LMFDB - Embedded newform 1110.2.bb.e.1009.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.19
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.03757 + 0.921047i) q^{5} -1.00000 q^{6} +(0.666623 - 0.384875i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.03757 + 0.921047i) q^{5} -1.00000 q^{6} +(0.666623 - 0.384875i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.30406 + 1.81643i) q^{10} -0.542466 q^{11} +(-0.866025 - 0.500000i) q^{12} +(5.71133 - 3.29744i) q^{13} +0.769750 q^{14} +(-2.22511 + 0.221132i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00556 + 1.73526i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.29036 - 2.23497i) q^{19} +(0.221132 + 2.22511i) q^{20} +(-0.384875 + 0.666623i) q^{21} +(-0.469789 - 0.271233i) q^{22} +3.05773i q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.30334 + 3.75339i) q^{25} +6.59487 q^{26} +1.00000i q^{27} +(0.666623 + 0.384875i) q^{28} +1.93051 q^{29} +(-2.03757 - 0.921047i) q^{30} -2.81660 q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.469789 - 0.271233i) q^{33} +(1.73526 + 3.00556i) q^{34} +(1.71278 - 0.170217i) q^{35} +1.00000 q^{36} +(1.40837 - 5.91747i) q^{37} -2.58072i q^{38} +(-3.29744 + 5.71133i) q^{39} +(-0.921047 + 2.03757i) q^{40} +(-4.40694 - 7.63305i) q^{41} +(-0.666623 + 0.384875i) q^{42} +6.99497i q^{43} +(-0.271233 - 0.469789i) q^{44} +(1.81643 - 1.30406i) q^{45} +(-1.52887 + 2.64807i) q^{46} +11.5001i q^{47} -1.00000i q^{48} +(-3.20374 + 5.54904i) q^{49} +(0.984087 + 4.90220i) q^{50} -3.47052 q^{51} +(5.71133 + 3.29744i) q^{52} +(-3.51035 - 2.02670i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.10531 - 0.499637i) q^{55} +(0.384875 + 0.666623i) q^{56} +(2.23497 + 1.29036i) q^{57} +(1.67187 + 0.965257i) q^{58} +(-2.29207 + 3.96998i) q^{59} +(-1.30406 - 1.81643i) q^{60} +(-2.02517 - 3.50769i) q^{61} +(-2.43925 - 1.40830i) q^{62} -0.769750i q^{63} -1.00000 q^{64} +(14.6743 - 1.45834i) q^{65} +0.542466 q^{66} +(8.50676 - 4.91138i) q^{67} +3.47052i q^{68} +(-1.52887 - 2.64807i) q^{69} +(1.56842 + 0.708976i) q^{70} +(-1.34544 - 2.33038i) q^{71} +(0.866025 + 0.500000i) q^{72} +9.10465i q^{73} +(4.17842 - 4.42050i) q^{74} +(-4.73747 - 1.59886i) q^{75} +(1.29036 - 2.23497i) q^{76} +(-0.361621 + 0.208782i) q^{77} +(-5.71133 + 3.29744i) q^{78} +(2.97540 + 5.15355i) q^{79} +(-1.81643 + 1.30406i) q^{80} +(-0.500000 - 0.866025i) q^{81} -8.81389i q^{82} +(-8.26377 - 4.77109i) q^{83} -0.769750 q^{84} +(4.52577 + 6.30397i) q^{85} +(-3.49748 + 6.05782i) q^{86} +(-1.67187 + 0.965257i) q^{87} -0.542466i q^{88} +(-6.24819 + 10.8222i) q^{89} +(2.22511 - 0.221132i) q^{90} +(2.53820 - 4.39630i) q^{91} +(-2.64807 + 1.52887i) q^{92} +(2.43925 - 1.40830i) q^{93} +(-5.75003 + 9.95934i) q^{94} +(-0.570681 - 5.74238i) q^{95} +(0.500000 - 0.866025i) q^{96} -16.8742i q^{97} +(-5.54904 + 3.20374i) q^{98} +(-0.271233 + 0.469789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.03757	+	0.921047i	0.911227	+	0.411905i
$5$	2.03757	+	0.921047i	0.911227	+	0.411905i
$6$	−1.00000			−0.408248
$7$	0.666623	−	0.384875i	0.251960	−	0.145469i	−0.368701	−	0.929548i	$-0.620198\pi$
$7$	0.666623	−	0.384875i	0.251960	−	0.145469i	0.620661	+	0.784079i	$0.286864\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.30406	+	1.81643i	0.412380	+	0.574406i
$11$	−0.542466			−0.163560			−0.0817799	−	0.996650i	$-0.526060\pi$
$11$	−0.542466			−0.163560			−0.0817799	+	0.996650i	$0.526060\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	5.71133	−	3.29744i	1.58404	−	0.914544i	0.589776	−	0.807567i	$-0.299216\pi$
$13$	5.71133	−	3.29744i	1.58404	−	0.914544i	0.994261	−	0.106977i	$-0.0341171\pi$
$14$	0.769750			0.205724
$15$	−2.22511	+	0.221132i	−0.574520	+	0.0570962i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00556	+	1.73526i	0.728955	+	0.420862i	0.818040	−	0.575162i	$-0.195061\pi$
$17$	3.00556	+	1.73526i	0.728955	+	0.420862i	−0.0890846	+	0.996024i	$0.528394\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−1.29036	−	2.23497i	−0.296029	−	0.512737i	0.679195	−	0.733958i	$-0.262329\pi$
$19$	−1.29036	−	2.23497i	−0.296029	−	0.512737i	−0.975224	+	0.221221i	$0.928996\pi$
$20$	0.221132	+	2.22511i	0.0494467	+	0.497549i
$21$	−0.384875	+	0.666623i	−0.0839866	+	0.145469i
$22$	−0.469789	−	0.271233i	−0.100159	−	0.0578271i
$23$			3.05773i			0.637581i	0.947825	+	0.318791i	$0.103277\pi$
$23$			3.05773i			0.637581i	−0.947825	+	0.318791i	$0.896723\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	3.30334	+	3.75339i	0.660669	+	0.750677i
$26$	6.59487			1.29336
$27$			1.00000i			0.192450i
$28$	0.666623	+	0.384875i	0.125980	+	0.0727346i
$29$	1.93051			0.358487			0.179244	−	0.983805i	$-0.442635\pi$
$29$	1.93051			0.358487			0.179244	+	0.983805i	$0.442635\pi$
$30$	−2.03757	−	0.921047i	−0.372007	−	0.168159i
$31$	−2.81660			−0.505876			−0.252938	−	0.967482i	$-0.581397\pi$
$31$	−2.81660			−0.505876			−0.252938	+	0.967482i	$0.581397\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.469789	−	0.271233i	0.0817799	−	0.0472156i
$34$	1.73526	+	3.00556i	0.297595	+	0.515449i
$35$	1.71278	−	0.170217i	0.289512	−	0.0287719i
$36$	1.00000			0.166667
$37$	1.40837	−	5.91747i	0.231534	−	0.972827i
$37$	1.40837	−	5.91747i	0.231534	−	0.972827i
$38$		−	2.58072i		−	0.418648i
$39$	−3.29744	+	5.71133i	−0.528012	+	0.914544i
$40$	−0.921047	+	2.03757i	−0.145630	+	0.322167i
$41$	−4.40694	−	7.63305i	−0.688249	−	1.19208i	−0.972404	−	0.233304i	$-0.925046\pi$
$41$	−4.40694	−	7.63305i	−0.688249	−	1.19208i	0.284155	−	0.958778i	$-0.408287\pi$
$42$	−0.666623	+	0.384875i	−0.102862	+	0.0593875i
$43$			6.99497i			1.06672i	0.845887	+	0.533361i	$0.179071\pi$
$43$			6.99497i			1.06672i	−0.845887	+	0.533361i	$0.820929\pi$
$44$	−0.271233	−	0.469789i	−0.0408899	−	0.0708234i
$45$	1.81643	−	1.30406i	0.270778	−	0.194398i
$46$	−1.52887	+	2.64807i	−0.225419	+	0.390437i
$47$			11.5001i			1.67746i	0.544551	+	0.838728i	$0.316700\pi$
$47$			11.5001i			1.67746i	−0.544551	+	0.838728i	$0.683300\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.20374	+	5.54904i	−0.457677	+	0.792721i
$50$	0.984087	+	4.90220i	0.139171	+	0.693276i
$51$	−3.47052			−0.485970
$52$	5.71133	+	3.29744i	0.792019	+	0.457272i
$53$	−3.51035	−	2.02670i	−0.482184	−	0.278389i	0.239142	−	0.970985i	$-0.423134\pi$
$53$	−3.51035	−	2.02670i	−0.482184	−	0.278389i	−0.721326	+	0.692595i	$0.756467\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−1.10531	−	0.499637i	−0.149040	−	0.0673710i
$56$	0.384875	+	0.666623i	0.0514311	+	0.0890813i
$57$	2.23497	+	1.29036i	0.296029	+	0.170912i
$58$	1.67187	+	0.965257i	0.219528	+	0.126744i
$59$	−2.29207	+	3.96998i	−0.298402	+	0.516848i	−0.975771	−	0.218796i	$-0.929787\pi$
$59$	−2.29207	+	3.96998i	−0.298402	+	0.516848i	0.677368	+	0.735644i	$0.263120\pi$
$60$	−1.30406	−	1.81643i	−0.168353	−	0.234500i
$61$	−2.02517	−	3.50769i	−0.259296	−	0.449114i	0.706758	−	0.707456i	$-0.250157\pi$
$61$	−2.02517	−	3.50769i	−0.259296	−	0.449114i	−0.966053	+	0.258342i	$0.916824\pi$
$62$	−2.43925	−	1.40830i	−0.309784	−	0.178854i
$63$		−	0.769750i		−	0.0969794i
$64$	−1.00000			−0.125000
$65$	14.6743	−	1.45834i	1.82012	−	0.180885i
$66$	0.542466			0.0667730
$67$	8.50676	−	4.91138i	1.03927	−	0.600021i	0.119641	−	0.992817i	$-0.461826\pi$
$67$	8.50676	−	4.91138i	1.03927	−	0.600021i	0.919625	+	0.392797i	$0.128492\pi$
$68$			3.47052i			0.420862i
$69$	−1.52887	−	2.64807i	−0.184054	−	0.318791i
$70$	1.56842	+	0.708976i	0.187462	+	0.0847389i
$71$	−1.34544	−	2.33038i	−0.159675	−	0.276565i	0.775077	−	0.631867i	$-0.217711\pi$
$71$	−1.34544	−	2.33038i	−0.159675	−	0.276565i	−0.934751	+	0.355302i	$0.884378\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			9.10465i			1.06562i	0.846235	+	0.532809i	$0.178864\pi$
$73$			9.10465i			1.06562i	−0.846235	+	0.532809i	$0.821136\pi$
$74$	4.17842	−	4.42050i	0.485731	−	0.513872i
$75$	−4.73747	−	1.59886i	−0.547036	−	0.184620i
$76$	1.29036	−	2.23497i	0.148014	−	0.256369i
$77$	−0.361621	+	0.208782i	−0.0412105	+	0.0237929i
$78$	−5.71133	+	3.29744i	−0.646680	+	0.373361i
$79$	2.97540	+	5.15355i	0.334759	+	0.579820i	0.983439	−	0.181242i	$-0.0580117\pi$
$79$	2.97540	+	5.15355i	0.334759	+	0.579820i	−0.648679	+	0.761062i	$0.724678\pi$
$80$	−1.81643	+	1.30406i	−0.203083	+	0.145798i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	8.81389i		−	0.973331i
$83$	−8.26377	−	4.77109i	−0.907067	−	0.523695i	−0.0275806	−	0.999620i	$-0.508780\pi$
$83$	−8.26377	−	4.77109i	−0.907067	−	0.523695i	−0.879486	+	0.475924i	$0.842114\pi$
$84$	−0.769750			−0.0839866
