LMFDB - Embedded newform 187.2.g.f.86.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (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:	$1.49320251780$
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			86.9
Character	$\chi$	$=$	187.86
Dual form			187.2.g.f.137.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.780378 - 2.40176i) q^{2} +(1.77278 - 1.28800i) q^{3} +(-3.54141 - 2.57299i) q^{4} +(0.678152 + 2.08714i) q^{5} +(-1.71003 - 5.26293i) q^{6} +(0.932422 + 0.677444i) q^{7} +(-4.85721 + 3.52897i) q^{8} +(0.556762 - 1.71354i) q^{9} +O(q^{10})$	\(q+(0.780378 - 2.40176i) q^{2} +(1.77278 - 1.28800i) q^{3} +(-3.54141 - 2.57299i) q^{4} +(0.678152 + 2.08714i) q^{5} +(-1.71003 - 5.26293i) q^{6} +(0.932422 + 0.677444i) q^{7} +(-4.85721 + 3.52897i) q^{8} +(0.556762 - 1.71354i) q^{9} +5.54201 q^{10} +(-3.01405 + 1.38401i) q^{11} -9.59217 q^{12} +(-0.288340 + 0.887418i) q^{13} +(2.35470 - 1.71079i) q^{14} +(3.89046 + 2.82658i) q^{15} +(1.97987 + 6.09341i) q^{16} +(0.309017 + 0.951057i) q^{17} +(-3.68101 - 2.67441i) q^{18} +(-4.23956 + 3.08022i) q^{19} +(2.96856 - 9.13628i) q^{20} +2.52553 q^{21} +(0.971950 + 8.31907i) q^{22} +5.52295 q^{23} +(-4.06546 + 12.5122i) q^{24} +(0.148835 - 0.108135i) q^{25} +(1.90635 + 1.38504i) q^{26} +(0.811409 + 2.49726i) q^{27} +(-1.55903 - 4.79822i) q^{28} +(-6.60719 - 4.80041i) q^{29} +(9.82479 - 7.13813i) q^{30} +(2.19710 - 6.76199i) q^{31} +4.17225 q^{32} +(-3.56066 + 6.33566i) q^{33} +2.52536 q^{34} +(-0.781595 + 2.40550i) q^{35} +(-6.38062 + 4.63579i) q^{36} +(-8.81621 - 6.40535i) q^{37} +(4.08948 + 12.5861i) q^{38} +(0.631833 + 1.94458i) q^{39} +(-10.6594 - 7.74448i) q^{40} +(6.89527 - 5.00971i) q^{41} +(1.97087 - 6.06572i) q^{42} -2.67260 q^{43} +(14.2350 + 2.85377i) q^{44} +3.95395 q^{45} +(4.30999 - 13.2648i) q^{46} +(2.54092 - 1.84609i) q^{47} +(11.3582 + 8.25223i) q^{48} +(-1.75264 - 5.39407i) q^{49} +(-0.143566 - 0.441851i) q^{50} +(1.77278 + 1.28800i) q^{51} +(3.30444 - 2.40082i) q^{52} +(-3.15753 + 9.71788i) q^{53} +6.63101 q^{54} +(-4.93260 - 5.35218i) q^{55} -6.91965 q^{56} +(-3.54849 + 10.9211i) q^{57} +(-16.6855 + 12.1227i) q^{58} +(5.17174 + 3.75749i) q^{59} +(-6.50495 - 20.0202i) q^{60} +(-0.628769 - 1.93515i) q^{61} +(-14.5261 - 10.5538i) q^{62} +(1.67996 - 1.22056i) q^{63} +(-0.703806 + 2.16609i) q^{64} -2.04770 q^{65} +(12.4381 + 13.4961i) q^{66} +12.3474 q^{67} +(1.35270 - 4.16318i) q^{68} +(9.79101 - 7.11358i) q^{69} +(5.16749 + 3.75440i) q^{70} +(4.48020 + 13.7886i) q^{71} +(3.34271 + 10.2878i) q^{72} +(0.700144 + 0.508684i) q^{73} +(-22.2641 + 16.1758i) q^{74} +(0.124574 - 0.383400i) q^{75} +22.9394 q^{76} +(-3.74796 - 0.751374i) q^{77} +5.16348 q^{78} +(-1.06880 + 3.28943i) q^{79} +(-11.3751 + 8.26451i) q^{80} +(9.02779 + 6.55908i) q^{81} +(-6.65118 - 20.4702i) q^{82} +(1.31184 + 4.03741i) q^{83} +(-8.94395 - 6.49816i) q^{84} +(-1.77542 + 1.28992i) q^{85} +(-2.08563 + 6.41892i) q^{86} -17.8961 q^{87} +(9.75577 - 17.3589i) q^{88} -6.94016 q^{89} +(3.08558 - 9.49643i) q^{90} +(-0.870030 + 0.632114i) q^{91} +(-19.5590 - 14.2105i) q^{92} +(-4.81448 - 14.8174i) q^{93} +(-2.45098 - 7.54333i) q^{94} +(-9.30391 - 6.75969i) q^{95} +(7.39650 - 5.37387i) q^{96} +(0.177752 - 0.547065i) q^{97} -14.3230 q^{98} +(0.693438 + 5.93525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.780378	−	2.40176i	0.551811	−	1.69830i	−0.152410	−	0.988317i	$-0.548704\pi$
$2$	0.780378	−	2.40176i	0.551811	−	1.69830i	0.704221	−	0.709981i	$-0.251296\pi$
$3$	1.77278	−	1.28800i	1.02352	−	0.743629i	0.0565167	−	0.998402i	$-0.482001\pi$
$3$	1.77278	−	1.28800i	1.02352	−	0.743629i	0.967001	+	0.254773i	$0.0820006\pi$
$4$	−3.54141	−	2.57299i	−1.77071	−	1.28649i
$5$	0.678152	+	2.08714i	0.303279	+	0.933396i	0.980314	+	0.197445i	$0.0632645\pi$
