LMFDB - Embedded newform 825.2.o.d.511.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(421,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 8]))

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

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

chi := DirichletCharacter("825.421");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.o (of order $5$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.12
Character	$\chi$	$=$	825.511
Dual form			825.2.o.d.691.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.786609 - 0.571505i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.325898 - 1.00301i) q^{4} +(-0.395116 - 2.20088i) q^{5} -0.972302 q^{6} +(-2.89935 + 2.10650i) q^{7} +(-0.917787 + 2.82466i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.947013 + 1.95704i) q^{10} +(2.59114 + 2.07027i) q^{11} +(-0.853212 - 0.619895i) q^{12} +(-0.838826 + 2.58164i) q^{13} +3.48453 q^{14} +(-1.61330 - 1.54831i) q^{15} +(0.629821 - 0.457592i) q^{16} -6.46236 q^{17} +(-0.786609 + 0.571505i) q^{18} +(-0.287574 + 0.885062i) q^{19} +(-2.07874 + 1.11357i) q^{20} +(-1.10745 + 3.40839i) q^{21} +(-0.855044 - 3.10934i) q^{22} +(-0.526966 + 0.382863i) q^{23} +(0.917787 + 2.82466i) q^{24} +(-4.68777 + 1.73921i) q^{25} +(2.13525 - 1.55135i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.05774 + 2.22158i) q^{28} +(0.0792663 + 0.243957i) q^{29} +(0.384172 + 2.13992i) q^{30} +(0.417537 - 0.303358i) q^{31} +5.18310 q^{32} +(3.31315 + 0.151849i) q^{33} +(5.08335 + 3.69327i) q^{34} +(5.78175 + 5.54882i) q^{35} -1.05463 q^{36} -5.82569 q^{37} +(0.732026 - 0.531848i) q^{38} +(0.838826 + 2.58164i) q^{39} +(6.57937 + 0.903873i) q^{40} +(3.77607 + 11.6215i) q^{41} +(2.81905 - 2.04816i) q^{42} -7.15991 q^{43} +(1.23205 - 3.27364i) q^{44} +(-2.21526 - 0.304332i) q^{45} +0.633324 q^{46} +(3.00606 - 2.18403i) q^{47} +(0.240570 - 0.740400i) q^{48} +(1.80577 - 5.55759i) q^{49} +(4.68141 + 1.31100i) q^{50} +(-5.22816 + 3.79848i) q^{51} +2.86278 q^{52} +7.99496 q^{53} +(-0.300458 + 0.924714i) q^{54} +(3.53261 - 6.52078i) q^{55} +(-3.28916 - 10.1230i) q^{56} +(0.287574 + 0.885062i) q^{57} +(0.0770708 - 0.237199i) q^{58} +5.74994 q^{59} +(-1.02720 + 2.12275i) q^{60} +(-4.72463 - 14.5409i) q^{61} -0.501809 q^{62} +(1.10745 + 3.40839i) q^{63} +(-5.33672 - 3.87735i) q^{64} +(6.01332 + 0.826109i) q^{65} +(-2.51937 - 2.01293i) q^{66} +(-0.133617 - 0.411231i) q^{67} +(2.10607 + 6.48182i) q^{68} +(-0.201283 + 0.619486i) q^{69} +(-1.37680 - 7.66905i) q^{70} +(1.76022 + 1.27887i) q^{71} +(2.40280 + 1.74574i) q^{72} +(-2.53640 + 7.80622i) q^{73} +(4.58254 + 3.32941i) q^{74} +(-2.77020 + 4.16245i) q^{75} +0.981447 q^{76} +(-11.8736 - 0.544197i) q^{77} +(0.815592 - 2.51013i) q^{78} -15.0300 q^{79} +(-1.25596 - 1.20536i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.67148 - 11.2996i) q^{82} +3.49315 q^{83} +3.77957 q^{84} +(2.55338 + 14.2229i) q^{85} +(5.63205 + 4.09193i) q^{86} +(0.207522 + 0.150773i) q^{87} +(-8.22591 + 5.41901i) q^{88} +(-13.0138 + 9.45511i) q^{89} +(1.56862 + 1.50542i) q^{90} +(-3.00618 - 9.25207i) q^{91} +(0.555753 + 0.403778i) q^{92} +(0.159485 - 0.490844i) q^{93} -3.61277 q^{94} +(2.06154 + 0.283214i) q^{95} +(4.19322 - 3.04655i) q^{96} -3.38663 q^{97} +(-4.59663 + 3.33965i) q^{98} +(2.76965 - 1.82457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - q^{2} + 29 q^{3} - 35 q^{4} - 3 q^{5} + 6 q^{6} - 2 q^{7} + q^{8} - 29 q^{9} + 2 q^{10} - 13 q^{11} + 30 q^{12} - 12 q^{14} + 3 q^{15} - 41 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} + 7 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 116 * q - q^2 + 29 * q^3 - 35 * q^4 - 3 * q^5 + 6 * q^6 - 2 * q^7 + q^8 - 29 * q^9 + 2 * q^10 - 13 * q^11 + 30 * q^12 - 12 * q^14 + 3 * q^15 - 41 * q^16 - 14 * q^17 - q^18 - 21 * q^19 + 7 * q^20 + 2 * q^21 + 16 * q^22 + 14 * q^23 - q^24 + 17 * q^25 - 16 * q^26 + 29 * q^27 - 7 * q^28 - 20 * q^29 + 8 * q^30 + 12 * q^31 - 94 * q^32 - 7 * q^33 + 20 * q^34 - 46 * q^35 + 130 * q^36 + 40 * q^37 + 29 * q^38 - 18 * q^40 - 16 * q^41 - 8 * q^42 - 46 * q^43 + 15 * q^44 + 2 * q^45 + 60 * q^46 + 5 * q^47 + 26 * q^48 - 5 * q^49 - 45 * q^50 - 11 * q^51 - 96 * q^52 + 44 * q^53 - 4 * q^54 - 6 * q^55 + 28 * q^56 + 21 * q^57 - 19 * q^58 + 26 * q^59 - 7 * q^60 + 5 * q^61 - 128 * q^62 - 2 * q^63 - 17 * q^64 + 10 * q^65 + 14 * q^66 - 35 * q^67 + 60 * q^68 + 6 * q^69 - 26 * q^70 - 10 * q^71 + 11 * q^72 - 40 * q^73 - 12 * q^74 - 27 * q^75 + 126 * q^76 + q^77 - 19 * q^78 + 126 * q^79 - 114 * q^80 - 29 * q^81 - 21 * q^82 - 78 * q^83 + 12 * q^84 - 6 * q^85 - 54 * q^86 - 5 * q^87 - 41 * q^88 + 13 * q^89 + 2 * q^90 - 25 * q^91 - 28 * q^92 + 43 * q^93 - 66 * q^94 + 49 * q^95 - 21 * q^96 - 80 * q^97 - 34 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.786609	−	0.571505i	−0.556217	−	0.404115i	0.273856	−	0.961771i	$-0.411701\pi$
$2$	−0.786609	−	0.571505i	−0.556217	−	0.404115i	−0.830072	+	0.557656i	$0.811701\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.325898	−	1.00301i	−0.162949	−	0.501506i
$5$	−0.395116	−	2.20088i	−0.176701	−	0.984265i
$5$	−0.395116	−	2.20088i	−0.176701	−	0.984265i
$6$	−0.972302			−0.396941
$7$	−2.89935	+	2.10650i	−1.09585	+	0.796183i	−0.980378	−	0.197127i	$-0.936839\pi$
$7$	−2.89935	+	2.10650i	−1.09585	+	0.796183i	−0.115474	+	0.993310i	$0.536839\pi$
$8$	−0.917787	+	2.82466i	−0.324487	+	0.998668i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.947013	+	1.95704i	−0.299472	+	0.618872i
$11$	2.59114	+	2.07027i	0.781257	+	0.624209i
$11$	2.59114	+	2.07027i	0.781257	+	0.624209i
$12$	−0.853212	−	0.619895i	−0.246301	−	0.178948i
$13$	−0.838826	+	2.58164i	−0.232648	+	0.716018i	0.764776	+	0.644296i	$0.222849\pi$
$13$	−0.838826	+	2.58164i	−0.232648	+	0.716018i	−0.997425	+	0.0717221i	$0.977151\pi$
$14$	3.48453			0.931281
$15$	−1.61330	−	1.54831i	−0.416553	−	0.399771i
$16$	0.629821	−	0.457592i	0.157455	−	0.114398i
$17$	−6.46236			−1.56735			−0.783676	−	0.621170i	$-0.786658\pi$
$17$	−6.46236			−1.56735			−0.783676	+	0.621170i	$0.786658\pi$
$18$	−0.786609	+	0.571505i	−0.185406	+	0.134705i
$19$	−0.287574	+	0.885062i	−0.0659740	+	0.203047i	−0.978609	−	0.205728i	$-0.934044\pi$
$19$	−0.287574	+	0.885062i	−0.0659740	+	0.203047i	0.912635	+	0.408775i	$0.134044\pi$
$20$	−2.07874	+	1.11357i	−0.464821	+	0.249002i
$21$	−1.10745	+	3.40839i	−0.241666	+	0.743772i
$22$	−0.855044	−	3.10934i	−0.182296	−	0.662913i
$23$	−0.526966	+	0.382863i	−0.109880	+	0.0798325i	−0.641368	−	0.767233i	$-0.721633\pi$
$23$	−0.526966	+	0.382863i	−0.109880	+	0.0798325i	0.531488	+	0.847066i	$0.321633\pi$
$24$	0.917787	+	2.82466i	0.187343	+	0.576581i
$25$	−4.68777	+	1.73921i	−0.937553	+	0.347842i
$26$	2.13525	−	1.55135i	0.418756	−	0.304244i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	3.05774	+	2.22158i	0.577858	+	0.419839i
$29$	0.0792663	+	0.243957i	0.0147194	+	0.0453016i	0.958146	−	0.286279i	$-0.0924183\pi$
$29$	0.0792663	+	0.243957i	0.0147194	+	0.0453016i	−0.943427	+	0.331580i	$0.892418\pi$
$30$	0.384172	+	2.13992i	0.0701400	+	0.390695i
$31$	0.417537	−	0.303358i	0.0749919	−	0.0544848i	−0.549658	−	0.835390i	$-0.685242\pi$
$31$	0.417537	−	0.303358i	0.0749919	−	0.0544848i	0.624650	+	0.780905i	$0.285242\pi$
$32$	5.18310			0.916252
$33$	3.31315	+	0.151849i	0.576745	+	0.0264336i
$34$	5.08335	+	3.69327i	0.871787	+	0.633390i
$35$	5.78175	+	5.54882i	0.977293	+	0.937922i
$36$	−1.05463			−0.175771
$37$	−5.82569			−0.957738			−0.478869	−	0.877886i	$-0.658953\pi$
$37$	−5.82569			−0.957738			−0.478869	+	0.877886i	$0.658953\pi$
$38$	0.732026	−	0.531848i	0.118750	−	0.0862771i
$39$	0.838826	+	2.58164i	0.134320	+	0.413393i
$40$	6.57937	+	0.903873i	1.04029	+	0.142915i
$41$	3.77607	+	11.6215i	0.589723	+	1.81498i	0.579415	+	0.815033i	$0.303281\pi$
$41$	3.77607	+	11.6215i	0.589723	+	1.81498i	0.0103074	+	0.999947i	$0.496719\pi$
$42$	2.81905	−	2.04816i	0.434988	−	0.316038i
$43$	−7.15991			−1.09188			−0.545938	−	0.837825i	$-0.683827\pi$
$43$	−7.15991			−1.09188			−0.545938	+	0.837825i	$0.683827\pi$
$44$	1.23205	−	3.27364i	0.185739	−	0.493519i
$45$	−2.21526	−	0.304332i	−0.330232	−	0.0453672i
$46$	0.633324			0.0933786
$47$	3.00606	−	2.18403i	0.438478	−	0.318573i	−0.346552	−	0.938031i	$-0.612647\pi$
$47$	3.00606	−	2.18403i	0.438478	−	0.318573i	0.785030	+	0.619458i	$0.212647\pi$
$48$	0.240570	−	0.740400i	0.0347233	−	0.106867i
$49$	1.80577	−	5.55759i	0.257967	−	0.793942i
$50$	4.68141	+	1.31100i	0.662051	+	0.185404i
$51$	−5.22816	+	3.79848i	−0.732088	+	0.531893i
$52$	2.86278			0.396997
$53$	7.99496			1.09819			0.549096	−	0.835759i	$-0.314972\pi$
$53$	7.99496			1.09819			0.549096	+	0.835759i	$0.314972\pi$
$54$	−0.300458	+	0.924714i	−0.0408871	+	0.125838i
$55$	3.53261	−	6.52078i	0.476338	−	0.879262i
$56$	−3.28916	−	10.1230i	−0.439533	−	1.35274i
$57$	0.287574	+	0.885062i	0.0380901	+	0.117229i
$58$	0.0770708	−	0.237199i	0.0101199	−	0.0311458i
$59$	5.74994			0.748578			0.374289	−	0.927312i	$-0.377887\pi$
$59$	5.74994			0.748578			0.374289	+	0.927312i	$0.377887\pi$
$60$	−1.02720	+	2.12275i	−0.132611	+	0.274046i
$61$	−4.72463	−	14.5409i	−0.604927	−	1.86177i	−0.497292	−	0.867583i	$-0.665672\pi$
$61$	−4.72463	−	14.5409i	−0.604927	−	1.86177i	−0.107635	−	0.994190i	$-0.534328\pi$
$62$	−0.501809			−0.0637298
$63$	1.10745	+	3.40839i	0.139526	+	0.429417i
