LMFDB - Embedded newform 385.2.n.f.36.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(36,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("385.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.n (of order $5$, degree $4$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.7
Character	$\chi$	$=$	385.36
Dual form			385.2.n.f.246.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60097 - 1.16317i) q^{2} +(0.925528 + 2.84848i) q^{3} +(0.592097 - 1.82229i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(4.79501 + 3.48378i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0513277 + 0.157970i) q^{8} +(-4.83020 + 3.50934i) q^{9} +O(q^{10})$	\(q+(1.60097 - 1.16317i) q^{2} +(0.925528 + 2.84848i) q^{3} +(0.592097 - 1.82229i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(4.79501 + 3.48378i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0513277 + 0.157970i) q^{8} +(-4.83020 + 3.50934i) q^{9} -1.97890 q^{10} +(0.944452 + 3.17931i) q^{11} +5.73875 q^{12} +(4.74103 - 3.44456i) q^{13} +(0.611515 + 1.88205i) q^{14} +(0.925528 - 2.84848i) q^{15} +(3.36618 + 2.44567i) q^{16} +(-5.74115 - 4.17119i) q^{17} +(-3.65102 + 11.2367i) q^{18} +(-1.24039 - 3.81752i) q^{19} +(-1.55013 + 1.12623i) q^{20} -2.99507 q^{21} +(5.21012 + 3.99141i) q^{22} +1.45156 q^{23} +(-0.402470 + 0.292412i) q^{24} +(0.309017 + 0.951057i) q^{25} +(3.58362 - 11.0293i) q^{26} +(-7.19759 - 5.22936i) q^{27} +(1.55013 + 1.12623i) q^{28} +(1.89295 - 5.82590i) q^{29} +(-1.83153 - 5.63688i) q^{30} +(3.81028 - 2.76833i) q^{31} +7.90168 q^{32} +(-8.18209 + 5.63280i) q^{33} -14.0432 q^{34} +(0.809017 - 0.587785i) q^{35} +(3.53508 + 10.8799i) q^{36} +(-0.0996537 + 0.306703i) q^{37} +(-6.42624 - 4.66894i) q^{38} +(14.1997 + 10.3167i) q^{39} +(0.0513277 - 0.157970i) q^{40} +(0.405358 + 1.24756i) q^{41} +(-4.79501 + 3.48378i) q^{42} -4.49398 q^{43} +(6.35282 + 0.161396i) q^{44} +5.97045 q^{45} +(2.32390 - 1.68841i) q^{46} +(2.82140 + 8.68339i) q^{47} +(-3.85096 + 11.8520i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.60097 + 1.16317i) q^{50} +(6.56797 - 20.2141i) q^{51} +(-3.46983 - 10.6790i) q^{52} +(-7.81580 + 5.67851i) q^{53} -17.6058 q^{54} +(1.10467 - 3.12725i) q^{55} -0.166100 q^{56} +(9.72611 - 7.06643i) q^{57} +(-3.74597 - 11.5289i) q^{58} +(2.15769 - 6.64069i) q^{59} +(-4.64275 - 3.37315i) q^{60} +(-10.0768 - 7.32123i) q^{61} +(2.88010 - 8.86402i) q^{62} +(-1.84497 - 5.67824i) q^{63} +(5.91797 - 4.29966i) q^{64} -5.86024 q^{65} +(-6.54736 + 18.5351i) q^{66} -6.02821 q^{67} +(-11.0004 + 7.99227i) q^{68} +(1.34346 + 4.13474i) q^{69} +(0.611515 - 1.88205i) q^{70} +(-0.689967 - 0.501290i) q^{71} +(-0.802295 - 0.582901i) q^{72} +(4.67488 - 14.3878i) q^{73} +(0.197205 + 0.606935i) q^{74} +(-2.42306 + 1.76046i) q^{75} -7.69103 q^{76} +(-3.31555 - 0.0842331i) q^{77} +34.7334 q^{78} +(-1.21249 + 0.880928i) q^{79} +(-1.28577 - 3.95718i) q^{80} +(2.69925 - 8.30742i) q^{81} +(2.10009 + 1.52581i) q^{82} +(7.32947 + 5.32517i) q^{83} +(-1.77337 + 5.45788i) q^{84} +(2.19292 + 6.74913i) q^{85} +(-7.19472 + 5.22727i) q^{86} +18.3470 q^{87} +(-0.453760 + 0.312382i) q^{88} -7.33214 q^{89} +(9.55850 - 6.94466i) q^{90} +(1.81091 + 5.57342i) q^{91} +(0.859464 - 2.64516i) q^{92} +(11.4121 + 8.29135i) q^{93} +(14.6172 + 10.6200i) q^{94} +(-1.24039 + 3.81752i) q^{95} +(7.31322 + 22.5078i) q^{96} +(-0.494932 + 0.359589i) q^{97} -1.97890 q^{98} +(-15.7192 - 12.0423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9}+O(q^{10}) $ 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9	\( 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9} - 4 q^{10} - 3 q^{11} + 30 q^{12} - q^{13} - q^{14} + 3 q^{16} + 5 q^{17} - 34 q^{18} - 5 q^{19} - 7 q^{20} - 10 q^{21} - 5 q^{22} + 8 q^{23} - 41 q^{24} - 9 q^{25} + 28 q^{26} + 7 q^{28} - 33 q^{29} + 12 q^{30} - q^{31} + 12 q^{32} - 14 q^{33} + 88 q^{34} + 9 q^{35} - 104 q^{36} - 18 q^{37} - 27 q^{38} + 6 q^{39} + 3 q^{40} + 36 q^{41} + 13 q^{42} - 20 q^{43} - 30 q^{44} + 74 q^{45} + 20 q^{46} - 7 q^{47} + 75 q^{48} - 9 q^{49} + q^{50} + 22 q^{51} - 6 q^{52} - 4 q^{53} - 26 q^{54} - 3 q^{55} + 12 q^{56} - 43 q^{57} - 41 q^{58} + 25 q^{59} - 15 q^{60} + 21 q^{61} + 31 q^{62} + 26 q^{63} + 43 q^{64} - 16 q^{65} - 12 q^{66} + 58 q^{67} - 43 q^{68} - 37 q^{69} - q^{70} - 29 q^{71} + 34 q^{72} + 19 q^{73} - 59 q^{74} - 5 q^{75} - 94 q^{76} + 3 q^{77} + 20 q^{78} + 11 q^{79} - 47 q^{80} - 10 q^{81} - 58 q^{82} + 47 q^{83} - 10 q^{85} + 35 q^{86} - 46 q^{87} - 110 q^{88} + 118 q^{89} + 36 q^{90} - 9 q^{91} + 107 q^{92} - 29 q^{93} - 27 q^{94} - 5 q^{95} + 67 q^{96} - 4 q^{98} + 16 q^{99}+O(q^{100}) \) 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9 - 4 * q^10 - 3 * q^11 + 30 * q^12 - q^13 - q^14 + 3 * q^16 + 5 * q^17 - 34 * q^18 - 5 * q^19 - 7 * q^20 - 10 * q^21 - 5 * q^22 + 8 * q^23 - 41 * q^24 - 9 * q^25 + 28 * q^26 + 7 * q^28 - 33 * q^29 + 12 * q^30 - q^31 + 12 * q^32 - 14 * q^33 + 88 * q^34 + 9 * q^35 - 104 * q^36 - 18 * q^37 - 27 * q^38 + 6 * q^39 + 3 * q^40 + 36 * q^41 + 13 * q^42 - 20 * q^43 - 30 * q^44 + 74 * q^45 + 20 * q^46 - 7 * q^47 + 75 * q^48 - 9 * q^49 + q^50 + 22 * q^51 - 6 * q^52 - 4 * q^53 - 26 * q^54 - 3 * q^55 + 12 * q^56 - 43 * q^57 - 41 * q^58 + 25 * q^59 - 15 * q^60 + 21 * q^61 + 31 * q^62 + 26 * q^63 + 43 * q^64 - 16 * q^65 - 12 * q^66 + 58 * q^67 - 43 * q^68 - 37 * q^69 - q^70 - 29 * q^71 + 34 * q^72 + 19 * q^73 - 59 * q^74 - 5 * q^75 - 94 * q^76 + 3 * q^77 + 20 * q^78 + 11 * q^79 - 47 * q^80 - 10 * q^81 - 58 * q^82 + 47 * q^83 - 10 * q^85 + 35 * q^86 - 46 * q^87 - 110 * q^88 + 118 * q^89 + 36 * q^90 - 9 * q^91 + 107 * q^92 - 29 * q^93 - 27 * q^94 - 5 * q^95 + 67 * q^96 - 4 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	1.60097	−	1.16317i	1.13206	−	0.822486i	0.146063	−	0.989275i	$-0.453340\pi$
$2$	1.60097	−	1.16317i	1.13206	−	0.822486i	0.985993	+	0.166789i	$0.0533399\pi$
$3$	0.925528	+	2.84848i	0.534354	+	1.64457i	0.745041	+	0.667018i	$0.232430\pi$
$3$	0.925528	+	2.84848i	0.534354	+	1.64457i	−0.210687	+	0.977553i	$0.567570\pi$
$4$	0.592097	−	1.82229i	0.296048	−	0.911143i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	4.79501	+	3.48378i	1.95756	+	1.42225i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.0513277	+	0.157970i	0.0181471	+	0.0558509i
$9$	−4.83020	+	3.50934i	−1.61007	+	1.16978i
$10$	−1.97890			−0.625785
$11$	0.944452	+	3.17931i	0.284763	+	0.958598i
$11$	0.944452	+	3.17931i	0.284763	+	0.958598i
$12$	5.73875			1.65663
$13$	4.74103	−	3.44456i	1.31493	−	0.955349i	0.314945	−	0.949110i	$-0.398014\pi$
$13$	4.74103	−	3.44456i	1.31493	−	0.955349i	0.999981	−	0.00623953i	$-0.00198612\pi$
$14$	0.611515	+	1.88205i	0.163434	+	0.502999i
$15$	0.925528	−	2.84848i	0.238970	−	0.735475i
$16$	3.36618	+	2.44567i	0.841545	+	0.611418i
$17$	−5.74115	−	4.17119i	−1.39243	−	1.01166i	−0.995593	−	0.0937748i	$-0.970107\pi$
$17$	−5.74115	−	4.17119i	−1.39243	−	1.01166i	−0.396840	−	0.917888i	$-0.629893\pi$
$18$	−3.65102	+	11.2367i	−0.860554	+	2.64851i
$19$	−1.24039	−	3.81752i	−0.284564	−	0.875798i	−0.986529	−	0.163587i	$-0.947694\pi$
$19$	−1.24039	−	3.81752i	−0.284564	−	0.875798i	0.701965	−	0.712212i	$-0.252306\pi$
$20$	−1.55013	+	1.12623i	−0.346619	+	0.251834i
$21$	−2.99507			−0.653578
$22$	5.21012	+	3.99141i	1.11080	+	0.850972i
$23$	1.45156			0.302671			0.151336	−	0.988482i	$-0.451643\pi$
$23$	1.45156			0.302671			0.151336	+	0.988482i	$0.451643\pi$
$24$	−0.402470	+	0.292412i	−0.0821539	+	0.0596883i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	3.58362	−	11.0293i	0.702807	−	2.16302i
$27$	−7.19759	−	5.22936i	−1.38518	−	1.00639i
$28$	1.55013	+	1.12623i	0.292947	+	0.212838i
$29$	1.89295	−	5.82590i	0.351512	−	1.08184i	−0.606492	−	0.795090i	$-0.707424\pi$
$29$	1.89295	−	5.82590i	0.351512	−	1.08184i	0.958004	−	0.286754i	$-0.0925762\pi$
$30$	−1.83153	−	5.63688i	−0.334390	−	1.02915i
$31$	3.81028	−	2.76833i	0.684347	−	0.497207i	−0.190450	−	0.981697i	$-0.560995\pi$
$31$	3.81028	−	2.76833i	0.684347	−	0.497207i	0.874797	+	0.484490i	$0.160995\pi$
$32$	7.90168			1.39683
$33$	−8.18209	+	5.63280i	−1.42432	+	0.980544i
$34$	−14.0432			−2.40839
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	3.53508	+	10.8799i	0.589181	+	1.81331i
$37$	−0.0996537	+	0.306703i	−0.0163830	+	0.0504216i	−0.958914	−	0.283698i	$-0.908439\pi$
$37$	−0.0996537	+	0.306703i	−0.0163830	+	0.0504216i	0.942531	+	0.334119i	$0.108439\pi$
$38$	−6.42624	−	4.66894i	−1.04247	−	0.757402i
$39$	14.1997	+	10.3167i	2.27378	+	1.65200i
$40$	0.0513277	−	0.157970i	0.00811562	−	0.0249773i
$41$	0.405358	+	1.24756i	0.0633062	+	0.194837i	0.977707	−	0.209973i	$-0.0673377\pi$
$41$	0.405358	+	1.24756i	0.0633062	+	0.194837i	−0.914401	+	0.404810i	$0.867338\pi$
$42$	−4.79501	+	3.48378i	−0.739886	+	0.537559i
$43$	−4.49398			−0.685326			−0.342663	−	0.939458i	$-0.611329\pi$
$43$	−4.49398			−0.685326			−0.342663	+	0.939458i	$0.611329\pi$
$44$	6.35282	+	0.161396i	0.957723	+	0.0243314i
$45$	5.97045			0.890022
$46$	2.32390	−	1.68841i	0.342640	−	0.248943i
$47$	2.82140	+	8.68339i	0.411544	+	1.26660i	0.915306	+	0.402760i	$0.131949\pi$
$47$	2.82140	+	8.68339i	0.411544	+	1.26660i	−0.503762	+	0.863843i	$0.668051\pi$
$48$	−3.85096	+	11.8520i	−0.555838	+	1.71069i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	1.60097	+	1.16317i	0.226411	+	0.164497i
$51$	6.56797	−	20.2141i	0.919699	−	2.83054i
$52$	−3.46983	−	10.6790i	−0.481178	−	1.48091i
