LMFDB - Embedded newform 276.2.i.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.1
Root			$-1.54238 + 1.78001i$ of defining polynomial
Character	$\chi$	$=$	276.25
Dual form			276.2.i.a.265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{3} +(-2.38954 - 0.701632i) q^{5} +(2.64891 - 3.05701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{3} +(-2.38954 - 0.701632i) q^{5} +(2.64891 - 3.05701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-4.05943 + 2.60884i) q^{11} +(-2.81278 - 3.24612i) q^{13} +(-0.354423 + 2.46507i) q^{15} +(1.87409 - 4.10368i) q^{17} +(-1.84032 - 4.02974i) q^{19} +(-3.40287 - 2.18689i) q^{21} +(4.75085 - 0.655317i) q^{23} +(1.01134 + 0.649950i) q^{25} +(0.415415 + 0.909632i) q^{27} +(-0.207351 + 0.454036i) q^{29} +(-0.727870 + 5.06245i) q^{31} +(3.16000 + 3.64683i) q^{33} +(-8.47457 + 5.44627i) q^{35} +(10.2392 - 3.00650i) q^{37} +(-2.81278 + 3.24612i) q^{39} +(7.29593 + 2.14228i) q^{41} +(1.07935 + 7.50707i) q^{43} +2.49042 q^{45} -7.67725 q^{47} +(-1.33235 - 9.26672i) q^{49} +(-4.32862 - 1.27100i) q^{51} +(5.00164 - 5.77220i) q^{53} +(11.5306 - 3.38569i) q^{55} +(-3.72681 + 2.39508i) q^{57} +(-1.85219 - 2.13754i) q^{59} +(-0.225996 + 1.57184i) q^{61} +(-1.68035 + 3.67946i) q^{63} +(4.44366 + 9.73025i) q^{65} +(10.1121 + 6.49867i) q^{67} +(-1.32476 - 4.60923i) q^{69} +(3.18977 + 2.04994i) q^{71} +(-3.09627 - 6.77988i) q^{73} +(0.499405 - 1.09354i) q^{75} +(-2.77784 + 19.3203i) q^{77} +(7.62471 + 8.79938i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-5.09163 + 1.49504i) q^{83} +(-7.35747 + 8.49098i) q^{85} +(0.478924 + 0.140625i) q^{87} +(-1.58627 - 11.0327i) q^{89} -17.3742 q^{91} +5.11451 q^{93} +(1.57012 + 10.9204i) q^{95} +(-6.84457 - 2.00975i) q^{97} +(3.16000 - 3.64683i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$	$1$

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
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$3$	−0.142315	−	0.989821i	−0.0821655	−	0.571474i
$4$		0			0
$5$	−2.38954	−	0.701632i	−1.06863	−	0.313779i	−0.300311	−	0.953841i	$-0.597090\pi$
$5$	−2.38954	−	0.701632i	−1.06863	−	0.313779i	−0.768323	+	0.640062i	$0.778909\pi$
$6$		0			0
$7$	2.64891	−	3.05701i	1.00119	−	1.15544i	0.0133629	−	0.999911i	$-0.495746\pi$
$7$	2.64891	−	3.05701i	1.00119	−	1.15544i	0.987831	−	0.155529i	$-0.0497082\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	−4.05943	+	2.60884i	−1.22396	+	0.786594i	−0.982940	−	0.183925i	$-0.941120\pi$
$11$	−4.05943	+	2.60884i	−1.22396	+	0.786594i	−0.241024	+	0.970519i	$0.577483\pi$
$12$		0			0
$13$	−2.81278	−	3.24612i	−0.780123	−	0.900310i	0.216995	−	0.976173i	$-0.430375\pi$
$13$	−2.81278	−	3.24612i	−0.780123	−	0.900310i	−0.997118	+	0.0758623i	$0.975829\pi$
$14$		0			0
$15$	−0.354423	+	2.46507i	−0.0915118	+	0.636478i
$16$		0			0
$17$	1.87409	−	4.10368i	0.454533	−	0.995288i	−0.534167	−	0.845379i	$-0.679375\pi$
$17$	1.87409	−	4.10368i	0.454533	−	0.995288i	0.988700	−	0.149909i	$-0.0478981\pi$
$18$		0			0
$19$	−1.84032	−	4.02974i	−0.422198	−	0.924485i	−0.994529	−	0.104462i	$-0.966688\pi$
$19$	−1.84032	−	4.02974i	−0.422198	−	0.924485i	0.572331	−	0.820023i	$-0.306039\pi$
$20$		0			0
$21$	−3.40287	−	2.18689i	−0.742567	−	0.477219i
$22$		0			0
$23$	4.75085	−	0.655317i	0.990620	−	0.136643i
$23$	4.75085	−	0.655317i	0.990620	−	0.136643i
$24$		0			0
$25$	1.01134	+	0.649950i	0.202268	+	0.129990i
$26$		0			0
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$		0			0
$29$	−0.207351	+	0.454036i	−0.0385042	+	0.0843124i	−0.927907	−	0.372812i	$-0.878393\pi$
$29$	−0.207351	+	0.454036i	−0.0385042	+	0.0843124i	0.889403	+	0.457125i	$0.151121\pi$
$30$		0			0
$31$	−0.727870	+	5.06245i	−0.130729	+	0.909243i	0.813877	+	0.581037i	$0.197353\pi$
$31$	−0.727870	+	5.06245i	−0.130729	+	0.909243i	−0.944606	+	0.328206i	$0.893556\pi$
$32$		0			0
$33$	3.16000	+	3.64683i	0.550085	+	0.634832i
$34$		0			0
$35$	−8.47457	+	5.44627i	−1.43246	+	0.920588i
$36$		0			0
$37$	10.2392	−	3.00650i	1.68331	−	0.494265i	0.706384	−	0.707829i	$-0.250325\pi$
$37$	10.2392	−	3.00650i	1.68331	−	0.494265i	0.976929	+	0.213564i	$0.0685071\pi$
$38$		0			0
$39$	−2.81278	+	3.24612i	−0.450404	+	0.519794i
$40$		0			0
$41$	7.29593	+	2.14228i	1.13943	+	0.334568i	0.796409	−	0.604759i	$-0.206731\pi$
$41$	7.29593	+	2.14228i	1.13943	+	0.334568i	0.343024	+	0.939327i	$0.388549\pi$
$42$		0			0
$43$	1.07935	+	7.50707i	0.164600	+	1.14482i	0.889824	+	0.456305i	$0.150827\pi$
$43$	1.07935	+	7.50707i	0.164600	+	1.14482i	−0.725224	+	0.688513i	$0.758264\pi$
$44$		0			0
$45$	2.49042			0.371250
$46$		0			0
$47$	−7.67725			−1.11984			−0.559921	−	0.828546i	$-0.689169\pi$
$47$	−7.67725			−1.11984			−0.559921	+	0.828546i	$0.689169\pi$
$48$		0			0
$49$	−1.33235	−	9.26672i	−0.190336	−	1.32382i
$50$		0			0
$51$	−4.32862	−	1.27100i	−0.606128	−	0.177975i
$52$		0			0
$53$	5.00164	−	5.77220i	0.687028	−	0.792873i	−0.299911	−	0.953967i	$-0.596957\pi$
$53$	5.00164	−	5.77220i	0.687028	−	0.792873i	0.986939	+	0.161095i	$0.0515024\pi$
$54$		0			0
$55$	11.5306	−	3.38569i	1.55479	−	0.456527i
$56$		0			0
$57$	−3.72681	+	2.39508i	−0.493629	+	0.317236i
$58$		0			0
$59$	−1.85219	−	2.13754i	−0.241134	−	0.278284i	0.622263	−	0.782808i	$-0.286213\pi$
$59$	−1.85219	−	2.13754i	−0.241134	−	0.278284i	−0.863397	+	0.504524i	$0.831668\pi$
$60$		0			0
$61$	−0.225996	+	1.57184i	−0.0289358	+	0.201253i	−0.999161	−	0.0409511i	$-0.986961\pi$
$61$	−0.225996	+	1.57184i	−0.0289358	+	0.201253i	0.970225	+	0.242204i	$0.0778703\pi$
$62$		0			0
$63$	−1.68035	+	3.67946i	−0.211705	+	0.463568i
$64$		0			0
$65$	4.44366	+	9.73025i	0.551168	+	1.20689i
$66$		0			0
$67$	10.1121	+	6.49867i	1.23539	+	0.793939i	0.984722	−	0.174134i	$-0.0557124\pi$
$67$	10.1121	+	6.49867i	1.23539	+	0.793939i	0.250671	+	0.968072i	$0.419349\pi$
$68$		0			0
$69$	−1.32476	−	4.60923i	−0.159483	−	0.554886i
$70$		0			0
$71$	3.18977	+	2.04994i	0.378556	+	0.243283i	0.716057	−	0.698042i	$-0.245945\pi$
$71$	3.18977	+	2.04994i	0.378556	+	0.243283i	−0.337501	+	0.941325i	$0.609582\pi$
$72$		0			0
$73$	−3.09627	−	6.77988i	−0.362391	−	0.793525i	−0.999737	−	0.0229473i	$-0.992695\pi$
$73$	−3.09627	−	6.77988i	−0.362391	−	0.793525i	0.637346	−	0.770578i	$-0.280032\pi$
$74$		0			0
$75$	0.499405	−	1.09354i	0.0576663	−	0.126272i
$76$		0			0
$77$	−2.77784	+	19.3203i	−0.316564	+	2.20175i
$78$		0			0
$79$	7.62471	+	8.79938i	0.857847	+	0.990008i	1.00000		0.000163051i	$5.19009e-5\pi$
$79$	7.62471	+	8.79938i	0.857847	+	0.990008i	−0.142153	+	0.989845i	$0.545403\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	−5.09163	+	1.49504i	−0.558879	+	0.164102i	−0.548959	−	0.835849i	$-0.684976\pi$
