LMFDB - Embedded newform 252.3.g.a.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,3,Mod(127,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("252.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1539727.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{3} - 8x + 8 $ x^6 - 2x^5 + 3x^3 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			127.6
Root			$0.841985 - 1.13625i$ of defining polynomial
Character	$\chi$	$=$	252.127
Dual form			252.3.g.a.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92411 + 0.545716i) q^{2} +(3.40439 + 2.10003i) q^{4} -1.36794 q^{5} +2.64575i q^{7} +(5.40439 + 5.89853i) q^{8} +O(q^{10})$	\(q+(1.92411 + 0.545716i) q^{2} +(3.40439 + 2.10003i) q^{4} -1.36794 q^{5} +2.64575i q^{7} +(5.40439 + 5.89853i) q^{8} +(-2.63206 - 0.746506i) q^{10} +15.3073i q^{11} +19.9460 q^{13} +(-1.44383 + 5.09071i) q^{14} +(7.17971 + 14.2987i) q^{16} +4.73588 q^{17} -13.2765i q^{19} +(-4.65699 - 2.87272i) q^{20} +(-8.35343 + 29.4528i) q^{22} -14.9487i q^{23} -23.1287 q^{25} +(38.3784 + 10.8849i) q^{26} +(-5.55617 + 9.00716i) q^{28} -6.20763 q^{29} -18.5385i q^{31} +(6.01152 + 31.4303i) q^{32} +(9.11234 + 2.58445i) q^{34} -3.61922i q^{35} -27.5216 q^{37} +(7.24518 - 25.5453i) q^{38} +(-7.39287 - 8.06882i) q^{40} +11.1064 q^{41} -27.0248i q^{43} +(-32.1458 + 52.1119i) q^{44} +(8.15777 - 28.7630i) q^{46} -30.9731i q^{47} -7.00000 q^{49} +(-44.5022 - 12.6217i) q^{50} +(67.9041 + 41.8874i) q^{52} +12.7857 q^{53} -20.9394i q^{55} +(-15.6060 + 14.2987i) q^{56} +(-11.9442 - 3.38760i) q^{58} -28.8289i q^{59} +6.52415 q^{61} +(10.1168 - 35.6701i) q^{62} +(-5.58519 + 63.7558i) q^{64} -27.2850 q^{65} -102.863i q^{67} +(16.1228 + 9.94551i) q^{68} +(1.97507 - 6.96378i) q^{70} +45.8085i q^{71} -70.0997 q^{73} +(-52.9546 - 15.0190i) q^{74} +(27.8810 - 45.1982i) q^{76} -40.4992 q^{77} +33.3739i q^{79} +(-9.82140 - 19.5597i) q^{80} +(21.3698 + 6.06092i) q^{82} -159.301i q^{83} -6.47839 q^{85} +(14.7478 - 51.9986i) q^{86} +(-90.2903 + 82.7264i) q^{88} +50.0417 q^{89} +52.7723i q^{91} +(31.3929 - 50.8913i) q^{92} +(16.9025 - 59.5955i) q^{94} +18.1614i q^{95} +89.7343 q^{97} +(-13.4688 - 3.82001i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + q^{4} + 4 q^{5} + 13 q^{8}+O(q^{10}) $ 6 * q + q^2 + q^4 + 4 * q^5 + 13 * q^8	$ 6 q + q^{2} + q^{4} + 4 q^{5} + 13 q^{8} - 28 q^{10} + 12 q^{13} - 7 q^{14} + 17 q^{16} + 4 q^{17} + 32 q^{20} + 52 q^{22} - 30 q^{25} + 56 q^{26} - 35 q^{28} + 36 q^{29} + 101 q^{32} + 58 q^{34} + 28 q^{37} + 190 q^{38} + 40 q^{40} + 20 q^{41} - 164 q^{44} + 120 q^{46} - 42 q^{49} - 161 q^{50} + 292 q^{52} - 92 q^{53} + 49 q^{56} - 166 q^{58} - 164 q^{61} - 148 q^{62} - 215 q^{64} + 136 q^{65} - 62 q^{68} + 84 q^{70} - 132 q^{73} - 250 q^{74} - 78 q^{76} - 112 q^{77} - 312 q^{80} - 86 q^{82} - 232 q^{85} + 164 q^{86} - 100 q^{88} - 348 q^{89} + 104 q^{92} - 276 q^{94} + 252 q^{97} - 7 q^{98}+O(q^{100}) $ 6 * q + q^2 + q^4 + 4 * q^5 + 13 * q^8 - 28 * q^10 + 12 * q^13 - 7 * q^14 + 17 * q^16 + 4 * q^17 + 32 * q^20 + 52 * q^22 - 30 * q^25 + 56 * q^26 - 35 * q^28 + 36 * q^29 + 101 * q^32 + 58 * q^34 + 28 * q^37 + 190 * q^38 + 40 * q^40 + 20 * q^41 - 164 * q^44 + 120 * q^46 - 42 * q^49 - 161 * q^50 + 292 * q^52 - 92 * q^53 + 49 * q^56 - 166 * q^58 - 164 * q^61 - 148 * q^62 - 215 * q^64 + 136 * q^65 - 62 * q^68 + 84 * q^70 - 132 * q^73 - 250 * q^74 - 78 * q^76 - 112 * q^77 - 312 * q^80 - 86 * q^82 - 232 * q^85 + 164 * q^86 - 100 * q^88 - 348 * q^89 + 104 * q^92 - 276 * q^94 + 252 * q^97 - 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	1.92411	+	0.545716i	0.962054	+	0.272858i
$2$	1.92411	+	0.545716i	0.962054	+	0.272858i
$3$		0			0
$3$		0			0
$4$	3.40439	+	2.10003i	0.851097	+	0.525009i
$5$	−1.36794			−0.273588			−0.136794	−	0.990600i	$-0.543680\pi$
$5$	−1.36794			−0.273588			−0.136794	+	0.990600i	$0.543680\pi$
$6$		0			0
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	5.40439	+	5.89853i	0.675548	+	0.737316i
$9$		0			0
$10$	−2.63206	−	0.746506i	−0.263206	−	0.0746506i
$11$			15.3073i			1.39157i	0.718250	+	0.695785i	$0.244943\pi$
$11$			15.3073i			1.39157i	−0.718250	+	0.695785i	$0.755057\pi$
$12$		0			0
$13$	19.9460			1.53431			0.767156	−	0.641461i	$-0.221671\pi$
$13$	19.9460			1.53431			0.767156	+	0.641461i	$0.221671\pi$
$14$	−1.44383	+	5.09071i	−0.103131	+	0.363622i
$15$		0			0
$16$	7.17971	+	14.2987i	0.448732	+	0.893667i
$17$	4.73588			0.278581			0.139290	−	0.990252i	$-0.455518\pi$
$17$	4.73588			0.278581			0.139290	+	0.990252i	$0.455518\pi$
$18$		0			0
$19$		−	13.2765i		−	0.698761i	−0.936981	−	0.349380i	$-0.886392\pi$
$19$		−	13.2765i		−	0.698761i	0.936981	−	0.349380i	$-0.113608\pi$
$20$	−4.65699	−	2.87272i	−0.232850	−	0.143636i
$21$		0			0
$22$	−8.35343	+	29.4528i	−0.379701	+	1.33877i
$23$		−	14.9487i		−	0.649945i	−0.945723	−	0.324973i	$-0.894645\pi$
$23$		−	14.9487i		−	0.649945i	0.945723	−	0.324973i	$-0.105355\pi$
$24$		0			0
$25$	−23.1287			−0.925150
$26$	38.3784	+	10.8849i	1.47609	+	0.418649i
$27$		0			0
$28$	−5.55617	+	9.00716i	−0.198435	+	0.321684i
$29$	−6.20763			−0.214056			−0.107028	−	0.994256i	$-0.534133\pi$
$29$	−6.20763			−0.214056			−0.107028	+	0.994256i	$0.534133\pi$
$30$		0			0
$31$		−	18.5385i		−	0.598017i	−0.954251	−	0.299008i	$-0.903344\pi$
$31$		−	18.5385i		−	0.598017i	0.954251	−	0.299008i	$-0.0966558\pi$
$32$	6.01152	+	31.4303i	0.187860	+	0.982196i
$33$		0			0
$34$	9.11234	+	2.58445i	0.268010	+	0.0760131i
$35$		−	3.61922i		−	0.103406i
$36$		0			0
$37$	−27.5216			−0.743827			−0.371914	−	0.928267i	$-0.621298\pi$
$37$	−27.5216			−0.743827			−0.371914	+	0.928267i	$0.621298\pi$
$38$	7.24518	−	25.5453i	0.190663	−	0.672246i
$39$		0			0
$40$	−7.39287	−	8.06882i	−0.184822	−	0.201720i
$41$	11.1064			0.270887			0.135443	−	0.990785i	$-0.456754\pi$
$41$	11.1064			0.270887			0.135443	+	0.990785i	$0.456754\pi$
$42$		0			0
$43$		−	27.0248i		−	0.628483i	−0.949343	−	0.314241i	$-0.898250\pi$
$43$		−	27.0248i		−	0.628483i	0.949343	−	0.314241i	$-0.101750\pi$
$44$	−32.1458	+	52.1119i	−0.730586	+	1.18436i
$45$		0			0
$46$	8.15777	−	28.7630i	0.177343	−	0.625282i
$47$		−	30.9731i		−	0.659001i	−0.944155	−	0.329501i	$-0.893120\pi$
$47$		−	30.9731i		−	0.659001i	0.944155	−	0.329501i	$-0.106880\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−44.5022	−	12.6217i	−0.890044	−	0.252435i
$51$		0			0
$52$	67.9041	+	41.8874i	1.30585	+	0.805527i
$53$	12.7857			0.241240			0.120620	−	0.992699i	$-0.461512\pi$
$53$	12.7857			0.241240			0.120620	+	0.992699i	$0.461512\pi$
$54$		0			0
$55$		−	20.9394i		−	0.380716i
$56$	−15.6060	+	14.2987i	−0.278679	+	0.255333i
$57$		0			0
$58$	−11.9442	−	3.38760i	−0.205934	−	0.0584070i
$59$		−	28.8289i		−	0.488626i	−0.969696	−	0.244313i	$-0.921438\pi$
$59$		−	28.8289i		−	0.488626i	0.969696	−	0.244313i	$-0.0785625\pi$
$60$		0			0
$61$	6.52415			0.106953			0.0534767	−	0.998569i	$-0.482970\pi$
