LMFDB - Embedded newform 126.2.l.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(5,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("126.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.l (of order $6$, degree $2$, 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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Root			$1.73109 - 0.0577511i$ of defining polynomial
Character	$\chi$	$=$	126.5
Dual form			126.2.l.a.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.890915 + 1.48535i) q^{3} -1.00000 q^{4} +(1.14095 + 1.97618i) q^{5} +(1.48535 + 0.890915i) q^{6} +(1.42337 + 2.23025i) q^{7} +1.00000i q^{8} +(-1.41254 - 2.64665i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.890915 + 1.48535i) q^{3} -1.00000 q^{4} +(1.14095 + 1.97618i) q^{5} +(1.48535 + 0.890915i) q^{6} +(1.42337 + 2.23025i) q^{7} +1.00000i q^{8} +(-1.41254 - 2.64665i) q^{9} +(1.97618 - 1.14095i) q^{10} +(-0.946590 - 0.546514i) q^{11} +(0.890915 - 1.48535i) q^{12} +(5.91448 + 3.41473i) q^{13} +(2.23025 - 1.42337i) q^{14} +(-3.95182 - 0.0659003i) q^{15} +1.00000 q^{16} +(-3.35863 - 5.81732i) q^{17} +(-2.64665 + 1.41254i) q^{18} +(-2.47987 - 1.43175i) q^{19} +(-1.14095 - 1.97618i) q^{20} +(-4.58081 + 0.127243i) q^{21} +(-0.546514 + 0.946590i) q^{22} +(-3.38264 + 1.95297i) q^{23} +(-1.48535 - 0.890915i) q^{24} +(-0.103535 + 0.179327i) q^{25} +(3.41473 - 5.91448i) q^{26} +(5.18965 + 0.259820i) q^{27} +(-1.42337 - 2.23025i) q^{28} +(1.59933 - 0.923371i) q^{29} +(-0.0659003 + 3.95182i) q^{30} +2.02166i q^{31} -1.00000i q^{32} +(1.65510 - 0.919121i) q^{33} +(-5.81732 + 3.35863i) q^{34} +(-2.78339 + 5.35745i) q^{35} +(1.41254 + 2.64665i) q^{36} +(3.57920 - 6.19935i) q^{37} +(-1.43175 + 2.47987i) q^{38} +(-10.3414 + 5.74285i) q^{39} +(-1.97618 + 1.14095i) q^{40} +(2.45515 - 4.25245i) q^{41} +(0.127243 + 4.58081i) q^{42} +(-3.74246 - 6.48214i) q^{43} +(0.946590 + 0.546514i) q^{44} +(3.61862 - 5.81113i) q^{45} +(1.95297 + 3.38264i) q^{46} +6.80349 q^{47} +(-0.890915 + 1.48535i) q^{48} +(-2.94803 + 6.34895i) q^{49} +(0.179327 + 0.103535i) q^{50} +(11.6330 + 0.193992i) q^{51} +(-5.91448 - 3.41473i) q^{52} +(0.222069 - 0.128212i) q^{53} +(0.259820 - 5.18965i) q^{54} -2.49418i q^{55} +(-2.23025 + 1.42337i) q^{56} +(4.33601 - 2.40791i) q^{57} +(-0.923371 - 1.59933i) q^{58} +1.94202 q^{59} +(3.95182 + 0.0659003i) q^{60} +1.33154i q^{61} +2.02166 q^{62} +(3.89211 - 6.91748i) q^{63} -1.00000 q^{64} +15.5841i q^{65} +(-0.919121 - 1.65510i) q^{66} +5.09918 q^{67} +(3.35863 + 5.81732i) q^{68} +(0.112802 - 6.76433i) q^{69} +(5.35745 + 2.78339i) q^{70} -0.233507i q^{71} +(2.64665 - 1.41254i) q^{72} +(5.89272 - 3.40216i) q^{73} +(-6.19935 - 3.57920i) q^{74} +(-0.174124 - 0.313551i) q^{75} +(2.47987 + 1.43175i) q^{76} +(-0.128486 - 2.88902i) q^{77} +(5.74285 + 10.3414i) q^{78} -7.27248 q^{79} +(1.14095 + 1.97618i) q^{80} +(-5.00947 + 7.47698i) q^{81} +(-4.25245 - 2.45515i) q^{82} +(-2.91353 - 5.04638i) q^{83} +(4.58081 - 0.127243i) q^{84} +(7.66407 - 13.2746i) q^{85} +(-6.48214 + 3.74246i) q^{86} +(-0.0533331 + 3.19821i) q^{87} +(0.546514 - 0.946590i) q^{88} +(-8.99707 + 15.5834i) q^{89} +(-5.81113 - 3.61862i) q^{90} +(0.802809 + 18.0512i) q^{91} +(3.38264 - 1.95297i) q^{92} +(-3.00288 - 1.80113i) q^{93} -6.80349i q^{94} -6.53424i q^{95} +(1.48535 + 0.890915i) q^{96} +(-4.13903 + 2.38967i) q^{97} +(6.34895 + 2.94803i) q^{98} +(-0.109333 + 3.27726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^7	$ 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.890915	+	1.48535i	−0.514370	+	0.857568i
$3$	−0.890915	+	1.48535i	−0.514370	+	0.857568i
$4$	−1.00000			−0.500000
$5$	1.14095	+	1.97618i	0.510248	+	0.883776i	0.999929	+	0.0118746i	$0.00377989\pi$
$5$	1.14095	+	1.97618i	0.510248	+	0.883776i	−0.489681	+	0.871902i	$0.662887\pi$
$6$	1.48535	+	0.890915i	0.606392	+	0.363715i
$7$	1.42337	+	2.23025i	0.537984	+	0.842955i
$7$	1.42337	+	2.23025i	0.537984	+	0.842955i
$8$			1.00000i			0.353553i
$9$	−1.41254	−	2.64665i	−0.470846	−	0.882215i
$10$	1.97618	−	1.14095i	0.624924	−	0.360800i
$11$	−0.946590	−	0.546514i	−0.285408	−	0.164780i	0.350461	−	0.936577i	$-0.386025\pi$
$11$	−0.946590	−	0.546514i	−0.285408	−	0.164780i	−0.635869	+	0.771797i	$0.719358\pi$
$12$	0.890915	−	1.48535i	0.257185	−	0.428784i
$13$	5.91448	+	3.41473i	1.64038	+	0.947075i	0.980697	+	0.195533i	$0.0626436\pi$
$13$	5.91448	+	3.41473i	1.64038	+	0.947075i	0.659685	+	0.751542i	$0.270690\pi$
$14$	2.23025	−	1.42337i	0.596059	−	0.380412i
$15$	−3.95182	−	0.0659003i	−1.02036	−	0.0170154i
$16$	1.00000			0.250000
$17$	−3.35863	−	5.81732i	−0.814588	−	1.41091i	−0.909623	−	0.415434i	$-0.863630\pi$
$17$	−3.35863	−	5.81732i	−0.814588	−	1.41091i	0.0950352	−	0.995474i	$-0.469704\pi$
$18$	−2.64665	+	1.41254i	−0.623820	+	0.332939i
$19$	−2.47987	−	1.43175i	−0.568922	−	0.328467i	0.187797	−	0.982208i	$-0.439865\pi$
$19$	−2.47987	−	1.43175i	−0.568922	−	0.328467i	−0.756718	+	0.653741i	$0.773199\pi$
$20$	−1.14095	−	1.97618i	−0.255124	−	0.441888i
$21$	−4.58081	+	0.127243i	−0.999614	+	0.0277668i
$22$	−0.546514	+	0.946590i	−0.116517	+	0.201814i
$23$	−3.38264	+	1.95297i	−0.705328	+	0.407221i	−0.809329	−	0.587356i	$-0.800169\pi$
$23$	−3.38264	+	1.95297i	−0.705328	+	0.407221i	0.104001	+	0.994577i	$0.466836\pi$
$24$	−1.48535	−	0.890915i	−0.303196	−	0.181857i
$25$	−0.103535	+	0.179327i	−0.0207069	+	0.0358655i
$26$	3.41473	−	5.91448i	0.669683	−	1.15993i
$27$	5.18965	+	0.259820i	0.998749	+	0.0500023i
$28$	−1.42337	−	2.23025i	−0.268992	−	0.421478i
$29$	1.59933	−	0.923371i	0.296987	−	0.171466i	−0.344101	−	0.938933i	$-0.611816\pi$
$29$	1.59933	−	0.923371i	0.296987	−	0.171466i	0.641089	+	0.767467i	$0.278483\pi$
$30$	−0.0659003	+	3.95182i	−0.0120317	+	0.721500i
$31$			2.02166i			0.363102i	0.983382	+	0.181551i	$0.0581117\pi$
$31$			2.02166i			0.363102i	−0.983382	+	0.181551i	$0.941888\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.65510	−	0.919121i	0.288115	−	0.159998i
$34$	−5.81732	+	3.35863i	−0.997663	+	0.576001i
$35$	−2.78339	+	5.35745i	−0.470478	+	0.905574i
$36$	1.41254	+	2.64665i	0.235423	+	0.441108i
$37$	3.57920	−	6.19935i	0.588416	−	1.01917i	−0.406024	−	0.913863i	$-0.633085\pi$
$37$	3.57920	−	6.19935i	0.588416	−	1.01917i	0.994440	−	0.105305i	$-0.0335818\pi$
$38$	−1.43175	+	2.47987i	−0.232261	+	0.402288i
$39$	−10.3414	+	5.74285i	−1.65595	+	0.919592i
$40$	−1.97618	+	1.14095i	−0.312462	+	0.180400i
$41$	2.45515	−	4.25245i	0.383431	−	0.664121i	−0.608120	−	0.793845i	$-0.708076\pi$
$41$	2.45515	−	4.25245i	0.383431	−	0.664121i	0.991550	+	0.129724i	$0.0414092\pi$
$42$	0.127243	+	4.58081i	0.0196341	+	0.706834i
$43$	−3.74246	−	6.48214i	−0.570721	−	0.988517i	−0.996492	−	0.0836863i	$-0.973331\pi$
$43$	−3.74246	−	6.48214i	−0.570721	−	0.988517i	0.425772	−	0.904831i	$-0.360003\pi$
$44$	0.946590	+	0.546514i	0.142704	+	0.0823901i
$45$	3.61862	−	5.81113i	0.539432	−	0.866272i
$46$	1.95297	+	3.38264i	0.287949	+	0.498742i
$47$	6.80349			0.992391			0.496195	−	0.868211i	$-0.334730\pi$
$47$	6.80349			0.992391			0.496195	+	0.868211i	$0.334730\pi$
$48$	−0.890915	+	1.48535i	−0.128593	+	0.214392i
$49$	−2.94803	+	6.34895i	−0.421147	+	0.906992i
$50$	0.179327	+	0.103535i	0.0253607	+	0.0146420i
$51$	11.6330	+	0.193992i	1.62895	+	0.0271643i
$52$	−5.91448	−	3.41473i	−0.820191	−	0.473538i
$53$	0.222069	−	0.128212i	0.0305036	−	0.0176112i	−0.484671	−	0.874697i	$-0.661061\pi$
$53$	0.222069	−	0.128212i	0.0305036	−	0.0176112i	0.515174	+	0.857085i	$0.327727\pi$
$54$	0.259820	−	5.18965i	0.0353570	−	0.706222i
$55$		−	2.49418i		−	0.336315i
$56$	−2.23025	+	1.42337i	−0.298030	+	0.190206i
$57$	4.33601	−	2.40791i	0.574319	−	0.318935i
$58$	−0.923371	−	1.59933i	−0.121245	−	0.210002i
$59$	1.94202			0.252829			0.126415	−	0.991977i	$-0.459653\pi$
$59$	1.94202			0.252829			0.126415	+	0.991977i	$0.459653\pi$
$60$	3.95182	+	0.0659003i	0.510178	+	0.00850769i
$61$			1.33154i			0.170486i	0.996360	+	0.0852432i	$0.0271667\pi$
$61$			1.33154i			0.170486i	−0.996360	+	0.0852432i	$0.972833\pi$
$62$	2.02166			0.256752
$63$	3.89211	−	6.91748i	0.490360	−	0.871520i
$64$	−1.00000			−0.125000
$65$			15.5841i			1.93297i
$66$	−0.919121	−	1.65510i	−0.113136	−	0.203728i
$67$	5.09918			0.622964			0.311482	−	0.950252i	$-0.399175\pi$
$67$	5.09918			0.622964			0.311482	+	0.950252i	$0.399175\pi$
$68$	3.35863	+	5.81732i	0.407294	+	0.705454i
$69$	0.112802	−	6.76433i	0.0135797	−	0.814330i
$70$	5.35745	+	2.78339i	0.640337	+	0.332678i
$71$		−	0.233507i		−	0.0277121i	−0.999904	−	0.0138561i	$-0.995589\pi$
$71$		−	0.233507i		−	0.0277121i	0.999904	−	0.0138561i	$-0.00441066\pi$
$72$	2.64665	−	1.41254i	0.311910	−	0.166469i
$73$	5.89272	−	3.40216i	0.689690	−	0.398193i	−0.113806	−	0.993503i	$-0.536304\pi$
$73$	5.89272	−	3.40216i	0.689690	−	0.398193i	0.803496	+	0.595310i	$0.202971\pi$
$74$	−6.19935	−	3.57920i	−0.720660	−	0.416073i
$75$	−0.174124	−	0.313551i	−0.0201061	−	0.0362058i
$76$	2.47987	+	1.43175i	0.284461	+	0.164233i
$77$	−0.128486	−	2.88902i	−0.0146424	−	0.329235i
$78$	5.74285	+	10.3414i	0.650250	+	1.17093i
$79$	−7.27248			−0.818218			−0.409109	−	0.912485i	$-0.634161\pi$
$79$	−7.27248			−0.818218			−0.409109	+	0.912485i	$0.634161\pi$
$80$	1.14095	+	1.97618i	0.127562	+	0.220944i
$81$	−5.00947	+	7.47698i	−0.556607	+	0.830776i
$82$	−4.25245	−	2.45515i	−0.469605	−	0.271126i