$53$	−7.81580	+	5.67851i	−1.07358	+	0.780004i	−0.976553	−	0.215277i	$-0.930934\pi$
$53$	−7.81580	+	5.67851i	−1.07358	+	0.780004i	−0.0970304	+	0.995281i	$0.530934\pi$
$54$	−17.6058			−2.39584
$55$	1.10467	−	3.12725i	0.148954	−	0.421678i
$56$	−0.166100			−0.0221960
$57$	9.72611	−	7.06643i	1.28826	−	0.935972i
$58$	−3.74597	−	11.5289i	−0.491870	−	1.51382i
$59$	2.15769	−	6.64069i	0.280907	−	0.864544i	−0.706688	−	0.707525i	$-0.749812\pi$
$59$	2.15769	−	6.64069i	0.280907	−	0.864544i	0.987596	−	0.157019i	$-0.0501884\pi$
$60$	−4.64275	−	3.37315i	−0.599376	−	0.435472i
$61$	−10.0768	−	7.32123i	−1.29020	−	0.937387i	−0.290393	−	0.956907i	$-0.593786\pi$
$61$	−10.0768	−	7.32123i	−1.29020	−	0.937387i	−0.999809	+	0.0195202i	$0.993786\pi$
$62$	2.88010	−	8.86402i	0.365772	−	1.12573i
$63$	−1.84497	−	5.67824i	−0.232445	−	0.715391i
$64$	5.91797	−	4.29966i	0.739747	−	0.537458i
$65$	−5.86024			−0.726873
$66$	−6.54736	+	18.5351i	−0.805924	+	2.28151i
$67$	−6.02821			−0.736463			−0.368231	−	0.929734i	$-0.620037\pi$
$67$	−6.02821			−0.736463			−0.368231	+	0.929734i	$0.620037\pi$
$68$	−11.0004	+	7.99227i	−1.33400	+	0.969205i
$69$	1.34346	+	4.13474i	0.161733	+	0.497764i
$70$	0.611515	−	1.88205i	0.0730901	−	0.224948i
$71$	−0.689967	−	0.501290i	−0.0818840	−	0.0594922i	0.546090	−	0.837726i	$-0.316116\pi$
$71$	−0.689967	−	0.501290i	−0.0818840	−	0.0594922i	−0.627974	+	0.778234i	$0.716116\pi$
$72$	−0.802295	−	0.582901i	−0.0945514	−	0.0686956i
$73$	4.67488	−	14.3878i	0.547154	−	1.68397i	−0.168659	−	0.985674i	$-0.553944\pi$
$73$	4.67488	−	14.3878i	0.547154	−	1.68397i	0.715813	−	0.698292i	$-0.246056\pi$
$74$	0.197205	+	0.606935i	0.0229246	+	0.0705548i
$75$	−2.42306	+	1.76046i	−0.279791	+	0.203280i
$76$	−7.69103			−0.882222
$77$	−3.31555	−	0.0842331i	−0.377843	−	0.00959925i
$78$	34.7334			3.93278
$79$	−1.21249	+	0.880928i	−0.136416	+	0.0991121i	−0.653901	−	0.756581i	$-0.726869\pi$
$79$	−1.21249	+	0.880928i	−0.136416	+	0.0991121i	0.517484	+	0.855693i	$0.326869\pi$
$80$	−1.28577	−	3.95718i	−0.143753	−	0.442426i
$81$	2.69925	−	8.30742i	0.299916	−	0.923047i
$82$	2.10009	+	1.52581i	0.231917	+	0.168497i
$83$	7.32947	+	5.32517i	0.804514	+	0.584514i	0.912235	−	0.409668i	$-0.134355\pi$
$83$	7.32947	+	5.32517i	0.804514	+	0.584514i	−0.107721	+	0.994181i	$0.534355\pi$
$84$	−1.77337	+	5.45788i	−0.193491	+	0.595503i
$85$	2.19292	+	6.74913i	0.237856	+	0.732046i
$86$	−7.19472	+	5.22727i	−0.775827	+	0.563671i
$87$	18.3470			1.96700
$88$	−0.453760	+	0.312382i	−0.0483710	+	0.0333000i
$89$	−7.33214			−0.777205			−0.388603	−	0.921405i	$-0.627042\pi$
$89$	−7.33214			−0.777205			−0.388603	+	0.921405i	$0.627042\pi$
$90$	9.55850	−	6.94466i	1.00755	−	0.732031i
$91$	1.81091	+	5.57342i	0.189835	+	0.584253i
$92$	0.859464	−	2.64516i	0.0896053	−	0.275777i
$93$	11.4121	+	8.29135i	1.18338	+	0.859773i
$94$	14.6172	+	10.6200i	1.50765	+	1.09537i
$95$	−1.24039	+	3.81752i	−0.127261	+	0.391669i
$96$	7.31322	+	22.5078i	0.746403	+	2.29719i
$97$	−0.494932	+	0.359589i	−0.0502527	+	0.0365107i	−0.612628	−	0.790371i	$-0.709888\pi$
$97$	−0.494932	+	0.359589i	−0.0502527	+	0.0365107i	0.562375	+	0.826882i	$0.309888\pi$
$98$	−1.97890			−0.199900
$99$	−15.7192	−	12.0423i	−1.57984	−	1.21030i
$100$	1.91606			0.191606
$101$	−13.5242	+	9.82592i	−1.34571	+	0.977716i	−0.346498	+	0.938051i	$0.612629\pi$
$101$	−13.5242	+	9.82592i	−1.34571	+	0.977716i	−0.999213	+	0.0396652i	$0.987371\pi$
$102$	−12.9974	−	40.0018i	−1.28693	−	3.96077i
$103$	0.913807	−	2.81241i	0.0900401	−	0.277115i	−0.895889	−	0.444277i	$-0.853460\pi$
$103$	0.913807	−	2.81241i	0.0900401	−	0.277115i	0.985929	+	0.167162i	$0.0534604\pi$
$104$	0.787485	+	0.572141i	0.0772192	+	0.0561030i
$105$	2.42306	+	1.76046i	0.236467	+	0.171803i
$106$	−5.90777	+	18.1822i	−0.573813	+	1.76601i
$107$	0.210144	+	0.646757i	0.0203154	+	0.0625244i	0.960700	−	0.277588i	$-0.0895349\pi$
$107$	0.210144	+	0.646757i	0.0203154	+	0.0625244i	−0.940385	+	0.340112i	$0.889535\pi$
$108$	−13.7911	+	10.0198i	−1.32705	+	0.964155i
$109$	16.4335			1.57404			0.787021	−	0.616927i	$-0.211623\pi$
$109$	16.4335			1.57404			0.787021	+	0.616927i	$0.211623\pi$
$110$	−1.86898	−	6.29155i	−0.178200	−	0.599876i
$111$	−0.965869			−0.0916762
$112$	−3.36618	+	2.44567i	−0.318074	+	0.231094i
$113$	1.84578	+	5.68072i	0.173636	+	0.534397i	0.999569	−	0.0293722i	$-0.00935082\pi$
$113$	1.84578	+	5.68072i	0.173636	+	0.534397i	−0.825933	+	0.563769i	$0.809351\pi$
$114$	7.35172	−	22.6263i	0.688552	−	2.11914i
$115$	−1.17434	−	0.853205i	−0.109507	−	0.0795618i
$116$	−9.49565	−	6.89900i	−0.881649	−	0.640556i
$117$	−10.8120	+	33.2758i	−0.999567	+	3.07635i
$118$	−4.26987	−	13.1413i	−0.393073	−	1.20975i
$119$	5.74115	−	4.17119i	0.526291	−	0.382372i
$120$	0.497481			0.0454136
$121$	−9.21602	+	6.00541i	−0.837820	+	0.545947i
$122$	−24.6485			−2.23157
$123$	−3.17849	+	2.30931i	−0.286595	+	0.208223i
$124$	−2.78864	−	8.58255i	−0.250427	−	0.770735i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−9.55850	−	6.94466i	−0.851539	−	0.618679i
$127$	3.72965	+	2.70975i	0.330953	+	0.240451i	0.740835	−	0.671687i	$-0.234430\pi$
$127$	3.72965	+	2.70975i	0.330953	+	0.240451i	−0.409882	+	0.912139i	$0.634430\pi$
$128$	−0.410260	+	1.26265i	−0.0362622	+	0.111604i
$129$	−4.15931	−	12.8010i	−0.366207	−	1.12707i
$130$	−9.38205	+	6.81646i	−0.822860	+	0.597843i
$131$	10.5612			0.922735			0.461368	−	0.887209i	$-0.347359\pi$
$131$	10.5612			0.922735			0.461368	+	0.887209i	$0.347359\pi$
$132$	5.41998	+	18.2453i	0.471748	+	1.58805i
$133$	4.01397			0.348056
$134$	−9.65097	+	7.01184i	−0.833716	+	0.605730i
$135$	2.74924	+	8.46128i	0.236617	+	0.728231i
$136$	0.364244	−	1.12103i	0.0312337	−	0.0961275i
$137$	9.95978	+	7.23621i	0.850922	+	0.618231i	0.925400	−	0.378992i	$-0.123729\pi$
$137$	9.95978	+	7.23621i	0.850922	+	0.618231i	−0.0744784	+	0.997223i	$0.523729\pi$
$138$	6.96025	+	5.05692i	0.592496	+	0.430473i
$139$	−3.32666	+	10.2384i	−0.282164	+	0.868411i	0.705070	+	0.709137i	$0.250915\pi$
$139$	−3.32666	+	10.2384i	−0.282164	+	0.868411i	−0.987234	+	0.159274i	$0.949085\pi$
$140$	−0.592097	−	1.82229i	−0.0500413	−	0.154011i
$141$	−22.1232	+	16.0734i	−1.86311	+	1.35363i
$142$	−1.68770			−0.141629
$143$	15.4290	+	11.8200i	1.29024	+	0.988437i
$144$	−24.8420			−2.07017
$145$	−4.95581	+	3.60061i	−0.411558	+	0.299014i
$146$	−9.25115	−	28.4721i	−0.765631	−	2.35637i
$147$	0.925528	−	2.84848i	0.0763363	−	0.234939i
$148$	0.499895	+	0.363195i	0.0410911	+	0.0298545i
$149$	−0.515816	−	0.374762i	−0.0422573	−	0.0307017i	0.566456	−	0.824092i	$-0.308314\pi$
$149$	−0.515816	−	0.374762i	−0.0422573	−	0.0307017i	−0.608713	+	0.793390i	$0.708314\pi$
$150$	−1.83153	+	5.63688i	−0.149544	+	0.460249i
$151$	−0.123132	−	0.378960i	−0.0100203	−	0.0308393i	0.945921	−	0.324396i	$-0.105161\pi$
$151$	−0.123132	−	0.378960i	−0.0100203	−	0.0308393i	−0.955942	+	0.293557i	$0.905161\pi$
$152$	0.539388	−	0.391888i	0.0437501	−	0.0317863i
$153$	42.3690			3.42533
$154$	−5.40607	+	3.72170i	−0.435634	+	0.299903i
$155$	−4.70977			−0.378298
$156$	27.2076	−	19.7675i	2.17835	−	1.58266i
$157$	3.21591	+	9.89755i	0.256657	+	0.789910i	0.993499	+	0.113845i	$0.0363166\pi$
$157$	3.21591	+	9.89755i	0.256657	+	0.789910i	−0.736841	+	0.676066i	$0.763683\pi$
$158$	−0.916492	+	2.82067i	−0.0729122	+	0.224401i
$159$	−23.4089	−	17.0076i	−1.85645	−	1.34879i
$160$	−6.39259	−	4.64449i	−0.505379	−	0.367179i
$161$	−0.448557	+	1.38052i	−0.0353512	+	0.108800i
$162$	−5.34155	−	16.4396i	−0.419672	−	1.29162i
$163$	−6.11418	+	4.44221i	−0.478900	+	0.347941i	−0.800900	−	0.598799i	$-0.795645\pi$
$163$	−6.11418	+	4.44221i	−0.478900	+	0.347941i	0.322000	+	0.946740i	$0.395645\pi$
$164$	2.51343			0.196266
$165$	9.93032	+	0.252284i	0.773075	+	0.0196403i
$166$	17.9283			1.39151
$167$	−9.94722	+	7.22708i	−0.769739	+	0.559248i	−0.901882	−	0.431982i	$-0.857814\pi$
$167$	−9.94722	+	7.22708i	−0.769739	+	0.559248i	0.132143	+	0.991231i	$0.457814\pi$
$168$	−0.153730	−	0.473132i	−0.0118605	−	0.0365030i
$169$	6.59516	−	20.2978i	0.507320	−	1.56137i
$170$	11.3612	+	8.25439i	0.871364	+	0.633083i
$171$	19.3883	+	14.0864i	1.48266	+	1.07721i
$172$	−2.66087	+	8.18932i	−0.202890	+	0.624430i
$173$	6.08508	+	18.7279i	0.462640	+	1.42386i	0.861927	+	0.507033i	$0.169258\pi$
$173$	6.08508	+	18.7279i	0.462640	+	1.42386i	−0.399287	+	0.916826i	$0.630742\pi$
$174$	29.3729	−	21.3407i	2.22675	−	1.61783i
$175$	−1.00000			−0.0755929
$176$	−4.59635	+	13.0119i	−0.346463	+	0.980812i
$177$	20.9129			1.57191
$178$	−11.7385	+	8.52853i	−0.879839	+	0.639240i
$179$	−4.01152	−	12.3462i	−0.299835	−	0.922798i	−0.981554	−	0.191184i	$-0.938767\pi$
$179$	−4.01152	−	12.3462i	−0.299835	−	0.922798i	0.681719	−	0.731614i	$-0.261233\pi$
$180$	3.53508	−	10.8799i	0.263490	−	0.810938i
$181$	−7.26641	−	5.27935i	−0.540108	−	0.392411i	0.284017	−	0.958819i	$-0.408333\pi$
$181$	−7.26641	−	5.27935i	−0.540108	−	0.392411i	−0.824125	+	0.566408i	$0.808333\pi$
$182$	9.38205	+	6.81646i	0.695444	+	0.505270i
$183$	11.5280	−	35.4796i	0.852176	−	2.62273i
$184$	0.0745052	+	0.229303i	0.00549259	+	0.0169045i
$185$	0.260897	−	0.189553i	0.0191815	−	0.0139362i
$186$	27.9146			2.04680
$187$	7.83926	−	22.1924i	0.573264	−	1.62287i
$188$	17.4942			1.27589
$189$	7.19759	−	5.22936i	0.523548	−	0.380380i
$190$	2.45461	+	7.55450i	0.178076	+	0.548061i
$191$	4.80212	−	14.7794i	0.347469	−	1.06940i	−0.612779	−	0.790254i	$-0.709948\pi$