$61$	6.52415			0.106953			0.0534767	+	0.998569i	$0.482970\pi$
$62$	10.1168	−	35.6701i	0.163174	−	0.575324i
$63$		0			0
$64$	−5.58519	+	63.7558i	−0.0872687	+	0.996185i
$65$	−27.2850			−0.419769
$66$		0			0
$67$		−	102.863i		−	1.53526i	−0.640891	−	0.767632i	$-0.721435\pi$
$67$		−	102.863i		−	1.53526i	0.640891	−	0.767632i	$-0.278565\pi$
$68$	16.1228	+	9.94551i	0.237099	+	0.146257i
$69$		0			0
$70$	1.97507	−	6.96378i	0.0282153	−	0.0994826i
$71$			45.8085i			0.645190i	0.946537	+	0.322595i	$0.104555\pi$
$71$			45.8085i			0.645190i	−0.946537	+	0.322595i	$0.895445\pi$
$72$		0			0
$73$	−70.0997			−0.960270			−0.480135	−	0.877195i	$-0.659412\pi$
$73$	−70.0997			−0.960270			−0.480135	+	0.877195i	$0.659412\pi$
$74$	−52.9546	−	15.0190i	−0.715602	−	0.202959i
$75$		0			0
$76$	27.8810	−	45.1982i	0.366856	−	0.594713i
$77$	−40.4992			−0.525964
$78$		0			0
$79$			33.3739i			0.422455i	0.977437	+	0.211228i	$0.0677461\pi$
$79$			33.3739i			0.422455i	−0.977437	+	0.211228i	$0.932254\pi$
$80$	−9.82140	−	19.5597i	−0.122767	−	0.244496i
$81$		0			0
$82$	21.3698	+	6.06092i	0.260608	+	0.0739136i
$83$		−	159.301i		−	1.91930i	−0.281206	−	0.959648i	$-0.590734\pi$
$83$		−	159.301i		−	1.91930i	0.281206	−	0.959648i	$-0.409266\pi$
$84$		0			0
$85$	−6.47839			−0.0762163
$86$	14.7478	−	51.9986i	0.171487	−	0.604634i
$87$		0			0
$88$	−90.2903	+	82.7264i	−1.02603	+	0.940073i
$89$	50.0417			0.562266			0.281133	−	0.959669i	$-0.409290\pi$
$89$	50.0417			0.562266			0.281133	+	0.959669i	$0.409290\pi$
$90$		0			0
$91$			52.7723i			0.579915i
$92$	31.3929	−	50.8913i	0.341227	−	0.553166i
$93$		0			0
$94$	16.9025	−	59.5955i	0.179814	−	0.633995i
$95$			18.1614i			0.191172i
$96$		0			0
$97$	89.7343			0.925096			0.462548	−	0.886594i	$-0.346935\pi$
$97$	89.7343			0.925096			0.462548	+	0.886594i	$0.346935\pi$
$98$	−13.4688	−	3.82001i	−0.137436	−	0.0389797i
$99$		0			0
$100$	−78.7392	−	48.5712i	−0.787392	−	0.485712i
$101$	−162.881			−1.61269			−0.806343	−	0.591448i	$-0.798557\pi$
$101$	−162.881			−1.61269			−0.806343	+	0.591448i	$0.798557\pi$
$102$		0			0
$103$			86.1212i			0.836129i	0.908417	+	0.418064i	$0.137291\pi$
$103$			86.1212i			0.836129i	−0.908417	+	0.418064i	$0.862709\pi$
$104$	107.796	+	117.652i	1.03650	+	1.13127i
$105$		0			0
$106$	24.6011	+	6.97739i	0.232086	+	0.0658244i
$107$			102.146i			0.954632i	0.878732	+	0.477316i	$0.158390\pi$
$107$			102.146i			0.954632i	−0.878732	+	0.477316i	$0.841610\pi$
$108$		0			0
$109$	152.037			1.39483			0.697416	−	0.716667i	$-0.254333\pi$
$109$	152.037			1.39483			0.697416	+	0.716667i	$0.254333\pi$
$110$	11.4270	−	40.2897i	0.103882	−	0.366270i
$111$		0			0
$112$	−37.8307	+	18.9957i	−0.337774	+	0.169605i
$113$	168.112			1.48772			0.743860	−	0.668335i	$-0.232993\pi$
$113$	168.112			1.48772			0.743860	+	0.668335i	$0.232993\pi$
$114$		0			0
$115$			20.4489i			0.177817i
$116$	−21.1332	−	13.0362i	−0.182183	−	0.112381i
$117$		0			0
$118$	15.7324	−	55.4700i	0.133326	−	0.470085i
$119$			12.5300i			0.105294i
$120$		0			0
$121$	−113.312			−0.936466
$122$	12.5532	+	3.56034i	0.102895	+	0.0291831i
$123$		0			0
$124$	38.9315	−	63.1123i	0.313964	−	0.508970i
$125$	65.8372			0.526697
$126$		0			0
$127$		−	87.8953i		−	0.692089i	−0.938218	−	0.346044i	$-0.887525\pi$
$127$		−	87.8953i		−	0.692089i	0.938218	−	0.346044i	$-0.112475\pi$
$128$	−45.5391	+	119.625i	−0.355774	+	0.934572i
$129$		0			0
$130$	−52.4992	−	14.8898i	−0.403840	−	0.114537i
$131$		−	140.141i		−	1.06978i	−0.844923	−	0.534888i	$-0.820354\pi$
$131$		−	140.141i		−	1.06978i	0.844923	−	0.534888i	$-0.179646\pi$
$132$		0			0
$133$	35.1262			0.264107
$134$	56.1338	−	197.919i	0.418909	−	1.47701i
$135$		0			0
$136$	25.5945	+	27.9347i	0.188195	+	0.205402i
$137$	−118.725			−0.866603			−0.433301	−	0.901249i	$-0.642651\pi$
$137$	−118.725			−0.866603			−0.433301	+	0.901249i	$0.642651\pi$
$138$		0			0
$139$		−	72.1046i		−	0.518738i	−0.965778	−	0.259369i	$-0.916485\pi$
$139$		−	72.1046i		−	0.518738i	0.965778	−	0.259369i	$-0.0835147\pi$
$140$	7.60050	−	12.3212i	0.0542893	−	0.0880089i
$141$		0			0
$142$	−24.9984	+	88.1405i	−0.176045	+	0.620708i
$143$			305.319i			2.13510i
$144$		0			0
$145$	8.49165			0.0585631
$146$	−134.879	−	38.2546i	−0.923832	−	0.262018i
$147$		0			0
$148$	−93.6942	−	57.7963i	−0.633069	−	0.390516i
$149$	−218.299			−1.46510			−0.732548	−	0.680716i	$-0.761669\pi$
$149$	−218.299			−1.46510			−0.732548	+	0.680716i	$0.761669\pi$
$150$		0			0
$151$			180.946i			1.19832i	0.800629	+	0.599160i	$0.204499\pi$
$151$			180.946i			1.19832i	−0.800629	+	0.599160i	$0.795501\pi$
$152$	78.3115	−	71.7511i	0.515207	−	0.472047i
$153$		0			0
$154$	−77.9249	−	22.1011i	−0.506006	−	0.143514i
$155$			25.3595i			0.163610i
$156$		0			0
$157$	−191.081			−1.21708			−0.608538	−	0.793525i	$-0.708244\pi$
$157$	−191.081			−1.21708			−0.608538	+	0.793525i	$0.708244\pi$
$158$	−18.2127	+	64.2151i	−0.115270	+	0.406425i
$159$		0			0
$160$	−8.22339	−	42.9947i	−0.0513962	−	0.268717i
$161$	39.5506			0.245656
$162$		0			0
$163$			287.743i			1.76530i	0.470035	+	0.882648i	$0.344241\pi$
$163$			287.743i			1.76530i	−0.470035	+	0.882648i	$0.655759\pi$
$164$	37.8103	+	23.3237i	0.230551	+	0.142218i
$165$		0			0
$166$	86.9334	−	306.513i	0.523695	−	1.84647i
$167$			124.859i			0.747659i	0.927497	+	0.373829i	$0.121955\pi$
$167$			124.859i			0.747659i	−0.927497	+	0.373829i	$0.878045\pi$
$168$		0			0
$169$	228.845			1.35411
$170$	−12.4651	−	3.53536i	−0.0733242	−	0.0207962i
$171$		0			0
$172$	56.7529	−	92.0027i	0.329959	−	0.534900i
$173$	275.207			1.59079			0.795396	−	0.606090i	$-0.207263\pi$
$173$	275.207			1.59079			0.795396	+	0.606090i	$0.207263\pi$
$174$		0			0
$175$		−	61.1929i		−	0.349674i
$176$	−218.873	+	109.902i	−1.24360	+	0.624441i
$177$		0			0
$178$	96.2856	+	27.3086i	0.540930	+	0.153419i
$179$			7.42479i			0.0414792i	0.999785	+	0.0207396i	$0.00660210\pi$
$179$			7.42479i			0.0414792i	−0.999785	+	0.0207396i	$0.993398\pi$
$180$		0			0
$181$	99.5623			0.550068			0.275034	−	0.961435i	$-0.411311\pi$
$181$	99.5623			0.550068			0.275034	+	0.961435i	$0.411311\pi$
$182$	−28.7987	+	101.540i	−0.158235	+	0.557910i
$183$		0			0
$184$	88.1755	−	80.7888i	0.479215	−	0.439069i
$185$	37.6479			0.203502
$186$		0			0
$187$			72.4933i			0.387665i
$188$	65.0445	−	105.444i	0.345981	−	0.560874i
$189$		0			0
$190$	−9.91096	+	34.9445i	−0.0521629	+	0.183918i
$191$			58.2058i			0.304743i	0.988323	+	0.152371i	$0.0486909\pi$
$191$			58.2058i			0.304743i	−0.988323	+	0.152371i	$0.951309\pi$
$192$		0			0
$193$	−103.881			−0.538246			−0.269123	−	0.963106i	$-0.586734\pi$
$193$	−103.881			−0.538246			−0.269123	+	0.963106i	$0.586734\pi$
$194$	172.659	+	48.9695i	0.889993	+	0.252420i
$195$		0			0
$196$	−23.8307	−	14.7002i	−0.121585	−	0.0750012i
$197$	181.201			0.919802			0.459901	−	0.887970i	$-0.347885\pi$
$197$	181.201			0.919802			0.459901	+	0.887970i	$0.347885\pi$
