LMFDB - Embedded newform 138.2.f.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	138.5
Dual form			138.2.f.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281733 + 0.959493i) q^{2} +(1.60896 + 0.641290i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.239432 + 1.66529i) q^{5} +(-1.06861 + 1.36311i) q^{6} +(-0.935173 + 0.427079i) q^{7} +(0.755750 - 0.654861i) q^{8} +(2.17749 + 2.06362i) q^{9} +O(q^{10})$	\(q+(-0.281733 + 0.959493i) q^{2} +(1.60896 + 0.641290i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.239432 + 1.66529i) q^{5} +(-1.06861 + 1.36311i) q^{6} +(-0.935173 + 0.427079i) q^{7} +(0.755750 - 0.654861i) q^{8} +(2.17749 + 2.06362i) q^{9} +(-1.53038 - 0.698899i) q^{10} +(0.0982102 - 0.0288371i) q^{11} +(-1.00683 - 1.40936i) q^{12} +(2.01205 - 4.40578i) q^{13} +(-0.146311 - 1.01761i) q^{14} +(-1.45317 + 2.52583i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-3.64007 + 2.33933i) q^{17} +(-2.59350 + 1.50790i) q^{18} +(0.916723 - 1.42645i) q^{19} +(1.10175 - 1.27148i) q^{20} +(-1.77854 + 0.0874352i) q^{21} +0.102356i q^{22} +(0.252958 - 4.78916i) q^{23} +(1.63593 - 0.568989i) q^{24} +(2.08161 + 0.611216i) q^{25} +(3.66045 + 3.17180i) q^{26} +(2.18012 + 4.71668i) q^{27} +(1.01761 + 0.146311i) q^{28} +(-3.25993 - 5.07256i) q^{29} +(-2.01411 - 2.10591i) q^{30} +(-2.77619 - 3.20389i) q^{31} +(-0.989821 + 0.142315i) q^{32} +(0.176509 + 0.0165835i) q^{33} +(-1.21904 - 4.15168i) q^{34} +(-0.487299 - 1.65959i) q^{35} +(-0.716147 - 2.91327i) q^{36} +(7.82633 - 1.12526i) q^{37} +(1.11040 + 1.28147i) q^{38} +(6.06269 - 5.79840i) q^{39} +(0.909580 + 1.41533i) q^{40} +(2.19341 + 0.315364i) q^{41} +(0.417178 - 1.73113i) q^{42} +(-4.63477 - 4.01605i) q^{43} +(-0.0982102 - 0.0288371i) q^{44} +(-3.95788 + 3.13205i) q^{45} +(4.52389 + 1.59197i) q^{46} -7.70215i q^{47} +(0.0850471 + 1.72996i) q^{48} +(-3.89187 + 4.49146i) q^{49} +(-1.17292 + 1.82509i) q^{50} +(-7.35690 + 1.42954i) q^{51} +(-4.07459 + 2.61858i) q^{52} +(4.36713 + 9.56268i) q^{53} +(-5.13983 + 0.762964i) q^{54} +(0.0245074 + 0.170453i) q^{55} +(-0.427079 + 0.935173i) q^{56} +(2.38974 - 1.70721i) q^{57} +(5.78551 - 1.69878i) q^{58} +(-7.37789 - 3.36937i) q^{59} +(2.58805 - 1.33922i) q^{60} +(-8.87756 + 7.69245i) q^{61} +(3.85625 - 1.76109i) q^{62} +(-2.91766 - 0.999879i) q^{63} +(0.142315 - 0.989821i) q^{64} +(6.85513 + 4.40553i) q^{65} +(-0.0656402 + 0.164687i) q^{66} +(-4.14663 + 14.1221i) q^{67} +4.32695 q^{68} +(3.47824 - 7.54333i) q^{69} +1.72965 q^{70} +(-2.05377 + 6.99449i) q^{71} +(2.99702 + 0.133624i) q^{72} +(9.69633 + 6.23145i) q^{73} +(-1.12526 + 7.82633i) q^{74} +(2.95726 + 2.31834i) q^{75} +(-1.54239 + 0.704387i) q^{76} +(-0.0795279 + 0.0689113i) q^{77} +(3.85547 + 7.45070i) q^{78} +(-12.6271 - 5.76662i) q^{79} +(-1.61426 + 0.473990i) q^{80} +(0.482954 + 8.98703i) q^{81} +(-0.920544 + 2.01571i) q^{82} +(0.779795 + 5.42359i) q^{83} +(1.54347 + 0.887994i) q^{84} +(-3.02410 - 6.62186i) q^{85} +(5.15914 - 3.31558i) q^{86} +(-1.99212 - 10.2521i) q^{87} +(0.0553380 - 0.0861077i) q^{88} +(5.91320 - 6.82420i) q^{89} +(-1.89012 - 4.67996i) q^{90} +4.97947i q^{91} +(-2.80202 + 3.89213i) q^{92} +(-2.41215 - 6.93527i) q^{93} +(7.39016 + 2.16995i) q^{94} +(2.15595 + 1.86814i) q^{95} +(-1.68385 - 0.405784i) q^{96} +(5.66160 + 0.814016i) q^{97} +(-3.21306 - 4.99962i) q^{98} +(0.273361 + 0.139876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.281733	+	0.959493i	−0.199215	+	0.678464i
$2$	−0.281733	+	0.959493i	−0.199215	+	0.678464i
$3$	1.60896	+	0.641290i	0.928932	+	0.370249i
$3$	1.60896	+	0.641290i	0.928932	+	0.370249i
$4$	−0.841254	−	0.540641i	−0.420627	−	0.270320i
$5$	−0.239432	+	1.66529i	−0.107077	+	0.744739i	0.863570	+	0.504230i	$0.168224\pi$
$5$	−0.239432	+	1.66529i	−0.107077	+	0.744739i	−0.970647	+	0.240509i	$0.922686\pi$
$6$	−1.06861	+	1.36311i	−0.436258	+	0.556488i
$7$	−0.935173	+	0.427079i	−0.353462	+	0.161421i	−0.584230	−	0.811588i	$-0.698603\pi$
$7$	−0.935173	+	0.427079i	−0.353462	+	0.161421i	0.230768	+	0.973009i	$0.425876\pi$
$8$	0.755750	−	0.654861i	0.267198	−	0.231528i
$9$	2.17749	+	2.06362i	0.725831	+	0.687873i
$10$	−1.53038	−	0.698899i	−0.483947	−	0.221011i
$11$	0.0982102	−	0.0288371i	0.0296115	−	0.00869472i	−0.266893	−	0.963726i	$-0.585997\pi$
$11$	0.0982102	−	0.0288371i	0.0296115	−	0.00869472i	0.296505	+	0.955031i	$0.404179\pi$
$12$	−1.00683	−	1.40936i	−0.290648	−	0.406846i
$13$	2.01205	−	4.40578i	0.558042	−	1.22194i	−0.394881	−	0.918732i	$-0.629214\pi$
$13$	2.01205	−	4.40578i	0.558042	−	1.22194i	0.952924	−	0.303210i	$-0.0980585\pi$
$14$	−0.146311	−	1.01761i	−0.0391032	−	0.271969i
$15$	−1.45317	+	2.52583i	−0.375207	+	0.652167i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−3.64007	+	2.33933i	−0.882846	+	0.567370i	−0.901657	−	0.432453i	$-0.857648\pi$
$17$	−3.64007	+	2.33933i	−0.882846	+	0.567370i	0.0188111	+	0.999823i	$0.494012\pi$
$18$	−2.59350	+	1.50790i	−0.611293	+	0.355416i
$19$	0.916723	−	1.42645i	0.210311	−	0.327250i	−0.720032	−	0.693941i	$-0.755873\pi$
$19$	0.916723	−	1.42645i	0.210311	−	0.327250i	0.930343	+	0.366691i	$0.119509\pi$
$20$	1.10175	−	1.27148i	0.246358	−	0.284312i
$21$	−1.77854	+	0.0874352i	−0.388108	+	0.0190799i
$22$			0.102356i			0.0218225i
$23$	0.252958	−	4.78916i	0.0527455	−	0.998608i
$23$	0.252958	−	4.78916i	0.0527455	−	0.998608i
$24$	1.63593	−	0.568989i	0.333932	−	0.116144i
$25$	2.08161	+	0.611216i	0.416322	+	0.122243i
$26$	3.66045	+	3.17180i	0.717874	+	0.622041i
$27$	2.18012	+	4.71668i	0.419564	+	0.907726i
$28$	1.01761	+	0.146311i	0.192311	+	0.0276502i
$29$	−3.25993	−	5.07256i	−0.605355	−	0.941950i	−0.999735	−	0.0230031i	$-0.992677\pi$
$29$	−3.25993	−	5.07256i	−0.605355	−	0.941950i	0.394381	−	0.918947i	$-0.370959\pi$
$30$	−2.01411	−	2.10591i	−0.367725	−	0.384486i
$31$	−2.77619	−	3.20389i	−0.498618	−	0.575436i	0.449530	−	0.893265i	$-0.351592\pi$
$31$	−2.77619	−	3.20389i	−0.498618	−	0.575436i	−0.948148	+	0.317829i	$0.897046\pi$
$32$	−0.989821	+	0.142315i	−0.174977	+	0.0251579i
$33$	0.176509	+	0.0165835i	0.0307263	+	0.00288683i
$34$	−1.21904	−	4.15168i	−0.209064	−	0.712008i
$35$	−0.487299	−	1.65959i	−0.0823686	−	0.280522i
$36$	−0.716147	−	2.91327i	−0.119358	−	0.485545i
$37$	7.82633	−	1.12526i	1.28664	−	0.184991i	0.535163	−	0.844749i	$-0.320250\pi$
$37$	7.82633	−	1.12526i	1.28664	−	0.184991i	0.751478	+	0.659758i	$0.229341\pi$
$38$	1.11040	+	1.28147i	0.180130	+	0.207881i
$39$	6.06269	−	5.79840i	0.970807	−	0.928487i
$40$	0.909580	+	1.41533i	0.143817	+	0.223784i
$41$	2.19341	+	0.315364i	0.342552	+	0.0492516i	0.311444	−	0.950264i	$-0.399187\pi$
$41$	2.19341	+	0.315364i	0.342552	+	0.0492516i	0.0311082	+	0.999516i	$0.490096\pi$
$42$	0.417178	−	1.73113i	0.0643720	−	0.267119i
$43$	−4.63477	−	4.01605i	−0.706796	−	0.612442i	0.225455	−	0.974253i	$-0.427613\pi$
$43$	−4.63477	−	4.01605i	−0.706796	−	0.612442i	−0.932251	+	0.361811i	$0.882158\pi$
$44$	−0.0982102	−	0.0288371i	−0.0148058	−	0.00434736i
$45$	−3.95788	+	3.13205i	−0.590006	+	0.466899i
$46$	4.52389	+	1.59197i	0.667012	+	0.234724i
$47$		−	7.70215i		−	1.12347i	−0.827316	−	0.561737i	$-0.810133\pi$
$47$		−	7.70215i		−	1.12347i	0.827316	−	0.561737i	$-0.189867\pi$
$48$	0.0850471	+	1.72996i	0.0122755	+	0.249698i
$49$	−3.89187	+	4.49146i	−0.555982	+	0.641637i
$50$	−1.17292	+	1.82509i	−0.165875	+	0.258107i
$51$	−7.35690	+	1.42954i	−1.03017	+	0.200176i
$52$	−4.07459	+	2.61858i	−0.565044	+	0.363131i
$53$	4.36713	+	9.56268i	0.599871	+	1.31353i	0.929290	+	0.369351i	$0.120420\pi$
$53$	4.36713	+	9.56268i	0.599871	+	1.31353i	−0.329419	+	0.944184i	$0.606853\pi$
$54$	−5.13983	+	0.762964i	−0.699443	+	0.103826i
$55$	0.0245074	+	0.170453i	0.00330458	+	0.0229839i
$56$	−0.427079	+	0.935173i	−0.0570709	+	0.124968i
$57$	2.38974	−	1.70721i	0.316528	−	0.226126i
$58$	5.78551	−	1.69878i	0.759675	−	0.223061i
$59$	−7.37789	−	3.36937i	−0.960520	−	0.438655i	−0.127464	−	0.991843i	$-0.540684\pi$
$59$	−7.37789	−	3.36937i	−0.960520	−	0.438655i	−0.833056	+	0.553189i	$0.813411\pi$
$60$	2.58805	−	1.33922i	0.334116	−	0.172893i
$61$	−8.87756	+	7.69245i	−1.13666	+	0.984918i	−0.999984	−	0.00569884i	$-0.998186\pi$
$61$	−8.87756	+	7.69245i	−1.13666	+	0.984918i	−0.136672	+	0.990616i	$0.543641\pi$
$62$	3.85625	−	1.76109i	0.489745	−	0.223659i
$63$	−2.91766	−	0.999879i	−0.367591	−	0.125973i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	6.85513	+	4.40553i	0.850275	+	0.546438i
$66$	−0.0656402	+	0.164687i	−0.00807975	+	0.0202716i
$67$	−4.14663	+	14.1221i	−0.506591	+	1.72529i	0.166788	+	0.985993i	$0.446661\pi$
$67$	−4.14663	+	14.1221i	−0.506591	+	1.72529i	−0.673379	+	0.739298i	$0.735158\pi$
$68$	4.32695			0.524720
$69$	3.47824	−	7.54333i	0.418731	−	0.908110i
$70$	1.72965			0.206733
$71$	−2.05377	+	6.99449i	−0.243737	+	0.830093i	0.743211	+	0.669057i	$0.233302\pi$
$71$	−2.05377	+	6.99449i	−0.243737	+	0.830093i	−0.986949	+	0.161036i	$0.948516\pi$
$72$	2.99702	+	0.133624i	0.353203	+	0.0157478i
$73$	9.69633	+	6.23145i	1.13487	+	0.729336i	0.966571	−	0.256400i	$-0.0825364\pi$
$73$	9.69633	+	6.23145i	1.13487	+	0.729336i	0.168298	+	0.985736i	$0.446173\pi$
$74$	−1.12526	+	7.82633i	−0.130808	+	0.909793i
$75$	2.95726	+	2.31834i	0.341475	+	0.267699i
$76$	−1.54239	+	0.704387i	−0.176925	+	0.0807988i
$77$	−0.0795279	+	0.0689113i	−0.00906304	+	0.00785317i
