LMFDB - Embedded newform 1110.2.bb.e.1009.2

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			1009.2
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.221132 + 2.22511i) q^{5} -1.00000 q^{6} +(-0.666623 + 0.384875i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.221132 + 2.22511i) 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} +(0.921047 + 2.03757i) 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} +(-2.03757 + 0.921047i) q^{20} +(-0.384875 + 0.666623i) q^{21} +(0.469789 + 0.271233i) q^{22} -3.05773i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.90220 - 0.984087i) q^{25} +6.59487 q^{26} -1.00000i q^{27} +(-0.666623 - 0.384875i) q^{28} +1.93051 q^{29} +(0.221132 - 2.22511i) q^{30} -2.81660 q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.469789 + 0.271233i) q^{33} +(1.73526 + 3.00556i) q^{34} +(-0.708976 - 1.56842i) q^{35} +1.00000 q^{36} +(-1.40837 + 5.91747i) q^{37} +2.58072i q^{38} +(-3.29744 + 5.71133i) q^{39} +(2.22511 + 0.221132i) 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} +(3.75339 + 3.30334i) q^{50} -3.47052 q^{51} +(-5.71133 - 3.29744i) q^{52} +(3.51035 + 2.02670i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.119957 - 1.20705i) 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} +(-6.07419 - 13.4375i) q^{65} +0.542466 q^{66} +(-8.50676 + 4.91138i) q^{67} -3.47052i q^{68} +(-1.52887 - 2.64807i) q^{69} +(-0.170217 + 1.71278i) 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} +(-0.921047 - 2.03757i) 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} +(5.25839 - 2.37696i) 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
$5$	−0.221132	+	2.22511i	−0.0988935	+	0.995098i
$5$	−0.221132	+	2.22511i	−0.0988935	+	0.995098i
$6$	−1.00000			−0.408248
$7$	−0.666623	+	0.384875i	−0.251960	+	0.145469i	−0.620661	−	0.784079i	$-0.713136\pi$
$7$	−0.666623	+	0.384875i	−0.251960	+	0.145469i	0.368701	+	0.929548i	$0.379802\pi$
$8$		−	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	$0.700784\pi$
$13$	−5.71133	+	3.29744i	−1.58404	+	0.914544i	−0.994261	+	0.106977i	$0.965883\pi$
$14$	0.769750			0.205724
$15$	0.921047	+	2.03757i	0.237813	+	0.526097i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00556	−	1.73526i	−0.728955	−	0.420862i	0.0890846	−	0.996024i	$-0.471606\pi$
$17$	−3.00556	−	1.73526i	−0.728955	−	0.420862i	−0.818040	+	0.575162i	$0.804939\pi$
$18$	−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	$0.928996\pi$
$20$	−2.03757	+	0.921047i	−0.455613	+	0.205952i
$21$	−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	$-0.896723\pi$
$23$		−	3.05773i		−	0.637581i	0.947825	−	0.318791i	$-0.103277\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.90220	−	0.984087i	−0.980440	−	0.196817i
$26$	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	$0.442635\pi$
$30$	0.221132	−	2.22511i	0.0403731	−	0.406247i
$31$	−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
$35$	−0.708976	−	1.56842i	−0.119839	−	0.265111i
$36$	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
$40$	2.22511	+	0.221132i	0.351820	+	0.0349641i
$41$	−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	$-0.820929\pi$
$43$		−	6.99497i		−	1.06672i	0.845887	−	0.533361i	$-0.179071\pi$
$44$	−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	$-0.683300\pi$
$47$		−	11.5001i		−	1.67746i	0.544551	−	0.838728i	$-0.316700\pi$
$48$			1.00000i			0.144338i
$49$	−3.20374	+	5.54904i	−0.457677	+	0.792721i
$50$	3.75339	+	3.30334i	0.530809	+	0.467163i
$51$	−3.47052			−0.485970
$52$	−5.71133	−	3.29744i	−0.792019	−	0.457272i
$53$	3.51035	+	2.02670i	0.482184	+	0.278389i	0.721326	−	0.692595i	$-0.243533\pi$
$53$	3.51035	+	2.02670i	0.482184	+	0.278389i	−0.239142	+	0.970985i	$0.576866\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	0.119957	−	1.20705i	0.0161750	−	0.162758i
$56$	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
$65$	−6.07419	−	13.4375i	−0.753410	−	1.66671i
$66$	0.542466			0.0667730
$67$	−8.50676	+	4.91138i	−1.03927	+	0.600021i	−0.919625	−	0.392797i	$-0.871508\pi$
$67$	−8.50676	+	4.91138i	−1.03927	+	0.600021i	−0.119641	+	0.992817i	$0.538174\pi$
$68$		−	3.47052i		−	0.420862i
$69$	−1.52887	−	2.64807i	−0.184054	−	0.318791i
$70$	−0.170217	+	1.71278i	−0.0203448	+	0.204716i
$71$	−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	$-0.821136\pi$
$73$		−	9.10465i		−	1.06562i	0.846235	−	0.532809i	$-0.178864\pi$
$74$	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	0.879486	−	0.475924i	$-0.157886\pi$