$5$	0.678152	+	2.08714i	0.303279	+	0.933396i	−0.677035	+	0.735951i	$0.736736\pi$
$6$	−1.71003	−	5.26293i	−0.698116	−	2.14858i
$7$	0.932422	+	0.677444i	0.352422	+	0.256050i	0.749885	−	0.661569i	$-0.230109\pi$
$7$	0.932422	+	0.677444i	0.352422	+	0.256050i	−0.397462	+	0.917619i	$0.630109\pi$
$8$	−4.85721	+	3.52897i	−1.71728	+	1.24768i
$9$	0.556762	−	1.71354i	0.185587	−	0.571179i
$10$	5.54201			1.75254
$11$	−3.01405	+	1.38401i	−0.908771	+	0.417294i
$11$	−3.01405	+	1.38401i	−0.908771	+	0.417294i
$12$	−9.59217			−2.76902
$13$	−0.288340	+	0.887418i	−0.0799710	+	0.246125i	−0.983047	−	0.183356i	$-0.941304\pi$
$13$	−0.288340	+	0.887418i	−0.0799710	+	0.246125i	0.903076	+	0.429482i	$0.141304\pi$
$14$	2.35470	−	1.71079i	0.629319	−	0.457227i
$15$	3.89046	+	2.82658i	1.00451	+	0.729820i
$16$	1.97987	+	6.09341i	0.494967	+	1.52335i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−3.68101	−	2.67441i	−0.867623	−	0.630365i
$19$	−4.23956	+	3.08022i	−0.972623	+	0.706652i	−0.956048	−	0.293211i	$-0.905276\pi$
$19$	−4.23956	+	3.08022i	−0.972623	+	0.706652i	−0.0165748	+	0.999863i	$0.505276\pi$
$20$	2.96856	−	9.13628i	0.663790	−	2.04293i
$21$	2.52553			0.551117
$22$	0.971950	+	8.31907i	0.207220	+	1.77363i
$23$	5.52295			1.15162			0.575808	−	0.817585i	$-0.304688\pi$
$23$	5.52295			1.15162			0.575808	+	0.817585i	$0.304688\pi$
$24$	−4.06546	+	12.5122i	−0.829859	+	2.55404i
$25$	0.148835	−	0.108135i	0.0297670	−	0.0216270i
$26$	1.90635	+	1.38504i	0.373866	+	0.271629i
$27$	0.811409	+	2.49726i	0.156156	+	0.480598i
$28$	−1.55903	−	4.79822i	−0.294630	−	0.906778i
$29$	−6.60719	−	4.80041i	−1.22693	−	0.891413i	−0.230269	−	0.973127i	$-0.573961\pi$
$29$	−6.60719	−	4.80041i	−1.22693	−	0.891413i	−0.996656	+	0.0817137i	$0.973961\pi$
$30$	9.82479	−	7.13813i	1.79375	−	1.30324i
$31$	2.19710	−	6.76199i	0.394612	−	1.21449i	−0.534652	−	0.845072i	$-0.679557\pi$
$31$	2.19710	−	6.76199i	0.394612	−	1.21449i	0.929264	−	0.369417i	$-0.120443\pi$
$32$	4.17225			0.737556
$33$	−3.56066	+	6.33566i	−0.619832	+	1.10290i
$34$	2.52536			0.433095
$35$	−0.781595	+	2.40550i	−0.132114	+	0.406604i
$36$	−6.38062	+	4.63579i	−1.06344	+	0.772632i
$37$	−8.81621	−	6.40535i	−1.44938	−	1.05303i	−0.985977	−	0.166884i	$-0.946630\pi$
$37$	−8.81621	−	6.40535i	−1.44938	−	1.05303i	−0.463399	−	0.886150i	$-0.653370\pi$
$38$	4.08948	+	12.5861i	0.663402	+	2.04174i
$39$	0.631833	+	1.94458i	0.101174	+	0.311382i
$40$	−10.6594	−	7.74448i	−1.68539	−	1.22451i
$41$	6.89527	−	5.00971i	1.07686	−	0.782385i	0.0997273	−	0.995015i	$-0.468203\pi$
$41$	6.89527	−	5.00971i	1.07686	−	0.782385i	0.977133	+	0.212630i	$0.0682030\pi$
$42$	1.97087	−	6.06572i	0.304112	−	0.935961i
$43$	−2.67260			−0.407567			−0.203784	−	0.979016i	$-0.565324\pi$
$43$	−2.67260			−0.407567			−0.203784	+	0.979016i	$0.565324\pi$
$44$	14.2350	+	2.85377i	2.14601	+	0.430223i
$45$	3.95395			0.589420
$46$	4.30999	−	13.2648i	0.635473	−	1.95579i
$47$	2.54092	−	1.84609i	0.370632	−	0.269280i	−0.386841	−	0.922146i	$-0.626434\pi$
$47$	2.54092	−	1.84609i	0.370632	−	0.269280i	0.757473	+	0.652867i	$0.226434\pi$
$48$	11.3582	+	8.25223i	1.63942	+	1.19111i
$49$	−1.75264	−	5.39407i	−0.250377	−	0.770581i
$50$	−0.143566	−	0.441851i	−0.0203033	−	0.0624872i
$51$	1.77278	+	1.28800i	0.248239	+	0.180357i
$52$	3.30444	−	2.40082i	0.458244	−	0.332933i
$53$	−3.15753	+	9.71788i	−0.433720	+	1.33485i	0.460672	+	0.887570i	$0.347608\pi$
$53$	−3.15753	+	9.71788i	−0.433720	+	1.33485i	−0.894393	+	0.447283i	$0.852392\pi$
$54$	6.63101			0.902367
$55$	−4.93260	−	5.35218i	−0.665112	−	0.721687i
$56$	−6.91965			−0.924677
$57$	−3.54849	+	10.9211i	−0.470010	+	1.44654i
$58$	−16.6855	+	12.1227i	−2.19092	+	1.59179i
$59$	5.17174	+	3.75749i	0.673303	+	0.489183i	0.871129	−	0.491054i	$-0.163388\pi$