$64$	−5.33672	−	3.87735i	−0.667090	−	0.484669i
$65$	6.01332	+	0.826109i	0.745860	+	0.102466i
$66$	−2.51937	−	2.01293i	−0.310113	−	0.247774i
$67$	−0.133617	−	0.411231i	−0.0163239	−	0.0502399i	0.942563	−	0.334029i	$-0.108408\pi$
$67$	−0.133617	−	0.411231i	−0.0163239	−	0.0502399i	−0.958887	+	0.283789i	$0.908408\pi$
$68$	2.10607	+	6.48182i	0.255398	+	0.786036i
$69$	−0.201283	+	0.619486i	−0.0242316	+	0.0745773i
$70$	−1.37680	−	7.66905i	−0.164559	−	0.916627i
$71$	1.76022	+	1.27887i	0.208899	+	0.151774i	0.687316	−	0.726359i	$-0.258789\pi$
$71$	1.76022	+	1.27887i	0.208899	+	0.151774i	−0.478416	+	0.878133i	$0.658789\pi$
$72$	2.40280	+	1.74574i	0.283172	+	0.205737i
$73$	−2.53640	+	7.80622i	−0.296863	+	0.913649i	0.685727	+	0.727859i	$0.259484\pi$
$73$	−2.53640	+	7.80622i	−0.296863	+	0.913649i	−0.982589	+	0.185790i	$0.940516\pi$
$74$	4.58254	+	3.32941i	0.532710	+	0.387036i
$75$	−2.77020	+	4.16245i	−0.319875	+	0.480638i
$76$	0.981447			0.112580
$77$	−11.8736	−	0.544197i	−1.35313	−	0.0620170i
$78$	0.815592	−	2.51013i	0.0923476	−	0.284217i
$79$	−15.0300			−1.69101			−0.845504	−	0.533970i	$-0.820700\pi$
$79$	−15.0300			−1.69101			−0.845504	+	0.533970i	$0.820700\pi$
$80$	−1.25596	−	1.20536i	−0.140420	−	0.134763i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.67148	−	11.2996i	0.405447	−	1.24784i
$83$	3.49315			0.383423			0.191712	−	0.981451i	$-0.438596\pi$
$83$	3.49315			0.383423			0.191712	+	0.981451i	$0.438596\pi$
$84$	3.77957			0.412385
$85$	2.55338	+	14.2229i	0.276953	+	1.54269i
$86$	5.63205	+	4.09193i	0.607320	+	0.441244i
$87$	0.207522	+	0.150773i	0.0222487	+	0.0161646i
$88$	−8.22591	+	5.41901i	−0.876885	+	0.577669i
$89$	−13.0138	+	9.45511i	−1.37947	+	1.00224i	−0.382535	+	0.923941i	$0.624949\pi$
$89$	−13.0138	+	9.45511i	−1.37947	+	1.00224i	−0.996930	+	0.0782991i	$0.975051\pi$
$90$	1.56862	+	1.50542i	0.165347	+	0.158686i
$91$	−3.00618	−	9.25207i	−0.315133	−	0.969881i
$92$	0.555753	+	0.403778i	0.0579413	+	0.0420968i
$93$	0.159485	−	0.490844i	0.0165378	−	0.0508982i
$94$	−3.61277			−0.372629
$95$	2.06154	+	0.283214i	0.211510	+	0.0290572i
$96$	4.19322	−	3.04655i	0.427969	−	0.310937i
$97$	−3.38663			−0.343860			−0.171930	−	0.985109i	$-0.555000\pi$
$97$	−3.38663			−0.343860			−0.171930	+	0.985109i	$0.555000\pi$
$98$	−4.59663	+	3.33965i	−0.464329	+	0.337355i
$99$	2.76965	−	1.82457i	0.278360	−	0.183376i
$100$	3.27218	+	4.13508i	0.327218	+	0.413508i
$101$	2.65112	+	8.15931i	0.263796	+	0.811881i	0.991968	+	0.126487i	$0.0403702\pi$
$101$	2.65112	+	8.15931i	0.263796	+	0.811881i	−0.728172	+	0.685394i	$0.759630\pi$
$102$	6.28336			0.622146
$103$	1.20387	+	3.70512i	0.118621	+	0.365077i	0.992685	−	0.120733i	$-0.0385246\pi$
$103$	1.20387	+	3.70512i	0.118621	+	0.365077i	−0.874064	+	0.485810i	$0.838525\pi$
$104$	−6.52239	−	4.73879i	−0.639573	−	0.464677i
$105$	7.93905	+	1.09066i	0.774772	+	0.106438i
$106$	−6.28891	−	4.56916i	−0.610833	−	0.443796i
$107$	−9.82131	−	7.13560i	−0.949462	−	0.689825i	0.00121733	−	0.999999i	$-0.499613\pi$
$107$	−9.82131	−	7.13560i	−0.949462	−	0.689825i	−0.950680	+	0.310175i	$0.899613\pi$
$108$	−0.853212	+	0.619895i	−0.0821004	+	0.0596494i
$109$	5.27702	+	3.83398i	0.505447	+	0.367228i	0.811094	−	0.584916i	$-0.198873\pi$
$109$	5.27702	+	3.83398i	0.505447	+	0.367228i	−0.305647	+	0.952145i	$0.598873\pi$
$110$	−6.50545	+	3.11040i	−0.620270	+	0.296565i
$111$	−4.71308	+	3.42426i	−0.447346	+	0.325016i
$112$	−0.862155	+	2.65344i	−0.0814660	+	0.250727i
$113$	1.39620	+	4.29705i	0.131343	+	0.404233i	0.995003	−	0.0998418i	$-0.0318337\pi$
$113$	1.39620	+	4.29705i	0.131343	+	0.404233i	−0.863660	+	0.504075i	$0.831834\pi$
$114$	0.279609	−	0.860548i	0.0261878	−	0.0805977i
$115$	1.05085	+	1.00851i	0.0979922	+	0.0940445i
$116$	0.218858	−	0.159010i	0.0203205	−	0.0147637i
$117$	2.19607	+	1.59554i	0.203027	+	0.147508i
$118$	−4.52295	−	3.28612i	−0.416372	−	0.302512i
$119$	18.7366	−	13.6130i	1.71759	−	1.24790i
$120$	5.85411	−	3.13601i	0.534405	−	0.286277i
$121$	2.42798	+	10.7287i	0.220726	+	0.975336i
$122$	−4.59377	+	14.1382i	−0.415900	+	1.28001i
$123$	9.88587	+	7.18251i	0.891379	+	0.647625i
$124$	−0.440346	−	0.319930i	−0.0395443	−	0.0287306i
$125$	5.68001	+	9.63003i	0.508035	+	0.861336i
$126$	1.07678	−	3.31399i	0.0959272	−	0.295234i
$127$	0.424479	+	1.30641i	0.0376664	+	0.115925i	0.968122	−	0.250480i	$-0.0805884\pi$
$127$	0.424479	+	1.30641i	0.0376664	+	0.115925i	−0.930455	+	0.366405i	$0.880588\pi$
$128$	−1.22135	−	3.75893i	−0.107953	−	0.332245i
$129$	−5.79249	+	4.20849i	−0.510000	+	0.370537i
$130$	−4.25801	−	4.08647i	−0.373452	−	0.358407i
$131$	−6.93483	−	21.3432i	−0.605899	−	1.86476i	−0.490491	−	0.871446i	$-0.663183\pi$
$131$	−6.93483	−	21.3432i	−0.605899	−	1.86476i	−0.115408	−	0.993318i	$-0.536817\pi$
$132$	−0.927442	−	3.37261i	−0.0807234	−	0.293548i
$133$	−1.03061	−	3.17188i	−0.0893650	−	0.275037i
$134$	−0.129916	+	0.399841i	−0.0112230	+	0.0345410i
$135$	−1.97107	+	1.05589i	−0.169642	+	0.0908764i
$136$	5.93107	−	18.2540i	0.508585	−	1.56526i
$137$	−14.4199	+	10.4767i	−1.23198	+	0.895083i	−0.997037	−	0.0769270i	$-0.975489\pi$
$137$	−14.4199	+	10.4767i	−1.23198	+	0.895083i	−0.234939	+	0.972010i	$0.575489\pi$
$138$	0.512370	−	0.372259i	0.0436158	−	0.0316888i
$139$	−2.40473	+	7.40099i	−0.203966	+	0.627744i	0.795788	+	0.605576i	$0.207057\pi$
$139$	−2.40473	+	7.40099i	−0.203966	+	0.627744i	−0.999754	+	0.0221685i	$0.992943\pi$
$140$	3.68127	−	7.60751i	0.311124	−	0.642952i
$141$	1.14821	−	3.53383i	0.0966968	−	0.297602i
$142$	−0.653721	−	2.01195i	−0.0548590	−	0.168839i
$143$	−7.51820	+	4.95279i	−0.628703	+	0.414173i
$144$	−0.240570	−	0.740400i	−0.0200475	−	0.0617000i
$145$	0.505600	−	0.270847i	0.0419878	−	0.0224926i
$146$	6.45645	−	4.69088i	0.534339	−	0.388220i
$147$	−1.80577	−	5.55759i	−0.148938	−	0.458383i
$148$	1.89858	+	5.84323i	0.156062	+	0.480311i
$149$	4.80944	−	14.8019i	0.394005	−	1.21262i	−0.535730	−	0.844390i	$-0.679963\pi$
$149$	4.80944	−	14.8019i	0.394005	−	1.21262i	0.929734	−	0.368232i	$-0.120037\pi$
$150$	4.55793	−	1.69104i	0.372153	−	0.138073i
$151$	−11.2598	−	8.18073i	−0.916310	−	0.665738i	0.0262926	−	0.999654i	$-0.491630\pi$
$151$	−11.2598	−	8.18073i	−0.916310	−	0.665738i	−0.942603	+	0.333916i	$0.891630\pi$
$152$	−2.23607	−	1.62460i	−0.181369	−	0.131772i
$153$	−1.99698	+	6.14607i	−0.161446	+	0.496880i
$154$	9.02890	+	7.21392i	0.727570	+	0.581314i
$155$	−0.832632	−	0.799088i	−0.0668786	−	0.0641843i
$156$	2.31604	−	1.68270i	0.185432	−	0.134724i
$157$	−8.49225	−	6.16998i	−0.677755	−	0.492418i	0.194857	−	0.980832i	$-0.437576\pi$
$157$	−8.49225	−	6.16998i	−0.677755	−	0.492418i	−0.872612	+	0.488414i	$0.837576\pi$
$158$	11.8227	+	8.58972i	0.940566	+	0.683361i
$159$	6.46806	−	4.69932i	0.512951	−	0.372680i
$160$	−2.04793	−	11.4074i	−0.161903	−	0.901834i
$161$	0.721358	−	2.22011i	0.0568509	−	0.174969i
$162$	0.300458	+	0.924714i	0.0236062	+	0.0726524i
$163$	−1.19577	+	3.68020i	−0.0936599	+	0.288256i	−0.986902	−	0.161320i	$-0.948425\pi$
$163$	−1.19577	+	3.68020i	−0.0936599	+	0.288256i	0.893242	+	0.449576i	$0.148425\pi$
$164$	10.4259	−	7.57487i	0.814128	−	0.591498i
$165$	−0.974876	−	7.35184i	−0.0758940	−	0.572340i
$166$	−2.74775	−	1.99635i	−0.213266	−	0.154947i
$167$	−6.71153	+	4.87621i	−0.519354	+	0.377333i	−0.816360	−	0.577543i	$-0.804012\pi$
$167$	−6.71153	+	4.87621i	−0.519354	+	0.377333i	0.297007	+	0.954875i	$0.404012\pi$
$168$	−8.61114	−	6.25636i	−0.664364	−	0.482689i
$169$	4.55599	+	3.31012i	0.350461	+	0.254624i
$170$	6.11994	−	12.6471i	0.469378	−	0.969990i
$171$	0.752879	+	0.546998i	0.0575741	+	0.0418300i
$172$	2.33340	+	7.18147i	0.177920	+	0.547582i
$173$	−14.8878			−1.13190			−0.565951	−	0.824439i	$-0.691491\pi$
$173$	−14.8878			−1.13190			−0.565951	+	0.824439i	$0.691491\pi$
$174$	−0.0770708	−	0.237199i	−0.00584272	−	0.0179820i
$175$	9.92784	−	14.9174i	0.750474	−	1.12765i
$176$	2.57929	+	0.118215i	0.194421	+	0.00891079i
$177$	4.65180	−	3.37973i	0.349651	−	0.254036i
$178$	15.6405			1.17230
$179$	−9.99892	+	7.26464i	−0.747354	+	0.542985i	−0.895006	−	0.446055i	$-0.852829\pi$
$179$	−9.99892	+	7.26464i	−0.747354	+	0.542985i	0.147651	+	0.989039i	$0.452829\pi$
$180$	0.416701	+	2.32111i	0.0310590	+	0.173006i
$181$	5.84777			0.434661			0.217331	−	0.976098i	$-0.430265\pi$
$181$	5.84777			0.434661			0.217331	+	0.976098i	$0.430265\pi$
$182$	−2.92292	+	8.99581i	−0.216661	+	0.666814i
$183$	−12.3692	−	8.98678i	−0.914361	−	0.664322i
$184$	−0.597815	−	1.83989i	−0.0440715	−	0.135638i
$185$	2.30183	+	12.8217i	0.169234	+	0.942667i
$186$	−0.405972	+	0.294956i	−0.0297673	+	0.0216272i
$187$	−16.7449	−	13.3788i	−1.22450	−	0.978355i
$188$	−3.17027	−	2.30334i	−0.231216	−	0.167988i
$189$	2.89935	+	2.10650i	0.210897	+	0.153226i
$190$	−1.45977	−	1.40096i	−0.105903	−	0.101636i
$191$	17.7544			1.28466			0.642332	−	0.766427i	$-0.277967\pi$
$191$	17.7544			1.28466			0.642332	+	0.766427i	$0.277967\pi$
$192$	−6.59655			−0.476065
$193$	2.84124	−	8.74443i	0.204517	−	0.629438i	−0.795216	−	0.606326i	$-0.792643\pi$
$193$	2.84124	−	8.74443i	0.204517	−	0.629438i	0.999733	−	0.0231116i	$-0.00735732\pi$
$194$	2.66395	+	1.93547i	0.191260	+	0.138959i
$195$	5.35045	−	2.86620i	0.383154	−	0.205253i
$196$	−6.16283			−0.440202
$197$	0.228584	−	0.703511i	0.0162860	−	0.0501231i	−0.942583	−	0.333971i	$-0.891611\pi$