$83$	−5.09163	+	1.49504i	−0.558879	+	0.164102i	−0.00991953	+	0.999951i	$0.503158\pi$
$84$		0			0
$85$	−7.35747	+	8.49098i	−0.798030	+	0.920976i
$86$		0			0
$87$	0.478924	+	0.140625i	0.0513460	+	0.0150766i
$88$		0			0
$89$	−1.58627	−	11.0327i	−0.168144	−	1.16947i	−0.882717	−	0.469905i	$-0.844288\pi$
$89$	−1.58627	−	11.0327i	−0.168144	−	1.16947i	0.714573	−	0.699561i	$-0.246621\pi$
$90$		0			0
$91$	−17.3742			−1.82131
$92$		0			0
$93$	5.11451			0.530350
$94$		0			0
$95$	1.57012	+	10.9204i	0.161091	+	1.12041i
$96$		0			0
$97$	−6.84457	−	2.00975i	−0.694961	−	0.204059i	−0.0848721	−	0.996392i	$-0.527048\pi$
$97$	−6.84457	−	2.00975i	−0.694961	−	0.204059i	−0.610089	+	0.792333i	$0.708866\pi$
$98$		0			0
$99$	3.16000	−	3.64683i	0.317592	−	0.366521i
$100$		0			0
$101$	5.07150	−	1.48913i	0.504633	−	0.148174i	−0.0195002	−	0.999810i	$-0.506208\pi$
$101$	5.07150	−	1.48913i	0.504633	−	0.148174i	0.524133	+	0.851636i	$0.324389\pi$
$102$		0			0
$103$	16.1144	−	10.3561i	1.58780	−	1.02042i	0.615074	−	0.788470i	$-0.289126\pi$
$103$	16.1144	−	10.3561i	1.58780	−	1.02042i	0.972728	−	0.231949i	$-0.0745102\pi$
$104$		0			0
$105$	6.59690	+	7.61322i	0.643791	+	0.742975i
$106$		0			0
$107$	1.56999	−	10.9195i	0.151777	−	1.05563i	−0.761463	−	0.648209i	$-0.775518\pi$
$107$	1.56999	−	10.9195i	0.151777	−	1.05563i	0.913240	−	0.407423i	$-0.133572\pi$
$108$		0			0
$109$	−0.724276	+	1.58594i	−0.0693731	+	0.151906i	−0.941142	−	0.338011i	$-0.890246\pi$
$109$	−0.724276	+	1.58594i	−0.0693731	+	0.151906i	0.871769	+	0.489917i	$0.162973\pi$
$110$		0			0
$111$	−4.43309	−	9.70710i	−0.420770	−	0.921357i
$112$		0			0
$113$	−14.5328	−	9.33966i	−1.36713	−	0.878601i	−0.368434	−	0.929654i	$-0.620106\pi$
$113$	−14.5328	−	9.33966i	−1.36713	−	0.878601i	−0.998696	+	0.0510528i	$0.983742\pi$
$114$		0			0
$115$	−11.8121	−	1.76744i	−1.10149	−	0.164815i
$116$		0			0
$117$	3.61337	+	2.32217i	0.334057	+	0.214685i
$118$		0			0
$119$	−7.58068	−	16.5994i	−0.694920	−	1.52166i
$120$		0			0
$121$	5.10337	−	11.1748i	0.463943	−	1.01589i
$122$		0			0
$123$	1.08215	−	7.52654i	0.0975745	−	0.678646i
$124$		0			0
$125$	6.19377	+	7.14799i	0.553988	+	0.639336i
$126$		0			0
$127$	−12.0209	+	7.72538i	−1.06668	+	0.685516i	−0.951444	−	0.307821i	$-0.900400\pi$
$127$	−12.0209	+	7.72538i	−1.06668	+	0.685516i	−0.115240	+	0.993338i	$0.536764\pi$
$128$		0			0
$129$	7.27706	−	2.13674i	0.640709	−	0.188129i
$130$		0			0
$131$	6.51189	−	7.51512i	0.568946	−	0.656599i	−0.396245	−	0.918145i	$-0.629687\pi$
$131$	6.51189	−	7.51512i	0.568946	−	0.656599i	0.965191	+	0.261546i	$0.0842323\pi$
$132$		0			0
$133$	−17.1938	−	5.04854i	−1.49089	−	0.437764i
$134$		0			0
$135$	−0.354423	−	2.46507i	−0.0305039	−	0.212159i
$136$		0			0
$137$	−8.14309			−0.695711			−0.347855	−	0.937548i	$-0.613090\pi$
$137$	−8.14309			−0.695711			−0.347855	+	0.937548i	$0.613090\pi$
$138$		0			0
$139$	−10.1303			−0.859242			−0.429621	−	0.903009i	$-0.641353\pi$
$139$	−10.1303			−0.859242			−0.429621	+	0.903009i	$0.641353\pi$
$140$		0			0
$141$	1.09259	+	7.59911i	0.0920124	+	0.639960i
$142$		0			0
$143$	19.8869	+	5.83931i	1.66302	+	0.488307i
$144$		0			0
$145$	0.814041	−	0.939453i	0.0676024	−	0.0780173i
$146$		0			0
$147$	−8.98279	+	2.63758i	−0.740888	+	0.217544i
$148$		0			0
$149$	5.58068	−	3.58648i	0.457187	−	0.293816i	−0.291705	−	0.956508i	$-0.594223\pi$
$149$	5.58068	−	3.58648i	0.457187	−	0.293816i	0.748892	+	0.662692i	$0.230586\pi$
$150$		0			0
$151$	5.56561	+	6.42306i	0.452923	+	0.522701i	0.935583	−	0.353107i	$-0.114875\pi$
$151$	5.56561	+	6.42306i	0.452923	+	0.522701i	−0.482660	+	0.875808i	$0.660329\pi$
$152$		0			0
$153$	−0.642033	+	4.46544i	−0.0519053	+	0.361010i
$154$		0			0
$155$	5.29125	−	11.5862i	0.425004	−	0.930628i
$156$		0			0
$157$	3.89510	+	8.52909i	0.310863	+	0.680695i	0.998992	−	0.0448934i	$-0.0142948\pi$
$157$	3.89510	+	8.52909i	0.310863	+	0.680695i	−0.688129	+	0.725589i	$0.741568\pi$
$158$		0			0
$159$	−6.42525	−	4.12926i	−0.509556	−	0.327472i
$160$		0			0
$161$	10.5813	−	16.2592i	0.833921	−	1.28141i
$162$		0			0
$163$	−4.07886	−	2.62132i	−0.319481	−	0.205318i	0.371064	−	0.928607i	$-0.378993\pi$
$163$	−4.07886	−	2.62132i	−0.319481	−	0.205318i	−0.690545	+	0.723289i	$0.742629\pi$
$164$		0			0
$165$	−4.99221	−	10.9314i	−0.388643	−	0.851009i
$166$		0			0
$167$	−5.54815	+	12.1488i	−0.429329	+	0.940099i	0.564107	+	0.825702i	$0.309221\pi$
$167$	−5.54815	+	12.1488i	−0.429329	+	0.940099i	−0.993435	+	0.114397i	$0.963507\pi$
$168$		0			0
$169$	−0.775469	+	5.39351i	−0.0596515	+	0.414885i
$170$		0			0
$171$	2.90108	+	3.34802i	0.221851	+	0.256030i
$172$		0			0
$173$	8.57692	−	5.51205i	0.652091	−	0.419073i	−0.172339	−	0.985038i	$-0.555132\pi$
$173$	8.57692	−	5.51205i	0.652091	−	0.419073i	0.824430	+	0.565964i	$0.191496\pi$
$174$		0			0
$175$	4.66585	−	1.37002i	0.352705	−	0.103564i
$176$		0			0
$177$	−1.85219	+	2.13754i	−0.139219	+	0.160667i
$178$		0			0
$179$	−5.83694	−	1.71388i	−0.436274	−	0.128102i	0.0562183	−	0.998419i	$-0.482096\pi$
$179$	−5.83694	−	1.71388i	−0.436274	−	0.128102i	−0.492492	+	0.870317i	$0.663914\pi$
$180$		0			0
$181$	0.660855	+	4.59635i	0.0491209	+	0.341644i	0.999530	+	0.0306423i	$0.00975529\pi$
$181$	0.660855	+	4.59635i	0.0491209	+	0.341644i	−0.950409	+	0.311001i	$0.899336\pi$
$182$		0			0
$183$	1.58800			0.117388
$184$		0			0
$185$	−26.5764			−1.95394
$186$		0			0
$187$	3.09810	+	21.5478i	0.226556	+	1.57573i
$188$		0			0
$189$	3.88115	+	1.13961i	0.282312	+	0.0828943i
$190$		0			0
$191$	7.73126	−	8.92235i	0.559414	−	0.645599i	−0.403636	−	0.914920i	$-0.632254\pi$
$191$	7.73126	−	8.92235i	0.559414	−	0.645599i	0.963050	+	0.269321i	$0.0867992\pi$
$192$		0			0
$193$	−21.4550	+	6.29975i	−1.54436	+	0.453466i	−0.939410	−	0.342795i	$-0.888626\pi$
$193$	−21.4550	+	6.29975i	−1.54436	+	0.453466i	−0.604953	+	0.796261i	$0.706808\pi$
$194$		0			0
$195$	8.99881	−	5.78319i	0.644418	−	0.414143i
$196$		0			0
$197$	−5.93139	−	6.84519i	−0.422594	−	0.487699i	0.504031	−	0.863685i	$-0.331850\pi$
$197$	−5.93139	−	6.84519i	−0.422594	−	0.487699i	−0.926625	+	0.375986i	$0.877304\pi$
$198$		0			0
$199$	0.513726	−	3.57304i	0.0364171	−	0.253286i	−0.963478	−	0.267788i	$-0.913707\pi$
$199$	0.513726	−	3.57304i	0.0364171	−	0.253286i	0.999895	+	0.0145021i	$0.00461632\pi$
$200$		0			0
$201$	4.99342	−	10.9341i	0.352208	−	0.771229i
$202$		0			0
$203$	0.838736	+	1.83658i	0.0588677	+	0.128902i
$204$		0			0
$205$	−15.9308	−	10.2381i	−1.11266	−	0.715061i
$206$		0			0
$207$	−4.37378	+	1.96724i	−0.303999	+	0.136733i
$208$		0			0
$209$	17.9836	+	11.5573i	1.24395	+	0.799438i
$210$		0			0
$211$	−1.02026	−	2.23405i	−0.0702374	−	0.153798i	0.871257	−	0.490827i	$-0.163305\pi$
$211$	−1.02026	−	2.23405i	−0.0702374	−	0.153798i	−0.941494	+	0.337029i	$0.890578\pi$