$191$	4.80212	−	14.7794i	0.347469	−	1.06940i	0.960249	−	0.279147i	$-0.0900515\pi$
$192$	17.7248	+	12.8778i	1.27917	+	0.929374i
$193$	−4.21258	−	3.06062i	−0.303228	−	0.220308i	0.425757	−	0.904837i	$-0.360008\pi$
$193$	−4.21258	−	3.06062i	−0.303228	−	0.220308i	−0.728985	+	0.684529i	$0.760008\pi$
$194$	−0.374106	+	1.15138i	−0.0268593	+	0.0826643i
$195$	−5.42381	−	16.6928i	−0.388407	−	1.19539i
$196$	−1.55013	+	1.12623i	−0.110723	+	0.0804453i
$197$	−15.9632			−1.13733			−0.568664	−	0.822570i	$-0.692540\pi$
$197$	−15.9632			−1.13733			−0.568664	+	0.822570i	$0.692540\pi$
$198$	−39.1731	−	0.995210i	−2.78391	−	0.0707265i
$199$	−16.0008			−1.13427			−0.567133	−	0.823626i	$-0.691947\pi$
$199$	−16.0008			−1.13427			−0.567133	+	0.823626i	$0.691947\pi$
$200$	−0.134378	+	0.0976310i	−0.00950193	+	0.00690356i
$201$	−5.57927	−	17.1712i	−0.393532	−	1.21117i
$202$	−10.2226	+	31.4620i	−0.719261	+	2.21366i
$203$	4.95581	+	3.60061i	0.347830	+	0.252713i
$204$	−32.9470	−	23.9374i	−2.30675	−	1.67595i
$205$	0.405358	−	1.24756i	0.0283114	−	0.0871336i
$206$	−1.80834	−	5.56549i	−0.125993	−	0.387766i
$207$	−7.01132	+	5.09402i	−0.487320	+	0.354059i
$208$	24.3834			1.69069
$209$	10.9656	−	7.54903i	0.758505	−	0.522178i
$210$	5.92696			0.408999
$211$	16.1129	−	11.7067i	1.10926	−	0.805924i	0.126712	−	0.991940i	$-0.459558\pi$
$211$	16.1129	−	11.7067i	1.10926	−	0.805924i	0.982547	+	0.186016i	$0.0595576\pi$
$212$	5.72017	+	17.6049i	0.392863	+	1.20911i
$213$	0.789332	−	2.42932i	0.0540842	−	0.166454i
$214$	1.08872	+	0.791004i	0.0744236	+	0.0540719i
$215$	3.63571	+	2.64150i	0.247953	+	0.180149i
$216$	0.456648	−	1.40542i	0.0310709	−	0.0956265i
$217$	1.45540	+	4.47926i	0.0987989	+	0.304072i
$218$	26.3095	−	19.1149i	1.78190	−	1.29463i
$219$	45.3102			3.06178
$220$	−5.04467	−	3.86466i	−0.340112	−	0.260556i
$221$	−41.5869			−2.79744
$222$	−1.54633	+	1.12347i	−0.103783	+	0.0754024i
$223$	1.12441	+	3.46058i	0.0752962	+	0.231738i	0.981620	−	0.190846i	$-0.0611232\pi$
$223$	1.12441	+	3.46058i	0.0752962	+	0.231738i	−0.906324	+	0.422584i	$0.861123\pi$
$224$	−2.44175	+	7.51494i	−0.163146	+	0.502113i
$225$	−4.83020	−	3.50934i	−0.322013	−	0.233956i
$226$	9.56267	+	6.94769i	0.636100	+	0.462153i
$227$	−6.39361	+	19.6775i	−0.424359	+	1.30604i	0.479248	+	0.877679i	$0.340909\pi$
$227$	−6.39361	+	19.6775i	−0.424359	+	1.30604i	−0.903607	+	0.428363i	$0.859091\pi$
$228$	−7.11827	−	21.9078i	−0.471419	−	1.45088i
$229$	8.89984	−	6.46612i	0.588118	−	0.427293i	−0.253523	−	0.967329i	$-0.581590\pi$
$229$	8.89984	−	6.46612i	0.588118	−	0.427293i	0.841642	+	0.540036i	$0.181590\pi$
$230$	−2.87250			−0.189407
$231$	−2.82870	−	9.52226i	−0.186115	−	0.626519i
$232$	1.01748			0.0668009
$233$	−0.141833	+	0.103048i	−0.00929180	+	0.00675089i	−0.592421	−	0.805628i	$-0.701828\pi$
$233$	−0.141833	+	0.103048i	−0.00929180	+	0.00675089i	0.583130	+	0.812379i	$0.301828\pi$
$234$	21.3959	+	65.8497i	1.39869	+	4.30473i
$235$	2.82140	−	8.68339i	0.184048	−	0.566442i
$236$	−10.8237	−	7.86386i	−0.704561	−	0.511894i
$237$	−3.63150	−	2.63844i	−0.235891	−	0.171385i
$238$	4.33959	−	13.3559i	0.281294	−	0.865733i
$239$	1.29196	+	3.97626i	0.0835702	+	0.257203i	0.984107	−	0.177578i	$-0.0568261\pi$
$239$	1.29196	+	3.97626i	0.0835702	+	0.257203i	−0.900537	+	0.434780i	$0.856826\pi$
$240$	10.0819	−	7.32496i	0.650787	−	0.472824i
$241$	−6.06222			−0.390502			−0.195251	−	0.980753i	$-0.562552\pi$
$241$	−6.06222			−0.390502			−0.195251	+	0.980753i	$0.562552\pi$
$242$	−7.76923	+	20.3343i	−0.499425	+	1.30714i
$243$	−0.528375			−0.0338952
$244$	−19.3078	+	14.0279i	−1.23606	+	0.898047i
$245$	0.309017	+	0.951057i	0.0197424	+	0.0607608i
$246$	−2.40254	+	7.39426i	−0.153180	+	0.471441i
$247$	−19.0304	−	13.8264i	−1.21087	−	0.879751i
$248$	0.632887	+	0.459820i	0.0401884	+	0.0291986i
$249$	−8.38503	+	25.8065i	−0.531380	+	1.63542i
$250$	−0.611515	−	1.88205i	−0.0386756	−	0.119031i
$251$	−8.40823	+	6.10894i	−0.530723	+	0.385593i	−0.820628	−	0.571463i	$-0.806376\pi$
$251$	−8.40823	+	6.10894i	−0.530723	+	0.385593i	0.289905	+	0.957055i	$0.406376\pi$
$252$	−11.4398			−0.720638
$253$	1.37093	+	4.61496i	0.0861896	+	0.290140i
$254$	9.12294			0.572424
$255$	−17.1952	+	12.4930i	−1.07680	+	0.782343i
$256$	5.33280	+	16.4127i	0.333300	+	1.02579i
$257$	−1.20170	+	3.69844i	−0.0749598	+	0.230702i	−0.981515	−	0.191384i	$-0.938702\pi$
$257$	−1.20170	+	3.69844i	−0.0749598	+	0.230702i	0.906555	+	0.422087i	$0.138702\pi$
$258$	−21.5487	−	15.6561i	−1.34156	−	0.974703i
$259$	−0.260897	−	0.189553i	−0.0162113	−	0.0117782i
$260$	−3.46983	+	10.6790i	−0.215190	+	0.662285i
$261$	11.3018	+	34.7833i	0.699562	+	2.15303i
$262$	16.9081	−	12.2845i	1.04459	−	0.758937i
$263$	−5.37305			−0.331316			−0.165658	−	0.986183i	$-0.552975\pi$
$263$	−5.37305			−0.331316			−0.165658	+	0.986183i	$0.552975\pi$
$264$	−1.30978	−	1.00341i	−0.0806115	−	0.0617556i
$265$	9.66087			0.593462
$266$	6.42624	−	4.66894i	0.394018	−	0.286271i
$267$	−6.78610	−	20.8855i	−0.415302	−	1.27817i
$268$	−3.56928	+	10.9851i	−0.218029	+	0.671023i
$269$	−12.5598	−	9.12522i	−0.765784	−	0.556374i	0.134895	−	0.990860i	$-0.456930\pi$
$269$	−12.5598	−	9.12522i	−0.765784	−	0.556374i	−0.900679	+	0.434486i	$0.856930\pi$
$270$	14.2434	+	10.3484i	0.866823	+	0.629784i
$271$	−4.20149	+	12.9308i	−0.255222	+	0.785493i	0.738564	+	0.674184i	$0.235504\pi$
$271$	−4.20149	+	12.9308i	−0.255222	+	0.785493i	−0.993786	+	0.111309i	$0.964496\pi$
$272$	−9.12438	−	28.0819i	−0.553247	−	1.70272i
$273$	−14.1997	+	10.3167i	−0.859407	+	0.624395i
$274$	24.3622			1.47178
$275$	−2.73185	+	1.88069i	−0.164737	+	0.113410i
$276$	8.33014			0.501415
$277$	10.9432	−	7.95072i	0.657515	−	0.477713i	−0.208308	−	0.978063i	$-0.566796\pi$
$277$	10.9432	−	7.95072i	0.657515	−	0.477713i	0.865823	+	0.500351i	$0.166796\pi$
$278$	6.58315	+	20.2609i	0.394831	+	1.21517i
$279$	−8.68939	+	26.7432i	−0.520220	+	1.60107i
$280$	0.134378	+	0.0976310i	0.00803060	+	0.00583457i
$281$	−8.74464	−	6.35336i	−0.521662	−	0.379009i	0.295568	−	0.955322i	$-0.404491\pi$
$281$	−8.74464	−	6.35336i	−0.521662	−	0.379009i	−0.817230	+	0.576312i	$0.804491\pi$
$282$	−16.7224	+	51.4661i	−0.995802	+	3.06476i
$283$	−7.94186	−	24.4425i	−0.472094	−	1.45296i	−0.849837	−	0.527046i	$-0.823299\pi$
$283$	−7.94186	−	24.4425i	−0.472094	−	1.45296i	0.377742	−	0.925911i	$-0.376701\pi$
$284$	−1.32202	+	0.960504i	−0.0784475	+	0.0569954i
$285$	−12.0221			−0.712130
$286$	38.4500	+	0.976838i	2.27360	+	0.0577617i
$287$	−1.31177			−0.0774311
$288$	−38.1667	+	27.7297i	−2.24899	+	1.63399i
$289$	10.3087	+	31.7269i	0.606394	+	1.86629i
$290$	−3.74597	+	11.5289i	−0.219971	+	0.677001i
$291$	−1.48236	−	1.07699i	−0.0868972	−	0.0631345i
$292$	−23.4507	−	17.0380i	−1.37235	−	0.997071i
$293$	−0.891186	+	2.74279i	−0.0520637	+	0.160235i	−0.973708	−	0.227801i	$-0.926846\pi$
$293$	−0.891186	+	2.74279i	−0.0520637	+	0.160235i	0.921644	+	0.388036i	$0.126846\pi$
$294$	−1.83153	−	5.63688i	−0.106817	−	0.328749i
$295$	−5.64891	+	4.10417i	−0.328892	+	0.238954i
$296$	−0.0535649			−0.00311340
$297$	9.82796	−	27.8223i	0.570276	−	1.61441i
$298$	−1.26172			−0.0730893
$299$	6.88189	−	4.99999i	0.397990	−	0.289157i
$300$	1.77337	+	5.45788i	0.102386	+	0.315111i
$301$	1.38872	−	4.27403i	0.0800443	−	0.246351i
$302$	−0.637925	−	0.463479i	−0.0367084	−	0.0266702i
$303$	−40.5060	−	29.4293i	−2.32701	−	1.69067i
$304$	5.16103	−	15.8840i	0.296005	−	0.911011i
$305$	3.84900	+	11.8460i	0.220393	+	0.678300i
$306$	67.8315	−	49.2824i	3.87767	−	2.81729i
$307$	0.0453798			0.00258996			0.00129498	−	0.999999i	$-0.499588\pi$
$307$	0.0453798			0.00258996			0.00129498	+	0.999999i	$0.499588\pi$
$308$	−2.11663	+	5.99201i	−0.120606	+	0.341427i
$309$	8.85685			0.503849
$310$	−7.54019	+	5.47827i	−0.428254	+	0.311145i
$311$	−9.73897	−	29.9735i	−0.552246	−	1.69964i	−0.703107	−	0.711084i	$-0.748205\pi$
$311$	−9.73897	−	29.9735i	−0.552246	−	1.69964i	0.150861	−	0.988555i	$-0.451795\pi$
$312$	−0.900895	+	2.77267i	−0.0510031	+	0.156971i
$313$	18.7104	+	13.5939i	1.05758	+	0.768374i	0.973639	−	0.228096i	$-0.0732502\pi$
$313$	18.7104	+	13.5939i	1.05758	+	0.768374i	0.0839382	+	0.996471i	$0.473250\pi$
$314$	16.6611	+	12.1050i	0.940241	+	0.683125i
$315$	−1.84497	+	5.67824i	−0.103952	+	0.319932i
$316$	0.887389	+	2.73110i	0.0499195	+	0.153637i
$317$	21.9525	−	15.9494i	1.23298	−	0.895810i	0.235867	−	0.971785i	$-0.424207\pi$
$317$	21.9525	−	15.9494i	1.23298	−	0.895810i	0.997110	+	0.0759752i	$0.0242070\pi$
$318$	−57.2596			−3.21096
$319$	20.3102	+	0.515988i	1.13715	+	0.0288898i
$320$	−7.31502			−0.408922
$321$	−1.64778	+	1.19718i	−0.0919702	+	0.0668203i
$322$	0.887651	+	2.73191i	0.0494669	+	0.152243i
$323$	−8.80234	+	27.0908i	−0.489775	+	1.50737i
$324$	−13.5403	−	9.83759i	−0.752238	−	0.546533i
$325$	4.74103	+	3.44456i	0.262985	+	0.191070i
$326$	−4.62155	+	14.2237i	−0.255964	+	0.787777i
$327$	15.2096	+	46.8104i	0.841095	+	2.58862i
$328$	−0.176272	+	0.128069i	−0.00973298	+	0.00707143i
$329$	−9.13026			−0.503367
$330$	16.1916	−	11.1468i	0.891317	−	0.613609i
$331$	−6.70591			−0.368590			−0.184295	−	0.982871i	$-0.559000\pi$
$331$	−6.70591			−0.368590			−0.184295	+	0.982871i	$0.559000\pi$
$332$	14.0437	−	10.2034i	0.770750	−	0.559983i
$333$	−0.594978	−	1.83115i	−0.0326046	−	0.100347i
$334$	−7.51885	+	23.1406i	−0.411413	+	1.26620i
$335$	4.87692	+	3.54329i	0.266455	+	0.193591i
$336$	−10.0819	−	7.32496i	−0.550015	−	0.399609i
$337$	−0.936658	+	2.88274i	−0.0510230	+	0.157033i	−0.973321	−	0.229446i	$-0.926309\pi$
