LMFDB - Embedded newform 735.2.u.b.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(106,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("735.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.u (of order $7$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			211.3
Character	$\chi$	$=$	735.211
Dual form			735.2.u.b.526.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.105053 + 0.460266i) q^{2} +(0.623490 - 0.781831i) q^{3} +(1.60113 + 0.771063i) q^{4} +(0.623490 - 0.781831i) q^{5} +(0.294351 + 0.369105i) q^{6} +(-2.25104 + 1.39025i) q^{7} +(-1.11180 + 1.39415i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(0.294351 + 0.369105i) q^{10} +(1.04085 - 4.56028i) q^{11} +(1.60113 - 0.771063i) q^{12} +(0.142281 - 0.623373i) q^{13} +(-0.403407 - 1.18213i) q^{14} +(-0.222521 - 0.974928i) q^{15} +(1.69115 + 2.12063i) q^{16} +(2.90536 - 1.39915i) q^{17} +0.472103 q^{18} +8.07611 q^{19} +(1.60113 - 0.771063i) q^{20} +(-0.316561 + 2.62674i) q^{21} +(1.98960 + 0.958140i) q^{22} +(7.66877 + 3.69308i) q^{23} +(0.396797 + 1.73848i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.271971 + 0.130974i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-4.67618 + 0.490274i) q^{28} +(0.216794 - 0.104402i) q^{29} +0.472103 q^{30} -3.02572 q^{31} +(-4.36691 + 2.10299i) q^{32} +(-2.91641 - 3.65706i) q^{33} +(0.338764 + 1.48422i) q^{34} +(-0.316561 + 2.62674i) q^{35} +(0.395446 - 1.73256i) q^{36} +(-7.07650 + 3.40786i) q^{37} +(-0.848418 + 3.71716i) q^{38} +(-0.398662 - 0.499907i) q^{39} +(0.396797 + 1.73848i) q^{40} +(3.23194 - 4.05272i) q^{41} +(-1.17575 - 0.421649i) q^{42} +(0.0362347 + 0.0454369i) q^{43} +(5.18281 - 6.49903i) q^{44} +(-0.900969 - 0.433884i) q^{45} +(-2.50543 + 3.14170i) q^{46} +(-0.410884 + 1.80020i) q^{47} +2.71239 q^{48} +(3.13440 - 6.25904i) q^{49} +0.472103 q^{50} +(0.717563 - 3.14385i) q^{51} +(0.708470 - 0.888393i) q^{52} +(1.50869 + 0.726547i) q^{53} +(0.294351 - 0.369105i) q^{54} +(-2.91641 - 3.65706i) q^{55} +(0.564488 - 4.68398i) q^{56} +(5.03537 - 6.31416i) q^{57} +(0.0252781 + 0.110751i) q^{58} +(1.86356 + 2.33684i) q^{59} +(0.395446 - 1.73256i) q^{60} +(-8.53161 + 4.10861i) q^{61} +(0.317860 - 1.39264i) q^{62} +(1.85630 + 1.88525i) q^{63} +(0.697947 + 3.05791i) q^{64} +(-0.398662 - 0.499907i) q^{65} +(1.98960 - 0.958140i) q^{66} -15.6802 q^{67} +5.73068 q^{68} +(7.66877 - 3.69308i) q^{69} +(-1.17575 - 0.421649i) q^{70} +(-10.7509 - 5.17735i) q^{71} +(1.60660 + 0.773696i) q^{72} +(2.95342 + 12.9398i) q^{73} +(-0.825118 - 3.61508i) q^{74} +(-0.900969 - 0.433884i) q^{75} +(12.9309 + 6.22719i) q^{76} +(3.99693 + 11.7124i) q^{77} +(0.271971 - 0.130974i) q^{78} -10.1427 q^{79} +2.71239 q^{80} +(-0.900969 + 0.433884i) q^{81} +(1.52581 + 1.91330i) q^{82} +(-3.07907 - 13.4903i) q^{83} +(-2.53224 + 3.96167i) q^{84} +(0.717563 - 3.14385i) q^{85} +(-0.0247196 + 0.0119044i) q^{86} +(0.0535436 - 0.234590i) q^{87} +(5.20050 + 6.52123i) q^{88} +(-0.0120501 - 0.0527949i) q^{89} +(0.294351 - 0.369105i) q^{90} +(0.546365 + 1.60105i) q^{91} +(9.43109 + 11.8262i) q^{92} +(-1.88650 + 2.36560i) q^{93} +(-0.785406 - 0.378232i) q^{94} +(5.03537 - 6.31416i) q^{95} +(-1.07854 + 4.72538i) q^{96} +10.9940 q^{97} +(2.55154 + 2.10019i) q^{98} -4.67756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) $ 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$	$1$

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 $

$2$	−0.105053	+	0.460266i	−0.0742835	+	0.325457i	−0.998393	−	0.0566707i	$-0.981951\pi$
$2$	−0.105053	+	0.460266i	−0.0742835	+	0.325457i	0.924109	+	0.382128i	$0.124809\pi$
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$4$	1.60113	+	0.771063i	0.800564	+	0.385532i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$6$	0.294351	+	0.369105i	0.120168	+	0.150686i
$7$	−2.25104	+	1.39025i	−0.850815	+	0.525466i
$7$	−2.25104	+	1.39025i	−0.850815	+	0.525466i
$8$	−1.11180	+	1.39415i	−0.393080	+	0.492907i
$9$	−0.222521	−	0.974928i	−0.0741736	−	0.324976i
$10$	0.294351	+	0.369105i	0.0930820	+	0.116721i
$11$	1.04085	−	4.56028i	0.313829	−	1.37498i	−0.534348	−	0.845264i	$-0.679443\pi$
$11$	1.04085	−	4.56028i	0.313829	−	1.37498i	0.848178	−	0.529712i	$-0.177700\pi$
$12$	1.60113	−	0.771063i	0.462206	−	0.222587i
$13$	0.142281	−	0.623373i	0.0394616	−	0.172893i	−0.951357	−	0.308091i	$-0.900310\pi$
$13$	0.142281	−	0.623373i	0.0394616	−	0.172893i	0.990819	+	0.135198i	$0.0431671\pi$
$14$	−0.403407	−	1.18213i	−0.107815	−	0.315937i
$15$	−0.222521	−	0.974928i	−0.0574547	−	0.251725i
$16$	1.69115	+	2.12063i	0.422787	+	0.530158i
$17$	2.90536	−	1.39915i	0.704652	−	0.339343i	−0.0470068	−	0.998895i	$-0.514968\pi$
$17$	2.90536	−	1.39915i	0.704652	−	0.339343i	0.751659	+	0.659552i	$0.229254\pi$
$18$	0.472103			0.111276
$19$	8.07611			1.85279			0.926394	−	0.376556i	$-0.122892\pi$
$19$	8.07611			1.85279			0.926394	+	0.376556i	$0.122892\pi$
$20$	1.60113	−	0.771063i	0.358023	−	0.172415i
$21$	−0.316561	+	2.62674i	−0.0690793	+	0.573203i
$22$	1.98960	+	0.958140i	0.424184	+	0.204276i
$23$	7.66877	+	3.69308i	1.59905	+	0.770061i	0.999541	−	0.0303076i	$-0.00964870\pi$
$23$	7.66877	+	3.69308i	1.59905	+	0.770061i	0.599508	+	0.800369i	$0.295363\pi$
$24$	0.396797	+	1.73848i	0.0809958	+	0.354866i
$25$	−0.222521	−	0.974928i	−0.0445042	−	0.194986i
$26$	0.271971	+	0.130974i	0.0533378	+	0.0256861i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−4.67618	+	0.490274i	−0.883716	+	0.0926532i
$29$	0.216794	−	0.104402i	0.0402576	−	0.0193870i	−0.413647	−	0.910438i	$-0.635745\pi$
$29$	0.216794	−	0.104402i	0.0402576	−	0.0193870i	0.453904	+	0.891050i	$0.350031\pi$
$30$	0.472103			0.0861938
$31$	−3.02572			−0.543435			−0.271718	−	0.962377i	$-0.587592\pi$
$31$	−3.02572			−0.543435			−0.271718	+	0.962377i	$0.587592\pi$
$32$	−4.36691	+	2.10299i	−0.771968	+	0.371760i
$33$	−2.91641	−	3.65706i	−0.507682	−	0.636613i
$34$	0.338764	+	1.48422i	0.0580975	+	0.254542i
$35$	−0.316561	+	2.62674i	−0.0535086	+	0.444001i
$36$	0.395446	−	1.73256i	0.0659077	−	0.288760i
$37$	−7.07650	+	3.40786i	−1.16337	+	0.560249i	−0.913023	−	0.407907i	$-0.866259\pi$
$37$	−7.07650	+	3.40786i	−1.16337	+	0.560249i	−0.250346	+	0.968156i	$0.580544\pi$
$38$	−0.848418	+	3.71716i	−0.137632	+	0.603003i
$39$	−0.398662	−	0.499907i	−0.0638370	−	0.0800491i
$40$	0.396797	+	1.73848i	0.0627391	+	0.274878i
$41$	3.23194	−	4.05272i	0.504744	−	0.632929i	−0.462548	−	0.886594i	$-0.653065\pi$
$41$	3.23194	−	4.05272i	0.504744	−	0.632929i	0.967292	+	0.253665i	$0.0816362\pi$
$42$	−1.17575	−	0.421649i	−0.181422	−	0.0650619i
$43$	0.0362347	+	0.0454369i	0.00552575	+	0.00692907i	0.784587	−	0.620019i	$-0.212875\pi$
$43$	0.0362347	+	0.0454369i	0.00552575	+	0.00692907i	−0.779061	+	0.626948i	$0.784304\pi$
$44$	5.18281	−	6.49903i	0.781337	−	0.979766i
$45$	−0.900969	−	0.433884i	−0.134309	−	0.0646796i
$46$	−2.50543	+	3.14170i	−0.369405	+	0.463219i
$47$	−0.410884	+	1.80020i	−0.0599335	+	0.262586i	−0.996014	−	0.0892009i	$-0.971569\pi$
$47$	−0.410884	+	1.80020i	−0.0599335	+	0.262586i	0.936080	+	0.351787i	$0.114426\pi$
$48$	2.71239			0.391500
$49$	3.13440	−	6.25904i	0.447772	−	0.894148i
$50$	0.472103			0.0667654
$51$	0.717563	−	3.14385i	0.100479	−	0.440227i
$52$	0.708470	−	0.888393i	0.0982471	−	0.123198i
$53$	1.50869	+	0.726547i	0.207235	+	0.0997989i	0.534622	−	0.845091i	$-0.320454\pi$
$53$	1.50869	+	0.726547i	0.207235	+	0.0997989i	−0.327388	+	0.944890i	$0.606168\pi$
$54$	0.294351	−	0.369105i	0.0400561	−	0.0502288i
$55$	−2.91641	−	3.65706i	−0.393248	−	0.493118i
$56$	0.564488	−	4.68398i	0.0754328	−	0.625923i
$57$	5.03537	−	6.31416i	0.666952	−	0.836331i
$58$	0.0252781	+	0.110751i	0.00331918	+	0.0145423i
$59$	1.86356	+	2.33684i	0.242615	+	0.304230i	0.888198	−	0.459460i	$-0.151957\pi$
$59$	1.86356	+	2.33684i	0.242615	+	0.304230i	−0.645583	+	0.763690i	$0.723386\pi$
$60$	0.395446	−	1.73256i	0.0510519	−	0.223673i
$61$	−8.53161	+	4.10861i	−1.09236	+	0.526053i	−0.891249	−	0.453515i	$-0.850170\pi$
$61$	−8.53161	+	4.10861i	−1.09236	+	0.526053i	−0.201112	+	0.979568i	$0.564456\pi$
$62$	0.317860	−	1.39264i	0.0403683	−	0.176865i
$63$	1.85630	+	1.88525i	0.233872	+	0.237519i
$64$	0.697947	+	3.05791i	0.0872434	+	0.382238i
$65$	−0.398662	−	0.499907i	−0.0494480	−	0.0620058i
$66$	1.98960	−	0.958140i	0.244903	−	0.117939i
$67$	−15.6802			−1.91564			−0.957819	−	0.287373i	$-0.907218\pi$
$67$	−15.6802			−1.91564			−0.957819	+	0.287373i	$0.907218\pi$
$68$	5.73068			0.694947
$69$	7.66877	−	3.69308i	0.923211	−	0.444595i
$70$	−1.17575	−	0.421649i	−0.140529	−	0.0503967i
$71$	−10.7509	−	5.17735i	−1.27590	−	0.614439i	−0.331563	−	0.943433i	$-0.607576\pi$
$71$	−10.7509	−	5.17735i	−1.27590	−	0.614439i	−0.944332	+	0.328994i	$0.893290\pi$
$72$	1.60660	+	0.773696i	0.189339	+	0.0911810i
$73$	2.95342	+	12.9398i	0.345671	+	1.51449i	0.786894	+	0.617088i	$0.211688\pi$
$73$	2.95342	+	12.9398i	0.345671	+	1.51449i	−0.441223	+	0.897398i	$0.645455\pi$
$74$	−0.825118	−	3.61508i	−0.0959180	−	0.420244i
$75$	−0.900969	−	0.433884i	−0.104035	−	0.0501006i
$76$	12.9309	+	6.22719i	1.48328	+	0.714308i
$77$	3.99693	+	11.7124i	0.455492	+	1.33476i
$78$	0.271971	−	0.130974i	0.0307946	−	0.0148299i
$79$	−10.1427			−1.14115			−0.570574	−	0.821246i	$-0.693279\pi$