$85$	4.52577	+	6.30397i	0.490888	+	0.683761i
$86$	−3.49748	+	6.05782i	−0.377143	+	0.653232i
$87$	−1.67187	+	0.965257i	−0.179244	+	0.103486i
$88$		−	0.542466i		−	0.0578271i
$89$	−6.24819	+	10.8222i	−0.662307	+	1.14715i	0.317701	+	0.948191i	$0.397089\pi$
$89$	−6.24819	+	10.8222i	−0.662307	+	1.14715i	−0.980008	+	0.198958i	$0.936244\pi$
$90$	2.22511	−	0.221132i	0.234547	−	0.0233094i
$91$	2.53820	−	4.39630i	0.266076	−	0.460857i
$92$	−2.64807	+	1.52887i	−0.276081	+	0.159395i
$93$	2.43925	−	1.40830i	0.252938	−	0.146034i
$94$	−5.75003	+	9.95934i	−0.593070	+	1.02723i
$95$	−0.570681	−	5.74238i	−0.0585506	−	0.589156i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	16.8742i		−	1.71332i	−0.515882	−	0.856660i	$-0.672536\pi$
$97$		−	16.8742i		−	1.71332i	0.515882	−	0.856660i	$-0.327464\pi$
$98$	−5.54904	+	3.20374i	−0.560538	+	0.323627i
$99$	−0.271233	+	0.469789i	−0.0272600	+	0.0472156i
$100$	−1.59886	+	4.73747i	−0.159886	+	0.473747i
$101$	11.2588			1.12029			0.560147	−	0.828393i	$-0.310745\pi$
$101$	11.2588			1.12029			0.560147	+	0.828393i	$0.310745\pi$
$102$	−3.00556	−	1.73526i	−0.297595	−	0.171816i
$103$		−	18.5120i		−	1.82405i	−0.410139	−	0.912023i	$-0.634520\pi$
$103$		−	18.5120i		−	1.82405i	0.410139	−	0.912023i	$-0.365480\pi$
$104$	3.29744	+	5.71133i	0.323340	+	0.560042i
$105$	−1.39820	+	1.00380i	−0.136450	+	0.0979609i
$106$	−2.02670	−	3.51035i	−0.196851	−	0.340956i
$107$	3.09274	−	1.78559i	0.298986	−	0.172620i	−0.343001	−	0.939335i	$-0.611443\pi$
$107$	3.09274	−	1.78559i	0.298986	−	0.172620i	0.641987	+	0.766715i	$0.278110\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−4.51885	+	7.82688i	−0.432827	+	0.749679i	−0.997116	−	0.0758990i	$-0.975817\pi$
$109$	−4.51885	+	7.82688i	−0.432827	+	0.749679i	0.564288	+	0.825578i	$0.309151\pi$
$110$	−0.707408	−	0.985353i	−0.0674487	−	0.0939498i
$111$	1.73905	+	5.82887i	0.165064	+	0.553252i
$112$			0.769750i			0.0727346i
$113$	16.7865	+	9.69168i	1.57914	+	0.911717i	0.994980	+	0.100079i	$0.0319094\pi$
$113$	16.7865	+	9.69168i	1.57914	+	0.911717i	0.584160	+	0.811638i	$0.301424\pi$
$114$	1.29036	+	2.23497i	0.120853	+	0.209324i
$115$	−2.81632	+	6.23033i	−0.262623	+	0.580981i
$116$	0.965257	+	1.67187i	0.0896219	+	0.155230i
$117$		−	6.59487i		−	0.609696i
$118$	−3.96998	+	2.29207i	−0.365467	+	0.211002i
$119$	2.67143			0.244890
$120$	−0.221132	−	2.22511i	−0.0201865	−	0.203124i
$121$	−10.7057			−0.973248
$122$		−	4.05033i		−	0.366700i
$123$	7.63305	+	4.40694i	0.688249	+	0.397361i
$124$	−1.40830	−	2.43925i	−0.126469	−	0.219051i
$125$	3.27373	+	10.6903i	0.292812	+	0.956170i
$126$	0.384875	−	0.666623i	0.0342874	−	0.0593875i
$127$	−12.9477	−	7.47537i	−1.14893	−	0.663332i	−0.200300	−	0.979735i	$-0.564192\pi$
$127$	−12.9477	−	7.47537i	−1.14893	−	0.663332i	−0.948625	+	0.316402i	$0.897525\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−3.49748	−	6.05782i	−0.307936	−	0.533361i
$130$	13.4375	+	6.07419i	1.17855	+	0.532742i
$131$	2.52822	−	4.37901i	0.220892	−	0.382596i	−0.734187	−	0.678947i	$-0.762436\pi$
$131$	2.52822	−	4.37901i	0.220892	−	0.382596i	0.955079	+	0.296351i	$0.0957698\pi$
$132$	0.469789	+	0.271233i	0.0408899	+	0.0236078i
$133$	−1.72037	−	0.993255i	−0.149175	−	0.0861261i
$134$	9.82276			0.848557
$135$	−0.921047	+	2.03757i	−0.0792711	+	0.175366i
$136$	−1.73526	+	3.00556i	−0.148797	+	0.257725i
$137$		−	7.12759i		−	0.608951i	−0.952520	−	0.304475i	$-0.901519\pi$
$137$		−	7.12759i		−	0.608951i	0.952520	−	0.304475i	$-0.0984812\pi$
$138$		−	3.05773i		−	0.260292i
$139$	−7.74292	+	13.4111i	−0.656746	+	1.13752i	0.324707	+	0.945815i	$0.394734\pi$
$139$	−7.74292	+	13.4111i	−0.656746	+	1.13752i	−0.981453	+	0.191703i	$0.938599\pi$
$140$	1.00380	+	1.39820i	0.0848366	+	0.118169i
$141$	−5.75003	−	9.95934i	−0.484240	−	0.838728i
$142$		−	2.69089i		−	0.225814i
$143$	−3.09820	+	1.78875i	−0.259085	+	0.149583i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.93355	+	1.77809i	0.326663	+	0.147663i
$146$	−4.55232	+	7.88486i	−0.376753	+	0.652555i
$147$		−	6.40748i		−	0.528480i
$148$	5.82887	−	1.73905i	0.479130	−	0.142949i
$149$	−4.63852			−0.380002			−0.190001	−	0.981784i	$-0.560849\pi$
$149$	−4.63852			−0.380002			−0.190001	+	0.981784i	$0.560849\pi$
$150$	−3.30334	−	3.75339i	−0.269717	−	0.306463i
$151$	−4.61736	−	7.99750i	−0.375755	−	0.650827i	0.614684	−	0.788773i	$-0.289283\pi$
$151$	−4.61736	−	7.99750i	−0.375755	−	0.650827i	−0.990440	+	0.137946i	$0.955950\pi$
$152$	2.23497	−	1.29036i	0.181280	−	0.104662i
$153$	3.00556	−	1.73526i	0.242985	−	0.140287i
$154$	−0.417563			−0.0336482
$155$	−5.73900	−	2.59422i	−0.460968	−	0.208373i
$156$	−6.59487			−0.528012
$157$	−8.57966	−	4.95347i	−0.684731	−	0.395330i	0.116904	−	0.993143i	$-0.462703\pi$
$157$	−8.57966	−	4.95347i	−0.684731	−	0.395330i	−0.801635	+	0.597813i	$0.796036\pi$
$158$			5.95081i			0.473421i
$159$	4.05341			0.321456
$160$	−2.22511	+	0.221132i	−0.175910	+	0.0174821i
$161$	1.17685	+	2.03836i	0.0927484	+	0.160645i
$162$		−	1.00000i		−	0.0785674i
$163$	0.578357	+	0.333914i	0.0453004	+	0.0261542i	0.522479	−	0.852652i	$-0.325007\pi$
$163$	0.578357	+	0.333914i	0.0453004	+	0.0261542i	−0.477179	+	0.878806i	$0.658341\pi$
$164$	4.40694	−	7.63305i	0.344124	−	0.596041i
$165$	1.20705	−	0.119957i	0.0939683	−	0.00933863i
$166$	−4.77109	−	8.26377i	−0.370308	−	0.641393i
$167$	12.2475	−	7.07110i	0.947740	−	0.547178i	0.0553617	−	0.998466i	$-0.482369\pi$
$167$	12.2475	−	7.07110i	0.947740	−	0.547178i	0.892378	+	0.451289i	$0.149035\pi$
$168$	−0.666623	−	0.384875i	−0.0514311	−	0.0296938i
$169$	15.2462	−	26.4071i	1.17278	−	2.03132i
$170$	0.767445	+	7.72228i	0.0588603	+	0.592272i
$171$	−2.58072			−0.197353
$172$	−6.05782	+	3.49748i	−0.461905	+	0.266681i
$173$	3.29150	+	1.90035i	0.250248	+	0.144481i	0.619878	−	0.784698i	$-0.287182\pi$
$173$	3.29150	+	1.90035i	0.250248	+	0.144481i	−0.369630	+	0.929179i	$0.620515\pi$
$174$	−1.93051			−0.146352
$175$	3.64667	+	1.23072i	0.275662	+	0.0930337i
$176$	0.271233	−	0.469789i	0.0204450	−	0.0354117i
$177$		−	4.58414i		−	0.344565i
$178$	−10.8222	+	6.24819i	−0.811157	+	0.468322i
$179$	9.26039			0.692154			0.346077	−	0.938206i	$-0.387514\pi$
$179$	9.26039			0.692154			0.346077	+	0.938206i	$0.387514\pi$
$180$	2.03757	+	0.921047i	0.151871	+	0.0686508i
$181$	−11.9533	−	20.7037i	−0.888481	−	1.53889i	−0.841671	−	0.539991i	$-0.818428\pi$
$181$	−11.9533	−	20.7037i	−0.888481	−	1.53889i	−0.0468108	−	0.998904i	$-0.514906\pi$
$182$	4.39630	−	2.53820i	0.325875	−	0.188144i
$183$	3.50769	+	2.02517i	0.259296	+	0.149705i
$184$	−3.05773			−0.225419
$185$	8.31992	−	10.7601i	0.611692	−	0.791096i
$186$	2.81660			0.206523
$187$	−1.63041	−	0.941320i	−0.119228	−	0.0688361i
$188$	−9.95934	+	5.75003i	−0.726360	+	0.419364i
$189$	0.384875	+	0.666623i	0.0279955	+	0.0484897i
$190$	2.37696	−	5.25839i	0.172443	−	0.381483i
$191$	−6.75889			−0.489056			−0.244528	−	0.969642i	$-0.578633\pi$
$191$	−6.75889			−0.489056			−0.244528	+	0.969642i	$0.578633\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$		−	0.828880i		−	0.0596641i	−0.999555	−	0.0298321i	$-0.990503\pi$
$193$		−	0.828880i		−	0.0596641i	0.999555	−	0.0298321i	$-0.00949725\pi$
$194$	8.43712	−	14.6135i	0.605750	−	1.04919i
$195$	−11.9791	+	8.60011i	−0.857844	+	0.615866i
$196$	−6.40748			−0.457677
$197$	−15.7441	−	9.08987i	−1.12172	−	0.647626i	−0.179882	−	0.983688i	$-0.557572\pi$
$197$	−15.7441	−	9.08987i	−1.12172	−	0.647626i	−0.941840	+	0.336062i	$0.890905\pi$
$198$	−0.469789	+	0.271233i	−0.0333865	+	0.0192757i
$199$	−14.7857			−1.04813			−0.524065	−	0.851678i	$-0.675585\pi$
$199$	−14.7857			−1.04813			−0.524065	+	0.851678i	$0.675585\pi$
$200$	−3.75339	+	3.30334i	−0.265405	+	0.233582i
$201$	−4.91138	+	8.50676i	−0.346422	+	0.600021i
$202$	9.75043	+	5.62941i	0.686038	+	0.396084i
$203$	1.28693	−	0.743007i	0.0903245	−	0.0521489i
$204$	−1.73526	−	3.00556i	−0.121493	−	0.210431i
$205$	−1.94904	−	19.6118i	−0.136127	−	1.36975i
$206$	9.25602	−	16.0319i	0.644898	−	1.11700i
$207$	2.64807	+	1.52887i	0.184054	+	0.106264i
$208$			6.59487i			0.457272i
$209$	0.699977	+	1.21240i	0.0484184	+	0.0838631i
$210$	−1.71278	+	0.170217i	−0.118193	+	0.0117461i
$211$	2.89788			0.199498			0.0997492	−	0.995013i	$-0.468196\pi$
$211$	2.89788			0.199498			0.0997492	+	0.995013i	$0.468196\pi$
$212$		−	4.05341i		−	0.278389i
$213$	2.33038	+	1.34544i	0.159675	+	0.0921883i
$214$	3.57119			0.244121
$215$	−6.44270	+	14.2527i	−0.439388	+	0.972027i
$216$	−1.00000			−0.0680414
$217$	−1.87761	+	1.08404i	−0.127460	+	0.0735893i
$218$	−7.82688	+	4.51885i	−0.530103	+	0.306055i
