LMFDB - Embedded newform 429.2.bd.b.76.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.8
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.b.175.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.225205 + 0.0603434i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.68498 - 0.972821i) q^{4} +(-1.03093 - 1.03093i) q^{5} +(0.0603434 + 0.225205i) q^{6} +(1.55041 - 0.415430i) q^{7} +(-0.650483 - 0.650483i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.225205 + 0.0603434i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.68498 - 0.972821i) q^{4} +(-1.03093 - 1.03093i) q^{5} +(0.0603434 + 0.225205i) q^{6} +(1.55041 - 0.415430i) q^{7} +(-0.650483 - 0.650483i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.169960 - 0.294380i) q^{10} +(3.31637 + 0.0413457i) q^{11} -1.94564i q^{12} +(-1.84135 - 3.09991i) q^{13} +0.374227 q^{14} +(0.377347 - 1.40828i) q^{15} +(1.83840 + 3.18421i) q^{16} +(3.85391 - 6.67516i) q^{17} +(-0.164861 + 0.164861i) q^{18} +(-1.30123 - 4.85627i) q^{19} +(0.734181 + 2.74000i) q^{20} +(1.13498 + 1.13498i) q^{21} +(0.744366 + 0.209432i) q^{22} +(-1.19156 + 0.687946i) q^{23} +(0.238093 - 0.888576i) q^{24} -2.87437i q^{25} +(-0.227622 - 0.809227i) q^{26} -1.00000 q^{27} +(-3.01653 - 0.808278i) q^{28} +(2.26196 - 1.30594i) q^{29} +(0.169960 - 0.294380i) q^{30} +(-2.16319 - 2.16319i) q^{31} +(0.698058 + 2.60519i) q^{32} +(1.62238 + 2.89273i) q^{33} +(1.27072 - 1.27072i) q^{34} +(-2.02664 - 1.17008i) q^{35} +(1.68498 - 0.972821i) q^{36} +(6.44205 + 1.72614i) q^{37} -1.17217i q^{38} +(1.76392 - 3.14461i) q^{39} +1.34121i q^{40} +(8.17249 + 2.18981i) q^{41} +(0.187113 + 0.324090i) q^{42} +(-5.90068 + 10.2203i) q^{43} +(-5.54777 - 3.29590i) q^{44} +(1.40828 - 0.377347i) q^{45} +(-0.309857 + 0.0830260i) q^{46} +(-8.06778 + 8.06778i) q^{47} +(-1.83840 + 3.18421i) q^{48} +(-3.83100 + 2.21183i) q^{49} +(0.173449 - 0.647320i) q^{50} +7.70782 q^{51} +(0.0869765 + 7.01457i) q^{52} +6.94558 q^{53} +(-0.225205 - 0.0603434i) q^{54} +(-3.37632 - 3.46157i) q^{55} +(-1.27874 - 0.738282i) q^{56} +(3.55503 - 3.55503i) q^{57} +(0.588209 - 0.157610i) q^{58} +(0.876879 + 3.27256i) q^{59} +(-2.00582 + 2.00582i) q^{60} +(-8.07072 - 4.65963i) q^{61} +(-0.356626 - 0.617694i) q^{62} +(-0.415430 + 1.55041i) q^{63} -6.72479i q^{64} +(-1.29748 + 5.09409i) q^{65} +(0.190810 + 0.749356i) q^{66} +(-1.34349 + 5.01396i) q^{67} +(-12.9875 + 7.49832i) q^{68} +(-1.19156 - 0.687946i) q^{69} +(-0.385802 - 0.385802i) q^{70} +(4.47194 - 1.19825i) q^{71} +(0.888576 - 0.238093i) q^{72} +(-6.00059 - 6.00059i) q^{73} +(1.34662 + 0.777470i) q^{74} +(2.48927 - 1.43718i) q^{75} +(-2.53173 + 9.44855i) q^{76} +(5.15889 - 1.31362i) q^{77} +(0.587000 - 0.601740i) q^{78} +0.938747i q^{79} +(1.38743 - 5.17796i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.70834 + 0.986311i) q^{82} +(7.48790 - 7.48790i) q^{83} +(-0.808278 - 3.01653i) q^{84} +(-10.8547 + 2.90852i) q^{85} +(-1.94559 + 1.94559i) q^{86} +(2.26196 + 1.30594i) q^{87} +(-2.13035 - 2.18414i) q^{88} +(0.781475 + 0.209396i) q^{89} +0.339921 q^{90} +(-4.14264 - 4.04116i) q^{91} +2.67699 q^{92} +(0.791781 - 2.95497i) q^{93} +(-2.30374 + 1.33006i) q^{94} +(-3.66499 + 6.34795i) q^{95} +(-1.90713 + 1.90713i) q^{96} +(-8.12074 + 2.17595i) q^{97} +(-0.996229 + 0.266939i) q^{98} +(-1.69399 + 2.85139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.225205	+	0.0603434i	0.159244	+	0.0426692i	0.337560	−	0.941304i	$-0.390398\pi$
$2$	0.225205	+	0.0603434i	0.159244	+	0.0426692i	−0.178316	+	0.983973i	$0.557065\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.68498	−	0.972821i	−0.842488	−	0.486410i
$5$	−1.03093	−	1.03093i	−0.461046	−	0.461046i	0.437952	−	0.898998i	$-0.355704\pi$
$5$	−1.03093	−	1.03093i	−0.461046	−	0.461046i	−0.898998	+	0.437952i	$0.855704\pi$
$6$	0.0603434	+	0.225205i	0.0246351	+	0.0919394i
$7$	1.55041	−	0.415430i	0.585998	−	0.157018i	0.0463746	−	0.998924i	$-0.485233\pi$
$7$	1.55041	−	0.415430i	0.585998	−	0.157018i	0.539624	+	0.841906i	$0.318567\pi$
$8$	−0.650483	−	0.650483i	−0.229981	−	0.229981i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.169960	−	0.294380i	−0.0537462	−	0.0930911i
$11$	3.31637	+	0.0413457i	0.999922	+	0.0124662i
$11$	3.31637	+	0.0413457i	0.999922	+	0.0124662i
$12$		−	1.94564i		−	0.561658i
$13$	−1.84135	−	3.09991i	−0.510699	−	0.859760i
$13$	−1.84135	−	3.09991i	−0.510699	−	0.859760i
$14$	0.374227			0.100016
$15$	0.377347	−	1.40828i	0.0974305	−	0.363616i
$16$	1.83840	+	3.18421i	0.459601	+	0.796051i
$17$	3.85391	−	6.67516i	0.934710	−	1.61897i	0.159560	−	0.987188i	$-0.448993\pi$
$17$	3.85391	−	6.67516i	0.934710	−	1.61897i	0.775150	−	0.631777i	$-0.217674\pi$
$18$	−0.164861	+	0.164861i	−0.0388582	+	0.0388582i
$19$	−1.30123	−	4.85627i	−0.298523	−	1.11410i	−0.938379	−	0.345609i	$-0.887673\pi$
$19$	−1.30123	−	4.85627i	−0.298523	−	1.11410i	0.639856	−	0.768495i	$-0.278994\pi$
$20$	0.734181	+	2.74000i	0.164168	+	0.612683i
$21$	1.13498	+	1.13498i	0.247672	+	0.247672i
$22$	0.744366	+	0.209432i	0.158699	+	0.0446511i
$23$	−1.19156	+	0.687946i	−0.248457	+	0.143447i	−0.619058	−	0.785346i	$-0.712485\pi$
$23$	−1.19156	+	0.687946i	−0.248457	+	0.143447i	0.370601	+	0.928792i	$0.379152\pi$
$24$	0.238093	−	0.888576i	0.0486006	−	0.181380i
$25$		−	2.87437i		−	0.574873i
$26$	−0.227622	−	0.809227i	−0.0446403	−	0.158702i
$27$	−1.00000			−0.192450
$28$	−3.01653	−	0.808278i	−0.570071	−	0.152750i
$29$	2.26196	−	1.30594i	0.420036	−	0.242508i	−0.275057	−	0.961428i	$-0.588697\pi$
$29$	2.26196	−	1.30594i	0.420036	−	0.242508i	0.695093	+	0.718920i	$0.255363\pi$
$30$	0.169960	−	0.294380i	0.0310304	−	0.0537462i
$31$	−2.16319	−	2.16319i	−0.388520	−	0.388520i	0.485639	−	0.874159i	$-0.338587\pi$
$31$	−2.16319	−	2.16319i	−0.388520	−	0.388520i	−0.874159	+	0.485639i	$0.838587\pi$
$32$	0.698058	+	2.60519i	0.123400	+	0.460536i
$33$	1.62238	+	2.89273i	0.282420	+	0.503560i
$34$	1.27072	−	1.27072i	0.217927	−	0.217927i
$35$	−2.02664	−	1.17008i	−0.342565	−	0.197780i
$36$	1.68498	−	0.972821i	0.280829	−	0.162137i
$37$	6.44205	+	1.72614i	1.05907	+	0.283776i	0.745993	−	0.665953i	$-0.231975\pi$
$37$	6.44205	+	1.72614i	1.05907	+	0.283776i	0.313072	+	0.949729i	$0.398642\pi$
$38$		−	1.17217i		−	0.190152i
$39$	1.76392	−	3.14461i	0.282454	−	0.503541i
$40$			1.34121i			0.212063i
$41$	8.17249	+	2.18981i	1.27633	+	0.341991i	0.832452	−	0.554097i	$-0.186936\pi$
$41$	8.17249	+	2.18981i	1.27633	+	0.341991i	0.443876	+	0.896088i	$0.353603\pi$
$42$	0.187113	+	0.324090i	0.0288722	+	0.0500082i
$43$	−5.90068	+	10.2203i	−0.899845	+	1.55858i	−0.0721532	+	0.997394i	$0.522987\pi$
$43$	−5.90068	+	10.2203i	−0.899845	+	1.55858i	−0.827692	+	0.561183i	$0.810346\pi$
$44$	−5.54777	−	3.29590i	−0.836358	−	0.496875i
$45$	1.40828	−	0.377347i	0.209934	−	0.0562515i
$46$	−0.309857	+	0.0830260i	−0.0456860	+	0.0122415i
$47$	−8.06778	+	8.06778i	−1.17681	+	1.17681i	−0.196253	+	0.980553i	$0.562878\pi$
$47$	−8.06778	+	8.06778i	−1.17681	+	1.17681i	−0.980553	+	0.196253i	$0.937122\pi$
$48$	−1.83840	+	3.18421i	−0.265350	+	0.459601i
$49$	−3.83100	+	2.21183i	−0.547286	+	0.315976i
$50$	0.173449	−	0.647320i	0.0245294	−	0.0915449i
$51$	7.70782			1.07931
$52$	0.0869765	+	7.01457i	0.0120615	+	0.972746i
$53$	6.94558			0.954049			0.477025	−	0.878890i	$-0.341715\pi$
$53$	6.94558			0.954049			0.477025	+	0.878890i	$0.341715\pi$
$54$	−0.225205	−	0.0603434i	−0.0306465	−	0.00821169i
$55$	−3.37632	−	3.46157i	−0.455263	−	0.466758i
$56$	−1.27874	−	0.738282i	−0.170879	−	0.0986571i
$57$	3.55503	−	3.55503i	0.470876	−	0.470876i
$58$	0.588209	−	0.157610i	0.0772356	−	0.0206952i
$59$	0.876879	+	3.27256i	0.114160	+	0.426051i	0.999223	−	0.0394210i	$-0.0125513\pi$
$59$	0.876879	+	3.27256i	0.114160	+	0.426051i	−0.885063	+	0.465472i	$0.845885\pi$
$60$	−2.00582	+	2.00582i	−0.258950	+	0.258950i
$61$	−8.07072	−	4.65963i	−1.03335	−	0.596605i	−0.115407	−	0.993318i	$-0.536817\pi$
$61$	−8.07072	−	4.65963i	−1.03335	−	0.596605i	−0.917942	+	0.396714i	$0.870151\pi$
$62$	−0.356626	−	0.617694i	−0.0452915	−	0.0784472i
$63$	−0.415430	+	1.55041i	−0.0523392	+	0.195333i
$64$		−	6.72479i		−	0.840598i
$65$	−1.29748	+	5.09409i	−0.160933	+	0.631844i
$66$	0.190810	+	0.749356i	0.0234870	+	0.0922393i
$67$	−1.34349	+	5.01396i	−0.164133	+	0.612552i	0.834016	+	0.551740i	$0.186036\pi$
$67$	−1.34349	+	5.01396i	−0.164133	+	0.612552i	−0.998149	+	0.0608125i	$0.980631\pi$
$68$	−12.9875	+	7.49832i	−1.57496	+	0.909305i
$69$	−1.19156	−	0.687946i	−0.143447	−	0.0828190i
$70$	−0.385802	−	0.385802i	−0.0461121	−	0.0461121i
$71$	4.47194	−	1.19825i	0.530721	−	0.142206i	0.0165000	−	0.999864i	$-0.494748\pi$
$71$	4.47194	−	1.19825i	0.530721	−	0.142206i	0.514221	+	0.857658i	$0.328081\pi$
$72$	0.888576	−	0.238093i	0.104720	−	0.0280596i
$73$	−6.00059	−	6.00059i	−0.702315	−	0.702315i	0.262592	−	0.964907i	$-0.415423\pi$
$73$	−6.00059	−	6.00059i	−0.702315	−	0.702315i	−0.964907	+	0.262592i	$0.915423\pi$
$74$	1.34662	+	0.777470i	0.156541	+	0.0903790i
$75$	2.48927	−	1.43718i	0.287437	−	0.165952i
$76$	−2.53173	+	9.44855i	−0.290410	+	1.08382i
$77$	5.15889	−	1.31362i	0.587910	−	0.149700i
