LMFDB - Embedded newform 538.2.d.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(5,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([104]))

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

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

chi := DirichletCharacter("538.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.d (of order $67$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$726$
Relative dimension:	$11$ over $\Q(\zeta_{67})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{67}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	538.5
Dual form			538.2.d.a.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.762685 - 0.646770i) q^{2} +(-0.456170 + 1.45008i) q^{3} +(0.163377 - 0.986564i) q^{4} +(-0.177575 - 0.829052i) q^{5} +(0.589953 + 1.40099i) q^{6} +(-0.732047 + 0.749414i) q^{7} +(-0.513474 - 0.858105i) q^{8} +(0.565057 + 0.394562i) q^{9} +(-0.671640 - 0.517455i) q^{10} +(-0.0878511 + 3.74647i) q^{11} +(1.35607 + 0.686951i) q^{12} +(5.07749 + 3.91188i) q^{13} +(-0.0736229 + 1.04503i) q^{14} +(1.28320 + 0.120691i) q^{15} +(-0.946616 - 0.322364i) q^{16} +(-0.0664010 - 2.83172i) q^{17} +(0.686152 - 0.0645358i) q^{18} +(0.423494 + 0.101147i) q^{19} +(-0.846924 + 0.0397409i) q^{20} +(-0.752771 - 1.40339i) q^{21} +(2.35610 + 2.91420i) q^{22} +(0.0289765 - 0.0921110i) q^{23} +(1.47855 - 0.353136i) q^{24} +(3.90555 - 1.75351i) q^{25} +(6.40261 - 0.300435i) q^{26} +(-4.44250 + 3.42266i) q^{27} +(0.619745 + 0.844648i) q^{28} +(2.89047 + 1.29776i) q^{29} +(1.05673 - 0.737883i) q^{30} +(7.18020 + 0.336923i) q^{31} +(-0.930465 + 0.366380i) q^{32} +(-5.39261 - 1.83642i) q^{33} +(-1.88211 - 2.11676i) q^{34} +(0.751296 + 0.473828i) q^{35} +(0.481578 - 0.493003i) q^{36} +(0.448874 + 3.81166i) q^{37} +(0.388412 - 0.196760i) q^{38} +(-7.98873 + 5.57828i) q^{39} +(-0.620233 + 0.578075i) q^{40} +(-2.94134 - 2.49430i) q^{41} +(-1.48180 - 0.583472i) q^{42} +(-8.75588 - 3.93121i) q^{43} +(3.68178 + 0.698760i) q^{44} +(0.226772 - 0.538526i) q^{45} +(-0.0374746 - 0.0889929i) q^{46} +(-4.22213 + 2.39385i) q^{47} +(0.899272 - 1.22561i) q^{48} +(0.138369 + 5.90086i) q^{49} +(1.84459 - 3.86337i) q^{50} +(4.13650 + 1.19546i) q^{51} +(4.68886 - 4.37015i) q^{52} +(3.08056 + 1.21300i) q^{53} +(-1.17455 + 5.48368i) q^{54} +(3.12162 - 0.592448i) q^{55} +(1.01896 + 0.243368i) q^{56} +(-0.339857 + 0.567960i) q^{57} +(3.04387 - 0.879685i) q^{58} +(-1.67581 + 10.1195i) q^{59} +(0.328714 - 1.24624i) q^{60} +(-7.01750 - 10.5694i) q^{61} +(5.69414 - 4.38697i) q^{62} +(-0.709339 + 0.134624i) q^{63} +(-0.472689 + 0.881230i) q^{64} +(2.34151 - 4.90415i) q^{65} +(-5.30060 + 2.08717i) q^{66} +(-0.860457 - 5.19592i) q^{67} +(-2.80452 - 0.397130i) q^{68} +(0.120350 + 0.0840366i) q^{69} +(0.879460 - 0.124535i) q^{70} +(-0.893368 - 12.6808i) q^{71} +(0.0484329 - 0.687476i) q^{72} +(9.83975 + 1.39334i) q^{73} +(2.80761 + 2.61678i) q^{74} +(0.761136 + 6.46326i) q^{75} +(0.168977 - 0.401279i) q^{76} +(-2.74335 - 2.80843i) q^{77} +(-2.48502 + 9.42134i) q^{78} +(-3.84763 - 4.75903i) q^{79} +(-0.0991613 + 0.842038i) q^{80} +(-2.22439 - 6.06228i) q^{81} -3.85656 q^{82} +(-2.88727 - 7.86887i) q^{83} +(-1.50752 + 0.513375i) q^{84} +(-2.33585 + 0.557893i) q^{85} +(-9.22057 + 2.66476i) q^{86} +(-3.20040 + 3.59941i) q^{87} +(3.25998 - 1.84833i) q^{88} +(-13.3076 - 8.39285i) q^{89} +(-0.175347 - 0.557395i) q^{90} +(-6.64857 + 0.941462i) q^{91} +(-0.0861392 - 0.0436361i) q^{92} +(-3.76396 + 10.2582i) q^{93} +(-1.67189 + 4.55650i) q^{94} +(0.00865410 - 0.369060i) q^{95} +(-0.106830 - 1.51638i) q^{96} +(9.30948 - 14.0214i) q^{97} +(3.92203 + 4.41101i) q^{98} +(-1.52786 + 2.08231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 726 q + 11 q^{2} + q^{3} - 11 q^{4} + q^{5} - q^{6} + 4 q^{7} + 11 q^{8} - 10 q^{9} - q^{10} + 5 q^{11} + q^{12} - 7 q^{13} - 4 q^{14} - 2 q^{15} - 11 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} + q^{20}+ \cdots + 25 q^{99}+O(q^{100}) $ 726 * q + 11 * q^2 + q^3 - 11 * q^4 + q^5 - q^6 + 4 * q^7 + 11 * q^8 - 10 * q^9 - q^10 + 5 * q^11 + q^12 - 7 * q^13 - 4 * q^14 - 2 * q^15 - 11 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 + q^20 - 191 * q^21 - 5 * q^22 + 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 185 * q^27 + 4 * q^28 + 7 * q^29 - 65 * q^30 + 4 * q^31 + 11 * q^32 + 18 * q^33 - 4 * q^34 + 22 * q^35 - 10 * q^36 + 216 * q^37 - 5 * q^38 - 4 * q^39 - q^40 - 122 * q^41 - 10 * q^42 + 5 * q^43 - 62 * q^44 + 9 * q^45 - 6 * q^46 + 211 * q^47 + q^48 + 9 * q^49 + 8 * q^50 + 18 * q^51 - 7 * q^52 - 141 * q^53 - 16 * q^54 - 28 * q^55 - 4 * q^56 + 4 * q^57 - 7 * q^58 + q^59 + 132 * q^60 - 60 * q^61 - 4 * q^62 - 11 * q^64 + 24 * q^65 - 18 * q^66 + 15 * q^67 + 4 * q^68 - 8 * q^69 - 22 * q^70 + 8 * q^71 + 10 * q^72 + 65 * q^73 - 15 * q^74 - 15 * q^75 + 5 * q^76 - 2 * q^77 + 4 * q^78 - 61 * q^79 + q^80 - 315 * q^81 - 280 * q^82 + 198 * q^83 - 258 * q^84 - 126 * q^85 - 5 * q^86 + 6 * q^87 - 5 * q^88 - 36 * q^89 - 9 * q^90 + 28 * q^91 + 6 * q^92 + 152 * q^93 - 10 * q^94 + 6 * q^95 - q^96 - 24 * q^97 - 9 * q^98 + 25 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{52}{67}\right)$

Coefficient data

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

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

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

$2$	0.762685	−	0.646770i	0.539300	−	0.457335i
$2$	0.762685	−	0.646770i	0.539300	−	0.457335i
$3$	−0.456170	+	1.45008i	−0.263370	+	0.837203i	0.725474	+	0.688249i	$0.241621\pi$
$3$	−0.456170	+	1.45008i	−0.263370	+	0.837203i	−0.988844	+	0.148954i	$0.952409\pi$
$4$	0.163377	−	0.986564i	0.0816887	−	0.493282i
$5$	−0.177575	−	0.829052i	−0.0794141	−	0.370763i	0.920381	−	0.391024i	$-0.127879\pi$
$5$	−0.177575	−	0.829052i	−0.0794141	−	0.370763i	−0.999795	+	0.0202602i	$0.993551\pi$
$6$	0.589953	+	1.40099i	0.240847	+	0.571952i
$7$	−0.732047	+	0.749414i	−0.276688	+	0.283252i	−0.839531	−	0.543312i	$-0.817170\pi$
$7$	−0.732047	+	0.749414i	−0.276688	+	0.283252i	0.562843	+	0.826564i	$0.309707\pi$
$8$	−0.513474	−	0.858105i	−0.181541	−	0.303386i
$9$	0.565057	+	0.394562i	0.188352	+	0.131521i
$10$	−0.671640	−	0.517455i	−0.212391	−	0.163634i
$11$	−0.0878511	+	3.74647i	−0.0264881	+	1.12960i	0.811649	+	0.584145i	$0.198570\pi$
$11$	−0.0878511	+	3.74647i	−0.0264881	+	1.12960i	−0.838137	+	0.545459i	$0.816355\pi$
$12$	1.35607	+	0.686951i	0.391463	+	0.198306i
$13$	5.07749	+	3.91188i	1.40824	+	1.08496i	0.983753	+	0.179526i	$0.0574565\pi$
$13$	5.07749	+	3.91188i	1.40824	+	1.08496i	0.424488	+	0.905433i	$0.360454\pi$
$14$	−0.0736229	+	1.04503i	−0.0196766	+	0.279297i
$15$	1.28320	+	0.120691i	0.331320	+	0.0311622i
$16$	−0.946616	−	0.322364i	−0.236654	−	0.0805911i
$17$	−0.0664010	−	2.83172i	−0.0161046	−	0.686793i	−0.946950	−	0.321380i	$-0.895853\pi$
$17$	−0.0664010	−	2.83172i	−0.0161046	−	0.686793i	0.930846	−	0.365412i	$-0.119072\pi$
$18$	0.686152	−	0.0645358i	0.161727	−	0.0152112i
$19$	0.423494	+	0.101147i	0.0971563	+	0.0232047i	0.280594	−	0.959827i	$-0.409469\pi$
$19$	0.423494	+	0.101147i	0.0971563	+	0.0232047i	−0.183437	+	0.983031i	$0.558722\pi$
$20$	−0.846924	+	0.0397409i	−0.189378	+	0.00888634i
$21$	−0.752771	−	1.40339i	−0.164268	−	0.306244i
$22$	2.35610	+	2.91420i	0.502323	+	0.621310i
$23$	0.0289765	−	0.0921110i	0.00604203	−	0.0192065i	−0.950843	−	0.309673i	$-0.899781\pi$
$23$	0.0289765	−	0.0921110i	0.00604203	−	0.0192065i	0.956885	+	0.290466i	$0.0938104\pi$
$24$	1.47855	−	0.353136i	0.301808	−	0.0720836i
$25$	3.90555	−	1.75351i	0.781111	−	0.350703i
$26$	6.40261	−	0.300435i	1.25565	−	0.0589201i
$27$	−4.44250	+	3.42266i	−0.854959	+	0.658691i
$28$	0.619745	+	0.844648i	0.117121	+	0.159623i
$29$	2.89047	+	1.29776i	0.536747	+	0.240988i	0.659839	−	0.751407i	$-0.270624\pi$
$29$	2.89047	+	1.29776i	0.536747	+	0.240988i	−0.123092	+	0.992395i	$0.539281\pi$
$30$	1.05673	−	0.737883i	0.192932	−	0.134718i
$31$	7.18020	+	0.336923i	1.28960	+	0.0605131i	0.680600	−	0.732655i	$-0.261719\pi$
$31$	7.18020	+	0.336923i	1.28960	+	0.0605131i	0.609002	+	0.793169i	$0.291570\pi$
$32$	−0.930465	+	0.366380i	−0.164485	+	0.0647675i
$33$	−5.39261	−	1.83642i	−0.938733	−	0.319680i
$34$	−1.88211	−	2.11676i	−0.322780	−	0.363022i
$35$	0.751296	+	0.473828i	0.126992	+	0.0800915i
$36$	0.481578	−	0.493003i	0.0802630	−	0.0821671i
$37$	0.448874	+	3.81166i	0.0737944	+	0.626633i	0.979317	+	0.202334i	$0.0648525\pi$
$37$	0.448874	+	3.81166i	0.0737944	+	0.626633i	−0.905522	+	0.424299i	$0.860521\pi$
$38$	0.388412	−	0.196760i	0.0630087	−	0.0319187i
$39$	−7.98873	+	5.57828i	−1.27922	+	0.893239i
$40$	−0.620233	+	0.578075i	−0.0980675	+	0.0914017i
$41$	−2.94134	−	2.49430i	−0.459360	−	0.389545i	0.387066	−	0.922052i	$-0.373489\pi$
$41$	−2.94134	−	2.49430i	−0.459360	−	0.389545i	−0.846425	+	0.532507i	$0.821250\pi$
$42$	−1.48180	−	0.583472i	−0.228646	−	0.0900317i
$43$	−8.75588	−	3.93121i	−1.33526	−	0.599504i	−0.388501	−	0.921448i	$-0.627007\pi$
$43$	−8.75588	−	3.93121i	−1.33526	−	0.599504i	−0.946759	+	0.321944i	$0.895664\pi$
$44$	3.68178	+	0.698760i	0.555050	+	0.105342i
$45$	0.226772	−	0.538526i	0.0338052	−	0.0802788i
$46$	−0.0374746	−	0.0889929i	−0.00552533	−	0.0131213i
$47$	−4.22213	+	2.39385i	−0.615861	+	0.349179i	−0.769213	−	0.638993i	$-0.779351\pi$
$47$	−4.22213	+	2.39385i	−0.615861	+	0.349179i	0.153352	+	0.988172i	$0.450993\pi$
$48$	0.899272	−	1.22561i	0.129799	−	0.176902i
$49$	0.138369	+	5.90086i	0.0197671	+	0.842981i
$50$	1.84459	−	3.86337i	0.260864	−	0.546364i
$51$	4.13650	+	1.19546i	0.579227	+	0.167398i
$52$	4.68886	−	4.37015i	0.650228	−	0.606031i
$53$	3.08056	+	1.21300i	0.423148	+	0.166619i	0.568356	−	0.822782i	$-0.307579\pi$
$53$	3.08056	+	1.21300i	0.423148	+	0.166619i	−0.145209	+	0.989401i	$0.546385\pi$
$54$	−1.17455	+	5.48368i	−0.159837	+	0.746235i
$55$	3.12162	−	0.592448i	0.420919	−	0.0798857i
$56$	1.01896	+	0.243368i	0.136165	+	0.0325215i