$79$	−10.1427			−1.14115			−0.570574	+	0.821246i	$0.693279\pi$
$80$	2.71239			0.303254
$81$	−0.900969	+	0.433884i	−0.100108	+	0.0482093i
$82$	1.52581	+	1.91330i	0.168497	+	0.211289i
$83$	−3.07907	−	13.4903i	−0.337971	−	1.48075i	−0.803280	−	0.595601i	$-0.796914\pi$
$83$	−3.07907	−	13.4903i	−0.337971	−	1.48075i	0.465309	−	0.885148i	$-0.345943\pi$
$84$	−2.53224	+	3.96167i	−0.276290	+	0.432254i
$85$	0.717563	−	3.14385i	0.0778307	−	0.340999i
$86$	−0.0247196	+	0.0119044i	−0.00266559	+	0.00128368i
$87$	0.0535436	−	0.234590i	0.00574048	−	0.0251507i
$88$	5.20050	+	6.52123i	0.554376	+	0.695165i
$89$	−0.0120501	−	0.0527949i	−0.00127731	−	0.00559624i	0.974285	−	0.225318i	$-0.0723421\pi$
$89$	−0.0120501	−	0.0527949i	−0.00127731	−	0.00559624i	−0.975563	+	0.219722i	$0.929485\pi$
$90$	0.294351	−	0.369105i	0.0310273	−	0.0389071i
$91$	0.546365	+	1.60105i	0.0572746	+	0.167835i
$92$	9.43109	+	11.8262i	0.983259	+	1.23297i
$93$	−1.88650	+	2.36560i	−0.195621	+	0.245302i
$94$	−0.785406	−	0.378232i	−0.0810085	−	0.0390116i
$95$	5.03537	−	6.31416i	0.516619	−	0.647819i
$96$	−1.07854	+	4.72538i	−0.110078	+	0.482282i
$97$	10.9940			1.11627			0.558135	−	0.829750i	$-0.311517\pi$
$97$	10.9940			1.11627			0.558135	+	0.829750i	$0.311517\pi$
$98$	2.55154	+	2.10019i	0.257745	+	0.212151i
$99$	−4.67756			−0.470112
$100$	0.395446	−	1.73256i	0.0395446	−	0.173256i
$101$	0.549100	−	0.688550i	0.0546375	−	0.0685133i	−0.753762	−	0.657148i	$-0.771763\pi$
$101$	0.549100	−	0.688550i	0.0546375	−	0.0685133i	0.808399	+	0.588634i	$0.200334\pi$
$102$	1.37163	+	0.660540i	0.135811	+	0.0654032i
$103$	0.489390	−	0.613676i	0.0482210	−	0.0604673i	−0.757136	−	0.653257i	$-0.773402\pi$
$103$	0.489390	−	0.613676i	0.0482210	−	0.0604673i	0.805357	+	0.592790i	$0.201974\pi$
$104$	0.710890	+	0.891427i	0.0697085	+	0.0874116i
$105$	1.85630	+	1.88525i	0.181156	+	0.183981i
$106$	−0.492897	+	0.618073i	−0.0478744	+	0.0600326i
$107$	−2.28946	−	10.0308i	−0.221331	−	0.969714i	−0.956478	−	0.291806i	$-0.905744\pi$
$107$	−2.28946	−	10.0308i	−0.221331	−	0.969714i	0.735147	−	0.677908i	$-0.237113\pi$
$108$	−1.10802	−	1.38941i	−0.106619	−	0.133696i
$109$	0.910665	−	3.98988i	0.0872258	−	0.382161i	−0.912406	−	0.409286i	$-0.865778\pi$
$109$	0.910665	−	3.98988i	0.0872258	−	0.382161i	0.999632	+	0.0271244i	$0.00863503\pi$
$110$	1.98960	−	0.958140i	0.189701	−	0.0913550i
$111$	−1.74775	+	7.65740i	−0.165889	+	0.726808i
$112$	−6.75506	−	2.42252i	−0.638293	−	0.228906i
$113$	4.05686	+	17.7743i	0.381637	+	1.67206i	0.692353	+	0.721559i	$0.256574\pi$
$113$	4.05686	+	17.7743i	0.381637	+	1.67206i	−0.310716	+	0.950503i	$0.600569\pi$
$114$	2.37721	+	2.98093i	0.222646	+	0.279190i
$115$	7.66877	−	3.69308i	0.715116	−	0.344382i
$116$	0.427616			0.0397031
$117$	−0.639404			−0.0591130
$118$	−1.27134	+	0.612244i	−0.117036	+	0.0563617i
$119$	−4.59492	+	7.18871i	−0.421216	+	0.658988i
$120$	1.60660	+	0.773696i	0.146662	+	0.0706285i
$121$	−9.80212	−	4.72045i	−0.891102	−	0.429132i
$122$	−0.994784	−	4.35843i	−0.0900635	−	0.394594i
$123$	−1.15347	−	5.05366i	−0.104004	−	0.455673i
$124$	−4.84457	−	2.33302i	−0.435055	−	0.209511i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	−1.06272	+	0.656341i	−0.0946750	+	0.0584715i
$127$	−3.83987	+	1.84919i	−0.340734	+	0.164089i	−0.596423	−	0.802670i	$-0.703412\pi$
$127$	−3.83987	+	1.84919i	−0.340734	+	0.164089i	0.255689	+	0.966759i	$0.417698\pi$
$128$	−11.1746			−0.987702
$129$	0.0581160			0.00511683
$130$	0.271971	−	0.130974i	0.0238534	−	0.0114872i
$131$	6.42025	+	8.05074i	0.560940	+	0.703396i	0.978731	−	0.205147i	$-0.0657671\pi$
$131$	6.42025	+	8.05074i	0.560940	+	0.703396i	−0.417791	+	0.908543i	$0.637196\pi$
$132$	−1.84972	−	8.10416i	−0.160998	−	0.705377i
$133$	−18.1797	+	11.2278i	−1.57638	+	0.973576i
$134$	1.64724	−	7.21705i	0.142300	−	0.623458i
$135$	−0.900969	+	0.433884i	−0.0775431	+	0.0373428i
$136$	−1.27955	+	5.60608i	−0.109721	+	0.480717i
$137$	−9.05625	−	11.3562i	−0.773727	−	0.970223i	0.226265	−	0.974066i	$-0.427348\pi$
$137$	−9.05625	−	11.3562i	−0.773727	−	0.970223i	−0.999993	+	0.00384226i	$0.998777\pi$
$138$	0.894176	+	3.91764i	0.0761173	+	0.333492i
$139$	11.7924	−	14.7872i	1.00022	−	1.25424i	0.0332249	−	0.999448i	$-0.489422\pi$
$139$	11.7924	−	14.7872i	1.00022	−	1.25424i	0.966996	−	0.254790i	$-0.0820063\pi$
$140$	−2.53224	+	3.96167i	−0.214013	+	0.334822i
$141$	1.15127	+	1.44365i	0.0969545	+	0.121577i
$142$	3.51237	−	4.40437i	0.294751	−	0.369607i
$143$	−2.69466	−	1.29768i	−0.225339	−	0.108518i
$144$	1.69115	−	2.12063i	0.140929	−	0.176719i
$145$	0.0535436	−	0.234590i	0.00444656	−	0.0194816i
$146$	−6.26600			−0.518578
$147$	−2.93924	−	6.35302i	−0.242425	−	0.523988i
$148$	−13.9581			−1.14735
$149$	2.43406	−	10.6643i	0.199406	−	0.873656i	−0.771885	−	0.635762i	$-0.780686\pi$
$149$	2.43406	−	10.6643i	0.199406	−	0.873656i	0.971291	−	0.237894i	$-0.0764570\pi$
$150$	0.294351	−	0.369105i	0.0240337	−	0.0301373i
$151$	−17.7840	−	8.56433i	−1.44724	−	0.696955i	−0.465128	−	0.885243i	$-0.653992\pi$
$151$	−17.7840	−	8.56433i	−1.44724	−	0.696955i	−0.982114	+	0.188289i	$0.939706\pi$
$152$	−8.97902	+	11.2593i	−0.728295	+	0.913253i
$153$	−2.01057	−	2.52117i	−0.162545	−	0.203825i
$154$	−5.81073	+	0.609226i	−0.468242	+	0.0490928i
$155$	−1.88650	+	2.36560i	−0.151528	+	0.190010i
$156$	−0.252850	−	1.10781i	−0.0202442	−	0.0886957i
$157$	1.09705	+	1.37566i	0.0875541	+	0.109789i	0.823679	−	0.567056i	$-0.191918\pi$
$157$	1.09705	+	1.37566i	0.0875541	+	0.109789i	−0.736125	+	0.676846i	$0.763346\pi$
$158$	1.06552	−	4.66836i	0.0847684	−	0.371395i
$159$	1.50869	−	0.726547i	0.119647	−	0.0576189i
$160$	−1.07854	+	4.72538i	−0.0852659	+	0.373574i
$161$	−22.3971	+	2.34822i	−1.76513	+	0.185066i
$162$	−0.105053	−	0.460266i	−0.00825372	−	0.0361619i
$163$	−3.44367	−	4.31823i	−0.269729	−	0.338230i	0.628457	−	0.777844i	$-0.283687\pi$
$163$	−3.44367	−	4.31823i	−0.269729	−	0.338230i	−0.898187	+	0.439614i	$0.855115\pi$
$164$	8.29966	−	3.99690i	0.648094	−	0.312106i
$165$	−4.67756			−0.364147
$166$	6.53258			0.507026
$167$	−4.10611	+	1.97740i	−0.317740	+	0.153016i	−0.585955	−	0.810343i	$-0.699281\pi$
$167$	−4.10611	+	1.97740i	−0.317740	+	0.153016i	0.268215	+	0.963359i	$0.413566\pi$
$168$	−3.31013	−	3.36175i	−0.255382	−	0.259364i
$169$	11.3442	+	5.46310i	0.872634	+	0.420238i
$170$	1.37163	+	0.660540i	0.105199	+	0.0506611i
$171$	−1.79710	−	7.87363i	−0.137428	−	0.602111i
$172$	0.0229818	+	0.100690i	0.00175234	+	0.00767752i
$173$	−13.0425	−	6.28092i	−0.991601	−	0.477530i	−0.133521	−	0.991046i	$-0.542628\pi$
$173$	−13.0425	−	6.28092i	−0.991601	−	0.477530i	−0.858080	+	0.513516i	$0.828343\pi$
$174$	0.102349	+	0.0492886i	0.00775905	+	0.00373656i
$175$	1.85630	+	1.88525i	0.140323	+	0.142511i
$176$	11.4309	−	5.50484i	0.861638	−	0.414943i
$177$	2.98892			0.224661
$178$	0.0255656			0.00191622
$179$	8.47336	−	4.08055i	0.633328	−	0.304995i	−0.0895373	−	0.995983i	$-0.528539\pi$
$179$	8.47336	−	4.08055i	0.633328	−	0.304995i	0.722866	+	0.690989i	$0.242825\pi$
$180$	−1.10802	−	1.38941i	−0.0825866	−	0.103560i
$181$	2.95987	+	12.9681i	0.220006	+	0.963908i	0.957472	+	0.288525i	$0.0931647\pi$
$181$	2.95987	+	12.9681i	0.220006	+	0.963908i	−0.737467	+	0.675384i	$0.763978\pi$
$182$	−0.794305	+	0.0832789i	−0.0588778	+	0.00617304i
$183$	−2.10713	+	9.23196i	−0.155764	+	0.682446i
$184$	−13.6749	+	6.58546i	−1.00812	+	0.485487i
$185$	−1.74775	+	7.65740i	−0.128497	+	0.562983i
$186$	−0.890624	−	1.11681i	−0.0653037	−	0.0818883i
$187$	−3.35644	−	14.7055i	−0.245447	−	1.07538i
$188$	−2.04594	+	2.56553i	−0.149216	+	0.187111i
$189$	2.63133	−	0.275882i	0.191401	−	0.0200674i
$190$	2.37721	+	2.98093i	0.172461	+	0.216260i
$191$	−15.5650	+	19.5179i	−1.12625	+	1.41227i	−0.227512	+	0.973775i	$0.573059\pi$
$191$	−15.5650	+	19.5179i	−1.12625	+	1.41227i	−0.898734	+	0.438493i	$0.855512\pi$
$192$	2.82593	+	1.36090i	0.203944	+	0.0982142i
$193$	−9.09031	+	11.3989i	−0.654335	+	0.820510i	−0.992713	−	0.120500i	$-0.961550\pi$
$193$	−9.09031	+	11.3989i	−0.654335	+	0.820510i	0.338378	+	0.941010i	$0.390122\pi$
$194$	−1.15495	+	5.06016i	−0.0829204	+	0.363298i
$195$	−0.639404			−0.0457887
$196$	9.84469	−	7.60470i	0.703192	−	0.543193i
$197$	21.3129			1.51848			0.759241	−	0.650809i	$-0.225570\pi$
$197$	21.3129			1.51848			0.759241	+	0.650809i	$0.225570\pi$
$198$	0.491390	−	2.15292i	0.0349216	−	0.153001i
$199$	−11.7271	+	14.7053i	−0.831310	+	1.04243i	0.167093	+	0.985941i	$0.446562\pi$
$199$	−11.7271	+	14.7053i	−0.831310	+	1.04243i	−0.998403	+	0.0564887i	$0.982010\pi$
$200$	1.60660	+	0.773696i	0.113604	+	0.0547086i
$201$	−9.77642	+	12.2592i	−0.689576	+	0.864701i
$202$	0.259232	+	0.325066i	0.0182395	+	0.0228716i
$203$	−0.342867	+	0.536412i	−0.0240645	+	0.0376488i
$204$	3.57302	−	4.48042i	0.250161	−	0.313692i
$205$	−1.15347	−	5.05366i	−0.0805615	−	0.352963i
$206$	0.231042	+	0.289718i	0.0160975	+	0.0201856i
$207$	1.89403	−	8.29828i	0.131644	−	0.576771i
$208$	1.56256	−	0.752491i	0.108344	−	0.0521759i
$209$	8.40606	−	36.8293i	0.581459	−	2.54754i
$210$	−1.06272	+	0.656341i	−0.0733349	+	0.0452919i
$211$	1.06839	+	4.68090i	0.0735507	+	0.322247i	0.998297	−	0.0583377i	$-0.0185800\pi$
$211$	1.06839	+	4.68090i	0.0735507	+	0.322247i	−0.924746	+	0.380584i	$0.875723\pi$
$212$	1.85539	+	2.32659i	0.127429	+	0.159791i