$78$	0.587000	−	0.601740i	0.0664647	−	0.0681336i
$79$			0.938747i			0.105617i	0.998605	+	0.0528086i	$0.0168173\pi$
$79$			0.938747i			0.105617i	−0.998605	+	0.0528086i	$0.983183\pi$
$80$	1.38743	−	5.17796i	0.155119	−	0.578913i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.70834	+	0.986311i	0.188655	+	0.108920i
$83$	7.48790	−	7.48790i	0.821904	−	0.821904i	−0.164477	−	0.986381i	$-0.552594\pi$
$83$	7.48790	−	7.48790i	0.821904	−	0.821904i	0.986381	+	0.164477i	$0.0525936\pi$
$84$	−0.808278	−	3.01653i	−0.0881903	−	0.329131i
$85$	−10.8547	+	2.90852i	−1.17736	+	0.315473i
$86$	−1.94559	+	1.94559i	−0.209798	+	0.209798i
$87$	2.26196	+	1.30594i	0.242508	+	0.140012i
$88$	−2.13035	−	2.18414i	−0.227096	−	0.232830i
$89$	0.781475	+	0.209396i	0.0828362	+	0.0221959i	0.299999	−	0.953939i	$-0.403014\pi$
$89$	0.781475	+	0.209396i	0.0828362	+	0.0221959i	−0.217163	+	0.976135i	$0.569680\pi$
$90$	0.339921			0.0358308
$91$	−4.14264	−	4.04116i	−0.434266	−	0.423629i
$92$	2.67699			0.279096
$93$	0.791781	−	2.95497i	0.0821039	−	0.306416i
$94$	−2.30374	+	1.33006i	−0.237612	+	0.137186i
$95$	−3.66499	+	6.34795i	−0.376020	+	0.651286i
$96$	−1.90713	+	1.90713i	−0.194645	+	0.194645i
$97$	−8.12074	+	2.17595i	−0.824536	+	0.220934i	−0.646329	−	0.763059i	$-0.723697\pi$
$97$	−8.12074	+	2.17595i	−0.824536	+	0.220934i	−0.178208	+	0.983993i	$0.557030\pi$
$98$	−0.996229	+	0.266939i	−0.100634	+	0.0269649i
$99$	−1.69399	+	2.85139i	−0.170252	+	0.286575i
$100$	−2.79624	+	4.84323i	−0.279624	+	0.484323i
$101$	1.57988	+	2.73642i	0.157203	+	0.272284i	0.933859	−	0.357641i	$-0.116419\pi$
$101$	1.57988	+	2.73642i	0.157203	+	0.272284i	−0.776656	+	0.629925i	$0.783085\pi$
$102$	1.73584	+	0.465116i	0.171873	+	0.0460533i
$103$		−	12.8037i		−	1.26159i	−0.775950	−	0.630795i	$-0.782729\pi$
$103$		−	12.8037i		−	1.26159i	0.775950	−	0.630795i	$-0.217271\pi$
$104$	−0.818670	+	3.21421i	−0.0802772	+	0.315179i
$105$		−	2.34016i		−	0.228376i
$106$	1.56418	+	0.419120i	0.151926	+	0.0407085i
$107$	14.4279	−	8.32993i	1.39479	−	0.805285i	0.400953	−	0.916099i	$-0.368679\pi$
$107$	14.4279	−	8.32993i	1.39479	−	0.805285i	0.993841	+	0.110814i	$0.0353457\pi$
$108$	1.68498	+	0.972821i	0.162137	+	0.0936097i
$109$	−8.79167	+	8.79167i	−0.842089	+	0.842089i	−0.989130	−	0.147041i	$-0.953025\pi$
$109$	−8.79167	+	8.79167i	−0.842089	+	0.842089i	0.147041	+	0.989130i	$0.453025\pi$
$110$	−0.551480	−	0.983299i	−0.0525815	−	0.0937539i
$111$	1.72614	+	6.44205i	0.163838	+	0.611452i
$112$	4.17308	+	4.17308i	0.394319	+	0.394319i
$113$	2.68660	−	4.65332i	0.252734	−	0.437748i	−0.711544	−	0.702642i	$-0.752004\pi$
$113$	2.68660	−	4.65332i	0.252734	−	0.437748i	0.964278	+	0.264894i	$0.0853370\pi$
$114$	1.01513	−	0.586087i	0.0950759	−	0.0548921i
$115$	1.93764	+	0.519188i	0.180686	+	0.0484146i
$116$	−5.08180			−0.471833
$117$	3.60527	−	0.0447033i	0.333308	−	0.00413282i
$118$			0.789909i			0.0727170i
$119$	3.20206	−	11.9502i	0.293532	−	1.09548i
$120$	−1.16152	+	0.670603i	−0.106032	+	0.0612174i
$121$	10.9966	+	0.274235i	0.999689	+	0.0249305i
$122$	−1.53638	−	1.53638i	−0.139098	−	0.139098i
$123$	2.18981	+	8.17249i	0.197449	+	0.736889i
$124$	1.54052	+	5.74931i	0.138343	+	0.516303i
$125$	−8.11792	+	8.11792i	−0.726089	+	0.726089i
$126$	−0.187113	+	0.324090i	−0.0166694	+	0.0288722i
$127$	2.24733	+	3.89249i	0.199419	+	0.345403i	0.948340	−	0.317256i	$-0.102761\pi$
$127$	2.24733	+	3.89249i	0.199419	+	0.345403i	−0.748922	+	0.662659i	$0.769428\pi$
$128$	1.80191	−	6.72482i	0.159268	−	0.594396i
$129$	−11.8014			−1.03905
$130$	−0.599594	+	1.06892i	−0.0525879	+	0.0937503i
$131$			14.4866i			1.26570i	0.774274	+	0.632851i	$0.218115\pi$
$131$			14.4866i			1.26570i	−0.774274	+	0.632851i	$0.781885\pi$
$132$	0.0804440	−	6.45246i	0.00700175	−	0.561615i
$133$	−4.03488	−	6.98861i	−0.349868	−	0.605989i
$134$	−0.605118	+	1.04810i	−0.0522743	+	0.0905417i
$135$	1.03093	+	1.03093i	0.0887283	+	0.0887283i
$136$	−6.84898	+	1.83518i	−0.587296	+	0.157365i
$137$	1.64135	+	6.12562i	0.140230	+	0.523347i	0.999921	+	0.0125326i	$0.00398937\pi$
$137$	1.64135	+	6.12562i	0.140230	+	0.523347i	−0.859691	+	0.510814i	$0.829344\pi$
$138$	−0.226831	−	0.226831i	−0.0193092	−	0.0193092i
$139$	16.0453	+	9.26376i	1.36094	+	0.785742i	0.989750	−	0.142813i	$-0.0456147\pi$
$139$	16.0453	+	9.26376i	1.36094	+	0.785742i	0.371195	+	0.928555i	$0.378948\pi$
$140$	2.27656	+	3.94311i	0.192404	+	0.333254i
$141$	−11.0208	−	2.95301i	−0.928118	−	0.248689i
$142$	1.07941			0.0905818
$143$	−5.97843	−	10.3566i	−0.499941	−	0.866059i
$144$	−3.67680			−0.306400
$145$	−3.67826	−	0.985587i	−0.305463	−	0.0818486i
$146$	−0.989264	−	1.71345i	−0.0818720	−	0.141807i
$147$	−3.83100	−	2.21183i	−0.315976	−	0.182429i
$148$	−9.17546	−	9.17546i	−0.754218	−	0.754218i
$149$	2.71084	+	10.1170i	0.222081	+	0.828817i	0.983553	+	0.180619i	$0.0578102\pi$
$149$	2.71084	+	10.1170i	0.222081	+	0.828817i	−0.761472	+	0.648198i	$0.775523\pi$
$150$	0.647320	−	0.173449i	0.0528535	−	0.0141620i
$151$	−0.879577	−	0.879577i	−0.0715790	−	0.0715790i	0.670411	−	0.741990i	$-0.266118\pi$
$151$	−0.879577	−	0.879577i	−0.0715790	−	0.0715790i	−0.741990	+	0.670411i	$0.766118\pi$
$152$	−2.31249	+	4.00535i	−0.187568	+	0.324877i
$153$	3.85391	+	6.67516i	0.311570	+	0.539655i
$154$	1.24107	+	0.0154727i	0.100009	+	0.00124682i
$155$			4.46019i			0.358251i
$156$	−6.03131	+	3.58261i	−0.482891	+	0.286838i
$157$	23.5033			1.87577			0.937884	−	0.346949i	$-0.112782\pi$
$157$	23.5033			1.87577			0.937884	+	0.346949i	$0.112782\pi$
$158$	−0.0566472	+	0.211410i	−0.00450661	+	0.0168189i
$159$	3.47279	+	6.01505i	0.275410	+	0.477025i
$160$	1.96612	−	3.40541i	0.155435	−	0.269222i
$161$	−1.56160	+	1.56160i	−0.123072	+	0.123072i
$162$	−0.0603434	−	0.225205i	−0.00474102	−	0.0176937i
$163$	4.82535	+	18.0084i	0.377950	+	1.41053i	0.848986	+	0.528416i	$0.177214\pi$
$163$	4.82535	+	18.0084i	0.377950	+	1.41053i	−0.471035	+	0.882114i	$0.656120\pi$
$164$	−11.6401	−	11.6401i	−0.908943	−	0.908943i
$165$	1.30965	−	4.65476i	0.101956	−	0.362373i
$166$	2.13816	−	1.23446i	0.165953	−	0.0958130i
$167$	−5.01072	+	18.7002i	−0.387741	+	1.44707i	0.446060	+	0.895003i	$0.352827\pi$
$167$	−5.01072	+	18.7002i	−0.387741	+	1.44707i	−0.833801	+	0.552066i	$0.813840\pi$
$168$		−	1.47656i		−	0.113919i
$169$	−6.21885	+	11.4160i	−0.478373	+	0.878157i
$170$	−2.62005			−0.200948
$171$	4.85627	+	1.30123i	0.371368	+	0.0995077i
$172$	19.8850	−	11.4806i	1.51622	−	0.875388i
$173$	1.58134	−	2.73896i	0.120227	−	0.208239i	−0.799630	−	0.600493i	$-0.794971\pi$
$173$	1.58134	−	2.73896i	0.120227	−	0.208239i	0.919857	+	0.392254i	$0.128304\pi$
$174$	0.430599	+	0.430599i	0.0326436	+	0.0326436i
$175$	−1.19410	−	4.45643i	−0.0902653	−	0.336875i
$176$	5.96516	+	10.6360i	0.449641	+	0.801719i
$177$	−2.39568	+	2.39568i	−0.180070	+	0.180070i
$178$	0.163356	+	0.0943136i	0.0122441	+	0.00706911i
$179$	6.89345	−	3.97994i	0.515241	−	0.297474i	−0.219745	−	0.975557i	$-0.570522\pi$
$179$	6.89345	−	3.97994i	0.515241	−	0.297474i	0.734985	+	0.678083i	$0.237189\pi$
$180$	−2.74000	−	0.734181i	−0.204228	−	0.0547226i
$181$		−	17.5622i		−	1.30539i	−0.757623	−	0.652693i	$-0.773639\pi$
$181$		−	17.5622i		−	1.30539i	0.757623	−	0.652693i	$-0.226361\pi$
$182$	−0.689083	−	1.16007i	−0.0510782	−	0.0859900i
$183$		−	9.31926i		−	0.688900i
$184$	1.22259	+	0.327591i	0.0901302	+	0.0241503i
$185$	−4.86177	−	8.42083i	−0.357444	−	0.619112i
$186$	0.356626	−	0.617694i	0.0261491	−	0.0452915i
$187$	13.0570	−	21.9780i	0.954820	−	1.60719i
$188$	21.4425	−	5.74550i	1.56386	−	0.419034i
$189$	−1.55041	+	0.415430i	−0.112775	+	0.0302181i
$190$	−1.20843	+	1.20843i	−0.0876687	+	0.0876687i
$191$	2.40528	−	4.16607i	0.174040	−	0.301447i	−0.765788	−	0.643093i	$-0.777651\pi$
$191$	2.40528	−	4.16607i	0.174040	−	0.301447i	0.939829	+	0.341646i	$0.110984\pi$
$192$	5.82384	−	3.36239i	0.420299	−	0.242660i
$193$	3.00563	−	11.2172i	0.216350	−	0.807429i	−0.769337	−	0.638843i	$-0.779413\pi$
$193$	3.00563	−	11.2172i	0.216350	−	0.807429i	0.985687	−	0.168586i	$-0.0539200\pi$
$194$	−1.96013			−0.140729
$195$	−5.06036	+	1.42339i	−0.362380	+	0.101931i
$196$	8.60686			0.614776
$197$	−19.0207	−	5.09658i	−1.35517	−	0.363116i	−0.493128	−	0.869957i	$-0.664147\pi$
$197$	−19.0207	−	5.09658i	−1.35517	−	0.363116i	−0.862040	+	0.506841i	$0.830813\pi$
$198$	−0.553556	+	0.539924i	−0.0393395	+	0.0383707i
$199$	3.66669	+	2.11697i	0.259925	+	0.150068i	0.624300	−	0.781184i	$-0.285384\pi$
$199$	3.66669	+	2.11697i	0.259925	+	0.150068i	−0.364375	+	0.931252i	$0.618717\pi$
$200$	−1.86973	+	1.86973i	−0.132210	+	0.132210i
$201$	−5.01396	+	1.34349i	−0.353657	+	0.0947622i
$202$	0.190670	+	0.711590i	0.0134155	+	0.0500673i
$203$	2.96443	−	2.96443i	0.208062	−	0.208062i
$204$	−12.9875	−	7.49832i	−0.909305	−	0.524988i
$205$	−6.16772	−	10.6828i	−0.430772	−	0.746120i
$206$	0.772621	−	2.88346i	0.0538310	−	0.200900i
$207$		−	1.37589i		−	0.0956311i
$208$	6.48560	−	11.5621i	0.449695	−	0.801689i
$209$	−4.11458	−	16.1590i	−0.284611	−	1.11774i
$210$	0.141213	−	0.527015i	0.00974464	−	0.0363675i
$211$	4.80671	−	2.77516i	0.330908	−	0.191050i	−0.325336	−	0.945598i	$-0.605477\pi$
