1.13138i	0.0676601	−	0.0434825i	−0.506373	−	0.862314i	$-0.669014\pi$
$677$	1.76046	−	1.13138i	0.0676601	−	0.0434825i	0.574034	+	0.818832i	$0.305378\pi$
$678$		0			0
$679$	2.62606	+	18.2646i	0.100779	+	0.700932i
$680$	−15.3624	+	9.87283i	−0.589122	+	0.378606i
$681$		0			0
$682$	4.79264	−	10.4944i	0.183520	−	0.401852i
$683$	11.4861	+	7.38168i	0.439504	+	0.282452i	0.741622	−	0.670818i	$-0.234057\pi$
$683$	11.4861	+	7.38168i	0.439504	+	0.282452i	−0.302117	+	0.953271i	$0.597693\pi$
$684$		0			0
$685$	14.6855	+	16.9480i	0.561104	+	0.647548i
$686$	18.7967	+	5.51922i	0.717663	+	0.210725i
$687$		0			0
$688$	1.21913	−	8.47922i	0.0464788	−	0.323267i
$689$	−6.18777			−0.235735
$690$		0			0
$691$	−19.2615			−0.732744			−0.366372	−	0.930469i	$-0.619400\pi$
$691$	−19.2615			−0.732744			−0.366372	+	0.930469i	$0.619400\pi$
$692$	2.19552	−	15.2702i	0.0834611	−	0.580485i
$693$		0			0
$694$	−0.125556	−	0.0368665i	−0.00476603	−	0.00139943i
$695$	21.4541	+	24.7593i	0.813799	+	0.939174i
$696$		0			0
$697$	4.34815	+	2.79439i	0.164698	+	0.105845i
$698$	7.76320	−	16.9990i	0.293841	−	0.643423i
$699$		0			0
$700$	1.43046	−	0.919299i	0.0540662	−	0.0347462i
$701$	−0.843289	−	5.86520i	−0.0318506	−	0.221526i	0.967679	−	0.252184i	$-0.0811488\pi$
$701$	−0.843289	−	5.86520i	−0.0318506	−	0.221526i	−0.999530	+	0.0306582i	$0.990240\pi$
$702$		0			0
$703$	−29.1322	+	18.7221i	−1.09874	+	0.706118i
$704$	3.63667	−	4.19694i	0.137062	−	0.158178i
$705$		0			0
$706$	27.6621	+	17.7773i	1.04108	+	0.669059i
$707$	−8.74708	+	2.56838i	−0.328968	+	0.0965937i
$708$		0			0
$709$	6.20193	+	1.82105i	0.232918	+	0.0683910i	0.396109	−	0.918204i	$-0.370360\pi$
$709$	6.20193	+	1.82105i	0.232918	+	0.0683910i	−0.163190	+	0.986595i	$0.552179\pi$
$710$	15.2274	+	33.3433i	0.571473	+	1.25135i
$711$		0			0
$712$	−10.7758			−0.403839
$713$	−9.90522	+	1.07406i	−0.370953	+	0.0402239i
$714$		0			0
$715$	2.20745	−	15.3531i	0.0825538	−	0.574174i
$716$	2.51322	+	5.50319i	0.0939236	+	0.205664i
$717$		0			0
$718$	4.29811	+	4.96028i	0.160404	+	0.185116i
$719$	−47.9418	+	14.0770i	−1.78793	+	0.524983i	−0.996294	−	0.0860135i	$-0.972587\pi$
$719$	−47.9418	+	14.0770i	−1.78793	+	0.524983i	−0.791633	+	0.610996i	$0.790769\pi$
$720$		0			0
$721$	−6.04670	+	13.2404i	−0.225191	+	0.493099i
$722$	−0.673779	+	0.777583i	−0.0250755	+	0.0289386i
$723$		0			0
$724$	0.892008	+	6.20405i	0.0331512	+	0.230572i
$725$	0.383099	+	2.66451i	0.0142280	+	0.0989576i
$726$		0			0
$727$	−14.5447	+	16.7855i	−0.539434	+	0.622540i	−0.958388	−	0.285467i	$-0.907851\pi$
$727$	−14.5447	+	16.7855i	−0.539434	+	0.622540i	0.418955	+	0.908007i	$0.362397\pi$