$197$	0.228584	−	0.703511i	0.0162860	−	0.0501231i	0.958869	+	0.283848i	$0.0916112\pi$
$198$	−3.22138	−	0.147643i	−0.228934	−	0.0104926i
$199$	−25.6888			−1.82103			−0.910517	−	0.413472i	$-0.864316\pi$
$199$	−25.6888			−1.82103			−0.910517	+	0.413472i	$0.864316\pi$
$200$	−0.610299	−	14.8376i	−0.0431546	−	1.04917i
$201$	−0.349814	−	0.254155i	−0.0246740	−	0.0179267i
$202$	2.57769	−	7.93331i	0.181366	−	0.558186i
$203$	−0.743716	−	0.540341i	−0.0521986	−	0.0379245i
$204$	5.51376	+	4.00598i	0.386041	+	0.280475i
$205$	24.0857	−	12.9025i	1.68222	−	0.901152i
$206$	1.17052	−	3.60250i	0.0815542	−	0.250998i
$207$	0.201283	+	0.619486i	0.0139901	+	0.0430572i
$208$	0.653027	+	2.00981i	0.0452793	+	0.139355i
$209$	−2.57746	+	1.69796i	−0.178287	+	0.117450i
$210$	−5.62160	−	5.39513i	−0.387928	−	0.372299i
$211$	1.61279	+	1.17176i	0.111029	+	0.0806671i	0.641914	−	0.766776i	$-0.278141\pi$
$211$	1.61279	+	1.17176i	0.111029	+	0.0806671i	−0.530885	+	0.847444i	$0.678141\pi$
$212$	−2.60554	−	8.01904i	−0.178949	−	0.550750i
$213$	2.17575			0.149080
$214$	3.64750	+	11.2259i	0.249338	+	0.767384i
$215$	2.82900	+	15.7581i	0.192936	+	1.07470i
$216$	2.97002			0.202084
$217$	−0.571562	+	1.75909i	−0.0388001	+	0.119415i
$218$	−1.95981	−	6.03168i	−0.132735	−	0.408517i
$219$	2.53640	+	7.80622i	0.171394	+	0.527496i
$220$	−7.69169	−	1.41814i	−0.518574	−	0.0956110i
$221$	5.42079	−	16.6835i	0.364642	−	1.12225i
$222$	5.66433			0.380165
$223$	−11.5052			−0.770448			−0.385224	−	0.922823i	$-0.625876\pi$
$223$	−11.5052			−0.770448			−0.385224	+	0.922823i	$0.625876\pi$
$224$	−15.0276	+	10.9182i	−1.00408	+	0.729505i
$225$	0.205486	+	4.99578i	0.0136991	+	0.333052i
$226$	1.35753	−	4.17804i	0.0903013	−	0.277919i
$227$	6.82733	−	21.0124i	0.453146	−	1.39464i	−0.420152	−	0.907454i	$-0.638023\pi$
$227$	6.82733	−	21.0124i	0.453146	−	1.39464i	0.873298	−	0.487186i	$-0.161977\pi$
$228$	0.794007	−	0.576880i	0.0525844	−	0.0382048i
$229$	4.17374			0.275808			0.137904	−	0.990446i	$-0.455963\pi$
$229$	4.17374			0.275808			0.137904	+	0.990446i	$0.455963\pi$
$230$	−0.250237	−	1.39387i	−0.0165001	−	0.0919092i
$231$	−9.92585	+	6.53889i	−0.653073	+	0.430227i
$232$	−0.761844			−0.0500175
$233$	5.17209	−	3.75774i	0.338835	−	0.246178i	−0.405335	−	0.914168i	$-0.632845\pi$
$233$	5.17209	−	3.75774i	0.338835	−	0.246178i	0.744170	+	0.667990i	$0.232845\pi$
$234$	−0.815592	−	2.51013i	−0.0533169	−	0.164093i
$235$	−5.99453	−	5.75303i	−0.391040	−	0.375286i
$236$	−1.87389	−	5.76725i	−0.121980	−	0.375416i
$237$	−12.1595	+	8.83441i	−0.789846	+	0.573857i
$238$	−22.5183			−1.45964
$239$	8.39561			0.543067			0.271533	−	0.962429i	$-0.412469\pi$
$239$	8.39561			0.543067			0.271533	+	0.962429i	$0.412469\pi$
$240$	−1.72459	−	0.236923i	−0.111322	−	0.0152933i
$241$	−15.6423	−	11.3648i	−1.00761	−	0.732069i	−0.0439007	−	0.999036i	$-0.513979\pi$
$241$	−15.6423	−	11.3648i	−1.00761	−	0.732069i	−0.963706	+	0.266967i	$0.913979\pi$
$242$	4.22163	−	9.82689i	0.271376	−	0.631697i
$243$	−1.00000			−0.0641500
$244$	−13.0450	+	9.47771i	−0.835118	+	0.606749i
$245$	−12.9451	−	1.77840i	−0.827032	−	0.113618i
$246$	−3.67148	−	11.2996i	−0.234085	−	0.720439i
$247$	−2.04369	−	1.48483i	−0.130037	−	0.0944772i
$248$	0.473674	+	1.45782i	0.0300783	+	0.0925716i
$249$	2.82602	−	2.05322i	0.179092	−	0.130118i
$250$	1.03567	−	10.8212i	0.0655013	−	0.684394i
$251$	−2.81111	−	8.65171i	−0.177436	−	0.546091i	0.822301	−	0.569053i	$-0.192690\pi$
$251$	−2.81111	−	8.65171i	−0.177436	−	0.546091i	−0.999736	+	0.0229624i	$0.992690\pi$
$252$	3.05774	−	2.22158i	0.192619	−	0.139946i
$253$	−2.15807	−	0.0989094i	−0.135677	−	0.00621838i
$254$	0.412722	−	1.27023i	0.0258965	−	0.0797012i
$255$	10.4257	+	10.0057i	0.652885	+	0.626582i
$256$	−5.26441	+	16.2022i	−0.329026	+	1.01264i
$257$	−19.4514	+	14.1323i	−1.21335	+	0.881548i	−0.995530	−	0.0944416i	$-0.969893\pi$
$257$	−19.4514	+	14.1323i	−1.21335	+	0.881548i	−0.217817	+	0.975990i	$0.569893\pi$
$258$	6.96160			0.433410
$259$	16.8907	−	12.2718i	1.04954	−	0.762535i
$260$	−1.13113	−	6.30065i	−0.0701499	−	0.390750i
$261$	0.256511			0.0158776
$262$	−6.74275	+	20.7520i	−0.416568	+	1.28207i
$263$	17.7293	+	12.8811i	1.09324	+	0.794282i	0.979943	−	0.199280i	$-0.0638602\pi$
$263$	17.7293	+	12.8811i	1.09324	+	0.794282i	0.113293	+	0.993562i	$0.463860\pi$
$264$	−3.46969	+	9.21914i	−0.213544	+	0.567399i
$265$	−3.15894	−	17.5960i	−0.194052	−	1.08091i
$266$	−1.00206	+	3.08403i	−0.0614403	+	0.189094i
$267$	−4.97085	+	15.2987i	−0.304211	+	0.936265i
$268$	−0.368924	+	0.268039i	−0.0225356	+	0.0163731i
$269$	3.20211			0.195236			0.0976182	−	0.995224i	$-0.468878\pi$
$269$	3.20211			0.195236			0.0976182	+	0.995224i	$0.468878\pi$
$270$	2.15390	+	0.295903i	0.131082	+	0.0180081i
$271$	6.69551	+	20.6067i	0.406723	+	1.25177i	0.919448	+	0.393212i	$0.128636\pi$
$271$	6.69551	+	20.6067i	0.406723	+	1.25177i	−0.512724	+	0.858553i	$0.671364\pi$
$272$	−4.07013	+	2.95712i	−0.246788	+	0.179302i
$273$	−7.87028	−	5.71809i	−0.476331	−	0.346075i
$274$	17.3303			1.04696
$275$	−15.7473	−	5.19840i	−0.949596	−	0.313475i
$276$	0.686949			0.0413495
$277$	19.1756	+	13.9319i	1.15215	+	0.837085i	0.988765	−	0.149478i	$-0.0477593\pi$
$277$	19.1756	+	13.9319i	1.15215	+	0.837085i	0.163383	+	0.986563i	$0.447759\pi$
$278$	6.12129	−	4.44737i	0.367130	−	0.266736i
$279$	−0.159485	−	0.490844i	−0.00954812	−	0.0293861i
$280$	−20.9799	+	11.2388i	−1.25379	+	0.671648i
$281$	−23.3567			−1.39335			−0.696673	−	0.717389i	$-0.745337\pi$
$281$	−23.3567			−1.39335			−0.696673	+	0.717389i	$0.745337\pi$
$282$	−2.92279	+	2.12353i	−0.174050	+	0.126455i
$283$	−3.85032	+	11.8501i	−0.228878	+	0.704413i	0.768997	+	0.639252i	$0.220756\pi$
$283$	−3.85032	+	11.8501i	−0.228878	+	0.704413i	−0.997875	+	0.0651606i	$0.979244\pi$
$284$	0.709072	−	2.18230i	0.0420757	−	0.129496i
$285$	1.83429	−	0.982619i	0.108654	−	0.0582053i
$286$	8.74442	+	0.400778i	0.517069	+	0.0236985i
$287$	−35.4290	−	25.7406i	−2.09130	−	1.51942i
$288$	1.60167	−	4.92943i	0.0943792	−	0.290469i
$289$	24.7621			1.45659
$290$	−0.552500	−	0.0759024i	−0.0324439	−	0.00445714i
$291$	−2.73984	+	1.99061i	−0.160612	+	0.116692i
$292$	8.65633			0.506574
$293$	13.0893	−	9.50992i	0.764684	−	0.555575i	−0.135659	−	0.990756i	$-0.543315\pi$
$293$	13.0893	−	9.50992i	0.764684	−	0.555575i	0.900343	+	0.435180i	$0.143315\pi$
$294$	−1.75576	+	5.40366i	−0.102398	+	0.315148i
$295$	−2.27189	−	12.6549i	−0.132275	−	0.736799i
$296$	5.34674	−	16.4556i	0.310773	−	0.956462i
$297$	1.16824	−	3.10407i	0.0677879	−	0.180116i
$298$	−12.2425	+	8.89471i	−0.709190	+	0.515257i
$299$	−0.546382	−	1.68159i	−0.0315981	−	0.0972489i
$300$	5.07779	+	1.42201i	0.293166	+	0.0820997i
$301$	20.7591	−	15.0824i	1.19654	−	0.869334i
$302$	4.18174	+	12.8701i	0.240632	+	0.740589i
$303$	6.94072	+	5.04273i	0.398734	+	0.289697i
$304$	0.223877	+	0.689023i	0.0128402	+	0.0395182i
$305$	−30.1361	+	16.1437i	−1.72559	+	0.924386i
$306$	5.08335	−	3.69327i	0.290596	−	0.211130i
$307$	7.85750			0.448451			0.224226	−	0.974537i	$-0.428015\pi$
$307$	7.85750			0.448451			0.224226	+	0.974537i	$0.428015\pi$
$308$	3.32376	+	12.0868i	0.189389	+	0.688707i
$309$	3.15177	+	2.28989i	0.179298	+	0.130267i
$310$	0.198273	+	1.10442i	0.0112611	+	0.0627270i
$311$	24.2110			1.37288			0.686441	−	0.727185i	$-0.259172\pi$
$311$	24.2110			1.37288			0.686441	+	0.727185i	$0.259172\pi$
$312$	−8.06211			−0.456427
$313$	6.40000	−	4.64987i	0.361749	−	0.262826i	−0.392032	−	0.919952i	$-0.628228\pi$
$313$	6.40000	−	4.64987i	0.361749	−	0.262826i	0.753781	+	0.657125i	$0.228228\pi$
$314$	3.15390	+	9.70672i	0.177985	+	0.547782i
$315$	7.06390	−	3.78409i	0.398006	−	0.213209i
$316$	4.89825	+	15.0753i	0.275548	+	0.848050i
$317$	27.0457	−	19.6498i	1.51904	−	1.10364i	0.557072	−	0.830464i	$-0.311925\pi$
$317$	27.0457	−	19.6498i	1.51904	−	1.10364i	0.961963	−	0.273180i	$-0.0880753\pi$
$318$	−7.77352			−0.435917
$319$	−0.299665	+	0.796227i	−0.0167780	+	0.0445802i
$320$	−6.42498	+	13.2775i	−0.359167	+	0.742235i
$321$	−12.1398			−0.677578
$322$	−1.83623	+	1.33410i	−0.102329	+	0.0743464i
$323$	1.85841	−	5.71959i	0.103404	−	0.318246i
$324$	−0.325898	+	1.00301i	−0.0181054	+	0.0557228i
$325$	−0.557792	−	13.5610i	−0.0309407	−	0.752230i
$326$	3.04386	−	2.21149i	0.168584	−	0.122483i
$327$	6.52275			0.360709
$328$	−36.2925			−2.00392
$329$	−4.11496	+	12.6645i	−0.226865	+	0.698218i
$330$	−3.43477	+	6.34017i	−0.189078	+	0.349015i
$331$	0.868363	+	2.67255i	0.0477296	+	0.146896i	0.972081	−	0.234646i	$-0.0753931\pi$
$331$	0.868363	+	2.67255i	0.0477296	+	0.146896i	−0.924351	+	0.381542i	$0.875393\pi$
$332$	−1.13841	−	3.50367i	−0.0624785	−	0.192289i
$333$	−1.80024	+	5.54056i	−0.0986524	+	0.303621i
$334$	8.06613			0.441359
$335$	−0.852277	+	0.456559i	−0.0465649	+	0.0249445i
$336$	0.862155	+	2.65344i	0.0470344	+	0.144757i
$337$	31.7367			1.72881			0.864405	−	0.502796i	$-0.167695\pi$
$337$	31.7367			1.72881			0.864405	+	0.502796i	$0.167695\pi$
$338$	−1.69203	−	5.20754i	−0.0920344	−	0.283253i
$339$	3.65529	+	2.65573i	0.198528	+	0.144239i
$340$	13.4336	−	7.19628i	0.728538	−	0.390273i
$341$	1.70993	+	0.0783701i	0.0925979	+	0.00424398i
$342$	−0.279609	−	0.860548i	−0.0151195	−	0.0465331i
$343$	−1.28066	−	3.94147i	−0.0691492	−	0.212819i
$344$	6.57128	−	20.2243i	0.354299	−	1.09042i
$345$	1.44294	+	0.198232i	0.0776855	+	0.0106724i
