LMFDB - Embedded newform 87.2.i.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(4,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("87.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.i (of order $14$, degree $6$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	87.4
Dual form			87.2.i.a.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26950 + 0.289755i) q^{2} +(0.433884 + 0.900969i) q^{3} +(-0.274272 - 0.132082i) q^{4} +(-0.0725658 + 0.317931i) q^{5} +(0.289755 + 1.26950i) q^{6} +(0.994220 - 0.478791i) q^{7} +(-2.34603 - 1.87090i) q^{8} +(-0.623490 + 0.781831i) q^{9} +(-0.184244 + 0.382587i) q^{10} +(-0.600556 + 0.478928i) q^{11} -0.304418i q^{12} +(-2.99941 - 3.76114i) q^{13} +(1.40089 - 0.319744i) q^{14} +(-0.317931 + 0.0725658i) q^{15} +(-2.05658 - 2.57887i) q^{16} +5.18289i q^{17} +(-1.01806 + 0.811874i) q^{18} +(1.81600 - 3.77095i) q^{19} +(0.0618958 - 0.0776149i) q^{20} +(0.862752 + 0.688022i) q^{21} +(-0.901176 + 0.433984i) q^{22} +(0.314479 + 1.37782i) q^{23} +(0.667716 - 2.92545i) q^{24} +(4.40903 + 2.12328i) q^{25} +(-2.71794 - 5.64386i) q^{26} +(-0.974928 - 0.222521i) q^{27} -0.335926 q^{28} +(-0.401521 + 5.37018i) q^{29} -0.424639 q^{30} +(-4.40253 - 1.00485i) q^{31} +(0.740318 + 1.53729i) q^{32} +(-0.692070 - 0.333284i) q^{33} +(-1.50177 + 6.57967i) q^{34} +(0.0800764 + 0.350838i) q^{35} +(0.274272 - 0.132082i) q^{36} +(1.40085 + 1.11714i) q^{37} +(3.39805 - 4.26102i) q^{38} +(2.08728 - 4.33428i) q^{39} +(0.765059 - 0.610114i) q^{40} +1.34344i q^{41} +(0.895904 + 1.12343i) q^{42} +(7.02843 - 1.60419i) q^{43} +(0.227973 - 0.0520334i) q^{44} +(-0.203325 - 0.254961i) q^{45} +1.84026i q^{46} +(0.354469 - 0.282680i) q^{47} +(1.43116 - 2.97184i) q^{48} +(-3.60520 + 4.52077i) q^{49} +(4.98202 + 3.97303i) q^{50} +(-4.66963 + 2.24877i) q^{51} +(0.325873 + 1.42774i) q^{52} +(1.96455 - 8.60725i) q^{53} +(-1.17319 - 0.564980i) q^{54} +(-0.108686 - 0.225689i) q^{55} +(-3.22824 - 0.736825i) q^{56} +4.18544 q^{57} +(-2.06576 + 6.70108i) q^{58} +3.67450 q^{59} +(0.0967842 + 0.0220904i) q^{60} +(3.83753 + 7.96872i) q^{61} +(-5.29784 - 2.55131i) q^{62} +(-0.245552 + 1.07583i) q^{63} +(1.96236 + 8.59768i) q^{64} +(1.41344 - 0.680677i) q^{65} +(-0.782011 - 0.623633i) q^{66} +(9.51550 - 11.9321i) q^{67} +(0.684568 - 1.42152i) q^{68} +(-1.10493 + 0.881149i) q^{69} +0.468590i q^{70} +(-9.37723 - 11.7587i) q^{71} +(2.92545 - 0.667716i) q^{72} +(-13.3579 + 3.04884i) q^{73} +(1.45468 + 1.82412i) q^{74} +4.89365i q^{75} +(-0.996152 + 0.794405i) q^{76} +(-0.367779 + 0.763701i) q^{77} +(3.90567 - 4.89756i) q^{78} +(-4.56304 - 3.63890i) q^{79} +(0.969139 - 0.466713i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-0.389269 + 1.70550i) q^{82} +(-11.4666 - 5.52203i) q^{83} +(-0.145753 - 0.302659i) q^{84} +(-1.64780 - 0.376101i) q^{85} +9.38739 q^{86} +(-5.01257 + 1.96827i) q^{87} +2.30495 q^{88} +(-8.07964 - 1.84412i) q^{89} +(-0.184244 - 0.382587i) q^{90} +(-4.78288 - 2.30331i) q^{91} +(0.0957331 - 0.419434i) q^{92} +(-1.00485 - 4.40253i) q^{93} +(0.531905 - 0.256152i) q^{94} +(1.06713 + 0.851004i) q^{95} +(-1.06383 + 1.33401i) q^{96} +(-0.670747 + 1.39282i) q^{97} +(-5.88670 + 4.69449i) q^{98} -0.768140i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 4 q^{5} - 2 q^{6} + 8 q^{7} + 4 q^{9} - 28 q^{11} - 10 q^{13} - 14 q^{15} - 22 q^{16} - 20 q^{20} + 4 q^{22} + 18 q^{23} - 18 q^{25} + 28 q^{26} + 8 q^{28} + 28 q^{29} - 40 q^{30} + 28 q^{31}+ \cdots - 42 q^{98}+O(q^{100}) $ 24 * q - 2 * q^4 - 4 * q^5 - 2 * q^6 + 8 * q^7 + 4 * q^9 - 28 * q^11 - 10 * q^13 - 14 * q^15 - 22 * q^16 - 20 * q^20 + 4 * q^22 + 18 * q^23 - 18 * q^25 + 28 * q^26 + 8 * q^28 + 28 * q^29 - 40 * q^30 + 28 * q^31 - 14 * q^32 + 34 * q^34 + 2 * q^36 - 28 * q^37 - 4 * q^38 + 14 * q^42 - 14 * q^43 + 14 * q^44 - 10 * q^45 + 56 * q^48 + 20 * q^49 + 42 * q^50 + 2 * q^51 - 68 * q^52 + 6 * q^53 + 2 * q^54 - 14 * q^55 + 32 * q^57 + 50 * q^58 + 28 * q^59 + 42 * q^60 - 8 * q^62 + 6 * q^63 - 20 * q^64 + 18 * q^65 - 28 * q^66 + 8 * q^67 + 14 * q^68 + 28 * q^69 - 42 * q^71 + 14 * q^72 - 84 * q^73 + 10 * q^74 - 14 * q^76 - 70 * q^77 + 2 * q^78 - 14 * q^79 + 36 * q^80 - 4 * q^81 - 50 * q^82 - 32 * q^83 + 14 * q^85 - 128 * q^86 - 44 * q^87 - 20 * q^88 - 14 * q^89 + 34 * q^91 - 58 * q^92 - 20 * q^93 - 44 * q^94 - 52 * q^96 + 56 * q^97 - 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$1$

Coefficient data

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

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

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

$2$	1.26950	+	0.289755i	0.897670	+	0.204887i	0.646372	−	0.763022i	$-0.276285\pi$
$2$	1.26950	+	0.289755i	0.897670	+	0.204887i	0.251298	+	0.967910i	$0.419143\pi$
$3$	0.433884	+	0.900969i	0.250503	+	0.520175i
$3$	0.433884	+	0.900969i	0.250503	+	0.520175i
$4$	−0.274272	−	0.132082i	−0.137136	−	0.0660411i
$5$	−0.0725658	+	0.317931i	−0.0324524	+	0.142183i	−0.988559	−	0.150837i	$-0.951803\pi$
$5$	−0.0725658	+	0.317931i	−0.0324524	+	0.142183i	0.956106	+	0.293020i	$0.0946603\pi$
$6$	0.289755	+	1.26950i	0.118292	+	0.518270i
$7$	0.994220	−	0.478791i	0.375780	−	0.180966i	−0.236454	−	0.971643i	$-0.575985\pi$
$7$	0.994220	−	0.478791i	0.375780	−	0.180966i	0.612234	+	0.790677i	$0.290271\pi$
$8$	−2.34603	−	1.87090i	−0.829447	−	0.661462i
$9$	−0.623490	+	0.781831i	−0.207830	+	0.260610i
$10$	−0.184244	+	0.382587i	−0.0582631	+	0.120985i
$11$	−0.600556	+	0.478928i	−0.181075	+	0.144402i	−0.709832	−	0.704371i	$-0.751229\pi$
$11$	−0.600556	+	0.478928i	−0.181075	+	0.144402i	0.528758	+	0.848773i	$0.322658\pi$
$12$		−	0.304418i		−	0.0878780i
$13$	−2.99941	−	3.76114i	−0.831887	−	1.04315i	−0.998368	−	0.0571090i	$-0.981812\pi$
$13$	−2.99941	−	3.76114i	−0.831887	−	1.04315i	0.166481	−	0.986045i	$-0.446760\pi$
$14$	1.40089	−	0.319744i	0.374404	−	0.0854553i
$15$	−0.317931	+	0.0725658i	−0.0820895	+	0.0187364i
$16$	−2.05658	−	2.57887i	−0.514144	−	0.644716i
$17$			5.18289i			1.25704i	0.777795	+	0.628518i	$0.216338\pi$
$17$			5.18289i			1.25704i	−0.777795	+	0.628518i	$0.783662\pi$
$18$	−1.01806	+	0.811874i	−0.239959	+	0.191361i
$19$	1.81600	−	3.77095i	0.416618	−	0.865116i	−0.582032	−	0.813166i	$-0.697742\pi$
$19$	1.81600	−	3.77095i	0.416618	−	0.865116i	0.998650	−	0.0519502i	$-0.0165437\pi$
$20$	0.0618958	−	0.0776149i	0.0138403	−	0.0173552i
$21$	0.862752	+	0.688022i	0.188268	+	0.150139i
$22$	−0.901176	+	0.433984i	−0.192131	+	0.0925256i
$23$	0.314479	+	1.37782i	0.0655733	+	0.287295i	0.997074	−	0.0764445i	$-0.0243568\pi$
$23$	0.314479	+	1.37782i	0.0655733	+	0.287295i	−0.931501	+	0.363740i	$0.881500\pi$
$24$	0.667716	−	2.92545i	0.136297	−	0.597156i
$25$	4.40903	+	2.12328i	0.881806	+	0.424655i
$26$	−2.71794	−	5.64386i	−0.533032	−	1.10685i
$27$	−0.974928	−	0.222521i	−0.187625	−	0.0428242i
$28$	−0.335926			−0.0634841
$29$	−0.401521	+	5.37018i	−0.0745606	+	0.997216i
$29$	−0.401521	+	5.37018i	−0.0745606	+	0.997216i
$30$	−0.424639			−0.0775282
$31$	−4.40253	−	1.00485i	−0.790718	−	0.180476i	−0.191956	−	0.981403i	$-0.561483\pi$
$31$	−4.40253	−	1.00485i	−0.790718	−	0.180476i	−0.598762	+	0.800927i	$0.704340\pi$
$32$	0.740318	+	1.53729i	0.130871	+	0.271756i
$33$	−0.692070	−	0.333284i	−0.120474	−	0.0580172i
$34$	−1.50177	+	6.57967i	−0.257551	+	1.12840i
$35$	0.0800764	+	0.350838i	0.0135354	+	0.0593024i
$36$	0.274272	−	0.132082i	0.0457119	−	0.0220137i
$37$	1.40085	+	1.11714i	0.230299	+	0.183657i	0.731840	−	0.681477i	$-0.238662\pi$
$37$	1.40085	+	1.11714i	0.230299	+	0.183657i	−0.501541	+	0.865134i	$0.667233\pi$
$38$	3.39805	−	4.26102i	0.551237	−	0.691229i
$39$	2.08728	−	4.33428i	0.334232	−	0.694040i
$40$	0.765059	−	0.610114i	0.120966	−	0.0964675i
$41$			1.34344i			0.209811i	0.994482	+	0.104905i	$0.0334540\pi$
$41$			1.34344i			0.209811i	−0.994482	+	0.104905i	$0.966546\pi$
$42$	0.895904	+	1.12343i	0.138241	+	0.173349i
$43$	7.02843	−	1.60419i	1.07182	−	0.244637i	0.350026	−	0.936740i	$-0.386173\pi$
$43$	7.02843	−	1.60419i	1.07182	−	0.244637i	0.721799	+	0.692103i	$0.243316\pi$
$44$	0.227973	−	0.0520334i	0.0343683	−	0.00784433i
$45$	−0.203325	−	0.254961i	−0.0303099	−	0.0380074i
$46$			1.84026i			0.271332i
$47$	0.354469	−	0.282680i	0.0517046	−	0.0412331i	−0.597297	−	0.802020i	$-0.703758\pi$
$47$	0.354469	−	0.282680i	0.0517046	−	0.0412331i	0.649001	+	0.760787i	$0.275187\pi$
$48$	1.43116	−	2.97184i	0.206570	−	0.428948i
$49$	−3.60520	+	4.52077i	−0.515028	+	0.645825i
$50$	4.98202	+	3.97303i	0.704564	+	0.561871i
$51$	−4.66963	+	2.24877i	−0.653878	+	0.314891i
$52$	0.325873	+	1.42774i	0.0451905	+	0.197992i
$53$	1.96455	−	8.60725i	0.269851	−	1.18230i	−0.640334	−	0.768096i	$-0.721204\pi$
$53$	1.96455	−	8.60725i	0.269851	−	1.18230i	0.910186	−	0.414200i	$-0.135939\pi$
$54$	−1.17319	−	0.564980i	−0.159651	−	0.0768840i
$55$	−0.108686	−	0.225689i	−0.0146553	−	0.0304320i
$56$	−3.22824	−	0.736825i	−0.431392	−	0.0984624i
$57$	4.18544			0.554376
$58$	−2.06576	+	6.70108i	−0.271248	+	0.879895i
$59$	3.67450			0.478379			0.239190	−	0.970973i	$-0.423118\pi$
$59$	3.67450			0.478379			0.239190	+	0.970973i	$0.423118\pi$
$60$	0.0967842	+	0.0220904i	0.0124948	+	0.00285185i
$61$	3.83753	+	7.96872i	0.491346	+	1.02029i	0.988301	+	0.152514i	$0.0487369\pi$
$61$	3.83753	+	7.96872i	0.491346	+	1.02029i	−0.496956	+	0.867776i	$0.665549\pi$
$62$	−5.29784	−	2.55131i	−0.672827	−	0.324016i
$63$	−0.245552	+	1.07583i	−0.0309367	+	0.135542i