$78$	3.85547	+	7.45070i	0.436546	+	0.843626i
$79$	−12.6271	−	5.76662i	−1.42066	−	0.648795i	−0.450840	−	0.892605i	$-0.648875\pi$
$79$	−12.6271	−	5.76662i	−1.42066	−	0.648795i	−0.969823	+	0.243810i	$0.921603\pi$
$80$	−1.61426	+	0.473990i	−0.180480	+	0.0529937i
$81$	0.482954	+	8.98703i	0.0536615	+	0.998559i
$82$	−0.920544	+	2.01571i	−0.101657	+	0.222598i
$83$	0.779795	+	5.42359i	0.0855936	+	0.595317i	0.986802	+	0.161931i	$0.0517721\pi$
$83$	0.779795	+	5.42359i	0.0855936	+	0.595317i	−0.901209	+	0.433386i	$0.857319\pi$
$84$	1.54347	+	0.887994i	0.168407	+	0.0968881i
$85$	−3.02410	−	6.62186i	−0.328010	−	0.718242i
$86$	5.15914	−	3.31558i	0.556324	−	0.357528i
$87$	−1.99212	−	10.2521i	−0.213577	−	1.09914i
$88$	0.0553380	−	0.0861077i	0.00589906	−	0.00917911i
$89$	5.91320	−	6.82420i	0.626798	−	0.723363i	−0.350185	−	0.936681i	$-0.613881\pi$
$89$	5.91320	−	6.82420i	0.626798	−	0.723363i	0.976983	+	0.213317i	$0.0684268\pi$
$90$	−1.89012	−	4.67996i	−0.199236	−	0.493311i
$91$			4.97947i			0.521990i
$92$	−2.80202	+	3.89213i	−0.292130	+	0.405783i
$93$	−2.41215	−	6.93527i	−0.250128	−	0.719154i
$94$	7.39016	+	2.16995i	0.762237	+	0.223813i
$95$	2.15595	+	1.86814i	0.221196	+	0.191668i
$96$	−1.68385	−	0.405784i	−0.171857	−	0.0414152i
$97$	5.66160	+	0.814016i	0.574849	+	0.0826508i	0.423607	−	0.905846i	$-0.360764\pi$
$97$	5.66160	+	0.814016i	0.574849	+	0.0826508i	0.151242	+	0.988497i	$0.451673\pi$
$98$	−3.21306	−	4.99962i	−0.324568	−	0.505037i
$99$	0.273361	+	0.139876i	0.0274738	+	0.0140581i
$100$	−1.42071	−	1.63959i	−0.142071	−	0.163959i
$101$	−6.05689	+	0.870849i	−0.602683	+	0.0866527i	−0.436901	−	0.899510i	$-0.643924\pi$
$101$	−6.05689	+	0.870849i	−0.602683	+	0.0866527i	−0.165782	+	0.986162i	$0.553015\pi$
$102$	0.701043	−	7.46164i	0.0694136	−	0.738813i
$103$	−2.78006	−	9.46801i	−0.273927	−	0.932910i	−0.975442	−	0.220256i	$-0.929311\pi$
$103$	−2.78006	−	9.46801i	−0.273927	−	0.932910i	0.701515	−	0.712655i	$-0.252507\pi$
$104$	−1.36456	−	4.64728i	−0.133806	−	0.455703i
$105$	0.280234	−	2.98271i	0.0273481	−	0.291083i
$106$	−10.4057	+	1.49611i	−1.01069	+	0.145315i
$107$	−9.30606	−	10.7398i	−0.899651	−	1.03825i	−0.999066	−	0.0432068i	$-0.986243\pi$
$107$	−9.30606	−	10.7398i	−0.899651	−	1.03825i	0.0994149	−	0.995046i	$-0.468303\pi$
$108$	0.716000	−	5.14659i	0.0688971	−	0.495230i
$109$	3.18167	+	4.95077i	0.304748	+	0.474198i	0.959524	−	0.281625i	$-0.0908735\pi$
$109$	3.18167	+	4.95077i	0.304748	+	0.474198i	−0.654776	+	0.755823i	$0.727237\pi$
$110$	−0.170453	−	0.0245074i	−0.0162520	−	0.00233669i
$111$	13.3139	+	3.20846i	1.26370	+	0.304534i
$112$	−0.776970	−	0.673248i	−0.0734168	−	0.0636160i
$113$	−7.89619	−	2.31853i	−0.742811	−	0.218109i	−0.111635	−	0.993749i	$-0.535609\pi$
$113$	−7.89619	−	2.31853i	−0.742811	−	0.218109i	−0.631175	+	0.775640i	$0.717427\pi$
$114$	0.964790	+	2.77391i	0.0903609	+	0.259801i
$115$	7.91475	+	1.56793i	0.738055	+	0.146210i
$116$			6.02976i			0.559849i
$117$	13.4731	−	5.44144i	1.24559	−	0.503062i
$118$	5.31148	−	6.12977i	0.488961	−	0.564292i
$119$	2.40501	−	3.74227i	0.220467	−	0.343054i
$120$	0.555836	+	2.86052i	0.0507407	+	0.261129i
$121$	−9.24498	+	5.94138i	−0.840452	+	0.540126i
$122$	−4.87976	−	10.6852i	−0.441792	−	0.967390i
$123$	3.32686	+	1.91402i	0.299973	+	0.172581i
$124$	0.603323	+	4.19621i	0.0541800	+	0.376830i
$125$	−5.01075	+	10.9720i	−0.448175	+	0.981367i
$126$	1.78138	−	2.51778i	0.158698	−	0.224301i
$127$	11.5199	−	3.38255i	1.02223	−	0.300153i	0.272681	−	0.962105i	$-0.412090\pi$
$127$	11.5199	−	3.38255i	1.02223	−	0.300153i	0.749547	+	0.661952i	$0.230272\pi$
$128$	0.909632	+	0.415415i	0.0804009	+	0.0367178i
$129$	−4.88170	−	9.43389i	−0.429810	−	0.830608i
$130$	−6.15839	+	5.33627i	−0.540126	+	0.468022i
$131$	0.425028	−	0.194104i	0.0371348	−	0.0169589i	−0.396761	−	0.917922i	$-0.629866\pi$
$131$	0.425028	−	0.194104i	0.0371348	−	0.0169589i	0.433896	+	0.900963i	$0.357139\pi$
$132$	−0.139523	−	0.109379i	−0.0121439	−	0.00952022i
$133$	−0.248088	+	1.72549i	−0.0215120	+	0.149619i
$134$	−12.3818	−	7.95732i	−1.06963	−	0.687407i
$135$	−8.37662	+	2.50119i	−0.720945	+	0.215269i
$136$	−1.21904	+	4.15168i	−0.104532	+	0.356004i
$137$	9.87770			0.843909			0.421955	−	0.906617i	$-0.361344\pi$
$137$	9.87770			0.843909			0.421955	+	0.906617i	$0.361344\pi$
$138$	6.25784	+	5.46255i	0.532703	+	0.465003i
$139$	12.4546			1.05639			0.528195	−	0.849123i	$-0.322869\pi$
$139$	12.4546			1.05639			0.528195	+	0.849123i	$0.322869\pi$
$140$	−0.487299	+	1.65959i	−0.0411843	+	0.140261i
$141$	4.93931	−	12.3924i	0.415965	−	1.04363i
$142$	−6.13255	−	3.94115i	−0.514632	−	0.330734i
$143$	0.0705540	−	0.490714i	0.00590003	−	0.0410356i
$144$	−0.972570	+	2.83798i	−0.0810475	+	0.236498i
$145$	9.22780	−	4.21419i	0.766327	−	0.349970i
$146$	−8.71080	+	7.54795i	−0.720911	+	0.624673i
$147$	−9.14219	+	4.73075i	−0.754035	+	0.390186i
$148$	−7.19229	−	3.28461i	−0.591203	−	0.269993i
$149$	5.25077	−	1.54176i	0.430160	−	0.126306i	−0.0594833	−	0.998229i	$-0.518945\pi$
$149$	5.25077	−	1.54176i	0.430160	−	0.126306i	0.489643	+	0.871923i	$0.337127\pi$
$150$	−3.05759	+	2.18432i	−0.249651	+	0.178349i
$151$	−1.56471	+	3.42623i	−0.127334	+	0.278823i	−0.962552	−	0.271096i	$-0.912614\pi$
$151$	−1.56471	+	3.42623i	−0.127334	+	0.278823i	0.835218	+	0.549919i	$0.185341\pi$
$152$	−0.241312	−	1.67836i	−0.0195730	−	0.136133i
$153$	−12.7537	−	2.41784i	−1.03108	−	0.195471i
$154$	−0.0437143	−	0.0957210i	−0.00352260	−	0.00771342i
$155$	6.00011	−	3.85604i	0.481940	−	0.309724i
$156$	−8.23511	+	1.60019i	−0.659336	+	0.128118i
$157$	−1.08150	+	1.68285i	−0.0863131	+	0.134306i	−0.881726	−	0.471763i	$-0.843618\pi$
$157$	−1.08150	+	1.68285i	−0.0863131	+	0.134306i	0.795412	+	0.606068i	$0.207254\pi$
$158$	9.09050	−	10.4910i	0.723201	−	0.834619i
$159$	0.894074	+	18.1865i	0.0709047	+	1.44229i
$160$		−	1.68241i		−	0.133006i
$161$	1.80879	+	4.58672i	0.142553	+	0.361484i
$162$	−8.75906	−	2.06855i	−0.688177	−	0.162521i
$163$	13.4116	+	3.93799i	1.05047	+	0.308447i	0.761009	−	0.648741i	$-0.224704\pi$
$163$	13.4116	+	3.93799i	1.05047	+	0.308447i	0.289465	+	0.957188i	$0.406522\pi$
$164$	−1.67471	−	1.45115i	−0.130773	−	0.113315i
$165$	−0.0698783	+	0.289968i	−0.00544002	+	0.0225740i
$166$	−5.42359	−	0.779795i	−0.420952	−	0.0605238i
$167$	−6.46981	−	10.0672i	−0.500649	−	0.779025i	0.495321	−	0.868710i	$-0.335050\pi$
$167$	−6.46981	−	10.0672i	−0.500649	−	0.779025i	−0.995970	+	0.0896851i	$0.971414\pi$
$168$	−1.28687	+	1.23077i	−0.0992842	+	0.0949562i
$169$	−6.84933	−	7.90455i	−0.526871	−	0.608042i
$170$	7.20562	−	1.03601i	0.552646	−	0.0794585i
$171$	4.93980	−	1.21432i	0.377756	−	0.0928610i
$172$	1.72778	+	5.88426i	0.131742	+	0.448671i
$173$	−0.469675	−	1.59957i	−0.0357087	−	0.121613i	0.939710	−	0.341973i	$-0.111095\pi$
$173$	−0.469675	−	1.59957i	−0.0357087	−	0.121613i	−0.975419	+	0.220360i	$0.929277\pi$
$174$	10.3981	+	0.976928i	0.788275	+	0.0740607i
$175$	−2.20770	+	0.317420i	−0.166887	+	0.0239947i
$176$	0.0670292	+	0.0773558i	0.00505252	+	0.00583091i
$177$	−9.70998	−	10.1525i	−0.729846	−	0.763112i
$178$	4.88183	+	7.59627i	0.365908	+	0.569365i
$179$	11.5704	+	1.66358i	0.864815	+	0.124342i	0.560424	−	0.828206i	$-0.310638\pi$
$179$	11.5704	+	1.66358i	0.864815	+	0.124342i	0.304391	+	0.952547i	$0.401547\pi$
$180$	5.02290	−	0.495061i	0.374385	−	0.0368996i
$181$	−18.9383	−	16.4101i	−1.40767	−	1.21976i	−0.942356	−	0.334611i	$-0.891395\pi$
$181$	−18.9383	−	16.4101i	−1.40767	−	1.21976i	−0.465317	−	0.885144i	$-0.654060\pi$
$182$	−4.77777	−	1.40288i	−0.354152	−	0.103988i
$183$	−19.2167	+	6.68374i	−1.42054	+	0.494076i
$184$	−2.94506	−	3.78505i	−0.217112	−	0.279038i
$185$			13.3025i			0.978020i
$186$	7.33392	−	0.360545i	0.537749	−	0.0264365i
$187$	−0.290032	+	0.334715i	−0.0212093	+	0.0244768i
$188$	−4.16410	+	6.47946i	−0.303698	+	0.472563i
$189$	−4.05318	−	3.47983i	−0.294826	−	0.253121i
$190$	−2.39987	+	1.54231i	−0.174105	+	0.111891i
$191$	6.95687	+	15.2334i	0.503382	+	1.10225i	0.975355	+	0.220639i	$0.0708144\pi$
$191$	6.95687	+	15.2334i	0.503382	+	1.10225i	−0.471974	+	0.881613i	$0.656458\pi$
$192$	0.863742	−	1.50132i	0.0623352	−	0.108348i
$193$	−3.01735	−	20.9861i	−0.217193	−	1.51061i	−0.748330	−	0.663326i	$-0.769144\pi$
$193$	−3.01735	−	20.9861i	−0.217193	−	1.51061i	0.531137	−	0.847286i	$-0.321765\pi$
$194$	−2.37610	+	5.20293i	−0.170594	+	0.373549i
$195$	8.20440	+	11.4844i	0.587529	+	0.822418i
$196$	5.70232	−	1.67435i	0.407308	−	0.119597i
$197$	19.5577	+	8.93169i	1.39343	+	0.636357i	0.963794	−	0.266647i	$-0.0859159\pi$
$197$	19.5577	+	8.93169i	1.39343	+	0.636357i	0.429632	+	0.903004i	$0.358643\pi$
$198$	−0.211225	+	0.222880i	−0.0150111	+	0.0158394i
$199$	0.280888	−	0.243391i	0.0199116	−	0.0172535i	−0.644848	−	0.764311i	$-0.723079\pi$
$199$	0.280888	−	0.243391i	0.0199116	−	0.0172535i	0.664760	+	0.747057i	$0.268534\pi$
$200$	1.97344	−	0.901239i	0.139543	−	0.0637272i
$201$	−15.7281	+	20.0627i	−1.10938	+	1.41511i
$202$	0.870849	−	6.05689i	0.0612727	−	0.426161i
$203$	5.21499	+	3.35147i	0.366020	+	0.235227i
$204$	6.96189	+	2.77483i	0.487430	+	0.194277i
$205$	−1.05034	+	3.57714i	−0.0733592	+	0.249838i
$206$	9.86772			0.687516
$207$	10.4338	−	9.90634i	0.725200	−	0.688539i
$208$	4.84347			0.335834
$209$	0.0488969	−	0.166528i	0.00338227	−	0.0115190i
$210$	2.78294	+	1.10921i	0.192041	+	0.0765427i
