LMFDB - Embedded newform 384.2.v.a.229.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			229.23
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.910468 + 1.08215i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-0.342097 + 1.97053i) q^{4} +(2.63552 + 3.21139i) q^{5} +(-1.31308 - 0.525180i) q^{6} +(1.69443 - 1.13218i) q^{7} +(-2.44387 + 1.42390i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(0.910468 + 1.08215i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-0.342097 + 1.97053i) q^{4} +(2.63552 + 3.21139i) q^{5} +(-1.31308 - 0.525180i) q^{6} +(1.69443 - 1.13218i) q^{7} +(-2.44387 + 1.42390i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-1.07565 + 5.77590i) q^{10} +(4.28043 - 1.29845i) q^{11} +(-0.627197 - 1.89911i) q^{12} +(-2.85407 - 2.34227i) q^{13} +(2.76791 + 0.802812i) q^{14} +(-3.83816 - 1.58982i) q^{15} +(-3.76594 - 1.34822i) q^{16} +(-5.40218 + 2.23766i) q^{17} +(1.40560 - 0.155816i) q^{18} +(-0.269906 - 2.74040i) q^{19} +(-7.22974 + 4.09476i) q^{20} +(-0.960647 + 1.79724i) q^{21} +(5.30231 + 3.44986i) q^{22} +(3.31698 - 0.659788i) q^{23} +(1.48408 - 2.40780i) q^{24} +(-2.39162 + 12.0235i) q^{25} +(-0.0638462 - 5.22110i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(1.65133 + 3.72623i) q^{28} +(0.408901 - 1.34797i) q^{29} +(-1.77410 - 5.60095i) q^{30} +(-4.32488 - 4.32488i) q^{31} +(-1.96979 - 5.30282i) q^{32} +(-3.16291 + 3.16291i) q^{33} +(-7.33999 - 3.80866i) q^{34} +(8.10159 + 2.45759i) q^{35} +(1.44837 + 1.37921i) q^{36} +(8.05373 + 0.793223i) q^{37} +(2.71978 - 2.78712i) q^{38} +(3.62121 + 0.720303i) q^{39} +(-11.0136 - 4.09552i) q^{40} +(-1.11095 - 5.58514i) q^{41} +(-2.81952 + 0.596769i) q^{42} +(-3.16625 - 1.69240i) q^{43} +(1.09431 + 8.87889i) q^{44} +(4.13440 - 0.407202i) q^{45} +(3.73399 + 2.98875i) q^{46} +(0.865264 + 2.08893i) q^{47} +(3.95681 - 0.586226i) q^{48} +(-1.08953 + 2.63035i) q^{49} +(-15.1887 + 8.35890i) q^{50} +(3.70947 - 4.52001i) q^{51} +(5.59188 - 4.82273i) q^{52} +(0.581978 + 1.91853i) q^{53} +(-1.16618 + 0.800014i) q^{54} +(15.4510 + 10.3240i) q^{55} +(-2.52886 + 5.17960i) q^{56} +(1.52985 + 2.28958i) q^{57} +(1.83099 - 0.784788i) q^{58} +(9.18901 - 7.54123i) q^{59} +(4.44580 - 7.01933i) q^{60} +(-5.57402 - 10.4283i) q^{61} +(0.742506 - 8.61784i) q^{62} -2.03787i q^{63} +(3.94502 - 6.95966i) q^{64} -15.3387i q^{65} +(-6.30248 - 0.543016i) q^{66} +(3.26315 + 6.10493i) q^{67} +(-2.56129 - 11.4106i) q^{68} +(-2.61429 + 2.14550i) q^{69} +(4.71676 + 11.0047i) q^{70} +(-4.41388 - 6.60584i) q^{71} +(-0.173813 + 2.82308i) q^{72} +(5.61024 + 3.74864i) q^{73} +(6.47427 + 9.43755i) q^{74} +(-3.55861 - 11.7312i) q^{75} +(5.49235 + 0.405626i) q^{76} +(5.78280 - 7.04636i) q^{77} +(2.51752 + 4.57450i) q^{78} +(-4.82549 + 11.6498i) q^{79} +(-5.59555 - 15.6472i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(5.03247 - 6.28731i) q^{82} +(-5.18996 + 0.511166i) q^{83} +(-3.21288 - 2.50781i) q^{84} +(-21.4236 - 11.4511i) q^{85} +(-1.05134 - 4.96723i) q^{86} +(0.274809 + 1.38156i) q^{87} +(-8.61195 + 9.26815i) q^{88} +(5.64347 + 1.12256i) q^{89} +(4.20489 + 4.10329i) q^{90} +(-7.48790 - 0.737494i) q^{91} +(0.165401 + 6.76191i) q^{92} +(5.85294 + 1.77547i) q^{93} +(-1.47274 + 2.83825i) q^{94} +(8.08915 - 8.08915i) q^{95} +(4.23693 + 3.74812i) q^{96} +(8.36665 + 8.36665i) q^{97} +(-3.83842 + 1.21582i) q^{98} +(1.29845 - 4.28043i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	0.910468	+	1.08215i	0.643798	+	0.765196i
$2$	0.910468	+	1.08215i	0.643798	+	0.765196i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$3$	−0.881921	+	0.471397i	−0.509177	+	0.272161i
$4$	−0.342097	+	1.97053i	−0.171048	+	0.985263i
$5$	2.63552	+	3.21139i	1.17864	+	1.43618i	0.875490	+	0.483237i	$0.160539\pi$
$5$	2.63552	+	3.21139i	1.17864	+	1.43618i	0.303152	+	0.952942i	$0.401961\pi$
$6$	−1.31308	−	0.525180i	−0.536064	−	0.214404i
$7$	1.69443	−	1.13218i	0.640434	−	0.427924i	−0.192500	−	0.981297i	$-0.561659\pi$
$7$	1.69443	−	1.13218i	0.640434	−	0.427924i	0.832934	+	0.553373i	$0.186659\pi$
$8$	−2.44387	+	1.42390i	−0.864039	+	0.503424i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−1.07565	+	5.77590i	−0.340151	+	1.82650i
$11$	4.28043	−	1.29845i	1.29060	−	0.391498i	0.430945	−	0.902378i	$-0.358180\pi$
$11$	4.28043	−	1.29845i	1.29060	−	0.391498i	0.859652	+	0.510880i	$0.170680\pi$
$12$	−0.627197	−	1.89911i	−0.181056	−	0.548226i
$13$	−2.85407	−	2.34227i	−0.791577	−	0.649630i	0.149143	−	0.988816i	$-0.452349\pi$
$13$	−2.85407	−	2.34227i	−0.791577	−	0.649630i	−0.940720	+	0.339186i	$0.889849\pi$
$14$	2.76791	+	0.802812i	0.739756	+	0.214561i
$15$	−3.83816	−	1.58982i	−0.991010	−	0.410490i
$16$	−3.76594	−	1.34822i	−0.941485	−	0.337055i
$17$	−5.40218	+	2.23766i	−1.31022	+	0.542712i	−0.924949	−	0.380091i	$-0.875893\pi$
$17$	−5.40218	+	2.23766i	−1.31022	+	0.542712i	−0.385273	+	0.922803i	$0.625893\pi$
$18$	1.40560	−	0.155816i	0.331304	−	0.0367262i
$19$	−0.269906	−	2.74040i	−0.0619206	−	0.628690i	−0.975195	−	0.221346i	$-0.928955\pi$
$19$	−0.269906	−	2.74040i	−0.0619206	−	0.628690i	0.913275	−	0.407344i	$-0.133545\pi$
$20$	−7.22974	+	4.09476i	−1.61662	+	0.915615i
$21$	−0.960647	+	1.79724i	−0.209630	+	0.392191i
$22$	5.30231	+	3.44986i	1.13046	+	0.735514i
$23$	3.31698	−	0.659788i	0.691638	−	0.137575i	0.163258	−	0.986583i	$-0.447800\pi$
$23$	3.31698	−	0.659788i	0.691638	−	0.137575i	0.528380	+	0.849008i	$0.322800\pi$
$24$	1.48408	−	2.40780i	0.302937	−	0.491490i
$25$	−2.39162	+	12.0235i	−0.478324	+	2.40470i
$26$	−0.0638462	−	5.22110i	−0.0125213	−	1.02394i
$27$	−0.0980171	+	0.995185i	−0.0188634	+	0.191523i
$28$	1.65133	+	3.72623i	0.312073	+	0.704192i
$29$	0.408901	−	1.34797i	0.0759311	−	0.250311i	−0.910755	−	0.412947i	$-0.864500\pi$
$29$	0.408901	−	1.34797i	0.0759311	−	0.250311i	0.986686	+	0.162636i	$0.0519995\pi$
$30$	−1.77410	−	5.60095i	−0.323905	−	1.02259i
$31$	−4.32488	−	4.32488i	−0.776772	−	0.776772i	0.202508	−	0.979281i	$-0.435091\pi$
$31$	−4.32488	−	4.32488i	−0.776772	−	0.776772i	−0.979281	+	0.202508i	$0.935091\pi$
$32$	−1.96979	−	5.30282i	−0.348213	−	0.937416i
$33$	−3.16291	+	3.16291i	−0.550593	+	0.550593i
$34$	−7.33999	−	3.80866i	−1.25880	−	0.653179i
$35$	8.10159	+	2.45759i	1.36942	+	0.415409i
$36$	1.44837	+	1.37921i	0.241395	+	0.229868i
$37$	8.05373	+	0.793223i	1.32403	+	0.130405i	0.735197	−	0.677853i	$-0.237090\pi$
$37$	8.05373	+	0.793223i	1.32403	+	0.130405i	0.588828	+	0.808258i	$0.299590\pi$
$38$	2.71978	−	2.78712i	0.441207	−	0.452131i
$39$	3.62121	+	0.720303i	0.579857	+	0.115341i
$40$	−11.0136	−	4.09552i	−1.74140	−	0.647558i
$41$	−1.11095	−	5.58514i	−0.173502	−	0.872253i	−0.965235	−	0.261385i	$-0.915821\pi$
$41$	−1.11095	−	5.58514i	−0.173502	−	0.872253i	0.791733	−	0.610868i	$-0.209179\pi$
$42$	−2.81952	+	0.596769i	−0.435062	+	0.0920834i
$43$	−3.16625	−	1.69240i	−0.482849	−	0.258088i	0.211966	−	0.977277i	$-0.432014\pi$
$43$	−3.16625	−	1.69240i	−0.482849	−	0.258088i	−0.694814	+	0.719189i	$0.744514\pi$
$44$	1.09431	+	8.87889i	0.164974	+	1.33854i
$45$	4.13440	−	0.407202i	0.616319	−	0.0607021i
$46$	3.73399	+	2.98875i	0.550547	+	0.440668i
$47$	0.865264	+	2.08893i	0.126212	+	0.304702i	0.974337	−	0.225093i	$-0.0722687\pi$
$47$	0.865264	+	2.08893i	0.126212	+	0.304702i	−0.848125	+	0.529795i	$0.822269\pi$
$48$	3.95681	−	0.586226i	0.571116	−	0.0846145i
$49$	−1.08953	+	2.63035i	−0.155647	+	0.375765i
$50$	−15.1887	+	8.35890i	−2.14801	+	1.18213i
$51$	3.70947	−	4.52001i	0.519430	−	0.632928i
$52$	5.59188	−	4.82273i	0.775454	−	0.668793i
$53$	0.581978	+	1.91853i	0.0799409	+	0.263530i	0.987796	−	0.155755i	$-0.0497810\pi$
$53$	0.581978	+	1.91853i	0.0799409	+	0.263530i	−0.907855	+	0.419285i	$0.862281\pi$
$54$	−1.16618	+	0.800014i	−0.158697	+	0.108868i
$55$	15.4510	+	10.3240i	2.08341	+	1.39209i
$56$	−2.52886	+	5.17960i	−0.337933	+	0.692154i
$57$	1.52985	+	2.28958i	0.202634	+	0.303262i
$58$	1.83099	−	0.784788i	0.240421	−	0.103048i
$59$	9.18901	−	7.54123i	1.19631	−	0.981784i	0.196308	−	0.980542i	$-0.437105\pi$
$59$	9.18901	−	7.54123i	1.19631	−	0.981784i	0.999999	−	0.00124159i	$-0.000395210\pi$
$60$	4.44580	−	7.01933i	0.573951	−	0.906191i
$61$	−5.57402	−	10.4283i	−0.713680	−	1.33520i	−0.933116	−	0.359575i	$-0.882922\pi$
$61$	−5.57402	−	10.4283i	−0.713680	−	1.33520i	0.219436	−	0.975627i	$-0.429578\pi$
$62$	0.742506	−	8.61784i	0.0942983	−	1.09447i
$63$		−	2.03787i		−	0.256748i
$64$	3.94502	−	6.95966i	0.493128	−	0.869957i
$65$		−	15.3387i		−	1.90253i
$66$	−6.30248	−	0.543016i	−0.775781	−	0.0668406i
$67$	3.26315	+	6.10493i	0.398657	+	0.745836i	0.998527	−	0.0542625i	$-0.0172808\pi$
$67$	3.26315	+	6.10493i	0.398657	+	0.745836i	−0.599869	+	0.800098i	$0.704781\pi$
$68$	−2.56129	−	11.4106i	−0.310602	−	1.38374i
$69$	−2.61429	+	2.14550i	−0.314724	+	0.258287i
$70$	4.71676	+	11.0047i	0.563760	+	1.31531i
$71$	−4.41388	−	6.60584i	−0.523831	−	0.783969i	0.471358	−	0.881942i	$-0.343764\pi$
$71$	−4.41388	−	6.60584i	−0.523831	−	0.783969i	−0.995189	+	0.0979730i	$0.968764\pi$
$72$	−0.173813	+	2.82308i	−0.0204841	+	0.332703i
$73$	5.61024	+	3.74864i	0.656629	+	0.438745i	0.838740	−	0.544533i	$-0.183293\pi$
$73$	5.61024	+	3.74864i	0.656629	+	0.438745i	−0.182111	+	0.983278i	$0.558293\pi$
$74$	6.47427	+	9.43755i	0.752619	+	1.09709i
$75$	−3.55861	−	11.7312i	−0.410913	−	1.35460i