$57$	−0.339857	+	0.567960i	−0.0450151	+	0.0752281i
$58$	3.04387	−	0.879685i	0.399680	−	0.115508i
$59$	−1.67581	+	10.1195i	−0.218172	+	1.31745i	0.625347	+	0.780347i	$0.284958\pi$
$59$	−1.67581	+	10.1195i	−0.218172	+	1.31745i	−0.843519	+	0.537099i	$0.819520\pi$
$60$	0.328714	−	1.24624i	0.0424368	−	0.160888i
$61$	−7.01750	−	10.5694i	−0.898499	−	1.35327i	−0.935267	−	0.353944i	$-0.884840\pi$
$61$	−7.01750	−	10.5694i	−0.898499	−	1.35327i	0.0367675	−	0.999324i	$-0.488294\pi$
$62$	5.69414	−	4.38697i	0.723157	−	0.557146i
$63$	−0.709339	+	0.134624i	−0.0893683	+	0.0169611i
$64$	−0.472689	+	0.881230i	−0.0590861	+	0.110154i
$65$	2.34151	−	4.90415i	0.290429	−	0.608285i
$66$	−5.30060	+	2.08717i	−0.652459	+	0.256912i
$67$	−0.860457	−	5.19592i	−0.105122	−	0.634783i	−0.986676	−	0.162700i	$-0.947980\pi$
$67$	−0.860457	−	5.19592i	−0.105122	−	0.634783i	0.881554	−	0.472083i	$-0.156498\pi$
$68$	−2.80452	−	0.397130i	−0.340098	−	0.0481591i
$69$	0.120350	+	0.0840366i	0.0144884	+	0.0101168i
$70$	0.879460	−	0.124535i	0.105116	−	0.0148847i
$71$	−0.893368	−	12.6808i	−0.106023	−	1.50494i	−0.707880	−	0.706332i	$-0.750348\pi$
$71$	−0.893368	−	12.6808i	−0.106023	−	1.50494i	0.601857	−	0.798604i	$-0.294428\pi$
$72$	0.0484329	−	0.687476i	0.00570788	−	0.0810198i
$73$	9.83975	+	1.39334i	1.15166	+	0.163079i	0.689884	−	0.723920i	$-0.257662\pi$
$73$	9.83975	+	1.39334i	1.15166	+	0.163079i	0.461772	+	0.886999i	$0.347214\pi$
$74$	2.80761	+	2.61678i	0.326379	+	0.304194i
$75$	0.761136	+	6.46326i	0.0878885	+	0.746313i
$76$	0.168977	−	0.401279i	0.0193830	−	0.0460299i
$77$	−2.74335	−	2.80843i	−0.312634	−	0.320050i
$78$	−2.48502	+	9.42134i	−0.281374	+	1.06676i
$79$	−3.84763	−	4.75903i	−0.432892	−	0.535433i	0.513655	−	0.857997i	$-0.328291\pi$
$79$	−3.84763	−	4.75903i	−0.432892	−	0.535433i	−0.946548	+	0.322564i	$0.895455\pi$
$80$	−0.0991613	+	0.842038i	−0.0110866	+	0.0941427i
$81$	−2.22439	−	6.06228i	−0.247155	−	0.673587i
$82$	−3.85656			−0.425885
$83$	−2.88727	−	7.86887i	−0.316919	−	0.863721i	−0.992030	−	0.126004i	$-0.959785\pi$
$83$	−2.88727	−	7.86887i	−0.316919	−	0.863721i	0.675111	−	0.737716i	$-0.264096\pi$
$84$	−1.50752	+	0.513375i	−0.164483	+	0.0560138i
$85$	−2.33585	+	0.557893i	−0.253359	+	0.0605120i
$86$	−9.22057	+	2.66476i	−0.994280	+	0.287349i
$87$	−3.20040	+	3.59941i	−0.343119	+	0.385897i
$88$	3.25998	−	1.84833i	0.347515	−	0.197033i
$89$	−13.3076	−	8.39285i	−1.41061	−	0.889640i	−0.410849	−	0.911704i	$-0.634767\pi$
$89$	−13.3076	−	8.39285i	−1.41061	−	0.889640i	−0.999757	+	0.0220633i	$0.992976\pi$
$90$	−0.175347	−	0.557395i	−0.0184832	−	0.0587546i
$91$	−6.64857	+	0.941462i	−0.696960	+	0.0986920i
$92$	−0.0861392	−	0.0436361i	−0.00898064	−	0.00454937i
$93$	−3.76396	+	10.2582i	−0.390304	+	1.06372i
$94$	−1.67189	+	4.55650i	−0.172442	+	0.469967i
$95$	0.00865410	−	0.369060i	0.000887892	−	0.0378648i
$96$	−0.106830	−	1.51638i	−0.0109032	−	0.154765i
$97$	9.30948	−	14.0214i	0.945235	−	1.42366i	0.0397830	−	0.999208i	$-0.487333\pi$
$97$	9.30948	−	14.0214i	0.945235	−	1.42366i	0.905452	−	0.424449i	$-0.139532\pi$
$98$	3.92203	+	4.41101i	0.396185	+	0.445579i
$99$	−1.52786	+	2.08231i	−0.153555	+	0.209280i
$100$	−1.09187	−	4.13956i	−0.109187	−	0.413956i
$101$	0.709960	−	1.18647i	0.0706436	−	0.118058i	−0.820751	−	0.571287i	$-0.806444\pi$
$101$	0.709960	−	1.18647i	0.0706436	−	0.118058i	0.891394	+	0.453229i	$0.149728\pi$
$102$	3.92804	−	1.76361i	0.388934	−	0.174623i
$103$	−10.2263	−	5.79808i	−1.00763	−	0.571302i	−0.101736	−	0.994811i	$-0.532440\pi$
$103$	−10.2263	−	5.79808i	−1.00763	−	0.571302i	−0.905892	+	0.423510i	$0.860798\pi$
$104$	0.749643	−	6.36567i	0.0735086	−	0.624205i
$105$	−1.02981	+	0.873293i	−0.100499	+	0.0852247i
$106$	3.13403	−	1.06728i	0.304404	−	0.103663i
$107$	2.37443	+	1.34625i	0.229545	+	0.130147i	0.603678	−	0.797229i	$-0.293701\pi$
$107$	2.37443	+	1.34625i	0.229545	+	0.130147i	−0.374133	+	0.927375i	$0.622060\pi$
$108$	2.65087	+	4.94199i	0.255080	+	0.475543i
$109$	3.42567	+	5.15955i	0.328120	+	0.494195i	0.959666	−	0.281143i	$-0.0907136\pi$
$109$	3.42567	+	5.15955i	0.328120	+	0.494195i	−0.631546	+	0.775338i	$0.717579\pi$
$110$	1.99764	−	2.47082i	0.190467	−	0.235584i
$111$	−5.73197	−	1.08786i	−0.544054	−	0.103255i
$112$	0.934551	−	0.473421i	0.0883068	−	0.0447341i
$113$	−3.42010	−	7.16319i	−0.321736	−	0.673856i	0.676291	−	0.736634i	$-0.263586\pi$
$113$	−3.42010	−	7.16319i	−0.321736	−	0.673856i	−0.998028	+	0.0627779i	$0.980004\pi$
$114$	0.108136	+	0.652984i	0.0101278	+	0.0611575i
$115$	−0.0815103	−	0.00766643i	−0.00760088	−	0.000714899i
$116$	1.75256	−	2.63961i	0.162721	−	0.245081i
$117$	1.32560	+	4.21382i	0.122551	+	0.389568i
$118$	5.26687	+	8.80186i	0.484854	+	0.810276i
$119$	2.17074	+	2.02319i	0.198991	+	0.185465i
$120$	−0.555322	−	1.16309i	−0.0506938	−	0.106175i
$121$	−3.04044	−	0.142669i	−0.276404	−	0.0129699i
$122$	−12.1881	−	3.52238i	−1.10346	−	0.318902i
$123$	4.95869	−	3.12734i	0.447110	−	0.281983i
$124$	1.50548	−	7.02868i	0.135196	−	0.631194i
$125$	−4.65512	−	6.34446i	−0.416367	−	0.567465i
$126$	−0.453931	+	0.561455i	−0.0404394	+	0.0500184i
$127$	4.19226	+	4.29172i	0.372003	+	0.380829i	0.875540	−	0.483145i	$-0.160506\pi$
$127$	4.19226	+	4.29172i	0.372003	+	0.380829i	−0.503537	+	0.863974i	$0.667968\pi$
$128$	0.209440	+	0.977821i	0.0185121	+	0.0864280i
$129$	9.69474	−	10.9034i	0.853574	−	0.959992i
$130$	−1.38602	−	5.25475i	−0.121562	−	0.460872i
$131$	18.4233	−	1.73280i	1.60965	−	0.151395i	0.749700	−	0.661778i	$-0.230198\pi$
$131$	18.4233	−	1.73280i	1.60965	−	0.151395i	0.859947	+	0.510383i	$0.170496\pi$
$132$	−2.69278	+	5.02012i	−0.234376	+	0.436946i
$133$	−0.385819	+	0.243328i	−0.0334547	+	0.0210992i
$134$	−4.01682	−	3.40633i	−0.347001	−	0.294262i
$135$	3.62644	+	3.07528i	0.312114	+	0.264678i
$136$	−2.39582	+	1.51099i	−0.205440	+	0.129567i
$137$	−1.75764	+	3.27675i	−0.150165	+	0.279951i	−0.945124	−	0.326712i	$-0.894059\pi$
$137$	−1.75764	+	3.27675i	−0.150165	+	0.279951i	0.794959	+	0.606663i	$0.207492\pi$
$138$	0.146141	−	0.0137453i	0.0124404	−	0.00117008i
$139$	1.18912	+	4.50824i	0.100860	+	0.382384i	0.998269	−	0.0588155i	$-0.0187324\pi$
$139$	1.18912	+	4.50824i	0.100860	+	0.382384i	−0.897409	+	0.441199i	$0.854553\pi$
$140$	0.590206	−	0.663789i	0.0498815	−	0.0561004i
$141$	−1.54526	−	7.21442i	−0.130135	−	0.607564i
$142$	−8.88293	−	9.09367i	−0.745439	−	0.763124i
$143$	−15.1018	+	18.6790i	−1.26288	+	1.56202i
$144$	−0.407700	−	0.555653i	−0.0339750	−	0.0463044i
$145$	0.562636	−	2.62680i	0.0467244	−	0.218144i
$146$	8.40581	−	5.30137i	0.695669	−	0.438745i
$147$	−8.61984	−	2.49115i	−0.710952	−	0.205467i
$148$	3.83378	+	0.179896i	0.315135	+	0.0147873i
$149$	−0.749655	−	1.57010i	−0.0614141	−	0.128628i	0.869415	−	0.494082i	$-0.164496\pi$
$149$	−0.749655	−	1.57010i	−0.0614141	−	0.128628i	−0.930829	+	0.365454i	$0.880914\pi$
$150$	4.76075	+	4.43715i	0.388714	+	0.362292i
$151$	9.37478	+	15.6669i	0.762909	+	1.27495i	0.955882	+	0.293750i	$0.0949034\pi$
$151$	9.37478	+	15.6669i	0.762909	+	1.27495i	−0.192973	+	0.981204i	$0.561813\pi$
$152$	−0.130659	−	0.415339i	−0.0105978	−	0.0336884i
$153$	1.07977	−	1.62628i	0.0872940	−	0.131477i
$154$	−3.90872	−	0.367634i	−0.314974	−	0.0296248i
$155$	−0.995699	−	6.01259i	−0.0799765	−	0.482943i
$156$	4.19815	+	8.79275i	0.336121	+	0.703984i
$157$	−13.2581	+	6.71622i	−1.05811	+	0.536013i	−0.892904	−	0.450246i	$-0.851336\pi$
$157$	−13.2581	+	6.71622i	−1.05811	+	0.536013i	−0.165205	+	0.986259i	$0.552829\pi$
$158$	−6.01253	−	1.14111i	−0.478331	−	0.0907817i
$159$	−3.16421	+	3.91372i	−0.250938	+	0.310378i
$160$	0.468976	+	0.706344i	0.0370758	+	0.0558414i
$161$	0.0478171	+	0.0891450i	0.00376851	+	0.00702561i
$162$	−5.61741	−	3.18494i	−0.441346	−	0.250233i
$163$	17.6460	−	6.00922i	1.38214	−	0.470679i	0.470764	−	0.882259i	$-0.343978\pi$
$163$	17.6460	−	6.00922i	1.38214	−	0.470679i	0.911373	+	0.411580i	$0.135023\pi$
$164$	−2.94134	+	2.49430i	−0.229680	+	0.194772i
$165$	−0.564895	+	4.79686i	−0.0439770	+	0.373435i
$166$	−7.29143	−	4.13407i	−0.565924	−	0.320866i
$167$	−18.5073	+	8.30938i	−1.43213	+	0.642999i	−0.969843	−	0.243729i	$-0.921629\pi$
$167$	−18.5073	+	8.30938i	−1.43213	+	0.642999i	−0.462292	+	0.886728i	$0.652973\pi$
$168$	−0.817724	+	1.36656i	−0.0630888	+	0.105432i
$169$	7.16254	+	27.1549i	0.550964	+	2.08884i
$170$	−1.42069	+	1.93625i	−0.108962	+	0.148504i
$171$	0.199390	+	0.224249i	0.0152477	+	0.0171487i
$172$	−5.30890	+	7.99596i	−0.404800	+	0.609687i
$173$	−0.615667	−	8.73901i	−0.0468083	−	0.664415i	−0.963989	−	0.265943i	$-0.914317\pi$
$173$	−0.615667	−	8.73901i	−0.0468083	−	0.664415i	0.917181	−	0.398472i	$-0.130459\pi$
$174$	−0.112910	+	4.81514i	−0.00855971	+	0.365035i
$175$	−1.54494	+	4.21053i	−0.116787	+	0.318286i
$176$	1.29089	−	3.51815i	0.0973046	−	0.265191i
$177$	−13.9096	−	7.04627i	−1.04551	−	0.529630i
$178$	−15.5778	+	2.20587i	−1.16760	+	0.165337i
$179$	3.44481	+	10.9504i	0.257477	+	0.818471i	0.990409	+	0.138169i	$0.0441216\pi$
$179$	3.44481	+	10.9504i	0.257477	+	0.818471i	−0.732932	+	0.680302i	$0.761849\pi$
$180$	−0.494241	−	0.311708i	−0.0368386	−	0.0232333i
$181$	−1.61290	+	0.914479i	−0.119886	+	0.0679727i	−0.551988	−	0.833852i	$-0.686130\pi$
$181$	−1.61290	+	0.914479i	−0.119886	+	0.0679727i	0.432101	+	0.901825i	$0.357772\pi$
$182$	−4.46186	+	5.01814i	−0.330735	+	0.371969i
$183$	18.5276	−	5.35451i	1.36960	−	0.395817i
$184$	−0.0939196	+	0.0224317i	−0.00692385	+	0.00165369i
$185$	3.08035	−	1.04900i	0.226472	−	0.0771237i
$186$	3.76396	+	10.2582i	0.275987	+	0.752165i
$187$	10.6148			0.776230
$188$	1.67189	+	4.55650i	0.121935	+	0.332317i
$189$	0.687128	−	5.83482i	0.0499812	−	0.424420i
$190$	−0.232097	−	0.287074i	−0.0168381	−	0.0208265i
$191$	−2.26182	+	8.57511i	−0.163660	+	0.620473i	0.833979	+	0.551796i	$0.186057\pi$
$191$	−2.26182	+	8.57511i	−0.163660	+	0.620473i	−0.997639	+	0.0686778i	$0.978122\pi$
$192$	−1.06223	−	1.08743i	−0.0766596	−	0.0784782i