$219$	−4.55232	−	7.88486i	−0.307618	−	0.532809i
$220$	−0.119957	−	1.20705i	−0.00808749	−	0.0813790i
$221$	22.8876			1.53959
$222$	−1.40837	+	5.91747i	−0.0945235	+	0.397155i
$223$		−	24.1686i		−	1.61845i	−0.587499	−	0.809225i	$-0.699887\pi$
$223$		−	24.1686i		−	1.61845i	0.587499	−	0.809225i	$-0.300113\pi$
$224$	−0.384875	+	0.666623i	−0.0257156	+	0.0445406i
$225$	4.90220	−	0.984087i	0.326813	−	0.0656058i
$226$	9.69168	+	16.7865i	0.644681	+	1.11662i
$227$	3.23949	−	1.87032i	0.215013	−	0.124138i	−0.388626	−	0.921396i	$-0.627050\pi$
$227$	3.23949	−	1.87032i	0.215013	−	0.124138i	0.603639	+	0.797258i	$0.293717\pi$
$228$			2.58072i			0.170912i
$229$	−0.869057	−	1.50525i	−0.0574289	−	0.0994698i	0.835882	−	0.548910i	$-0.184957\pi$
$229$	−0.869057	−	1.50525i	−0.0574289	−	0.0994698i	−0.893311	+	0.449440i	$0.851624\pi$
$230$	−5.55417	+	3.98747i	−0.366231	+	0.262926i
$231$	0.208782	−	0.361621i	0.0137368	−	0.0237929i
$232$			1.93051i			0.126744i
$233$		−	7.05019i		−	0.461874i	−0.972969	−	0.230937i	$-0.925821\pi$
$233$		−	7.05019i		−	0.461874i	0.972969	−	0.230937i	$-0.0741791\pi$
$234$	3.29744	−	5.71133i	0.215560	−	0.373361i
$235$	−10.5921	+	23.4321i	−0.690952	+	1.52854i
$236$	−4.58414			−0.298402
$237$	−5.15355	−	2.97540i	−0.334759	−	0.193273i
$238$	2.31353	+	1.33572i	0.149964	+	0.0865817i
$239$	5.47005	−	9.47441i	0.353828	−	0.612848i	−0.633088	−	0.774079i	$-0.718213\pi$
$239$	5.47005	−	9.47441i	0.353828	−	0.612848i	0.986917	+	0.161231i	$0.0515464\pi$
$240$	0.921047	−	2.03757i	0.0594533	−	0.131524i
$241$	−4.49573	−	7.78684i	−0.289596	−	0.501594i	0.684118	−	0.729372i	$-0.260187\pi$
$241$	−4.49573	−	7.78684i	−0.289596	−	0.501594i	−0.973713	+	0.227777i	$0.926854\pi$
$242$	−9.27143	−	5.35287i	−0.595990	−	0.344095i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	2.02517	−	3.50769i	0.129648	−	0.224557i
$245$	−11.6388	+	8.35574i	−0.743573	+	0.533829i
$246$	4.40694	+	7.63305i	0.280976	+	0.486665i
$247$	−14.7393	−	8.50976i	−0.937842	−	0.541463i
$248$		−	2.81660i		−	0.178854i
$249$	9.54218			0.604711
$250$	−2.51002	+	10.8949i	−0.158747	+	0.689057i
$251$	5.88384			0.371384			0.185692	−	0.982608i	$-0.440547\pi$
$251$	5.88384			0.371384			0.185692	+	0.982608i	$0.440547\pi$
$252$	0.666623	−	0.384875i	0.0419933	−	0.0242449i
$253$		−	1.65872i		−	0.104283i
$254$	−7.47537	−	12.9477i	−0.469047	−	0.812413i
$255$	−7.07141	−	3.19651i	−0.442829	−	0.200173i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.7354	−	8.50750i	−0.919170	−	0.530683i	−0.0358001	−	0.999359i	$-0.511398\pi$
$257$	−14.7354	−	8.50750i	−0.919170	−	0.530683i	−0.883370	+	0.468676i	$0.844731\pi$
$258$		−	6.99497i		−	0.435488i
$259$	−1.33864	−	4.48677i	−0.0831789	−	0.278794i
$260$	8.60011	+	11.9791i	0.533356	+	0.742915i
$261$	0.965257	−	1.67187i	0.0597479	−	0.103486i
$262$	4.37901	−	2.52822i	0.270536	−	0.156194i
$263$	−25.3139	+	14.6150i	−1.56092	+	0.901198i	−0.563756	+	0.825941i	$0.690644\pi$
$263$	−25.3139	+	14.6150i	−1.56092	+	0.901198i	−0.997164	+	0.0752567i	$0.976022\pi$
$264$	0.271233	+	0.469789i	0.0166932	+	0.0289135i
$265$	−5.28588	−	7.36274i	−0.324709	−	0.452290i
$266$	−0.993255	−	1.72037i	−0.0609004	−	0.105483i
$267$		−	12.4964i		−	0.764766i
$268$	8.50676	+	4.91138i	0.519633	+	0.300010i
$269$	18.6554			1.13744			0.568720	−	0.822531i	$-0.307439\pi$
$269$	18.6554			1.13744			0.568720	+	0.822531i	$0.307439\pi$
$270$	−1.81643	+	1.30406i	−0.110545	+	0.0793626i
$271$	10.9535	−	18.9720i	0.665378	−	1.15247i	−0.313805	−	0.949487i	$-0.601604\pi$
$271$	10.9535	−	18.9720i	0.665378	−	1.15247i	0.979183	−	0.202980i	$-0.0650628\pi$
$272$	−3.00556	+	1.73526i	−0.182239	+	0.105216i
$273$			5.07640i			0.307238i
$274$	3.56379	−	6.17267i	0.215297	−	0.372905i
$275$	−1.79195	−	2.03609i	−0.108059	−	0.122781i
$276$	1.52887	−	2.64807i	0.0920269	−	0.159395i
$277$	−0.767485	+	0.443108i	−0.0461137	+	0.0266238i	−0.522880	−	0.852407i	$-0.675142\pi$
$277$	−0.767485	+	0.443108i	−0.0461137	+	0.0266238i	0.476766	+	0.879030i	$0.341809\pi$
$278$	−13.4111	+	7.74292i	−0.804346	+	0.464390i
$279$	−1.40830	+	2.43925i	−0.0843127	+	0.146034i
$280$	0.170217	+	1.71278i	0.0101724	+	0.102358i
$281$	−6.61630	+	11.4598i	−0.394695	+	0.683632i	−0.993062	−	0.117590i	$-0.962483\pi$
$281$	−6.61630	+	11.4598i	−0.394695	+	0.683632i	0.598367	+	0.801222i	$0.295816\pi$
$282$		−	11.5001i		−	0.684818i
$283$	−11.7426	+	6.77958i	−0.698024	+	0.403004i	−0.806611	−	0.591083i	$-0.798701\pi$
$283$	−11.7426	+	6.77958i	−0.698024	+	0.403004i	0.108587	+	0.994087i	$0.465367\pi$
$284$	1.34544	−	2.33038i	0.0798374	−	0.138282i
$285$	3.36541	+	4.68770i	0.199350	+	0.277676i
$286$	−3.57750			−0.211542
$287$	−5.87554	−	3.39225i	−0.346822	−	0.200238i
$288$			1.00000i			0.0589256i
$289$	−2.47774	−	4.29157i	−0.145750	−	0.252446i
$290$	2.51751	+	3.50665i	0.147833	+	0.205918i
$291$	8.43712	+	14.6135i	0.494593	+	0.856660i
$292$	−7.88486	+	4.55232i	−0.461426	+	0.266405i
$293$	2.88440	−	1.66531i	0.168508	−	0.0972884i	−0.413374	−	0.910561i	$-0.635650\pi$
$293$	2.88440	−	1.66531i	0.168508	−	0.0972884i	0.581882	+	0.813273i	$0.302316\pi$
$294$	3.20374	−	5.54904i	0.186846	−	0.323627i
$295$	−8.32679	+	5.97800i	−0.484804	+	0.348052i
$296$	5.91747	+	1.40837i	0.343946	+	0.0818598i
$297$		−	0.542466i		−	0.0314771i
$298$	−4.01708	−	2.31926i	−0.232703	−	0.134351i
$299$	10.0827	+	17.4637i	0.583096	+	1.00995i
$300$	−0.984087	−	4.90220i	−0.0568163	−	0.283029i
$301$	2.69219	+	4.66301i	0.155175	+	0.268771i
$302$		−	9.23472i		−	0.531398i
$303$	−9.75043	+	5.62941i	−0.560147	+	0.323401i
$304$	2.58072			0.148014
$305$	−0.895660	−	9.01242i	−0.0512853	−	0.516050i
$306$	3.47052			0.198396
$307$		−	2.73317i		−	0.155990i	−0.996954	−	0.0779950i	$-0.975148\pi$
$307$		−	2.73317i		−	0.155990i	0.996954	−	0.0779950i	$-0.0248518\pi$
$308$	−0.361621	−	0.208782i	−0.0206052	−	0.0118964i
$309$	9.25602	+	16.0319i	0.526557	+	0.912023i
$310$	−3.67301	−	5.11616i	−0.208613	−	0.290578i
$311$	−6.52821	+	11.3072i	−0.370181	+	0.641172i	−0.989593	−	0.143894i	$-0.954038\pi$
$311$	−6.52821	+	11.3072i	−0.370181	+	0.641172i	0.619412	+	0.785066i	$0.287371\pi$
$312$	−5.71133	−	3.29744i	−0.323340	−	0.186681i
$313$	27.7040	+	15.9949i	1.56592	+	0.904085i	0.996637	+	0.0819448i	$0.0261131\pi$
$313$	27.7040	+	15.9949i	1.56592	+	0.904085i	0.569285	+	0.822140i	$0.307220\pi$
$314$	−4.95347	−	8.57966i	−0.279540	−	0.484178i
$315$	0.708976	−	1.56842i	0.0399463	−	0.0883703i
$316$	−2.97540	+	5.15355i	−0.167380	+	0.289910i
$317$	19.2122	+	11.0922i	1.07907	+	0.623000i	0.930645	−	0.365924i	$-0.119247\pi$
$317$	19.2122	+	11.0922i	1.07907	+	0.623000i	0.148423	+	0.988924i	$0.452580\pi$
$318$	3.51035	+	2.02670i	0.196851	+	0.113652i
$319$	−1.04724			−0.0586341
$320$	−2.03757	−	0.921047i	−0.113903	−	0.0514881i
$321$	−1.78559	+	3.09274i	−0.0996622	+	0.172620i
$322$			2.35369i			0.131166i
$323$		−	8.95644i		−	0.498350i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	31.2430	+	10.5443i	1.73305	+	0.584890i
$326$	0.333914	+	0.578357i	0.0184938	+	0.0320322i
$327$		−	9.03770i		−	0.499786i
$328$	7.63305	−	4.40694i	0.421465	−	0.243333i
$329$	4.42609	+	7.66621i	0.244018	+	0.422652i
$330$	1.10531	+	0.499637i	0.0608453	+	0.0275041i
$331$	11.2486	−	19.4831i	0.618279	−	1.07089i	−0.371521	−	0.928425i	$-0.621164\pi$
$331$	11.2486	−	19.4831i	0.618279	−	1.07089i	0.989800	−	0.142466i	$-0.0455031\pi$
$332$		−	9.54218i		−	0.523695i
$333$	−4.42050	−	4.17842i	−0.242242	−	0.228976i
$334$	14.1422			0.773826
$335$	21.8567	−	2.17213i	1.19416	−	0.118676i
$336$	−0.384875	−	0.666623i	−0.0209967	−	0.0363673i
$337$	−11.9426	+	6.89508i	−0.650557	+	0.375599i	−0.788669	−	0.614818i	$-0.789230\pi$
$337$	−11.9426	+	6.89508i	−0.650557	+	0.375599i	0.138113	+	0.990416i	$0.455896\pi$
$338$	26.4071	−	15.2462i	1.43636	−	0.829282i
$339$	−19.3834			−1.05276
$340$	−3.19651	+	7.07141i	−0.173355	+	0.383501i
$341$	1.52791			0.0827409
$342$	−2.23497	−	1.29036i	−0.120853	−	0.0697747i
$343$			10.3204i			0.557250i
$344$	−6.99497			−0.377143
$345$	−0.676164	−	6.80378i	−0.0364035	−	0.366303i
$346$	1.90035	+	3.29150i	0.102163	+	0.176952i
$347$			10.5992i			0.568995i	0.958677	+	0.284497i	$0.0918267\pi$
$347$			10.5992i			0.568995i	−0.958677	+	0.284497i	$0.908173\pi$
$348$	−1.67187	−	0.965257i	−0.0896219	−	0.0517432i
$349$	0.379291	−	0.656952i	0.0203030	−	0.0351658i	−0.855695	−	0.517480i	$-0.826870\pi$
$349$	0.379291	−	0.656952i	0.0203030	−	0.0351658i	0.875998	+	0.482314i	$0.160204\pi$
$350$	2.54275	+	2.88917i	0.135916	+	0.154433i
$351$	3.29744	+	5.71133i	0.176004	+	0.304848i
$352$	0.469789	−	0.271233i	0.0250399	−	0.0144568i