$76$	5.49235	+	0.405626i	0.630016	+	0.0465285i
$77$	5.78280	−	7.04636i	0.659011	−	0.803007i
$78$	2.51752	+	4.57450i	0.285053	+	0.517960i
$79$	−4.82549	+	11.6498i	−0.542910	+	1.31070i	0.379751	+	0.925089i	$0.376010\pi$
$79$	−4.82549	+	11.6498i	−0.542910	+	1.31070i	−0.922661	+	0.385612i	$0.873990\pi$
$80$	−5.59555	−	15.6472i	−0.625601	−	1.74941i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	5.03247	−	6.28731i	0.555744	−	0.694317i
$83$	−5.18996	+	0.511166i	−0.569672	+	0.0561078i	−0.378753	−	0.925498i	$-0.623647\pi$
$83$	−5.18996	+	0.511166i	−0.569672	+	0.0561078i	−0.190919	+	0.981606i	$0.561147\pi$
$84$	−3.21288	−	2.50781i	−0.350554	−	0.273625i
$85$	−21.4236	−	11.4511i	−2.32371	−	1.24205i
$86$	−1.05134	−	4.96723i	−0.113369	−	0.535630i
$87$	0.274809	+	1.38156i	0.0294626	+	0.148118i
$88$	−8.61195	+	9.26815i	−0.918037	+	0.987988i
$89$	5.64347	+	1.12256i	0.598206	+	0.118991i	0.484900	−	0.874569i	$-0.338856\pi$
$89$	5.64347	+	1.12256i	0.598206	+	0.118991i	0.113306	+	0.993560i	$0.463856\pi$
$90$	4.20489	+	4.10329i	0.443234	+	0.432525i
$91$	−7.48790	−	0.737494i	−0.784945	−	0.0773104i
$92$	0.165401	+	6.76191i	0.0172442	+	0.704977i
$93$	5.85294	+	1.77547i	0.606922	+	0.184108i
$94$	−1.47274	+	2.83825i	−0.151902	+	0.292743i
$95$	8.08915	−	8.08915i	0.829930	−	0.829930i
$96$	4.23693	+	3.74812i	0.432430	+	0.382541i
$97$	8.36665	+	8.36665i	0.849505	+	0.849505i	0.990071	−	0.140566i	$-0.0448923\pi$
$97$	8.36665	+	8.36665i	0.849505	+	0.849505i	−0.140566	+	0.990071i	$0.544892\pi$
$98$	−3.83842	+	1.21582i	−0.387739	+	0.122816i
$99$	1.29845	−	4.28043i	0.130499	−	0.430199i
$100$	−22.8744	−	8.82594i	−2.28744	−	0.882594i
$101$	0.231973	−	2.35526i	0.0230821	−	0.234357i	−0.976721	−	0.214514i	$-0.931183\pi$
$101$	0.231973	−	2.35526i	0.0230821	−	0.234357i	0.999803	−	0.0198432i	$-0.00631669\pi$
$102$	8.26868	−	0.101114i	0.818722	−	0.0100117i
$103$	0.473584	−	2.38087i	0.0466636	−	0.234594i	−0.950414	−	0.310987i	$-0.899340\pi$
$103$	0.473584	−	2.38087i	0.0466636	−	0.234594i	0.997078	+	0.0763932i	$0.0243404\pi$
$104$	10.3101	+	1.66031i	1.01099	+	0.162807i
$105$	−8.30346	+	1.65166i	−0.810335	+	0.161186i
$106$	−1.54626	+	2.37654i	−0.150186	+	0.230830i
$107$	4.90834	−	9.18286i	0.474507	−	0.887741i	−0.524825	−	0.851210i	$-0.675869\pi$
$107$	4.90834	−	9.18286i	0.474507	−	0.887741i	0.999333	−	0.0365309i	$-0.0116307\pi$
$108$	−1.92751	−	0.533595i	−0.185474	−	0.0513452i
$109$	1.36107	+	13.8192i	0.130367	+	1.32364i	0.808411	+	0.588619i	$0.200328\pi$
$109$	1.36107	+	13.8192i	0.130367	+	1.32364i	−0.678044	+	0.735022i	$0.737172\pi$
$110$	2.89549	+	26.1200i	0.276074	+	2.49045i
$111$	−7.47668	+	3.09694i	−0.709655	+	0.293949i
$112$	−7.90755	+	1.97926i	−0.747193	+	0.187023i
$113$	15.8769	+	6.57643i	1.49357	+	0.618658i	0.972091	−	0.234604i	$-0.0753795\pi$
$113$	15.8769	+	6.57643i	1.49357	+	0.618658i	0.521482	+	0.853262i	$0.325379\pi$
$114$	−1.08479	+	3.74012i	−0.101600	+	0.350294i
$115$	10.8608	+	8.91324i	1.01278	+	0.831164i
$116$	2.51632	+	1.26689i	0.233634	+	0.117627i
$117$	−3.53317	+	1.07177i	−0.326641	+	0.0990856i
$118$	16.5270	+	3.07784i	1.52144	+	0.283338i
$119$	−6.62018	+	9.90780i	−0.606871	+	0.908247i
$120$	11.6437	−	1.57984i	1.06292	−	0.144219i
$121$	7.48992	−	5.00460i	0.680901	−	0.454964i
$122$	6.20997	−	15.5265i	0.562225	−	1.40571i
$123$	3.61259	+	4.40196i	0.325736	+	0.396911i
$124$	10.0018	−	7.04276i	0.898190	−	0.632459i
$125$	−26.5960	+	14.2159i	−2.37882	+	1.27151i
$126$	2.20528	−	1.85542i	0.196462	−	0.165294i
$127$	−18.1249			−1.60832			−0.804161	−	0.594411i	$-0.797385\pi$
$127$	−18.1249			−1.60832			−0.804161	+	0.594411i	$0.797385\pi$
$128$	11.1232	−	2.06744i	0.983162	−	0.182737i
$129$	3.59017			0.316097
$130$	16.5987	−	13.9654i	1.45581	−	1.22484i
$131$	−4.28977	+	2.29293i	−0.374799	+	0.200334i	−0.648031	−	0.761614i	$-0.724407\pi$
$131$	−4.28977	+	2.29293i	−0.374799	+	0.200334i	0.273232	+	0.961948i	$0.411907\pi$
$132$	−5.15058	−	7.31462i	−0.448300	−	0.636656i
$133$	−3.55996	−	4.33783i	−0.308688	−	0.376137i
$134$	−3.63545	+	9.08956i	−0.314055	+	0.785218i
$135$	−3.45426	+	2.30806i	−0.297295	+	0.198646i
$136$	10.0160	−	13.1607i	0.858869	−	1.12852i
$137$	−5.92010	+	8.86005i	−0.505788	+	0.756966i	−0.993227	−	0.116192i	$-0.962931\pi$
$137$	−5.92010	+	8.86005i	−0.505788	+	0.756966i	0.487439	+	0.873157i	$0.337931\pi$
$138$	−4.70198	−	0.875653i	−0.400259	−	0.0745406i
$139$	7.13718	−	2.16504i	0.605367	−	0.183636i	0.0273028	−	0.999627i	$-0.491308\pi$
$139$	7.13718	−	2.16504i	0.605367	−	0.183636i	0.578065	+	0.815991i	$0.303808\pi$
$140$	−7.61427	+	15.1237i	−0.643524	+	1.27818i
$141$	−1.74781	−	1.43439i	−0.147192	−	0.120798i
$142$	3.12981	−	10.7909i	0.262648	−	0.905551i
$143$	−15.2580	−	6.32006i	−1.27594	−	0.528510i
$144$	−3.21325	+	2.38223i	−0.267771	+	0.198519i
$145$	5.40652	−	2.23946i	0.448987	−	0.185977i
$146$	1.05135	+	9.48413i	0.0870102	+	0.784912i
$147$	−0.279062	−	2.83336i	−0.0230166	−	0.233692i
$148$	−4.31822	+	15.5987i	−0.354956	+	1.28221i
$149$	−5.37475	+	10.0554i	−0.440317	+	0.823774i	−0.999988	−	0.00494035i	$-0.998427\pi$
$149$	−5.37475	+	10.0554i	−0.440317	+	0.823774i	0.559671	+	0.828715i	$0.310927\pi$
$150$	9.45488	−	14.5318i	0.771988	−	1.18652i
$151$	−0.437213	+	0.0869670i	−0.0355799	+	0.00707727i	−0.212848	−	0.977085i	$-0.568274\pi$
$151$	−0.437213	+	0.0869670i	−0.0355799	+	0.00707727i	0.177268	+	0.984163i	$0.443274\pi$
$152$	4.56166	+	6.31286i	0.370000	+	0.512041i
$153$	−1.14075	+	5.73493i	−0.0922240	+	0.463641i
$154$	12.8903	−	0.157629i	1.03873	−	0.0127021i
$155$	2.49058	−	25.2872i	0.200048	−	2.03112i
$156$	−2.65818	+	6.88926i	−0.212825	+	0.551583i
$157$	−3.12812	+	10.3120i	−0.249651	+	0.822988i	0.739123	+	0.673570i	$0.235240\pi$
$157$	−3.12812	+	10.3120i	−0.249651	+	0.822988i	−0.988774	+	0.149418i	$0.952260\pi$
$158$	−17.0002	+	5.38483i	−1.35247	+	0.428394i
$159$	−1.41765	−	1.41765i	−0.112427	−	0.112427i
$160$	11.8380	−	20.3015i	0.935879	−	1.60497i
$161$	4.87339	−	4.87339i	0.384077	−	0.384077i
$162$	0.651355	−	1.25528i	0.0511753	−	0.0986244i
$163$	−21.5919	−	6.54982i	−1.69121	−	0.513022i	−0.709708	−	0.704496i	$-0.751173\pi$
$163$	−21.5919	−	6.54982i	−1.69121	−	0.513022i	−0.981498	+	0.191474i	$0.938673\pi$
$164$	11.3857	−	0.278502i	0.889075	−	0.0217474i
$165$	−18.4933	−	1.82143i	−1.43970	−	0.141798i
$166$	−5.27845	−	5.15091i	−0.409687	−	0.399788i
$167$	−9.17731	−	1.82548i	−0.710161	−	0.141260i	−0.173225	−	0.984882i	$-0.555419\pi$
$167$	−9.17731	−	1.82548i	−0.710161	−	0.141260i	−0.536937	+	0.843623i	$0.680419\pi$
$168$	−0.211397	−	5.76010i	−0.0163096	−	0.444401i
$169$	0.123291	+	0.619824i	0.00948390	+	0.0476788i
$170$	−7.11362	−	33.6094i	−0.545590	−	2.57772i
$171$	−2.42851	−	1.29806i	−0.185713	−	0.0992655i
$172$	4.41807	−	5.66021i	0.336875	−	0.431587i
$173$	−12.3052	+	1.21195i	−0.935545	+	0.0921432i	−0.554287	−	0.832326i	$-0.687009\pi$
$173$	−12.3052	+	1.21195i	−0.935545	+	0.0921432i	−0.381258	+	0.924469i	$0.624509\pi$
$174$	−1.24485	+	1.55525i	−0.0943716	+	0.117903i
$175$	9.56034	+	23.0807i	0.722693	+	1.74474i
$176$	−17.8704	−	0.881067i	−1.34703	−	0.0664129i
$177$	−4.54907	+	10.9824i	−0.341929	+	0.825490i
$178$	3.92342	+	7.12913i	0.294073	+	0.534351i
$179$	15.3886	−	18.7510i	1.15020	−	1.40152i	0.248784	−	0.968559i	$-0.419969\pi$
$179$	15.3886	−	18.7510i	1.15020	−	1.40152i	0.901413	−	0.432960i	$-0.142531\pi$
$180$	−0.611961	+	8.28623i	−0.0456129	+	0.617619i
$181$	−7.38815	−	24.3555i	−0.549157	−	1.81033i	−0.585083	−	0.810973i	$-0.698938\pi$
$181$	−7.38815	−	24.3555i	−0.549157	−	1.81033i	0.0359264	−	0.999354i	$-0.488562\pi$
$182$	−6.01941	−	8.77450i	−0.446189	−	0.650409i
$183$	9.83169	+	6.56933i	0.726780	+	0.485619i
$184$	−7.16680	+	6.33548i	−0.528344	+	0.467058i
$185$	18.6784	+	27.9543i	1.37327	+	2.05524i
$186$	3.40759	+	7.95027i	0.249857	+	0.582942i
$187$	−20.2182	+	16.5926i	−1.47850	+	1.21337i
$188$	−4.41230	+	0.990408i	−0.321800	+	0.0722329i
$189$	0.960647	+	1.79724i	0.0698768	+	0.130730i
$190$	16.1186	+	1.38876i	1.16937	+	0.100751i
$191$			16.9418i			1.22587i	0.790134	+	0.612934i	$0.210011\pi$
$191$			16.9418i			1.22587i	−0.790134	+	0.612934i	$0.789989\pi$
$192$	−0.198439	+	7.99754i	−0.0143211	+	0.577173i
$193$		−	9.81720i		−	0.706657i	−0.935499	−	0.353329i	$-0.885050\pi$
$193$		−	9.81720i		−	0.706657i	0.935499	−	0.353329i	$-0.114950\pi$
$194$	−1.43641	+	16.6715i	−0.103128	+	1.19695i
$195$	7.23060	+	13.5275i	0.517794	+	0.968724i
$196$	−4.81045	−	3.04678i	−0.343604	−	0.217627i
$197$	7.72442	−	6.33927i	0.550342	−	0.451654i	−0.317667	−	0.948202i	$-0.602899\pi$
$197$	7.72442	−	6.33927i	0.550342	−	0.451654i	0.868009	+	0.496548i	$0.165399\pi$
$198$	5.81426	−	2.49207i	0.413202	−	0.177104i
$199$	−9.39602	−	14.0621i	−0.666066	−	0.996838i	−0.998555	−	0.0537311i	$-0.982889\pi$
$199$	−9.39602	−	14.0621i	−0.666066	−	0.996838i	0.332490	−	0.943107i	$-0.392111\pi$
$200$	−11.2754	−	32.7893i	−0.797292	−	2.31855i
$201$	−5.75569	−	3.84583i	−0.405975	−	0.271264i
$202$	2.75995	−	1.89336i	0.194189	−	0.133216i
$203$	−0.833289	−	2.74699i	−0.0584854	−	0.192801i
$204$	7.63779	+	8.85589i	0.534752	+	0.620037i
$205$	15.0081	−	18.2875i	1.04821	−	1.27725i
$206$	3.00764	−	1.65521i	0.209552	−	0.115324i
$207$	1.29422	−	3.12453i	0.0899546	−	0.217170i
$208$	7.59035	+	12.6688i	0.526296	+	0.878422i
$209$	−4.71359	−	11.3796i	−0.326046	−	0.787144i