$64$	1.96236	+	8.59768i	0.245295	+	1.07471i
$65$	1.41344	−	0.680677i	0.175316	−	0.0844276i
$66$	−0.782011	−	0.623633i	−0.0962589	−	0.0767639i
$67$	9.51550	−	11.9321i	1.16250	−	1.45773i	0.298384	−	0.954446i	$-0.403552\pi$
$67$	9.51550	−	11.9321i	1.16250	−	1.45773i	0.864119	−	0.503287i	$-0.167876\pi$
$68$	0.684568	−	1.42152i	0.0830161	−	0.172385i
$69$	−1.10493	+	0.881149i	−0.133018	+	0.106078i
$70$			0.468590i			0.0560072i
$71$	−9.37723	−	11.7587i	−1.11287	−	1.39550i	−0.909150	−	0.416469i	$-0.863267\pi$
$71$	−9.37723	−	11.7587i	−1.11287	−	1.39550i	−0.203722	−	0.979029i	$-0.565304\pi$
$72$	2.92545	−	0.667716i	0.344768	−	0.0786910i
$73$	−13.3579	+	3.04884i	−1.56342	+	0.356840i	−0.914683	−	0.404173i	$-0.867559\pi$
$73$	−13.3579	+	3.04884i	−1.56342	+	0.356840i	−0.648737	+	0.761013i	$0.724702\pi$
$74$	1.45468	+	1.82412i	0.169104	+	0.212049i
$75$			4.89365i			0.565070i
$76$	−0.996152	+	0.794405i	−0.114266	+	0.0911245i
$77$	−0.367779	+	0.763701i	−0.0419123	+	0.0870318i
$78$	3.90567	−	4.89756i	0.442230	−	0.554539i
$79$	−4.56304	−	3.63890i	−0.513382	−	0.409408i	0.332237	−	0.943196i	$-0.392197\pi$
$79$	−4.56304	−	3.63890i	−0.513382	−	0.409408i	−0.845619	+	0.533788i	$0.820768\pi$
$80$	0.969139	−	0.466713i	0.108353	−	0.0521801i
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−0.389269	+	1.70550i	−0.0429876	+	0.188341i
$83$	−11.4666	−	5.52203i	−1.25862	−	0.606122i	−0.318814	−	0.947817i	$-0.603285\pi$
$83$	−11.4666	−	5.52203i	−1.25862	−	0.606122i	−0.939811	+	0.341695i	$0.888999\pi$
$84$	−0.145753	−	0.302659i	−0.0159029	−	0.0330228i
$85$	−1.64780	−	0.376101i	−0.178730	−	0.0407938i
$86$	9.38739			1.01227
$87$	−5.01257	+	1.96827i	−0.537404	+	0.211021i
$88$	2.30495			0.245708
$89$	−8.07964	−	1.84412i	−0.856440	−	0.195477i	−0.228313	−	0.973588i	$-0.573321\pi$
$89$	−8.07964	−	1.84412i	−0.856440	−	0.195477i	−0.628127	+	0.778111i	$0.716178\pi$
$90$	−0.184244	−	0.382587i	−0.0194210	−	0.0403282i
$91$	−4.78288	−	2.30331i	−0.501382	−	0.241453i
$92$	0.0957331	−	0.419434i	0.00998086	−	0.0437290i
$93$	−1.00485	−	4.40253i	−0.104198	−	0.456521i
$94$	0.531905	−	0.256152i	0.0548618	−	0.0264201i
$95$	1.06713	+	0.851004i	0.109485	+	0.0873112i
$96$	−1.06383	+	1.33401i	−0.108577	+	0.136151i
$97$	−0.670747	+	1.39282i	−0.0681040	+	0.141419i	−0.932242	−	0.361836i	$-0.882150\pi$
$97$	−0.670747	+	1.39282i	−0.0681040	+	0.141419i	0.864138	+	0.503255i	$0.167864\pi$
$98$	−5.88670	+	4.69449i	−0.594647	+	0.474215i
$99$		−	0.768140i		−	0.0772010i
$100$	−0.928824	−	1.16471i	−0.0928824	−	0.116471i
$101$	15.7570	−	3.59643i	1.56788	−	0.357858i	0.651651	−	0.758519i	$-0.274077\pi$
$101$	15.7570	−	3.59643i	1.56788	−	0.357858i	0.916226	+	0.400661i	$0.131219\pi$
$102$	−6.57967	+	1.50177i	−0.651485	+	0.148697i
$103$	−6.82835	−	8.56248i	−0.672818	−	0.843687i	0.321853	−	0.946790i	$-0.395694\pi$
$103$	−6.82835	−	8.56248i	−0.672818	−	0.843687i	−0.994671	+	0.103103i	$0.967123\pi$
$104$			14.4354i			1.41550i
$105$	−0.281350	+	0.224369i	−0.0274569	+	0.0218962i
$106$	4.98798	−	10.3576i	0.484475	−	1.00602i
$107$	−7.79954	+	9.78032i	−0.754010	+	0.945499i	−0.999716	−	0.0238458i	$-0.992409\pi$
$107$	−7.79954	+	9.78032i	−0.754010	+	0.945499i	0.245706	+	0.969345i	$0.420980\pi$
$108$	0.238004	+	0.189802i	0.0229019	+	0.0182637i
$109$	7.93042	−	3.81909i	0.759597	−	0.365802i	−0.0136509	−	0.999907i	$-0.504345\pi$
$109$	7.93042	−	3.81909i	0.759597	−	0.365802i	0.773247	+	0.634104i	$0.218631\pi$
$110$	−0.0725825	−	0.318005i	−0.00692047	−	0.0303205i
$111$	−0.398704	+	1.74684i	−0.0378433	+	0.165802i
$112$	−3.27943	−	1.57929i	−0.309877	−	0.149229i
$113$	−1.06799	−	2.21771i	−0.100468	−	0.208624i	0.844676	−	0.535278i	$-0.179793\pi$
$113$	−1.06799	−	2.21771i	−0.100468	−	0.208624i	−0.945144	+	0.326654i	$0.894079\pi$
$114$	5.31341	+	1.21275i	0.497647	+	0.113585i
$115$	−0.460873			−0.0429766
$116$	0.819430	−	1.41985i	0.0760822	−	0.131830i
$117$	4.81068			0.444748
$118$	4.66477	+	1.06470i	0.429427	+	0.0980139i
$119$	2.48152	+	5.15294i	0.227481	+	0.472369i
$120$	0.881640	+	0.424576i	0.0804824	+	0.0387583i
$121$	−2.31643	+	10.1490i	−0.210585	+	0.922633i
$122$	2.56277	+	11.2282i	0.232022	+	1.01655i
$123$	−1.21040	+	0.582899i	−0.109138	+	0.0525582i
$124$	1.07477	+	0.857097i	0.0965169	+	0.0769696i
$125$	−2.01162	+	2.52250i	−0.179925	+	0.225619i
$126$	−0.623456	+	1.29462i	−0.0555418	+	0.115334i
$127$	11.9351	−	9.51790i	1.05907	−	0.844577i	0.0708265	−	0.997489i	$-0.477436\pi$
$127$	11.9351	−	9.51790i	1.05907	−	0.844577i	0.988240	+	0.152911i	$0.0488649\pi$
$128$			8.07081i			0.713366i
$129$	4.49485	+	5.63636i	0.395749	+	0.496254i
$130$	1.99159	−	0.454567i	0.174674	−	0.0398682i
$131$	8.52336	−	1.94540i	0.744689	−	0.169970i	0.166692	−	0.986009i	$-0.446692\pi$
$131$	8.52336	−	1.94540i	0.744689	−	0.169970i	0.577997	+	0.816039i	$0.303834\pi$
$132$	0.145794	+	0.182820i	0.0126898	+	0.0159125i
$133$		−	4.61864i		−	0.400487i
$134$	15.5373	−	12.3906i	1.34222	−	1.07038i
$135$	0.141493	−	0.293813i	0.0121778	−	0.0252874i
$136$	9.69667	−	12.1592i	0.831482	−	1.04265i
$137$	18.2169	+	14.5275i	1.55638	+	1.24117i	0.838305	+	0.545202i	$0.183547\pi$
$137$	18.2169	+	14.5275i	1.55638	+	1.24117i	0.718073	+	0.695968i	$0.245025\pi$
$138$	−1.65802	+	0.798460i	−0.141140	+	0.0679694i
$139$	3.01052	+	13.1900i	0.255349	+	1.11876i	0.926160	+	0.377130i	$0.123089\pi$
$139$	3.01052	+	13.1900i	0.255349	+	1.11876i	−0.670811	+	0.741628i	$0.734054\pi$
$140$	0.0243767	−	0.106801i	0.00206021	−	0.00902637i
$141$	0.408484	+	0.196715i	0.0344005	+	0.0165664i
$142$	−8.49724	−	17.6447i	−0.713073	−	1.48071i
$143$	3.60263	+	0.822277i	0.301267	+	0.0687623i
$144$	3.29849			0.274874
$145$	−1.67821	−	0.517347i	−0.139368	−	0.0429633i
$146$	−17.8412			−1.47655
$147$	−5.63731	−	1.28668i	−0.464958	−	0.106124i
$148$	−0.236660	−	0.491429i	−0.0194533	−	0.0403952i
$149$	−1.19555	−	0.575745i	−0.0979430	−	0.0471668i	0.384271	−	0.923220i	$-0.374453\pi$
$149$	−1.19555	−	0.575745i	−0.0979430	−	0.0471668i	−0.482214	+	0.876054i	$0.660167\pi$
$150$	−1.41796	+	6.21248i	−0.115776	+	0.507247i
$151$	3.19768	+	14.0099i	0.260223	+	1.14011i	0.921010	+	0.389539i	$0.127366\pi$
$151$	3.19768	+	14.0099i	0.260223	+	1.14011i	−0.660787	+	0.750574i	$0.729777\pi$
$152$	−11.3155	+	5.44924i	−0.917805	+	0.441991i
$153$	−4.05215	−	3.23148i	−0.327597	−	0.261250i
$154$	−0.688180	+	0.862950i	−0.0554551	+	0.0695385i
$155$	0.638946	−	1.32679i	0.0513214	−	0.106570i
$156$	−1.14496	+	0.913076i	−0.0916703	+	0.0731046i
$157$		−	13.1931i		−	1.05292i	−0.850199	−	0.526462i	$-0.823518\pi$
$157$		−	13.1931i		−	1.05292i	0.850199	−	0.526462i	$-0.176482\pi$
$158$	−4.73838	−	5.94174i	−0.376965	−	0.472699i
$159$	8.60725	−	1.96455i	0.682599	−	0.155799i
$160$	−0.542473	+	0.123816i	−0.0428863	+	0.00978851i
$161$	0.972350	+	1.21929i	0.0766319	+	0.0960933i
$162$		−	1.30214i		−	0.102306i
$163$	2.35391	−	1.87718i	0.184373	−	0.147032i	−0.526954	−	0.849894i	$-0.676666\pi$
$163$	2.35391	−	1.87718i	0.184373	−	0.147032i	0.711327	+	0.702861i	$0.248095\pi$
$164$	0.177445	−	0.368469i	0.0138561	−	0.0287726i
$165$	0.156182	−	0.195846i	0.0121587	−	0.0152466i
$166$	−12.9568	−	10.3327i	−1.00564	−	0.801974i
$167$	−1.23842	+	0.596394i	−0.0958321	+	0.0461503i	−0.481186	−	0.876619i	$-0.659794\pi$
$167$	−1.23842	+	0.596394i	−0.0958321	+	0.0461503i	0.385354	+	0.922769i	$0.374079\pi$
$168$	−0.736825	−	3.22824i	−0.0568473	−	0.249064i
$169$	−2.25696	+	9.88838i	−0.173612	+	0.760645i
$170$	−1.98291	−	0.954918i	−0.152082	−	0.0732389i
$171$	1.81600	+	3.77095i	0.138873	+	0.288372i
$172$	−2.13958	−	0.488346i	−0.163142	−	0.0372360i
$173$	−13.2857			−1.01009			−0.505045	−	0.863093i	$-0.668524\pi$
$173$	−13.2857			−1.01009			−0.505045	+	0.863093i	$0.668524\pi$
$174$	−6.93377	+	1.04630i	−0.525647	+	0.0793200i
$175$	5.40015			0.408213
$176$	2.47018	+	0.563802i	0.186197	+	0.0424982i
$177$	1.59431	+	3.31061i	0.119835	+	0.248841i
$178$	−9.72273	−	4.68222i	−0.728750	−	0.350947i
$179$	1.36940	−	5.99973i	0.102354	−	0.448441i	−0.897617	−	0.440777i	$-0.854703\pi$
$179$	1.36940	−	5.99973i	0.102354	−	0.448441i	0.999971	−	0.00766454i	$-0.00243972\pi$
$180$	0.0220904	+	0.0967842i	0.00164652	+	0.00721387i
$181$	−21.7247	+	10.4620i	−1.61478	+	0.777638i	−0.999939	−	0.0110120i	$-0.996495\pi$
$181$	−21.7247	+	10.4620i	−1.61478	+	0.777638i	−0.614842	+	0.788650i	$0.710780\pi$
$182$	−5.40446	−	4.30991i	−0.400605	−	0.319472i
$183$	−5.51452	+	6.91500i	−0.407645	+	0.511171i
$184$	1.83999	−	3.82077i	0.135645	−	0.281671i
$185$	−0.456829	+	0.364309i	−0.0335868	+	0.0267845i
$186$		−	5.88016i		−	0.431154i
$187$	−2.48223	−	3.11262i	−0.181519	−	0.227617i
$188$	−0.134558	+	0.0307119i	−0.00981363	+	0.00223990i
$189$	−1.07583	+	0.245552i	−0.0782554	+	0.0178613i
$190$	1.10813	+	1.38955i	0.0803923	+	0.100809i
$191$		−	5.15567i		−	0.373051i	−0.982450	−	0.186526i	$-0.940277\pi$
$191$		−	5.15567i		−	0.373051i	0.982450	−	0.186526i	$-0.0597228\pi$
$192$	−6.89480	+	5.49842i	−0.497589	+	0.396814i
$193$	−1.20357	+	2.49924i	−0.0866349	+	0.179899i	−0.939785	−	0.341766i	$-0.888975\pi$
$193$	−1.20357	+	2.49924i	−0.0866349	+	0.179899i	0.853150	+	0.521666i	$0.174689\pi$
$194$	−1.25509	+	1.57383i	−0.0901100	+	0.112994i
$195$	1.22654	+	0.978131i	0.0878342	+	0.0700454i
$196$	1.58592	−	0.763737i	0.113280	−	0.0545526i
$197$	−5.49393	−	24.0705i	−0.391426	−	1.71495i	−0.659631	−	0.751589i	$-0.729288\pi$
$197$	−5.49393	−	24.0705i	−0.391426	−	1.71495i	0.268205	−	0.963362i	$-0.413570\pi$