$346$	11.7109	+	8.50848i	0.629583	+	0.457419i
$347$	−11.5326	−	8.37893i	−0.619103	−	0.449804i	0.233505	−	0.972356i	$-0.424980\pi$
$347$	−11.5326	−	8.37893i	−0.619103	−	0.449804i	−0.852608	+	0.522551i	$0.824980\pi$
$348$	0.0835965	−	0.257283i	0.00448124	−	0.0137918i
$349$	−4.72955	−	3.43622i	−0.253167	−	0.183937i	0.453962	−	0.891021i	$-0.350010\pi$
$349$	−4.72955	−	3.43622i	−0.253167	−	0.183937i	−0.707129	+	0.707084i	$0.750010\pi$
$350$	−16.3347	+	6.06033i	−0.873125	+	0.323938i
$351$	2.71450			0.144889
$352$	13.4301	+	10.7304i	0.715829	+	0.571933i
$353$	−2.74069	+	8.43498i	−0.145872	+	0.448949i	−0.997122	−	0.0758120i	$-0.975845\pi$
$353$	−2.74069	+	8.43498i	−0.145872	+	0.448949i	0.851250	+	0.524761i	$0.175845\pi$
$354$	−5.59068			−0.297141
$355$	2.11916	−	4.37933i	0.112473	−	0.232431i
$356$	13.7248	+	9.97163i	0.727411	+	0.528495i
$357$	7.15676	−	22.0263i	0.378776	−	1.16575i
$358$	12.0170			0.635119
$359$	3.45169			0.182173			0.0910867	−	0.995843i	$-0.470966\pi$
$359$	3.45169			0.182173			0.0910867	+	0.995843i	$0.470966\pi$
$360$	2.89277	−	5.97804i	0.152463	−	0.315071i
$361$	14.6707	+	10.6589i	0.772141	+	0.560994i
$362$	−4.59991	−	3.34203i	−0.241766	−	0.175653i
$363$	8.27045	+	7.25256i	0.434086	+	0.380661i
$364$	−8.30022	+	6.03046i	−0.435050	+	0.316082i
$365$	18.1827	+	2.49794i	0.951728	+	0.130748i
$366$	4.59377	+	14.1382i	0.240120	+	0.739014i
$367$	11.9641	+	8.69246i	0.624523	+	0.453743i	0.854499	−	0.519454i	$-0.173864\pi$
$367$	11.9641	+	8.69246i	0.624523	+	0.453743i	−0.229975	+	0.973196i	$0.573864\pi$
$368$	−0.156699	+	0.482271i	−0.00816852	+	0.0251401i
$369$	12.2196			0.636127
$370$	5.51701	−	11.4011i	0.286815	−	0.592717i
$371$	−23.1802	+	16.8414i	−1.20346	+	0.874362i
$372$	−0.544298			−0.0282205
$373$	11.7320	−	8.52377i	0.607458	−	0.441344i	−0.241060	−	0.970510i	$-0.577495\pi$
$373$	11.7320	−	8.52377i	0.607458	−	0.441344i	0.848518	+	0.529166i	$0.177495\pi$
$374$	5.52560	+	20.0937i	0.285722	+	1.03902i
$375$	10.2556	+	4.45224i	0.529598	+	0.229912i
$376$	3.41021	+	10.4956i	0.175868	+	0.541267i
$377$	−0.696298			−0.0358612
$378$	−1.07678	−	3.31399i	−0.0553836	−	0.170453i
$379$	−28.8814	−	20.9836i	−1.48354	−	1.07786i	−0.976394	−	0.215995i	$-0.930701\pi$
$379$	−28.8814	−	20.9836i	−1.48354	−	1.07786i	−0.507146	−	0.861860i	$-0.669299\pi$
$380$	−0.387786	−	2.16005i	−0.0198930	−	0.110808i
$381$	1.11130	+	0.807407i	0.0569336	+	0.0413647i
$382$	−13.9658	−	10.1467i	−0.714551	−	0.519152i
$383$	−11.9106	+	8.65359i	−0.608605	+	0.442178i	−0.848923	−	0.528517i	$-0.822748\pi$
$383$	−11.9106	+	8.65359i	−0.608605	+	0.442178i	0.240318	+	0.970694i	$0.422748\pi$
$384$	−3.19753	−	2.32315i	−0.163174	−	0.118553i
$385$	3.49376	+	26.3475i	0.178058	+	1.34279i
$386$	−7.23242	+	5.25466i	−0.368121	+	0.267455i
$387$	−2.21253	+	6.80948i	−0.112469	+	0.346145i
$388$	1.10369	+	3.39682i	0.0560316	+	0.172448i
$389$	0.355078	−	1.09282i	0.0180032	−	0.0554081i	−0.941651	−	0.336590i	$-0.890726\pi$
$389$	0.355078	−	1.09282i	0.0180032	−	0.0554081i	0.959655	+	0.281182i	$0.0907264\pi$
$390$	−5.84676	−	0.803227i	−0.296062	−	0.0406730i
$391$	3.40544	−	2.47420i	0.172221	−	0.125126i
$392$	14.0410	+	10.2014i	0.709177	+	0.515247i
$393$	−18.1556	−	13.1908i	−0.915830	−	0.665389i
$394$	−0.581866	+	0.422751i	−0.0293140	+	0.0212979i
$395$	5.93860	+	33.0793i	0.298803	+	1.66440i
$396$	−2.73269	−	2.18336i	−0.137323	−	0.109718i
$397$	−2.26085	+	6.95817i	−0.113469	+	0.349221i	−0.991625	−	0.129154i	$-0.958774\pi$
$397$	−2.26085	+	6.95817i	−0.113469	+	0.349221i	0.878156	+	0.478375i	$0.158774\pi$
$398$	20.2071	+	14.6813i	1.01289	+	0.735907i
$399$	−2.69816	−	1.96033i	−0.135077	−	0.0981393i
$400$	−2.15661	+	3.24048i	−0.107830	+	0.162024i
$401$	7.21973	−	22.2200i	0.360536	−	1.10962i	−0.592194	−	0.805796i	$-0.701738\pi$
$401$	7.21973	−	22.2200i	0.360536	−	1.10962i	0.952730	−	0.303820i	$-0.0982621\pi$
$402$	0.129916	+	0.399841i	0.00647963	+	0.0199422i
$403$	0.432921	+	1.33240i	0.0215654	+	0.0663713i
$404$	7.31988	−	5.31820i	0.364178	−	0.264591i
$405$	−0.973990	+	2.01279i	−0.0483980	+	0.100017i
$406$	0.276206	+	0.850075i	0.0137079	+	0.0421885i
$407$	−15.0952	−	12.0607i	−0.748240	−	0.597829i
$408$	−5.93107	−	18.2540i	−0.293632	−	0.903705i
$409$	−2.49486	+	7.67838i	−0.123363	+	0.379672i	−0.993599	−	0.112963i	$-0.963966\pi$
$409$	−2.49486	+	7.67838i	−0.123363	+	0.379672i	0.870236	+	0.492634i	$0.163966\pi$
$410$	−26.3199	−	3.61582i	−1.29985	−	0.178572i
$411$	−5.50792	+	16.9516i	−0.271685	+	0.836162i
$412$	3.32394	−	2.41499i	0.163759	−	0.118978i
$413$	−16.6711	+	12.1123i	−0.820331	+	0.596005i
$414$	0.195708	−	0.602327i	0.00961852	−	0.0296028i
$415$	−1.38020	−	7.68802i	−0.0677514	−	0.377390i
$416$	−4.34772	+	13.3809i	−0.213165	+	0.656053i
$417$	2.40473	+	7.40099i	0.117760	+	0.362428i
$418$	2.99785	+	0.137398i	0.146629	+	0.00672037i
$419$	9.88478	+	30.4222i	0.482903	+	1.48622i	0.834995	+	0.550258i	$0.185470\pi$
$419$	9.88478	+	30.4222i	0.482903	+	1.48622i	−0.352092	+	0.935965i	$0.614530\pi$
$420$	−1.49337	−	8.31840i	−0.0728690	−	0.405896i
$421$	−9.19019	+	6.67706i	−0.447902	+	0.325420i	−0.788767	−	0.614692i	$-0.789280\pi$
$421$	−9.19019	+	6.67706i	−0.447902	+	0.325420i	0.340865	+	0.940112i	$0.389280\pi$
$422$	−0.598967	−	1.84343i	−0.0291573	−	0.0897368i
$423$	−1.14821	−	3.53383i	−0.0558279	−	0.171821i
$424$	−7.33767	+	22.5830i	−0.356349	+	1.09673i
$425$	30.2940	−	11.2394i	1.46948	−	0.545190i
$426$	−1.71146	−	1.24345i	−0.0829207	−	0.0602454i
$427$	44.3289	+	32.2068i	2.14522	+	1.55860i
$428$	−3.95634	+	12.1764i	−0.191237	+	0.588567i
$429$	−3.17117	+	8.42598i	−0.153106	+	0.406810i
$430$	6.78053	−	14.0123i	0.326986	−	0.675732i
$431$	−11.9482	+	8.68086i	−0.575523	+	0.418142i	−0.837107	−	0.547038i	$-0.815755\pi$
$431$	−11.9482	+	8.68086i	−0.575523	+	0.418142i	0.261584	+	0.965181i	$0.415755\pi$
$432$	−0.629821	−	0.457592i	−0.0303023	−	0.0220159i
$433$	−8.13916	−	5.91344i	−0.391143	−	0.284182i	0.374781	−	0.927113i	$-0.377718\pi$
$433$	−8.13916	−	5.91344i	−0.391143	−	0.284182i	−0.765924	+	0.642931i	$0.777718\pi$
$434$	1.45492	−	1.05706i	0.0698385	−	0.0507406i
$435$	0.249839	−	0.516304i	0.0119789	−	0.0247549i
$436$	2.12575	−	6.54239i	0.101805	−	0.313324i
$437$	−0.187316	−	0.576499i	−0.00896053	−	0.0275777i
$438$	2.46614	−	7.59001i	0.117837	−	0.362665i
$439$	17.8347	−	12.9577i	0.851204	−	0.618436i	−0.0742739	−	0.997238i	$-0.523664\pi$
$439$	17.8347	−	12.9577i	0.851204	−	0.618436i	0.925478	+	0.378802i	$0.123664\pi$
$440$	15.1768	+	15.9631i	0.723526	+	0.761012i
$441$	−4.72757	−	3.43478i	−0.225122	−	0.163561i
$442$	−13.7987	+	10.0254i	−0.656339	+	0.476858i
$443$	27.0453	+	19.6496i	1.28496	+	0.933578i	0.999691	−	0.0248689i	$-0.00791685\pi$
$443$	27.0453	+	19.6496i	1.28496	+	0.933578i	0.285270	+	0.958447i	$0.407917\pi$
$444$	4.97055	+	3.61132i	0.235892	+	0.171386i
$445$	25.9516	+	24.9061i	1.23022	+	1.18066i
$446$	9.05013	+	6.57530i	0.428536	+	0.311350i
$447$	−4.80944	−	14.8019i	−0.227479	−	0.700107i
$448$	23.6407			1.11692
$449$	10.5201	+	32.3777i	0.496476	+	1.52800i	0.814643	+	0.579963i	$0.196933\pi$
$449$	10.5201	+	32.3777i	0.496476	+	1.52800i	−0.318167	+	0.948035i	$0.603067\pi$
$450$	2.69347	−	4.04716i	0.126972	−	0.190785i
$451$	−14.2754	+	37.9305i	−0.672202	+	1.78608i
$452$	3.85498	−	2.80080i	0.181323	−	0.131739i
$453$	−13.9179			−0.653919
$454$	−17.3791	+	12.6267i	−0.815642	+	0.592599i
$455$	−19.1749	+	10.2719i	−0.898935	+	0.481554i
$456$	−2.76393			−0.129433
$457$	−6.71954	+	20.6806i	−0.314327	+	0.967399i	0.661704	+	0.749765i	$0.269834\pi$
$457$	−6.71954	+	20.6806i	−0.314327	+	0.967399i	−0.976031	+	0.217633i	$0.930166\pi$
$458$	−3.28310	−	2.38531i	−0.153409	−	0.111458i
$459$	1.99698	+	6.14607i	0.0932109	+	0.286874i
$460$	0.669081	−	1.38269i	0.0311961	−	0.0644681i
$461$	22.8087	−	16.5715i	1.06231	−	0.771810i	0.0877918	−	0.996139i	$-0.472019\pi$
$461$	22.8087	−	16.5715i	1.06231	−	0.771810i	0.974513	+	0.224329i	$0.0720190\pi$
$462$	11.5448	+	0.529124i	0.537111	+	0.0246171i
$463$	−30.3913	−	22.0806i	−1.41241	−	1.02617i	−0.992967	−	0.118388i	$-0.962227\pi$
$463$	−30.3913	−	22.0806i	−1.41241	−	1.02617i	−0.419438	−	0.907784i	$-0.637773\pi$
$464$	0.161556	+	0.117377i	0.00750006	+	0.00544911i
$465$	−1.14331	−	0.157067i	−0.0530195	−	0.00728381i
$466$	−6.21598			−0.287950
$467$	−32.3326			−1.49617			−0.748087	−	0.663600i	$-0.769028\pi$
$467$	−32.3326			−1.49617			−0.748087	+	0.663600i	$0.769028\pi$
$468$	0.884649	−	2.72267i	0.0408929	−	0.125855i
$469$	1.25366	+	0.910839i	0.0578887	+	0.0420586i
$470$	1.42747	+	7.95129i	0.0658441	+	0.366766i
$471$	−10.4970			−0.483676
$472$	−5.27722	+	16.2416i	−0.242904	+	0.747581i
$473$	−18.5523	−	14.8229i	−0.853036	−	0.681559i
$474$	14.6137			0.671230
$475$	−0.191227	−	4.64912i	−0.00877412	−	0.213316i
$476$	−19.7602	−	14.3566i	−0.905707	−	0.658035i
$477$	2.47058	−	7.60366i	0.113120	−	0.348148i
$478$	−6.60406	−	4.79813i	−0.302063	−	0.219461i
$479$	−31.7346	−	23.0565i	−1.44999	−	1.05348i	−0.985833	−	0.167728i	$-0.946357\pi$
$479$	−31.7346	−	23.0565i	−1.44999	−	1.05348i	−0.464158	−	0.885753i	$-0.653643\pi$
$480$	−8.36191	−	8.02504i	−0.381667	−	0.366291i
$481$	4.88674	−	15.0398i	0.222816	−	0.685757i
$482$	5.80932	+	17.8793i	0.264607	+	0.814378i
$483$	−0.721358	−	2.22011i	−0.0328229	−	0.101019i