$198$		0			0
$199$			217.919i			1.09507i	0.836783	+	0.547535i	$0.184434\pi$
$199$			217.919i			1.09507i	−0.836783	+	0.547535i	$0.815566\pi$
$200$	−124.997	−	136.425i	−0.624983	−	0.682127i
$201$		0			0
$202$	−313.401	−	88.8870i	−1.55149	−	0.440035i
$203$		−	16.4238i		−	0.0809056i
$204$		0			0
$205$	−15.1928			−0.0741113
$206$	−46.9978	+	165.707i	−0.228145	+	0.804401i
$207$		0			0
$208$	143.207	+	285.202i	0.688494	+	1.37116i
$209$	203.226			0.972375
$210$		0			0
$211$		−	107.401i		−	0.509007i	−0.967072	−	0.254504i	$-0.918088\pi$
$211$		−	107.401i		−	0.509007i	0.967072	−	0.254504i	$-0.0819121\pi$
$212$	43.5276	+	26.8505i	0.205319	+	0.126653i
$213$		0			0
$214$	−55.7425	+	196.539i	−0.260479	+	0.918407i
$215$			36.9682i			0.171945i
$216$		0			0
$217$	49.0483			0.226029
$218$	292.535	+	82.9689i	1.34190	+	0.380591i
$219$		0			0
$220$	43.9735	−	71.2858i	0.199879	−	0.324026i
$221$	94.4620			0.427430
$222$		0			0
$223$			349.685i			1.56809i	0.620702	+	0.784047i	$0.286848\pi$
$223$			349.685i			1.56809i	−0.620702	+	0.784047i	$0.713152\pi$
$224$	−83.1567	+	15.9050i	−0.371235	+	0.0710044i
$225$		0			0
$226$	323.466	+	91.7417i	1.43127	+	0.405937i
$227$			18.3421i			0.0808020i	0.999184	+	0.0404010i	$0.0128635\pi$
$227$			18.3421i			0.0808020i	−0.999184	+	0.0404010i	$0.987136\pi$
$228$		0			0
$229$	68.5444			0.299320			0.149660	−	0.988737i	$-0.452182\pi$
$229$	68.5444			0.299320			0.149660	+	0.988737i	$0.452182\pi$
$230$	−11.1593	+	39.3460i	−0.0485188	+	0.171070i
$231$		0			0
$232$	−33.5484	−	36.6159i	−0.144605	−	0.157827i
$233$	−61.4788			−0.263858			−0.131929	−	0.991259i	$-0.542117\pi$
$233$	−61.4788			−0.263858			−0.131929	+	0.991259i	$0.542117\pi$
$234$		0			0
$235$			42.3692i			0.180295i
$236$	60.5418	−	98.1449i	0.256533	−	0.415868i
$237$		0			0
$238$	−6.83780	+	24.1090i	−0.0287302	+	0.101298i
$239$		−	204.645i		−	0.856256i	−0.903718	−	0.428128i	$-0.859173\pi$
$239$		−	204.645i		−	0.856256i	0.903718	−	0.428128i	$-0.140827\pi$
$240$		0			0
$241$	−389.266			−1.61521			−0.807606	−	0.589723i	$-0.799237\pi$
$241$	−389.266			−1.61521			−0.807606	+	0.589723i	$0.799237\pi$
$242$	−218.025	−	61.8364i	−0.900931	−	0.255522i
$243$		0			0
$244$	22.2107	+	13.7009i	0.0910276	+	0.0561514i
$245$	9.57557			0.0390840
$246$		0			0
$247$		−	264.813i		−	1.07212i
$248$	109.350	−	100.189i	0.440927	−	0.403989i
$249$		0			0
$250$	126.678	+	35.9284i	0.506711	+	0.143714i
$251$			115.082i			0.458494i	0.973368	+	0.229247i	$0.0736264\pi$
$251$			115.082i			0.458494i	−0.973368	+	0.229247i	$0.926374\pi$
$252$		0			0
$253$	228.824			0.904444
$254$	47.9659	−	169.120i	0.188842	−	0.665827i
$255$		0			0
$256$	−152.904	+	205.320i	−0.597280	+	0.802033i
$257$	−337.233			−1.31219			−0.656094	−	0.754679i	$-0.727793\pi$
$257$	−337.233			−1.31219			−0.656094	+	0.754679i	$0.727793\pi$
$258$		0			0
$259$		−	72.8153i		−	0.281140i
$260$	−92.8886	−	57.2994i	−0.357264	−	0.220382i
$261$		0			0
$262$	76.4770	−	269.646i	0.291897	−	1.02918i
$263$			163.729i			0.622543i	0.950321	+	0.311271i	$0.100755\pi$
$263$			163.729i			0.622543i	−0.950321	+	0.311271i	$0.899245\pi$
$264$		0			0
$265$	−17.4901			−0.0660004
$266$	67.5866	+	19.1689i	0.254085	+	0.0720637i
$267$		0			0
$268$	216.015	−	350.184i	0.806027	−	1.30666i
$269$	−290.784			−1.08098			−0.540490	−	0.841350i	$-0.681761\pi$
$269$	−290.784			−1.08098			−0.540490	+	0.841350i	$0.681761\pi$
$270$		0			0
$271$		−	368.628i		−	1.36025i	−0.733096	−	0.680126i	$-0.761925\pi$
$271$		−	368.628i		−	1.36025i	0.733096	−	0.680126i	$-0.238075\pi$
$272$	34.0022	+	67.7167i	0.125008	+	0.248958i
$273$		0			0
$274$	−228.439	−	64.7899i	−0.833719	−	0.236460i
$275$		−	354.038i		−	1.28741i
$276$		0			0
$277$	254.425			0.918503			0.459252	−	0.888306i	$-0.348118\pi$
$277$	254.425			0.918503			0.459252	+	0.888306i	$0.348118\pi$
$278$	39.3487	−	138.737i	0.141542	−	0.499055i
$279$		0			0
$280$	21.3481	−	19.5597i	0.0762432	−	0.0698560i
$281$	−146.631			−0.521819			−0.260909	−	0.965363i	$-0.584022\pi$
$281$	−146.631			−0.521819			−0.260909	+	0.965363i	$0.584022\pi$
$282$		0			0
$283$		−	191.554i		−	0.676868i	−0.940990	−	0.338434i	$-0.890103\pi$
$283$		−	191.554i		−	0.676868i	0.940990	−	0.338434i	$-0.109897\pi$
$284$	−96.1994	+	155.950i	−0.338730	+	0.549119i
$285$		0			0
$286$	−166.618	+	587.468i	−0.582580	+	2.05408i
$287$			29.3847i			0.102386i
$288$		0			0
$289$	−266.571			−0.922393
$290$	16.3389	+	4.63403i	0.0563409	+	0.0159794i
$291$		0			0
$292$	−238.647	−	147.212i	−0.817283	−	0.504150i
$293$	−315.496			−1.07678			−0.538389	−	0.842696i	$-0.680967\pi$
$293$	−315.496			−1.07678			−0.538389	+	0.842696i	$0.680967\pi$
$294$		0			0
$295$			39.4362i			0.133682i
$296$	−148.737	−	162.337i	−0.502491	−	0.548436i
$297$		0			0
$298$	−420.031	−	119.129i	−1.40950	−	0.399763i
$299$		−	298.168i		−	0.997218i
$300$		0			0
$301$	71.5008			0.237544
$302$	−98.7454	+	348.161i	−0.326972	+	1.15285i
$303$		0			0
$304$	189.836	−	95.3211i	0.624459	−	0.313556i
$305$	−8.92464			−0.0292611
$306$		0			0
$307$		−	452.508i		−	1.47397i	−0.675911	−	0.736983i	$-0.736250\pi$
$307$		−	452.508i		−	1.47397i	0.675911	−	0.736983i	$-0.263750\pi$
$308$	−137.875	−	85.0498i	−0.447646	−	0.276136i
$309$		0			0
$310$	−13.8391	+	48.7945i	−0.0446423	+	0.157402i
$311$		−	477.817i		−	1.53639i	−0.640217	−	0.768194i	$-0.721155\pi$
$311$		−	477.817i		−	1.53639i	0.640217	−	0.768194i	$-0.278845\pi$
$312$		0			0
$313$	209.435			0.669122			0.334561	−	0.942374i	$-0.391412\pi$
$313$	209.435			0.669122			0.334561	+	0.942374i	$0.391412\pi$
$314$	−367.660	−	104.276i	−1.17089	−	0.332089i
$315$		0			0
$316$	−70.0865	+	113.618i	−0.221793	+	0.359550i
$317$	−1.74873			−0.00551651			−0.00275825	−	0.999996i	$-0.500878\pi$
$317$	−1.74873			−0.00551651			−0.00275825	+	0.999996i	$0.500878\pi$
$318$		0			0
$319$		−	95.0218i		−	0.297874i
$320$	7.64020	−	87.2140i	0.0238756	−	0.272544i
$321$		0			0
$322$	76.0997	+	21.5834i	0.236335	+	0.0670293i
$323$		−	62.8757i		−	0.194662i
$324$		0			0
$325$	−461.327			−1.41947
$326$	−157.026	+	553.649i	−0.481675	+	1.69831i
$327$		0			0
$328$	60.0230	+	65.5111i	0.182997	+	0.199729i
$329$	81.9470			0.249079
$330$		0			0
$331$		−	375.049i		−	1.13308i	−0.824035	−	0.566539i	$-0.808282\pi$
$331$		−	375.049i		−	1.13308i	0.824035	−	0.566539i	$-0.191718\pi$
$332$	334.539	−	542.324i	1.00765	−	1.63351i
$333$		0			0
$334$	−68.1376	+	240.242i	−0.204005	+	0.719288i
$335$			140.710i			0.420029i
$336$		0			0
$337$	254.740			0.755906			0.377953	−	0.925825i	$-0.376628\pi$
$337$	254.740			0.755906			0.377953	+	0.925825i	$0.376628\pi$
$338$	440.322	+	124.884i	1.30273	+	0.369480i
$339$		0			0
$340$	−22.0549	−	13.6048i	−0.0648675	−	0.0400142i
$341$	283.774			0.832182
$342$		0			0
$343$		−	18.5203i		−	0.0539949i
$344$	159.406	−	146.052i	0.463390	−	0.424570i
$345$		0			0
$346$	529.528	+	150.185i	1.53043	+	0.434061i