$337$	−0.936658	+	2.88274i	−0.0510230	+	0.157033i	0.922298	+	0.386478i	$0.126309\pi$
$338$	−13.0512	−	40.1674i	−0.709891	−	2.18482i
$339$	−14.4731	+	10.5153i	−0.786071	+	0.571114i
$340$	13.5973			0.737415
$341$	12.4000	+	9.49951i	0.671499	+	0.514427i
$342$	47.4249			2.56445
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−0.230666	−	0.709916i	−0.0124367	−	0.0382761i
$345$	1.34346	−	4.13474i	0.0723294	−	0.222607i
$346$	31.5258	+	22.9048i	1.69484	+	1.23137i
$347$	−2.25507	−	1.63841i	−0.121059	−	0.0879543i	0.525608	−	0.850727i	$-0.323838\pi$
$347$	−2.25507	−	1.63841i	−0.121059	−	0.0879543i	−0.646667	+	0.762772i	$0.723838\pi$
$348$	10.8632	−	33.4334i	0.582327	−	1.79222i
$349$	−6.85774	−	21.1060i	−0.367087	−	1.12978i	−0.948664	−	0.316285i	$-0.897564\pi$
$349$	−6.85774	−	21.1060i	−0.367087	−	1.12978i	0.581577	−	0.813491i	$-0.302436\pi$
$350$	−1.60097	+	1.16317i	−0.0855753	+	0.0621741i
$351$	−52.1369			−2.78286
$352$	7.46276	+	25.1219i	0.397766	+	1.33900i
$353$	−15.8853			−0.845492			−0.422746	−	0.906248i	$-0.638934\pi$
$353$	−15.8853			−0.845492			−0.422746	+	0.906248i	$0.638934\pi$
$354$	33.4809	−	24.3253i	1.77949	−	1.29287i
$355$	0.263544	+	0.811104i	0.0139875	+	0.0430490i
$356$	−4.34133	+	13.3613i	−0.230090	+	0.708145i
$357$	17.1952	+	12.4930i	0.910064	+	0.661200i
$358$	−20.7830	−	15.0998i	−1.09842	−	0.798048i
$359$	2.32851	−	7.16641i	0.122894	−	0.378228i	−0.870618	−	0.491960i	$-0.836280\pi$
$359$	2.32851	−	7.16641i	0.122894	−	0.378228i	0.993511	+	0.113732i	$0.0362805\pi$
$360$	0.306449	+	0.943154i	0.0161513	+	0.0497086i
$361$	2.33646	−	1.69753i	0.122971	−	0.0893439i
$362$	−17.7741			−0.934185
$363$	−25.6360	−	20.6935i	−1.34554	−	1.08613i
$364$	11.2286			0.588538
$365$	−12.2390	+	8.89216i	−0.640619	+	0.465437i
$366$	−22.8129	−	70.2108i	−1.19245	−	3.66998i
$367$	−1.50800	+	4.64115i	−0.0787170	+	0.242266i	−0.982669	−	0.185367i	$-0.940653\pi$
$367$	−1.50800	+	4.64115i	−0.0787170	+	0.242266i	0.903952	+	0.427633i	$0.140653\pi$
$368$	4.88621	+	3.55004i	0.254711	+	0.185059i
$369$	−6.33608	−	4.60343i	−0.329843	−	0.239645i
$370$	0.197205	−	0.606935i	0.0102522	−	0.0315531i
$371$	−2.98537	−	9.18803i	−0.154993	−	0.477019i
$372$	21.8663	−	15.8868i	1.13371	−	0.823691i
$373$	21.9126			1.13459			0.567296	−	0.823514i	$-0.307990\pi$
$373$	21.9126			1.13459			0.567296	+	0.823514i	$0.307990\pi$
$374$	−13.2631	−	44.6477i	−0.685821	−	2.30868i
$375$	2.99507			0.154665
$376$	−1.22690	+	0.891396i	−0.0632726	+	0.0459702i
$377$	−11.0931	−	34.1412i	−0.571326	−	1.75836i
$378$	5.44048	−	16.7441i	0.279828	−	0.861222i
$379$	−2.29894	−	1.67028i	−0.118089	−	0.0857964i	0.527173	−	0.849758i	$-0.323252\pi$
$379$	−2.29894	−	1.67028i	−0.118089	−	0.0857964i	−0.645262	+	0.763961i	$0.723252\pi$
$380$	6.22218	+	4.52068i	0.319191	+	0.231906i
$381$	−4.26677	+	13.1318i	−0.218593	+	0.672761i
$382$	−9.50294	−	29.2471i	−0.486213	−	1.49641i
$383$	−3.21459	+	2.33554i	−0.164258	+	0.119340i	−0.666878	−	0.745167i	$-0.732370\pi$
$383$	−3.21459	+	2.33554i	−0.164258	+	0.119340i	0.502620	+	0.864508i	$0.332370\pi$
$384$	−3.97634			−0.202917
$385$	2.63283	+	2.01698i	0.134181	+	0.102795i
$386$	−10.3042			−0.524471
$387$	21.7068	−	15.7709i	1.10342	−	0.801682i
$388$	0.362226	+	1.11482i	0.0183893	+	0.0565963i
$389$	4.23694	−	13.0400i	0.214822	−	0.661153i	−0.784345	−	0.620325i	$-0.787001\pi$
$389$	4.23694	−	13.0400i	0.214822	−	0.661153i	0.999166	−	0.0408274i	$-0.0129994\pi$
$390$	−28.0999	−	20.4158i	−1.42289	−	1.03379i
$391$	−8.33362	−	6.05473i	−0.421450	−	0.306201i
$392$	0.0513277	−	0.157970i	0.00259244	−	0.00797871i
$393$	9.77468	+	30.0834i	0.493067	+	1.51750i
$394$	−25.5565	+	18.5679i	−1.28752	+	0.935437i
$395$	1.49872			0.0754090
$396$	−31.2518	+	21.5146i	−1.57046	+	1.08115i
$397$	4.20724			0.211155			0.105578	−	0.994411i	$-0.466331\pi$
$397$	4.20724			0.211155			0.105578	+	0.994411i	$0.466331\pi$
$398$	−25.6167	+	18.6117i	−1.28405	+	0.932918i
$399$	3.71504	+	11.4337i	0.185985	+	0.572402i
$400$	−1.28577	+	3.95718i	−0.0642883	+	0.197859i
$401$	−10.0969	−	7.33586i	−0.504217	−	0.366335i	0.306408	−	0.951900i	$-0.400873\pi$
$401$	−10.0969	−	7.33586i	−0.504217	−	0.366335i	−0.810625	+	0.585565i	$0.800873\pi$
$402$	−28.9053	−	21.0010i	−1.44167	−	1.04743i
$403$	8.52898	−	26.2495i	0.424859	−	1.30758i
$404$	9.89800	+	30.4629i	0.492444	+	1.51559i
$405$	−7.06672	+	5.13427i	−0.351148	+	0.255124i
$406$	12.1222			0.601615
$407$	−1.06922	−	0.0271640i	−0.0529993	−	0.00134647i
$408$	3.53035			0.174778
$409$	28.7613	−	20.8963i	1.42215	−	1.03325i	0.430742	−	0.902475i	$-0.358252\pi$
$409$	28.7613	−	20.8963i	1.42215	−	1.03325i	0.991411	−	0.130779i	$-0.0417480\pi$
$410$	−0.802164	−	2.46881i	−0.0396161	−	0.121926i
$411$	−11.3941	+	35.0676i	−0.562032	+	1.72976i
$412$	−4.58395	−	3.33044i	−0.225835	−	0.164079i
$413$	5.64891	+	4.10417i	0.277965	+	0.201953i
$414$	−5.29968	+	16.3107i	−0.260465	+	0.801629i
$415$	−2.79961	−	8.61631i	−0.137427	−	0.422958i
$416$	37.4621	−	27.2178i	1.83673	−	1.33446i
$417$	−32.2429			−1.57894
$418$	8.77472	−	24.8406i	0.429186	−	1.21499i
$419$	−12.5901			−0.615069			−0.307534	−	0.951537i	$-0.599504\pi$
$419$	−12.5901			−0.615069			−0.307534	+	0.951537i	$0.599504\pi$
$420$	4.64275	−	3.37315i	0.226543	−	0.164593i
$421$	7.14245	+	21.9822i	0.348102	+	1.07135i	0.959902	+	0.280335i	$0.0904455\pi$
$421$	7.14245	+	21.9822i	0.348102	+	1.07135i	−0.611801	+	0.791012i	$0.709555\pi$
$422$	12.1793	−	37.4841i	0.592881	−	1.82470i
$423$	−44.1009	−	32.0412i	−2.14426	−	1.55790i
$424$	−1.29820	−	0.943200i	−0.0630464	−	0.0458059i
$425$	2.19292	−	6.74913i	0.106372	−	0.327381i
$426$	−1.56201	−	4.80738i	−0.0756798	−	0.232919i
$427$	10.0768	−	7.32123i	0.487651	−	0.354299i
$428$	1.30300			0.0629830
$429$	−19.3890	+	54.8890i	−0.936112	+	2.65006i
$430$	8.89317			0.428867
$431$	−29.0422	+	21.1004i	−1.39892	+	1.01637i	−0.404096	+	0.914717i	$0.632414\pi$
$431$	−29.0422	+	21.1004i	−1.39892	+	1.01637i	−0.994820	+	0.101655i	$0.967586\pi$
$432$	−11.4391	−	35.2059i	−0.550364	−	1.69384i
$433$	−6.30850	+	19.4156i	−0.303167	+	0.933053i	0.677187	+	0.735811i	$0.263199\pi$
$433$	−6.30850	+	19.4156i	−0.303167	+	0.933053i	−0.980355	+	0.197243i	$0.936801\pi$
$434$	7.54019	+	5.47827i	0.361941	+	0.262965i
$435$	−14.8430	−	10.7841i	−0.711668	−	0.517057i
$436$	9.73020	−	29.9465i	0.465992	−	1.43418i
$437$	−1.80049	−	5.54135i	−0.0861293	−	0.265079i
$438$	72.5401	−	52.7035i	3.46610	−	2.51827i
$439$	0.415510			0.0198312			0.00991561	−	0.999951i	$-0.496844\pi$
$439$	0.415510			0.0198312			0.00991561	+	0.999951i	$0.496844\pi$
$440$	0.550713	+	0.0139911i	0.0262542	+	0.000666999i
$441$	5.97045			0.284307
$442$	−66.5793	+	48.3727i	−3.16685	+	2.30085i
$443$	5.60969	+	17.2649i	0.266525	+	0.820278i	0.991338	+	0.131333i	$0.0419259\pi$
$443$	5.60969	+	17.2649i	0.266525	+	0.820278i	−0.724814	+	0.688945i	$0.758074\pi$
$444$	−0.571888	+	1.76009i	−0.0271406	+	0.0835302i
$445$	5.93182	+	4.30972i	0.281195	+	0.204300i
$446$	5.82540	+	4.23240i	0.275841	+	0.200410i
$447$	0.590101	−	1.81614i	0.0279108	−	0.0859007i
$448$	2.26047	+	6.95700i	0.106797	+	0.328687i
$449$	0.995188	−	0.723046i	0.0469658	−	0.0341227i	−0.564055	−	0.825737i	$-0.690759\pi$
$449$	0.995188	−	0.723046i	0.0469658	−	0.0341227i	0.611020	+	0.791615i	$0.290759\pi$
$450$	−11.8150			−0.556962
$451$	−3.58355	+	2.46702i	−0.168743	+	0.116168i
$452$	11.4448			0.538317
$453$	0.965499	−	0.701476i	0.0453631	−	0.0329582i
$454$	12.6523	+	38.9399i	0.593804	+	1.82754i
$455$	1.81091	−	5.57342i	0.0848969	−	0.261286i
$456$	1.61551	+	1.17373i	0.0756530	+	0.0549651i
$457$	6.09391	+	4.42748i	0.285061	+	0.207109i	0.721122	−	0.692808i	$-0.243627\pi$
$457$	6.09391	+	4.42748i	0.285061	+	0.207109i	−0.436061	+	0.899917i	$0.643627\pi$
$458$	6.72716	−	20.7041i	0.314340	−	0.967438i
$459$	19.5098	+	60.0451i	0.910641	+	2.80266i
$460$	−2.25010	+	1.63480i	−0.104912	+	0.0762228i
$461$	31.9357			1.48739			0.743696	−	0.668518i	$-0.233071\pi$
$461$	31.9357			1.48739			0.743696	+	0.668518i	$0.233071\pi$
$462$	−15.6047	−	11.9546i	−0.725995	−	0.556177i
$463$	18.9621			0.881242			0.440621	−	0.897693i	$-0.354758\pi$
$463$	18.9621			0.881242			0.440621	+	0.897693i	$0.354758\pi$
$464$	20.6203	−	14.9815i	0.957272	−	0.695499i
$465$	−4.35902	−	13.4157i	−0.202145	−	0.622138i
$466$	−0.107208	+	0.329953i	−0.00496632	+	0.0152848i
$467$	6.04576	+	4.39250i	0.279764	+	0.203261i	0.718815	−	0.695202i	$-0.244685\pi$
$467$	6.04576	+	4.39250i	0.279764	+	0.203261i	−0.439050	+	0.898463i	$0.644685\pi$
$468$	54.2363	+	39.4050i	2.50708	+	1.82150i
$469$	1.86282	−	5.73317i	0.0860170	−	0.264733i
$470$	−5.58329	−	17.1836i	−0.257538	−	0.792620i
$471$	−25.2166	+	18.3209i	−1.16192	+	0.844183i
$472$	1.15978			0.0533833
$473$	−4.24435	−	14.2878i	−0.195156	−	0.656952i
$474$	−8.88288			−0.408004
$475$	3.24737	−	2.35935i	0.149000	−	0.108255i
$476$	−4.20179	−	12.9318i	−0.192589	−	0.592727i
$477$	17.8240	−	54.8567i	0.816106	−	2.51172i
$478$	6.69346	+	4.86308i	0.306152	+	0.222432i
$479$	−5.01428	−	3.64309i	−0.229109	−	0.166457i	0.467309	−	0.884094i	$-0.345224\pi$
$479$	−5.01428	−	3.64309i	−0.229109	−	0.166457i	−0.696417	+	0.717637i	$0.745224\pi$
$480$	7.31322	−	22.5078i	0.333801	−	1.02734i
$481$	0.583994	+	1.79735i	0.0266279	+	0.0819521i
$482$	−9.70542	+	7.05140i	−0.442070	+	0.321183i
$483$	−4.34752			−0.197819
$484$	5.48681	+	20.3500i	0.249400	+	0.925000i
$485$	0.611769			0.0277790