$211$	6.53129	+	4.19740i	0.449632	+	0.288961i	0.745794	−	0.666177i	$-0.232070\pi$
$211$	6.53129	+	4.19740i	0.449632	+	0.288961i	−0.296162	+	0.955138i	$0.595707\pi$
$212$	1.49611	−	10.4057i	0.102753	−	0.714665i
$213$	−7.78992	+	9.93678i	−0.533757	+	0.680857i
$214$	12.9266	−	5.90336i	0.883641	−	0.403545i
$215$	7.79759	−	6.75665i	0.531791	−	0.460800i
$216$	4.73639	+	2.13696i	0.322271	+	0.145402i
$217$	3.96453	+	1.81054i	0.269130	+	0.122908i
$218$	−5.64661	+	1.65799i	−0.382436	+	0.112293i
$219$	11.6048	+	16.2443i	0.784181	+	1.09769i
$220$	0.0715368	−	0.156644i	0.00482301	−	0.0105609i
$221$	2.98256	+	20.7442i	0.200629	+	1.39540i
$222$	−6.82944	+	11.8706i	−0.458362	+	0.796704i
$223$	−6.79607	−	14.8813i	−0.455099	−	0.996527i	−0.988577	−	0.150714i	$-0.951843\pi$
$223$	−6.79607	−	14.8813i	−0.455099	−	0.996527i	0.533479	−	0.845814i	$-0.320884\pi$
$224$	0.864875	−	0.555821i	0.0577869	−	0.0371374i
$225$	3.27138	+	5.62657i	0.218092	+	0.375105i
$226$	4.44922	−	6.92313i	0.295958	−	0.460520i
$227$	−6.29072	+	7.25988i	−0.417530	+	0.481855i	−0.925083	−	0.379765i	$-0.876005\pi$
$227$	−6.29072	+	7.25988i	−0.417530	+	0.481855i	0.507553	+	0.861621i	$0.330550\pi$
$228$	−2.93336	+	0.144208i	−0.194267	+	0.00955040i
$229$			14.2379i			0.940870i	0.882435	+	0.470435i	$0.155903\pi$
$229$			14.2379i			0.940870i	−0.882435	+	0.470435i	$0.844097\pi$
$230$	−3.73426	+	7.15241i	−0.246230	+	0.471616i
$231$	−0.172149	+	0.0598749i	−0.0113266	+	0.00393948i
$232$	−5.78551	−	1.69878i	−0.379838	−	0.111530i
$233$	−3.26410	−	2.82836i	−0.213839	−	0.185292i	0.541355	−	0.840794i	$-0.317912\pi$
$233$	−3.26410	−	2.82836i	−0.213839	−	0.185292i	−0.755193	+	0.655502i	$0.772457\pi$
$234$	1.42522	+	14.4603i	0.0931698	+	0.945303i
$235$	12.8263	+	1.84414i	0.836695	+	0.120299i
$236$	4.38506	+	6.82328i	0.285443	+	0.444158i
$237$	−16.6184	−	17.3759i	−1.07948	−	1.12869i
$238$	2.91311	+	3.36191i	0.188829	+	0.217920i
$239$	−13.7002	+	1.96980i	−0.886195	+	0.127416i	−0.570357	−	0.821397i	$-0.693195\pi$
$239$	−13.7002	+	1.96980i	−0.886195	+	0.127416i	−0.315839	+	0.948813i	$0.602286\pi$
$240$	−2.90125	−	0.272580i	−0.187275	−	0.0175950i
$241$	−3.31655	−	11.2951i	−0.213638	−	0.727584i	−0.994672	−	0.103095i	$-0.967125\pi$
$241$	−3.31655	−	11.2951i	−0.213638	−	0.727584i	0.781034	−	0.624489i	$-0.214693\pi$
$242$	−3.09611	−	10.5444i	−0.199025	−	0.677818i
$243$	−4.98625	+	14.7695i	−0.319868	+	0.947462i
$244$	11.6271	−	1.67173i	0.744351	−	0.107022i
$245$	−6.54773	−	7.55649i	−0.418319	−	0.482766i
$246$	−2.77377	+	2.65286i	−0.176849	+	0.169140i
$247$	−4.44012	−	6.90896i	−0.282518	−	0.439607i
$248$	−4.19621	−	0.603323i	−0.266459	−	0.0383111i
$249$	−2.22344	+	9.22641i	−0.140905	+	0.584700i
$250$	−9.11588	−	7.89895i	−0.576539	−	0.499574i
$251$	−5.86387	−	1.72179i	−0.370124	−	0.108678i	0.0913804	−	0.995816i	$-0.470872\pi$
$251$	−5.86387	−	1.72179i	−0.370124	−	0.108678i	−0.461505	+	0.887138i	$0.652690\pi$
$252$	1.91392	+	2.41856i	0.120566	+	0.152355i
$253$	−0.113262	−	0.477639i	−0.00712075	−	0.0300289i
$254$			12.0063i			0.753339i
$255$	−0.619119	−	12.5936i	−0.0387707	−	0.788644i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	11.0714	−	17.2274i	0.690614	−	1.07462i	−0.302000	−	0.953308i	$-0.597654\pi$
$257$	11.0714	−	17.2274i	0.690614	−	1.07462i	0.992615	−	0.121309i	$-0.0387092\pi$
$258$	10.4271	−	2.02612i	0.649162	−	0.126141i
$259$	−6.83840	+	4.39478i	−0.424918	+	0.273078i
$260$	−3.38510	−	7.41233i	−0.209935	−	0.459693i
$261$	3.36934	−	17.7727i	0.208557	−	1.10010i
$262$	0.0664969	+	0.462496i	0.00410819	+	0.0285731i
$263$	8.96471	−	19.6300i	0.552788	−	1.21044i	−0.402680	−	0.915341i	$-0.631921\pi$
$263$	8.96471	−	19.6300i	0.552788	−	1.21044i	0.955468	−	0.295096i	$-0.0953516\pi$
$264$	0.144257	−	0.103056i	0.00887838	−	0.00634265i
$265$	−16.9702	+	4.98291i	−1.04247	+	0.306098i
$266$	−1.58570	−	0.724165i	−0.0972256	−	0.0444014i
$267$	13.8904	−	7.18777i	0.850078	−	0.439884i
$268$	11.1234	−	9.63844i	0.679467	−	0.588761i
$269$	−23.9682	+	10.9459i	−1.46137	+	0.667384i	−0.978109	−	0.208094i	$-0.933274\pi$
$269$	−23.9682	+	10.9459i	−1.46137	+	0.667384i	−0.483258	+	0.875478i	$0.660547\pi$
$270$	−0.0399123	−	8.74198i	−0.00242899	−	0.532020i
$271$	−2.20066	+	15.3059i	−0.133680	+	0.929768i	0.807019	+	0.590526i	$0.201080\pi$
$271$	−2.20066	+	15.3059i	−0.133680	+	0.929768i	−0.940699	+	0.339242i	$0.889829\pi$
$272$	−3.64007	−	2.33933i	−0.220711	−	0.141843i
$273$	−3.19329	+	8.01176i	−0.193266	+	0.484894i
$274$	−2.78287	+	9.47759i	−0.168119	+	0.572562i
$275$	0.222061			0.0133908
$276$	−7.00431	+	4.46538i	−0.421610	+	0.268784i
$277$	−10.5440			−0.633527			−0.316763	−	0.948505i	$-0.602596\pi$
$277$	−10.5440			−0.633527			−0.316763	+	0.948505i	$0.602596\pi$
$278$	−3.50888	+	11.9501i	−0.210449	+	0.716722i
$279$	0.566481	−	12.7054i	0.0339143	−	0.760655i
$280$	−1.45508	−	0.935120i	−0.0869574	−	0.0558841i
$281$	4.64648	−	32.3170i	0.277186	−	1.92787i	−0.0862990	−	0.996269i	$-0.527504\pi$
$281$	4.64648	−	32.3170i	0.277186	−	1.92787i	0.363485	−	0.931600i	$-0.381587\pi$
$282$	10.4989	+	8.23059i	0.625200	+	0.490124i
$283$	−4.25254	+	1.94207i	−0.252787	+	0.115444i	−0.537779	−	0.843086i	$-0.680736\pi$
$283$	−4.25254	+	1.94207i	−0.252787	+	0.115444i	0.284992	+	0.958530i	$0.408009\pi$
$284$	5.50924	−	4.77379i	0.326913	−	0.283272i
$285$	2.27082	+	4.38836i	0.134512	+	0.259944i
$286$	0.450959	+	0.205946i	0.0266658	+	0.0121779i
$287$	−2.18590	+	0.641838i	−0.129030	+	0.0378865i
$288$	−2.44901	−	1.73272i	−0.144309	−	0.102102i
$289$	0.715565	−	1.56687i	0.0420921	−	0.0921688i
$290$	1.44372	+	10.0413i	0.0847781	+	0.589644i
$291$	8.58726	+	4.94045i	0.503394	+	0.289614i
$292$	−4.78809	−	10.4845i	−0.280202	−	0.613557i
$293$	1.86542	−	1.19883i	0.108979	−	0.0700364i	−0.485016	−	0.874505i	$-0.661186\pi$
$293$	1.86542	−	1.19883i	0.108979	−	0.0700364i	0.593995	+	0.804469i	$0.297550\pi$
$294$	−1.96347	−	10.1047i	−0.114512	−	0.589317i
$295$	7.37747	−	11.4796i	0.429533	−	0.668367i
$296$	5.17786	−	5.97557i	0.300957	−	0.347323i
$297$	0.350125	+	0.400358i	0.0203163	+	0.0232311i
$298$			5.47244i			0.317010i
$299$	−20.5910	−	10.7505i	−1.19081	−	0.621718i
$300$	−1.23442	−	3.54913i	−0.0712690	−	0.204909i
$301$	6.04949	+	1.77629i	0.348687	+	0.102384i
$302$	−2.84662	−	2.46661i	−0.163804	−	0.141937i
$303$	−10.3037	−	2.48306i	−0.591935	−	0.142648i
$304$	1.67836	+	0.241312i	0.0962608	+	0.0138402i
$305$	−10.6846	−	16.6255i	−0.611797	−	0.951974i
$306$	5.91303	−	11.5559i	0.338025	−	0.660607i
$307$	9.59763	+	11.0763i	0.547765	+	0.632155i	0.960361	−	0.278759i	$-0.0899232\pi$
$307$	9.59763	+	11.0763i	0.547765	+	0.632155i	−0.412596	+	0.910914i	$0.635378\pi$
$308$	0.104159	−	0.0149759i	0.00593503	−	0.000853328i
$309$	1.59875	−	17.0164i	0.0909494	−	0.968032i
$310$	2.00941	+	6.84343i	0.114127	+	0.388681i
$311$	3.02751	+	10.3107i	0.171674	+	0.584669i	0.999712	+	0.0239966i	$0.00763909\pi$
$311$	3.02751	+	10.3107i	0.171674	+	0.584669i	−0.828038	+	0.560672i	$0.810543\pi$
$312$	0.784728	−	8.35236i	0.0444265	−	0.472859i
$313$	−2.87718	+	0.413675i	−0.162628	+	0.0233823i	−0.223148	−	0.974785i	$-0.571633\pi$
$313$	−2.87718	+	0.413675i	−0.162628	+	0.0233823i	0.0605200	+	0.998167i	$0.480724\pi$
$314$	−1.30999	−	1.51180i	−0.0739268	−	0.0853161i
$315$	2.36367	−	4.61934i	0.133178	−	0.260270i
$316$	7.50495	+	11.6779i	0.422186	+	0.656935i
$317$	24.0748	+	3.46143i	1.35217	+	0.194413i	0.780031	−	0.625741i	$-0.215203\pi$
$317$	24.0748	+	3.46143i	1.35217	+	0.194413i	0.572142	+	0.820154i	$0.306113\pi$
$318$	−17.7018	−	4.26588i	−0.992665	−	0.239219i
$319$	−0.466437	−	0.404170i	−0.0261155	−	0.0226292i
$320$	1.61426	+	0.473990i	0.0902400	+	0.0264969i
$321$	−8.08576	−	23.2477i	−0.451303	−	1.29756i
$322$	−4.91052	+	0.443291i	−0.273653	+	0.0247037i
$323$			7.33688i			0.408235i
$324$	4.45247	−	7.82148i	0.247359	−	0.434527i
$325$	6.88119	−	7.94132i	0.381700	−	0.440505i
$326$	−7.55695	+	11.7588i	−0.418541	+	0.651262i
$327$	1.94429	+	10.0060i	0.107519	+	0.553330i
$328$	1.86419	−	1.19804i	0.102932	−	0.0661506i
$329$	3.28943	+	7.20284i	0.181352	+	0.397106i
$330$	−0.258535	−	0.148741i	−0.0142319	−	0.00818793i
$331$	4.43045	+	30.8145i	0.243520	+	1.69372i	0.634184	+	0.773182i	$0.281336\pi$
$331$	4.43045	+	30.8145i	0.243520	+	1.69372i	−0.390664	+	0.920533i	$0.627755\pi$
$332$	2.27621	−	4.98421i	0.124923	−	0.273544i
$333$	19.3639	+	13.7003i	1.06113	+	0.750774i
$334$	11.4822	−	3.37147i	0.628277	−	0.184479i
$335$	−22.5245	−	10.2866i	−1.23065	−	0.562018i
$336$	−0.818365	−	1.58149i	−0.0446454	−	0.0862775i
$337$	8.30491	−	7.19625i	0.452397	−	0.392005i	−0.398642	−	0.917107i	$-0.630518\pi$
$337$	8.30491	−	7.19625i	0.452397	−	0.392005i	0.851039	+	0.525102i	$0.175973\pi$
$338$	9.51404	−	4.34491i	0.517495	−	0.236332i
$339$	−11.2178	−	8.79416i	−0.609266	−	0.477633i
$340$	−1.03601	+	7.20562i	−0.0561856	+	0.390780i
$341$	−0.365041	−	0.234598i	−0.0197681	−	0.0127042i
$342$	−0.226576	+	5.08182i	−0.0122519	+	0.274793i
$343$	3.74887	−	12.7675i	0.202420	−	0.689379i
$344$	−6.13268			−0.330652
$345$	11.7290	+	7.59838i	0.631469	+	0.409083i
$346$	1.66710			0.0896236
$347$	−9.14891	+	31.1583i	−0.491139	+	1.67267i	0.224721	+	0.974423i	$0.427853\pi$
$347$	−9.14891	+	31.1583i	−0.491139	+	1.67267i	−0.715860	+	0.698244i	$0.753965\pi$
$348$	−3.86683	+	9.70163i	−0.207284	+	0.520062i