$83$	8.26377	+	4.77109i	0.907067	+	0.523695i	0.0275806	+	0.999620i	$0.491220\pi$
$84$	−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	$0.936244\pi$
$90$	−0.921047	−	2.03757i	−0.0970869	−	0.214778i
$91$	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
$95$	5.25839	−	2.37696i	0.539499	−	0.243871i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			16.8742i			1.71332i	0.515882	+	0.856660i	$0.327464\pi$
$97$			16.8742i			1.71332i	−0.515882	+	0.856660i	$0.672536\pi$
$98$	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	$0.365480\pi$
$103$			18.5120i			1.82405i	−0.410139	+	0.912023i	$0.634520\pi$
$104$	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	−0.641987	−	0.766715i	$-0.721890\pi$
$107$	−3.09274	+	1.78559i	−0.298986	+	0.172620i	0.343001	+	0.939335i	$0.388557\pi$
$108$	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	$-0.968091\pi$
$113$	−16.7865	−	9.69168i	−1.57914	−	0.911717i	−0.584160	−	0.811638i	$-0.698576\pi$
$114$	1.29036	+	2.23497i	0.120853	+	0.209324i
$115$	6.80378	+	0.676164i	0.634456	+	0.0630526i
$116$	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
$120$	2.03757	−	0.921047i	0.186003	−	0.0840797i
$121$	−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	0.948625	−	0.316402i	$-0.102475\pi$
$127$	12.9477	+	7.47537i	1.14893	+	0.663332i	0.200300	+	0.979735i	$0.435808\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−3.49748	−	6.05782i	−0.307936	−	0.533361i
$130$	−1.45834	+	14.6743i	−0.127905	+	1.28702i
$131$	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
$135$	2.22511	+	0.221132i	0.191507	+	0.0190321i
$136$	−1.73526	+	3.00556i	−0.148797	+	0.257725i
$137$			7.12759i			0.608951i	0.952520	+	0.304475i	$0.0984812\pi$
$137$			7.12759i			0.608951i	−0.952520	+	0.304475i	$0.901519\pi$
$138$			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
$145$	−0.426899	+	4.29560i	−0.0354521	+	0.356730i
$146$	−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	$0.560849\pi$
$150$	4.90220	+	0.984087i	0.400263	+	0.0803504i
$151$	−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
$155$	0.622841	−	6.26723i	0.0500278	−	0.503396i
$156$	−6.59487			−0.528012
$157$	8.57966	+	4.95347i	0.684731	+	0.395330i	0.801635	−	0.597813i	$-0.203964\pi$
$157$	8.57966	+	4.95347i	0.684731	+	0.395330i	−0.116904	+	0.993143i	$0.537297\pi$
$158$		−	5.95081i		−	0.473421i
$159$	4.05341			0.321456
$160$	0.921047	+	2.03757i	0.0728152	+	0.161084i
$161$	1.17685	+	2.03836i	0.0927484	+	0.160645i
$162$			1.00000i			0.0785674i
$163$	−0.578357	−	0.333914i	−0.0453004	−	0.0261542i	0.477179	−	0.878806i	$-0.341659\pi$
$163$	−0.578357	−	0.333914i	−0.0453004	−	0.0261542i	−0.522479	+	0.852652i	$0.674993\pi$
$164$	4.40694	−	7.63305i	0.344124	−	0.596041i
$165$	−0.499637	−	1.10531i	−0.0388967	−	0.0860483i
$166$	−4.77109	−	8.26377i	−0.370308	−	0.641393i
$167$	−12.2475	+	7.07110i	−0.947740	+	0.547178i	−0.892378	−	0.451289i	$-0.850965\pi$
$167$	−12.2475	+	7.07110i	−0.947740	+	0.547178i	−0.0553617	+	0.998466i	$0.517631\pi$
$168$	0.666623	+	0.384875i	0.0514311	+	0.0296938i
$169$	15.2462	−	26.4071i	1.17278	−	2.03132i
$170$	−7.07141	+	3.19651i	−0.542353	+	0.245161i
$171$	−2.58072			−0.197353
$172$	6.05782	−	3.49748i	0.461905	−	0.266681i
$173$	−3.29150	−	1.90035i	−0.250248	−	0.144481i	0.369630	−	0.929179i	$-0.379485\pi$
$173$	−3.29150	−	1.90035i	−0.250248	−	0.144481i	−0.619878	+	0.784698i	$0.712818\pi$
$174$	−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	$0.387514\pi$
$180$	−0.221132	+	2.22511i	−0.0164822	+	0.165850i
$181$	−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
$185$	−12.8556	−	4.44232i	−0.945161	−	0.326606i
$186$	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
$190$	−5.74238	−	0.570681i	−0.416596	−	0.0414016i
$191$	−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	$0.00949725\pi$
$193$			0.828880i			0.0596641i	−0.999555	+	0.0298321i	$0.990503\pi$
$194$	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	0.941840	−	0.336062i	$-0.109095\pi$
$197$	15.7441	+	9.08987i	1.12172	+	0.647626i	0.179882	+	0.983688i	$0.442428\pi$
$198$	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	$0.675585\pi$
$200$	−0.984087	+	4.90220i	−0.0695854	+	0.346638i
$201$	−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
$205$	17.9589	−	8.11800i	1.25430	−	0.566986i
$206$	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
$210$	0.708976	+	1.56842i	0.0489240	+	0.108231i