$193$	1.25422	−	2.97846i	0.0902809	−	0.214395i	−0.870225	−	0.492655i	$-0.836026\pi$
$193$	1.25422	−	2.97846i	0.0902809	−	0.214395i	0.960506	+	0.278260i	$0.0897578\pi$
$194$	−1.96842	−	16.7150i	−0.141324	−	1.20007i
$195$	6.04328	+	5.63251i	0.432768	+	0.403352i
$196$	5.84418	+	0.827557i	0.417442	+	0.0591112i
$197$	0.620852	−	8.81262i	0.0442339	−	0.627873i	−0.924723	−	0.380642i	$-0.875703\pi$
$197$	0.620852	−	8.81262i	0.0442339	−	0.627873i	0.968956	−	0.247231i	$-0.0795208\pi$
$198$	0.181503	+	2.57632i	0.0128988	+	0.183091i
$199$	1.23405	−	0.174746i	0.0874794	−	0.0123874i	−0.0963283	−	0.995350i	$-0.530710\pi$
$199$	1.23405	−	0.174746i	0.0874794	−	0.0123874i	0.183808	+	0.982962i	$0.441158\pi$
$200$	−3.51010	−	2.45099i	−0.248202	−	0.173311i
$201$	7.92701	+	1.12249i	0.559128	+	0.0791745i
$202$	−0.225895	−	1.36408i	−0.0158939	−	0.0959764i
$203$	−3.08852	+	1.21614i	−0.216772	+	0.0853560i
$204$	1.85521	−	3.88561i	0.129890	−	0.272047i
$205$	−1.54560	+	2.88145i	−0.107949	+	0.201249i
$206$	−11.5495	+	2.19196i	−0.804690	+	0.152721i
$207$	0.0527169	−	0.0406150i	0.00366408	−	0.00282294i
$208$	−3.54538	−	5.33985i	−0.245828	−	0.370252i
$209$	−0.416149	+	1.57772i	−0.0287857	+	0.109134i
$210$	−0.220598	+	1.33210i	−0.0152227	+	0.0919233i
$211$	15.8383	−	4.57730i	1.09035	−	0.315114i	0.316573	−	0.948568i	$-0.397468\pi$
$211$	15.8383	−	4.57730i	1.09035	−	0.315114i	0.773781	+	0.633454i	$0.218363\pi$
$212$	1.70000	−	2.84099i	0.116756	−	0.195120i
$213$	18.7957	+	4.48916i	1.28786	+	0.307592i
$214$	2.68165	−	0.508947i	0.183314	−	0.0347909i
$215$	−1.70435	+	7.95717i	−0.116236	+	0.542674i
$216$	5.21811	+	2.05468i	0.355047	+	0.139803i
$217$	−5.50874	+	5.13430i	−0.373957	+	0.348539i
$218$	5.94975	+	1.71949i	0.402968	+	0.116459i
$219$	−6.50906	+	13.6328i	−0.439841	+	0.921220i
$220$	−0.0744851	−	3.17647i	−0.00502179	−	0.214158i
$221$	10.7402	−	14.6378i	0.722463	−	0.984643i
$222$	−5.07528	+	2.87757i	−0.340631	+	0.193130i
$223$	−1.71136	−	4.06406i	−0.114601	−	0.272149i	0.854219	−	0.519913i	$-0.174036\pi$
$223$	−1.71136	−	4.06406i	−0.114601	−	0.272149i	−0.968821	+	0.247764i	$0.920304\pi$
$224$	0.406574	−	0.965511i	0.0271654	−	0.0645109i
$225$	2.89873	+	0.550146i	0.193249	+	0.0366764i
$226$	−7.24140	−	3.25124i	−0.481691	−	0.216269i
$227$	−22.7549	−	8.95999i	−1.51030	−	0.594695i	−0.541096	−	0.840961i	$-0.681991\pi$
$227$	−22.7549	−	8.95999i	−1.51030	−	0.594695i	−0.969202	+	0.246265i	$0.920796\pi$
$228$	0.504804	+	0.428082i	0.0334314	+	0.0283504i
$229$	−12.5328	+	11.6810i	−0.828193	+	0.771899i	−0.976151	−	0.217095i	$-0.930342\pi$
$229$	−12.5328	+	11.6810i	−0.828193	+	0.771899i	0.147958	+	0.988994i	$0.452730\pi$
$230$	−0.0671251	+	0.0468713i	−0.00442610	+	0.00309061i
$231$	5.32388	−	2.69695i	0.350286	−	0.177446i
$232$	−0.370566	−	3.14669i	−0.0243288	−	0.206591i
$233$	9.47794	−	9.70279i	0.620920	−	0.635651i	−0.330405	−	0.943839i	$-0.607185\pi$
$233$	9.47794	−	9.70279i	0.620920	−	0.635651i	0.951325	+	0.308188i	$0.0997227\pi$
$234$	3.73638	+	2.35646i	0.244255	+	0.154047i
$235$	2.73437	+	3.07528i	0.178371	+	0.200609i
$236$	9.70974	+	3.30659i	0.632050	+	0.215241i
$237$	8.65614	−	3.40844i	0.562277	−	0.221402i
$238$	2.96413	+	0.139088i	0.192136	+	0.00901575i
$239$	17.2541	−	12.0480i	1.11607	−	0.779318i	0.138593	−	0.990349i	$-0.455742\pi$
$239$	17.2541	−	12.0480i	1.11607	−	0.779318i	0.977479	+	0.211031i	$0.0676822\pi$
$240$	−1.17579	−	0.527904i	−0.0758967	−	0.0340761i
$241$	−0.690535	−	0.941128i	−0.0444813	−	0.0606234i	0.783441	−	0.621466i	$-0.213462\pi$
$241$	−0.690535	−	0.941128i	−0.0444813	−	0.0606234i	−0.827923	+	0.560842i	$0.810477\pi$
$242$	−2.41117	+	1.85765i	−0.154996	+	0.119415i
$243$	−7.00021	+	0.328477i	−0.449064	+	0.0210718i
$244$	−11.5738	+	5.19642i	−0.740940	+	0.332667i
$245$	4.86755	−	1.16256i	0.310976	−	0.0742734i
$246$	1.75925	−	5.59231i	0.112165	−	0.356553i
$247$	1.75461	+	2.17023i	0.111643	+	0.138089i
$248$	−3.39773	−	6.33437i	−0.215756	−	0.402233i
$249$	12.7276	−	0.597226i	0.806577	−	0.0378477i
$250$	−7.65380	−	1.82803i	−0.484069	−	0.115615i
$251$	24.5438	−	2.30846i	1.54919	−	0.145709i	0.715764	−	0.698342i	$-0.246079\pi$
$251$	24.5438	−	2.30846i	1.54919	−	0.145709i	0.833424	+	0.552634i	$0.186377\pi$
$252$	0.0169256	+	0.721802i	0.00106621	+	0.0454693i
$253$	0.342546	+	0.116652i	0.0215357	+	0.00733385i
$254$	5.97313	+	0.561802i	0.374788	+	0.0352506i
$255$	0.256556	−	3.64166i	0.0160662	−	0.228050i
$256$	0.792162	+	0.610310i	0.0495102	+	0.0381444i
$257$	−27.0258	−	13.6906i	−1.68582	−	0.853997i	−0.990851	−	0.134960i	$-0.956909\pi$
$257$	−27.0258	−	13.6906i	−1.68582	−	0.853997i	−0.694972	−	0.719037i	$-0.744583\pi$
$258$	0.342031	−	14.5861i	0.0212939	−	0.908093i
$259$	−3.18511	−	2.45392i	−0.197913	−	0.152479i
$260$	−4.45571	−	3.11128i	−0.276331	−	0.192953i
$261$	1.12123	+	1.87378i	0.0694027	+	0.115984i
$262$	12.9304	−	13.2372i	0.798844	−	0.817796i
$263$	−2.10321	−	4.99460i	−0.129690	−	0.307980i	0.843820	−	0.536626i	$-0.180302\pi$
$263$	−2.10321	−	4.99460i	−0.129690	−	0.307980i	−0.973510	+	0.228646i	$0.926570\pi$
$264$	1.19312	+	5.57038i	0.0734317	+	0.342833i
$265$	0.458610	−	2.76934i	0.0281722	−	0.170119i
$266$	−0.136881	+	0.435119i	−0.00839271	+	0.0266788i
$267$	18.2408	−	15.4685i	1.11632	−	0.946659i
$268$	−5.26669			−0.321714
$269$	7.27040	−	14.7017i	0.443284	−	0.896381i
$269$	7.27040	−	14.7017i	0.443284	−	0.896381i
$270$	4.75483			0.289370
$271$	−3.97341	+	3.36952i	−0.241367	+	0.204684i	−0.759305	−	0.650735i	$-0.774461\pi$
$271$	−3.97341	+	3.36952i	−0.241367	+	0.204684i	0.517938	+	0.855418i	$0.326700\pi$
$272$	−0.849989	+	2.70195i	−0.0515381	+	0.163830i
$273$	1.66769	−	10.0704i	0.100933	−	0.609490i
$274$	0.778778	+	3.63591i	0.0470477	+	0.219653i
$275$	6.22639	+	14.7861i	0.375465	+	0.891636i
$276$	0.102570	−	0.105003i	0.00617398	−	0.00632045i
$277$	−4.39433	−	7.34369i	−0.264030	−	0.441240i	0.697245	−	0.716833i	$-0.254409\pi$
$277$	−4.39433	−	7.34369i	−0.264030	−	0.441240i	−0.961274	+	0.275594i	$0.911126\pi$
$278$	3.82271	+	2.66928i	0.229271	+	0.160093i
$279$	3.92429	+	3.02341i	0.234941	+	0.181007i
$280$	0.0208225	−	0.887989i	0.00124438	−	0.0530675i
$281$	5.87772	+	2.97751i	0.350636	+	0.177624i	0.618405	−	0.785859i	$-0.287779\pi$
$281$	5.87772	+	2.97751i	0.350636	+	0.177624i	−0.267770	+	0.963483i	$0.586287\pi$
$282$	−5.84462	−	4.50290i	−0.348042	−	0.268144i
$283$	−1.29186	+	18.3372i	−0.0767934	+	1.09004i	0.797077	+	0.603877i	$0.206378\pi$
$283$	−1.29186	+	18.3372i	−0.0767934	+	1.09004i	−0.873871	+	0.486158i	$0.838398\pi$
$284$	−12.6564	−	1.19039i	−0.751019	−	0.0706369i
$285$	0.531219	+	0.180903i	0.0314667	+	0.0107158i
$286$	0.563095	+	24.0136i	0.0332965	+	1.41995i
$287$	4.02246	−	0.378332i	0.237438	−	0.0223322i
$288$	−0.670326	−	0.160100i	−0.0394993	−	0.00943399i
$289$	8.96710	−	0.420771i	0.527476	−	0.0247512i
$290$	−1.26982	−	2.36732i	−0.0745665	−	0.139014i
$291$	16.0854	+	19.8956i	0.942945	+	1.16630i
$292$	2.98222	−	9.47990i	0.174521	−	0.554769i
$293$	−15.0591	+	3.59669i	−0.879759	+	0.210121i	−0.647071	−	0.762430i	$-0.724006\pi$
$293$	−15.0591	+	3.59669i	−0.879759	+	0.210121i	−0.232689	+	0.972551i	$0.574752\pi$
$294$	−8.18543	+	3.67509i	−0.477384	+	0.214336i
$295$	8.68717	−	0.407635i	0.505787	−	0.0237334i
$296$	3.04032	−	2.34237i	0.176715	−	0.136147i
$297$	−12.4326	−	16.9444i	−0.721414	−	0.983213i
$298$	−1.58725	−	0.712641i	−0.0919467	−	0.0412822i
$299$	0.507455	−	0.354340i	0.0293469	−	0.0204920i
$300$	6.50077	+	0.305041i	0.375322	+	0.0176116i
$301$	9.35582	−	3.68395i	0.539261	−	0.212339i
$302$	17.2829	+	5.88558i	0.994518	+	0.338677i
$303$	1.39661	+	1.57073i	0.0802330	+	0.0902360i
$304$	−0.368280	−	0.232267i	−0.0211223	−	0.0133214i
$305$	−7.51641	+	7.69473i	−0.430389	+	0.440599i
$306$	−0.228308	−	1.93870i	−0.0130515	−	0.110828i
$307$	13.2704	−	6.72245i	0.757381	−	0.383671i	−0.0304711	−	0.999536i	$-0.509701\pi$
$307$	13.2704	−	6.72245i	0.757381	−	0.383671i	0.787852	+	0.615865i	$0.211193\pi$
$308$	−3.21890	+	2.24765i	−0.183414	+	0.128072i
$309$	13.0726	−	12.1840i	0.743675	−	0.693126i
$310$	−4.64817	−	3.94172i	−0.263998	−	0.223875i
$311$	−10.6572	−	4.19640i	−0.604317	−	0.237956i	0.0443651	−	0.999015i	$-0.485874\pi$
$311$	−10.6572	−	4.19640i	−0.604317	−	0.237956i	−0.648682	+	0.761060i	$0.724679\pi$
$312$	8.88875	+	3.99087i	0.503227	+	0.225938i
$313$	31.7837	+	6.03217i	1.79652	+	0.340958i	0.973785	−	0.227469i	$-0.0730451\pi$
$313$	31.7837	+	6.03217i	1.79652	+	0.340958i	0.822733	+	0.568428i	$0.192448\pi$
$314$	−5.76789	+	13.6973i	−0.325501	+	0.772983i
$315$	0.237571	+	0.564173i	0.0133856	+	0.0317875i
$316$	−5.32370	+	3.01842i	−0.299482	+	0.169799i
$317$	−2.61314	+	3.56145i	−0.146769	+	0.200031i	−0.873409	−	0.486988i	$-0.838096\pi$
$317$	−2.61314	+	3.56145i	−0.146769	+	0.200031i	0.726640	+	0.687018i	$0.241081\pi$
$318$	0.117983	+	5.03145i	0.00661614	+	0.282150i
$319$	−5.11596	+	10.7151i	−0.286439	+	0.599928i
$320$	0.814523	+	0.235399i	0.0455332	+	0.0131592i
$321$	−3.03531	+	2.82899i	−0.169414	+	0.157899i
$322$	0.0941257	+	0.0370629i	0.00524542	+	0.00206544i
$323$	0.258300	−	1.20593i	0.0143722	−	0.0670999i
$324$	−6.34424	+	1.20406i	−0.352458	+	0.0668925i
$325$	26.6899	+	6.37460i	1.48049	+	0.353599i
$326$	9.57172	−	15.9960i	0.530129	−	0.885937i
$327$	−9.04444	+	2.61386i	−0.500159	+	0.144547i
$328$	−0.630074	+	3.80474i	−0.0347900	+	0.210081i
$329$	1.29681	−	4.91653i	0.0714956	−	0.271057i
$330$	2.67163	+	4.02385i	0.147068	+	0.221506i
$331$	7.31785	−	5.63793i	0.402225	−	0.309889i	−0.389202	−	0.921153i	$-0.627249\pi$
$331$	7.31785	−	5.63793i	0.402225	−	0.309889i	0.791427	+	0.611264i	$0.209339\pi$
$332$	−8.23486	+	1.56288i	−0.451946	+	0.0857742i
$333$	−1.25029	+	2.33091i	−0.0685157	+	0.127733i
$334$	−8.74096	+	18.3074i	−0.478284	+	1.00174i
$335$	−4.15489	+	1.63603i	−0.227006	+	0.0893859i
$336$	0.260184	+	1.57113i	0.0141942	+	0.0857124i