$210$	−9.34738	−	7.48181i	−0.645031	−	0.516294i
$211$	4.86187	−	0.478852i	0.334705	−	0.0329655i	0.0707310	−	0.997495i	$-0.477467\pi$
$211$	4.86187	−	0.478852i	0.334705	−	0.0329655i	0.263974	+	0.964530i	$0.414967\pi$
$212$	−3.97960	+	0.490481i	−0.273320	+	0.0336864i
$213$	7.00667	+	3.74514i	0.480089	+	0.256613i
$214$	14.4061	−	3.04914i	0.984782	−	0.208435i
$215$	−2.90978	−	14.6284i	−0.198445	−	0.997651i
$216$	−1.17750	−	2.57167i	−0.0801188	−	0.174980i
$217$	−12.2248	−	2.43166i	−0.829871	−	0.165072i
$218$	−13.7152	+	14.0548i	−0.928914	+	0.951913i
$219$	−6.71488	−	0.661358i	−0.453750	−	0.0446905i
$220$	−25.6295	+	26.9148i	−1.72794	+	1.81459i
$221$	20.6594	+	6.26696i	1.38970	+	0.421562i
$222$	−10.1586	−	5.27122i	−0.681803	−	0.353781i
$223$	6.60843	−	6.60843i	0.442533	−	0.442533i	−0.450329	−	0.892863i	$-0.648693\pi$
$223$	6.60843	−	6.60843i	0.442533	−	0.442533i	0.892863	+	0.450329i	$0.148693\pi$
$224$	−9.34143	−	6.75510i	−0.624150	−	0.451344i
$225$	8.66845	+	8.66845i	0.577897	+	0.577897i
$226$	7.33872	+	23.1688i	0.488165	+	1.54117i
$227$	0.343765	−	1.13324i	0.0228165	−	0.0752158i	−0.944793	−	0.327668i	$-0.893737\pi$
$227$	0.343765	−	1.13324i	0.0228165	−	0.0752158i	0.967609	+	0.252453i	$0.0812372\pi$
$228$	−5.03504	+	2.23135i	−0.333453	+	0.147775i
$229$	0.501229	−	5.08906i	0.0331221	−	0.336294i	−0.964316	−	0.264755i	$-0.914709\pi$
$229$	0.501229	−	5.08906i	0.0331221	−	0.336294i	0.997438	−	0.0715393i	$-0.0227911\pi$
$230$	0.242959	+	19.8683i	0.0160203	+	1.31007i
$231$	−1.77834	+	8.94033i	−0.117006	+	0.588230i
$232$	0.920067	+	3.87649i	0.0604054	+	0.254504i
$233$	−10.0389	+	1.99687i	−0.657672	+	0.130819i	−0.512634	−	0.858607i	$-0.671330\pi$
$233$	−10.0389	+	1.99687i	−0.657672	+	0.130819i	−0.145037	+	0.989426i	$0.546330\pi$
$234$	−4.37665	−	2.84760i	−0.286111	−	0.186153i
$235$	−4.42796	+	8.28414i	−0.288848	+	0.540398i
$236$	11.7166	+	20.6870i	0.762688	+	1.34661i
$237$	−1.23596	−	12.5489i	−0.0802841	−	0.815138i
$238$	−16.7492	+	1.85671i	−1.08569	+	0.120352i
$239$	−9.18309	+	3.80376i	−0.594004	+	0.246045i	−0.659372	−	0.751817i	$-0.729178\pi$
$239$	−9.18309	+	3.80376i	−0.594004	+	0.246045i	0.0653679	+	0.997861i	$0.479178\pi$
$240$	12.3109	+	11.1619i	0.794663	+	0.720495i
$241$	−24.3464	−	10.0846i	−1.56829	−	0.649606i	−0.581785	−	0.813343i	$-0.697645\pi$
$241$	−24.3464	−	10.0846i	−1.56829	−	0.649606i	−0.986504	+	0.163736i	$0.947645\pi$
$242$	12.2351	+	3.54868i	0.786499	+	0.228118i
$243$	0.773010	+	0.634393i	0.0495886	+	0.0406963i
$244$	22.4560	−	7.41627i	1.43760	−	0.474778i
$245$	−11.3186	+	3.43345i	−0.723117	+	0.219355i
$246$	−1.47443	+	7.91720i	−0.0940061	+	0.504782i
$247$	−5.64843	+	8.45348i	−0.359401	+	0.537882i
$248$	16.7277	+	4.41126i	1.06221	+	0.280116i
$249$	4.33617	−	2.89734i	0.274794	−	0.183611i
$250$	−39.5986	−	15.8378i	−2.50443	−	1.00167i
$251$	11.8762	+	14.4712i	0.749620	+	0.913415i	0.998479	−	0.0551249i	$-0.0175557\pi$
$251$	11.8762	+	14.4712i	0.749620	+	0.913415i	−0.248859	+	0.968540i	$0.580056\pi$
$252$	4.01568	+	0.697150i	0.252964	+	0.0439163i
$253$	13.3414	−	7.13112i	0.838766	−	0.448330i
$254$	−16.5021	−	19.6138i	−1.03543	−	1.23068i
$255$	24.2919			1.52122
$256$	12.3646	+	10.1546i	0.772787	+	0.634665i
$257$	−2.70853			−0.168953			−0.0844767	−	0.996425i	$-0.526922\pi$
$257$	−2.70853			−0.168953			−0.0844767	+	0.996425i	$0.526922\pi$
$258$	3.26874	+	3.88511i	0.203503	+	0.241876i
$259$	14.5446	−	7.77422i	0.903754	−	0.483067i
$260$	30.2252	+	5.24731i	1.87449	+	0.325424i
$261$	−0.893620	−	1.08888i	−0.0553137	−	0.0674000i
$262$	−6.38699	−	2.55454i	−0.394590	−	0.157820i
$263$	−3.39621	+	2.26927i	−0.209419	+	0.139929i	−0.655857	−	0.754885i	$-0.727692\pi$
$263$	−3.39621	+	2.26927i	−0.209419	+	0.139929i	0.446438	+	0.894815i	$0.352692\pi$
$264$	3.22609	−	12.2334i	0.198552	−	0.752915i
$265$	−4.62732	+	6.92528i	−0.284254	+	0.425417i
$266$	1.45295	−	7.80187i	0.0890860	−	0.478363i
$267$	−5.50626	+	1.67031i	−0.336978	+	0.102221i
$268$	−13.1462	+	4.34165i	−0.803034	+	0.265208i
$269$	4.96162	+	4.07190i	0.302515	+	0.248268i	0.773388	−	0.633933i	$-0.218561\pi$
$269$	4.96162	+	4.07190i	0.302515	+	0.248268i	−0.470872	+	0.882201i	$0.656061\pi$
$270$	−5.64266	−	1.63661i	−0.343401	−	0.0996009i
$271$	−12.7011	−	5.26095i	−0.771534	−	0.319580i	−0.0380404	−	0.999276i	$-0.512112\pi$
$271$	−12.7011	−	5.26095i	−0.771534	−	0.319580i	−0.733494	+	0.679696i	$0.762112\pi$
$272$	23.3611	−	1.14354i	1.41648	−	0.0693375i
$273$	6.95139	−	2.87936i	0.420717	−	0.174267i
$274$	−14.9780	+	1.66036i	−0.904852	+	0.100306i
$275$	5.37478	+	54.5711i	0.324111	+	3.29076i
$276$	−3.33341	−	5.88550i	−0.200648	−	0.354265i
$277$	−1.79671	+	3.36142i	−0.107954	+	0.201968i	−0.930098	−	0.367312i	$-0.880278\pi$
$277$	−1.79671	+	3.36142i	−0.107954	+	0.201968i	0.822144	+	0.569280i	$0.192778\pi$
$278$	8.84107	+	5.75230i	0.530252	+	0.345000i
$279$	−5.99879	+	1.19323i	−0.359138	+	0.0714370i
$280$	−23.2986	+	5.52981i	−1.39236	+	0.330470i
$281$	−4.40340	+	22.1374i	−0.262685	+	1.32060i	0.593875	+	0.804557i	$0.297597\pi$
$281$	−4.40340	+	22.1374i	−0.262685	+	1.32060i	−0.856560	+	0.516048i	$0.827403\pi$
$282$	−0.0390990	−	3.19736i	−0.00232831	−	0.190400i
$283$	−0.0508846	+	0.516640i	−0.00302478	+	0.0307111i	−0.996579	−	0.0826499i	$-0.973662\pi$
$283$	−0.0508846	+	0.516640i	−0.00302478	+	0.0307111i	0.993554	+	0.113361i	$0.0361617\pi$
$284$	14.5270	−	6.43783i	0.862016	−	0.382015i
$285$	−3.32080	+	10.9472i	−0.196707	+	0.648456i
$286$	−7.05264	−	22.2656i	−0.417031	−	1.31659i
$287$	−8.20583	−	8.20583i	−0.484375	−	0.484375i
$288$	−5.50349	−	1.30827i	−0.324296	−	0.0770906i
$289$	12.1556	−	12.1556i	0.715038	−	0.715038i
$290$	7.34589	+	3.81172i	0.431366	+	0.223832i
$291$	−11.3227	−	3.43472i	−0.663751	−	0.201347i
$292$	−9.30603	+	9.77271i	−0.544595	+	0.571905i
$293$	7.61556	+	0.750067i	0.444906	+	0.0438194i	0.317990	−	0.948094i	$-0.396992\pi$
$293$	7.61556	+	0.750067i	0.444906	+	0.0438194i	0.126916	+	0.991913i	$0.459492\pi$
$294$	2.81205	−	2.88167i	0.164002	−	0.168063i
$295$	48.4357	+	9.63446i	2.82004	+	0.560940i
$296$	−20.8118	+	9.52917i	−1.20966	+	0.553871i
$297$	0.872646	+	4.38709i	0.0506361	+	0.254565i
$298$	−15.7750	+	3.33888i	−0.913823	+	0.193416i
$299$	−11.0123	−	5.88620i	−0.636858	−	0.340408i
$300$	24.3339	−	2.99914i	1.40492	−	0.173155i
$301$	−7.28109	+	0.717125i	−0.419675	+	0.0413344i
$302$	−0.492179	−	0.393949i	−0.0283217	−	0.0226692i
$303$	0.905679	+	2.18650i	0.0520299	+	0.125611i
$304$	−2.67821	+	10.6841i	−0.153606	+	0.612773i
$305$	18.7988	−	45.3843i	1.07642	−	2.59870i
$306$	−7.24466	+	3.98700i	−0.414150	+	0.227922i
$307$	0.363981	−	0.443512i	0.0207735	−	0.0253125i	−0.762520	−	0.646965i	$-0.776038\pi$
$307$	0.363981	−	0.443512i	0.0207735	−	0.0253125i	0.783294	+	0.621652i	$0.213538\pi$
$308$	11.9068	+	13.8057i	0.678450	+	0.786652i
$309$	0.704669	+	2.32298i	0.0400872	+	0.132150i
$310$	29.6322	−	20.3280i	1.68299	−	1.15456i
$311$	−20.5106	−	13.7047i	−1.16305	−	0.777123i	−0.184437	−	0.982844i	$-0.559046\pi$
$311$	−20.5106	−	13.7047i	−1.16305	−	0.777123i	−0.978611	+	0.205721i	$0.934046\pi$
$312$	−9.87540	+	3.39591i	−0.559085	+	0.192255i
$313$	−16.2383	−	24.3023i	−0.917843	−	1.37365i	−0.927551	−	0.373696i	$-0.878090\pi$
$313$	−16.2383	−	24.3023i	−0.917843	−	1.37365i	0.00970865	−	0.999953i	$-0.496910\pi$
$314$	−14.0072	+	6.00367i	−0.790472	+	0.338807i
$315$	6.54441	−	5.37086i	0.368736	−	0.302614i
$316$	−21.3054	−	13.4941i	−1.19852	−	0.759102i
$317$	9.10110	+	17.0270i	0.511169	+	0.956330i	0.996627	+	0.0820695i	$0.0261530\pi$
$317$	9.10110	+	17.0270i	0.511169	+	0.956330i	−0.485458	+	0.874260i	$0.661347\pi$
$318$	0.243385	−	2.82483i	0.0136483	−	0.158408i
$319$		−	6.30082i		−	0.352778i
$320$	32.7474	−	5.67332i	1.83063	−	0.317148i
$321$			10.4123i			0.581160i
$322$	9.71080	+	0.836674i	0.541162	+	0.0466260i
$323$	7.59015	+	14.2002i	0.422327	+	0.790118i
$324$	1.95144	−	0.438031i	0.108413	−	0.0243351i
$325$	34.9881	−	28.7140i	1.94079	−	1.59277i
$326$	−12.5708	−	29.3290i	−0.696233	−	1.62439i
$327$	−7.71469	−	11.5459i	−0.426623	−	0.638487i
$328$	10.6677	+	12.0675i	0.589026	+	0.666315i
$329$	3.83118	+	2.55991i	0.211220	+	0.141133i
$330$	−14.8665	−	21.6709i	−0.818373	−	1.19294i
$331$	2.87364	+	9.47311i	0.157949	+	0.520689i	0.999820	−	0.0189907i	$-0.00604528\pi$
$331$	2.87364	+	9.47311i	0.157949	+	0.520689i	−0.841870	+	0.539680i	$0.818545\pi$
$332$	0.768203	−	10.4018i	0.0421606	−	0.570874i
$333$	5.13395	−	6.25574i	0.281339	−	0.342812i
$334$	−6.38020	−	11.5933i	−0.349109	−	0.634355i
$335$	−11.0052	+	26.5689i	−0.601279	+	1.45162i
$336$	6.04082	−	5.47315i	0.329554	−	0.298585i
$337$	−8.73191	−	21.0807i	−0.475657	−	1.14834i	−0.961626	−	0.274362i	$-0.911533\pi$
$337$	−8.73191	−	21.0807i	−0.475657	−	1.14834i	0.485969	−	0.873976i	$-0.338467\pi$
$338$	−0.558491	+	0.697749i	−0.0303779	+	0.0379525i
$339$	−17.1023	+	1.68443i	−0.928868	+	0.0914855i
$340$	29.8937	−	38.2983i	1.62121	−	2.07702i
$341$	−24.1280	−	12.8967i	−1.30661	−	0.698395i
$342$	−0.806378	−	3.80986i	−0.0436039	−	0.206013i
$343$	3.91489	+	19.6815i	0.211384	+	1.06270i
$344$	10.1477	−	0.372423i	0.547128	−	0.0200797i
$345$	−13.7801	−	2.74102i	−0.741894	−	0.147572i
$346$	−12.5150	−	12.2126i	−0.672810	−	0.656553i
$347$	27.9788	+	2.75567i	1.50198	+	0.147932i	0.815305	−	0.579031i	$-0.196569\pi$