$211$	4.80671	−	2.77516i	0.330908	−	0.191050i	0.656244	+	0.754549i	$0.272144\pi$
$212$	−11.7031	−	6.75681i	−0.803775	−	0.464060i
$213$	3.27369	+	3.27369i	0.224309	+	0.224309i
$214$	3.75188	−	1.00531i	0.256473	−	0.0687217i
$215$	16.6196	−	4.45320i	1.13345	−	0.303706i
$216$	0.650483	+	0.650483i	0.0442598	+	0.0442598i
$217$	−4.25247	−	2.45516i	−0.288676	−	0.166667i
$218$	−2.51044	+	1.44941i	−0.170029	+	0.0981661i
$219$	2.19637	−	8.19695i	0.148417	−	0.553899i
$220$	2.32153	+	9.11721i	0.156517	+	0.614682i
$221$	−27.7888	+	0.344564i	−1.86928	+	0.0231779i
$222$			1.55494i			0.104361i
$223$	−5.00409	+	18.6755i	−0.335099	+	1.25061i	0.568663	+	0.822571i	$0.307461\pi$
$223$	−5.00409	+	18.6755i	−0.335099	+	1.25061i	−0.903762	+	0.428036i	$0.859206\pi$
$224$	2.16454	+	3.74910i	0.144625	+	0.250497i
$225$	2.48927	+	1.43718i	0.165952	+	0.0958122i
$226$	0.885831	−	0.885831i	0.0589246	−	0.0589246i
$227$	−6.43668	−	24.0220i	−0.427218	−	1.59440i	−0.759032	−	0.651053i	$-0.774327\pi$
$227$	−6.43668	−	24.0220i	−0.427218	−	1.59440i	0.331815	−	0.943345i	$-0.392339\pi$
$228$	−9.44855	+	2.53173i	−0.625746	+	0.167668i
$229$	5.70239	−	5.70239i	0.376825	−	0.376825i	−0.493131	−	0.869955i	$-0.664148\pi$
$229$	5.70239	−	5.70239i	0.376825	−	0.376825i	0.869955	+	0.493131i	$0.164148\pi$
$230$	0.405035	+	0.233847i	0.0267072	+	0.0154194i
$231$	3.71707	+	3.81092i	0.244565	+	0.250740i
$232$	−2.32086	−	0.621873i	−0.152372	−	0.0408280i
$233$	−9.10917			−0.596762			−0.298381	−	0.954447i	$-0.596447\pi$
$233$	−9.10917			−0.596762			−0.298381	+	0.954447i	$0.596447\pi$
$234$	0.814622	+	0.207487i	0.0532535	+	0.0135639i
$235$	16.6346			1.08512
$236$	1.70609	−	6.36722i	0.111057	−	0.414471i
$237$	−0.812979	+	0.469373i	−0.0528086	+	0.0304891i
$238$	1.44224	−	2.49803i	0.0934863	−	0.161923i
$239$	−3.80148	+	3.80148i	−0.245897	+	0.245897i	−0.819284	−	0.573387i	$-0.805629\pi$
$239$	−3.80148	+	3.80148i	−0.245897	+	0.245897i	0.573387	+	0.819284i	$0.305629\pi$
$240$	5.17796	−	1.38743i	0.334236	−	0.0895582i
$241$	−3.84559	+	1.03042i	−0.247716	+	0.0663754i	−0.380541	−	0.924764i	$-0.624262\pi$
$241$	−3.84559	+	1.03042i	−0.247716	+	0.0663754i	0.132824	+	0.991140i	$0.457595\pi$
$242$	2.45993	+	0.725330i	0.158130	+	0.0466260i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	9.06597	+	15.7027i	0.580389	+	1.00526i
$245$	6.22974	+	1.66925i	0.398003	+	0.106645i
$246$			1.97262i			0.125770i
$247$	−12.6579	+	12.9758i	−0.805406	+	0.825630i
$248$			2.81423i			0.178704i
$249$	10.2287	+	2.74076i	0.648215	+	0.173689i
$250$	−2.31806	+	1.33833i	−0.146607	+	0.0846434i
$251$	13.0444	+	7.53120i	0.823357	+	0.475365i	0.851573	−	0.524237i	$-0.175649\pi$
$251$	13.0444	+	7.53120i	0.823357	+	0.475365i	−0.0282160	+	0.999602i	$0.508983\pi$
$252$	2.20826	−	2.20826i	0.139107	−	0.139107i
$253$	−3.98009	+	2.23222i	−0.250226	+	0.140338i
$254$	0.271223	+	1.01222i	0.0170181	+	0.0635123i
$255$	−7.94622	−	7.94622i	−0.497612	−	0.497612i
$256$	−5.91319	+	10.2419i	−0.369574	+	0.640121i
$257$	26.1259	−	15.0838i	1.62969	−	0.940900i	0.645500	−	0.763760i	$-0.276649\pi$
$257$	26.1259	−	15.0838i	1.62969	−	0.940900i	0.984186	−	0.177140i	$-0.0566844\pi$
$258$	−2.65772	−	0.712134i	−0.165462	−	0.0443355i
$259$	10.7049			0.665168
$260$	7.14187	−	7.32120i	0.442920	−	0.454042i
$261$			2.61189i			0.161672i
$262$	−0.874171	+	3.26245i	−0.0540065	+	0.201555i
$263$	−14.7105	+	8.49312i	−0.907089	+	0.523708i	−0.879493	−	0.475911i	$-0.842118\pi$
$263$	−14.7105	+	8.49312i	−0.907089	+	0.523708i	−0.0275955	+	0.999619i	$0.508785\pi$
$264$	0.826344	−	2.93700i	0.0508579	−	0.180760i
$265$	−7.16041	−	7.16041i	−0.439861	−	0.439861i
$266$	−0.486956	−	1.81734i	−0.0298572	−	0.111429i
$267$	0.209396	+	0.781475i	0.0128148	+	0.0478255i
$268$	7.14142	−	7.14142i	0.436232	−	0.436232i
$269$	−13.2889	+	23.0170i	−0.810238	+	1.40337i	0.102460	+	0.994737i	$0.467329\pi$
$269$	−13.2889	+	23.0170i	−0.810238	+	1.40337i	−0.912697	+	0.408636i	$0.866005\pi$
$270$	0.169960	+	0.294380i	0.0103435	+	0.0179154i
$271$	5.15177	−	19.2267i	0.312948	−	1.16794i	−0.612938	−	0.790131i	$-0.710012\pi$
$271$	5.15177	−	19.2267i	0.312948	−	1.16794i	0.925885	−	0.377805i	$-0.123321\pi$
$272$	28.3401			1.71837
$273$	1.42843	−	5.60821i	0.0864525	−	0.339424i
$274$			1.47856i			0.0893232i
$275$	0.118843	−	9.53245i	0.00716649	−	0.574829i
$276$	1.33850	+	2.31834i	0.0805680	+	0.139548i
$277$	−0.328662	+	0.569260i	−0.0197474	+	0.0342035i	−0.875730	−	0.482801i	$-0.839620\pi$
$277$	−0.328662	+	0.569260i	−0.0197474	+	0.0342035i	0.855983	+	0.517004i	$0.172953\pi$
$278$	3.05447	+	3.05447i	0.183195	+	0.183195i
$279$	2.95497	−	0.791781i	0.176909	−	0.0474027i
$280$	0.557177	+	2.07941i	0.0332977	+	0.124269i
$281$	8.96037	+	8.96037i	0.534531	+	0.534531i	0.921917	−	0.387386i	$-0.126622\pi$
$281$	8.96037	+	8.96037i	0.534531	+	0.534531i	−0.387386	+	0.921917i	$0.626622\pi$
$282$	−2.30374	−	1.33006i	−0.137186	−	0.0792041i
$283$	−4.28987	−	7.43028i	−0.255006	−	0.441684i	0.709891	−	0.704312i	$-0.248744\pi$
$283$	−4.28987	−	7.43028i	−0.255006	−	0.441684i	−0.964897	+	0.262628i	$0.915411\pi$
$284$	−8.70079	−	2.33137i	−0.516297	−	0.138341i
$285$	−7.32998			−0.434191
$286$	−0.721419	−	2.69310i	−0.0426584	−	0.159247i
$287$	13.5804			0.801625
$288$	−2.60519	−	0.698058i	−0.153512	−	0.0411334i
$289$	−21.2052	−	36.7285i	−1.24737	−	2.16050i
$290$	−0.768888	−	0.443917i	−0.0451506	−	0.0260677i
$291$	−5.94479	−	5.94479i	−0.348490	−	0.348490i
$292$	4.27334	+	15.9483i	0.250078	+	0.933306i
$293$	−16.7250	+	4.48145i	−0.977085	+	0.261809i	−0.711817	−	0.702365i	$-0.752127\pi$
$293$	−16.7250	+	4.48145i	−0.977085	+	0.261809i	−0.265269	+	0.964175i	$0.585461\pi$
$294$	−0.729290	−	0.729290i	−0.0425331	−	0.0425331i
$295$	2.46978	−	4.27778i	0.143796	−	0.249062i
$296$	−3.06762	−	5.31327i	−0.178302	−	0.308827i
$297$	−3.31637	−	0.0413457i	−0.192435	−	0.00239912i
$298$			2.44198i			0.141460i
$299$	4.32665	+	2.42697i	0.250216	+	0.140355i
$300$	−5.59249			−0.322882
$301$	−4.90264	+	18.2969i	−0.282583	+	1.05461i
$302$	−0.145008	−	0.251162i	−0.00834428	−	0.0144527i
$303$	−1.57988	+	2.73642i	−0.0907615	+	0.157203i
$304$	13.0712	−	13.0712i	0.749682	−	0.749682i
$305$	3.51659	+	13.1241i	0.201360	+	0.751484i
$306$	0.465116	+	1.73584i	0.0265889	+	0.0992311i
$307$	20.7581	+	20.7581i	1.18473	+	1.18473i	0.978504	+	0.206226i	$0.0661180\pi$
$307$	20.7581	+	20.7581i	1.18473	+	1.18473i	0.206226	+	0.978504i	$0.433882\pi$
$308$	−9.97051	−	2.80527i	−0.568123	−	0.159845i
$309$	11.0884	−	6.40187i	0.630795	−	0.364190i
$310$	−0.269143	+	1.00446i	−0.0152863	+	0.0570492i
$311$			13.2287i			0.750131i	0.926998	+	0.375066i	$0.122380\pi$
$311$			13.2287i			0.750131i	−0.926998	+	0.375066i	$0.877620\pi$
$312$	−3.19292	+	0.898114i	−0.180763	+	0.0508457i
$313$	24.5212			1.38602			0.693009	−	0.720929i	$-0.256284\pi$
$313$	24.5212			1.38602			0.693009	+	0.720929i	$0.256284\pi$
$314$	5.29305	+	1.41827i	0.298704	+	0.0800375i
$315$	2.02664	−	1.17008i	0.114188	−	0.0659266i
$316$	0.913233	−	1.58177i	0.0513733	−	0.0889812i
$317$	6.13342	+	6.13342i	0.344487	+	0.344487i	0.858051	−	0.513564i	$-0.171675\pi$
$317$	6.13342	+	6.13342i	0.344487	+	0.344487i	−0.513564	+	0.858051i	$0.671675\pi$
$318$	0.419120	+	1.56418i	0.0235031	+	0.0877147i
$319$	7.55549	−	4.23747i	0.423026	−	0.237253i
$320$	−6.93278	+	6.93278i	−0.387554	+	0.387554i
$321$	14.4279	+	8.32993i	0.805285	+	0.464931i
$322$	−0.445913	+	0.257448i	−0.0248498	+	0.0143470i
$323$	−37.4312	−	10.0297i	−2.08273	−	0.558065i
$324$			1.94564i			0.108091i
$325$	−8.91027	+	5.29272i	−0.494253	+	0.293587i
$326$			4.34676i			0.240745i
$327$	−12.0096	−	3.21797i	−0.664135	−	0.177954i
$328$	−3.89163	−	6.74050i	−0.214879	−	0.372182i
$329$	−9.15673	+	15.8599i	−0.504827	+	0.874386i
$330$	0.575822	−	0.969245i	0.0316980	−	0.0533552i
$331$	11.7335	−	3.14398i	0.644931	−	0.172809i	0.0784949	−	0.996915i	$-0.474989\pi$
$331$	11.7335	−	3.14398i	0.644931	−	0.172809i	0.566436	+	0.824106i	$0.308322\pi$
$332$	−19.9013	+	5.33254i	−1.09223	+	0.292661i
$333$	−4.71590	+	4.71590i	−0.258430	+	0.258430i
$334$	−2.25687	+	3.90902i	−0.123491	+	0.213892i
$335$	6.55408	−	3.78400i	0.358088	−	0.206742i
$336$	−1.52745	+	5.70054i	−0.0833295	+	0.310990i
$337$	−3.83601			−0.208961			−0.104480	−	0.994527i	$-0.533318\pi$
$337$	−3.83601			−0.208961			−0.104480	+	0.994527i	$0.533318\pi$
$338$	−2.08940	+	2.19568i	−0.113648	+	0.119429i
$339$	5.37319			0.291832
$340$	21.1194	+	5.65893i	1.14536	+	0.306899i
$341$	−7.08448	−	7.26336i	−0.383646	−	0.393333i
$342$	1.01513	+	0.586087i	0.0548921	+	0.0316920i
$343$	−12.9656	+	12.9656i	−0.700075	+	0.700075i
$344$	10.4864	−	2.80982i	0.565389	−	0.151496i
$345$	0.519188	+	1.93764i	0.0279522	+	0.104319i
$346$	0.521403	−	0.521403i	0.0280308	−	0.0280308i
$347$	2.29398	+	1.32443i	0.123147	+	0.0710991i	0.560308	−	0.828284i	$-0.310683\pi$
$347$	2.29398	+	1.32443i	0.123147	+	0.0710991i	−0.437161	+	0.899383i	$0.644016\pi$
$348$	−2.54090	−	4.40097i	−0.136206	−	0.235917i
$349$	−7.29648	+	27.2308i	−0.390572	+	1.45763i	0.438622	+	0.898672i	$0.355467\pi$