$337$	−14.6360	−	2.07251i	−0.797273	−	0.112897i	−0.270297	−	0.962777i	$-0.587122\pi$
$337$	−14.6360	−	2.07251i	−0.797273	−	0.112897i	−0.526976	+	0.849880i	$0.676674\pi$
$338$	23.0258	+	16.0782i	1.25244	+	0.874536i
$339$	11.9473	−	1.69179i	0.648891	−	0.0918852i
$340$	0.168772	+	2.39561i	0.00915293	+	0.129920i
$341$	−1.89306	+	26.8708i	−0.102515	+	1.45514i
$342$	0.297109	+	0.0420717i	0.0160658	+	0.00227498i
$343$	−9.88807	−	9.21596i	−0.533905	−	0.497615i
$344$	1.12253	+	9.53204i	0.0605226	+	0.513933i
$345$	0.0482995	−	0.114699i	0.00260036	−	0.00617520i
$346$	−6.12169	−	6.26692i	−0.329104	−	0.336912i
$347$	4.29097	−	16.2681i	0.230351	−	0.873318i	−0.747542	−	0.664214i	$-0.768766\pi$
$347$	4.29097	−	16.2681i	0.230351	−	0.873318i	0.977893	−	0.209104i	$-0.0670546\pi$
$348$	3.02817	+	3.74546i	0.162327	+	0.200778i
$349$	0.575980	−	4.89099i	0.0308315	−	0.261809i	−0.969056	−	0.246839i	$-0.920608\pi$
$349$	0.575980	−	4.89099i	0.0308315	−	0.261809i	0.999888	−	0.0149694i	$-0.00476509\pi$
$350$	1.54494	+	4.21053i	0.0825806	+	0.225062i
$351$	−35.9457			−1.91864
$352$	−1.29089	−	3.51815i	−0.0688047	−	0.187518i
$353$	−23.1660	+	7.88904i	−1.23300	+	0.419891i	−0.861126	−	0.508391i	$-0.830240\pi$
$353$	−23.1660	+	7.88904i	−1.23300	+	0.419891i	−0.371875	+	0.928283i	$0.621285\pi$
$354$	−15.1660	+	3.62223i	−0.806062	+	0.192519i
$355$	−10.3544	+	2.99245i	−0.549555	+	0.158823i
$356$	−10.4542	+	11.7576i	−0.554074	+	0.623152i
$357$	−3.92401	+	2.22482i	−0.207681	+	0.117750i
$358$	9.70969	+	6.12371i	0.513173	+	0.323648i
$359$	−6.14456	−	19.5324i	−0.324297	−	1.03088i	−0.964813	−	0.262935i	$-0.915309\pi$
$359$	−6.14456	−	19.5324i	−0.324297	−	1.03088i	0.640516	−	0.767945i	$-0.278720\pi$
$360$	−0.578554	+	0.0819253i	−0.0304925	+	0.00431784i
$361$	−16.7802	−	8.50044i	−0.883168	−	0.447391i
$362$	−0.638680	+	1.74064i	−0.0335683	+	0.0914858i
$363$	1.59384	−	4.34380i	0.0836549	−	0.227990i
$364$	−0.157415	+	6.71306i	−0.00825076	+	0.351860i
$365$	−0.592142	−	8.40509i	−0.0309941	−	0.439942i
$366$	10.6676	−	16.0669i	0.557603	−	0.839830i
$367$	−10.9819	−	12.3510i	−0.573249	−	0.644718i	0.387588	−	0.921833i	$-0.373308\pi$
$367$	−10.9819	−	12.3510i	−0.573249	−	0.644718i	−0.960837	+	0.277114i	$0.910622\pi$
$368$	−0.0571230	+	0.0778527i	−0.00297774	+	0.00405835i
$369$	−0.677868	−	2.56996i	−0.0352884	−	0.133787i
$370$	1.67088	−	2.79233i	0.0868649	−	0.145166i
$371$	−3.16416	+	1.42064i	−0.164275	+	0.0737560i
$372$	9.50539	+	5.38933i	0.492831	+	0.279424i
$373$	−3.08911	+	26.2315i	−0.159948	+	1.35822i	0.644687	+	0.764446i	$0.276988\pi$
$373$	−3.08911	+	26.2315i	−0.159948	+	1.35822i	−0.804636	+	0.593769i	$0.797639\pi$
$374$	8.09574	−	6.86533i	0.418621	−	0.354998i
$375$	11.3235	−	3.85615i	0.584742	−	0.199131i
$376$	4.22213	+	2.39385i	0.217740	+	0.123453i
$377$	9.59964	+	17.8965i	0.494407	+	0.921719i
$378$	−3.24972	−	4.89454i	−0.167148	−	0.251748i
$379$	13.9301	−	17.2298i	0.715542	−	0.885034i	−0.281681	−	0.959508i	$-0.590892\pi$
$379$	13.9301	−	17.2298i	0.715542	−	0.885034i	0.997223	+	0.0744738i	$0.0237277\pi$
$380$	−0.362687	−	0.0688339i	−0.0186055	−	0.00353110i
$381$	−8.13572	+	4.12136i	−0.416805	+	0.211144i
$382$	3.82107	+	8.00299i	0.195503	+	0.409468i
$383$	4.54125	+	27.4226i	0.232047	+	1.40123i	0.810607	+	0.585590i	$0.199137\pi$
$383$	4.54125	+	27.4226i	0.232047	+	1.40123i	−0.578560	+	0.815640i	$0.696385\pi$
$384$	−1.51346	−	0.142348i	−0.0772334	−	0.00726417i
$385$	−1.84119	+	2.77309i	−0.0938355	+	0.141330i
$386$	−0.969804	−	3.08282i	−0.0493617	−	0.156912i
$387$	−3.39647	−	5.67610i	−0.172652	−	0.288532i
$388$	−12.3120	−	11.4752i	−0.625050	−	0.582564i
$389$	5.28376	+	11.0665i	0.267897	+	0.561094i	0.991649	−	0.128967i	$-0.0411660\pi$
$389$	5.28376	+	11.0665i	0.267897	+	0.561094i	−0.723752	+	0.690060i	$0.757584\pi$
$390$	8.25206	+	0.387218i	0.417859	+	0.0196076i
$391$	−0.262756	−	0.0759372i	−0.0132882	−	0.00384031i
$392$	4.99251	−	3.14868i	0.252160	−	0.159032i
$393$	−5.89145	+	27.5056i	−0.297184	+	1.38748i
$394$	−5.22622	−	7.12280i	−0.263293	−	0.358842i
$395$	−3.26224	+	4.03497i	−0.164141	+	0.203022i
$396$	1.80471	+	1.84753i	0.0906903	+	0.0928419i
$397$	4.05638	+	18.9382i	0.203584	+	0.950479i	0.956357	+	0.292200i	$0.0943872\pi$
$397$	4.05638	+	18.9382i	0.203584	+	0.950479i	−0.752773	+	0.658280i	$0.771284\pi$
$398$	0.828170	−	0.931422i	0.0415124	−	0.0466879i
$399$	−0.176846	−	0.670467i	−0.00885338	−	0.0335653i
$400$	−4.26233	+	0.400892i	−0.213116	+	0.0200446i
$401$	3.40864	−	6.35470i	0.170219	−	0.317339i	−0.781718	−	0.623633i	$-0.785656\pi$
$401$	3.40864	−	6.35470i	0.170219	−	0.317339i	0.951937	+	0.306294i	$0.0990890\pi$
$402$	6.77181	−	4.27084i	0.337747	−	0.213010i
$403$	35.1394	+	29.7988i	1.75042	+	1.48438i
$404$	−1.05453	−	0.894262i	−0.0524650	−	0.0444912i
$405$	−4.63095	+	2.92065i	−0.230114	+	0.145128i
$406$	−1.56901	+	2.92509i	−0.0778686	+	0.145170i
$407$	−14.3197	+	1.34684i	−0.709802	+	0.0667602i
$408$	−1.09816	−	4.16339i	−0.0543670	−	0.206119i
$409$	3.84796	−	4.32770i	0.190269	−	0.213991i	−0.644480	−	0.764621i	$-0.722926\pi$
$409$	3.84796	−	4.32770i	0.190269	−	0.213991i	0.834749	+	0.550630i	$0.185613\pi$
$410$	0.684829	+	3.19728i	0.0338213	+	0.157903i
$411$	−3.94976	−	4.04346i	−0.194827	−	0.199449i
$412$	−7.39092	+	9.14163i	−0.364125	+	0.450376i
$413$	−6.35692	−	8.66382i	−0.312803	−	0.426319i
$414$	0.0139378	−	0.0650721i	0.000685008	−	0.00319812i
$415$	−6.01099	+	3.79101i	−0.295068	+	0.186094i
$416$	−6.15766	−	1.77958i	−0.301904	−	0.0872509i
$417$	−7.07974	−	0.332208i	−0.346696	−	0.0162683i
$418$	0.703034	+	1.47246i	0.0343865	+	0.0720204i
$419$	−6.24790	−	5.82322i	−0.305230	−	0.284483i	0.514190	−	0.857676i	$-0.328093\pi$
$419$	−6.24790	−	5.82322i	−0.305230	−	0.284483i	−0.819420	+	0.573193i	$0.805704\pi$
$420$	0.693312	+	1.15865i	0.0338302	+	0.0565361i
$421$	7.44125	+	23.6543i	0.362665	+	1.15284i	0.941390	+	0.337320i	$0.109520\pi$
$421$	7.44125	+	23.6543i	0.362665	+	1.15284i	−0.578725	+	0.815522i	$0.696450\pi$
$422$	9.11918	−	13.7348i	0.443915	−	0.668598i
$423$	−3.33027	−	0.313228i	−0.161923	−	0.0152296i
$424$	−0.540906	−	3.26629i	−0.0262687	−	0.158625i
$425$	−5.22479	−	10.9430i	−0.253439	−	0.530813i
$426$	17.2387	−	8.73269i	0.835216	−	0.423100i
$427$	13.0580	+	2.47825i	0.631919	+	0.119931i
$428$	1.71609	−	2.12258i	0.0829501	−	0.102599i
$429$	−20.1970	−	30.4196i	−0.975123	−	1.46867i
$430$	3.84657	+	7.17114i	0.185498	+	0.345823i
$431$	−1.40535	−	0.796801i	−0.0676933	−	0.0383805i	0.458997	−	0.888438i	$-0.348209\pi$
$431$	−1.40535	−	0.796801i	−0.0676933	−	0.0383805i	−0.526690	+	0.850057i	$0.676567\pi$
$432$	5.30868	−	1.80784i	0.255414	−	0.0869797i
$433$	18.4977	−	15.6863i	0.888941	−	0.753837i	−0.0811182	−	0.996704i	$-0.525849\pi$
$433$	18.4977	−	15.6863i	0.888941	−	0.753837i	0.970060	+	0.242867i	$0.0780879\pi$
$434$	−0.880723	+	7.47874i	−0.0422760	+	0.358991i
$435$	3.55241	+	2.01414i	0.170325	+	0.0965704i
$436$	5.64990	−	2.53669i	0.270581	−	0.121485i
$437$	0.0215882	−	0.0360776i	0.00103270	−	0.00172583i
$438$	3.85293	+	14.6074i	0.184100	+	0.697969i
$439$	−12.2241	+	16.6603i	−0.583427	+	0.795151i	−0.993124	−	0.117071i	$-0.962649\pi$
$439$	−12.2241	+	16.6603i	−0.583427	+	0.795151i	0.409697	+	0.912222i	$0.365635\pi$
$440$	−2.11125	−	2.37447i	−0.100650	−	0.113199i
$441$	−2.25007	+	3.38892i	−0.107146	+	0.161377i
$442$	−1.27589	−	18.1104i	−0.0606877	−	0.861426i
$443$	0.320384	−	13.6630i	0.0152219	−	0.649150i	−0.937959	−	0.346748i	$-0.887286\pi$
$443$	0.320384	−	13.6630i	0.0152219	−	0.649150i	0.953180	−	0.302402i	$-0.0977886\pi$
$444$	−2.00972	+	5.47722i	−0.0953770	+	0.259937i
$445$	−4.59500	+	12.5231i	−0.217824	+	0.593651i
$446$	−3.93374	−	1.99274i	−0.186268	−	0.0943589i
$447$	2.61875	−	0.370824i	0.123862	−	0.0175394i
$448$	−0.314376	−	0.999341i	−0.0148528	−	0.0472144i
$449$	−26.0003	−	16.3978i	−1.22703	−	0.773862i	−0.246291	−	0.969196i	$-0.579212\pi$
$449$	−26.0003	−	16.3978i	−1.22703	−	0.773862i	−0.980737	+	0.195334i	$0.937421\pi$
$450$	2.56664	−	1.45522i	0.120992	−	0.0685999i
$451$	9.60325	−	10.8005i	0.452199	−	0.508577i
$452$	−7.62571	+	2.20385i	−0.358683	+	0.103660i
$453$	−26.9947	+	6.44740i	−1.26832	+	0.302925i
$454$	−23.1499	+	7.88356i	−1.08648	+	0.369994i
$455$	1.96114	+	5.34483i	0.0919398	+	0.250570i
$456$	0.661877			0.0309952
$457$	−11.9982	−	32.6994i	−0.561251	−	1.52962i	−0.825063	−	0.565041i	$-0.808860\pi$
$457$	−11.9982	−	32.6994i	−0.561251	−	1.52962i	0.263812	−	0.964574i	$-0.415020\pi$
$458$	−2.00372	+	17.0147i	−0.0936275	+	0.795047i
$459$	9.98699	+	12.3526i	0.466153	+	0.576571i
$460$	−0.0208804	+	0.0791626i	−0.000973552	+	0.00369098i
$461$	11.6963	+	11.9738i	0.544750	+	0.557674i	0.931140	−	0.364662i	$-0.118815\pi$
$461$	11.6963	+	11.9738i	0.544750	+	0.557674i	−0.386390	+	0.922336i	$0.626278\pi$
$462$	2.31614	−	5.50025i	0.107757	−	0.255895i
$463$	4.18087	+	35.5022i	0.194301	+	1.64993i	0.650102	+	0.759847i	$0.274726\pi$
$463$	4.18087	+	35.5022i	0.194301	+	1.64993i	−0.455801	+	0.890082i	$0.650647\pi$
$464$	−2.31781	−	2.16027i	−0.107602	−	0.100288i
$465$	9.17294	+	1.29892i	0.425385	+	0.0602360i
$466$	0.953209	−	13.5302i	0.0441566	−	0.626775i
$467$	1.14869	+	16.3049i	0.0531549	+	0.754502i	0.950018	+	0.312194i	$0.101064\pi$
$467$	1.14869	+	16.3049i	0.0531549	+	0.754502i	−0.896863	+	0.442308i	$0.854160\pi$
$468$	4.37377	−	0.619342i	0.202178	−	0.0286291i
$469$	4.52379	+	3.15882i	0.208889	+	0.145861i
$470$	4.07446	+	0.576958i	0.187941	+	0.0266131i
$471$	−3.69111	−	22.2890i	−0.170078	−	1.02702i
$472$	9.54408	−	3.75808i	0.439302	−	0.172979i
$473$	15.4974	−	32.4583i	0.712571	−	1.49244i
$474$	4.39743	−	8.19810i	0.201981	−	0.376551i
$475$	1.83134	−	0.347568i	0.0840278	−	0.0159475i
$476$	2.35065	−	1.81103i	0.107742	−	0.0830083i
$477$	1.26209	+	1.90089i	0.0577871	+	0.0870356i
$478$	5.36716	−	20.3482i	0.245488	−	0.930706i
$479$	1.44687	−	8.73698i	0.0661090	−	0.399203i	−0.933107	−	0.359600i	$-0.882913\pi$