$347$	27.9788	+	2.75567i	1.50198	+	0.147932i	0.686676	+	0.726964i	$0.259069\pi$
$348$	−2.81640	+	0.0688911i	−0.150975	+	0.00369295i
$349$	12.9991	+	3.94322i	0.695823	+	0.211076i	0.618332	−	0.785917i	$-0.287809\pi$
$349$	12.9991	+	3.94322i	0.695823	+	0.211076i	0.0774917	+	0.996993i	$0.475309\pi$
$350$	−16.2724	+	31.3599i	−0.869796	+	1.67626i
$351$	2.61074	−	2.61074i	0.139351	−	0.139351i
$352$	−15.3170	−	20.1407i	−0.816399	−	1.07350i
$353$	20.5229	+	20.5229i	1.09232	+	1.09232i	0.995280	+	0.0970423i	$0.0309382\pi$
$353$	20.5229	+	20.5229i	1.09232	+	1.09232i	0.0970423	+	0.995280i	$0.469062\pi$
$354$	−16.0264	+	5.07637i	−0.851795	+	0.269806i
$355$	9.58107	−	31.5846i	0.508511	−	1.67633i
$356$	−4.14264	+	10.7366i	−0.219559	+	0.569037i
$357$	1.16797	−	11.8586i	0.0618157	−	0.627625i
$358$	34.3023	−	0.419465i	1.81293	−	0.0221694i
$359$	0.783929	−	3.94108i	0.0413742	−	0.208002i	−0.954569	−	0.297991i	$-0.903683\pi$
$359$	0.783929	−	3.94108i	0.0413742	−	0.208002i	0.995943	+	0.0899894i	$0.0286833\pi$
$360$	−9.52412	+	6.88211i	−0.501965	+	0.362719i
$361$	11.1980	−	2.22742i	0.589368	−	0.117233i
$362$	19.6296	−	30.1700i	1.03171	−	1.58570i
$363$	−4.24636	+	7.94439i	−0.222876	+	0.416972i
$364$	4.01484	−	14.5028i	0.210435	−	0.760153i
$365$	2.74755	+	27.8963i	0.143813	+	1.46016i
$366$	1.84244	+	16.6205i	0.0963060	+	0.868769i
$367$	−20.5821	+	8.52538i	−1.07438	+	0.445021i	−0.848533	−	0.529143i	$-0.822514\pi$
$367$	−20.5821	+	8.52538i	−1.07438	+	0.445021i	−0.225843	+	0.974164i	$0.572514\pi$
$368$	−13.3811	−	1.98730i	−0.697537	−	0.103595i
$369$	−5.26109	−	2.17921i	−0.273881	−	0.113445i
$370$	−13.2446	+	45.6643i	−0.688553	+	2.37398i
$371$	3.15824	+	2.59190i	0.163968	+	0.134565i
$372$	−5.50088	+	10.9260i	−0.285208	+	0.566486i
$373$	−3.69152	+	1.11981i	−0.191139	+	0.0579815i	−0.384403	−	0.923165i	$-0.625593\pi$
$373$	−3.69152	+	1.11981i	−0.191139	+	0.0579815i	0.193264	+	0.981147i	$0.438093\pi$
$374$	−36.3637	−	6.77204i	−1.88032	−	0.350174i
$375$	16.7543	−	25.0746i	0.865188	−	1.29485i
$376$	−5.08903	−	3.87304i	−0.262446	−	0.199737i
$377$	−4.32434	+	2.88943i	−0.222715	+	0.148813i
$378$	−1.07025	+	2.67590i	−0.0550477	+	0.137633i
$379$	2.50472	+	3.05201i	0.128659	+	0.156771i	0.833355	−	0.552738i	$-0.186417\pi$
$379$	2.50472	+	3.05201i	0.128659	+	0.156771i	−0.704697	+	0.709509i	$0.748917\pi$
$380$	13.1726	+	18.7072i	0.675740	+	0.959657i
$381$	15.9847	−	8.54401i	0.818922	−	0.437723i
$382$	−18.3336	+	15.4250i	−0.938029	+	0.789211i
$383$	19.9282			1.01828			0.509141	−	0.860683i	$-0.329963\pi$
$383$	19.9282			1.01828			0.509141	+	0.860683i	$0.329963\pi$
$384$	−8.83521	+	7.06676i	−0.450870	+	0.360624i
$385$	37.8693			1.93000
$386$	10.6237	−	8.93824i	0.540731	−	0.454944i
$387$	−3.16625	+	1.69240i	−0.160950	+	0.0860293i
$388$	−19.3489	+	13.6245i	−0.982292	+	0.691679i
$389$	−12.5423	−	15.2829i	−0.635921	−	0.774872i	0.350948	−	0.936395i	$-0.385859\pi$
$389$	−12.5423	−	15.2829i	−0.635921	−	0.774872i	−0.986869	+	0.161523i	$0.948359\pi$
$390$	−8.05555	+	20.1409i	−0.407909	+	1.01988i
$391$	−16.4425	+	10.9866i	−0.831535	+	0.555614i
$392$	−1.08269	−	7.97962i	−0.0546842	−	0.403032i
$393$	2.70236	−	4.04437i	0.136316	−	0.204011i
$394$	13.8929	+	2.58728i	0.699913	+	0.130345i
$395$	−50.1297	+	15.2067i	−2.52230	+	0.765130i
$396$	7.99049	+	4.02296i	0.401537	+	0.202161i
$397$	4.38943	+	3.60232i	0.220299	+	0.180795i	0.738069	−	0.674725i	$-0.235738\pi$
$397$	4.38943	+	3.60232i	0.220299	+	0.180795i	−0.517770	+	0.855520i	$0.673238\pi$
$398$	6.66257	−	22.9710i	0.333964	−	1.15143i
$399$	5.18444	+	2.14747i	0.259547	+	0.107508i
$400$	25.2170	−	42.0553i	1.26085	−	2.10276i
$401$	15.4019	−	6.37969i	0.769136	−	0.318586i	0.0366135	−	0.999330i	$-0.488343\pi$
$401$	15.4019	−	6.37969i	0.769136	−	0.318586i	0.732522	+	0.680743i	$0.238343\pi$
$402$	−1.07861	−	9.73001i	−0.0537960	−	0.485289i
$403$	2.21346	+	22.4736i	0.110260	+	1.11949i
$404$	4.56174	+	1.26283i	0.226955	+	0.0628284i
$405$	1.95837	−	3.66385i	0.0973122	−	0.182058i
$406$	2.21397	−	3.40279i	0.109877	−	0.168877i
$407$	35.5034	−	7.06206i	1.75984	−	0.350053i
$408$	−2.62944	+	16.3282i	−0.130177	+	0.808368i
$409$	−4.01893	+	20.2045i	−0.198723	+	0.999049i	0.744685	+	0.667416i	$0.232600\pi$
$409$	−4.01893	+	20.2045i	−0.198723	+	0.999049i	−0.943408	+	0.331633i	$0.892400\pi$
$410$	33.4542	−	0.409095i	1.65219	−	0.0202038i
$411$	1.04446	−	10.6046i	0.0515194	−	0.523086i
$412$	4.52955	+	1.74770i	0.223155	+	0.0861028i
$413$	7.03209	−	23.1817i	0.346027	−	1.14070i
$414$	4.55955	−	1.44424i	0.224090	−	0.0709805i
$415$	−15.3198	−	15.3198i	−0.752020	−	0.752020i
$416$	−6.79875	+	19.7484i	−0.333336	+	0.968246i
$417$	−5.27384	+	5.27384i	−0.258261	+	0.258261i
$418$	8.02287	−	15.4616i	0.392412	−	0.756251i
$419$	12.8661	+	3.90288i	0.628549	+	0.190668i	0.588458	−	0.808528i	$-0.299735\pi$
$419$	12.8661	+	3.90288i	0.628549	+	0.190668i	0.0400908	+	0.999196i	$0.487235\pi$
$420$	−0.414051	−	16.9272i	−0.0202036	−	0.825964i
$421$	−15.1499	−	1.49214i	−0.738362	−	0.0727223i	−0.278158	−	0.960535i	$-0.589724\pi$
$421$	−15.1499	−	1.49214i	−0.738362	−	0.0727223i	−0.460204	+	0.887813i	$0.652224\pi$
$422$	4.94476	+	4.82529i	0.240707	+	0.234891i
$423$	2.21760	+	0.441108i	0.107823	+	0.0214474i
$424$	−4.15407	−	3.85995i	−0.201739	−	0.187456i
$425$	−13.9845	−	70.3047i	−0.678346	−	3.41028i
$426$	2.32654	+	10.9921i	0.112721	+	0.532569i
$427$	−21.2515	−	11.3591i	−1.02843	−	0.549708i
$428$	16.4159	+	12.8134i	0.793494	+	0.619361i
$429$	16.4356	−	1.61876i	0.793518	−	0.0781547i
$430$	13.1809	−	16.4675i	0.635639	−	0.794135i
$431$	−12.2591	−	29.5962i	−0.590502	−	1.42560i	−0.883019	−	0.469338i	$-0.844493\pi$
$431$	−12.2591	−	29.5962i	−0.590502	−	1.42560i	0.292517	−	0.956260i	$-0.405507\pi$
$432$	1.71086	−	3.61566i	0.0823136	−	0.173958i
$433$	−8.58927	+	20.7363i	−0.412774	+	0.996525i	0.571615	+	0.820522i	$0.306317\pi$
$433$	−8.58927	+	20.7363i	−0.412774	+	0.996525i	−0.984390	+	0.176003i	$0.943683\pi$
$434$	−8.49884	−	15.4430i	−0.407957	−	0.741287i
$435$	−3.71246	+	4.52364i	−0.177999	+	0.216892i
$436$	−27.6967	−	2.04548i	−1.32643	−	0.0979608i
$437$	−2.70335	−	8.91176i	−0.129319	−	0.426307i
$438$	−5.39800	−	7.86866i	−0.257926	−	0.375979i
$439$	−9.98262	−	6.67017i	−0.476444	−	0.318350i	0.294058	−	0.955788i	$-0.404994\pi$
$439$	−9.98262	−	6.67017i	−0.476444	−	0.318350i	−0.770502	+	0.637438i	$0.779994\pi$
$440$	−52.4607	−	3.22994i	−2.50097	−	0.153981i
$441$	1.58175	+	2.36725i	0.0753214	+	0.112726i
$442$	12.0279	+	28.0625i	0.572110	+	1.33479i
$443$	21.0656	−	17.2881i	1.00086	−	0.821383i	0.0169132	−	0.999857i	$-0.494616\pi$
$443$	21.0656	−	17.2881i	1.00086	−	0.821383i	0.983945	+	0.178474i	$0.0571161\pi$
$444$	−3.54485	−	15.7924i	−0.168231	−	0.749476i
$445$	11.2685	+	21.0819i	0.534179	+	0.999379i
$446$	13.1681	+	1.13455i	0.623527	+	0.0537225i
$447$		−	11.4018i		−	0.539284i
$448$	−1.19503	−	16.2591i	−0.0564601	−	0.768172i
$449$		−	5.17891i		−	0.244408i	−0.992505	−	0.122204i	$-0.961004\pi$
$449$		−	5.17891i		−	0.244408i	0.992505	−	0.122204i	$-0.0389962\pi$
$450$	−1.48822	+	17.2729i	−0.0701553	+	0.814252i
$451$	−12.0074	−	22.4643i	−0.565407	−	1.05780i
$452$	−18.3904	+	29.0360i	−0.865014	+	1.36574i
$453$	0.344591	−	0.282799i	0.0161903	−	0.0132870i
$454$	1.53932	−	0.659774i	0.0722440	−	0.0309647i
$455$	−17.3662	−	25.9903i	−0.814138	−	1.21844i
$456$	−6.99889	−	3.41709i	−0.327753	−	0.160020i
$457$	34.7768	+	23.2371i	1.62679	+	1.08699i	0.928603	+	0.371074i	$0.121010\pi$
$457$	34.7768	+	23.2371i	1.62679	+	1.08699i	0.698188	+	0.715914i	$0.253990\pi$
$458$	5.96348	−	4.09102i	0.278655	−	0.191161i
$459$	−1.69738	−	5.59550i	−0.0792267	−	0.261175i
$460$	−21.2792	+	18.3523i	−0.992149	+	0.855682i
$461$	15.1437	−	18.4526i	0.705311	−	0.859424i	−0.289912	−	0.957053i	$-0.593626\pi$
$461$	15.1437	−	18.4526i	0.705311	−	0.859424i	0.995223	+	0.0976294i	$0.0311260\pi$
$462$	−11.2939	+	6.21545i	−0.525440	+	0.289169i
$463$	−4.78321	+	11.5477i	−0.222295	+	0.536667i	−0.995201	−	0.0978536i	$-0.968802\pi$
$463$	−4.78321	+	11.5477i	−0.222295	+	0.536667i	0.772906	+	0.634520i	$0.218802\pi$
$464$	−3.35726	+	4.52507i	−0.155857	+	0.210071i
$465$	9.72383	+	23.4754i	0.450932	+	1.08865i
$466$	−11.3010	−	9.04554i	−0.523510	−	0.419026i
$467$	−28.9267	+	2.84903i	−1.33857	+	0.131837i	−0.741824	−	0.670595i	$-0.766039\pi$
$467$	−28.9267	+	2.84903i	−1.33857	+	0.131837i	−0.596744	+	0.802432i	$0.703539\pi$
$468$	−0.903273	−	7.32884i	−0.0417538	−	0.338776i
$469$	12.4411	+	6.64989i	0.574475	+	0.307063i
$470$	−12.9962	+	2.75072i	−0.599470	+	0.126881i
$471$	−2.10230	−	10.5690i	−0.0968688	−	0.486992i
$472$	−11.7188	+	31.5140i	−0.539402	+	1.45055i
$473$	−15.7504	−	3.13295i	−0.724205	−	0.144053i
$474$	12.4545	−	12.7628i	0.572053	−	0.586217i
$475$	33.5946	+	3.30878i	1.54143	+	0.151817i
$476$	−17.2588	−	16.4347i	−0.791057	−	0.753282i
$477$	1.91853	+	0.581978i	0.0878433	+	0.0266470i
$478$	−12.4771	−	6.47428i	−0.570691	−	0.296127i
$479$	−12.6950	+	12.6950i	−0.580049	+	0.580049i	−0.934917	−	0.354867i	$-0.884526\pi$
$479$	−12.6950	+	12.6950i	−0.580049	+	0.580049i	0.354867	+	0.934917i	$0.384526\pi$
$480$	−0.870161	+	23.4847i	−0.0397172	+	1.07193i
$481$	−21.1280	−	21.1280i	−0.963352	−	0.963352i
$482$	−11.2535	−	35.5281i	−0.512585	−	1.61826i
$483$	−2.00065	+	6.59525i	−0.0910325	+	0.300094i
$484$	7.29942	+	16.4711i	0.331792	+	0.748688i