$349$	−7.29648	+	27.2308i	−0.390572	+	1.45763i	−0.829193	+	0.558962i	$0.811200\pi$
$350$		−	1.07566i		−	0.0574967i
$351$	1.84135	+	3.09991i	0.0982841	+	0.165461i
$352$	2.20730	+	8.66862i	0.117650	+	0.462039i
$353$	1.62549	−	6.06639i	0.0865159	−	0.322882i	−0.909081	−	0.416619i	$-0.863215\pi$
$353$	1.62549	−	6.06639i	0.0865159	−	0.322882i	0.995597	+	0.0937377i	$0.0298815\pi$
$354$	−0.684081	+	0.394954i	−0.0363585	+	0.0209916i
$355$	−5.84557	−	3.37494i	−0.310251	−	0.179123i
$356$	−1.11306	−	1.11306i	−0.0589921	−	0.0589921i
$357$	11.9502	−	3.20206i	0.632474	−	0.169471i
$358$	1.79260	−	0.480326i	0.0947418	−	0.0253860i
$359$	−14.1067	−	14.1067i	−0.744523	−	0.744523i	0.228921	−	0.973445i	$-0.426480\pi$
$359$	−14.1067	−	14.1067i	−0.744523	−	0.744523i	−0.973445	+	0.228921i	$0.926480\pi$
$360$	−1.16152	−	0.670603i	−0.0612174	−	0.0353439i
$361$	−5.43563	+	3.13826i	−0.286086	+	0.165172i
$362$	1.05976	−	3.95508i	0.0556998	−	0.207874i
$363$	5.26080	+	9.66044i	0.276120	+	0.507041i
$364$	3.04891	+	10.8393i	0.159806	+	0.568134i
$365$			12.3724i			0.647599i
$366$	0.562356	−	2.09874i	0.0293948	−	0.109703i
$367$	−8.64996	−	14.9822i	−0.451524	−	0.782063i	0.546957	−	0.837161i	$-0.315786\pi$
$367$	−8.64996	−	14.9822i	−0.451524	−	0.782063i	−0.998481	+	0.0550978i	$0.982453\pi$
$368$	−4.38112	−	2.52944i	−0.228382	−	0.131856i
$369$	−5.98268	+	5.98268i	−0.311446	+	0.311446i
$370$	−0.586751	−	2.18978i	−0.0305037	−	0.113842i
$371$	10.7685	−	2.88540i	0.559071	−	0.149803i
$372$	−4.20879	+	4.20879i	−0.218215	+	0.218215i
$373$	−25.0285	−	14.4502i	−1.29593	−	0.748203i	−0.316228	−	0.948683i	$-0.602416\pi$
$373$	−25.0285	−	14.4502i	−1.29593	−	0.748203i	−0.979698	+	0.200480i	$0.935750\pi$
$374$	4.26671	−	4.16163i	0.220626	−	0.215193i
$375$	−11.0893	−	2.97137i	−0.572648	−	0.153441i
$376$	10.4959			0.541285
$377$	−8.21337	−	4.60717i	−0.423010	−	0.237281i
$378$	−0.374227			−0.0192482
$379$	−5.26611	+	19.6534i	−0.270502	+	1.00953i	0.688294	+	0.725432i	$0.258360\pi$
$379$	−5.26611	+	19.6534i	−0.270502	+	1.00953i	−0.958796	+	0.284095i	$0.908307\pi$
$380$	12.3508	−	7.13076i	0.633585	−	0.365800i
$381$	−2.24733	+	3.89249i	−0.115134	+	0.199419i
$382$	0.793076	−	0.793076i	0.0405773	−	0.0405773i
$383$	−32.1721	+	8.62049i	−1.64392	+	0.440486i	−0.957901	−	0.287100i	$-0.907309\pi$
$383$	−32.1721	+	8.62049i	−1.64392	+	0.440486i	−0.686016	+	0.727586i	$0.740642\pi$
$384$	6.72482	−	1.80191i	0.343175	−	0.0919534i
$385$	−6.67270	−	3.96421i	−0.340072	−	0.202035i
$386$	1.35376	−	2.34479i	0.0689047	−	0.119346i
$387$	−5.90068	−	10.2203i	−0.299948	−	0.519526i
$388$	15.8000	+	4.23361i	0.802126	+	0.214929i
$389$		−	7.87750i		−	0.399405i	−0.979857	−	0.199703i	$-0.936002\pi$
$389$		−	7.87750i		−	0.399405i	0.979857	−	0.199703i	$-0.0639976\pi$
$390$	−1.22551	+	0.0151956i	−0.0620560	+	0.000769457i
$391$			10.6051i			0.536324i
$392$	3.93076	+	1.05324i	0.198533	+	0.0531969i
$393$	−12.5458	+	7.24331i	−0.632851	+	0.365376i
$394$	−3.97600	−	2.29554i	−0.200308	−	0.115648i
$395$	0.967783	−	0.967783i	0.0486944	−	0.0486944i
$396$	5.62822	−	3.15656i	0.282829	−	0.158623i
$397$	1.16677	+	4.35446i	0.0585588	+	0.218544i	0.989004	−	0.147885i	$-0.0472467\pi$
$397$	1.16677	+	4.35446i	0.0585588	+	0.218544i	−0.930446	+	0.366430i	$0.880580\pi$
$398$	0.698011	+	0.698011i	0.0349881	+	0.0349881i
$399$	4.03488	−	6.98861i	0.201996	−	0.349868i
$400$	9.15257	−	5.28424i	0.457629	−	0.264212i
$401$	2.26254	+	0.606247i	0.112986	+	0.0302745i	0.314869	−	0.949135i	$-0.398039\pi$
$401$	2.26254	+	0.606247i	0.112986	+	0.0302745i	−0.201883	+	0.979410i	$0.564706\pi$
$402$	−1.21024			−0.0603611
$403$	−2.72249	+	10.6889i	−0.135617	+	0.532450i
$404$		−	6.14774i		−	0.305862i
$405$	−0.377347	+	1.40828i	−0.0187505	+	0.0699778i
$406$	0.846487	−	0.488719i	0.0420104	−	0.0242547i
$407$	21.2928	+	5.99087i	1.05545	+	0.296956i
$408$	−5.01380	−	5.01380i	−0.248220	−	0.248220i
$409$	−0.766998	−	2.86248i	−0.0379256	−	0.141540i	0.944367	−	0.328894i	$-0.106676\pi$
$409$	−0.766998	−	2.86248i	−0.0379256	−	0.141540i	−0.982293	+	0.187353i	$0.940009\pi$
$410$	−0.744362	−	2.77800i	−0.0367614	−	0.137196i
$411$	−4.48426	+	4.48426i	−0.221192	+	0.221192i
$412$	−12.4557	+	21.5740i	−0.613650	+	1.06287i
$413$	2.71904	+	4.70951i	0.133795	+	0.231740i
$414$	0.0830260	−	0.309857i	0.00408051	−	0.0152287i
$415$	−15.4390			−0.757871
$416$	6.79047	−	6.96098i	0.332930	−	0.341290i
$417$			18.5275i			0.907297i
$418$	0.0484644	−	3.88736i	0.00237047	−	0.190137i
$419$	0.785023	+	1.35970i	0.0383509	+	0.0664256i	0.884564	−	0.466419i	$-0.154456\pi$
$419$	0.785023	+	1.35970i	0.0383509	+	0.0664256i	−0.846213	+	0.532845i	$0.821123\pi$
$420$	−2.27656	+	3.94311i	−0.111085	+	0.192404i
$421$	12.8659	+	12.8659i	0.627047	+	0.627047i	0.947324	−	0.320277i	$-0.103776\pi$
$421$	12.8659	+	12.8659i	0.627047	+	0.627047i	−0.320277	+	0.947324i	$0.603776\pi$
$422$	1.24996	−	0.334925i	0.0608469	−	0.0163039i
$423$	−2.95301	−	11.0208i	−0.143580	−	0.535849i
$424$	−4.51799	−	4.51799i	−0.219413	−	0.219413i
$425$	−19.1869	−	11.0775i	−0.930700	−	0.537340i
$426$	0.539704	+	0.934794i	0.0261487	+	0.0452909i
$427$	−14.4486	−	3.87150i	−0.699219	−	0.187355i
$428$	−32.4141			−1.56680
$429$	5.97983	−	10.3558i	0.288709	−	0.499980i
$430$	4.01152			0.193453
$431$	16.4737	+	4.41410i	0.793508	+	0.212620i	0.632732	−	0.774371i	$-0.281934\pi$
$431$	16.4737	+	4.41410i	0.793508	+	0.212620i	0.160776	+	0.986991i	$0.448600\pi$
$432$	−1.83840	−	3.18421i	−0.0884502	−	0.153200i
$433$	1.84836	+	1.06715i	0.0888265	+	0.0512840i	0.543755	−	0.839244i	$-0.317002\pi$
$433$	1.84836	+	1.06715i	0.0888265	+	0.0512840i	−0.454929	+	0.890528i	$0.650335\pi$
$434$	−0.809523	−	0.809523i	−0.0388583	−	0.0388583i
$435$	−0.985587	−	3.67826i	−0.0472553	−	0.176359i
$436$	23.3665	−	6.26103i	1.11905	−	0.299849i
$437$	4.89134	+	4.89134i	0.233985	+	0.233985i
$438$	0.989264	−	1.71345i	0.0472688	−	0.0818720i
$439$	8.07097	+	13.9793i	0.385206	+	0.667197i	0.991798	−	0.127817i	$-0.0407969\pi$
$439$	8.07097	+	13.9793i	0.385206	+	0.667197i	−0.606591	+	0.795014i	$0.707464\pi$
$440$	−0.0554531	+	4.44793i	−0.00264362	+	0.212047i
$441$		−	4.42366i		−	0.210651i
$442$	−6.27895	−	1.59927i	−0.298659	−	0.0760696i
$443$	8.89814			0.422763			0.211382	−	0.977404i	$-0.432204\pi$
$443$	8.89814			0.422763			0.211382	+	0.977404i	$0.432204\pi$
$444$	3.35845	−	12.5339i	0.159385	−	0.594833i
$445$	−0.589774	−	1.02152i	−0.0279580	−	0.0484246i
$446$	−2.25389	+	3.90385i	−0.106725	+	0.184853i
$447$	−7.40616	+	7.40616i	−0.350299	+	0.350299i
$448$	−2.79368	−	10.4261i	−0.131989	−	0.492589i
$449$	3.15735	+	11.7834i	0.149004	+	0.556092i	0.999544	+	0.0301815i	$0.00960854\pi$
$449$	3.15735	+	11.7834i	0.149004	+	0.556092i	−0.850540	+	0.525910i	$0.823725\pi$
$450$	0.473871	+	0.473871i	0.0223385	+	0.0223385i
$451$	27.0124	+	7.60012i	1.27197	+	0.357876i
$452$	−9.05370	+	5.22715i	−0.425850	+	0.245865i
$453$	0.321948	−	1.20152i	0.0151264	−	0.0564526i
$454$		−	5.79828i		−	0.272127i
$455$	0.104613	+	8.43692i	0.00490433	+	0.395529i
$456$	−4.62498			−0.216584
$457$	−17.6329	−	4.72471i	−0.824831	−	0.221013i	−0.178373	−	0.983963i	$-0.557084\pi$
$457$	−17.6329	−	4.72471i	−0.824831	−	0.221013i	−0.646457	+	0.762950i	$0.723750\pi$
$458$	1.62831	−	0.940103i	0.0760858	−	0.0439281i
$459$	−3.85391	+	6.67516i	−0.179885	+	0.311570i
$460$	−2.75979	−	2.75979i	−0.128676	−	0.128676i
$461$	3.48774	+	13.0164i	0.162440	+	0.606234i	0.998353	+	0.0573722i	$0.0182722\pi$
$461$	3.48774	+	13.0164i	0.162440	+	0.606234i	−0.835913	+	0.548862i	$0.815061\pi$
$462$	0.607137	+	1.08254i	0.0282466	+	0.0503642i
$463$	20.5790	−	20.5790i	0.956388	−	0.956388i	−0.0427003	−	0.999088i	$-0.513596\pi$
$463$	20.5790	−	20.5790i	0.956388	−	0.956388i	0.999088	+	0.0427003i	$0.0135961\pi$
$464$	8.31679	+	4.80170i	0.386097	+	0.222913i
$465$	−3.86264	+	2.23009i	−0.179126	+	0.103418i
$466$	−2.05143	−	0.549678i	−0.0950306	−	0.0254634i
$467$		−	32.4403i		−	1.50116i	−0.660781	−	0.750579i	$-0.729775\pi$
$467$		−	32.4403i		−	1.50116i	0.660781	−	0.750579i	$-0.270225\pi$
$468$	−6.11829	−	3.43196i	−0.282818	−	0.158642i
$469$			8.33179i			0.384726i
$470$	3.74620	+	1.00379i	0.172799	+	0.0463014i
$471$	11.7517	+	20.3545i	0.541487	+	0.937884i
$472$	1.55835	−	2.69914i	0.0717288	−	0.124238i
$473$	−19.9914	+	33.6502i	−0.919204	+	1.54724i
$474$	−0.211410	+	0.0566472i	−0.00971039	+	0.00260189i
$475$	−13.9587	+	3.74022i	−0.640468	+	0.171613i
$476$	−17.0208	+	17.0208i	−0.780148	+	0.780148i
$477$	−3.47279	+	6.01505i	−0.159008	+	0.275410i
$478$	−1.08550	+	0.626716i	−0.0496498	+	0.0286653i
$479$	5.77805	−	21.5640i	0.264006	−	0.985283i	−0.698850	−	0.715268i	$-0.746305\pi$
$479$	5.77805	−	21.5640i	0.264006	−	0.985283i	0.962856	−	0.270015i	$-0.0870286\pi$
$480$	3.93223			0.179481
$481$	−6.51119	−	23.1482i	−0.296885	−	1.05547i
$482$	−0.928224			−0.0422794
$483$	−2.13319	−	0.571587i	−0.0970636	−	0.0260081i
$484$	−18.2622	−	11.1598i	−0.830099	−	0.507263i
$485$	10.6152	+	6.12867i	0.482010	+	0.278288i
$486$	0.164861	−	0.164861i	0.00747826	−	0.00747826i
$487$	−7.34545	+	1.96821i	−0.332854	+	0.0891879i	−0.421375	−	0.906886i	$-0.638452\pi$