$479$	1.44687	−	8.73698i	0.0661090	−	0.399203i	0.999216	−	0.0396028i	$-0.0126093\pi$
$480$	−1.23819	+	0.357839i	−0.0565153	+	0.0163330i
$481$	−12.6316	+	21.1096i	−0.575951	+	0.962514i
$482$	−1.13535	−	0.271167i	−0.0517139	−	0.0123513i
$483$	−0.151080	+	0.0286732i	−0.00687438	+	0.00130468i
$484$	−0.637492	+	2.97628i	−0.0289769	+	0.135285i
$485$	−13.2776	−	5.22819i	−0.602905	−	0.237400i
$486$	−5.12651	+	4.77805i	−0.232543	+	0.216737i
$487$	−12.2459	−	3.53908i	−0.554913	−	0.160371i	−0.0116476	−	0.999932i	$-0.503708\pi$
$487$	−12.2459	−	3.53908i	−0.554913	−	0.160371i	−0.543265	+	0.839561i	$0.682812\pi$
$488$	−5.46631	+	11.4488i	−0.247448	+	0.518265i
$489$	0.664293	+	28.3292i	0.0300404	+	1.28109i
$490$	2.96050	−	4.03486i	0.133742	−	0.182276i
$491$	12.3325	−	6.99226i	0.556559	−	0.315556i	−0.189020	−	0.981973i	$-0.560531\pi$
$491$	12.3325	−	6.99226i	0.556559	−	0.315556i	0.745579	+	0.666417i	$0.232173\pi$
$492$	−2.27519	−	5.40300i	−0.102573	−	0.243586i
$493$	3.48297	−	8.27117i	0.156865	−	0.372515i
$494$	2.74186	+	0.520373i	0.123362	+	0.0234127i
$495$	1.99765	+	0.896905i	0.0897878	+	0.0403129i
$496$	−6.68828	−	2.63358i	−0.300313	−	0.118251i
$497$	10.1572	+	8.61345i	0.455611	+	0.386366i
$498$	9.32086	−	8.68730i	0.417678	−	0.389287i
$499$	−17.9583	+	12.5397i	−0.803922	+	0.561353i	−0.900947	−	0.433929i	$-0.857127\pi$
$499$	−17.9583	+	12.5397i	−0.803922	+	0.561353i	0.0970251	+	0.995282i	$0.469067\pi$
$500$	−7.01975	+	3.55604i	−0.313933	+	0.159031i
$501$	−3.60680	−	30.6275i	−0.161140	−	1.36834i
$502$	17.2261	−	17.6348i	0.768839	−	0.787079i
$503$	−25.1871	−	15.8850i	−1.12304	−	0.708277i	−0.162578	−	0.986696i	$-0.551981\pi$
$503$	−25.1871	−	15.8850i	−1.12304	−	0.708277i	−0.960460	+	0.278418i	$0.910190\pi$
$504$	0.479749	+	0.539561i	0.0213697	+	0.0240340i
$505$	−1.10971	−	0.377906i	−0.0493816	−	0.0168166i
$506$	0.336702	−	0.132580i	0.0149682	−	0.00589388i
$507$	−42.6441	−	2.00103i	−1.89389	−	0.0888687i
$508$	4.91898	−	3.43476i	0.218244	−	0.152393i
$509$	2.18332	+	0.980265i	0.0967738	+	0.0434495i	0.457401	−	0.889261i	$-0.348781\pi$
$509$	2.18332	+	0.980265i	0.0967738	+	0.0434495i	−0.360627	+	0.932710i	$0.617437\pi$
$510$	−2.15965	−	2.94337i	−0.0956307	−	0.130335i
$511$	−8.24735	+	6.35405i	−0.364841	+	0.281087i
$512$	0.998901	−	0.0468723i	0.0441456	−	0.00207148i
$513$	−2.22756	+	1.00013i	−0.0983494	+	0.0441569i
$514$	−29.4669	+	7.03784i	−1.29973	+	0.310426i
$515$	−2.99097	+	9.50773i	−0.131798	+	0.418961i
$516$	−9.17302	−	11.3458i	−0.403819	−	0.499473i
$517$	−8.59758	−	16.0284i	−0.378121	−	0.704928i
$518$	−4.01635	+	0.188463i	−0.176468	+	0.00828058i
$519$	12.9531	+	3.09371i	0.568578	+	0.135799i
$520$	−5.41059	+	0.508891i	−0.237270	+	0.0223164i
$521$	−0.953895	−	40.6795i	−0.0417909	−	1.78220i	−0.474094	−	0.880474i	$-0.657224\pi$
$521$	−0.953895	−	40.6795i	−0.0417909	−	1.78220i	0.432303	−	0.901729i	$-0.357701\pi$
$522$	2.06705	+	0.703923i	0.0904725	+	0.0308099i
$523$	−1.42743	−	0.134257i	−0.0624173	−	0.00587065i	0.0623868	−	0.998052i	$-0.480129\pi$
$523$	−1.42743	−	0.134257i	−0.0624173	−	0.00587065i	−0.124804	+	0.992181i	$0.539830\pi$
$524$	1.30043	−	18.4588i	0.0568096	−	0.806377i
$525$	−5.40085	−	4.16100i	−0.235712	−	0.181601i
$526$	−4.83445	−	2.44902i	−0.210792	−	0.106782i
$527$	0.477297	−	20.3547i	0.0207914	−	0.886664i
$528$	4.51273	+	3.47677i	0.196391	+	0.151307i
$529$	18.8500	+	13.1624i	0.819566	+	0.572277i
$530$	−1.44135	−	2.40875i	−0.0626084	−	0.104630i
$531$	−4.93970	+	5.05688i	−0.214365	+	0.219450i
$532$	0.177025	+	0.420389i	0.00767499	+	0.0182262i
$533$	−5.17719	−	24.1709i	−0.224249	−	1.04696i
$534$	3.90743	−	23.5952i	0.169091	−	1.02107i
$535$	0.694468	−	2.20758i	0.0300245	−	0.0954422i
$536$	−4.01682	+	3.40633i	−0.173500	+	0.147131i
$537$	−17.4504			−0.753039
$538$	−3.96362	−	15.9151i	−0.170884	−	0.686148i
$539$	−22.1196			−0.952758
$540$	3.62644	−	3.07528i	0.156057	−	0.132339i
$541$	2.64272	−	8.40072i	0.113619	−	0.361175i	−0.879853	−	0.475246i	$-0.842359\pi$
$541$	2.64272	−	8.40072i	0.113619	−	0.361175i	0.993473	+	0.114071i	$0.0363890\pi$
$542$	−0.851157	+	5.13976i	−0.0365603	+	0.220772i
$543$	−0.590308	−	2.75599i	−0.0253326	−	0.118271i
$544$	1.09927	+	2.61049i	0.0471308	+	0.111924i
$545$	3.66922	−	3.75627i	0.157172	−	0.160901i
$546$	−5.24133	−	8.75917i	−0.224308	−	0.374858i
$547$	−9.26129	−	6.46686i	−0.395984	−	0.276503i	0.357574	−	0.933885i	$-0.383604\pi$
$547$	−9.26129	−	6.46686i	−0.395984	−	0.276503i	−0.753558	+	0.657382i	$0.771664\pi$
$548$	2.94556	+	2.26937i	0.125828	+	0.0969425i
$549$	0.204971	−	8.74113i	0.00874795	−	0.373062i
$550$	14.3120	+	7.25010i	0.610265	+	0.309145i
$551$	1.09283	+	0.841958i	0.0465563	+	0.0358686i
$552$	0.0103156	−	0.146424i	0.000439061	−	0.00623220i
$553$	6.38313	+	0.600364i	0.271438	+	0.0255301i
$554$	−8.10117	−	2.75880i	−0.344186	−	0.117210i
$555$	0.115962	+	4.94527i	0.00492231	+	0.209915i
$556$	4.64194	−	0.436596i	0.196862	−	0.0185158i
$557$	21.0105	+	5.01813i	0.890243	+	0.212625i	0.651673	−	0.758500i	$-0.274068\pi$
$557$	21.0105	+	5.01813i	0.890243	+	0.212625i	0.238570	+	0.971125i	$0.423321\pi$
$558$	4.94845	−	0.232200i	0.209485	−	0.00982982i
$559$	−29.0795	−	54.2126i	−1.22993	−	2.29295i
$560$	−0.558444	−	0.690724i	−0.0235986	−	0.0291884i
$561$	−4.84215	+	15.3923i	−0.204436	+	0.649863i
$562$	6.40862	−	1.53063i	0.270331	−	0.0645657i
$563$	−17.6770	+	7.93662i	−0.744997	+	0.334489i	−0.746389	−	0.665510i	$-0.768214\pi$
$563$	−17.6770	+	7.93662i	−0.744997	+	0.334489i	0.00139115	+	0.999999i	$0.499557\pi$
$564$	−7.36995	+	0.345826i	−0.310331	+	0.0145619i
$565$	−5.33133	+	4.10745i	−0.224291	+	0.172802i
$566$	10.8747	+	14.8211i	0.457097	+	0.622976i
$567$	6.17152	+	2.77089i	0.259179	+	0.116366i
$568$	−10.4228	+	7.27788i	−0.437329	+	0.305373i
$569$	15.6446	+	0.734107i	0.655858	+	0.0307754i	0.372203	−	0.928151i	$-0.378602\pi$
$569$	15.6446	+	0.734107i	0.655858	+	0.0307754i	0.283654	+	0.958927i	$0.408453\pi$
$570$	0.522155	−	0.205604i	0.0218707	−	0.00861180i
$571$	35.3760	+	12.0471i	1.48044	+	0.504155i	0.941157	−	0.337970i	$-0.109740\pi$
$571$	35.3760	+	12.0471i	1.48044	+	0.504155i	0.539282	+	0.842125i	$0.318696\pi$
$572$	15.9607	+	17.9506i	0.667352	+	0.750553i
$573$	−11.4028	−	7.19153i	−0.476359	−	0.300430i
$574$	2.82318	−	2.89016i	0.117837	−	0.120633i
$575$	−0.0483484	−	0.410555i	−0.00201627	−	0.0171213i
$576$	−0.614796	+	0.311441i	−0.0256165	+	0.0129767i
$577$	−27.3539	+	19.1004i	−1.13876	+	0.795159i	−0.981322	−	0.192371i	$-0.938382\pi$
$577$	−27.3539	+	19.1004i	−1.13876	+	0.795159i	−0.157436	+	0.987529i	$0.550323\pi$
$578$	6.56693	−	6.12056i	0.273148	−	0.254582i
$579$	3.74687	+	3.17741i	0.155715	+	0.132049i
$580$	−2.49958	−	0.984236i	−0.103790	−	0.0408682i
$581$	8.01066	+	3.59662i	0.332338	+	0.149213i
$582$	25.1360	+	4.77053i	1.04192	+	0.197745i
$583$	−4.81511	+	11.4347i	−0.199421	+	0.473576i
$584$	−3.85682	−	9.15899i	−0.159596	−	0.379002i
$585$	3.25808	−	1.84726i	0.134705	−	0.0763747i
$586$	−9.15908	+	12.4829i	−0.378358	+	0.515663i
$587$	−0.346430	−	14.7737i	−0.0142987	−	0.609778i	−0.959249	−	0.282563i	$-0.908815\pi$
$587$	−0.346430	−	14.7737i	−0.0142987	−	0.609778i	0.944950	−	0.327215i	$-0.106110\pi$
$588$	−3.86597	+	8.09702i	−0.159430	+	0.333916i
$589$	3.00670	+	0.868941i	0.123889	+	0.0358041i
$590$	6.36193	−	5.92950i	0.261917	−	0.244114i
$591$	12.4958	+	4.92034i	0.514008	+	0.202396i
$592$	0.803831	−	3.75287i	0.0330372	−	0.154242i
$593$	−26.9957	+	5.12347i	−1.10858	+	0.210396i	−0.708240	−	0.705972i	$-0.750511\pi$
$593$	−26.9957	+	5.12347i	−1.10858	+	0.210396i	−0.400339	+	0.916367i	$0.631108\pi$
$594$	−20.4413	−	4.88219i	−0.838717	−	0.200318i
$595$	1.29186	−	2.15892i	0.0529611	−	0.0885072i
$596$	−1.67148	+	0.483063i	−0.0684667	+	0.0197870i
$597$	−0.309541	+	1.86918i	−0.0126687	+	0.0765005i
$598$	0.157852	−	0.598456i	0.00645505	−	0.0244727i
$599$	−0.483616	−	0.728394i	−0.0197600	−	0.0297614i	0.823081	−	0.567924i	$-0.192253\pi$
$599$	−0.483616	−	0.728394i	−0.0197600	−	0.0297614i	−0.842841	+	0.538162i	$0.819119\pi$
$600$	5.15533	−	3.97185i	0.210466	−	0.162150i
$601$	−25.4608	+	4.83217i	−1.03857	+	0.197108i	−0.677570	−	0.735458i	$-0.736967\pi$
$601$	−25.4608	+	4.83217i	−1.03857	+	0.197108i	−0.360998	+	0.932567i	$0.617564\pi$
$602$	4.75288	−	8.86076i	0.193713	−	0.361137i
$603$	1.56390	−	3.27550i	0.0636871	−	0.133389i
$604$	16.9880	−	6.68920i	0.691233	−	0.272180i
$605$	0.421627	+	2.54602i	0.0171416	+	0.103510i
$606$	2.08107	+	0.294687i	0.0845377	+	0.0119708i
$607$	−26.3266	−	18.3830i	−1.06856	−	0.746145i	−0.100020	−	0.994985i	$-0.531891\pi$
$607$	−26.3266	−	18.3830i	−1.06856	−	0.746145i	−0.968544	+	0.248841i	$0.919950\pi$
$608$	−0.431105	+	0.0610460i	−0.0174836	+	0.00247574i
$609$	−0.354602	−	5.03336i	−0.0143692	−	0.203962i
$610$	−0.755936	+	10.7300i	−0.0306069	+	0.434447i
$611$	−30.8023	−	4.36171i	−1.24613	−	0.176456i
$612$	−1.42802	−	1.33096i	−0.0577244	−	0.0538007i
$613$	−0.613434	−	5.20903i	−0.0247764	−	0.210391i	0.975162	−	0.221493i	$-0.0710929\pi$
$613$	−0.613434	−	5.20903i	−0.0247764	−	0.210391i	−0.999938	+	0.0111020i	$0.996466\pi$
$614$	5.77324	−	13.7100i	0.232989	−	0.553291i
$615$	−3.47327	−	3.55567i	−0.140056	−	0.143378i
$616$	−1.00129	+	3.79614i	−0.0403431	+	0.152951i
$617$	15.5811	+	19.2719i	0.627273	+	0.775857i	0.987604	−	0.156968i	$-0.0501719\pi$
$617$	15.5811	+	19.2719i	0.627273	+	0.775857i	−0.360330	+	0.932825i	$0.617336\pi$
$618$	2.09001	−	17.7476i	0.0840727	−	0.713911i
$619$	−0.477391	−	1.30107i	−0.0191880	−	0.0522943i	0.928840	−	0.370480i	$-0.120807\pi$
$619$	−0.477391	−	1.30107i	−0.0191880	−	0.0522943i	−0.948028	+	0.318186i	$0.896926\pi$
$620$	−6.09448			−0.244760
$621$	0.186536	+	0.508380i	0.00748544	+	0.0204006i
$622$	−10.8422	+	3.69226i	−0.434734	+	0.148046i
$623$	16.0315	−	3.82896i	0.642289	−	0.153404i
$624$	9.36049	−	2.70520i	0.374720	−	0.108295i
$625$	9.79023	−	11.0108i	0.391609	−	0.440433i