$213$	−10.7509	+	5.17735i	−0.736638	+	0.354746i
$214$	4.85735			0.332042
$215$	0.0581160			0.00396348
$216$	1.60660	−	0.773696i	0.109315	−	0.0526434i
$217$	6.81103	−	4.20651i	0.462363	−	0.285556i
$218$	1.74074	+	0.838296i	0.117898	+	0.0567766i
$219$	11.9581	+	5.75874i	0.808057	+	0.389140i
$220$	−1.84972	−	8.10416i	−0.124708	−	0.546382i
$221$	−0.458813	−	2.01019i	−0.0308631	−	0.135220i
$222$	−3.34083	−	1.60886i	−0.224222	−	0.107980i
$223$	−7.07910	−	3.40911i	−0.474051	−	0.228291i	0.181574	−	0.983377i	$-0.441881\pi$
$223$	−7.07910	−	3.40911i	−0.474051	−	0.228291i	−0.655626	+	0.755086i	$0.727595\pi$
$224$	6.90642	−	10.8050i	0.461454	−	0.721941i
$225$	−0.900969	+	0.433884i	−0.0600646	+	0.0289256i
$226$	−8.60707			−0.572534
$227$	−21.6089			−1.43423			−0.717115	−	0.696955i	$-0.754538\pi$
$227$	−21.6089			−1.43423			−0.717115	+	0.696955i	$0.754538\pi$
$228$	12.9309	−	6.22719i	0.856370	−	0.412406i
$229$	17.9038	+	22.4506i	1.18312	+	1.48358i	0.838556	+	0.544816i	$0.183400\pi$
$229$	17.9038	+	22.4506i	1.18312	+	1.48358i	0.344560	+	0.938764i	$0.388028\pi$
$230$	0.894176	+	3.91764i	0.0589602	+	0.258322i
$231$	11.6492	+	4.17767i	0.766461	+	0.274870i
$232$	−0.0954784	+	0.418318i	−0.00626846	+	0.0274639i
$233$	−16.2363	+	7.81897i	−1.06367	+	0.512238i	−0.882062	−	0.471132i	$-0.843845\pi$
$233$	−16.2363	+	7.81897i	−1.06367	+	0.512238i	−0.181611	+	0.983370i	$0.558131\pi$
$234$	0.0671712	−	0.294296i	0.00439112	−	0.0192387i
$235$	1.15127	+	1.44365i	0.0751006	+	0.0941732i
$236$	1.18196	+	5.17850i	0.0769390	+	0.337092i
$237$	−6.32389	+	7.92991i	−0.410781	+	0.515103i
$238$	−2.82601	−	2.87008i	−0.183183	−	0.186040i
$239$	−4.85196	−	6.08416i	−0.313847	−	0.393552i	0.599740	−	0.800195i	$-0.295271\pi$
$239$	−4.85196	−	6.08416i	−0.313847	−	0.393552i	−0.913587	+	0.406643i	$0.866699\pi$
$240$	1.69115	−	2.12063i	0.109163	−	0.136886i
$241$	18.6515	+	8.98209i	1.20145	+	0.578587i	0.924088	−	0.382179i	$-0.124826\pi$
$241$	18.6515	+	8.98209i	1.20145	+	0.578587i	0.277360	+	0.960766i	$0.410540\pi$
$242$	3.20240	−	4.01569i	0.205858	−	0.258138i
$243$	−0.222521	+	0.974928i	−0.0142747	+	0.0625417i
$244$	−16.8282			−1.07732
$245$	−2.93924	−	6.35302i	−0.187781	−	0.405879i
$246$	2.44720			0.156028
$247$	1.14908	−	5.03443i	0.0731140	−	0.320333i
$248$	3.36399	−	4.21831i	0.213614	−	0.267863i
$249$	−12.4669	−	6.00374i	−0.790057	−	0.380471i
$250$	0.294351	−	0.369105i	0.0186164	−	0.0233442i
$251$	4.83497	+	6.06286i	0.305181	+	0.382684i	0.910646	−	0.413187i	$-0.135584\pi$
$251$	4.83497	+	6.06286i	0.305181	+	0.382684i	−0.605465	+	0.795872i	$0.707013\pi$
$252$	1.51853	+	4.44985i	0.0956585	+	0.280314i
$253$	24.8236	−	31.1278i	1.56064	−	1.95699i
$254$	−0.447728	−	1.96163i	−0.0280930	−	0.123083i
$255$	−2.01057	−	2.52117i	−0.125907	−	0.157882i
$256$	−0.221974	+	0.972532i	−0.0138734	+	0.0607833i
$257$	−20.3919	+	9.82021i	−1.27201	+	0.612568i	−0.943325	−	0.331872i	$-0.892320\pi$
$257$	−20.3919	+	9.82021i	−1.27201	+	0.612568i	−0.328686	+	0.944439i	$0.606606\pi$
$258$	−0.00610525	+	0.0267488i	−0.000380096	+	0.00166531i
$259$	11.1917	−	17.5094i	0.695420	−	1.08798i
$260$	−0.252850	−	1.10781i	−0.0156811	−	0.0687034i
$261$	−0.150026	−	0.188127i	−0.00928637	−	0.0116447i
$262$	−4.37995	+	2.10927i	−0.270594	+	0.130311i
$263$	−6.82973			−0.421139			−0.210570	−	0.977579i	$-0.567532\pi$
$263$	−6.82973			−0.421139			−0.210570	+	0.977579i	$0.567532\pi$
$264$	8.34096			0.513351
$265$	1.50869	−	0.726547i	0.0926781	−	0.0446314i
$266$	−3.25796	−	9.54701i	−0.199758	−	0.585365i
$267$	−0.0487898	−	0.0234959i	−0.00298589	−	0.00143793i
$268$	−25.1060	−	12.0904i	−1.53359	−	0.738539i
$269$	−2.22556	−	9.75080i	−0.135695	−	0.594517i	−0.996352	−	0.0853331i	$-0.972805\pi$
$269$	−2.22556	−	9.75080i	−0.135695	−	0.594517i	0.860658	−	0.509184i	$-0.170053\pi$
$270$	−0.105053	−	0.460266i	−0.00639331	−	0.0280109i
$271$	7.63996	+	3.67921i	0.464095	+	0.223496i	0.651294	−	0.758826i	$-0.274227\pi$
$271$	7.63996	+	3.67921i	0.464095	+	0.223496i	−0.187199	+	0.982322i	$0.559941\pi$
$272$	7.88046	+	3.79503i	0.477823	+	0.230107i
$273$	1.59240	+	0.571071i	0.0963765	+	0.0345628i
$274$	6.17825	−	2.97529i	0.373241	−	0.179744i
$275$	−4.67756			−0.282067
$276$	15.1263			0.910495
$277$	9.33985	−	4.49784i	0.561177	−	0.270249i	−0.131718	−	0.991287i	$-0.542049\pi$
$277$	9.33985	−	4.49784i	0.561177	−	0.270249i	0.692895	+	0.721039i	$0.256335\pi$
$278$	5.56724	+	6.98110i	0.333901	+	0.418698i
$279$	0.673286	+	2.94986i	0.0403086	+	0.176603i
$280$	−3.31013	−	3.36175i	−0.197818	−	0.200903i
$281$	−1.48843	+	6.52123i	−0.0887922	+	0.389024i	−0.999723	−	0.0235350i	$-0.992508\pi$
$281$	−1.48843	+	6.52123i	−0.0887922	+	0.389024i	0.910931	+	0.412559i	$0.135365\pi$
$282$	−0.785406	+	0.378232i	−0.0467703	+	0.0225234i
$283$	−4.81061	+	21.0766i	−0.285961	+	1.25288i	0.604053	+	0.796944i	$0.293551\pi$
$283$	−4.81061	+	21.0766i	−0.285961	+	1.25288i	−0.890014	+	0.455933i	$0.849306\pi$
$284$	−13.2215	−	16.5792i	−0.784551	−	0.983796i
$285$	−1.79710	−	7.87363i	−0.106451	−	0.466393i
$286$	0.880360	−	1.10394i	0.0520568	−	0.0652772i
$287$	−1.64093	+	13.6161i	−0.0968613	+	0.803731i
$288$	3.02199	+	3.78946i	0.178073	+	0.223296i
$289$	−4.11585	+	5.16111i	−0.242109	+	0.303595i
$290$	0.102349	+	0.0492886i	0.00601013	+	0.00289433i
$291$	6.85464	−	8.59544i	0.401826	−	0.503874i
$292$	−5.24858	+	22.9955i	−0.307150	+	1.34571i
$293$	0.0138888			0.000811390			0.000405695	−	1.00000i	$-0.499871\pi$
$293$	0.0138888			0.000811390			0.000405695		1.00000i	$0.499871\pi$
$294$	3.23285	−	0.685432i	0.188544	−	0.0399752i
$295$	2.98892			0.174022
$296$	3.11657	−	13.6546i	0.181147	−	0.793656i
$297$	−2.91641	+	3.65706i	−0.169227	+	0.212204i
$298$	4.65273	+	2.24063i	0.269525	+	0.129796i
$299$	3.39329	−	4.25505i	0.196239	−	0.246076i
$300$	−1.10802	−	1.38941i	−0.0639713	−	0.0802175i
$301$	−0.144735	−	0.0519052i	−0.00834237	−	0.00299176i
$302$	5.81013	−	7.28567i	0.334335	−	0.419243i
$303$	−0.195972	−	0.858608i	−0.0112583	−	0.0493257i
$304$	13.6579	+	17.1265i	0.783334	+	0.982270i
$305$	−2.10713	+	9.23196i	−0.120654	+	0.528621i
$306$	1.37163	−	0.660540i	0.0784106	−	0.0377606i
$307$	1.04355	−	4.57209i	0.0595585	−	0.260943i	−0.936379	−	0.350991i	$-0.885845\pi$
$307$	1.04355	−	4.57209i	0.0595585	−	0.260943i	0.995937	+	0.0900479i	$0.0287020\pi$
$308$	−2.63144	+	21.8350i	−0.149940	+	1.24417i
$309$	−0.174661	−	0.765241i	−0.00993613	−	0.0435330i
$310$	−0.890624	−	1.11681i	−0.0505840	−	0.0634304i
$311$	19.0146	−	9.15694i	1.07822	−	0.519242i	0.191471	−	0.981498i	$-0.438674\pi$
$311$	19.0146	−	9.15694i	1.07822	−	0.519242i	0.886746	+	0.462256i	$0.152960\pi$
$312$	1.14018			0.0645499
$313$	16.9297			0.956926			0.478463	−	0.878108i	$-0.341194\pi$
$313$	16.9297			0.956926			0.478463	+	0.878108i	$0.341194\pi$
$314$	−0.748416	+	0.360418i	−0.0422356	+	0.0203396i
$315$	2.63133	−	0.275882i	0.148259	−	0.0155442i
$316$	−16.2398	−	7.82069i	−0.913562	−	0.439948i
$317$	25.2337	+	12.1519i	1.41727	+	0.682520i	0.976583	−	0.215142i	$-0.0690216\pi$
$317$	25.2337	+	12.1519i	1.41727	+	0.682520i	0.440684	+	0.897662i	$0.354736\pi$
$318$	0.175913	+	0.770725i	0.00986470	+	0.0432201i
$319$	−0.250453	−	1.09731i	−0.0140227	−	0.0614374i
$320$	2.82593	+	1.36090i	0.157974	+	0.0760764i
$321$	−9.26985	−	4.46412i	−0.517393	−	0.249163i
$322$	1.27207	−	10.5553i	0.0708895	−	0.588223i
$323$	23.4640	−	11.2997i	1.30557	−	0.628730i
$324$	−1.77712			−0.0987288
$325$	−0.639404			−0.0354678
$326$	2.34930	−	1.13136i	0.130116	−	0.0626605i
$327$	−2.55163	−	3.19964i	−0.141105	−	0.176940i
$328$	2.05685	+	9.01163i	0.113570	+	0.497584i
$329$	−1.57781	−	4.62356i	−0.0869876	−	0.254905i
$330$	0.491390	−	2.15292i	0.0270501	−	0.118514i
$331$	−4.38594	+	2.11216i	−0.241073	+	0.116095i	−0.550520	−	0.834822i	$-0.685570\pi$
$331$	−4.38594	+	2.11216i	−0.241073	+	0.116095i	0.309447	+	0.950917i	$0.399856\pi$
$332$	5.47187	−	23.9738i	0.300308	−	1.31573i
$333$	4.89709	+	6.14076i	0.268359	+	0.336511i
$334$	−0.478771	−	2.09763i	−0.0261972	−	0.114777i
$335$	−9.77642	+	12.2592i	−0.534143	+	0.669794i
$336$	−6.10571	+	3.77090i	−0.333094	+	0.205720i
$337$	−1.53434	−	1.92400i	−0.0835809	−	0.104807i	0.738283	−	0.674491i	$-0.235637\pi$
$337$	−1.53434	−	1.92400i	−0.0835809	−	0.104807i	−0.821864	+	0.569684i	$0.807066\pi$
$338$	−3.70622	+	4.64746i	−0.201592	+	0.252788i
$339$	16.4259	+	7.91029i	0.892132	+	0.429628i
$340$	3.57302	−	4.48042i	0.193774	−	0.242985i
$341$	−3.14933	+	13.7981i	−0.170546	+	0.747210i
$342$	3.81275			0.206170
$343$	1.64595	+	18.4470i	0.0888731	+	0.996043i
$344$	−0.103632			−0.00558745
$345$	1.89403	−	8.29828i	0.101971	−	0.446765i
$346$	4.26104	−	5.34318i	0.229075	−	0.287251i
$347$	11.7835	+	5.67463i	0.632570	+	0.304630i	0.722555	−	0.691313i	$-0.242968\pi$
$347$	11.7835	+	5.67463i	0.632570	+	0.304630i	−0.0899847	+	0.995943i	$0.528682\pi$
$348$	0.266614	−	0.334323i	0.0142920	−	0.0179216i
$349$	−12.8385	−	16.0990i	−0.687230	−	0.861759i	0.308768	−	0.951138i	$-0.400083\pi$
$349$	−12.8385	−	16.0990i	−0.687230	−	0.861759i	−0.995998	+	0.0893782i	$0.971512\pi$
$350$	−1.06272	+	0.656341i	−0.0568050	+	0.0350829i
$351$	−0.398662	+	0.499907i	−0.0212790	+	0.0266830i
$352$	5.04492	+	22.1032i	0.268895	+	1.17811i
$353$	−12.1114	−	15.1872i	−0.644624	−	0.808332i	0.346949	−	0.937884i	$-0.387218\pi$