$212$		0			0
$213$	1.57512	−	3.44904i	0.107926	−	0.236324i
$214$		0			0
$215$	2.68804	−	18.6958i	0.183323	−	1.27504i
$216$		0			0
$217$	13.5479	+	15.6351i	0.919690	+	1.06138i
$218$		0			0
$219$	−6.27023	+	4.02963i	−0.423703	+	0.272297i
$220$		0			0
$221$	−18.5924	+	5.45922i	−1.25066	+	0.367227i
$222$		0			0
$223$	10.9606	−	12.6492i	0.733976	−	0.847053i	−0.258938	−	0.965894i	$-0.583372\pi$
$223$	10.9606	−	12.6492i	0.733976	−	0.847053i	0.992913	+	0.118841i	$0.0379179\pi$
$224$		0			0
$225$	−1.15349	−	0.338694i	−0.0768991	−	0.0225796i
$226$		0			0
$227$	1.94100	+	13.5000i	0.128829	+	0.896024i	0.947042	+	0.321109i	$0.104056\pi$
$227$	1.94100	+	13.5000i	0.128829	+	0.896024i	−0.818213	+	0.574915i	$0.805035\pi$
$228$		0			0
$229$	−6.76866			−0.447286			−0.223643	−	0.974671i	$-0.571795\pi$
$229$	−6.76866			−0.447286			−0.223643	+	0.974671i	$0.571795\pi$
$230$		0			0
$231$	19.5190			1.28425
$232$		0			0
$233$	1.54002	+	10.7111i	0.100890	+	0.701705i	0.975998	+	0.217778i	$0.0698809\pi$
$233$	1.54002	+	10.7111i	0.100890	+	0.701705i	−0.875108	+	0.483927i	$0.839210\pi$
$234$		0			0
$235$	18.3451	+	5.38661i	1.19670	+	0.351383i
$236$		0			0
$237$	7.62471	−	8.79938i	0.495278	−	0.571581i
$238$		0			0
$239$	−18.3881	+	5.39923i	−1.18943	+	0.349247i	−0.815801	−	0.578333i	$-0.803704\pi$
$239$	−18.3881	+	5.39923i	−1.18943	+	0.349247i	−0.373625	+	0.927580i	$0.621885\pi$
$240$		0			0
$241$	−8.37372	+	5.38147i	−0.539399	+	0.346651i	−0.781804	−	0.623525i	$-0.785700\pi$
$241$	−8.37372	+	5.38147i	−0.539399	+	0.346651i	0.242405	+	0.970175i	$0.422064\pi$
$242$		0			0
$243$	−0.654861	−	0.755750i	−0.0420093	−	0.0484814i
$244$		0			0
$245$	−3.31812	+	23.0780i	−0.211987	+	1.47440i
$246$		0			0
$247$	−7.90458	+	17.3086i	−0.502957	+	1.10132i
$248$		0			0
$249$	2.20443	+	4.82703i	0.139700	+	0.305901i
$250$		0			0
$251$	9.59137	+	6.16400i	0.605402	+	0.389068i	0.807130	−	0.590373i	$-0.201019\pi$
$251$	9.59137	+	6.16400i	0.605402	+	0.389068i	−0.201728	+	0.979442i	$0.564656\pi$
$252$		0			0
$253$	−17.5761	+	15.0544i	−1.10500	+	0.946462i
$254$		0			0
$255$	9.45163	+	6.07419i	0.591884	+	0.380381i
$256$		0			0
$257$	10.8691	+	23.8000i	0.677995	+	1.48460i	0.864754	+	0.502196i	$0.167474\pi$
$257$	10.8691	+	23.8000i	0.677995	+	1.48460i	−0.186759	+	0.982406i	$0.559798\pi$
$258$		0			0
$259$	17.9318	−	39.2652i	1.11423	−	2.43982i
$260$		0			0
$261$	0.0710354	−	0.494062i	0.00439698	−	0.0305817i
$262$		0			0
$263$	19.2160	+	22.1764i	1.18491	+	1.36746i	0.914438	+	0.404727i	$0.132633\pi$
$263$	19.2160	+	22.1764i	1.18491	+	1.36746i	0.270469	+	0.962729i	$0.412821\pi$
$264$		0			0
$265$	−16.0016	+	10.2836i	−0.982969	+	0.631716i
$266$		0			0
$267$	−10.6947	+	3.14024i	−0.654504	+	0.192180i
$268$		0			0
$269$	18.5100	−	21.3616i	1.12857	−	1.30244i	0.180790	−	0.983522i	$-0.442134\pi$
$269$	18.5100	−	21.3616i	1.12857	−	1.30244i	0.947782	−	0.318920i	$-0.103320\pi$
$270$		0			0
$271$	0.108543	+	0.0318710i	0.00659349	+	0.00193602i	0.285028	−	0.958519i	$-0.407997\pi$
$271$	0.108543	+	0.0318710i	0.00659349	+	0.00193602i	−0.278434	+	0.960455i	$0.589815\pi$
$272$		0			0
$273$	2.47260	+	17.1973i	0.149649	+	1.04083i
$274$		0			0
$275$	−5.80108			−0.349818
$276$		0			0
$277$	−3.96519			−0.238245			−0.119123	−	0.992880i	$-0.538008\pi$
$277$	−3.96519			−0.238245			−0.119123	+	0.992880i	$0.538008\pi$
$278$		0			0
$279$	−0.727870	−	5.06245i	−0.0435765	−	0.303081i
$280$		0			0
$281$	15.9629	+	4.68713i	0.952267	+	0.279611i	0.720730	−	0.693215i	$-0.243807\pi$
$281$	15.9629	+	4.68713i	0.952267	+	0.279611i	0.231536	+	0.972826i	$0.425625\pi$
$282$		0			0
$283$	11.0836	−	12.7911i	0.658851	−	0.760354i	−0.323738	−	0.946147i	$-0.604940\pi$
$283$	11.0836	−	12.7911i	0.658851	−	0.760354i	0.982589	+	0.185792i	$0.0594852\pi$
$284$		0			0
$285$	10.5858	−	3.10828i	0.627050	−	0.184119i
$286$		0			0
$287$	25.8752	−	16.6290i	1.52737	−	0.981579i
$288$		0			0
$289$	−2.19534	−	2.53355i	−0.129137	−	0.149032i
$290$		0			0
$291$	−1.01521	+	7.06092i	−0.0595125	+	0.413919i
$292$		0			0
$293$	8.50419	−	18.6216i	0.496820	−	1.08788i	−0.480670	−	0.876902i	$-0.659607\pi$
$293$	8.50419	−	18.6216i	0.496820	−	1.08788i	0.977490	−	0.210982i	$-0.0676662\pi$
$294$		0			0
$295$	2.92611	+	6.40728i	0.170365	+	0.373046i
$296$		0			0
$297$	−4.05943	−	2.60884i	−0.235552	−	0.151380i
$298$		0			0
$299$	−15.4903	−	13.5785i	−0.895827	−	0.785267i
$300$		0			0
$301$	25.8083	+	16.5860i	1.48756	+	0.956000i
$302$		0			0
$303$	−2.19572	−	4.80796i	−0.126141	−	0.276210i
$304$		0			0
$305$	1.64288	−	3.59740i	0.0940708	−	0.205986i
$306$		0			0
$307$	−2.39426	+	16.6525i	−0.136648	+	0.950407i	0.799967	+	0.600045i	$0.204851\pi$
$307$	−2.39426	+	16.6525i	−0.136648	+	0.950407i	−0.936614	+	0.350362i	$0.886059\pi$
$308$		0			0
$309$	−12.5440	−	14.4766i	−0.713605	−	0.823544i
$310$		0			0
$311$	−25.0518	+	16.0998i	−1.42055	+	0.912935i	−0.420571	+	0.907260i	$0.638170\pi$
$311$	−25.0518	+	16.0998i	−1.42055	+	0.912935i	−0.999984	+	0.00567544i	$0.998193\pi$
$312$		0			0
$313$	28.9943	−	8.51351i	1.63886	−	0.481212i	0.672861	−	0.739769i	$-0.265065\pi$
$313$	28.9943	−	8.51351i	1.63886	−	0.481212i	0.965996	+	0.258557i	$0.0832470\pi$
$314$		0			0
$315$	6.59690	−	7.61322i	0.371693	−	0.428957i
$316$		0			0
$317$	5.02982	+	1.47689i	0.282503	+	0.0829504i	0.419914	−	0.907564i	$-0.362060\pi$
$317$	5.02982	+	1.47689i	0.282503	+	0.0829504i	−0.137411	+	0.990514i	$0.543878\pi$
$318$		0			0
$319$	−0.342778	−	2.38407i	−0.0191919	−	0.133483i
$320$		0			0
$321$	−11.0318			−0.615736
$322$		0			0
$323$	−19.9856			−1.11203
$324$		0			0
$325$	−0.734864	−	5.11109i	−0.0407629	−	0.283512i
$326$		0			0
$327$	1.67288	+	0.491201i	0.0925102	+	0.0271635i
$328$		0			0
$329$	−20.3364	+	23.4694i	−1.12118	+	1.29391i
$330$		0			0
$331$	−18.1389	+	5.32606i	−0.997003	+	0.292747i	−0.739226	−	0.673458i	$-0.764808\pi$
$331$	−18.1389	+	5.32606i	−0.997003	+	0.292747i	−0.257778	+	0.966204i	$0.582990\pi$
$332$		0			0
$333$	−8.97741	+	5.76943i	−0.491959	+	0.316163i
$334$		0			0
$335$	−19.6036	−	22.6238i	−1.07106	−	1.23607i
$336$		0			0
$337$	1.73565	−	12.0717i	0.0945470	−	0.657589i	−0.886344	−	0.463028i	$-0.846763\pi$
$337$	1.73565	−	12.0717i	0.0945470	−	0.657589i	0.980891	−	0.194560i	$-0.0623280\pi$
$338$		0			0
$339$	−7.17636	+	15.7140i	−0.389766	+	0.853470i
$340$		0			0
$341$	−10.2524	−	22.4496i	−0.555197	−	1.21571i
$342$		0			0
$343$	−8.03763	−	5.16547i	−0.433991	−	0.278909i
$344$		0			0
$345$	−0.0684114	+	11.9434i	−0.00368315	+	0.643013i
$346$		0			0
$347$	7.06027	+	4.53736i	0.379015	+	0.243578i	0.716252	−	0.697842i	$-0.245856\pi$
$347$	7.06027	+	4.53736i	0.379015	+	0.243578i	−0.337237	+	0.941420i	$0.609492\pi$