$349$	1.33425	+	0.857468i	0.0714206	+	0.0458992i	0.575864	−	0.817546i	$-0.304666\pi$
$349$	1.33425	+	0.857468i	0.0714206	+	0.0458992i	−0.504443	+	0.863445i	$0.668302\pi$
$350$	0.317420	−	2.20770i	0.0169668	−	0.118007i
$351$	25.1672	−	0.114903i	1.34332	−	0.00613307i
$352$	−0.0931067	+	0.0425204i	−0.00496260	+	0.00226634i
$353$	6.14635	−	5.32584i	0.327137	−	0.283466i	−0.475770	−	0.879570i	$-0.657831\pi$
$353$	6.14635	−	5.32584i	0.327137	−	0.283466i	0.802908	+	0.596103i	$0.203285\pi$
$354$	12.4769	−	6.45635i	0.663141	−	0.343151i
$355$	−11.1561	−	5.09482i	−0.592104	−	0.270405i
$356$	−8.66394	+	2.54396i	−0.459188	+	0.134830i
$357$	6.26945	−	4.47885i	0.331814	−	0.237046i
$358$	−4.85596	+	10.6331i	−0.256646	+	0.561975i
$359$	−0.984961	−	6.85055i	−0.0519842	−	0.361558i	−0.999165	−	0.0408580i	$-0.986991\pi$
$359$	−0.984961	−	6.85055i	−0.0519842	−	0.361558i	0.947181	−	0.320700i	$-0.103918\pi$
$360$	−0.940106	+	4.95891i	−0.0495480	+	0.261357i
$361$	6.69851	+	14.6677i	0.352553	+	0.771984i
$362$	21.0809	−	13.5479i	1.10799	−	0.712062i
$363$	−18.6849	+	3.63073i	−0.980705	+	0.190564i
$364$	2.69210	−	4.18900i	0.141105	−	0.219563i
$365$	−12.6988	+	14.6552i	−0.664684	+	0.767086i
$366$	−0.999023	−	20.3213i	−0.0522198	−	1.06221i
$367$		−	4.70919i		−	0.245818i	−0.992418	−	0.122909i	$-0.960778\pi$
$367$		−	4.70919i		−	0.245818i	0.992418	−	0.122909i	$-0.0392223\pi$
$368$	4.46145	−	1.75939i	0.232569	−	0.0917144i
$369$	4.12534	+	5.21306i	0.214756	+	0.271381i
$370$	−12.7637	−	3.74775i	−0.663552	−	0.194836i
$371$	−8.16804	−	7.07765i	−0.424064	−	0.367453i
$372$	−1.72026	+	7.13843i	−0.0891916	+	0.370110i
$373$	8.83662	+	1.27051i	0.457543	+	0.0657847i	0.367233	−	0.930129i	$-0.380305\pi$
$373$	8.83662	+	1.27051i	0.457543	+	0.0657847i	0.0903099	+	0.995914i	$0.471214\pi$
$374$	−0.239445	−	0.372584i	−0.0123814	−	0.0192659i
$375$	−15.0983	+	14.4402i	−0.779675	+	0.745687i
$376$	−5.04383	−	5.82090i	−0.260116	−	0.300190i
$377$	−28.9077	+	4.15630i	−1.48882	+	0.214060i
$378$	4.48079	−	2.90862i	0.230467	−	0.149603i
$379$	−5.62273	−	19.1493i	−0.288820	−	0.983631i	−0.968269	−	0.249909i	$-0.919599\pi$
$379$	−5.62273	−	19.1493i	−0.288820	−	0.983631i	0.679449	−	0.733722i	$-0.262219\pi$
$380$	−0.803709	−	2.73718i	−0.0412294	−	0.140414i
$381$	20.7043	+	1.94523i	1.06071	+	0.0996569i
$382$	−16.5763	+	2.38332i	−0.848119	+	0.121941i
$383$	22.0312	+	25.4253i	1.12574	+	1.29917i	0.949127	+	0.314894i	$0.101969\pi$
$383$	22.0312	+	25.4253i	1.12574	+	1.29917i	0.176614	+	0.984280i	$0.443486\pi$
$384$	1.19716	+	1.25172i	0.0610922	+	0.0638768i
$385$	−0.0957155	−	0.148936i	−0.00487812	−	0.00759050i
$386$	20.9861	+	3.01735i	1.06816	+	0.153579i
$387$	−1.80458	−	18.3093i	−0.0917320	−	0.930715i
$388$	−4.32275	−	3.74569i	−0.219455	−	0.190158i
$389$	26.9591	+	7.91591i	1.36688	+	0.401353i	0.881184	−	0.472774i	$-0.156747\pi$
$389$	26.9591	+	7.91591i	1.36688	+	0.401353i	0.485698	+	0.874127i	$0.338565\pi$
$390$	−13.3307	+	4.63652i	−0.675026	+	0.234780i
$391$	10.2826	+	18.0246i	0.520014	+	0.911543i
$392$			5.94305i			0.300170i
$393$	0.808328	−	0.0397385i	0.0407748	−	0.00200454i
$394$	−14.0799	+	16.2491i	−0.709336	+	0.818618i
$395$	12.6264	−	19.6471i	0.635304	−	0.988552i
$396$	−0.154343	−	0.265461i	−0.00775604	−	0.0133399i
$397$	−9.40607	+	6.04491i	−0.472077	+	0.303385i	−0.754962	−	0.655768i	$-0.772345\pi$
$397$	−9.40607	+	6.04491i	−0.472077	+	0.303385i	0.282885	+	0.959154i	$0.408708\pi$
$398$	0.154396	+	0.338081i	0.00773920	+	0.0169465i
$399$	−1.50570	+	2.61715i	−0.0753795	+	0.131021i
$400$	0.308751	+	2.14741i	0.0154375	+	0.107370i
$401$	−2.81245	+	6.15841i	−0.140447	+	0.307536i	−0.966765	−	0.255668i	$-0.917704\pi$
$401$	−2.81245	+	6.15841i	−0.140447	+	0.307536i	0.826317	+	0.563205i	$0.190432\pi$
$402$	−14.8189	−	20.7433i	−0.739099	−	1.03458i
$403$	−19.7015	+	5.78487i	−0.981400	+	0.288165i
$404$	5.56619	+	2.54200i	0.276928	+	0.126469i
$405$	−15.0816	−	1.34753i	−0.749412	−	0.0669592i
$406$	−4.68494	+	4.05953i	−0.232510	+	0.201471i
$407$	0.736177	−	0.336201i	0.0364909	−	0.0166649i
$408$	−4.62382	+	5.89812i	−0.228913	+	0.292001i
$409$	−1.18146	+	8.21722i	−0.0584193	+	0.406315i	0.939539	+	0.342443i	$0.111254\pi$
$409$	−1.18146	+	8.21722i	−0.0584193	+	0.406315i	−0.997958	+	0.0638728i	$0.979655\pi$
$410$	−3.13633	−	2.01559i	−0.154892	−	0.0995431i
$411$	15.8928	+	6.33448i	0.783935	+	0.312457i
$412$	−2.78006	+	9.46801i	−0.136964	+	0.466455i
$413$	8.33860			0.410315
$414$	6.56552	+	12.8021i	0.322678	+	0.629189i
$415$	−9.21855			−0.452521
$416$	−1.36456	+	4.64728i	−0.0669032	+	0.227851i
$417$	20.0390	+	7.98704i	0.981314	+	0.391127i
$418$	0.146006	+	0.0938325i	0.00714139	+	0.00458950i
$419$	0.368763	−	2.56481i	0.0180153	−	0.125299i	−0.978829	−	0.204679i	$-0.934385\pi$
$419$	0.368763	−	2.56481i	0.0180153	−	0.125299i	0.996844	+	0.0793800i	$0.0252941\pi$
$420$	−1.84832	+	2.35771i	−0.0901889	+	0.115044i
$421$	4.79936	−	2.19179i	0.233907	−	0.106822i	−0.295014	−	0.955493i	$-0.595324\pi$
$421$	4.79936	−	2.19179i	0.233907	−	0.106822i	0.528920	+	0.848671i	$0.322597\pi$
$422$	−5.86745	+	5.08418i	−0.285623	+	0.247494i
$423$	15.8943	−	16.7714i	0.772807	−	0.815452i
$424$	9.56268	+	4.36713i	0.464405	+	0.212086i
$425$	−9.00704	+	2.64470i	−0.436905	+	0.128287i
$426$	−7.33959	−	10.2739i	−0.355604	−	0.497772i
$427$	5.01677	−	10.9852i	0.242779	−	0.531611i
$428$	2.02240	+	14.0661i	0.0977564	+	0.679911i
$429$	0.428209	−	0.744293i	0.0206741	−	0.0359348i
$430$	4.28613	+	9.38531i	0.206695	+	0.452600i
$431$	9.99945	−	6.42626i	0.481656	−	0.309542i	−0.277186	−	0.960816i	$-0.589402\pi$
$431$	9.99945	−	6.42626i	0.481656	−	0.309542i	0.758842	+	0.651275i	$0.225765\pi$
$432$	−3.38479	+	3.94248i	−0.162851	+	0.189683i
$433$	−16.4326	+	25.5697i	−0.789701	+	1.22880i	0.179797	+	0.983704i	$0.442456\pi$
$433$	−16.4326	+	25.5697i	−0.789701	+	1.22880i	−0.969499	+	0.245096i	$0.921181\pi$
$434$	−2.85414	+	3.29385i	−0.137003	+	0.158110i
$435$	17.5497	−	0.862764i	0.841442	−	0.0413664i
$436$		−	5.88499i		−	0.281840i
$437$	−6.59959	−	4.75116i	−0.315701	−	0.227279i
$438$	−18.8557	+	6.55819i	−0.900963	+	0.313362i
$439$	−9.58092	−	2.81321i	−0.457272	−	0.134267i	0.0449808	−	0.998988i	$-0.485677\pi$
$439$	−9.58092	−	2.81321i	−0.457272	−	0.134267i	−0.502253	+	0.864721i	$0.667496\pi$
$440$	0.130144	+	0.112771i	0.00620439	+	0.00537613i
$441$	−17.7432	+	1.74878i	−0.844914	+	0.0832754i
$442$	−20.7442	−	2.98256i	−0.986699	−	0.141866i
$443$	−7.42289	−	11.5502i	−0.352672	−	0.548769i	0.618913	−	0.785460i	$-0.287573\pi$
$443$	−7.42289	−	11.5502i	−0.352672	−	0.548769i	−0.971585	+	0.236691i	$0.923937\pi$
$444$	−9.46571	−	9.89715i	−0.449223	−	0.469698i
$445$	9.94844	+	11.4811i	0.471601	+	0.544257i
$446$	16.1932	−	2.32823i	0.766770	−	0.110245i
$447$	9.43698	+	0.886632i	0.446354	+	0.0419363i
$448$	0.289643	+	0.986434i	0.0136844	+	0.0466046i
$449$	−0.790513	−	2.69224i	−0.0373066	−	0.127055i	0.938734	−	0.344642i	$-0.112000\pi$
$449$	−0.790513	−	2.69224i	−0.0373066	−	0.127055i	−0.976041	+	0.217587i	$0.930181\pi$
$450$	−6.32031	+	1.55367i	−0.297942	+	0.0732409i
$451$	0.224509	−	0.0322795i	0.0105717	−	0.00151998i
$452$	5.38920	+	6.21947i	0.253487	+	0.292539i
$453$	−4.71476	+	4.50923i	−0.221519	+	0.211862i
$454$	−5.19350	−	8.08125i	−0.243743	−	0.379272i
$455$	−8.29225	−	1.19225i	−0.388747	−	0.0558933i
$456$	0.688057	−	2.85517i	0.0322212	−	0.133706i
$457$	30.6167	+	26.5295i	1.43219	+	1.24100i	0.925434	+	0.378908i	$0.123700\pi$
$457$	30.6167	+	26.5295i	1.43219	+	1.24100i	0.506754	+	0.862091i	$0.330845\pi$
$458$	−13.6612	−	4.01129i	−0.638346	−	0.187435i
$459$	−18.9696	−	12.0690i	−0.885427	−	0.563334i
$460$	−5.81063	−	5.59806i	−0.270922	−	0.261011i
$461$		−	5.60337i		−	0.260975i	−0.991450	−	0.130487i	$-0.958346\pi$
$461$		−	5.60337i		−	0.260975i	0.991450	−	0.130487i	$-0.0416542\pi$
$462$	−0.00894955	−	0.182045i	−0.000416371	−	0.00846948i
$463$	−9.18037	+	10.5947i	−0.426648	+	0.492378i	−0.927851	−	0.372952i	$-0.878346\pi$
$463$	−9.18037	+	10.5947i	−0.426648	+	0.492378i	0.501203	+	0.865330i	$0.332891\pi$
$464$	3.25993	−	5.07256i	0.151339	−	0.235488i
$465$	12.1268	−	2.35639i	0.562365	−	0.109275i
$466$	3.63340	−	2.33504i	0.168314	−	0.108169i
$467$	16.5185	+	36.1704i	0.764383	+	1.67376i	0.738644	+	0.674096i	$0.235467\pi$
$467$	16.5185	+	36.1704i	0.764383	+	1.67376i	0.0257390	+	0.999669i	$0.491806\pi$
$468$	−14.2761	−	2.70646i	−0.659915	−	0.125106i
$469$	−2.15345	−	14.9776i	−0.0994370	−	0.691599i
$470$	−5.38302	+	11.7872i	−0.248300	+	0.543702i
$471$	−2.81928	+	2.01407i	−0.129906	+	0.0928037i
$472$	−7.78231	+	2.28509i	−0.358210	+	0.105180i
$473$	−0.570993	−	0.260764i	−0.0262543	−	0.0119899i
$474$	21.3540	−	11.0499i	0.980822	−	0.507540i
$475$	2.78013	−	2.40900i	0.127561	−	0.110532i
$476$	−4.04645	+	1.84795i	−0.185469	+	0.0847008i
$477$	−10.2243	+	29.8348i	−0.468140	+	1.36604i
$478$	1.96980	−	13.7002i	0.0900965	−	0.626635i
$479$	−7.70739	−	4.95324i	−0.352160	−	0.226319i	0.352586	−	0.935780i	$-0.385302\pi$
$479$	−7.70739	−	4.95324i	−0.352160	−	0.226319i	−0.704746	+	0.709460i	$0.748939\pi$
$480$	1.07891	−	2.70693i	0.0492455	−	0.123554i
$481$	10.7893	−	36.7452i	0.491952	−	1.67543i
$482$	11.7720			0.536199
$483$	−0.0311551	+	8.53981i	−0.00141761	+	0.388575i
$484$	10.9895			0.499524
$485$	−2.71114	+	9.23329i	−0.123106	+	0.419262i
$486$	−12.7664	−	8.94531i	−0.579097	−	0.405767i