$353$	−12.1114	−	15.1872i	−0.644624	−	0.808332i	−0.991573	+	0.129552i	$0.958646\pi$
$354$	−0.313995	+	1.37570i	−0.0166886	+	0.0731177i
$355$	−10.7509	+	5.17735i	−0.570598	+	0.274785i
$356$	0.0214144	−	0.0938227i	0.00113496	−	0.00497260i
$357$	2.75548	+	8.07454i	0.145835	+	0.427350i
$358$	0.987991	+	4.32867i	0.0522169	+	0.228777i
$359$	−10.4033	−	13.0453i	−0.549064	−	0.688504i	0.427430	−	0.904048i	$-0.359419\pi$
$359$	−10.4033	−	13.0453i	−0.549064	−	0.688504i	−0.976494	+	0.215544i	$0.930847\pi$
$360$	1.60660	−	0.773696i	0.0846751	−	0.0407774i
$361$	46.2236			2.43282
$362$	−6.27970			−0.330054
$363$	−9.80212	+	4.72045i	−0.514478	+	0.247759i
$364$	−0.359708	+	2.98476i	−0.0188538	+	0.156444i
$365$	11.9581	+	5.75874i	0.625918	+	0.301426i
$366$	−4.02780	−	1.93969i	−0.210536	−	0.101389i
$367$	−0.658193	−	2.88373i	−0.0343574	−	0.150530i	0.954840	−	0.297122i	$-0.0960267\pi$
$367$	−0.658193	−	2.88373i	−0.0343574	−	0.150530i	−0.989197	+	0.146592i	$0.953170\pi$
$368$	5.13735	+	22.5082i	0.267803	+	1.17332i
$369$	−4.67029	−	2.24909i	−0.243125	−	0.117083i
$370$	−3.34083	−	1.60886i	−0.173682	−	0.0836407i
$371$	−4.40621	+	0.461969i	−0.228759	+	0.0239842i
$372$	−4.84457	+	2.33302i	−0.251179	+	0.120961i
$373$	−10.2174			−0.529034			−0.264517	−	0.964381i	$-0.585213\pi$
$373$	−10.2174			−0.529034			−0.264517	+	0.964381i	$0.585213\pi$
$374$	7.12106			0.368221
$375$	−0.900969	+	0.433884i	−0.0465258	+	0.0224057i
$376$	−2.05293	−	2.57429i	−0.105872	−	0.132759i
$377$	−0.0342360	−	0.149998i	−0.00176325	−	0.00772528i
$378$	−0.149449	+	1.24009i	−0.00768684	+	0.0637835i
$379$	1.43498	−	6.28705i	0.0737099	−	0.322944i	−0.924608	−	0.380920i	$-0.875607\pi$
$379$	1.43498	−	6.28705i	0.0737099	−	0.322944i	0.998318	+	0.0579756i	$0.0184646\pi$
$380$	12.9309	−	6.22719i	0.663341	−	0.319448i
$381$	−0.948370	+	4.15508i	−0.0485865	+	0.212871i
$382$	−7.34830	−	9.21447i	−0.375972	−	0.471453i
$383$	−1.30084	−	5.69934i	−0.0664697	−	0.291223i	0.930758	−	0.365636i	$-0.119149\pi$
$383$	−1.30084	−	5.69934i	−0.0664697	−	0.291223i	−0.997227	+	0.0744137i	$0.976291\pi$
$384$	−6.96723	+	8.73664i	−0.355545	+	0.445840i
$385$	11.6492	+	4.17767i	0.593698	+	0.212914i
$386$	−4.29156	−	5.38145i	−0.218435	−	0.273908i
$387$	0.0362347	−	0.0454369i	0.00184192	−	0.00230969i
$388$	17.6028	+	8.47706i	0.893646	+	0.430357i
$389$	−3.02243	+	3.79001i	−0.153243	+	0.192161i	−0.852527	−	0.522683i	$-0.824931\pi$
$389$	−3.02243	+	3.79001i	−0.153243	+	0.192161i	0.699284	+	0.714844i	$0.253502\pi$
$390$	0.0671712	−	0.294296i	0.00340134	−	0.0149023i
$391$	27.4477			1.38809
$392$	5.24122	+	11.3286i	0.264722	+	0.572182i
$393$	10.2973			0.519429
$394$	−2.23898	+	9.80962i	−0.112798	+	0.494201i
$395$	−6.32389	+	7.92991i	−0.318190	+	0.398997i
$396$	−7.48937	−	3.60669i	−0.376355	−	0.181243i
$397$	7.05589	−	8.84781i	0.354125	−	0.444059i	−0.572580	−	0.819849i	$-0.694057\pi$
$397$	7.05589	−	8.84781i	0.354125	−	0.444059i	0.926705	+	0.375790i	$0.122629\pi$
$398$	−5.53638	−	6.94240i	−0.277514	−	0.347991i
$399$	−2.55658	+	21.2139i	−0.127989	+	1.06202i
$400$	1.69115	−	2.12063i	0.0845574	−	0.106032i
$401$	6.59660	+	28.9016i	0.329419	+	1.44328i	0.820241	+	0.572018i	$0.193839\pi$
$401$	6.59660	+	28.9016i	0.329419	+	1.44328i	−0.490822	+	0.871260i	$0.663304\pi$
$402$	−4.61548	−	5.78762i	−0.230199	−	0.288660i
$403$	−0.430502	+	1.88615i	−0.0214448	+	0.0939559i
$404$	1.41010	−	0.679067i	0.0701549	−	0.0337848i
$405$	−0.222521	+	0.974928i	−0.0110572	+	0.0484446i
$406$	−0.210873	−	0.214162i	−0.0104655	−	0.0106287i
$407$	8.17520	+	35.8179i	0.405230	+	1.77543i
$408$	3.58522	+	4.49572i	0.177495	+	0.222572i
$409$	0.480088	−	0.231198i	0.0237388	−	0.0114320i	−0.421977	−	0.906607i	$-0.638664\pi$
$409$	0.480088	−	0.231198i	0.0237388	−	0.0114320i	0.445715	+	0.895175i	$0.352949\pi$
$410$	2.44720			0.120859
$411$	−14.5251			−0.716470
$412$	1.25676	−	0.605223i	0.0619161	−	0.0298172i
$413$	−7.44375	−	2.66950i	−0.366283	−	0.131357i
$414$	3.62045	+	1.74351i	0.177935	+	0.0856891i
$415$	−12.4669	−	6.00374i	−0.611975	−	0.294712i
$416$	0.689622	+	3.02143i	0.0338115	+	0.148138i
$417$	−4.20867	−	18.4394i	−0.206100	−	0.902981i
$418$	16.0682	+	7.73804i	0.785922	+	0.378480i
$419$	17.5432	+	8.44837i	0.857042	+	0.412730i	0.810187	−	0.586172i	$-0.199366\pi$
$419$	17.5432	+	8.44837i	0.857042	+	0.412730i	0.0468555	+	0.998902i	$0.485080\pi$
$420$	1.51853	+	4.44985i	0.0740967	+	0.217130i
$421$	−10.8289	+	5.21491i	−0.527767	+	0.254159i	−0.678740	−	0.734379i	$-0.737474\pi$
$421$	−10.8289	+	5.21491i	−0.527767	+	0.254159i	0.150973	+	0.988538i	$0.451759\pi$
$422$	−2.26670			−0.110341
$423$	1.84649			0.0897796
$424$	−2.69028	+	1.29557i	−0.130651	+	0.0629184i
$425$	−2.01057	−	2.52117i	−0.0975269	−	0.122295i
$426$	−1.25355	−	5.49216i	−0.0607347	−	0.266096i
$427$	13.4930	−	21.1098i	0.652974	−	1.02157i
$428$	4.06865	−	17.8259i	0.196666	−	0.861648i
$429$	−2.69466	+	1.29768i	−0.130100	+	0.0626526i
$430$	−0.00610525	+	0.0267488i	−0.000294421	+	0.00128994i
$431$	−12.5261	−	15.7073i	−0.603363	−	0.756593i	0.382535	−	0.923941i	$-0.375051\pi$
$431$	−12.5261	−	15.7073i	−0.603363	−	0.756593i	−0.985898	+	0.167348i	$0.946480\pi$
$432$	−0.603564	−	2.64439i	−0.0290390	−	0.127228i
$433$	23.3883	−	29.3280i	1.12397	−	1.40941i	0.223384	−	0.974730i	$-0.428289\pi$
$433$	23.3883	−	29.3280i	1.12397	−	1.40941i	0.900584	−	0.434682i	$-0.143139\pi$
$434$	1.22060	+	3.57679i	0.0585905	+	0.171691i
$435$	−0.150026	−	0.188127i	−0.00719319	−	0.00901998i
$436$	4.53454	−	5.68614i	0.217165	−	0.272317i
$437$	61.9338	+	29.8258i	2.96270	+	1.42676i
$438$	−3.90679	+	4.89896i	−0.186674	+	0.234081i
$439$	0.823637	−	3.60859i	0.0393100	−	0.172228i	−0.951462	−	0.307765i	$-0.900419\pi$
$439$	0.823637	−	3.60859i	0.0393100	−	0.172228i	0.990772	+	0.135537i	$0.0432759\pi$
$440$	8.34096			0.397640
$441$	−6.79958	−	1.66305i	−0.323789	−	0.0791929i
$442$	0.973423			0.0463010
$443$	7.24631	−	31.7482i	0.344283	−	1.50840i	−0.445650	−	0.895207i	$-0.647027\pi$
$443$	7.24631	−	31.7482i	0.344283	−	1.50840i	0.789933	−	0.613194i	$-0.210116\pi$
$444$	−8.70271	+	10.9129i	−0.413012	+	0.517901i
$445$	−0.0487898	−	0.0234959i	−0.00231286	−	0.00111381i
$446$	2.31278	−	2.90013i	0.109513	−	0.137325i
$447$	−6.82010	−	8.55213i	−0.322580	−	0.404502i
$448$	−5.82237	−	5.91316i	−0.275081	−	0.279371i
$449$	−10.7838	+	13.5224i	−0.508918	+	0.638163i	−0.968215	−	0.250120i	$-0.919530\pi$
$449$	−10.7838	+	13.5224i	−0.508918	+	0.638163i	0.459297	+	0.888283i	$0.348102\pi$
$450$	−0.105053	−	0.460266i	−0.00495223	−	0.0216972i
$451$	−15.1176	−	18.9568i	−0.711859	−	0.892643i
$452$	−7.20952	+	31.5870i	−0.339107	+	1.48573i
$453$	−17.7840	+	8.56433i	−0.835565	+	0.402387i
$454$	2.27007	−	9.94582i	0.106540	−	0.466781i
$455$	1.59240	+	0.571071i	0.0746530	+	0.0267722i
$456$	3.20457	+	14.0402i	0.150068	+	0.657491i
$457$	−6.23980	−	7.82446i	−0.291885	−	0.366013i	0.614169	−	0.789175i	$-0.289491\pi$
$457$	−6.23980	−	7.82446i	−0.291885	−	0.366013i	−0.906054	+	0.423162i	$0.860920\pi$
$458$	−12.2141	+	5.88201i	−0.570728	+	0.274848i
$459$	−3.22470			−0.150516
$460$	15.1263			0.705267
$461$	5.22400	−	2.51574i	0.243306	−	0.117170i	−0.308257	−	0.951303i	$-0.599746\pi$
$461$	5.22400	−	2.51574i	0.243306	−	0.117170i	0.551563	+	0.834133i	$0.314032\pi$
$462$	−3.14662	+	4.92286i	−0.146394	+	0.229032i
$463$	3.68630	+	1.77523i	0.171317	+	0.0825018i	0.517577	−	0.855637i	$-0.326834\pi$
$463$	3.68630	+	1.77523i	0.171317	+	0.0825018i	−0.346260	+	0.938139i	$0.612548\pi$
$464$	0.588029	+	0.283180i	0.0272986	+	0.0131463i
$465$	0.673286	+	2.94986i	0.0312229	+	0.136796i
$466$	−1.89314	−	8.29441i	−0.0876982	−	0.384231i
$467$	−5.80944	−	2.79768i	−0.268829	−	0.129461i	0.294614	−	0.955616i	$-0.404809\pi$
$467$	−5.80944	−	2.79768i	−0.268829	−	0.129461i	−0.563442	+	0.826155i	$0.690523\pi$
$468$	−1.02377	−	0.493021i	−0.0473237	−	0.0227899i
$469$	35.2968	−	21.7994i	1.62985	−	1.00660i
$470$	−0.785406	+	0.378232i	−0.0362281	+	0.0174465i
$471$	1.75953			0.0810749
$472$	−5.32981			−0.245325
$473$	0.244920	−	0.117947i	0.0112614	−	0.00542323i
$474$	−2.98553	−	3.74373i	−0.137130	−	0.171955i
$475$	−1.79710	−	7.87363i	−0.0824568	−	0.361267i
$476$	−12.9000	+	7.96708i	−0.591271	+	0.365171i
$477$	0.372616	−	1.63254i	0.0170609	−	0.0747487i
$478$	3.31004	−	1.59403i	0.151398	−	0.0729094i
$479$	−7.31731	+	32.0592i	−0.334336	+	1.46482i	0.476305	+	0.879280i	$0.341976\pi$
$479$	−7.31731	+	32.0592i	−0.334336	+	1.46482i	−0.810641	+	0.585543i	$0.800881\pi$
$480$	3.02199	+	3.78946i	0.137935	+	0.172964i
$481$	1.11752	+	4.89617i	0.0509545	+	0.223246i
$482$	−6.09354	+	7.64106i	−0.277553	+	0.348041i
$483$	−12.1284	+	18.9748i	−0.551862	+	0.863384i
$484$	−12.0547	−	15.1161i	−0.547940	−	0.687096i
$485$	6.85464	−	8.59544i	0.311253	−	0.390299i
$486$	−0.425350	−	0.204838i	−0.0192943	−	0.00929163i
$487$	11.5497	−	14.4829i	0.523368	−	0.656283i	−0.447952	−	0.894058i	$-0.647847\pi$
$487$	11.5497	−	14.4829i	0.523368	−	0.656283i	0.971320	+	0.237775i	$0.0764179\pi$
$488$	3.75742	−	16.4623i	0.170090	−	0.745214i
$489$	−5.52322			−0.249769
$490$	3.23285	−	0.685432i	0.146045	−	0.0309647i
$491$	−21.3576			−0.963857			−0.481928	−	0.876211i	$-0.660063\pi$
$491$	−21.3576			−0.963857			−0.481928	+	0.876211i	$0.660063\pi$