$211$	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
$215$	15.5646	+	1.54681i	1.06149	+	0.105492i
$216$	−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
$220$	1.10531	−	0.499637i	0.0745200	−	0.0336855i
$221$	22.8876			1.53959
$222$	1.40837	−	5.91747i	0.0945235	−	0.397155i
$223$			24.1686i			1.61845i	0.587499	+	0.809225i	$0.300113\pi$
$223$			24.1686i			1.61845i	−0.587499	+	0.809225i	$0.699887\pi$
$224$	−0.384875	+	0.666623i	−0.0257156	+	0.0445406i
$225$	−3.30334	+	3.75339i	−0.220223	+	0.250226i
$226$	9.69168	+	16.7865i	0.644681	+	1.11662i
$227$	−3.23949	+	1.87032i	−0.215013	+	0.124138i	−0.603639	−	0.797258i	$-0.706283\pi$
$227$	−3.23949	+	1.87032i	−0.215013	+	0.124138i	0.388626	+	0.921396i	$0.372950\pi$
$228$		−	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	$0.0741791\pi$
$233$			7.05019i			0.461874i	−0.972969	+	0.230937i	$0.925821\pi$
$234$	3.29744	−	5.71133i	0.215560	−	0.373361i
$235$	25.5889	+	2.54304i	1.66923	+	0.165889i
$236$	−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	$0.0515464\pi$
$240$	−2.22511	−	0.221132i	−0.143630	−	0.0142740i
$241$	−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
$250$	−8.18029	+	7.62121i	−0.517367	+	0.482008i
$251$	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
$255$	0.767445	−	7.72228i	0.0480593	−	0.483588i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.7354	+	8.50750i	0.919170	+	0.530683i	0.883370	−	0.468676i	$-0.155269\pi$
$257$	14.7354	+	8.50750i	0.919170	+	0.530683i	0.0358001	+	0.999359i	$0.488602\pi$
$258$			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	$-0.309356\pi$
$263$	25.3139	−	14.6150i	1.56092	−	0.901198i	0.997164	−	0.0752567i	$-0.0239776\pi$
$264$	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
$275$	2.65928	+	0.533834i	0.160361	+	0.0321914i
$276$	1.52887	−	2.64807i	0.0920269	−	0.159395i
$277$	0.767485	−	0.443108i	0.0461137	−	0.0266238i	−0.476766	−	0.879030i	$-0.658191\pi$
$277$	0.767485	−	0.443108i	0.0461137	−	0.0266238i	0.522880	+	0.852407i	$0.324858\pi$
$278$	13.4111	−	7.74292i	0.804346	−	0.464390i
$279$	−1.40830	+	2.43925i	−0.0843127	+	0.146034i
$280$	−1.56842	+	0.708976i	−0.0937308	+	0.0423694i
$281$	−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	−0.108587	−	0.994087i	$-0.534633\pi$
$283$	11.7426	−	6.77958i	0.698024	−	0.403004i	0.806611	+	0.591083i	$0.201299\pi$
$284$	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	−0.581882	−	0.813273i	$-0.697684\pi$
$293$	−2.88440	+	1.66531i	−0.168508	+	0.0972884i	0.413374	+	0.910561i	$0.364350\pi$
$294$	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
$300$	−3.75339	−	3.30334i	−0.216702	−	0.190719i
$301$	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
$305$	8.25281	−	3.73055i	0.472555	−	0.213610i
$306$	3.47052			0.198396
$307$			2.73317i			0.155990i	0.996954	+	0.0779950i	$0.0248518\pi$
$307$			2.73317i			0.155990i	−0.996954	+	0.0779950i	$0.975148\pi$
$308$	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	$-0.973887\pi$
$313$	−27.7040	−	15.9949i	−1.56592	−	0.904085i	−0.569285	−	0.822140i	$-0.692780\pi$
$314$	−4.95347	−	8.57966i	−0.279540	−	0.484178i
$315$	−1.71278	−	0.170217i	−0.0965040	−	0.00959063i
$316$	−2.97540	+	5.15355i	−0.167380	+	0.289910i
$317$	−19.2122	−	11.0922i	−1.07907	−	0.623000i	−0.148423	−	0.988924i	$-0.547420\pi$
$317$	−19.2122	−	11.0922i	−1.07907	−	0.623000i	−0.930645	+	0.365924i	$0.880753\pi$
$318$	−3.51035	−	2.02670i	−0.196851	−	0.113652i
$319$	−1.04724			−0.0586341
$320$	0.221132	−	2.22511i	0.0123617	−	0.124387i
$321$	−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
$330$	−0.119957	+	1.20705i	−0.00660341	+	0.0664457i
$331$	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
$335$	−9.04722	−	20.0145i	−0.494303	−	1.09351i
$336$	−0.384875	−	0.666623i	−0.0209967	−	0.0363673i
$337$	11.9426	−	6.89508i	0.650557	−	0.375599i	−0.138113	−	0.990416i	$-0.544104\pi$
$337$	11.9426	−	6.89508i	0.650557	−	0.375599i	0.788669	+	0.614818i	$0.210770\pi$
$338$	−26.4071	+	15.2462i	−1.43636	+	0.829282i
$339$	−19.3834			−1.05276
$340$	7.72228	+	0.767445i	0.418799	+	0.0416205i
$341$	1.52791			0.0827409
$342$	2.23497	+	1.29036i	0.120853	+	0.0697747i
$343$		−	10.3204i		−	0.557250i
$344$	−6.99497			−0.377143
$345$	6.23033	−	2.81632i	0.335430	−	0.151625i
$346$	1.90035	+	3.29150i	0.102163	+	0.176952i
$347$		−	10.5992i		−	0.568995i	−0.958677	−	0.284497i	$-0.908173\pi$
$347$		−	10.5992i		−	0.568995i	0.958677	−	0.284497i	$-0.0918267\pi$