$347$		−	511.422i		−	1.47384i	−0.675981	−	0.736919i	$-0.736280\pi$
$347$		−	511.422i		−	1.47384i	0.675981	−	0.736919i	$-0.263720\pi$
$348$		0			0
$349$	−383.129			−1.09779			−0.548895	−	0.835891i	$-0.684951\pi$
$349$	−383.129			−1.09779			−0.548895	+	0.835891i	$0.684951\pi$
$350$	33.3940	−	117.742i	0.0954113	−	0.336405i
$351$		0			0
$352$	−481.111	+	92.0199i	−1.36679	+	0.261420i
$353$	−217.384			−0.615819			−0.307909	−	0.951416i	$-0.599629\pi$
$353$	−217.384			−0.615819			−0.307909	+	0.951416i	$0.599629\pi$
$354$		0			0
$355$		−	62.6632i		−	0.176516i
$356$	170.361	+	105.089i	0.478543	+	0.295195i
$357$		0			0
$358$	−4.05183	+	14.2861i	−0.0113180	+	0.0399053i
$359$			483.099i			1.34568i	0.739788	+	0.672840i	$0.234926\pi$
$359$			483.099i			1.34568i	−0.739788	+	0.672840i	$0.765074\pi$
$360$		0			0
$361$	184.736			0.511733
$362$	191.569	+	54.3328i	0.529195	+	0.150091i
$363$		0			0
$364$	−110.824	+	179.657i	−0.304461	+	0.493564i
$365$	95.8921			0.262718
$366$		0			0
$367$			470.944i			1.28323i	0.767028	+	0.641614i	$0.221735\pi$
$367$			470.944i			1.28323i	−0.767028	+	0.641614i	$0.778265\pi$
$368$	213.747	−	107.328i	0.580834	−	0.291651i
$369$		0			0
$370$	72.4386	+	20.5451i	0.195780	+	0.0555272i
$371$			33.8279i			0.0911803i
$372$		0			0
$373$	−179.535			−0.481326			−0.240663	−	0.970609i	$-0.577365\pi$
$373$	−179.535			−0.481326			−0.240663	+	0.970609i	$0.577365\pi$
$374$	−39.5608	+	139.485i	−0.105778	+	0.372955i
$375$		0			0
$376$	182.695	−	167.390i	0.485892	−	0.445187i
$377$	−123.818			−0.328429
$378$		0			0
$379$		−	87.8468i		−	0.231786i	−0.993262	−	0.115893i	$-0.963027\pi$
$379$		−	87.8468i		−	0.231786i	0.993262	−	0.115893i	$-0.0369729\pi$
$380$	−38.1395	+	61.8284i	−0.100367	+	0.162706i
$381$		0			0
$382$	−31.7639	+	111.994i	−0.0831515	+	0.293179i
$383$			653.584i			1.70649i	0.521513	+	0.853243i	$0.325368\pi$
$383$			653.584i			1.70649i	−0.521513	+	0.853243i	$0.674632\pi$
$384$		0			0
$385$	55.4004			0.143897
$386$	−199.879	−	56.6898i	−0.517822	−	0.146865i
$387$		0			0
$388$	305.490	+	188.445i	0.787346	+	0.485684i
$389$	168.861			0.434090			0.217045	−	0.976162i	$-0.430358\pi$
$389$	168.861			0.434090			0.217045	+	0.976162i	$0.430358\pi$
$390$		0			0
$391$		−	70.7954i		−	0.181062i
$392$	−37.8307	−	41.2897i	−0.0965069	−	0.105331i
$393$		0			0
$394$	348.650	+	98.8843i	0.884899	+	0.250975i
$395$		−	45.6535i		−	0.115578i
$396$		0			0
$397$	−691.521			−1.74187			−0.870934	−	0.491401i	$-0.836485\pi$
$397$	−691.521			−1.74187			−0.870934	+	0.491401i	$0.836485\pi$
$398$	−118.922	+	419.300i	−0.298799	+	1.05352i
$399$		0			0
$400$	−166.058	−	330.710i	−0.415144	−	0.826775i
$401$	399.834			0.997091			0.498546	−	0.866864i	$-0.333868\pi$
$401$	399.834			0.997091			0.498546	+	0.866864i	$0.333868\pi$
$402$		0			0
$403$		−	369.770i		−	0.917544i
$404$	−554.511	−	342.057i	−1.37255	−	0.846675i
$405$		0			0
$406$	8.96276	−	31.6013i	0.0220758	−	0.0778356i
$407$		−	421.281i		−	1.03509i
$408$		0			0
$409$	111.079			0.271586			0.135793	−	0.990737i	$-0.456642\pi$
$409$	111.079			0.271586			0.135793	+	0.990737i	$0.456642\pi$
$410$	−29.2326	−	8.29096i	−0.0712990	−	0.0202219i
$411$		0			0
$412$	−180.858	+	293.190i	−0.438975	+	0.711626i
$413$	76.2742			0.184683
$414$		0			0
$415$			217.915i			0.525095i
$416$	119.906	+	626.910i	0.288236	+	1.50699i
$417$		0			0
$418$	391.029	+	110.904i	0.935477	+	0.265320i
$419$		−	641.986i		−	1.53219i	−0.642729	−	0.766094i	$-0.722198\pi$
$419$		−	641.986i		−	1.53219i	0.642729	−	0.766094i	$-0.277802\pi$
$420$		0			0
$421$	151.970			0.360975			0.180487	−	0.983577i	$-0.442233\pi$
$421$	151.970			0.360975			0.180487	+	0.983577i	$0.442233\pi$
$422$	58.6102	−	206.650i	0.138887	−	0.489693i
$423$		0			0
$424$	69.0991	+	75.4170i	0.162970	+	0.177870i
$425$	−109.535			−0.257729
$426$		0			0
$427$			17.2613i			0.0404246i
$428$	−214.509	+	347.743i	−0.501190	+	0.812484i
$429$		0			0
$430$	−20.1741	+	71.1308i	−0.0469166	+	0.165421i
$431$			459.854i			1.06695i	0.845817	+	0.533473i	$0.179113\pi$
$431$			459.854i			1.06695i	−0.845817	+	0.533473i	$0.820887\pi$
$432$		0			0
$433$	534.370			1.23411			0.617056	−	0.786919i	$-0.288325\pi$
$433$	534.370			1.23411			0.617056	+	0.786919i	$0.288325\pi$
$434$	94.3743	+	26.7665i	0.217452	+	0.0616739i
$435$		0			0
$436$	517.591	+	319.282i	1.18714	+	0.732299i
$437$	−198.466			−0.454156
$438$		0			0
$439$		−	201.259i		−	0.458449i	−0.973374	−	0.229224i	$-0.926381\pi$
$439$		−	201.259i		−	0.458449i	0.973374	−	0.229224i	$-0.0736189\pi$
$440$	123.512	−	113.165i	0.280708	−	0.257192i
$441$		0			0
$442$	181.755	+	51.5495i	0.411211	+	0.116628i
$443$			73.4928i			0.165898i	0.996554	+	0.0829490i	$0.0264339\pi$
$443$			73.4928i			0.165898i	−0.996554	+	0.0829490i	$0.973566\pi$
$444$		0			0
$445$	−68.4539			−0.153829
$446$	−190.829	+	672.832i	−0.427867	+	1.50859i
$447$		0			0
$448$	−168.682	−	14.7770i	−0.376522	−	0.0329845i
$449$	41.4382			0.0922899			0.0461450	−	0.998935i	$-0.485306\pi$
$449$	41.4382			0.0922899			0.0461450	+	0.998935i	$0.485306\pi$
$450$		0			0
$451$			170.008i			0.376958i
$452$	572.320	+	353.042i	1.26619	+	0.781066i
$453$		0			0
$454$	−10.0096	+	35.2921i	−0.0220475	+	0.0777359i
$455$		−	72.1892i		−	0.158658i
$456$		0			0
$457$	270.205			0.591258			0.295629	−	0.955303i	$-0.404471\pi$
$457$	270.205			0.591258			0.295629	+	0.955303i	$0.404471\pi$
$458$	131.887	+	37.4058i	0.287962	+	0.0816720i
$459$		0			0
$460$	−42.9435	+	69.6161i	−0.0933554	+	0.151339i
$461$	735.133			1.59465			0.797324	−	0.603552i	$-0.206248\pi$
$461$	735.133			1.59465			0.797324	+	0.603552i	$0.206248\pi$
$462$		0			0
$463$			742.356i			1.60336i	0.597753	+	0.801681i	$0.296060\pi$
$463$			742.356i			1.60336i	−0.597753	+	0.801681i	$0.703940\pi$
$464$	−44.5690	−	88.7608i	−0.0960538	−	0.191295i
$465$		0			0
$466$	−118.292	−	33.5500i	−0.253845	−	0.0719957i
$467$			402.152i			0.861140i	0.902557	+	0.430570i	$0.141687\pi$
$467$			402.152i			0.861140i	−0.902557	+	0.430570i	$0.858313\pi$
$468$		0			0
$469$	272.149			0.580275
$470$	−23.1216	+	81.5230i	−0.0491949	+	0.173453i
$471$		0			0
$472$	170.048	−	155.803i	0.360272	−	0.330091i
$473$	413.675			0.874577
$474$		0			0
$475$			307.068i			0.646459i
$476$	−26.3133	+	42.6568i	−0.0552801	+	0.0896151i
$477$		0			0
$478$	111.678	−	393.760i	0.233636	−	0.823765i
$479$			356.741i			0.744763i	0.928080	+	0.372381i	$0.121459\pi$
$479$			356.741i			0.744763i	−0.928080	+	0.372381i	$0.878541\pi$
$480$		0			0
$481$	−548.947			−1.14126
$482$	−748.990	−	212.429i	−1.55392	−	0.440724i
$483$		0			0
$484$	−385.759	−	237.960i	−0.797024	−	0.491653i
$485$	−122.751			−0.253095
$486$		0			0
$487$		−	121.123i		−	0.248713i	−0.992238	−	0.124356i	$-0.960313\pi$
$487$		−	121.123i		−	0.248713i	0.992238	−	0.124356i	$-0.0396866\pi$
$488$	35.2590	+	38.4829i	0.0722521	+	0.0788584i
$489$		0			0
$490$	18.4244	+	5.22554i	0.0376009	+	0.0106644i