$348$		0			0
$349$	9.08565	+	19.8948i	0.486344	+	1.06494i	0.980670	+	0.195668i	$0.0626875\pi$
$349$	9.08565	+	19.8948i	0.486344	+	1.06494i	−0.494326	+	0.869276i	$0.664585\pi$
$350$		0			0
$351$	1.78430	−	3.90708i	0.0952390	−	0.208544i
$352$		0			0
$353$	−2.92984	+	20.3775i	−0.155940	+	1.08459i	0.750079	+	0.661348i	$0.230015\pi$
$353$	−2.92984	+	20.3775i	−0.155940	+	1.08459i	−0.906019	+	0.423237i	$0.860894\pi$
$354$		0			0
$355$	−6.18378	−	7.13646i	−0.328201	−	0.378764i
$356$		0			0
$357$	−15.3516	+	9.86585i	−0.812491	+	0.522156i
$358$		0			0
$359$	20.5158	−	6.02397i	1.08278	−	0.317933i	0.308790	−	0.951130i	$-0.400076\pi$
$359$	20.5158	−	6.02397i	1.08278	−	0.317933i	0.773991	+	0.633197i	$0.218258\pi$
$360$		0			0
$361$	−0.409640	+	0.472749i	−0.0215600	+	0.0248815i
$362$		0			0
$363$	−11.7874	−	3.46109i	−0.618677	−	0.181660i
$364$		0			0
$365$	2.64167	+	18.3732i	0.138271	+	0.961699i
$366$		0			0
$367$	11.1339			0.581182			0.290591	−	0.956847i	$-0.406148\pi$
$367$	11.1339			0.581182			0.290591	+	0.956847i	$0.406148\pi$
$368$		0			0
$369$	−7.60394			−0.395845
$370$		0			0
$371$	−4.39675	−	30.5801i	−0.228268	−	1.58764i
$372$		0			0
$373$	−12.8571	−	3.77518i	−0.665714	−	0.195471i	−0.0686206	−	0.997643i	$-0.521860\pi$
$373$	−12.8571	−	3.77518i	−0.665714	−	0.195471i	−0.597094	+	0.802171i	$0.703678\pi$
$374$		0			0
$375$	6.19377	−	7.14799i	0.319845	−	0.369121i
$376$		0			0
$377$	2.05709	−	0.604015i	0.105945	−	0.0311084i
$378$		0			0
$379$	−0.457570	+	0.294062i	−0.0235038	+	0.0151050i	−0.552340	−	0.833619i	$-0.686265\pi$
$379$	−0.457570	+	0.294062i	−0.0235038	+	0.0151050i	0.528836	+	0.848724i	$0.322629\pi$
$380$		0			0
$381$	9.35750	+	10.7991i	0.479399	+	0.553256i
$382$		0			0
$383$	0.358061	−	2.49037i	0.0182961	−	0.127252i	−0.978626	−	0.205646i	$-0.934070\pi$
$383$	0.358061	−	2.49037i	0.0182961	−	0.127252i	0.996922	+	0.0783945i	$0.0249794\pi$
$384$		0			0
$385$	20.1935	−	44.2175i	1.02915	−	2.25353i
$386$		0			0
$387$	−3.15062	−	6.89890i	−0.160155	−	0.350691i
$388$		0			0
$389$	−10.5193	−	6.76037i	−0.533352	−	0.342764i	0.246082	−	0.969249i	$-0.420857\pi$
$389$	−10.5193	−	6.76037i	−0.533352	−	0.342764i	−0.779434	+	0.626485i	$0.784493\pi$
$390$		0			0
$391$	6.21429	−	20.7241i	0.314270	−	1.04806i
$392$		0			0
$393$	−8.36536	−	5.37609i	−0.421977	−	0.271188i
$394$		0			0
$395$	−12.0456	−	26.3762i	−0.606080	−	1.32713i
$396$		0			0
$397$	9.36806	−	20.5132i	0.470169	−	1.02953i	−0.514881	−	0.857262i	$-0.672164\pi$
$397$	9.36806	−	20.5132i	0.470169	−	1.02953i	0.985051	−	0.172266i	$-0.0551087\pi$
$398$		0			0
$399$	−2.55023	+	17.7372i	−0.127671	+	0.887973i
$400$		0			0
$401$	0.939019	+	1.08369i	0.0468924	+	0.0541167i	0.778711	−	0.627383i	$-0.215874\pi$
$401$	0.939019	+	1.08369i	0.0468924	+	0.0541167i	−0.731819	+	0.681499i	$0.761328\pi$
$402$		0			0
$403$	18.4806	−	11.8768i	0.920586	−	0.591625i
$404$		0			0
$405$	−2.38954	+	0.701632i	−0.118737	+	0.0348644i
$406$		0			0
$407$	−33.7218	+	38.9171i	−1.67153	+	1.92905i
$408$		0			0
$409$	−2.01920	−	0.592891i	−0.0998430	−	0.0293166i	0.231429	−	0.972852i	$-0.425660\pi$
$409$	−2.01920	−	0.592891i	−0.0998430	−	0.0293166i	−0.331272	+	0.943535i	$0.607478\pi$
$410$		0			0
$411$	1.15888	+	8.06020i	0.0571634	+	0.397580i
$412$		0			0
$413$	−11.4407			−0.562962
$414$		0			0
$415$	13.2156			0.648729
$416$		0			0
$417$	1.44169	+	10.0272i	0.0706001	+	0.491034i
$418$		0			0
$419$	14.1544	+	4.15610i	0.691486	+	0.203039i	0.608549	−	0.793516i	$-0.291752\pi$
$419$	14.1544	+	4.15610i	0.691486	+	0.203039i	0.0829368	+	0.996555i	$0.473570\pi$
$420$		0			0
$421$	1.55784	−	1.79785i	0.0759246	−	0.0876216i	−0.716516	−	0.697570i	$-0.754264\pi$
$421$	1.55784	−	1.79785i	0.0759246	−	0.0876216i	0.792441	+	0.609949i	$0.208810\pi$
$422$		0			0
$423$	7.36627	−	2.16293i	0.358160	−	0.105165i
$424$		0			0
$425$	4.56252	−	2.93216i	0.221315	−	0.142230i
$426$		0			0
$427$	4.20647	+	4.85452i	0.203565	+	0.234927i
$428$		0			0
$429$	2.94968	−	20.5155i	0.142412	−	0.990495i
$430$		0			0
$431$	7.23072	−	15.8331i	0.348291	−	0.762652i	−0.651700	−	0.758477i	$-0.725944\pi$
$431$	7.23072	−	15.8331i	0.348291	−	0.762652i	0.999991	−	0.00417490i	$-0.00132892\pi$
$432$		0			0
$433$	−8.20769	−	17.9723i	−0.394436	−	0.863695i	−0.997804	−	0.0662322i	$-0.978902\pi$
$433$	−8.20769	−	17.9723i	−0.394436	−	0.863695i	0.603368	−	0.797463i	$-0.293825\pi$
$434$		0			0
$435$	−1.04574	−	0.672057i	−0.0501394	−	0.0322227i
$436$		0			0
$437$	−11.3838	−	17.9387i	−0.544562	−	0.858123i
$438$		0			0
$439$	−15.4395	−	9.92238i	−0.736888	−	0.473569i	0.117586	−	0.993063i	$-0.462484\pi$
$439$	−15.4395	−	9.92238i	−0.736888	−	0.473569i	−0.854474	+	0.519493i	$0.826121\pi$
$440$		0			0
$441$	3.88912	+	8.51599i	0.185196	+	0.405523i
$442$		0			0
$443$	−0.532229	+	1.16542i	−0.0252869	+	0.0553707i	−0.921854	−	0.387537i	$-0.873326\pi$
$443$	−0.532229	+	1.16542i	−0.0252869	+	0.0553707i	0.896567	+	0.442908i	$0.146053\pi$
$444$		0			0
$445$	−3.95047	+	27.4761i	−0.187270	+	1.30249i
$446$		0			0
$447$	−4.34419	−	5.01346i	−0.205473	−	0.237129i
$448$		0			0
$449$	7.96730	−	5.12027i	0.376000	−	0.241641i	−0.338968	−	0.940798i	$-0.610078\pi$
$449$	7.96730	−	5.12027i	0.376000	−	0.241641i	0.714968	+	0.699157i	$0.246441\pi$
$450$		0			0
$451$	−35.2062	+	10.3375i	−1.65779	+	0.486772i
$452$		0			0
$453$	5.56561	−	6.42306i	0.261495	−	0.301782i
$454$		0			0
$455$	41.5163	+	12.1903i	1.94631	+	0.571489i
$456$		0			0
$457$	−2.98099	−	20.7333i	−0.139445	−	0.969861i	−0.932618	−	0.360865i	$-0.882482\pi$
$457$	−2.98099	−	20.7333i	−0.139445	−	0.969861i	0.793173	−	0.608996i	$-0.208428\pi$
$458$		0			0
$459$	4.51136			0.210572
$460$		0			0
$461$	7.43095			0.346094			0.173047	−	0.984914i	$-0.444639\pi$
$461$	7.43095			0.346094			0.173047	+	0.984914i	$0.444639\pi$
$462$		0			0
$463$	3.90134	+	27.1344i	0.181310	+	1.26104i	0.853669	+	0.520816i	$0.174372\pi$
$463$	3.90134	+	27.1344i	0.181310	+	1.26104i	−0.672358	+	0.740226i	$0.734719\pi$
$464$		0			0
$465$	−12.2213	−	3.58850i	−0.566750	−	0.166413i
$466$		0			0
$467$	−24.5015	+	28.2762i	−1.13379	+	1.30847i	−0.188563	+	0.982061i	$0.560383\pi$
$467$	−24.5015	+	28.2762i	−1.13379	+	1.30847i	−0.945230	+	0.326405i	$0.894163\pi$
$468$		0			0
$469$	46.6526	−	13.6984i	2.15422	−	0.632535i
$470$		0			0
$471$	7.88794	−	5.06927i	0.363457	−	0.233580i
$472$		0			0
$473$	−23.9663	−	27.6586i	−1.10197	−	1.27174i
$474$		0			0
$475$	0.757935	−	5.27155i	0.0347764	−	0.241875i
$476$		0			0
$477$	−3.17282	+	6.94751i	−0.145274	+	0.318105i
$478$		0			0
$479$	6.62333	+	14.5031i	0.302628	+	0.662662i	0.998456	−	0.0555460i	$-0.0176900\pi$
$479$	6.62333	+	14.5031i	0.302628	+	0.662662i	−0.695829	+	0.718208i	$0.744963\pi$