$728$	0.885331	−	1.93861i	0.0328126	−	0.0718495i
$729$		0			0
$730$	26.8145	−	7.87345i	0.992449	−	0.291409i
$731$	−42.1172	−	48.6059i	−1.55776	−	1.79775i
$732$		0			0
$733$	16.0918	+	35.2361i	0.594364	+	1.30148i	0.932769	+	0.360475i	$0.117385\pi$
$733$	16.0918	+	35.2361i	0.594364	+	1.30148i	−0.338405	+	0.941001i	$0.609887\pi$
$734$	2.24121	−	15.5880i	0.0827245	−	0.575362i
$735$		0			0
$736$	−4.72041	−	0.847210i	−0.173996	−	0.0312286i
$737$	−16.3985			−0.604047
$738$		0			0
$739$	−3.39732	−	7.43909i	−0.124972	−	0.273651i	0.836796	−	0.547514i	$-0.184426\pi$
$739$	−3.39732	−	7.43909i	−0.124972	−	0.273651i	−0.961769	+	0.273863i	$0.911699\pi$
$740$	−18.0585	−	5.30244i	−0.663842	−	0.194922i
$741$		0			0
$742$	9.59558	−	2.81752i	0.352265	−	0.103434i
$743$	−5.79535	−	3.72445i	−0.212611	−	0.136637i	0.430001	−	0.902828i	$-0.358513\pi$
$743$	−5.79535	−	3.72445i	−0.212611	−	0.136637i	−0.642612	+	0.766191i	$0.722149\pi$
$744$		0			0
$745$	−17.7699	+	20.5076i	−0.651039	+	0.751339i
$746$	13.5773	−	8.72558i	0.497099	−	0.319466i
$747$		0			0
$748$	−5.93357	−	41.2689i	−0.216953	−	1.50894i
$749$	14.5261	−	9.33539i	0.530774	−	0.341108i
$750$		0			0
$751$	−6.35324	+	13.9117i	−0.231833	+	0.507643i	−0.989418	−	0.145093i	$-0.953652\pi$
$751$	−6.35324	+	13.9117i	−0.231833	+	0.507643i	0.757585	+	0.652736i	$0.226379\pi$
$752$	−5.97283	−	3.83850i	−0.217807	−	0.139976i
$753$		0			0
$754$	2.20946	+	2.54985i	0.0804638	+	0.0928601i
$755$	−35.7085	−	10.4849i	−1.29956	−	0.381586i
$756$		0			0
$757$	1.52276	−	10.5910i	0.0553456	−	0.384937i	−0.943256	−	0.332067i	$-0.892254\pi$
$757$	1.52276	−	10.5910i	0.0553456	−	0.384937i	0.998601	−	0.0528700i	$-0.0168369\pi$
$758$	21.2866			0.773163
$759$		0			0
$760$	−10.8855			−0.394860
$761$	0.756832	−	5.26388i	0.0274351	−	0.190816i	−0.971495	−	0.237060i	$-0.923816\pi$
$761$	0.756832	−	5.26388i	0.0274351	−	0.190816i	0.998930	+	0.0462444i	$0.0147253\pi$
$762$		0			0
$763$	−25.8003	−	7.57566i	−0.934035	−	0.274257i
$764$	12.6330	+	14.5792i	0.457045	+	0.527457i
$765$		0			0
$766$	−22.6282	−	14.5423i	−0.817591	−	0.525434i
$767$	1.92455	−	4.21419i	0.0694916	−	0.152165i
$768$		0			0
$769$	17.4129	−	11.1906i	0.627924	−	0.403542i	−0.187616	−	0.982242i	$-0.560076\pi$
$769$	17.4129	−	11.1906i	0.627924	−	0.403542i	0.815540	+	0.578700i	$0.196440\pi$
$770$	3.56768	+	24.8137i	0.128570	+	0.894225i
$771$		0			0
$772$	−21.7720	+	13.9920i	−0.783592	+	0.503584i
$773$	−17.5087	+	20.2061i	−0.629743	+	0.726762i	−0.977526	−	0.210813i	$-0.932389\pi$
$773$	−17.5087	+	20.2061i	−0.629743	+	0.726762i	0.347784	+	0.937575i	$0.386934\pi$
$774$		0			0