$83$	−2.91353	−	5.04638i	−0.319801	−	0.553912i	0.660645	−	0.750698i	$-0.270283\pi$
$83$	−2.91353	−	5.04638i	−0.319801	−	0.553912i	−0.980446	+	0.196786i	$0.936950\pi$
$84$	4.58081	−	0.127243i	0.499807	−	0.0138834i
$85$	7.66407	−	13.2746i	0.831285	−	1.43983i
$86$	−6.48214	+	3.74246i	−0.698987	+	0.403560i
$87$	−0.0533331	+	3.19821i	−0.00571791	+	0.342884i
$88$	0.546514	−	0.946590i	0.0582586	−	0.100907i
$89$	−8.99707	+	15.5834i	−0.953687	+	1.65184i	−0.216344	+	0.976317i	$0.569413\pi$
$89$	−8.99707	+	15.5834i	−0.953687	+	1.65184i	−0.737344	+	0.675518i	$0.763920\pi$
$90$	−5.81113	−	3.61862i	−0.612547	−	0.381436i
$91$	0.802809	+	18.0512i	0.0841573	+	1.89228i
$92$	3.38264	−	1.95297i	0.352664	−	0.203611i
$93$	−3.00288	−	1.80113i	−0.311384	−	0.186769i
$94$		−	6.80349i		−	0.701726i
$95$		−	6.53424i		−	0.670399i
$96$	1.48535	+	0.890915i	0.151598	+	0.0909287i
$97$	−4.13903	+	2.38967i	−0.420255	+	0.242634i	−0.695186	−	0.718830i	$-0.744678\pi$
$97$	−4.13903	+	2.38967i	−0.420255	+	0.242634i	0.274931	+	0.961464i	$0.411345\pi$
$98$	6.34895	+	2.94803i	0.641341	+	0.297796i
$99$	−0.109333	+	3.27726i	−0.0109884	+	0.329377i
$100$	0.103535	−	0.179327i	0.0103535	−	0.0179327i
$101$	−5.22981	+	9.05829i	−0.520385	+	0.901334i	0.479334	+	0.877633i	$0.340878\pi$
$101$	−5.22981	+	9.05829i	−0.520385	+	0.901334i	−0.999719	+	0.0237012i	$0.992455\pi$
$102$	0.193992	−	11.6330i	0.0192080	−	1.15184i
$103$	−11.0398	+	6.37383i	−1.08778	+	0.628033i	−0.932986	−	0.359914i	$-0.882806\pi$
$103$	−11.0398	+	6.37383i	−1.08778	+	0.628033i	−0.154799	+	0.987946i	$0.549473\pi$
$104$	−3.41473	+	5.91448i	−0.334842	+	0.579963i
$105$	−5.47793	−	8.90734i	−0.534591	−	0.869268i
$106$	−0.128212	−	0.222069i	−0.0124530	−	0.0215693i
$107$	8.25865	+	4.76813i	0.798394	+	0.460953i	0.842909	−	0.538056i	$-0.180841\pi$
$107$	8.25865	+	4.76813i	0.798394	+	0.460953i	−0.0445153	+	0.999009i	$0.514174\pi$
$108$	−5.18965	−	0.259820i	−0.499375	−	0.0250012i
$109$	−2.88251	−	4.99266i	−0.276095	−	0.478210i	0.694316	−	0.719670i	$-0.255707\pi$
$109$	−2.88251	−	4.99266i	−0.276095	−	0.478210i	−0.970411	+	0.241460i	$0.922374\pi$
$110$	−2.49418			−0.237811
$111$	6.01946	+	10.8395i	0.571341	+	1.02884i
$112$	1.42337	+	2.23025i	0.134496	+	0.210739i
$113$	−10.3333	−	5.96592i	−0.972073	−	0.561227i	−0.0722053	−	0.997390i	$-0.523004\pi$
$113$	−10.3333	−	5.96592i	−0.972073	−	0.561227i	−0.899868	+	0.436163i	$0.856337\pi$
$114$	−2.40791	−	4.33601i	−0.225521	−	0.406105i
$115$	−7.71884	−	4.45647i	−0.719785	−	0.415568i
$116$	−1.59933	+	0.923371i	−0.148494	+	0.0857329i
$117$	0.683135	−	20.4770i	0.0631559	−	1.89310i
$118$		−	1.94202i		−	0.178777i
$119$	8.19350	−	15.7708i	0.751097	−	1.44571i
$120$	0.0659003	−	3.95182i	0.00601584	−	0.360750i
$121$	−4.90265	−	8.49163i	−0.445695	−	0.771966i
$122$	1.33154			0.120552
$123$	4.12905	+	7.43534i	0.372304	+	0.670422i
$124$		−	2.02166i		−	0.181551i
$125$	10.9370			0.978234
$126$	−6.91748	−	3.89211i	−0.616258	−	0.346737i
$127$	−10.9133			−0.968400			−0.484200	−	0.874957i	$-0.660889\pi$
$127$	−10.9133			−0.968400			−0.484200	+	0.874957i	$0.660889\pi$
$128$			1.00000i			0.0883883i
$129$	12.9625	+	0.216161i	1.14128	+	0.0190320i
$130$	15.5841			1.36682
$131$	0.989677	+	1.71417i	0.0864684	+	0.149768i	0.906016	−	0.423243i	$-0.139108\pi$
$131$	0.989677	+	1.71417i	0.0864684	+	0.149768i	−0.819548	+	0.573011i	$0.805775\pi$
$132$	−1.65510	+	0.919121i	−0.144058	+	0.0799992i
$133$	−0.336608	−	7.56865i	−0.0291876	−	0.656285i
$134$		−	5.09918i		−	0.440502i
$135$	5.40768	+	10.5521i	0.465419	+	0.908184i
$136$	5.81732	−	3.35863i	0.498831	−	0.288000i
$137$	2.86923	+	1.65655i	0.245135	+	0.141528i	0.617534	−	0.786544i	$-0.288132\pi$
$137$	2.86923	+	1.65655i	0.245135	+	0.141528i	−0.372400	+	0.928072i	$0.621465\pi$
$138$	−6.76433	−	0.112802i	−0.575818	−	0.00960230i
$139$	−3.00698	−	1.73608i	−0.255048	−	0.147252i	0.367025	−	0.930211i	$-0.380376\pi$
$139$	−3.00698	−	1.73608i	−0.255048	−	0.147252i	−0.622074	+	0.782959i	$0.713710\pi$
$140$	2.78339	−	5.35745i	0.235239	−	0.452787i
$141$	−6.06133	+	10.1056i	−0.510456	+	0.851043i
$142$	−0.233507			−0.0195954
$143$	−3.73239	−	6.46469i	−0.312118	−	0.540605i
$144$	−1.41254	−	2.64665i	−0.117712	−	0.220554i
$145$	3.64950	+	2.10704i	0.303075	+	0.174980i
$146$	−3.40216	−	5.89272i	−0.281565	−	0.487685i
$147$	−6.80398	−	10.0352i	−0.561183	−	0.827692i
$148$	−3.57920	+	6.19935i	−0.294208	+	0.509584i
$149$	−11.5534	+	6.67036i	−0.946492	+	0.546457i	−0.891989	−	0.452056i	$-0.850691\pi$
$149$	−11.5534	+	6.67036i	−0.946492	+	0.546457i	−0.0545027	+	0.998514i	$0.517357\pi$
$150$	−0.313551	+	0.174124i	−0.0256013	+	0.0142171i
$151$	2.66995	−	4.62450i	0.217278	−	0.376336i	−0.736697	−	0.676223i	$-0.763616\pi$
$151$	2.66995	−	4.62450i	0.217278	−	0.376336i	0.953975	+	0.299887i	$0.0969489\pi$
$152$	1.43175	−	2.47987i	0.116131	−	0.201144i
$153$	−10.6522	+	17.1063i	−0.861179	+	1.38296i
$154$	−2.88902	+	0.128486i	−0.232804	+	0.0103537i
$155$	−3.99518	+	2.30662i	−0.320901	+	0.185272i
$156$	10.3414	−	5.74285i	0.827973	−	0.459796i
$157$			17.6673i			1.41000i	0.709206	+	0.705002i	$0.249054\pi$
$157$			17.6673i			1.41000i	−0.709206	+	0.705002i	$0.750946\pi$
$158$			7.27248i			0.578568i
$159$	−0.00740540	+	0.444077i	−0.000587286	+	0.0352176i
$160$	1.97618	−	1.14095i	0.156231	−	0.0902000i
$161$	−9.17035	−	4.76433i	−0.722725	−	0.375481i
$162$	7.47698	+	5.00947i	0.587447	+	0.393581i
$163$	7.94915	−	13.7683i	0.622625	−	1.07842i	−0.366370	−	0.930469i	$-0.619400\pi$
$163$	7.94915	−	13.7683i	0.622625	−	1.07842i	0.988995	−	0.147949i	$-0.0472672\pi$
$164$	−2.45515	+	4.25245i	−0.191715	+	0.332061i
$165$	3.70474	+	2.22210i	0.288413	+	0.172991i
$166$	−5.04638	+	2.91353i	−0.391675	+	0.226134i
$167$	2.85878	−	4.95155i	0.221219	−	0.383163i	−0.733959	−	0.679193i	$-0.762330\pi$
$167$	2.85878	−	4.95155i	0.221219	−	0.383163i	0.955178	+	0.296031i	$0.0956631\pi$
$168$	−0.127243	−	4.58081i	−0.00981703	−	0.353417i
$169$	16.8207	+	29.1344i	1.29390	+	2.24110i
$170$	−13.2746	−	7.66407i	−1.01811	−	0.587807i
$171$	−0.286431	+	8.58575i	−0.0219039	+	0.656569i
$172$	3.74246	+	6.48214i	0.285360	+	0.494258i
$173$	15.2052			1.15603			0.578013	−	0.816027i	$-0.303828\pi$
$173$	15.2052			1.15603			0.578013	+	0.816027i	$0.303828\pi$
$174$	3.19821	+	0.0533331i	0.242456	+	0.00404317i
$175$	−0.547313	+	0.0243412i	−0.0413730	+	0.00184002i
$176$	−0.946590	−	0.546514i	−0.0713519	−	0.0411950i
$177$	−1.73017	+	2.88458i	−0.130048	+	0.216818i
$178$	15.5834	+	8.99707i	1.16802	+	0.674359i
$179$	3.51582	−	2.02986i	0.262785	−	0.151719i	−0.362819	−	0.931859i	$-0.618186\pi$
$179$	3.51582	−	2.02986i	0.262785	−	0.151719i	0.625604	+	0.780141i	$0.284852\pi$
$180$	−3.61862	+	5.81113i	−0.269716	+	0.433136i
$181$		−	3.68452i		−	0.273869i	−0.990580	−	0.136934i	$-0.956275\pi$
$181$		−	3.68452i		−	0.273869i	0.990580	−	0.136934i	$-0.0437249\pi$
$182$	18.0512	−	0.802809i	1.33804	−	0.0595082i
$183$	−1.97781	−	1.18629i	−0.146204	−	0.0876931i
$184$	−1.95297	−	3.38264i	−0.143975	−	0.249371i
$185$	16.3347			1.20095
$186$	−1.80113	+	3.00288i	−0.132065	+	0.220182i
$187$			7.34216i			0.536912i
$188$	−6.80349			−0.496195
$189$	6.80734	+	11.9440i	0.495161	+	0.868801i
$190$	−6.53424			−0.474044
$191$		−	25.7989i		−	1.86674i	−0.358916	−	0.933370i	$-0.616854\pi$
$191$		−	25.7989i		−	1.86674i	0.358916	−	0.933370i	$-0.383146\pi$
$192$	0.890915	−	1.48535i	0.0642963	−	0.107196i
$193$	−9.28662			−0.668466			−0.334233	−	0.942491i	$-0.608477\pi$
$193$	−9.28662			−0.668466			−0.334233	+	0.942491i	$0.608477\pi$
$194$	2.38967	+	4.13903i	0.171568	+	0.297165i
$195$	−23.1479	−	13.8841i	−1.65766	−	0.994265i
$196$	2.94803	−	6.34895i	0.210573	−	0.453496i
$197$			5.86237i			0.417677i	0.977950	+	0.208838i	$0.0669683\pi$
$197$			5.86237i			0.417677i	−0.977950	+	0.208838i	$0.933032\pi$
$198$	3.27726	+	0.109333i	0.232905	+	0.00776997i
$199$	−13.9117	+	8.03191i	−0.986173	+	0.569367i	−0.904128	−	0.427262i	$-0.859478\pi$
$199$	−13.9117	+	8.03191i	−0.986173	+	0.569367i	−0.0820447	+	0.996629i	$0.526145\pi$
$200$	−0.179327	−	0.103535i	−0.0126804	−	0.00732101i
$201$	−4.54294	+	7.57408i	−0.320434	+	0.534234i
$202$	9.05829	+	5.22981i	0.637339	+	0.367968i
$203$	4.33578	+	2.25260i	0.304312	+	0.158101i
$204$	−11.6330	−	0.193992i	−0.814475	−	0.0135821i
$205$	11.2048			0.782579
$206$	6.37383	+	11.0398i	0.444086	+	0.769180i
$207$	9.94691	+	6.19400i	0.691358	+	0.430512i
$208$	5.91448	+	3.41473i	0.410096	+	0.236769i
$209$	1.56495	+	2.71057i	0.108250	+	0.187494i
$210$	−8.90734	+	5.47793i	−0.614665	+	0.378013i
$211$	12.3741	−	21.4325i	0.851867	−	1.47548i	−0.0276550	−	0.999618i	$-0.508804\pi$
$211$	12.3741	−	21.4325i	0.851867	−	1.47548i	0.879522	−	0.475859i	$-0.157863\pi$
$212$	−0.222069	+	0.128212i	−0.0152518	+	0.00880562i
$213$	0.346839	+	0.208035i	0.0237650	+	0.0142543i
$214$	4.76813	−	8.25865i	0.325943	−	0.564550i
$215$	8.53993	−	14.7916i	0.582419	−	1.00878i
$216$	−0.259820	+	5.18965i	−0.0176785	+	0.353111i
$217$	−4.50882	+	2.87758i	−0.306078	+	0.195343i
$218$	−4.99266	+	2.88251i	−0.338146	+	0.195228i
$219$	−0.196506	+	11.7838i	−0.0132786	+	0.796275i
$220$			2.49418i			0.168158i
$221$		−	45.8753i		−	3.08590i
$222$	10.8395	−	6.01946i	0.727497	−	0.403999i
$223$	3.20041	−	1.84776i	0.214315	−	0.123735i	−0.389000	−	0.921238i	$-0.627179\pi$