$353$	20.0758	+	11.5908i	1.06853	+	0.616915i	0.927779	−	0.373130i	$-0.121715\pi$
$353$	20.0758	+	11.5908i	1.06853	+	0.616915i	0.140750	+	0.990045i	$0.455049\pi$
$354$	2.29207	−	3.96998i	0.121822	−	0.211002i
$355$	−0.595043	−	5.98751i	−0.0315816	−	0.317784i
$356$	−12.4964			−0.662307
$357$	−2.31353	+	1.33572i	−0.122445	+	0.0706937i
$358$	8.01973	+	4.63019i	0.423856	+	0.244713i
$359$	−18.2560			−0.963513			−0.481756	−	0.876305i	$-0.660001\pi$
$359$	−18.2560			−0.963513			−0.481756	+	0.876305i	$0.660001\pi$
$360$	1.30406	+	1.81643i	0.0687300	+	0.0957344i
$361$	6.16994	−	10.6867i	0.324734	−	0.562455i
$362$		−	23.9066i		−	1.25650i
$363$	9.27143	−	5.35287i	0.486624	−	0.280953i
$364$	5.07640			0.266076
$365$	−8.38581	+	18.5513i	−0.438933	+	0.971020i
$366$	2.02517	+	3.50769i	0.105857	+	0.183350i
$367$	4.49957	−	2.59783i	0.234876	−	0.135606i	−0.377944	−	0.925829i	$-0.623369\pi$
$367$	4.49957	−	2.59783i	0.234876	−	0.135606i	0.612819	+	0.790223i	$0.290035\pi$
$368$	−2.64807	−	1.52887i	−0.138040	−	0.0796977i
$369$	−8.81389			−0.458833
$370$	12.5853	−	5.15853i	0.654278	−	0.268179i
$371$	−3.12011			−0.161988
$372$	2.43925	+	1.40830i	0.126469	+	0.0730169i
$373$	−26.7185	+	15.4260i	−1.38343	+	0.798726i	−0.992564	−	0.121720i	$-0.961159\pi$
$373$	−26.7185	+	15.4260i	−1.38343	+	0.798726i	−0.390869	+	0.920446i	$0.627826\pi$
$374$	−0.941320	−	1.63041i	−0.0486745	−	0.0843067i
$375$	−8.18029	−	7.62121i	−0.422428	−	0.393558i
$376$	−11.5001			−0.593070
$377$	11.0258	−	6.36575i	0.567857	−	0.327853i
$378$			0.769750i			0.0395917i
$379$	−15.6609	+	27.1255i	−0.804448	+	1.39335i	0.112215	+	0.993684i	$0.464206\pi$
$379$	−15.6609	+	27.1255i	−0.804448	+	1.39335i	−0.916663	+	0.399661i	$0.869128\pi$
$380$	4.68770	−	3.36541i	0.240474	−	0.172642i
$381$	14.9507			0.765950
$382$	−5.85337	−	3.37945i	−0.299485	−	0.172907i
$383$	9.68429	−	5.59123i	0.494844	−	0.285698i	−0.231738	−	0.972778i	$-0.574441\pi$
$383$	9.68429	−	5.59123i	0.494844	−	0.285698i	0.726582	+	0.687080i	$0.241108\pi$
$384$	1.00000			0.0510310
$385$	−0.929123	+	0.0923369i	−0.0473525	+	0.00470592i
$386$	0.414440	−	0.717831i	0.0210944	−	0.0365367i
$387$	6.05782	+	3.49748i	0.307936	+	0.177787i
$388$	14.6135	−	8.43712i	0.741889	−	0.428330i
$389$	−0.695306	−	1.20430i	−0.0352534	−	0.0610607i	0.847860	−	0.530220i	$-0.177890\pi$
$389$	−0.695306	−	1.20430i	−0.0352534	−	0.0610607i	−0.883114	+	0.469159i	$0.844557\pi$
$390$	−14.6743	+	1.45834i	−0.743062	+	0.0738459i
$391$	−5.30596	+	9.19020i	−0.268334	+	0.464768i
$392$	−5.54904	−	3.20374i	−0.280269	−	0.161813i
$393$			5.05645i			0.255064i
$394$	−9.08987	−	15.7441i	−0.457941	−	0.793177i
$395$	1.31592	+	13.2412i	0.0662110	+	0.666236i
$396$	−0.542466			−0.0272600
$397$			8.51192i			0.427201i	0.976921	+	0.213601i	$0.0685191\pi$
$397$			8.51192i			0.427201i	−0.976921	+	0.213601i	$0.931481\pi$
$398$	−12.8048	−	7.39285i	−0.641846	−	0.370570i
$399$	1.98651			0.0994499
$400$	−4.90220	+	0.984087i	−0.245110	+	0.0492043i
$401$	29.6466			1.48048			0.740240	−	0.672343i	$-0.234712\pi$
$401$	29.6466			1.48048			0.740240	+	0.672343i	$0.234712\pi$
$402$	−8.50676	+	4.91138i	−0.424279	+	0.244957i
$403$	−16.0865	+	9.28755i	−0.801326	+	0.462646i
$404$	5.62941	+	9.75043i	0.280074	+	0.485102i
$405$	−0.221132	−	2.22511i	−0.0109882	−	0.110566i
$406$	1.48601			0.0737496
$407$	−0.763993	+	3.21003i	−0.0378697	+	0.159115i
$408$		−	3.47052i		−	0.171816i
$409$	−2.37075	+	4.10626i	−0.117226	+	0.203042i	−0.918667	−	0.395032i	$-0.870734\pi$
$409$	−2.37075	+	4.10626i	−0.117226	+	0.203042i	0.801441	+	0.598073i	$0.204067\pi$
$410$	8.11800	−	17.9589i	0.400920	−	0.886925i
$411$	3.56379	+	6.17267i	0.175789	+	0.304475i
$412$	16.0319	−	9.25602i	0.789835	−	0.456011i
$413$			3.52865i			0.173633i
$414$	1.52887	+	2.64807i	0.0751397	+	0.130146i
$415$	−12.4436	−	17.3327i	−0.610831	−	0.850830i
$416$	−3.29744	+	5.71133i	−0.161670	+	0.280021i
$417$		−	15.4858i		−	0.758345i
$418$			1.39995i			0.0684740i
$419$	−14.4699	+	25.0626i	−0.706900	+	1.22439i	0.259101	+	0.965850i	$0.416574\pi$
$419$	−14.4699	+	25.0626i	−0.706900	+	1.22439i	−0.966001	+	0.258537i	$0.916760\pi$
$420$	−1.56842	−	0.708976i	−0.0765309	−	0.0345945i
$421$	−3.42062			−0.166711			−0.0833555	−	0.996520i	$-0.526564\pi$
$421$	−3.42062			−0.166711			−0.0833555	+	0.996520i	$0.526564\pi$
$422$	2.50964	+	1.44894i	0.122167	+	0.0705333i
$423$	9.95934	+	5.75003i	0.484240	+	0.279576i
$424$	2.02670	−	3.51035i	0.0984254	−	0.170478i
$425$	3.41529	+	17.0132i	0.165666	+	0.825261i
$426$	1.34544	+	2.33038i	0.0651870	+	0.112907i
$427$	−2.70005	−	1.55887i	−0.130664	−	0.0754391i
$428$	3.09274	+	1.78559i	0.149493	+	0.0863100i
$429$	1.78875	−	3.09820i	0.0863615	−	0.149583i
$430$	−12.7059	+	9.12186i	−0.612733	+	0.439895i
$431$	8.64674	+	14.9766i	0.416499	+	0.721397i	0.995584	−	0.0938698i	$-0.0299237\pi$
$431$	8.64674	+	14.9766i	0.416499	+	0.721397i	−0.579086	+	0.815267i	$0.696590\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			23.3604i			1.12263i	0.827602	+	0.561315i	$0.189704\pi$
$433$			23.3604i			1.12263i	−0.827602	+	0.561315i	$0.810296\pi$
$434$	−2.16808			−0.104071
$435$	−4.29560	+	0.426899i	−0.205958	+	0.0204683i
$436$	−9.03770			−0.432827
$437$	6.83394	−	3.94558i	0.326912	−	0.188743i
$438$		−	9.10465i		−	0.435037i
$439$	14.6814	+	25.4289i	0.700705	+	1.21366i	0.968219	+	0.250103i	$0.0804644\pi$
$439$	14.6814	+	25.4289i	0.700705	+	1.21366i	−0.267514	+	0.963554i	$0.586202\pi$
$440$	0.499637	−	1.10531i	0.0238193	−	0.0526936i
$441$	3.20374	+	5.54904i	0.152559	+	0.264240i
$442$	19.8213	+	11.4438i	0.942802	+	0.544327i
$443$			3.62878i			0.172409i	0.996277	+	0.0862043i	$0.0274738\pi$
$443$			3.62878i			0.172409i	−0.996277	+	0.0862043i	$0.972526\pi$
$444$	−4.17842	+	4.42050i	−0.198299	+	0.209788i
$445$	−22.6988	+	16.2960i	−1.07603	+	0.772506i
$446$	12.0843	−	20.9306i	0.572209	−	0.991094i
$447$	4.01708	−	2.31926i	0.190001	−	0.109697i
$448$	−0.666623	+	0.384875i	−0.0314950	+	0.0181836i
$449$	−9.83669	−	17.0376i	−0.464222	−	0.804056i	0.534944	−	0.844887i	$-0.320333\pi$
$449$	−9.83669	−	17.0376i	−0.464222	−	0.804056i	−0.999166	+	0.0408314i	$0.986999\pi$
$450$	4.73747	+	1.59886i	0.223327	+	0.0753708i
$451$	2.39062	+	4.14067i	0.112570	+	0.194977i
$452$			19.3834i			0.911717i
$453$	7.99750	+	4.61736i	0.375755	+	0.216942i
$454$	3.74064			0.175557
$455$	9.22095	−	6.61994i	0.432285	−	0.310347i
$456$	−1.29036	+	2.23497i	−0.0604266	+	0.104662i
$457$	−9.90061	+	5.71612i	−0.463131	+	0.267389i	−0.713360	−	0.700798i	$-0.752827\pi$
$457$	−9.90061	+	5.71612i	−0.463131	+	0.267389i	0.250229	+	0.968187i	$0.419494\pi$
$458$		−	1.73811i		−	0.0812168i
$459$	−1.73526	+	3.00556i	−0.0809950	+	0.140287i
$460$	−6.80378	+	0.676164i	−0.317228	+	0.0315263i
$461$	−11.3754	+	19.7029i	−0.529807	+	0.917653i	0.469588	+	0.882886i	$0.344402\pi$
$461$	−11.3754	+	19.7029i	−0.529807	+	0.917653i	−0.999395	+	0.0347677i	$0.988931\pi$
$462$	0.361621	−	0.208782i	0.0168241	−	0.00971341i
$463$	−16.2637	+	9.38987i	−0.755840	+	0.436384i	−0.827800	−	0.561023i	$-0.810408\pi$
$463$	−16.2637	+	9.38987i	−0.755840	+	0.436384i	0.0719602	+	0.997408i	$0.477075\pi$
$464$	−0.965257	+	1.67187i	−0.0448109	+	0.0776148i
$465$	6.26723	−	0.622841i	0.290636	−	0.0288836i
$466$	3.52510	−	6.10565i	0.163297	−	0.282839i
$467$			12.9857i			0.600907i	0.953796	+	0.300453i	$0.0971380\pi$
$467$			12.9857i			0.600907i	−0.953796	+	0.300453i	$0.902862\pi$
$468$	5.71133	−	3.29744i	0.264006	−	0.152424i
$469$	3.78054	−	6.54808i	0.174569	−	0.302362i
$470$	−20.8891	+	14.9968i	−0.963542	+	0.691749i
$471$	9.90694			0.456488
$472$	−3.96998	−	2.29207i	−0.182733	−	0.105501i
$473$		−	3.79453i		−	0.174473i
$474$	−2.97540	−	5.15355i	−0.136665	−	0.236710i
$475$	4.12620	−	12.2261i	0.189323	−	0.560972i
$476$	1.33572	+	2.31353i	0.0612225	+	0.106040i
$477$	−3.51035	+	2.02670i	−0.160728	+	0.0927964i
$478$	9.47441	−	5.47005i	0.433349	−	0.250194i
$479$	7.95632	−	13.7808i	0.363534	−	0.629659i	−0.625006	−	0.780620i	$-0.714904\pi$
$479$	7.95632	−	13.7808i	0.363534	−	0.629659i	0.988540	+	0.150961i	$0.0482368\pi$
$480$	1.81643	−	1.30406i	0.0829084	−	0.0595219i
$481$	−11.4688	−	38.4406i	−0.522934	−	1.75274i
$482$		−	8.99146i		−	0.409550i
$483$	−2.03836	−	1.17685i	−0.0927484	−	0.0535483i
$484$	−5.35287	−	9.27143i	−0.243312	−	0.421429i
$485$	15.5420	−	34.3824i	0.705725	−	1.56122i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$		−	20.3959i		−	0.924226i	−0.886821	−	0.462113i	$-0.847091\pi$
$487$		−	20.3959i		−	0.924226i	0.886821	−	0.462113i	$-0.152909\pi$