$775$	−1.60123	−	1.02905i	−0.0575178	−	0.0369645i
$776$	9.53973	−	2.80112i	0.342457	−	0.100554i
$777$		0			0
$778$	28.0116	+	8.22496i	1.00427	+	0.294879i
$779$	1.27990	+	2.80260i	0.0458573	+	0.100413i
$780$		0			0
$781$	−83.6905			−2.99468
$782$	−28.0152	+	22.6182i	−1.00182	+	0.808826i
$783$		0			0
$784$	0.506008	−	3.51936i	0.0180717	−	0.125692i
$785$	2.86312	+	6.26937i	0.102189	+	0.223763i
$786$		0			0
$787$	28.3878	+	32.7612i	1.01191	+	1.16781i	0.985761	+	0.168154i	$0.0537806\pi$
$787$	28.3878	+	32.7612i	1.01191	+	1.16781i	0.0261540	+	0.999658i	$0.491674\pi$
$788$	17.6386	−	5.17917i	0.628350	−	0.184500i
$789$		0			0
$790$	10.6464	−	23.3124i	0.378783	−	0.829418i
$791$	17.8714	−	20.6246i	0.635432	−	0.733328i
$792$		0			0
$793$	0.0619771	+	0.431060i	0.00220087	+	0.0153074i
$794$	0.307965	+	2.14195i	0.0109293	+	0.0760148i
$795$		0			0
$796$	−5.66954	+	6.54299i	−0.200951	+	0.231910i
$797$	15.9326	−	34.8875i	0.564361	−	1.23578i	−0.385385	−	0.922756i	$-0.625931\pi$
$797$	15.9326	−	34.8875i	0.564361	−	1.23578i	0.949746	−	0.313022i	$-0.101341\pi$
$798$		0			0
$799$	−51.1454	+	15.0176i	−1.80939	+	0.531286i
$800$	−0.599980	−	0.692414i	−0.0212125	−	0.0244805i
$801$		0			0
$802$	2.83253	+	6.20238i	0.100020	+	0.219014i
$803$	−9.08053	+	63.1565i	−0.320445	+	2.22874i
$804$		0			0
$805$	16.8447	−	13.5997i	0.593697	−	0.479325i
$806$	−2.38563			−0.0840301
$807$		0			0
$808$	2.04053	+	4.46815i	0.0717858	+	0.157189i
$809$	6.58065	+	1.93225i	0.231363	+	0.0679344i	0.395359	−	0.918527i	$-0.370620\pi$
$809$	6.58065	+	1.93225i	0.231363	+	0.0679344i	−0.163996	+	0.986461i	$0.552438\pi$
$810$		0			0
$811$	2.26053	−	0.663751i	0.0793779	−	0.0233075i	−0.241802	−	0.970325i	$-0.577739\pi$
$811$	2.26053	−	0.663751i	0.0793779	−	0.0233075i	0.321180	+	0.947018i	$0.395920\pi$
$812$	−4.58733	−	2.94810i	−0.160984	−	0.103458i
$813$		0			0
$814$	28.1398	−	32.4751i	0.986299	−	1.13825i
$815$	51.0826	−	32.8288i	1.78935	−	1.14994i
$816$		0			0
$817$	−5.45604	−	37.9476i	−0.190883	−	1.32762i
$818$	−10.8384	+	6.96545i	−0.378957	+	0.243541i
$819$		0			0
$820$	−0.695617	+	1.52319i	−0.0242920	+	0.0531920i
$821$	−13.3148	−	8.55691i	−0.464690	−	0.298638i	0.287267	−	0.957851i	$-0.407253\pi$
$821$	−13.3148	−	8.55691i	−0.464690	−	0.298638i	−0.751957	+	0.659212i	$0.770890\pi$
$822$		0			0
$823$	−2.96189	−	3.41821i	−0.103245	−	0.119151i	0.701775	−	0.712398i	$-0.252391\pi$
$823$	−2.96189	−	3.41821i	−0.103245	−	0.119151i	−0.805020	+	0.593247i	$0.797846\pi$
$824$	7.52521	+	2.20960i	0.262153	+	0.0769751i
$825$		0			0
$826$	−1.06560	+	7.41140i	−0.0370769	+	0.257876i
$827$	6.29678			0.218961			0.109480	−	0.993989i	$-0.465081\pi$