$484$	9.96973	−	5.93176i	0.453169	−	0.269625i
$485$	1.33811	+	7.45356i	0.0607605	+	0.338449i
$486$	0.786609	+	0.571505i	0.0356813	+	0.0259240i
$487$	5.89871	+	18.1544i	0.267296	+	0.822652i	0.991156	+	0.132705i	$0.0423663\pi$
$487$	5.89871	+	18.1544i	0.267296	+	0.822652i	−0.723860	+	0.689947i	$0.757634\pi$
$488$	45.4093			2.05558
$489$	1.19577	+	3.68020i	0.0540746	+	0.166424i
$490$	9.16637	+	8.79709i	0.414094	+	0.397412i
$491$	−33.2778			−1.50180			−0.750902	−	0.660413i	$-0.770381\pi$
$491$	−33.2778			−1.50180			−0.750902	+	0.660413i	$0.770381\pi$
$492$	3.98235	−	12.2564i	0.179538	−	0.552561i
$493$	−0.512247	−	1.57653i	−0.0230704	−	0.0710035i
$494$	0.758997	+	2.33595i	0.0341489	+	0.105100i
$495$	−5.11000	−	5.37475i	−0.229677	−	0.241577i
$496$	0.124159	−	0.382123i	0.00557492	−	0.0171578i
$497$	−7.79744			−0.349763
$498$	−3.39640			−0.152196
$499$	4.54963	−	3.30550i	0.203670	−	0.147975i	−0.481275	−	0.876570i	$-0.659826\pi$
$499$	4.54963	−	3.30550i	0.203670	−	0.147975i	0.684945	+	0.728595i	$0.259826\pi$
$500$	7.80793	−	8.83552i	0.349181	−	0.395136i
$501$	−2.56358	+	7.88988i	−0.114532	+	0.352494i
$502$	−2.73325	+	8.41208i	−0.121991	+	0.375449i
$503$	7.40590	−	5.38070i	0.330213	−	0.239913i	−0.410308	−	0.911947i	$-0.634579\pi$
$503$	7.40590	−	5.38070i	0.330213	−	0.239913i	0.740521	+	0.672033i	$0.234579\pi$
$504$	−10.6440			−0.474119
$505$	16.9102	−	9.05868i	0.752493	−	0.403106i
$506$	1.64103	+	1.31115i	0.0729527	+	0.0582878i
$507$	5.63151			0.250104
$508$	1.17201	−	0.851514i	0.0519995	−	0.0377798i
$509$	−8.27076	−	25.4548i	−0.366595	−	1.12826i	−0.948976	−	0.315348i	$-0.897879\pi$
$509$	−8.27076	−	25.4548i	−0.366595	−	1.12826i	0.582381	−	0.812916i	$-0.302121\pi$
$510$	−2.48266	−	13.8289i	−0.109934	−	0.612356i
$511$	−9.08992	−	27.9759i	−0.402115	−	1.23758i
$512$	7.00560	−	5.08986i	0.309607	−	0.224942i
$513$	0.930609			0.0410874
$514$	23.3773			1.03113
$515$	7.67887	−	4.11353i	0.338372	−	0.181264i
$516$	6.10893	+	4.43839i	0.268930	+	0.195389i
$517$	12.3106	+	0.564225i	0.541421	+	0.0248146i
$518$	−20.2998			−0.891923
$519$	−12.0445	+	8.75086i	−0.528696	+	0.384120i
$520$	−7.85242	+	16.2274i	−0.344351	+	0.711618i
$521$	−3.31820	−	10.2124i	−0.145373	−	0.447412i	0.851686	−	0.524053i	$-0.175581\pi$
$521$	−3.31820	−	10.2124i	−0.145373	−	0.447412i	−0.997059	+	0.0766408i	$0.975581\pi$
$522$	−0.201774	−	0.146597i	−0.00883140	−	0.00641639i
$523$	10.6713	+	32.8430i	0.466625	+	1.43612i	0.856928	+	0.515437i	$0.172370\pi$
$523$	10.6713	+	32.8430i	0.466625	+	1.43612i	−0.390303	+	0.920686i	$0.627630\pi$
$524$	−19.1474	+	13.9114i	−0.836459	+	0.607723i
$525$	−0.736421	−	17.9038i	−0.0321400	−	0.781388i
$526$	−6.58442	−	20.2648i	−0.287094	−	0.883586i
$527$	−2.69827	+	1.96041i	−0.117539	+	0.0853968i
$528$	2.15618	−	1.42043i	0.0938355	−	0.0618164i
$529$	−6.97628	+	21.4708i	−0.303317	+	0.933513i
$530$	−7.57133	+	15.6465i	−0.328878	+	0.679640i
$531$	1.77683	−	5.46852i	0.0771078	−	0.237313i
$532$	−2.84556	+	2.06742i	−0.123371	+	0.0896341i
$533$	−33.1701			−1.43676
$534$	12.6534	−	9.19323i	0.547566	−	0.397830i
$535$	−11.8241	+	24.4350i	−0.511199	+	1.05642i
$536$	1.28422			0.0554698
$537$	−3.81925	+	11.7544i	−0.164813	+	0.507241i
$538$	−2.51881	−	1.83002i	−0.108594	−	0.0788980i
$539$	16.1847	−	10.6621i	0.697125	−	0.459247i
$540$	1.70143	+	1.63289i	0.0732181	+	0.0702684i
$541$	−3.18915	+	9.81518i	−0.137112	+	0.421988i	−0.995913	−	0.0903226i	$-0.971210\pi$
$541$	−3.18915	+	9.81518i	−0.137112	+	0.421988i	0.858800	+	0.512310i	$0.171210\pi$
$542$	6.51006	−	20.0359i	0.279631	−	0.860616i
$543$	4.73095	−	3.43723i	0.203024	−	0.147506i
$544$	−33.4951			−1.43609
$545$	6.35310	−	13.1290i	0.272137	−	0.562383i
$546$	2.92292	+	8.99581i	0.125089	+	0.384985i
$547$	13.1910	−	9.58382i	0.564006	−	0.409774i	−0.268917	−	0.963163i	$-0.586666\pi$
$547$	13.1910	−	9.58382i	0.564006	−	0.409774i	0.832923	+	0.553389i	$0.186666\pi$
$548$	15.2076	+	11.0490i	0.649639	+	0.471990i
$549$	−15.2892			−0.652528
$550$	9.41603	+	13.0888i	0.401501	+	0.558106i
$551$	−0.238712			−0.0101695
$552$	−1.56510	−	1.13711i	−0.0666151	−	0.0483987i
$553$	43.5773	−	31.6607i	1.85309	−	1.34635i
$554$	−7.12154	−	21.9179i	−0.302565	−	0.931201i
$555$	9.39860	+	9.01996i	0.398948	+	0.382876i
$556$	8.20698			0.348053
$557$	5.01346	−	3.64249i	0.212427	−	0.154337i	−0.476484	−	0.879183i	$-0.658089\pi$
$557$	5.01346	−	3.64249i	0.212427	−	0.154337i	0.688911	+	0.724846i	$0.258089\pi$
$558$	−0.155068	+	0.477249i	−0.00656453	+	0.0202036i
$559$	6.00592	−	18.4843i	0.254023	−	0.781803i
$560$	6.18056	+	0.849085i	0.261177	+	0.0358804i
$561$	−21.4107	−	0.981305i	−0.903962	−	0.0414307i
$562$	18.3726	+	13.3485i	0.775002	+	0.563072i
$563$	−2.28117	+	7.02071i	−0.0961397	+	0.295887i	−0.987549	−	0.157312i	$-0.949717\pi$
$563$	−2.28117	+	7.02071i	−0.0961397	+	0.295887i	0.891409	+	0.453199i	$0.149717\pi$
$564$	−3.91867			−0.165006
$565$	8.90565	−	4.77070i	0.374664	−	0.200705i
$566$	9.80106	−	7.12089i	0.411969	−	0.299313i
$567$	3.58380			0.150505
$568$	−5.22788	+	3.79828i	−0.219357	+	0.159372i
$569$	9.56704	−	29.4443i	0.401071	−	1.23437i	−0.523060	−	0.852296i	$-0.675210\pi$
$569$	9.56704	−	29.4443i	0.401071	−	1.23437i	0.924131	−	0.382075i	$-0.124790\pi$
$570$	−2.00444	−	0.275370i	−0.0839569	−	0.0115340i
$571$	−4.26493	+	13.1261i	−0.178482	+	0.549310i	−0.999775	−	0.0211955i	$-0.993253\pi$
$571$	−4.26493	+	13.1261i	−0.178482	+	0.549310i	0.821294	+	0.570506i	$0.193253\pi$
$572$	7.41787	+	5.92673i	0.310157	+	0.247809i
$573$	14.3636	−	10.4358i	0.600048	−	0.435961i
$574$	13.1578	+	40.4956i	0.549197	+	1.69026i
$575$	1.80441	−	2.71128i	0.0752493	−	0.113068i
$576$	−5.33672	+	3.87735i	−0.222363	+	0.161556i
$577$	0.950761	+	2.92614i	0.0395807	+	0.121817i	0.968894	−	0.247474i	$-0.0796005\pi$
$577$	0.950761	+	2.92614i	0.0395807	+	0.121817i	−0.929314	+	0.369291i	$0.879601\pi$
$578$	−19.4781	−	14.1516i	−0.810180	−	0.588630i
$579$	−2.84124	−	8.74443i	−0.118078	−	0.363406i
$580$	−0.436437	−	0.418854i	−0.0181220	−	0.0173920i
$581$	−10.1279	+	7.35834i	−0.420175	+	0.305275i
$582$	3.29282			0.136492
$583$	20.7160	+	16.5517i	0.857971	+	0.685502i
$584$	−19.7220	−	14.3289i	−0.816104	−	0.592934i
$585$	2.64389	−	5.46372i	0.109312	−	0.225897i
$586$	−15.7311			−0.649846
$587$	27.7138			1.14387			0.571935	−	0.820299i	$-0.306193\pi$
$587$	27.7138			1.14387			0.571935	+	0.820299i	$0.306193\pi$
$588$	−4.98583	+	3.62242i	−0.205612	+	0.149386i
$589$	0.148418	+	0.456784i	0.00611547	+	0.0188215i
$590$	−5.44527	+	11.2529i	−0.224178	+	0.463274i
$591$	−0.228584	−	0.703511i	−0.00940271	−	0.0289386i
$592$	−3.66915	+	2.66579i	−0.150801	+	0.109563i
$593$	6.15688			0.252833			0.126416	−	0.991977i	$-0.459652\pi$
$593$	6.15688			0.252833			0.126416	+	0.991977i	$0.459652\pi$
$594$	−2.69293	+	1.77403i	−0.110492	+	0.0727895i
$595$	−37.3637	−	35.8585i	−1.53176	−	1.47005i
$596$	−16.4139			−0.672339
$597$	−20.7827	+	15.0995i	−0.850580	+	0.617982i
$598$	−0.531249	+	1.63501i	−0.0217244	+	0.0668607i
$599$	4.89942	−	15.0789i	0.200185	−	0.616106i	−0.799692	−	0.600411i	$-0.795004\pi$
$599$	4.89942	−	15.0789i	0.200185	−	0.616106i	0.999877	−	0.0156954i	$-0.00499621\pi$
$600$	−9.21504	−	11.6451i	−0.376203	−	0.475410i
$601$	−30.9273	+	22.4700i	−1.26155	+	0.916571i	−0.998833	−	0.0483018i	$-0.984619\pi$
$601$	−30.9273	+	22.4700i	−1.26155	+	0.916571i	−0.262719	+	0.964873i	$0.584619\pi$
$602$	−24.9490			−1.01684
$603$	−0.432394			−0.0176084
$604$	−4.53581	+	13.9598i	−0.184560	+	0.568016i
$605$	22.6533	−	9.58279i	0.920986	−	0.389596i
$606$	−2.57769	−	7.93331i	−0.104711	−	0.322269i
$607$	−11.9797	−	36.8696i	−0.486239	−	1.49649i	−0.830178	−	0.557499i	$-0.811761\pi$
$607$	−11.9797	−	36.8696i	−0.486239	−	1.49649i	0.343938	−	0.938992i	$-0.388239\pi$
$608$	−1.49053	+	4.58737i	−0.0604488	+	0.186042i
$609$	−0.919284			−0.0372512
$610$	32.9315	+	4.52413i	1.33336	+	0.183176i
$611$	3.11681	+	9.59257i	0.126093	+	0.388074i
$612$	6.81538			0.275496
$613$	−3.45069	−	10.6201i	−0.139372	−	0.428943i	0.856872	−	0.515529i	$-0.172404\pi$
$613$	−3.45069	−	10.6201i	−0.139372	−	0.428943i	−0.996244	+	0.0865854i	$0.972404\pi$
$614$	−6.18078	−	4.49060i	−0.249436	−	0.181226i
$615$	11.9018	−	24.5956i	0.479926	−	0.991789i
$616$	12.4347	−	33.0395i	0.501006	−	1.33120i
$617$	4.35213	+	13.3945i	0.175210	+	0.539241i	0.999643	−	0.0267185i	$-0.00850577\pi$
$617$	4.35213	+	13.3945i	0.175210	+	0.539241i	−0.824433	+	0.565960i	$0.808506\pi$
$618$	−1.17052	−	3.60250i	−0.0470853	−	0.144914i
$619$	5.97154	−	18.3785i	0.240016	−	0.738694i	−0.756400	−	0.654109i	$-0.773044\pi$
$619$	5.97154	−	18.3785i	0.240016	−	0.738694i	0.996416	−	0.0845850i	$-0.0269564\pi$
$620$	−0.530141	+	1.09556i	−0.0212910	+	0.0439988i
$621$	0.526966	+	0.382863i	0.0211464	+	0.0153638i
$622$	−19.0446	−	13.8367i	−0.763620	−	0.554802i
$623$	17.8145	−	54.8274i	0.713723	−	2.19661i
$624$	1.70965	+	1.24213i	0.0684407	+	0.0497251i
$625$	18.9503	−	16.3060i	0.758012	−	0.652240i
$626$	−7.69172			−0.307423
$627$	−1.08717	+	2.88867i	−0.0434174	+	0.115362i
$628$	−3.42095	+	10.5286i	−0.136511	+	0.420137i
$629$	37.6477			1.50111
$630$	−7.71915	−	1.06046i	−0.307538	−	0.0422496i
$631$	−10.4292	−	7.57729i	−0.415182	−	0.301647i	0.360514	−	0.932754i	$-0.382601\pi$
$631$	−10.4292	−	7.57729i	−0.415182	−	0.301647i	−0.775696	+	0.631106i	$0.782601\pi$