$348$	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	$0.160204\pi$
$350$	−3.77347	−	0.757501i	−0.201700	−	0.0404901i
$351$	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	−0.140750	−	0.990045i	$-0.544951\pi$
$353$	−20.0758	−	11.5908i	−1.06853	−	0.616915i	−0.927779	+	0.373130i	$0.878285\pi$
$354$	2.29207	−	3.96998i	0.121822	−	0.211002i
$355$	5.48286	−	2.47843i	0.291000	−	0.131542i
$356$	−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
$365$	20.2588	+	2.01333i	1.06039	+	0.105383i
$366$	2.02517	+	3.50769i	0.105857	+	0.183350i
$367$	−4.49957	+	2.59783i	−0.234876	+	0.135606i	−0.612819	−	0.790223i	$-0.709965\pi$
$367$	−4.49957	+	2.59783i	−0.234876	+	0.135606i	0.377944	+	0.925829i	$0.376631\pi$
$368$	2.64807	+	1.52887i	0.138040	+	0.0796977i
$369$	−8.81389			−0.458833
$370$	8.91210	+	10.2749i	0.463318	+	0.534169i
$371$	−3.12011			−0.161988
$372$	−2.43925	−	1.40830i	−0.126469	−	0.0730169i
$373$	26.7185	−	15.4260i	1.38343	−	0.798726i	0.390869	−	0.920446i	$-0.372174\pi$
$373$	26.7185	−	15.4260i	1.38343	−	0.798726i	0.992564	+	0.121720i	$0.0388412\pi$
$374$	−0.941320	−	1.63041i	−0.0486745	−	0.0843067i
$375$	−2.51002	−	10.8949i	−0.129617	−	0.562613i
$376$	−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	−0.726582	−	0.687080i	$-0.758892\pi$
$383$	−9.68429	+	5.59123i	−0.494844	+	0.285698i	0.231738	+	0.972778i	$0.425559\pi$
$384$	1.00000			0.0510310
$385$	0.384596	+	0.850813i	0.0196008	+	0.0433614i
$386$	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	$0.844557\pi$
$390$	6.07419	+	13.4375i	0.307578	+	0.680433i
$391$	−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
$395$	−12.1252	+	5.48097i	−0.610083	+	0.275778i
$396$	−0.542466			−0.0272600
$397$		−	8.51192i		−	0.427201i	−0.976921	−	0.213601i	$-0.931481\pi$
$397$		−	8.51192i		−	0.427201i	0.976921	−	0.213601i	$-0.0685191\pi$
$398$	12.8048	+	7.39285i	0.641846	+	0.370570i
$399$	1.98651			0.0994499
$400$	3.30334	−	3.75339i	0.165167	−	0.187669i
$401$	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
$405$	2.03757	−	0.921047i	0.101247	−	0.0457672i
$406$	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	$0.204067\pi$
$410$	−19.6118	−	1.94904i	−0.968560	−	0.0962561i
$411$	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	$0.916760\pi$
$420$	0.170217	−	1.71278i	0.00830573	−	0.0835749i
$421$	−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
$425$	13.0262	+	11.4643i	0.631864	+	0.556102i
$426$	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	$-0.810296\pi$
$433$		−	23.3604i		−	1.12263i	0.827602	−	0.561315i	$-0.189704\pi$
$434$	−2.16808			−0.104071
$435$	1.77809	+	3.93355i	0.0852531	+	0.188599i
$436$	−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	$0.586202\pi$
$440$	−1.20705	−	0.119957i	−0.0575436	−	0.00571872i
$441$	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	$-0.972526\pi$
$443$		−	3.62878i		−	0.172409i	0.996277	−	0.0862043i	$-0.0274738\pi$
$444$	−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	−0.250229	−	0.968187i	$-0.580506\pi$
$457$	9.90061	−	5.71612i	0.463131	−	0.267389i	0.713360	+	0.700798i	$0.247173\pi$
$458$			1.73811i			0.0812168i
$459$	−1.73526	+	3.00556i	−0.0809950	+	0.140287i
$460$	2.81632	+	6.23033i	0.131311	+	0.290491i
$461$	−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	−0.0719602	−	0.997408i	$-0.522925\pi$
$463$	16.2637	−	9.38987i	0.755840	−	0.436384i	0.827800	+	0.561023i	$0.189592\pi$
$464$	−0.965257	+	1.67187i	−0.0448109	+	0.0776148i
$465$	−2.59422	−	5.73900i	−0.120304	−	0.266140i
$466$	3.52510	−	6.10565i	0.163297	−	0.282839i
$467$		−	12.9857i		−	0.600907i	−0.953796	−	0.300453i	$-0.902862\pi$
$467$		−	12.9857i		−	0.600907i	0.953796	−	0.300453i	$-0.0971380\pi$
$468$	−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
$485$	−37.5470	−	3.73144i	−1.70492	−	0.169436i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$			20.3959i			0.924226i	0.886821	+	0.462113i	$0.152909\pi$
$487$			20.3959i			0.924226i	−0.886821	+	0.462113i	$0.847091\pi$
$488$	−3.50769	+	2.02517i	−0.158786	+	0.0916749i
$489$	−0.667829			−0.0302003
$490$	5.90159	+	13.0557i	0.266607	+	0.589795i
$491$	−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	$0.871999\pi$
$500$	10.8949	−	2.51002i	0.487237	−	0.112251i
$501$	−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	0.991997	−	0.126262i	$-0.0402979\pi$
$503$	30.9199	+	17.8516i	1.37865	+	0.795964i	0.386653	+	0.922225i	$0.373631\pi$