$827$	6.29678			0.218961			0.109480	+	0.993989i	$0.465081\pi$
$828$		0			0
$829$	6.30959			0.219141			0.109570	−	0.993979i	$-0.465052\pi$
$829$	6.30959			0.219141			0.109570	+	0.993979i	$0.465052\pi$
$830$	3.61679	−	25.1553i	0.125541	−	0.873154i
$831$		0			0
$832$	−1.10181	−	0.323520i	−0.0381983	−	0.0112160i
$833$	−17.4811	−	20.1742i	−0.605683	−	0.698995i
$834$		0			0
$835$	−17.7600	−	11.4137i	−0.614610	−	0.394986i
$836$	10.3244	−	22.6073i	0.357077	−	0.781890i
$837$		0			0
$838$	−6.27442	+	4.03233i	−0.216746	+	0.139294i
$839$	−0.626028	−	4.35412i	−0.0216129	−	0.150321i	0.976157	−	0.217064i	$-0.0696482\pi$
$839$	−0.626028	−	4.35412i	−0.0216129	−	0.150321i	−0.997770	+	0.0667435i	$0.978739\pi$
$840$		0			0
$841$	−17.1341	+	11.0114i	−0.590830	+	0.379703i
$842$	−0.560671	+	0.647048i	−0.0193220	+	0.0222988i
$843$		0			0
$844$	11.6814	+	7.50718i	0.402090	+	0.258408i
$845$	27.2619	−	8.00482i	0.937838	−	0.275374i
$846$		0			0
$847$	−35.3293	−	10.3736i	−1.21393	−	0.356441i
$848$	−2.23847	−	4.90157i	−0.0768695	−	0.168321i
$849$		0			0
$850$	−6.87859			−0.235934
$851$	−36.5256	−	6.55554i	−1.25208	−	0.224721i
$852$		0			0
$853$	−0.505055	+	3.51274i	−0.0172928	+	0.120274i	−0.996639	−	0.0819151i	$-0.973896\pi$
$853$	−0.505055	+	3.51274i	−0.0172928	+	0.120274i	0.979347	+	0.202189i	$0.0648055\pi$
$854$	−0.292387	−	0.640239i	−0.0100053	−	0.0219085i
$855$		0			0
$856$	−6.09274	−	7.03140i	−0.208246	−	0.240328i
$857$	45.7825	−	13.4430i	1.56390	−	0.459203i	0.618683	−	0.785641i	$-0.287666\pi$
$857$	45.7825	−	13.4430i	1.56390	−	0.459203i	0.945219	+	0.326437i	$0.105848\pi$
$858$		0			0
$859$	−14.0609	+	30.7891i	−0.479752	+	1.05051i	0.502779	+	0.864415i	$0.332311\pi$
$859$	−14.0609	+	30.7891i	−0.479752	+	1.05051i	−0.982532	+	0.186096i	$0.940416\pi$
$860$	13.6449	−	15.7470i	0.465286	−	0.536969i
$861$		0			0
$862$	−3.84759	−	26.7606i	−0.131049	−	0.911469i
$863$	−1.82291	−	12.6786i	−0.0620525	−	0.431585i	−0.997039	−	0.0769006i	$-0.975498\pi$
$863$	−1.82291	−	12.6786i	−0.0620525	−	0.431585i	0.934986	−	0.354684i	$-0.115412\pi$
$864$		0			0
$865$	24.5729	−	28.3587i	0.835505	−	0.964224i
$866$	−9.04977	+	19.8162i	−0.307524	+	0.673383i
$867$		0			0
$868$	3.69947	−	1.08626i	0.125568	−	0.0368702i
$869$	38.3181	+	44.2214i	1.29985	+	1.50011i
$870$		0			0
$871$	1.40863	+	3.08446i	0.0477295	+	0.104513i
$872$	−2.06193	+	14.3410i	−0.0698258	+	0.485649i
$873$		0			0
$874$	−21.3380	+	2.31376i	−0.721769	+	0.0782643i
$875$	−18.4351			−0.623221
$876$		0			0
$877$	−17.5440	−	38.4159i	−0.592417	−	1.29721i	−0.933970	−	0.357350i	$-0.883680\pi$