$491$			18.4535i			0.0375835i	0.999823	+	0.0187917i	$0.00598195\pi$
$491$			18.4535i			0.0375835i	−0.999823	+	0.0187917i	$0.994018\pi$
$492$		0			0
$493$	−29.3986			−0.0596320
$494$	144.513	−	509.529i	0.292536	−	1.03143i
$495$		0			0
$496$	265.076	−	133.101i	0.534427	−	0.268349i
$497$	−121.198			−0.243859
$498$		0			0
$499$			149.571i			0.299742i	0.988706	+	0.149871i	$0.0478859\pi$
$499$			149.571i			0.299742i	−0.988706	+	0.149871i	$0.952114\pi$
$500$	224.135	+	138.260i	0.448270	+	0.276521i
$501$		0			0
$502$	−62.8022	+	221.430i	−0.125104	+	0.441097i
$503$			651.239i			1.29471i	0.762189	+	0.647354i	$0.224125\pi$
$503$			651.239i			1.29471i	−0.762189	+	0.647354i	$0.775875\pi$
$504$		0			0
$505$	222.812			0.441211
$506$	440.283	+	124.873i	0.870124	+	0.246785i
$507$		0			0
$508$	184.583	−	299.230i	0.363353	−	0.589035i
$509$	−817.972			−1.60702			−0.803509	−	0.595293i	$-0.797036\pi$
$509$	−817.972			−1.60702			−0.803509	+	0.595293i	$0.797036\pi$
$510$		0			0
$511$		−	185.466i		−	0.362948i
$512$	−406.250	+	311.617i	−0.793457	+	0.608627i
$513$		0			0
$514$	−648.872	−	184.033i	−1.26240	−	0.358041i
$515$		−	117.809i		−	0.228754i
$516$		0			0
$517$	474.113			0.917046
$518$	39.7365	−	140.105i	0.0767114	−	0.270472i
$519$		0			0
$520$	−147.458	−	160.941i	−0.283574	−	0.309502i
$521$	173.603			0.333211			0.166606	−	0.986024i	$-0.446719\pi$
$521$	173.603			0.333211			0.166606	+	0.986024i	$0.446719\pi$
$522$		0			0
$523$			680.630i			1.30139i	0.759337	+	0.650697i	$0.225523\pi$
$523$			680.630i			1.30139i	−0.759337	+	0.650697i	$0.774477\pi$
$524$	294.300	−	477.093i	0.561642	−	0.910483i
$525$		0			0
$526$	−89.3494	+	315.032i	−0.169866	+	0.598920i
$527$		−	87.7961i		−	0.166596i
$528$		0			0
$529$	305.535			0.577571
$530$	−33.6528	−	9.54463i	−0.0634959	−	0.0180087i
$531$		0			0
$532$	119.583	+	73.7663i	0.224780	+	0.138658i
$533$	221.528			0.415624
$534$		0			0
$535$		−	139.729i		−	0.261175i
$536$	606.738	−	555.910i	1.13197	−	1.03714i
$537$		0			0
$538$	−559.499	−	158.685i	−1.03996	−	0.294954i
$539$		−	107.151i		−	0.198796i
$540$		0			0
$541$	−313.190			−0.578909			−0.289454	−	0.957192i	$-0.593474\pi$
$541$	−313.190			−0.578909			−0.289454	+	0.957192i	$0.593474\pi$
$542$	201.166	−	709.280i	0.371156	−	1.30864i
$543$		0			0
$544$	28.4698	+	148.850i	0.0523342	+	0.273621i
$545$	−207.977			−0.381609
$546$		0			0
$547$		−	352.784i		−	0.644944i	−0.946579	−	0.322472i	$-0.895486\pi$
$547$		−	352.784i		−	0.644944i	0.946579	−	0.322472i	$-0.104514\pi$
$548$	−404.184	−	249.326i	−0.737563	−	0.454974i
$549$		0			0
$550$	193.204	−	681.207i	0.351280	−	1.23856i
$551$			82.4153i			0.149574i
$552$		0			0
$553$	−88.2992			−0.159673
$554$	489.542	+	138.844i	0.883650	+	0.250621i
$555$		0			0
$556$	151.422	−	245.472i	0.272342	−	0.441497i
$557$	135.925			0.244030			0.122015	−	0.992528i	$-0.461064\pi$
$557$	135.925			0.244030			0.122015	+	0.992528i	$0.461064\pi$
$558$		0			0
$559$		−	539.037i		−	0.964288i
$560$	51.7501	−	25.9850i	0.0924109	−	0.0464017i
$561$		0			0
$562$	−282.134	−	80.0190i	−0.502018	−	0.142383i
$563$			160.363i			0.284836i	0.989807	+	0.142418i	$0.0454878\pi$
$563$			160.363i			0.284836i	−0.989807	+	0.142418i	$0.954512\pi$
$564$		0			0
$565$	−229.967			−0.407022
$566$	104.534	−	368.570i	0.184689	−	0.651184i
$567$		0			0
$568$	−270.203	+	247.567i	−0.475709	+	0.435857i
$569$	−611.297			−1.07434			−0.537168	−	0.843475i	$-0.680506\pi$
$569$	−611.297			−1.07434			−0.537168	+	0.843475i	$0.680506\pi$
$570$		0			0
$571$			286.952i			0.502542i	0.967917	+	0.251271i	$0.0808486\pi$
$571$			286.952i			0.502542i	−0.967917	+	0.251271i	$0.919151\pi$
$572$	−641.182	+	1039.43i	−1.12095	+	1.81718i
$573$		0			0
$574$	−16.0357	+	56.5393i	−0.0279367	+	0.0985004i
$575$			345.746i			0.601297i
$576$		0			0
$577$	−530.428			−0.919286			−0.459643	−	0.888104i	$-0.652023\pi$
$577$	−530.428			−0.919286			−0.459643	+	0.888104i	$0.652023\pi$
$578$	−512.912	−	145.472i	−0.887392	−	0.251682i
$579$		0			0
$580$	28.9089	+	17.8328i	0.0498429	+	0.0307462i
$581$	421.472			0.725425
$582$		0			0
$583$			195.715i			0.335703i
$584$	−378.846	−	413.485i	−0.648709	−	0.708022i
$585$		0			0
$586$	−607.049	−	172.171i	−1.03592	−	0.293808i
$587$		−	10.9359i		−	0.0186301i	−0.999957	−	0.00931506i	$-0.997035\pi$
$587$		−	10.9359i		−	0.0186301i	0.999957	−	0.00931506i	$-0.00296512\pi$
$588$		0			0
$589$	−246.126			−0.417871
$590$	−21.5210	+	75.8796i	−0.0364763	+	0.128609i
$591$		0			0
$592$	−197.597	−	393.522i	−0.333779	−	0.664734i
$593$	−119.459			−0.201449			−0.100725	−	0.994914i	$-0.532116\pi$
$593$	−119.459			−0.201449			−0.100725	+	0.994914i	$0.532116\pi$
$594$		0			0
$595$		−	17.1402i		−	0.0288071i
$596$	−743.175	−	458.436i	−1.24694	−	0.769188i
$597$		0			0
$598$	162.715	−	573.708i	0.272099	−	0.959378i
$599$		−	1020.35i		−	1.70342i	−0.524014	−	0.851710i	$-0.675566\pi$
$599$		−	1020.35i		−	1.70342i	0.524014	−	0.851710i	$-0.324434\pi$
$600$		0			0
$601$	−109.785			−0.182671			−0.0913356	−	0.995820i	$-0.529114\pi$
$601$	−109.785			−0.182671			−0.0913356	+	0.995820i	$0.529114\pi$
$602$	137.575	+	39.0191i	0.228530	+	0.0648159i
$603$		0			0
$604$	−379.994	+	616.012i	−0.629129	+	1.01989i
$605$	155.004			0.256206
$606$		0			0
$607$			649.557i			1.07011i	0.844817	+	0.535055i	$0.179709\pi$
$607$			649.557i			1.07011i	−0.844817	+	0.535055i	$0.820291\pi$
$608$	417.283	−	79.8117i	0.686320	−	0.131269i
$609$		0			0
$610$	−17.1720	−	4.87032i	−0.0281508	−	0.00798413i
$611$		−	617.790i		−	1.01111i
$612$		0			0
$613$	802.148			1.30856			0.654281	−	0.756252i	$-0.272971\pi$
$613$	802.148			1.30856			0.654281	+	0.756252i	$0.272971\pi$
$614$	246.941	−	870.674i	0.402184	−	1.41804i
$615$		0			0
$616$	−218.873	−	238.886i	−0.355314	−	0.387801i
$617$	−1151.11			−1.86565			−0.932825	−	0.360329i	$-0.882664\pi$
$617$	−1151.11			−1.86565			−0.932825	+	0.360329i	$0.882664\pi$
$618$		0			0
$619$		−	223.829i		−	0.361598i	−0.983520	−	0.180799i	$-0.942132\pi$
$619$		−	223.829i		−	0.361598i	0.983520	−	0.180799i	$-0.0578683\pi$
$620$	−53.2559	+	86.3337i	−0.0858967	+	0.139248i
$621$		0			0
$622$	260.752	−	919.371i	0.419216	−	1.47809i
$623$			132.398i			0.212517i
$624$		0			0
$625$	488.157			0.781052
$626$	402.976	+	114.292i	0.643732	+	0.182575i
$627$		0			0
$628$	−650.513	−	401.276i	−1.03585	−	0.638975i
$629$	−130.339			−0.207216
$630$		0			0
$631$			385.557i			0.611026i	0.952188	+	0.305513i	$0.0988279\pi$
$631$			385.557i			0.611026i	−0.952188	+	0.305513i	$0.901172\pi$
$632$	−196.857	+	180.366i	−0.311483	+	0.285389i
$633$		0			0
$634$	−3.36475	−	0.954312i	−0.00530718	−	0.00150522i
$635$			120.235i			0.189347i
$636$		0			0
$637$	−139.622			−0.219187
$638$	51.8550	−	182.832i	0.0812774	−	0.286571i
$639$		0			0
$640$	62.2947	−	163.640i	0.0973355	−	0.255687i
$641$	289.861			0.452201			0.226100	−	0.974104i	$-0.427402\pi$
$641$	289.861			0.452201			0.226100	+	0.974104i	$0.427402\pi$