$504$	0.769750			0.0342874
$505$	−2.48969	+	25.0521i	−0.110790	+	1.11480i
$506$	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
$515$	−41.1913	−	4.09361i	−1.81510	−	0.180386i
$516$	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
$520$	−13.4375	+	6.07419i	−0.589273	+	0.266371i
$521$	−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	−0.990527	−	0.137316i	$-0.956152\pi$
$523$	−31.2593	+	18.0475i	−1.36687	+	0.789164i	−0.376344	+	0.926480i	$0.622819\pi$
$524$	5.05645			0.220892
$525$	2.54275	−	2.88917i	0.110975	−	0.126094i
$526$	−29.2299			−1.27449
$527$	8.46545	+	4.88753i	0.368761	+	0.212904i
$528$		−	0.542466i		−	0.0236078i
$529$	13.6503			0.593490
$530$	8.25908	−	3.73338i	0.358752	−	0.162168i
$531$	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
$535$	−3.28923	−	7.27653i	−0.142206	−	0.314592i
$536$	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
$540$	0.921047	+	2.03757i	0.0396356	+	0.0876828i
$541$	−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	$0.198588\pi$
$547$			27.3262i			1.16838i	−0.811616	+	0.584192i	$0.801412\pi$
$548$	−6.17267	+	3.56379i	−0.263683	+	0.152238i
$549$	−4.05033			−0.172864
$550$	−2.03609	−	1.79195i	−0.0868190	−	0.0764091i
$551$	−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
$555$	−13.3544	+	2.58063i	−0.566863	+	0.109542i
$556$	−15.4858			−0.656746
$557$	−39.0111	−	22.5231i	−1.65295	−	0.954333i	−0.975849	−	0.218445i	$-0.929902\pi$
$557$	−39.0111	−	22.5231i	−1.65295	−	0.954333i	−0.677103	−	0.735888i	$-0.736765\pi$
$558$	2.43925	−	1.40830i	0.103261	−	0.0596181i
$559$	23.0655	+	39.9506i	0.975565	+	1.68973i
$560$	1.71278	+	0.170217i	0.0723780	+	0.00719297i
$561$	1.88264			0.0794851
$562$	11.4598	−	6.61630i	0.483401	−	0.279092i
$563$		−	17.5550i		−	0.739856i	−0.929061	−	0.369928i	$-0.879382\pi$
$563$		−	17.5550i		−	0.739856i	0.929061	−	0.369928i	$-0.120618\pi$
$564$	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	$0.663673\pi$
$570$	−5.25839	+	2.37696i	−0.220250	+	0.0995601i
$571$	−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
$575$	−3.00907	+	14.9896i	−0.125487	+	0.625110i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.31132	−	4.22119i	−0.304374	−	0.175731i	0.340032	−	0.940414i	$-0.389562\pi$
$577$	−7.31132	−	4.22119i	−0.304374	−	0.175731i	−0.644406	+	0.764683i	$0.722895\pi$
$578$			4.95548i			0.206121i
$579$	0.414440	+	0.717831i	0.0172235	+	0.0298321i
$580$	−3.93355	+	1.77809i	−0.163332	+	0.0738314i
$581$	−7.34510			−0.304726
$582$		−	16.8742i		−	0.699460i
$583$	−1.90425	−	1.09942i	−0.0788659	−	0.0455332i
$584$	−9.10465			−0.376753
$585$	−14.6743	−	1.45834i	−0.606707	−	0.0602950i
$586$	3.33062			0.137587
$587$	−16.3387	+	9.43316i	−0.674371	+	0.389348i	−0.797731	−	0.603014i	$-0.793966\pi$
$587$	−16.3387	+	9.43316i	−0.674371	+	0.389348i	0.123360	+	0.992362i	$0.460633\pi$
$588$	−5.54904	+	3.20374i	−0.228839	+	0.132120i
$589$	3.63443	+	6.29501i	0.149754	+	0.259381i
$590$	4.22221	+	9.34049i	0.173826	+	0.384542i
$591$	18.1797			0.747815
$592$	−4.42050	−	4.17842i	−0.181681	−	0.171732i
$593$			18.8965i			0.775985i	0.921663	+	0.387992i	$0.126831\pi$
$593$			18.8965i			0.775985i	−0.921663	+	0.387992i	$0.873169\pi$
$594$	0.271233	−	0.469789i	0.0111288	−	0.0192757i
$595$	−0.590741	+	5.94423i	−0.0242180	+	0.243690i
$596$	−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
$605$	2.36738	−	23.8214i	0.0962479	−	0.968477i
$606$	−11.2588			−0.457358
$607$	23.1934	+	13.3907i	0.941391	+	0.543512i	0.890396	−	0.455187i	$-0.150427\pi$
$607$	23.1934	+	13.3907i	0.941391	+	0.543512i	0.0509949	+	0.998699i	$0.483761\pi$
$608$	−2.23497	−	1.29036i	−0.0906400	−	0.0523310i
$609$	−0.743007	+	1.28693i	−0.0301082	+	0.0521489i
$610$	−9.01242	−	0.895660i	−0.364902	−	0.0362642i
$611$	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	0.432177	−	0.901789i	$-0.357746\pi$
$613$	−3.28567	−	1.89698i	−0.132707	−	0.0766184i	−0.564884	+	0.825171i	$0.691079\pi$
$614$	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	0.775323	−	0.631565i	$-0.217587\pi$
$617$	15.3019	+	8.83457i	0.616032	+	0.355666i	−0.159290	+	0.987232i	$0.550921\pi$
$618$		−	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	$0.523627\pi$
$620$	5.73900	−	2.59422i	0.230484	−	0.104186i
$621$	−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
$625$	23.0631	+	9.64838i	0.922526	+	0.385935i
$626$	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	$-0.994399\pi$