$877$	−17.5440	−	38.4159i	−0.592417	−	1.29721i	0.341553	−	0.939862i	$-0.389047\pi$
$878$	−14.5232	−	4.26441i	−0.490136	−	0.143917i
$879$		0			0
$880$	12.9604	−	3.80551i	0.436894	−	0.128284i
$881$	−34.4876	−	22.1638i	−1.16192	−	0.746718i	−0.189939	−	0.981796i	$-0.560829\pi$
$881$	−34.4876	−	22.1638i	−1.16192	−	0.746718i	−0.971976	+	0.235078i	$0.924465\pi$
$882$		0			0
$883$	−36.2725	+	41.8607i	−1.22067	+	1.40873i	−0.336418	+	0.941713i	$0.609215\pi$
$883$	−36.2725	+	41.8607i	−1.22067	+	1.40873i	−0.884250	+	0.467013i	$0.845330\pi$
$884$	−7.25274	+	4.66106i	−0.243936	+	0.156768i
$885$		0			0
$886$	−2.17227	−	15.1084i	−0.0729787	−	0.507578i
$887$	−24.3710	+	15.6623i	−0.818299	+	0.525889i	−0.881540	−	0.472109i	$-0.843493\pi$
$887$	−24.3710	+	15.6623i	−0.818299	+	0.525889i	0.0632409	+	0.997998i	$0.479856\pi$
$888$		0			0
$889$	5.34789	−	11.7102i	0.179362	−	0.392749i
$890$	−22.0494	−	14.1703i	−0.739097	−	0.474989i
$891$		0			0
$892$	−2.47863	−	2.86050i	−0.0829908	−	0.0957765i
$893$	−30.4876	−	8.95197i	−1.02023	−	0.299566i
$894$		0			0
$895$	−2.09421	+	14.5656i	−0.0700018	+	0.486873i
$896$	1.85592			0.0620020
$897$		0			0
$898$	−28.3538			−0.946180
$899$	−0.868684	+	6.04183i	−0.0289722	+	0.201506i
$900$		0			0
$901$	−38.8171	−	11.3977i	−1.29318	−	0.379713i
$902$	−2.50363	−	2.88934i	−0.0833617	−	0.0962046i
$903$		0			0
$904$	−12.3702	−	7.94983i	−0.411426	−	0.264407i
$905$	−6.33318	+	13.8677i	−0.210522	+	0.460979i
$906$		0			0
$907$	−18.8032	+	12.0841i	−0.624348	+	0.401244i	−0.814213	−	0.580566i	$-0.802831\pi$
$907$	−18.8032	+	12.0841i	−0.624348	+	0.401244i	0.189865	+	0.981810i	$0.439195\pi$
$908$	1.39927	+	9.73215i	0.0464365	+	0.322973i
$909$		0			0
$910$	4.36086	−	2.80255i	0.144561	−	0.0929037i
$911$	−22.0772	+	25.4785i	−0.731451	+	0.844139i	−0.992634	−	0.121150i	$-0.961342\pi$
$911$	−22.0772	+	25.4785i	−0.731451	+	0.844139i	0.261184	+	0.965289i	$0.415887\pi$
$912$		0			0
$913$	48.8127	+	31.3700i	1.61547	+	1.03820i
$914$	18.9817	−	5.57352i	0.627858	−	0.184356i
$915$		0			0
$916$	18.9717	+	5.57060i	0.626843	+	0.184058i
$917$	−2.61581	−	5.72781i	−0.0863815	−	0.189149i
$918$		0			0
$919$	41.0403			1.35380			0.676898	−	0.736077i	$-0.263324\pi$
$919$	41.0403			1.35380			0.676898	+	0.736077i	$0.263324\pi$
$920$	−8.54481	−	7.94096i	−0.281714	−	0.261806i
$921$		0			0
$922$	1.55841	−	10.8390i	0.0513237	−	0.356964i
$923$	7.18899	+	15.7417i	0.236629	+	0.518144i
$924$		0			0
$925$	−4.64253	−	5.35776i	−0.152645	−	0.176162i
$926$	9.22426	−	2.70849i	0.303128	−	0.0890064i
$927$		0			0
$928$	−1.22055	+	2.67263i	−0.0400665	+	0.0877334i
$929$	−22.4388	+	25.8958i	−0.736194	+	0.849613i	−0.993154	−	0.116809i	$-0.962734\pi$