$59$	5.17174	+	3.75749i	0.673303	+	0.489183i	−0.197826	+	0.980237i	$0.563388\pi$
$60$	−6.50495	−	20.0202i	−0.839785	−	2.58459i
$61$	−0.628769	−	1.93515i	−0.0805056	−	0.247771i	0.902700	−	0.430270i	$-0.141581\pi$
$61$	−0.628769	−	1.93515i	−0.0805056	−	0.247771i	−0.983206	+	0.182499i	$0.941581\pi$
$62$	−14.5261	−	10.5538i	−1.84481	−	1.34034i
$63$	1.67996	−	1.22056i	0.211655	−	0.153777i
$64$	−0.703806	+	2.16609i	−0.0879758	+	0.270762i
$65$	−2.04770			−0.253986
$66$	12.4381	+	13.4961i	1.53102	+	1.66125i
$67$	12.3474			1.50848			0.754240	−	0.656599i	$-0.228006\pi$
$67$	12.3474			1.50848			0.754240	+	0.656599i	$0.228006\pi$
$68$	1.35270	−	4.16318i	0.164039	−	0.504859i
$69$	9.79101	−	7.11358i	1.17870	−	0.856375i
$70$	5.16749	+	3.75440i	0.617633	+	0.448737i
$71$	4.48020	+	13.7886i	0.531702	+	1.63641i	0.750670	+	0.660678i	$0.229731\pi$
$71$	4.48020	+	13.7886i	0.531702	+	1.63641i	−0.218968	+	0.975732i	$0.570269\pi$
$72$	3.34271	+	10.2878i	0.393942	+	1.21243i
$73$	0.700144	+	0.508684i	0.0819457	+	0.0595370i	0.628004	−	0.778210i	$-0.283872\pi$
$73$	0.700144	+	0.508684i	0.0819457	+	0.0595370i	−0.546058	+	0.837747i	$0.683872\pi$
$74$	−22.2641	+	16.1758i	−2.58815	+	1.88040i
$75$	0.124574	−	0.383400i	0.0143846	−	0.0442712i
$76$	22.9394			2.63133
$77$	−3.74796	−	0.751374i	−0.427120	−	0.0856270i
$78$	5.16348			0.584649
$79$	−1.06880	+	3.28943i	−0.120249	+	0.370090i	−0.993006	−	0.118066i	$-0.962330\pi$
$79$	−1.06880	+	3.28943i	−0.120249	+	0.370090i	0.872756	+	0.488156i	$0.162330\pi$
$80$	−11.3751	+	8.26451i	−1.27178	+	0.924001i
$81$	9.02779	+	6.55908i	1.00309	+	0.728786i
$82$	−6.65118	−	20.4702i	−0.734500	−	2.26056i
$83$	1.31184	+	4.03741i	0.143993	+	0.443164i	0.996880	−	0.0789311i	$-0.0251507\pi$
$83$	1.31184	+	4.03741i	0.143993	+	0.443164i	−0.852887	+	0.522095i	$0.825151\pi$
$84$	−8.94395	−	6.49816i	−0.975865	−	0.709008i
$85$	−1.77542	+	1.28992i	−0.192572	+	0.139912i
$86$	−2.08563	+	6.41892i	−0.224900	+	0.692170i
$87$	−17.8961			−1.91866
$88$	9.75577	−	17.3589i	1.03997	−	1.85047i
$89$	−6.94016			−0.735655			−0.367828	−	0.929894i	$-0.619898\pi$
$89$	−6.94016			−0.735655			−0.367828	+	0.929894i	$0.619898\pi$
$90$	3.08558	−	9.49643i	0.325248	−	1.00101i
$91$	−0.870030	+	0.632114i	−0.0912040	+	0.0662636i
$92$	−19.5590	−	14.2105i	−2.03917	−	1.48154i
$93$	−4.81448	−	14.8174i	−0.499238	−	1.53650i
$94$	−2.45098	−	7.54333i	−0.252799	−	0.778035i
$95$	−9.30391	−	6.75969i	−0.954561	−	0.693530i
$96$	7.39650	−	5.37387i	0.754902	−	0.548468i
$97$	0.177752	−	0.547065i	0.0180480	−	0.0555460i	−0.941627	−	0.336658i	$-0.890703\pi$
$97$	0.177752	−	0.547065i	0.0180480	−	0.0555460i	0.959675	+	0.281112i	$0.0907033\pi$
$98$	−14.3230			−1.44684
$99$	0.693438	+	5.93525i	0.0696932	+	0.596515i
$100$	−0.805315			−0.0805315
$101$	3.13752	−	9.65629i	0.312195	−	0.960837i	−0.664699	−	0.747111i	$-0.731440\pi$
$101$	3.13752	−	9.65629i	0.312195	−	0.960837i	0.976894	−	0.213726i	$-0.0685598\pi$
$102$	4.47691	−	3.25267i	0.443280	−	0.322062i
$103$	−2.04018	−	1.48228i	−0.201025	−	0.146053i	0.482719	−	0.875775i	$-0.339649\pi$
$103$	−2.04018	−	1.48228i	−0.201025	−	0.146053i	−0.683744	+	0.729722i	$0.739649\pi$
$104$	−1.73114	−	5.32792i	−0.169753	−	0.522445i
$105$	1.71270	+	5.27114i	0.167142	+	0.514410i
$106$	20.8759	+	15.1672i	2.02765	+	1.47317i
$107$	−10.0218	+	7.28126i	−0.968844	+	0.703906i	−0.955188	−	0.296000i	$-0.904347\pi$
$107$	−10.0218	+	7.28126i	−0.968844	+	0.703906i	−0.0136561	+	0.999907i	$0.504347\pi$
$108$	3.55188	−	10.9316i	0.341780	−	1.05189i
$109$	−13.0709			−1.25197			−0.625983	−	0.779836i	$-0.715302\pi$
$109$	−13.0709			−1.25197			−0.625983	+	0.779836i	$0.715302\pi$
$110$	−16.7039	+	7.67019i	−1.59266	+	0.731324i
$111$	−23.8794			−2.26653
$112$	−2.28187	+	7.02288i	−0.215617	+	0.663600i