$487$	16.3164	+	10.4859i	0.739367	+	0.475162i	0.855325	−	0.518092i	$-0.173357\pi$
$487$	16.3164	+	10.4859i	0.739367	+	0.475162i	−0.115958	+	0.993254i	$0.536994\pi$
$488$	−1.67173	+	11.6271i	−0.0756756	+	0.526336i
$489$	19.0532	+	14.9368i	0.861618	+	0.675464i
$490$	9.09510	−	4.15360i	0.410875	−	0.187640i
$491$	7.82690	−	6.78204i	0.353223	−	0.306069i	−0.460117	−	0.887858i	$-0.652193\pi$
$491$	7.82690	−	6.78204i	0.353223	−	0.306069i	0.813340	+	0.581789i	$0.197647\pi$
$492$	−1.76394	−	3.40881i	−0.0795243	−	0.153681i
$493$	23.7328	+	10.8384i	1.06887	+	0.488136i
$494$	7.88003	−	2.31379i	0.354539	−	0.104102i
$495$	−0.298385	+	0.421734i	−0.0134114	+	0.0189555i
$496$	1.76109	−	3.85625i	0.0790754	−	0.173151i
$497$	−1.06657	−	7.41818i	−0.0478423	−	0.332751i
$498$	−8.22626	−	4.73276i	−0.368627	−	0.212080i
$499$	7.88426	+	17.2641i	0.352948	+	0.772848i	0.999946	+	0.0103568i	$0.00329674\pi$
$499$	7.88426	+	17.2641i	0.352948	+	0.772848i	−0.646998	+	0.762491i	$0.723976\pi$
$500$	10.1472	−	6.52123i	0.453798	−	0.291638i
$501$	−3.95364	−	20.3468i	−0.176636	−	0.909026i
$502$	3.30409	−	5.14126i	0.147469	−	0.229466i
$503$	11.8379	−	13.6617i	0.527825	−	0.609143i	−0.427747	−	0.903898i	$-0.640693\pi$
$503$	11.8379	−	13.6617i	0.527825	−	0.609143i	0.955573	+	0.294755i	$0.0952382\pi$
$504$	−2.85980	+	1.15500i	−0.127386	+	0.0514480i
$505$		−	10.2950i		−	0.458120i
$506$	0.490201	+	0.0258919i	0.0217921	+	0.00115104i
$507$	−5.95117	−	17.1105i	−0.264301	−	0.759904i
$508$	−11.5199	−	3.38255i	−0.511114	−	0.150076i
$509$	−17.5241	−	15.1847i	−0.776742	−	0.673051i	0.173406	−	0.984850i	$-0.444523\pi$
$509$	−17.5241	−	15.1847i	−0.776742	−	0.673051i	−0.950148	+	0.311800i	$0.899068\pi$
$510$	12.2579	+	2.95400i	0.542790	+	0.130805i
$511$	−11.7291	−	1.68639i	−0.518863	−	0.0746013i
$512$	−0.540641	−	0.841254i	−0.0238932	−	0.0371785i
$513$	8.72667	+	1.21407i	0.385292	+	0.0536023i
$514$	13.4104	+	15.4764i	0.591508	+	0.682637i
$515$	16.4326	−	2.36265i	0.724106	−	0.104111i
$516$	−0.993603	+	10.5755i	−0.0437409	+	0.465562i
$517$	−0.222108	−	0.756430i	−0.00976829	−	0.0332677i
$518$	−2.29015	−	7.79955i	−0.100624	−	0.342693i
$519$	0.270099	−	2.87483i	0.0118560	−	0.126191i
$520$	8.06577	−	1.15968i	0.353707	−	0.0508555i
$521$	−28.3772	−	32.7490i	−1.24323	−	1.43476i	−0.859361	−	0.511370i	$-0.829138\pi$
$521$	−28.3772	−	32.7490i	−1.24323	−	1.43476i	−0.383865	−	0.923389i	$-0.625407\pi$
$522$	16.1035	+	8.24001i	0.704833	+	0.360656i
$523$	−16.6607	−	25.9245i	−0.728521	−	1.13360i	−0.985907	−	0.167292i	$-0.946498\pi$
$523$	−16.6607	−	25.9245i	−0.728521	−	1.13360i	0.257387	−	0.966309i	$-0.417139\pi$
$524$	−0.462496	−	0.0664969i	−0.0202042	−	0.00290493i
$525$	−3.75566	−	0.905064i	−0.163911	−	0.0395002i
$526$	16.3092	+	14.1320i	0.711114	+	0.616184i
$527$	17.6005	+	5.16796i	0.766688	+	0.225120i
$528$	0.0582396	+	0.167447i	0.00253455	+	0.00728721i
$529$	−22.8720	−	2.42291i	−0.994436	−	0.105344i
$530$		−	17.6867i		−	0.768260i
$531$	−9.11221	−	22.5619i	−0.395436	−	0.979105i
$532$	1.14158	−	1.31745i	0.0494936	−	0.0571186i
$533$	5.80267	−	9.02913i	0.251341	−	0.391095i
$534$	2.98324	+	15.3528i	0.129097	+	0.664379i
$535$	20.1130	−	12.9258i	0.869560	−	0.558832i
$536$	6.11421	+	13.3882i	0.264093	+	0.578284i
$537$	17.5495	+	10.0966i	0.757318	+	0.435702i
$538$	−3.74990	−	26.0811i	−0.161670	−	1.12444i
$539$	−0.252701	+	0.553338i	−0.0108846	+	0.0238340i
$540$	8.39911	+	2.42460i	0.361440	+	0.104338i
$541$	−7.97010	+	2.34023i	−0.342661	+	0.100614i	−0.448535	−	0.893765i	$-0.648054\pi$
$541$	−7.97010	+	2.34023i	−0.342661	+	0.100614i	0.105874	+	0.994380i	$0.466236\pi$
$542$	−14.0659	−	6.42369i	−0.604183	−	0.275921i
$543$	−19.9473	−	38.5482i	−0.856020	−	1.65426i
$544$	3.27009	−	2.83355i	0.140204	−	0.121488i
$545$	−9.00625	+	4.11301i	−0.385785	+	0.176182i
$546$	−6.78757	−	5.32111i	−0.290481	−	0.227722i
$547$	3.61830	−	25.1658i	0.154707	−	1.07601i	−0.753487	−	0.657463i	$-0.771630\pi$
$547$	3.61830	−	25.1658i	0.154707	−	1.07601i	0.908194	−	0.418549i	$-0.137461\pi$
$548$	−8.30965	−	5.34029i	−0.354971	−	0.228126i
$549$	−35.2051	−	1.56964i	−1.50252	−	0.0669908i
$550$	−0.0625619	+	0.213066i	−0.00266765	+	0.00908518i
$551$	−10.2242			−0.435566
$552$	−2.31115	−	7.97863i	−0.0983693	−	0.339593i
$553$	14.2714			0.606880
$554$	2.97058	−	10.1169i	0.126208	−	0.429825i
$555$	−8.53078	+	21.4032i	−0.362111	+	0.908515i
$556$	−10.4775	−	6.73349i	−0.444346	−	0.285564i
$557$	−3.58680	+	24.9467i	−0.151978	+	1.05703i	0.760922	+	0.648843i	$0.224747\pi$
$557$	−3.58680	+	24.9467i	−0.151978	+	1.05703i	−0.912900	+	0.408184i	$0.866162\pi$
$558$	12.0312	+	4.12307i	0.509321	+	0.174544i
$559$	−27.0192	+	12.3393i	−1.14279	+	0.521895i
$560$	1.30718	−	1.13268i	0.0552386	−	0.0478645i
$561$	−0.681299	+	0.352548i	−0.0287645	+	0.0148846i
$562$	29.6989	+	13.5630i	1.25277	+	0.572121i
$563$	−35.0882	+	10.3028i	−1.47879	+	0.434212i	−0.918945	−	0.394386i	$-0.870957\pi$
$563$	−35.0882	+	10.3028i	−1.47879	+	0.434212i	−0.559844	+	0.828598i	$0.689139\pi$
$564$	−10.8551	+	7.75479i	−0.457081	+	0.326535i
$565$	5.75162	−	12.5943i	0.241972	−	0.529846i
$566$	−0.665323	−	4.62742i	−0.0279656	−	0.194505i
$567$	−4.28982	−	8.19817i	−0.180156	−	0.344291i
$568$	3.02828	+	6.63101i	0.127064	+	0.278231i
$569$	18.0839	−	11.6218i	0.758115	−	0.487211i	−0.103590	−	0.994620i	$-0.533033\pi$
$569$	18.0839	−	11.6218i	0.758115	−	0.487211i	0.861705	+	0.507409i	$0.169397\pi$
$570$	−4.85036	+	0.942489i	−0.203159	+	0.0394765i
$571$	−7.47682	+	11.6342i	−0.312895	+	0.486875i	−0.961709	−	0.274073i	$-0.911629\pi$
$571$	−7.47682	+	11.6342i	−0.312895	+	0.486875i	0.648814	+	0.760947i	$0.275265\pi$
$572$	−0.324654	+	0.374671i	−0.0135745	+	0.0156658i
$573$	1.42427	+	28.9713i	0.0594996	+	1.21029i
$574$		−	2.27818i		−	0.0950895i
$575$	3.45377	−	9.81455i	0.144032	−	0.409295i
$576$	2.35250	−	1.86165i	0.0980210	−	0.0775686i
$577$	−36.4284	−	10.6963i	−1.51653	−	0.445295i	−0.585636	−	0.810574i	$-0.699155\pi$
$577$	−36.4284	−	10.6963i	−1.51653	−	0.445295i	−0.930898	+	0.365280i	$0.880973\pi$
$578$	1.30180	+	1.12802i	0.0541478	+	0.0469194i
$579$	8.60340	−	35.7007i	0.357545	−	1.48367i
$580$	−10.0413	−	1.44372i	−0.416942	−	0.0599471i
$581$	−3.04555	−	4.73896i	−0.126351	−	0.196605i
$582$	−7.15964	+	6.84753i	−0.296777	+	0.283839i
$583$	0.704657	+	0.813217i	0.0291839	+	0.0336800i
$584$	11.4087	−	1.64033i	0.472096	−	0.0678772i
$585$	5.83568	+	23.7394i	0.241276	+	0.981503i
$586$	0.624720	+	2.12760i	0.0258070	+	0.0878905i
$587$	−2.78661	−	9.49033i	−0.115016	−	0.391708i	0.881783	−	0.471655i	$-0.156343\pi$
$587$	−2.78661	−	9.49033i	−0.115016	−	0.391708i	−0.996799	+	0.0799470i	$0.974525\pi$
$588$	10.2485	+	0.962880i	0.422643	+	0.0397085i
$589$	−7.11518	+	1.02301i	−0.293176	+	0.0421523i
$590$	8.93610	+	10.3128i	0.367893	+	0.424571i
$591$	25.7397	+	26.9129i	1.05879	+	1.10705i
$592$	4.27475	+	6.65163i	0.175691	+	0.273381i
$593$	0.458775	+	0.0659619i	0.0188396	+	0.00270873i	0.151728	−	0.988422i	$-0.451516\pi$
$593$	0.458775	+	0.0659619i	0.0188396	+	0.00270873i	−0.132889	+	0.991131i	$0.542425\pi$
$594$	−0.482783	+	0.223149i	−0.0198088	+	0.00915591i
$595$	5.65612	+	4.90106i	0.231878	+	0.200924i
$596$	−5.25077	−	1.54176i	−0.215080	−	0.0631531i
$597$	0.608021	−	0.211475i	0.0248847	−	0.00865509i
$598$	16.1162	−	16.7281i	0.659040	−	0.684064i
$599$		−	2.23680i		−	0.0913932i	−0.998955	−	0.0456966i	$-0.985449\pi$
$599$		−	2.23680i		−	0.0913932i	0.998955	−	0.0456966i	$-0.0145507\pi$
$600$	3.75314	−	0.184509i	0.153221	−	0.00753255i
$601$	−4.37348	+	5.04726i	−0.178398	+	0.205882i	−0.837905	−	0.545816i	$-0.816220\pi$
$601$	−4.37348	+	5.04726i	−0.178398	+	0.205882i	0.659507	+	0.751698i	$0.270765\pi$
$602$	−3.40867	+	5.30400i	−0.138927	+	0.216175i
$603$	−38.1719	+	22.1937i	−1.55448	+	0.903799i
$604$	3.16868	−	2.03639i	0.128932	−	0.0828594i
$605$	−7.68057	−	16.8181i	−0.312259	−	0.683753i
$606$	5.28538	−	9.18681i	0.214704	−	0.373189i
$607$	1.19191	+	8.28993i	0.0483782	+	0.336478i	0.999608	+	0.0279948i	$0.00891219\pi$
$607$	1.19191	+	8.28993i	0.0483782	+	0.336478i	−0.951230	+	0.308483i	$0.900179\pi$
$608$	−0.704387	+	1.54239i	−0.0285667	+	0.0625523i
$609$	6.24143	+	8.73670i	0.252916	+	0.354029i
$610$	18.9623	−	5.56782i	0.767759	−	0.225434i
$611$	−33.9339	−	15.4971i	−1.37282	−	0.626946i
$612$	9.42191	+	8.92918i	0.380858	+	0.360941i
$613$	25.3844	−	21.9958i	1.02527	−	0.888400i	0.0314596	−	0.999505i	$-0.489984\pi$
$613$	25.3844	−	21.9958i	1.02527	−	0.888400i	0.993809	+	0.111105i	$0.0354390\pi$
$614$	−13.3315	+	6.08831i	−0.538017	+	0.245704i
$615$	−3.98395	+	5.08190i	−0.160648	+	0.204922i
$616$	−0.0149759	+	0.104159i	−0.000603394	+	0.00419670i
$617$	6.60446	+	4.24443i	0.265886	+	0.170874i	0.666790	−	0.745246i	$-0.267668\pi$
$617$	6.60446	+	4.24443i	0.265886	+	0.170874i	−0.400905	+	0.916120i	$0.631304\pi$
$618$	15.8767	+	6.32807i	0.638656	+	0.254552i
$619$	6.97404	−	23.7514i	0.280310	−	0.954649i	−0.692184	−	0.721721i	$-0.743351\pi$
$619$	6.97404	−	23.7514i	0.280310	−	0.954649i	0.972494	−	0.232928i	$-0.0748306\pi$
$620$	−7.13234			−0.286442
$621$	23.1404	−	9.24779i	0.928592	−	0.371101i
$622$	−10.7460			−0.430877
$623$	−2.61539	+	8.90721i	−0.104784	+	0.356860i
$624$	7.79294	+	3.10607i	0.311967	+	0.124342i
$625$	−7.94636	−	5.10681i	−0.317854	−	0.204273i
$626$	0.413675	−	2.87718i	0.0165338	−	0.114995i