$487$	−7.34545	+	1.96821i	−0.332854	+	0.0891879i	0.0885214	+	0.996074i	$0.471786\pi$
$488$	2.21885	+	8.28088i	0.100443	+	0.374858i
$489$	−13.1831	+	13.1831i	−0.596160	+	0.596160i
$490$	1.30224	+	0.751847i	0.0588291	+	0.0339650i
$491$	11.5353	+	19.9798i	0.520582	+	0.901675i	0.999714	+	0.0239314i	$0.00761834\pi$
$491$	11.5353	+	19.9798i	0.520582	+	0.901675i	−0.479132	+	0.877743i	$0.659048\pi$
$492$	4.26059	−	15.9007i	0.192082	−	0.716860i
$493$		−	20.1320i		−	0.906697i
$494$	−3.63363	+	2.15838i	−0.163485	+	0.0971103i
$495$	4.68596	−	1.19319i	0.210618	−	0.0536301i
$496$	2.91123	−	10.8648i	0.130718	−	0.487846i
$497$	6.43553	−	3.71555i	0.288673	−	0.166665i
$498$	2.13816	+	1.23446i	0.0958130	+	0.0553177i
$499$	5.97354	+	5.97354i	0.267412	+	0.267412i	0.828057	−	0.560644i	$-0.189446\pi$
$499$	5.97354	+	5.97354i	0.267412	+	0.267412i	−0.560644	+	0.828057i	$0.689446\pi$
$500$	21.5758	−	5.78121i	0.964898	−	0.258544i
$501$	−18.7002	+	5.01072i	−0.835466	+	0.223862i
$502$	2.48321	+	2.48321i	0.110831	+	0.110831i
$503$	15.3334	+	8.85276i	0.683684	+	0.394725i	0.801242	−	0.598341i	$-0.204173\pi$
$503$	15.3334	+	8.85276i	0.683684	+	0.394725i	−0.117558	+	0.993066i	$0.537507\pi$
$504$	1.27874	−	0.738282i	0.0569597	−	0.0328857i
$505$	1.19232	−	4.44980i	0.0530576	−	0.198014i
$506$	−1.03103	+	0.262533i	−0.0458350	+	0.0116710i
$507$	−12.9960	+	0.322335i	−0.577173	+	0.0143154i
$508$		−	8.74501i		−	0.387997i
$509$	−2.20052	+	8.21246i	−0.0975364	+	0.364011i	−0.997392	−	0.0721775i	$-0.977005\pi$
$509$	−2.20052	+	8.21246i	−0.0975364	+	0.364011i	0.899855	+	0.436188i	$0.143672\pi$
$510$	−1.31002	−	2.26903i	−0.0580088	−	0.100474i
$511$	−11.7962	−	6.81052i	−0.521832	−	0.301280i
$512$	−11.7955	+	11.7955i	−0.521294	+	0.521294i
$513$	1.30123	+	4.85627i	0.0574508	+	0.214409i
$514$	6.79387	−	1.82041i	0.299665	−	0.0802949i
$515$	−13.1998	+	13.1998i	−0.581651	+	0.581651i
$516$	19.8850	+	11.4806i	0.875388	+	0.505405i
$517$	−27.0893	+	26.4222i	−1.19139	+	1.16204i
$518$	2.41079	+	0.645968i	0.105924	+	0.0283822i
$519$	3.16268			0.138826
$520$	4.15761	−	2.46963i	0.182323	−	0.108300i
$521$	1.50270			0.0658344			0.0329172	−	0.999458i	$-0.489520\pi$
$521$	1.50270			0.0658344			0.0329172	+	0.999458i	$0.489520\pi$
$522$	−0.157610	+	0.588209i	−0.00689841	+	0.0257452i
$523$	23.5301	−	13.5851i	1.02890	−	0.594036i	0.112232	−	0.993682i	$-0.464200\pi$
$523$	23.5301	−	13.5851i	1.02890	−	0.594036i	0.916670	+	0.399646i	$0.130867\pi$
$524$	14.0929	−	24.4096i	0.615650	−	1.06634i
$525$	3.26234	−	3.26234i	0.142380	−	0.142380i
$526$	−3.82538	+	1.02501i	−0.166794	+	0.0446924i
$527$	−22.7764	+	6.10290i	−0.992153	+	0.265847i
$528$	−6.22847	+	10.4840i	−0.271059	+	0.456257i
$529$	−10.5535	+	18.2791i	−0.458846	+	0.794745i
$530$	−1.18047	−	2.04464i	−0.0512765	−	0.0888135i
$531$	−3.27256	−	0.876879i	−0.142017	−	0.0380533i
$532$			15.7008i			0.680718i
$533$	−8.26021	−	29.3662i	−0.357789	−	1.27199i
$534$			0.188627i			0.00816270i
$535$	−23.4617	−	6.28654i	−1.01434	−	0.271791i
$536$	4.13541	−	2.38758i	0.178622	−	0.103128i
$537$	6.89345	+	3.97994i	0.297474	+	0.171747i
$538$	−4.38164	+	4.38164i	−0.188906	+	0.188906i
$539$	−12.7965	+	7.17685i	−0.551183	+	0.309129i
$540$	−0.734181	−	2.74000i	−0.0315941	−	0.117911i
$541$	2.98881	+	2.98881i	0.128499	+	0.128499i	0.768431	−	0.639932i	$-0.221038\pi$
$541$	2.98881	+	2.98881i	0.128499	+	0.128499i	−0.639932	+	0.768431i	$0.721038\pi$
$542$	2.32040	−	4.01906i	0.0996698	−	0.172633i
$543$	15.2093	−	8.78108i	0.652693	−	0.376832i
$544$	20.0803	+	5.38050i	0.860935	+	0.230687i
$545$	18.1272			0.776484
$546$	0.660107	−	1.17680i	0.0282500	−	0.0503623i
$547$			10.3332i			0.441815i	0.975295	+	0.220908i	$0.0709019\pi$
$547$			10.3332i			0.441815i	−0.975295	+	0.220908i	$0.929098\pi$
$548$	3.19349	−	11.9183i	0.136419	−	0.509123i
$549$	8.07072	−	4.65963i	0.344450	−	0.198868i
$550$	0.601984	−	2.13958i	0.0256687	−	0.0912320i
$551$	−9.28535	−	9.28535i	−0.395569	−	0.395569i
$552$	0.327591	+	1.22259i	0.0139432	+	0.0520367i
$553$	0.389984	+	1.45544i	0.0165838	+	0.0618915i
$554$	−0.108367	+	0.108367i	−0.00460409	+	0.00460409i
$555$	4.86177	−	8.42083i	0.206371	−	0.357444i
$556$	−18.0240	−	31.2184i	−0.764386	−	1.32396i
$557$	−5.43779	+	20.2941i	−0.230407	+	0.859889i	0.749759	+	0.661711i	$0.230169\pi$
$557$	−5.43779	+	20.2941i	−0.230407	+	0.859889i	−0.980166	+	0.198178i	$0.936497\pi$
$558$	0.713251			0.0301943
$559$	42.5471	−	0.527559i	1.79955	−	0.0223134i
$560$		−	8.60431i		−	0.363599i
$561$	25.5619	+	0.318685i	1.07923	+	0.0134549i
$562$	1.47722	+	2.55862i	0.0623127	+	0.107929i
$563$	13.4703	−	23.3312i	0.567705	−	0.983295i	−0.429087	−	0.903263i	$-0.641165\pi$
$563$	13.4703	−	23.3312i	0.567705	−	0.983295i	0.996792	−	0.0800314i	$-0.0255020\pi$
$564$	15.6970	+	15.6970i	0.660963	+	0.660963i
$565$	−7.56694	+	2.02756i	−0.318344	+	0.0852999i
$566$	−0.517731	−	1.93220i	−0.0217618	−	0.0812163i
$567$	−1.13498	−	1.13498i	−0.0476645	−	0.0476645i
$568$	−3.68836	−	2.12948i	−0.154760	−	0.0893509i
$569$	−0.0149005	−	0.0258085i	−0.000624663	−	0.00108195i	0.865713	−	0.500541i	$-0.166866\pi$
$569$	−0.0149005	−	0.0258085i	−0.000624663	−	0.00108195i	−0.866338	+	0.499459i	$0.833532\pi$
$570$	−1.65075	−	0.442316i	−0.0691421	−	0.0185266i
$571$	24.8271			1.03898			0.519490	−	0.854476i	$-0.326122\pi$
$571$	24.8271			1.03898			0.519490	+	0.854476i	$0.326122\pi$
$572$	−0.00157647	+	23.2665i	−6.59155e−5	+	0.972821i
$573$	4.81057			0.200964
$574$	3.05836	+	0.819486i	0.127654	+	0.0342047i
$575$	1.97741	+	3.42497i	0.0824637	+	0.142831i
$576$	5.82384	+	3.36239i	0.242660	+	0.140100i
$577$	−21.9824	−	21.9824i	−0.915138	−	0.915138i	0.0815327	−	0.996671i	$-0.474018\pi$
$577$	−21.9824	−	21.9824i	−0.915138	−	0.915138i	−0.996671	+	0.0815327i	$0.974018\pi$
$578$	−2.55919	−	9.55102i	−0.106448	−	0.397270i
$579$	11.2172	−	3.00563i	0.466169	−	0.124910i
$580$	5.23898	+	5.23898i	0.217537	+	0.217537i
$581$	8.49859	−	14.7200i	0.352581	−	0.610688i
$582$	−0.980066	−	1.69752i	−0.0406250	−	0.0703646i
$583$	23.0341	+	0.287170i	0.953975	+	0.0118934i
$584$			7.80656i			0.323038i
$585$	−3.76287	−	3.67070i	−0.155576	−	0.151765i
$586$	−4.03697			−0.166766
$587$	−6.99631	+	26.1106i	−0.288769	+	1.07770i	0.657272	+	0.753653i	$0.271710\pi$
$587$	−6.99631	+	26.1106i	−0.288769	+	1.07770i	−0.946041	+	0.324047i	$0.894957\pi$
$588$	4.30343	+	7.45376i	0.177470	+	0.307388i
$589$	−7.69020	+	13.3198i	−0.316869	+	0.548834i
$590$	0.814341	−	0.814341i	0.0335259	−	0.0335259i
$591$	−5.09658	−	19.0207i	−0.209645	−	0.782406i
$592$	6.34668	+	23.6861i	0.260847	+	0.973494i
$593$	−12.6029	−	12.6029i	−0.517538	−	0.517538i	0.399288	−	0.916826i	$-0.369257\pi$
$593$	−12.6029	−	12.6029i	−0.517538	−	0.517538i	−0.916826	+	0.399288i	$0.869257\pi$
$594$	−0.744366	−	0.209432i	−0.0305417	−	0.00859310i
$595$	−15.6210	+	9.01877i	−0.640397	+	0.369733i
$596$	5.27433	−	19.6841i	0.216045	−	0.806290i
$597$			4.23393i			0.173283i
$598$	0.827929	+	0.807649i	0.0338565	+	0.0330272i
$599$	−3.92609			−0.160415			−0.0802077	−	0.996778i	$-0.525558\pi$
$599$	−3.92609			−0.160415			−0.0802077	+	0.996778i	$0.525558\pi$
$600$	−2.55409	−	0.684367i	−0.104270	−	0.0279392i
$601$	−34.2368	+	19.7666i	−1.39655	+	0.806297i	−0.994029	−	0.109115i	$-0.965198\pi$
$601$	−34.2368	+	19.7666i	−1.39655	+	0.806297i	−0.402518	+	0.915412i	$0.631865\pi$
$602$	−2.20819	+	3.82470i	−0.0899992	+	0.155883i
$603$	−3.67047	−	3.67047i	−0.149473	−	0.149473i
$604$	0.626395	+	2.33774i	0.0254876	+	0.0951212i
$605$	−11.0540	−	11.6194i	−0.449409	−	0.472397i
$606$	−0.520920	+	0.520920i	−0.0211609	+	0.0211609i
$607$	−27.9880	−	16.1589i	−1.13600	−	0.655869i	−0.190562	−	0.981675i	$-0.561031\pi$
$607$	−27.9880	−	16.1589i	−1.13600	−	0.655869i	−0.945437	+	0.325806i	$0.894364\pi$
$608$	11.7431	−	6.77991i	0.476247	−	0.274961i
$609$	4.04949	+	1.08506i	0.164093	+	0.0439687i
$610$			3.16781i			0.128261i
$611$	39.8650	+	10.1538i	1.61276	+	0.410777i
$612$		−	14.9966i		−	0.606204i
$613$	−21.1196	−	5.65898i	−0.853013	−	0.228564i	−0.194285	−	0.980945i	$-0.562239\pi$
$613$	−21.1196	−	5.65898i	−0.853013	−	0.228564i	−0.658728	+	0.752381i	$0.728905\pi$
$614$	3.42221	+	5.92745i	0.138109	+	0.239212i
$615$	6.16772	−	10.6828i	0.248707	−	0.430772i
$616$	−4.21026	−	2.50129i	−0.169636	−	0.100780i
$617$	8.27439	−	2.21712i	0.333114	−	0.0892578i	−0.0883850	−	0.996086i	$-0.528171\pi$
$617$	8.27439	−	2.21712i	0.333114	−	0.0892578i	0.421500	+	0.906829i	$0.361504\pi$
$618$	2.88346	−	0.772621i	0.115990	−	0.0310794i
$619$	−11.7450	+	11.7450i	−0.472073	+	0.472073i	−0.902585	−	0.430512i	$-0.858333\pi$
$619$	−11.7450	+	11.7450i	−0.472073	+	0.472073i	0.430512	+	0.902585i	$0.358333\pi$
$620$	4.33897	−	7.51531i	0.174257	−	0.301822i
$621$	1.19156	−	0.687946i	0.0478156	−	0.0276063i
$622$	−0.798265	+	2.97916i	−0.0320075	+	0.119454i
$623$	1.29859			0.0520270
$624$	13.2559	−	0.164365i	0.530660	−	0.00657987i
$625$	2.36619			0.0946477
$626$	5.52228	+	1.47969i	0.220715	+	0.0591403i
$627$	11.9368	−	11.6428i	0.476709	−	0.464969i
$628$	−39.6025	−	22.8645i	−1.58031	−	0.912393i