$485$	−4.81811	+	48.9191i	−0.218779	+	2.22130i
$486$	0.0172924	+	1.41411i	0.000784401	+	0.0641452i
$487$	2.27774	−	11.4510i	0.103214	−	0.518893i	−0.894240	−	0.447587i	$-0.852283\pi$
$487$	2.27774	−	11.4510i	0.103214	−	0.518893i	0.997454	−	0.0713059i	$-0.0227167\pi$
$488$	28.4710	+	17.5485i	1.28882	+	0.794383i
$489$	22.1299	−	4.40191i	1.00075	−	0.199061i
$490$	−14.0207	−	9.12235i	−0.633391	−	0.412106i
$491$	3.52201	−	6.58922i	0.158946	−	0.297367i	−0.789824	−	0.613333i	$-0.789828\pi$
$491$	3.52201	−	6.58922i	0.158946	−	0.297367i	0.948771	+	0.315965i	$0.102328\pi$
$492$	−9.91002	+	5.61281i	−0.446778	+	0.253045i
$493$	0.807329	+	8.19695i	0.0363603	+	0.369172i
$494$	−14.2906	+	1.58417i	−0.642967	+	0.0712750i
$495$	17.1682	−	7.11132i	0.771655	−	0.319630i
$496$	10.4564	+	22.1182i	0.469504	+	0.993134i
$497$	−14.9580	−	6.19582i	−0.670959	−	0.277920i
$498$	7.08330	+	2.05446i	0.317410	+	0.0920624i
$499$	20.6329	+	16.9330i	0.923657	+	0.758025i	0.970556	−	0.240874i	$-0.0774341\pi$
$499$	20.6329	+	16.9330i	0.923657	+	0.758025i	−0.0468996	+	0.998900i	$0.514934\pi$
$500$	−18.9143	−	57.2714i	−0.845874	−	2.56125i
$501$	8.95419	−	2.71622i	0.400044	−	0.121352i
$502$	−4.84711	+	26.0274i	−0.216337	+	1.16166i
$503$	−10.2486	+	15.3381i	−0.456962	+	0.683892i	−0.986383	−	0.164467i	$-0.947409\pi$
$503$	−10.2486	+	15.3381i	−0.456962	+	0.683892i	0.529420	+	0.848360i	$0.322409\pi$
$504$	2.90173	+	4.98030i	0.129253	+	0.221840i
$505$	8.17503	−	5.46238i	0.363784	−	0.243073i
$506$	19.8638	+	7.94473i	0.883056	+	0.353186i
$507$	−0.400916	−	0.488517i	−0.0178053	−	0.0216958i
$508$	6.20046	−	35.7155i	0.275101	−	1.58462i
$509$	13.9495	−	7.45616i	0.618300	−	0.330488i	−0.132335	−	0.991205i	$-0.542247\pi$
$509$	13.9495	−	7.45616i	0.618300	−	0.330488i	0.750635	+	0.660717i	$0.229747\pi$
$510$	22.1170	+	26.2875i	0.979358	+	1.16403i
$511$	13.7503			0.608277
$512$	0.268725	+	22.6258i	0.0118761	+	0.999929i
$513$	2.75366			0.121577
$514$	−2.46603	−	2.93104i	−0.108772	−	0.129282i
$515$	8.89404	−	4.75397i	0.391918	−	0.209485i
$516$	−1.22819	+	7.07453i	−0.0540680	+	0.311439i
$517$	6.41608	+	7.81802i	0.282179	+	0.343836i
$518$	21.6552	+	8.66120i	0.951476	+	0.380551i
$519$	10.2809	−	6.86947i	0.451281	−	0.301536i
$520$	21.8407	+	37.4857i	0.957779	+	1.64386i
$521$	3.98005	−	5.95657i	0.174369	−	0.260962i	−0.733983	−	0.679168i	$-0.762341\pi$
$521$	3.98005	−	5.95657i	0.174369	−	0.260962i	0.908352	+	0.418206i	$0.137341\pi$
$522$	0.364718	−	1.95842i	0.0159633	−	0.0857178i
$523$	14.4634	−	4.38742i	0.632440	−	0.191849i	0.0422424	−	0.999107i	$-0.486550\pi$
$523$	14.4634	−	4.38742i	0.632440	−	0.191849i	0.590198	+	0.807259i	$0.299050\pi$
$524$	−3.05076	−	9.23751i	−0.133273	−	0.403542i
$525$	−19.3116	−	15.8486i	−0.842828	−	0.691691i
$526$	−5.54783	−	1.60911i	−0.241897	−	0.0701604i
$527$	33.0414	+	13.6862i	1.43931	+	0.596180i
$528$	16.1756	−	7.64703i	0.703955	−	0.332794i
$529$	−10.6822	+	4.42471i	−0.464443	+	0.192379i
$530$	−11.7072	+	1.29779i	−0.508529	+	0.0563722i
$531$	−1.16516	−	11.8301i	−0.0505636	−	0.513381i
$532$	9.76565	−	5.53104i	0.423395	−	0.239801i
$533$	−9.91120	+	18.5425i	−0.429302	+	0.803167i
$534$	−6.82080	−	4.43784i	−0.295165	−	0.192044i
$535$	42.4259	−	8.43903i	1.83423	−	0.364851i
$536$	−16.6675	−	10.2733i	−0.719927	−	0.443737i
$537$	−4.73234	+	23.7911i	−0.204216	+	1.02666i
$538$	0.110993	+	9.07655i	0.00478523	+	0.391318i
$539$	−1.24825	+	12.6737i	−0.0537661	+	0.545896i
$540$	−3.36640	−	7.59628i	−0.144867	−	0.326892i
$541$	0.635635	−	2.09541i	0.0273281	−	0.0900886i	−0.942216	−	0.335007i	$-0.891261\pi$
$541$	0.635635	−	2.09541i	0.0273281	−	0.0900886i	0.969544	+	0.244919i	$0.0787612\pi$
$542$	−5.87076	−	18.5344i	−0.252171	−	0.796119i
$543$	17.9969	+	17.9969i	0.772319	+	0.772319i
$544$	22.5071	+	24.2391i	0.964982	+	1.03924i
$545$	−40.7918	+	40.7918i	−1.74733	+	1.74733i
$546$	9.44492	+	4.90088i	0.404205	+	0.209738i
$547$	−26.7264	−	8.10736i	−1.14274	−	0.346646i	−0.338507	−	0.940964i	$-0.609922\pi$
$547$	−26.7264	−	8.10736i	−1.14274	−	0.346646i	−0.804230	+	0.594318i	$0.797422\pi$
$548$	−15.4337	−	14.6967i	−0.659296	−	0.627812i
$549$	−11.7675	−	1.15900i	−0.502226	−	0.0494650i
$550$	−54.1605	+	55.5015i	−2.30941	+	2.36659i
$551$	−3.80433	−	0.756728i	−0.162070	−	0.0322377i
$552$	3.33403	−	8.96581i	0.141906	−	0.381610i
$553$	5.01319	+	25.2030i	0.213183	+	1.07174i
$554$	−5.27341	+	1.11615i	−0.224046	+	0.0474205i
$555$	−29.6505	−	15.8485i	−1.25859	−	0.672731i
$556$	1.82466	+	14.8046i	0.0773827	+	0.627857i
$557$	−25.7889	+	2.53998i	−1.09271	+	0.107623i	−0.628280	−	0.777987i	$-0.716241\pi$
$557$	−25.7889	+	2.53998i	−1.09271	+	0.107623i	−0.464430	+	0.885610i	$0.653741\pi$
$558$	−6.75296	−	5.40519i	−0.285876	−	0.228820i
$559$	5.07264	+	12.2464i	0.214550	+	0.517970i
$560$	−27.1967	−	20.1779i	−1.14927	−	0.852671i
$561$	10.0091	−	24.1641i	0.422585	−	1.02021i
$562$	−27.9651	+	15.3902i	−1.17964	+	0.649197i
$563$	−20.7743	+	25.3136i	−0.875533	+	1.06684i	0.121705	+	0.992566i	$0.461164\pi$
$563$	−20.7743	+	25.3136i	−0.875533	+	1.06684i	−0.997238	+	0.0742741i	$0.976336\pi$
$564$	3.42443	−	2.95341i	0.144194	−	0.124361i
$565$	20.7244	+	68.3193i	0.871883	+	2.87421i
$566$	−0.605411	+	0.415319i	−0.0254473	+	0.0174572i
$567$	−1.69443	−	1.13218i	−0.0711594	−	0.0475472i
$568$	20.1930	+	9.85891i	0.847280	+	0.413671i
$569$	−20.1851	−	30.2092i	−0.846204	−	1.26643i	−0.961969	−	0.273158i	$-0.911932\pi$
$569$	−20.1851	−	30.2092i	−0.846204	−	1.26643i	0.115765	−	0.993277i	$-0.463068\pi$
$570$	−14.8700	+	6.37347i	−0.622835	+	0.266955i
$571$	9.12441	−	7.48821i	0.381845	−	0.313372i	−0.423817	−	0.905748i	$-0.639310\pi$
$571$	9.12441	−	7.48821i	0.381845	−	0.313372i	0.805662	+	0.592376i	$0.201810\pi$
$572$	17.6735	−	27.9042i	0.738968	−	1.16673i
$573$	−7.98633	−	14.9414i	−0.333634	−	0.624184i
$574$	1.40879	−	16.3511i	0.0588019	−	0.682481i
$575$			41.4596i			1.72899i
$576$	−3.59501	−	7.14674i	−0.149792	−	0.297781i
$577$			12.4652i			0.518933i	0.965752	+	0.259466i	$0.0835467\pi$
$577$			12.4652i			0.518933i	−0.965752	+	0.259466i	$0.916453\pi$
$578$	24.2215	+	2.08691i	1.00748	+	0.0868039i
$579$	4.62779	+	8.65799i	0.192325	+	0.359814i
$580$	2.56335	+	11.4198i	0.106437	+	0.474182i
$581$	−8.21529	+	6.74211i	−0.340828	+	0.279710i
$582$	−6.59211	−	15.3801i	−0.273252	−	0.637526i
$583$	4.98223	+	7.45644i	0.206343	+	0.308814i
$584$	−19.0484	−	1.17278i	−0.788228	−	0.0485302i
$585$	−12.7536	−	8.52171i	−0.527298	−	0.352329i
$586$	6.12203	+	8.92409i	0.252899	+	0.368651i
$587$	5.91284	+	19.4920i	0.244049	+	0.804522i	0.990311	+	0.138869i	$0.0443468\pi$
$587$	5.91284	+	19.4920i	0.244049	+	0.804522i	−0.746262	+	0.665653i	$0.768153\pi$
$588$	5.67868	+	0.419387i	0.234185	+	0.0172952i
$589$	−10.6846	+	13.0192i	−0.440251	+	0.536447i
$590$	33.6732	+	61.1865i	1.38630	+	2.51901i
$591$	−3.82402	+	9.23200i	−0.157299	+	0.379754i
$592$	−29.2604	−	13.8454i	−1.20260	−	0.569044i
$593$	7.18715	+	17.3513i	0.295141	+	0.712533i	0.999995	+	0.00318086i	$0.00101250\pi$
$593$	7.18715	+	17.3513i	0.295141	+	0.712533i	−0.704854	+	0.709352i	$0.748987\pi$
$594$	−3.95297	+	4.93864i	−0.162192	+	0.202635i
$595$	−49.2655	+	4.85223i	−2.01969	+	0.198922i
$596$	−17.9758	−	14.0310i	−0.736319	−	0.574733i
$597$	14.9154	+	7.97244i	0.610446	+	0.326290i
$598$	−3.65660	−	17.2762i	−0.149529	−	0.706474i
$599$	6.05846	+	30.4579i	0.247542	+	1.24448i	0.881899	+	0.471437i	$0.156265\pi$
$599$	6.05846	+	30.4579i	0.247542	+	1.24448i	−0.634358	+	0.773040i	$0.718735\pi$
$600$	25.4008	+	23.6024i	1.03698	+	0.963563i
$601$	−8.78745	−	1.74793i	−0.358448	−	0.0712997i	0.0125816	−	0.999921i	$-0.495995\pi$
$601$	−8.78745	−	1.74793i	−0.358448	−	0.0712997i	−0.371029	+	0.928621i	$0.620995\pi$
$602$	−7.40523	−	7.22631i	−0.301815	−	0.294522i
$603$	6.88897	+	0.678504i	0.280541	+	0.0276308i
$604$	−0.0218015	−	0.891290i	−0.000887092	−	0.0362661i
$605$	35.8116	+	10.8633i	1.45595	+	0.441657i
$606$	−1.54153	+	2.97082i	−0.0626205	+	0.120681i
$607$	−25.5155	+	25.5155i	−1.03564	+	1.03564i	−0.0363017	+	0.999341i	$0.511558\pi$
$607$	−25.5155	+	25.5155i	−1.03564	+	1.03564i	−0.999341	+	0.0363017i	$0.988442\pi$
$608$	−14.0002	+	6.82926i	−0.567782	+	0.276963i
$609$	2.02982	+	2.02982i	0.0822523	+	0.0822523i
$610$	66.2283	−	20.9778i	2.68151	−	0.849367i
$611$	2.42333	−	7.98865i	0.0980374	−	0.323186i
$612$	−10.9106	−	4.20977i	−0.441034	−	0.170170i
$613$	2.44954	−	24.8706i	0.0989359	−	1.00451i	−0.809677	−	0.586875i	$-0.800358\pi$
$613$	2.44954	−	24.8706i	0.0989359	−	1.00451i	0.908613	−	0.417638i	$-0.137142\pi$
$614$	0.811339	−	0.00992146i	0.0327430	−	0.000400398i
$615$	−4.61535	+	23.2029i	−0.186109	+	0.935632i
$616$	−4.09911	+	25.4545i	−0.165158	+	1.02559i
$617$	3.05533	−	0.607743i	0.123003	−	0.0244668i	−0.133205	−	0.991089i	$-0.542527\pi$
$617$	3.05533	−	0.607743i	0.123003	−	0.0244668i	0.256208	+	0.966622i	$0.417527\pi$
$618$	−1.87224	+	2.87756i	−0.0753124	+	0.115752i
$619$	−6.90692	+	12.9219i	−0.277612	+	0.519376i	−0.981627	−	0.190809i	$-0.938889\pi$
$619$	−6.90692	+	12.9219i	−0.277612	+	0.519376i	0.704015	+	0.710185i	$0.251389\pi$
$620$	48.9771	+	13.5584i	1.96697	+	0.544520i
$621$	0.331490	+	3.36568i	0.0133023	+	0.135060i
$622$	−3.84364	−	34.6732i	−0.154116	−	1.39027i
$623$	10.8334	−	4.48734i	0.434031	−	0.179781i
$624$	−12.6661	−	7.59480i	−0.507050	−	0.304035i