$198$	0.222572	−	0.975152i	0.0158175	−	0.0693010i
$199$	4.73656	+	2.28101i	0.335766	+	0.161696i	0.594168	−	0.804341i	$-0.297482\pi$
$199$	4.73656	+	2.28101i	0.335766	+	0.161696i	−0.258402	+	0.966038i	$0.583196\pi$
$200$	−6.37129	−	13.2301i	−0.450518	−	0.935511i
$201$	14.8790	+	3.39604i	1.04949	+	0.239538i
$202$	21.0455			1.48076
$203$	2.17199	+	5.53138i	0.152444	+	0.388227i
$204$	1.57777			0.110466
$205$	−0.427123	−	0.0974881i	−0.0298316	−	0.00680886i
$206$	−6.18756	−	12.8486i	−0.431108	−	0.895204i
$207$	−1.27330	−	0.613188i	−0.0885003	−	0.0426195i
$208$	−3.53096	+	15.4702i	−0.244828	+	1.07266i
$209$	0.715407	+	3.13440i	0.0494857	+	0.216811i
$210$	−0.422185	+	0.203314i	−0.0291335	+	0.0140300i
$211$	18.9222	+	15.0899i	1.30266	+	1.03883i	0.996213	+	0.0869434i	$0.0277099\pi$
$211$	18.9222	+	15.0899i	1.30266	+	1.03883i	0.306442	+	0.951889i	$0.400862\pi$
$212$	−1.67568	+	2.10124i	−0.115086	+	0.144314i
$213$	6.52557	−	13.5505i	0.447125	−	0.928464i
$214$	−12.7354	+	10.1561i	−0.870573	+	0.694259i
$215$			2.35097i			0.160335i
$216$	1.87090	+	2.34603i	0.127298	+	0.159627i
$217$	−4.85820	+	1.10885i	−0.329796	+	0.0752738i
$218$	11.1742	−	2.55045i	0.756816	−	0.172738i
$219$	−8.54267	−	10.7122i	−0.577260	−	0.723861i
$220$			0.0762557i			0.00514116i
$221$	19.4936	−	15.5456i	1.31128	−	1.04571i
$222$	−1.01231	+	2.10208i	−0.0679417	+	0.141082i
$223$	0.757116	−	0.949394i	0.0507003	−	0.0635761i	−0.755835	−	0.654762i	$-0.772769\pi$
$223$	0.757116	−	0.949394i	0.0507003	−	0.0635761i	0.806535	+	0.591186i	$0.201340\pi$
$224$	1.47208	+	1.17394i	0.0983573	+	0.0784374i
$225$	−4.40903	+	2.12328i	−0.293935	+	0.141552i
$226$	−0.713222	−	3.12483i	−0.0474428	−	0.207861i
$227$	−3.55503	+	15.5756i	−0.235956	+	1.03379i	0.708645	+	0.705566i	$0.249307\pi$
$227$	−3.55503	+	15.5756i	−0.235956	+	1.03379i	−0.944600	+	0.328223i	$0.893550\pi$
$228$	−1.14795	−	0.552823i	−0.0760247	−	0.0366116i
$229$	6.65454	+	13.8183i	0.439745	+	0.913139i	0.996589	+	0.0825223i	$0.0262976\pi$
$229$	6.65454	+	13.8183i	0.439745	+	0.913139i	−0.556845	+	0.830617i	$0.687988\pi$
$230$	−0.585077	−	0.133540i	−0.0385788	−	0.00880537i
$231$	−0.847644			−0.0557709
$232$	10.9890	−	11.8474i	0.721465	−	0.777820i
$233$	12.9851			0.850684			0.425342	−	0.905033i	$-0.360154\pi$
$233$	12.9851			0.850684			0.425342	+	0.905033i	$0.360154\pi$
$234$	6.10715	+	1.39392i	0.399237	+	0.0911232i
$235$	0.0641504	+	0.133210i	0.00418471	+	0.00868964i
$236$	−1.00781	−	0.485336i	−0.0656029	−	0.0315927i
$237$	1.29871	−	5.69002i	0.0843602	−	0.369606i
$238$	1.65720	+	7.26068i	0.107420	+	0.470640i
$239$	−0.229801	+	0.110667i	−0.0148646	+	0.00715842i	−0.441301	−	0.897359i	$-0.645483\pi$
$239$	−0.229801	+	0.110667i	−0.0148646	+	0.00715842i	0.426437	+	0.904517i	$0.359769\pi$
$240$	0.840988	+	0.670665i	0.0542855	+	0.0432913i
$241$	−5.23484	+	6.56429i	−0.337206	+	0.422843i	−0.921306	−	0.388839i	$-0.872876\pi$
$241$	−5.23484	+	6.56429i	−0.337206	+	0.422843i	0.584100	+	0.811682i	$0.301448\pi$
$242$	−5.88141	+	12.2129i	−0.378072	+	0.785074i
$243$	0.781831	−	0.623490i	0.0501545	−	0.0399969i
$244$		−	2.69246i		−	0.172367i
$245$	−1.17568	−	1.47426i	−0.0751115	−	0.0941869i
$246$	−1.70550	+	0.389269i	−0.108739	+	0.0248189i
$247$	−19.6300	+	4.48043i	−1.24903	+	0.285083i
$248$	8.44851	+	10.5941i	0.536481	+	0.672726i
$249$		−	12.7270i		−	0.806540i
$250$	−3.28466	+	2.61943i	−0.207740	+	0.165667i
$251$	−8.09013	+	16.7993i	−0.510644	+	1.06036i	0.473136	+	0.880989i	$0.343122\pi$
$251$	−8.09013	+	16.7993i	−0.510644	+	1.06036i	−0.983781	+	0.179375i	$0.942593\pi$
$252$	0.209447	−	0.262638i	0.0131939	−	0.0165446i
$253$	−0.848739	−	0.676846i	−0.0533597	−	0.0425530i
$254$	17.9094	−	8.62471i	1.12374	−	0.541163i
$255$	−0.376101	−	1.64780i	−0.0235523	−	0.103190i
$256$	1.58617	−	6.94947i	0.0991357	−	0.434342i
$257$	−22.1806	−	10.6816i	−1.38359	−	0.666301i	−0.413827	−	0.910355i	$-0.635808\pi$
$257$	−22.1806	−	10.6816i	−1.38359	−	0.666301i	−0.969762	+	0.244054i	$0.921523\pi$
$258$	4.07304	+	8.45775i	0.253576	+	0.526556i
$259$	1.92764	+	0.439971i	0.119778	+	0.0273384i
$260$	−0.477572			−0.0296177
$261$	−3.94823	−	3.66217i	−0.244389	−	0.226683i
$262$	11.3841			0.703310
$263$	9.91282	+	2.26254i	0.611251	+	0.139514i	0.516930	−	0.856028i	$-0.327075\pi$
$263$	9.91282	+	2.26254i	0.611251	+	0.139514i	0.0943210	+	0.995542i	$0.469932\pi$
$264$	1.00008	+	2.07669i	0.0615506	+	0.127811i
$265$	2.59396	+	1.24918i	0.159345	+	0.0767367i
$266$	1.33827	−	5.86336i	0.0820548	−	0.359505i
$267$	−1.84412	−	8.07964i	−0.112859	−	0.494466i
$268$	−4.18584	+	2.01580i	−0.255691	+	0.123134i
$269$	0.522286	+	0.416509i	0.0318444	+	0.0253950i	0.639283	−	0.768972i	$-0.279231\pi$
$269$	0.522286	+	0.416509i	0.0318444	+	0.0253950i	−0.607438	+	0.794367i	$0.707803\pi$
$270$	0.264758	−	0.331996i	0.0161127	−	0.0202047i
$271$	−4.03127	+	8.37102i	−0.244882	+	0.508504i	−0.986791	−	0.161997i	$-0.948206\pi$
$271$	−4.03127	+	8.37102i	−0.244882	+	0.508504i	0.741909	+	0.670501i	$0.233921\pi$
$272$	13.3660	−	10.6590i	0.810432	−	0.646298i
$273$		−	5.30860i		−	0.321291i
$274$	18.9169	+	23.7211i	1.14281	+	1.43304i
$275$	−3.66477	+	0.836459i	−0.220994	+	0.0504404i
$276$	0.419434	−	0.0957331i	0.0252470	−	0.00576245i
$277$	−9.19224	−	11.5267i	−0.552308	−	0.692572i	0.424807	−	0.905284i	$-0.360342\pi$
$277$	−9.19224	−	11.5267i	−0.552308	−	0.692572i	−0.977115	+	0.212712i	$0.931770\pi$
$278$			17.6169i			1.05659i
$279$	3.53056	−	2.81552i	0.211369	−	0.168561i
$280$	0.468520	−	0.972891i	0.0279994	−	0.0581414i
$281$	−13.4220	+	16.8307i	−0.800690	+	1.00403i	0.199021	+	0.979995i	$0.436224\pi$
$281$	−13.4220	+	16.8307i	−0.800690	+	1.00403i	−0.999711	+	0.0240385i	$0.992348\pi$
$282$	0.461570	+	0.368090i	0.0274861	+	0.0219194i
$283$	9.29893	−	4.47813i	0.552764	−	0.266197i	−0.136583	−	0.990629i	$-0.543612\pi$
$283$	9.29893	−	4.47813i	0.552764	−	0.266197i	0.689347	+	0.724431i	$0.257898\pi$
$284$	1.01880	+	4.46363i	0.0604544	+	0.264868i
$285$	−0.303720	+	1.33068i	−0.0179908	+	0.0788229i
$286$	4.33527	+	2.08776i	0.256350	+	0.123452i
$287$	0.643229	+	1.33568i	0.0379686	+	0.0788427i
$288$	−1.66348	−	0.379678i	−0.0980214	−	0.0223728i
$289$	−9.86239			−0.580141
$290$	−1.98058	−	1.14304i	−0.116304	−	0.0671216i
$291$	−1.54591			−0.0906230
$292$	4.06638	+	0.928124i	0.237967	+	0.0543144i
$293$	−10.9372	−	22.7113i	−0.638958	−	1.32681i	−0.929101	−	0.369826i	$-0.879417\pi$
$293$	−10.9372	−	22.7113i	−0.638958	−	1.32681i	0.290143	−	0.956983i	$-0.406297\pi$
$294$	−6.78373	−	3.26687i	−0.395635	−	0.190528i
$295$	−0.266643	+	1.16824i	−0.0155246	+	0.0680175i
$296$	−1.19639	−	5.24171i	−0.0695385	−	0.304668i
$297$	0.692070	−	0.333284i	0.0401580	−	0.0193391i
$298$	−1.35092	−	1.07732i	−0.0782566	−	0.0624075i
$299$	4.23893	−	5.31545i	0.245144	−	0.307401i
$300$	0.646365	−	1.34219i	0.0373179	−	0.0774914i
$301$	6.21973	−	4.96007i	0.358499	−	0.285894i
$302$			18.7121i			1.07676i
$303$	10.0770	+	12.6361i	0.578906	+	0.725926i
$304$	−13.4595	+	3.07205i	−0.771956	+	0.176194i
$305$	−2.81198	+	0.641816i	−0.161013	+	0.0367503i
$306$	−4.20786	−	5.27649i	−0.240547	−	0.301637i
$307$		−	17.7845i		−	1.01502i	−0.861647	−	0.507508i	$-0.830567\pi$
$307$		−	17.7845i		−	1.01502i	0.861647	−	0.507508i	$-0.169433\pi$
$308$	0.201743	−	0.160884i	0.0114953	−	0.00916723i
$309$	4.75182	−	9.86726i	0.270322	−	0.561329i
$310$	1.19558	−	1.49921i	0.0679045	−	0.0851496i
$311$	6.56620	+	5.23637i	0.372335	+	0.296927i	0.791724	−	0.610880i	$-0.209184\pi$
$311$	6.56620	+	5.23637i	0.372335	+	0.296927i	−0.419388	+	0.907807i	$0.637755\pi$
$312$	−13.0058	+	6.26327i	−0.736309	+	0.354588i
$313$	0.467343	+	2.04756i	0.0264158	+	0.115735i	0.986417	−	0.164261i	$-0.0525239\pi$
$313$	0.467343	+	2.04756i	0.0264158	+	0.115735i	−0.960001	+	0.279996i	$0.909667\pi$
$314$	3.82276	−	16.7486i	0.215731	−	0.945179i
$315$	−0.324223	−	0.156137i	−0.0182679	−	0.00879735i
$316$	0.770877	+	1.60074i	0.0433652	+	0.0900489i
$317$	4.90180	+	1.11880i	0.275312	+	0.0628382i	0.357948	−	0.933742i	$-0.383477\pi$
$317$	4.90180	+	1.11880i	0.275312	+	0.0628382i	−0.0826355	+	0.996580i	$0.526334\pi$
$318$	11.4961			0.644670
$319$	−2.33079	−	3.41739i	−0.130499	−	0.191337i
$320$	−2.87587			−0.160766
$321$	−12.1959	−	2.78362i	−0.680706	−	0.155367i
$322$	0.881101	+	1.82963i	0.0491018	+	0.101961i
$323$	19.5445	+	9.41212i	1.08748	+	0.523704i
$324$	−0.0677395	+	0.296786i	−0.00376330	+	0.0164881i
$325$	−5.23855	−	22.9516i	−0.290582	−	1.27312i
$326$	3.53221	−	1.70102i	0.195631	−	0.0942108i
$327$	6.88176	+	5.48802i	0.380562	+	0.303488i
$328$	2.51345	−	3.15176i	0.138782	−	0.174027i
$329$	0.217076	−	0.450762i	0.0119678	−	0.0248513i
$330$	0.255020	−	0.203372i	0.0140384	−	0.0111952i
$331$		−	3.80922i		−	0.209374i	−0.994505	−	0.104687i	$-0.966616\pi$
$331$		−	3.80922i		−	0.209374i	0.994505	−	0.104687i	$-0.0333840\pi$
$332$	2.41560	+	3.02907i	0.132574	+	0.166242i
$333$	−1.74684	+	0.398704i	−0.0957261	+	0.0218489i
$334$	−1.74498	+	0.398281i	−0.0954813	+	0.0217930i
$335$	3.10308	+	3.89113i	0.169539	+	0.212595i
$336$		−	3.63989i		−	0.198572i
$337$	−1.18125	+	0.942012i	−0.0643466	+	0.0513147i	−0.655135	−	0.755512i	$-0.727388\pi$
$337$	−1.18125	+	0.942012i	−0.0643466	+	0.0513147i	0.590788	+	0.806827i	$0.298817\pi$
$338$	−5.73041	+	11.8993i	−0.311693	+	0.647237i
$339$	1.53470	−	1.92445i	0.0833535	−	0.104522i
$340$	0.402270	+	0.320799i	0.0218161	+	0.0173978i
$341$	3.12522	−	1.50503i	0.169240	−	0.0815017i