$223$	3.20041	−	1.84776i	0.214315	−	0.123735i	0.603315	+	0.797503i	$0.293846\pi$
$224$	2.23025	−	1.42337i	0.149015	−	0.0951030i
$225$	0.620863	+	0.0207127i	0.0413909	+	0.00138085i
$226$	−5.96592	+	10.3333i	−0.396847	+	0.687359i
$227$	2.30549	−	3.99322i	0.153020	−	0.265039i	−0.779316	−	0.626631i	$-0.784433\pi$
$227$	2.30549	−	3.99322i	0.153020	−	0.265039i	0.932336	+	0.361592i	$0.117767\pi$
$228$	−4.33601	+	2.40791i	−0.287160	+	0.159468i
$229$	−13.8220	+	7.98016i	−0.913386	+	0.527344i	−0.881519	−	0.472148i	$-0.843479\pi$
$229$	−13.8220	+	7.98016i	−0.913386	+	0.527344i	−0.0318672	+	0.999492i	$0.510145\pi$
$230$	−4.45647	+	7.71884i	−0.293851	+	0.508965i
$231$	4.40569	+	2.38303i	0.289873	+	0.156792i
$232$	0.923371	+	1.59933i	0.0606223	+	0.105001i
$233$	−6.17609	−	3.56577i	−0.404609	−	0.233601i	0.283862	−	0.958865i	$-0.408384\pi$
$233$	−6.17609	−	3.56577i	−0.404609	−	0.233601i	−0.688471	+	0.725264i	$0.741718\pi$
$234$	−20.4770	−	0.683135i	−1.33862	−	0.0446580i
$235$	7.76244	+	13.4449i	0.506366	+	0.877051i
$236$	−1.94202			−0.126415
$237$	6.47917	−	10.8022i	0.420867	−	0.701678i
$238$	−15.7708	−	8.19350i	−1.02227	−	0.531106i
$239$	13.6219	+	7.86462i	0.881129	+	0.508720i	0.871031	−	0.491229i	$-0.163452\pi$
$239$	13.6219	+	7.86462i	0.881129	+	0.508720i	0.0100987	+	0.999949i	$0.496785\pi$
$240$	−3.95182	−	0.0659003i	−0.255089	−	0.00425384i
$241$	1.39292	+	0.804201i	0.0897257	+	0.0518031i	0.544191	−	0.838961i	$-0.316837\pi$
$241$	1.39292	+	0.804201i	0.0897257	+	0.0518031i	−0.454466	+	0.890764i	$0.650170\pi$
$242$	−8.49163	+	4.90265i	−0.545863	+	0.315154i
$243$	−6.64294	−	14.1022i	−0.426145	−	0.904655i
$244$		−	1.33154i		−	0.0852432i
$245$	−15.9102	+	1.41799i	−1.01647	+	0.0905920i
$246$	7.43534	−	4.12905i	0.474060	−	0.263259i
$247$	−9.77810	−	16.9362i	−0.622166	−	1.07762i
$248$	−2.02166			−0.128376
$249$	10.0914	+	0.168283i	0.639514	+	0.0106645i
$250$		−	10.9370i		−	0.691716i
$251$	−18.3728			−1.15968			−0.579841	−	0.814729i	$-0.696885\pi$
$251$	−18.3728			−1.15968			−0.579841	+	0.814729i	$0.696885\pi$
$252$	−3.89211	+	6.91748i	−0.245180	+	0.435760i
$253$	4.26929			0.268408
$254$			10.9133i			0.684762i
$255$	12.8893	+	23.2103i	0.807162	+	1.45349i
$256$	1.00000			0.0625000
$257$	8.73678	+	15.1326i	0.544986	+	0.943943i	0.998608	+	0.0527487i	$0.0167982\pi$
$257$	8.73678	+	15.1326i	0.544986	+	0.943943i	−0.453622	+	0.891194i	$0.649868\pi$
$258$	0.216161	−	12.9625i	0.0134576	−	0.807009i
$259$	18.9206	−	0.841476i	1.17567	−	0.0522868i
$260$		−	15.5841i		−	0.966487i
$261$	−4.70295	−	2.92855i	−0.291105	−	0.181273i
$262$	1.71417	−	0.989677i	0.105902	−	0.0611424i
$263$	23.9148	+	13.8072i	1.47465	+	0.851389i	0.999592	−	0.0285666i	$-0.00909427\pi$
$263$	23.9148	+	13.8072i	1.47465	+	0.851389i	0.475057	+	0.879955i	$0.342428\pi$
$264$	0.919121	+	1.65510i	0.0565680	+	0.101864i
$265$	0.506740	+	0.292567i	0.0311288	+	0.0179722i
$266$	−7.56865	+	0.336608i	−0.464064	+	0.0206388i
$267$	−15.1312	−	27.2473i	−0.926013	−	1.66751i
$268$	−5.09918			−0.311482
$269$	−3.38607	−	5.86484i	−0.206452	−	0.357586i	0.744142	−	0.668021i	$-0.232858\pi$
$269$	−3.38607	−	5.86484i	−0.206452	−	0.357586i	−0.950594	+	0.310435i	$0.899525\pi$
$270$	10.5521	−	5.40768i	0.642183	−	0.329101i
$271$	7.23822	+	4.17899i	0.439691	+	0.253856i	0.703466	−	0.710729i	$-0.251635\pi$
$271$	7.23822	+	4.17899i	0.439691	+	0.253856i	−0.263776	+	0.964584i	$0.584968\pi$
$272$	−3.35863	−	5.81732i	−0.203647	−	0.352727i
$273$	−27.5276	−	14.8896i	−1.66605	−	0.901162i
$274$	1.65655	−	2.86923i	0.100076	−	0.173336i
$275$	0.196010	−	0.113166i	0.0118198	−	0.00682419i
$276$	−0.112802	+	6.76433i	−0.00678985	+	0.407165i
$277$	8.10617	−	14.0403i	0.487053	−	0.843600i	−0.512837	−	0.858486i	$-0.671405\pi$
$277$	8.10617	−	14.0403i	0.487053	−	0.843600i	0.999889	+	0.0148865i	$0.00473868\pi$
$278$	−1.73608	+	3.00698i	−0.104123	+	0.180346i
$279$	5.35063	−	2.85568i	0.320334	−	0.170965i
$280$	−5.35745	−	2.78339i	−0.320169	−	0.166339i
$281$	−25.3352	+	14.6273i	−1.51137	+	0.872590i	−0.511458	+	0.859308i	$0.670895\pi$
$281$	−25.3352	+	14.6273i	−1.51137	+	0.872590i	−0.999912	+	0.0132818i	$0.995772\pi$
$282$	10.1056	+	6.06133i	0.601778	+	0.360947i
$283$		−	1.43448i		−	0.0852712i	−0.999091	−	0.0426356i	$-0.986425\pi$
$283$		−	1.43448i		−	0.0852712i	0.999091	−	0.0426356i	$-0.0135754\pi$
$284$			0.233507i			0.0138561i
$285$	9.70565	+	5.82146i	0.574913	+	0.344833i
$286$	−6.46469	+	3.73239i	−0.382265	+	0.220701i
$287$	12.9786	−	0.577211i	0.766104	−	0.0340717i
$288$	−2.64665	+	1.41254i	−0.155955	+	0.0832347i
$289$	−14.0608	+	24.3541i	−0.827108	+	1.43259i
$290$	2.10704	−	3.64950i	0.123730	−	0.214306i
$291$	0.138025	−	8.27691i	0.00809118	−	0.485201i
$292$	−5.89272	+	3.40216i	−0.344845	+	0.199096i
$293$	−10.8260	+	18.7511i	−0.632459	+	1.09545i	0.354588	+	0.935023i	$0.384621\pi$
$293$	−10.8260	+	18.7511i	−0.632459	+	1.09545i	−0.987047	+	0.160429i	$0.948712\pi$
$294$	−10.0352	+	6.80398i	−0.585267	+	0.396816i
$295$	2.21575	+	3.83779i	0.129006	+	0.223444i
$296$	6.19935	+	3.57920i	0.360330	+	0.208037i
$297$	−4.77048	−	3.08216i	−0.276811	−	0.178845i
$298$	6.67036	+	11.5534i	0.386404	+	0.669271i
$299$	−26.6754			−1.54268
$300$	0.174124	+	0.313551i	0.0100530	+	0.0181029i
$301$	9.12987	−	17.5731i	0.526237	−	1.01290i
$302$	−4.62450	−	2.66995i	−0.266110	−	0.153639i
$303$	−8.79544	−	15.8383i	−0.505285	−	0.909885i
$304$	−2.47987	−	1.43175i	−0.142230	−	0.0821167i
$305$	−2.63137	+	1.51922i	−0.150672	+	0.0869904i
$306$	17.1063	+	10.6522i	0.977903	+	0.608945i
$307$		−	13.4732i		−	0.768957i	−0.923134	−	0.384479i	$-0.874381\pi$
$307$		−	13.4732i		−	0.768957i	0.923134	−	0.384479i	$-0.125619\pi$
$308$	0.128486	+	2.88902i	0.00732120	+	0.164617i
$309$	0.368147	−	22.0765i	0.0209432	−	1.25589i
$310$	2.30662	+	3.99518i	0.131007	+	0.226911i
$311$	−28.7338			−1.62934			−0.814672	−	0.579922i	$-0.803083\pi$
$311$	−28.7338			−1.62934			−0.814672	+	0.579922i	$0.803083\pi$
$312$	−5.74285	−	10.3414i	−0.325125	−	0.585465i
$313$		−	23.6293i		−	1.33561i	−0.744337	−	0.667805i	$-0.767234\pi$
$313$		−	23.6293i		−	1.33561i	0.744337	−	0.667805i	$-0.232766\pi$
$314$	17.6673			0.997023
$315$	18.1109	−	0.200966i	1.02043	−	0.0113231i
$316$	7.27248			0.409109
$317$			0.877680i			0.0492954i	0.999696	+	0.0246477i	$0.00784641\pi$
$317$			0.877680i			0.0492954i	−0.999696	+	0.0246477i	$0.992154\pi$
$318$	0.444077	+	0.00740540i	0.0249026	+	0.000415274i
$319$	−2.01854			−0.113017
$320$	−1.14095	−	1.97618i	−0.0637811	−	0.110472i
$321$	−14.4401	+	8.01900i	−0.805969	+	0.447577i
$322$	−4.76433	+	9.17035i	−0.265505	+	0.511043i
$323$			19.2349i			1.07026i
$324$	5.00947	−	7.47698i	0.278304	−	0.415388i
$325$	−1.22471	+	0.707086i	−0.0679346	+	0.0392221i
$326$	−13.7683	−	7.94915i	−0.762557	−	0.440262i
$327$	9.98393	+	0.166491i	0.552113	+	0.00920700i
$328$	4.25245	+	2.45515i	0.234802	+	0.135563i
$329$	9.68389	+	15.1735i	0.533890	+	0.836541i
$330$	2.22210	−	3.70474i	0.122323	−	0.203939i
$331$	−20.1830			−1.10936			−0.554680	−	0.832064i	$-0.687159\pi$
$331$	−20.1830			−1.10936			−0.554680	+	0.832064i	$0.687159\pi$
$332$	2.91353	+	5.04638i	0.159901	+	0.276956i
$333$	−21.4632	−	0.716039i	−1.17618	−	0.0392387i
$334$	−4.95155	−	2.85878i	−0.270937	−	0.156425i
$335$	5.81791	+	10.0769i	0.317866	+	0.550561i
$336$	−4.58081	+	0.127243i	−0.249904	+	0.00694169i
$337$	0.757605	−	1.31221i	0.0412694	−	0.0714807i	−0.844653	−	0.535314i	$-0.820193\pi$
$337$	0.757605	−	1.31221i	0.0412694	−	0.0714807i	0.885922	+	0.463834i	$0.153526\pi$
$338$	29.1344	−	16.8207i	1.58470	−	0.914927i
$339$	18.0676	−	10.0334i	0.981295	−	0.544941i
$340$	−7.66407	+	13.2746i	−0.415642	+	0.719914i
$341$	1.10487	−	1.91369i	0.0598319	−	0.103632i
$342$	8.58575	+	0.286431i	0.464264	+	0.0154884i
$343$	−18.3559	+	2.46207i	−0.991124	+	0.132939i
$344$	6.48214	−	3.74246i	0.349494	−	0.201780i
$345$	13.4963	−	7.49485i	0.726614	−	0.403509i
$346$		−	15.2052i		−	0.817434i
$347$			36.0985i			1.93787i	0.247320	+	0.968934i	$0.420450\pi$
$347$			36.0985i			1.93787i	−0.247320	+	0.968934i	$0.579550\pi$
$348$	0.0533331	−	3.19821i	0.00285895	−	0.171442i
$349$	−16.7962	+	9.69727i	−0.899078	+	0.519083i	−0.876901	−	0.480671i	$-0.840393\pi$
$349$	−16.7962	+	9.69727i	−0.899078	+	0.519083i	−0.0221769	+	0.999754i	$0.507060\pi$
$350$	0.0243412	+	0.547313i	0.00130109	+	0.0292551i
$351$	29.8069	+	19.2579i	1.59097	+	1.02791i
$352$	−0.546514	+	0.946590i	−0.0291293	+	0.0504534i
$353$	2.01909	−	3.49717i	0.107465	−	0.186136i	−0.807277	−	0.590172i	$-0.799060\pi$
$353$	2.01909	−	3.49717i	0.107465	−	0.186136i	0.914743	+	0.404037i	$0.132393\pi$
$354$	2.88458	+	1.73017i	0.153314	+	0.0919577i
$355$	0.461452	−	0.266419i	0.0244913	−	0.0141401i
$356$	8.99707	−	15.5834i	0.476844	−	0.825918i
$357$	16.1255	+	26.2207i	0.853450	+	1.38775i
$358$	−2.02986	−	3.51582i	−0.107281	−	0.185817i
$359$	21.2649	+	12.2773i	1.12232	+	0.647970i	0.941991	−	0.335637i	$-0.108952\pi$
$359$	21.2649	+	12.2773i	1.12232	+	0.647970i	0.180326	+	0.983607i	$0.442285\pi$
$360$	5.81113	+	3.61862i	0.306273	+	0.190718i
$361$	−5.40016	−	9.35335i	−0.284219	−	0.492282i
$362$	−3.68452			−0.193654
$363$	16.9809	+	0.283172i	0.891266	+	0.0148627i
$364$	−0.802809	−	18.0512i	−0.0420786	−	0.946140i
$365$	13.4466	+	7.76339i	0.703827	+	0.406354i
$366$	−1.18629	+	1.97781i	−0.0620084	+	0.103382i