$492$	2.04985	−	8.98096i	0.0924142	−	0.404893i
$493$	0.483789	−	0.606652i	0.0217887	−	0.0273222i
$494$	2.19646	+	1.05776i	0.0988236	+	0.0475910i
$495$	−2.91641	+	3.65706i	−0.131083	+	0.164373i
$496$	−5.11694	−	6.41644i	−0.229757	−	0.288107i
$497$	31.3985	−	3.29198i	1.40842	−	0.147665i
$498$	4.07300	−	5.10738i	0.182515	−	0.228867i
$499$	5.98549	+	26.2241i	0.267947	+	1.17395i	0.912397	+	0.409307i	$0.134229\pi$
$499$	5.98549	+	26.2241i	0.267947	+	1.17395i	−0.644449	+	0.764647i	$0.722913\pi$
$500$	−1.10802	−	1.38941i	−0.0495520	−	0.0621362i
$501$	−1.01413	+	4.44318i	−0.0453078	+	0.198506i
$502$	−3.29846	+	1.58845i	−0.147217	+	0.0708961i
$503$	2.83835	−	12.4356i	0.126556	−	0.554477i	−0.871400	−	0.490573i	$-0.836788\pi$
$503$	2.83835	−	12.4356i	0.126556	−	0.554477i	0.997956	−	0.0639042i	$-0.0203552\pi$
$504$	−4.69215	+	0.491949i	−0.209005	+	0.0219131i
$505$	−0.195972	−	0.858608i	−0.00872063	−	0.0382076i
$506$	11.7193	+	14.6955i	0.520985	+	0.653295i
$507$	11.3442	−	5.46310i	0.503816	−	0.242625i
$508$	−7.57397			−0.336041
$509$	−17.9627			−0.796182			−0.398091	−	0.917346i	$-0.630327\pi$
$509$	−17.9627			−0.796182			−0.398091	+	0.917346i	$0.630327\pi$
$510$	1.37163	−	0.660540i	0.0607366	−	0.0292492i
$511$	−24.6378	−	25.0220i	−1.08991	−	1.10691i
$512$	−20.5602	−	9.90127i	−0.908641	−	0.437578i
$513$	−7.27633	−	3.50409i	−0.321258	−	0.154710i
$514$	−2.37769	−	10.4173i	−0.104875	−	0.459489i
$515$	−0.174661	−	0.765241i	−0.00769650	−	0.0337206i
$516$	0.0930513	+	0.0448111i	0.00409635	+	0.00197270i
$517$	7.78174	+	3.74749i	0.342241	+	0.164814i
$518$	6.88324	+	6.99058i	0.302432	+	0.307148i
$519$	−13.0425	+	6.28092i	−0.572501	+	0.275702i
$520$	1.14018			0.0500001
$521$	−10.6790			−0.467855			−0.233927	−	0.972254i	$-0.575158\pi$
$521$	−10.6790			−0.467855			−0.233927	+	0.972254i	$0.575158\pi$
$522$	0.102349	−	0.0492886i	0.00447969	−	0.00215730i
$523$	−16.0754	−	20.1579i	−0.702927	−	0.881442i	0.294312	−	0.955710i	$-0.404910\pi$
$523$	−16.0754	−	20.1579i	−0.702927	−	0.881442i	−0.997238	+	0.0742672i	$0.976338\pi$
$524$	4.07202	+	17.8407i	0.177887	+	0.779374i
$525$	2.63133	−	0.275882i	0.114841	−	0.0120405i
$526$	0.717482	−	3.14349i	0.0312837	−	0.137063i
$527$	−8.79079	+	4.23342i	−0.382933	+	0.184411i
$528$	2.82320	−	12.3693i	0.122864	−	0.538303i
$529$	30.8309	+	38.6607i	1.34047	+	1.68090i
$530$	0.175913	+	0.770725i	0.00764117	+	0.0334781i
$531$	1.86356	−	2.33684i	0.0808718	−	0.101410i
$532$	−37.7654	+	3.95951i	−1.63734	+	0.171667i
$533$	−2.06652	−	2.59133i	−0.0895107	−	0.112243i
$534$	0.0159399	−	0.0199880i	0.000689786	−	0.000864964i
$535$	−9.26985	−	4.46412i	−0.400771	−	0.193001i
$536$	17.4332	−	21.8605i	0.753000	−	0.944232i
$537$	2.09275	−	9.16892i	0.0903087	−	0.395668i
$538$	4.72176			0.203570
$539$	−25.2805	−	20.8085i	−1.08891	−	0.896285i
$540$	−1.77712			−0.0764750
$541$	6.02485	−	26.3966i	0.259029	−	1.13488i	−0.663264	−	0.748386i	$-0.730829\pi$
$541$	6.02485	−	26.3966i	0.259029	−	1.13488i	0.922292	−	0.386493i	$-0.126314\pi$
$542$	−2.49602	+	3.12990i	−0.107213	+	0.134441i
$543$	11.9843	+	5.77133i	0.514295	+	0.247671i
$544$	−9.74503	+	12.2199i	−0.417815	+	0.523923i
$545$	−2.55163	−	3.19964i	−0.109300	−	0.137057i
$546$	−0.430131	+	0.672936i	−0.0184079	+	0.0287990i
$547$	11.8446	−	14.8526i	0.506438	−	0.635053i	−0.461230	−	0.887281i	$-0.652592\pi$
$547$	11.8446	−	14.8526i	0.506438	−	0.635053i	0.967668	+	0.252228i	$0.0811632\pi$
$548$	−5.74389	−	25.1656i	−0.245367	−	1.07502i
$549$	5.90406	+	7.40346i	0.251979	+	0.315972i
$550$	0.491390	−	2.15292i	0.0209529	−	0.0918008i
$551$	1.75085	−	0.843165i	0.0745888	−	0.0359200i
$552$	−3.37741	+	14.7974i	−0.143752	+	0.629819i
$553$	22.8318	−	14.1010i	0.970905	−	0.599634i
$554$	1.08902	+	4.77133i	0.0462682	+	0.202714i
$555$	4.89709	+	6.14076i	0.207870	+	0.260661i
$556$	30.2831	−	14.5836i	1.28429	−	0.618481i
$557$	−31.4774			−1.33374			−0.666871	−	0.745173i	$-0.732367\pi$
$557$	−31.4774			−1.33374			−0.666871	+	0.745173i	$0.732367\pi$
$558$	−1.42845			−0.0604711
$559$	0.0334797	−	0.0161230i	0.00141604	−	0.000681929i
$560$	−6.10571	+	3.77090i	−0.258013	+	0.159350i
$561$	−13.5900	−	6.54458i	−0.573769	−	0.276312i
$562$	−2.84514	−	1.37015i	−0.120015	−	0.0577962i
$563$	−2.25041	−	9.85971i	−0.0948436	−	0.415537i	0.905110	−	0.425178i	$-0.139788\pi$
$563$	−2.25041	−	9.85971i	−0.0948436	−	0.415537i	−0.999954	+	0.00964061i	$0.996931\pi$
$564$	0.730189	+	3.19917i	0.0307465	+	0.134709i
$565$	16.4259	+	7.91029i	0.691042	+	0.332788i
$566$	−9.19550	−	4.42832i	−0.386516	−	0.186136i
$567$	1.42491	−	2.22926i	0.0598407	−	0.0936203i
$568$	19.1708	−	9.23219i	0.804391	−	0.387374i
$569$	−1.70320			−0.0714018			−0.0357009	−	0.999363i	$-0.511366\pi$
$569$	−1.70320			−0.0714018			−0.0357009	+	0.999363i	$0.511366\pi$
$570$	3.81275			0.159699
$571$	1.86047	−	0.895957i	0.0778584	−	0.0374946i	−0.394549	−	0.918875i	$-0.629099\pi$
$571$	1.86047	−	0.895957i	0.0778584	−	0.0374946i	0.472408	+	0.881380i	$0.343385\pi$
$572$	−3.31391	−	4.15551i	−0.138561	−	0.173751i
$573$	5.55510	+	24.3385i	0.232068	+	1.01675i
$574$	−6.09463	−	2.18567i	−0.254385	−	0.0912282i
$575$	1.89403	−	8.29828i	0.0789865	−	0.346062i
$576$	2.82593	−	1.36090i	0.117747	−	0.0567040i
$577$	−5.45848	+	23.9152i	−0.227239	+	0.995601i	0.724640	+	0.689128i	$0.242006\pi$
$577$	−5.45848	+	23.9152i	−0.227239	+	0.995601i	−0.951879	+	0.306473i	$0.900851\pi$
$578$	−1.94310	−	2.43657i	−0.0808224	−	0.101348i
$579$	3.24430	+	14.2142i	0.134828	+	0.590721i
$580$	0.266614	−	0.334323i	0.0110705	−	0.0138820i
$581$	25.6860	+	26.0865i	1.06563	+	1.08225i
$582$	3.23609	+	4.05793i	0.134140	+	0.168207i
$583$	4.88358	−	6.12382i	0.202257	−	0.253623i
$584$	−21.3236	−	10.2689i	−0.882378	−	0.424931i
$585$	−0.398662	+	0.499907i	−0.0164827	+	0.0206686i
$586$	−0.00145905	+	0.00639252i	−6.02728e−5	+	0.000264073i
$587$	7.53433			0.310975			0.155488	−	0.987838i	$-0.450305\pi$
$587$	7.53433			0.310975			0.155488	+	0.987838i	$0.450305\pi$
$588$	0.192471	−	12.4383i	0.00793738	−	0.512949i
$589$	−24.4360			−1.00687
$590$	−0.313995	+	1.37570i	−0.0129270	+	0.0566367i
$591$	13.2884	−	16.6631i	0.546611	−	0.685429i
$592$	−19.1942	−	9.24345i	−0.788878	−	0.379904i
$593$	7.83857	−	9.82926i	0.321892	−	0.403639i	−0.594388	−	0.804178i	$-0.702606\pi$
$593$	7.83857	−	9.82926i	0.321892	−	0.403639i	0.916280	+	0.400539i	$0.131177\pi$
$594$	−1.37684	−	1.72651i	−0.0564926	−	0.0708395i
$595$	2.75548	+	8.07454i	0.112963	+	0.331024i
$596$	12.1201	−	15.1982i	0.496460	−	0.622541i
$597$	4.18534	+	18.3372i	0.171295	+	0.750491i
$598$	1.60198	+	2.00882i	0.0655099	+	0.0821468i
$599$	3.42303	−	14.9973i	0.139861	−	0.612772i	−0.855603	−	0.517633i	$-0.826813\pi$
$599$	3.42303	−	14.9973i	0.139861	−	0.612772i	0.995464	−	0.0951391i	$-0.0303296\pi$
$600$	1.60660	−	0.773696i	0.0655890	−	0.0315860i
$601$	8.43744	−	36.9668i	0.344170	−	1.50791i	−0.446006	−	0.895030i	$-0.647154\pi$
$601$	8.43744	−	36.9668i	0.344170	−	1.50791i	0.790177	−	0.612879i	$-0.209989\pi$
$602$	0.0390950	−	0.0611637i	0.00159339	−	0.00249285i
$603$	3.48917	+	15.2870i	0.142090	+	0.622536i
$604$	−21.8708	−	27.4252i	−0.889912	−	1.11591i
$605$	−9.80212	+	4.72045i	−0.398513	+	0.191914i
$606$	0.415776			0.0168897
$607$	15.4755			0.628133			0.314067	−	0.949401i	$-0.398308\pi$
$607$	15.4755			0.628133			0.314067	+	0.949401i	$0.398308\pi$
$608$	−35.2676	+	16.9840i	−1.43029	+	0.688792i
$609$	0.205610	+	0.602512i	0.00833174	+	0.0244150i
$610$	−4.02780	−	1.93969i	−0.163081	−	0.0785356i
$611$	1.06374	+	0.512268i	0.0430341	+	0.0207241i
$612$	−1.27520	−	5.58700i	−0.0515467	−	0.225841i
$613$	4.66257	+	20.4281i	0.188320	+	0.825082i	0.977503	+	0.210924i	$0.0676472\pi$
$613$	4.66257	+	20.4281i	0.188320	+	0.825082i	−0.789183	+	0.614158i	$0.789496\pi$
$614$	1.99475	+	0.960620i	0.0805015	+	0.0387675i
$615$	−4.67029	−	2.24909i	−0.188324	−	0.0906921i
$616$	−20.7727	−	7.44956i	−0.836956	−	0.300151i
$617$	−13.4102	+	6.45799i	−0.539873	+	0.259989i	−0.683889	−	0.729586i	$-0.739713\pi$
$617$	−13.4102	+	6.45799i	−0.539873	+	0.259989i	0.144016	+	0.989575i	$0.453998\pi$
$618$	0.370563			0.0149062
$619$	−18.6571			−0.749891			−0.374945	−	0.927047i	$-0.622339\pi$
$619$	−18.6571			−0.749891			−0.374945	+	0.927047i	$0.622339\pi$
$620$	−4.84457	+	2.33302i	−0.194562	+	0.0936963i
$621$	−5.30695	−	6.65471i	−0.212961	−	0.267044i
$622$	2.21709	+	9.71372i	0.0888974	+	0.389485i
$623$	0.100523	+	0.102091i	0.00402738	+	0.00409019i
$624$	0.385921	−	1.69083i	0.0154492	−	0.0676874i
$625$	−0.900969	+	0.433884i	−0.0360388	+	0.0173553i
$626$	−1.77852	+	7.79219i	−0.0710838	+	0.311438i
$627$	−23.5532	−	29.5348i	−0.940626	−	1.17951i
$628$	0.695800	+	3.04850i	0.0277654	+	0.121648i
$629$	−15.7917	+	19.8021i	−0.629654	+	0.789562i
$630$	−0.149449	+	1.24009i	−0.00595420	+	0.0494065i
$631$	−17.7995	−	22.3198i	−0.708586	−	0.888538i	0.289047	−	0.957315i	$-0.406662\pi$
$631$	−17.7995	−	22.3198i	−0.708586	−	0.888538i	−0.997632	+	0.0687769i	$0.978090\pi$
$632$	11.2767	−	14.1405i	0.448563	−	0.562480i
$633$	4.32580	+	2.08320i	0.171935	+	0.0827997i
$634$	−8.24399	+	10.3376i	−0.327411	+	0.410560i
$635$	−0.948370	+	4.15508i	−0.0376349	+	0.164889i
$636$	2.97582			0.117999
$637$	−3.45575	−	2.84444i	−0.136922	−	0.112701i
$638$	0.531364			0.0210369