$342$	1.21275	+	5.31341i	0.0655781	+	0.287316i
$343$	−3.13872	+	13.7516i	−0.169475	+	0.742518i
$344$	−19.4902	−	9.38598i	−1.05084	−	0.506058i
$345$	−0.199965	−	0.415232i	−0.0107658	−	0.0223553i
$346$	−16.8661	−	3.84958i	−0.906729	−	0.206955i
$347$	−23.3601			−1.25404			−0.627019	−	0.779004i	$-0.715725\pi$
$347$	−23.3601			−1.25404			−0.627019	+	0.779004i	$0.715725\pi$
$348$	1.63478	+	0.122230i	0.0876334	+	0.00655224i
$349$	−15.0240			−0.804216			−0.402108	−	0.915592i	$-0.631722\pi$
$349$	−15.0240			−0.804216			−0.402108	+	0.915592i	$0.631722\pi$
$350$	6.85548	+	1.56472i	0.366441	+	0.0836377i
$351$	2.08728	+	4.33428i	0.111411	+	0.231347i
$352$	−1.18085	−	0.568668i	−0.0629396	−	0.0303101i
$353$	3.57377	−	15.6577i	0.190213	−	0.833377i	−0.786288	−	0.617861i	$-0.788000\pi$
$353$	3.57377	−	15.6577i	0.190213	−	0.833377i	0.976500	−	0.215516i	$-0.0691433\pi$
$354$	1.06470	+	4.66477i	0.0565883	+	0.247930i
$355$	4.41892	−	2.12804i	0.234532	−	0.112945i
$356$	1.97244	+	1.57297i	0.104539	+	0.0833671i
$357$	−3.56594	+	4.47155i	−0.188730	+	0.236660i
$358$	3.47690	−	7.21986i	0.183760	−	0.381581i
$359$	−20.7505	+	16.5480i	−1.09517	+	0.873370i	−0.992609	−	0.121357i	$-0.961275\pi$
$359$	−20.7505	+	16.5480i	−1.09517	+	0.873370i	−0.102562	+	0.994727i	$0.532704\pi$
$360$			0.978547i			0.0515739i
$361$	0.924048	+	1.15872i	0.0486341	+	0.0609852i
$362$	−30.6108	+	6.98672i	−1.60887	+	0.367214i
$363$	−10.1490	+	2.31643i	−0.532682	+	0.121581i
$364$	1.00758	+	1.26347i	0.0528116	+	0.0662236i
$365$		−	4.46812i		−	0.233872i
$366$	−9.00433	+	7.18071i	−0.470664	+	0.375342i
$367$	7.37679	−	15.3181i	0.385065	−	0.799597i	−0.614874	−	0.788625i	$-0.710793\pi$
$367$	7.37679	−	15.3181i	0.385065	−	0.799597i	0.999940	−	0.0109716i	$-0.00349242\pi$
$368$	2.90646	−	3.64459i	0.151510	−	0.189987i
$369$	−1.05035	−	0.837624i	−0.0546789	−	0.0436050i
$370$	−0.685504	+	0.330121i	−0.0356377	+	0.0171622i
$371$	−2.16788	−	9.49811i	−0.112551	−	0.493117i
$372$	−0.305895	+	1.34021i	−0.0158599	+	0.0694867i
$373$	10.5705	+	5.09050i	0.547322	+	0.263576i	0.687046	−	0.726614i	$-0.258907\pi$
$373$	10.5705	+	5.09050i	0.547322	+	0.263576i	−0.139724	+	0.990190i	$0.544622\pi$
$374$	−2.24929	−	4.67070i	−0.116308	−	0.241516i
$375$	−3.14550	−	0.717941i	−0.162433	−	0.0370743i
$376$	−1.36046			−0.0701604
$377$	21.4023	−	14.5972i	1.10228	−	0.751794i
$378$	−1.43692			−0.0739071
$379$	−7.51780	−	1.71589i	−0.386163	−	0.0881392i	0.0250318	−	0.999687i	$-0.492031\pi$
$379$	−7.51780	−	1.71589i	−0.386163	−	0.0881392i	−0.411195	+	0.911547i	$0.634888\pi$
$380$	−0.180280	−	0.374355i	−0.00924815	−	0.0192040i
$381$	13.7538	+	6.62347i	0.704627	+	0.339330i
$382$	1.49388	−	6.54511i	0.0764335	−	0.334877i
$383$	−3.92927	−	17.2153i	−0.200776	−	0.879659i	−0.970466	−	0.241240i	$-0.922446\pi$
$383$	−3.92927	−	17.2153i	−0.200776	−	0.879659i	0.769689	−	0.638419i	$-0.220411\pi$
$384$	−7.27155	+	3.50180i	−0.371075	+	0.178700i
$385$	−0.216116	−	0.172347i	−0.0110143	−	0.00878361i
$386$	−2.25210	+	2.82404i	−0.114629	+	0.143740i
$387$	−3.12794	+	6.49524i	−0.159002	+	0.330172i
$388$	0.367933	−	0.293417i	0.0186790	−	0.0148960i
$389$			17.4066i			0.882550i	0.897372	+	0.441275i	$0.145474\pi$
$389$			17.4066i			0.882550i	−0.897372	+	0.441275i	$0.854526\pi$
$390$	1.27367	+	1.59713i	0.0644947	+	0.0808738i
$391$	−7.14110	+	1.62991i	−0.361141	+	0.0824281i
$392$	16.9158	−	3.86092i	0.854377	−	0.195006i
$393$	5.45089	+	6.83520i	0.274961	+	0.344790i
$394$		−	32.1493i		−	1.61966i
$395$	1.48804	−	1.18667i	0.0748715	−	0.0597080i
$396$	−0.101458	+	0.210679i	−0.00509844	+	0.0105870i
$397$	5.44605	−	6.82914i	0.273330	−	0.342744i	−0.626154	−	0.779700i	$-0.715372\pi$
$397$	5.44605	−	6.82914i	0.273330	−	0.342744i	0.899483	+	0.436955i	$0.143943\pi$
$398$	5.35212	+	4.26817i	0.268278	+	0.213944i
$399$	4.16125	−	2.00395i	0.208323	−	0.100323i
$400$	−3.59186	−	15.7370i	−0.179593	−	0.786849i
$401$	−2.21564	+	9.70733i	−0.110644	+	0.484761i	0.888996	+	0.457915i	$0.151404\pi$
$401$	−2.21564	+	9.70733i	−0.110644	+	0.484761i	−0.999640	+	0.0268462i	$0.991454\pi$
$402$	17.9049	+	8.62253i	0.893014	+	0.430053i
$403$	9.42562	+	19.5725i	0.469524	+	0.974976i
$404$	−4.79671	−	1.09482i	−0.238645	−	0.0544693i
$405$	0.326108			0.0162044
$406$	1.15460	+	7.65142i	0.0573016	+	0.379734i
$407$	−1.37632			−0.0682218
$408$	15.1623	+	3.46070i	0.750647	+	0.171330i
$409$	−8.84673	−	18.3704i	−0.437443	−	0.908359i	−0.996838	−	0.0794584i	$-0.974681\pi$
$409$	−8.84673	−	18.3704i	−0.437443	−	0.908359i	0.559395	−	0.828901i	$-0.311033\pi$
$410$	−0.513984	−	0.247522i	−0.0253839	−	0.0122242i
$411$	−5.18481	+	22.7161i	−0.255748	+	1.12050i
$412$	0.741871	+	3.25035i	0.0365494	+	0.160133i
$413$	3.65326	−	1.75932i	0.179765	−	0.0865704i
$414$	−1.43877	−	1.14738i	−0.0707119	−	0.0563909i
$415$	2.58771	−	3.24489i	0.127026	−	0.159285i
$416$	3.56143	−	7.39540i	0.174614	−	0.362589i
$417$	−10.5775	+	8.43530i	−0.517984	+	0.413078i
$418$			4.18641i			0.204764i
$419$	−22.7123	−	28.4803i	−1.10957	−	1.39135i	−0.911567	−	0.411153i	$-0.865126\pi$
$419$	−22.7123	−	28.4803i	−1.10957	−	1.39135i	−0.198002	−	0.980202i	$-0.563445\pi$
$420$	0.106801	−	0.0243767i	0.00521138	−	0.00118946i
$421$	19.3547	−	4.41759i	0.943292	−	0.215300i	0.276897	−	0.960900i	$-0.410694\pi$
$421$	19.3547	−	4.41759i	0.943292	−	0.215300i	0.666394	+	0.745599i	$0.267837\pi$
$422$	19.6493	+	24.6394i	0.956511	+	1.19943i
$423$			0.453383i			0.0220442i
$424$	−20.7122	+	16.5174i	−1.00587	+	0.802156i
$425$	−11.0047	+	22.8515i	−0.533807	+	1.10846i
$426$	12.2105	−	15.3115i	0.591601	−	0.741844i
$427$	7.63071	+	6.08528i	0.369276	+	0.294488i
$428$	3.43100	−	1.65228i	0.165844	−	0.0798660i
$429$	0.822277	+	3.60263i	0.0396999	+	0.173937i
$430$	−0.681203	+	2.98455i	−0.0328505	+	0.143928i
$431$	32.2188	+	15.5158i	1.55193	+	0.747369i	0.996452	−	0.0841645i	$-0.0268221\pi$
$431$	32.2188	+	15.5158i	1.55193	+	0.747369i	0.555475	+	0.831533i	$0.312536\pi$
$432$	1.43116	+	2.97184i	0.0688568	+	0.142983i
$433$	36.6041	+	8.35464i	1.75908	+	0.401498i	0.975536	−	0.219839i	$-0.0705532\pi$
$433$	36.6041	+	8.35464i	1.75908	+	0.401498i	0.783543	+	0.621337i	$0.213410\pi$
$434$	−6.48877			−0.311471
$435$	−0.262035	−	1.73648i	−0.0125636	−	0.0832580i
$436$	−2.67952			−0.128326
$437$	5.76679	+	1.31623i	0.275863	+	0.0629639i
$438$	−7.74100	−	16.0744i	−0.369879	−	0.768062i
$439$	6.21349	+	2.99226i	0.296554	+	0.142813i	0.576244	−	0.817277i	$-0.304518\pi$
$439$	6.21349	+	2.99226i	0.296554	+	0.142813i	−0.279691	+	0.960090i	$0.590232\pi$
$440$	−0.167260	+	0.732815i	−0.00797382	+	0.0349356i
$441$	−1.28668	−	5.63731i	−0.0612705	−	0.268443i
$442$	29.2515	−	14.0868i	1.39135	−	0.670040i
$443$	−10.8106	−	8.62118i	−0.513628	−	0.409605i	0.332080	−	0.943251i	$-0.392250\pi$
$443$	−10.8106	−	8.62118i	−0.513628	−	0.409605i	−0.845707	+	0.533647i	$0.820821\pi$
$444$	0.340079	−	0.426446i	0.0161395	−	0.0202382i
$445$	1.17261	−	2.43495i	0.0555870	−	0.115428i
$446$	1.23625	−	0.985875i	0.0585381	−	0.0466826i
$447$		−	1.32696i		−	0.0627629i
$448$	6.06751	+	7.60842i	0.286663	+	0.359464i
$449$	19.5253	−	4.45651i	0.921454	−	0.210316i	0.264622	−	0.964352i	$-0.414753\pi$
$449$	19.5253	−	4.45651i	0.921454	−	0.210316i	0.656833	+	0.754036i	$0.271896\pi$
$450$	−6.21248	+	1.41796i	−0.292859	+	0.0668432i
$451$	−0.643413	−	0.806814i	−0.0302971	−	0.0379914i
$452$			0.749317i			0.0352449i
$453$	−11.2351	+	8.95969i	−0.527871	+	0.420963i
$454$	−9.02620	+	18.7431i	−0.423621	+	0.879657i
$455$	1.07937	−	1.35349i	0.0506016	−	0.0634524i
$456$	−9.81918	−	7.83054i	−0.459825	−	0.366699i
$457$	−22.0357	+	10.6119i	−1.03079	+	0.496402i	−0.871276	−	0.490794i	$-0.836707\pi$
$457$	−22.0357	+	10.6119i	−1.03079	+	0.496402i	−0.159513	+	0.987196i	$0.550992\pi$
$458$	4.44401	+	19.4705i	0.207655	+	0.909796i
$459$	1.15330	−	5.05295i	0.0538316	−	0.235851i
$460$	0.126404	+	0.0608731i	0.00589363	+	0.00283822i
$461$	9.66512	+	20.0698i	0.450150	+	0.934746i	0.995339	+	0.0964329i	$0.0307433\pi$
$461$	9.66512	+	20.0698i	0.450150	+	0.934746i	−0.545190	+	0.838313i	$0.683542\pi$
$462$	−1.07608	−	0.245609i	−0.0500638	−	0.0114267i
$463$	−27.5102			−1.27851			−0.639254	−	0.768996i	$-0.720757\pi$
$463$	−27.5102			−1.27851			−0.639254	+	0.768996i	$0.720757\pi$
$464$	14.6747	−	10.0087i	0.681257	−	0.464643i
$465$	1.47262			0.0682911
$466$	16.4846	+	3.76250i	0.763634	+	0.174294i
$467$	10.3029	+	21.3941i	0.476760	+	0.990002i	0.991187	+	0.132468i	$0.0422902\pi$
$467$	10.3029	+	21.3941i	0.476760	+	0.990002i	−0.514428	+	0.857534i	$0.671996\pi$
$468$	−1.31943	−	0.635406i	−0.0609908	−	0.0293716i
$469$	3.74754	−	16.4190i	0.173045	−	0.758160i
$470$	0.0428407	+	0.187697i	0.00197609	+	0.00865783i
$471$	11.8866	−	5.72427i	0.547704	−	0.263761i
$472$	−8.62050	−	6.87462i	−0.396791	−	0.316430i
$473$	−3.45267	+	4.32951i	−0.158754	+	0.199071i
$474$	3.29742	−	6.84715i	0.151455	−	0.314500i
$475$	16.0136	−	12.7704i	0.734753	−	0.585946i
$476$		−	1.74107i		−	0.0798018i
$477$	5.50454	+	6.90248i	0.252036	+	0.316043i
$478$	−0.323798	+	0.0739049i	−0.0148102	+	0.00338033i
$479$	25.5186	−	5.82446i	1.16598	−	0.266126i	0.404635	−	0.914478i	$-0.367399\pi$
$479$	25.5186	−	5.82446i	1.16598	−	0.266126i	0.761341	+	0.648352i	$0.224541\pi$
$480$	−0.346925	−	0.435030i	−0.0158349	−	0.0198563i
$481$		−	8.61959i		−	0.393020i
$482$	−8.54765	+	6.81652i	−0.389335	+	0.310484i
$483$	−0.676654	+	1.40509i	−0.0307888	+	0.0639336i
$484$	1.97583	−	2.47761i	0.0898104	−	0.112619i