$113$	7.40800	−	5.38223i	0.696886	−	0.506318i	−0.182030	−	0.983293i	$-0.558267\pi$
$113$	7.40800	−	5.38223i	0.696886	−	0.506318i	0.878917	+	0.476975i	$0.158267\pi$
$114$	23.4608	+	17.0452i	2.19730	+	1.59643i
$115$	3.74540	+	11.5272i	0.349260	+	1.07491i
$116$	11.0474	+	34.0004i	1.02573	+	3.15686i
$117$	1.36009	+	0.988160i	0.125740	+	0.0913554i
$118$	13.0605	−	9.48899i	1.20231	−	0.873533i
$119$	−0.356154	+	1.09613i	−0.0326485	+	0.100482i
$120$	−28.8717			−2.63561
$121$	7.16904	−	8.34295i	0.651731	−	0.758450i
$122$	−5.13844			−0.465213
$123$	5.77131	−	17.7623i	0.520381	−	1.60157i
$124$	−25.1793	+	18.2939i	−2.26117	+	1.64284i
$125$	9.20375	+	6.68691i	0.823208	+	0.598096i
$126$	−1.62049	−	4.98736i	−0.144365	−	0.444309i
$127$	−2.93478	−	9.03232i	−0.260419	−	0.801489i	−0.992713	−	0.120500i	$-0.961550\pi$
$127$	−2.93478	−	9.03232i	−0.260419	−	0.801489i	0.732294	−	0.680989i	$-0.238450\pi$
$128$	11.4040	+	8.28552i	1.00798	+	0.732343i
$129$	−4.73794	+	3.44231i	−0.417152	+	0.303079i
$130$	−1.59798	+	4.91808i	−0.140152	+	0.431344i
$131$	−1.53700			−0.134288			−0.0671442	−	0.997743i	$-0.521389\pi$
$131$	−1.53700			−0.134288			−0.0671442	+	0.997743i	$0.521389\pi$
$132$	28.9113	−	13.2756i	2.51641	−	1.15550i
$133$	−6.03974			−0.523712
$134$	9.63567	−	29.6555i	0.832395	−	2.56185i
$135$	−4.66186	+	3.38704i	−0.401229	+	0.291510i
$136$	−4.85721	−	3.52897i	−0.416502	−	0.302607i
$137$	4.27382	+	13.1535i	0.365137	+	1.12378i	0.949895	+	0.312568i	$0.101189\pi$
$137$	4.27382	+	13.1535i	0.365137	+	1.12378i	−0.584758	+	0.811208i	$0.698811\pi$
$138$	−9.44441	−	29.0669i	−0.803961	−	2.47434i
$139$	1.23631	+	0.898231i	0.104862	+	0.0761870i	0.638981	−	0.769223i	$-0.279356\pi$
$139$	1.23631	+	0.898231i	0.104862	+	0.0761870i	−0.534118	+	0.845410i	$0.679356\pi$
$140$	8.95727	−	6.50784i	0.757028	−	0.550013i
$141$	2.12674	−	6.54544i	0.179104	−	0.551225i
$142$	36.6132			3.07251
$143$	−0.359123	−	3.07379i	−0.0300314	−	0.257043i
$144$	11.5436			0.961966
$145$	5.53843	−	17.0455i	0.459941	−	1.41555i
$146$	1.76811	−	1.28461i	0.146330	−	0.106315i
$147$	−10.0546	−	7.30512i	−0.829292	−	0.602516i
$148$	14.7409	+	45.3680i	1.21170	+	3.72922i
$149$	0.179935	+	0.553783i	0.0147409	+	0.0453677i	0.958156	−	0.286245i	$-0.0924072\pi$
$149$	0.179935	+	0.553783i	0.0147409	+	0.0453677i	−0.943416	+	0.331613i	$0.892407\pi$
$150$	−0.823618	−	0.598393i	−0.0672481	−	0.0488586i
$151$	0.667251	−	0.484786i	0.0543001	−	0.0394513i	−0.560304	−	0.828287i	$-0.689316\pi$
$151$	0.667251	−	0.484786i	0.0543001	−	0.0394513i	0.614604	+	0.788836i	$0.289316\pi$
$152$	9.72243	−	29.9226i	0.788594	−	2.42704i
$153$	1.80172			0.145660
$154$	−4.72944	+	8.41533i	−0.381109	+	0.678127i
$155$	15.6032			1.25328
$156$	2.76580	−	8.51226i	0.221441	−	0.681526i
$157$	−0.941367	+	0.683943i	−0.0751293	+	0.0545846i	−0.624716	−	0.780852i	$-0.714785\pi$
$157$	−0.941367	+	0.683943i	−0.0751293	+	0.0545846i	0.549587	+	0.835437i	$0.314785\pi$
$158$	7.06634	+	5.13400i	0.562168	+	0.408439i
$159$	6.91904	+	21.2946i	0.548715	+	1.68877i
$160$	2.82942	+	8.70806i	0.223685	+	0.688432i
$161$	5.14972	+	3.74149i	0.405855	+	0.294871i
$162$	22.7984	−	16.5640i	1.79121	−	1.30139i
$163$	5.59999	−	17.2350i	0.438625	−	1.34995i	−0.450701	−	0.892675i	$-0.648826\pi$
$163$	5.59999	−	17.2350i	0.438625	−	1.34995i	0.889326	−	0.457274i	$-0.151174\pi$
$164$	−37.3089			−2.91333
$165$	−15.6381	−	3.13505i	−1.21742	−	0.244063i
$166$	10.7206			0.832081
$167$	−5.86654	+	18.0554i	−0.453967	+	1.39717i	0.418377	+	0.908273i	$0.362599\pi$
$167$	−5.86654	+	18.0554i	−0.453967	+	1.39717i	−0.872344	+	0.488892i	$0.837401\pi$
$168$	−12.2670	+	8.91253i	−0.946423	+	0.687617i
$169$	9.81285	+	7.12945i	0.754835	+	0.548419i
$170$	1.71257	+	5.27076i	0.131349	+	0.404249i
$171$	2.91765	+	8.97959i	0.223118	+	0.686687i