$486$	−0.845911	+	0.614590i	−0.0383713	+	0.0278784i
$487$	−4.59511	−	14.1423i	−0.208224	−	0.640848i	−0.999566	−	0.0294737i	$-0.990617\pi$
$487$	−4.59511	−	14.1423i	−0.208224	−	0.640848i	0.791341	−	0.611375i	$-0.209383\pi$
$488$	0.639318	−	1.96762i	0.0289406	−	0.0890699i
$489$	−18.3124	−	13.3047i	−0.828116	−	0.601661i
$490$	1.60097	+	1.16317i	0.0723243	+	0.0525467i
$491$	7.47378	−	23.0019i	0.337287	−	1.03806i	−0.628298	−	0.777973i	$-0.716248\pi$
$491$	7.47378	−	23.0019i	0.337287	−	1.03806i	0.965585	−	0.260089i	$-0.0837520\pi$
$492$	2.32625	+	7.15945i	0.104875	+	0.322773i
$493$	−35.1687	+	25.5515i	−1.58392	+	1.15078i
$494$	−46.5495			−2.09436
$495$	5.63881	+	18.9819i	0.253446	+	0.853174i
$496$	19.5965			0.879910
$497$	0.689967	−	0.501290i	0.0309492	−	0.0224859i
$498$	16.5932	+	51.0685i	0.743558	+	2.28844i
$499$	−7.01151	+	21.5792i	−0.313878	+	0.966018i	0.662335	+	0.749208i	$0.269565\pi$
$499$	−7.01151	+	21.5792i	−0.313878	+	0.966018i	−0.976214	+	0.216811i	$0.930435\pi$
$500$	−1.55013	−	1.12623i	−0.0693239	−	0.0503667i
$501$	−29.7926	−	21.6456i	−1.33104	−	0.967055i
$502$	−6.35556	+	19.5604i	−0.283663	+	0.873024i
$503$	2.68940	+	8.27713i	0.119915	+	0.369059i	0.992940	−	0.118615i	$-0.0378454\pi$
$503$	2.68940	+	8.27713i	0.119915	+	0.369059i	−0.873026	+	0.487674i	$0.837845\pi$
$504$	0.802295	−	0.582901i	0.0357371	−	0.0259645i
$505$	16.7169			0.743891
$506$	7.56280	+	5.79377i	0.336207	+	0.257565i
$507$	63.9220			2.83887
$508$	7.14624	−	5.19205i	0.317063	−	0.230360i
$509$	8.00960	+	24.6510i	0.355019	+	1.09264i	0.955998	+	0.293372i	$0.0947774\pi$
$509$	8.00960	+	24.6510i	0.355019	+	1.09264i	−0.600979	+	0.799265i	$0.705223\pi$
$510$	−12.9974	+	40.0018i	−0.575534	+	1.77131i
$511$	12.2390	+	8.89216i	0.541422	+	0.393366i
$512$	25.4802	+	18.5125i	1.12608	+	0.818143i
$513$	−11.0354	+	33.9633i	−0.487223	+	1.49952i
$514$	2.37804	+	7.31886i	0.104891	+	0.322821i
$515$	−2.39238	+	1.73816i	−0.105421	+	0.0765927i
$516$	−25.7899			−1.13533
$517$	−24.9425	+	17.1712i	−1.09697	+	0.755187i
$518$	−0.638169			−0.0280396
$519$	−47.7143	+	34.6665i	−2.09442	+	1.52169i
$520$	−0.300792	−	0.925744i	−0.0131906	−	0.0405965i
$521$	12.6444	−	38.9155i	0.553962	−	1.70492i	−0.144707	−	0.989474i	$-0.546224\pi$
$521$	12.6444	−	38.9155i	0.553962	−	1.70492i	0.698669	−	0.715445i	$-0.253776\pi$
$522$	58.5527	+	42.5410i	2.56278	+	1.86197i
$523$	15.0718	+	10.9503i	0.659046	+	0.478825i	0.866341	−	0.499454i	$-0.166466\pi$
$523$	15.0718	+	10.9503i	0.659046	+	0.478825i	−0.207295	+	0.978279i	$0.566466\pi$
$524$	6.25324	−	19.2455i	0.273174	−	0.840744i
$525$	−0.925528	−	2.84848i	−0.0403934	−	0.124318i
$526$	−8.60208	+	6.24978i	−0.375069	+	0.272503i
$527$	−33.4227			−1.45591
$528$	−41.3183	−	1.04971i	−1.79815	−	0.0456828i
$529$	−20.8930			−0.908390
$530$	15.4667	−	11.2372i	0.671832	−	0.488115i
$531$	12.8824	+	39.6479i	0.559048	+	1.72057i
$532$	2.37666	−	7.31461i	0.103041	−	0.317128i
$533$	6.21912	+	4.51846i	0.269380	+	0.195716i
$534$	−35.1577	−	25.5436i	−1.52142	−	1.10538i
$535$	0.210144	−	0.646757i	0.00908532	−	0.0279618i
$536$	−0.309414	−	0.952278i	−0.0133646	−	0.0411321i
$537$	31.4551	−	22.8535i	1.35739	−	0.986201i
$538$	−30.7220			−1.32452
$539$	1.10467	−	3.12725i	0.0475816	−	0.134700i
$540$	17.0467			0.733572
$541$	−12.9952	+	9.44160i	−0.558709	+	0.405926i	−0.830986	−	0.556293i	$-0.812223\pi$
$541$	−12.9952	+	9.44160i	−0.558709	+	0.405926i	0.272277	+	0.962219i	$0.412223\pi$
$542$	8.31434	+	25.5889i	0.357132	+	1.09914i
$543$	8.31288	−	25.5844i	0.356740	−	1.09793i
$544$	−45.3647	−	32.9594i	−1.94500	−	1.41312i
$545$	−13.2950	−	9.65935i	−0.569493	−	0.413761i
$546$	−10.7332	+	33.0334i	−0.459339	+	1.41370i
$547$	−5.33639	−	16.4237i	−0.228168	−	0.702228i	−0.997955	−	0.0639270i	$-0.979638\pi$
$547$	−5.33639	−	16.4237i	−0.228168	−	0.702228i	0.769787	−	0.638301i	$-0.220362\pi$
$548$	19.0836	−	13.8650i	0.815210	−	0.592285i
$549$	74.3657			3.17385
$550$	−2.18604	+	6.18853i	−0.0932132	+	0.263880i
$551$	−24.5885			−1.04750
$552$	−0.584210	+	0.424453i	−0.0248656	+	0.0180659i
$553$	−0.463131	−	1.42537i	−0.0196943	−	0.0606129i
$554$	8.27171	−	25.4577i	0.351431	−	1.08159i
$555$	0.781404	+	0.567724i	0.0331688	+	0.0240985i
$556$	16.6876	+	12.1243i	0.707713	+	0.514183i
$557$	−13.8951	+	42.7646i	−0.588753	+	1.81200i	−0.00510875	+	0.999987i	$0.501626\pi$
$557$	−13.8951	+	42.7646i	−0.588753	+	1.81200i	−0.583645	+	0.812009i	$0.698374\pi$
$558$	17.1955	+	52.9222i	0.727942	+	2.24038i
$559$	−21.3061	+	15.4798i	−0.901153	+	0.654726i
$560$	4.16083			0.175827
$561$	70.4701	+	1.79032i	2.97525	+	0.0755875i
$562$	−21.3899			−0.902280
$563$	−23.7729	+	17.2720i	−1.00191	+	0.727928i	−0.962496	−	0.271295i	$-0.912548\pi$
$563$	−23.7729	+	17.2720i	−1.00191	+	0.727928i	−0.0394107	+	0.999223i	$0.512548\pi$
$564$	16.1913	+	49.8318i	0.681778	+	2.09830i
$565$	1.84578	−	5.68072i	0.0776524	−	0.238990i
$566$	−41.1455	−	29.8940i	−1.72947	−	1.25654i
$567$	7.06672	+	5.13427i	0.296774	+	0.215619i
$568$	0.0437746	−	0.134724i	0.00183674	−	0.00565291i
$569$	7.17778	+	22.0909i	0.300908	+	0.926100i	0.981173	+	0.193133i	$0.0618650\pi$
$569$	7.17778	+	22.0909i	0.300908	+	0.926100i	−0.680264	+	0.732967i	$0.738135\pi$
$570$	−19.2471	+	13.9838i	−0.806170	+	0.585717i
$571$	27.8192			1.16420			0.582098	−	0.813119i	$-0.302232\pi$
$571$	27.8192			1.16420			0.582098	+	0.813119i	$0.302232\pi$
$572$	30.6749	−	21.1175i	1.28258	−	0.882967i
$573$	46.5434			1.94438
$574$	−2.10009	+	1.52581i	−0.0876562	+	0.0636860i
$575$	0.448557	+	1.38052i	0.0187061	+	0.0575715i
$576$	−13.4960	+	41.5364i	−0.562333	+	1.73068i
$577$	−24.2956	−	17.6518i	−1.01144	−	0.734853i	−0.0469284	−	0.998898i	$-0.514943\pi$
$577$	−24.2956	−	17.6518i	−1.01144	−	0.734853i	−0.964510	+	0.264045i	$0.914943\pi$
$578$	53.4077	+	38.8030i	2.22147	+	1.61399i
$579$	4.81925	−	14.8321i	0.200281	−	0.616402i
$580$	3.62702	+	11.1628i	0.150604	+	0.463510i
$581$	−7.32947	+	5.32517i	−0.304078	+	0.220925i
$582$	−3.62593			−0.150300
$583$	−25.4354	−	19.4858i	−1.05343	−	0.807018i
$584$	2.51280			0.103980
$585$	28.3061	−	20.5656i	1.17031	−	0.850282i
$586$	1.76357	+	5.42772i	0.0728525	+	0.224217i
$587$	4.07242	−	12.5336i	0.168087	−	0.517318i	−0.831164	−	0.556028i	$-0.812325\pi$
$587$	4.07242	−	12.5336i	0.168087	−	0.517318i	0.999250	+	0.0387100i	$0.0123249\pi$
$588$	−4.64275	−	3.37315i	−0.191464	−	0.139106i
$589$	−15.2944	−	11.1120i	−0.630194	−	0.457863i
$590$	−4.26987	+	13.1413i	−0.175788	+	0.541018i
$591$	−14.7744	−	45.4708i	−0.607736	−	1.87042i
$592$	−1.08555	+	0.788695i	−0.0446157	+	0.0324152i
$593$	−20.0435			−0.823086			−0.411543	−	0.911390i	$-0.635010\pi$
$593$	−20.0435			−0.823086			−0.411543	+	0.911390i	$0.635010\pi$
$594$	−16.6278	−	55.9741i	−0.682247	−	2.29665i
$595$	−7.09645			−0.290926
$596$	−0.988336	+	0.718068i	−0.0404838	+	0.0294132i
$597$	−14.8092	−	45.5780i	−0.606099	−	1.86538i
$598$	5.20185	−	16.0096i	0.212719	−	0.654683i
$599$	19.9897	+	14.5234i	0.816757	+	0.593409i	0.915782	−	0.401676i	$-0.131572\pi$
$599$	19.9897	+	14.5234i	0.816757	+	0.593409i	−0.0990245	+	0.995085i	$0.531572\pi$
$600$	−0.402470	−	0.292412i	−0.0164308	−	0.0119377i
$601$	7.53891	−	23.2024i	0.307519	−	0.946445i	−0.671207	−	0.741270i	$-0.734224\pi$
$601$	7.53891	−	23.2024i	0.307519	−	0.946445i	0.978725	−	0.205175i	$-0.0657764\pi$
$602$	−2.74814	−	8.45790i	−0.112006	−	0.344718i
$603$	29.1174	−	21.1551i	1.18575	−	0.861500i
$604$	−0.763479			−0.0310655
$605$	10.9858	+	0.558559i	0.446637	+	0.0227086i
$606$	−99.0802			−4.02486
$607$	29.3359	−	21.3138i	1.19071	−	0.865100i	0.197369	−	0.980329i	$-0.436760\pi$
$607$	29.3359	−	21.3138i	1.19071	−	0.865100i	0.993339	+	0.115230i	$0.0367604\pi$
$608$	−9.80113	−	30.1648i	−0.397488	−	1.22334i
$609$	−5.66952	+	17.4490i	−0.229741	+	0.707069i
$610$	19.9410	+	14.4880i	0.807389	+	0.586603i
$611$	43.2868	+	31.4497i	1.75120	+	1.27232i
$612$	25.0866	−	77.2085i	1.01406	−	3.12097i
$613$	−0.0385615	−	0.118680i	−0.00155749	−	0.00479345i	0.950275	−	0.311413i	$-0.100802\pi$
$613$	−0.0385615	−	0.118680i	−0.00155749	−	0.00479345i	−0.951832	+	0.306619i	$0.900802\pi$
$614$	0.0726516	−	0.0527845i	0.00293198	−	0.00213021i
$615$	3.92883			0.158426
$616$	−0.156873	−	0.528083i	−0.00632061	−	0.0212771i
$617$	−3.76668			−0.151641			−0.0758204	−	0.997121i	$-0.524158\pi$
$617$	−3.76668			−0.151641			−0.0758204	+	0.997121i	$0.524158\pi$
$618$	14.1795	−	10.3020i	0.570385	−	0.414409i
$619$	−13.5647	−	41.7477i	−0.545210	−	1.67798i	−0.720491	−	0.693464i	$-0.756084\pi$
$619$	−13.5647	−	41.7477i	−0.545210	−	1.67798i	0.175282	−	0.984518i	$-0.443916\pi$
$620$	−2.78864	+	8.58255i	−0.111994	+	0.344683i
$621$	−10.4477	−	7.59073i	−0.419253	−	0.304605i
$622$	−50.4560	−	36.6584i	−2.02310	−	1.46987i
$623$	2.26576	−	6.97328i	0.0907756	−	0.279378i
$624$	22.5675	+	69.4557i	0.903425	+	2.78046i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	45.7669			1.82921
$627$	31.6522	+	24.2484i	1.26407	+	0.968388i
$628$	19.9403			0.795704
$629$	1.85144	−	1.34515i	0.0738218	−	0.0536347i
$630$	3.65102	+	11.2367i	0.145460	+	0.447681i
$631$	3.21951	−	9.90864i	0.128167	−	0.394457i	−0.866298	−	0.499528i	$-0.833507\pi$
$631$	3.21951	−	9.90864i	0.128167	−	0.394457i	0.994465	+	0.105071i	$0.0335069\pi$
$632$	−0.201395	−	0.146322i	−0.00801106	−	0.00582037i
$633$	48.2593	+	35.0624i	1.91814	+	1.39361i
$634$	16.5934	−	51.0691i	0.659006	−	2.02821i
$635$	−1.42460	−	4.38446i	−0.0565335	−	0.173992i