$367$	−6.28109	−	3.62639i	−0.327870	−	0.189296i	0.327025	−	0.945016i	$-0.393954\pi$
$367$	−6.28109	−	3.62639i	−0.327870	−	0.189296i	−0.654895	+	0.755720i	$0.727287\pi$
$368$	−3.38264	+	1.95297i	−0.176332	+	0.101805i
$369$	−14.7227	−	0.491167i	−0.766435	−	0.0255691i
$370$		−	16.3347i		−	0.849203i
$371$	0.602031	+	0.312777i	0.0312559	+	0.0162386i
$372$	3.00288	+	1.80113i	0.155692	+	0.0933843i
$373$	14.8921	+	25.7939i	0.771083	+	1.33556i	0.936970	+	0.349410i	$0.113618\pi$
$373$	14.8921	+	25.7939i	0.771083	+	1.33556i	−0.165887	+	0.986145i	$0.553049\pi$
$374$	7.34216			0.379654
$375$	−9.74393	+	16.2453i	−0.503175	+	0.838902i
$376$			6.80349i			0.350863i
$377$	12.6122			0.649564
$378$	11.9440	−	6.80734i	0.614335	−	0.350132i
$379$	6.11280			0.313993			0.156997	−	0.987599i	$-0.449819\pi$
$379$	6.11280			0.313993			0.156997	+	0.987599i	$0.449819\pi$
$380$			6.53424i			0.335200i
$381$	9.72284	−	16.2101i	0.498116	−	0.830469i
$382$	−25.7989			−1.31998
$383$	−16.2451	−	28.1374i	−0.830088	−	1.43775i	−0.897968	−	0.440061i	$-0.854957\pi$
$383$	−16.2451	−	28.1374i	−0.830088	−	1.43775i	0.0678797	−	0.997694i	$-0.478377\pi$
$384$	−1.48535	−	0.890915i	−0.0757990	−	0.0454643i
$385$	5.56265	−	3.55015i	0.283499	−	0.180932i
$386$			9.28662i			0.472677i
$387$	−11.8695	+	19.0613i	−0.603363	+	0.968938i
$388$	4.13903	−	2.38967i	0.210127	−	0.121317i
$389$	1.80316	+	1.04105i	0.0914236	+	0.0527834i	0.545015	−	0.838426i	$-0.316524\pi$
$389$	1.80316	+	1.04105i	0.0914236	+	0.0527834i	−0.453591	+	0.891210i	$0.649857\pi$
$390$	−13.8841	+	23.1479i	−0.703051	+	1.17214i
$391$	22.7221	+	13.1186i	1.14910	+	0.663435i
$392$	−6.34895	−	2.94803i	−0.320670	−	0.148898i
$393$	−3.42786	−	0.0571628i	−0.172913	−	0.00288348i
$394$	5.86237			0.295342
$395$	−8.29754	−	14.3718i	−0.417495	−	0.723122i
$396$	0.109333	−	3.27726i	0.00549420	−	0.164689i
$397$	16.3994	+	9.46822i	0.823064	+	0.475196i	0.851472	−	0.524400i	$-0.175710\pi$
$397$	16.3994	+	9.46822i	0.823064	+	0.475196i	−0.0284077	+	0.999596i	$0.509044\pi$
$398$	8.03191	+	13.9117i	0.402603	+	0.697329i
$399$	11.5420	+	6.24305i	0.577823	+	0.312543i
$400$	−0.103535	+	0.179327i	−0.00517674	+	0.00896637i
$401$	3.35718	−	1.93827i	0.167650	−	0.0967926i	−0.413827	−	0.910355i	$-0.635808\pi$
$401$	3.35718	−	1.93827i	0.167650	−	0.0967926i	0.581477	+	0.813563i	$0.302475\pi$
$402$	7.57408	+	4.54294i	0.377761	+	0.226581i
$403$	−6.90343	+	11.9571i	−0.343884	+	0.595625i
$404$	5.22981	−	9.05829i	0.260193	−	0.450667i
$405$	−20.4914	−	1.36876i	−1.01823	−	0.0680142i
$406$	2.25260	−	4.33578i	0.111794	−	0.215181i
$407$	−6.77606	+	3.91216i	−0.335877	+	0.193919i
$408$	−0.193992	+	11.6330i	−0.00960402	+	0.575921i
$409$		−	16.1988i		−	0.800979i	−0.916301	−	0.400490i	$-0.868840\pi$
$409$		−	16.1988i		−	0.800979i	0.916301	−	0.400490i	$-0.131160\pi$
$410$		−	11.2048i		−	0.553367i
$411$	−5.01680	+	2.78597i	−0.247460	+	0.137422i
$412$	11.0398	−	6.37383i	0.543892	−	0.314016i
$413$	2.76421	+	4.33119i	0.136018	+	0.213124i
$414$	6.19400	−	9.94691i	0.304418	−	0.488864i
$415$	6.64838	−	11.5153i	0.326356	−	0.565266i
$416$	3.41473	−	5.91448i	0.167421	−	0.289981i
$417$	5.25765	−	2.91972i	0.257468	−	0.142979i
$418$	2.71057	−	1.56495i	0.132578	−	0.0765441i
$419$	−1.63790	+	2.83692i	−0.0800165	+	0.138593i	−0.903257	−	0.429100i	$-0.858831\pi$
$419$	−1.63790	+	2.83692i	−0.0800165	+	0.138593i	0.823240	+	0.567693i	$0.192164\pi$
$420$	5.47793	+	8.90734i	0.267296	+	0.434634i
$421$	−0.844823	−	1.46328i	−0.0411741	−	0.0713157i	0.844704	−	0.535234i	$-0.179777\pi$
$421$	−0.844823	−	1.46328i	−0.0411741	−	0.0713157i	−0.885878	+	0.463918i	$0.846443\pi$
$422$	−21.4325	−	12.3741i	−1.04332	−	0.602361i
$423$	−9.61019	−	18.0064i	−0.467264	−	0.875502i
$424$	0.128212	+	0.222069i	0.00622651	+	0.0107846i
$425$	1.39094			0.0674705
$426$	0.208035	−	0.346839i	0.0100793	−	0.0168044i
$427$	−2.96967	+	1.89528i	−0.143712	+	0.0917189i
$428$	−8.25865	−	4.76813i	−0.399197	−	0.230476i
$429$	12.9276	+	0.215580i	0.624150	+	0.0104083i
$430$	−14.7916	−	8.53993i	−0.713314	−	0.411832i
$431$	0.0157083	−	0.00906921i	0.000756644	−	0.000436848i	−0.499622	−	0.866244i	$-0.666528\pi$
$431$	0.0157083	−	0.00906921i	0.000756644	−	0.000436848i	0.500378	+	0.865807i	$0.333194\pi$
$432$	5.18965	+	0.259820i	0.249687	+	0.0125006i
$433$			5.36964i			0.258048i	0.991641	+	0.129024i	$0.0411845\pi$
$433$			5.36964i			0.258048i	−0.991641	+	0.129024i	$0.958815\pi$
$434$	2.87758	+	4.50882i	0.138128	+	0.216430i
$435$	−6.38110	+	3.54360i	−0.305950	+	0.169903i
$436$	2.88251	+	4.99266i	0.138047	+	0.239105i
$437$	11.1847			0.535035
$438$	11.7838	+	0.196506i	0.563051	+	0.00938941i
$439$		−	21.8401i		−	1.04237i	−0.853443	−	0.521186i	$-0.825490\pi$
$439$		−	21.8401i		−	1.04237i	0.853443	−	0.521186i	$-0.174510\pi$
$440$	2.49418			0.118905
$441$	20.9676	−	1.16575i	0.998458	−	0.0555121i
$442$	−45.8753			−2.18206
$443$		−	2.09931i		−	0.0997413i	−0.998756	−	0.0498707i	$-0.984119\pi$
$443$		−	2.09931i		−	0.0997413i	0.998756	−	0.0498707i	$-0.0158809\pi$
$444$	−6.01946	−	10.8395i	−0.285671	−	0.514418i
$445$	−41.0608			−1.94647
$446$	−1.84776	−	3.20041i	−0.0874938	−	0.151544i
$447$	0.385274	−	23.1036i	0.0182228	−	1.09276i
$448$	−1.42337	−	2.23025i	−0.0672480	−	0.105369i
$449$		−	27.1356i		−	1.28061i	−0.768122	−	0.640303i	$-0.778809\pi$
$449$		−	27.1356i		−	1.28061i	0.768122	−	0.640303i	$-0.221191\pi$
$450$	0.0207127	−	0.620863i	0.000976406	−	0.0292678i
$451$	−4.64805	+	2.68355i	−0.218868	+	0.126364i
$452$	10.3333	+	5.96592i	0.486036	+	0.280613i
$453$	4.49030	+	8.08586i	0.210973	+	0.379907i
$454$	−3.99322	−	2.30549i	−0.187411	−	0.108202i
$455$	−34.7565	+	22.1820i	−1.62941	+	1.03991i
$456$	2.40791	+	4.33601i	0.112761	+	0.203052i
$457$	8.43196			0.394431			0.197215	−	0.980360i	$-0.436810\pi$
$457$	8.43196			0.394431			0.197215	+	0.980360i	$0.436810\pi$
$458$	7.98016	+	13.8220i	0.372888	+	0.645862i
$459$	−15.9187	−	31.0625i	−0.743020	−	1.44987i
$460$	7.71884	+	4.45647i	0.359893	+	0.207784i
$461$	4.67153	+	8.09133i	0.217575	+	0.376851i	0.954066	−	0.299596i	$-0.0968520\pi$
$461$	4.67153	+	8.09133i	0.217575	+	0.376851i	−0.736491	+	0.676447i	$0.763519\pi$
$462$	2.38303	−	4.40569i	0.110869	−	0.204971i
$463$	−12.7281	+	22.0458i	−0.591526	+	1.02455i	0.402501	+	0.915420i	$0.368141\pi$
$463$	−12.7281	+	22.0458i	−0.591526	+	1.02455i	−0.994027	+	0.109134i	$0.965192\pi$
$464$	1.59933	−	0.923371i	0.0742469	−	0.0428664i
$465$	0.133228	−	7.98925i	0.00617831	−	0.370493i
$466$	−3.56577	+	6.17609i	−0.165181	+	0.286102i
$467$	−10.3199	+	17.8746i	−0.477547	+	0.827136i	−0.999669	−	0.0257351i	$-0.991807\pi$
$467$	−10.3199	+	17.8746i	−0.477547	+	0.827136i	0.522122	+	0.852871i	$0.325141\pi$
$468$	−0.683135	+	20.4770i	−0.0315779	+	0.946548i
$469$	7.25803	+	11.3724i	0.335145	+	0.525131i
$470$	13.4449	−	7.76244i	0.620169	−	0.358055i
$471$	−26.2421	−	15.7401i	−1.20917	−	0.725264i
$472$			1.94202i			0.0893886i
$473$			8.18124i			0.376174i
$474$	−10.8022	−	6.47917i	−0.496161	−	0.297598i
$475$	0.513506	−	0.296473i	0.0235613	−	0.0136031i
$476$	−8.19350	+	15.7708i	−0.375548	+	0.722853i
$477$	−0.653013	−	0.406635i	−0.0298994	−	0.0186185i
$478$	7.86462	−	13.6219i	0.359720	−	0.623053i
$479$	3.07442	−	5.32505i	0.140474	−	0.243308i	−0.787201	−	0.616696i	$-0.788471\pi$
$479$	3.07442	−	5.32505i	0.140474	−	0.243308i	0.927675	+	0.373388i	$0.121804\pi$
$480$	−0.0659003	+	3.95182i	−0.00300792	+	0.180375i
$481$	42.3382	−	24.4440i	1.93046	−	1.11455i
$482$	0.804201	−	1.39292i	0.0366303	−	0.0634456i
$483$	15.2467	−	9.37658i	0.693749	−	0.426649i
$484$	4.90265	+	8.49163i	0.222848	+	0.385983i
$485$	−9.44486	−	5.45299i	−0.428869	−	0.247608i
$486$	−14.1022	+	6.64294i	−0.639688	+	0.301330i
$487$	−9.86365	−	17.0843i	−0.446965	−	0.774166i	0.551222	−	0.834359i	$-0.314162\pi$
$487$	−9.86365	−	17.0843i	−0.446965	−	0.774166i	−0.998187	+	0.0601930i	$0.980828\pi$
$488$	−1.33154			−0.0602760
$489$	13.3688	+	24.0737i	0.604557	+	1.08865i
$490$	1.41799	+	15.9102i	0.0640582	+	0.718751i
$491$	3.42935	+	1.97994i	0.154764	+	0.0893533i	0.575382	−	0.817885i	$-0.304853\pi$
$491$	3.42935	+	1.97994i	0.154764	+	0.0893533i	−0.420618	+	0.907238i	$0.638187\pi$
$492$	−4.12905	−	7.43534i	−0.186152	−	0.335211i
$493$	−10.7431	−	6.20253i	−0.483845	−	0.279348i
$494$	−16.9362	+	9.77810i	−0.761994	+	0.439938i
$495$	−6.60121	+	3.52313i	−0.296702	+	0.158353i
$496$			2.02166i			0.0907754i
$497$	0.520778	−	0.332367i	0.0233601	−	0.0149087i
$498$	0.168283	−	10.0914i	0.00754094	−	0.452205i
$499$	18.4092	+	31.8856i	0.824108	+	1.42740i	0.902599	+	0.430482i	$0.141656\pi$
$499$	18.4092	+	31.8856i	0.824108	+	1.42740i	−0.0784916	+	0.996915i	$0.525010\pi$
$500$	−10.9370			−0.489117
$501$	4.80786	+	8.65771i	0.214800	+	0.386798i
$502$			18.3728i			0.820019i
$503$	12.3802			0.552004			0.276002	−	0.961157i	$-0.410990\pi$
$503$	12.3802			0.552004			0.276002	+	0.961157i	$0.410990\pi$
$504$	6.91748	+	3.89211i	0.308129	+	0.173368i
$505$	−23.8678			−1.06210
$506$		−	4.26929i		−	0.189793i
$507$	−58.2606	−	0.971551i	−2.58745	−	0.0431481i
$508$	10.9133			0.484200
$509$	−7.54528	−	13.0688i	−0.334438	−	0.579264i	0.648938	−	0.760841i	$-0.275213\pi$
$509$	−7.54528	−	13.0688i	−0.334438	−	0.579264i	−0.983377	+	0.181577i	$0.941880\pi$
$510$	23.2103	−	12.8893i	1.02777	−	0.570750i
$511$	15.9752	+	8.29969i	0.706701	+	0.367157i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.4977	−	8.07463i	−0.551786	−	0.356504i