$642$		0			0
$643$			525.629i			0.817463i	0.912655	+	0.408731i	$0.134029\pi$
$643$			525.629i			0.817463i	−0.912655	+	0.408731i	$0.865971\pi$
$644$	134.646	+	83.0577i	0.209077	+	0.128972i
$645$		0			0
$646$	34.3123	−	120.980i	0.0531150	−	0.187275i
$647$		−	95.6042i		−	0.147765i	−0.997267	−	0.0738827i	$-0.976461\pi$
$647$		−	95.6042i		−	0.147765i	0.997267	−	0.0738827i	$-0.0235390\pi$
$648$		0			0
$649$	441.292			0.679958
$650$	−887.643	−	251.754i	−1.36560	−	0.387313i
$651$		0			0
$652$	−604.271	+	979.589i	−0.926796	+	1.50244i
$653$	627.508			0.960962			0.480481	−	0.877005i	$-0.340462\pi$
$653$	627.508			0.960962			0.480481	+	0.877005i	$0.340462\pi$
$654$		0			0
$655$			191.704i			0.292677i
$656$	79.7404	+	158.806i	0.121555	+	0.242082i
$657$		0			0
$658$	157.675	+	44.7198i	0.239628	+	0.0679633i
$659$			220.070i			0.333945i	0.985962	+	0.166972i	$0.0533991\pi$
$659$			220.070i			0.333945i	−0.985962	+	0.166972i	$0.946601\pi$
$660$		0			0
$661$	743.710			1.12513			0.562564	−	0.826754i	$-0.309815\pi$
$661$	743.710			1.12513			0.562564	+	0.826754i	$0.309815\pi$
$662$	204.670	−	721.635i	0.309170	−	1.09008i
$663$		0			0
$664$	939.644	−	860.927i	1.41513	−	1.29658i
$665$	−48.0505			−0.0722564
$666$		0			0
$667$			92.7962i			0.139125i
$668$	−262.208	+	425.068i	−0.392527	+	0.636330i
$669$		0			0
$670$	−76.7876	+	270.741i	−0.114608	+	0.404091i
$671$			99.8669i			0.148833i
$672$		0			0
$673$	−1017.05			−1.51122			−0.755610	−	0.655022i	$-0.772659\pi$
$673$	−1017.05			−1.51122			−0.755610	+	0.655022i	$0.772659\pi$
$674$	490.148	+	139.016i	0.727223	+	0.206255i
$675$		0			0
$676$	779.076	+	480.582i	1.15248	+	0.710920i
$677$	−861.905			−1.27312			−0.636562	−	0.771225i	$-0.719644\pi$
$677$	−861.905			−1.27312			−0.636562	+	0.771225i	$0.719644\pi$
$678$		0			0
$679$			237.415i			0.349653i
$680$	−35.0117	−	38.2129i	−0.0514878	−	0.0561955i
$681$		0			0
$682$	546.012	+	154.860i	0.800604	+	0.227068i
$683$			635.790i			0.930879i	0.885080	+	0.465440i	$0.154104\pi$
$683$			635.790i			0.930879i	−0.885080	+	0.465440i	$0.845896\pi$
$684$		0			0
$685$	162.408			0.237092
$686$	10.1068	−	35.6350i	0.0147330	−	0.0519460i
$687$		0			0
$688$	386.418	−	194.030i	0.561654	−	0.282020i
$689$	255.025			0.370138
$690$		0			0
$691$		−	214.780i		−	0.310825i	−0.987850	−	0.155412i	$-0.950329\pi$
$691$		−	214.780i		−	0.310825i	0.987850	−	0.155412i	$-0.0496706\pi$
$692$	936.911	+	577.944i	1.35392	+	0.835180i
$693$		0			0
$694$	279.091	−	984.031i	0.402149	−	1.41791i
$695$			98.6347i			0.141920i
$696$		0			0
$697$	52.5983			0.0754639
$698$	−737.181	−	209.080i	−1.05613	−	0.299541i
$699$		0			0
$700$	128.507	−	208.324i	0.183582	−	0.297606i
$701$	271.746			0.387655			0.193828	−	0.981036i	$-0.437910\pi$
$701$	271.746			0.387655			0.193828	+	0.981036i	$0.437910\pi$
$702$		0			0
$703$			365.390i			0.519758i
$704$	−975.927	−	85.4941i	−1.38626	−	0.121440i
$705$		0			0
$706$	−418.271	−	118.630i	−0.592451	−	0.168031i
$707$		−	430.944i		−	0.609538i
$708$		0			0
$709$	−616.894			−0.870090			−0.435045	−	0.900409i	$-0.643267\pi$
$709$	−616.894			−0.870090			−0.435045	+	0.900409i	$0.643267\pi$
$710$	34.1963	−	120.571i	0.0481638	−	0.169818i
$711$		0			0
$712$	270.445	+	295.172i	0.379838	+	0.414567i
$713$	−277.127			−0.388678
$714$		0			0
$715$		−	417.658i		−	0.584137i
$716$	−15.5923	+	25.2768i	−0.0217770	+	0.0353029i
$717$		0			0
$718$	−263.635	+	929.536i	−0.367180	+	1.29462i
$719$		−	55.3428i		−	0.0769719i	−0.999259	−	0.0384859i	$-0.987747\pi$
$719$		−	55.3428i		−	0.0769719i	0.999259	−	0.0384859i	$-0.0122535\pi$
$720$		0			0
$721$	−227.855			−0.316027
$722$	355.451	+	100.813i	0.492315	+	0.139631i
$723$		0			0
$724$	338.949	+	209.084i	0.468161	+	0.288790i
$725$	143.575			0.198034
$726$		0			0
$727$		−	1046.07i		−	1.43888i	−0.694554	−	0.719440i	$-0.744398\pi$
$727$		−	1046.07i		−	1.43888i	0.694554	−	0.719440i	$-0.255602\pi$
$728$	−311.279	+	285.202i	−0.427580	+	0.391761i
$729$		0			0
$730$	184.507	+	52.3299i	0.252749	+	0.0716848i
$731$		−	127.986i		−	0.175083i
$732$		0			0
$733$	851.328			1.16143			0.580715	−	0.814107i	$-0.302773\pi$
$733$	851.328			1.16143			0.580715	+	0.814107i	$0.302773\pi$
$734$	−257.002	+	906.148i	−0.350139	+	1.23453i
$735$		0			0
$736$	469.843	−	89.8646i	0.638373	−	0.122099i
$737$	1574.55			2.13643
$738$		0			0
$739$		−	789.585i		−	1.06845i	−0.845342	−	0.534226i	$-0.820603\pi$
$739$		−	789.585i		−	1.06845i	0.845342	−	0.534226i	$-0.179397\pi$
$740$	128.168	+	79.0618i	0.173200	+	0.106840i
$741$		0			0
$742$	−18.4604	+	65.0885i	−0.0248793	+	0.0877204i
$743$			892.788i			1.20160i	0.799400	+	0.600799i	$0.205151\pi$
$743$			892.788i			1.20160i	−0.799400	+	0.600799i	$0.794849\pi$
$744$		0			0
$745$	298.620			0.400832
$746$	−345.444	−	97.9751i	−0.463062	−	0.131334i
$747$		0			0
$748$	−152.239	+	246.795i	−0.203527	+	0.329940i
$749$	−270.252			−0.360817
$750$		0			0
$751$			406.211i			0.540894i	0.962735	+	0.270447i	$0.0871715\pi$
$751$			406.211i			0.540894i	−0.962735	+	0.270447i	$0.912829\pi$
$752$	442.873	−	222.378i	0.588928	−	0.295715i
$753$		0			0
$754$	−238.239	−	67.5693i	−0.315966	−	0.0896145i
$755$		−	247.524i		−	0.327846i
$756$		0			0
$757$	89.9062			0.118766			0.0593832	−	0.998235i	$-0.481087\pi$
$757$	89.9062			0.118766			0.0593832	+	0.998235i	$0.481087\pi$
$758$	47.9394	−	169.027i	0.0632446	−	0.222990i
$759$		0			0
$760$	−107.125	+	98.1511i	−0.140954	+	0.129146i
$761$	261.751			0.343956			0.171978	−	0.985101i	$-0.444984\pi$
$761$	261.751			0.343956			0.171978	+	0.985101i	$0.444984\pi$
$762$		0			0
$763$			402.251i			0.527197i
$764$	−122.234	+	198.155i	−0.159992	+	0.259365i
$765$		0			0
$766$	−356.672	+	1257.57i	−0.465629	+	1.64173i
$767$		−	575.024i		−	0.749705i
$768$		0			0
$769$	−753.905			−0.980370			−0.490185	−	0.871618i	$-0.663071\pi$
$769$	−753.905			−0.980370			−0.490185	+	0.871618i	$0.663071\pi$
$770$	106.596	+	30.2329i	0.138437	+	0.0392635i
$771$		0			0
$772$	−353.653	−	218.155i	−0.458099	−	0.282584i
$773$	463.530			0.599650			0.299825	−	0.953994i	$-0.403072\pi$
$773$	463.530			0.599650			0.299825	+	0.953994i	$0.403072\pi$
$774$		0			0
$775$			428.773i			0.553255i
$776$	484.959	+	529.300i	0.624947	+	0.682088i
$777$		0			0
$778$	324.907	+	92.1501i	0.417618	+	0.118445i
$779$		−	147.453i		−	0.189285i
$780$		0			0
$781$	−701.203			−0.897827
$782$	38.6342	−	136.218i	0.0494043	−	0.174192i
$783$		0			0
$784$	−50.2579	−	100.091i	−0.0641045	−	0.127667i
$785$	261.387			0.332977
$786$		0			0
$787$		−	618.821i		−	0.786304i	−0.919473	−	0.393152i	$-0.871385\pi$
$787$		−	618.821i		−	0.786304i	0.919473	−	0.393152i	$-0.128615\pi$
$788$	616.878	+	380.528i	0.782841	+	0.482904i
$789$		0			0
$790$	24.9139	−	87.8423i	0.0315365	−	0.111193i
$791$			444.784i			0.562305i
$792$		0			0
$793$	130.131			0.164100
$794$	−1330.56	−	377.375i	−1.67577	−	0.475283i
$795$		0			0