$626$	28.1424	−	15.9561i	1.12479	−	0.637733i
$627$	−2.09799	−	1.32316i	−0.0837857	−	0.0528419i
$628$	4.45991	+	14.1772i	0.177970	+	0.565733i
$629$	10.7637	−	1.52418i	0.429178	−	0.0607731i
$630$	0.546082	+	0.276632i	0.0217564	+	0.0110213i
$631$	−0.695416	+	1.89526i	−0.0276841	+	0.0754493i	−0.951882	−	0.306464i	$-0.900854\pi$
$631$	−0.695416	+	1.89526i	−0.0276841	+	0.0754493i	0.924198	+	0.381913i	$0.124735\pi$
$632$	−2.10809	+	5.74531i	−0.0838552	+	0.228536i
$633$	−0.587511	+	25.0548i	−0.0233515	+	0.995840i
$634$	0.310430	+	4.40636i	0.0123288	+	0.174999i
$635$	2.81362	−	4.23771i	0.111655	−	0.168168i
$636$	3.34418	+	3.76111i	0.132605	+	0.149138i
$637$	−22.3809	+	30.5028i	−0.886763	+	1.20857i
$638$	3.02831	+	11.4811i	0.119892	+	0.454540i
$639$	4.49856	−	7.51788i	0.177960	−	0.297403i
$640$	0.773473	−	0.347274i	0.0305742	−	0.0137272i
$641$	31.2963	+	17.7443i	1.23613	+	0.700858i	0.965143	−	0.261724i	$-0.0842912\pi$
$641$	31.2963	+	17.7443i	1.23613	+	0.700858i	0.270989	+	0.962583i	$0.412649\pi$
$642$	−0.485277	+	4.12077i	−0.0191523	+	0.162634i
$643$	16.1049	−	13.6572i	0.635114	−	0.538588i	−0.270484	−	0.962725i	$-0.587184\pi$
$643$	16.1049	−	13.6572i	0.635114	−	0.538588i	0.905598	+	0.424137i	$0.139422\pi$
$644$	0.0957594	−	0.0326103i	0.00377345	−	0.00128503i
$645$	−10.7610	−	6.10127i	−0.423716	−	0.240237i
$646$	−0.582960	−	1.08681i	−0.0229362	−	0.0427599i
$647$	−24.3125	−	36.6181i	−0.955825	−	1.43961i	−0.897350	−	0.441319i	$-0.854511\pi$
$647$	−24.3125	−	36.6181i	−0.955825	−	1.43961i	−0.0584745	−	0.998289i	$-0.518624\pi$
$648$	−4.05991	+	5.02159i	−0.159488	+	0.197267i
$649$	−37.7652	−	7.16740i	−1.48241	−	0.281345i
$650$	24.4789	−	12.4004i	0.960142	−	0.486385i
$651$	−4.93222	−	10.3302i	−0.193309	−	0.404873i
$652$	−3.04553	−	18.3906i	−0.119272	−	0.720232i
$653$	−15.4053	−	1.44894i	−0.602855	−	0.0567014i	−0.212181	−	0.977230i	$-0.568057\pi$
$653$	−15.4053	−	1.44894i	−0.602855	−	0.0567014i	−0.390674	+	0.920529i	$0.627758\pi$
$654$	−5.20750	+	7.84323i	−0.203629	+	0.306695i
$655$	−4.70809	−	14.9661i	−0.183960	−	0.584775i
$656$	1.98024	+	3.30933i	0.0773154	+	0.129208i
$657$	5.01027	+	4.66971i	0.195469	+	0.182183i
$658$	−2.19081	−	4.58851i	−0.0854065	−	0.178879i
$659$	−25.1683	−	1.18100i	−0.980419	−	0.0460050i	−0.449370	−	0.893346i	$-0.648351\pi$
$659$	−25.1683	−	1.18100i	−0.980419	−	0.0460050i	−0.531050	+	0.847341i	$0.678202\pi$
$660$	4.64011	+	1.34100i	0.180616	+	0.0521984i
$661$	−6.71001	+	4.23187i	−0.260989	+	0.164601i	−0.657557	−	0.753405i	$-0.728410\pi$
$661$	−6.71001	+	4.23187i	−0.260989	+	0.164601i	0.396568	+	0.918005i	$0.370201\pi$
$662$	1.93477	−	9.03293i	0.0751969	−	0.351075i
$663$	16.3266	+	22.2514i	0.634071	+	0.864174i
$664$	−5.26978	+	6.51804i	−0.204507	+	0.252949i
$665$	0.270244	+	0.276655i	0.0104796	+	0.0107282i
$666$	0.553984	+	2.58641i	0.0214664	+	0.100221i
$667$	0.203294	−	0.228639i	0.00787158	−	0.00885296i
$668$	5.17407	+	19.6162i	0.200191	+	0.758972i
$669$	6.67388	−	0.627710i	0.258027	−	0.0242687i
$670$	−2.11074	+	3.93504i	−0.0815450	+	0.152024i
$671$	40.2143	−	25.3624i	1.55246	−	0.979103i
$672$	1.21460	+	1.03000i	0.0468542	+	0.0397332i
$673$	28.2758	+	23.9784i	1.08995	+	0.924298i	0.997447	−	0.0714142i	$-0.0227512\pi$
$673$	28.2758	+	23.9784i	1.08995	+	0.924298i	0.0925056	+	0.995712i	$0.470512\pi$
$674$	−12.5031	+	7.88545i	−0.481601	+	0.303736i
$675$	−11.3487	+	21.1574i	−0.436813	+	0.814347i
$676$	27.9603	−	2.62980i	1.07539	−	0.101146i
$677$	7.41599	+	28.1158i	0.285020	+	1.08058i	0.944408	+	0.328777i	$0.106636\pi$
$677$	7.41599	+	28.1158i	0.285020	+	1.08058i	−0.659388	+	0.751803i	$0.729185\pi$
$678$	8.01787	−	9.01748i	0.307924	−	0.346314i
$679$	3.69286	+	17.2410i	0.141719	+	0.661648i
$680$	1.67813	+	1.71794i	0.0643533	+	0.0658800i
$681$	23.3728	−	28.9092i	0.895648	−	1.10780i
$682$	15.9354	+	21.7184i	0.610200	+	0.831639i
$683$	−0.633596	+	2.95809i	−0.0242439	+	0.113188i	−0.988304	−	0.152495i	$-0.951269\pi$
$683$	−0.633596	+	2.95809i	−0.0242439	+	0.113188i	0.964060	+	0.265683i	$0.0855975\pi$
$684$	0.253811	−	0.160074i	0.00970472	−	0.00612057i
$685$	3.02871	+	0.875302i	0.115721	+	0.0334436i
$686$	−13.5021	−	0.633570i	−0.515512	−	0.0241898i
$687$	−11.2212	−	23.5021i	−0.428116	−	0.896661i
$688$	7.02117	+	6.54393i	0.267680	+	0.249485i
$689$	10.8964	+	18.2098i	0.415120	+	0.693737i
$690$	−0.0373467	−	0.118718i	−0.00142176	−	0.00451952i
$691$	2.03196	−	3.06043i	0.0772995	−	0.116424i	−0.792408	−	0.609991i	$-0.791173\pi$
$691$	2.03196	−	3.06043i	0.0772995	−	0.116424i	0.869708	+	0.493567i	$0.164307\pi$
$692$	−8.72218	−	0.820362i	−0.331567	−	0.0311855i
$693$	−0.442050	−	2.66935i	−0.0167921	−	0.101400i
$694$	−7.24907	−	15.1827i	−0.275171	−	0.576328i
$695$	3.52640	−	1.78639i	0.133764	−	0.0677617i
$696$	4.73200	+	0.898078i	0.179366	+	0.0340416i
$697$	−6.86786	+	8.49466i	−0.260139	+	0.321758i
$698$	−2.72405	−	4.10281i	−0.103107	−	0.155294i
$699$	9.74626	+	18.1699i	0.368637	+	0.687248i
$700$	3.90155	+	2.21209i	0.147465	+	0.0836091i
$701$	5.90685	−	2.01154i	0.223099	−	0.0759749i	−0.208569	−	0.978008i	$-0.566881\pi$
$701$	5.90685	−	2.01154i	0.223099	−	0.0759749i	0.431668	+	0.902033i	$0.357925\pi$
$702$	−27.4153	+	23.2486i	−1.03472	+	0.877463i
$703$	−0.195442	+	1.65962i	−0.00737125	+	0.0625937i
$704$	−3.25998	−	1.84833i	−0.122865	−	0.0696616i
$705$	−5.70673	+	2.56221i	−0.214928	+	0.0964983i
$706$	−12.5660	+	20.9999i	−0.472926	+	0.790343i
$707$	0.369431	+	1.40060i	0.0138939	+	0.0526751i
$708$	−9.22411	+	12.5715i	−0.346663	+	0.472467i
$709$	28.6118	+	32.1789i	1.07454	+	1.20850i	0.976993	+	0.213274i	$0.0684126\pi$
$709$	28.6118	+	32.1789i	1.07454	+	1.20850i	0.0975454	+	0.995231i	$0.468901\pi$
$710$	−5.96174	+	8.97922i	−0.223740	+	0.336984i
$711$	−0.296403	−	4.20725i	−0.0111160	−	0.157784i
$712$	−0.368826	+	15.7288i	−0.0138223	+	0.589464i
$713$	0.239092	−	0.651613i	0.00895405	−	0.0244031i
$714$	−1.55383	+	4.23477i	−0.0581508	+	0.158482i
$715$	18.1676	+	9.20326i	0.679429	+	0.344182i
$716$	11.3661	−	1.60948i	0.424770	−	0.0601489i
$717$	9.59971	+	30.5157i	0.358508	+	1.13963i
$718$	−17.3193	−	10.9229i	−0.646351	−	0.407641i
$719$	2.68480	−	1.52222i	0.100126	−	0.0567692i	−0.442336	−	0.896849i	$-0.645850\pi$
$719$	2.68480	−	1.52222i	0.100126	−	0.0567692i	0.542463	+	0.840080i	$0.317492\pi$
$720$	−0.388268	+	0.436674i	−0.0144699	+	0.0162739i
$721$	11.8313	−	3.41927i	0.440621	−	0.127340i
$722$	−18.2958	+	4.36976i	−0.680900	+	0.162626i
$723$	1.67971	−	0.572016i	0.0624691	−	0.0212735i
$724$	0.638680	+	1.74064i	0.0237363	+	0.0646902i
$725$	13.5645			0.503774
$726$	−1.59384	−	4.34380i	−0.0591530	−	0.161214i
$727$	−1.42633	+	12.1118i	−0.0528997	+	0.449202i	0.940957	+	0.338526i	$0.109928\pi$
$727$	−1.42633	+	12.1118i	−0.0528997	+	0.449202i	−0.993857	+	0.110676i	$0.964698\pi$
$728$	4.22174	+	5.22176i	0.156468	+	0.193531i
$729$	7.65778	−	29.0325i	0.283621	−	1.07528i
$730$	−5.88778	−	6.02746i	−0.217916	−	0.223086i
$731$	−10.5507	+	25.0552i	−0.390231	+	0.926701i
$732$	−2.25558	−	19.1534i	−0.0833685	−	0.707932i
$733$	−15.4890	−	14.4362i	−0.572099	−	0.533213i	0.341472	−	0.939892i	$-0.389075\pi$
$733$	−15.4890	−	14.4362i	−0.572099	−	0.533213i	−0.913571	+	0.406679i	$0.866687\pi$
$734$	−16.3640	−	2.31720i	−0.604006	−	0.0855294i
$735$	−0.534624	+	7.58866i	−0.0197199	+	0.279912i
$736$	0.00678596	+	0.0963225i	0.000250134	+	0.00355049i
$737$	19.5420	−	2.76721i	0.719838	−	0.101932i
$738$	−2.17918	−	1.52165i	−0.0802166	−	0.0560127i
$739$	−23.6508	−	3.34903i	−0.870007	−	0.123196i	−0.309055	−	0.951044i	$-0.600013\pi$
$739$	−23.6508	−	3.34903i	−0.870007	−	0.123196i	−0.560952	+	0.827848i	$0.689565\pi$
$740$	−0.531641	−	3.21035i	−0.0195435	−	0.118015i
$741$	−3.94741	+	1.55433i	−0.145012	+	0.0570998i
$742$	−1.49443	+	3.12998i	−0.0548621	+	0.114905i
$743$	9.07080	−	16.9106i	0.332775	−	0.620391i	−0.658442	−	0.752631i	$-0.728784\pi$
$743$	9.07080	−	16.9106i	0.332775	−	0.620391i	0.991218	+	0.132241i	$0.0422172\pi$
$744$	10.7353	−	2.03743i	0.393574	−	0.0746959i
$745$	−1.16858	+	0.900314i	−0.0428134	+	0.0329850i
$746$	14.6097	+	22.0043i	0.534900	+	0.805635i
$747$	1.47328	−	5.58557i	0.0539045	−	0.204365i
$748$	1.73422	−	10.4722i	0.0634092	−	0.382900i
$749$	−2.74709	+	0.793914i	−0.100376	+	0.0290090i
$750$	6.14222	−	10.2647i	0.224282	−	0.374815i
$751$	−31.4280	−	7.50625i	−1.14683	−	0.273907i	−0.385771	−	0.922595i	$-0.626064\pi$
$751$	−31.4280	−	7.50625i	−1.14683	−	0.273907i	−0.761055	+	0.648688i	$0.775318\pi$
$752$	4.76843	−	0.904992i	0.173887	−	0.0330017i
$753$	−7.84868	+	36.6434i	−0.286022	+	1.33536i
$754$	18.8964	+	7.44067i	0.688168	+	0.270973i
$755$	11.3239	−	10.5542i	0.412121	−	0.384108i
$756$	−5.64416	−	1.63117i	−0.205276	−	0.0593252i
$757$	−6.83293	+	14.3111i	−0.248347	+	0.520147i	−0.988302	−	0.152509i	$-0.951265\pi$
$757$	−6.83293	+	14.3111i	−0.248347	+	0.520147i	0.739955	+	0.672656i	$0.234847\pi$
$758$	−0.519407	−	22.1505i	−0.0188657	−	0.804542i
$759$	−0.325414	+	0.443505i	−0.0118118	+	0.0160982i
$760$	−0.321136	+	0.182077i	−0.0116488	+	0.00660462i
$761$	15.1712	+	36.0277i	0.549954	+	1.30600i	0.925342	+	0.379135i	$0.123778\pi$
$761$	15.1712	+	36.0277i	0.549954	+	1.30600i	−0.375388	+	0.926868i	$0.622490\pi$
$762$	−3.53942	+	8.40524i	−0.128220	+	0.304490i
$763$	−6.37439	−	1.20979i	−0.230768	−	0.0437972i
$764$	8.09036	+	3.63241i	0.292699	+	0.131416i
$765$	−1.54001	−	0.606395i	−0.0556793	−	0.0219243i
$766$	21.1997	+	17.9777i	0.765975	+	0.649560i
$767$	−48.0951	+	44.8260i	−1.73662	+	1.61857i
$768$	−1.24636	+	0.870293i	−0.0449741	+	0.0314040i
$769$	−15.8379	+	8.02311i	−0.571130	+	0.289321i	−0.713686	−	0.700466i	$-0.752975\pi$
$769$	−15.8379	+	8.02311i	−0.571130	+	0.289321i	0.142556	+	0.989787i	$0.454468\pi$
$770$	0.389304	+	3.30582i	0.0140296	+	0.119133i
$771$	32.1808	−	32.9443i	1.15896	−	1.18646i
$772$	−2.73353	−	1.72398i	−0.0983820	−	0.0620476i