$172$	9.46476	+	6.87655i	0.721681	+	0.524332i
$173$	10.9961	−	7.98913i	0.836018	−	0.607402i	−0.0852378	−	0.996361i	$-0.527165\pi$
$173$	10.9961	−	7.98913i	0.836018	−	0.607402i	0.921255	+	0.388958i	$0.127165\pi$
$174$	−13.9657	+	42.9820i	−1.05874	+	3.25846i
$175$	0.212032			0.0160281
$176$	−14.4008	−	15.6257i	−1.08550	−	1.17783i
$177$	14.0080			1.05291
$178$	−5.41595	+	16.6686i	−0.405942	+	1.24936i
$179$	3.18756	−	2.31590i	0.238250	−	0.173099i	−0.462253	−	0.886748i	$-0.652959\pi$
$179$	3.18756	−	2.31590i	0.238250	−	0.173099i	0.700503	+	0.713649i	$0.252959\pi$
$180$	−14.0026	−	10.1735i	−1.04369	−	0.758285i
$181$	−0.880222	−	2.70905i	−0.0654264	−	0.201362i	0.912999	−	0.407961i	$-0.133760\pi$
$181$	−0.880222	−	2.70905i	−0.0654264	−	0.201362i	−0.978426	+	0.206600i	$0.933760\pi$
$182$	0.839231	+	2.58289i	0.0622080	+	0.191456i
$183$	−3.60716	−	2.62075i	−0.266649	−	0.193732i
$184$	−26.8261	+	19.4903i	−1.97765	+	1.43685i
$185$	7.39012	−	22.7444i	0.543332	−	1.67220i
$186$	−39.3450			−2.88491
$187$	−2.24766	−	2.43885i	−0.164365	−	0.178347i
$188$	−13.7484			−1.00271
$189$	−0.935179	+	2.87818i	−0.0680242	+	0.209357i
$190$	−23.4957	+	17.0706i	−1.70456	+	1.23843i
$191$	−5.03321	−	3.65684i	−0.364190	−	0.264600i	0.390607	−	0.920557i	$-0.372265\pi$
$191$	−5.03321	−	3.65684i	−0.364190	−	0.264600i	−0.754798	+	0.655958i	$0.772265\pi$
$192$	1.54224	+	4.74652i	0.111301	+	0.342551i
$193$	−6.59956	−	20.3113i	−0.475047	−	1.46204i	−0.845895	−	0.533349i	$-0.820933\pi$
$193$	−6.59956	−	20.3113i	−0.475047	−	1.46204i	0.370848	−	0.928693i	$-0.379067\pi$
$194$	−1.17520	−	0.853835i	−0.0843746	−	0.0613018i
$195$	−3.63013	+	2.63744i	−0.259959	+	0.188871i
$196$	−7.67204	+	23.6121i	−0.548003	+	1.68658i
$197$	−2.12956			−0.151725			−0.0758626	−	0.997118i	$-0.524171\pi$
$197$	−2.12956			−0.151725			−0.0758626	+	0.997118i	$0.524171\pi$
$198$	14.7962	+	2.96627i	1.05152	+	0.210804i
$199$	−22.1126			−1.56752			−0.783759	−	0.621065i	$-0.786700\pi$
$199$	−22.1126			−1.56752			−0.783759	+	0.621065i	$0.786700\pi$
$200$	−0.341318	+	1.05047i	−0.0241348	+	0.0742793i
$201$	21.8894	−	15.9035i	1.54396	−	1.12175i
$202$	−20.7436	−	15.0711i	−1.45952	−	1.06040i
$203$	−2.90869	−	8.95201i	−0.204150	−	0.628308i
$204$	−2.96414	−	9.12270i	−0.207532	−	0.638717i
$205$	15.1320	+	10.9940i	1.05686	+	0.767856i
$206$	−5.15218	+	3.74328i	−0.358969	+	0.260806i
$207$	3.07497	−	9.46378i	0.213725	−	0.657778i
$208$	−5.97827			−0.414519
$209$	8.51522	−	15.1515i	0.589010	−	1.04805i
$210$	13.9965			0.965853
$211$	−3.55970	+	10.9556i	−0.245060	+	0.754218i	0.750566	+	0.660795i	$0.229781\pi$
$211$	−3.55970	+	10.9556i	−0.245060	+	0.754218i	−0.995627	+	0.0934226i	$0.970219\pi$
$212$	36.1861	−	26.2907i	2.48527	−	1.80565i
$213$	25.7022	+	18.6738i	1.76109	+	1.27951i
$214$	9.66703	+	29.7521i	0.660824	+	2.03381i
$215$	−1.81243	−	5.57807i	−0.123606	−	0.380421i
$216$	−12.7539	−	9.26628i	−0.867795	−	0.630490i
$217$	6.62950	−	4.81661i	0.450040	−	0.326973i
$218$	−10.2003	+	31.3932i	−0.690848	+	2.12621i
$219$	1.89639			0.128146
$220$	3.69730	+	31.6458i	0.249272	+	2.13356i
$221$	−0.933086			−0.0627662
$222$	−18.6349	+	57.3524i	−1.25069	+	3.84924i
$223$	−1.78145	+	1.29430i	−0.119295	+	0.0866727i	−0.645833	−	0.763479i	$-0.723490\pi$
$223$	−1.78145	+	1.29430i	−0.119295	+	0.0866727i	0.526538	+	0.850152i	$0.323490\pi$
$224$	3.89030	+	2.82647i	0.259931	+	0.188851i
$225$	−0.102427	−	0.315239i	−0.00682850	−	0.0210160i
$226$	−7.14576	−	21.9924i	−0.475329	−	1.46291i
$227$	9.07422	+	6.59280i	0.602277	+	0.437580i	0.846686	−	0.532092i	$-0.178594\pi$
$227$	9.07422	+	6.59280i	0.602277	+	0.437580i	−0.244409	+	0.969672i	$0.578594\pi$
$228$	40.6666	−	29.5460i	2.69321	−	1.95673i
$229$	2.74561	−	8.45012i	0.181435	−	0.558400i	−0.818434	−	0.574601i	$-0.805157\pi$