$485$	−0.394148	−	0.314322i	−0.0178973	−	0.0142726i
$486$	1.17319	−	0.564980i	0.0532171	−	0.0256280i
$487$	3.63049	+	15.9062i	0.164513	+	0.720780i	0.988128	+	0.153631i	$0.0490966\pi$
$487$	3.63049	+	15.9062i	0.164513	+	0.720780i	−0.823615	+	0.567149i	$0.808046\pi$
$488$	5.90569	−	25.8745i	0.267338	−	1.17128i
$489$	2.71261	+	1.30632i	0.122668	+	0.0590739i
$490$	−1.06535	−	2.21223i	−0.0481277	−	0.0999382i
$491$	−32.0763	−	7.32121i	−1.44758	−	0.330402i	−0.574714	−	0.818354i	$-0.694887\pi$
$491$	−32.0763	−	7.32121i	−1.44758	−	0.330402i	−0.872870	+	0.487952i	$0.837744\pi$
$492$	0.408969			0.0184378
$493$	−27.8331	−	2.08104i	−1.25354	−	0.0937254i
$494$	−26.2185			−1.17963
$495$	0.244216	+	0.0557407i	0.0109767	+	0.00250536i
$496$	6.46277	+	13.4201i	0.290187	+	0.602580i
$497$	−14.9530	−	7.20098i	−0.670733	−	0.323008i
$498$	3.68770	−	16.1569i	0.165250	−	0.724007i
$499$	−4.93194	−	21.6082i	−0.220784	−	0.967317i	−0.956890	−	0.290451i	$-0.906195\pi$
$499$	−4.93194	−	21.6082i	−0.220784	−	0.967317i	0.736106	−	0.676866i	$-0.236662\pi$
$500$	0.884908	−	0.426149i	0.0395743	−	0.0190580i
$501$	−1.07466	−	0.857016i	−0.0480125	−	0.0382887i
$502$	−15.1381	+	18.9825i	−0.675645	+	0.847233i
$503$	−17.2581	+	35.8369i	−0.769503	+	1.59789i	0.0317009	+	0.999497i	$0.489908\pi$
$503$	−17.2581	+	35.8369i	−0.769503	+	1.59789i	−0.801204	+	0.598392i	$0.795807\pi$
$504$	2.58885	−	2.06454i	0.115316	−	0.0919618i
$505$			5.27061i			0.234539i
$506$	−0.881352	−	1.10518i	−0.0391809	−	0.0491313i
$507$	−9.88838	+	2.25696i	−0.439159	+	0.100235i
$508$	−4.53060	+	1.03408i	−0.201013	+	0.0458798i
$509$	−6.35541	−	7.96943i	−0.281699	−	0.353239i	0.620771	−	0.783992i	$-0.286820\pi$
$509$	−6.35541	−	7.96943i	−0.281699	−	0.353239i	−0.902470	+	0.430753i	$0.858248\pi$
$510$		−	2.20086i		−	0.0974558i
$511$	−11.8209	+	9.42685i	−0.522926	+	0.417019i
$512$	11.0309	−	22.9058i	0.487500	−	1.01230i
$513$	−2.60958	+	3.27231i	−0.115216	+	0.144476i
$514$	−25.0632	−	19.9872i	−1.10549	−	0.881599i
$515$	3.21779	−	1.54960i	0.141793	−	0.0682837i
$516$	−0.488346	−	2.13958i	−0.0214982	−	0.0941899i
$517$	−0.0774955	+	0.339530i	−0.00340825	+	0.0149325i
$518$	2.31965	+	1.11708i	0.101919	+	0.0490818i
$519$	−5.76444	−	11.9700i	−0.253031	−	0.525424i
$520$	−4.58945	−	1.04751i	−0.201261	−	0.0459365i
$521$	−7.09229			−0.310719			−0.155359	−	0.987858i	$-0.549654\pi$
$521$	−7.09229			−0.310719			−0.155359	+	0.987858i	$0.549654\pi$
$522$	−3.95113	−	5.79313i	−0.172936	−	0.253559i
$523$	10.9937			0.480723			0.240361	−	0.970683i	$-0.422734\pi$
$523$	10.9937			0.480723			0.240361	+	0.970683i	$0.422734\pi$
$524$	−2.59467	−	0.592216i	−0.113349	−	0.0258711i
$525$	2.34304	+	4.86537i	0.102259	+	0.212342i
$526$	11.9287	+	5.74457i	0.520117	+	0.250475i
$527$	5.20803	−	22.8179i	0.226865	−	0.993961i
$528$	0.563802	+	2.47018i	0.0245364	+	0.107501i
$529$	18.9228	−	9.11274i	0.822730	−	0.396206i
$530$	2.93106	+	2.33745i	0.127317	+	0.101532i
$531$	−2.29101	+	2.87284i	−0.0994215	+	0.124671i
$532$	−0.610041	+	1.26676i	−0.0264486	+	0.0549211i
$533$	5.05289	−	4.02954i	0.218865	−	0.174539i
$534$		−	10.7914i		−	0.466990i
$535$	−2.54349	−	3.18943i	−0.109965	−	0.137891i
$536$	−44.6473	+	10.1905i	−1.92847	+	0.440161i
$537$	5.99973	−	1.36940i	0.258908	−	0.0590940i
$538$	0.542356	+	0.680093i	0.0233826	+	0.0293209i
$539$		−	4.44161i		−	0.191314i
$540$	−0.0776149	+	0.0618958i	−0.00334001	+	0.00266357i
$541$	−2.09471	+	4.34971i	−0.0900586	+	0.187009i	−0.941133	−	0.338037i	$-0.890237\pi$
$541$	−2.09471	+	4.34971i	−0.0900586	+	0.187009i	0.851074	+	0.525045i	$0.175952\pi$
$542$	−7.54323	+	9.45892i	−0.324010	+	0.406295i
$543$	−18.8520	−	15.0339i	−0.809015	−	0.645168i
$544$	−7.96759	+	3.83699i	−0.341608	+	0.164510i
$545$	0.638731	+	2.79847i	0.0273602	+	0.119873i
$546$	1.53819	−	6.73925i	0.0658284	−	0.288413i
$547$	30.9219	+	14.8912i	1.32212	+	0.636701i	0.955864	−	0.293811i	$-0.0949236\pi$
$547$	30.9219	+	14.8912i	1.32212	+	0.636701i	0.366261	+	0.930512i	$0.380638\pi$
$548$	−3.07756	−	6.39062i	−0.131467	−	0.272994i
$549$	−8.62286	−	1.96811i	−0.368015	−	0.0839969i
$550$	−4.89478			−0.208714
$551$	19.5215	+	11.2663i	0.831645	+	0.479962i
$552$	4.24073			0.180498
$553$	−6.27894	−	1.43313i	−0.267008	−	0.0609428i
$554$	−8.32961	−	17.2966i	−0.353891	−	0.734862i
$555$	−0.526442	−	0.253521i	−0.0223462	−	0.0107614i
$556$	0.916459	−	4.01527i	0.0388665	−	0.170285i
$557$	−2.97941	−	13.0536i	−0.126242	−	0.553101i	−0.998003	−	0.0631697i	$-0.979879\pi$
$557$	−2.97941	−	13.0536i	−0.126242	−	0.553101i	0.871761	−	0.489931i	$-0.162978\pi$
$558$	5.29784	−	2.55131i	0.224276	−	0.108005i
$559$	−27.1147	−	21.6233i	−1.14683	−	0.914568i
$560$	0.740080	−	0.928031i	0.0312741	−	0.0392165i
$561$	1.72737	−	3.58693i	0.0729298	−	0.151440i
$562$	−21.9160	+	17.4774i	−0.924470	+	0.737240i
$563$		−	1.89811i		−	0.0799960i	−0.999200	−	0.0399980i	$-0.987265\pi$
$563$		−	1.89811i		−	0.0799960i	0.999200	−	0.0399980i	$-0.0127352\pi$
$564$	−0.0860529	−	0.107907i	−0.00362348	−	0.00454370i
$565$	0.782578	−	0.178618i	0.0329233	−	0.00751453i
$566$	13.1025	−	2.99057i	0.550741	−	0.125703i
$567$	−0.688022	−	0.862752i	−0.0288942	−	0.0362322i
$568$			45.1301i			1.89362i
$569$	−8.72457	+	6.95761i	−0.365753	+	0.291678i	−0.789070	−	0.614303i	$-0.789437\pi$
$569$	−8.72457	+	6.95761i	−0.365753	+	0.291678i	0.423317	+	0.905982i	$0.360866\pi$
$570$	−0.771143	+	1.60130i	−0.0322996	+	0.0670709i
$571$	−8.23671	+	10.3285i	−0.344696	+	0.432235i	−0.923716	−	0.383079i	$-0.874864\pi$
$571$	−8.23671	+	10.3285i	−0.344696	+	0.432235i	0.579020	+	0.815313i	$0.303435\pi$
$572$	−0.879491	−	0.701371i	−0.0367734	−	0.0293258i
$573$	4.64510	−	2.23696i	0.194052	−	0.0934505i
$574$	0.429559	+	1.88202i	0.0179294	+	0.0785540i
$575$	−1.53895	+	6.74258i	−0.0641786	+	0.281185i
$576$	−7.94545	−	3.82633i	−0.331060	−	0.159430i
$577$	6.01524	+	12.4908i	0.250418	+	0.519998i	0.987848	−	0.155426i	$-0.0496750\pi$
$577$	6.01524	+	12.4908i	0.250418	+	0.519998i	−0.737430	+	0.675424i	$0.763961\pi$
$578$	−12.5203	−	2.85767i	−0.520775	−	0.118864i
$579$	−2.77395			−0.115281
$580$	0.391953	+	0.363555i	0.0162750	+	0.0150958i
$581$	−14.0442			−0.582653
$582$	−1.96253	−	0.447935i	−0.0813496	−	0.0185675i
$583$	2.94243	+	6.11001i	0.121863	+	0.253051i
$584$	37.0420	+	17.8385i	1.53281	+	0.738163i
$585$	−0.349091	+	1.52947i	−0.0144331	+	0.0632357i
$586$	−7.30403	−	32.0011i	−0.301727	−	1.32195i
$587$	25.0371	−	12.0572i	1.03339	−	0.497655i	0.161253	−	0.986913i	$-0.448447\pi$
$587$	25.0371	−	12.0572i	1.03339	−	0.497655i	0.872139	+	0.489258i	$0.162732\pi$
$588$	1.37621	+	1.09749i	0.0567538	+	0.0452596i
$589$	−11.7842	+	14.7769i	−0.485560	+	0.608873i
$590$	−0.677005	+	1.40582i	−0.0278719	+	0.0578765i
$591$	19.3030	−	15.3937i	0.794021	−	0.633210i
$592$		−	5.91011i		−	0.242904i
$593$	5.03568	+	6.31455i	0.206791	+	0.259307i	0.874401	−	0.485203i	$-0.161254\pi$
$593$	5.03568	+	6.31455i	0.206791	+	0.259307i	−0.667611	+	0.744511i	$0.732683\pi$
$594$	0.975152	−	0.222572i	0.0400110	−	0.00913224i
$595$	−1.81835	+	0.415028i	−0.0745453	+	0.0170145i
$596$	0.251859	+	0.315821i	0.0103165	+	0.0129365i
$597$			5.25719i			0.215162i
$598$	6.92149	−	5.51970i	0.283041	−	0.225717i
$599$	8.35658	−	17.3526i	0.341440	−	0.709008i	−0.657574	−	0.753390i	$-0.728417\pi$
$599$	8.35658	−	17.3526i	0.341440	−	0.709008i	0.999015	+	0.0443814i	$0.0141317\pi$
$600$	9.15553	−	11.4807i	0.373773	−	0.468696i
$601$	17.3000	+	13.7963i	0.705681	+	0.562762i	0.909226	−	0.416304i	$-0.136675\pi$
$601$	17.3000	+	13.7963i	0.705681	+	0.562762i	−0.203544	+	0.979066i	$0.565246\pi$
$602$	9.33313	−	4.49460i	0.380390	−	0.183186i
$603$	3.39604	+	14.8790i	0.138298	+	0.605921i
$604$	0.973432	−	4.26488i	0.0396084	−	0.173536i
$605$	−3.05858	−	1.47293i	−0.124349	−	0.0598833i
$606$	9.13131	+	18.9614i	0.370934	+	0.770253i
$607$	11.5672	+	2.64014i	0.469499	+	0.107160i	0.450723	−	0.892664i	$-0.351166\pi$
$607$	11.5672	+	2.64014i	0.469499	+	0.107160i	0.0187755	+	0.999824i	$0.494023\pi$
$608$	7.14145			0.289624
$609$	−4.04121	+	4.35687i	−0.163758	+	0.176549i
$610$	−3.75577			−0.152067
$611$	−2.12640	−	0.485336i	−0.0860248	−	0.0196346i
$612$	0.684568	+	1.42152i	0.0276720	+	0.0574616i
$613$	30.4811	+	14.6789i	1.23112	+	0.592876i	0.932387	−	0.361461i	$-0.117722\pi$
$613$	30.4811	+	14.6789i	1.23112	+	0.592876i	0.298733	+	0.954337i	$0.403436\pi$
$614$	5.15314	−	22.5774i	0.207964	−	0.911150i
$615$	−0.0974881	−	0.427123i	−0.00393110	−	0.0172233i
$616$	2.29163	−	1.10359i	0.0923323	−	0.0444649i
$617$	1.32047	+	1.05304i	0.0531601	+	0.0423938i	0.649709	−	0.760183i	$-0.274891\pi$
$617$	1.32047	+	1.05304i	0.0531601	+	0.0423938i	−0.596549	+	0.802576i	$0.703462\pi$
$618$	8.89151	−	11.1496i	0.357669	−	0.448502i
$619$	−6.73642	+	13.9883i	−0.270759	+	0.562238i	−0.991369	−	0.131104i	$-0.958148\pi$
$619$	−6.73642	+	13.9883i	−0.270759	+	0.562238i	0.720609	+	0.693341i	$0.243862\pi$
$620$	−0.350489	+	0.279506i	−0.0140760	+	0.0112252i
$621$		−	1.41325i		−	0.0567119i
$622$	6.81851	+	8.55014i	0.273397	+	0.342830i
$623$	−8.91589	+	2.03499i	−0.357208	+	0.0815303i
$624$	−15.4702	+	3.53096i	−0.619302	+	0.141352i
$625$	14.5997	+	18.3075i	0.583988	+	0.732298i
$626$			2.73479i			0.109304i
$627$	−2.51359	+	2.00452i	−0.100383	+	0.0800530i
$628$	−1.74257	+	3.61849i	−0.0695363	+	0.144394i
$629$	−5.79004	+	7.26048i	−0.230864	+	0.289494i
$630$	−0.366358	−	0.292161i	−0.0145961	−	0.0116400i