$625$	−59.1179	−	24.4874i	−2.36472	−	0.979498i
$626$	11.5143	−	39.6988i	0.460205	−	1.58668i
$627$	9.52133	+	7.81395i	0.380245	+	0.312059i
$628$	−19.2500	−	9.69174i	−0.768157	−	0.386743i
$629$	−45.2827	+	13.7363i	−1.80554	+	0.547704i
$630$	11.7706	+	2.19204i	0.468950	+	0.0873330i
$631$	−1.95435	+	2.92489i	−0.0778014	+	0.116438i	−0.868330	−	0.495988i	$-0.834806\pi$
$631$	−1.95435	+	2.92489i	−0.0778014	+	0.116438i	0.790528	+	0.612426i	$0.209806\pi$
$632$	−4.79521	−	35.3415i	−0.190743	−	1.40581i
$633$	−4.06205	+	2.71418i	−0.161452	+	0.107879i
$634$	−10.1395	+	25.3513i	−0.402690	+	1.00683i
$635$	−47.7685	−	58.2061i	−1.89564	−	2.30984i
$636$	3.27848	−	2.30853i	0.130000	−	0.0915393i
$637$	9.27060	−	4.95524i	0.367314	−	0.196334i
$638$	6.81843	−	5.73669i	0.269944	−	0.227118i
$639$	−7.94478			−0.314291
$640$	35.9548	+	30.2722i	1.42124	+	1.19661i
$641$	−4.87386			−0.192506			−0.0962529	−	0.995357i	$-0.530686\pi$
$641$	−4.87386			−0.192506			−0.0962529	+	0.995357i	$0.530686\pi$
$642$	−11.2677	+	9.48010i	−0.444701	+	0.374150i
$643$	−3.65896	+	1.95575i	−0.144295	+	0.0771274i	−0.541964	−	0.840401i	$-0.682319\pi$
$643$	−3.65896	+	1.95575i	−0.144295	+	0.0771274i	0.397669	+	0.917529i	$0.369819\pi$
$644$	7.93596	+	11.2703i	0.312721	+	0.444112i
$645$	9.46199	+	11.5295i	0.372565	+	0.453972i
$646$	−8.45612	+	21.1425i	−0.332702	+	0.831839i
$647$	−3.61547	+	2.41578i	−0.142139	+	0.0949742i	−0.624607	−	0.780940i	$-0.714741\pi$
$647$	−3.61547	+	2.41578i	−0.142139	+	0.0949742i	0.482468	+	0.875914i	$0.339741\pi$
$648$	2.25074	+	1.71294i	0.0884175	+	0.0672907i
$649$	29.5410	−	44.2112i	1.15958	−	1.73544i
$650$	62.9285	+	11.7192i	2.46826	+	0.459666i
$651$	11.9276	−	3.61818i	0.467478	−	0.141808i
$652$	20.2931	−	40.3067i	0.794739	−	1.57853i
$653$	−13.2734	−	10.8932i	−0.519429	−	0.426285i	0.337801	−	0.941217i	$-0.390317\pi$
$653$	−13.2734	−	10.8932i	−0.519429	−	0.426285i	−0.857231	+	0.514933i	$0.827817\pi$
$654$	5.47036	−	18.8606i	0.213908	−	0.737507i
$655$	−18.6693	−	7.73308i	−0.729470	−	0.302156i
$656$	−3.34622	+	22.5311i	−0.130648	+	0.879692i
$657$	6.23376	−	2.58211i	0.243202	−	0.100738i
$658$	0.717957	+	6.47663i	0.0279889	+	0.252485i
$659$	0.600506	+	6.09704i	0.0233924	+	0.237507i	0.999770	+	0.0214368i	$0.00682406\pi$
$659$	0.600506	+	6.09704i	0.0233924	+	0.237507i	−0.976378	+	0.216070i	$0.930676\pi$
$660$	9.91567	−	35.8184i	0.385967	−	1.39423i
$661$	19.7562	−	36.9612i	0.768426	−	1.43762i	−0.126761	−	0.991933i	$-0.540458\pi$
$661$	19.7562	−	36.9612i	0.768426	−	1.43762i	0.895187	−	0.445691i	$-0.147042\pi$
$662$	−7.63497	+	11.7347i	−0.296742	+	0.456081i
$663$	−21.1742	+	4.21181i	−0.822338	+	0.163573i
$664$	11.9557	−	8.63921i	0.463973	−	0.335266i
$665$	4.54811	−	22.8649i	0.176368	−	0.886662i
$666$	11.4439	−	0.139942i	0.443444	−	0.00542266i
$667$	0.466945	−	4.74097i	0.0180802	−	0.183571i
$668$	6.73668	−	17.4596i	0.260650	−	0.675533i
$669$	−2.71292	+	8.94331i	−0.104888	+	0.345768i
$670$	−38.7715	+	12.2809i	−1.49787	+	0.474451i
$671$	−37.3998	−	37.3998i	−1.44380	−	1.44380i
$672$	11.4227	+	1.55395i	0.440642	+	0.0599449i
$673$	7.41492	−	7.41492i	0.285824	−	0.285824i	−0.549602	−	0.835426i	$-0.685221\pi$
$673$	7.41492	−	7.41492i	0.285824	−	0.285824i	0.835426	+	0.549602i	$0.185221\pi$
$674$	14.8623	−	28.6425i	0.572476	−	1.10327i
$675$	−11.7312	−	3.55861i	−0.451533	−	0.136971i
$676$	−1.26356	+	0.0309075i	−0.0485983	+	0.00118875i
$677$	20.1170	+	1.98135i	0.773159	+	0.0761495i	0.476899	−	0.878958i	$-0.341761\pi$
$677$	20.1170	+	1.98135i	0.773159	+	0.0761495i	0.296260	+	0.955107i	$0.404261\pi$
$678$	−17.3939	−	16.9736i	−0.668008	−	0.651868i
$679$	23.6493	+	4.70413i	0.907576	+	0.180528i
$680$	68.6617	−	2.51990i	2.63306	−	0.0966337i
$681$	0.231032	+	1.16148i	0.00885318	+	0.0445079i
$682$	−8.01162	−	37.8522i	−0.306781	−	1.44943i
$683$	25.3442	+	13.5468i	0.969769	+	0.518353i	0.878639	−	0.477486i	$-0.158452\pi$
$683$	25.3442	+	13.5468i	0.969769	+	0.518353i	0.0911303	+	0.995839i	$0.470952\pi$
$684$	3.38865	−	4.34137i	0.129568	−	0.165997i
$685$	−44.0557	+	4.33911i	−1.68328	+	0.165789i
$686$	−17.7340	+	22.1559i	−0.677085	+	0.845915i
$687$	1.95692	+	4.72443i	0.0746612	+	0.180248i
$688$	9.64218	+	10.6423i	0.367605	+	0.405733i
$689$	2.83271	−	6.83876i	0.107918	−	0.260536i
$690$	−9.58010	−	17.4077i	−0.364708	−	0.662700i
$691$	−9.73426	+	11.8612i	−0.370309	+	0.451222i	−0.924509	−	0.381161i	$-0.875524\pi$
$691$	−9.73426	+	11.8612i	−0.370309	+	0.451222i	0.554200	+	0.832384i	$0.313024\pi$
$692$	1.82138	−	24.6623i	0.0692384	−	0.937519i
$693$	−2.64608	−	8.72297i	−0.100516	−	0.331358i
$694$	22.4918	+	32.7862i	0.853775	+	1.24455i
$695$	25.7630	+	17.2143i	0.977246	+	0.652975i
$696$	−2.63879	−	2.98505i	−0.100023	−	0.113148i
$697$	18.4992	+	27.6860i	0.700707	+	1.04868i
$698$	7.56806	+	17.6571i	0.286455	+	0.668331i
$699$	7.91222	−	6.49339i	0.299268	−	0.245603i
$700$	−48.7516	+	10.9430i	−1.84264	+	0.413608i
$701$	8.34904	+	15.6200i	0.315339	+	0.589958i	0.988797	−	0.149268i	$-0.0476917\pi$
$701$	8.34904	+	15.6200i	0.315339	+	0.589958i	−0.673458	+	0.739226i	$0.735192\pi$
$702$	5.20221	+	0.448218i	0.196345	+	0.0169169i
$703$		−	22.2845i		−	0.840476i
$704$	7.84959	−	34.9127i	0.295842	−	1.31582i
$705$		−	9.39328i		−	0.353772i
$706$	−3.52341	+	40.8942i	−0.132605	+	1.53908i
$707$	−2.27352	−	4.25345i	−0.0855045	−	0.159968i
$708$	−20.0849	−	12.7211i	−0.754838	−	0.478089i
$709$	3.71648	−	3.05004i	0.139575	−	0.114547i	−0.562015	−	0.827127i	$-0.689974\pi$
$709$	3.71648	−	3.05004i	0.139575	−	0.114547i	0.701590	+	0.712581i	$0.252474\pi$
$710$	42.9025	−	18.3886i	1.61010	−	0.690111i
$711$	7.00552	+	10.4845i	0.262728	+	0.393200i
$712$	−15.3903	+	5.29235i	−0.576777	+	0.198339i
$713$	−17.1991	−	11.4920i	−0.644110	−	0.430381i
$714$	13.8962	−	9.53298i	0.520053	−	0.356763i
$715$	−19.9165	−	65.6560i	−0.744837	−	2.45540i
$716$	31.6850	+	36.7383i	1.18412	+	1.37297i
$717$	6.30568	−	7.68349i	0.235490	−	0.286945i
$718$	4.97858	−	2.73989i	0.185799	−	0.102252i
$719$	15.2736	−	36.8738i	0.569609	−	1.37516i	−0.332275	−	0.943182i	$-0.607816\pi$
$719$	15.2736	−	36.8738i	0.569609	−	1.37516i	0.901885	−	0.431977i	$-0.142184\pi$
$720$	−16.1189	−	4.04058i	−0.600715	−	0.150584i
$721$	−1.89312	−	4.57039i	−0.0705034	−	0.170210i
$722$	12.6058	+	10.0899i	0.469140	+	0.375508i
$723$	26.2254	−	2.58298i	0.975335	−	0.0960621i
$724$	50.5205	−	6.22660i	1.87758	−	0.231410i
$725$	15.2293	+	8.14024i	0.565603	+	0.302321i
$726$	−12.4632	+	2.63791i	−0.462552	+	0.0979019i
$727$	0.300108	+	1.50874i	0.0111304	+	0.0559562i	0.985951	−	0.167033i	$-0.0534186\pi$
$727$	0.300108	+	1.50874i	0.0111304	+	0.0559562i	−0.974821	+	0.222989i	$0.928419\pi$
$728$	19.3496	−	8.85968i	0.717143	−	0.328361i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−27.6864	+	28.3719i	−1.02472	+	1.05009i
$731$	20.8917	+	2.05765i	0.772706	+	0.0761049i
$732$	−16.3084	+	17.1263i	−0.602777	+	0.633005i
$733$	−11.3351	−	3.43847i	−0.418672	−	0.127003i	0.0739178	−	0.997264i	$-0.476450\pi$
$733$	−11.3351	−	3.43847i	−0.418672	−	0.127003i	−0.492590	+	0.870262i	$0.663950\pi$
$734$	−27.9651	−	14.5108i	−1.03221	−	0.535604i
$735$	8.36357	−	8.36357i	0.308495	−	0.308495i
$736$	−10.0325	−	16.2897i	−0.369803	−	0.600447i
$737$	21.8946	+	21.8946i	0.806500	+	0.806500i
$738$	−2.43181	−	7.67739i	−0.0895163	−	0.282609i
$739$	−6.20938	+	20.4696i	−0.228416	+	0.752986i	0.765558	+	0.643367i	$0.222463\pi$
$739$	−6.20938	+	20.4696i	−0.228416	+	0.752986i	−0.993974	+	0.109619i	$0.965037\pi$
$740$	−61.4744	+	27.2433i	−2.25984	+	1.00148i
$741$	0.996532	−	10.1180i	0.0366085	−	0.371692i
$742$	0.0706506	+	5.77753i	0.00259367	+	0.212100i
$743$	0.0475193	−	0.238896i	0.00174331	−	0.00876423i	−0.979904	−	0.199470i	$-0.936078\pi$
$743$	0.0475193	−	0.238896i	0.00174331	−	0.00876423i	0.981647	+	0.190706i	$0.0610778\pi$
$744$	−16.8319	+	3.99498i	−0.617089	+	0.146463i
$745$	−46.4573	+	9.24093i	−1.70206	+	0.338561i
$746$	−4.57281	−	2.97522i	−0.167422	−	0.108931i
$747$	−2.45837	+	4.59928i	−0.0899470	+	0.168279i
$748$	−25.7796	−	45.5167i	−0.942595	−	1.66425i
$749$	−2.07983	−	21.1169i	−0.0759953	−	0.771593i
$750$	42.3887	−	4.69893i	1.54782	−	0.171581i
$751$	26.8718	−	11.1307i	0.980566	−	0.406164i	0.165931	−	0.986137i	$-0.446937\pi$
$751$	26.8718	−	11.1307i	0.980566	−	0.406164i	0.814635	+	0.579974i	$0.196937\pi$
$752$	−0.442189	−	9.03336i	−0.0161250	−	0.329413i
$753$	−17.2956	−	7.16406i	−0.630286	−	0.261073i
$754$	−7.06398	−	2.04885i	−0.257255	−	0.0746148i
$755$	−1.43157	−	1.17486i	−0.0521001	−	0.0427575i
$756$	−3.87015	+	1.27815i	−0.140756	+	0.0464858i
$757$	−29.4023	+	8.91909i	−1.06865	+	0.324170i	−0.775141	−	0.631788i	$-0.782321\pi$
$757$	−29.4023	+	8.91909i	−1.06865	+	0.324170i	−0.293504	+	0.955958i	$0.594821\pi$
$758$	−1.02226	+	5.48923i	−0.0371303	+	0.199378i
$759$	−8.40447	+	12.5782i	−0.305063	+	0.456559i
$760$	−8.25071	+	31.2870i	−0.299285	+	1.13490i
$761$	−16.4303	+	10.9784i	−0.595598	+	0.397966i	−0.816513	−	0.577327i	$-0.804096\pi$
$761$	−16.4303	+	10.9784i	−0.595598	+	0.397966i	0.220915	+	0.975293i	$0.429096\pi$
$762$	23.7995	+	9.51881i	0.862164	+	0.344830i
$763$	17.9521	+	21.8747i	0.649910	+	0.791917i
$764$	−33.3843	−	5.79575i	−1.20780	−	0.209683i
$765$	−21.4236	+	11.4511i	−0.774571	+	0.414017i
$766$	18.1440	+	21.5653i	0.655568	+	0.779185i