$480$		0			0
$481$	−38.5600	−	24.7810i	−1.75818	−	1.12992i
$482$		0			0
$483$	−17.5996	−	8.15963i	−0.800811	−	0.371276i
$484$		0			0
$485$	14.9453	+	9.60474i	0.678630	+	0.436129i
$486$		0			0
$487$	6.29565	+	13.7855i	0.285283	+	0.624683i	0.996968	−	0.0778164i	$-0.0247948\pi$
$487$	6.29565	+	13.7855i	0.285283	+	0.624683i	−0.711685	+	0.702499i	$0.752068\pi$
$488$		0			0
$489$	−2.01416	+	4.41040i	−0.0910835	+	0.199445i
$490$		0			0
$491$	−5.02270	+	34.9336i	−0.226671	+	1.57653i	0.485315	+	0.874340i	$0.338705\pi$
$491$	−5.02270	+	34.9336i	−0.226671	+	1.57653i	−0.711986	+	0.702194i	$0.752204\pi$
$492$		0			0
$493$	1.47462	+	1.70181i	0.0664137	+	0.0766455i
$494$		0			0
$495$	−10.1097	+	6.49710i	−0.454396	+	0.292023i
$496$		0			0
$497$	14.7161	−	4.32104i	0.660107	−	0.193825i
$498$		0			0
$499$	15.9697	−	18.4300i	0.714902	−	0.825041i	−0.275782	−	0.961220i	$-0.588937\pi$
$499$	15.9697	−	18.4300i	0.714902	−	0.825041i	0.990684	+	0.136179i	$0.0434824\pi$
$500$		0			0
$501$	12.8147	+	3.76273i	0.572518	+	0.168106i
$502$		0			0
$503$	−4.74046	−	32.9706i	−0.211367	−	1.47009i	−0.768599	−	0.639731i	$-0.779046\pi$
$503$	−4.74046	−	32.9706i	−0.211367	−	1.47009i	0.557232	−	0.830357i	$-0.311863\pi$
$504$		0			0
$505$	−13.1634			−0.585762
$506$		0			0
$507$	5.44897			0.241997
$508$		0			0
$509$	−2.84114	−	19.7605i	−0.125931	−	0.875870i	−0.950636	−	0.310307i	$-0.899568\pi$
$509$	−2.84114	−	19.7605i	−0.125931	−	0.875870i	0.824705	−	0.565563i	$-0.191341\pi$
$510$		0			0
$511$	−28.9279	−	8.49399i	−1.27969	−	0.375752i
$512$		0			0
$513$	2.90108	−	3.34802i	0.128086	−	0.147819i
$514$		0			0
$515$	−45.7722	+	13.4399i	−2.01697	+	0.592235i
$516$		0			0
$517$	31.1653	−	20.0287i	1.37065	−	0.880861i
$518$		0			0
$519$	−6.67657	−	7.70517i	−0.293069	−	0.338219i
$520$		0			0
$521$	−5.86877	+	40.8182i	−0.257116	+	1.78828i	0.296014	+	0.955184i	$0.404343\pi$
$521$	−5.86877	+	40.8182i	−0.257116	+	1.78828i	−0.553130	+	0.833095i	$0.686567\pi$
$522$		0			0
$523$	4.28867	−	9.39088i	0.187530	−	0.410634i	−0.792392	−	0.610012i	$-0.791165\pi$
$523$	4.28867	−	9.39088i	0.187530	−	0.410634i	0.979923	+	0.199377i	$0.0638920\pi$
$524$		0			0
$525$	−2.02009	−	4.42339i	−0.0881641	−	0.193052i
$526$		0			0
$527$	19.4106	+	12.4744i	0.845538	+	0.543394i
$528$		0			0
$529$	22.1411	−	6.22662i	0.962657	−	0.270723i
$530$		0			0
$531$	2.37937	+	1.52913i	0.103256	+	0.0663586i
$532$		0			0
$533$	−13.5677	−	29.7092i	−0.587683	−	1.28685i
$534$		0			0
$535$	−11.4131	+	24.9911i	−0.493429	+	1.08046i
$536$		0			0
$537$	−0.865753	+	6.02144i	−0.0373600	+	0.259844i
$538$		0			0
$539$	29.5840	+	34.1417i	1.27427	+	1.47059i
$540$		0			0
$541$	−29.0203	+	18.6502i	−1.24768	+	0.801834i	−0.986548	−	0.163469i	$-0.947732\pi$
$541$	−29.0203	+	18.6502i	−1.24768	+	0.801834i	−0.261130	+	0.965304i	$0.584095\pi$
$542$		0			0
$543$	4.45551	−	1.30826i	0.191204	−	0.0561427i
$544$		0			0
$545$	2.84343	−	3.28150i	0.121799	−	0.140564i
$546$		0			0
$547$	9.85374	+	2.89332i	0.421315	+	0.123709i	0.485516	−	0.874228i	$-0.338632\pi$
$547$	9.85374	+	2.89332i	0.421315	+	0.123709i	−0.0642009	+	0.997937i	$0.520450\pi$
$548$		0			0
$549$	−0.225996	−	1.57184i	−0.00964527	−	0.0670843i
$550$		0			0
$551$	2.21124			0.0942019
$552$		0			0
$553$	47.0969			2.00277
$554$		0			0
$555$	3.78222	+	26.3059i	0.160546	+	1.11662i
$556$		0			0
$557$	−29.0734	−	8.53672i	−1.23188	−	0.361712i	−0.399921	−	0.916550i	$-0.630962\pi$
$557$	−29.0734	−	8.53672i	−1.23188	−	0.361712i	−0.831959	+	0.554837i	$0.812780\pi$
$558$		0			0
$559$	21.3329	−	24.6194i	0.902283	−	1.04129i
$560$		0			0
$561$	20.8875	−	6.13314i	0.881873	−	0.258941i
$562$		0			0
$563$	−26.7756	+	17.2076i	−1.12846	+	0.725214i	−0.965237	−	0.261376i	$-0.915824\pi$
$563$	−26.7756	+	17.2076i	−1.12846	+	0.725214i	−0.163218	+	0.986590i	$0.552187\pi$
$564$		0			0
$565$	28.1737	+	32.5141i	1.18528	+	1.36788i
$566$		0			0
$567$	0.575663	−	4.00383i	0.0241756	−	0.168145i
$568$		0			0
$569$	−0.827716	+	1.81245i	−0.0346997	+	0.0759817i	−0.926188	−	0.377062i	$-0.876934\pi$
$569$	−0.827716	+	1.81245i	−0.0346997	+	0.0759817i	0.891488	+	0.453043i	$0.149662\pi$
$570$		0			0
$571$	−4.19617	−	9.18833i	−0.175604	−	0.384520i	0.801280	−	0.598290i	$-0.204153\pi$
$571$	−4.19617	−	9.18833i	−0.175604	−	0.384520i	−0.976884	+	0.213770i	$0.931426\pi$
$572$		0			0
$573$	−9.93181	−	6.38279i	−0.414907	−	0.266645i
$574$		0			0
$575$	5.23065	+	2.42506i	0.218133	+	0.101132i
$576$		0			0
$577$	9.09996	+	5.84819i	0.378836	+	0.243463i	0.716176	−	0.697920i	$-0.245891\pi$
$577$	9.09996	+	5.84819i	0.378836	+	0.243463i	−0.337340	+	0.941383i	$0.609527\pi$
$578$		0			0
$579$	9.28899	+	20.3401i	0.386037	+	0.845304i
$580$		0			0
$581$	−8.91693	+	19.5254i	−0.369937	+	0.810048i
$582$		0			0
$583$	−5.24508	+	36.4803i	−0.217229	+	1.51086i
$584$		0			0
$585$	−7.00499	−	8.08419i	−0.289621	−	0.334240i
$586$		0			0
$587$	19.2092	−	12.3450i	0.792848	−	0.509532i	−0.0804270	−	0.996761i	$-0.525628\pi$
$587$	19.2092	−	12.3450i	0.792848	−	0.509532i	0.873275	+	0.487228i	$0.161992\pi$
$588$		0			0
$589$	21.7398	−	6.38340i	0.895775	−	0.263023i
$590$		0			0
$591$	−5.93139	+	6.84519i	−0.243985	+	0.281573i
$592$		0			0
$593$	12.7448	+	3.74220i	0.523365	+	0.153674i	0.532735	−	0.846282i	$-0.321164\pi$
$593$	12.7448	+	3.74220i	0.523365	+	0.153674i	−0.00936967	+	0.999956i	$0.502983\pi$
$594$		0			0
$595$	6.46768	+	44.9837i	0.265149	+	1.84415i
$596$		0			0
$597$	−3.60978			−0.147739
$598$		0			0
$599$	15.3103			0.625563			0.312781	−	0.949825i	$-0.398739\pi$
$599$	15.3103			0.625563			0.312781	+	0.949825i	$0.398739\pi$
$600$		0			0
$601$	3.13065	+	21.7741i	0.127702	+	0.888185i	0.948457	+	0.316905i	$0.102644\pi$
$601$	3.13065	+	21.7741i	0.127702	+	0.888185i	−0.820755	+	0.571280i	$0.806447\pi$
$602$		0			0
$603$	−11.5334	−	3.38651i	−0.469676	−	0.137909i
$604$		0			0
$605$	−20.0353	+	23.1220i	−0.814552	+	0.940043i
$606$		0			0
$607$	−1.82069	+	0.534602i	−0.0738994	+	0.0216988i	−0.318473	−	0.947932i	$-0.603170\pi$
$607$	−1.82069	+	0.534602i	−0.0738994	+	0.0216988i	0.244574	+	0.969631i	$0.421352\pi$
$608$		0			0
$609$	1.69852	−	1.09157i	0.0688274	−	0.0442327i
$610$		0			0
$611$	21.5944	+	24.9212i	0.873615	+	1.00821i
$612$		0			0
$613$	−2.90508	+	20.2052i	−0.117335	+	0.816082i	0.843136	+	0.537701i	$0.180707\pi$
$613$	−2.90508	+	20.2052i	−0.117335	+	0.816082i	−0.960471	+	0.278381i	$0.910202\pi$
$614$		0			0
$615$	−7.86671	+	17.2257i	−0.317216	+	0.694607i
$616$		0			0
$617$	8.44479	+	18.4915i	0.339975	+	0.744440i	0.999977	−	0.00682330i	$-0.00217194\pi$
$617$	8.44479	+	18.4915i	0.339975	+	0.744440i	−0.660002	+	0.751264i	$0.729445\pi$
$618$		0			0