$643$		−	0.892405i		−	0.0351930i	0.999845	−	0.0175965i	$-0.00560143\pi$
$644$	−1.17685	+	2.03836i	−0.0463742	+	0.0803225i
$645$	14.2527	−	6.44270i	0.561200	−	0.253681i
$646$	4.47822	−	7.75651i	0.176193	−	0.305176i
$647$	−31.7515	+	18.3317i	−1.24828	+	0.720695i	−0.970766	−	0.240026i	$-0.922844\pi$
$647$	−31.7515	+	18.3317i	−1.24828	+	0.720695i	−0.277514	+	0.960722i	$0.589511\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	1.24337	−	2.15358i	0.0488066	−	0.0845355i
$650$	−32.3294	−	6.48993i	−1.26806	−	0.254556i
$651$	1.08404	−	1.87761i	0.0424868	−	0.0735893i
$652$		−	0.667829i		−	0.0261542i
$653$	14.7693	−	8.52708i	0.577969	−	0.333690i	−0.182357	−	0.983232i	$-0.558373\pi$
$653$	14.7693	−	8.52708i	0.577969	−	0.333690i	0.760326	+	0.649542i	$0.225039\pi$
$654$	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
$670$	−2.17213	+	21.8567i	−0.0839167	+	0.844398i
$671$	1.09858	+	1.90280i	0.0424104	+	0.0734569i
$672$			0.769750i			0.0296938i
$673$	16.1356	−	9.31590i	0.621982	−	0.359102i	−0.155658	−	0.987811i	$-0.549750\pi$
$673$	16.1356	−	9.31590i	0.621982	−	0.359102i	0.777640	+	0.628709i	$0.216417\pi$
$674$	−13.7902			−0.531177
$675$	−0.984087	+	4.90220i	−0.0378775	+	0.188686i
$676$	30.4923			1.17278
$677$		−	38.7308i		−	1.48855i	−0.667875	−	0.744273i	$-0.732796\pi$
$677$		−	38.7308i		−	1.48855i	0.667875	−	0.744273i	$-0.267204\pi$
$678$	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	0.422403	−	0.906408i	$-0.361187\pi$
$683$	−3.95588	−	2.28393i	−0.151368	−	0.0873922i	−0.573771	+	0.819016i	$0.694520\pi$
$684$	−1.29036	−	2.23497i	−0.0493382	−	0.0854562i
$685$	−15.8596	−	1.57614i	−0.605966	−	0.0602213i
$686$	−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
$690$	−6.80378	−	0.676164i	−0.259016	−	0.0257411i
$691$	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
$700$	2.88917	+	2.54275i	0.109200	+	0.0961069i
$701$	−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
$705$	23.4321	−	10.5921i	0.882505	−	0.398921i
$706$	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	$0.309060\pi$
$710$	−5.98751	−	0.595043i	−0.224707	−	0.0223315i
$711$	5.95081			0.223173
$712$	10.8222	+	6.24819i	0.405578	+	0.234161i
$713$			8.61240i			0.322537i
$714$	−2.67143			−0.0999759
$715$	3.29504	+	7.28938i	0.123228	+	0.272607i
$716$	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	$0.917597\pi$
$720$	−2.03757	+	0.921047i	−0.0759356	+	0.0343254i
$721$	−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
$725$	−9.46377	−	1.89979i	−0.351476	−	0.0705566i
$726$	10.7057			0.397327
$727$	−43.9282	+	25.3620i	−1.62921	+	0.940624i	−0.644879	+	0.764285i	$0.723092\pi$
$727$	−43.9282	+	25.3620i	−1.62921	+	0.940624i	−0.984329	+	0.176339i	$0.943574\pi$
$728$	−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	−0.995228	−	0.0975813i	$-0.968889\pi$
$733$	−38.1292	+	22.0139i	−1.40833	+	0.813102i	−0.413106	+	0.910683i	$0.635556\pi$
$734$	5.19566			0.191775
$735$	−14.2573	−	1.41690i	−0.525890	−	0.0522633i
$736$	−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	$0.219113\pi$
$740$	−2.58063	−	13.3544i	−0.0948658	−	0.490918i
$741$	17.0195			0.625228
$742$	2.70210	+	1.56006i	0.0991970	+	0.0572714i
$743$	−22.7858	+	13.1554i	−0.835928	+	0.482623i	−0.855878	−	0.517178i	$-0.826983\pi$
$743$	−22.7858	+	13.1554i	−0.835928	+	0.482623i	0.0199498	+	0.999801i	$0.493649\pi$
$744$	1.40830	+	2.43925i	0.0516307	+	0.0894271i
$745$	1.02573	−	10.3212i	0.0375797	−	0.378140i
$746$	−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
$755$	18.8163	−	8.50561i	0.684797	−	0.309551i
$756$	−0.384875	+	0.666623i	−0.0139978	+	0.0242449i
$757$	−0.128003	−	0.0739027i	−0.00465236	−	0.00268604i	0.497672	−	0.867365i	$-0.334188\pi$
$757$	−0.128003	−	0.0739027i	−0.00465236	−	0.00268604i	−0.502324	+	0.864679i	$0.667522\pi$
$758$	27.1255	−	15.6609i	0.985244	−	0.568831i
$759$	0.829358	+	1.43649i	0.0301038	+	0.0521413i
$760$	−2.37696	−	5.25839i	−0.0862216	−	0.190742i
$761$	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
$765$	−3.19651	−	7.07141i	−0.115570	−	0.255667i
$766$	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	$0.640248\pi$
$770$	0.0923369	−	0.929123i	0.00332759	−	0.0334833i
$771$	17.0150			0.612780
$772$	−0.717831	+	0.414440i	−0.0258353	+	0.0149160i
$773$	−40.7775	+	23.5429i	−1.46666	+	0.846778i	−0.999305	−	0.0372892i	$-0.988128\pi$
$773$	−40.7775	+	23.5429i	−1.46666	+	0.846778i	−0.467359	+	0.884068i	$0.654794\pi$
$774$	3.49748	+	6.05782i	0.125714	+	0.217744i