$229$	2.74561	−	8.45012i	0.181435	−	0.558400i	0.999869	+	0.0162013i	$0.00515726\pi$
$230$	30.6083			2.01825
$231$	−7.61210	+	3.49536i	−0.500839	+	0.229978i
$232$	49.0330			3.21918
$233$	1.79480	−	5.52384i	0.117581	−	0.361878i	−0.874895	−	0.484312i	$-0.839070\pi$
$233$	1.79480	−	5.52384i	0.117581	−	0.361878i	0.992477	+	0.122434i	$0.0390699\pi$
$234$	3.43470	−	2.49546i	0.224533	−	0.163133i
$235$	5.57617	+	4.05133i	0.363750	+	0.264280i
$236$	−8.64728	−	26.6136i	−0.562890	−	1.73240i
$237$	2.34204	+	7.20807i	0.152132	+	0.468215i
$238$	2.35470	+	1.71079i	0.152632	+	0.110894i
$239$	9.04572	−	6.57210i	0.585119	−	0.425114i	−0.255447	−	0.966823i	$-0.582223\pi$
$239$	9.04572	−	6.57210i	0.585119	−	0.425114i	0.840566	+	0.541709i	$0.182223\pi$
$240$	−9.52093	+	29.3024i	−0.614573	+	1.89146i
$241$	−10.9676			−0.706483			−0.353242	−	0.935532i	$-0.614921\pi$
$241$	−10.9676			−0.706483			−0.353242	+	0.935532i	$0.614921\pi$
$242$	−14.4432	−	23.7289i	−0.928442	−	1.52535i
$243$	16.5751			1.06329
$244$	−2.75239	+	8.47098i	−0.176204	+	0.542299i
$245$	10.0696	−	7.31599i	0.643323	−	0.467402i
$246$	−38.1568	−	27.7226i	−2.43279	−	1.76753i
$247$	−1.51101	−	4.65041i	−0.0961433	−	0.295899i
$248$	13.1911	+	40.5979i	0.837633	+	2.57797i
$249$	7.52580	+	5.46782i	0.476928	+	0.346509i
$250$	23.2427	−	16.8868i	1.47000	−	1.06802i
$251$	−1.76018	+	5.41729i	−0.111102	+	0.341936i	−0.991114	−	0.133015i	$-0.957534\pi$
$251$	−1.76018	+	5.41729i	−0.111102	+	0.341936i	0.880012	+	0.474951i	$0.157534\pi$
$252$	−9.08993			−0.572611
$253$	−16.6465	+	7.64381i	−1.04656	+	0.480562i
$254$	−23.9837			−1.50487
$255$	−1.48602	+	4.57351i	−0.0930583	+	0.286404i
$256$	25.1141	−	18.2464i	1.56963	−	1.14040i
$257$	−22.8400	−	16.5943i	−1.42472	−	1.03512i	−0.990969	−	0.134090i	$-0.957189\pi$
$257$	−22.8400	−	16.5943i	−1.42472	−	1.03512i	−0.433754	−	0.901031i	$-0.642811\pi$
$258$	4.57021	+	14.0657i	0.284529	+	0.875691i
$259$	−3.88116	−	11.9450i	−0.241164	−	0.742225i
$260$	7.25175	+	5.26870i	0.449734	+	0.326751i
$261$	−11.9043	+	8.64898i	−0.736858	+	0.535358i
$262$	−1.19944	+	3.69150i	−0.0741018	+	0.228062i
$263$	−13.9941			−0.862916			−0.431458	−	0.902133i	$-0.642001\pi$
$263$	−13.9941			−0.862916			−0.431458	+	0.902133i	$0.642001\pi$
$264$	−5.06347	−	43.3391i	−0.311635	−	2.66734i
$265$	−22.4238			−1.37748
$266$	−4.71328	+	14.5060i	−0.288990	+	0.889419i
$267$	−12.3034	+	8.93895i	−0.752956	+	0.547055i
$268$	−43.7274	−	31.7698i	−2.67107	−	1.94065i
$269$	−8.49346	−	26.1402i	−0.517855	−	1.59380i	−0.778026	−	0.628232i	$-0.783779\pi$
$269$	−8.49346	−	26.1402i	−0.517855	−	1.59380i	0.260170	−	0.965563i	$-0.416221\pi$
$270$	4.49683	+	13.8398i	0.273669	+	0.842265i
$271$	21.4510	+	15.5850i	1.30305	+	0.946724i	0.999981	−	0.00624300i	$-0.00198722\pi$
$271$	21.4510	+	15.5850i	1.30305	+	0.946724i	0.303074	+	0.952967i	$0.401987\pi$
$272$	−5.18336	+	3.76593i	−0.314288	+	0.228343i
$273$	−0.728211	+	2.24120i	−0.0440734	+	0.135644i
$274$	34.9266			2.10999
$275$	−0.298937	+	0.531913i	−0.0180266	+	0.0320756i
$276$	−52.9771			−3.18885
$277$	3.23137	−	9.94513i	0.194154	−	0.597545i	−0.805831	−	0.592145i	$-0.798281\pi$
$277$	3.23137	−	9.94513i	0.194154	−	0.597545i	0.999985	−	0.00539961i	$-0.00171876\pi$
$278$	3.12212	−	2.26835i	0.187252	−	0.136047i
$279$	−10.3636	−	7.52963i	−0.620455	−	0.450787i
$280$	−4.69257	−	14.4423i	−0.280435	−	0.863090i
$281$	8.63210	+	26.5669i	0.514948	+	1.58485i	0.783377	+	0.621547i	$0.213495\pi$
$281$	8.63210	+	26.5669i	0.514948	+	1.58485i	−0.268430	+	0.963299i	$0.586505\pi$
$282$	−14.0609	−	10.2158i	−0.837314	−	0.608344i
$283$	12.1455	−	8.82424i	0.721976	−	0.524547i	−0.165039	−	0.986287i	$-0.552775\pi$
$283$	12.1455	−	8.82424i	0.721976	−	0.524547i	0.887015	+	0.461741i	$0.152775\pi$