$636$	−44.8530	+	32.5876i	−1.77854	+	1.29218i
$637$	−5.86024			−0.232191
$638$	33.1161	−	22.7981i	1.31108	−	0.902586i
$639$	5.09187			0.201431
$640$	1.07407	−	0.780360i	0.0424565	−	0.0308465i
$641$	−0.546290	−	1.68131i	−0.0215772	−	0.0664077i	0.939688	−	0.342032i	$-0.111115\pi$
$641$	−0.546290	−	1.68131i	−0.0215772	−	0.0664077i	−0.961265	+	0.275625i	$0.911115\pi$
$642$	−1.24552	+	3.83330i	−0.0491566	+	0.151288i
$643$	13.0049	+	9.44861i	0.512863	+	0.372617i	0.813909	−	0.580993i	$-0.197336\pi$
$643$	13.0049	+	9.44861i	0.512863	+	0.372617i	−0.301045	+	0.953610i	$0.597336\pi$
$644$	2.25010	+	1.63480i	0.0886666	+	0.0644200i
$645$	−4.15931	+	12.8010i	−0.163773	+	0.504040i
$646$	17.4190	+	53.6102i	0.685341	+	2.10926i
$647$	−32.9341	+	23.9280i	−1.29477	+	0.940706i	−0.999890	−	0.0148274i	$-0.995280\pi$
$647$	−32.9341	+	23.9280i	−1.29477	+	0.940706i	−0.294881	+	0.955534i	$0.595280\pi$
$648$	1.45087			0.0569956
$649$	23.1506	+	0.588152i	0.908742	+	0.0230870i
$650$	11.5969			0.454866
$651$	−11.4121	+	8.29135i	−0.447274	+	0.324964i
$652$	4.47480	+	13.7720i	0.175247	+	0.539353i
$653$	−15.2672	+	46.9876i	−0.597451	+	1.83877i	−0.0553261	+	0.998468i	$0.517620\pi$
$653$	−15.2672	+	46.9876i	−0.597451	+	1.83877i	−0.542125	+	0.840298i	$0.682380\pi$
$654$	78.7987	+	57.2506i	3.08127	+	2.23868i
$655$	−8.54418	−	6.20771i	−0.333849	−	0.242555i
$656$	−1.68662	+	5.19089i	−0.0658516	+	0.202670i
$657$	27.9112	+	85.9018i	1.08892	+	3.35135i
$658$	−14.6172	+	10.6200i	−0.569839	+	0.414013i
$659$	42.1007			1.64001			0.820005	−	0.572357i	$-0.193971\pi$
$659$	42.1007			1.64001			0.820005	+	0.572357i	$0.193971\pi$
$660$	6.33944	−	17.9465i	0.246763	−	0.698567i
$661$	36.0059			1.40047			0.700234	−	0.713914i	$-0.253079\pi$
$661$	36.0059			1.40047			0.700234	+	0.713914i	$0.253079\pi$
$662$	−10.7360	+	7.80013i	−0.417265	+	0.303161i
$663$	−38.4898	−	118.460i	−1.49482	−	4.60059i
$664$	−0.465015	+	1.43117i	−0.0180461	+	0.0555401i
$665$	−3.24737	−	2.35935i	−0.125928	−	0.0914918i
$666$	−3.08248	−	2.23956i	−0.119444	−	0.0867810i
$667$	2.74773	−	8.45665i	0.106393	−	0.327443i
$668$	7.28009	+	22.4058i	0.281675	+	0.866907i
$669$	−8.81674	+	6.40573i	−0.340875	+	0.247660i
$670$	11.9292			0.460867
$671$	13.7594	−	38.9518i	0.531175	−	1.50372i
$672$	−23.6661			−0.912939
$673$	32.8757	−	23.8856i	1.26727	−	0.920722i	0.268175	−	0.963370i	$-0.413579\pi$
$673$	32.8757	−	23.8856i	1.26727	−	0.920722i	0.999090	+	0.0426483i	$0.0135795\pi$
$674$	1.85356	+	5.70466i	0.0713963	+	0.219735i
$675$	2.74924	−	8.46128i	0.105818	−	0.325675i
$676$	−33.0835	−	24.0365i	−1.27244	−	0.924482i
$677$	−6.00240	−	4.36100i	−0.230691	−	0.167607i	0.466435	−	0.884556i	$-0.345538\pi$
$677$	−6.00240	−	4.36100i	−0.230691	−	0.167607i	−0.697126	+	0.716949i	$0.745538\pi$
$678$	−10.9398	+	33.6694i	−0.420142	+	1.29306i
$679$	−0.189047	−	0.581827i	−0.00725496	−	0.0223285i
$680$	−0.953604	+	0.692834i	−0.0365691	+	0.0265690i
$681$	−61.9685			−2.37464
$682$	30.9016	+	0.785068i	1.18328	+	0.0300618i
$683$	0.354974			0.0135827			0.00679135	−	0.999977i	$-0.497838\pi$
$683$	0.354974			0.0135827			0.00679135	+	0.999977i	$0.497838\pi$
$684$	37.1492	−	26.9905i	1.42044	−	1.03201i
$685$	−3.80430	−	11.7084i	−0.145355	−	0.447356i
$686$	0.611515	−	1.88205i	0.0233478	−	0.0718570i
$687$	26.6557	+	19.3665i	1.01698	+	0.738877i
$688$	−15.1276	−	10.9908i	−0.576732	−	0.419021i
$689$	−17.4950	+	53.8440i	−0.666506	+	2.05129i
$690$	−2.65858	−	8.18226i	−0.101210	−	0.311493i
$691$	18.2265	−	13.2423i	0.693368	−	0.503761i	−0.184398	−	0.982852i	$-0.559033\pi$
$691$	18.2265	−	13.2423i	0.693368	−	0.503761i	0.877766	+	0.479090i	$0.159033\pi$
$692$	37.7306			1.43430
$693$	16.3104	−	11.2286i	0.619580	−	0.426538i
$694$	−5.51605			−0.209386
$695$	8.70932	−	6.32769i	0.330363	−	0.240023i
$696$	0.941707	+	2.89828i	0.0356953	+	0.109859i
$697$	2.87660	−	8.85327i	0.108959	−	0.335342i
$698$	−35.5289	−	25.8132i	−1.34479	−	0.977045i
$699$	−0.424801	−	0.308636i	−0.0160674	−	0.0116737i
$700$	−0.592097	+	1.82229i	−0.0223791	+	0.0688759i
$701$	1.15946	+	3.56844i	0.0437921	+	0.134778i	0.970562	−	0.240851i	$-0.0774266\pi$
$701$	1.15946	+	3.56844i	0.0437921	+	0.134778i	−0.926770	+	0.375629i	$0.877427\pi$
$702$	−83.4694	+	60.6441i	−3.15035	+	2.28886i
$703$	1.29445			0.0488211
$704$	19.2592	+	14.7542i	0.725858	+	0.556072i
$705$	27.3458			1.02990
$706$	−25.4319	+	18.4774i	−0.957143	+	0.695405i
$707$	−5.16579	−	15.8987i	−0.194280	−	0.597931i
$708$	12.3824	−	38.1093i	0.465361	−	1.43223i
$709$	−12.7539	−	9.26624i	−0.478982	−	0.348001i	0.321949	−	0.946757i	$-0.395662\pi$
$709$	−12.7539	−	9.26624i	−0.478982	−	0.348001i	−0.800932	+	0.598756i	$0.795662\pi$
$710$	1.36538	+	0.992005i	0.0512417	+	0.0372293i
$711$	2.76510	−	8.51011i	0.103699	−	0.319154i
$712$	−0.376342	−	1.15826i	−0.0141040	−	0.0434076i
$713$	5.53085	−	4.01840i	0.207132	−	0.150490i
$714$	42.0604			1.57407
$715$	−5.53472	−	18.6315i	−0.206987	−	0.696779i
$716$	−24.8735			−0.929566
$717$	−10.1305	+	7.36027i	−0.378332	+	0.274874i
$718$	−4.60789	−	14.1816i	−0.171965	−	0.529254i
$719$	−0.141243	+	0.434701i	−0.00526747	+	0.0162116i	−0.953656	−	0.300900i	$-0.902713\pi$
$719$	−0.141243	+	0.434701i	−0.00526747	+	0.0162116i	0.948388	+	0.317112i	$0.102713\pi$
$720$	20.0976	+	14.6018i	0.748994	+	0.544176i
$721$	2.39238	+	1.73816i	0.0890968	+	0.0647326i
$722$	1.76607	−	5.43540i	0.0657262	−	0.202285i
$723$	−5.61076	−	17.2681i	−0.208666	−	0.642209i
$724$	−13.9229	+	10.1156i	−0.517441	+	0.375943i
$725$	6.12572			0.227503
$726$	−65.1125	−	3.31056i	−2.41655	−	0.122866i
$727$	27.1484			1.00688			0.503440	−	0.864030i	$-0.332068\pi$
$727$	27.1484			1.00688			0.503440	+	0.864030i	$0.332068\pi$
$728$	−0.787485	+	0.572141i	−0.0291861	+	0.0212050i
$729$	−8.58676	−	26.4273i	−0.318028	−	0.978790i
$730$	−9.25115	+	28.4721i	−0.342401	+	1.05380i
$731$	25.8006	+	18.7453i	0.954271	+	0.693319i
$732$	−57.8283	−	42.0147i	−2.13739	−	1.55291i
$733$	−6.20234	+	19.0888i	−0.229089	+	0.705062i	0.768762	+	0.639535i	$0.220873\pi$
$733$	−6.20234	+	19.0888i	−0.229089	+	0.705062i	−0.997851	+	0.0655274i	$0.979127\pi$
$734$	2.98419	+	9.18439i	0.110148	+	0.339002i
$735$	−2.42306	+	1.76046i	−0.0893760	+	0.0649355i
$736$	11.4698			0.422781
$737$	−5.69336	−	19.1655i	−0.209717	−	0.705972i
$738$	−15.4984			−0.570506
$739$	−6.01368	+	4.36919i	−0.221217	+	0.160723i	−0.692874	−	0.721059i	$-0.743656\pi$
$739$	−6.01368	+	4.36919i	−0.221217	+	0.160723i	0.471658	+	0.881782i	$0.343656\pi$
$740$	−0.190943	−	0.587662i	−0.00701920	−	0.0216029i
$741$	21.7710	−	67.0044i	0.799779	−	2.46147i
$742$	−15.4667	−	11.2372i	−0.567802	−	0.412532i
$743$	12.9242	+	9.38999i	0.474143	+	0.344485i	0.799054	−	0.601259i	$-0.205334\pi$
$743$	12.9242	+	9.38999i	0.474143	+	0.344485i	−0.324911	+	0.945745i	$0.605334\pi$
$744$	−0.724033	+	2.22834i	−0.0265443	+	0.0816951i
$745$	0.197024	+	0.606378i	0.00721840	+	0.0222160i
$746$	35.0814	−	25.4881i	1.28442	−	0.933185i
$747$	−54.0907			−1.97907
$748$	−35.7993	−	27.4254i	−1.30895	−	1.00277i
$749$	−0.680041			−0.0248481
$750$	4.79501	−	3.48378i	0.175089	−	0.127210i
$751$	2.54523	+	7.83340i	0.0928766	+	0.285845i	0.986694	−	0.162585i	$-0.0519833\pi$
$751$	2.54523	+	7.83340i	0.0928766	+	0.285845i	−0.893818	+	0.448430i	$0.851983\pi$
$752$	−11.7394	+	36.1301i	−0.428091	+	1.31753i
$753$	−25.1832	−	18.2967i	−0.917728	−	0.666769i
$754$	−57.4718	−	41.7557i	−2.09300	−	1.52065i
$755$	−0.123132	+	0.378960i	−0.00448121	+	0.0137918i
$756$	−5.26771	−	16.2124i	−0.191585	−	0.589638i
$757$	−38.9973	+	28.3332i	−1.41738	+	1.02979i	−0.425182	+	0.905108i	$0.639790\pi$
$757$	−38.9973	+	28.3332i	−1.41738	+	1.02979i	−0.992197	+	0.124679i	$0.960210\pi$
$758$	−5.62335			−0.204249
$759$	−11.8768	+	8.17634i	−0.431100	+	0.296782i
$760$	−0.666720			−0.0241845
$761$	−15.4834	+	11.2493i	−0.561272	+	0.407788i	−0.831924	−	0.554889i	$-0.812761\pi$
$761$	−15.4834	+	11.2493i	−0.561272	+	0.407788i	0.270652	+	0.962677i	$0.412761\pi$
$762$	8.44354	+	25.9865i	0.305877	+	0.941393i
$763$	−5.07822	+	15.6292i	−0.183844	+	0.565814i
$764$	−24.0890	−	17.5017i	−0.871509	−	0.633188i
$765$	−34.2773	−	24.9039i	−1.23930	−	0.900402i
$766$	−2.42983	+	7.47825i	−0.0877933	+	0.270200i
$767$	−12.6446	−	38.9160i	−0.456569	−	1.40518i
$768$	−41.8155	+	30.3807i	−1.50889	+	1.09627i
$769$	−49.9853			−1.80252			−0.901259	−	0.433281i	$-0.857356\pi$
$769$	−49.9853			−1.80252			−0.901259	+	0.433281i	$0.857356\pi$
$770$	6.56117	+	0.166689i	0.236448	+	0.00600706i
$771$	−11.6471			−0.419462
$772$	−8.07157	+	5.86434i	−0.290502	+	0.211062i
$773$	8.53264	+	26.2608i	0.306898	+	0.944534i	0.978962	+	0.204041i	$0.0654077\pi$
$773$	8.53264	+	26.2608i	0.306898	+	0.944534i	−0.672065	+	0.740493i	$0.734592\pi$
$774$	16.4076	−	50.4975i	0.589760	−	1.81510i
$775$	3.81028	+	2.76833i	0.136869	+	0.0994414i
$776$	−0.0822081	−	0.0597277i	−0.00295110	−	0.00214410i
$777$	0.298470	−	0.918596i	0.0107075	−	0.0329544i
$778$	−8.38451	−	25.8049i	−0.300599	−	0.925149i
$779$	4.25979	−	3.09492i	0.152623	−	0.110887i
$780$	−33.6304			−1.20416
$781$	0.942116	−	2.66706i	0.0337116	−	0.0954350i
$782$	−20.3846			−0.728950
$783$	−44.0904	+	32.0336i	−1.57566	+	1.14479i
$784$	−1.28577	−	3.95718i	−0.0459202	−	0.141328i
$785$	3.21591	−	9.89755i	0.114781	−	0.353259i
$786$	50.6410	+	36.7929i	1.80631	+	1.31236i
$787$	15.7687	+	11.4567i	0.562095	+	0.408386i	0.832225	−	0.554438i	$-0.187067\pi$