$775$	13.8075	+	2.77178i	0.495981	+	0.0995652i
$776$	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
$780$	1.45834	−	14.6743i	0.0522170	−	0.525424i
$781$	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	$-0.953197\pi$
$787$		−	8.22013i		−	0.293016i	0.989209	−	0.146508i	$-0.0468034\pi$
$788$			18.1797i			0.647626i
$789$	14.6150	−	25.3139i	0.520307	−	0.901198i
$790$	13.2412	+	1.31592i	0.471100	+	0.0468182i
$791$	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
$795$	−0.896340	+	9.01926i	−0.0317899	+	0.319880i
$796$	−7.39285	−	12.8048i	−0.262033	−	0.453854i
$797$	29.4580	+	17.0076i	1.04346	+	0.602440i	0.920811	−	0.390010i	$-0.127528\pi$
$797$	29.4580	+	17.0076i	1.04346	+	0.602440i	0.122647	+	0.992450i	$0.460862\pi$
$798$	−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
$805$	−4.79580	+	2.16786i	−0.169030	+	0.0764070i
$806$	−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	$0.804115\pi$
$810$	−2.22511	−	0.221132i	−0.0781823	−	0.00776980i
$811$	−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	0.511560	−	0.859248i	$-0.329068\pi$
$823$	0.665818	+	0.384410i	0.0232090	+	0.0133997i	−0.488351	+	0.872647i	$0.662401\pi$
$824$	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	$-0.275906\pi$
$827$	46.9051	−	27.0807i	1.63105	−	0.941687i	0.983770	−	0.179435i	$-0.0574269\pi$
$828$		−	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	$0.222701\pi$
$830$	19.4428	−	8.78880i	0.674870	−	0.305064i
$831$	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
$835$	−13.0256	−	28.8156i	−0.450770	−	0.997206i
$836$	−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	0.0224093	−	0.999749i	$-0.492866\pi$
$853$	−24.3052	−	14.0326i	−0.832194	−	0.480467i	−0.854603	+	0.519281i	$0.826200\pi$
$854$	−1.55887	−	2.70005i	−0.0533435	−	0.0923936i
$855$	0.570681	−	5.74238i	0.0195169	−	0.196385i
$856$	1.78559	+	3.09274i	0.0610304	+	0.105708i
$857$		−	22.3241i		−	0.762576i	−0.924456	−	0.381288i	$-0.875481\pi$
$857$		−	22.3241i		−	0.762576i	0.924456	−	0.381288i	$-0.124519\pi$
$858$	−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	$0.477847\pi$
$860$	6.44270	+	14.2527i	0.219694	+	0.486013i
$861$	6.78449			0.231215
$862$		−	17.2935i		−	0.589018i
$863$	11.8959	+	6.86812i	0.404942	+	0.233794i	0.688614	−	0.725128i	$-0.258219\pi$
$863$	11.8959	+	6.86812i	0.404942	+	0.233794i	−0.283672	+	0.958921i	$0.591553\pi$
$864$	−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
$870$	0.426899	−	4.29560i	0.0144732	−	0.145634i
$871$	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
$875$	1.93209	+	8.38639i	0.0653164	+	0.283512i
$876$	4.55232	−	7.88486i	0.153809	−	0.266405i
$877$		−	20.5882i		−	0.695215i	−0.937640	−	0.347608i	$-0.886994\pi$
$877$		−	20.5882i		−	0.695215i	0.937640	−	0.347608i	$-0.113006\pi$
$878$		−	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	−0.394094	−	0.919070i	$-0.628942\pi$
$883$	6.08562	−	3.51353i	0.204797	−	0.118240i	0.598891	+	0.800830i	$0.295608\pi$
$884$	11.4438	+	19.8213i	0.384897	+	0.666662i
$885$	−10.2002	−	1.01370i	−0.342876	−	0.0340753i
$886$	−1.81439	+	3.14262i	−0.0609556	+	0.105578i
$887$		−	50.3834i		−	1.69171i	−0.533415	−	0.845854i	$-0.679091\pi$
$887$		−	50.3834i		−	1.69171i	0.533415	−	0.845854i	$-0.320909\pi$
$888$	5.82887	−	1.73905i	0.195604	−	0.0583588i
$889$	−11.5083			−0.385977
$890$	11.5098	+	25.4622i	0.385808	+	0.853494i
$891$	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
$895$	−2.04777	+	20.6054i	−0.0684495	+	0.688761i
$896$	−0.769750			−0.0257156
$897$	17.4637	+	10.0827i	0.583096	+	0.336651i
$898$			19.6734i			0.656509i
$899$	−5.43748			−0.181350
$900$	−4.90220	−	0.984087i	−0.163407	−	0.0328029i
$901$	−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
$905$	48.7112	−	22.0191i	1.61922	−	0.731939i
$906$	4.61736	+	7.99750i	0.153401	+	0.265699i
$907$	23.9196	−	13.8100i	0.794238	−	0.458554i	−0.0472142	−	0.998885i	$-0.515034\pi$
$907$	23.9196	−	13.8100i	0.794238	−	0.458554i	0.841452	+	0.540331i	$0.181701\pi$
$908$	−3.23949	−	1.87032i	−0.107506	−	0.0620688i
$909$	5.62941	−	9.75043i	0.186716	−	0.323401i
$910$	−4.67561	−	10.3435i	−0.154995	−	0.342884i
$911$	−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	$0.206649\pi$
$920$	0.676164	−	6.80378i	0.0222925	−	0.224314i
$921$	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
$925$	12.7274	−	27.6227i	0.418475	−	0.908228i
$926$	−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	$0.862953\pi$