$488$	3.50769	−	2.02517i	0.158786	−	0.0916749i
$489$	−0.667829			−0.0302003
$490$	−14.2573	+	1.41690i	−0.644081	+	0.0640092i
$491$	−24.5248			−1.10679			−0.553395	−	0.832919i	$-0.686668\pi$
$491$	−24.5248			−1.10679			−0.553395	+	0.832919i	$0.686668\pi$
$492$			8.81389i			0.397361i
$493$	5.80227	+	3.34994i	0.261321	+	0.150874i
$494$	−8.50976	−	14.7393i	−0.382872	−	0.663154i
$495$	−0.985353	+	0.707408i	−0.0442883	+	0.0317956i
$496$	1.40830	−	2.43925i	0.0632345	−	0.109525i
$497$	−1.79381	−	1.03566i	−0.0804633	−	0.0464555i
$498$	8.26377	+	4.77109i	0.370308	+	0.213798i
$499$	−2.70684	−	4.68838i	−0.121175	−	0.209881i	0.799056	−	0.601256i	$-0.205333\pi$
$499$	−2.70684	−	4.68838i	−0.121175	−	0.209881i	−0.920231	+	0.391375i	$0.871999\pi$
$500$	−7.62121	+	8.18029i	−0.340831	+	0.365834i
$501$	−7.07110	+	12.2475i	−0.315913	+	0.547178i
$502$	5.09555	+	2.94192i	0.227426	+	0.131304i
$503$	−30.9199	−	17.8516i	−1.37865	−	0.795964i	−0.386653	−	0.922225i	$-0.626369\pi$
$503$	−30.9199	−	17.8516i	−1.37865	−	0.795964i	−0.991997	+	0.126262i	$0.959702\pi$
$504$	0.769750			0.0342874
$505$	22.9406	+	10.3699i	1.02084	+	0.461455i
$506$	0.829358	−	1.43649i	0.0368695	−	0.0638598i
$507$			30.4923i			1.35421i
$508$		−	14.9507i		−	0.663332i
$509$	−4.68806	+	8.11996i	−0.207795	+	0.359911i	−0.951020	−	0.309131i	$-0.899962\pi$
$509$	−4.68806	+	8.11996i	−0.207795	+	0.359911i	0.743225	+	0.669042i	$0.233295\pi$
$510$	−4.52577	−	6.30397i	−0.200404	−	0.279144i
$511$	3.50415	+	6.06937i	0.155015	+	0.268493i
$512$		−	1.00000i		−	0.0441942i
$513$	2.23497	−	1.29036i	0.0986763	−	0.0569708i
$514$	−8.50750	−	14.7354i	−0.375250	−	0.649952i
$515$	17.0505	−	37.7195i	0.751333	−	1.66212i
$516$	3.49748	−	6.05782i	0.153968	−	0.266681i
$517$		−	6.23839i		−	0.274364i
$518$	1.08409	−	4.55498i	0.0476323	−	0.200134i
$519$	−3.80070			−0.166832
$520$	1.45834	+	14.6743i	0.0639525	+	0.643510i
$521$	−3.40599	−	5.89935i	−0.149219	−	0.258455i	0.781720	−	0.623630i	$-0.214343\pi$
$521$	−3.40599	−	5.89935i	−0.149219	−	0.258455i	−0.930939	+	0.365175i	$0.881009\pi$
$522$	1.67187	−	0.965257i	0.0731759	−	0.0422482i
$523$	31.2593	−	18.0475i	1.36687	−	0.789164i	0.376344	−	0.926480i	$-0.377181\pi$
$523$	31.2593	−	18.0475i	1.36687	−	0.789164i	0.990527	+	0.137316i	$0.0438476\pi$
$524$	5.05645			0.220892
$525$	−3.77347	+	0.757501i	−0.164688	+	0.0330601i
$526$	−29.2299			−1.27449
$527$	−8.46545	−	4.88753i	−0.368761	−	0.212904i
$528$			0.542466i			0.0236078i
$529$	13.6503			0.593490
$530$	−0.896340	−	9.01926i	−0.0389345	−	0.391772i
$531$	2.29207	+	3.96998i	0.0994674	+	0.172283i
$532$		−	1.98651i		−	0.0861261i
$533$	−50.3390	−	29.0632i	−2.18042	−	1.25887i
$534$	6.24819	−	10.8222i	0.270386	−	0.468322i
$535$	7.94628	−	0.789706i	0.343547	−	0.0341420i
$536$	4.91138	+	8.50676i	0.212139	+	0.367436i
$537$	−8.01973	+	4.63019i	−0.346077	+	0.199808i
$538$	16.1560	+	9.32770i	0.696537	+	0.402146i
$539$	1.73792	−	3.01017i	0.0748576	−	0.129657i
$540$	−2.22511	+	0.221132i	−0.0957534	+	0.00951603i
$541$	−36.5319			−1.57063			−0.785313	−	0.619098i	$-0.787498\pi$
$541$	−36.5319			−1.57063			−0.785313	+	0.619098i	$0.787498\pi$
$542$	18.9720	−	10.9535i	0.814918	−	0.470493i
$543$	20.7037	+	11.9533i	0.888481	+	0.512965i
$544$	−3.47052			−0.148797
$545$	−16.4164	+	11.7857i	−0.703200	+	0.504844i
$546$	−2.53820	+	4.39630i	−0.108625	+	0.188144i
$547$		−	27.3262i		−	1.16838i	−0.811616	−	0.584192i	$-0.801412\pi$
$547$		−	27.3262i		−	1.16838i	0.811616	−	0.584192i	$-0.198588\pi$
$548$	6.17267	−	3.56379i	0.263683	−	0.152238i
$549$	−4.05033			−0.172864
$550$	−0.533834	−	2.65928i	−0.0227628	−	0.113392i
$551$	−2.49106	−	4.31464i	−0.106123	−	0.183810i
$552$	2.64807	−	1.52887i	0.112710	−	0.0650729i
$553$	3.96695	+	2.29032i	0.168692	+	0.0973942i
$554$	−0.886215			−0.0376517
$555$	−1.82523	+	13.4784i	−0.0774765	+	0.572128i
$556$	−15.4858			−0.656746
$557$	39.0111	+	22.5231i	1.65295	+	0.954333i	0.975849	+	0.218445i	$0.0700983\pi$
$557$	39.0111	+	22.5231i	1.65295	+	0.954333i	0.677103	+	0.735888i	$0.263235\pi$
$558$	−2.43925	+	1.40830i	−0.103261	+	0.0596181i
$559$	23.0655	+	39.9506i	0.975565	+	1.68973i
$560$	−0.708976	+	1.56842i	−0.0299597	+	0.0662777i
$561$	1.88264			0.0794851
$562$	−11.4598	+	6.61630i	−0.483401	+	0.279092i
$563$			17.5550i			0.739856i	0.929061	+	0.369928i	$0.120618\pi$
$563$			17.5550i			0.739856i	−0.929061	+	0.369928i	$0.879382\pi$
$564$	5.75003	−	9.95934i	0.242120	−	0.419364i
$565$	25.2771	+	35.2086i	1.06341	+	1.48124i
$566$	−13.5592			−0.569934
$567$	−0.666623	−	0.384875i	−0.0279955	−	0.0161632i
$568$	2.33038	−	1.34544i	0.0977804	−	0.0564536i
$569$	−23.4641			−0.983665			−0.491832	−	0.870690i	$-0.663673\pi$
$569$	−23.4641			−0.983665			−0.491832	+	0.870690i	$0.663673\pi$
$570$	0.570681	+	5.74238i	0.0239032	+	0.240522i
$571$	−6.16416	+	10.6766i	−0.257962	+	0.446804i	−0.965696	−	0.259676i	$-0.916384\pi$
$571$	−6.16416	+	10.6766i	−0.257962	+	0.446804i	0.707734	+	0.706479i	$0.249718\pi$
$572$	−3.09820	−	1.78875i	−0.129542	−	0.0747913i
$573$	5.85337	−	3.37945i	0.244528	−	0.141178i
$574$	−3.39225	−	5.87554i	−0.141590	−	0.245240i
$575$	−11.4769	+	10.1007i	−0.478618	+	0.421230i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	7.31132	+	4.22119i	0.304374	+	0.175731i	0.644406	−	0.764683i	$-0.277105\pi$
$577$	7.31132	+	4.22119i	0.304374	+	0.175731i	−0.340032	+	0.940414i	$0.610438\pi$
$578$		−	4.95548i		−	0.206121i
$579$	0.414440	+	0.717831i	0.0172235	+	0.0298321i
$580$	0.426899	+	4.29560i	0.0177260	+	0.178365i
$581$	−7.34510			−0.304726
$582$			16.8742i			0.699460i
$583$	1.90425	+	1.09942i	0.0788659	+	0.0455332i
$584$	−9.10465			−0.376753
$585$	6.07419	−	13.4375i	0.251137	−	0.555572i
$586$	3.33062			0.137587
$587$	16.3387	−	9.43316i	0.674371	−	0.389348i	−0.123360	−	0.992362i	$-0.539367\pi$
$587$	16.3387	−	9.43316i	0.674371	−	0.389348i	0.797731	+	0.603014i	$0.206034\pi$
$588$	5.54904	−	3.20374i	0.228839	−	0.132120i
$589$	3.63443	+	6.29501i	0.149754	+	0.259381i
$590$	−10.2002	+	1.01370i	−0.419936	+	0.0417335i
$591$	18.1797			0.747815
$592$	4.42050	+	4.17842i	0.181681	+	0.171732i
$593$		−	18.8965i		−	0.775985i	−0.921663	−	0.387992i	$-0.873169\pi$
$593$		−	18.8965i		−	0.775985i	0.921663	−	0.387992i	$-0.126831\pi$
$594$	0.271233	−	0.469789i	0.0111288	−	0.0192757i
$595$	5.44322	+	2.46052i	0.223150	+	0.100871i
$596$	−2.31926	−	4.01708i	−0.0950006	−	0.164546i
$597$	12.8048	−	7.39285i	0.524065	−	0.302569i
$598$			20.1654i			0.824623i
$599$	−22.1683	−	38.3966i	−0.905773	−	1.56884i	−0.819876	−	0.572540i	$-0.805958\pi$
$599$	−22.1683	−	38.3966i	−0.905773	−	1.56884i	−0.0858964	−	0.996304i	$-0.527375\pi$
$600$	1.59886	−	4.73747i	0.0652730	−	0.193407i
$601$	0.236379	−	0.409421i	0.00964212	−	0.0167006i	−0.861164	−	0.508327i	$-0.830264\pi$
$601$	0.236379	−	0.409421i	0.00964212	−	0.0167006i	0.870806	+	0.491626i	$0.163597\pi$
$602$			5.38438i			0.219451i
$603$		−	9.82276i		−	0.400014i
$604$	4.61736	−	7.99750i	0.187878	−	0.325414i
$605$	−21.8136	−	9.86048i	−0.886850	−	0.400886i
$606$	−11.2588			−0.457358
$607$	−23.1934	−	13.3907i	−0.941391	−	0.543512i	−0.0509949	−	0.998699i	$-0.516239\pi$
$607$	−23.1934	−	13.3907i	−0.941391	−	0.543512i	−0.890396	+	0.455187i	$0.849573\pi$
$608$	2.23497	+	1.29036i	0.0906400	+	0.0523310i
$609$	−0.743007	+	1.28693i	−0.0301082	+	0.0521489i
$610$	3.73055	−	8.25281i	0.151045	−	0.334147i
$611$	37.9207	+	65.6806i	1.53411	+	2.65715i
$612$	3.00556	+	1.73526i	0.121493	+	0.0701437i
$613$	3.28567	+	1.89698i	0.132707	+	0.0766184i	0.564884	−	0.825171i	$-0.308921\pi$
$613$	3.28567	+	1.89698i	0.132707	+	0.0766184i	−0.432177	+	0.901789i	$0.642254\pi$
$614$	1.36658	−	2.36699i	0.0551508	−	0.0955240i
$615$	11.4938	+	16.0098i	0.463476	+	0.645579i
$616$	−0.208782	−	0.361621i	−0.00841206	−	0.0145701i
$617$	−15.3019	−	8.83457i	−0.616032	−	0.355666i	0.159290	−	0.987232i	$-0.449079\pi$
$617$	−15.3019	−	8.83457i	−0.616032	−	0.355666i	−0.775323	+	0.631565i	$0.782413\pi$
$618$			18.5120i			0.744664i
$619$	−3.69004			−0.148315			−0.0741576	−	0.997247i	$-0.523627\pi$
$619$	−3.69004			−0.148315			−0.0741576	+	0.997247i	$0.523627\pi$
$620$	−0.622841	−	6.26723i	−0.0250139	−	0.251698i
$621$	−3.05773			−0.122703
$622$	−11.3072	+	6.52821i	−0.453377	+	0.261757i
$623$			9.61909i			0.385381i
$624$	−3.29744	−	5.71133i	−0.132003	−	0.228636i
$625$	−3.17583	+	24.7975i	−0.127033	+	0.991898i
$626$	15.9949	+	27.7040i	0.639285	+	1.10727i
$627$	−1.21240	−	0.699977i	−0.0484184	−	0.0279544i
$628$		−	9.90694i		−	0.395330i
$629$	14.5013	−	15.3414i	0.578205	−	0.611703i