$787$	15.7687	+	11.4567i	0.562095	+	0.408386i	−0.270130	+	0.962824i	$0.587067\pi$
$788$	−9.45174	+	29.0895i	−0.336704	+	1.03627i
$789$	−4.97291	−	15.3050i	−0.177040	−	0.544874i
$790$	2.39941	−	1.74327i	0.0853671	−	0.0620228i
$791$	−5.97306			−0.212377
$792$	1.09549	−	3.10127i	0.0389267	−	0.110199i
$793$	−72.9929			−2.59205
$794$	6.73565	−	4.89374i	0.239039	−	0.173672i
$795$	8.94140	+	27.5188i	0.317119	+	0.975991i
$796$	−9.47401	+	29.1580i	−0.335797	+	1.03348i
$797$	24.6422	+	17.9036i	0.872873	+	0.634179i	0.931356	−	0.364109i	$-0.118627\pi$
$797$	24.6422	+	17.9036i	0.872873	+	0.634179i	−0.0584835	+	0.998288i	$0.518627\pi$
$798$	19.2471	+	13.9838i	0.681338	+	0.495021i
$799$	20.0220	−	61.6213i	0.708326	−	2.18000i
$800$	2.44175	+	7.51494i	0.0863290	+	0.265693i
$801$	35.4157	−	25.7310i	1.25135	−	0.909160i
$802$	−24.6977			−0.872107
$803$	50.1585	+	1.27430i	1.77006	+	0.0449690i
$804$	−34.5944			−1.22005
$805$	1.17434	−	0.853205i	0.0413899	−	0.0300715i
$806$	−16.8780	−	51.9453i	−0.594504	−	1.82969i
$807$	14.3686	−	44.2220i	0.505798	−	1.55669i
$808$	−2.24637	−	1.63208i	−0.0790271	−	0.0574165i
$809$	1.97550	+	1.43529i	0.0694550	+	0.0504620i	0.621971	−	0.783040i	$-0.286332\pi$
$809$	1.97550	+	1.43529i	0.0694550	+	0.0504620i	−0.552516	+	0.833502i	$0.686332\pi$
$810$	−5.34155	+	16.4396i	−0.187683	+	0.577629i
$811$	11.8461	+	36.4587i	0.415974	+	1.28024i	0.911377	+	0.411573i	$0.135020\pi$
$811$	11.8461	+	36.4587i	0.415974	+	1.28024i	−0.495403	+	0.868663i	$0.664980\pi$
$812$	9.49565	−	6.89900i	0.333232	−	0.242107i
$813$	−40.7219			−1.42818
$814$	−1.74338	+	1.20020i	−0.0611056	+	0.0420669i
$815$	7.55754			0.264729
$816$	71.5461	−	51.9813i	2.50461	−	1.81971i
$817$	5.57427	+	17.1559i	0.195019	+	0.600207i
$818$	21.7399	−	66.9086i	0.760118	−	2.33940i
$819$	−28.3061	−	20.5656i	−0.989095	−	0.718620i
$820$	−2.03341	−	1.47736i	−0.0710096	−	0.0515915i
$821$	7.84806	−	24.1538i	0.273899	−	0.842975i	−0.715609	−	0.698501i	$-0.753851\pi$
$821$	7.84806	−	24.1538i	0.273899	−	0.842975i	0.989509	−	0.144474i	$-0.0461491\pi$
$822$	22.5479	+	69.3954i	0.786449	+	2.42044i
$823$	−27.3870	+	19.8978i	−0.954651	+	0.693595i	−0.951902	−	0.306401i	$-0.900875\pi$
$823$	−27.3870	+	19.8978i	−0.954651	+	0.693595i	−0.00274906	+	0.999996i	$0.500875\pi$
$824$	0.491181			0.0171111
$825$	−7.88551	−	6.04100i	−0.274538	−	0.210321i
$826$	13.8176			0.480775
$827$	31.3854	−	22.8028i	1.09138	−	0.792932i	0.111746	−	0.993737i	$-0.464356\pi$
$827$	31.3854	−	22.8028i	1.09138	−	0.792932i	0.979631	+	0.200805i	$0.0643557\pi$
$828$	5.13139	+	15.7928i	0.178328	+	0.548837i
$829$	−3.31739	+	10.2099i	−0.115218	+	0.354603i	−0.991992	−	0.126298i	$-0.959690\pi$
$829$	−3.31739	+	10.2099i	−0.115218	+	0.354603i	0.876775	+	0.480901i	$0.159690\pi$
$830$	−14.5043	−	10.5380i	−0.503453	−	0.365780i
$831$	32.7758	+	23.8130i	1.13698	+	0.826063i
$832$	13.2469	−	40.7697i	0.459252	−	1.41343i
$833$	2.19292	+	6.74913i	0.0759803	+	0.233843i
$834$	−51.6198	+	37.5040i	−1.78745	+	1.29866i
$835$	12.2954			0.425501
$836$	−7.26381	−	24.4522i	−0.251224	−	0.845696i
$837$	−41.9015			−1.44833
$838$	−20.1564	+	14.6445i	−0.696292	+	0.505885i
$839$	10.5994	+	32.6217i	0.365933	+	1.12623i	0.949395	+	0.314086i	$0.101698\pi$
$839$	10.5994	+	32.6217i	0.365933	+	1.12623i	−0.583461	+	0.812141i	$0.698302\pi$
$840$	−0.153730	+	0.473132i	−0.00530419	+	0.0163246i
$841$	−6.89641	−	5.01053i	−0.237807	−	0.172777i
$842$	37.0039	+	26.8849i	1.27524	+	0.926515i
$843$	10.0040	−	30.7892i	0.344556	−	1.06044i
$844$	−11.7926	−	36.2938i	−0.405917	−	1.24929i
$845$	−17.2664	+	12.5447i	−0.593981	+	0.431552i
$846$	−107.874			−3.70877
$847$	−2.86358	−	10.6207i	−0.0983938	−	0.364933i
$848$	−40.1972			−1.38038
$849$	62.2737	−	45.2445i	2.13723	−	1.55279i
$850$	−4.33959	−	13.3559i	−0.148847	−	0.458103i
$851$	−0.144653	+	0.445197i	−0.00495865	+	0.0152612i
$852$	−3.95955	−	2.87678i	−0.135652	−	0.0985568i
$853$	4.78920	+	3.47956i	0.163979	+	0.119138i	0.666748	−	0.745283i	$-0.267686\pi$
$853$	4.78920	+	3.47956i	0.163979	+	0.119138i	−0.502769	+	0.864421i	$0.667686\pi$
$854$	7.61680	−	23.4421i	0.260642	−	0.802172i
$855$	−7.40566	−	22.7923i	−0.253268	−	0.779480i
$856$	−0.0913822	+	0.0663931i	−0.00312338	+	0.00226927i
$857$	1.71800			0.0586857			0.0293428	−	0.999569i	$-0.490659\pi$
$857$	1.71800			0.0586857			0.0293428	+	0.999569i	$0.490659\pi$
$858$	32.8040	+	110.428i	1.11991	+	3.76996i
$859$	55.3643			1.88901			0.944503	−	0.328502i	$-0.106544\pi$
$859$	55.3643			1.88901			0.944503	+	0.328502i	$0.106544\pi$
$860$	6.96625	−	5.06128i	0.237547	−	0.172588i
$861$	−1.21408	−	3.73654i	−0.0413756	−	0.127341i
$862$	−21.9523	+	67.5622i	−0.747698	+	2.30118i
$863$	40.1974	+	29.2051i	1.36833	+	0.994153i	0.997865	+	0.0653079i	$0.0208030\pi$
$863$	40.1974	+	29.2051i	1.36833	+	0.994153i	0.370469	+	0.928845i	$0.379197\pi$
$864$	−56.8731	−	41.3207i	−1.93486	−	1.40576i
$865$	6.08508	−	18.7279i	0.206899	−	0.636769i
$866$	12.4839	+	38.4216i	0.424221	+	1.30562i
$867$	−80.8326	+	58.7283i	−2.74522	+	1.99452i
$868$	9.02422			0.306302
$869$	−3.94588	−	3.02290i	−0.133855	−	0.102545i
$870$	−36.3069			−1.23092
$871$	−28.5799	+	20.7645i	−0.968394	+	0.703579i
$872$	0.843492	+	2.59600i	0.0285642	+	0.0879117i
$873$	1.12870	−	3.47377i	0.0382006	−	0.117569i
$874$	−9.32807	−	6.77724i	−0.315527	−	0.229244i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	26.8280	−	82.5681i	0.906434	−	2.78972i
$877$	1.11047	+	3.41768i	0.0374980	+	0.115407i	0.968053	−	0.250744i	$-0.0806753\pi$
$877$	1.11047	+	3.41768i	0.0374980	+	0.115407i	−0.930555	+	0.366151i	$0.880675\pi$
$878$	0.665219	−	0.483310i	0.0224500	−	0.0163109i
$879$	−8.63761			−0.291339
$880$	11.3668	−	7.82522i	0.383173	−	0.263788i
$881$	−10.4748			−0.352906			−0.176453	−	0.984309i	$-0.556462\pi$
$881$	−10.4748			−0.352906			−0.176453	+	0.984309i	$0.556462\pi$
$882$	9.55850	−	6.94466i	0.321851	−	0.233839i
$883$	−3.76579	−	11.5899i	−0.126729	−	0.390032i	0.867483	−	0.497467i	$-0.165736\pi$
$883$	−3.76579	−	11.5899i	−0.126729	−	0.390032i	−0.994212	+	0.107435i	$0.965736\pi$
$884$	−24.6235	+	75.7832i	−0.828177	+	2.54887i
$885$	−16.9189	−	12.2923i	−0.568722	−	0.413201i
$886$	29.0629	+	21.1155i	0.976388	+	0.709388i
$887$	1.70711	−	5.25395i	0.0573192	−	0.176410i	−0.918298	−	0.395890i	$-0.870436\pi$
$887$	1.70711	−	5.25395i	0.0573192	−	0.176410i	0.975617	+	0.219480i	$0.0704360\pi$
$888$	−0.0495758	−	0.152579i	−0.00166366	−	0.00512020i
$889$	−3.72965	+	2.70975i	−0.125088	+	0.0908820i
$890$	14.5096			0.486363
$891$	28.9612	+	0.735771i	0.970236	+	0.0246493i
$892$	6.97193			0.233438
$893$	29.6493	−	21.5415i	0.992177	−	0.720859i
$894$	−1.16775	−	3.59398i	−0.0390555	−	0.120201i
$895$	−4.01152	+	12.3462i	−0.134090	+	0.412688i
$896$	−1.07407	−	0.780360i	−0.0358823	−	0.0260700i
$897$	20.6118	+	14.9753i	0.688206	+	0.500011i
$898$	0.752237	−	2.31515i	0.0251025	−	0.0772575i
$899$	−8.91536	−	27.4387i	−0.297344	−	0.915131i
$900$	−9.25497	+	6.72413i	−0.308499	+	0.224138i
$901$	68.5579			2.28399
$902$	−2.86758	+	8.11790i	−0.0954798	+	0.270297i
$903$	13.4598			0.447914
$904$	−0.802645	+	0.583156i	−0.0266956	+	0.0193955i
$905$	2.77552	+	8.54217i	0.0922614	+	0.283951i
$906$	0.729796	−	2.24608i	0.0242458	−	0.0746210i
$907$	20.4441	+	14.8535i	0.678834	+	0.493202i	0.872971	−	0.487773i	$-0.162190\pi$
$907$	20.4441	+	14.8535i	0.678834	+	0.493202i	−0.194137	+	0.980975i	$0.562190\pi$
$908$	32.0724	+	23.3020i	1.06436	+	0.773303i
$909$	30.8421	−	94.9223i	1.02297	−	3.14837i
$910$	−3.58362	−	11.0293i	−0.118796	−	0.365617i
$911$	22.5595	−	16.3905i	0.747431	−	0.543041i	−0.147598	−	0.989047i	$-0.547154\pi$
$911$	22.5595	−	16.3905i	0.747431	−	0.543041i	0.895030	+	0.446007i	$0.147154\pi$
$912$	50.0220			1.65639
$913$	−10.0080	+	28.3320i	−0.331218	+	0.937653i
$914$	14.9061			0.493049
$915$	−30.1808	+	21.9276i	−0.997745	+	0.724904i
$916$	−6.51354	−	20.0466i	−0.215214	−	0.662359i
$917$	−3.26359	+	10.0443i	−0.107773	+	0.331692i
$918$	101.077	+	73.4370i	3.33605	+	2.42378i
$919$	46.4671	+	33.7603i	1.53281	+	1.11365i	0.954652	+	0.297725i	$0.0962277\pi$
$919$	46.4671	+	33.7603i	1.53281	+	1.11365i	0.578157	+	0.815926i	$0.303772\pi$
$920$	0.0745052	−	0.229303i	0.00245636	−	0.00755991i
$921$	0.0420003	+	0.129264i	0.00138396	+	0.00425938i
$922$	51.1279	−	37.1466i	1.68381	−	1.22336i
$923$	−4.99788			−0.164507
$924$	−19.0271	−	0.483393i	−0.625947	−	0.0159024i
$925$	−0.322486			−0.0106033
$926$	30.3577	−	22.0561i	0.997615	−	0.724810i
$927$	5.45584	+	16.7914i	0.179193	+	0.551501i
$928$	14.9575	−	46.0344i	0.491004	−	1.51115i
$929$	−28.9308	−	21.0194i	−0.949188	−	0.689625i	0.00142698	−	0.999999i	$-0.499546\pi$
$929$	−28.9308	−	21.0194i	−0.949188	−	0.689625i	−0.950615	+	0.310374i	$0.899546\pi$
$930$	−22.5834	−	16.4078i	−0.740539	−	0.538033i
$931$	−1.24039	+	3.81752i	−0.0406520	+	0.125114i
$932$	0.103804	+	0.319475i	0.00340020	+	0.0104648i
$933$	76.3652	−	55.4825i	2.50008	−	1.81642i
$934$	14.7883			0.483888
$935$	−19.3865	+	13.3462i	−0.634005	+	0.436468i
$936$	−5.81155			−0.189956
$937$	25.4413	−	18.4842i	0.831130	−	0.603851i	−0.0887489	−	0.996054i	$-0.528287\pi$
$937$	25.4413	−	18.4842i	0.831130	−	0.603851i	0.919879	+	0.392203i	$0.128287\pi$
$938$	−3.68634	−	11.3454i	−0.120363	−	0.370440i
$939$	−21.4050	+	65.8779i	−0.698527	+	2.14984i
$940$	−14.1531	−	10.2828i	−0.461622	−	0.335388i
$941$	22.5083	+	16.3533i	0.733750	+	0.533101i	0.890748	−	0.454498i	$-0.150181\pi$