$929$	−22.4388	+	25.8958i	−0.736194	+	0.849613i	0.256960	+	0.966422i	$0.417279\pi$
$930$		0			0
$931$	−2.26457	−	15.7504i	−0.0742183	−	0.516200i
$932$	−2.37893	−	16.5458i	−0.0779244	−	0.541976i
$933$		0			0
$934$	−10.3864	+	11.9866i	−0.339855	+	0.392213i
$935$	42.1278	−	92.2471i	1.37773	−	3.01680i
$936$		0			0
$937$	−9.52597	+	2.79708i	−0.311200	+	0.0913766i	−0.433603	−	0.901104i	$-0.642758\pi$
$937$	−9.52597	+	2.79708i	−0.311200	+	0.0913766i	0.122403	+	0.992480i	$0.460940\pi$
$938$	−3.58888	−	4.14179i	−0.117181	−	0.135234i
$939$		0			0
$940$	−7.17392	−	15.7087i	−0.233988	−	0.512361i
$941$	2.54908	−	17.7293i	0.0830977	−	0.577957i	−0.905150	−	0.425093i	$-0.860241\pi$
$941$	2.54908	−	17.7293i	0.0830977	−	0.577957i	0.988247	−	0.152864i	$-0.0488496\pi$
$942$		0			0
$943$	−1.03980	+	3.13364i	−0.0338606	+	0.102045i
$944$	4.03445			0.131310
$945$		0			0
$946$	19.7622	+	43.2732i	0.642525	+	1.40693i
$947$	34.9446	+	10.2607i	1.13555	+	0.333427i	0.794886	−	0.606759i	$-0.207531\pi$
$947$	34.9446	+	10.2607i	1.13555	+	0.333427i	0.340662	+	0.940186i	$0.389349\pi$
$948$		0			0
$949$	12.6594	−	3.71713i	0.410941	−	0.120663i
$950$	−3.44940	−	2.21679i	−0.111913	−	0.0719223i
$951$		0			0
$952$	9.12473	−	10.5305i	0.295734	−	0.341295i
$953$	37.7109	−	24.2353i	1.22157	−	0.785058i	0.239016	−	0.971016i	$-0.423175\pi$
$953$	37.7109	−	24.2353i	1.22157	−	0.785058i	0.982558	+	0.185957i	$0.0595386\pi$
$954$		0			0
$955$	6.67771	+	46.4445i	0.216086	+	1.50291i
$956$	7.19559	−	4.62433i	0.232722	−	0.149561i
$957$		0			0
$958$	−11.7357	+	25.6977i	−0.379164	+	0.830254i
$959$	−14.3948	−	9.25096i	−0.464831	−	0.298729i
$960$		0			0
$961$	17.4743	+	20.1665i	0.563688	+	0.650531i
$962$	−8.52557	−	2.50333i	−0.274875	−	0.0807107i
$963$		0			0
$964$	−3.00884	+	20.9269i	−0.0969082	+	0.674011i
$965$	−62.9496			−2.02642
$966$		0			0
$967$	−15.8234			−0.508846			−0.254423	−	0.967093i	$-0.581885\pi$
$967$	−15.8234			−0.508846			−0.254423	+	0.967093i	$0.581885\pi$
$968$	−2.82347	+	19.6377i	−0.0907498	+	0.631179i
$969$		0			0
$970$	23.2037	+	6.81323i	0.745026	+	0.218759i
$971$	−15.9576	−	18.4161i	−0.512105	−	0.591001i	0.439531	−	0.898227i	$-0.355144\pi$
$971$	−15.9576	−	18.4161i	−0.512105	−	0.591001i	−0.951636	+	0.307227i	$0.900599\pi$
$972$		0			0
$973$	−21.0293	−	13.5147i	−0.674170	−	0.433263i
$974$	−0.840018	+	1.83938i	−0.0269159	+	0.0589377i
$975$		0			0
$976$	−0.319039	+	0.205034i	−0.0102122	+	0.00656298i
$977$	−0.300639	−	2.09099i	−0.00961831	−	0.0668968i	0.984447	−	0.175682i	$-0.0562130\pi$
$977$	−0.300639	−	2.09099i	−0.00961831	−	0.0668968i	−0.994065	+	0.108785i	$0.965304\pi$