$619$	−29.4504	−	18.9266i	−1.18371	−	0.760725i	−0.207647	−	0.978204i	$-0.566580\pi$
$619$	−29.4504	−	18.9266i	−1.18371	−	0.760725i	−0.976065	+	0.217479i	$0.930217\pi$
$620$		0			0
$621$	2.56967	+	4.04930i	0.103117	+	0.162493i
$622$		0			0
$623$	−37.9290	−	24.3755i	−1.51959	−	0.976583i
$624$		0			0
$625$	−12.2820	−	26.8939i	−0.491281	−	1.07576i
$626$		0			0
$627$	8.88037	−	19.4453i	0.354648	−	0.776570i
$628$		0			0
$629$	6.85144	−	47.6528i	0.273185	−	1.90004i
$630$		0			0
$631$	−20.2459	−	23.3650i	−0.805976	−	0.930146i	0.192717	−	0.981254i	$-0.438270\pi$
$631$	−20.2459	−	23.3650i	−0.805976	−	0.930146i	−0.998693	+	0.0511081i	$0.983725\pi$
$632$		0			0
$633$	−2.06611	+	1.32781i	−0.0821207	+	0.0527758i
$634$		0			0
$635$	34.1448	−	10.0258i	1.35500	−	0.397863i
$636$		0			0
$637$	−26.3332	+	30.3902i	−1.04336	+	1.20410i
$638$		0			0
$639$	−3.63810	−	1.06824i	−0.143921	−	0.0422590i
$640$		0			0
$641$	−7.05443	−	49.0646i	−0.278633	−	1.93794i	−0.341422	−	0.939910i	$-0.610908\pi$
$641$	−7.05443	−	49.0646i	−0.278633	−	1.93794i	0.0627883	−	0.998027i	$-0.480001\pi$
$642$		0			0
$643$	36.1135			1.42418			0.712089	−	0.702089i	$-0.247749\pi$
$643$	36.1135			1.42418			0.712089	+	0.702089i	$0.247749\pi$
$644$		0			0
$645$	−18.8880			−0.743715
$646$		0			0
$647$	−2.05843	−	14.3167i	−0.0809251	−	0.562846i	−0.989434	−	0.144982i	$-0.953688\pi$
$647$	−2.05843	−	14.3167i	−0.0809251	−	0.562846i	0.908509	−	0.417865i	$-0.137221\pi$
$648$		0			0
$649$	13.0953	+	3.84513i	0.514036	+	0.150935i
$650$		0			0
$651$	13.5479	−	15.6351i	0.530983	−	0.612787i
$652$		0			0
$653$	39.8195	−	11.6921i	1.55826	−	0.457545i	0.614701	−	0.788760i	$-0.289277\pi$
$653$	39.8195	−	11.6921i	1.55826	−	0.457545i	0.943555	+	0.331215i	$0.107458\pi$
$654$		0			0
$655$	−20.8333	+	13.3887i	−0.814023	+	0.523141i
$656$		0			0
$657$	4.88096	+	5.63293i	0.190424	+	0.219762i
$658$		0			0
$659$	−3.38046	+	23.5116i	−0.131684	+	0.915881i	0.811675	+	0.584109i	$0.198556\pi$
$659$	−3.38046	+	23.5116i	−0.131684	+	0.915881i	−0.943359	+	0.331773i	$0.892353\pi$
$660$		0			0
$661$	−18.6367	+	40.8086i	−0.724882	+	1.58727i	0.0820519	+	0.996628i	$0.473853\pi$
$661$	−18.6367	+	40.8086i	−0.724882	+	1.58727i	−0.806934	+	0.590642i	$0.798875\pi$
$662$		0			0
$663$	8.04963	+	17.6262i	0.312622	+	0.684546i
$664$		0			0
$665$	37.5429	+	24.1274i	1.45585	+	0.935620i
$666$		0			0
$667$	−0.687558	+	2.29294i	−0.0266223	+	0.0887829i
$668$		0			0
$669$	−14.0803	−	9.04886i	−0.544376	−	0.349849i
$670$		0			0
$671$	−3.18325	−	6.97034i	−0.122888	−	0.269087i
$672$		0			0
$673$	−18.4662	+	40.4353i	−0.711819	+	1.55867i	0.113207	+	0.993571i	$0.463888\pi$
$673$	−18.4662	+	40.4353i	−0.711819	+	1.55867i	−0.825026	+	0.565095i	$0.808840\pi$
$674$		0			0
$675$	−0.171089	+	1.18995i	−0.00658520	+	0.0458011i
$676$		0			0
$677$	16.0916	+	18.5707i	0.618451	+	0.713731i	0.975412	−	0.220389i	$-0.0707326\pi$
$677$	16.0916	+	18.5707i	0.618451	+	0.713731i	−0.356961	+	0.934119i	$0.616187\pi$
$678$		0			0
$679$	−24.2745	+	15.6003i	−0.931569	+	0.598683i
$680$		0			0
$681$	13.0863	−	3.84249i	0.501469	−	0.147245i
$682$		0			0
$683$	23.6796	−	27.3277i	0.906076	−	1.04567i	−0.0926750	−	0.995696i	$-0.529542\pi$
$683$	23.6796	−	27.3277i	0.906076	−	1.04567i	0.998751	−	0.0499707i	$-0.0159128\pi$
$684$		0			0
$685$	19.4582	+	5.71345i	0.743461	+	0.218300i
$686$		0			0
$687$	0.963281	+	6.69977i	0.0367515	+	0.255612i
$688$		0			0
$689$	−32.8057			−1.24980
$690$		0			0
$691$	−29.9939			−1.14102			−0.570511	−	0.821290i	$-0.693255\pi$
$691$	−29.9939			−1.14102			−0.570511	+	0.821290i	$0.693255\pi$
$692$		0			0
$693$	−2.77784	−	19.3203i	−0.105521	−	0.733917i
$694$		0			0
$695$	24.2068	+	7.10776i	0.918216	+	0.269613i
$696$		0			0
$697$	22.4644	−	25.9253i	0.850901	−	0.981992i
$698$		0			0
$699$	10.3829	−	3.04869i	0.392716	−	0.115312i
$700$		0			0
$701$	38.9924	−	25.0589i	1.47272	−	0.946462i	0.474934	−	0.880022i	$-0.342472\pi$
$701$	38.9924	−	25.0589i	1.47272	−	0.946462i	0.997790	−	0.0664406i	$-0.0211643\pi$
$702$		0			0
$703$	−30.9588	−	35.7283i	−1.16763	−	1.34752i
$704$		0			0
$705$	2.72100	−	18.9250i	0.102479	−	0.712755i
$706$		0			0
$707$	8.88168	−	19.4482i	0.334030	−	0.731424i
$708$		0			0
$709$	−0.678476	−	1.48565i	−0.0254807	−	0.0557949i	0.896464	−	0.443117i	$-0.146127\pi$
$709$	−0.678476	−	1.48565i	−0.0254807	−	0.0557949i	−0.921944	+	0.387322i	$0.873400\pi$
$710$		0			0
$711$	−9.79492	−	6.29482i	−0.367338	−	0.236074i
$712$		0			0
$713$	−0.140495	+	24.5279i	−0.00526157	+	0.918578i
$714$		0			0
$715$	−43.4234	−	27.9065i	−1.62394	−	1.04364i
$716$		0			0
$717$	7.96117	+	17.4325i	0.297315	+	0.651030i
$718$		0			0
$719$	1.86499	−	4.08377i	0.0695525	−	0.152299i	−0.871663	−	0.490106i	$-0.836958\pi$
$719$	1.86499	−	4.08377i	0.0695525	−	0.152299i	0.941215	+	0.337807i	$0.109685\pi$
$720$		0			0
$721$	11.0270	−	76.6943i	0.410666	−	2.85625i
$722$		0			0
$723$	6.51839	+	7.52263i	0.242422	+	0.279770i
$724$		0			0
$725$	−0.504804	+	0.324418i	−0.0187479	+	0.0120486i
$726$		0			0
$727$	−25.1042	+	7.37125i	−0.931062	+	0.273384i	−0.711881	−	0.702300i	$-0.752157\pi$
$727$	−25.1042	+	7.37125i	−0.931062	+	0.273384i	−0.219181	+	0.975684i	$0.570338\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	32.8294	+	9.63959i	1.21424	+	0.356533i
$732$		0			0
$733$	4.67175	+	32.4927i	0.172555	+	1.20015i	0.873461	+	0.486894i	$0.161870\pi$
$733$	4.67175	+	32.4927i	0.172555	+	1.20015i	−0.700906	+	0.713253i	$0.747221\pi$
$734$		0			0
$735$	23.3153			0.859999
$736$		0			0
$737$	−58.0034			−2.13658
$738$		0			0
$739$	1.53138	+	10.6510i	0.0563328	+	0.391803i	0.998408	+	0.0564017i	$0.0179628\pi$
$739$	1.53138	+	10.6510i	0.0563328	+	0.391803i	−0.942075	+	0.335401i	$0.891128\pi$
$740$		0			0
$741$	18.2574	+	5.36085i	0.670702	+	0.196936i
$742$		0			0
$743$	−8.99673	+	10.3828i	−0.330058	+	0.380907i	−0.896387	−	0.443272i	$-0.853818\pi$
$743$	−8.99673	+	10.3828i	−0.330058	+	0.380907i	0.566329	+	0.824179i	$0.308363\pi$
$744$		0			0
$745$	−15.8516	+	4.65446i	−0.580759	+	0.170526i
$746$		0			0
$747$	4.46418	−	2.86895i	0.163336	−	0.104970i
$748$		0			0
$749$	−29.2223	−	33.7244i	−1.06776	−	1.23226i
$750$		0			0
$751$	1.35281	−	9.40898i	0.0493646	−	0.343338i	−0.950139	−	0.311827i	$-0.899059\pi$
$751$	1.35281	−	9.40898i	0.0493646	−	0.343338i	0.999503	−	0.0315111i	$-0.0100319\pi$
$752$		0			0
$753$	4.73627	−	10.3710i	0.172599	−	0.377939i
$754$		0			0
$755$	−8.79262	−	19.2532i	−0.319996	−	0.700694i
$756$		0			0
$757$	34.4271	+	22.1249i	1.25127	+	0.804144i	0.987065	−	0.160322i	$-0.0512531\pi$
$757$	34.4271	+	22.1249i	1.25127	+	0.804144i	0.264208	+	0.964466i	$0.414889\pi$
$758$		0			0
$759$	17.4025	+	15.2548i	0.631671	+	0.553713i