$627$	0.185466	−	0.236579i	0.00740678	−	0.00944805i
$628$	1.81963	−	0.830998i	0.0726112	−	0.0331604i
$629$	−25.8560	+	22.4044i	−1.03095	+	0.893321i
$630$	3.76630	+	3.56934i	0.150053	+	0.142206i
$631$	−22.5499	−	10.2982i	−0.897696	−	0.409964i	−0.0875280	−	0.996162i	$-0.527897\pi$
$631$	−22.5499	−	10.2982i	−0.897696	−	0.409964i	−0.810168	+	0.586198i	$0.800624\pi$
$632$	−13.3193	+	3.91089i	−0.529812	+	0.155567i
$633$	7.81681	+	10.9419i	0.310690	+	0.434901i
$634$	−10.1039	+	22.1244i	−0.401275	+	0.878671i
$635$	2.87468	+	19.9939i	0.114078	+	0.793432i
$636$	9.08025	−	15.7829i	0.360055	−	0.625831i
$637$	11.9577	+	26.1838i	0.473782	+	1.03744i
$638$	0.519209	−	0.333675i	0.0205557	−	0.0132103i
$639$	−18.9060	+	10.9923i	−0.747911	+	0.434847i
$640$	−0.909580	+	1.41533i	−0.0359543	+	0.0559460i
$641$	10.5629	−	12.1902i	0.417208	−	0.481484i	−0.507776	−	0.861489i	$-0.669532\pi$
$641$	10.5629	−	12.1902i	0.417208	−	0.481484i	0.924984	+	0.380005i	$0.124078\pi$
$642$	24.5841	−	1.20858i	0.970255	−	0.0476990i
$643$		−	30.4292i		−	1.20001i	−0.799996	−	0.600005i	$-0.795165\pi$
$643$		−	30.4292i		−	1.20001i	0.799996	−	0.600005i	$-0.204835\pi$
$644$	0.958119	−	4.83650i	0.0377552	−	0.190585i
$645$	16.8790	−	5.87065i	0.664609	−	0.231157i
$646$	−7.03969	−	2.06704i	−0.276973	−	0.0813265i
$647$	19.3372	+	16.7558i	0.760224	+	0.658738i	0.946114	−	0.323833i	$-0.104972\pi$
$647$	19.3372	+	16.7558i	0.760224	+	0.658738i	−0.185891	+	0.982570i	$0.559517\pi$
$648$	6.25025	+	6.47568i	0.245533	+	0.254389i
$649$	−0.821748	−	0.118149i	−0.0322564	−	0.00463777i
$650$	5.68098	+	8.83978i	0.222826	+	0.346725i
$651$	5.21768	+	5.45550i	0.204497	+	0.213818i
$652$	−9.15348	−	10.5637i	−0.358478	−	0.413706i
$653$	−19.7902	+	2.84540i	−0.774449	+	0.111349i	−0.518197	−	0.855261i	$-0.673397\pi$
$653$	−19.7902	+	2.84540i	−0.774449	+	0.111349i	−0.256252	+	0.966610i	$0.582488\pi$
$654$	−10.1484	−	0.953473i	−0.396834	−	0.0372837i
$655$	0.221473	+	0.754268i	0.00865366	+	0.0294717i
$656$	0.624308	+	2.12620i	0.0243751	+	0.0830141i
$657$	8.25435	+	33.5785i	0.322033	+	1.31002i
$658$	−7.83782	+	1.12691i	−0.305550	+	0.0439314i
$659$	29.0804	+	33.5606i	1.13281	+	1.30734i	0.945716	+	0.324994i	$0.105362\pi$
$659$	29.0804	+	33.5606i	1.13281	+	1.30734i	0.187096	+	0.982342i	$0.440092\pi$
$660$	0.215554	−	0.206157i	0.00839042	−	0.00802466i
$661$	2.59155	+	4.03253i	0.100800	+	0.156847i	0.887990	−	0.459863i	$-0.152101\pi$
$661$	2.59155	+	4.03253i	0.100800	+	0.156847i	−0.787190	+	0.616710i	$0.788465\pi$
$662$	−30.8145	−	4.43045i	−1.19764	−	0.172194i
$663$	−8.50422	+	35.2892i	−0.330276	+	1.37052i
$664$	4.14103	+	3.58822i	0.160703	+	0.139250i
$665$	−2.81404	−	0.826276i	−0.109124	−	0.0320416i
$666$	−18.6008	+	14.7197i	−0.720767	+	0.570376i
$667$	−25.1179	+	14.3292i	−0.972569	+	0.554828i
$668$			11.9669i			0.463014i
$669$	−1.39135	−	28.3017i	−0.0537926	−	1.09421i
$670$	16.2158	−	18.7141i	0.626472	−	0.722987i
$671$	−0.650039	+	1.01148i	−0.0250945	+	0.0390478i
$672$	1.74799	−	0.339657i	0.0674302	−	0.0131026i
$673$	29.9188	−	19.2276i	1.15328	−	0.741171i	0.182994	−	0.983114i	$-0.441421\pi$
$673$	29.9188	−	19.2276i	1.15328	−	0.741171i	0.970290	+	0.241943i	$0.0777847\pi$
$674$	4.56498	+	9.99592i	0.175837	+	0.385028i
$675$	1.65524	+	11.1508i	0.0637103	+	0.429195i
$676$	1.48850	+	10.3528i	0.0572501	+	0.398183i
$677$	−6.54304	+	14.3273i	−0.251469	+	0.550641i	−0.992700	−	0.120609i	$-0.961515\pi$
$677$	−6.54304	+	14.3273i	−0.251469	+	0.550641i	0.741231	+	0.671250i	$0.234242\pi$
$678$	11.5984	−	8.28578i	0.445432	−	0.318213i
$679$	−5.64223	+	1.65671i	−0.216529	+	0.0635786i
$680$	−6.62186	−	3.02410i	−0.253937	−	0.115969i
$681$	−14.7772	+	7.64666i	−0.566263	+	0.293021i
$682$	0.327939	−	0.284161i	0.0125574	−	0.0108811i
$683$	45.0288	−	20.5640i	1.72298	−	0.786858i	0.728135	−	0.685433i	$-0.240387\pi$
$683$	45.0288	−	20.5640i	1.72298	−	0.786858i	0.994843	−	0.101424i	$-0.0323400\pi$
$684$	−4.81214	−	1.64911i	−0.183997	−	0.0630554i
$685$	−2.36504	+	16.4492i	−0.0903635	+	0.628492i
$686$	11.1941	+	7.19402i	0.427394	+	0.274669i
$687$	−9.13065	+	22.9083i	−0.348356	+	0.874004i
$688$	1.72778	−	5.88426i	0.0658708	−	0.224335i
$689$	50.9179			1.93982
$690$	−10.5950	+	9.11319i	−0.403346	+	0.346933i
$691$	−11.4429			−0.435308			−0.217654	−	0.976026i	$-0.569840\pi$
$691$	−11.4429			−0.435308			−0.217654	+	0.976026i	$0.569840\pi$
$692$	−0.469675	+	1.59957i	−0.0178544	+	0.0608064i
$693$	−0.315378	−	0.0140613i	−0.0119802	−	0.000534146i
$694$	−27.3187	−	17.5566i	−1.03700	−	0.666441i
$695$	−2.98204	+	20.7406i	−0.113115	+	0.786734i
$696$	−8.21924	−	6.44346i	−0.311549	−	0.244239i
$697$	−8.72188	+	3.98315i	−0.330365	+	0.150873i
$698$	−1.19864	+	1.03862i	−0.0453690	+	0.0393125i
$699$	−3.43801	−	6.64396i	−0.130037	−	0.251298i
$700$	2.02885	+	0.926545i	0.0766833	+	0.0350201i
$701$	14.8215	−	4.35198i	0.559800	−	0.164372i	0.0104214	−	0.999946i	$-0.496683\pi$
$701$	14.8215	−	4.35198i	0.559800	−	0.164372i	0.549378	+	0.835574i	$0.314865\pi$
$702$	−6.98016	+	24.1801i	−0.263449	+	0.912618i
$703$	5.56946	−	12.1954i	0.210056	−	0.459959i
$704$	−0.0145668	−	0.101315i	−0.000549008	−	0.00381844i
$705$	19.4543	+	11.1925i	0.732693	+	0.421535i
$706$	3.37848	+	7.39785i	0.127151	+	0.278422i
$707$	5.29232	−	3.40116i	0.199038	−	0.127914i
$708$	2.67967	+	13.7905i	0.100708	+	0.518278i
$709$	4.02008	−	6.25537i	0.150977	−	0.234925i	−0.757524	−	0.652807i	$-0.773591\pi$
$709$	4.02008	−	6.25537i	0.150977	−	0.234925i	0.908501	+	0.417882i	$0.137227\pi$
$710$	8.03148	−	9.26882i	0.301416	−	0.347852i
$711$	−15.5954	−	38.6144i	−0.584873	−	1.44815i
$712$		−	9.02971i		−	0.338403i
$713$	−16.0462	+	12.4851i	−0.600935	+	0.467572i
$714$	2.53112	+	7.27733i	0.0947247	+	0.272347i
$715$	0.800287	+	0.234985i	0.0299290	+	0.00878796i
$716$	−8.83428	−	7.65494i	−0.330152	−	0.286079i
$717$	−23.3063	−	5.61651i	−0.870391	−	0.209753i
$718$	6.85055	+	0.984961i	0.255660	+	0.0367584i
$719$	8.35006	+	12.9929i	0.311405	+	0.484555i	0.961313	−	0.275457i	$-0.0888293\pi$
$719$	8.35006	+	12.9929i	0.311405	+	0.484555i	−0.649909	+	0.760012i	$0.725193\pi$
$720$	−4.49318	−	2.29911i	−0.167451	−	0.0856828i
$721$	6.64342	+	7.66692i	0.247414	+	0.285531i
$722$	−15.9607	+	2.29481i	−0.593997	+	0.0854039i
$723$	1.90727	−	20.3003i	0.0709321	−	0.754975i
$724$	7.05993	+	24.0439i	0.262380	+	0.893584i
$725$	−3.68549	−	12.5516i	−0.136876	−	0.466155i
$726$	1.78050	−	18.9510i	0.0660805	−	0.703336i
$727$	24.5659	−	3.53204i	0.911099	−	0.130996i	0.329203	−	0.944259i	$-0.393220\pi$
$727$	24.5659	−	3.53204i	0.911099	−	0.130996i	0.581896	+	0.813263i	$0.302311\pi$
$728$	3.26086	+	3.76323i	0.120855	+	0.139475i
$729$	−17.4942	+	20.5658i	−0.647933	+	0.761698i
$730$	−10.4839	−	16.3132i	−0.388025	−	0.603779i
$731$	26.2657	+	3.77644i	0.971473	+	0.139677i
$732$	19.7796	+	4.76663i	0.731076	+	0.176180i
$733$	−3.96930	−	3.43942i	−0.146610	−	0.127038i	0.578468	−	0.815705i	$-0.303651\pi$
$733$	−3.96930	−	3.43942i	−0.146610	−	0.127038i	−0.725078	+	0.688667i	$0.758196\pi$
$734$	4.51843	+	1.32673i	0.166778	+	0.0489706i
$735$	−5.68913	−	16.3571i	−0.209847	−	0.603340i
$736$	0.431184	+	4.77641i	0.0158937	+	0.176061i
$737$			1.50651i			0.0554931i
$738$	−6.16413	+	2.48954i	−0.226905	+	0.0916413i
$739$	−2.04564	+	2.36080i	−0.0752502	+	0.0868434i	−0.792126	−	0.610357i	$-0.791026\pi$
$739$	−2.04564	+	2.36080i	−0.0752502	+	0.0868434i	0.716876	+	0.697201i	$0.245571\pi$
$740$	7.19188	−	11.1908i	0.264379	−	0.411382i
$741$	−2.71332	−	13.9636i	−0.0996762	−	0.512967i
$742$	9.09216	−	5.84318i	0.333784	−	0.214510i
$743$	−7.60500	−	16.6526i	−0.279000	−	0.610926i	0.717309	−	0.696755i	$-0.245373\pi$
$743$	−7.60500	−	16.6526i	−0.279000	−	0.610926i	−0.996310	+	0.0858289i	$0.972646\pi$
$744$	−6.36462	−	3.66171i	−0.233338	−	0.134245i
$745$	1.31028	+	9.11318i	0.0480049	+	0.333881i
$746$	−3.70861	+	8.12073i	−0.135782	+	0.297321i
$747$	−9.49423	+	13.4190i	−0.347376	+	0.490977i
$748$	0.424951	−	0.124777i	0.0155378	−	0.00456230i
$749$	13.2895	+	6.06912i	0.485588	+	0.221761i
$750$	−9.60154	−	18.5550i	−0.350599	−	0.677533i
$751$	19.7209	−	17.0883i	0.719626	−	0.623559i	−0.216066	−	0.976379i	$-0.569323\pi$
$751$	19.7209	−	17.0883i	0.719626	−	0.623559i	0.935691	+	0.352820i	$0.114777\pi$
$752$	7.00612	−	3.19959i	0.255487	−	0.116677i
$753$	−8.33056	−	6.53073i	−0.303582	−	0.237993i
$754$	4.15630	−	28.9077i	0.151364	−	1.05276i
$755$	−5.33102	−	3.42604i	−0.194016	−	0.124686i
$756$	1.52842	+	5.11874i	0.0555880	+	0.186167i
$757$	5.09428	−	17.3495i	0.185155	−	0.630580i	−0.813634	−	0.581378i	$-0.802514\pi$
$757$	5.09428	−	17.3495i	0.185155	−	0.630580i	0.998789	−	0.0492022i	$-0.0156679\pi$
$758$	19.9577			0.724895
$759$	0.124071	−	0.841135i	0.00450348	−	0.0305313i
$760$	2.85274			0.103480
$761$	13.2516	−	45.1307i	0.480370	−	1.63599i	−0.261325	−	0.965251i	$-0.584160\pi$
$761$	13.2516	−	45.1307i	0.480370	−	1.63599i	0.741695	−	0.670738i	$-0.234022\pi$
$762$	−7.69949	+	19.3176i	−0.278923	+	0.699801i
$763$	−5.08978	−	3.27100i	−0.184262	−	0.118418i
$764$	2.38332	−	16.5763i	0.0862254	−	0.599711i
$765$	7.08004	−	20.6597i	0.255979	−	0.746952i
$766$	−30.6023	+	13.9756i	−1.10571	+	0.504960i
$767$	−29.6894	+	25.7260i	−1.07202	+	0.928912i
$768$	−1.53830	+	0.796014i	−0.0555086	+	0.0287237i
$769$	6.32838	+	2.89007i	0.228207	+	0.104219i	0.526237	−	0.850338i	$-0.323602\pi$