$514$	15.1326	−	8.73678i	0.667468	−	0.385363i
$515$	−25.1917	−	14.5445i	−1.11008	−	0.640905i
$516$	−12.9625	−	0.216161i	−0.570641	−	0.00951598i
$517$	−6.44011	−	3.71820i	−0.283236	−	0.163526i
$518$	−0.841476	−	18.9206i	−0.0369723	−	0.831325i
$519$	−13.5465	+	22.5850i	−0.594626	+	0.991372i
$520$	−15.5841			−0.683410
$521$	−12.4908	−	21.6347i	−0.547231	−	0.947832i	−0.998463	−	0.0554255i	$-0.982348\pi$
$521$	−12.4908	−	21.6347i	−0.547231	−	0.947832i	0.451232	−	0.892407i	$-0.350985\pi$
$522$	−2.92855	+	4.70295i	−0.128179	+	0.205842i
$523$	21.6818	+	12.5180i	0.948077	+	0.547372i	0.892483	−	0.451081i	$-0.148961\pi$
$523$	21.6818	+	12.5180i	0.948077	+	0.547372i	0.0555939	+	0.998453i	$0.482295\pi$
$524$	−0.989677	−	1.71417i	−0.0432342	−	0.0748839i
$525$	0.451455	−	0.834639i	0.0197031	−	0.0364266i
$526$	13.8072	−	23.9148i	0.602023	−	1.04273i
$527$	11.7607	−	6.79003i	0.512303	−	0.295778i
$528$	1.65510	−	0.919121i	0.0720289	−	0.0399996i
$529$	−3.87185	+	6.70625i	−0.168341	+	0.291576i
$530$	0.292567	−	0.506740i	0.0127083	−	0.0220114i
$531$	−2.74318	−	5.13983i	−0.119044	−	0.223050i
$532$	0.336608	+	7.56865i	0.0145938	+	0.328143i
$533$	29.0419	−	16.7674i	1.25795	−	0.726275i
$534$	−27.2473	+	15.1312i	−1.17911	+	0.654790i
$535$			21.7608i			0.940802i
$536$			5.09918i			0.220251i
$537$	−0.117243	+	7.03067i	−0.00505941	+	0.303396i
$538$	−5.86484	+	3.38607i	−0.252851	+	0.145984i
$539$	6.26036	−	4.39871i	0.269653	−	0.189466i
$540$	−5.40768	−	10.5521i	−0.232710	−	0.454092i
$541$	7.23042	−	12.5235i	0.310860	−	0.538426i	−0.667689	−	0.744441i	$-0.732716\pi$
$541$	7.23042	−	12.5235i	0.310860	−	0.538426i	0.978549	+	0.206015i	$0.0660496\pi$
$542$	4.17899	−	7.23822i	0.179503	−	0.310908i
$543$	5.47281	+	3.28260i	0.234861	+	0.140870i
$544$	−5.81732	+	3.35863i	−0.249416	+	0.144000i
$545$	6.57761	−	11.3928i	0.281754	−	0.488012i
$546$	−14.8896	+	27.5276i	−0.637218	+	1.17807i
$547$	16.9160	+	29.2994i	0.723277	+	1.25275i	0.959679	+	0.281098i	$0.0906985\pi$
$547$	16.9160	+	29.2994i	0.723277	+	1.25275i	−0.236402	+	0.971655i	$0.575968\pi$
$548$	−2.86923	−	1.65655i	−0.122567	−	0.0707642i
$549$	3.52412	−	1.88085i	0.150406	−	0.0802729i
$550$	−0.113166	−	0.196010i	−0.00482543	−	0.00835789i
$551$	−5.28816			−0.225283
$552$	6.76433	+	0.112802i	0.287909	+	0.00480115i
$553$	−10.3514	−	16.2195i	−0.440188	−	0.689721i
$554$	−14.0403	−	8.10617i	−0.596515	−	0.344398i
$555$	−14.5529	+	24.2628i	−0.617735	+	1.02990i
$556$	3.00698	+	1.73608i	0.127524	+	0.0736261i
$557$	−5.09456	+	2.94134i	−0.215863	+	0.124629i	−0.604033	−	0.796959i	$-0.706441\pi$
$557$	−5.09456	+	2.94134i	−0.215863	+	0.124629i	0.388170	+	0.921588i	$0.373107\pi$
$558$	−2.85568	−	5.35063i	−0.120891	−	0.226510i
$559$		−	51.1180i		−	2.16206i
$560$	−2.78339	+	5.35745i	−0.117620	+	0.226393i
$561$	−10.9057	−	6.54124i	−0.460438	−	0.276171i
$562$	14.6273	+	25.3352i	0.617014	+	1.06870i
$563$	15.5637			0.655931			0.327966	−	0.944690i	$-0.393637\pi$
$563$	15.5637			0.655931			0.327966	+	0.944690i	$0.393637\pi$
$564$	6.06133	−	10.1056i	0.255228	−	0.425521i
$565$		−	27.2273i		−	1.14546i
$566$	−1.43448			−0.0602958
$567$	−23.8059	−	0.529836i	−0.999752	−	0.0222510i
$568$	0.233507			0.00979772
$569$		−	26.2110i		−	1.09882i	−0.835553	−	0.549410i	$-0.814852\pi$
$569$		−	26.2110i		−	1.09882i	0.835553	−	0.549410i	$-0.185148\pi$
$570$	5.82146	−	9.70565i	0.243834	−	0.406525i
$571$	25.6181			1.07208			0.536041	−	0.844192i	$-0.319919\pi$
$571$	25.6181			1.07208			0.536041	+	0.844192i	$0.319919\pi$
$572$	3.73239	+	6.46469i	0.156059	+	0.270302i
$573$	38.3204	+	22.9846i	1.60086	+	0.960195i
$574$	−0.577211	−	12.9786i	−0.0240923	−	0.541717i
$575$		−	0.808799i		−	0.0337292i
$576$	1.41254	+	2.64665i	0.0588558	+	0.110277i
$577$	28.0540	−	16.1970i	1.16790	−	0.674288i	0.214717	−	0.976676i	$-0.431117\pi$
$577$	28.0540	−	16.1970i	1.16790	−	0.674288i	0.953185	+	0.302388i	$0.0977839\pi$
$578$	24.3541	+	14.0608i	1.01300	+	0.584853i
$579$	8.27360	−	13.7939i	0.343839	−	0.573255i
$580$	−3.64950	−	2.10704i	−0.151537	−	0.0874901i
$581$	7.10766	−	13.6808i	0.294875	−	0.567574i
$582$	−8.27691	−	0.138025i	−0.343089	−	0.00572133i
$583$	−0.280278			−0.0116079
$584$	3.40216	+	5.89272i	0.140782	+	0.243842i
$585$	41.2457	−	22.0132i	1.70530	−	0.910134i
$586$	18.7511	+	10.8260i	0.774601	+	0.447216i
$587$	−4.76851	−	8.25931i	−0.196818	−	0.340898i	0.750677	−	0.660669i	$-0.229727\pi$
$587$	−4.76851	−	8.25931i	−0.196818	−	0.340898i	−0.947495	+	0.319771i	$0.896394\pi$
$588$	6.80398	+	10.0352i	0.280591	+	0.413846i
$589$	2.89453	−	5.01347i	0.119267	−	0.206576i
$590$	3.83779	−	2.21575i	0.157999	−	0.0912208i
$591$	−8.70769	−	5.22288i	−0.358186	−	0.214841i
$592$	3.57920	−	6.19935i	0.147104	−	0.254792i
$593$	−1.89409	+	3.28065i	−0.0777808	+	0.134720i	−0.902292	−	0.431125i	$-0.858117\pi$
$593$	−1.89409	+	3.28065i	−0.0777808	+	0.134720i	0.824511	+	0.565845i	$0.191450\pi$
$594$	−3.08216	+	4.77048i	−0.126463	+	0.195735i
$595$	40.5144	−	1.80184i	1.66093	−	0.0738681i
$596$	11.5534	−	6.67036i	0.473246	−	0.273229i
$597$	0.463916	−	27.8195i	0.0189868	−	1.13858i
$598$			26.6754i			1.09084i
$599$			36.1388i			1.47659i	0.674478	+	0.738295i	$0.264369\pi$
$599$			36.1388i			1.47659i	−0.674478	+	0.738295i	$0.735631\pi$
$600$	0.313551	−	0.174124i	0.0128007	−	0.00710857i
$601$	−13.8275	+	7.98332i	−0.564036	+	0.325646i	−0.754764	−	0.655997i	$-0.772249\pi$
$601$	−13.8275	+	7.98332i	−0.564036	+	0.325646i	0.190728	+	0.981643i	$0.438915\pi$
$602$	−17.5731	−	9.12987i	−0.716227	−	0.372106i
$603$	−7.20279	−	13.4957i	−0.293320	−	0.549588i
$604$	−2.66995	+	4.62450i	−0.108639	+	0.188168i
$605$	11.1873	−	19.3771i	0.454830	−	0.787789i
$606$	−15.8383	+	8.79544i	−0.643386	+	0.357290i
$607$	−19.6190	+	11.3270i	−0.796309	+	0.459749i	−0.842179	−	0.539198i	$-0.818727\pi$
$607$	−19.6190	+	11.3270i	−0.796309	+	0.459749i	0.0458701	+	0.998947i	$0.485394\pi$
$608$	−1.43175	+	2.47987i	−0.0580653	+	0.100572i
$609$	−7.20871	+	4.43329i	−0.292112	+	0.179646i
$610$	1.51922	+	2.63137i	0.0615115	+	0.106541i
$611$	40.2391	+	23.2321i	1.62790	+	0.939868i
$612$	10.6522	−	17.1063i	0.430589	−	0.691481i
$613$	−1.84758	−	3.20011i	−0.0746232	−	0.129251i	0.826299	−	0.563231i	$-0.190442\pi$
$613$	−1.84758	−	3.20011i	−0.0746232	−	0.129251i	−0.900922	+	0.433980i	$0.857109\pi$
$614$	−13.4732			−0.543735
$615$	−9.98256	+	16.6431i	−0.402536	+	0.671115i
$616$	2.88902	−	0.128486i	0.116402	−	0.00517687i
$617$	22.5187	+	13.0011i	0.906567	+	0.523407i	0.879325	−	0.476222i	$-0.157994\pi$
$617$	22.5187	+	13.0011i	0.906567	+	0.523407i	0.0272418	+	0.999629i	$0.491328\pi$
$618$	−22.0765	−	0.368147i	−0.888049	−	0.0148090i
$619$	20.5526	+	11.8660i	0.826079	+	0.476937i	0.852508	−	0.522714i	$-0.175080\pi$
$619$	20.5526	+	11.8660i	0.826079	+	0.476937i	−0.0264296	+	0.999651i	$0.508414\pi$
$620$	3.99518	−	2.30662i	0.160450	−	0.0926360i
$621$	−18.0621	+	9.25634i	−0.724808	+	0.371444i
$622$			28.7338i			1.15212i
$623$	−47.5610	+	2.11523i	−1.90549	+	0.0847448i
$624$	−10.3414	+	5.74285i	−0.413986	+	0.229898i
$625$	12.9962	+	22.5101i	0.519849	+	0.900406i
$626$	−23.6293			−0.944418
$627$	−5.42038	−	0.0903900i	−0.216469	−	0.00360983i
$628$		−	17.6673i		−	0.705002i
$629$	−48.0848			−1.91727
$630$	−0.200966	−	18.1109i	−0.00800666	−	0.721556i
$631$	−0.664631			−0.0264586			−0.0132293	−	0.999912i	$-0.504211\pi$
$631$	−0.664631			−0.0264586			−0.0132293	+	0.999912i	$0.504211\pi$
$632$		−	7.27248i		−	0.289284i
$633$	20.8106	+	37.4744i	0.827147	+	1.48947i
$634$	0.877680			0.0348571
$635$	−12.4515	−	21.5667i	−0.494125	−	0.855849i
$636$	0.00740540	−	0.444077i	0.000293643	−	0.0176088i
$637$	−39.1160	+	27.4840i	−1.54983	+	1.08896i
$638$			2.01854i			0.0799148i
$639$	−0.618009	+	0.329837i	−0.0244481	+	0.0130482i
$640$	−1.97618	+	1.14095i	−0.0781155	+	0.0451000i
$641$	7.27466	+	4.20003i	0.287332	+	0.165891i	0.636738	−	0.771080i	$-0.280283\pi$
$641$	7.27466	+	4.20003i	0.287332	+	0.165891i	−0.349406	+	0.936971i	$0.613617\pi$
$642$	8.01900	+	14.4401i	0.316485	+	0.569906i
$643$	−0.237974	−	0.137394i	−0.00938478	−	0.00541831i	0.495300	−	0.868722i	$-0.335058\pi$
$643$	−0.237974	−	0.137394i	−0.00938478	−	0.00541831i	−0.504685	+	0.863304i	$0.668391\pi$
$644$	9.17035	+	4.76433i	0.361362	+	0.187741i
$645$	14.3624	+	25.8629i	0.565518	+	1.01835i
$646$	19.2349			0.756789
$647$	17.0508	+	29.5328i	0.670335	+	1.16105i	0.977809	+	0.209498i	$0.0671829\pi$
$647$	17.0508	+	29.5328i	0.670335	+	1.16105i	−0.307474	+	0.951556i	$0.599484\pi$
$648$	−7.47698	−	5.00947i	−0.293724	−	0.196790i
$649$	−1.83830	−	1.06134i	−0.0721594	−	0.0416612i
$650$	0.707086	+	1.22471i	0.0277342	+	0.0480370i
$651$	−0.257243	−	9.26086i	−0.0100822	−	0.362962i
$652$	−7.94915	+	13.7683i	−0.311313	+	0.539209i
$653$	−1.48356	+	0.856531i	−0.0580560	+	0.0335187i	−0.528747	−	0.848779i	$-0.677338\pi$
$653$	−1.48356	+	0.856531i	−0.0580560	+	0.0335187i	0.470691	+	0.882298i	$0.344005\pi$
$654$	0.166491	−	9.98393i	0.00651033	−	0.390403i
$655$	−2.25834	+	3.91157i	−0.0882408	+	0.152838i
$656$	2.45515	−	4.25245i	0.0958576	−	0.166030i
$657$	−17.3280	−	10.7902i	−0.676030	−	0.420967i
$658$	15.1735	−	9.68389i	0.591524	−	0.377517i
$659$	30.0556	−	17.3526i	1.17080	−	0.675961i	0.216930	−	0.976187i	$-0.430396\pi$