$773$	3.22807	+	3.63053i	0.116106	+	0.130581i	0.802509	−	0.596640i	$-0.203498\pi$
$773$	3.22807	+	3.63053i	0.116106	+	0.130581i	−0.686403	+	0.727221i	$0.740811\pi$
$774$	−6.26157	−	2.13234i	−0.225067	−	0.0766453i
$775$	28.6335	−	11.2747i	1.02854	−	0.405000i
$776$	−16.8120	−	0.788884i	−0.603516	−	0.0283193i
$777$	5.01133	−	3.49925i	0.179780	−	0.125535i
$778$	11.1873	+	5.02288i	0.401085	+	0.180079i
$779$	−0.993348	−	1.35383i	−0.0355904	−	0.0485060i
$780$	6.54416	−	5.04186i	0.234319	−	0.180527i
$781$	47.5868	−	2.23296i	1.70279	−	0.0799015i
$782$	−0.249514	+	0.112027i	−0.00892261	+	0.00400607i
$783$	−17.2827	+	4.12779i	−0.617633	+	0.147515i
$784$	1.77125	−	5.63046i	0.0632588	−	0.201088i
$785$	7.92240	+	9.79900i	0.282763	+	0.349741i
$786$	13.2965	+	24.7885i	0.474270	+	0.884178i
$787$	−12.1076	+	0.568136i	−0.431590	+	0.0202519i	−0.261561	−	0.965187i	$-0.584237\pi$
$787$	−12.1076	+	0.568136i	−0.431590	+	0.0202519i	−0.170030	+	0.985439i	$0.554386\pi$
$788$	−8.59278	−	2.05229i	−0.306105	−	0.0731099i
$789$	8.20199	−	0.771437i	0.291999	−	0.0274639i
$790$	0.121638	+	5.18733i	0.00432768	+	0.184557i
$791$	7.87187	+	2.68072i	0.279892	+	0.0953154i
$792$	2.57136	+	0.241848i	0.0913692	+	0.00859370i
$793$	5.71475	−	81.1174i	0.202937	−	2.88056i
$794$	15.3424	+	11.8203i	0.544481	+	0.419487i
$795$	3.80656	+	1.92831i	0.135005	+	0.0683902i
$796$	0.0292179	−	1.24602i	0.00103560	−	0.0441639i
$797$	35.8186	+	27.5959i	1.26876	+	0.977498i	0.999897	+	0.0143198i	$0.00455829\pi$
$797$	35.8186	+	27.5959i	1.26876	+	0.977498i	0.268863	+	0.963178i	$0.413352\pi$
$798$	−0.568516	−	0.396976i	−0.0201252	−	0.0140528i
$799$	7.05906	+	11.7969i	0.249732	+	0.417345i
$800$	−2.99153	+	3.06250i	−0.105767	+	0.108276i
$801$	−4.20807	−	9.99312i	−0.148685	−	0.353090i
$802$	−1.51031	−	7.05125i	−0.0533309	−	0.248988i
$803$	−6.08456	+	36.7420i	−0.214719	+	1.29660i
$804$	2.40250	−	7.63711i	0.0847298	−	0.269340i
$805$	0.0654147	−	0.0554728i	0.00230557	−	0.00195516i
$806$	46.0732			1.62286
$807$	18.0022	+	17.2492i	0.633706	+	0.607199i
$808$	−1.38266			−0.0486418
$809$	18.7621	−	15.9106i	0.659641	−	0.559387i	−0.253346	−	0.967376i	$-0.581531\pi$
$809$	18.7621	−	15.9106i	0.659641	−	0.559387i	0.912987	+	0.407989i	$0.133770\pi$
$810$	−1.64297	+	5.22269i	−0.0577281	+	0.183507i
$811$	−7.77059	+	46.9231i	−0.272862	+	1.64769i	0.406324	+	0.913729i	$0.366810\pi$
$811$	−7.77059	+	46.9231i	−0.272862	+	1.64769i	−0.679187	+	0.733966i	$0.737667\pi$
$812$	0.695201	+	3.24571i	0.0243968	+	0.113902i
$813$	−3.07351	−	7.29883i	−0.107793	−	0.255981i
$814$	−10.0503	+	10.2888i	−0.352264	+	0.360621i
$815$	−8.11544	−	13.5623i	−0.284272	−	0.475067i
$816$	−3.53031	−	2.46510i	−0.123585	−	0.0862958i
$817$	−3.31044	−	2.55048i	−0.115817	−	0.0892299i
$818$	0.135756	−	5.78941i	0.00474660	−	0.202422i
$819$	−4.12829	−	2.09129i	−0.144254	−	0.0730757i
$820$	2.59022	+	1.99560i	0.0904543	+	0.0696892i
$821$	−2.46596	+	35.0027i	−0.0860624	+	1.22160i	0.745627	+	0.666363i	$0.232150\pi$
$821$	−2.46596	+	35.0027i	−0.0860624	+	1.22160i	−0.831690	+	0.555241i	$0.812626\pi$
$822$	−5.62761	−	0.529304i	−0.196286	−	0.0184616i
$823$	−10.9931	−	3.74362i	−0.383194	−	0.130494i	0.124095	−	0.992270i	$-0.460397\pi$
$823$	−10.9931	−	3.74362i	−0.383194	−	0.130494i	−0.507289	+	0.861776i	$0.669352\pi$
$824$	0.275582	+	11.7524i	0.00960037	+	0.409415i
$825$	−24.2813	+	2.28377i	−0.845367	+	0.0795108i
$826$	−10.4518	−	2.49631i	−0.363666	−	0.0868576i
$827$	32.5605	−	1.52786i	1.13224	−	0.0531289i	0.527501	−	0.849554i	$-0.323129\pi$
$827$	32.5605	−	1.52786i	1.13224	−	0.0531289i	0.604737	+	0.796425i	$0.293278\pi$
$828$	−0.0314565	−	0.0586441i	−0.00109319	−	0.00203802i
$829$	−12.1075	−	14.9754i	−0.420510	−	0.520118i	0.522609	−	0.852573i	$-0.324959\pi$
$829$	−12.1075	−	14.9754i	−0.420510	−	0.520118i	−0.943119	+	0.332455i	$0.892123\pi$
$830$	−2.13258	+	6.77908i	−0.0740230	+	0.235305i
$831$	12.6535	−	3.02215i	0.438945	−	0.104837i
$832$	−5.84733	+	2.62533i	−0.202720	+	0.0910170i
$833$	16.7004	−	0.783647i	0.578634	−	0.0271517i
$834$	−5.61447	+	4.32559i	−0.194413	+	0.149783i
$835$	10.1753	+	13.8679i	0.352132	+	0.479920i
$836$	1.48854	+	0.668323i	0.0514821	+	0.0231144i
$837$	−33.0512	+	23.0786i	−1.14242	+	0.797713i
$838$	−8.53147	−	0.400329i	−0.294715	−	0.0138291i
$839$	35.5102	−	13.9825i	1.22595	−	0.482729i	0.337334	−	0.941385i	$-0.390475\pi$
$839$	35.5102	−	13.9825i	1.22595	−	0.482729i	0.888614	+	0.458656i	$0.151669\pi$
$840$	1.27816	+	0.435269i	0.0441006	+	0.0150182i
$841$	−12.5990	−	14.1698i	−0.434450	−	0.488614i
$842$	20.9743	+	13.2280i	0.722821	+	0.455868i
$843$	−6.99887	+	7.16491i	−0.241054	+	0.246773i
$844$	−1.92818	−	16.3733i	−0.0663707	−	0.563593i
$845$	21.2410	−	10.7602i	0.730711	−	0.370161i
$846$	−2.74253	+	1.91502i	−0.0942902	+	0.0658398i
$847$	2.33266	−	2.17411i	0.0801513	−	0.0747033i
$848$	−2.52508	−	2.14131i	−0.0867116	−	0.0735329i
$849$	−26.0011	−	10.2382i	−0.892356	−	0.351374i
$850$	−11.0625	−	4.96682i	−0.379439	−	0.170361i
$851$	0.364102	+	0.0691024i	0.0124813	+	0.00236880i
$852$	7.49963	−	17.8097i	0.256933	−	0.610152i
$853$	−17.2150	−	40.8813i	−0.589431	−	1.39975i	−0.894348	−	0.447372i	$-0.852360\pi$
$853$	−17.2150	−	40.8813i	−0.589431	−	1.39975i	0.304917	−	0.952379i	$-0.401371\pi$
$854$	11.5620	−	6.55537i	0.395643	−	0.224320i
$855$	0.150507	−	0.205126i	0.00514723	−	0.00701515i
$856$	−0.0639870	−	2.72877i	−0.00218703	−	0.0932675i
$857$	−16.2732	+	34.0833i	−0.555883	+	1.16426i	0.411609	+	0.911361i	$0.364967\pi$
$857$	−16.2732	+	34.0833i	−0.555883	+	1.16426i	−0.967492	+	0.252901i	$0.918615\pi$
$858$	−35.0785	−	10.1378i	−1.19756	−	0.346097i
$859$	32.9952	−	30.7525i	1.12578	−	1.04926i	0.127431	−	0.991847i	$-0.459327\pi$
$859$	32.9952	−	30.7525i	1.12578	−	1.04926i	0.998351	−	0.0574127i	$-0.0182851\pi$
$860$	7.57180	+	2.98147i	0.258196	+	0.101667i
$861$	−1.28632	+	6.00547i	−0.0438375	+	0.204666i
$862$	−1.58719	+	0.301230i	−0.0540598	+	0.0102599i
$863$	−29.8371	−	7.12627i	−1.01567	−	0.242581i	−0.309706	−	0.950832i	$-0.600231\pi$
$863$	−29.8371	−	7.12627i	−1.01567	−	0.242581i	−0.705961	+	0.708251i	$0.749484\pi$
$864$	2.87960	−	4.81231i	0.0979658	−	0.163718i
$865$	−7.13577	+	2.06225i	−0.242623	+	0.0701187i
$866$	3.96245	−	23.9275i	0.134649	−	0.813089i
$867$	−3.48037	+	13.1949i	−0.118200	+	0.448124i
$868$	4.16531	+	6.27355i	0.141380	+	0.212938i
$869$	18.1676	−	13.9970i	0.616294	−	0.474815i
$870$	4.01205	−	0.761441i	0.136021	−	0.0258153i
$871$	15.9568	−	29.7482i	0.540677	−	1.00798i
$872$	2.66844	−	5.58888i	0.0903648	−	0.189263i
$873$	10.7927	−	4.24973i	0.365278	−	0.143832i
$874$	−0.00686893	−	0.0414784i	−0.000232345	−	0.00140303i
$875$	8.16239	+	1.15582i	0.275939	+	0.0390740i
$876$	12.3862	+	8.64889i	0.418491	+	0.292219i
$877$	10.0134	−	1.41794i	0.338130	−	0.0478804i	0.0309192	−	0.999522i	$-0.490157\pi$
$877$	10.0134	−	1.41794i	0.338130	−	0.0478804i	0.307211	+	0.951641i	$0.400604\pi$
$878$	1.45218	+	20.6127i	0.0490085	+	0.695646i
$879$	1.65400	−	23.4775i	0.0557880	−	0.791877i
$880$	−3.14596	−	0.445479i	−0.106050	−	0.0150171i
$881$	18.4516	+	17.1974i	0.621651	+	0.579396i	0.928026	−	0.372515i	$-0.121504\pi$
$881$	18.4516	+	17.1974i	0.621651	+	0.579396i	−0.306376	+	0.951911i	$0.599116\pi$
$882$	0.475760	+	4.03996i	0.0160197	+	0.136032i
$883$	13.6224	−	32.3498i	0.458431	−	1.08866i	−0.514485	−	0.857499i	$-0.672017\pi$
$883$	13.6224	−	32.3498i	0.458431	−	1.08866i	0.972916	−	0.231159i	$-0.0742519\pi$
$884$	−12.6864	−	12.9874i	−0.426689	−	0.436812i
$885$	−3.37172	+	12.7830i	−0.113339	+	0.429697i
$886$	−8.59248	−	10.6278i	−0.288670	−	0.357048i
$887$	−3.81906	+	32.4299i	−0.128232	+	1.08889i	0.766487	+	0.642260i	$0.222003\pi$
$887$	−3.81906	+	32.4299i	−0.128232	+	1.08889i	−0.894718	+	0.446631i	$0.852624\pi$
$888$	2.00972	+	5.47722i	0.0674417	+	0.183803i
$889$	−6.28521			−0.210799
$890$	4.59500	+	12.5231i	0.154025	+	0.419774i
$891$	22.9076	−	7.80105i	0.767434	−	0.261345i
$892$	−4.28905	+	1.02439i	−0.143608	+	0.0342992i
$893$	−2.03018	+	0.586726i	−0.0679374	+	0.0196340i
$894$	1.75744	−	1.97655i	0.0587776	−	0.0661056i
$895$	8.46673	−	4.80044i	0.283012	−	0.160461i
$896$	−0.886113	−	0.558854i	−0.0296030	−	0.0186700i
$897$	0.282335	+	0.897489i	0.00942688	+	0.0299663i
$898$	−30.4356	+	4.30980i	−1.01565	+	0.143820i
$899$	20.3169	+	10.2921i	0.677607	+	0.343259i
$900$	1.01634	−	2.76990i	0.0338780	−	0.0923301i
$901$	3.23033	−	8.80382i	0.107618	−	0.293298i
$902$	0.338803	−	14.4485i	0.0112809	−	0.481082i
$903$	1.07417	+	15.2472i	0.0357461	+	0.507395i
$904$	−4.39064	+	6.61292i	−0.146030	+	0.219943i
$905$	1.04456	+	1.17479i	0.0347224	+	0.0390514i
$906$	−16.4185	+	22.3767i	−0.545468	+	0.743417i
$907$	−2.73372	−	10.3642i	−0.0907718	−	0.344138i	0.906110	−	0.423041i	$-0.139037\pi$
$907$	−2.73372	−	10.3642i	−0.0907718	−	0.344138i	−0.996882	+	0.0789029i	$0.974858\pi$
$908$	−12.5572	+	20.9853i	−0.416727	+	0.696423i
$909$	0.869302	−	0.390299i	0.0288329	−	0.0129454i
$910$	4.95261	+	2.80802i	0.164177	+	0.0930849i
$911$	0.996675	−	8.46336i	0.0330213	−	0.280404i	−0.966681	−	0.255986i	$-0.917600\pi$
$911$	0.996675	−	8.46336i	0.0330213	−	0.280404i	0.999702	−	0.0244178i	$-0.00777319\pi$
$912$	0.504804	−	0.428082i	0.0167157	−	0.0141752i
$913$	29.7342	−	10.1258i	0.984057	−	0.335115i
$914$	−30.2998	−	17.1793i	−1.00223	−	0.568241i
$915$	−7.72920	−	14.4095i	−0.255520	−	0.476363i
$916$	9.47642	+	14.2728i	0.313110	+	0.471588i
$917$	−12.1881	+	15.0751i	−0.402487	+	0.497825i
$918$	15.6062	+	2.96188i	0.515083	+	0.0977567i
$919$	39.6813	−	20.1016i	1.30897	−	0.663090i	0.347413	−	0.937712i	$-0.387060\pi$
$919$	39.6813	−	20.1016i	1.30897	−	0.663090i	0.961552	+	0.274622i	$0.0885526\pi$
$920$	0.0352748	+	0.0738809i	0.00116298	+	0.00243578i
$921$	3.69454	+	22.3097i	0.121739	+	0.735129i
$922$	16.6649	+	1.56741i	0.548828	+	0.0516199i
$923$	45.0697	−	67.8814i	1.48349	−	2.23434i
$924$	−1.79091	−	5.69297i	−0.0589166	−	0.187285i