$796$	−457.638	+	741.881i	−0.574922	+	0.932011i
$797$	441.998			0.554577			0.277289	−	0.960787i	$-0.410564\pi$
$797$	441.998			0.554577			0.277289	+	0.960787i	$0.410564\pi$
$798$		0			0
$799$		−	146.685i		−	0.183585i
$800$	−139.039	−	726.943i	−0.173799	−	0.908678i
$801$		0			0
$802$	769.323	+	218.196i	0.959256	+	0.272064i
$803$		−	1073.04i		−	1.33628i
$804$		0			0
$805$	−54.1028			−0.0672085
$806$	201.790	−	711.478i	0.250359	−	0.882727i
$807$		0			0
$808$	−880.274	−	960.760i	−1.08945	−	1.18906i
$809$	−311.447			−0.384978			−0.192489	−	0.981299i	$-0.561656\pi$
$809$	−311.447			−0.384978			−0.192489	+	0.981299i	$0.561656\pi$
$810$		0			0
$811$			965.110i			1.19002i	0.803717	+	0.595012i	$0.202853\pi$
$811$			965.110i			1.19002i	−0.803717	+	0.595012i	$0.797147\pi$
$812$	34.4906	−	55.9131i	0.0424762	−	0.0688585i
$813$		0			0
$814$	229.900	−	810.590i	0.282432	−	0.995811i
$815$		−	393.615i		−	0.482963i
$816$		0			0
$817$	−358.793			−0.439159
$818$	213.728	+	60.6175i	0.261281	+	0.0741045i
$819$		0			0
$820$	−51.7222	−	31.9054i	−0.0630759	−	0.0389091i
$821$	−1464.81			−1.78417			−0.892087	−	0.451864i	$-0.850759\pi$
$821$	−1464.81			−1.78417			−0.892087	+	0.451864i	$0.850759\pi$
$822$		0			0
$823$			967.159i			1.17516i	0.809165	+	0.587581i	$0.199920\pi$
$823$			967.159i			1.17516i	−0.809165	+	0.587581i	$0.800080\pi$
$824$	−507.988	+	465.433i	−0.616491	+	0.564845i
$825$		0			0
$826$	146.760	+	41.6241i	0.177675	+	0.0503924i
$827$			1298.46i			1.57009i	0.619441	+	0.785043i	$0.287359\pi$
$827$			1298.46i			1.57009i	−0.619441	+	0.785043i	$0.712641\pi$
$828$		0			0
$829$	−771.397			−0.930515			−0.465258	−	0.885175i	$-0.654038\pi$
$829$	−771.397			−0.930515			−0.465258	+	0.885175i	$0.654038\pi$
$830$	−118.920	+	419.291i	−0.143277	+	0.505170i
$831$		0			0
$832$	−111.403	+	1271.68i	−0.133897	+	1.52846i
$833$	−33.1511			−0.0397973
$834$		0			0
$835$		−	170.799i		−	0.204550i
$836$	691.861	+	426.782i	0.827585	+	0.510505i
$837$		0			0
$838$	350.343	−	1235.25i	0.418070	−	1.47405i
$839$		−	1088.04i		−	1.29683i	−0.761287	−	0.648415i	$-0.775432\pi$
$839$		−	1088.04i		−	1.29683i	0.761287	−	0.648415i	$-0.224568\pi$
$840$		0			0
$841$	−802.465			−0.954180
$842$	292.407	+	82.9327i	0.347277	+	0.0984949i
$843$		0			0
$844$	225.545	−	365.633i	0.267233	−	0.433215i
$845$	−313.045			−0.370468
$846$		0			0
$847$		−	299.797i		−	0.353951i
$848$	91.7978	+	182.819i	0.108252	+	0.215588i
$849$		0			0
$850$	−210.757	−	59.7750i	−0.247949	−	0.0703235i
$851$			411.413i			0.483447i
$852$		0			0
$853$	126.051			0.147774			0.0738870	−	0.997267i	$-0.476460\pi$
$853$	126.051			0.147774			0.0738870	+	0.997267i	$0.476460\pi$
$854$	−9.41976	+	33.2126i	−0.0110302	+	0.0388906i
$855$		0			0
$856$	−602.508	+	552.034i	−0.703865	+	0.644900i
$857$	1135.93			1.32547			0.662736	−	0.748853i	$-0.269395\pi$
$857$	1135.93			1.32547			0.662736	+	0.748853i	$0.269395\pi$
$858$		0			0
$859$		−	590.556i		−	0.687492i	−0.939063	−	0.343746i	$-0.888304\pi$
$859$		−	590.556i		−	0.687492i	0.939063	−	0.343746i	$-0.111696\pi$
$860$	−77.6345	+	125.854i	−0.0902727	+	0.146342i
$861$		0			0
$862$	−250.950	+	884.809i	−0.291125	+	1.02646i
$863$			292.067i			0.338432i	0.985579	+	0.169216i	$0.0541235\pi$
$863$			292.067i			0.338432i	−0.985579	+	0.169216i	$0.945876\pi$
$864$		0			0
$865$	−376.466			−0.435221
$866$	1028.19	+	291.615i	1.18728	+	0.336737i
$867$		0			0
$868$	166.979	+	103.003i	0.192373	+	0.118667i
$869$	−510.864			−0.587876
$870$		0			0
$871$		−	2051.70i		−	2.35557i
$872$	821.665	+	896.792i	0.942276	+	1.02843i
$873$		0			0
$874$	−381.871	−	108.306i	−0.436923	−	0.123920i
$875$			174.189i			0.199073i
$876$		0			0
$877$	1087.23			1.23971			0.619856	−	0.784715i	$-0.287191\pi$
$877$	1087.23			1.23971			0.619856	+	0.784715i	$0.287191\pi$
$878$	109.830	−	387.244i	0.125091	−	0.441053i
$879$		0			0
$880$	299.405	−	150.339i	0.340233	−	0.170839i
$881$	−1217.53			−1.38198			−0.690991	−	0.722863i	$-0.742826\pi$
$881$	−1217.53			−1.38198			−0.690991	+	0.722863i	$0.742826\pi$
$882$		0			0
$883$		−	1141.10i		−	1.29230i	−0.763212	−	0.646148i	$-0.776379\pi$
$883$		−	1141.10i		−	1.29230i	0.763212	−	0.646148i	$-0.223621\pi$
$884$	321.585	+	198.374i	0.363784	+	0.224404i
$885$		0			0
$886$	−40.1062	+	141.408i	−0.0452666	+	0.159603i
$887$			368.518i			0.415466i	0.978186	+	0.207733i	$0.0666085\pi$
$887$			368.518i			0.415466i	−0.978186	+	0.207733i	$0.933391\pi$
$888$		0			0
$889$	232.549			0.261585
$890$	−131.713	−	37.3564i	−0.147992	−	0.0419735i
$891$		0			0
$892$	−734.350	+	1190.46i	−0.823263	+	1.33460i
$893$	−411.213			−0.460484
$894$		0			0
$895$		−	10.1566i		−	0.0113482i
$896$	−316.499	−	120.485i	−0.353235	−	0.134470i
$897$		0			0
$898$	79.7315	+	22.6135i	0.0887879	+	0.0251821i
$899$			115.080i			0.128009i
$900$		0			0
$901$	60.5517			0.0672050
$902$	−92.7761	+	327.114i	−0.102856	+	0.362654i
$903$		0			0
$904$	908.544	+	991.615i	1.00503	+	1.09692i
$905$	−136.195			−0.150492
$906$		0			0
$907$			341.525i			0.376544i	0.982117	+	0.188272i	$0.0602886\pi$
$907$			341.525i			0.376544i	−0.982117	+	0.188272i	$0.939711\pi$
$908$	−38.5190	+	62.4435i	−0.0424218	+	0.0687703i
$909$		0			0
$910$	39.3948	−	138.900i	0.0432910	−	0.152637i
$911$		−	536.979i		−	0.589439i	−0.955584	−	0.294719i	$-0.904774\pi$
$911$		−	536.979i		−	0.589439i	0.955584	−	0.294719i	$-0.0952262\pi$
$912$		0			0
$913$	2438.47			2.67083
$914$	519.904	+	147.455i	0.568823	+	0.161330i
$915$		0			0
$916$	233.352	+	143.946i	0.254751	+	0.157146i
$917$	370.777			0.404337
$918$		0			0
$919$		−	987.383i		−	1.07441i	−0.843452	−	0.537205i	$-0.819480\pi$
$919$		−	987.383i		−	1.07441i	0.843452	−	0.537205i	$-0.180520\pi$
$920$	−120.619	+	110.514i	−0.131107	+	0.120124i
$921$		0			0
$922$	1414.47	+	401.174i	1.53414	+	0.435113i
$923$			913.698i			0.989922i
$924$		0			0
$925$	636.540			0.688152
$926$	−405.116	+	1428.37i	−0.437490	+	1.54252i
$927$		0			0
$928$	−37.3173	−	195.107i	−0.0402126	−	0.210245i
$929$	1285.67			1.38393			0.691965	−	0.721932i	$-0.256745\pi$
$929$	1285.67			1.38393			0.691965	+	0.721932i	$0.256745\pi$
$930$		0			0
$931$			92.9352i			0.0998230i
$932$	−209.298	−	129.108i	−0.224568	−	0.138527i
$933$		0			0
$934$	−219.461	+	773.785i	−0.234969	+	0.828463i
$935$		−	99.1664i		−	0.106060i
$936$		0			0
$937$	−887.657			−0.947339			−0.473670	−	0.880703i	$-0.657071\pi$
$937$	−887.657			−0.947339			−0.473670	+	0.880703i	$0.657071\pi$
$938$	523.644	+	148.516i	0.558256	+	0.158333i
$939$		0			0
$940$	−88.9769	+	144.241i	−0.0946563	+	0.153448i
$941$	−380.526			−0.404385			−0.202192	−	0.979346i	$-0.564807\pi$
$941$	−380.526			−0.404385			−0.202192	+	0.979346i	$0.564807\pi$
$942$		0			0
$943$		−	166.026i		−	0.176061i
$944$	412.215	−	206.983i	0.436669	−	0.219262i
$945$		0			0
$946$	795.956	+	225.749i	0.841391	+	0.238636i
$947$			363.169i			0.383494i	0.981444	+	0.191747i	$0.0614153\pi$