$629$	36.3493	−	36.3493i	1.44934	−	1.44934i
$630$	0.527015	−	0.141213i	0.0209968	−	0.00562607i
$631$	−3.27112	−	12.2080i	−0.130221	−	0.485993i	0.869750	−	0.493492i	$-0.164280\pi$
$631$	−3.27112	−	12.2080i	−0.130221	−	0.485993i	−0.999972	+	0.00749885i	$0.997613\pi$
$632$	0.610639	−	0.610639i	0.0242899	−	0.0242899i
$633$	4.80671	+	2.77516i	0.191050	+	0.110303i
$634$	1.01116	+	1.75139i	0.0401584	+	0.0695564i
$635$	1.69605	−	6.32973i	0.0673056	−	0.251188i
$636$		−	13.5136i		−	0.535850i
$637$	13.9107	+	7.80300i	0.551162	+	0.309166i
$638$	1.95723	−	0.498373i	0.0774876	−	0.0197308i
$639$	−1.19825	+	4.47194i	−0.0474021	+	0.176907i
$640$	−8.79047	+	5.07518i	−0.347474	+	0.200614i
$641$	4.94629	+	2.85574i	0.195367	+	0.112795i	0.594493	−	0.804101i	$-0.297353\pi$
$641$	4.94629	+	2.85574i	0.195367	+	0.112795i	−0.399126	+	0.916896i	$0.630686\pi$
$642$	2.74656	+	2.74656i	0.108398	+	0.108398i
$643$	16.6057	−	4.44947i	0.654863	−	0.175470i	0.0839366	−	0.996471i	$-0.473251\pi$
$643$	16.6057	−	4.44947i	0.654863	−	0.175470i	0.570927	+	0.821001i	$0.306584\pi$
$644$	4.15043	−	1.11210i	0.163550	−	0.0438230i
$645$	12.1664	+	12.1664i	0.479050	+	0.479050i
$646$	−7.82445	−	4.51745i	−0.307849	−	0.177737i
$647$	12.9204	−	7.45959i	0.507953	−	0.293267i	−0.224039	−	0.974580i	$-0.571924\pi$
$647$	12.9204	−	7.45959i	0.507953	−	0.293267i	0.731992	+	0.681313i	$0.238591\pi$
$648$	−0.238093	+	0.888576i	−0.00935319	+	0.0349066i
$649$	2.77275	+	10.8893i	0.108840	+	0.427441i
$650$	−2.32601	+	0.654268i	−0.0912338	+	0.0256625i
$651$		−	4.91033i		−	0.192451i
$652$	9.38840	−	35.0380i	0.367678	−	1.37219i
$653$	8.13965	+	14.0983i	0.318529	+	0.551709i	0.980181	−	0.198102i	$-0.0634778\pi$
$653$	8.13965	+	14.0983i	0.318529	+	0.551709i	−0.661652	+	0.749811i	$0.730144\pi$
$654$	−2.51044	−	1.44941i	−0.0981661	−	0.0566762i
$655$	14.9347	−	14.9347i	0.583546	−	0.583546i
$656$	8.05151	+	30.0486i	0.314359	+	1.17320i
$657$	8.19695	−	2.19637i	0.319794	−	0.0856884i
$658$	−3.01918	+	3.01918i	−0.117700	+	0.117700i
$659$	−5.71438	−	3.29920i	−0.222600	−	0.128518i	0.384553	−	0.923103i	$-0.374355\pi$
$659$	−5.71438	−	3.29920i	−0.222600	−	0.128518i	−0.607154	+	0.794584i	$0.707689\pi$
$660$	−6.73497	+	6.56911i	−0.262158	+	0.255702i
$661$	20.2672	+	5.43058i	0.788302	+	0.211225i	0.630442	−	0.776236i	$-0.282874\pi$
$661$	20.2672	+	5.43058i	0.788302	+	0.211225i	0.157861	+	0.987461i	$0.449540\pi$
$662$	2.83215			0.110075
$663$	−14.1928	−	23.8935i	−0.551203	−	0.927947i
$664$	−9.74151			−0.378044
$665$	−3.04509	+	11.3644i	−0.118084	+	0.440694i
$666$	−1.34662	+	0.777470i	−0.0521803	+	0.0301263i
$667$	−1.79684	+	3.11222i	−0.0695739	+	0.120505i
$668$	26.6349	−	26.6349i	1.03054	−	1.03054i
$669$	−18.6755	+	5.00409i	−0.722038	+	0.193469i
$670$	1.70435	−	0.456679i	0.0658447	−	0.0176430i
$671$	−26.5728	−	15.7867i	−1.02583	−	0.609440i
$672$	−2.16454	+	3.74910i	−0.0834991	+	0.144625i
$673$	−17.0513	−	29.5336i	−0.657278	−	1.13844i	−0.981318	−	0.192395i	$-0.938375\pi$
$673$	−17.0513	−	29.5336i	−0.657278	−	1.13844i	0.324040	−	0.946043i	$-0.394959\pi$
$674$	−0.863888	−	0.231478i	−0.0332757	−	0.00891620i
$675$			2.87437i			0.110634i
$676$	21.5844	−	13.1859i	0.830168	−	0.507150i
$677$		−	23.1888i		−	0.891217i	−0.895228	−	0.445608i	$-0.852987\pi$
$677$		−	23.1888i		−	0.891217i	0.895228	−	0.445608i	$-0.147013\pi$
$678$	1.21007	+	0.324237i	0.0464724	+	0.0124522i
$679$	−11.6865	+	6.74720i	−0.448486	+	0.258934i
$680$	8.95277	+	5.16888i	0.343323	+	0.198218i
$681$	17.5853	−	17.5853i	0.673872	−	0.673872i
$682$	−1.15716	−	2.06324i	−0.0443100	−	0.0790057i
$683$	−1.59042	−	5.93552i	−0.0608557	−	0.227117i	0.928800	−	0.370582i	$-0.120842\pi$
$683$	−1.59042	−	5.93552i	−0.0608557	−	0.227117i	−0.989655	+	0.143466i	$0.954175\pi$
$684$	−6.91682	−	6.91682i	−0.264471	−	0.264471i
$685$	4.62296	−	8.00721i	0.176634	−	0.305940i
$686$	−3.70229	+	2.13752i	−0.141354	+	0.0816109i
$687$	7.78962	+	2.08722i	0.297192	+	0.0796325i
$688$	−43.3913			−1.65428
$689$	−12.7893	−	21.5307i	−0.487232	−	0.820253i
$690$			0.467694i			0.0178048i
$691$	−4.16924	+	15.5598i	−0.158605	+	0.591923i	0.840164	+	0.542332i	$0.182458\pi$
$691$	−4.16924	+	15.5598i	−0.158605	+	0.591923i	−0.998770	+	0.0495910i	$0.984208\pi$
$692$	−5.32903	+	3.07672i	−0.202579	+	0.116959i
$693$	−1.44182	+	5.12454i	−0.0547702	+	0.194665i
$694$	0.436694	+	0.436694i	0.0165767	+	0.0165767i
$695$	−6.99130	−	26.0919i	−0.265195	−	0.989721i
$696$	−0.621873	−	2.32086i	−0.0235720	−	0.0879721i
$697$	46.1134	−	46.1134i	1.74667	−	1.74667i
$698$	−3.28640	+	5.69222i	−0.124392	+	0.215454i
$699$	−4.55459	−	7.88878i	−0.172270	−	0.298381i
$700$	−2.32329	+	8.67062i	−0.0878119	+	0.327719i
$701$	25.6394			0.968388			0.484194	−	0.874961i	$-0.339113\pi$
$701$	25.6394			0.968388			0.484194	+	0.874961i	$0.339113\pi$
$702$	0.227622	+	0.809227i	0.00859103	+	0.0305423i
$703$		−	33.5304i		−	1.26462i
$704$	0.278041	−	22.3019i	0.0104791	−	0.840533i
$705$	8.31732	+	14.4060i	0.313248	+	0.542562i
$706$	0.732133	−	1.26809i	0.0275542	−	0.0477253i
$707$	3.58624	+	3.58624i	0.134874	+	0.134874i
$708$	6.36722	−	1.70609i	0.239295	−	0.0641189i
$709$	−10.9689	−	40.9365i	−0.411946	−	1.53740i	−0.790876	−	0.611977i	$-0.790375\pi$
$709$	−10.9689	−	40.9365i	−0.411946	−	1.53740i	0.378930	−	0.925425i	$-0.376292\pi$
$710$	−1.11279	−	1.11279i	−0.0417624	−	0.0417624i
$711$	−0.812979	−	0.469373i	−0.0304891	−	0.0176029i
$712$	−0.372128	−	0.644544i	−0.0139461	−	0.0241553i
$713$	4.06572	+	1.08941i	0.152262	+	0.0407986i
$714$	2.88447			0.107949
$715$	−4.51355	+	16.8402i	−0.168797	+	0.629789i
$716$	−15.4871			−0.578779
$717$	−5.19292	−	1.39144i	−0.193933	−	0.0519642i
$718$	−2.32565	−	4.02814i	−0.0867924	−	0.150329i
$719$	13.9578	+	8.05856i	0.520540	+	0.300534i	0.737155	−	0.675723i	$-0.236169\pi$
$719$	13.9578	+	8.05856i	0.520540	+	0.300534i	−0.216616	+	0.976257i	$0.569502\pi$
$720$	3.79053	+	3.79053i	0.141265	+	0.141265i
$721$	−5.31906	−	19.8510i	−0.198092	−	0.739289i
$722$	−1.41350	+	0.378746i	−0.0526051	+	0.0140955i
$723$	−2.81517	−	2.81517i	−0.104697	−	0.104697i
$724$	−17.0848	+	29.5918i	−0.634953	+	1.09977i
$725$	−3.75376	−	6.50170i	−0.139411	−	0.241467i
$726$	0.601812	+	2.49303i	0.0223353	+	0.0925250i
$727$		−	0.319366i		−	0.0118446i	−0.999982	−	0.00592231i	$-0.998115\pi$
$727$		−	0.319366i		−	0.0118446i	0.999982	−	0.00592231i	$-0.00188514\pi$
$728$	0.0660073	+	5.32342i	0.00244639	+	0.197299i
$729$	1.00000			0.0370370
$730$	−0.746591	+	2.78631i	−0.0276326	+	0.103126i
$731$	45.4813	+	78.7760i	1.68219	+	2.91363i
$732$	−9.06597	+	15.7027i	−0.335088	+	0.580389i
$733$	5.54310	−	5.54310i	0.204739	−	0.204739i	−0.597288	−	0.802027i	$-0.703755\pi$
$733$	5.54310	−	5.54310i	0.204739	−	0.204739i	0.802027	+	0.597288i	$0.203755\pi$
$734$	−1.04394	−	3.89602i	−0.0385324	−	0.143805i
$735$	1.66925	+	6.22974i	0.0615713	+	0.229787i
$736$	−2.62400	−	2.62400i	−0.0967221	−	0.0967221i
$737$	−4.66280	+	16.5726i	−0.171756	+	0.610459i
$738$	−1.70834	+	0.986311i	−0.0628849	+	0.0363066i
$739$	−9.03192	+	33.7076i	−0.332245	+	1.23995i	0.574581	+	0.818448i	$0.305165\pi$
$739$	−9.03192	+	33.7076i	−0.332245	+	1.23995i	−0.906826	+	0.421506i	$0.861502\pi$
$740$			18.9185i			0.695459i
$741$	−17.5663	−	4.47421i	−0.645316	−	0.164364i
$742$	2.59922			0.0954205
$743$	6.37576	+	1.70838i	0.233904	+	0.0626743i	0.373867	−	0.927482i	$-0.378032\pi$
$743$	6.37576	+	1.70838i	0.233904	+	0.0626743i	−0.139963	+	0.990157i	$0.544698\pi$
$744$	−2.43720	+	1.40712i	−0.0893520	+	0.0515874i
$745$	7.63523	−	13.2246i	0.279733	−	0.484512i
$746$	−4.76455	−	4.76455i	−0.174443	−	0.174443i
$747$	2.74076	+	10.2287i	0.100279	+	0.374247i
$748$	−43.3813	+	24.3302i	−1.58618	+	0.889601i
$749$	18.9085	−	18.9085i	0.690903	−	0.690903i
$750$	−2.31806	−	1.33833i	−0.0846434	−	0.0488689i
$751$	−12.2214	+	7.05606i	−0.445967	+	0.257479i	−0.706125	−	0.708087i	$-0.749559\pi$
$751$	−12.2214	+	7.05606i	−0.445967	+	0.257479i	0.260158	+	0.965566i	$0.416225\pi$
$752$	−40.5213	−	10.8576i	−1.47766	−	0.395938i
$753$			15.0624i			0.548904i
$754$	−1.57168	−	1.53318i	−0.0572371	−	0.0558351i
$755$			1.81357i			0.0660024i
$756$	3.01653	+	0.808278i	0.109710	+	0.0293968i
$757$	−13.4900	−	23.3653i	−0.490302	−	0.849227i	0.509636	−	0.860390i	$-0.329780\pi$
$757$	−13.4900	−	23.3653i	−0.490302	−	0.849227i	−0.999938	+	0.0111628i	$0.996447\pi$
$758$	−2.37190	+	4.10826i	−0.0861515	+	0.149219i
$759$	−3.92320	−	2.33075i	−0.142403	−	0.0846008i
$760$	6.51325	−	1.74522i	0.236260	−	0.0633058i
$761$	47.2018	−	12.6477i	1.71106	−	0.458478i	0.735378	−	0.677657i	$-0.237004\pi$
$761$	47.2018	−	12.6477i	1.71106	−	0.458478i	0.975685	+	0.219179i	$0.0703377\pi$
$762$	−0.740996	+	0.740996i	−0.0268434	+	0.0268434i
$763$	−9.97833	+	17.2830i	−0.361240	+	0.625686i
$764$	−8.10569	+	4.67982i	−0.293253	+	0.169310i
$765$	2.90852	−	10.8547i	0.105158	−	0.392454i
$766$	−7.76549			−0.280579
$767$	8.52998	−	8.74417i	0.308000	−	0.315734i
$768$	−11.8264			−0.426748
$769$	8.58341	+	2.29992i	0.309526	+	0.0829371i	0.410238	−	0.911978i	$-0.365446\pi$
$769$	8.58341	+	2.29992i	0.309526	+	0.0829371i	−0.100713	+	0.994916i	$0.532112\pi$