$978$		0			0
$979$	50.3419	−	32.3528i	1.60893	−	1.03400i
$980$	5.66340	−	6.53592i	0.180911	−	0.208782i
$981$		0			0
$982$	−15.4989	−	9.96053i	−0.494590	−	0.317853i
$983$	−5.63251	+	1.65385i	−0.179649	+	0.0527497i	−0.370320	−	0.928904i	$-0.620752\pi$
$983$	−5.63251	+	1.65385i	−0.179649	+	0.0527497i	0.190671	+	0.981654i	$0.438934\pi$
$984$		0			0
$985$	42.9029	+	12.5974i	1.36700	+	0.401387i
$986$	9.16361	+	20.0655i	0.291829	+	0.639016i
$987$		0			0
$988$	−5.13916			−0.163499
$989$	23.3998	−	33.7679i	0.744071	−	1.07376i
$990$		0			0
$991$	7.05110	−	49.0415i	0.223985	−	1.55785i	−0.498761	−	0.866740i	$-0.666211\pi$
$991$	7.05110	−	49.0415i	0.223985	−	1.55785i	0.722746	−	0.691114i	$-0.242880\pi$
$992$	−0.863019	−	1.88975i	−0.0274009	−	0.0599996i
$993$		0			0
$994$	−18.3160	−	21.1378i	−0.580948	−	0.670450i
$995$	−20.2051	+	5.93276i	−0.640546	+	0.188081i
$996$		0			0
$997$	−0.732045	+	1.60296i	−0.0231841	+	0.0507661i	−0.920870	−	0.389870i	$-0.872520\pi$
$997$	−0.732045	+	1.60296i	−0.0231841	+	0.0507661i	0.897686	+	0.440636i	$0.145247\pi$
$998$	8.27053	−	9.54470i	0.261799	−	0.302132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.b.307.1		10
3.2	odd	2		138.2.e.c.31.1	✓	10
23.3	even	11	inner	414.2.i.b.325.1		10
23.7	odd	22		9522.2.a.ca.1.1		5
23.16	even	11		9522.2.a.bv.1.5		5
69.26	odd	22		138.2.e.c.49.1	yes	10
69.53	even	22		3174.2.a.y.1.5		5
69.62	odd	22		3174.2.a.z.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.c.31.1	✓	10	3.2	odd	2
138.2.e.c.49.1	yes	10	69.26	odd	22
414.2.i.b.307.1		10	1.1	even	1	trivial
414.2.i.b.325.1		10	23.3	even	11	inner
3174.2.a.y.1.5		5	69.53	even	22
3174.2.a.z.1.1		5	69.62	odd	22
9522.2.a.bv.1.5		5	23.16	even	11
9522.2.a.ca.1.1		5	23.7	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-1.59283 - 1.83823i) q^{5} +(1.56130 + 1.00339i) q^{7} +(0.415415 - 0.909632i) q^{8} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-1.59283 - 1.83823i) q^{5} +(1.56130 + 1.00339i) q^{7} +(0.415415 - 0.909632i) q^{8} +(2.04620 - 1.31501i) q^{10} +(0.790323 + 5.49682i) q^{11} +(0.966031 - 0.620830i) q^{13} +(-1.21537 + 1.40261i) q^{14} +(0.841254 + 0.540641i) q^{16} +(7.20366 - 2.11519i) q^{17} +(4.29408 + 1.26086i) q^{19} +(1.01042 + 2.21252i) q^{20} -5.55334 q^{22} +(2.45093 + 4.12225i) q^{23} +(-0.130388 + 0.906870i) q^{25} +(0.477031 + 1.04455i) q^{26} +(-1.21537 - 1.40261i) q^{28} +(2.81913 - 0.827771i) q^{29} +(-0.863019 + 1.88975i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.06847 + 7.43136i) q^{34} +(-0.642438 - 4.46825i) q^{35} +(-5.06718 + 5.84784i) q^{37} +(-1.85913 + 4.07093i) q^{38} +(-2.33380 + 0.685265i) q^{40} +(0.450833 + 0.520289i) q^{41} +(-3.55862 - 7.79229i) q^{43} +(0.790323 - 5.49682i) q^{44} +(-4.42909 + 1.83933i) q^{46} -7.09992 q^{47} +(-1.47703 - 3.23425i) q^{49} +(-0.879083 - 0.258122i) q^{50} +(-1.10181 + 0.323520i) q^{52} +(-4.53311 - 2.91326i) q^{53} +(8.84555 - 10.2083i) q^{55} +(1.56130 - 1.00339i) q^{56} +(0.418141 + 2.90824i) q^{58} +(3.39399 - 2.18119i) q^{59} +(-0.157543 + 0.344971i) q^{61} +(-1.74769 - 1.12317i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(-2.67995 - 0.786905i) q^{65} +(-0.420243 + 2.92285i) q^{67} -7.50778 q^{68} +4.51420 q^{70} +(-2.14473 + 14.9169i) q^{71} +(11.0242 + 3.23701i) q^{73} +(-5.06718 - 5.84784i) q^{74} +(-3.76492 - 2.41956i) q^{76} +(-4.28150 + 9.37518i) q^{77} +(8.86394 - 5.69651i) q^{79} +(-0.346156 - 2.40757i) q^{80} +(-0.579153 + 0.372199i) q^{82} +(6.84228 - 7.89641i) q^{83} +(-15.3624 - 9.87283i) q^{85} +(8.21942 - 2.41344i) q^{86} +(5.32839 + 1.56456i) q^{88} +(-4.47642 - 9.80199i) q^{89} +2.13120 q^{91} +(-1.19028 - 4.64578i) q^{92} +(1.01042 - 7.02765i) q^{94} +(-4.52201 - 9.90183i) q^{95} +(6.51094 + 7.51402i) q^{97} +(3.41153 - 1.00172i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{7} - q^{8} + 11 q^{10} - 11 q^{11} - 13 q^{13} - 13 q^{14} - q^{16} - 2 q^{19} + 11 q^{20} - 22 q^{22} + 10 q^{23} + 5 q^{25} + 9 q^{26} - 13 q^{28} + 27 q^{29} - 18 q^{31} - q^{32} + 33 q^{34} - 44 q^{35} - q^{37} - 13 q^{38} - 11 q^{40} + 16 q^{41} + 20 q^{43} - 11 q^{44} - q^{46} - 19 q^{49} + 27 q^{50} - 2 q^{52} + q^{53} + 33 q^{55} - 2 q^{56} - 17 q^{58} + q^{59} - 34 q^{61} + 4 q^{62} - q^{64} - 11 q^{65} + 8 q^{67} - 22 q^{68} + 22 q^{70} + 22 q^{71} + 31 q^{73} - q^{74} - 2 q^{76} - 22 q^{77} + 32 q^{79} - 28 q^{82} - 33 q^{83} - 11 q^{85} + 20 q^{86} + 22 q^{88} + 23 q^{89} + 18 q^{91} - 23 q^{92} + 11 q^{94} + 22 q^{95} - q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^7 - q^8 + 11 * q^10 - 11 * q^11 - 13 * q^13 - 13 * q^14 - q^16 - 2 * q^19 + 11 * q^20 - 22 * q^22 + 10 * q^23 + 5 * q^25 + 9 * q^26 - 13 * q^28 + 27 * q^29 - 18 * q^31 - q^32 + 33 * q^34 - 44 * q^35 - q^37 - 13 * q^38 - 11 * q^40 + 16 * q^41 + 20 * q^43 - 11 * q^44 - q^46 - 19 * q^49 + 27 * q^50 - 2 * q^52 + q^53 + 33 * q^55 - 2 * q^56 - 17 * q^58 + q^59 - 34 * q^61 + 4 * q^62 - q^64 - 11 * q^65 + 8 * q^67 - 22 * q^68 + 22 * q^70 + 22 * q^71 + 31 * q^73 - q^74 - 2 * q^76 - 22 * q^77 + 32 * q^79 - 28 * q^82 - 33 * q^83 - 11 * q^85 + 20 * q^86 + 22 * q^88 + 23 * q^89 + 18 * q^91 - 23 * q^92 + 11 * q^94 + 22 * q^95 - q^97 + 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more