$630$	1.39820	−	1.00380i	0.0557056	−	0.0399924i
$631$	−10.1262	+	17.5391i	−0.403117	+	0.698219i	−0.994100	−	0.108465i	$-0.965407\pi$
$631$	−10.1262	+	17.5391i	−0.403117	+	0.698219i	0.590983	+	0.806684i	$0.298740\pi$
$632$	−5.15355	+	2.97540i	−0.204997	+	0.118355i
$633$	−2.50964	+	1.44894i	−0.0997492	+	0.0575902i
$634$	11.0922	+	19.2122i	0.440527	+	0.763016i
$635$	−19.4967	−	27.1570i	−0.773702	−	1.07769i
$636$	2.02670	+	3.51035i	0.0803640	+	0.139195i
$637$			42.2565i			1.67427i
$638$	−0.906935	−	0.523619i	−0.0359059	−	0.0207303i
$639$	−2.69089			−0.106450
$640$	−1.30406	−	1.81643i	−0.0515475	−	0.0718008i
$641$	−8.01769	+	13.8870i	−0.316680	+	0.548505i	−0.979793	−	0.200014i	$-0.935901\pi$
$641$	−8.01769	+	13.8870i	−0.316680	+	0.548505i	0.663114	+	0.748519i	$0.269235\pi$
$642$	−3.09274	+	1.78559i	−0.122061	+	0.0704718i
$643$			0.892405i			0.0351930i	0.999845	+	0.0175965i	$0.00560143\pi$
$643$			0.892405i			0.0351930i	−0.999845	+	0.0175965i	$0.994399\pi$
$644$	−1.17685	+	2.03836i	−0.0463742	+	0.0803225i
$645$	−1.54681	−	15.5646i	−0.0609058	−	0.612854i
$646$	4.47822	−	7.75651i	0.176193	−	0.305176i
$647$	31.7515	−	18.3317i	1.24828	−	0.720695i	0.277514	−	0.960722i	$-0.410489\pi$
$647$	31.7515	−	18.3317i	1.24828	−	0.720695i	0.970766	+	0.240026i	$0.0771561\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	1.24337	−	2.15358i	0.0488066	−	0.0845355i
$650$	21.7851	+	24.7531i	0.854483	+	0.970897i
$651$	1.08404	−	1.87761i	0.0424868	−	0.0735893i
$652$			0.667829i			0.0261542i
$653$	−14.7693	+	8.52708i	−0.577969	+	0.333690i	−0.760326	−	0.649542i	$-0.774961\pi$
$653$	−14.7693	+	8.52708i	−0.577969	+	0.333690i	0.182357	+	0.983232i	$0.441627\pi$
$654$	4.51885	−	7.82688i	0.176701	−	0.306055i
$655$	9.18470	−	6.59391i	0.358876	−	0.257645i
$656$	8.81389			0.344124
$657$	7.88486	+	4.55232i	0.307618	+	0.177603i
$658$			8.85217i			0.345094i
$659$	−2.94764	−	5.10547i	−0.114824	−	0.198881i	0.802885	−	0.596133i	$-0.203297\pi$
$659$	−2.94764	−	5.10547i	−0.114824	−	0.198881i	−0.917709	+	0.397253i	$0.869964\pi$
$660$	0.707408	+	0.985353i	0.0275358	+	0.0383548i
$661$	12.8330	+	22.2274i	0.499147	+	0.864547i	1.00000		0.000985045i	$-0.000313550\pi$
$661$	12.8330	+	22.2274i	0.499147	+	0.864547i	−0.500853	+	0.865532i	$0.666980\pi$
$662$	19.4831	−	11.2486i	0.757234	−	0.437189i
$663$	−19.8213	+	11.4438i	−0.769795	+	0.444441i
$664$	4.77109	−	8.26377i	0.185154	−	0.320697i
$665$	−2.59053	−	3.60836i	−0.100456	−	0.139926i
$666$	−1.73905	−	5.82887i	−0.0673870	−	0.225864i
$667$			5.90300i			0.228565i
$668$	12.2475	+	7.07110i	0.473870	+	0.273589i
$669$	12.0843	+	20.9306i	0.467206	+	0.809225i
$670$	20.0145	+	9.04722i	0.773228	+	0.349525i
$671$	1.09858	+	1.90280i	0.0424104	+	0.0734569i
$672$		−	0.769750i		−	0.0296938i
$673$	−16.1356	+	9.31590i	−0.621982	+	0.359102i	−0.777640	−	0.628709i	$-0.783583\pi$
$673$	−16.1356	+	9.31590i	−0.621982	+	0.359102i	0.155658	+	0.987811i	$0.450250\pi$
$674$	−13.7902			−0.531177
$675$	−3.75339	+	3.30334i	−0.144468	+	0.127146i
$676$	30.4923			1.17278
$677$			38.7308i			1.48855i	0.667875	+	0.744273i	$0.267204\pi$
$677$			38.7308i			1.48855i	−0.667875	+	0.744273i	$0.732796\pi$
$678$	−16.7865	−	9.69168i	−0.644681	−	0.372207i
$679$	−6.49448	−	11.2488i	−0.249235	−	0.431688i
$680$	−6.30397	+	4.52577i	−0.241746	+	0.173555i
$681$	−1.87032	+	3.23949i	−0.0716709	+	0.124138i
$682$	1.32321	+	0.763955i	0.0506683	+	0.0292533i
$683$	3.95588	+	2.28393i	0.151368	+	0.0873922i	0.573771	−	0.819016i	$-0.305480\pi$
$683$	3.95588	+	2.28393i	0.151368	+	0.0873922i	−0.422403	+	0.906408i	$0.638813\pi$
$684$	−1.29036	−	2.23497i	−0.0493382	−	0.0854562i
$685$	6.56484	−	14.5229i	0.250830	−	0.554892i
$686$	−5.16021	+	8.93774i	−0.197018	+	0.341245i
$687$	1.50525	+	0.869057i	0.0574289	+	0.0331566i
$688$	−6.05782	−	3.49748i	−0.230952	−	0.133340i
$689$	−26.7317			−1.01840
$690$	2.81632	−	6.23033i	0.107215	−	0.237185i
$691$	7.17049	−	12.4197i	0.272778	−	0.472466i	−0.696794	−	0.717271i	$-0.745391\pi$
$691$	7.17049	−	12.4197i	0.272778	−	0.472466i	0.969572	+	0.244805i	$0.0787241\pi$
$692$			3.80070i			0.144481i
$693$			0.417563i			0.0158619i
$694$	−5.29960	+	9.17918i	−0.201170	+	0.348437i
$695$	−28.1290	+	20.1945i	−1.06699	+	0.766020i
$696$	−0.965257	−	1.67187i	−0.0365880	−	0.0633722i
$697$		−	30.5888i		−	1.15863i
$698$	0.656952	−	0.379291i	0.0248660	−	0.0143564i
$699$	3.52510	+	6.10565i	0.133331	+	0.230937i
$700$	0.757501	+	3.77347i	0.0286309	+	0.142624i
$701$	−2.65641	+	4.60103i	−0.100331	+	0.173779i	−0.911821	−	0.410588i	$-0.865324\pi$
$701$	−2.65641	+	4.60103i	−0.100331	+	0.173779i	0.811490	+	0.584366i	$0.198657\pi$
$702$			6.59487i			0.248907i
$703$	−15.0427	+	4.48801i	−0.567345	+	0.169269i
$704$	0.542466			0.0204450
$705$	−2.54304	−	25.5889i	−0.0957763	−	0.963732i
$706$	11.5908	+	20.0758i	0.436225	+	0.755564i
$707$	7.50539	−	4.33324i	0.282269	−	0.162968i
$708$	3.96998	−	2.29207i	0.149201	−	0.0861413i
$709$	30.0632			1.12905			0.564524	−	0.825417i	$-0.309060\pi$
$709$	30.0632			1.12905			0.564524	+	0.825417i	$0.309060\pi$
$710$	2.47843	−	5.48286i	0.0930140	−	0.205768i
$711$	5.95081			0.223173
$712$	−10.8222	−	6.24819i	−0.405578	−	0.234161i
$713$		−	8.61240i		−	0.322537i
$714$	−2.67143			−0.0999759
$715$	−7.96031	+	0.791100i	−0.297699	+	0.0295855i
$716$	4.63019	+	8.01973i	0.173038	+	0.299711i
$717$			10.9401i			0.408566i
$718$	−15.8101	−	9.12798i	−0.590029	−	0.340653i
$719$	−18.9050	+	32.7444i	−0.705036	+	1.22116i	0.261642	+	0.965165i	$0.415736\pi$
$719$	−18.9050	+	32.7444i	−0.705036	+	1.22116i	−0.966679	+	0.255993i	$0.917597\pi$
$720$	0.221132	+	2.22511i	0.00824112	+	0.0829248i
$721$	−7.12483	−	12.3406i	−0.265342	−	0.459586i
$722$	10.6867	−	6.16994i	0.397716	−	0.229621i
$723$	7.78684	+	4.49573i	0.289596	+	0.167198i
$724$	11.9533	−	20.7037i	0.444241	−	0.769447i
$725$	6.37715	+	7.24597i	0.236842	+	0.269108i
$726$	10.7057			0.397327
$727$	43.9282	−	25.3620i	1.62921	−	0.940624i	0.644879	−	0.764285i	$-0.276908\pi$
$727$	43.9282	−	25.3620i	1.62921	−	0.940624i	0.984329	−	0.176339i	$-0.0564255\pi$
$728$	4.39630	+	2.53820i	0.162938	+	0.0940720i
$729$	−1.00000			−0.0370370
$730$	−16.5380	+	11.8730i	−0.612098	+	0.439440i
$731$	−12.1381	+	21.0238i	−0.448944	+	0.777593i
$732$			4.05033i			0.149705i
$733$	38.1292	−	22.0139i	1.40833	−	0.813102i	0.413106	−	0.910683i	$-0.364444\pi$
$733$	38.1292	−	22.0139i	1.40833	−	0.813102i	0.995228	+	0.0975813i	$0.0311106\pi$
$734$	5.19566			0.191775
$735$	5.90159	−	13.0557i	0.217684	−	0.481566i
$736$	−1.52887	−	2.64807i	−0.0563548	−	0.0976093i
$737$	−4.61463	+	2.66426i	−0.169982	+	0.0981392i
$738$	−7.63305	−	4.40694i	−0.280976	−	0.162222i
$739$	41.9885			1.54457			0.772286	−	0.635275i	$-0.219113\pi$
$739$	41.9885			1.54457			0.772286	+	0.635275i	$0.219113\pi$
$740$	13.4784	+	1.82523i	0.495478	+	0.0670966i
$741$	17.0195			0.625228
$742$	−2.70210	−	1.56006i	−0.0991970	−	0.0572714i
$743$	22.7858	−	13.1554i	0.835928	−	0.482623i	−0.0199498	−	0.999801i	$-0.506351\pi$
$743$	22.7858	−	13.1554i	0.835928	−	0.482623i	0.855878	+	0.517178i	$0.173017\pi$
$744$	1.40830	+	2.43925i	0.0516307	+	0.0894271i
$745$	−9.45129	−	4.27230i	−0.346268	−	0.156525i
$746$	−30.8519			−1.12957
$747$	−8.26377	+	4.77109i	−0.302356	+	0.174565i
$748$		−	1.88264i		−	0.0688361i
$749$	1.37446	−	2.38064i	0.0502217	−	0.0869866i
$750$	−3.27373	−	10.6903i	−0.119540	−	0.390355i
$751$	32.3655			1.18103			0.590517	−	0.807025i	$-0.298924\pi$
$751$	32.3655			1.18103			0.590517	+	0.807025i	$0.298924\pi$
$752$	−9.95934	−	5.75003i	−0.363180	−	0.209682i
$753$	−5.09555	+	2.94192i	−0.185692	+	0.107209i
$754$	12.7315			0.463654
$755$	−2.04210	−	20.5482i	−0.0743195	−	0.747827i
$756$	−0.384875	+	0.666623i	−0.0139978	+	0.0242449i
$757$	0.128003	+	0.0739027i	0.00465236	+	0.00268604i	0.502324	−	0.864679i	$-0.332478\pi$
$757$	0.128003	+	0.0739027i	0.00465236	+	0.00268604i	−0.497672	+	0.867365i	$0.665812\pi$
$758$	−27.1255	+	15.6609i	−0.985244	+	0.568831i
$759$	0.829358	+	1.43649i	0.0301038	+	0.0521413i
$760$	5.74238	−	0.570681i	0.208298	−	0.0207008i
$761$	8.49049	−	14.7060i	0.307780	−	0.533090i	−0.670097	−	0.742274i	$-0.733747\pi$
$761$	8.49049	−	14.7060i	0.307780	−	0.533090i	0.977876	+	0.209184i	$0.0670806\pi$
$762$	12.9477	+	7.47537i	0.469047	+	0.270804i
$763$			6.95677i			0.251852i
$764$	−3.37945	−	5.85337i	−0.122264	−	0.211768i
$765$	7.72228	−	0.767445i	0.279200	−	0.0277470i
$766$	11.1825			0.404039
$767$			30.2318i			1.09161i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−23.6536			−0.852971			−0.426485	−	0.904495i	$-0.640248\pi$