$947$			363.169i			0.383494i	−0.981444	+	0.191747i	$0.938585\pi$
$948$		0			0
$949$	−1398.21			−1.47335
$950$	−167.572	+	590.832i	−0.176391	+	0.621928i
$951$		0			0
$952$	−73.9082	+	67.7167i	−0.0776347	+	0.0711310i
$953$	679.479			0.712990			0.356495	−	0.934297i	$-0.383972\pi$
$953$	679.479			0.712990			0.356495	+	0.934297i	$0.383972\pi$
$954$		0			0
$955$		−	79.6220i		−	0.0833738i
$956$	429.762	−	696.692i	0.449542	−	0.728757i
$957$		0			0
$958$	−194.680	+	686.409i	−0.203215	+	0.716502i
$959$		−	314.116i		−	0.327545i
$960$		0			0
$961$	617.323			0.642376
$962$	−1056.23	−	299.570i	−1.09796	−	0.311403i
$963$		0			0
$964$	−1325.21	−	817.472i	−1.37470	−	0.848000i
$965$	142.103			0.147257
$966$		0			0
$967$			209.525i			0.216675i	0.994114	+	0.108337i	$0.0345527\pi$
$967$			209.525i			0.216675i	−0.994114	+	0.108337i	$0.965447\pi$
$968$	−612.384	−	668.376i	−0.632628	−	0.690471i
$969$		0			0
$970$	−236.186	−	66.9872i	−0.243491	−	0.0690590i
$971$		−	538.867i		−	0.554961i	−0.960731	−	0.277481i	$-0.910501\pi$
$971$		−	538.867i		−	0.554961i	0.960731	−	0.277481i	$-0.0894994\pi$
$972$		0			0
$973$	190.771			0.196065
$974$	66.0989	−	233.054i	0.0678633	−	0.239275i
$975$		0			0
$976$	46.8415	+	93.2867i	0.0479933	+	0.0955806i
$977$	−1028.30			−1.05250			−0.526252	−	0.850329i	$-0.676403\pi$
$977$	−1028.30			−1.05250			−0.526252	+	0.850329i	$0.676403\pi$
$978$		0			0
$979$			766.001i			0.782432i
$980$	32.5989	+	20.1090i	0.0332642	+	0.0205194i
$981$		0			0
$982$	−10.0704	+	35.5065i	−0.0102550	+	0.0361574i
$983$		−	520.479i		−	0.529480i	−0.964320	−	0.264740i	$-0.914714\pi$
$983$		−	520.479i		−	0.529480i	0.964320	−	0.264740i	$-0.0852862\pi$
$984$		0			0
$985$	−247.872			−0.251646
$986$	−56.5660	−	16.0433i	−0.0573692	−	0.0162711i
$987$		0			0
$988$	556.116	−	901.525i	0.562871	−	0.912475i
$989$	−403.986			−0.408479
$990$		0			0
$991$		−	1849.00i		−	1.86579i	−0.360148	−	0.932895i	$-0.617274\pi$
$991$		−	1849.00i		−	1.86579i	0.360148	−	0.932895i	$-0.382726\pi$
$992$	582.671	−	111.445i	0.587369	−	0.112343i
$993$		0			0
$994$	−233.198	−	66.1397i	−0.234606	−	0.0665389i
$995$		−	298.100i		−	0.299598i
$996$		0			0
$997$	1010.23			1.01327			0.506635	−	0.862161i	$-0.330889\pi$
$997$	1010.23			1.01327			0.506635	+	0.862161i	$0.330889\pi$
$998$	−81.6236	+	287.792i	−0.0817872	+	0.288368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.g.a.127.6		6
3.2	odd	2		28.3.c.a.15.1	✓	6
4.3	odd	2	inner	252.3.g.a.127.5		6
12.11	even	2		28.3.c.a.15.2	yes	6
21.2	odd	6		196.3.g.k.67.4		12
21.5	even	6		196.3.g.j.67.4		12
21.11	odd	6		196.3.g.k.79.5		12
21.17	even	6		196.3.g.j.79.5		12
21.20	even	2		196.3.c.g.99.1		6
24.5	odd	2		448.3.d.d.127.1		6
24.11	even	2		448.3.d.d.127.6		6
48.5	odd	4		1792.3.g.g.127.12		12
48.11	even	4		1792.3.g.g.127.2		12
48.29	odd	4		1792.3.g.g.127.1		12
48.35	even	4		1792.3.g.g.127.11		12
84.11	even	6		196.3.g.k.79.4		12
84.23	even	6		196.3.g.k.67.5		12
84.47	odd	6		196.3.g.j.67.5		12
84.59	odd	6		196.3.g.j.79.4		12
84.83	odd	2		196.3.c.g.99.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.c.a.15.1	✓	6	3.2	odd	2
28.3.c.a.15.2	yes	6	12.11	even	2
196.3.c.g.99.1		6	21.20	even	2
196.3.c.g.99.2		6	84.83	odd	2
196.3.g.j.67.4		12	21.5	even	6
196.3.g.j.67.5		12	84.47	odd	6
196.3.g.j.79.4		12	84.59	odd	6
196.3.g.j.79.5		12	21.17	even	6
196.3.g.k.67.4		12	21.2	odd	6
196.3.g.k.67.5		12	84.23	even	6
196.3.g.k.79.4		12	84.11	even	6
196.3.g.k.79.5		12	21.11	odd	6
252.3.g.a.127.5		6	4.3	odd	2	inner
252.3.g.a.127.6		6	1.1	even	1	trivial
448.3.d.d.127.1		6	24.5	odd	2
448.3.d.d.127.6		6	24.11	even	2
1792.3.g.g.127.1		12	48.29	odd	4
1792.3.g.g.127.2		12	48.11	even	4
1792.3.g.g.127.11		12	48.35	even	4
1792.3.g.g.127.12		12	48.5	odd	4

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92411 + 0.545716i) q^{2} +(3.40439 + 2.10003i) q^{4} -1.36794 q^{5} +2.64575i q^{7} +(5.40439 + 5.89853i) q^{8} +O(q^{10})\)	\(q+(1.92411 + 0.545716i) q^{2} +(3.40439 + 2.10003i) q^{4} -1.36794 q^{5} +2.64575i q^{7} +(5.40439 + 5.89853i) q^{8} +(-2.63206 - 0.746506i) q^{10} +15.3073i q^{11} +19.9460 q^{13} +(-1.44383 + 5.09071i) q^{14} +(7.17971 + 14.2987i) q^{16} +4.73588 q^{17} -13.2765i q^{19} +(-4.65699 - 2.87272i) q^{20} +(-8.35343 + 29.4528i) q^{22} -14.9487i q^{23} -23.1287 q^{25} +(38.3784 + 10.8849i) q^{26} +(-5.55617 + 9.00716i) q^{28} -6.20763 q^{29} -18.5385i q^{31} +(6.01152 + 31.4303i) q^{32} +(9.11234 + 2.58445i) q^{34} -3.61922i q^{35} -27.5216 q^{37} +(7.24518 - 25.5453i) q^{38} +(-7.39287 - 8.06882i) q^{40} +11.1064 q^{41} -27.0248i q^{43} +(-32.1458 + 52.1119i) q^{44} +(8.15777 - 28.7630i) q^{46} -30.9731i q^{47} -7.00000 q^{49} +(-44.5022 - 12.6217i) q^{50} +(67.9041 + 41.8874i) q^{52} +12.7857 q^{53} -20.9394i q^{55} +(-15.6060 + 14.2987i) q^{56} +(-11.9442 - 3.38760i) q^{58} -28.8289i q^{59} +6.52415 q^{61} +(10.1168 - 35.6701i) q^{62} +(-5.58519 + 63.7558i) q^{64} -27.2850 q^{65} -102.863i q^{67} +(16.1228 + 9.94551i) q^{68} +(1.97507 - 6.96378i) q^{70} +45.8085i q^{71} -70.0997 q^{73} +(-52.9546 - 15.0190i) q^{74} +(27.8810 - 45.1982i) q^{76} -40.4992 q^{77} +33.3739i q^{79} +(-9.82140 - 19.5597i) q^{80} +(21.3698 + 6.06092i) q^{82} -159.301i q^{83} -6.47839 q^{85} +(14.7478 - 51.9986i) q^{86} +(-90.2903 + 82.7264i) q^{88} +50.0417 q^{89} +52.7723i q^{91} +(31.3929 - 50.8913i) q^{92} +(16.9025 - 59.5955i) q^{94} +18.1614i q^{95} +89.7343 q^{97} +(-13.4688 - 3.82001i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + q^{4} + 4 q^{5} + 13 q^{8}+O(q^{10}) \) 6 * q + q^2 + q^4 + 4 * q^5 + 13 * q^8	\( 6 q + q^{2} + q^{4} + 4 q^{5} + 13 q^{8} - 28 q^{10} + 12 q^{13} - 7 q^{14} + 17 q^{16} + 4 q^{17} + 32 q^{20} + 52 q^{22} - 30 q^{25} + 56 q^{26} - 35 q^{28} + 36 q^{29} + 101 q^{32} + 58 q^{34} + 28 q^{37} + 190 q^{38} + 40 q^{40} + 20 q^{41} - 164 q^{44} + 120 q^{46} - 42 q^{49} - 161 q^{50} + 292 q^{52} - 92 q^{53} + 49 q^{56} - 166 q^{58} - 164 q^{61} - 148 q^{62} - 215 q^{64} + 136 q^{65} - 62 q^{68} + 84 q^{70} - 132 q^{73} - 250 q^{74} - 78 q^{76} - 112 q^{77} - 312 q^{80} - 86 q^{82} - 232 q^{85} + 164 q^{86} - 100 q^{88} - 348 q^{89} + 104 q^{92} - 276 q^{94} + 252 q^{97} - 7 q^{98}+O(q^{100}) \) 6 * q + q^2 + q^4 + 4 * q^5 + 13 * q^8 - 28 * q^10 + 12 * q^13 - 7 * q^14 + 17 * q^16 + 4 * q^17 + 32 * q^20 + 52 * q^22 - 30 * q^25 + 56 * q^26 - 35 * q^28 + 36 * q^29 + 101 * q^32 + 58 * q^34 + 28 * q^37 + 190 * q^38 + 40 * q^40 + 20 * q^41 - 164 * q^44 + 120 * q^46 - 42 * q^49 - 161 * q^50 + 292 * q^52 - 92 * q^53 + 49 * q^56 - 166 * q^58 - 164 * q^61 - 148 * q^62 - 215 * q^64 + 136 * q^65 - 62 * q^68 + 84 * q^70 - 132 * q^73 - 250 * q^74 - 78 * q^76 - 112 * q^77 - 312 * q^80 - 86 * q^82 - 232 * q^85 + 164 * q^86 - 100 * q^88 - 348 * q^89 + 104 * q^92 - 276 * q^94 + 252 * q^97 - 7 * q^98

Introduction

L-functions

Modular forms

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