$639$	−2.65525	+	11.6334i	−0.105040	+	0.460210i
$640$	−6.96723	+	8.73664i	−0.275404	+	0.345346i
$641$	−22.8508	−	11.0044i	−0.902552	−	0.434646i	−0.0757418	−	0.997127i	$-0.524132\pi$
$641$	−22.8508	−	11.0044i	−0.902552	−	0.434646i	−0.826810	+	0.562482i	$0.809847\pi$
$642$	3.02851	−	3.79763i	0.119526	−	0.149880i
$643$	15.2557	+	19.1300i	0.601625	+	0.754414i	0.985630	−	0.168917i	$-0.0540270\pi$
$643$	15.2557	+	19.1300i	0.601625	+	0.754414i	−0.384005	+	0.923331i	$0.625456\pi$
$644$	−37.6712	−	13.5097i	−1.48445	−	0.532358i
$645$	0.0362347	−	0.0454369i	0.00142674	−	0.00178908i
$646$	2.73589	+	11.9867i	0.107642	+	0.471612i
$647$	16.9501	+	21.2548i	0.666377	+	0.835611i	0.994021	−	0.109191i	$-0.0348259\pi$
$647$	16.9501	+	21.2548i	0.666377	+	0.835611i	−0.327643	+	0.944801i	$0.606254\pi$
$648$	0.396797	−	1.73848i	0.0155876	−	0.0682939i
$649$	12.5963	−	6.06607i	0.494449	−	0.238114i
$650$	0.0671712	−	0.294296i	0.00263467	−	0.0115432i
$651$	0.957824	−	7.94779i	0.0375401	−	0.311499i
$652$	−2.18414	−	9.56933i	−0.0855374	−	0.374764i
$653$	−2.52665	−	3.16832i	−0.0988755	−	0.123986i	0.729932	−	0.683520i	$-0.239552\pi$
$653$	−2.52665	−	3.16832i	−0.0988755	−	0.123986i	−0.828808	+	0.559534i	$0.810980\pi$
$654$	1.74074	−	0.838296i	0.0680683	−	0.0327800i
$655$	10.2973			0.402348
$656$	14.0600			0.548952
$657$	11.9581	−	5.75874i	0.466532	−	0.224670i
$658$	2.29382	−	0.240496i	0.0894225	−	0.00937550i
$659$	21.3016	+	10.2583i	0.829794	+	0.399608i	0.800038	−	0.599950i	$-0.204813\pi$
$659$	21.3016	+	10.2583i	0.829794	+	0.399608i	0.0297559	+	0.999557i	$0.490527\pi$
$660$	−7.48937	−	3.60669i	−0.291523	−	0.140390i
$661$	5.78809	+	25.3593i	0.225130	+	0.986361i	0.953551	+	0.301231i	$0.0973975\pi$
$661$	5.78809	+	25.3593i	0.225130	+	0.986361i	−0.728421	+	0.685130i	$0.759745\pi$
$662$	−0.511400	−	2.24059i	−0.0198761	−	0.0870829i
$663$	−1.85770	−	0.894620i	−0.0721470	−	0.0347441i
$664$	22.2308	+	10.7058i	0.862722	+	0.415465i
$665$	−2.55658	+	21.2139i	−0.0991400	+	0.822639i
$666$	−3.34083	+	1.60886i	−0.129455	+	0.0623421i
$667$	2.04811			0.0793030
$668$	−8.09911			−0.313364
$669$	−7.07910	+	3.40911i	−0.273694	+	0.131804i
$670$	−4.61548	−	5.78762i	−0.178311	−	0.223595i
$671$	9.85624	+	43.1830i	0.380496	+	1.66706i
$672$	−4.14163	−	12.1365i	−0.159767	−	0.468175i
$673$	0.621383	−	2.72246i	0.0239526	−	0.104943i	−0.961539	−	0.274670i	$-0.911431\pi$
$673$	0.621383	−	2.72246i	0.0239526	−	0.104943i	0.985491	+	0.169727i	$0.0542886\pi$
$674$	1.04674	−	0.504083i	0.0403189	−	0.0194166i
$675$	−0.222521	+	0.974928i	−0.00856483	+	0.0375250i
$676$	13.9512	+	17.4943i	0.536585	+	0.672856i
$677$	1.30942	+	5.73695i	0.0503252	+	0.220489i	0.993837	−	0.110849i	$-0.0353571\pi$
$677$	1.30942	+	5.73695i	0.0503252	+	0.220489i	−0.943512	+	0.331338i	$0.892500\pi$
$678$	−5.36642	+	6.72928i	−0.206096	+	0.258436i
$679$	−24.7480	+	15.2844i	−0.949739	+	0.586562i
$680$	3.58522	+	4.49572i	0.137487	+	0.172403i
$681$	−13.4729	+	16.8945i	−0.516283	+	0.647398i
$682$	−6.01996	−	2.89906i	−0.230516	−	0.111011i
$683$	0.689937	−	0.865153i	0.0263997	−	0.0331042i	−0.768456	−	0.639902i	$-0.778975\pi$
$683$	0.689937	−	0.865153i	0.0263997	−	0.0331042i	0.794856	+	0.606798i	$0.207546\pi$
$684$	3.19367	−	13.9924i	0.122113	−	0.535012i
$685$	−14.5251			−0.554975
$686$	−8.66343	−	1.18033i	−0.330771	−	0.0450651i
$687$	28.7154			1.09556
$688$	−0.0350767	+	0.153681i	−0.00133729	+	0.00585904i
$689$	0.667568	−	0.837103i	0.0254323	−	0.0318911i
$690$	3.62045	+	1.74351i	0.137828	+	0.0663745i
$691$	−12.0776	+	15.1449i	−0.459455	+	0.576138i	−0.956554	−	0.291556i	$-0.905827\pi$
$691$	−12.0776	+	15.1449i	−0.459455	+	0.576138i	0.497099	+	0.867694i	$0.334399\pi$
$692$	−16.0397	−	20.1131i	−0.609737	−	0.764587i
$693$	10.5294	−	6.50298i	0.399978	−	0.247028i
$694$	−3.84972	+	4.82740i	−0.146134	+	0.183246i
$695$	−4.20867	−	18.4394i	−0.159644	−	0.699446i
$696$	0.267524	+	0.335465i	0.0101405	+	0.0127158i
$697$	3.71958	−	16.2966i	0.140889	−	0.617276i
$698$	8.75854	−	4.21789i	0.331516	−	0.159650i
$699$	−4.01003	+	17.5691i	−0.151673	+	0.664524i
$700$	1.51853	+	4.44985i	0.0573951	+	0.168188i
$701$	1.94811	+	8.53521i	0.0735789	+	0.322370i	0.998301	−	0.0582735i	$-0.0185595\pi$
$701$	1.94811	+	8.53521i	0.0735789	+	0.322370i	−0.924722	+	0.380644i	$0.875702\pi$
$702$	−0.188209	−	0.236007i	−0.00710351	−	0.00890752i
$703$	−57.1506	+	27.5223i	−2.15548	+	1.03802i
$704$	14.6714			0.552948
$705$	1.84649			0.0695430
$706$	8.26248	−	3.97900i	0.310963	−	0.149752i
$707$	−0.278792	+	2.31334i	−0.0104850	+	0.0870023i
$708$	4.78565	+	2.30465i	0.179856	+	0.0866140i
$709$	46.3885	+	22.3395i	1.74216	+	0.838979i	0.981910	+	0.189346i	$0.0606369\pi$
$709$	46.3885	+	22.3395i	1.74216	+	0.838979i	0.760248	+	0.649633i	$0.225077\pi$
$710$	−1.25355	−	5.49216i	−0.0470449	−	0.206117i
$711$	2.25697	+	9.88844i	0.0846430	+	0.370845i
$712$	0.0870013	+	0.0418976i	0.00326051	+	0.00157018i
$713$	−23.2035	−	11.1742i	−0.868979	−	0.418478i
$714$	−4.00591	+	0.419999i	−0.149917	+	0.0157181i
$715$	−2.69466	+	1.29768i	−0.100775	+	0.0485305i
$716$	16.7133			0.624605
$717$	−7.78194			−0.290622
$718$	7.09720	−	3.41783i	0.264865	−	0.127552i
$719$	−30.6655	−	38.4533i	−1.14363	−	1.43407i	−0.883463	−	0.468501i	$-0.844794\pi$
$719$	−30.6655	−	38.4533i	−1.14363	−	1.43407i	−0.260166	−	0.965564i	$-0.583777\pi$
$720$	−0.603564	−	2.64439i	−0.0224935	−	0.0985504i
$721$	−0.248475	+	2.06179i	−0.00925370	+	0.0767849i
$722$	−4.85592	+	21.2752i	−0.180718	+	0.791779i
$723$	18.6515	−	8.98209i	0.693657	−	0.334048i
$724$	−5.26005	+	23.0458i	−0.195488	+	0.856490i
$725$	−0.150026	−	0.188127i	−0.00557182	−	0.00698684i
$726$	−1.14292	−	5.00748i	−0.0424179	−	0.185845i
$727$	−1.98043	+	2.48339i	−0.0734502	+	0.0921037i	−0.817199	−	0.576355i	$-0.804474\pi$
$727$	−1.98043	+	2.48339i	−0.0734502	+	0.0921037i	0.743749	+	0.668459i	$0.233046\pi$
$728$	−2.83955	−	1.01833i	−0.105241	−	0.0377417i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−3.90679	+	4.89896i	−0.144597	+	0.181319i
$731$	0.168848	+	0.0813128i	0.00624506	+	0.00300746i
$732$	−10.4922	+	13.1568i	−0.387804	+	0.486290i
$733$	7.74588	−	33.9369i	0.286101	−	1.25349i	−0.603726	−	0.797192i	$-0.706318\pi$
$733$	7.74588	−	33.9369i	0.286101	−	1.25349i	0.889827	−	0.456298i	$-0.150825\pi$
$734$	1.39643			0.0515431
$735$	−6.79958	−	1.66305i	−0.250806	−	0.0613425i
$736$	−41.2553			−1.52069
$737$	−16.3208	+	71.5060i	−0.601183	+	2.63396i
$738$	1.52581	−	1.91330i	0.0561657	−	0.0704296i
$739$	−33.4896	−	16.1277i	−1.23194	−	0.593269i	−0.299324	−	0.954151i	$-0.596761\pi$
$739$	−33.4896	−	16.1277i	−1.23194	−	0.593269i	−0.932611	+	0.360883i	$0.882475\pi$
$740$	−8.70271	+	10.9129i	−0.319918	+	0.401165i
$741$	−3.21964	−	4.03730i	−0.118276	−	0.148314i
$742$	0.250256	−	2.07656i	0.00918718	−	0.0762329i
$743$	26.2997	−	32.9788i	0.964844	−	1.20988i	−0.0128659	−	0.999917i	$-0.504095\pi$
$743$	26.2997	−	32.9788i	0.964844	−	1.20988i	0.977710	−	0.209959i	$-0.0673331\pi$
$744$	−1.20060	−	5.26015i	−0.0440160	−	0.192846i
$745$	−6.82010	−	8.55213i	−0.249869	−	0.313326i
$746$	1.07336	−	4.70270i	0.0392985	−	0.172178i
$747$	−12.4669	+	6.00374i	−0.456140	+	0.219665i
$748$	5.96480	−	26.1335i	0.218095	−	0.955535i
$749$	19.0990	+	19.3968i	0.697863	+	0.708745i
$750$	−0.105053	−	0.460266i	−0.00383598	−	0.0168065i
$751$	15.2130	+	19.0765i	0.555130	+	0.696111i	0.977649	−	0.210243i	$-0.0674256\pi$
$751$	15.2130	+	19.0765i	0.555130	+	0.696111i	−0.422519	+	0.906354i	$0.638854\pi$
$752$	−4.51243	+	2.17307i	−0.164551	+	0.0792437i
$753$	7.75469			0.282597
$754$	0.0726355			0.00264523
$755$	−17.7840	+	8.56433i	−0.647226	+	0.311688i
$756$	4.42582	+	1.58720i	0.160965	+	0.0577258i
$757$	−44.8731	−	21.6097i	−1.63094	−	0.785419i	−0.999954	−	0.00962582i	$-0.996936\pi$
$757$	−44.8731	−	21.6097i	−1.63094	−	0.785419i	−0.630987	−	0.775794i	$-0.717350\pi$
$758$	2.74297	+	1.32094i	0.0996291	+	0.0479788i
$759$	−8.85943	−	38.8157i	−0.321577	−	1.40892i
$760$	3.20457	+	14.0402i	0.116242	+	0.509290i
$761$	10.2724	+	4.94695i	0.372376	+	0.179327i	0.610706	−	0.791857i	$-0.290886\pi$
$761$	10.2724	+	4.94695i	0.372376	+	0.179327i	−0.238330	+	0.971184i	$0.576600\pi$
$762$	−1.81281	−	0.873005i	−0.0656713	−	0.0316256i
$763$	3.49699	+	10.2475i	0.126600	+	0.370983i
$764$	−39.9712	+	19.2491i	−1.44611	+	0.696408i
$765$	−3.22470			−0.116589
$766$	2.75987			0.0997181
$767$	1.72187	−	0.829209i	0.0621731	−	0.0299410i
$768$	0.621958	+	0.779910i	0.0224430	+	0.0281426i
$769$	1.74473	+	7.64415i	0.0629165	+	0.275655i	0.996594	−	0.0824586i	$-0.0262772\pi$
$769$	1.74473	+	7.64415i	0.0629165	+	0.275655i	−0.933678	+	0.358114i	$0.883420\pi$
$770$	−3.14662	+	4.92286i	−0.113396	+	0.177407i
$771$	−5.03638	+	22.0658i	−0.181381	+	0.794681i
$772$	−23.3440	+	11.2419i	−0.840170	+	0.404605i
$773$	−0.159823	+	0.700232i	−0.00574844	+	0.0251856i	−0.977721	−	0.209910i	$-0.932683\pi$
$773$	−0.159823	+	0.700232i	−0.00574844	+	0.0251856i	0.971972	+	0.235095i	$0.0755402\pi$
$774$	0.0171065	+	0.0214509i	0.000614881	+	0.000771037i
$775$	0.673286	+	2.94986i	0.0241851	+	0.105962i
$776$	−12.2231	+	15.3273i	−0.438784	+	0.550218i
$777$	−6.71144	−	19.6670i	−0.240772	−	0.705548i
$778$	−1.42690	−	1.78927i	−0.0511567	−	0.0641485i
$779$	26.1015	−	32.7303i	0.935183	−	1.17268i