$941$	22.5083	+	16.3533i	0.733750	+	0.533101i	−0.156997	+	0.987599i	$0.550181\pi$
$942$	−19.0606	+	58.6624i	−0.621027	+	1.91132i
$943$	0.588401	+	1.81091i	0.0191610	+	0.0589714i
$944$	23.5041	−	17.0767i	0.764994	−	0.555801i
$945$	−8.89672			−0.289410
$946$	−23.4142	−	17.9373i	−0.761261	−	0.583193i
$947$	0.153056			0.00497364			0.00248682	−	0.999997i	$-0.499208\pi$
$947$	0.153056			0.00497364			0.00248682	+	0.999997i	$0.499208\pi$
$948$	−6.95819	+	5.05542i	−0.225992	+	0.164193i
$949$	−27.3959	−	84.3160i	−0.889310	−	2.73701i
$950$	2.45461	−	7.55450i	0.0796379	−	0.245100i
$951$	65.7494	+	47.7697i	2.13207	+	1.54904i
$952$	0.953604	+	0.692834i	0.0309065	+	0.0224549i
$953$	17.1665	−	52.8331i	0.556078	−	1.71143i	−0.137002	−	0.990571i	$-0.543747\pi$
$953$	17.1665	−	52.8331i	0.556078	−	1.71143i	0.693080	−	0.720861i	$-0.256253\pi$
$954$	−35.2720	−	108.556i	−1.14197	−	3.51464i
$955$	−12.5721	+	9.13418i	−0.406824	+	0.295575i
$956$	8.01084			0.259089
$957$	17.3278	+	58.3307i	0.560129	+	1.88556i
$958$	−12.2652			−0.396272
$959$	−9.95978	+	7.23621i	−0.321618	+	0.233669i
$960$	−6.77025	−	20.8367i	−0.218509	−	0.672502i
$961$	−2.72494	+	8.38649i	−0.0879012	+	0.270532i
$962$	3.02558	+	2.19821i	0.0975487	+	0.0708733i
$963$	−3.28473	−	2.38650i	−0.105849	−	0.0769038i
$964$	−3.58942	+	11.0471i	−0.115607	+	0.355803i
$965$	1.60906	+	4.95218i	0.0517975	+	0.159416i
$966$	−6.96025	+	5.05692i	−0.223942	+	0.162704i
$967$	−15.1154			−0.486077			−0.243038	−	0.970017i	$-0.578144\pi$
$967$	−15.1154			−0.486077			−0.243038	+	0.970017i	$0.578144\pi$
$968$	−1.42171	−	1.14761i	−0.0456956	−	0.0368857i
$969$	−85.3145			−2.74070
$970$	0.979423	−	0.711592i	0.0314474	−	0.0228479i
$971$	17.1175	+	52.6822i	0.549326	+	1.69065i	0.710475	+	0.703723i	$0.248480\pi$
$971$	17.1175	+	52.6822i	0.549326	+	1.69065i	−0.161148	+	0.986930i	$0.551520\pi$
$972$	−0.312849	+	0.962849i	−0.0100346	+	0.0308834i
$973$	−8.70932	−	6.32769i	−0.279208	−	0.202856i
$974$	−23.8065	−	17.2965i	−0.762810	−	0.554214i
$975$	−5.42381	+	16.6928i	−0.173701	+	0.534597i
$976$	−16.0150	−	49.2891i	−0.512628	−	1.57771i
$977$	17.3771	−	12.6252i	0.555941	−	0.403915i	−0.274030	−	0.961721i	$-0.588357\pi$
$977$	17.3771	−	12.6252i	0.555941	−	0.403915i	0.829971	+	0.557806i	$0.188357\pi$
$978$	−44.7933			−1.43233
$979$	−6.92486	−	23.3111i	−0.221319	−	0.745027i
$980$	1.91606			0.0612064
$981$	−79.3769	+	57.6707i	−2.53431	+	1.84128i
$982$	−14.7899	−	45.5186i	−0.471964	−	1.45256i
$983$	13.9339	−	42.8841i	0.444422	−	1.36779i	−0.438695	−	0.898636i	$-0.644559\pi$
$983$	13.9339	−	42.8841i	0.444422	−	1.36779i	0.883117	−	0.469153i	$-0.155441\pi$
$984$	−0.527947	−	0.383576i	−0.0168303	−	0.0122279i
$985$	12.9145	+	9.38291i	0.411489	+	0.298964i
$986$	−26.5831	+	81.8144i	−0.846579	+	2.60550i
$987$	−8.45031	−	26.0074i	−0.268976	−	0.827824i
$988$	−36.4634	+	26.4922i	−1.16006	+	0.842830i
$989$	−6.52329			−0.207428
$990$	31.1068	+	23.8305i	0.988638	+	0.757384i
$991$	49.8800			1.58449			0.792246	−	0.610202i	$-0.208912\pi$
$991$	49.8800			1.58449			0.792246	+	0.610202i	$0.208912\pi$
$992$	30.1076	−	21.8745i	0.955918	−	0.694515i
$993$	−6.20651	−	19.1017i	−0.196958	−	0.606173i
$994$	0.521528	−	1.60510i	0.0165419	−	0.0509106i
$995$	12.9449	+	9.40503i	0.410381	+	0.298159i
$996$	42.0620	+	30.5598i	1.33279	+	0.968325i
$997$	−9.00166	+	27.7043i	−0.285086	+	0.877403i	0.701287	+	0.712879i	$0.252609\pi$
$997$	−9.00166	+	27.7043i	−0.285086	+	0.877403i	−0.986373	+	0.164525i	$0.947391\pi$
$998$	13.8751	+	42.7032i	0.439209	+	1.35175i
$999$	2.32112	−	1.68640i	0.0734371	−	0.0533552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.f.36.7	✓	36
11.2	odd	10		4235.2.a.bp.1.14		18
11.4	even	5	inner	385.2.n.f.246.7	yes	36
11.9	even	5		4235.2.a.bo.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.7	✓	36	1.1	even	1	trivial
385.2.n.f.246.7	yes	36	11.4	even	5	inner
4235.2.a.bo.1.5		18	11.9	even	5
4235.2.a.bp.1.14		18	11.2	odd	10

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60097 - 1.16317i) q^{2} +(0.925528 + 2.84848i) q^{3} +(0.592097 - 1.82229i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(4.79501 + 3.48378i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0513277 + 0.157970i) q^{8} +(-4.83020 + 3.50934i) q^{9} +O(q^{10})\)	\(q+(1.60097 - 1.16317i) q^{2} +(0.925528 + 2.84848i) q^{3} +(0.592097 - 1.82229i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(4.79501 + 3.48378i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.0513277 + 0.157970i) q^{8} +(-4.83020 + 3.50934i) q^{9} -1.97890 q^{10} +(0.944452 + 3.17931i) q^{11} +5.73875 q^{12} +(4.74103 - 3.44456i) q^{13} +(0.611515 + 1.88205i) q^{14} +(0.925528 - 2.84848i) q^{15} +(3.36618 + 2.44567i) q^{16} +(-5.74115 - 4.17119i) q^{17} +(-3.65102 + 11.2367i) q^{18} +(-1.24039 - 3.81752i) q^{19} +(-1.55013 + 1.12623i) q^{20} -2.99507 q^{21} +(5.21012 + 3.99141i) q^{22} +1.45156 q^{23} +(-0.402470 + 0.292412i) q^{24} +(0.309017 + 0.951057i) q^{25} +(3.58362 - 11.0293i) q^{26} +(-7.19759 - 5.22936i) q^{27} +(1.55013 + 1.12623i) q^{28} +(1.89295 - 5.82590i) q^{29} +(-1.83153 - 5.63688i) q^{30} +(3.81028 - 2.76833i) q^{31} +7.90168 q^{32} +(-8.18209 + 5.63280i) q^{33} -14.0432 q^{34} +(0.809017 - 0.587785i) q^{35} +(3.53508 + 10.8799i) q^{36} +(-0.0996537 + 0.306703i) q^{37} +(-6.42624 - 4.66894i) q^{38} +(14.1997 + 10.3167i) q^{39} +(0.0513277 - 0.157970i) q^{40} +(0.405358 + 1.24756i) q^{41} +(-4.79501 + 3.48378i) q^{42} -4.49398 q^{43} +(6.35282 + 0.161396i) q^{44} +5.97045 q^{45} +(2.32390 - 1.68841i) q^{46} +(2.82140 + 8.68339i) q^{47} +(-3.85096 + 11.8520i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.60097 + 1.16317i) q^{50} +(6.56797 - 20.2141i) q^{51} +(-3.46983 - 10.6790i) q^{52} +(-7.81580 + 5.67851i) q^{53} -17.6058 q^{54} +(1.10467 - 3.12725i) q^{55} -0.166100 q^{56} +(9.72611 - 7.06643i) q^{57} +(-3.74597 - 11.5289i) q^{58} +(2.15769 - 6.64069i) q^{59} +(-4.64275 - 3.37315i) q^{60} +(-10.0768 - 7.32123i) q^{61} +(2.88010 - 8.86402i) q^{62} +(-1.84497 - 5.67824i) q^{63} +(5.91797 - 4.29966i) q^{64} -5.86024 q^{65} +(-6.54736 + 18.5351i) q^{66} -6.02821 q^{67} +(-11.0004 + 7.99227i) q^{68} +(1.34346 + 4.13474i) q^{69} +(0.611515 - 1.88205i) q^{70} +(-0.689967 - 0.501290i) q^{71} +(-0.802295 - 0.582901i) q^{72} +(4.67488 - 14.3878i) q^{73} +(0.197205 + 0.606935i) q^{74} +(-2.42306 + 1.76046i) q^{75} -7.69103 q^{76} +(-3.31555 - 0.0842331i) q^{77} +34.7334 q^{78} +(-1.21249 + 0.880928i) q^{79} +(-1.28577 - 3.95718i) q^{80} +(2.69925 - 8.30742i) q^{81} +(2.10009 + 1.52581i) q^{82} +(7.32947 + 5.32517i) q^{83} +(-1.77337 + 5.45788i) q^{84} +(2.19292 + 6.74913i) q^{85} +(-7.19472 + 5.22727i) q^{86} +18.3470 q^{87} +(-0.453760 + 0.312382i) q^{88} -7.33214 q^{89} +(9.55850 - 6.94466i) q^{90} +(1.81091 + 5.57342i) q^{91} +(0.859464 - 2.64516i) q^{92} +(11.4121 + 8.29135i) q^{93} +(14.6172 + 10.6200i) q^{94} +(-1.24039 + 3.81752i) q^{95} +(7.31322 + 22.5078i) q^{96} +(-0.494932 + 0.359589i) q^{97} -1.97890 q^{98} +(-15.7192 - 12.0423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9}+O(q^{10}) \) 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9	\( 36 q + q^{2} - 17 q^{4} - 9 q^{5} - 13 q^{6} + 9 q^{7} + 3 q^{8} - 11 q^{9} - 4 q^{10} - 3 q^{11} + 30 q^{12} - q^{13} - q^{14} + 3 q^{16} + 5 q^{17} - 34 q^{18} - 5 q^{19} - 7 q^{20} - 10 q^{21} - 5 q^{22} + 8 q^{23} - 41 q^{24} - 9 q^{25} + 28 q^{26} + 7 q^{28} - 33 q^{29} + 12 q^{30} - q^{31} + 12 q^{32} - 14 q^{33} + 88 q^{34} + 9 q^{35} - 104 q^{36} - 18 q^{37} - 27 q^{38} + 6 q^{39} + 3 q^{40} + 36 q^{41} + 13 q^{42} - 20 q^{43} - 30 q^{44} + 74 q^{45} + 20 q^{46} - 7 q^{47} + 75 q^{48} - 9 q^{49} + q^{50} + 22 q^{51} - 6 q^{52} - 4 q^{53} - 26 q^{54} - 3 q^{55} + 12 q^{56} - 43 q^{57} - 41 q^{58} + 25 q^{59} - 15 q^{60} + 21 q^{61} + 31 q^{62} + 26 q^{63} + 43 q^{64} - 16 q^{65} - 12 q^{66} + 58 q^{67} - 43 q^{68} - 37 q^{69} - q^{70} - 29 q^{71} + 34 q^{72} + 19 q^{73} - 59 q^{74} - 5 q^{75} - 94 q^{76} + 3 q^{77} + 20 q^{78} + 11 q^{79} - 47 q^{80} - 10 q^{81} - 58 q^{82} + 47 q^{83} - 10 q^{85} + 35 q^{86} - 46 q^{87} - 110 q^{88} + 118 q^{89} + 36 q^{90} - 9 q^{91} + 107 q^{92} - 29 q^{93} - 27 q^{94} - 5 q^{95} + 67 q^{96} - 4 q^{98} + 16 q^{99}+O(q^{100}) \) 36 * q + q^2 - 17 * q^4 - 9 * q^5 - 13 * q^6 + 9 * q^7 + 3 * q^8 - 11 * q^9 - 4 * q^10 - 3 * q^11 + 30 * q^12 - q^13 - q^14 + 3 * q^16 + 5 * q^17 - 34 * q^18 - 5 * q^19 - 7 * q^20 - 10 * q^21 - 5 * q^22 + 8 * q^23 - 41 * q^24 - 9 * q^25 + 28 * q^26 + 7 * q^28 - 33 * q^29 + 12 * q^30 - q^31 + 12 * q^32 - 14 * q^33 + 88 * q^34 + 9 * q^35 - 104 * q^36 - 18 * q^37 - 27 * q^38 + 6 * q^39 + 3 * q^40 + 36 * q^41 + 13 * q^42 - 20 * q^43 - 30 * q^44 + 74 * q^45 + 20 * q^46 - 7 * q^47 + 75 * q^48 - 9 * q^49 + q^50 + 22 * q^51 - 6 * q^52 - 4 * q^53 - 26 * q^54 - 3 * q^55 + 12 * q^56 - 43 * q^57 - 41 * q^58 + 25 * q^59 - 15 * q^60 + 21 * q^61 + 31 * q^62 + 26 * q^63 + 43 * q^64 - 16 * q^65 - 12 * q^66 + 58 * q^67 - 43 * q^68 - 37 * q^69 - q^70 - 29 * q^71 + 34 * q^72 + 19 * q^73 - 59 * q^74 - 5 * q^75 - 94 * q^76 + 3 * q^77 + 20 * q^78 + 11 * q^79 - 47 * q^80 - 10 * q^81 - 58 * q^82 + 47 * q^83 - 10 * q^85 + 35 * q^86 - 46 * q^87 - 110 * q^88 + 118 * q^89 + 36 * q^90 - 9 * q^91 + 107 * q^92 - 29 * q^93 - 27 * q^94 - 5 * q^95 + 67 * q^96 - 4 * q^98 + 16 * q^99

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