$767$	−43.8897			−1.58477
$768$	−15.6915	−	3.12696i	−0.566217	−	0.112835i
$769$	−21.3929			−0.771446			−0.385723	−	0.922615i	$-0.626048\pi$
$769$	−21.3929			−0.771446			−0.385723	+	0.922615i	$0.626048\pi$
$770$	34.4788	+	40.9803i	1.24253	+	1.47683i
$771$	2.38871	−	1.27679i	0.0860273	−	0.0459826i
$772$	19.3450	+	3.35843i	0.696243	+	0.120873i
$773$	−16.7261	−	20.3808i	−0.601597	−	0.733048i	0.379794	−	0.925071i	$-0.375995\pi$
$773$	−16.7261	−	20.3808i	−0.601597	−	0.733048i	−0.981390	+	0.192024i	$0.938495\pi$
$774$	−4.71420	−	1.88549i	−0.169448	−	0.0677724i
$775$	62.3436	−	41.6567i	2.23945	−	1.49635i
$776$	−32.3603	−	8.53376i	−1.16167	−	0.306344i
$777$	−9.16240	+	13.7125i	−0.328699	+	0.491933i
$778$	5.11897	−	27.4872i	0.183524	−	0.985465i
$779$	−15.0057	+	4.55191i	−0.537633	+	0.163089i
$780$	−29.1298	+	9.62036i	−1.04302	+	0.344464i
$781$	−27.4707	−	22.5446i	−0.982978	−	0.806710i
$782$	−26.8595	−	7.79040i	−0.960494	−	0.278584i
$783$	1.30140	+	0.539056i	0.0465081	+	0.0192643i
$784$	7.64939	−	8.43682i	0.273193	−	0.301315i
$785$	−41.3602	+	17.1319i	−1.47621	+	0.611465i
$786$	6.83703	−	0.757908i	0.243869	−	0.0270337i
$787$	−0.0605382	−	0.614655i	−0.00215795	−	0.0219101i	0.994045	−	0.108966i	$-0.0347540\pi$
$787$	−0.0605382	−	0.614655i	−0.00215795	−	0.0219101i	−0.996203	+	0.0870562i	$0.972254\pi$
$788$	9.84919	+	17.3898i	0.350863	+	0.619486i
$789$	1.92546	−	3.60228i	0.0685482	−	0.128245i
$790$	−62.0973	−	40.4026i	−2.20932	−	1.43746i
$791$	34.3480	−	6.83224i	1.22127	−	0.242926i
$792$	2.92164	+	12.3097i	0.103816	+	0.437406i
$793$	−8.51720	+	42.8189i	−0.302455	+	1.52054i
$794$	0.0981927	+	8.02982i	0.00348473	+	0.284968i
$795$	0.816381	−	8.28886i	0.0289541	−	0.293976i
$796$	30.9241	−	13.7045i	1.09608	−	0.485742i
$797$	−9.47228	+	31.2259i	−0.335525	+	1.10608i	0.613187	+	0.789938i	$0.289887\pi$
$797$	−9.47228	+	31.2259i	−0.335525	+	1.10608i	−0.948712	+	0.316141i	$0.897613\pi$
$798$	2.39639	+	7.56555i	0.0848312	+	0.267817i
$799$	−9.34863	−	9.34863i	−0.330731	−	0.330731i
$800$	68.4694	−	11.0014i	2.42076	−	0.388958i
$801$	4.06871	−	4.06871i	0.143761	−	0.143761i
$802$	20.9267	+	10.8587i	0.738949	+	0.383434i
$803$	28.8816	+	8.76115i	1.01921	+	0.309174i
$804$	9.54730	−	10.0261i	0.336707	−	0.353592i
$805$	28.4943	+	2.80644i	1.00429	+	0.0989142i
$806$	−22.3045	+	22.8568i	−0.785643	+	0.805095i
$807$	−6.29524	−	1.25220i	−0.221603	−	0.0440796i
$808$	2.78674	+	6.08626i	0.0980371	+	0.214114i
$809$	3.12955	+	15.7333i	0.110029	+	0.553153i	0.995995	+	0.0894039i	$0.0284962\pi$
$809$	3.12955	+	15.7333i	0.110029	+	0.553153i	−0.885966	+	0.463749i	$0.846504\pi$
$810$	5.74787	−	1.21657i	0.201960	−	0.0427459i
$811$	20.8386	+	11.1384i	0.731741	+	0.391124i	0.794788	−	0.606887i	$-0.207582\pi$
$811$	20.8386	+	11.1384i	0.731741	+	0.391124i	−0.0630475	+	0.998011i	$0.520082\pi$
$812$	5.69807	−	0.702282i	0.199963	−	0.0246453i
$813$	13.6813	−	1.34749i	0.479825	−	0.0472586i
$814$	39.9669	+	31.9902i	1.40084	+	1.12126i
$815$	−35.8718	−	86.6022i	−1.25653	−	3.03354i
$816$	−20.0636	+	12.0209i	−0.702367	+	0.420815i
$817$	−3.78325	+	9.13357i	−0.132359	+	0.319543i
$818$	−25.5234	+	14.0465i	−0.892405	+	0.491124i
$819$	−4.77326	+	5.81623i	−0.166791	+	0.203236i
$820$	30.9017	+	35.8300i	1.07913	+	1.25124i
$821$	10.0153	+	33.0162i	0.349538	+	1.15227i	0.938838	+	0.344359i	$0.111904\pi$
$821$	10.0153	+	33.0162i	0.349538	+	1.15227i	−0.589300	+	0.807914i	$0.700596\pi$
$822$	12.4267	−	8.52487i	0.433431	−	0.297339i
$823$	−31.8991	−	21.3143i	−1.11193	−	0.742970i	−0.142859	−	0.989743i	$-0.545630\pi$
$823$	−31.8991	−	21.3143i	−1.11193	−	0.742970i	−0.969073	+	0.246773i	$0.920630\pi$
$824$	2.23274	+	6.49287i	0.0777811	+	0.226190i
$825$	−30.4647	−	45.5937i	−1.06065	−	1.58737i
$826$	31.4886	−	13.4964i	1.09563	−	0.469600i
$827$	−23.3302	+	19.1466i	−0.811271	+	0.665793i	−0.945668	−	0.325135i	$-0.894590\pi$
$827$	−23.3302	+	19.1466i	−0.811271	+	0.665793i	0.134397	+	0.990928i	$0.457090\pi$
$828$	5.71421	+	3.61919i	0.198583	+	0.125775i
$829$	−8.66509	−	16.2112i	−0.300951	−	0.563039i	0.685307	−	0.728255i	$-0.259668\pi$
$829$	−8.66509	−	16.2112i	−0.300951	−	0.563039i	−0.986258	+	0.165215i	$0.947168\pi$
$830$	2.63014	−	30.5265i	0.0912935	−	1.05959i
$831$		−	3.81147i		−	0.132218i
$832$	−27.5608	+	10.6230i	−0.955499	+	0.368287i
$833$		−	16.6476i		−	0.576806i
$834$	−10.5087	−	0.905424i	−0.363888	−	0.0313523i
$835$	−18.3247	−	34.2830i	−0.634151	−	1.18641i
$836$	24.0363	−	5.39532i	0.831313	−	0.186601i
$837$	4.72797	−	3.88015i	0.163423	−	0.134117i
$838$	7.49064	+	17.4765i	0.258760	+	0.603714i
$839$	1.71452	+	2.56596i	0.0591917	+	0.0885867i	0.859885	−	0.510488i	$-0.170535\pi$
$839$	1.71452	+	2.56596i	0.0591917	+	0.0885867i	−0.800693	+	0.599075i	$0.795535\pi$
$840$	17.9408	−	15.8597i	0.619017	−	0.547213i
$841$	22.4628	+	15.0092i	0.774579	+	0.517557i
$842$	−12.1788	−	17.7530i	−0.419709	−	0.611810i
$843$	−6.55203	−	21.5992i	−0.225664	−	0.743915i
$844$	−0.719640	+	9.74424i	−0.0247710	+	0.335411i
$845$	−1.66556	+	2.02950i	−0.0572972	+	0.0698168i
$846$	1.54171	+	2.80139i	0.0530050	+	0.0963138i
$847$	7.02502	−	16.9599i	0.241382	−	0.582749i
$848$	0.394902	−	8.00969i	0.0135610	−	0.275054i
$849$	−0.198666	−	0.479623i	−0.00681821	−	0.0164606i
$850$	63.3478	−	79.1434i	2.17281	−	2.71460i
$851$	27.2374	−	2.68265i	0.933687	−	0.0919601i
$852$	−9.77686	+	12.5256i	−0.334950	+	0.429121i
$853$	36.6891	+	19.6108i	1.25621	+	0.671459i	0.959015	−	0.283357i	$-0.0914480\pi$
$853$	36.6891	+	19.6108i	1.25621	+	0.671459i	0.297198	+	0.954816i	$0.403948\pi$
$854$	−7.05648	−	33.3394i	−0.241468	−	1.14085i
$855$	−2.23179	−	11.2200i	−0.0763257	−	0.383715i
$856$	1.08011	+	29.4307i	0.0369175	+	1.00592i
$857$	28.8463	+	5.73790i	0.985372	+	0.196003i	0.661375	−	0.750055i	$-0.269973\pi$
$857$	28.8463	+	5.73790i	0.985372	+	0.196003i	0.323997	+	0.946058i	$0.394973\pi$
$858$	16.7158	+	16.3119i	0.570669	+	0.556880i
$859$	14.8930	+	1.46683i	0.508143	+	0.0500477i	0.348840	−	0.937182i	$-0.386576\pi$
$859$	14.8930	+	1.46683i	0.508143	+	0.0500477i	0.159302	+	0.987230i	$0.449076\pi$
$860$	29.8211	−	0.729445i	1.01689	−	0.0248739i
$861$	11.1051	+	3.36869i	0.378461	+	0.114805i
$862$	20.8660	−	40.2126i	0.710697	−	1.36965i
$863$	40.0483	−	40.0483i	1.36326	−	1.36326i	0.493531	−	0.869728i	$-0.335706\pi$
$863$	40.0483	−	40.0483i	1.36326	−	1.36326i	0.869728	−	0.493531i	$-0.164294\pi$
$864$	5.47036	−	1.44054i	0.186105	−	0.0490080i
$865$	−36.3226	−	36.3226i	−1.23501	−	1.23501i
$866$	−30.2601	+	9.58489i	−1.02828	+	0.325708i
$867$	−4.99019	+	16.4504i	−0.169476	+	0.558687i
$868$	8.97370	−	23.2573i	0.304587	−	0.789406i
$869$	−5.52848	+	56.1316i	−0.187541	+	1.90413i
$870$	−8.27533	+	0.101195i	−0.280560	+	0.00343083i
$871$	4.98615	−	25.0671i	0.168949	−	0.849366i
$872$	−23.0035	−	31.8344i	−0.778995	−	1.07805i
$873$	11.6049	−	2.30835i	0.392766	−	0.0781260i
$874$	7.18255	−	11.0393i	0.242953	−	0.373410i
$875$	−28.9702	+	54.1994i	−0.979370	+	1.83227i
$876$	3.60036	−	13.0056i	0.121645	−	0.439418i
$877$	2.49524	+	25.3346i	0.0842582	+	0.855487i	0.940699	+	0.339242i	$0.110171\pi$
$877$	2.49524	+	25.3346i	0.0842582	+	0.855487i	−0.856441	+	0.516245i	$0.827329\pi$
$878$	−1.87073	−	16.8757i	−0.0631339	−	0.569526i
$879$	−7.06990	+	2.92845i	−0.238462	+	0.0987741i
$880$	−44.2685	−	59.7111i	−1.49229	−	2.01286i
$881$	11.8415	+	4.90493i	0.398952	+	0.165251i	0.573133	−	0.819462i	$-0.305728\pi$
$881$	11.8415	+	4.90493i	0.398952	+	0.165251i	−0.174181	+	0.984714i	$0.555728\pi$
$882$	−1.12159	+	3.86700i	−0.0377660	+	0.130209i
$883$	−11.5546	−	9.48263i	−0.388844	−	0.319116i	0.419578	−	0.907719i	$-0.362178\pi$
$883$	−11.5546	−	9.48263i	−0.388844	−	0.319116i	−0.808422	+	0.588603i	$0.799678\pi$
$884$	−19.4167	+	38.5660i	−0.653055	+	1.29711i
$885$	−47.2581	+	14.3356i	−1.58856	+	0.481886i
$886$	37.8879	+	7.05589i	1.27287	+	0.237047i
$887$	10.3250	−	15.4524i	0.346679	−	0.518842i	−0.616624	−	0.787258i	$-0.711500\pi$
$887$	10.3250	−	15.4524i	0.346679	−	0.518842i	0.963303	+	0.268416i	$0.0865002\pi$
$888$	13.8623	−	18.2146i	0.465189	−	0.611241i
$889$	−30.7113	+	20.5207i	−1.03002	+	0.688241i
$890$	−12.5542	+	31.3886i	−0.420817	+	1.05215i
$891$	−2.83766	−	3.45770i	−0.0950653	−	0.115837i
$892$	10.7614	+	15.2828i	0.360317	+	0.511706i
$893$	5.49097	−	2.93498i	0.183748	−	0.0982154i
$894$	12.3384	−	10.3809i	0.412658	−	0.347190i
$895$	100.774			3.36850
$896$	16.5068	−	16.0966i	0.551453	−	0.537750i
$897$	12.4867			0.416919
$898$	5.60436	−	4.71523i	0.187020	−	0.157349i
$899$	−7.59825	+	4.06135i	−0.253416	+	0.135454i
$900$	−20.0468	+	14.1159i	−0.668228	+	0.470531i
$901$	−7.43695	−	9.06196i	−0.247761	−	0.301898i
$902$	13.3774	−	33.4468i	0.445417	−	1.11366i
$903$	6.08330	−	4.06473i	0.202439	−	0.135266i
$904$	−48.1653	+	6.53516i	−1.60195	+	0.217356i
$905$	58.7434	−	87.9157i	1.95270	−	2.92242i
$906$	0.619770	+	0.115420i	0.0205905	+	0.00383458i
$907$	0.393055	−	0.119232i	0.0130512	−	0.00395903i	−0.283752	−	0.958898i	$-0.591579\pi$
$907$	0.393055	−	0.119232i	0.0130512	−	0.00395903i	0.296804	+	0.954939i	$0.404079\pi$
$908$	2.11548	+	1.06507i	0.0702046	+	0.0353457i
$909$	−1.82945	−	1.50139i	−0.0606790	−	0.0497979i
$910$	12.3141	−	42.4561i	0.408207	−	1.40741i
$911$	32.4866	+	13.4564i	1.07633	+	0.445830i	0.849220	−	0.528039i	$-0.177072\pi$