$780$	−1.02377	−	0.493021i	−0.0366568	−	0.0176530i
$781$	−34.8003	+	43.6382i	−1.24525	+	1.56150i
$782$	−2.88345	+	12.6332i	−0.103112	+	0.451763i
$783$	−0.240623			−0.00859916
$784$	18.5738	−	3.93804i	0.663352	−	0.140644i
$785$	1.75953			0.0628004
$786$	−1.08176	+	4.73949i	−0.0385850	+	0.169052i
$787$	28.8135	−	36.1310i	1.02709	−	1.28793i	0.0701855	−	0.997534i	$-0.477641\pi$
$787$	28.8135	−	36.1310i	1.02709	−	1.28793i	0.956906	−	0.290398i	$-0.0937877\pi$
$788$	34.1247	+	16.4336i	1.21564	+	0.585423i
$789$	−4.25827	+	5.33970i	−0.151598	+	0.190098i
$790$	−2.98553	−	3.74373i	−0.106220	−	0.133196i
$791$	−33.8429	−	34.3706i	−1.20331	−	1.22208i
$792$	5.20050	−	6.52123i	0.184792	−	0.231722i
$793$	1.34731	+	5.90296i	0.0478444	+	0.209620i
$794$	3.33111	+	4.17707i	0.118217	+	0.148239i
$795$	0.372616	−	1.63254i	0.0132153	−	0.0579001i
$796$	−30.1153	+	14.5027i	−1.06741	+	0.514036i
$797$	5.83436	−	25.5620i	0.206664	−	0.905453i	−0.760105	−	0.649800i	$-0.774853\pi$
$797$	5.83436	−	25.5620i	0.206664	−	0.905453i	0.966769	−	0.255653i	$-0.0822903\pi$
$798$	−9.49546	−	3.40528i	−0.336136	−	0.120546i
$799$	1.32498	+	5.80510i	0.0468743	+	0.205370i
$800$	3.02199	+	3.78946i	0.106844	+	0.133978i
$801$	−0.0487898	+	0.0234959i	−0.00172390	+	0.000830187i
$802$	−13.9954			−0.494195
$803$	62.0831			2.19086
$804$	−25.1060	+	12.0904i	−0.885419	+	0.426395i
$805$	−12.1284	+	18.9748i	−0.427471	+	0.668774i
$806$	−0.822906	−	0.396291i	−0.0289856	−	0.0139587i
$807$	−9.01109	−	4.33951i	−0.317206	−	0.152758i
$808$	0.349454	+	1.53106i	0.0122938	+	0.0538625i
$809$	1.05479	+	4.62133i	0.0370844	+	0.162477i	0.990079	−	0.140508i	$-0.0448737\pi$
$809$	1.05479	+	4.62133i	0.0370844	+	0.162477i	−0.952995	+	0.302986i	$0.902017\pi$
$810$	−0.425350	−	0.204838i	−0.0149453	−	0.00719726i
$811$	−7.56859	−	3.64484i	−0.265769	−	0.127988i	0.296254	−	0.955109i	$-0.404263\pi$
$811$	−7.56859	−	3.64484i	−0.265769	−	0.127988i	−0.562023	+	0.827122i	$0.689977\pi$
$812$	−0.962582	+	0.594493i	−0.0337800	+	0.0208626i
$813$	7.63996	−	3.67921i	0.267945	−	0.129036i
$814$	−17.3446			−0.607928
$815$	−5.52322			−0.193470
$816$	7.88046	−	3.79503i	0.275871	−	0.132853i
$817$	0.292636	+	0.366954i	0.0102380	+	0.0128381i
$818$	0.0559781	+	0.245256i	0.00195723	+	0.00857518i
$819$	1.43933	−	0.888933i	0.0502942	−	0.0310618i
$820$	2.04985	−	8.98096i	0.0715837	−	0.313629i
$821$	48.7867	−	23.4945i	1.70267	−	0.819962i	0.709311	−	0.704895i	$-0.249006\pi$
$821$	48.7867	−	23.4945i	1.70267	−	0.819962i	0.993358	−	0.115067i	$-0.0367082\pi$
$822$	1.52590	−	6.68541i	0.0532219	−	0.233180i
$823$	8.71629	+	10.9299i	0.303831	+	0.380992i	0.910184	−	0.414203i	$-0.135940\pi$
$823$	8.71629	+	10.9299i	0.303831	+	0.380992i	−0.606353	+	0.795195i	$0.707368\pi$
$824$	0.311454	+	1.36457i	0.0108500	+	0.0475370i
$825$	−2.91641	+	3.65706i	−0.101536	+	0.127323i
$826$	2.01067	−	3.14567i	0.0699600	−	0.109452i
$827$	−9.43372	−	11.8295i	−0.328042	−	0.411352i	0.590272	−	0.807205i	$-0.299021\pi$
$827$	−9.43372	−	11.8295i	−0.328042	−	0.411352i	−0.918314	+	0.395852i	$0.870449\pi$
$828$	9.43109	−	11.8262i	0.327753	−	0.410989i
$829$	21.7104	+	10.4552i	0.754032	+	0.363123i	0.771085	−	0.636732i	$-0.219714\pi$
$829$	21.7104	+	10.4552i	0.754032	+	0.363123i	−0.0170533	+	0.999855i	$0.505428\pi$
$830$	4.07300	−	5.10738i	0.141376	−	0.177280i
$831$	2.30675	−	10.1065i	0.0800204	−	0.350592i
$832$	2.00552			0.0695289
$833$	0.349252	−	22.5702i	0.0121009	−	0.782011i
$834$	8.92916			0.309192
$835$	−1.01413	+	4.44318i	−0.0350953	+	0.153762i
$836$	41.8569	−	52.4869i	1.44765	−	1.81530i
$837$	2.72608	+	1.31281i	0.0942271	+	0.0453774i
$838$	−5.73146	+	7.18702i	−0.197990	+	0.248272i
$839$	−11.2609	−	14.1207i	−0.388768	−	0.487500i	0.548480	−	0.836164i	$-0.315207\pi$
$839$	−11.2609	−	14.1207i	−0.388768	−	0.487500i	−0.937248	+	0.348664i	$0.886635\pi$
$840$	−4.69215	+	0.491949i	−0.161895	+	0.0169738i
$841$	−18.0451	+	22.6278i	−0.622245	+	0.780271i
$842$	−1.26264	−	5.53200i	−0.0435136	−	0.190645i
$843$	4.17049	+	5.22962i	0.143639	+	0.180118i
$844$	−1.89865	+	8.31852i	−0.0653542	+	0.286335i
$845$	11.3442	−	5.46310i	0.390254	−	0.187936i
$846$	−0.193979	+	0.849879i	−0.00666915	+	0.0292194i
$847$	28.6276	−	3.00146i	0.983657	−	0.103131i
$848$	1.01068	+	4.42808i	0.0347069	+	0.152061i
$849$	13.4790	+	16.9022i	0.462599	+	0.580081i
$850$	1.37163	−	0.660540i	0.0470464	−	0.0226563i
$851$	−66.8536			−2.29171
$852$	−21.2056			−0.726492
$853$	24.1882	−	11.6484i	0.828187	−	0.398834i	0.0287519	−	0.999587i	$-0.490847\pi$
$853$	24.1882	−	11.6484i	0.828187	−	0.398834i	0.799435	+	0.600753i	$0.205132\pi$
$854$	8.29862	+	8.42803i	0.283973	+	0.288401i
$855$	−7.27633	−	3.50409i	−0.248845	−	0.119837i
$856$	16.5299	+	7.96037i	0.564980	+	0.272080i
$857$	−2.36247	−	10.3507i	−0.0807005	−	0.353572i	0.918415	−	0.395618i	$-0.129470\pi$
$857$	−2.36247	−	10.3507i	−0.0807005	−	0.353572i	−0.999116	+	0.0420460i	$0.986612\pi$
$858$	−0.314197	−	1.37659i	−0.0107265	−	0.0469959i
$859$	−19.1934	−	9.24308i	−0.654872	−	0.315370i	0.0767800	−	0.997048i	$-0.475536\pi$
$859$	−19.1934	−	9.24308i	−0.654872	−	0.315370i	−0.731652	+	0.681678i	$0.761250\pi$
$860$	0.0930513	+	0.0448111i	0.00317302	+	0.00152805i
$861$	9.62236	+	9.77241i	0.327929	+	0.333043i
$862$	8.54543	−	4.11526i	0.291059	−	0.140166i
$863$	20.6500			0.702933			0.351467	−	0.936200i	$-0.385683\pi$
$863$	20.6500			0.702933			0.351467	+	0.936200i	$0.385683\pi$
$864$	4.84690			0.164895
$865$	−13.0425	+	6.28092i	−0.443457	+	0.213558i
$866$	11.0417	+	13.8458i	0.375211	+	0.470500i
$867$	1.46893	+	6.43580i	0.0498874	+	0.218571i
$868$	14.1488	−	1.48343i	0.480242	−	0.0503510i
$869$	−10.5571	+	46.2537i	−0.358125	+	1.56905i
$870$	0.102349	−	0.0492886i	0.00346995	−	0.00167104i
$871$	−2.23099	+	9.77460i	−0.0755941	+	0.331200i
$872$	4.55003	+	5.70555i	0.154083	+	0.193214i
$873$	−2.44639	−	10.7183i	−0.0827978	−	0.362761i
$874$	−20.2341	+	25.3728i	−0.684429	+	0.858247i
$875$	2.63133	−	0.275882i	0.0889551	−	0.00932650i
$876$	14.7062	+	18.4410i	0.496876	+	0.623063i
$877$	20.4170	−	25.6021i	0.689434	−	0.864523i	−0.306751	−	0.951790i	$-0.599242\pi$
$877$	20.4170	−	25.6021i	0.689434	−	0.864523i	0.996185	+	0.0872672i	$0.0278134\pi$
$878$	1.57439	+	0.758184i	0.0531329	+	0.0255875i
$879$	0.00865949	−	0.0108587i	0.000292078	−	0.000366254i
$880$	2.82320	−	12.3693i	0.0951701	−	0.416968i
$881$	12.0093			0.404605			0.202303	−	0.979323i	$-0.435158\pi$
$881$	12.0093			0.404605			0.202303	+	0.979323i	$0.435158\pi$
$882$	1.47976	−	2.95491i	0.0498261	−	0.0994969i
$883$	15.3426			0.516319			0.258159	−	0.966102i	$-0.416884\pi$
$883$	15.3426			0.516319			0.258159	+	0.966102i	$0.416884\pi$
$884$	0.815366	−	3.57235i	0.0274237	−	0.120151i
$885$	1.86356	−	2.33684i	0.0626430	−	0.0785519i
$886$	13.8514	+	6.67046i	0.465346	+	0.224099i
$887$	5.15810	−	6.46805i	0.173192	−	0.217176i	−0.687658	−	0.726035i	$-0.741361\pi$
$887$	5.15810	−	6.46805i	0.173192	−	0.217176i	0.860850	+	0.508859i	$0.169933\pi$
$888$	−8.73243	−	10.9501i	−0.293041	−	0.367462i
$889$	6.07289	−	9.50099i	0.203678	−	0.318653i
$890$	0.0159399	−	0.0199880i	0.000534306	−	0.000669998i
$891$	1.04085	+	4.56028i	0.0348699	+	0.152775i
$892$	−8.70591	−	10.9169i	−0.291495	−	0.365524i
$893$	−3.31834	+	14.5386i	−0.111044	+	0.486516i
$894$	4.65273	−	2.24063i	0.155610	−	0.0749380i
$895$	2.09275	−	9.16892i	0.0699528	−	0.306483i
$896$	25.1545	−	15.5355i	0.840352	−	0.519004i
$897$	−1.21105	−	5.30596i	−0.0404358	−	0.177161i
$898$	−5.09105	−	6.38398i	−0.169891	−	0.213036i
$899$	−0.655957	+	0.315892i	−0.0218774	+	0.0105356i
$900$	−1.77712			−0.0592373
$901$	5.39983			0.179894
$902$	10.3133	−	4.96664i	0.343396	−	0.165371i
$903$	−0.130822	+	0.0807959i	−0.00435348	+	0.00268872i
$904$	−29.2904	−	14.1055i	−0.974186	−	0.469143i
$905$	11.9843	+	5.77133i	0.398371	+	0.191845i
$906$	−2.07361	−	9.08508i	−0.0688911	−	0.301832i
$907$	12.1013	+	53.0194i	0.401818	+	1.76048i	0.620029	+	0.784579i	$0.287121\pi$
$907$	12.1013	+	53.0194i	0.401818	+	1.76048i	−0.218211	+	0.975902i	$0.570022\pi$
$908$	−34.5986	−	16.6618i	−1.14819	−	0.552941i
$909$	−0.793473	−	0.382117i	−0.0263178	−	0.0126740i
$910$	−0.430131	+	0.672936i	−0.0142587	+	0.0223076i
$911$	35.0607	−	16.8844i	1.16161	−	0.559404i	0.249111	−	0.968475i	$-0.419862\pi$
$911$	35.0607	−	16.8844i	1.16161	−	0.559404i	0.912502	+	0.409071i	$0.134147\pi$
$912$	21.9056			0.725366
$913$	−64.7243			−2.14206
$914$	4.25684	−	2.04999i	0.140804	−	0.0678075i
$915$	5.90406	+	7.40346i	0.195182	+	0.244751i
$916$	11.3554	+	49.7513i	0.375193	+	1.64383i
$917$	−25.6448	−	9.19681i	−0.846867	−	0.303705i
$918$	0.338764	−	1.48422i	0.0111809	−	0.0489866i
$919$	6.30332	−	3.03552i	0.207927	−	0.100133i	−0.327022	−	0.945017i	$-0.606045\pi$
$919$	6.30332	−	3.03552i	0.207927	−	0.100133i	0.534949	+	0.844884i	$0.320331\pi$
$920$	−3.37741	+	14.7974i	−0.111350	+	0.487856i
$921$	−2.92396	−	3.66653i	−0.0963477	−	0.120816i
$922$	0.609117	+	2.66871i	0.0200602	+	0.0878894i
$923$	−4.75707	+	5.96517i	−0.156581	+	0.196346i
$924$	15.4306	+	15.6712i	0.507630	+	0.515546i
$925$	4.89709	+	6.14076i	0.161015	+	0.201907i
$926$	−1.20433	+	1.51019i	−0.0395768	+	0.0496278i
$927$	−0.707189	−	0.340564i	−0.0232271	−	0.0111856i
$928$	−0.727161	+	0.911831i	−0.0238702	+	0.0299323i