$284$	19.6117	−	60.3587i	1.16374	−	3.58163i
$285$	−25.2003			−1.49274
$286$	−7.66274	−	1.53619i	−0.453108	−	0.0908369i
$287$	9.82310			0.579839
$288$	2.32295	−	7.14930i	0.136881	−	0.421276i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−36.6171	−	26.6039i	−2.15023	−	1.56223i
$291$	−0.389505	−	1.19877i	−0.0228332	−	0.0702733i
$292$	−1.17066	−	3.60292i	−0.0685077	−	0.210845i
$293$	17.5109	+	12.7224i	1.02300	+	0.743252i	0.966895	−	0.255173i	$-0.0821324\pi$
$293$	17.5109	+	12.7224i	1.02300	+	0.743252i	0.0561031	+	0.998425i	$0.482132\pi$
$294$	−25.3915	+	18.4480i	−1.48086	+	1.07591i
$295$	−4.33517	+	13.3423i	−0.252403	+	0.776817i
$296$	65.4265			3.80284
$297$	−5.90186	−	6.40388i	−0.342461	−	0.371591i
$298$	1.47047			0.0851820
$299$	−1.59249	+	4.90117i	−0.0920958	+	0.283442i
$300$	−1.42765	+	1.03725i	−0.0824254	+	0.0598856i
$301$	−2.49199	−	1.81053i	−0.143636	−	0.104357i
$302$	−0.643630	−	1.98089i	−0.0370368	−	0.113987i
$303$	−6.87519	−	21.1597i	−0.394969	−	1.21559i
$304$	−27.1628	−	19.7350i	−1.55790	−	1.13188i
$305$	3.61253	−	2.62465i	0.206853	−	0.150287i
$306$	1.40602	−	4.32729i	0.0803769	−	0.247375i
$307$	5.61922			0.320706			0.160353	−	0.987060i	$-0.448737\pi$
$307$	5.61922			0.320706			0.160353	+	0.987060i	$0.448737\pi$
$308$	11.3398	+	12.3044i	0.646144	+	0.701106i
$309$	−5.52597			−0.314362
$310$	12.1764	−	37.4750i	0.691571	−	2.12844i
$311$	−6.88425	+	5.00170i	−0.390370	+	0.283621i	−0.765607	−	0.643308i	$-0.777561\pi$
$311$	−6.88425	+	5.00170i	−0.390370	+	0.283621i	0.375237	+	0.926929i	$0.377561\pi$
$312$	−9.93132	−	7.21553i	−0.562250	−	0.408499i
$313$	1.42655	+	4.39046i	0.0806333	+	0.248164i	0.983244	−	0.182294i	$-0.0583522\pi$
$313$	1.42655	+	4.39046i	0.0806333	+	0.248164i	−0.902611	+	0.430458i	$0.858352\pi$
$314$	0.908043	+	2.79467i	0.0512438	+	0.157712i
$315$	3.68675	+	2.67858i	0.207725	+	0.150921i
$316$	12.2487	−	8.89922i	0.689044	−	0.500620i
$317$	−0.365109	+	1.12369i	−0.0205066	+	0.0631127i	−0.960786	−	0.277291i	$-0.910564\pi$
$317$	−0.365109	+	1.12369i	−0.0205066	+	0.0631127i	0.940280	+	0.340403i	$0.110564\pi$
$318$	56.5439			3.17083
$319$	26.5582	+	5.32428i	1.48698	+	0.298102i
$320$	−4.99822			−0.279409
$321$	−8.38820	+	25.8162i	−0.468184	+	1.44092i
$322$	13.0049	−	9.44860i	0.724734	−	0.526550i
$323$	−4.23956	−	3.08022i	−0.235896	−	0.171388i
$324$	−15.0947	−	46.4568i	−0.838595	−	2.58093i
$325$	0.0530458	+	0.163258i	0.00294245	+	0.00905594i
$326$	−37.0241	−	26.8996i	−2.05058	−	1.48983i
$327$	−23.1719	+	16.8354i	−1.28141	+	0.930999i
$328$	−15.8127	+	48.6664i	−0.873108	+	2.68715i
$329$	3.61984			0.199568
$330$	−19.7332	+	35.1123i	−1.08628	+	1.93287i
$331$	−6.99089			−0.384254			−0.192127	−	0.981370i	$-0.561539\pi$
$331$	−6.99089			−0.384254			−0.192127	+	0.981370i	$0.561539\pi$
$332$	5.74246	−	17.6735i	0.315158	−	0.969958i
$333$	−15.8843	+	11.5406i	−0.870456	+	0.632423i
$334$	38.7865	+	28.1800i	2.12230	+	1.54194i
$335$	8.37344	+	25.7708i	0.457490	+	1.40801i
$336$	5.00023	+	15.3891i	0.272785	+	0.839545i
$337$	−6.52070	−	4.73756i	−0.355205	−	0.258071i	0.395844	−	0.918318i	$-0.370452\pi$
$337$	−6.52070	−	4.73756i	−0.355205	−	0.258071i	−0.751049	+	0.660246i	$0.770452\pi$
$338$	24.7809	−	18.0044i	1.34791	−	0.979311i
$339$	6.20046	−	19.0831i	0.336763	−	1.03645i
$340$	9.60646			0.520983
$341$	2.73646	+	23.4218i	0.148188	+	1.26836i
$342$	23.8437			1.28932
$343$	4.51306	−	13.8898i	0.243682	−	0.749976i
$344$	12.9814	−	9.43151i	0.699908	−	0.508513i
$345$	21.4868	+	15.6111i	1.15681	+	0.840472i
$346$	−10.6068	−	32.6445i	−0.570227	−	1.75498i
$347$	9.42305	+	29.0012i	0.505856	+	1.55686i	0.799327	+	0.600896i	$0.205189\pi$
$347$	9.42305	+	29.0012i	0.505856	+	1.55686i	−0.293471	+	0.955968i	$0.594811\pi$
$348$	63.3773	+	46.0463i	3.39738	+	2.46834i