$631$	−16.5425	+	7.96642i	−0.658545	+	0.317138i	−0.733142	−	0.680075i	$-0.761947\pi$
$631$	−16.5425	+	7.96642i	−0.658545	+	0.317138i	0.0745977	+	0.997214i	$0.476233\pi$
$632$	3.89702	+	17.0740i	0.155015	+	0.679166i
$633$	−5.38553	+	23.5955i	−0.214056	+	0.937839i
$634$	5.89864	+	2.84064i	0.234265	+	0.112816i
$635$	2.15996	+	4.48521i	0.0857155	+	0.177990i
$636$	−2.62021	−	0.598045i	−0.103898	−	0.0237140i
$637$	27.8167			1.10214
$638$	−1.96873	−	5.01373i	−0.0779426	−	0.198495i
$639$	15.0399			0.594970
$640$	−2.56597	−	0.585665i	−0.101429	−	0.0231504i
$641$	2.23437	+	4.63971i	0.0882522	+	0.183258i	0.940424	−	0.340005i	$-0.110429\pi$
$641$	2.23437	+	4.63971i	0.0882522	+	0.183258i	−0.852171	+	0.523263i	$0.824715\pi$
$642$	−14.6760	−	7.06761i	−0.579217	−	0.278936i
$643$	6.29062	−	27.5610i	0.248078	−	1.08690i	−0.685372	−	0.728193i	$-0.740361\pi$
$643$	6.29062	−	27.5610i	0.248078	−	1.08690i	0.933450	−	0.358707i	$-0.116782\pi$
$644$	−0.105642	−	0.462846i	−0.00416286	−	0.0182387i
$645$	−2.11815	+	1.02005i	−0.0834020	+	0.0401643i
$646$	22.0844	+	17.6118i	0.868901	+	0.692925i
$647$	17.6767	−	22.1659i	0.694943	−	0.871431i	−0.301691	−	0.953406i	$-0.597551\pi$
$647$	17.6767	−	22.1659i	0.694943	−	0.871431i	0.996634	+	0.0819746i	$0.0261226\pi$
$648$	−1.30195	+	2.70353i	−0.0511454	+	0.106205i
$649$	−2.20674	+	1.75982i	−0.0866223	+	0.0690790i
$650$		−	30.6549i		−	1.20238i
$651$	−3.10693	−	3.89597i	−0.121770	−	0.152695i
$652$	−0.893553	+	0.203948i	−0.0349942	+	0.00798721i
$653$	39.3129	−	8.97291i	1.53843	−	0.351137i	0.632500	−	0.774561i	$-0.282029\pi$
$653$	39.3129	−	8.97291i	1.53843	−	0.351137i	0.905932	+	0.423424i	$0.139172\pi$
$654$	7.14620	+	8.96105i	0.279439	+	0.350405i
$655$			2.85101i			0.111398i
$656$	3.46456	−	2.76290i	0.135268	−	0.107873i
$657$	5.94481	−	12.3445i	0.231929	−	0.481606i
$658$	0.406188	−	0.509343i	0.0158348	−	0.0198563i
$659$	−38.6554	−	30.8267i	−1.50580	−	1.20084i	−0.920941	−	0.389701i	$-0.872578\pi$
$659$	−38.6554	−	30.8267i	−1.50580	−	1.20084i	−0.584859	−	0.811135i	$-0.698850\pi$
$660$	−0.0687040	+	0.0330861i	−0.00267430	+	0.00128788i
$661$	−3.53346	−	15.4811i	−0.137436	−	0.602146i	−0.995993	−	0.0894282i	$-0.971496\pi$
$661$	−3.53346	−	15.4811i	−0.137436	−	0.602146i	0.858557	−	0.512717i	$-0.171361\pi$
$662$	1.10374	−	4.83579i	0.0428980	−	0.187949i
$663$	22.4641	+	10.8181i	0.872433	+	0.420142i
$664$	16.5699	+	34.4077i	0.643036	+	1.33528i
$665$	1.46841	+	0.335155i	0.0569426	+	0.0129968i
$666$	−2.33313			−0.0904070
$667$	−7.52541	+	1.13558i	−0.291385	+	0.0439699i
$668$	0.418437			0.0161898
$669$	1.18387	+	0.270212i	0.0457712	+	0.0104470i
$670$	2.81187	+	5.83892i	0.108632	+	0.225577i
$671$	−6.12109	−	2.94776i	−0.236302	−	0.113797i
$672$	−0.418975	+	1.83565i	−0.0161623	+	0.0708118i
$673$	−2.60304	−	11.4047i	−0.100340	−	0.439617i	−0.999995	−	0.00301712i	$-0.999040\pi$
$673$	−2.60304	−	11.4047i	−0.100340	−	0.439617i	0.899656	−	0.436600i	$-0.143818\pi$
$674$	−1.77254	+	0.853611i	−0.0682757	+	0.0328799i
$675$	−3.82601	−	3.05114i	−0.147263	−	0.117439i
$676$	1.92510	−	2.41400i	0.0740423	−	0.0928461i
$677$	−8.46222	+	17.5720i	−0.325230	+	0.675346i	−0.997912	−	0.0645849i	$-0.979428\pi$
$677$	−8.46222	+	17.5720i	−0.325230	+	0.675346i	0.672683	+	0.739931i	$0.265142\pi$
$678$	2.50592	−	1.99840i	0.0962392	−	0.0767482i
$679$			1.70592i			0.0654671i
$680$	3.16216	+	3.96522i	0.121263	+	0.152059i
$681$	−15.5756	+	3.55503i	−0.596858	+	0.136229i
$682$	4.40354	−	1.00508i	0.168620	−	0.0384865i
$683$	15.4166	+	19.3318i	0.589900	+	0.739711i	0.983766	−	0.179457i	$-0.0574340\pi$
$683$	15.4166	+	19.3318i	0.589900	+	0.739711i	−0.393866	+	0.919168i	$0.628863\pi$
$684$		−	1.27413i		−	0.0487174i
$685$	−5.94068	+	4.73753i	−0.226982	+	0.181012i
$686$	−7.96919	+	16.5482i	−0.304265	+	0.631813i
$687$	−9.56256	+	11.9911i	−0.364834	+	0.457488i
$688$	−18.5915	−	14.8262i	−0.708794	−	0.565244i
$689$	−38.2656	+	18.4277i	−1.45780	+	0.702041i
$690$	−0.133540	−	0.585077i	−0.00508378	−	0.0222735i
$691$	10.6279	−	46.5640i	0.404306	−	1.77138i	−0.205324	−	0.978694i	$-0.565825\pi$
$691$	10.6279	−	46.5640i	0.404306	−	1.77138i	0.609630	−	0.792686i	$-0.291318\pi$
$692$	3.64388	+	1.75480i	0.138520	+	0.0667075i
$693$	−0.367779	−	0.763701i	−0.0139708	−	0.0290106i
$694$	−29.6556	−	6.76870i	−1.12571	−	0.256936i
$695$	−4.41197			−0.167355
$696$	15.4421	+	4.76038i	0.585331	+	0.180442i
$697$	−6.96293			−0.263740
$698$	−19.0729	−	4.35327i	−0.721921	−	0.164774i
$699$	5.63404	+	11.6992i	0.213099	+	0.442504i
$700$	−1.48111	−	0.713264i	−0.0559806	−	0.0269588i
$701$	−1.81198	+	7.93882i	−0.0684377	+	0.299845i	−0.997550	−	0.0699516i	$-0.977716\pi$
$701$	−1.81198	+	7.93882i	−0.0684377	+	0.299845i	0.929113	+	0.369797i	$0.120573\pi$
$702$	1.39392	+	6.10715i	0.0526100	+	0.230500i
$703$	6.75665	−	3.25383i	0.254832	−	0.122721i
$704$	−5.29617	−	4.22356i	−0.199607	−	0.159181i
$705$	−0.0921840	+	0.115595i	−0.00347185	+	0.00435356i
$706$	9.07379	−	18.8419i	0.341497	−	0.709125i
$707$	13.9440	−	11.1199i	0.524417	−	0.418208i
$708$		−	1.11859i		−	0.0420390i
$709$	1.10726	+	1.38847i	0.0415842	+	0.0521449i	0.802189	−	0.597071i	$-0.203669\pi$
$709$	1.10726	+	1.38847i	0.0415842	+	0.0521449i	−0.760605	+	0.649215i	$0.775097\pi$
$710$	6.22641	−	1.42114i	0.233673	−	0.0533344i
$711$	5.69002	−	1.29871i	0.213392	−	0.0487054i
$712$	15.5049	+	19.4425i	0.581071	+	0.728640i
$713$		−	6.38190i		−	0.239004i
$714$	−5.82261	+	4.64338i	−0.217906	+	0.173774i
$715$	−0.522855	+	1.08572i	−0.0195537	+	0.0406036i
$716$	−1.16805	+	1.46468i	−0.0436519	+	0.0547378i
$717$	−0.199414	−	0.159028i	−0.00744726	−	0.00593899i
$718$	−31.1376	+	14.9951i	−1.16204	+	0.559611i
$719$	−6.25224	−	27.3929i	−0.233169	−	1.02158i	−0.946992	−	0.321256i	$-0.895895\pi$
$719$	−6.25224	−	27.3929i	−0.233169	−	1.02158i	0.713823	−	0.700326i	$-0.246962\pi$
$720$	−0.239358	+	1.04869i	−0.00892033	+	0.0390825i
$721$	−10.8885	−	5.24364i	−0.405510	−	0.195283i
$722$	0.837332	+	1.73874i	0.0311623	+	0.0647091i
$723$	−8.18553	−	1.86829i	−0.304423	−	0.0694826i
$724$	7.34031			0.272800
$725$	−13.1727	+	22.8247i	−0.489221	+	0.847689i
$726$	−13.5553			−0.503084
$727$	−45.8409	−	10.4629i	−1.70015	−	0.388047i	−0.741121	−	0.671372i	$-0.765705\pi$
$727$	−45.8409	−	10.4629i	−1.70015	−	0.388047i	−0.959024	+	0.283325i	$0.908563\pi$
$728$	6.91152	+	14.3519i	0.256158	+	0.531918i
$729$	0.900969	+	0.433884i	0.0333692	+	0.0160698i
$730$	1.29466	−	5.67227i	0.0479175	−	0.209940i
$731$	8.31436	+	36.4276i	0.307518	+	1.34732i
$732$	2.42583	−	1.16822i	0.0896611	−	0.0431785i
$733$	−24.3427	−	19.4127i	−0.899119	−	0.717023i	0.0605475	−	0.998165i	$-0.480715\pi$
$733$	−24.3427	−	19.4127i	−0.899119	−	0.717023i	−0.959666	+	0.281142i	$0.909287\pi$
$734$	13.8033	−	17.3088i	0.509489	−	0.638879i
$735$	0.818152	−	1.69891i	0.0301780	−	0.0626652i
$736$	−1.88529	+	1.50347i	−0.0694927	+	0.0554186i
$737$			11.7231i			0.431826i
$738$	−1.09071	−	1.36770i	−0.0401495	−	0.0503459i
$739$	12.3734	−	2.82414i	0.455161	−	0.103888i	0.0112072	−	0.999937i	$-0.496433\pi$
$739$	12.3734	−	2.82414i	0.455161	−	0.103888i	0.443954	+	0.896050i	$0.353575\pi$
$740$	0.173414	−	0.0395806i	0.00637483	−	0.00145501i
$741$	−12.5539	−	15.7421i	−0.461178	−	0.578299i
$742$		−	12.6860i		−	0.465717i
$743$	−10.7328	+	8.55909i	−0.393747	+	0.314002i	−0.800272	−	0.599637i	$-0.795312\pi$
$743$	−10.7328	+	8.55909i	−0.393747	+	0.314002i	0.406525	+	0.913639i	$0.366740\pi$
$744$	−5.87928	+	12.2084i	−0.215545	+	0.447583i
$745$	0.269803	−	0.338322i	0.00988482	−	0.0123952i
$746$	11.9443	+	9.52524i	0.437311	+	0.348744i
$747$	11.4666	−	5.52203i	0.419542	−	0.202041i
$748$	0.269684	+	1.18156i	0.00986061	+	0.0432022i
$749$	−3.07173	+	13.4581i	−0.112239	+	0.491750i
$750$	−3.78518	−	1.82285i	−0.138215	−	0.0665610i
$751$	−2.11829	−	4.39867i	−0.0772973	−	0.160510i	0.858739	−	0.512414i	$-0.171249\pi$
$751$	−2.11829	−	4.39867i	−0.0772973	−	0.160510i	−0.936036	+	0.351904i	$0.885534\pi$
$752$	−1.45799	−	0.332776i	−0.0531672	−	0.0121351i
$753$	−18.6458			−0.679492
$754$	31.3998	−	12.3297i	1.14351	−	0.449020i
$755$	−4.68624			−0.170550
$756$	0.327504	+	0.0747506i	0.0119112	+	0.00271865i
$757$	−8.84210	−	18.3608i	−0.321372	−	0.667335i	0.676220	−	0.736700i	$-0.263617\pi$
$757$	−8.84210	−	18.3608i	−0.321372	−	0.667335i	−0.997591	+	0.0693651i	$0.977903\pi$
$758$	−9.04664	−	4.35663i	−0.328589	−	0.158240i
$759$	0.241564	−	1.05836i	0.00876821	−	0.0384160i
$760$	−0.911368	−	3.99297i	−0.0330588	−	0.144840i
$761$	32.2082	−	15.5107i	1.16755	−	0.562261i	0.253288	−	0.967391i	$-0.418488\pi$
$761$	32.2082	−	15.5107i	1.16755	−	0.562261i	0.914259	+	0.405130i	$0.132774\pi$
$762$	15.5412	+	12.3937i	0.562998	+	0.448976i
$763$	6.05604	−	7.59403i	0.219243	−	0.274922i
$764$	−0.680973	+	1.41405i	−0.0246367	+	0.0511587i
$765$	1.32144	−	1.05381i	0.0477767	−	0.0381006i
$766$		−	22.9933i		−	0.830780i
$767$	−11.0213	−	13.8203i	−0.397958	−	0.499023i
$768$	6.94947	−	1.58617i	0.250767	−	0.0572360i
$769$	22.6272	−	5.16452i	0.815959	−	0.186237i	0.205879	−	0.978577i	$-0.433995\pi$
$769$	22.6272	−	5.16452i	0.815959	−	0.186237i	0.610080	+	0.792340i	$0.291137\pi$
$770$	−0.224421	−	0.281415i	−0.00808756	−	0.0101415i
$771$		−	24.6186i		−	0.886618i
$772$	0.660210	−	0.526500i	0.0237615	−	0.0189492i
$773$	−18.5344	+	38.4871i	−0.666636	+	1.38428i	0.243470	+	0.969908i	$0.421714\pi$
$773$	−18.5344	+	38.4871i	−0.666636	+	1.38428i	−0.910106	+	0.414375i	$0.864000\pi$
$774$	−5.85294	+	7.33936i	−0.210380	+	0.263808i