$769$	−23.6536			−0.852971			−0.426485	+	0.904495i	$0.640248\pi$
$770$	−0.850813	−	0.384596i	−0.0306612	−	0.0138599i
$771$	17.0150			0.612780
$772$	0.717831	−	0.414440i	0.0258353	−	0.0149160i
$773$	40.7775	−	23.5429i	1.46666	−	0.846778i	0.467359	−	0.884068i	$-0.345206\pi$
$773$	40.7775	−	23.5429i	1.46666	−	0.846778i	0.999305	+	0.0372892i	$0.0118723\pi$
$774$	3.49748	+	6.05782i	0.125714	+	0.217744i
$775$	−9.30419	−	10.5718i	−0.334217	−	0.379750i
$776$	16.8742			0.605750
$777$	3.40268	+	3.21634i	0.122070	+	0.115386i
$778$		−	1.39061i		−	0.0498558i
$779$	−11.3731	+	19.6988i	−0.407483	+	0.705781i
$780$	−13.4375	−	6.07419i	−0.481139	−	0.217491i
$781$	0.729858	+	1.26415i	0.0261164	+	0.0452349i
$782$	−9.19020	+	5.30596i	−0.328641	+	0.189741i
$783$			1.93051i			0.0689909i
$784$	−3.20374	−	5.54904i	−0.114419	−	0.198180i
$785$	−12.9192	−	17.9953i	−0.461107	−	0.642279i
$786$	−2.52822	+	4.37901i	−0.0901788	+	0.156194i
$787$			8.22013i			0.293016i	0.989209	+	0.146508i	$0.0468034\pi$
$787$			8.22013i			0.293016i	−0.989209	+	0.146508i	$0.953197\pi$
$788$		−	18.1797i		−	0.647626i
$789$	14.6150	−	25.3139i	0.520307	−	0.901198i
$790$	−5.48097	+	12.1252i	−0.195004	+	0.431394i
$791$	14.9204			0.530507
$792$	−0.469789	−	0.271233i	−0.0166932	−	0.00963785i
$793$	−23.1328	−	13.3557i	−0.821469	−	0.474275i
$794$	−4.25596	+	7.37154i	−0.151038	+	0.261606i
$795$	8.25908	+	3.73338i	0.292919	+	0.132409i
$796$	−7.39285	−	12.8048i	−0.262033	−	0.453854i
$797$	−29.4580	−	17.0076i	−1.04346	−	0.602440i	−0.122647	−	0.992450i	$-0.539138\pi$
$797$	−29.4580	−	17.0076i	−1.04346	−	0.602440i	−0.920811	+	0.390010i	$0.872472\pi$
$798$	1.72037	+	0.993255i	0.0609004	+	0.0351608i
$799$	−19.9556	+	34.5641i	−0.705978	+	1.22279i
$800$	−4.73747	−	1.59886i	−0.167495	−	0.0565281i
$801$	6.24819	+	10.8222i	0.220769	+	0.382383i
$802$	25.6747	+	14.8233i	0.906605	+	0.523429i
$803$		−	4.93896i		−	0.174292i
$804$	−9.82276			−0.346422
$805$	0.520478	+	5.23721i	0.0183444	+	0.184588i
$806$	−18.5751			−0.654280
$807$	−16.1560	+	9.32770i	−0.568720	+	0.328350i
$808$			11.2588i			0.396084i
$809$	2.60716	+	4.51573i	0.0916627	+	0.158765i	0.908211	−	0.418513i	$-0.137449\pi$
$809$	2.60716	+	4.51573i	0.0916627	+	0.158765i	−0.816548	+	0.577277i	$0.804115\pi$
$810$	0.921047	−	2.03757i	0.0323623	−	0.0715927i
$811$	−9.31410	−	16.1325i	−0.327062	−	0.566489i	0.654865	−	0.755746i	$-0.272725\pi$
$811$	−9.31410	−	16.1325i	−0.327062	−	0.566489i	−0.981928	+	0.189257i	$0.939392\pi$
$812$	1.28693	+	0.743007i	0.0451622	+	0.0260744i
$813$			21.9070i			0.768312i
$814$	−2.26665	+	2.39797i	−0.0794461	+	0.0840488i
$815$	0.870889	+	1.21307i	0.0305059	+	0.0424919i
$816$	1.73526	−	3.00556i	0.0607463	−	0.105216i
$817$	15.6335	−	9.02603i	0.546948	−	0.315781i
$818$	−4.10626	+	2.37075i	−0.143572	+	0.0828914i
$819$	−2.53820	−	4.39630i	−0.0886920	−	0.153619i
$820$	16.0098	−	11.4938i	0.559088	−	0.401382i
$821$	−5.49890	−	9.52438i	−0.191913	−	0.332403i	0.753971	−	0.656908i	$-0.228136\pi$
$821$	−5.49890	−	9.52438i	−0.191913	−	0.332403i	−0.945884	+	0.324504i	$0.894802\pi$
$822$			7.12759i			0.248603i
$823$	−0.665818	−	0.384410i	−0.0232090	−	0.0133997i	0.488351	−	0.872647i	$-0.337599\pi$
$823$	−0.665818	−	0.384410i	−0.0232090	−	0.0133997i	−0.511560	+	0.859248i	$0.670932\pi$
$824$	18.5120			0.644898
$825$	2.56992	+	0.867325i	0.0894731	+	0.0301964i
$826$	−1.76432	+	3.05590i	−0.0613886	+	0.106328i
$827$	−46.9051	+	27.0807i	−1.63105	+	0.941687i	−0.647280	+	0.762252i	$0.724094\pi$
$827$	−46.9051	+	27.0807i	−1.63105	+	0.941687i	−0.983770	+	0.179435i	$0.942573\pi$
$828$			3.05773i			0.106264i
$829$	−5.04238	+	8.73366i	−0.175129	+	0.303333i	−0.940206	−	0.340606i	$-0.889368\pi$
$829$	−5.04238	+	8.73366i	−0.175129	+	0.303333i	0.765077	+	0.643939i	$0.222701\pi$
$830$	−2.11009	−	21.2324i	−0.0732422	−	0.736986i
$831$	0.443108	−	0.767485i	0.0153712	−	0.0266238i
$832$	−5.71133	+	3.29744i	−0.198005	+	0.114318i
$833$	−19.2581	+	11.1187i	−0.667253	+	0.385239i
$834$	7.74292	−	13.4111i	0.268115	−	0.464390i
$835$	31.4679	−	3.12730i	1.08899	−	0.108225i
$836$	−0.699977	+	1.21240i	−0.0242092	+	0.0419316i
$837$		−	2.81660i		−	0.0973559i
$838$	−25.0626	+	14.4699i	−0.865773	+	0.499854i
$839$	−9.03244	+	15.6446i	−0.311835	+	0.540113i	−0.978760	−	0.205012i	$-0.934277\pi$
$839$	−9.03244	+	15.6446i	−0.311835	+	0.540113i	0.666925	+	0.745125i	$0.267610\pi$
$840$	−1.00380	−	1.39820i	−0.0346344	−	0.0482425i
$841$	−25.2731			−0.871487
$842$	−2.96235	−	1.71031i	−0.102089	−	0.0589412i
$843$		−	13.2326i		−	0.455755i
$844$	1.44894	+	2.50964i	0.0498746	+	0.0863853i
$845$	55.3873	−	39.7638i	1.90538	−	1.36792i
$846$	5.75003	+	9.95934i	0.197690	+	0.342409i
$847$	−7.13669	+	4.12037i	−0.245220	+	0.141578i
$848$	3.51035	−	2.02670i	0.120546	−	0.0695973i
$849$	6.77958	−	11.7426i	0.232675	−	0.403004i
$850$	−5.54886	+	16.4415i	−0.190324	+	0.563939i
$851$	18.0941	+	4.30642i	0.620256	+	0.147622i
$852$			2.69089i			0.0921883i
$853$	24.3052	+	14.0326i	0.832194	+	0.480467i	0.854603	−	0.519281i	$-0.173800\pi$
$853$	24.3052	+	14.0326i	0.832194	+	0.480467i	−0.0224093	+	0.999749i	$0.507134\pi$
$854$	−1.55887	−	2.70005i	−0.0533435	−	0.0923936i
$855$	−5.25839	−	2.37696i	−0.179833	−	0.0812905i
$856$	1.78559	+	3.09274i	0.0610304	+	0.105708i
$857$			22.3241i			0.762576i	0.924456	+	0.381288i	$0.124519\pi$
$857$			22.3241i			0.762576i	−0.924456	+	0.381288i	$0.875481\pi$
$858$	3.09820	−	1.78875i	0.105771	−	0.0610668i
$859$	4.07618			0.139077			0.0695387	−	0.997579i	$-0.477847\pi$
$859$	4.07618			0.139077			0.0695387	+	0.997579i	$0.477847\pi$
$860$	−15.5646	+	1.54681i	−0.530747	+	0.0527460i
$861$	6.78449			0.231215
$862$			17.2935i			0.589018i
$863$	−11.8959	−	6.86812i	−0.404942	−	0.233794i	0.283672	−	0.958921i	$-0.408447\pi$
$863$	−11.8959	−	6.86812i	−0.404942	−	0.233794i	−0.688614	+	0.725128i	$0.741781\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	4.95633	+	6.90371i	0.168520	+	0.234733i
$866$	−11.6802	+	20.2307i	−0.396909	+	0.687467i
$867$	4.29157	+	2.47774i	0.145750	+	0.0841485i
$868$	−1.87761	−	1.08404i	−0.0637302	−	0.0367947i
$869$	−1.61406	−	2.79563i	−0.0547531	−	0.0948352i
$870$	−3.93355	−	1.77809i	−0.133360	−	0.0602830i
$871$	32.3899	−	56.1010i	1.09749	−	1.90091i
$872$	−7.82688	−	4.51885i	−0.265052	−	0.153028i
$873$	−14.6135	−	8.43712i	−0.494593	−	0.285553i
$874$	7.89115			0.266922
$875$	6.29678	+	5.86643i	0.212870	+	0.198321i
$876$	4.55232	−	7.88486i	0.153809	−	0.266405i
$877$			20.5882i			0.695215i	0.937640	+	0.347608i	$0.113006\pi$
$877$			20.5882i			0.695215i	−0.937640	+	0.347608i	$0.886994\pi$
$878$			29.3628i			0.990946i
$879$	−1.66531	+	2.88440i	−0.0561695	+	0.0972884i
$880$	0.985353	−	0.707408i	0.0332163	−	0.0238467i
$881$	−10.7066	−	18.5444i	−0.360715	−	0.624776i	0.627364	−	0.778726i	$-0.284134\pi$
$881$	−10.7066	−	18.5444i	−0.360715	−	0.624776i	−0.988079	+	0.153950i	$0.950801\pi$
$882$			6.40748i			0.215751i
$883$	−6.08562	+	3.51353i	−0.204797	+	0.118240i	−0.598891	−	0.800830i	$-0.704392\pi$
$883$	−6.08562	+	3.51353i	−0.204797	+	0.118240i	0.394094	+	0.919070i	$0.371058\pi$
$884$	11.4438	+	19.8213i	0.384897	+	0.666662i
$885$	4.22221	−	9.34049i	0.141928	−	0.313977i
$886$	−1.81439	+	3.14262i	−0.0609556	+	0.105578i
$887$			50.3834i			1.69171i	0.533415	+	0.845854i	$0.320909\pi$
$887$			50.3834i			1.69171i	−0.533415	+	0.845854i	$0.679091\pi$
$888$	−5.82887	+	1.73905i	−0.195604	+	0.0583588i
$889$	−11.5083			−0.385977
$890$	−27.8058	+	2.76336i	−0.932052	+	0.0926279i
$891$	0.271233	+	0.469789i	0.00908665	+	0.0157385i
$892$	20.9306	−	12.0843i	0.700809	−	0.404613i
$893$	25.7023	−	14.8392i	0.860094	−	0.496575i
$894$	4.63852			0.155135
$895$	18.8686	+	8.52925i	0.630709	+	0.285101i
$896$	−0.769750			−0.0257156
$897$	−17.4637	−	10.0827i	−0.583096	−	0.336651i
$898$		−	19.6734i		−	0.656509i
$899$	−5.43748			−0.181350
$900$	3.30334	+	3.75339i	0.110111	+	0.125113i
$901$	−7.03372	−	12.1828i	−0.234327	−	0.405866i
$902$			4.78124i			0.159198i
$903$	−4.66301	−	2.69219i	−0.155175	−	0.0895905i
$904$	−9.69168	+	16.7865i	−0.322341	+	0.558310i
$905$	−5.28652	−	53.1947i	−0.175730	−	1.76825i
$906$	4.61736	+	7.99750i	0.153401	+	0.265699i
$907$	−23.9196	+	13.8100i	−0.794238	+	0.458554i	−0.841452	−	0.540331i	$-0.818299\pi$
$907$	−23.9196	+	13.8100i	−0.794238	+	0.458554i	0.0472142	+	0.998885i	$0.484966\pi$
$908$	3.23949	+	1.87032i	0.107506	+	0.0620688i
$909$	5.62941	−	9.75043i	0.186716	−	0.323401i
$910$	11.2955	−	1.12256i	0.374444	−	0.0372124i
$911$	−42.5841			−1.41088			−0.705438	−	0.708772i	$-0.749249\pi$