$632$	13.7943	−	42.4546i	0.548709	−	1.68875i
$633$	1.99351			0.0792350
$634$	−32.5043			−1.29091
$635$	2.70754	−	1.45041i	0.107445	−	0.0575579i
$636$	−6.82140	−	4.95604i	−0.270486	−	0.196520i
$637$	12.8330	+	9.32370i	0.508461	+	0.369418i
$638$	0.690767	−	0.455059i	0.0273477	−	0.0180160i
$639$	1.76022	−	1.27887i	0.0696331	−	0.0505914i
$640$	−7.79038	+	4.17326i	−0.307942	+	0.164963i
$641$	7.04396	+	21.6791i	0.278220	+	0.856272i	0.988349	+	0.152201i	$0.0486363\pi$
$641$	7.04396	+	21.6791i	0.278220	+	0.856272i	−0.710130	+	0.704071i	$0.751364\pi$
$642$	9.54929	+	6.93796i	0.376880	+	0.273820i
$643$	6.32645	−	19.4708i	0.249491	−	0.767854i	−0.745374	−	0.666646i	$-0.767729\pi$
$643$	6.32645	−	19.4708i	0.249491	−	0.767854i	0.994865	−	0.101208i	$-0.0322707\pi$
$644$	−2.46188			−0.0970118
$645$	11.5511	+	11.0857i	0.454824	+	0.436501i
$646$	−4.73061	+	3.43699i	−0.186123	+	0.135227i
$647$	18.1640			0.714100			0.357050	−	0.934085i	$-0.383783\pi$
$647$	18.1640			0.714100			0.357050	+	0.934085i	$0.383783\pi$
$648$	2.40280	−	1.74574i	0.0943908	−	0.0685790i
$649$	14.8989	+	11.9039i	0.584832	+	0.467269i
$650$	−7.31142	+	10.9860i	−0.286778	+	0.430906i
$651$	0.571562	+	1.75909i	0.0224013	+	0.0689440i
$652$	4.08098			0.159824
$653$	−1.95918	−	6.02973i	−0.0766686	−	0.235962i	0.905376	−	0.424611i	$-0.139589\pi$
$653$	−1.95918	−	6.02973i	−0.0766686	−	0.235962i	−0.982045	+	0.188649i	$0.939589\pi$
$654$	−5.13086	−	3.72779i	−0.200632	−	0.145768i
$655$	−44.2338	+	23.6958i	−1.72836	+	0.925871i
$656$	7.69617	+	5.59160i	0.300485	+	0.218315i
$657$	6.64037	+	4.82451i	0.259065	+	0.188222i
$658$	10.4747	−	7.61032i	0.408346	−	0.296681i
$659$	−2.89285	−	2.10178i	−0.112689	−	0.0818736i	0.530013	−	0.847989i	$-0.322187\pi$
$659$	−2.89285	−	2.10178i	−0.112689	−	0.0818736i	−0.642703	+	0.766116i	$0.722187\pi$
$660$	−7.05627	+	3.37376i	−0.274665	+	0.131324i
$661$	−26.7112	+	19.4068i	−1.03895	+	0.754839i	−0.970080	−	0.242787i	$-0.921938\pi$
$661$	−26.7112	+	19.4068i	−1.03895	+	0.754839i	−0.0688670	+	0.997626i	$0.521938\pi$
$662$	0.844311	−	2.59852i	0.0328151	−	0.100994i
$663$	−5.42079	−	16.6835i	−0.210526	−	0.647932i
$664$	−3.20597	+	9.86697i	−0.124416	+	0.382913i
$665$	−6.57373	+	3.52151i	−0.254918	+	0.136558i
$666$	4.58254	−	3.32941i	0.177570	−	0.129012i
$667$	−0.135173	−	0.0982086i	−0.00523390	−	0.00380265i
$668$	7.07817	+	5.14259i	0.273863	+	0.198973i
$669$	−9.30794	+	6.76261i	−0.359866	+	0.261458i
$670$	0.931334	+	0.127947i	0.0359806	+	0.00494301i
$671$	17.8614	−	47.4588i	0.689533	−	1.83213i
$672$	−5.74005	+	17.6661i	−0.221427	+	0.681483i
$673$	−5.79638	−	4.21132i	−0.223434	−	0.162334i	0.470437	−	0.882434i	$-0.344096\pi$
$673$	−5.79638	−	4.21132i	−0.223434	−	0.162334i	−0.693871	+	0.720099i	$0.744096\pi$
$674$	−24.9644	−	18.1377i	−0.961593	−	0.698638i
$675$	3.10269	+	3.92089i	0.119422	+	0.150915i
$676$	1.83530	−	5.64847i	0.0705884	−	0.217249i
$677$	7.31928	+	22.5264i	0.281303	+	0.865761i	0.987483	+	0.157728i	$0.0504170\pi$
$677$	7.31928	+	22.5264i	0.281303	+	0.865761i	−0.706180	+	0.708033i	$0.749583\pi$
$678$	−1.35753	−	4.17804i	−0.0521355	−	0.160456i
$679$	9.81902	−	7.13394i	0.376819	−	0.273775i
$680$	−42.5183	−	5.84115i	−1.63050	−	0.223998i
$681$	−6.82733	−	21.0124i	−0.261624	−	0.805196i
$682$	−1.30026	−	1.03888i	−0.0497894	−	0.0397808i
$683$	0.166488	+	0.512397i	0.00637048	+	0.0196063i	0.954191	−	0.299197i	$-0.0967189\pi$
$683$	0.166488	+	0.512397i	0.00637048	+	0.0196063i	−0.947821	+	0.318804i	$0.896719\pi$
$684$	0.303284	−	0.933412i	0.0115963	−	0.0356899i
$685$	28.7555	+	27.5970i	1.09869	+	1.05443i
$686$	−1.24519	+	3.83230i	−0.0475416	+	0.146318i
$687$	3.37663	−	2.45326i	0.128826	−	0.0935978i
$688$	−4.50947	+	3.27632i	−0.171922	+	0.124909i
$689$	−6.70638	+	20.6401i	−0.255493	+	0.786326i
$690$	−1.02174	−	0.980581i	−0.0388971	−	0.0373301i
$691$	−13.0934	+	40.2972i	−0.498095	+	1.53298i	0.313982	+	0.949429i	$0.398337\pi$
$691$	−13.0934	+	40.2972i	−0.498095	+	1.53298i	−0.812077	+	0.583550i	$0.801663\pi$
$692$	4.85192	+	14.9327i	0.184442	+	0.567655i
$693$	−4.18672	+	11.1243i	−0.159040	+	0.422579i
$694$	4.28305	+	13.1819i	0.162582	+	0.500377i
$695$	17.2389	+	2.36827i	0.653907	+	0.0898337i
$696$	−0.616344	+	0.447800i	−0.0233625	+	0.0169738i
$697$	−24.4023	−	75.1025i	−0.924303	−	2.84471i
$698$	1.75649	+	5.40593i	0.0664842	+	0.204617i
$699$	1.97556	−	6.08016i	0.0747226	−	0.229973i
$700$	−18.1978	−	5.09619i	−0.687810	−	0.192618i
$701$	−9.96420	−	7.23941i	−0.376343	−	0.273429i	0.383494	−	0.923544i	$-0.374721\pi$
$701$	−9.96420	−	7.23941i	−0.376343	−	0.273429i	−0.759836	+	0.650115i	$0.774721\pi$
$702$	−2.13525	−	1.55135i	−0.0805897	−	0.0585519i
$703$	1.67532	−	5.15610i	0.0631858	−	0.194466i
$704$	−5.80101	−	21.0952i	−0.218634	−	0.795055i
$705$	−8.23122	−	1.13080i	−0.310006	−	0.0425885i
$706$	6.97648	−	5.06871i	0.262563	−	0.190763i
$707$	−24.8741	−	18.0721i	−0.935488	−	0.679672i
$708$	−4.90592	−	3.56436i	−0.184376	−	0.133957i
$709$	23.4857	−	17.0633i	0.882023	−	0.640827i	−0.0517627	−	0.998659i	$-0.516484\pi$
$709$	23.4857	−	17.0633i	0.882023	−	0.640827i	0.933786	+	0.357832i	$0.116484\pi$
$710$	−4.16976	+	2.23371i	−0.156488	+	0.0838298i
$711$	−4.64453	+	14.2944i	−0.174183	+	0.536081i
$712$	−14.7635	−	45.4375i	−0.553287	−	1.70284i
$713$	−0.103883	+	0.319719i	−0.00389045	+	0.0119736i
$714$	−18.2177	+	13.2359i	−0.681780	+	0.495342i
$715$	13.8711	+	14.5897i	0.518749	+	0.545625i
$716$	10.5451	+	7.66149i	0.394090	+	0.286324i
$717$	6.79219	−	4.93481i	0.253659	−	0.184294i
$718$	−2.71513	−	1.97266i	−0.101328	−	0.0736190i
$719$	−21.2601	−	15.4463i	−0.792867	−	0.576051i	0.115946	−	0.993256i	$-0.463010\pi$
$719$	−21.2601	−	15.4463i	−0.792867	−	0.576051i	−0.908813	+	0.417204i	$0.863010\pi$
$720$	−1.53448	+	0.822011i	−0.0571867	+	0.0306345i
$721$	−11.2953	−	8.20651i	−0.420659	−	0.305626i
$722$	−5.44849	−	16.7687i	−0.202772	−	0.624068i
$723$	−19.3349			−0.719072
$724$	−1.90578	−	5.86538i	−0.0708277	−	0.217985i
$725$	−0.795873	−	1.00575i	−0.0295580	−	0.0373526i
$726$	−2.36073	−	10.4315i	−0.0876151	−	0.387151i
$727$	−5.59717	+	4.06658i	−0.207588	+	0.150821i	−0.686721	−	0.726921i	$-0.740951\pi$
$727$	−5.59717	+	4.06658i	−0.207588	+	0.150821i	0.479134	+	0.877742i	$0.340951\pi$
$728$	28.8930			1.07084
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−12.8751	−	12.3564i	−0.476530	−	0.457332i
$731$	46.2699			1.71135
$732$	−4.98273	+	15.3353i	−0.184167	+	0.566808i
$733$	−6.65581	−	4.83573i	−0.245838	−	0.178612i	0.458042	−	0.888930i	$-0.348551\pi$
$733$	−6.65581	−	4.83573i	−0.245838	−	0.178612i	−0.703880	+	0.710319i	$0.748551\pi$
$734$	−4.44332	−	13.6751i	−0.164006	−	0.504759i
$735$	−11.5181	+	6.17019i	−0.424852	+	0.227591i
$736$	−2.73132	+	1.98442i	−0.100678	+	0.0731467i
$737$	0.505138	−	1.34218i	0.0186070	−	0.0494398i
$738$	−9.61205	−	6.98357i	−0.353825	−	0.257069i
$739$	−8.19337	−	5.95283i	−0.301398	−	0.218978i	0.426799	−	0.904347i	$-0.359641\pi$
$739$	−8.19337	−	5.95283i	−0.301398	−	0.218978i	−0.728197	+	0.685368i	$0.759641\pi$
$740$	12.1101	−	6.48731i	0.445176	−	0.238478i
$741$	−2.52614			−0.0927999
$742$	27.8587			1.02273
$743$	10.3747	−	31.9301i	0.380612	−	1.17140i	−0.559002	−	0.829166i	$-0.688816\pi$
$743$	10.3747	−	31.9301i	0.380612	−	1.17140i	0.939614	−	0.342236i	$-0.111184\pi$
$744$	1.24009	+	0.900981i	0.0454641	+	0.0330316i
$745$	−34.4776	−	4.73653i	−1.26316	−	0.173533i
$746$	−14.0998			−0.516232
$747$	1.07944	−	3.32219i	0.0394948	−	0.121552i
$748$	−7.96198	+	21.1554i	−0.291119	+	0.773518i
$749$	43.5066			1.58970
$750$	−5.52268	−	9.36330i	−0.201660	−	0.341899i
$751$	18.7124	+	13.5953i	0.682825	+	0.496101i	0.874294	−	0.485398i	$-0.161325\pi$
$751$	18.7124	+	13.5953i	0.682825	+	0.496101i	−0.191469	+	0.981499i	$0.561325\pi$
$752$	0.893885	−	2.75109i	0.0325966	−	0.100322i
$753$	−7.35958	−	5.34705i	−0.268198	−	0.194857i
$754$	0.547715	+	0.397938i	0.0199466	+	0.0144920i
$755$	−13.5559	+	28.0139i	−0.493349	+	1.01953i
$756$	1.16795	−	3.59459i	0.0424780	−	0.130734i
$757$	12.0656	+	37.1342i	0.438533	+	1.34966i	0.889423	+	0.457085i	$0.151107\pi$
$757$	12.0656	+	37.1342i	0.438533	+	1.34966i	−0.450890	+	0.892579i	$0.648893\pi$
$758$	10.7262	+	33.0118i	0.389592	+	1.19904i
$759$	−1.80405	+	1.18846i	−0.0654830	+	0.0431384i
$760$	−2.69204	+	5.56322i	−0.0976506	+	0.201799i
$761$	36.1090	+	26.2347i	1.30895	+	0.951007i	1.00000		7.12834e-5i	$-2.26902e-5\pi$
$761$	36.1090	+	26.2347i	1.30895	+	0.951007i	0.308949	+	0.951079i	$0.400023\pi$
$762$	−0.412722	−	1.27023i	−0.0149513	−	0.0460155i
$763$	−23.3762			−0.846276
$764$	−5.78612	−	17.8079i	−0.209335	−	0.644266i
$765$	14.3158	+	1.96670i	0.517589	+	0.0711063i
$766$	14.3146			0.517207
$767$	−4.82320	+	14.8443i	−0.174155	+	0.535995i
$768$	5.26441	+	16.2022i	0.189963	+	0.584646i
$769$	2.81057	+	8.65005i	0.101352	+	0.311929i	0.988857	−	0.148869i	$-0.0475633\pi$
$769$	2.81057	+	8.65005i	0.101352	+	0.311929i	−0.887505	+	0.460798i	$0.847563\pi$
$770$	12.3095	−	22.7219i	0.443604	−	0.818840i
$771$	−7.42979	+	22.8665i	−0.267577	+	0.823518i
$772$	−9.69671			−0.348992
$773$	7.44562			0.267800			0.133900	−	0.990995i	$-0.457250\pi$
$773$	7.44562			0.267800			0.133900	+	0.990995i	$0.457250\pi$
$774$	5.63205	−	4.09193i	0.202440	−	0.147081i
$775$	−1.42971	+	2.14826i	−0.0513568	+	0.0771677i
$776$	3.10820	−	9.56606i	0.111578	−	0.343402i