$775$	−17.2773	−	13.7782i	−0.620620	−	0.494928i
$776$	4.17942	−	2.01270i	0.150032	−	0.0722517i
$777$	0.439971	+	1.92764i	0.0157839	+	0.0691536i
$778$	−5.04364	+	22.0977i	−0.180823	+	0.792239i
$779$	5.06607	+	2.43969i	0.181511	+	0.0874110i
$780$	−0.207211	−	0.430277i	−0.00741933	−	0.0154064i
$781$	11.2631	+	2.57073i	0.403026	+	0.0919880i
$782$	−9.53788			−0.341074
$783$	1.58643	−	5.14619i	0.0566944	−	0.183910i
$784$	19.0728			0.681172
$785$	4.19450	+	0.957368i	0.149708	+	0.0341699i
$786$	4.93936	+	10.2567i	0.176181	+	0.365844i
$787$	−12.6203	−	6.07762i	−0.449866	−	0.216644i	0.195212	−	0.980761i	$-0.437461\pi$
$787$	−12.6203	−	6.07762i	−0.449866	−	0.216644i	−0.645077	+	0.764117i	$0.723175\pi$
$788$	−1.67245	+	7.32750i	−0.0595787	+	0.261031i
$789$	2.26254	+	9.91282i	0.0805484	+	0.352906i
$790$	2.23291	−	1.07531i	0.0794433	−	0.0382579i
$791$	−2.12364	−	1.69354i	−0.0755079	−	0.0602155i
$792$	−1.43711	+	1.80208i	−0.0510655	+	0.0640342i
$793$	18.4612	−	38.3350i	0.655575	−	1.36132i
$794$	8.89252	−	7.09155i	0.315584	−	0.251670i
$795$			2.87907i			0.102110i
$796$	−0.997823	−	1.25123i	−0.0353669	−	0.0443487i
$797$	8.94816	−	2.04236i	0.316960	−	0.0723441i	−0.0610812	−	0.998133i	$-0.519455\pi$
$797$	8.94816	−	2.04236i	0.316960	−	0.0723441i	0.378041	+	0.925789i	$0.376598\pi$
$798$	5.86336	−	1.33827i	0.207561	−	0.0473743i
$799$	1.46510	+	1.83718i	0.0518315	+	0.0649946i
$800$			8.34984i			0.295211i
$801$	6.47936	−	5.16712i	0.228937	−	0.182571i
$802$	−5.62549	+	11.6814i	−0.198643	+	0.412486i
$803$	6.56197	−	8.22845i	0.231567	−	0.290376i
$804$	−3.63234	−	2.89669i	−0.128103	−	0.102158i
$805$	−0.458209	+	0.220662i	−0.0161497	+	0.00777731i
$806$	6.29458	+	27.5784i	0.221717	+	0.971407i
$807$	−0.148651	+	0.651280i	−0.00523275	+	0.0229262i
$808$	−43.6949	−	21.0424i	−1.53718	−	0.740268i
$809$	−5.06054	−	10.5083i	−0.177919	−	0.369453i	0.792869	−	0.609392i	$-0.208587\pi$
$809$	−5.06054	−	10.5083i	−0.177919	−	0.369453i	−0.970788	+	0.239940i	$0.922872\pi$
$810$	0.413993	+	0.0944911i	0.0145462	+	0.00332008i
$811$	10.2506			0.359946			0.179973	−	0.983672i	$-0.442399\pi$
$811$	10.2506			0.359946			0.179973	+	0.983672i	$0.442399\pi$
$812$	0.134881	−	1.80398i	0.00473341	−	0.0633074i
$813$	−9.29114			−0.325854
$814$	−1.74724	−	0.398796i	−0.0612407	−	0.0139778i
$815$	0.426002	+	0.884601i	0.0149222	+	0.0309862i
$816$	15.4027	+	7.41756i	0.539203	+	0.259667i
$817$	6.71426	−	29.4171i	0.234902	−	1.02917i
$818$	−5.90799	−	25.8846i	−0.206568	−	0.905034i
$819$	4.78288	−	2.30331i	0.167127	−	0.0804843i
$820$	0.104271	+	0.0831536i	0.00364131	+	0.00290385i
$821$	−14.2411	+	17.8578i	−0.497019	+	0.623242i	−0.965554	−	0.260203i	$-0.916211\pi$
$821$	−14.2411	+	17.8578i	−0.497019	+	0.623242i	0.468535	+	0.883445i	$0.344782\pi$
$822$	−13.1642	+	27.3358i	−0.459155	+	0.953444i
$823$	0.386174	−	0.307963i	0.0134612	−	0.0107349i	−0.616736	−	0.787170i	$-0.711545\pi$
$823$	0.386174	−	0.307963i	0.0134612	−	0.0107349i	0.630197	+	0.776435i	$0.282974\pi$
$824$			32.8630i			1.14484i
$825$	−2.34371	−	2.93891i	−0.0815974	−	0.102320i
$826$	5.14758	−	1.17490i	0.179107	−	0.0408801i
$827$	−51.0365	+	11.6488i	−1.77471	+	0.405067i	−0.979530	−	0.201300i	$-0.935483\pi$
$827$	−51.0365	+	11.6488i	−1.77471	+	0.405067i	−0.795185	+	0.606367i	$0.792626\pi$
$828$	0.268238	+	0.336360i	0.00932192	+	0.0116893i
$829$			39.7417i			1.38029i	0.723673	+	0.690143i	$0.242452\pi$
$829$			39.7417i			1.38029i	−0.723673	+	0.690143i	$0.757548\pi$
$830$	4.22531	−	3.36958i	0.146663	−	0.116960i
$831$	6.39684	−	13.2832i	0.221904	−	0.460788i
$832$	26.4512	−	33.1687i	0.917029	−	1.14992i
$833$	−23.4307	−	18.6853i	−0.811825	−	0.647409i
$834$	−15.8723	+	7.64370i	−0.549613	+	0.264680i
$835$	−0.0997451	−	0.437012i	−0.00345182	−	0.0151234i
$836$	0.217783	−	0.954170i	0.00753218	−	0.0330006i
$837$	4.06855	+	1.95931i	0.140630	+	0.0677237i
$838$	−20.5809	−	42.7367i	−0.710955	−	1.47631i
$839$	31.1101	+	7.10068i	1.07404	+	0.245143i	0.722740	−	0.691120i	$-0.242882\pi$
$839$	31.1101	+	7.10068i	1.07404	+	0.245143i	0.351301	+	0.936263i	$0.385740\pi$
$840$	1.07983			0.0372576
$841$	−28.6776	−	4.31248i	−0.988881	−	0.148706i
$842$	25.8508			0.890877
$843$	−20.9875	−	4.79026i	−0.722848	−	0.164985i
$844$	−3.19670	−	6.63802i	−0.110035	−	0.228490i
$845$	−2.98005	−	1.43512i	−0.102517	−	0.0493695i
$846$	−0.131370	+	0.575568i	−0.00451658	+	0.0197884i
$847$	2.55619	+	11.1994i	0.0878317	+	0.384816i
$848$	−26.2372	+	12.6352i	−0.900988	+	0.433893i
$849$	8.06931	+	6.43506i	0.276938	+	0.220851i
$850$	−20.5918	+	25.8213i	−0.706293	+	0.885663i
$851$	−1.09869	+	2.28144i	−0.0376625	+	0.0782069i
$852$	−3.57956	+	2.85460i	−0.122634	+	0.0977970i
$853$			12.8451i			0.439806i	0.975522	+	0.219903i	$0.0705741\pi$
$853$			12.8451i			0.439806i	−0.975522	+	0.219903i	$0.929426\pi$
$854$	7.92392	+	9.93629i	0.271151	+	0.340013i
$855$	−1.33068	+	0.303720i	−0.0455084	+	0.0103870i
$856$	36.5959	−	8.35278i	1.25082	−	0.285492i
$857$	5.92373	+	7.42812i	0.202351	+	0.253740i	0.872644	−	0.488356i	$-0.162403\pi$
$857$	5.92373	+	7.42812i	0.202351	+	0.253740i	−0.670294	+	0.742096i	$0.733832\pi$
$858$			4.81179i			0.164272i
$859$	−14.5414	+	11.5964i	−0.496146	+	0.395663i	−0.839344	−	0.543600i	$-0.817061\pi$
$859$	−14.5414	+	11.5964i	−0.496146	+	0.395663i	0.343199	+	0.939263i	$0.388489\pi$
$860$	0.310521	−	0.644803i	0.0105887	−	0.0219876i
$861$	−0.924319	+	1.15906i	−0.0315007	+	0.0395006i
$862$	36.4060	+	29.0328i	1.23999	+	0.988861i
$863$	43.7868	−	21.0866i	1.49052	−	0.717796i	0.501441	−	0.865192i	$-0.332803\pi$
$863$	43.7868	−	21.0866i	1.49052	−	0.717796i	0.989078	+	0.147396i	$0.0470892\pi$
$864$	−0.379678	−	1.66348i	−0.0129169	−	0.0565927i
$865$	0.964085	−	4.22393i	0.0327799	−	0.143618i
$866$	44.0480	+	21.2124i	1.49681	+	0.720826i
$867$	−4.27913	−	8.88571i	−0.145327	−	0.301775i
$868$	1.47893	+	0.337555i	0.0501980	+	0.0114574i
$869$	4.48313			0.152080
$870$	0.170502	−	2.28039i	0.00578055	−	0.0773124i
$871$	−73.4191			−2.48771
$872$	−25.7501	−	5.87730i	−0.872010	−	0.199031i
$873$	−0.670747	−	1.39282i	−0.0227013	−	0.0471398i
$874$	6.93954	+	3.34191i	0.234734	+	0.113042i
$875$	−0.792248	+	3.47107i	−0.0267829	+	0.117343i
$876$	0.928124	+	4.06638i	0.0313584	+	0.137390i
$877$	−11.3140	+	5.44854i	−0.382047	+	0.183984i	−0.615043	−	0.788493i	$-0.710861\pi$
$877$	−11.3140	+	5.44854i	−0.382047	+	0.183984i	0.232996	+	0.972478i	$0.425147\pi$
$878$	7.02099	+	5.59905i	0.236947	+	0.188959i
$879$	15.7167	−	19.7081i	0.530112	−	0.664739i
$880$	−0.358501	+	0.744435i	−0.0120851	+	0.0250949i
$881$	−11.2267	+	8.95299i	−0.378237	+	0.301634i	−0.794093	−	0.607797i	$-0.792054\pi$
$881$	−11.2267	+	8.95299i	−0.378237	+	0.301634i	0.415856	+	0.909431i	$0.363482\pi$
$882$		−	7.52937i		−	0.253527i
$883$	15.4326	+	19.3518i	0.519347	+	0.651241i	0.970470	−	0.241221i	$-0.0775478\pi$
$883$	15.4326	+	19.3518i	0.519347	+	0.651241i	−0.451123	+	0.892462i	$0.648976\pi$
$884$	−7.39985	+	1.68897i	−0.248884	+	0.0568061i
$885$	−1.16824	+	0.266643i	−0.0392699	+	0.00896311i
$886$	−11.2260	−	14.0770i	−0.377146	−	0.472926i
$887$		−	17.0877i		−	0.573749i	−0.957968	−	0.286875i	$-0.907384\pi$
$887$		−	17.0877i		−	0.573749i	0.957968	−	0.286875i	$-0.0926163\pi$
$888$	4.20353	−	3.35220i	0.141061	−	0.112492i
$889$	7.30900	−	15.1773i	0.245136	−	0.509030i
$890$	2.19416	−	2.75139i	0.0735485	−	0.0922269i
$891$	0.600556	+	0.478928i	0.0201194	+	0.0160447i
$892$	−0.333054	+	0.160390i	−0.0111515	+	0.00537026i
$893$	−0.422258	−	1.85003i	−0.0141303	−	0.0619089i
$894$	0.384492	−	1.68457i	0.0128593	−	0.0563404i
$895$	1.80813	+	0.870750i	0.0604392	+	0.0291060i
$896$	3.86424	+	8.02417i	0.129095	+	0.268069i
$897$	6.62826	+	1.51286i	0.221311	+	0.0505128i
$898$	26.0786			0.870253
$899$	7.16392	−	23.2389i	0.238930	−	0.775061i
$900$	1.48972			0.0496573
$901$	44.6105	+	10.1820i	1.48619	+	0.339213i
$902$	−0.583033	−	1.21068i	−0.0194129	−	0.0403112i
$903$	7.16751	+	3.45169i	0.238520	+	0.114865i
$904$	−1.64356	+	7.20091i	−0.0546641	+	0.239499i
$905$	−1.74975	−	7.66614i	−0.0581635	−	0.254831i
$906$	−16.8590	+	8.11889i	−0.560104	+	0.269732i
$907$	−4.05424	−	3.23315i	−0.134619	−	0.107355i	0.553865	−	0.832606i	$-0.313152\pi$
$907$	−4.05424	−	3.23315i	−0.134619	−	0.107355i	−0.688484	+	0.725251i	$0.741724\pi$
$908$	3.03230	−	3.80239i	0.100631	−	0.126187i
$909$	−7.01251	+	14.5616i	−0.232590	+	0.482979i
$910$	1.76243	−	1.40549i	0.0584241	−	0.0465917i
$911$		−	18.0436i		−	0.597811i	−0.954283	−	0.298905i	$-0.903378\pi$
$911$		−	18.0436i		−	0.597811i	0.954283	−	0.298905i	$-0.0966215\pi$
$912$	−8.60769	−	10.7937i	−0.285029	−	0.357415i
$913$	9.53100	−	2.17539i	0.315430	−	0.0719949i
$914$	−31.0492	+	7.08677i	−1.02701	+	0.234409i
$915$	−1.79833	−	2.25503i	−0.0594509	−	0.0745491i
$916$		−	4.66891i		−	0.154265i
$917$	7.54265	−	6.01506i	0.249080	−	0.198635i
$918$	2.92823	−	6.08053i	0.0966460	−	0.200687i
$919$	−5.45496	+	6.84030i	−0.179943	+	0.225641i	−0.863620	−	0.504144i	$-0.831808\pi$
$919$	−5.45496	+	6.84030i	−0.179943	+	0.225641i	0.683677	+	0.729785i	$0.260380\pi$
$920$	1.08122	+	0.862246i	0.0356468	+	0.0284274i
$921$	16.0233	−	7.71641i	0.527986	−	0.254264i
$922$	6.45453	+	28.2791i	0.212568	+	0.931323i
$923$	−16.0999	+	70.5382i	−0.529934	+	2.32179i
$924$	0.232485	+	0.111959i	0.00764818	+	0.00368317i
$925$	3.80440	+	7.89992i	0.125088	+	0.259748i
$926$	−34.9241	−	7.97121i	−1.14768	−	0.261950i
$927$	10.9518			0.359705