$760$		0			0
$761$	17.7600	+	11.4136i	0.643798	+	0.413744i	0.821395	−	0.570359i	$-0.193196\pi$
$761$	17.7600	+	11.4136i	0.643798	+	0.413744i	−0.177597	+	0.984103i	$0.556832\pi$
$762$		0			0
$763$	2.92970	+	6.41514i	0.106062	+	0.232244i
$764$		0			0
$765$	4.66726	−	10.2199i	0.168745	−	0.369500i
$766$		0			0
$767$	−1.72891	+	12.0248i	−0.0624273	+	0.434191i
$768$		0			0
$769$	−16.4272	−	18.9580i	−0.592380	−	0.683643i	0.377839	−	0.925871i	$-0.376667\pi$
$769$	−16.4272	−	18.9580i	−0.592380	−	0.683643i	−0.970219	+	0.242228i	$0.922122\pi$
$770$		0			0
$771$	22.0109	−	14.1455i	0.792703	−	0.509439i
$772$		0			0
$773$	−25.5088	+	7.49005i	−0.917487	+	0.269399i	−0.706189	−	0.708023i	$-0.749587\pi$
$773$	−25.5088	+	7.49005i	−0.917487	+	0.269399i	−0.211298	+	0.977422i	$0.567769\pi$
$774$		0			0
$775$	−4.02646	+	4.64679i	−0.144635	+	0.166917i
$776$		0			0
$777$	−41.4175	−	12.1613i	−1.48585	−	0.436284i
$778$		0			0
$779$	−4.79402	−	33.3431i	−0.171764	−	1.19464i
$780$		0			0
$781$	−18.2966			−0.654704
$782$		0			0
$783$	−0.499143			−0.0178379
$784$		0			0
$785$	−3.32322	−	23.1135i	−0.118611	−	0.824957i
$786$		0			0
$787$	22.4544	+	6.59320i	0.800412	+	0.235022i	0.656262	−	0.754534i	$-0.272137\pi$
$787$	22.4544	+	6.59320i	0.800412	+	0.235022i	0.144151	+	0.989556i	$0.453955\pi$
$788$		0			0
$789$	19.2160	−	22.1764i	0.684106	−	0.789501i
$790$		0			0
$791$	−67.0475	+	19.6869i	−2.38393	+	0.699986i
$792$		0			0
$793$	5.73803	−	3.68761i	0.203764	−	0.130951i
$794$		0			0
$795$	12.4562	+	14.3752i	0.441775	+	0.509836i
$796$		0			0
$797$	−1.60649	+	11.1734i	−0.0569047	+	0.395781i	0.941386	+	0.337332i	$0.109525\pi$
$797$	−1.60649	+	11.1734i	−0.0569047	+	0.395781i	−0.998290	+	0.0584489i	$0.981385\pi$
$798$		0			0
$799$	−14.3878	+	31.5050i	−0.509005	+	1.11457i
$800$		0			0
$801$	4.63029	+	10.1389i	0.163603	+	0.358241i
$802$		0			0
$803$	30.2567	+	19.4448i	1.06774	+	0.686192i
$804$		0			0
$805$	−36.6924	+	31.4280i	−1.29324	+	1.10769i
$806$		0			0
$807$	−23.7784	−	15.2815i	−0.837041	−	0.537933i
$808$		0			0
$809$	14.3175	+	31.3510i	0.503377	+	1.10224i	0.975357	+	0.220633i	$0.0708123\pi$
$809$	14.3175	+	31.3510i	0.503377	+	1.10224i	−0.471980	+	0.881609i	$0.656460\pi$
$810$		0			0
$811$	−9.81825	+	21.4990i	−0.344765	+	0.754931i	−1.00000		0.000494599i	$-0.999843\pi$
$811$	−9.81825	+	21.4990i	−0.344765	+	0.754931i	0.655234	+	0.755426i	$0.272570\pi$
$812$		0			0
$813$	0.0160994	−	0.111973i	0.000564629	−	0.00392708i
$814$		0			0
$815$	7.90739	+	9.12562i	0.276984	+	0.319656i
$816$		0			0
$817$	28.2652	−	18.1649i	0.988873	−	0.635510i
$818$		0			0
$819$	16.6704	−	4.89487i	0.582511	−	0.171041i
$820$		0			0
$821$	7.23368	−	8.34811i	0.252457	−	0.291351i	−0.615348	−	0.788255i	$-0.710985\pi$
$821$	7.23368	−	8.34811i	0.252457	−	0.291351i	0.867805	+	0.496904i	$0.165530\pi$
$822$		0			0
$823$	−39.7025	−	11.6577i	−1.38394	−	0.406362i	−0.496802	−	0.867864i	$-0.665493\pi$
$823$	−39.7025	−	11.6577i	−1.38394	−	0.406362i	−0.887139	+	0.461502i	$0.847311\pi$
$824$		0			0
$825$	0.825580	+	5.74204i	0.0287430	+	0.199912i
$826$		0			0
$827$	−33.3095			−1.15828			−0.579142	−	0.815227i	$-0.696612\pi$
$827$	−33.3095			−1.15828			−0.579142	+	0.815227i	$0.696612\pi$
$828$		0			0
$829$	−26.7169			−0.927917			−0.463959	−	0.885857i	$-0.653571\pi$
$829$	−26.7169			−0.927917			−0.463959	+	0.885857i	$0.653571\pi$
$830$		0			0
$831$	0.564305	+	3.92483i	0.0195755	+	0.136151i
$832$		0			0
$833$	−40.5246	−	11.8991i	−1.40409	−	0.412279i
$834$		0			0
$835$	21.7815	−	25.1372i	0.753779	−	0.869907i
$836$		0			0
$837$	−4.90734	+	1.44092i	−0.169622	+	0.0498056i
$838$		0			0
$839$	−7.30959	+	4.69759i	−0.252355	+	0.162179i	−0.660703	−	0.750648i	$-0.729742\pi$
$839$	−7.30959	+	4.69759i	−0.252355	+	0.162179i	0.408348	+	0.912827i	$0.366105\pi$
$840$		0			0
$841$	18.8278	+	21.7284i	0.649235	+	0.749257i
$842$		0			0
$843$	2.36766	−	16.4675i	0.0815467	−	0.567170i
$844$		0			0
$845$	5.63727	−	12.3439i	0.193928	−	0.424643i
$846$		0			0
$847$	−20.6431	−	45.2022i	−0.709307	−	1.55317i
$848$		0			0
$849$	−14.2383	−	9.15040i	−0.488657	−	0.314041i
$850$		0			0
$851$	46.6746	−	20.9933i	1.59999	−	0.719642i
$852$		0			0
$853$	21.0828	+	13.5491i	0.721861	+	0.463912i	0.849284	−	0.527937i	$-0.177034\pi$
$853$	21.0828	+	13.5491i	0.721861	+	0.463912i	−0.127423	+	0.991848i	$0.540671\pi$
$854$		0			0
$855$	−4.58316	−	10.0357i	−0.156741	−	0.343215i
$856$		0			0
$857$	9.96621	−	21.8230i	0.340439	−	0.745458i	−0.659541	−	0.751668i	$-0.729249\pi$
$857$	9.96621	−	21.8230i	0.340439	−	0.745458i	0.999981	+	0.00621000i	$0.00197672\pi$
$858$		0			0
$859$	1.08109	−	7.51915i	0.0368863	−	0.256550i	−0.963031	−	0.269390i	$-0.913178\pi$
$859$	1.08109	−	7.51915i	0.0368863	−	0.256550i	0.999918	+	0.0128397i	$0.00408711\pi$
$860$		0			0
$861$	−20.1422	−	23.2453i	−0.686443	−	0.792198i
$862$		0			0
$863$	3.12515	−	2.00841i	0.106381	−	0.0683672i	−0.486368	−	0.873754i	$-0.661679\pi$
$863$	3.12515	−	2.00841i	0.106381	−	0.0683672i	0.592750	+	0.805387i	$0.298042\pi$
$864$		0			0
$865$	−24.3623	+	7.15342i	−0.828343	+	0.243224i
$866$		0			0
$867$	−2.19534	+	2.53355i	−0.0745575	+	0.0860439i
$868$		0			0
$869$	−53.9081	−	15.8289i	−1.82871	−	0.536957i
$870$		0			0
$871$	−7.34771	−	51.1044i	−0.248968	−	1.73161i
$872$		0			0
$873$	7.13353			0.241433
$874$		0			0
$875$	38.2582			1.29336
$876$		0			0
$877$	−4.74616	−	33.0103i	−0.160266	−	1.11468i	−0.898131	−	0.439729i	$-0.855075\pi$
$877$	−4.74616	−	33.0103i	−0.160266	−	1.11468i	0.737864	−	0.674949i	$-0.235834\pi$
$878$		0			0
$879$	−19.6423	−	5.76750i	−0.662518	−	0.194533i
$880$		0			0
$881$	15.9310	−	18.3853i	0.536728	−	0.619417i	−0.421011	−	0.907056i	$-0.638325\pi$
$881$	15.9310	−	18.3853i	0.536728	−	0.619417i	0.957739	+	0.287638i	$0.0928701\pi$
$882$		0			0
$883$	26.9814	−	7.92247i	0.907998	−	0.266612i	0.205800	−	0.978594i	$-0.434020\pi$
$883$	26.9814	−	7.92247i	0.907998	−	0.266612i	0.702198	+	0.711982i	$0.252202\pi$
$884$		0			0
$885$	5.92564	−	3.80818i	0.199188	−	0.128010i
$886$		0			0
$887$	−16.0130	−	18.4800i	−0.537665	−	0.620498i	0.420299	−	0.907385i	$-0.361925\pi$
$887$	−16.0130	−	18.4800i	−0.537665	−	0.620498i	−0.957964	+	0.286887i	$0.907380\pi$
$888$		0			0
$889$	−8.22583	+	57.2119i	−0.275885	+	1.91882i
$890$		0			0
$891$	−2.00457	+	4.38939i	−0.0671555	+	0.147050i
$892$		0			0
$893$	14.1286	+	30.9373i	0.472795	+	1.03528i
$894$		0			0
$895$	12.7451	+	8.19077i	0.426021	+	0.273787i
$896$		0			0
$897$	−11.2358	+	17.2651i	−0.375154	+	0.576464i
$898$		0			0
$899$	−2.14761	−	1.38019i	−0.0716268	−	0.0460318i
$900$		0			0
$901$	−14.3137	−	31.3427i	−0.476860	−	1.04418i
$902$		0			0
$903$	12.7443	−	27.9060i	0.424102	−	0.928654i