$929$	−3.98382	+	17.4543i	−0.130705	+	0.572656i	0.866581	+	0.499036i	$0.166312\pi$
$929$	−3.98382	+	17.4543i	−0.130705	+	0.572656i	−0.997286	+	0.0736203i	$0.976545\pi$
$930$	−1.42845			−0.0468407
$931$	25.3138	−	50.5487i	0.829626	−	1.65667i
$932$	−32.0253			−1.04902
$933$	4.69621	−	20.5754i	0.153747	−	0.673610i
$934$	1.89797	−	2.37999i	0.0621036	−	0.0778755i
$935$	−13.5900	−	6.54458i	−0.444439	−	0.214031i
$936$	0.710890	−	0.891427i	0.0232362	−	0.0291372i
$937$	3.89098	+	4.87913i	0.127113	+	0.159394i	0.841315	−	0.540545i	$-0.181782\pi$
$937$	3.89098	+	4.87913i	0.127113	+	0.159394i	−0.714202	+	0.699939i	$0.753210\pi$
$938$	6.32549	+	18.5360i	0.206535	+	0.605221i
$939$	10.5555	−	13.2362i	0.344467	−	0.431947i
$940$	0.730189	+	3.19917i	0.0238161	+	0.104345i
$941$	−32.2703	−	40.4657i	−1.05198	−	1.31915i	−0.945783	−	0.324801i	$-0.894703\pi$
$941$	−32.2703	−	40.4657i	−1.05198	−	1.31915i	−0.106201	−	0.994345i	$-0.533869\pi$
$942$	−0.184844	+	0.809853i	−0.00602253	+	0.0263864i
$943$	39.7520	−	19.1436i	1.29450	−	0.623400i
$944$	−1.80401	+	7.90387i	−0.0587154	+	0.257249i
$945$	1.42491	−	2.22926i	0.0463524	−	0.0725180i
$946$	0.0285576	+	0.125119i	0.000928489	+	0.00406798i
$947$	10.1072	+	12.6741i	0.328441	+	0.411852i	0.918445	−	0.395548i	$-0.129445\pi$
$947$	10.1072	+	12.6741i	0.328441	+	0.411852i	−0.590004	+	0.807400i	$0.700874\pi$
$948$	−16.2398	+	7.82069i	−0.527445	+	0.254004i
$949$	8.48652			0.275484
$950$	3.81275			0.123702
$951$	25.2337	−	12.1519i	0.818259	−	0.394053i
$952$	−4.91353	−	14.3984i	−0.159248	−	0.466656i
$953$	−13.3591	−	6.43343i	−0.432745	−	0.208399i	0.204813	−	0.978801i	$-0.434341\pi$
$953$	−13.3591	−	6.43343i	−0.432745	−	0.208399i	−0.637559	+	0.770402i	$0.720056\pi$
$954$	0.712257	+	0.343005i	0.0230602	+	0.0111052i
$955$	5.55510	+	24.3385i	0.179759	+	0.787574i
$956$	−3.07734	−	13.4827i	−0.0995282	−	0.436061i
$957$	−1.01406	−	0.488348i	−0.0327801	−	0.0157860i
$958$	−13.9871	−	6.73582i	−0.451902	−	0.217624i
$959$	36.1740	+	12.9728i	1.16812	+	0.418913i
$960$	2.82593	−	1.36090i	0.0912065	−	0.0439227i
$961$	−21.8450			−0.704678
$962$	−2.37094			−0.0764422
$963$	−9.26985	+	4.46412i	−0.298717	+	0.143854i
$964$	22.9377	+	28.7630i	0.738774	+	0.926393i
$965$	3.24430	+	14.2142i	0.104438	+	0.457571i
$966$	−7.45934	−	7.57566i	−0.240000	−	0.243743i
$967$	1.65673	−	7.25862i	0.0532769	−	0.233421i	−0.941278	−	0.337631i	$-0.890374\pi$
$967$	1.65673	−	7.25862i	0.0532769	−	0.233421i	0.994555	+	0.104210i	$0.0332314\pi$
$968$	17.4790	−	8.41745i	0.561797	−	0.270547i
$969$	5.79512	−	25.3901i	0.186166	−	0.815647i
$970$	3.23609	+	4.05793i	0.103905	+	0.130292i
$971$	−9.27674	−	40.6441i	−0.297705	−	1.30433i	−0.873535	−	0.486761i	$-0.838178\pi$
$971$	−9.27674	−	40.6441i	−0.297705	−	1.30433i	0.575830	−	0.817569i	$-0.304679\pi$
$972$	−1.10802	+	1.38941i	−0.0355396	+	0.0445653i
$973$	−5.98731	+	49.6812i	−0.191944	+	1.59271i
$974$	5.45266	+	6.83742i	0.174714	+	0.219085i
$975$	−0.398662	+	0.499907i	−0.0127674	+	0.0160098i
$976$	−23.1411	−	11.1442i	−0.740728	−	0.356716i
$977$	−11.4200	+	14.3203i	−0.365360	+	0.458147i	−0.930200	−	0.367054i	$-0.880366\pi$
$977$	−11.4200	+	14.3203i	−0.365360	+	0.458147i	0.564840	+	0.825200i	$0.308938\pi$
$978$	0.580230	−	2.54215i	0.0185537	−	0.0812890i
$979$	−0.253302			−0.00809556
$980$	0.192471	−	12.4383i	0.00614827	−	0.397328i
$981$	−4.09249			−0.130663
$982$	2.24368	−	9.83019i	0.0715986	−	0.313694i
$983$	34.8457	−	43.6951i	1.11140	−	1.39366i	0.201175	−	0.979555i	$-0.435524\pi$
$983$	34.8457	−	43.6951i	1.11140	−	1.39366i	0.910230	−	0.414102i	$-0.135904\pi$
$984$	8.32800	+	4.01055i	0.265487	+	0.127852i
$985$	13.2884	−	16.6631i	0.423403	−	0.530931i
$986$	0.228398	+	0.286402i	0.00727367	+	0.00912090i
$987$	−4.59859	−	1.64916i	−0.146375	−	0.0524933i
$988$	5.72168	−	7.17477i	0.182031	−	0.228260i
$989$	0.110073	+	0.482263i	0.00350013	+	0.0153351i
$990$	−1.37684	−	1.72651i	−0.0437590	−	0.0548720i
$991$	−8.07289	+	35.3697i	−0.256444	+	1.12355i	0.668578	+	0.743642i	$0.266903\pi$
$991$	−8.07289	+	35.3697i	−0.256444	+	1.12355i	−0.925022	+	0.379913i	$0.875954\pi$
$992$	13.2130	−	6.36306i	0.419514	−	0.202027i
$993$	−1.08324	+	4.74598i	−0.0343755	+	0.150609i
$994$	−1.78332	+	14.7975i	−0.0565633	+	0.469349i
$995$	4.18534	+	18.3372i	0.132684	+	0.581328i
$996$	−15.3318	−	19.2255i	−0.485808	−	0.609184i
$997$	−20.6615	+	9.95005i	−0.654356	+	0.315121i	−0.731443	−	0.681903i	$-0.761153\pi$
$997$	−20.6615	+	9.95005i	−0.654356	+	0.315121i	0.0770863	+	0.997024i	$0.475438\pi$
$998$	−12.6989			−0.401976
$999$	7.85432			0.248500

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.u.b.211.3	✓	48
49.36	even	7	inner	735.2.u.b.526.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.u.b.211.3	✓	48	1.1	even	1	trivial
735.2.u.b.526.3	yes	48	49.36	even	7	inner

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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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.105053 + 0.460266i) q^{2} +(0.623490 - 0.781831i) q^{3} +(1.60113 + 0.771063i) q^{4} +(0.623490 - 0.781831i) q^{5} +(0.294351 + 0.369105i) q^{6} +(-2.25104 + 1.39025i) q^{7} +(-1.11180 + 1.39415i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(0.294351 + 0.369105i) q^{10} +(1.04085 - 4.56028i) q^{11} +(1.60113 - 0.771063i) q^{12} +(0.142281 - 0.623373i) q^{13} +(-0.403407 - 1.18213i) q^{14} +(-0.222521 - 0.974928i) q^{15} +(1.69115 + 2.12063i) q^{16} +(2.90536 - 1.39915i) q^{17} +0.472103 q^{18} +8.07611 q^{19} +(1.60113 - 0.771063i) q^{20} +(-0.316561 + 2.62674i) q^{21} +(1.98960 + 0.958140i) q^{22} +(7.66877 + 3.69308i) q^{23} +(0.396797 + 1.73848i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.271971 + 0.130974i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-4.67618 + 0.490274i) q^{28} +(0.216794 - 0.104402i) q^{29} +0.472103 q^{30} -3.02572 q^{31} +(-4.36691 + 2.10299i) q^{32} +(-2.91641 - 3.65706i) q^{33} +(0.338764 + 1.48422i) q^{34} +(-0.316561 + 2.62674i) q^{35} +(0.395446 - 1.73256i) q^{36} +(-7.07650 + 3.40786i) q^{37} +(-0.848418 + 3.71716i) q^{38} +(-0.398662 - 0.499907i) q^{39} +(0.396797 + 1.73848i) q^{40} +(3.23194 - 4.05272i) q^{41} +(-1.17575 - 0.421649i) q^{42} +(0.0362347 + 0.0454369i) q^{43} +(5.18281 - 6.49903i) q^{44} +(-0.900969 - 0.433884i) q^{45} +(-2.50543 + 3.14170i) q^{46} +(-0.410884 + 1.80020i) q^{47} +2.71239 q^{48} +(3.13440 - 6.25904i) q^{49} +0.472103 q^{50} +(0.717563 - 3.14385i) q^{51} +(0.708470 - 0.888393i) q^{52} +(1.50869 + 0.726547i) q^{53} +(0.294351 - 0.369105i) q^{54} +(-2.91641 - 3.65706i) q^{55} +(0.564488 - 4.68398i) q^{56} +(5.03537 - 6.31416i) q^{57} +(0.0252781 + 0.110751i) q^{58} +(1.86356 + 2.33684i) q^{59} +(0.395446 - 1.73256i) q^{60} +(-8.53161 + 4.10861i) q^{61} +(0.317860 - 1.39264i) q^{62} +(1.85630 + 1.88525i) q^{63} +(0.697947 + 3.05791i) q^{64} +(-0.398662 - 0.499907i) q^{65} +(1.98960 - 0.958140i) q^{66} -15.6802 q^{67} +5.73068 q^{68} +(7.66877 - 3.69308i) q^{69} +(-1.17575 - 0.421649i) q^{70} +(-10.7509 - 5.17735i) q^{71} +(1.60660 + 0.773696i) q^{72} +(2.95342 + 12.9398i) q^{73} +(-0.825118 - 3.61508i) q^{74} +(-0.900969 - 0.433884i) q^{75} +(12.9309 + 6.22719i) q^{76} +(3.99693 + 11.7124i) q^{77} +(0.271971 - 0.130974i) q^{78} -10.1427 q^{79} +2.71239 q^{80} +(-0.900969 + 0.433884i) q^{81} +(1.52581 + 1.91330i) q^{82} +(-3.07907 - 13.4903i) q^{83} +(-2.53224 + 3.96167i) q^{84} +(0.717563 - 3.14385i) q^{85} +(-0.0247196 + 0.0119044i) q^{86} +(0.0535436 - 0.234590i) q^{87} +(5.20050 + 6.52123i) q^{88} +(-0.0120501 - 0.0527949i) q^{89} +(0.294351 - 0.369105i) q^{90} +(0.546365 + 1.60105i) q^{91} +(9.43109 + 11.8262i) q^{92} +(-1.88650 + 2.36560i) q^{93} +(-0.785406 - 0.378232i) q^{94} +(5.03537 - 6.31416i) q^{95} +(-1.07854 + 4.72538i) q^{96} +10.9940 q^{97} +(2.55154 + 2.10019i) q^{98} -4.67756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 8 q^{3} - q^{4} - 8 q^{5} + q^{6} - q^{7} + 15 q^{8} - 8 q^{9} + q^{10} + 10 q^{11} - q^{12} + 20 q^{13} - q^{14} - 8 q^{15} - 15 q^{16} + 7 q^{17} - 6 q^{18} - 2 q^{19} - q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) 48 * q + q^2 - 8 * q^3 - q^4 - 8 * q^5 + q^6 - q^7 + 15 * q^8 - 8 * q^9 + q^10 + 10 * q^11 - q^12 + 20 * q^13 - q^14 - 8 * q^15 - 15 * q^16 + 7 * q^17 - 6 * q^18 - 2 * q^19 - q^20 - q^21 - 17 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 - 12 * q^26 - 8 * q^27 + 29 * q^28 + 12 * q^29 - 6 * q^30 - 58 * q^31 + 9 * q^32 + 3 * q^33 + 36 * q^34 - q^35 - q^36 - 15 * q^37 - 5 * q^38 - 8 * q^39 - 6 * q^40 - 2 * q^41 + 6 * q^42 + 30 * q^43 + 33 * q^44 - 8 * q^45 + 52 * q^46 + 6 * q^47 + 6 * q^48 + 13 * q^49 - 6 * q^50 - 7 * q^51 + 3 * q^53 + q^54 + 3 * q^55 - 67 * q^56 + 19 * q^57 + 36 * q^58 + 9 * q^59 - q^60 - 7 * q^61 + 14 * q^62 - 15 * q^63 + 19 * q^64 - 8 * q^65 - 17 * q^66 + 14 * q^67 + 22 * q^68 + 12 * q^69 + 6 * q^70 - 24 * q^71 - 6 * q^72 + 2 * q^73 + 2 * q^74 - 8 * q^75 + 62 * q^76 + 42 * q^77 - 12 * q^78 + 22 * q^79 + 6 * q^80 - 8 * q^81 - 51 * q^82 + 53 * q^83 + 50 * q^84 - 7 * q^85 - 35 * q^86 + 19 * q^87 + 11 * q^88 - 51 * q^89 + q^90 - q^91 + 29 * q^92 + 26 * q^93 - 4 * q^94 + 19 * q^95 + 9 * q^96 - 102 * q^97 + 90 * q^98 - 32 * q^99

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