$911$	−42.5841			−1.41088			−0.705438	+	0.708772i	$0.749249\pi$
$912$	−2.23497	+	1.29036i	−0.0740072	+	0.0427281i
$913$	4.48282	+	2.58816i	0.148360	+	0.0856554i
$914$	−11.4322			−0.378145
$915$	5.28187	+	7.35715i	0.174613	+	0.243220i
$916$	0.869057	−	1.50525i	0.0287145	−	0.0497349i
$917$		−	3.89220i		−	0.128532i
$918$	−3.00556	+	1.73526i	−0.0991982	+	0.0572721i
$919$	48.2956			1.59313			0.796563	−	0.604556i	$-0.206649\pi$
$919$	48.2956			1.59313			0.796563	+	0.604556i	$0.206649\pi$
$920$	−6.23033	−	2.81632i	−0.205408	−	0.0928512i
$921$	1.36658	+	2.36699i	0.0450304	+	0.0779950i
$922$	−19.7029	+	11.3754i	−0.648879	+	0.374630i
$923$	−15.3685	−	8.87303i	−0.505862	−	0.292059i
$924$	0.417563			0.0137368
$925$	26.8629	−	14.2613i	0.883247	−	0.468909i
$926$	−18.7797			−0.617141
$927$	−16.0319	−	9.25602i	−0.526557	−	0.304008i
$928$	−1.67187	+	0.965257i	−0.0548820	+	0.0316861i
$929$	−2.83207	−	4.90529i	−0.0929172	−	0.160937i	0.815820	−	0.578306i	$-0.196286\pi$
$929$	−2.83207	−	4.90529i	−0.0929172	−	0.160937i	−0.908737	+	0.417368i	$0.862953\pi$
$930$	5.73900	+	2.59422i	0.188189	+	0.0850678i
$931$	16.5359			0.541943
$932$	6.10565	−	3.52510i	0.199997	−	0.115468i
$933$		−	13.0564i		−	0.427448i
$934$	−6.49285	+	11.2460i	−0.212453	+	0.367979i
$935$	−2.45508	−	3.41969i	−0.0802896	−	0.111836i
$936$	6.59487			0.215560
$937$	20.6589	+	11.9274i	0.674896	+	0.389651i	0.797929	−	0.602751i	$-0.205929\pi$
$937$	20.6589	+	11.9274i	0.674896	+	0.389651i	−0.123033	+	0.992403i	$0.539262\pi$
$938$	6.54808	−	3.78054i	0.213802	−	0.123439i
$939$	−31.9898			−1.04395
$940$	−25.5889	+	2.54304i	−0.834617	+	0.0829447i
$941$	11.8682	−	20.5563i	0.386891	−	0.670115i	−0.605138	−	0.796120i	$-0.706882\pi$
$941$	11.8682	−	20.5563i	0.386891	−	0.670115i	0.992030	+	0.126005i	$0.0402155\pi$
$942$	8.57966	+	4.95347i	0.279540	+	0.161393i
$943$	23.3398	−	13.4753i	0.760049	−	0.438815i
$944$	−2.29207	−	3.96998i	−0.0746006	−	0.129212i
$945$	0.170217	+	1.71278i	0.00553715	+	0.0557166i
$946$	1.89727	−	3.28616i	0.0616855	−	0.106842i
$947$	−28.5238	−	16.4682i	−0.926899	−	0.535145i	−0.0410694	−	0.999156i	$-0.513076\pi$
$947$	−28.5238	−	16.4682i	−0.926899	−	0.535145i	−0.885829	+	0.464011i	$0.846410\pi$
$948$		−	5.95081i		−	0.193273i
$949$	30.0220	+	51.9996i	0.974555	+	1.68798i
$950$	9.68644	−	8.52501i	0.314270	−	0.276588i
$951$	−22.1844			−0.719378
$952$			2.67143i			0.0865817i
$953$	−25.6624	−	14.8162i	−0.831285	−	0.479943i	0.0230074	−	0.999735i	$-0.492676\pi$
$953$	−25.6624	−	14.8162i	−0.831285	−	0.479943i	−0.854292	+	0.519793i	$0.826009\pi$
$954$	−4.05341			−0.131234
$955$	−13.7717	−	6.22526i	−0.445641	−	0.201445i
$956$	10.9401			0.353828
$957$	0.906935	−	0.523619i	0.0293171	−	0.0169262i
$958$	13.7808	−	7.95632i	0.445236	−	0.257057i
$959$	−2.74323	−	4.75142i	−0.0885836	−	0.153431i
$960$	2.22511	−	0.221132i	0.0718150	−	0.00713702i
$961$	−23.0668			−0.744090
$962$	9.28801	−	39.0250i	0.299458	−	1.25822i
$963$		−	3.57119i		−	0.115080i
$964$	4.49573	−	7.78684i	0.144798	−	0.250797i
$965$	0.763438	−	1.68890i	0.0245759	−	0.0543675i
$966$	−1.17685	−	2.03836i	−0.0378644	−	0.0655830i
$967$	8.33504	−	4.81224i	0.268037	−	0.154751i	−0.359958	−	0.932968i	$-0.617209\pi$
$967$	8.33504	−	4.81224i	0.268037	−	0.154751i	0.627995	+	0.778217i	$0.283876\pi$
$968$		−	10.7057i		−	0.344095i
$969$	4.47822	+	7.75651i	0.143861	+	0.249175i
$970$	30.6509	−	22.0050i	0.984142	−	0.706539i
$971$	18.1092	−	31.3660i	0.581152	−	1.00658i	−0.414192	−	0.910190i	$-0.635936\pi$
$971$	18.1092	−	31.3660i	0.581152	−	1.00658i	0.995343	−	0.0963944i	$-0.0307310\pi$
$972$			1.00000i			0.0320750i
$973$			11.9202i			0.382145i
$974$	10.1979	−	17.6634i	0.326763	−	0.565971i
$975$	−32.3294	+	6.48993i	−1.03537	+	0.207844i
$976$	4.05033			0.129648
$977$	−19.2807	−	11.1317i	−0.616845	−	0.356135i	0.158795	−	0.987312i	$-0.449239\pi$
$977$	−19.2807	−	11.1317i	−0.616845	−	0.356135i	−0.775639	+	0.631176i	$0.782572\pi$
$978$	−0.578357	−	0.333914i	−0.0184938	−	0.0106774i
$979$	3.38943	−	5.87067i	0.108327	−	0.187627i
$980$	−13.0557	−	5.90159i	−0.417048	−	0.188520i
$981$	4.51885	+	7.82688i	0.144276	+	0.249893i
$982$	−21.2391	−	12.2624i	−0.677768	−	0.391310i
$983$	−38.8577	−	22.4345i	−1.23937	−	0.715550i	−0.270404	−	0.962747i	$-0.587157\pi$
$983$	−38.8577	−	22.4345i	−1.23937	−	0.715550i	−0.968965	+	0.247196i	$0.920491\pi$
$984$	−4.40694	+	7.63305i	−0.140488	+	0.243333i
$985$	−23.7075	−	33.0223i	−0.755383	−	1.05218i
$986$	3.34994	+	5.80227i	0.106684	+	0.184782i
$987$	−7.66621	−	4.42609i	−0.244018	−	0.140884i
$988$		−	17.0195i		−	0.541463i
$989$	−21.3887			−0.680123
$990$	−1.20705	+	0.119957i	−0.0383624	+	0.00381248i
$991$	21.6734			0.688478			0.344239	−	0.938882i	$-0.388137\pi$
$991$	21.6734			0.688478			0.344239	+	0.938882i	$0.388137\pi$
$992$	2.43925	−	1.40830i	0.0774461	−	0.0447135i
$993$			22.4972i			0.713927i
$994$	−1.03566	−	1.79381i	−0.0328490	−	0.0568961i
$995$	−30.1268	−	13.6183i	−0.955084	−	0.431730i
$996$	4.77109	+	8.26377i	0.151178	+	0.261848i
$997$	27.5164	+	15.8866i	0.871452	+	0.503133i	0.867830	−	0.496861i	$-0.165514\pi$
$997$	27.5164	+	15.8866i	0.871452	+	0.503133i	0.00362128	+	0.999993i	$0.498847\pi$
$998$		−	5.41368i		−	0.171367i
$999$	5.91747	+	1.40837i	0.187221	+	0.0445588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.e.1009.19	yes	40
5.4	even	2	inner	1110.2.bb.e.1009.2	✓	40
37.26	even	3	inner	1110.2.bb.e.1099.2	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.e.1009.2	✓	40	5.4	even	2	inner
1110.2.bb.e.1009.19	yes	40	1.1	even	1	trivial
1110.2.bb.e.1099.2	yes	40	37.26	even	3	inner
1110.2.bb.e.1099.19	yes	40	185.174	even	6	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.03757 + 0.921047i) q^{5} -1.00000 q^{6} +(0.666623 - 0.384875i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.03757 + 0.921047i) q^{5} -1.00000 q^{6} +(0.666623 - 0.384875i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.30406 + 1.81643i) q^{10} -0.542466 q^{11} +(-0.866025 - 0.500000i) q^{12} +(5.71133 - 3.29744i) q^{13} +0.769750 q^{14} +(-2.22511 + 0.221132i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.00556 + 1.73526i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.29036 - 2.23497i) q^{19} +(0.221132 + 2.22511i) q^{20} +(-0.384875 + 0.666623i) q^{21} +(-0.469789 - 0.271233i) q^{22} +3.05773i q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.30334 + 3.75339i) q^{25} +6.59487 q^{26} +1.00000i q^{27} +(0.666623 + 0.384875i) q^{28} +1.93051 q^{29} +(-2.03757 - 0.921047i) q^{30} -2.81660 q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.469789 - 0.271233i) q^{33} +(1.73526 + 3.00556i) q^{34} +(1.71278 - 0.170217i) q^{35} +1.00000 q^{36} +(1.40837 - 5.91747i) q^{37} -2.58072i q^{38} +(-3.29744 + 5.71133i) q^{39} +(-0.921047 + 2.03757i) q^{40} +(-4.40694 - 7.63305i) q^{41} +(-0.666623 + 0.384875i) q^{42} +6.99497i q^{43} +(-0.271233 - 0.469789i) q^{44} +(1.81643 - 1.30406i) q^{45} +(-1.52887 + 2.64807i) q^{46} +11.5001i q^{47} -1.00000i q^{48} +(-3.20374 + 5.54904i) q^{49} +(0.984087 + 4.90220i) q^{50} -3.47052 q^{51} +(5.71133 + 3.29744i) q^{52} +(-3.51035 - 2.02670i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.10531 - 0.499637i) q^{55} +(0.384875 + 0.666623i) q^{56} +(2.23497 + 1.29036i) q^{57} +(1.67187 + 0.965257i) q^{58} +(-2.29207 + 3.96998i) q^{59} +(-1.30406 - 1.81643i) q^{60} +(-2.02517 - 3.50769i) q^{61} +(-2.43925 - 1.40830i) q^{62} -0.769750i q^{63} -1.00000 q^{64} +(14.6743 - 1.45834i) q^{65} +0.542466 q^{66} +(8.50676 - 4.91138i) q^{67} +3.47052i q^{68} +(-1.52887 - 2.64807i) q^{69} +(1.56842 + 0.708976i) q^{70} +(-1.34544 - 2.33038i) q^{71} +(0.866025 + 0.500000i) q^{72} +9.10465i q^{73} +(4.17842 - 4.42050i) q^{74} +(-4.73747 - 1.59886i) q^{75} +(1.29036 - 2.23497i) q^{76} +(-0.361621 + 0.208782i) q^{77} +(-5.71133 + 3.29744i) q^{78} +(2.97540 + 5.15355i) q^{79} +(-1.81643 + 1.30406i) q^{80} +(-0.500000 - 0.866025i) q^{81} -8.81389i q^{82} +(-8.26377 - 4.77109i) q^{83} -0.769750 q^{84} +(4.52577 + 6.30397i) q^{85} +(-3.49748 + 6.05782i) q^{86} +(-1.67187 + 0.965257i) q^{87} -0.542466i q^{88} +(-6.24819 + 10.8222i) q^{89} +(2.22511 - 0.221132i) q^{90} +(2.53820 - 4.39630i) q^{91} +(-2.64807 + 1.52887i) q^{92} +(2.43925 - 1.40830i) q^{93} +(-5.75003 + 9.95934i) q^{94} +(-0.570681 - 5.74238i) q^{95} +(0.500000 - 0.866025i) q^{96} -16.8742i q^{97} +(-5.54904 + 3.20374i) q^{98} +(-0.271233 + 0.469789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

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