$904$		0			0
$905$	1.64580	−	11.4468i	0.0547084	−	0.380505i
$906$		0			0
$907$	−5.09587	−	5.88095i	−0.169206	−	0.195274i	0.664813	−	0.747010i	$-0.268511\pi$
$907$	−5.09587	−	5.88095i	−0.169206	−	0.195274i	−0.834019	+	0.551736i	$0.813966\pi$
$908$		0			0
$909$	−4.44653	+	2.85761i	−0.147482	+	0.0947811i
$910$		0			0
$911$	−33.4926	+	9.83430i	−1.10966	+	0.325825i	−0.784683	−	0.619897i	$-0.787174\pi$
$911$	−33.4926	+	9.83430i	−1.10966	+	0.325825i	−0.324975	+	0.945723i	$0.605356\pi$
$912$		0			0
$913$	16.7688	−	19.3522i	0.554966	−	0.640465i
$914$		0			0
$915$	−3.79459	−	1.11419i	−0.125445	−	0.0368340i
$916$		0			0
$917$	−5.72435	−	39.8138i	−0.189035	−	1.31477i
$918$		0			0
$919$	17.9522			0.592187			0.296093	−	0.955159i	$-0.404316\pi$
$919$	17.9522			0.592187			0.296093	+	0.955159i	$0.404316\pi$
$920$		0			0
$921$	16.8237			0.554360
$922$		0			0
$923$	−2.31776	−	16.1204i	−0.0762900	−	0.530609i
$924$		0			0
$925$	12.3094	+	3.61436i	0.404730	+	0.118840i
$926$		0			0
$927$	−12.5440	+	14.4766i	−0.412000	+	0.475473i
$928$		0			0
$929$	−20.1532	+	5.91751i	−0.661205	+	0.194147i	−0.595083	−	0.803664i	$-0.702881\pi$
$929$	−20.1532	+	5.91751i	−0.661205	+	0.194147i	−0.0661220	+	0.997812i	$0.521063\pi$
$930$		0			0
$931$	−34.8905	+	22.4228i	−1.14349	+	0.734876i
$932$		0			0
$933$	19.5012	+	22.5055i	0.638439	+	0.736798i
$934$		0			0
$935$	7.71557	−	53.6630i	0.252326	−	1.75497i
$936$		0			0
$937$	−10.2393	+	22.4210i	−0.334504	+	0.732462i	−0.999902	−	0.0140270i	$-0.995535\pi$
$937$	−10.2393	+	22.4210i	−0.334504	+	0.732462i	0.665397	+	0.746489i	$0.268262\pi$
$938$		0			0
$939$	−12.5532	−	27.4876i	−0.409657	−	0.897025i
$940$		0			0
$941$	39.2493	+	25.2240i	1.27949	+	0.822279i	0.990825	−	0.135151i	$-0.0431520\pi$
$941$	39.2493	+	25.2240i	1.27949	+	0.822279i	0.288666	+	0.957430i	$0.406788\pi$
$942$		0			0
$943$	36.0657	+	5.39649i	1.17446	+	0.175734i
$944$		0			0
$945$	−8.47457	−	5.44627i	−0.275678	−	0.177167i
$946$		0			0
$947$	10.3997	+	22.7721i	0.337944	+	0.739995i	0.999955	−	0.00949957i	$-0.00302385\pi$
$947$	10.3997	+	22.7721i	0.337944	+	0.739995i	−0.662010	+	0.749495i	$0.730297\pi$
$948$		0			0
$949$	−13.2992	+	29.1211i	−0.431709	+	0.945312i
$950$		0			0
$951$	0.746038	−	5.18881i	0.0241919	−	0.168259i
$952$		0			0
$953$	21.6866	+	25.0277i	0.702499	+	0.810727i	0.989088	−	0.147326i	$-0.0470668\pi$
$953$	21.6866	+	25.0277i	0.702499	+	0.810727i	−0.286589	+	0.958054i	$0.592521\pi$
$954$		0			0
$955$	−24.7344	+	15.8958i	−0.800385	+	0.514376i
$956$		0			0
$957$	−2.31103	+	0.678578i	−0.0747049	+	0.0219353i
$958$		0			0
$959$	−21.5703	+	24.8935i	−0.696542	+	0.803852i
$960$		0			0
$961$	4.64567	+	1.36409i	0.149860	+	0.0440030i
$962$		0			0
$963$	1.56999	+	10.9195i	0.0505923	+	0.351877i
$964$		0			0
$965$	55.6876			1.79265
$966$		0			0
$967$	12.0764			0.388352			0.194176	−	0.980967i	$-0.437797\pi$
$967$	12.0764			0.388352			0.194176	+	0.980967i	$0.437797\pi$
$968$		0			0
$969$	2.84425	+	19.7822i	0.0913706	+	0.635497i
$970$		0			0
$971$	47.4911	+	13.9446i	1.52406	+	0.447505i	0.933227	−	0.359288i	$-0.116980\pi$
$971$	47.4911	+	13.9446i	1.52406	+	0.447505i	0.590834	+	0.806793i	$0.298799\pi$
$972$		0			0
$973$	−26.8343	+	30.9684i	−0.860269	+	0.992803i
$974$		0			0
$975$	−4.95449	+	1.45477i	−0.158671	+	0.0465899i
$976$		0			0
$977$	−18.3854	+	11.8156i	−0.588200	+	0.378013i	−0.800626	−	0.599164i	$-0.795500\pi$
$977$	−18.3854	+	11.8156i	−0.588200	+	0.378013i	0.212427	+	0.977177i	$0.431863\pi$
$978$		0			0
$979$	35.2219	+	40.6483i	1.12570	+	1.29912i
$980$		0			0
$981$	0.248126	−	1.72575i	0.00792205	−	0.0550991i
$982$		0			0
$983$	3.00858	−	6.58788i	0.0959589	−	0.210121i	−0.855565	−	0.517695i	$-0.826790\pi$
$983$	3.00858	−	6.58788i	0.0959589	−	0.210121i	0.951524	+	0.307575i	$0.0995174\pi$
$984$		0			0
$985$	9.37048	+	20.5185i	0.298568	+	0.653774i
$986$		0			0
$987$	26.1247	+	16.7893i	0.831558	+	0.534410i
$988$		0			0
$989$	10.0474	+	34.9577i	0.319487	+	1.11159i
$990$		0			0
$991$	47.3042	+	30.4005i	1.50267	+	0.965705i	0.994533	+	0.104427i	$0.0333008\pi$
$991$	47.3042	+	30.4005i	1.50267	+	0.965705i	0.508134	+	0.861278i	$0.330336\pi$
$992$		0			0
$993$	7.85328	+	17.1963i	0.249216	+	0.545707i
$994$		0			0
$995$	−3.73453	+	8.17747i	−0.118392	+	0.259243i
$996$		0			0
$997$	8.91121	−	61.9788i	0.282221	−	1.96289i	0.0126093	−	0.999920i	$-0.495986\pi$
$997$	8.91121	−	61.9788i	0.282221	−	1.96289i	0.269612	−	0.962969i	$-0.413105\pi$
$998$		0			0
$999$	6.98832	+	8.06495i	0.221101	+	0.255164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.25.1	✓	20
3.2	odd	2		828.2.q.c.577.2		20
23.9	even	11		6348.2.a.s.1.8		10
23.12	even	11	inner	276.2.i.a.265.1	yes	20
23.14	odd	22		6348.2.a.t.1.3		10
69.35	odd	22		828.2.q.c.541.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.25.1	✓	20	1.1	even	1	trivial
276.2.i.a.265.1	yes	20	23.12	even	11	inner
828.2.q.c.541.2		20	69.35	odd	22
828.2.q.c.577.2		20	3.2	odd	2
6348.2.a.s.1.8		10	23.9	even	11
6348.2.a.t.1.3		10	23.14	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{3} +(-2.38954 - 0.701632i) q^{5} +(2.64891 - 3.05701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{3} +(-2.38954 - 0.701632i) q^{5} +(2.64891 - 3.05701i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-4.05943 + 2.60884i) q^{11} +(-2.81278 - 3.24612i) q^{13} +(-0.354423 + 2.46507i) q^{15} +(1.87409 - 4.10368i) q^{17} +(-1.84032 - 4.02974i) q^{19} +(-3.40287 - 2.18689i) q^{21} +(4.75085 - 0.655317i) q^{23} +(1.01134 + 0.649950i) q^{25} +(0.415415 + 0.909632i) q^{27} +(-0.207351 + 0.454036i) q^{29} +(-0.727870 + 5.06245i) q^{31} +(3.16000 + 3.64683i) q^{33} +(-8.47457 + 5.44627i) q^{35} +(10.2392 - 3.00650i) q^{37} +(-2.81278 + 3.24612i) q^{39} +(7.29593 + 2.14228i) q^{41} +(1.07935 + 7.50707i) q^{43} +2.49042 q^{45} -7.67725 q^{47} +(-1.33235 - 9.26672i) q^{49} +(-4.32862 - 1.27100i) q^{51} +(5.00164 - 5.77220i) q^{53} +(11.5306 - 3.38569i) q^{55} +(-3.72681 + 2.39508i) q^{57} +(-1.85219 - 2.13754i) q^{59} +(-0.225996 + 1.57184i) q^{61} +(-1.68035 + 3.67946i) q^{63} +(4.44366 + 9.73025i) q^{65} +(10.1121 + 6.49867i) q^{67} +(-1.32476 - 4.60923i) q^{69} +(3.18977 + 2.04994i) q^{71} +(-3.09627 - 6.77988i) q^{73} +(0.499405 - 1.09354i) q^{75} +(-2.77784 + 19.3203i) q^{77} +(7.62471 + 8.79938i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-5.09163 + 1.49504i) q^{83} +(-7.35747 + 8.49098i) q^{85} +(0.478924 + 0.140625i) q^{87} +(-1.58627 - 11.0327i) q^{89} -17.3742 q^{91} +5.11451 q^{93} +(1.57012 + 10.9204i) q^{95} +(-6.84457 - 2.00975i) q^{97} +(3.16000 - 3.64683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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