$659$	30.0556	−	17.3526i	1.17080	−	0.675961i	0.953868	+	0.300226i	$0.0970622\pi$
$660$	−3.70474	−	2.22210i	−0.144207	−	0.0864953i
$661$			38.3447i			1.49144i	0.666261	+	0.745718i	$0.267894\pi$
$661$			38.3447i			1.49144i	−0.666261	+	0.745718i	$0.732106\pi$
$662$			20.1830i			0.784435i
$663$	68.1409	+	40.8710i	2.64637	+	1.58730i
$664$	5.04638	−	2.91353i	0.195838	−	0.113067i
$665$	14.5730	−	9.30065i	0.565116	−	0.360664i
$666$	−0.716039	+	21.4632i	−0.0277459	+	0.831684i
$667$	−3.60662	+	6.24686i	−0.139649	+	0.241879i
$668$	−2.85878	+	4.95155i	−0.110610	+	0.191581i
$669$	−0.106725	+	6.39993i	−0.00412622	+	0.247435i
$670$	10.0769	−	5.81791i	0.389305	−	0.224765i
$671$	0.727706	−	1.26042i	0.0280928	−	0.0486581i
$672$	0.127243	+	4.58081i	0.00490852	+	0.176709i
$673$	−8.33538	−	14.4373i	−0.321305	−	0.556517i	0.659452	−	0.751746i	$-0.270788\pi$
$673$	−8.33538	−	14.4373i	−0.321305	−	0.556517i	−0.980758	+	0.195229i	$0.937455\pi$
$674$	−1.31221	−	0.757605i	−0.0505445	−	0.0291819i
$675$	−0.583902	+	0.903747i	−0.0224744	+	0.0347852i
$676$	−16.8207	−	29.1344i	−0.646951	−	1.12055i
$677$	20.9365			0.804653			0.402327	−	0.915496i	$-0.368202\pi$
$677$	20.9365			0.804653			0.402327	+	0.915496i	$0.368202\pi$
$678$	−10.0334	−	18.0676i	−0.385331	−	0.693881i
$679$	−11.2209	−	5.82968i	−0.430620	−	0.223723i
$680$	13.2746	+	7.66407i	0.509056	+	0.293903i
$681$	3.87734	+	6.98208i	0.148580	+	0.267554i
$682$	−1.91369	−	1.10487i	−0.0732789	−	0.0423076i
$683$	6.62003	−	3.82208i	0.253308	−	0.146248i	−0.367970	−	0.929838i	$-0.619947\pi$
$683$	6.62003	−	3.82208i	0.253308	−	0.146248i	0.621278	+	0.783590i	$0.286614\pi$
$684$	0.286431	−	8.58575i	0.0109519	−	0.328284i
$685$			7.56016i			0.288859i
$686$	2.46207	+	18.3559i	0.0940024	+	0.700831i
$687$	0.460927	−	27.6402i	0.0175855	−	1.05454i
$688$	−3.74246	−	6.48214i	−0.142680	−	0.247129i
$689$	1.75123			0.0667167
$690$	−7.49485	−	13.4963i	−0.285324	−	0.513794i
$691$			10.5131i			0.399937i	0.979802	+	0.199969i	$0.0640840\pi$
$691$			10.5131i			0.399937i	−0.979802	+	0.199969i	$0.935916\pi$
$692$	−15.2052			−0.578013
$693$	−7.46473	+	4.42092i	−0.283562	+	0.167937i
$694$	36.0985			1.37028
$695$		−	7.92311i		−	0.300541i
$696$	−3.19821	−	0.0533331i	−0.121228	−	0.00202159i
$697$	−32.9838			−1.24935
$698$	9.69727	+	16.7962i	0.367047	+	0.635744i
$699$	10.7988	−	5.99687i	0.408448	−	0.226822i
$700$	0.547313	−	0.0243412i	0.0206865	−	0.000920011i
$701$		−	15.7336i		−	0.594250i	−0.954839	−	0.297125i	$-0.903972\pi$
$701$		−	15.7336i		−	0.594250i	0.954839	−	0.297125i	$-0.0960277\pi$
$702$	19.2579	−	29.8069i	0.726844	−	1.12499i
$703$	−17.7519	+	10.2491i	−0.669526	+	0.386551i
$704$	0.946590	+	0.546514i	0.0356759	+	0.0205975i
$705$	−26.8861	−	0.448352i	−1.01259	−	0.0168859i
$706$	−3.49717	−	2.01909i	−0.131618	−	0.0759895i
$707$	−27.6462	+	1.22954i	−1.03974	+	0.0462415i
$708$	1.73017	−	2.88458i	0.0650239	−	0.108409i
$709$	−2.89945			−0.108891			−0.0544456	−	0.998517i	$-0.517339\pi$
$709$	−2.89945			−0.108891			−0.0544456	+	0.998517i	$0.517339\pi$
$710$	−0.266419	−	0.461452i	−0.00999854	−	0.0173180i
$711$	10.2727	+	19.2477i	0.385255	+	0.721845i
$712$	−15.5834	−	8.99707i	−0.584012	−	0.337179i
$713$	−3.94824	−	6.83855i	−0.147863	−	0.256106i
$714$	26.2207	−	16.1255i	0.981284	−	0.603481i
$715$	8.51695	−	14.7518i	0.318516	−	0.551686i
$716$	−3.51582	+	2.02986i	−0.131392	+	0.0758595i
$717$	−23.8177	+	13.2266i	−0.889489	+	0.493958i
$718$	12.2773	−	21.2649i	0.458184	−	0.793598i
$719$	20.5644	−	35.6186i	0.766924	−	1.32835i	−0.172299	−	0.985045i	$-0.555120\pi$
$719$	20.5644	−	35.6186i	0.766924	−	1.32835i	0.939223	−	0.343307i	$-0.111547\pi$
$720$	3.61862	−	5.81113i	0.134858	−	0.216568i
$721$	−29.9290	−	15.5492i	−1.11461	−	0.579082i
$722$	−9.35335	+	5.40016i	−0.348096	+	0.200973i
$723$	−2.43549	+	1.35250i	−0.0905769	+	0.0502999i
$724$			3.68452i			0.136934i
$725$			0.382404i			0.0142021i
$726$	0.283172	−	16.9809i	0.0105095	−	0.630220i
$727$	−33.6212	+	19.4112i	−1.24694	+	0.719921i	−0.970498	−	0.241109i	$-0.922489\pi$
$727$	−33.6212	+	19.4112i	−1.24694	+	0.719921i	−0.276442	+	0.961031i	$0.589155\pi$
$728$	−18.0512	+	0.802809i	−0.669022	+	0.0297541i
$729$	26.8650	+	2.69675i	0.995000	+	0.0998795i
$730$	7.76339	−	13.4466i	0.287336	−	0.497681i
$731$	−25.1391	+	43.5423i	−0.929804	+	1.61047i
$732$	1.97781	+	1.18629i	0.0731019	+	0.0438466i
$733$	22.5362	−	13.0113i	0.832394	−	0.480583i	−0.0222778	−	0.999752i	$-0.507092\pi$
$733$	22.5362	−	13.0113i	0.832394	−	0.480583i	0.854672	+	0.519169i	$0.173758\pi$
$734$	−3.62639	+	6.28109i	−0.133852	+	0.231839i
$735$	12.0685	−	24.8956i	0.445152	−	0.918288i
$736$	1.95297	+	3.38264i	0.0719873	+	0.124686i
$737$	−4.82683	−	2.78677i	−0.177799	−	0.102652i
$738$	−0.491167	+	14.7227i	−0.0180801	+	0.541951i
$739$	−3.70004	−	6.40866i	−0.136108	−	0.235746i	0.789912	−	0.613220i	$-0.210126\pi$
$739$	−3.70004	−	6.40866i	−0.136108	−	0.235746i	−0.926020	+	0.377474i	$0.876793\pi$
$740$	−16.3347			−0.600477
$741$	33.8676	+	0.564775i	1.24416	+	0.0207475i
$742$	0.312777	−	0.602031i	0.0114824	−	0.0221013i
$743$	−24.3241	−	14.0435i	−0.892366	−	0.515208i	−0.0176504	−	0.999844i	$-0.505619\pi$
$743$	−24.3241	−	14.0435i	−0.892366	−	0.515208i	−0.874716	+	0.484636i	$0.838952\pi$
$744$	1.80113	−	3.00288i	0.0660327	−	0.110091i
$745$	−26.3637	−	15.2211i	−0.965892	−	0.557658i
$746$	25.7939	−	14.8921i	0.944380	−	0.545238i
$747$	−9.24051	+	14.8393i	−0.338092	+	0.542941i
$748$		−	7.34216i		−	0.268456i
$749$	1.12100	+	25.2057i	0.0409604	+	0.920996i
$750$	16.2453	+	9.74393i	0.593194	+	0.355798i
$751$	−21.1897	−	36.7016i	−0.773221	−	1.33926i	−0.935789	−	0.352561i	$-0.885311\pi$
$751$	−21.1897	−	36.7016i	−0.773221	−	1.33926i	0.162567	−	0.986697i	$-0.448023\pi$
$752$	6.80349			0.248098
$753$	16.3686	−	27.2901i	0.596506	−	0.994507i
$754$		−	12.6122i		−	0.459311i
$755$	12.1851			0.443463
$756$	−6.80734	−	11.9440i	−0.247581	−	0.434401i
$757$	−41.6462			−1.51366			−0.756828	−	0.653614i	$-0.773252\pi$
$757$	−41.6462			−1.51366			−0.756828	+	0.653614i	$0.773252\pi$
$758$		−	6.11280i		−	0.222027i
$759$	−3.80358	+	6.34140i	−0.138061	+	0.230178i
$760$	6.53424			0.237022
$761$	−17.4823	−	30.2802i	−0.633732	−	1.09766i	−0.986782	−	0.162051i	$-0.948189\pi$
$761$	−17.4823	−	30.2802i	−0.633732	−	1.09766i	0.353051	−	0.935604i	$-0.385144\pi$
$762$	−16.2101	−	9.72284i	−0.587230	−	0.352221i
$763$	7.03199	−	13.5351i	0.254575	−	0.490005i
$764$			25.7989i			0.933370i
$765$	−45.9588	−	1.53324i	−1.66164	−	0.0554344i
$766$	−28.1374	+	16.2451i	−1.01665	+	0.586961i
$767$	11.4860	+	6.63146i	0.414737	+	0.239448i
$768$	−0.890915	+	1.48535i	−0.0321481	+	0.0535980i
$769$	18.9307	+	10.9296i	0.682658	+	0.394133i	0.800856	−	0.598857i	$-0.204378\pi$
$769$	18.9307	+	10.9296i	0.682658	+	0.394133i	−0.118198	+	0.992990i	$0.537712\pi$
$770$	−3.55015	−	5.56265i	−0.127938	−	0.200464i
$771$	−30.2609	−	0.504629i	−1.08982	−	0.0181738i
$772$	9.28662			0.334233
$773$	10.6368	+	18.4235i	0.382579	+	0.662646i	0.991430	−	0.130638i	$-0.0417026\pi$
$773$	10.6368	+	18.4235i	0.382579	+	0.662646i	−0.608851	+	0.793285i	$0.708369\pi$
$774$	19.0613	+	11.8695i	0.685143	+	0.426642i
$775$	−0.362540	−	0.209312i	−0.0130228	−	0.00751872i
$776$	−2.38967	−	4.13903i	−0.0857842	−	0.148583i
$777$	−15.6068	+	28.8535i	−0.559891	+	1.03511i
$778$	1.04105	−	1.80316i	0.0373235	−	0.0646463i
$779$	−12.1769	+	7.03035i	−0.436284	+	0.251889i
$780$	23.1479	+	13.8841i	0.828829	+	0.497132i
$781$	−0.127615	+	0.221035i	−0.00456641	+	0.00790925i
$782$	13.1186	−	22.7221i	0.469120	−	0.812539i
$783$	8.53986	−	4.37644i	0.305190	−	0.156401i
$784$	−2.94803	+	6.34895i	−0.105287	+	0.226748i
$785$	−34.9138	+	20.1575i	−1.24613	+	0.719452i
$786$	−0.0571628	+	3.42786i	−0.00203893	+	0.122268i
$787$		−	47.0237i		−	1.67622i	−0.545505	−	0.838108i	$-0.683662\pi$
$787$		−	47.0237i		−	1.67622i	0.545505	−	0.838108i	$-0.316338\pi$
$788$		−	5.86237i		−	0.208838i
$789$	−41.8146	+	23.2208i	−1.48864	+	0.826683i
$790$	−14.3718	+	8.29754i	−0.511325	+	0.295213i
$791$	−1.40260	−	31.5375i	−0.0498707	−	1.12134i
$792$	−3.27726	−	0.109333i	−0.116452	−	0.00388499i
$793$	−4.54685	+	7.87538i	−0.161463	+	0.279663i
$794$	9.46822	−	16.3994i	0.336015	−	0.581994i
$795$	−0.886027	+	0.492035i	−0.0314241	+	0.0174507i
$796$	13.9117	−	8.03191i	0.493086	−	0.284684i
$797$	14.5203	−	25.1499i	0.514336	−	0.890856i	−0.485526	−	0.874222i	$-0.661372\pi$
$797$	14.5203	−	25.1499i	0.514336	−	0.890856i	0.999862	−	0.0166334i	$-0.00529483\pi$
$798$	6.24305	−	11.5420i	0.221001	−	0.408582i
$799$	−22.8504	−	39.5781i	−0.808390	−	1.40017i
$800$	0.179327	+	0.103535i	0.00634018	+	0.00366051i
$801$	53.9524	+	1.79991i	1.90631	+	0.0635968i
$802$	−1.93827	−	3.35718i	−0.0684427	−	0.118546i
$803$	−7.43731			−0.262457
$804$	4.54294	−	7.57408i	0.160217	−	0.267117i
$805$	−1.04773	−	23.5581i	−0.0369275	−	0.830316i
$806$	11.9571	+	6.90343i	0.421171	+	0.243163i
$807$	11.7281	+	0.195576i	0.412847	+	0.00688461i
$808$	−9.05829	−	5.22981i	−0.318670	−	0.183984i
$809$	47.5777	−	27.4690i	1.67274	−	0.965759i	0.706650	−	0.707563i	$-0.250205\pi$
$809$	47.5777	−	27.4690i	1.67274	−	0.965759i	0.966093	−	0.258195i	$-0.0831279\pi$
$810$	−1.36876	+	20.4914i	−0.0480933	+	0.719996i
$811$			34.0190i			1.19457i	0.802030	+	0.597284i	$0.203754\pi$
$811$			34.0190i			1.19457i	−0.802030	+	0.597284i	$0.796246\pi$
$812$	−4.33578	−	2.25260i	−0.152156	−	0.0790506i