$925$	8.43689	+	14.0995i	0.277403	+	0.463589i
$926$	26.1505	+	24.3730i	0.859357	+	0.800945i
$927$	−3.49075	−	7.31116i	−0.114651	−	0.240130i
$928$	−3.16496	−	0.148512i	−0.103895	−	0.00487514i
$929$	−0.729225	−	0.210748i	−0.0239251	−	0.00691440i	0.265656	−	0.964068i	$-0.414411\pi$
$929$	−0.729225	−	0.210748i	−0.0239251	−	0.00691440i	−0.289581	+	0.957154i	$0.593516\pi$
$930$	7.83616	−	4.94211i	0.256958	−	0.162058i
$931$	−0.538257	+	2.51298i	−0.0176406	+	0.0823595i
$932$	−8.02394	−	10.9358i	−0.262833	−	0.358214i
$933$	10.9466	−	13.5396i	0.358376	−	0.443266i
$934$	11.4216	+	11.6926i	0.373727	+	0.382593i
$935$	−1.88492	−	8.80021i	−0.0616436	−	0.287798i
$936$	2.93524	−	3.30119i	0.0959413	−	0.107903i
$937$	−10.1607	−	38.5217i	−0.331936	−	1.25845i	−0.900154	−	0.435572i	$-0.856546\pi$
$937$	−10.1607	−	38.5217i	−0.331936	−	1.25845i	0.568218	−	0.822878i	$-0.307633\pi$
$938$	5.49326	−	0.516667i	0.179361	−	0.0168698i
$939$	−23.2459	+	43.3371i	−0.758601	+	1.41425i
$940$	3.48069	−	2.19520i	0.113528	−	0.0715996i
$941$	−14.7462	−	12.5050i	−0.480711	−	0.407651i	0.373457	−	0.927647i	$-0.378172\pi$
$941$	−14.7462	−	12.5050i	−0.480711	−	0.407651i	−0.854169	+	0.519996i	$0.825933\pi$
$942$	−17.2310	−	14.6122i	−0.561417	−	0.476091i
$943$	−0.314983	+	0.198653i	−0.0102572	+	0.00646904i
$944$	4.84852	−	9.03905i	0.157806	−	0.294196i
$945$	−4.95938	+	0.466454i	−0.161329	+	0.0151737i
$946$	−9.17343	−	34.7787i	−0.298254	−	1.13075i
$947$	−7.52026	+	8.45783i	−0.244375	+	0.274843i	−0.856758	−	0.515719i	$-0.827525\pi$
$947$	−7.52026	+	8.45783i	−0.244375	+	0.274843i	0.612382	+	0.790562i	$0.290211\pi$
$948$	−1.94843	−	9.09670i	−0.0632820	−	0.295447i
$949$	44.5106	+	45.5666i	1.44488	+	1.47915i
$950$	1.17194	−	1.44954i	0.0380228	−	0.0470294i
$951$	−3.97234	−	5.41389i	−0.128812	−	0.175557i
$952$	0.621491	−	2.90158i	0.0201426	−	0.0940406i
$953$	−8.62595	+	5.44021i	−0.279422	+	0.176226i	−0.665833	−	0.746101i	$-0.731924\pi$
$953$	−8.62595	+	5.44021i	−0.279422	+	0.176226i	0.386411	+	0.922327i	$0.373715\pi$
$954$	2.19201	+	0.633496i	0.0709691	+	0.0205102i
$955$	7.51086	+	0.352438i	0.243046	+	0.0114046i
$956$	−9.06716	−	18.9906i	−0.293253	−	0.614200i
$957$	−13.2039	−	12.3064i	−0.426823	−	0.397811i
$958$	−4.54731	−	7.59936i	−0.146917	−	0.245524i
$959$	−1.16897	−	3.71593i	−0.0377479	−	0.119994i
$960$	−0.712908	+	1.07374i	−0.0230090	+	0.0346548i
$961$	20.5780	+	1.93546i	0.663805	+	0.0624341i
$962$	4.01912	+	24.2697i	0.129582	+	0.782486i
$963$	0.810511	+	1.69756i	0.0261184	+	0.0547033i
$964$	−1.04130	+	0.527498i	−0.0335380	+	0.0169896i
$965$	−2.69202	−	0.510914i	−0.0866592	−	0.0164469i
$966$	−0.0966815	+	0.119583i	−0.00311068	+	0.00384751i
$967$	−3.20211	−	4.82284i	−0.102973	−	0.155092i	0.777991	−	0.628276i	$-0.216239\pi$
$967$	−3.20211	−	4.82284i	−0.102973	−	0.155092i	−0.880964	+	0.473184i	$0.843105\pi$
$968$	1.43876	+	2.68228i	0.0462436	+	0.0862116i
$969$	1.63087	+	0.924665i	0.0523911	+	0.0297045i
$970$	−13.5081	+	4.60009i	−0.433718	+	0.147700i
$971$	−44.8025	+	37.9932i	−1.43778	+	1.21926i	−0.502876	+	0.864359i	$0.667725\pi$
$971$	−44.8025	+	37.9932i	−1.43778	+	1.21926i	−0.934903	+	0.354902i	$0.884514\pi$
$972$	−0.819612	+	6.95982i	−0.0262891	+	0.223236i
$973$	−4.24902	−	2.40910i	−0.136217	−	0.0772322i
$974$	−11.6287	+	5.22105i	−0.372608	+	0.167293i
$975$	−21.4188	+	35.7946i	−0.685951	+	1.14634i
$976$	3.23569	+	12.2673i	0.103572	+	0.392667i
$977$	−35.0304	+	47.7428i	−1.12072	+	1.52743i	−0.301934	+	0.953329i	$0.597632\pi$
$977$	−35.0304	+	47.7428i	−1.12072	+	1.52743i	−0.818786	+	0.574098i	$0.805353\pi$
$978$	18.8292	+	21.1767i	0.602090	+	0.677155i
$979$	32.6127	−	49.1193i	1.04231	−	1.56986i
$980$	−0.351694	−	4.99209i	−0.0112345	−	0.159466i
$981$	−0.100059	+	4.26708i	−0.00319463	+	0.136237i
$982$	4.88345	−	13.3092i	0.155837	−	0.424713i
$983$	−1.84235	+	5.02107i	−0.0587617	+	0.160147i	−0.964758	−	0.263138i	$-0.915243\pi$
$983$	−1.84235	+	5.02107i	−0.0587617	+	0.160147i	0.905996	+	0.423285i	$0.139123\pi$
$984$	−5.22975	−	2.64926i	−0.166718	−	0.0844555i
$985$	−7.41637	+	1.05018i	−0.236305	+	0.0334616i
$986$	−2.69314	−	8.56098i	−0.0857670	−	0.272637i
$987$	6.53779	+	4.12326i	0.208100	+	0.131245i
$988$	2.42774	−	1.37647i	0.0772365	−	0.0437913i
$989$	−0.615823	+	0.692600i	−0.0195820	+	0.0220234i
$990$	2.10367	−	0.607965i	0.0668591	−	0.0193224i
$991$	−16.1706	+	3.86217i	−0.513675	+	0.122686i	−0.480898	−	0.876777i	$-0.659689\pi$
$991$	−16.1706	+	3.86217i	−0.513675	+	0.122686i	−0.0327778	+	0.999463i	$0.510435\pi$
$992$	−6.80437	+	2.31719i	−0.216039	+	0.0735708i
$993$	4.83726	+	13.1833i	0.153506	+	0.418360i
$994$	13.3176			0.422410
$995$	−0.364010	−	0.992060i	−0.0115399	−	0.0314504i
$996$	1.49019	−	12.6541i	0.0472186	−	0.400961i
$997$	5.04554	+	6.24069i	0.159794	+	0.197645i	0.851230	−	0.524793i	$-0.175857\pi$
$997$	5.04554	+	6.24069i	0.159794	+	0.197645i	−0.691436	+	0.722438i	$0.743022\pi$
$998$	−5.58621	+	21.1787i	−0.176828	+	0.670400i
$999$	−15.0401	−	15.3969i	−0.475848	−	0.487137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.d.a.5.4	✓	726
269.54	even	67	inner	538.2.d.a.323.4	yes	726

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.d.a.5.4	✓	726	1.1	even	1	trivial
538.2.d.a.323.4	yes	726	269.54	even	67	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.d (of order \(67\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(0.762685 - 0.646770i) q^{2} +(-0.456170 + 1.45008i) q^{3} +(0.163377 - 0.986564i) q^{4} +(-0.177575 - 0.829052i) q^{5} +(0.589953 + 1.40099i) q^{6} +(-0.732047 + 0.749414i) q^{7} +(-0.513474 - 0.858105i) q^{8} +(0.565057 + 0.394562i) q^{9} +(-0.671640 - 0.517455i) q^{10} +(-0.0878511 + 3.74647i) q^{11} +(1.35607 + 0.686951i) q^{12} +(5.07749 + 3.91188i) q^{13} +(-0.0736229 + 1.04503i) q^{14} +(1.28320 + 0.120691i) q^{15} +(-0.946616 - 0.322364i) q^{16} +(-0.0664010 - 2.83172i) q^{17} +(0.686152 - 0.0645358i) q^{18} +(0.423494 + 0.101147i) q^{19} +(-0.846924 + 0.0397409i) q^{20} +(-0.752771 - 1.40339i) q^{21} +(2.35610 + 2.91420i) q^{22} +(0.0289765 - 0.0921110i) q^{23} +(1.47855 - 0.353136i) q^{24} +(3.90555 - 1.75351i) q^{25} +(6.40261 - 0.300435i) q^{26} +(-4.44250 + 3.42266i) q^{27} +(0.619745 + 0.844648i) q^{28} +(2.89047 + 1.29776i) q^{29} +(1.05673 - 0.737883i) q^{30} +(7.18020 + 0.336923i) q^{31} +(-0.930465 + 0.366380i) q^{32} +(-5.39261 - 1.83642i) q^{33} +(-1.88211 - 2.11676i) q^{34} +(0.751296 + 0.473828i) q^{35} +(0.481578 - 0.493003i) q^{36} +(0.448874 + 3.81166i) q^{37} +(0.388412 - 0.196760i) q^{38} +(-7.98873 + 5.57828i) q^{39} +(-0.620233 + 0.578075i) q^{40} +(-2.94134 - 2.49430i) q^{41} +(-1.48180 - 0.583472i) q^{42} +(-8.75588 - 3.93121i) q^{43} +(3.68178 + 0.698760i) q^{44} +(0.226772 - 0.538526i) q^{45} +(-0.0374746 - 0.0889929i) q^{46} +(-4.22213 + 2.39385i) q^{47} +(0.899272 - 1.22561i) q^{48} +(0.138369 + 5.90086i) q^{49} +(1.84459 - 3.86337i) q^{50} +(4.13650 + 1.19546i) q^{51} +(4.68886 - 4.37015i) q^{52} +(3.08056 + 1.21300i) q^{53} +(-1.17455 + 5.48368i) q^{54} +(3.12162 - 0.592448i) q^{55} +(1.01896 + 0.243368i) q^{56} +(-0.339857 + 0.567960i) q^{57} +(3.04387 - 0.879685i) q^{58} +(-1.67581 + 10.1195i) q^{59} +(0.328714 - 1.24624i) q^{60} +(-7.01750 - 10.5694i) q^{61} +(5.69414 - 4.38697i) q^{62} +(-0.709339 + 0.134624i) q^{63} +(-0.472689 + 0.881230i) q^{64} +(2.34151 - 4.90415i) q^{65} +(-5.30060 + 2.08717i) q^{66} +(-0.860457 - 5.19592i) q^{67} +(-2.80452 - 0.397130i) q^{68} +(0.120350 + 0.0840366i) q^{69} +(0.879460 - 0.124535i) q^{70} +(-0.893368 - 12.6808i) q^{71} +(0.0484329 - 0.687476i) q^{72} +(9.83975 + 1.39334i) q^{73} +(2.80761 + 2.61678i) q^{74} +(0.761136 + 6.46326i) q^{75} +(0.168977 - 0.401279i) q^{76} +(-2.74335 - 2.80843i) q^{77} +(-2.48502 + 9.42134i) q^{78} +(-3.84763 - 4.75903i) q^{79} +(-0.0991613 + 0.842038i) q^{80} +(-2.22439 - 6.06228i) q^{81} -3.85656 q^{82} +(-2.88727 - 7.86887i) q^{83} +(-1.50752 + 0.513375i) q^{84} +(-2.33585 + 0.557893i) q^{85} +(-9.22057 + 2.66476i) q^{86} +(-3.20040 + 3.59941i) q^{87} +(3.25998 - 1.84833i) q^{88} +(-13.3076 - 8.39285i) q^{89} +(-0.175347 - 0.557395i) q^{90} +(-6.64857 + 0.941462i) q^{91} +(-0.0861392 - 0.0436361i) q^{92} +(-3.76396 + 10.2582i) q^{93} +(-1.67189 + 4.55650i) q^{94} +(0.00865410 - 0.369060i) q^{95} +(-0.106830 - 1.51638i) q^{96} +(9.30948 - 14.0214i) q^{97} +(3.92203 + 4.41101i) q^{98} +(-1.52786 + 2.08231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 726 q + 11 q^{2} + q^{3} - 11 q^{4} + q^{5} - q^{6} + 4 q^{7} + 11 q^{8} - 10 q^{9} - q^{10} + 5 q^{11} + q^{12} - 7 q^{13} - 4 q^{14} - 2 q^{15} - 11 q^{16} + 4 q^{17} + 10 q^{18} + 5 q^{19} + q^{20}+ \cdots + 25 q^{99}+O(q^{100}) \) 726 * q + 11 * q^2 + q^3 - 11 * q^4 + q^5 - q^6 + 4 * q^7 + 11 * q^8 - 10 * q^9 - q^10 + 5 * q^11 + q^12 - 7 * q^13 - 4 * q^14 - 2 * q^15 - 11 * q^16 + 4 * q^17 + 10 * q^18 + 5 * q^19 + q^20 - 191 * q^21 - 5 * q^22 + 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 185 * q^27 + 4 * q^28 + 7 * q^29 - 65 * q^30 + 4 * q^31 + 11 * q^32 + 18 * q^33 - 4 * q^34 + 22 * q^35 - 10 * q^36 + 216 * q^37 - 5 * q^38 - 4 * q^39 - q^40 - 122 * q^41 - 10 * q^42 + 5 * q^43 - 62 * q^44 + 9 * q^45 - 6 * q^46 + 211 * q^47 + q^48 + 9 * q^49 + 8 * q^50 + 18 * q^51 - 7 * q^52 - 141 * q^53 - 16 * q^54 - 28 * q^55 - 4 * q^56 + 4 * q^57 - 7 * q^58 + q^59 + 132 * q^60 - 60 * q^61 - 4 * q^62 - 11 * q^64 + 24 * q^65 - 18 * q^66 + 15 * q^67 + 4 * q^68 - 8 * q^69 - 22 * q^70 + 8 * q^71 + 10 * q^72 + 65 * q^73 - 15 * q^74 - 15 * q^75 + 5 * q^76 - 2 * q^77 + 4 * q^78 - 61 * q^79 + q^80 - 315 * q^81 - 280 * q^82 + 198 * q^83 - 258 * q^84 - 126 * q^85 - 5 * q^86 + 6 * q^87 - 5 * q^88 - 36 * q^89 - 9 * q^90 + 28 * q^91 + 6 * q^92 + 152 * q^93 - 10 * q^94 + 6 * q^95 - q^96 - 24 * q^97 - 9 * q^98 + 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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