$770$	−1.26351	−	1.29541i	−0.0455337	−	0.0466834i
$771$	26.1259	+	15.0838i	0.940900	+	0.543229i
$772$	−15.9767	+	15.9767i	−0.575014	+	0.575014i
$773$	0.438804	−	0.117577i	0.0157827	−	0.00422896i	−0.250919	−	0.968008i	$-0.580733\pi$
$773$	0.438804	−	0.117577i	0.0157827	−	0.00422896i	0.266702	+	0.963779i	$0.414066\pi$
$774$	−0.712134	−	2.65772i	−0.0255971	−	0.0955297i
$775$	−6.21779	+	6.21779i	−0.223350	+	0.223350i
$776$	6.69782	+	3.86699i	0.240438	+	0.138817i
$777$	5.35244	+	9.27069i	0.192018	+	0.332584i
$778$	0.475355	−	1.77405i	0.0170423	−	0.0636027i
$779$		−	42.5372i		−	1.52405i
$780$	9.91128	+	2.52444i	0.354881	+	0.0903894i
$781$	14.8801	−	3.78895i	0.532453	−	0.135579i
$782$	−0.639949	+	2.38832i	−0.0228845	+	0.0854062i
$783$	−2.26196	+	1.30594i	−0.0808359	+	0.0466706i
$784$	−14.0858	−	8.13247i	−0.503066	−	0.290445i
$785$	−24.2303	−	24.2303i	−0.864815	−	0.864815i
$786$	−3.26245	+	0.874171i	−0.116368	+	0.0311807i
$787$	−10.4217	+	2.79248i	−0.371493	+	0.0995411i	−0.439735	−	0.898128i	$-0.644928\pi$
$787$	−10.4217	+	2.79248i	−0.371493	+	0.0995411i	0.0682423	+	0.997669i	$0.478261\pi$
$788$	27.0913	+	27.0913i	0.965088	+	0.965088i
$789$	−14.7105	−	8.49312i	−0.523708	−	0.302363i
$790$	0.276348	−	0.159550i	0.00983203	−	0.00567653i
$791$	2.23219	−	8.33063i	0.0793674	−	0.296203i
$792$	2.95669	−	0.752866i	0.105061	−	0.0267519i
$793$	0.416601	+	33.5985i	0.0147940	+	1.19312i
$794$			1.05105i			0.0373004i
$795$	2.62089	−	9.78131i	0.0929535	−	0.346907i
$796$	−4.11886	−	7.13407i	−0.145989	−	0.252860i
$797$	−22.2977	−	12.8736i	−0.789823	−	0.456005i	0.0500770	−	0.998745i	$-0.484053\pi$
$797$	−22.2977	−	12.8736i	−0.789823	−	0.456005i	−0.839900	+	0.542741i	$0.817387\pi$
$798$	1.33039	−	1.33039i	0.0470953	−	0.0470953i
$799$	22.7613	+	84.9462i	0.805236	+	3.00518i
$800$	7.48826	−	2.00647i	0.264750	−	0.0709395i
$801$	−0.572079	+	0.572079i	−0.0202134	+	0.0202134i
$802$	0.472952	+	0.273059i	0.0167005	+	0.00964205i
$803$	−19.6520	−	20.1482i	−0.693506	−	0.711016i
$804$	9.75536	+	2.61394i	0.344045	+	0.0921866i
$805$	3.21981			0.113483
$806$	−1.25812	+	2.24290i	−0.0443154	+	0.0790027i
$807$	−26.5778			−0.935582
$808$	0.752316	−	2.80768i	0.0264664	−	0.0987739i
$809$	0.941997	−	0.543862i	0.0331189	−	0.0191212i	−0.483349	−	0.875428i	$-0.660580\pi$
$809$	0.941997	−	0.543862i	0.0331189	−	0.0191212i	0.516468	+	0.856306i	$0.327247\pi$
$810$	−0.169960	+	0.294380i	−0.00597180	+	0.0103435i
$811$	−14.0346	+	14.0346i	−0.492821	+	0.492821i	−0.909194	−	0.416373i	$-0.863301\pi$
$811$	−14.0346	+	14.0346i	−0.492821	+	0.492821i	0.416373	+	0.909194i	$0.363301\pi$
$812$	−7.87885	+	2.11113i	−0.276493	+	0.0740862i
$813$	19.2267	−	5.15177i	0.674308	−	0.180680i
$814$	4.43373	+	2.63405i	0.155402	+	0.0923235i
$815$	13.5909	−	23.5400i	0.476067	−	0.824572i
$816$	14.1701	+	24.5433i	0.496051	+	0.859186i
$817$	57.3105	+	15.3563i	2.00504	+	0.537249i
$818$		−	0.690926i		−	0.0241577i
$819$	5.57107	−	1.56705i	0.194669	−	0.0547570i
$820$			24.0004i			0.838129i
$821$	−15.8308	−	4.24186i	−0.552500	−	0.148042i	−0.0282418	−	0.999601i	$-0.508991\pi$
$821$	−15.8308	−	4.24186i	−0.552500	−	0.148042i	−0.524259	+	0.851559i	$0.675657\pi$
$822$	−1.28047	+	0.739281i	−0.0446616	+	0.0257854i
$823$	−6.75835	−	3.90193i	−0.235581	−	0.136013i	0.377563	−	0.925984i	$-0.376762\pi$
$823$	−6.75835	−	3.90193i	−0.235581	−	0.136013i	−0.613144	+	0.789971i	$0.710096\pi$
$824$	−8.32862	+	8.32862i	−0.290141	+	0.290141i
$825$	8.31477	−	4.66331i	0.289483	−	0.162355i
$826$	0.328152	+	1.22468i	0.0114179	+	0.0426120i
$827$	11.3769	+	11.3769i	0.395615	+	0.395615i	0.876683	−	0.481068i	$-0.159751\pi$
$827$	11.3769	+	11.3769i	0.395615	+	0.395615i	−0.481068	+	0.876683i	$0.659751\pi$
$828$	−1.33850	+	2.31834i	−0.0465160	+	0.0805680i
$829$	−15.7047	+	9.06710i	−0.545446	+	0.314914i	−0.747283	−	0.664506i	$-0.768642\pi$
$829$	−15.7047	+	9.06710i	−0.545446	+	0.314914i	0.201837	+	0.979419i	$0.435309\pi$
$830$	−3.47694	−	0.931642i	−0.120686	−	0.0323378i
$831$	−0.657325			−0.0228023
$832$	−20.8462	+	12.3827i	−0.722712	+	0.429293i
$833$			34.0968i			1.18138i
$834$	−1.11801	+	4.17248i	−0.0387136	+	0.144481i
$835$	24.4444	−	14.1130i	0.845932	−	0.488399i
$836$	−8.78681	+	31.2302i	−0.303898	+	1.08012i
$837$	2.16319	+	2.16319i	0.0747707	+	0.0747707i
$838$	0.0947418	+	0.353581i	0.00327280	+	0.0122143i
$839$	−13.3935	−	49.9852i	−0.462395	−	1.72568i	−0.665384	−	0.746501i	$-0.731732\pi$
$839$	−13.3935	−	49.9852i	−0.462395	−	1.72568i	0.202989	−	0.979181i	$-0.434934\pi$
$840$	−1.52224	+	1.52224i	−0.0525221	+	0.0525221i
$841$	−11.0890	+	19.2067i	−0.382380	+	0.662302i
$842$	2.12109	+	3.67384i	0.0730976	+	0.126609i
$843$	−3.27972	+	12.2401i	−0.112960	+	0.421571i
$844$	−10.7989			−0.371714
$845$	18.1803	−	5.35794i	0.625423	−	0.184319i
$846$		−	2.66013i		−	0.0914571i
$847$	17.1631	−	4.14313i	0.589731	−	0.142360i
$848$	12.7688	+	22.1162i	0.438482	+	0.759472i
$849$	4.28987	−	7.43028i	0.147228	−	0.255006i
$850$	−3.65251	−	3.65251i	−0.125280	−	0.125280i
$851$	−8.86356	+	2.37498i	−0.303839	+	0.0814134i
$852$	−2.33137	−	8.70079i	−0.0798714	−	0.298084i
$853$	−10.3413	−	10.3413i	−0.354081	−	0.354081i	0.507545	−	0.861625i	$-0.330553\pi$
$853$	−10.3413	−	10.3413i	−0.354081	−	0.354081i	−0.861625	+	0.507545i	$0.830553\pi$
$854$	−3.02028	−	1.74376i	−0.103352	−	0.0596702i
$855$	−3.66499	−	6.34795i	−0.125340	−	0.217095i
$856$	−14.8036	−	3.96660i	−0.505975	−	0.135576i
$857$	−1.11246			−0.0380010			−0.0190005	−	0.999819i	$-0.506048\pi$
$857$	−1.11246			−0.0380010			−0.0190005	+	0.999819i	$0.506048\pi$
$858$	1.97159	−	1.97132i	0.0673089	−	0.0672997i
$859$	−43.6560			−1.48952			−0.744762	−	0.667330i	$-0.767437\pi$
$859$	−43.6560			−1.48952			−0.744762	+	0.667330i	$0.767437\pi$
$860$	−32.3357	−	8.66433i	−1.10264	−	0.295451i
$861$	6.79019	+	11.7610i	0.231409	+	0.400812i
$862$	3.44358	+	1.98815i	0.117289	+	0.0677167i
$863$	8.21522	+	8.21522i	0.279649	+	0.279649i	0.832969	−	0.553320i	$-0.186639\pi$
$863$	8.21522	+	8.21522i	0.279649	+	0.279649i	−0.553320	+	0.832969i	$0.686639\pi$
$864$	−0.698058	−	2.60519i	−0.0237484	−	0.0886302i
$865$	−4.45393	+	1.19343i	−0.151438	+	0.0405777i
$866$	0.351863	+	0.351863i	0.0119568	+	0.0119568i
$867$	21.2052	−	36.7285i	0.720167	−	1.24737i
$868$	4.77687	+	8.27378i	0.162138	+	0.280830i
$869$	−0.0388132	+	3.11323i	−0.00131665	+	0.105609i
$870$		−	0.887835i		−	0.0301004i
$871$	18.0166	−	5.06777i	0.610470	−	0.171715i
$872$	11.4377			0.387328
$873$	2.17595	−	8.12074i	0.0736446	−	0.274845i
$874$	0.806393	+	1.39671i	0.0272766	+	0.0472445i
$875$	−9.21364	+	15.9585i	−0.311478	+	0.539496i
$876$	−11.6750	+	11.6750i	−0.394461	+	0.394461i
$877$	−1.59608	−	5.95666i	−0.0538958	−	0.201142i	0.933728	−	0.357983i	$-0.116536\pi$
$877$	−1.59608	−	5.95666i	−0.0538958	−	0.201142i	−0.987624	+	0.156841i	$0.949869\pi$
$878$	0.974059	+	3.63524i	0.0328729	+	0.122683i
$879$	−12.2436	−	12.2436i	−0.412965	−	0.412965i
$880$	4.81531	−	17.1146i	0.162324	−	0.576935i
$881$	−15.6382	+	9.02873i	−0.526865	+	0.304186i	−0.739739	−	0.672894i	$-0.765051\pi$
$881$	−15.6382	+	9.02873i	−0.526865	+	0.304186i	0.212874	+	0.977080i	$0.431718\pi$
$882$	0.266939	−	0.996229i	0.00898829	−	0.0335448i
$883$			29.4396i			0.990720i	0.868688	+	0.495360i	$0.164964\pi$
$883$			29.4396i			0.990720i	−0.868688	+	0.495360i	$0.835036\pi$
$884$	47.1586	+	26.4529i	1.58612	+	0.889708i
$885$	4.93955			0.166041
$886$	2.00390	+	0.536944i	0.0673224	+	0.0180390i
$887$	−38.9394	+	22.4817i	−1.30746	+	0.754861i	−0.981671	−	0.190582i	$-0.938962\pi$
$887$	−38.9394	+	22.4817i	−1.30746	+	0.754861i	−0.325787	+	0.945443i	$0.605629\pi$
$888$	3.06762	−	5.31327i	0.102942	−	0.178302i
$889$	5.10133	+	5.10133i	0.171093	+	0.171093i
$890$	−0.0711779	−	0.265639i	−0.00238589	−	0.00890425i
$891$	−1.62238	−	2.89273i	−0.0543517	−	0.0969101i
$892$	26.5997	−	26.5997i	0.890624	−	0.890624i
$893$	49.6773	+	28.6812i	1.66239	+	0.959781i
$894$	−2.11481	+	1.22099i	−0.0707299	+	0.0408359i
$895$	−11.2097	−	3.00363i	−0.374699	−	0.100400i
$896$		−	11.1748i		−	0.373323i
$897$	0.0615069	+	4.96047i	0.00205365	+	0.165625i
$898$			2.84419i			0.0949120i
$899$	−7.71805	−	2.06804i	−0.257411	−	0.0689731i
$900$	−2.79624	−	4.84323i	−0.0932081	−	0.161441i
$901$	26.7676	−	46.3629i	0.891759	−	1.54457i
$902$	5.62471	+	3.34160i	0.187282	+	0.111263i
$903$	−18.2969	+	4.90264i	−0.608882	+	0.163149i
$904$	−4.77449	+	1.27932i	−0.158797	+	0.0425496i
$905$	−18.1054	+	18.1054i	−0.601843	+	0.601843i
$906$	0.145008	−	0.251162i	0.00481757	−	0.00834428i
$907$	−11.8268	+	6.82821i	−0.392703	+	0.226727i	−0.683330	−	0.730109i	$-0.739469\pi$
$907$	−11.8268	+	6.82821i	−0.392703	+	0.226727i	0.290628	+	0.956836i	$0.406136\pi$
$908$	−12.5235	+	46.7383i	−0.415606	+	1.55106i
$909$	−3.15975			−0.104802
$910$	−0.485553	+	1.90635i	−0.0160959	+	0.0631948i
$911$	−48.2305			−1.59795			−0.798975	−	0.601365i	$-0.794624\pi$
$911$	−48.2305			−1.59795			−0.798975	+	0.601365i	$0.794624\pi$
$912$	17.8555	+	4.78438i	0.591256	+	0.158427i
$913$	25.1422	−	24.5230i	0.832086	−	0.811594i
$914$	−3.68590	−	2.12805i	−0.121919	−	0.0703898i