$777$	6.45169	−	19.8562i	0.231453	−	0.712339i
$778$	−0.903859	+	0.656692i	−0.0324049	+	0.0235435i
$779$	−11.3717			−0.407433
$780$	−4.61854	−	4.43247i	−0.165370	−	0.158708i
$781$	1.91336	+	6.95786i	0.0684653	+	0.248972i
$782$	−4.09277			−0.146357
$783$	0.207522	−	0.150773i	0.00741622	−	0.00538820i
$784$	−1.40580	−	4.32660i	−0.0502070	−	0.154521i
$785$	−10.2240	+	21.1283i	−0.364909	+	0.754101i
$786$	6.74275	+	20.7520i	0.240506	+	0.740201i
$787$	29.3956	−	21.3571i	1.04784	−	0.761300i	0.0760390	−	0.997105i	$-0.475773\pi$
$787$	29.3956	−	21.3571i	1.04784	−	0.761300i	0.971800	+	0.235805i	$0.0757726\pi$
$788$	−0.780124			−0.0277908
$789$	21.9146			0.780181
$790$	14.2336	−	29.4144i	0.506409	−	1.04652i
$791$	−13.0998	−	9.51758i	−0.465776	−	0.338406i
$792$	2.61184	+	9.49787i	0.0928077	+	0.337492i
$793$	41.5025			1.47380
$794$	5.75503	−	4.18128i	0.204239	−	0.148388i
$795$	−12.8983	−	12.3787i	−0.457455	−	0.439026i
$796$	8.37195	+	25.7662i	0.296736	+	0.913259i
$797$	−9.57302	−	6.95521i	−0.339094	−	0.246366i	0.405186	−	0.914234i	$-0.367207\pi$
$797$	−9.57302	−	6.95521i	−0.339094	−	0.246366i	−0.744279	+	0.667868i	$0.767207\pi$
$798$	1.00206	+	3.08403i	0.0354726	+	0.109173i
$799$	−19.4262	+	14.1140i	−0.687250	+	0.499316i
$800$	−24.2972	+	9.01450i	−0.859035	+	0.318711i
$801$	4.97085	+	15.2987i	0.175636	+	0.540553i
$802$	−18.3780	+	13.3524i	−0.648948	+	0.471489i
$803$	−22.7331	+	14.9760i	−0.802234	+	0.528491i
$804$	−0.140916	+	0.433696i	−0.00496974	+	0.0152953i
$805$	−5.17122	−	0.710422i	−0.182262	−	0.0250391i
$806$	0.420930	−	1.29549i	0.0148266	−	0.0456317i
$807$	2.59057	−	1.88216i	0.0911922	−	0.0662550i
$808$	−25.4804			−0.896398
$809$	18.3659	−	13.3436i	0.645711	−	0.469136i	−0.216097	−	0.976372i	$-0.569333\pi$
$809$	18.3659	−	13.3436i	0.645711	−	0.469136i	0.861807	+	0.507236i	$0.169333\pi$
$810$	1.91647	−	1.02664i	0.0673380	−	0.0360725i
$811$	30.9271			1.08600			0.542998	−	0.839734i	$-0.317289\pi$
$811$	30.9271			1.08600			0.542998	+	0.839734i	$0.317289\pi$
$812$	−0.299593	+	0.922052i	−0.0105136	+	0.0323577i
$813$	17.5291	+	12.7356i	0.614772	+	0.446658i
$814$	4.98122	+	18.1140i	0.174592	+	0.634897i
$815$	8.57216	+	1.17764i	0.300270	+	0.0412510i
$816$	−1.55465	+	4.78473i	−0.0544237	+	0.167499i
$817$	2.05901	−	6.33697i	0.0720355	−	0.221702i
$818$	6.35071	−	4.61406i	0.222047	−	0.161327i
$819$	−9.72820			−0.339931
$820$	−20.7909	−	19.9533i	−0.726048	−	0.696798i
$821$	12.4683	+	38.3734i	0.435145	+	1.33924i	0.892938	+	0.450180i	$0.148640\pi$
$821$	12.4683	+	38.3734i	0.435145	+	1.33924i	−0.457792	+	0.889059i	$0.651360\pi$
$822$	14.0205	−	10.1865i	0.489021	−	0.355295i
$823$	−35.9438	−	26.1147i	−1.25292	−	0.910302i	−0.254535	−	0.967064i	$-0.581922\pi$
$823$	−35.9438	−	26.1147i	−1.25292	−	0.910302i	−0.998388	+	0.0567619i	$0.981922\pi$
$824$	−11.5706			−0.403081
$825$	−15.7954	+	5.05042i	−0.549924	+	0.175833i
$826$	20.0359			0.697136
$827$	37.4606	+	27.2168i	1.30263	+	0.946419i	0.999978	−	0.00668037i	$-0.00212644\pi$
$827$	37.4606	+	27.2168i	1.30263	+	0.946419i	0.302657	+	0.953100i	$0.402126\pi$
$828$	0.555753	−	0.403778i	0.0193138	−	0.0140323i
$829$	−5.19811	−	15.9981i	−0.180538	−	0.555639i	0.819305	−	0.573358i	$-0.194360\pi$
$829$	−5.19811	−	15.9981i	−0.180538	−	0.555639i	−0.999843	+	0.0177192i	$0.994360\pi$
$830$	−3.30806	+	6.83626i	−0.114825	+	0.237290i
$831$	23.7023			0.822224
$832$	14.4865	−	10.5251i	0.502229	−	0.364891i
$833$	−11.6695	+	35.9151i	−0.404326	+	1.24439i
$834$	2.33812	−	7.19600i	0.0809626	−	0.249177i
$835$	13.3838	+	12.8446i	0.463166	+	0.444506i
$836$	2.54306	+	2.03186i	0.0879537	+	0.0702733i
$837$	−0.417537	−	0.303358i	−0.0144322	−	0.0104856i
$838$	9.61099	−	29.5796i	0.332006	−	1.02181i
$839$	−21.5946			−0.745527			−0.372763	−	0.927926i	$-0.621590\pi$
$839$	−21.5946			−0.745527			−0.372763	+	0.927926i	$0.621590\pi$
$840$	−10.3671	+	21.4241i	−0.357699	+	0.739202i
$841$	23.4083	−	17.0071i	0.807181	−	0.586452i
$842$	11.0451			0.380638
$843$	−18.8960	+	13.7287i	−0.650812	+	0.472843i
$844$	0.649682	−	1.99952i	0.0223630	−	0.0688262i
$845$	5.48504	−	11.3351i	0.188691	−	0.389938i
$846$	−1.11641	+	3.43595i	−0.0383829	+	0.118130i
$847$	−29.6396	−	25.9917i	−1.01843	−	0.893086i
$848$	5.03540	−	3.65843i	0.172916	−	0.125631i
$849$	3.85032	+	11.8501i	0.132143	+	0.406693i
$850$	−30.2529	−	8.47218i	−1.03767	−	0.290593i
$851$	3.06994	−	2.23044i	0.105236	−	0.0764586i
$852$	−0.709072	−	2.18230i	−0.0242924	−	0.0747644i
$853$	41.0089	+	29.7947i	1.40412	+	1.02015i	0.994145	+	0.108052i	$0.0344613\pi$
$853$	41.0089	+	29.7947i	1.40412	+	1.02015i	0.409971	+	0.912098i	$0.365539\pi$
$854$	−16.4631	−	50.6683i	−0.563357	−	1.73383i
$855$	0.906405	−	1.87313i	0.0309984	−	0.0640595i
$856$	29.1695	−	21.1929i	0.996994	−	0.724358i
$857$	−8.21047			−0.280464			−0.140232	−	0.990119i	$-0.544785\pi$
$857$	−8.21047			−0.280464			−0.140232	+	0.990119i	$0.544785\pi$
$858$	7.30996	−	4.81561i	0.249558	−	0.164402i
$859$	−44.8410	−	32.5789i	−1.52995	−	1.11158i	−0.956264	−	0.292504i	$-0.905512\pi$
$859$	−44.8410	−	32.5789i	−1.52995	−	1.11158i	−0.573690	−	0.819073i	$-0.694488\pi$
$860$	14.8836	−	7.97306i	0.507527	−	0.271879i
$861$	−43.7926			−1.49245
$862$	14.3597			0.489093
$863$	37.8791	−	27.5208i	1.28942	−	0.936819i	0.289627	−	0.957140i	$-0.406469\pi$
$863$	37.8791	−	27.5208i	1.28942	−	0.936819i	0.999794	+	0.0203209i	$0.00646879\pi$
$864$	−1.60167	−	4.92943i	−0.0544898	−	0.167702i
$865$	5.88243	+	32.7664i	0.200009	+	1.11409i
$866$	3.02277	+	9.30314i	0.102718	+	0.316133i
$867$	20.0329	−	14.5548i	0.680354	−	0.494306i
$868$	1.95065			0.0662095
$869$	−38.9448	−	31.1161i	−1.32111	−	1.05554i
$870$	−0.491596	+	0.263345i	−0.0166667	+	0.00892823i
$871$	1.17373			0.0397704
$872$	−15.6729	+	11.3870i	−0.530750	+	0.385612i
$873$	−1.04652	+	3.22087i	−0.0354195	+	0.109010i
$874$	−0.182128	+	0.560531i	−0.00616056	+	0.0189603i
$875$	−36.7540	−	15.9559i	−1.24251	−	0.539408i
$876$	7.00312	−	5.08807i	0.236614	−	0.171910i
$877$	−11.9324			−0.402928			−0.201464	−	0.979496i	$-0.564570\pi$
$877$	−11.9324			−0.402928			−0.201464	+	0.979496i	$0.564570\pi$
$878$	−21.4343			−0.723373
$879$	4.99966	−	15.3874i	0.168634	−	0.519003i
$880$	−0.758943	−	5.72343i	−0.0255840	−	0.192937i
$881$	14.2507	+	43.8592i	0.480118	+	1.47765i	0.838928	+	0.544242i	$0.183183\pi$
$881$	14.2507	+	43.8592i	0.480118	+	1.47765i	−0.358810	+	0.933411i	$0.616817\pi$
$882$	1.75576	+	5.40366i	0.0591194	+	0.181951i
$883$	11.0638	−	34.0508i	0.372325	−	1.14590i	−0.572940	−	0.819597i	$-0.694197\pi$
$883$	11.0638	−	34.0508i	0.372325	−	1.14590i	0.945265	−	0.326302i	$-0.105803\pi$
$884$	−18.5003			−0.622234
$885$	−9.27639	−	8.90267i	−0.311822	−	0.299260i
$886$	−10.0443	−	30.9130i	−0.337443	−	1.03854i
$887$	−37.4380			−1.25704			−0.628522	−	0.777792i	$-0.716340\pi$
$887$	−37.4380			−1.25704			−0.628522	+	0.777792i	$0.716340\pi$
$888$	−5.34674	−	16.4556i	−0.179425	−	0.552213i
$889$	−3.98268	−	2.89358i	−0.133575	−	0.0970477i
$890$	−6.17980	−	34.4228i	−0.207147	−	1.15385i
$891$	−0.879401	−	3.19791i	−0.0294611	−	0.107134i
$892$	3.74954	+	11.5399i	0.125544	+	0.386384i
$893$	1.06854	+	3.28862i	0.0357572	+	0.110049i
$894$	−4.67623	+	14.3919i	−0.156396	+	0.481339i
$895$	19.9394	+	19.1361i	0.666499	+	0.639648i
$896$	11.4593	+	8.32568i	0.382829	+	0.278141i
$897$	−1.43045	−	1.03928i	−0.0477612	−	0.0347006i
$898$	10.2288	−	31.4809i	0.341338	−	1.05053i
$899$	0.107103	+	0.0778148i	0.00357208	+	0.00259527i
$900$	4.94385	−	1.83422i	0.164795	−	0.0611406i
$901$	−51.6663			−1.72125
$902$	32.9066	−	21.6780i	1.09567	−	0.721798i
$903$	7.92927	−	24.4038i	0.263870	−	0.812108i
$904$	−13.4191			−0.446313
$905$	−2.31055	−	12.8703i	−0.0768053	−	0.427822i
$906$	10.9479	+	7.95414i	0.363721	+	0.264259i
$907$	8.89677	−	27.3814i	0.295412	−	0.909185i	−0.687670	−	0.726023i	$-0.741367\pi$
$907$	8.89677	−	27.3814i	0.295412	−	0.909185i	0.983083	−	0.183162i	$-0.0586334\pi$
$908$	−23.3007			−0.773259
$909$	8.57920			0.284554
$910$	20.9536	+	2.87860i	0.694605	+	0.0954248i
$911$	8.74450	+	6.35325i	0.289718	+	0.210493i	0.723145	−	0.690696i	$-0.242696\pi$
$911$	8.74450	+	6.35325i	0.289718	+	0.210493i	−0.433427	+	0.901189i	$0.642696\pi$
$912$	0.586118	+	0.425839i	0.0194083	+	0.0141010i
$913$	9.05124	+	7.23176i	0.299552	+	0.239336i
$914$	17.1047	−	12.4273i	0.565774	−	0.411059i
$915$	−14.8916	+	30.7741i	−0.492300	+	1.01736i
$916$	−1.36021	−	4.18631i	−0.0449427	−	0.138319i
$917$	65.0660	+	47.2732i	2.14867	+	1.56110i
$918$	1.94167	−	5.97583i	0.0640845	−	0.197232i
$919$	26.9311			0.888374			0.444187	−	0.895934i	$-0.353493\pi$
$919$	26.9311			0.888374			0.444187	+	0.895934i	$0.353493\pi$
$920$	−3.81317	+	2.04269i	−0.125716	+	0.0673455i
$921$	6.35685	−	4.61852i	0.209465	−	0.152185i
$922$	−27.4122			−0.902772
$923$	−4.77810	+	3.47150i	−0.157273	+	0.114266i
$924$	9.79339	+	7.82473i	0.322179	+	0.257415i
$925$	27.3095	−	10.1321i	0.897930	−	0.333141i
$926$	11.2869	+	34.7376i	0.370912	+	1.14155i
$927$	3.89580			0.127955
$928$	0.410845	+	1.26445i	0.0134867	+	0.0415077i
$929$	10.9977	+	7.99033i	0.360824	+	0.262154i	0.753396	−	0.657567i	$-0.228414\pi$
$929$	10.9977	+	7.99033i	0.360824	+	0.262154i	−0.392572	+	0.919721i	$0.628414\pi$
$930$	0.809570	+	0.776955i	0.0265468	+	0.0254774i
$931$	4.39952	+	3.19644i	0.144188	+	0.104759i