$911$	32.4866	+	13.4564i	1.07633	+	0.445830i	0.227110	+	0.973869i	$0.427072\pi$
$912$	−2.67446	−	10.6850i	−0.0885601	−	0.353816i
$913$	−21.5515	+	8.92693i	−0.713251	+	0.295438i
$914$	6.51712	+	58.7904i	0.215567	+	1.94461i
$915$	4.81496	+	48.8871i	0.159178	+	1.61616i
$916$	9.85665	+	2.72864i	0.325673	+	0.0901566i
$917$	−4.67270	+	8.74201i	−0.154306	+	0.288687i
$918$	4.50976	−	6.93133i	0.148844	−	0.228768i
$919$	18.9684	−	3.77305i	0.625710	−	0.124461i	0.127956	−	0.991780i	$-0.459158\pi$
$919$	18.9684	−	3.77305i	0.625710	−	0.124461i	0.497754	+	0.867318i	$0.334158\pi$
$920$	−39.2340	−	6.31811i	−1.29351	−	0.208302i
$921$	−0.111932	+	0.562722i	−0.00368829	+	0.0185423i
$922$	33.7563	−	0.412789i	1.11171	−	0.0135945i
$923$	−2.87517	+	29.1921i	−0.0946373	+	0.960868i
$924$	−17.0088	−	6.56273i	−0.559548	−	0.215898i
$925$	−28.7988	+	94.9368i	−0.946897	+	3.12150i
$926$	−16.8513	+	5.33765i	−0.553768	+	0.175406i
$927$	−1.71651	−	1.71651i	−0.0563776	−	0.0563776i
$928$	−7.95348	+	0.486879i	−0.261086	+	0.0159826i
$929$	−22.2062	+	22.2062i	−0.728561	+	0.728561i	−0.970333	−	0.241772i	$-0.922271\pi$
$929$	−22.2062	+	22.2062i	−0.728561	+	0.728561i	0.241772	+	0.970333i	$0.422271\pi$
$930$	−16.5507	+	31.8962i	−0.542718	+	1.04592i
$931$	7.50228	+	2.27579i	0.245877	+	0.0745861i
$932$	−0.500590	−	20.4651i	−0.0163974	−	0.670356i
$933$	24.5491	+	2.41787i	0.803700	+	0.0791576i
$934$	−29.4199	−	28.7091i	−0.962649	−	0.939389i
$935$	−106.571	−	21.1983i	−3.48524	−	0.693257i
$936$	7.10851	−	7.65015i	0.232349	−	0.250053i
$937$	5.77307	+	29.0232i	0.188598	+	0.948146i	0.952899	+	0.303287i	$0.0980841\pi$
$937$	5.77307	+	29.0232i	0.188598	+	0.948146i	−0.764301	+	0.644859i	$0.776916\pi$
$938$	4.13101	+	19.5176i	0.134882	+	0.637272i
$939$	25.7769	+	13.7781i	0.841198	+	0.449630i
$940$	−14.8093	−	11.5594i	−0.483026	−	0.377026i
$941$	11.3333	−	1.11623i	0.369454	−	0.0363881i	0.0884134	−	0.996084i	$-0.471820\pi$
$941$	11.3333	−	1.11623i	0.369454	−	0.0363881i	0.281041	+	0.959696i	$0.409320\pi$
$942$	9.52313	−	11.8977i	0.310280	−	0.387648i
$943$	−7.37002	−	17.7928i	−0.240001	−	0.579414i
$944$	−44.7725	+	16.0110i	−1.45722	+	0.521113i
$945$	−3.23985	+	7.82169i	−0.105392	+	0.254440i
$946$	−10.9499	−	19.8968i	−0.356012	−	0.646899i
$947$	31.5381	−	38.4292i	1.02485	−	1.24878i	0.0567047	−	0.998391i	$-0.481941\pi$
$947$	31.5381	−	38.4292i	1.02485	−	1.24878i	0.968145	−	0.250392i	$-0.0805593\pi$
$948$	25.1507	+	1.85745i	0.816857	+	0.0603272i
$949$	−7.23166	−	23.8396i	−0.234750	−	0.773866i
$950$	27.0062	+	39.3670i	0.876198	+	1.27723i
$951$	−16.0529	−	10.7262i	−0.520551	−	0.347821i
$952$	2.07116	−	33.6399i	0.0671268	−	1.09027i
$953$	−14.9395	−	22.3585i	−0.483938	−	0.724264i	0.506497	−	0.862241i	$-0.330940\pi$
$953$	−14.9395	−	22.3585i	−0.483938	−	0.724264i	−0.990435	+	0.137977i	$0.955940\pi$
$954$	1.11697	+	2.60600i	0.0361632	+	0.0843725i
$955$	−54.4069	+	44.6506i	−1.76057	+	1.44486i
$956$	−4.35390	−	19.3968i	−0.140815	−	0.627336i
$957$	2.97018	+	5.55682i	0.0960124	+	0.179627i
$958$	−25.2963	−	2.17950i	−0.817286	−	0.0704166i
$959$			21.7154i			0.701226i
$960$	−26.2062	+	20.4404i	−0.845803	+	0.659712i
$961$			6.40925i			0.206750i
$962$	3.62729	−	42.1000i	0.116949	−	1.35736i
$963$	−4.90834	−	9.18286i	−0.158169	−	0.295914i
$964$	28.2008	−	44.5253i	0.908286	−	1.43406i
$965$	31.5269	−	25.8734i	1.01489	−	0.832896i
$966$	−8.95857	+	3.83976i	−0.288237	+	0.123542i
$967$	−19.4204	−	29.0647i	−0.624518	−	0.934657i	−0.999969	−	0.00781532i	$-0.997512\pi$
$967$	−19.4204	−	29.0647i	−0.624518	−	0.934657i	0.375451	−	0.926842i	$-0.377488\pi$
$968$	−11.1783	+	22.8955i	−0.359286	+	0.735889i
$969$	−13.3878	−	8.94546i	−0.430079	−	0.287369i
$970$	−57.3246	+	39.3254i	−1.84058	+	1.26266i
$971$	−3.62649	−	11.9549i	−0.116380	−	0.383652i	0.879327	−	0.476219i	$-0.157993\pi$
$971$	−3.62649	−	11.9549i	−0.116380	−	0.383652i	−0.995707	+	0.0925664i	$0.970493\pi$
$972$	−1.51453	+	1.30621i	−0.0485787	+	0.0418968i
$973$	9.64223	−	11.7491i	0.309116	−	0.376658i
$974$	14.4655	−	7.96089i	0.463504	−	0.255083i
$975$	−17.3211	+	41.8168i	−0.554719	+	1.33921i
$976$	6.93182	+	46.7872i	0.221882	+	1.49762i
$977$	−0.567698	−	1.37054i	−0.0181623	−	0.0438476i	0.914538	−	0.404499i	$-0.132554\pi$
$977$	−0.567698	−	1.37054i	−0.0181623	−	0.0438476i	−0.932701	+	0.360652i	$0.882554\pi$
$978$	24.9121	+	19.9401i	0.796601	+	0.637613i
$979$	25.6140	−	2.52276i	0.818628	−	0.0806279i
$980$	−2.89365	−	23.4781i	−0.0924344	−	0.749981i
$981$	12.2464	+	6.54585i	0.390998	+	0.208993i
$982$	10.3372	−	2.18793i	0.329874	−	0.0698196i
$983$	8.37815	+	42.1198i	0.267222	+	1.34341i	0.848278	+	0.529550i	$0.177639\pi$
$983$	8.37815	+	42.1198i	0.267222	+	1.34341i	−0.581057	+	0.813863i	$0.697361\pi$
$984$	−15.0967	−	5.61385i	−0.481264	−	0.178963i
$985$	40.7158	+	8.09887i	1.29731	+	0.258052i
$986$	−8.13528	+	8.33671i	−0.259080	+	0.265495i
$987$	−4.58554	−	0.451636i	−0.145959	−	0.0143757i
$988$	−14.7255	−	14.0223i	−0.468480	−	0.446108i
$989$	−11.6190	−	3.52459i	−0.369463	−	0.112075i
$990$	23.3266	+	12.1040i	0.741370	+	0.384690i
$991$	24.7120	−	24.7120i	0.785002	−	0.785002i	−0.195668	−	0.980670i	$-0.562687\pi$
$991$	24.7120	−	24.7120i	0.785002	−	0.785002i	0.980670	+	0.195668i	$0.0626874\pi$
$992$	−14.4150	+	31.4532i	−0.457676	+	0.998640i
$993$	−6.99991	−	6.99991i	−0.222136	−	0.222136i
$994$	−6.91400	−	21.8279i	−0.219299	−	0.692340i
$995$	20.3956	−	67.2354i	0.646585	−	2.13150i
$996$	4.22589	+	9.53571i	0.133902	+	0.302151i
$997$	−1.63142	+	16.5641i	−0.0516676	+	0.524590i	0.934163	+	0.356846i	$0.116148\pi$
$997$	−1.63142	+	16.5641i	−0.0516676	+	0.524590i	−0.985831	+	0.167743i	$0.946352\pi$
$998$	0.461564	+	37.7449i	0.0146105	+	1.19479i
$999$	−1.57881	+	7.93720i	−0.0499512	+	0.251122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.23	yes	512
128.109	even	32	inner	384.2.v.a.109.23	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.23	✓	512	128.109	even	32	inner
384.2.v.a.229.23	yes	512	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.910468 + 1.08215i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-0.342097 + 1.97053i) q^{4} +(2.63552 + 3.21139i) q^{5} +(-1.31308 - 0.525180i) q^{6} +(1.69443 - 1.13218i) q^{7} +(-2.44387 + 1.42390i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.910468 + 1.08215i) q^{2} +(-0.881921 + 0.471397i) q^{3} +(-0.342097 + 1.97053i) q^{4} +(2.63552 + 3.21139i) q^{5} +(-1.31308 - 0.525180i) q^{6} +(1.69443 - 1.13218i) q^{7} +(-2.44387 + 1.42390i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-1.07565 + 5.77590i) q^{10} +(4.28043 - 1.29845i) q^{11} +(-0.627197 - 1.89911i) q^{12} +(-2.85407 - 2.34227i) q^{13} +(2.76791 + 0.802812i) q^{14} +(-3.83816 - 1.58982i) q^{15} +(-3.76594 - 1.34822i) q^{16} +(-5.40218 + 2.23766i) q^{17} +(1.40560 - 0.155816i) q^{18} +(-0.269906 - 2.74040i) q^{19} +(-7.22974 + 4.09476i) q^{20} +(-0.960647 + 1.79724i) q^{21} +(5.30231 + 3.44986i) q^{22} +(3.31698 - 0.659788i) q^{23} +(1.48408 - 2.40780i) q^{24} +(-2.39162 + 12.0235i) q^{25} +(-0.0638462 - 5.22110i) q^{26} +(-0.0980171 + 0.995185i) q^{27} +(1.65133 + 3.72623i) q^{28} +(0.408901 - 1.34797i) q^{29} +(-1.77410 - 5.60095i) q^{30} +(-4.32488 - 4.32488i) q^{31} +(-1.96979 - 5.30282i) q^{32} +(-3.16291 + 3.16291i) q^{33} +(-7.33999 - 3.80866i) q^{34} +(8.10159 + 2.45759i) q^{35} +(1.44837 + 1.37921i) q^{36} +(8.05373 + 0.793223i) q^{37} +(2.71978 - 2.78712i) q^{38} +(3.62121 + 0.720303i) q^{39} +(-11.0136 - 4.09552i) q^{40} +(-1.11095 - 5.58514i) q^{41} +(-2.81952 + 0.596769i) q^{42} +(-3.16625 - 1.69240i) q^{43} +(1.09431 + 8.87889i) q^{44} +(4.13440 - 0.407202i) q^{45} +(3.73399 + 2.98875i) q^{46} +(0.865264 + 2.08893i) q^{47} +(3.95681 - 0.586226i) q^{48} +(-1.08953 + 2.63035i) q^{49} +(-15.1887 + 8.35890i) q^{50} +(3.70947 - 4.52001i) q^{51} +(5.59188 - 4.82273i) q^{52} +(0.581978 + 1.91853i) q^{53} +(-1.16618 + 0.800014i) q^{54} +(15.4510 + 10.3240i) q^{55} +(-2.52886 + 5.17960i) q^{56} +(1.52985 + 2.28958i) q^{57} +(1.83099 - 0.784788i) q^{58} +(9.18901 - 7.54123i) q^{59} +(4.44580 - 7.01933i) q^{60} +(-5.57402 - 10.4283i) q^{61} +(0.742506 - 8.61784i) q^{62} -2.03787i q^{63} +(3.94502 - 6.95966i) q^{64} -15.3387i q^{65} +(-6.30248 - 0.543016i) q^{66} +(3.26315 + 6.10493i) q^{67} +(-2.56129 - 11.4106i) q^{68} +(-2.61429 + 2.14550i) q^{69} +(4.71676 + 11.0047i) q^{70} +(-4.41388 - 6.60584i) q^{71} +(-0.173813 + 2.82308i) q^{72} +(5.61024 + 3.74864i) q^{73} +(6.47427 + 9.43755i) q^{74} +(-3.55861 - 11.7312i) q^{75} +(5.49235 + 0.405626i) q^{76} +(5.78280 - 7.04636i) q^{77} +(2.51752 + 4.57450i) q^{78} +(-4.82549 + 11.6498i) q^{79} +(-5.59555 - 15.6472i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(5.03247 - 6.28731i) q^{82} +(-5.18996 + 0.511166i) q^{83} +(-3.21288 - 2.50781i) q^{84} +(-21.4236 - 11.4511i) q^{85} +(-1.05134 - 4.96723i) q^{86} +(0.274809 + 1.38156i) q^{87} +(-8.61195 + 9.26815i) q^{88} +(5.64347 + 1.12256i) q^{89} +(4.20489 + 4.10329i) q^{90} +(-7.48790 - 0.737494i) q^{91} +(0.165401 + 6.76191i) q^{92} +(5.85294 + 1.77547i) q^{93} +(-1.47274 + 2.83825i) q^{94} +(8.08915 - 8.08915i) q^{95} +(4.23693 + 3.74812i) q^{96} +(8.36665 + 8.36665i) q^{97} +(-3.83842 + 1.21582i) q^{98} +(1.29845 - 4.28043i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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