$915$	−9.60751	+	9.60751i	−0.317615	+	0.317615i
$916$	−15.1558	+	4.06098i	−0.500762	+	0.134179i
$917$	6.01817	+	22.4601i	0.198738	+	0.741699i
$918$	−1.27072	+	1.27072i	−0.0419400	+	0.0419400i
$919$	12.4888	+	7.21043i	0.411968	+	0.237850i	0.691635	−	0.722247i	$-0.256891\pi$
$919$	12.4888	+	7.21043i	0.411968	+	0.237850i	−0.279667	+	0.960097i	$0.590224\pi$
$920$	−0.922677	−	1.59812i	−0.0304198	−	0.0526886i
$921$	−7.59801	+	28.3562i	−0.250363	+	0.934367i
$922$			3.14182i			0.103470i
$923$	−11.9489	−	11.6562i	−0.393302	−	0.383668i
$924$	−2.55582	−	10.0374i	−0.0840805	−	0.330205i
$925$	4.96156	−	18.5168i	0.163135	−	0.608829i
$926$	5.87629	−	3.39268i	0.193107	−	0.111490i
$927$	11.0884	+	6.40187i	0.364190	+	0.210265i
$928$	4.98121	+	4.98121i	0.163516	+	0.163516i
$929$	−7.27059	+	1.94815i	−0.238540	+	0.0639167i	−0.376109	−	0.926576i	$-0.622738\pi$
$929$	−7.27059	+	1.94815i	−0.238540	+	0.0639167i	0.137568	+	0.990492i	$0.456071\pi$
$930$	−1.00446	+	0.269143i	−0.0329374	+	0.00882554i
$931$	15.7263	+	15.7263i	0.515407	+	0.515407i
$932$	15.3487	+	8.86159i	0.502764	+	0.290271i
$933$	−11.4564	+	6.61435i	−0.375066	+	0.216544i
$934$	1.95756	−	7.30571i	0.0640532	−	0.239050i
$935$	−36.1186	+	9.19692i	−1.18120	+	0.300771i
$936$	−2.37425	−	2.31609i	−0.0776047	−	0.0757038i
$937$		−	5.96536i		−	0.194880i	−0.995241	−	0.0974399i	$-0.968935\pi$
$937$		−	5.96536i		−	0.194880i	0.995241	−	0.0974399i	$-0.0310654\pi$
$938$	−0.502768	+	1.87636i	−0.0164160	+	0.0612652i
$939$	12.2606	+	21.2360i	0.400109	+	0.693009i
$940$	−28.0289	−	16.1825i	−0.914203	−	0.527816i
$941$	−19.5901	+	19.5901i	−0.638619	+	0.638619i	−0.950215	−	0.311596i	$-0.899136\pi$
$941$	−19.5901	+	19.5901i	−0.638619	+	0.638619i	0.311596	+	0.950215i	$0.399136\pi$
$942$	1.41827	+	5.29305i	0.0462097	+	0.172457i
$943$	−11.2445	+	3.01295i	−0.366170	+	0.0981150i
$944$	−8.80844	+	8.80844i	−0.286690	+	0.286690i
$945$	2.02664	+	1.17008i	0.0659266	+	0.0380627i
$946$	−6.53272	+	6.37183i	−0.212397	+	0.207166i
$947$	18.0810	+	4.84478i	0.587552	+	0.157434i	0.540334	−	0.841450i	$-0.318298\pi$
$947$	18.0810	+	4.84478i	0.587552	+	0.157434i	0.0472180	+	0.998885i	$0.484964\pi$
$948$	1.82647			0.0593208
$949$	−7.55207	+	29.6504i	−0.245151	+	0.962494i
$950$	−3.36926			−0.109313
$951$	−2.24499	+	8.37841i	−0.0727987	+	0.271689i
$952$	−9.85631	+	5.69055i	−0.319445	+	0.184432i
$953$	−18.6200	+	32.2508i	−0.603162	+	1.04471i	0.389177	+	0.921163i	$0.372759\pi$
$953$	−18.6200	+	32.2508i	−0.603162	+	1.04471i	−0.992339	+	0.123544i	$0.960574\pi$
$954$	−1.14506	+	1.14506i	−0.0370726	+	0.0370726i
$955$	−6.77461	+	1.81525i	−0.219221	+	0.0587402i
$956$	10.1036	−	2.70724i	0.326772	−	0.0875584i
$957$	7.44750	+	4.42451i	0.240743	+	0.143024i
$958$	2.60249	−	4.50764i	0.0840825	−	0.145635i
$959$	5.08953	+	8.81533i	0.164350	+	0.284662i
$960$	−9.47036	−	2.53758i	−0.305655	−	0.0818999i
$961$		−	21.6412i		−	0.698105i
$962$	−0.0695109	−	5.60598i	−0.00224112	−	0.180744i
$963$			16.6599i			0.536857i
$964$	7.48214	+	2.00483i	0.240984	+	0.0645713i
$965$	−14.6627	+	8.46551i	−0.472009	+	0.272515i
$966$	−0.445913	−	0.257448i	−0.0143470	−	0.00828325i
$967$	11.2353	−	11.2353i	0.361304	−	0.361304i	−0.502989	−	0.864293i	$-0.667766\pi$
$967$	11.2353	−	11.2353i	0.361304	−	0.361304i	0.864293	+	0.502989i	$0.167766\pi$
$968$	−6.97471	−	7.33148i	−0.224176	−	0.235643i
$969$	−10.0297	−	37.4312i	−0.322199	−	1.20246i
$970$	2.02076	+	2.02076i	0.0648827	+	0.0648827i
$971$	27.6532	−	47.8967i	0.887432	−	1.53708i	0.0445318	−	0.999008i	$-0.485820\pi$
$971$	27.6532	−	47.8967i	0.887432	−	1.53708i	0.842900	−	0.538070i	$-0.180846\pi$
$972$	−1.68498	+	0.972821i	−0.0540456	+	0.0312032i
$973$	28.7252	+	7.69689i	0.920887	+	0.246751i
$974$	−1.77300			−0.0568105
$975$	−9.03876	−	5.07016i	−0.289472	−	0.162375i
$976$		−	34.2651i		−	1.09680i
$977$	−12.1993	+	45.5285i	−0.390291	+	1.45659i	0.439364	+	0.898309i	$0.355204\pi$
$977$	−12.1993	+	45.5285i	−0.390291	+	1.45659i	−0.829655	+	0.558277i	$0.811463\pi$
$978$	−3.76441	+	2.17338i	−0.120372	+	0.0694971i
$979$	2.58300	+	0.726743i	0.0825530	+	0.0232268i
$980$	−8.87307	−	8.87307i	−0.283440	−	0.283440i
$981$	−3.21797	−	12.0096i	−0.102742	−	0.383438i
$982$	1.39216	+	5.19562i	0.0444257	+	0.165799i
$983$	32.0352	−	32.0352i	1.02176	−	1.02176i	0.0220066	−	0.999758i	$-0.492995\pi$
$983$	32.0352	−	32.0352i	1.02176	−	1.02176i	0.999758	−	0.0220066i	$-0.00700548\pi$
$984$	3.89163	−	6.74050i	0.124061	−	0.214879i
$985$	14.3548	+	24.8632i	0.457381	+	0.792208i
$986$	1.21483	−	4.53381i	0.0386881	−	0.144386i
$987$	−18.3135			−0.582924
$988$	33.9514	−	9.54997i	1.08014	−	0.303825i
$989$		−	16.2374i		−	0.516319i
$990$	1.12730	+	0.0140543i	0.0358280	+	0.000446674i
$991$	−5.77566	−	10.0037i	−0.183470	−	0.317779i	0.759590	−	0.650402i	$-0.225400\pi$
$991$	−5.77566	−	10.0037i	−0.183470	−	0.317779i	−0.943060	+	0.332623i	$0.892066\pi$
$992$	4.12548	−	7.14553i	0.130984	−	0.226871i
$993$	8.58951	+	8.58951i	0.272580	+	0.272580i
$994$	1.67352	−	0.448418i	0.0530808	−	0.0142230i
$995$	−1.59766	−	5.96255i	−0.0506492	−	0.189026i
$996$	−14.5688	−	14.5688i	−0.461629	−	0.461629i
$997$	−2.40739	−	1.38990i	−0.0762427	−	0.0440187i	0.461394	−	0.887195i	$-0.347349\pi$
$997$	−2.40739	−	1.38990i	−0.0762427	−	0.0440187i	−0.537637	+	0.843177i	$0.680683\pi$
$998$	0.984805	+	1.70573i	0.0311735	+	0.0539940i
$999$	−6.44205	−	1.72614i	−0.203817	−	0.0546127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.b.76.8	yes	56
11.10	odd	2	inner	429.2.bd.b.76.7	✓	56
13.6	odd	12	inner	429.2.bd.b.175.7	yes	56
143.32	even	12	inner	429.2.bd.b.175.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.b.76.7	✓	56	11.10	odd	2	inner
429.2.bd.b.76.8	yes	56	1.1	even	1	trivial
429.2.bd.b.175.7	yes	56	13.6	odd	12	inner
429.2.bd.b.175.8	yes	56	143.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.225205 + 0.0603434i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.68498 - 0.972821i) q^{4} +(-1.03093 - 1.03093i) q^{5} +(0.0603434 + 0.225205i) q^{6} +(1.55041 - 0.415430i) q^{7} +(-0.650483 - 0.650483i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.225205 + 0.0603434i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.68498 - 0.972821i) q^{4} +(-1.03093 - 1.03093i) q^{5} +(0.0603434 + 0.225205i) q^{6} +(1.55041 - 0.415430i) q^{7} +(-0.650483 - 0.650483i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.169960 - 0.294380i) q^{10} +(3.31637 + 0.0413457i) q^{11} -1.94564i q^{12} +(-1.84135 - 3.09991i) q^{13} +0.374227 q^{14} +(0.377347 - 1.40828i) q^{15} +(1.83840 + 3.18421i) q^{16} +(3.85391 - 6.67516i) q^{17} +(-0.164861 + 0.164861i) q^{18} +(-1.30123 - 4.85627i) q^{19} +(0.734181 + 2.74000i) q^{20} +(1.13498 + 1.13498i) q^{21} +(0.744366 + 0.209432i) q^{22} +(-1.19156 + 0.687946i) q^{23} +(0.238093 - 0.888576i) q^{24} -2.87437i q^{25} +(-0.227622 - 0.809227i) q^{26} -1.00000 q^{27} +(-3.01653 - 0.808278i) q^{28} +(2.26196 - 1.30594i) q^{29} +(0.169960 - 0.294380i) q^{30} +(-2.16319 - 2.16319i) q^{31} +(0.698058 + 2.60519i) q^{32} +(1.62238 + 2.89273i) q^{33} +(1.27072 - 1.27072i) q^{34} +(-2.02664 - 1.17008i) q^{35} +(1.68498 - 0.972821i) q^{36} +(6.44205 + 1.72614i) q^{37} -1.17217i q^{38} +(1.76392 - 3.14461i) q^{39} +1.34121i q^{40} +(8.17249 + 2.18981i) q^{41} +(0.187113 + 0.324090i) q^{42} +(-5.90068 + 10.2203i) q^{43} +(-5.54777 - 3.29590i) q^{44} +(1.40828 - 0.377347i) q^{45} +(-0.309857 + 0.0830260i) q^{46} +(-8.06778 + 8.06778i) q^{47} +(-1.83840 + 3.18421i) q^{48} +(-3.83100 + 2.21183i) q^{49} +(0.173449 - 0.647320i) q^{50} +7.70782 q^{51} +(0.0869765 + 7.01457i) q^{52} +6.94558 q^{53} +(-0.225205 - 0.0603434i) q^{54} +(-3.37632 - 3.46157i) q^{55} +(-1.27874 - 0.738282i) q^{56} +(3.55503 - 3.55503i) q^{57} +(0.588209 - 0.157610i) q^{58} +(0.876879 + 3.27256i) q^{59} +(-2.00582 + 2.00582i) q^{60} +(-8.07072 - 4.65963i) q^{61} +(-0.356626 - 0.617694i) q^{62} +(-0.415430 + 1.55041i) q^{63} -6.72479i q^{64} +(-1.29748 + 5.09409i) q^{65} +(0.190810 + 0.749356i) q^{66} +(-1.34349 + 5.01396i) q^{67} +(-12.9875 + 7.49832i) q^{68} +(-1.19156 - 0.687946i) q^{69} +(-0.385802 - 0.385802i) q^{70} +(4.47194 - 1.19825i) q^{71} +(0.888576 - 0.238093i) q^{72} +(-6.00059 - 6.00059i) q^{73} +(1.34662 + 0.777470i) q^{74} +(2.48927 - 1.43718i) q^{75} +(-2.53173 + 9.44855i) q^{76} +(5.15889 - 1.31362i) q^{77} +(0.587000 - 0.601740i) q^{78} +0.938747i q^{79} +(1.38743 - 5.17796i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.70834 + 0.986311i) q^{82} +(7.48790 - 7.48790i) q^{83} +(-0.808278 - 3.01653i) q^{84} +(-10.8547 + 2.90852i) q^{85} +(-1.94559 + 1.94559i) q^{86} +(2.26196 + 1.30594i) q^{87} +(-2.13035 - 2.18414i) q^{88} +(0.781475 + 0.209396i) q^{89} +0.339921 q^{90} +(-4.14264 - 4.04116i) q^{91} +2.67699 q^{92} +(0.791781 - 2.95497i) q^{93} +(-2.30374 + 1.33006i) q^{94} +(-3.66499 + 6.34795i) q^{95} +(-1.90713 + 1.90713i) q^{96} +(-8.12074 + 2.17595i) q^{97} +(-0.996229 + 0.266939i) q^{98} +(-1.69399 + 2.85139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

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