$769$	6.32838	+	2.89007i	0.228207	+	0.104219i	−0.298030	+	0.954556i	$0.596330\pi$
$770$	0.169870	−	0.0498782i	0.00612167	−	0.00179749i
$771$	28.8612	−	20.6182i	1.03941	−	0.742547i
$772$	−8.80759	+	19.2859i	−0.316992	+	0.694116i
$773$	1.93188	+	13.4365i	0.0694850	+	0.483279i	0.994616	+	0.103630i	$0.0330459\pi$
$773$	1.93188	+	13.4365i	0.0694850	+	0.483279i	−0.925131	+	0.379648i	$0.876045\pi$
$774$	18.0761	+	3.42685i	0.649731	+	0.123176i
$775$	−3.82067	−	8.36611i	−0.137243	−	0.300520i
$776$	4.81182	−	3.09237i	0.172734	−	0.111010i
$777$	−13.8210	+	2.68561i	−0.495827	+	0.0963456i
$778$	−15.1905	+	23.6369i	−0.544607	+	0.847425i
$779$	2.46060	−	2.83968i	0.0881600	−	0.101742i
$780$	−0.693025	−	14.0970i	−0.0248143	−	0.504752i
$781$			0.746155i			0.0266995i
$782$	−20.1914	+	4.78799i	−0.722044	+	0.171218i
$783$	16.8186	−	26.4348i	0.601048	−	0.944704i
$784$	−5.70232	−	1.67435i	−0.203654	−	0.0597983i
$785$	−2.54348	−	2.20394i	−0.0907806	−	0.0786618i
$786$	−0.189604	+	0.786781i	−0.00676294	+	0.0280635i
$787$	−4.53843	−	0.652528i	−0.161778	−	0.0232601i	0.0609501	−	0.998141i	$-0.480587\pi$
$787$	−4.53843	−	0.652528i	−0.161778	−	0.0232601i	−0.222728	+	0.974881i	$0.571496\pi$
$788$	−11.6241	−	18.0875i	−0.414092	−	0.644340i
$789$	27.0124	−	25.8348i	0.961666	−	0.919745i
$790$	15.2940	+	17.6502i	0.544135	+	0.627965i
$791$	8.37450	−	1.20407i	0.297763	−	0.0428118i
$792$	0.298192	−	0.0733023i	0.0105958	−	0.00260468i
$793$	16.0291	+	54.5902i	0.569211	+	1.93855i
$794$	−3.15006	−	10.7281i	−0.111791	−	0.380726i
$795$	−30.4999	−	2.86555i	−1.08172	−	0.101631i
$796$	−0.367885	+	0.0528939i	−0.0130393	+	0.00187477i
$797$	11.2080	+	12.9347i	0.397008	+	0.458172i	0.918696	−	0.394964i	$-0.129243\pi$
$797$	11.2080	+	12.9347i	0.397008	+	0.458172i	−0.521688	+	0.853136i	$0.674698\pi$
$798$	−2.08693	−	2.18205i	−0.0738764	−	0.0772436i
$799$	18.0179	+	28.0363i	0.637426	+	0.991854i
$800$	−2.14741	−	0.308751i	−0.0759224	−	0.0109160i
$801$	26.9585	−	2.65705i	0.952532	−	0.0938823i
$802$	−5.11659	−	4.43355i	−0.180673	−	0.156554i
$803$	1.13198	+	0.332378i	0.0399466	+	0.0117294i
$804$	24.0781	−	8.37455i	0.849167	−	0.295348i
$805$	−8.07129	+	1.91394i	−0.284476	+	0.0674577i
$806$		−	20.5332i		−	0.723251i
$807$	−45.5833	+	2.24094i	−1.60461	+	0.0788847i
$808$	−4.00720	+	4.62456i	−0.140973	+	0.162691i
$809$	−17.3425	+	26.9854i	−0.609729	+	0.948756i	0.389882	+	0.920865i	$0.372516\pi$
$809$	−17.3425	+	26.9854i	−0.609729	+	0.948756i	−0.999611	+	0.0278917i	$0.991121\pi$
$810$	5.54193	−	14.0911i	0.194724	−	0.495110i
$811$	−12.7751	+	8.21008i	−0.448596	+	0.288295i	−0.745368	−	0.666653i	$-0.767726\pi$
$811$	−12.7751	+	8.21008i	−0.448596	+	0.288295i	0.296772	+	0.954948i	$0.404090\pi$
$812$	−2.57519	−	5.63887i	−0.0903713	−	0.197886i
$813$	−13.3563	+	23.2153i	−0.468426	+	0.814197i
$814$	0.115177	+	0.801075i	0.00403696	+	0.0280777i
$815$	−9.76904	+	21.3912i	−0.342195	+	0.749302i
$816$	−4.35652	−	6.09822i	−0.152509	−	0.213480i
$817$	−9.97749	+	2.92966i	−0.349068	+	0.102496i
$818$	−7.55151	−	3.44866i	−0.264032	−	0.120580i
$819$	−10.2757	+	10.8428i	−0.359063	+	0.378877i
$820$	2.81755	−	2.44142i	0.0983933	−	0.0852583i
$821$	−16.8460	+	7.69331i	−0.587929	+	0.268498i	−0.687089	−	0.726573i	$-0.741112\pi$
$821$	−16.8460	+	7.69331i	−0.587929	+	0.268498i	0.0991597	+	0.995072i	$0.468385\pi$
$822$	−10.5554	+	13.4644i	−0.368162	+	0.469625i
$823$	−2.67278	+	18.5896i	−0.0931674	+	0.647994i	0.888709	+	0.458472i	$0.151603\pi$
$823$	−2.67278	+	18.5896i	−0.0931674	+	0.647994i	−0.981876	+	0.189522i	$0.939306\pi$
$824$	−8.30125	−	5.33489i	−0.289188	−	0.185850i
$825$	0.357287	+	0.142406i	0.0124391	+	0.00495793i
$826$	−2.34925	+	8.00082i	−0.0817410	+	0.278384i
$827$	12.9030			0.448680			0.224340	−	0.974511i	$-0.427977\pi$
$827$	12.9030			0.448680			0.224340	+	0.974511i	$0.427977\pi$
$828$	−14.1333	+	2.69281i	−0.491164	+	0.0935814i
$829$	−14.7238			−0.511379			−0.255689	−	0.966759i	$-0.582302\pi$
$829$	−14.7238			−0.511379			−0.255689	+	0.966759i	$0.582302\pi$
$830$	2.59716	−	8.84513i	0.0901489	−	0.307019i
$831$	−16.9648	−	6.76176i	−0.588504	−	0.234563i
$832$	−4.07459	−	2.61858i	−0.141261	−	0.0907829i
$833$	3.65967	−	25.4536i	0.126800	−	0.881914i
$834$	−13.3092	+	16.9771i	−0.460858	+	0.587868i
$835$	18.3139	−	8.36367i	0.633778	−	0.289437i
$836$	−0.131166	+	0.113656i	−0.00453648	+	0.00393088i
$837$	9.05933	−	20.0793i	0.313136	−	0.694041i
$838$	2.35702	+	1.07642i	0.0814219	+	0.0371841i
$839$	−11.2000	+	3.28862i	−0.386667	+	0.113536i	−0.469288	−	0.883045i	$-0.655489\pi$
$839$	−11.2000	+	3.28862i	−0.386667	+	0.113536i	0.0826206	+	0.996581i	$0.473671\pi$
$840$	−1.74147	−	2.43770i	−0.0600865	−	0.0841085i
$841$	−3.05663	+	6.69309i	−0.105401	+	0.230796i
$842$	0.750875	+	5.22245i	0.0258769	+	0.179978i
$843$	28.2006	−	49.0169i	0.971279	−	1.68823i
$844$	−3.22518	−	7.06216i	−0.111015	−	0.243090i
$845$	14.8033	−	9.51350i	0.509249	−	0.327274i
$846$	11.6141	+	19.9755i	0.399300	+	0.686772i
$847$	6.10821	−	9.50456i	0.209881	−	0.326581i
$848$	−6.88435	+	7.94496i	−0.236409	+	0.272831i
$849$	−8.08758	+	0.397596i	−0.277565	+	0.0136455i
$850$		−	9.38729i		−	0.321981i
$851$	−3.40929	−	37.7662i	−0.116869	−	1.29461i
$852$	11.9255	−	4.14780i	0.408562	−	0.142101i
$853$	12.8931	+	3.78576i	0.441451	+	0.129622i	0.494902	−	0.868949i	$-0.335204\pi$
$853$	12.8931	+	3.78576i	0.441451	+	0.129622i	−0.0534509	+	0.998570i	$0.517022\pi$
$854$	9.12683	+	7.90845i	0.312314	+	0.270621i
$855$	0.839436	+	8.51694i	0.0287081	+	0.291273i
$856$	−14.0661	−	2.02240i	−0.480770	−	0.0691242i
$857$	5.50648	+	8.56826i	0.188098	+	0.292686i	0.922476	−	0.386055i	$-0.126162\pi$
$857$	5.50648	+	8.56826i	0.188098	+	0.292686i	−0.734378	+	0.678741i	$0.762526\pi$
$858$	0.593504	+	0.620555i	0.0202619	+	0.0211854i
$859$	−23.3397	−	26.9355i	−0.796341	−	0.919027i	0.201834	−	0.979420i	$-0.435310\pi$
$859$	−23.3397	−	26.9355i	−0.796341	−	0.919027i	−0.998175	+	0.0603933i	$0.980765\pi$
$860$	−10.2127	+	1.46836i	−0.348249	+	0.0500707i
$861$	−3.92863	−	0.369106i	−0.133887	−	0.0125791i
$862$	3.34878	+	11.4049i	0.114060	+	0.388452i
$863$	1.52467	+	5.19254i	0.0519002	+	0.176756i	0.981364	−	0.192157i	$-0.0615482\pi$
$863$	1.52467	+	5.19254i	0.0519002	+	0.176756i	−0.929464	+	0.368913i	$0.879730\pi$
$864$	−2.82918	−	4.35841i	−0.0962507	−	0.148276i
$865$	2.77619	−	0.399156i	0.0943934	−	0.0135717i
$866$	−19.9043	−	22.9708i	−0.676376	−	0.780579i
$867$	2.15613	−	2.06214i	0.0732261	−	0.0700340i
$868$	−2.35632	−	3.66651i	−0.0799789	−	0.124450i
$869$	−1.40641	−	0.202211i	−0.0477091	−	0.00685953i
$870$	−4.11650	+	17.0818i	−0.139562	+	0.579129i
$871$	53.8756	+	46.6835i	1.82551	+	1.58181i
$872$	5.64661	+	1.65799i	0.191218	+	0.0561467i
$873$	10.6483	+	13.4559i	0.360390	+	0.455413i
$874$	6.41803	−	4.99371i	0.217093	−	0.168915i
$875$		−	12.4007i		−	0.419221i
$876$	−0.980257	−	19.9396i	−0.0331198	−	0.673697i
$877$	−14.4567	+	16.6840i	−0.488169	+	0.563378i	−0.945376	−	0.325983i	$-0.894305\pi$
$877$	−14.4567	+	16.6840i	−0.488169	+	0.563378i	0.457206	+	0.889361i	$0.348850\pi$
$878$	5.39852	−	8.40025i	0.182191	−	0.283495i
$879$	3.77017	−	0.732594i	0.127165	−	0.0247098i
$880$	−0.144869	+	0.0931014i	−0.00488352	+	0.00313845i
$881$	−10.4323	−	22.8435i	−0.351473	−	0.769618i	−0.999965	−	0.00839660i	$-0.997327\pi$
$881$	−10.4323	−	22.8435i	−0.351473	−	0.769618i	0.648492	−	0.761222i	$-0.275400\pi$
$882$	3.32089	−	17.5172i	0.111820	−	0.589833i
$883$	−6.20267	−	43.1406i	−0.208737	−	1.45180i	−0.777287	−	0.629147i	$-0.783405\pi$
$883$	−6.20267	−	43.1406i	−0.208737	−	1.45180i	0.568550	−	0.822649i	$-0.307505\pi$
$884$	8.70605	−	19.0636i	0.292816	−	0.641178i
$885$	19.2318	−	13.7391i	0.646470	−	0.461833i
$886$	13.1737	−	3.86813i	0.442578	−	0.129952i
$887$	1.16036	+	0.529920i	0.0389612	+	0.0177930i	0.434800	−	0.900527i	$-0.356819\pi$
$887$	1.16036	+	0.529920i	0.0389612	+	0.0177930i	−0.395839	+	0.918320i	$0.629546\pi$
$888$	12.1630	−	6.29393i	0.408165	−	0.211211i
$889$	−9.32850	+	8.08319i	−0.312868	+	0.271101i
$890$	−13.8188	+	6.31085i	−0.463209	+	0.211540i
$891$	0.306591	+	0.868692i	0.0102712	+	0.0291023i
$892$	−2.32823	+	16.1932i	−0.0779550	+	0.542189i
$893$	−10.9867	−	7.06074i	−0.367657	−	0.236279i
$894$	−3.50942	+	8.80493i	−0.117373	+	0.294481i
$895$	−5.54067	+	18.8698i	−0.185204	+	0.630748i
$896$	−1.02808			−0.0343457
$897$	−26.2358	−	30.5019i	−0.875989	−	1.01843i
$898$	2.80590			0.0936340
$899$	−7.20173	+	24.5269i	−0.240191	+	0.818016i
$900$	0.289897	−	6.50201i	0.00966322	−	0.216734i
$901$	−38.2669	−	24.5926i	−1.27485	−	0.819299i
$902$	−0.0322795	+	0.224509i	−0.00107479	+	0.00747534i
$903$	8.59425	+	6.73745i	0.285999	+	0.224208i
$904$	−7.48585	+	3.41867i	−0.248976	+	0.113703i
$905$	31.8620	−	27.6086i	1.05913	−	0.917741i
$906$	−2.99828	−	5.79418i	−0.0996111	−	0.192499i
$907$	38.3590	+	17.5180i	1.27369	+	0.581674i	0.933464	−	0.358670i	$-0.116770\pi$
$907$	38.3590	+	17.5180i	1.27369	+	0.581674i	0.340225	+	0.940344i	$0.389497\pi$
$908$	9.21708	−	2.70638i	0.305879	−	0.0898143i
$909$	−14.9859	−	10.6028i	−0.497052	−	0.351674i
$910$	3.48015	−	7.62046i	0.115366	−	0.252616i
$911$	−0.466916	−	3.24747i	−0.0154696	−	0.107594i	0.980624	−	0.195901i	$-0.0627632\pi$
$911$	−0.466916	−	3.24747i	−0.0154696	−	0.107594i	−0.996093	+	0.0883077i	$0.971854\pi$
$912$	2.54567	+	1.46458i	0.0842954	+	0.0484971i