$928$	−8.55275	+	3.35838i	−0.280758	+	0.110244i
$929$	42.8899			1.40717			0.703587	−	0.710609i	$-0.251581\pi$
$929$	42.8899			1.40717			0.703587	+	0.710609i	$0.251581\pi$
$930$	1.86949	+	0.426698i	0.0613029	+	0.0139920i
$931$	10.5006	+	21.8047i	0.344144	+	0.714621i
$932$	−3.56145	−	1.71510i	−0.116659	−	0.0561801i
$933$	−1.86884	+	8.18792i	−0.0611830	+	0.268060i
$934$	6.88042	+	30.1451i	0.225134	+	0.986377i
$935$	1.16972	−	0.563310i	0.0382541	−	0.0184222i
$936$	−11.2860	−	9.00030i	−0.368895	−	0.294184i
$937$	−10.3965	+	13.0367i	−0.339637	+	0.425892i	−0.922092	−	0.386972i	$-0.873521\pi$
$937$	−10.3965	+	13.0367i	−0.339637	+	0.425892i	0.582454	+	0.812863i	$0.302093\pi$
$938$	9.51498	−	19.7581i	0.310675	−	0.645123i
$939$	−1.64202	+	1.30947i	−0.0535853	+	0.0427328i
$940$		−	0.0450088i		−	0.00146802i
$941$	−10.3481	−	12.9761i	−0.337337	−	0.423007i	0.584011	−	0.811746i	$-0.301482\pi$
$941$	−10.3481	−	12.9761i	−0.337337	−	0.423007i	−0.921348	+	0.388738i	$0.872911\pi$
$942$	16.7486	−	3.82276i	0.545699	−	0.124552i
$943$	−1.85103	+	0.422485i	−0.0602777	+	0.0137580i
$944$	−7.55689	−	9.47604i	−0.245956	−	0.308419i
$945$		−	0.359860i		−	0.0117063i
$946$	−5.63766	+	4.49588i	−0.183296	+	0.146174i
$947$	19.5444	−	40.5843i	0.635107	−	1.31881i	−0.296391	−	0.955067i	$-0.595783\pi$
$947$	19.5444	−	40.5843i	0.635107	−	1.31881i	0.931498	−	0.363746i	$-0.118502\pi$
$948$	−1.10775	+	1.38907i	−0.0359780	+	0.0451150i
$949$	51.5329	+	41.0961i	1.67283	+	1.33404i
$950$	24.0295	−	11.5720i	0.779618	−	0.375444i
$951$	1.11880	+	4.90180i	0.0362797	+	0.158952i
$952$	3.81889	−	16.7316i	0.123771	−	0.542275i
$953$	−17.4621	−	8.40933i	−0.565655	−	0.272405i	0.129124	−	0.991628i	$-0.458783\pi$
$953$	−17.4621	−	8.40933i	−0.565655	−	0.272405i	−0.694779	+	0.719224i	$0.744498\pi$
$954$	4.98798	+	10.3576i	0.161492	+	0.335341i
$955$	1.63915	+	0.374125i	0.0530417	+	0.0121064i
$956$	0.0776451			0.00251122
$957$	2.06767	−	3.58272i	0.0668384	−	0.115813i
$958$	34.0835			1.10119
$959$	25.0673	+	5.72145i	0.809465	+	0.184755i
$960$	−1.24779	−	2.59107i	−0.0402724	−	0.0836264i
$961$	−9.55748	−	4.60264i	−0.308306	−	0.148472i
$962$	2.49757	−	10.9426i	0.0805248	−	0.352802i
$963$	−2.78362	−	12.1959i	−0.0897010	−	0.393006i
$964$	2.30279	−	1.10897i	0.0741680	−	0.0357174i
$965$	−0.707249	−	0.564012i	−0.0227671	−	0.0181562i
$966$	−1.26614	+	1.58769i	−0.0407374	+	0.0510831i
$967$	−11.2078	+	23.2732i	−0.360417	+	0.748414i	−0.999790	−	0.0204826i	$-0.993480\pi$
$967$	−11.2078	+	23.2732i	−0.360417	+	0.748414i	0.639373	+	0.768897i	$0.279194\pi$
$968$	24.4221	−	19.4760i	0.784956	−	0.625981i
$969$			21.6927i			0.696870i
$970$	−0.409293	−	0.513238i	−0.0131416	−	0.0164791i
$971$	27.5064	−	6.27816i	0.882723	−	0.201476i	0.242949	−	0.970039i	$-0.421885\pi$
$971$	27.5064	−	6.27816i	0.882723	−	0.201476i	0.639774	+	0.768563i	$0.279028\pi$
$972$	−0.296786	+	0.0677395i	−0.00951942	+	0.00217274i
$973$	9.30836	+	11.6723i	0.298412	+	0.374197i
$974$			21.2449i			0.680729i
$975$	18.4057	−	14.6781i	0.589455	−	0.470075i
$976$	12.6581	−	26.2848i	0.405175	−	0.841355i
$977$	17.8073	−	22.3297i	0.569707	−	0.714390i	−0.410612	−	0.911810i	$-0.634685\pi$
$977$	17.8073	−	22.3297i	0.569707	−	0.714390i	0.980319	+	0.197420i	$0.0632563\pi$
$978$	3.06513	+	2.44436i	0.0980122	+	0.0781621i
$979$	5.73548	−	2.76206i	0.183307	−	0.0882758i
$980$	0.127733	+	0.559634i	0.00408027	+	0.0178768i
$981$	−1.95865	+	8.58142i	−0.0625350	+	0.273984i
$982$	−38.5995	−	18.5885i	−1.23176	−	0.593184i
$983$	−9.85199	−	20.4579i	−0.314230	−	0.652505i	0.682709	−	0.730690i	$-0.260802\pi$
$983$	−9.85199	−	20.4579i	−0.314230	−	0.652505i	−0.996939	+	0.0781854i	$0.975087\pi$
$984$	3.93018	+	0.897039i	0.125290	+	0.0285966i
$985$	8.05143			0.256540
$986$	−34.7310	−	10.7066i	−1.10606	−	0.340969i
$987$	0.500309			0.0159250
$988$	5.97574	+	1.36392i	0.190114	+	0.0433922i
$989$	4.42058	+	9.17943i	0.140566	+	0.291889i
$990$	0.293880	+	0.141525i	0.00934013	+	0.00449797i
$991$	−10.4378	+	45.7310i	−0.331568	+	1.45269i	0.484528	+	0.874776i	$0.338991\pi$
$991$	−10.4378	+	45.7310i	−0.331568	+	1.45269i	−0.816096	+	0.577917i	$0.803866\pi$
$992$	−1.71453	−	7.51186i	−0.0544364	−	0.238502i
$993$	3.43199	−	1.65276i	0.108911	−	0.0524487i
$994$	−16.8963	−	13.4743i	−0.535917	−	0.427379i
$995$	−1.06892	+	1.34038i	−0.0338869	+	0.0424929i
$996$	−1.68101	+	3.49065i	−0.0532648	+	0.110605i
$997$	−28.3877	+	22.6385i	−0.899048	+	0.716967i	−0.959651	−	0.281195i	$-0.909269\pi$
$997$	−28.3877	+	22.6385i	−0.899048	+	0.716967i	0.0606024	+	0.998162i	$0.480698\pi$
$998$		−	28.8606i		−	0.913567i
$999$	−1.11714	−	1.40085i	−0.0353449	−	0.0443211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.i.a.4.3	✓	24
3.2	odd	2		261.2.o.b.91.2		24
29.14	odd	28		2523.2.a.v.1.3		12
29.15	odd	28		2523.2.a.s.1.10		12
29.22	even	14	inner	87.2.i.a.22.3	yes	24
87.14	even	28		7569.2.a.bn.1.10		12
87.44	even	28		7569.2.a.bt.1.3		12
87.80	odd	14		261.2.o.b.109.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.i.a.4.3	✓	24	1.1	even	1	trivial
87.2.i.a.22.3	yes	24	29.22	even	14	inner
261.2.o.b.91.2		24	3.2	odd	2
261.2.o.b.109.2		24	87.80	odd	14
2523.2.a.s.1.10		12	29.15	odd	28
2523.2.a.v.1.3		12	29.14	odd	28
7569.2.a.bn.1.10		12	87.14	even	28
7569.2.a.bt.1.3		12	87.44	even	28

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.i (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26950 + 0.289755i) q^{2} +(0.433884 + 0.900969i) q^{3} +(-0.274272 - 0.132082i) q^{4} +(-0.0725658 + 0.317931i) q^{5} +(0.289755 + 1.26950i) q^{6} +(0.994220 - 0.478791i) q^{7} +(-2.34603 - 1.87090i) q^{8} +(-0.623490 + 0.781831i) q^{9} +(-0.184244 + 0.382587i) q^{10} +(-0.600556 + 0.478928i) q^{11} -0.304418i q^{12} +(-2.99941 - 3.76114i) q^{13} +(1.40089 - 0.319744i) q^{14} +(-0.317931 + 0.0725658i) q^{15} +(-2.05658 - 2.57887i) q^{16} +5.18289i q^{17} +(-1.01806 + 0.811874i) q^{18} +(1.81600 - 3.77095i) q^{19} +(0.0618958 - 0.0776149i) q^{20} +(0.862752 + 0.688022i) q^{21} +(-0.901176 + 0.433984i) q^{22} +(0.314479 + 1.37782i) q^{23} +(0.667716 - 2.92545i) q^{24} +(4.40903 + 2.12328i) q^{25} +(-2.71794 - 5.64386i) q^{26} +(-0.974928 - 0.222521i) q^{27} -0.335926 q^{28} +(-0.401521 + 5.37018i) q^{29} -0.424639 q^{30} +(-4.40253 - 1.00485i) q^{31} +(0.740318 + 1.53729i) q^{32} +(-0.692070 - 0.333284i) q^{33} +(-1.50177 + 6.57967i) q^{34} +(0.0800764 + 0.350838i) q^{35} +(0.274272 - 0.132082i) q^{36} +(1.40085 + 1.11714i) q^{37} +(3.39805 - 4.26102i) q^{38} +(2.08728 - 4.33428i) q^{39} +(0.765059 - 0.610114i) q^{40} +1.34344i q^{41} +(0.895904 + 1.12343i) q^{42} +(7.02843 - 1.60419i) q^{43} +(0.227973 - 0.0520334i) q^{44} +(-0.203325 - 0.254961i) q^{45} +1.84026i q^{46} +(0.354469 - 0.282680i) q^{47} +(1.43116 - 2.97184i) q^{48} +(-3.60520 + 4.52077i) q^{49} +(4.98202 + 3.97303i) q^{50} +(-4.66963 + 2.24877i) q^{51} +(0.325873 + 1.42774i) q^{52} +(1.96455 - 8.60725i) q^{53} +(-1.17319 - 0.564980i) q^{54} +(-0.108686 - 0.225689i) q^{55} +(-3.22824 - 0.736825i) q^{56} +4.18544 q^{57} +(-2.06576 + 6.70108i) q^{58} +3.67450 q^{59} +(0.0967842 + 0.0220904i) q^{60} +(3.83753 + 7.96872i) q^{61} +(-5.29784 - 2.55131i) q^{62} +(-0.245552 + 1.07583i) q^{63} +(1.96236 + 8.59768i) q^{64} +(1.41344 - 0.680677i) q^{65} +(-0.782011 - 0.623633i) q^{66} +(9.51550 - 11.9321i) q^{67} +(0.684568 - 1.42152i) q^{68} +(-1.10493 + 0.881149i) q^{69} +0.468590i q^{70} +(-9.37723 - 11.7587i) q^{71} +(2.92545 - 0.667716i) q^{72} +(-13.3579 + 3.04884i) q^{73} +(1.45468 + 1.82412i) q^{74} +4.89365i q^{75} +(-0.996152 + 0.794405i) q^{76} +(-0.367779 + 0.763701i) q^{77} +(3.90567 - 4.89756i) q^{78} +(-4.56304 - 3.63890i) q^{79} +(0.969139 - 0.466713i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-0.389269 + 1.70550i) q^{82} +(-11.4666 - 5.52203i) q^{83} +(-0.145753 - 0.302659i) q^{84} +(-1.64780 - 0.376101i) q^{85} +9.38739 q^{86} +(-5.01257 + 1.96827i) q^{87} +2.30495 q^{88} +(-8.07964 - 1.84412i) q^{89} +(-0.184244 - 0.382587i) q^{90} +(-4.78288 - 2.30331i) q^{91} +(0.0957331 - 0.419434i) q^{92} +(-1.00485 - 4.40253i) q^{93} +(0.531905 - 0.256152i) q^{94} +(1.06713 + 0.851004i) q^{95} +(-1.06383 + 1.33401i) q^{96} +(-0.670747 + 1.39282i) q^{97} +(-5.88670 + 4.69449i) q^{98} -0.768140i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 4 q^{5} - 2 q^{6} + 8 q^{7} + 4 q^{9} - 28 q^{11} - 10 q^{13} - 14 q^{15} - 22 q^{16} - 20 q^{20} + 4 q^{22} + 18 q^{23} - 18 q^{25} + 28 q^{26} + 8 q^{28} + 28 q^{29} - 40 q^{30} + 28 q^{31}+ \cdots - 42 q^{98}+O(q^{100}) \) 24 * q - 2 * q^4 - 4 * q^5 - 2 * q^6 + 8 * q^7 + 4 * q^9 - 28 * q^11 - 10 * q^13 - 14 * q^15 - 22 * q^16 - 20 * q^20 + 4 * q^22 + 18 * q^23 - 18 * q^25 + 28 * q^26 + 8 * q^28 + 28 * q^29 - 40 * q^30 + 28 * q^31 - 14 * q^32 + 34 * q^34 + 2 * q^36 - 28 * q^37 - 4 * q^38 + 14 * q^42 - 14 * q^43 + 14 * q^44 - 10 * q^45 + 56 * q^48 + 20 * q^49 + 42 * q^50 + 2 * q^51 - 68 * q^52 + 6 * q^53 + 2 * q^54 - 14 * q^55 + 32 * q^57 + 50 * q^58 + 28 * q^59 + 42 * q^60 - 8 * q^62 + 6 * q^63 - 20 * q^64 + 18 * q^65 - 28 * q^66 + 8 * q^67 + 14 * q^68 + 28 * q^69 - 42 * q^71 + 14 * q^72 - 84 * q^73 + 10 * q^74 - 14 * q^76 - 70 * q^77 + 2 * q^78 - 14 * q^79 + 36 * q^80 - 4 * q^81 - 50 * q^82 - 32 * q^83 + 14 * q^85 - 128 * q^86 - 44 * q^87 - 20 * q^88 - 14 * q^89 + 34 * q^91 - 58 * q^92 - 20 * q^93 - 44 * q^94 - 52 * q^96 + 56 * q^97 - 42 * q^98

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