$930$	−0.622841	+	6.26723i	−0.0204238	+	0.205511i
$931$	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	0.123033	−	0.992403i	$-0.460738\pi$
$937$	−20.6589	−	11.9274i	−0.674896	−	0.389651i	−0.797929	+	0.602751i	$0.794071\pi$
$938$	−6.54808	+	3.78054i	−0.213802	+	0.123439i
$939$	−31.9898			−1.04395
$940$	10.5921	+	23.4321i	0.345476	+	0.764271i
$941$	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
$945$	−1.56842	+	0.708976i	−0.0510206	+	0.0230630i
$946$	1.89727	−	3.28616i	0.0616855	−	0.106842i
$947$	28.5238	+	16.4682i	0.926899	+	0.535145i	0.885829	−	0.464011i	$-0.153590\pi$
$947$	28.5238	+	16.4682i	0.926899	+	0.535145i	0.0410694	+	0.999156i	$0.486924\pi$
$948$			5.95081i			0.193273i
$949$	30.0220	+	51.9996i	0.974555	+	1.68798i
$950$	2.53965	−	12.6512i	0.0823972	−	0.410459i
$951$	−22.1844			−0.719378
$952$		−	2.67143i		−	0.0865817i
$953$	25.6624	+	14.8162i	0.831285	+	0.479943i	0.854292	−	0.519793i	$-0.173991\pi$
$953$	25.6624	+	14.8162i	0.831285	+	0.479943i	−0.0230074	+	0.999735i	$0.507324\pi$
$954$	−4.05341			−0.131234
$955$	1.49461	−	15.0393i	0.0483645	−	0.486659i
$956$	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
$960$	−0.921047	−	2.03757i	−0.0297267	−	0.0657621i
$961$	−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
$965$	−1.84435	−	0.183292i	−0.0593716	−	0.00590039i
$966$	−1.17685	−	2.03836i	−0.0378644	−	0.0655830i
$967$	−8.33504	+	4.81224i	−0.268037	+	0.154751i	−0.627995	−	0.778217i	$-0.716124\pi$
$967$	−8.33504	+	4.81224i	−0.268037	+	0.154751i	0.359958	+	0.932968i	$0.382791\pi$
$968$			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
$975$	21.7851	−	24.7531i	0.697683	−	0.792734i
$976$	4.05033			0.129648
$977$	19.2807	+	11.1317i	0.616845	+	0.356135i	0.775639	−	0.631176i	$-0.217428\pi$
$977$	19.2807	+	11.1317i	0.616845	+	0.356135i	−0.158795	+	0.987312i	$0.550761\pi$
$978$	0.578357	+	0.333914i	0.0184938	+	0.0106774i
$979$	3.38943	−	5.87067i	0.108327	−	0.187627i
$980$	1.41690	−	14.2573i	0.0452613	−	0.455434i
$981$	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	0.968965	−	0.247196i	$-0.0795093\pi$
$983$	38.8577	+	22.4345i	1.23937	+	0.715550i	0.270404	+	0.962747i	$0.412843\pi$
$984$	−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
$990$	0.499637	+	1.10531i	0.0158795	+	0.0351291i
$991$	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
$995$	3.26960	−	32.8997i	0.103653	−	1.04299i
$996$	4.77109	+	8.26377i	0.151178	+	0.261848i
$997$	−27.5164	−	15.8866i	−0.871452	−	0.503133i	−0.00362128	−	0.999993i	$-0.501153\pi$
$997$	−27.5164	−	15.8866i	−0.871452	−	0.503133i	−0.867830	+	0.496861i	$0.834486\pi$
$998$			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.1009.2	✓	40
5.4	even	2	inner	1110.2.bb.e.1009.19	yes	40
37.26	even	3	inner	1110.2.bb.e.1099.19	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.2	yes	40

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.221132 + 2.22511i) q^{5} -1.00000 q^{6} +(-0.666623 + 0.384875i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.221132 + 2.22511i) 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} +(0.921047 + 2.03757i) 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} +(-2.03757 + 0.921047i) q^{20} +(-0.384875 + 0.666623i) q^{21} +(0.469789 + 0.271233i) q^{22} -3.05773i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.90220 - 0.984087i) q^{25} +6.59487 q^{26} -1.00000i q^{27} +(-0.666623 - 0.384875i) q^{28} +1.93051 q^{29} +(0.221132 - 2.22511i) q^{30} -2.81660 q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.469789 + 0.271233i) q^{33} +(1.73526 + 3.00556i) q^{34} +(-0.708976 - 1.56842i) q^{35} +1.00000 q^{36} +(-1.40837 + 5.91747i) q^{37} +2.58072i q^{38} +(-3.29744 + 5.71133i) q^{39} +(2.22511 + 0.221132i) 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} +(3.75339 + 3.30334i) q^{50} -3.47052 q^{51} +(-5.71133 - 3.29744i) q^{52} +(3.51035 + 2.02670i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.119957 - 1.20705i) 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} +(-6.07419 - 13.4375i) q^{65} +0.542466 q^{66} +(-8.50676 + 4.91138i) q^{67} -3.47052i q^{68} +(-1.52887 - 2.64807i) q^{69} +(-0.170217 + 1.71278i) 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} +(-0.921047 - 2.03757i) 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} +(5.25839 - 2.37696i) 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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