$813$	−12.6559	+	7.02818i	−0.443862	+	0.246489i
$814$	3.91216	+	6.77606i	0.137121	+	0.237501i
$815$	36.2783			1.27077
$816$	11.6330	+	0.193992i	0.407237	+	0.00679107i
$817$			21.4332i			0.749851i
$818$	−16.1988			−0.566378
$819$	46.6411	−	27.6228i	1.62977	−	0.965218i
$820$	−11.2048			−0.391290
$821$			8.00116i			0.279243i	0.990205	+	0.139621i	$0.0445885\pi$
$821$			8.00116i			0.279243i	−0.990205	+	0.139621i	$0.955411\pi$
$822$	2.78597	+	5.01680i	0.0971717	+	0.174981i
$823$	7.02491			0.244873			0.122436	−	0.992476i	$-0.460929\pi$
$823$	7.02491			0.244873			0.122436	+	0.992476i	$0.460929\pi$
$824$	−6.37383	−	11.0398i	−0.222043	−	0.384590i
$825$	−0.00653639	+	0.391965i	−0.000227568	+	0.0136465i
$826$	4.33119	−	2.76421i	0.150701	−	0.0961793i
$827$			37.4952i			1.30384i	0.758290	+	0.651918i	$0.226035\pi$
$827$			37.4952i			1.30384i	−0.758290	+	0.651918i	$0.773965\pi$
$828$	−9.94691	−	6.19400i	−0.345679	−	0.215256i
$829$	−2.96310	+	1.71074i	−0.102913	+	0.0594166i	−0.550573	−	0.834787i	$-0.685591\pi$
$829$	−2.96310	+	1.71074i	−0.102913	+	0.0594166i	0.447660	+	0.894204i	$0.352257\pi$
$830$	−11.5153	−	6.64838i	−0.399703	−	0.230769i
$831$	13.6329	+	24.5492i	0.472919	+	0.851603i
$832$	−5.91448	−	3.41473i	−0.205048	−	0.118384i
$833$	46.8352	−	4.17416i	1.62274	−	0.144626i
$834$	−2.91972	−	5.25765i	−0.101102	−	0.182057i
$835$	13.0469			0.451507
$836$	−1.56495	−	2.71057i	−0.0541248	−	0.0937470i
$837$	−0.525268	+	10.4917i	−0.0181559	+	0.362647i
$838$	2.83692	+	1.63790i	0.0979998	+	0.0565802i
$839$	4.87530	+	8.44428i	0.168314	+	0.291529i	0.937827	−	0.347102i	$-0.112834\pi$
$839$	4.87530	+	8.44428i	0.168314	+	0.291529i	−0.769513	+	0.638631i	$0.779501\pi$
$840$	8.90734	−	5.47793i	0.307332	−	0.189007i
$841$	−12.7948	+	22.1612i	−0.441199	+	0.764179i
$842$	−1.46328	+	0.844823i	−0.0504278	+	0.0291145i
$843$	0.844858	−	50.6633i	0.0290985	−	1.74494i
$844$	−12.3741	+	21.4325i	−0.425933	+	0.737738i
$845$	−38.3832	+	66.4817i	−1.32042	+	2.28704i
$846$	−18.0064	+	9.61019i	−0.619073	+	0.330405i
$847$	11.9602	−	23.0209i	0.410956	−	0.791006i
$848$	0.222069	−	0.128212i	0.00762589	−	0.00440281i
$849$	2.13071	+	1.27800i	0.0731259	+	0.0438610i
$850$		−	1.39094i		−	0.0477089i
$851$			27.9602i			0.958463i
$852$	−0.346839	−	0.208035i	−0.0118825	−	0.00712715i
$853$	−21.2846	+	12.2887i	−0.728771	+	0.420756i	−0.817972	−	0.575258i	$-0.804902\pi$
$853$	−21.2846	+	12.2887i	−0.728771	+	0.420756i	0.0892016	+	0.996014i	$0.471568\pi$
$854$	1.89528	+	2.96967i	0.0648551	+	0.101620i
$855$	−17.2938	+	9.22987i	−0.591436	+	0.315655i
$856$	−4.76813	+	8.25865i	−0.162971	+	0.282275i
$857$	−14.9684	+	25.9260i	−0.511309	+	0.885614i	0.488605	+	0.872505i	$0.337506\pi$
$857$	−14.9684	+	25.9260i	−0.511309	+	0.885614i	−0.999914	+	0.0131086i	$0.995827\pi$
$858$	0.215580	−	12.9276i	0.00735977	−	0.441341i
$859$	−46.6403	+	26.9278i	−1.59135	+	0.918765i	−0.598271	+	0.801294i	$0.704145\pi$
$859$	−46.6403	+	26.9278i	−1.59135	+	0.918765i	−0.993076	+	0.117471i	$0.962521\pi$
$860$	−8.53993	+	14.7916i	−0.291209	+	0.504389i
$861$	−10.7055	+	19.7921i	−0.364842	+	0.674512i
$862$	−0.00906921	−	0.0157083i	−0.000308899	−	0.000535028i
$863$	−42.6599	−	24.6297i	−1.45216	−	0.838404i	−0.453555	−	0.891228i	$-0.649844\pi$
$863$	−42.6599	−	24.6297i	−1.45216	−	0.838404i	−0.998604	+	0.0528239i	$0.983178\pi$
$864$	0.259820	−	5.18965i	0.00883924	−	0.176556i
$865$	17.3483	+	30.0482i	0.589861	+	1.02167i
$866$	5.36964			0.182468
$867$	−23.6473	−	42.5827i	−0.803106	−	1.44618i
$868$	4.50882	−	2.87758i	0.153039	−	0.0976714i
$869$	6.88406	+	3.97451i	0.233526	+	0.134826i
$870$	3.54360	+	6.38110i	0.120139	+	0.216339i
$871$	30.1590	+	17.4123i	1.02190	+	0.589994i
$872$	4.99266	−	2.88251i	0.169073	−	0.0976142i
$873$	12.1712	+	7.57904i	0.411931	+	0.256512i
$874$		−	11.1847i		−	0.378327i
$875$	15.5674	+	24.3922i	0.526274	+	0.824608i
$876$	0.196506	−	11.7838i	0.00663931	−	0.398137i
$877$	−9.80382	−	16.9807i	−0.331051	−	0.573398i	0.651667	−	0.758505i	$-0.274070\pi$
$877$	−9.80382	−	16.9807i	−0.331051	−	0.573398i	−0.982718	+	0.185108i	$0.940737\pi$
$878$	−21.8401			−0.737068
$879$	−18.2070	−	32.7860i	−0.614106	−	1.10584i
$880$		−	2.49418i		−	0.0840788i
$881$	−6.20452			−0.209036			−0.104518	−	0.994523i	$-0.533330\pi$
$881$	−6.20452			−0.209036			−0.104518	+	0.994523i	$0.533330\pi$
$882$	−1.16575	−	20.9676i	−0.0392530	−	0.706016i
$883$	26.8733			0.904359			0.452180	−	0.891927i	$-0.350647\pi$
$883$	26.8733			0.904359			0.452180	+	0.891927i	$0.350647\pi$
$884$			45.8753i			1.54295i
$885$	−7.67450	−	0.127980i	−0.257976	−	0.00430199i
$886$	−2.09931			−0.0705278
$887$	2.93679	+	5.08668i	0.0986079	+	0.170794i	0.911109	−	0.412166i	$-0.135228\pi$
$887$	2.93679	+	5.08668i	0.0986079	+	0.170794i	−0.812501	+	0.582960i	$0.801894\pi$
$888$	−10.8395	+	6.01946i	−0.363749	+	0.202000i
$889$	−15.5337	−	24.3394i	−0.520983	−	0.816318i
$890$			41.0608i			1.37636i
$891$	8.82818	−	4.33989i	0.295755	−	0.145392i
$892$	−3.20041	+	1.84776i	−0.107158	+	0.0618675i
$893$	−16.8718	−	9.74092i	−0.564592	−	0.325968i
$894$	−23.1036	−	0.385274i	−0.772700	−	0.0128855i
$895$	8.02276	+	4.63194i	0.268171	+	0.154829i
$896$	−2.23025	+	1.42337i	−0.0745074	+	0.0475515i
$897$	23.7655	−	39.6223i	0.793507	−	1.32295i
$898$	−27.1356			−0.905525
$899$	1.86675	+	3.23330i	0.0622595	+	0.107837i
$900$	−0.620863	−	0.0207127i	−0.0206954	−	0.000690423i
$901$	−1.49170	−	0.861233i	−0.0496957	−	0.0286918i
$902$	2.68355	+	4.64805i	0.0893525	+	0.154763i
$903$	17.9683	+	29.2172i	0.597948	+	0.972289i
$904$	5.96592	−	10.3333i	0.198424	−	0.343680i
$905$	7.28130	−	4.20386i	0.242039	−	0.139741i
$906$	8.08586	−	4.49030i	0.268635	−	0.149180i
$907$	24.6305	−	42.6613i	0.817842	−	1.41654i	−0.0894269	−	0.995993i	$-0.528504\pi$
$907$	24.6305	−	42.6613i	0.817842	−	1.41654i	0.907269	−	0.420551i	$-0.138163\pi$
$908$	−2.30549	+	3.99322i	−0.0765102	+	0.132520i
$909$	31.3614	+	1.04625i	1.04019	+	0.0347020i
$910$	22.1820	+	34.7565i	0.735327	+	1.15217i
$911$	14.0032	−	8.08474i	0.463946	−	0.267859i	−0.249756	−	0.968309i	$-0.580350\pi$
$911$	14.0032	−	8.08474i	0.463946	−	0.267859i	0.713702	+	0.700450i	$0.247017\pi$
$912$	4.33601	−	2.40791i	0.143580	−	0.0797338i
$913$			6.36914i			0.210788i
$914$		−	8.43196i		−	0.278905i
$915$	0.0877489	−	5.26201i	0.00290089	−	0.173957i
$916$	13.8220	−	7.98016i	0.456693	−	0.263672i
$917$	−2.41435	+	4.64713i	−0.0797289	+	0.153462i
$918$	−31.0625	+	15.9187i	−1.02522	+	0.525395i
$919$	−26.5159	+	45.9269i	−0.874680	+	1.51499i	−0.0175762	+	0.999846i	$0.505595\pi$
$919$	−26.5159	+	45.9269i	−0.874680	+	1.51499i	−0.857104	+	0.515144i	$0.827738\pi$
$920$	4.45647	−	7.71884i	0.146926	−	0.254482i
$921$	20.0125	+	12.0035i	0.659433	+	0.395529i
$922$	8.09133	−	4.67153i	0.266474	−	0.153849i
$923$	0.797361	−	1.38107i	0.0262455	−	0.0454585i
$924$	−4.40569	−	2.38303i	−0.144936	−	0.0783959i
$925$	0.741142	+	1.28370i	0.0243686	+	0.0422077i
$926$	22.0458	+	12.7281i	0.724469	+	0.418272i
$927$	32.4634	+	20.2152i	1.06624	+	0.663953i
$928$	−0.923371	−	1.59933i	−0.0303112	−	0.0525005i
$929$	2.95169			0.0968418			0.0484209	−	0.998827i	$-0.484581\pi$
$929$	2.95169			0.0968418			0.0484209	+	0.998827i	$0.484581\pi$
$930$	−7.98925	−	0.133228i	−0.261978	−	0.00436873i
$931$	16.4009	−	11.5237i	0.537517	−	0.377675i
$932$	6.17609	+	3.56577i	0.202305	+	0.116801i
$933$	25.5994	−	42.6798i	0.838086	−	1.39727i
$934$	17.8746	+	10.3199i	0.584873	+	0.337677i
$935$	−14.5095	+	8.37704i	−0.474510	+	0.273958i
$936$	20.4770	+	0.683135i	0.669311	+	0.0223290i
$937$		−	27.1986i		−	0.888540i	−0.895893	−	0.444270i	$-0.853463\pi$
$937$		−	27.1986i		−	0.888540i	0.895893	−	0.444270i	$-0.146537\pi$
$938$	11.3724	−	7.25803i	0.371323	−	0.236983i
$939$	35.0979	+	21.0517i	1.14538	+	0.686998i
$940$	−7.76244	−	13.4449i	−0.253183	−	0.438526i
$941$	−15.1273			−0.493137			−0.246568	−	0.969125i	$-0.579303\pi$
$941$	−15.1273			−0.493137			−0.246568	+	0.969125i	$0.579303\pi$
$942$	−15.7401	+	26.2421i	−0.512839	+	0.855015i
$943$			19.1793i			0.624565i
$944$	1.94202			0.0632073
$945$	−15.8368	+	27.0801i	−0.515171	+	0.880916i
$946$	8.18124			0.265995
$947$		−	18.1062i		−	0.588371i	−0.955748	−	0.294186i	$-0.904952\pi$
$947$		−	18.1062i		−	0.588371i	0.955748	−	0.294186i	$-0.0950484\pi$
$948$	−6.47917	+	10.8022i	−0.210434	+	0.350839i
$949$	46.4698			1.50847
$950$	−0.296473	−	0.513506i	−0.00961884	−	0.0166603i
$951$	−1.30366	−	0.781939i	−0.0422742	−	0.0253561i
$952$	15.7708	+	8.19350i	0.511135	+	0.265553i
$953$		−	31.8552i		−	1.03189i	−0.856621	−	0.515946i	$-0.827441\pi$
$953$		−	31.8552i		−	1.03189i	0.856621	−	0.515946i	$-0.172559\pi$
$954$	−0.406635	+	0.653013i	−0.0131653	+	0.0211421i
$955$	50.9833	−	29.4352i	1.64978	−	0.952501i
$956$	−13.6219	−	7.86462i	−0.440565	−	0.254360i
$957$	1.79835	−	2.99824i	0.0581324	−	0.0969195i
$958$	−5.32505	−	3.07442i	−0.172045	−	0.0993300i
$959$	0.389458	+	8.75697i	0.0125762	+	0.282777i
$960$	3.95182	+	0.0659003i	0.127544	+	0.00212692i
$961$	26.9129			0.868157
$962$	−24.4440	−	42.3382i	−0.788105	−	1.36504i
$963$	0.953892	−	28.5929i	0.0307387	−	0.921393i
$964$	−1.39292	−	0.804201i	−0.0448628	−	0.0259016i
$965$	−10.5956	−	18.3521i	−0.341084	−	0.590774i
$966$	−9.37658	−	15.2467i	−0.301686	−	0.490555i
$967$	1.32305	−	2.29159i	0.0425464	−	0.0736925i	−0.843968	−	0.536393i	$-0.819786\pi$