$932$	−5.45463	−	3.96302i	−0.178672	−	0.129813i
$933$	19.5871	−	14.2309i	0.641254	−	0.465899i
$934$	25.4331	+	18.4782i	0.832197	+	0.604627i
$935$	−22.8290	+	42.1396i	−0.746589	+	1.37811i
$936$	−6.52239	+	4.73879i	−0.213191	+	0.154892i
$937$	−5.25954	+	16.1872i	−0.171822	+	0.528813i	−0.999474	−	0.0324284i	$-0.989676\pi$
$937$	−5.25954	+	16.1872i	−0.171822	+	0.528813i	0.827652	+	0.561241i	$0.189676\pi$
$938$	−0.465593	−	1.43295i	−0.0152022	−	0.0467874i
$939$	2.44458	−	7.52365i	0.0797759	−	0.245525i
$940$	−3.81675	+	7.88748i	−0.124489	+	0.257261i
$941$	0.0282090	−	0.0204950i	0.000919586	−	0.000668119i	−0.587325	−	0.809351i	$-0.699819\pi$
$941$	0.0282090	−	0.0204950i	0.000919586	−	0.000668119i	0.588245	+	0.808683i	$0.299819\pi$
$942$	8.25703	+	5.99908i	0.269029	+	0.195461i
$943$	−6.43932	−	4.67844i	−0.209693	−	0.152351i
$944$	3.62143	−	2.63113i	0.117868	−	0.0856359i
$945$	3.49058	−	7.21345i	0.113549	−	0.234653i
$946$	6.12204	+	22.2626i	0.199045	+	0.723819i
$947$	−3.63566	+	11.1894i	−0.118143	+	0.363607i	−0.992590	−	0.121515i	$-0.961225\pi$
$947$	−3.63566	+	11.1894i	−0.118143	+	0.363607i	0.874447	+	0.485122i	$0.161225\pi$
$948$	12.8238	+	9.31702i	0.416497	+	0.302603i
$949$	−18.0253	−	13.0961i	−0.585125	−	0.425118i
$950$	−2.50657	+	3.76632i	−0.0813239	+	0.122196i
$951$	10.3305	−	31.7941i	0.334990	−	1.03099i
$952$	21.2557	+	65.4185i	0.688903	+	2.12022i
$953$	5.32019	+	16.3739i	0.172338	+	0.530401i	0.999502	−	0.0315593i	$-0.0100473\pi$
$953$	5.32019	+	16.3739i	0.172338	+	0.530401i	−0.827164	+	0.561960i	$0.810047\pi$
$954$	−6.28891	+	4.56916i	−0.203611	+	0.147932i
$955$	−7.01505	−	39.0753i	−0.227002	−	1.26445i
$956$	−2.73611	−	8.42089i	−0.0884922	−	0.272351i
$957$	0.225576	+	0.820300i	0.00729184	+	0.0265165i
$958$	11.7858	+	36.2730i	0.380782	+	1.17193i
$959$	19.7393	−	60.7512i	0.637414	−	1.96176i
$960$	2.60640	+	14.5182i	0.0841213	+	0.468574i
$961$	−9.49722	+	29.2294i	−0.306362	+	0.942885i
$962$	−12.4393	+	9.03767i	−0.401059	+	0.291386i
$963$	−9.82131	+	7.13560i	−0.316487	+	0.229942i
$964$	−6.30120	+	19.3931i	−0.202948	+	0.624610i
$965$	−20.3681	−	2.79816i	−0.655671	−	0.0900760i
$966$	−0.701378	+	2.15862i	−0.0225665	+	0.0694524i
$967$	−12.8835	−	39.6512i	−0.414304	−	1.27510i	−0.912872	−	0.408246i	$-0.866141\pi$
$967$	−12.8835	−	39.6512i	−0.414304	−	1.27510i	0.498568	−	0.866851i	$-0.333859\pi$
$968$	−32.5333	−	2.98843i	−1.04566	−	0.0960518i
$969$	−1.85841	−	5.71959i	−0.0597006	−	0.183740i
$970$	3.20718	−	6.62778i	0.102976	−	0.212805i
$971$	8.25741	−	5.99936i	0.264993	−	0.192529i	−0.447352	−	0.894358i	$-0.647633\pi$
$971$	8.25741	−	5.99936i	0.264993	−	0.192529i	0.712345	+	0.701829i	$0.247633\pi$
$972$	0.325898	+	1.00301i	0.0104532	+	0.0321716i
$973$	−8.61806	−	26.5237i	−0.276282	−	0.850309i
$974$	5.73533	−	17.6515i	0.183772	−	0.565591i
$975$	−8.42223	−	10.6432i	−0.269727	−	0.340856i
$976$	−9.62948	−	6.99623i	−0.308232	−	0.223944i
$977$	−32.0388	−	23.2775i	−1.02501	−	0.744714i	−0.0577071	−	0.998334i	$-0.518379\pi$
$977$	−32.0388	−	23.2775i	−1.02501	−	0.744714i	−0.967304	+	0.253619i	$0.918379\pi$
$978$	1.16265	−	3.57827i	0.0371774	−	0.114420i
$979$	−53.2953	−	2.44265i	−1.70332	−	0.0780674i
$980$	2.43503	+	13.5637i	0.0777843	+	0.433275i
$981$	5.27702	−	3.83398i	0.168482	−	0.122409i
$982$	26.1766	+	19.0184i	0.835329	+	0.606902i
$983$	−16.6600	−	12.1042i	−0.531372	−	0.386064i	0.289499	−	0.957178i	$-0.406511\pi$
$983$	−16.6600	−	12.1042i	−0.531372	−	0.386064i	−0.820871	+	0.571114i	$0.806511\pi$
$984$	−29.3613	+	21.3322i	−0.936003	+	0.680046i
$985$	−1.63866	−	0.225119i	−0.0522121	−	0.00717289i
$986$	−0.498059	+	1.53287i	−0.0158614	+	0.0488164i
$987$	4.11496	+	12.6645i	0.130980	+	0.403116i
$988$	−0.823263	+	2.53374i	−0.0261915	+	0.0806091i
$989$	3.77303	−	2.74127i	0.119975	−	0.0871672i
$990$	0.947874	+	7.14821i	0.0301254	+	0.227185i
$991$	28.4658	+	20.6816i	0.904247	+	0.656974i	0.939553	−	0.342402i	$-0.111241\pi$
$991$	28.4658	+	20.6816i	0.904247	+	0.656974i	−0.0353062	+	0.999377i	$0.511241\pi$
$992$	2.16414	−	1.57234i	0.0687115	−	0.0499218i
$993$	2.27340	+	1.65172i	0.0721443	+	0.0524159i
$994$	6.13354	+	4.45627i	0.194544	+	0.141344i
$995$	10.1501	+	56.5381i	0.321779	+	1.79238i
$996$	−2.98040	−	2.16539i	−0.0944376	−	0.0686130i
$997$	2.55922	+	7.87646i	0.0810512	+	0.249450i	0.983368	−	0.181623i	$-0.0581351\pi$
$997$	2.55922	+	7.87646i	0.0810512	+	0.249450i	−0.902317	+	0.431073i	$0.858135\pi$
$998$	−5.46789			−0.173083
$999$	1.80024	+	5.54056i	0.0569570	+	0.175296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.o.d.511.12	yes	116
11.9	even	5		825.2.m.d.361.18	yes	116
25.16	even	5		825.2.m.d.16.18	✓	116
275.141	even	5	inner	825.2.o.d.691.12	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.d.16.18	✓	116	25.16	even	5
825.2.m.d.361.18	yes	116	11.9	even	5
825.2.o.d.511.12	yes	116	1.1	even	1	trivial
825.2.o.d.691.12	yes	116	275.141	even	5	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.o (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.786609 - 0.571505i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.325898 - 1.00301i) q^{4} +(-0.395116 - 2.20088i) q^{5} -0.972302 q^{6} +(-2.89935 + 2.10650i) q^{7} +(-0.917787 + 2.82466i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.947013 + 1.95704i) q^{10} +(2.59114 + 2.07027i) q^{11} +(-0.853212 - 0.619895i) q^{12} +(-0.838826 + 2.58164i) q^{13} +3.48453 q^{14} +(-1.61330 - 1.54831i) q^{15} +(0.629821 - 0.457592i) q^{16} -6.46236 q^{17} +(-0.786609 + 0.571505i) q^{18} +(-0.287574 + 0.885062i) q^{19} +(-2.07874 + 1.11357i) q^{20} +(-1.10745 + 3.40839i) q^{21} +(-0.855044 - 3.10934i) q^{22} +(-0.526966 + 0.382863i) q^{23} +(0.917787 + 2.82466i) q^{24} +(-4.68777 + 1.73921i) q^{25} +(2.13525 - 1.55135i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(3.05774 + 2.22158i) q^{28} +(0.0792663 + 0.243957i) q^{29} +(0.384172 + 2.13992i) q^{30} +(0.417537 - 0.303358i) q^{31} +5.18310 q^{32} +(3.31315 + 0.151849i) q^{33} +(5.08335 + 3.69327i) q^{34} +(5.78175 + 5.54882i) q^{35} -1.05463 q^{36} -5.82569 q^{37} +(0.732026 - 0.531848i) q^{38} +(0.838826 + 2.58164i) q^{39} +(6.57937 + 0.903873i) q^{40} +(3.77607 + 11.6215i) q^{41} +(2.81905 - 2.04816i) q^{42} -7.15991 q^{43} +(1.23205 - 3.27364i) q^{44} +(-2.21526 - 0.304332i) q^{45} +0.633324 q^{46} +(3.00606 - 2.18403i) q^{47} +(0.240570 - 0.740400i) q^{48} +(1.80577 - 5.55759i) q^{49} +(4.68141 + 1.31100i) q^{50} +(-5.22816 + 3.79848i) q^{51} +2.86278 q^{52} +7.99496 q^{53} +(-0.300458 + 0.924714i) q^{54} +(3.53261 - 6.52078i) q^{55} +(-3.28916 - 10.1230i) q^{56} +(0.287574 + 0.885062i) q^{57} +(0.0770708 - 0.237199i) q^{58} +5.74994 q^{59} +(-1.02720 + 2.12275i) q^{60} +(-4.72463 - 14.5409i) q^{61} -0.501809 q^{62} +(1.10745 + 3.40839i) q^{63} +(-5.33672 - 3.87735i) q^{64} +(6.01332 + 0.826109i) q^{65} +(-2.51937 - 2.01293i) q^{66} +(-0.133617 - 0.411231i) q^{67} +(2.10607 + 6.48182i) q^{68} +(-0.201283 + 0.619486i) q^{69} +(-1.37680 - 7.66905i) q^{70} +(1.76022 + 1.27887i) q^{71} +(2.40280 + 1.74574i) q^{72} +(-2.53640 + 7.80622i) q^{73} +(4.58254 + 3.32941i) q^{74} +(-2.77020 + 4.16245i) q^{75} +0.981447 q^{76} +(-11.8736 - 0.544197i) q^{77} +(0.815592 - 2.51013i) q^{78} -15.0300 q^{79} +(-1.25596 - 1.20536i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.67148 - 11.2996i) q^{82} +3.49315 q^{83} +3.77957 q^{84} +(2.55338 + 14.2229i) q^{85} +(5.63205 + 4.09193i) q^{86} +(0.207522 + 0.150773i) q^{87} +(-8.22591 + 5.41901i) q^{88} +(-13.0138 + 9.45511i) q^{89} +(1.56862 + 1.50542i) q^{90} +(-3.00618 - 9.25207i) q^{91} +(0.555753 + 0.403778i) q^{92} +(0.159485 - 0.490844i) q^{93} -3.61277 q^{94} +(2.06154 + 0.283214i) q^{95} +(4.19322 - 3.04655i) q^{96} -3.38663 q^{97} +(-4.59663 + 3.33965i) q^{98} +(2.76965 - 1.82457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - q^{2} + 29 q^{3} - 35 q^{4} - 3 q^{5} + 6 q^{6} - 2 q^{7} + q^{8} - 29 q^{9} + 2 q^{10} - 13 q^{11} + 30 q^{12} - 12 q^{14} + 3 q^{15} - 41 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} + 7 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 116 * q - q^2 + 29 * q^3 - 35 * q^4 - 3 * q^5 + 6 * q^6 - 2 * q^7 + q^8 - 29 * q^9 + 2 * q^10 - 13 * q^11 + 30 * q^12 - 12 * q^14 + 3 * q^15 - 41 * q^16 - 14 * q^17 - q^18 - 21 * q^19 + 7 * q^20 + 2 * q^21 + 16 * q^22 + 14 * q^23 - q^24 + 17 * q^25 - 16 * q^26 + 29 * q^27 - 7 * q^28 - 20 * q^29 + 8 * q^30 + 12 * q^31 - 94 * q^32 - 7 * q^33 + 20 * q^34 - 46 * q^35 + 130 * q^36 + 40 * q^37 + 29 * q^38 - 18 * q^40 - 16 * q^41 - 8 * q^42 - 46 * q^43 + 15 * q^44 + 2 * q^45 + 60 * q^46 + 5 * q^47 + 26 * q^48 - 5 * q^49 - 45 * q^50 - 11 * q^51 - 96 * q^52 + 44 * q^53 - 4 * q^54 - 6 * q^55 + 28 * q^56 + 21 * q^57 - 19 * q^58 + 26 * q^59 - 7 * q^60 + 5 * q^61 - 128 * q^62 - 2 * q^63 - 17 * q^64 + 10 * q^65 + 14 * q^66 - 35 * q^67 + 60 * q^68 + 6 * q^69 - 26 * q^70 - 10 * q^71 + 11 * q^72 - 40 * q^73 - 12 * q^74 - 27 * q^75 + 126 * q^76 + q^77 - 19 * q^78 + 126 * q^79 - 114 * q^80 - 29 * q^81 - 21 * q^82 - 78 * q^83 + 12 * q^84 - 6 * q^85 - 54 * q^86 - 5 * q^87 - 41 * q^88 + 13 * q^89 + 2 * q^90 - 25 * q^91 - 28 * q^92 + 43 * q^93 - 66 * q^94 + 49 * q^95 - 21 * q^96 - 80 * q^97 - 34 * q^98 - 3 * q^99

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