$913$	0.232985	+	0.510165i	0.00771067	+	0.0168840i
$914$	−34.0806	+	21.9023i	−1.12729	+	0.724463i
$915$	−6.52924	−	33.6017i	−0.215850	−	1.11084i
$916$	7.69761	−	11.9777i	0.254336	−	0.395755i
$917$	−0.314577	+	0.363041i	−0.0103882	+	0.0119887i
$918$	16.9245	−	14.8010i	0.558592	−	0.488506i
$919$			50.8788i			1.67834i	0.543872	+	0.839168i	$0.316958\pi$
$919$			50.8788i			1.67834i	−0.543872	+	0.839168i	$0.683042\pi$
$920$	7.00834	−	3.99810i	0.231058	−	0.131814i
$921$	8.33909	+	23.9761i	0.274782	+	0.790039i
$922$	5.37639	+	1.57865i	0.177062	+	0.0519901i
$923$	26.6839	+	23.1217i	0.878310	+	0.761060i
$924$	0.177192	+	0.0427009i	0.00582919	+	0.00140476i
$925$	16.9792	+	2.44123i	0.558271	+	0.0802673i
$926$	−7.57914	−	11.7934i	−0.249066	−	0.387554i
$927$	13.4848	−	26.3535i	0.442899	−	0.865562i
$928$	3.94865	+	4.55699i	0.129621	+	0.149590i
$929$	20.0276	−	2.87953i	0.657084	−	0.0944744i	0.194295	−	0.980943i	$-0.437758\pi$
$929$	20.0276	−	2.87953i	0.657084	−	0.0944744i	0.462789	+	0.886469i	$0.346849\pi$
$930$	−1.15557	+	12.2994i	−0.0378925	+	0.403314i
$931$	2.83907	+	9.66898i	0.0930467	+	0.316888i
$932$	1.21681	+	4.14408i	0.0398580	+	0.135744i
$933$	−1.74105	+	18.5311i	−0.0569994	+	0.606680i
$934$	−39.3590	+	5.65897i	−1.28787	+	0.185167i
$935$	−0.487954	−	0.563128i	−0.0159578	−	0.0184163i
$936$	6.61888	−	12.9354i	0.216345	−	0.422805i
$937$	−24.5665	−	38.2263i	−0.802554	−	1.24880i	−0.965044	−	0.262088i	$-0.915589\pi$
$937$	−24.5665	−	38.2263i	−0.802554	−	1.24880i	0.162490	−	0.986710i	$-0.448047\pi$
$938$	14.9776	+	2.15345i	0.489035	+	0.0703126i
$939$	−4.89454	−	1.17952i	−0.159727	−	0.0384921i
$940$	−9.79314	−	8.48581i	−0.319417	−	0.276776i
$941$	−56.5694	−	16.6103i	−1.84411	−	0.541479i	−0.999986	−	0.00533093i	$-0.998303\pi$
$941$	−56.5694	−	16.6103i	−1.84411	−	0.541479i	−0.844124	−	0.536148i	$-0.819879\pi$
$942$	−1.13821	−	3.27251i	−0.0370848	−	0.106624i
$943$	2.06517	−	10.4248i	0.0672511	−	0.339478i
$944$		−	8.11085i		−	0.263986i
$945$	6.76538	−	5.91653i	0.220078	−	0.192465i
$946$	0.411069	−	0.474399i	0.0133650	−	0.0154240i
$947$	−3.00007	+	4.66820i	−0.0974891	+	0.151696i	−0.886572	−	0.462591i	$-0.846920\pi$
$947$	−3.00007	+	4.66820i	−0.0974891	+	0.151696i	0.789083	+	0.614287i	$0.210556\pi$
$948$	4.58621	+	23.6022i	0.148953	+	0.766562i
$949$	46.9639	−	30.1819i	1.52451	−	0.979744i
$950$	1.52816	+	3.34621i	0.0495801	+	0.108565i
$951$	36.5155	+	21.0082i	1.18410	+	0.681238i
$952$	−0.633080	−	4.40317i	−0.0205183	−	0.142708i
$953$	−2.67821	+	5.86446i	−0.0867558	+	0.189969i	−0.948037	−	0.318160i	$-0.896935\pi$
$953$	−2.67821	+	5.86446i	−0.0867558	+	0.189969i	0.861281	+	0.508128i	$0.169662\pi$
$954$	−25.7457	−	18.2156i	−0.833548	−	0.589752i
$955$	−27.0337	+	7.93782i	−0.874791	+	0.256862i
$956$	12.5903	+	5.74981i	0.407201	+	0.185962i
$957$	−0.491287	−	0.949414i	−0.0158811	−	0.0306902i
$958$	6.92402	−	5.99970i	0.223705	−	0.193842i
$959$	−9.23736	+	4.21856i	−0.298290	+	0.136224i
$960$	2.29332	+	1.79784i	0.0740164	+	0.0580251i
$961$	1.85406	−	12.8953i	0.0598083	−	0.415976i
$962$	32.2170	+	20.7046i	1.03872	+	0.667543i
$963$	1.89890	−	42.5899i	0.0611913	−	1.37244i
$964$	−3.31655	+	11.2951i	−0.106819	+	0.363792i
$965$	35.6703			1.14827
$966$	−8.18511	−	2.43583i	−0.263351	−	0.0783717i
$967$	−29.5117			−0.949033			−0.474516	−	0.880247i	$-0.657377\pi$
$967$	−29.5117			−0.949033			−0.474516	+	0.880247i	$0.657377\pi$
$968$	−3.09611	+	10.5444i	−0.0995126	+	0.338909i
$969$	−4.70507	+	11.8047i	−0.151149	+	0.379223i
$970$	−8.09546	−	5.20264i	−0.259930	−	0.167047i
$971$	1.43939	−	10.0111i	0.0461921	−	0.321273i	−0.953604	−	0.301065i	$-0.902658\pi$
$971$	1.43939	−	10.0111i	0.0461921	−	0.321273i	0.999796	−	0.0202083i	$-0.00643294\pi$
$972$	12.1797	−	9.72910i	0.390663	−	0.312061i
$973$	−11.6472	+	5.31912i	−0.373394	+	0.170523i
$974$	−14.6580	+	12.7013i	−0.469674	+	0.406975i
$975$	16.1642	−	8.36441i	0.517670	−	0.267875i
$976$	−10.6852	−	4.87976i	−0.342024	−	0.156197i
$977$	33.1589	−	9.73634i	1.06085	−	0.311493i	0.295656	−	0.955295i	$-0.404462\pi$
$977$	33.1589	−	9.73634i	1.06085	−	0.311493i	0.765193	+	0.643802i	$0.222644\pi$
$978$	−19.6996	+	14.0733i	−0.629925	+	0.450014i
$979$	0.383947	−	0.840726i	0.0122710	−	0.0268697i
$980$	1.42296	+	9.89689i	0.0454547	+	0.316145i
$981$	−3.28844	+	17.3460i	−0.104992	+	0.553816i
$982$	4.30223	+	9.42057i	0.137290	+	0.300623i
$983$	−31.3429	+	20.1429i	−0.999684	+	0.642458i	−0.934703	−	0.355429i	$-0.884335\pi$
$983$	−31.3429	+	20.1429i	−0.999684	+	0.642458i	−0.0649805	+	0.997887i	$0.520699\pi$
$984$	3.76769	−	0.732111i	0.120109	−	0.0233388i
$985$	−19.5566	+	30.4306i	−0.623124	+	0.969600i
$986$	−17.0856	+	19.7179i	−0.544118	+	0.627945i
$987$	0.673439	+	13.6986i	0.0214358	+	0.436030i
$988$			8.21270i			0.261281i
$989$	−20.4059	+	21.1807i	−0.648870	+	0.673509i
$990$	−0.320586	−	0.405114i	−0.0101889	−	0.0128754i
$991$	6.86845	+	2.01676i	0.218183	+	0.0640644i	0.388997	−	0.921239i	$-0.372822\pi$
$991$	6.86845	+	2.01676i	0.218183	+	0.0640644i	−0.170814	+	0.985303i	$0.554640\pi$
$992$	3.20389	+	2.77619i	0.101724	+	0.0881441i
$993$	−12.6326	+	52.4204i	−0.400884	+	1.66351i
$994$	7.41818	+	1.06657i	0.235290	+	0.0338296i
$995$	0.338062	+	0.526035i	0.0107173	+	0.0166764i
$996$	6.85865	−	6.55967i	0.217325	−	0.207851i
$997$	−29.3334	−	33.8525i	−0.928998	−	1.07212i	−0.997225	−	0.0744508i	$-0.976280\pi$
$997$	−29.3334	−	33.8525i	−0.928998	−	1.07212i	0.0682269	−	0.997670i	$-0.478266\pi$
$998$	−18.7861	+	2.70103i	−0.594662	+	0.0854995i
$999$	22.3698	+	34.4611i	0.707749	+	1.09030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.5.4	✓	80
3.2	odd	2	inner	138.2.f.a.5.5	yes	80
23.14	odd	22	inner	138.2.f.a.83.5	yes	80
69.14	even	22	inner	138.2.f.a.83.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.5.4	✓	80	1.1	even	1	trivial
138.2.f.a.5.5	yes	80	3.2	odd	2	inner
138.2.f.a.83.4	yes	80	69.14	even	22	inner
138.2.f.a.83.5	yes	80	23.14	odd	22	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281733 + 0.959493i) q^{2} +(1.60896 + 0.641290i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.239432 + 1.66529i) q^{5} +(-1.06861 + 1.36311i) q^{6} +(-0.935173 + 0.427079i) q^{7} +(0.755750 - 0.654861i) q^{8} +(2.17749 + 2.06362i) q^{9} +O(q^{10})\)	\(q+(-0.281733 + 0.959493i) q^{2} +(1.60896 + 0.641290i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.239432 + 1.66529i) q^{5} +(-1.06861 + 1.36311i) q^{6} +(-0.935173 + 0.427079i) q^{7} +(0.755750 - 0.654861i) q^{8} +(2.17749 + 2.06362i) q^{9} +(-1.53038 - 0.698899i) q^{10} +(0.0982102 - 0.0288371i) q^{11} +(-1.00683 - 1.40936i) q^{12} +(2.01205 - 4.40578i) q^{13} +(-0.146311 - 1.01761i) q^{14} +(-1.45317 + 2.52583i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-3.64007 + 2.33933i) q^{17} +(-2.59350 + 1.50790i) q^{18} +(0.916723 - 1.42645i) q^{19} +(1.10175 - 1.27148i) q^{20} +(-1.77854 + 0.0874352i) q^{21} +0.102356i q^{22} +(0.252958 - 4.78916i) q^{23} +(1.63593 - 0.568989i) q^{24} +(2.08161 + 0.611216i) q^{25} +(3.66045 + 3.17180i) q^{26} +(2.18012 + 4.71668i) q^{27} +(1.01761 + 0.146311i) q^{28} +(-3.25993 - 5.07256i) q^{29} +(-2.01411 - 2.10591i) q^{30} +(-2.77619 - 3.20389i) q^{31} +(-0.989821 + 0.142315i) q^{32} +(0.176509 + 0.0165835i) q^{33} +(-1.21904 - 4.15168i) q^{34} +(-0.487299 - 1.65959i) q^{35} +(-0.716147 - 2.91327i) q^{36} +(7.82633 - 1.12526i) q^{37} +(1.11040 + 1.28147i) q^{38} +(6.06269 - 5.79840i) q^{39} +(0.909580 + 1.41533i) q^{40} +(2.19341 + 0.315364i) q^{41} +(0.417178 - 1.73113i) q^{42} +(-4.63477 - 4.01605i) q^{43} +(-0.0982102 - 0.0288371i) q^{44} +(-3.95788 + 3.13205i) q^{45} +(4.52389 + 1.59197i) q^{46} -7.70215i q^{47} +(0.0850471 + 1.72996i) q^{48} +(-3.89187 + 4.49146i) q^{49} +(-1.17292 + 1.82509i) q^{50} +(-7.35690 + 1.42954i) q^{51} +(-4.07459 + 2.61858i) q^{52} +(4.36713 + 9.56268i) q^{53} +(-5.13983 + 0.762964i) q^{54} +(0.0245074 + 0.170453i) q^{55} +(-0.427079 + 0.935173i) q^{56} +(2.38974 - 1.70721i) q^{57} +(5.78551 - 1.69878i) q^{58} +(-7.37789 - 3.36937i) q^{59} +(2.58805 - 1.33922i) q^{60} +(-8.87756 + 7.69245i) q^{61} +(3.85625 - 1.76109i) q^{62} +(-2.91766 - 0.999879i) q^{63} +(0.142315 - 0.989821i) q^{64} +(6.85513 + 4.40553i) q^{65} +(-0.0656402 + 0.164687i) q^{66} +(-4.14663 + 14.1221i) q^{67} +4.32695 q^{68} +(3.47824 - 7.54333i) q^{69} +1.72965 q^{70} +(-2.05377 + 6.99449i) q^{71} +(2.99702 + 0.133624i) q^{72} +(9.69633 + 6.23145i) q^{73} +(-1.12526 + 7.82633i) q^{74} +(2.95726 + 2.31834i) q^{75} +(-1.54239 + 0.704387i) q^{76} +(-0.0795279 + 0.0689113i) q^{77} +(3.85547 + 7.45070i) q^{78} +(-12.6271 - 5.76662i) q^{79} +(-1.61426 + 0.473990i) q^{80} +(0.482954 + 8.98703i) q^{81} +(-0.920544 + 2.01571i) q^{82} +(0.779795 + 5.42359i) q^{83} +(1.54347 + 0.887994i) q^{84} +(-3.02410 - 6.62186i) q^{85} +(5.15914 - 3.31558i) q^{86} +(-1.99212 - 10.2521i) q^{87} +(0.0553380 - 0.0861077i) q^{88} +(5.91320 - 6.82420i) q^{89} +(-1.89012 - 4.67996i) q^{90} +4.97947i q^{91} +(-2.80202 + 3.89213i) q^{92} +(-2.41215 - 6.93527i) q^{93} +(7.39016 + 2.16995i) q^{94} +(2.15595 + 1.86814i) q^{95} +(-1.68385 - 0.405784i) q^{96} +(5.66160 + 0.814016i) q^{97} +(-3.21306 - 4.99962i) q^{98} +(0.273361 + 0.139876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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