$967$	1.32305	−	2.29159i	0.0425464	−	0.0736925i	0.886514	+	0.462701i	$0.153120\pi$
$968$	8.49163	−	4.90265i	0.272931	−	0.157577i
$969$	−28.5707	−	17.1367i	−0.917822	−	0.550511i
$970$	−5.45299	+	9.44486i	−0.175085	+	0.303256i
$971$	−17.9023	+	31.0077i	−0.574513	+	0.995086i	0.421581	+	0.906791i	$0.361475\pi$
$971$	−17.9023	+	31.0077i	−0.574513	+	0.995086i	−0.996094	+	0.0882950i	$0.971858\pi$
$972$	6.64294	+	14.1022i	0.213072	+	0.452328i
$973$	−0.408155	−	9.17739i	−0.0130849	−	0.294214i
$974$	−17.0843	+	9.86365i	−0.547418	+	0.316052i
$975$	0.0408406	−	2.44908i	0.00130795	−	0.0784332i
$976$			1.33154i			0.0426216i
$977$			4.42710i			0.141636i	0.997489	+	0.0708178i	$0.0225609\pi$
$977$			4.42710i			0.141636i	−0.997489	+	0.0708178i	$0.977439\pi$
$978$	24.0737	−	13.3688i	0.769792	−	0.427487i
$979$	17.0331	−	9.83405i	0.544379	−	0.314298i
$980$	15.9102	−	1.41799i	0.508234	−	0.0452960i
$981$	−9.14214	+	14.6813i	−0.291886	+	0.468738i
$982$	1.97994	−	3.42935i	0.0631823	−	0.109435i
$983$	−8.90634	+	15.4262i	−0.284068	+	0.492021i	−0.972383	−	0.233392i	$-0.925018\pi$
$983$	−8.90634	+	15.4262i	−0.284068	+	0.492021i	0.688315	+	0.725412i	$0.258351\pi$
$984$	−7.43534	+	4.12905i	−0.237030	+	0.131629i
$985$	−11.5851	+	6.68868i	−0.369133	+	0.213119i
$986$	−6.20253	+	10.7431i	−0.197529	+	0.342130i
$987$	−31.1655	+	0.865698i	−0.992008	+	0.0275555i
$988$	9.77810	+	16.9362i	0.311083	+	0.538811i
$989$	25.3188	+	14.6178i	0.805091	+	0.464819i
$990$	3.52313	+	6.60121i	0.111972	+	0.209800i
$991$	7.62877	+	13.2134i	0.242336	+	0.419738i	0.961379	−	0.275227i	$-0.0887531\pi$
$991$	7.62877	+	13.2134i	0.242336	+	0.419738i	−0.719043	+	0.694965i	$0.755420\pi$
$992$	2.02166			0.0641879
$993$	17.9814	−	29.9789i	0.570621	−	0.951351i
$994$	−0.332367	−	0.520778i	−0.0105420	−	0.0165181i
$995$	−31.7451	−	18.3280i	−1.00639	−	0.581037i
$996$	−10.0914	−	0.168283i	−0.319757	−	0.00533225i
$997$	35.7668	+	20.6500i	1.13275	+	0.653991i	0.944624	−	0.328155i	$-0.106427\pi$
$997$	35.7668	+	20.6500i	1.13275	+	0.653991i	0.188122	+	0.982146i	$0.439760\pi$
$998$	31.8856	−	18.4092i	1.00932	−	0.582732i
$999$	20.1855	−	31.2425i	0.638641	−	0.988470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.l.a.5.1	✓	16
3.2	odd	2		378.2.l.a.341.5		16
4.3	odd	2		1008.2.ca.c.257.6		16
7.2	even	3		882.2.m.b.293.2		16
7.3	odd	6		126.2.t.a.59.5	yes	16
7.4	even	3		882.2.t.a.815.8		16
7.5	odd	6		882.2.m.a.293.3		16
7.6	odd	2		882.2.l.b.509.4		16
9.2	odd	6		126.2.t.a.47.5	yes	16
9.4	even	3		1134.2.k.a.971.8		16
9.5	odd	6		1134.2.k.b.971.1		16
9.7	even	3		378.2.t.a.89.1		16
12.11	even	2		3024.2.ca.c.2609.2		16
21.2	odd	6		2646.2.m.b.881.5		16
21.5	even	6		2646.2.m.a.881.8		16
21.11	odd	6		2646.2.t.b.2285.4		16
21.17	even	6		378.2.t.a.17.1		16
21.20	even	2		2646.2.l.a.1097.8		16
28.3	even	6		1008.2.df.c.689.8		16
36.7	odd	6		3024.2.df.c.1601.2		16
36.11	even	6		1008.2.df.c.929.8		16
63.2	odd	6		882.2.m.a.587.3		16
63.11	odd	6		882.2.l.b.227.8		16
63.16	even	3		2646.2.m.a.1763.8		16
63.20	even	6		882.2.t.a.803.8		16
63.25	even	3		2646.2.l.a.521.4		16
63.31	odd	6		1134.2.k.b.647.1		16
63.34	odd	6		2646.2.t.b.1979.4		16
63.38	even	6	inner	126.2.l.a.101.5	yes	16
63.47	even	6		882.2.m.b.587.2		16
63.52	odd	6		378.2.l.a.143.1		16
63.59	even	6		1134.2.k.a.647.8		16
63.61	odd	6		2646.2.m.b.1763.5		16
84.59	odd	6		3024.2.df.c.17.2		16
252.115	even	6		3024.2.ca.c.2033.2		16
252.227	odd	6		1008.2.ca.c.353.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.1	✓	16	1.1	even	1	trivial
126.2.l.a.101.5	yes	16	63.38	even	6	inner
126.2.t.a.47.5	yes	16	9.2	odd	6
126.2.t.a.59.5	yes	16	7.3	odd	6
378.2.l.a.143.1		16	63.52	odd	6
378.2.l.a.341.5		16	3.2	odd	2
378.2.t.a.17.1		16	21.17	even	6
378.2.t.a.89.1		16	9.7	even	3
882.2.l.b.227.8		16	63.11	odd	6
882.2.l.b.509.4		16	7.6	odd	2
882.2.m.a.293.3		16	7.5	odd	6
882.2.m.a.587.3		16	63.2	odd	6
882.2.m.b.293.2		16	7.2	even	3
882.2.m.b.587.2		16	63.47	even	6
882.2.t.a.803.8		16	63.20	even	6
882.2.t.a.815.8		16	7.4	even	3
1008.2.ca.c.257.6		16	4.3	odd	2
1008.2.ca.c.353.6		16	252.227	odd	6
1008.2.df.c.689.8		16	28.3	even	6
1008.2.df.c.929.8		16	36.11	even	6
1134.2.k.a.647.8		16	63.59	even	6
1134.2.k.a.971.8		16	9.4	even	3
1134.2.k.b.647.1		16	63.31	odd	6
1134.2.k.b.971.1		16	9.5	odd	6
2646.2.l.a.521.4		16	63.25	even	3
2646.2.l.a.1097.8		16	21.20	even	2
2646.2.m.a.881.8		16	21.5	even	6
2646.2.m.a.1763.8		16	63.16	even	3
2646.2.m.b.881.5		16	21.2	odd	6
2646.2.m.b.1763.5		16	63.61	odd	6
2646.2.t.b.1979.4		16	63.34	odd	6
2646.2.t.b.2285.4		16	21.11	odd	6
3024.2.ca.c.2033.2		16	252.115	even	6
3024.2.ca.c.2609.2		16	12.11	even	2
3024.2.df.c.17.2		16	84.59	odd	6
3024.2.df.c.1601.2		16	36.7	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.890915 + 1.48535i) q^{3} -1.00000 q^{4} +(1.14095 + 1.97618i) q^{5} +(1.48535 + 0.890915i) q^{6} +(1.42337 + 2.23025i) q^{7} +1.00000i q^{8} +(-1.41254 - 2.64665i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.890915 + 1.48535i) q^{3} -1.00000 q^{4} +(1.14095 + 1.97618i) q^{5} +(1.48535 + 0.890915i) q^{6} +(1.42337 + 2.23025i) q^{7} +1.00000i q^{8} +(-1.41254 - 2.64665i) q^{9} +(1.97618 - 1.14095i) q^{10} +(-0.946590 - 0.546514i) q^{11} +(0.890915 - 1.48535i) q^{12} +(5.91448 + 3.41473i) q^{13} +(2.23025 - 1.42337i) q^{14} +(-3.95182 - 0.0659003i) q^{15} +1.00000 q^{16} +(-3.35863 - 5.81732i) q^{17} +(-2.64665 + 1.41254i) q^{18} +(-2.47987 - 1.43175i) q^{19} +(-1.14095 - 1.97618i) q^{20} +(-4.58081 + 0.127243i) q^{21} +(-0.546514 + 0.946590i) q^{22} +(-3.38264 + 1.95297i) q^{23} +(-1.48535 - 0.890915i) q^{24} +(-0.103535 + 0.179327i) q^{25} +(3.41473 - 5.91448i) q^{26} +(5.18965 + 0.259820i) q^{27} +(-1.42337 - 2.23025i) q^{28} +(1.59933 - 0.923371i) q^{29} +(-0.0659003 + 3.95182i) q^{30} +2.02166i q^{31} -1.00000i q^{32} +(1.65510 - 0.919121i) q^{33} +(-5.81732 + 3.35863i) q^{34} +(-2.78339 + 5.35745i) q^{35} +(1.41254 + 2.64665i) q^{36} +(3.57920 - 6.19935i) q^{37} +(-1.43175 + 2.47987i) q^{38} +(-10.3414 + 5.74285i) q^{39} +(-1.97618 + 1.14095i) q^{40} +(2.45515 - 4.25245i) q^{41} +(0.127243 + 4.58081i) q^{42} +(-3.74246 - 6.48214i) q^{43} +(0.946590 + 0.546514i) q^{44} +(3.61862 - 5.81113i) q^{45} +(1.95297 + 3.38264i) q^{46} +6.80349 q^{47} +(-0.890915 + 1.48535i) q^{48} +(-2.94803 + 6.34895i) q^{49} +(0.179327 + 0.103535i) q^{50} +(11.6330 + 0.193992i) q^{51} +(-5.91448 - 3.41473i) q^{52} +(0.222069 - 0.128212i) q^{53} +(0.259820 - 5.18965i) q^{54} -2.49418i q^{55} +(-2.23025 + 1.42337i) q^{56} +(4.33601 - 2.40791i) q^{57} +(-0.923371 - 1.59933i) q^{58} +1.94202 q^{59} +(3.95182 + 0.0659003i) q^{60} +1.33154i q^{61} +2.02166 q^{62} +(3.89211 - 6.91748i) q^{63} -1.00000 q^{64} +15.5841i q^{65} +(-0.919121 - 1.65510i) q^{66} +5.09918 q^{67} +(3.35863 + 5.81732i) q^{68} +(0.112802 - 6.76433i) q^{69} +(5.35745 + 2.78339i) q^{70} -0.233507i q^{71} +(2.64665 - 1.41254i) q^{72} +(5.89272 - 3.40216i) q^{73} +(-6.19935 - 3.57920i) q^{74} +(-0.174124 - 0.313551i) q^{75} +(2.47987 + 1.43175i) q^{76} +(-0.128486 - 2.88902i) q^{77} +(5.74285 + 10.3414i) q^{78} -7.27248 q^{79} +(1.14095 + 1.97618i) q^{80} +(-5.00947 + 7.47698i) q^{81} +(-4.25245 - 2.45515i) q^{82} +(-2.91353 - 5.04638i) q^{83} +(4.58081 - 0.127243i) q^{84} +(7.66407 - 13.2746i) q^{85} +(-6.48214 + 3.74246i) q^{86} +(-0.0533331 + 3.19821i) q^{87} +(0.546514 - 0.946590i) q^{88} +(-8.99707 + 15.5834i) q^{89} +(-5.81113 - 3.61862i) q^{90} +(0.802809 + 18.0512i) q^{91} +(3.38264 - 1.95297i) q^{92} +(-3.00288 - 1.80113i) q^{93} -6.80349i q^{94} -6.53424i q^{95} +(1.48535 + 0.890915i) q^{96} +(-4.13903 + 2.38967i) q^{97} +(6.34895 + 2.94803i) q^{98} +(-0.109333 + 3.27726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^7	\( 16 q - 16 q^{4} + 2 q^{7} + 12 q^{11} + 6 q^{13} - 6 q^{14} - 18 q^{15} + 16 q^{16} - 18 q^{17} - 12 q^{18} - 12 q^{21} - 6 q^{23} - 8 q^{25} + 12 q^{26} + 36 q^{27} - 2 q^{28} + 6 q^{29} + 30 q^{35} - 2 q^{37} - 12 q^{39} - 6 q^{41} - 2 q^{43} - 12 q^{44} - 30 q^{45} + 6 q^{46} - 36 q^{47} - 8 q^{49} - 12 q^{50} + 6 q^{51} - 6 q^{52} - 36 q^{53} + 18 q^{54} + 6 q^{56} + 6 q^{57} + 6 q^{58} + 60 q^{59} + 18 q^{60} + 36 q^{62} + 36 q^{63} - 16 q^{64} + 24 q^{66} - 28 q^{67} + 18 q^{68} - 42 q^{69} - 18 q^{70} + 12 q^{72} + 18 q^{74} + 60 q^{75} - 42 q^{77} + 32 q^{79} - 36 q^{81} + 12 q^{84} - 12 q^{85} + 24 q^{86} - 24 q^{87} - 24 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} - 42 q^{93} + 6 q^{97} - 24 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^7 + 12 * q^11 + 6 * q^13 - 6 * q^14 - 18 * q^15 + 16 * q^16 - 18 * q^17 - 12 * q^18 - 12 * q^21 - 6 * q^23 - 8 * q^25 + 12 * q^26 + 36 * q^27 - 2 * q^28 + 6 * q^29 + 30 * q^35 - 2 * q^37 - 12 * q^39 - 6 * q^41 - 2 * q^43 - 12 * q^44 - 30 * q^45 + 6 * q^46 - 36 * q^47 - 8 * q^49 - 12 * q^50 + 6 * q^51 - 6 * q^52 - 36 * q^53 + 18 * q^54 + 6 * q^56 + 6 * q^57 + 6 * q^58 + 60 * q^59 + 18 * q^60 + 36 * q^62 + 36 * q^63 - 16 * q^64 + 24 * q^66 - 28 * q^67 + 18 * q^68 - 42 * q^69 - 18 * q^70 + 12 * q^72 + 18 * q^74 + 60 * q^75 - 42 * q^77 + 32 * q^79 - 36 * q^81 + 12 * q^84 - 12 * q^85 + 24 * q^86 - 24 * q^87 - 24 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 - 42 * q^93 + 6 * q^97 - 24 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more