$349$	−6.40725	+	4.65514i	−0.342972	+	0.249184i	−0.745915	−	0.666041i	$-0.767987\pi$
$349$	−6.40725	+	4.65514i	−0.342972	+	0.249184i	0.402943	+	0.915225i	$0.367987\pi$
$350$	0.165465	−	0.509250i	0.00884450	−	0.0272206i
$351$	−2.45007			−0.130775
$352$	−12.5754	+	5.77443i	−0.670270	+	0.307778i
$353$	−3.05023			−0.162347			−0.0811736	−	0.996700i	$-0.525867\pi$
$353$	−3.05023			−0.162347			−0.0811736	+	0.996700i	$0.525867\pi$
$354$	10.9316	−	33.6439i	0.581006	−	1.78815i
$355$	−25.7405	+	18.7016i	−1.36616	+	0.992576i
$356$	24.5779	+	17.8569i	1.30263	+	0.946415i
$357$	0.780433	+	2.40193i	0.0413049	+	0.127123i
$358$	−3.07472	−	9.46303i	−0.162504	−	0.500137i
$359$	−1.49466	−	1.08594i	−0.0788853	−	0.0573135i	0.547644	−	0.836712i	$-0.315525\pi$
$359$	−1.49466	−	1.08594i	−0.0788853	−	0.0573135i	−0.626529	+	0.779398i	$0.715525\pi$
$360$	−19.2052	+	13.9534i	−1.01220	+	0.735408i
$361$	2.61480	−	8.04753i	0.137621	−	0.423554i
$362$	−7.19338			−0.378075
$363$	1.96342	−	24.0240i	0.103053	−	1.26093i
$364$	4.70755			0.246743
$365$	−0.586890	+	1.80626i	−0.0307192	+	0.0945440i
$366$	−9.10935	+	6.61833i	−0.476153	+	0.345946i
$367$	−23.6783	−	17.2033i	−1.23600	−	0.898004i	−0.238672	−	0.971100i	$-0.576712\pi$
$367$	−23.6783	−	17.2033i	−1.23600	−	0.898004i	−0.997325	+	0.0730962i	$0.976712\pi$
$368$	10.9347	+	33.6536i	0.570012	+	1.75432i
$369$	−4.74529	−	14.6045i	−0.247030	−	0.760280i
$370$	−48.8595	−	35.4985i	−2.54009	−	1.84548i
$371$	−9.52747	+	6.92211i	−0.494642	+	0.359378i
$372$	−21.0750	+	64.8622i	−1.09269	+	3.36295i
$373$	−6.59617			−0.341537			−0.170768	−	0.985311i	$-0.554625\pi$
$373$	−6.59617			−0.341537			−0.170768	+	0.985311i	$0.554625\pi$
$374$	−7.61156	+	3.49511i	−0.393584	+	0.180728i
$375$	24.9290			1.28733
$376$	−5.82701	+	17.9337i	−0.300505	+	0.924859i
$377$	6.16508	−	4.47919i	0.317518	−	0.230690i
$378$	6.18290	+	4.49214i	0.318014	+	0.231051i
$379$	7.23256	+	22.2595i	0.371511	+	1.14339i	0.945802	+	0.324743i	$0.105278\pi$
$379$	7.23256	+	22.2595i	0.371511	+	1.14339i	−0.574291	+	0.818651i	$0.694722\pi$
$380$	15.5564	+	47.8777i	0.798026	+	2.45607i
$381$	−16.8364	−	12.2324i	−0.862554	−	0.626682i
$382$	−12.7106	+	9.23482i	−0.650333	+	0.472495i
$383$	−2.27884	+	7.01355i	−0.116443	+	0.358376i	−0.992245	−	0.124295i	$-0.960333\pi$
$383$	−2.27884	+	7.01355i	−0.116443	+	0.358376i	0.875802	+	0.482671i	$0.160333\pi$
$384$	30.8887			1.57628
$385$	−0.973466	−	8.33205i	−0.0496124	−	0.424641i
$386$	−53.9331			−2.74512
$387$	−1.48800	+	4.57959i	−0.0756392	+	0.232794i
$388$	−2.03708	+	1.48003i	−0.103417	+	0.0751370i
$389$	3.22979	+	2.34658i	0.163757	+	0.118976i	0.666646	−	0.745375i	$-0.267729\pi$
$389$	3.22979	+	2.34658i	0.163757	+	0.118976i	−0.502889	+	0.864351i	$0.667729\pi$
$390$	3.50163	+	10.7769i	0.177312	+	0.545709i
$391$	1.70669	+	5.25264i	0.0863108	+	0.265637i
$392$	27.5484	+	20.0151i	1.39141	+	1.01092i
$393$	−2.72477	+	1.97966i	−0.137447	+	0.0998608i
$394$	−1.66186	+	5.11469i	−0.0837235	+	0.257675i
$395$	−7.59030			−0.381910
$396$	12.8156	−	22.8034i	0.644006	−	1.14591i
$397$	−3.81129			−0.191283			−0.0956417	−	0.995416i	$-0.530490\pi$
$397$	−3.81129			−0.191283			−0.0956417	+	0.995416i	$0.530490\pi$
$398$	−17.2562	+	53.1090i	−0.864973	+	2.66211i
$399$	−10.7072	+	7.77921i	−0.536029	+	0.389448i
$400$	0.953584	+	0.692819i	0.0476792	+	0.0346410i
$401$	−0.563344	−	1.73379i	−0.0281320	−	0.0865815i	0.936005	−	0.351987i	$-0.114494\pi$
$401$	−0.563344	−	1.73379i	−0.0281320	−	0.0865815i	−0.964137	+	0.265406i	$0.914494\pi$
$402$	−21.1145	−	64.9837i	−1.05309	−	3.24109i
$403$	5.36720	+	3.89950i	0.267359	+	0.194248i
$404$	−35.9567	+	26.1241i	−1.78891	+	1.29972i
$405$	−7.56747	+	23.2903i	−0.376031	+	1.15730i
$406$	−23.7704			−1.17971
$407$	35.4376	+	7.10437i	1.75658	+	0.352150i
$408$	−13.1561			−0.651325
$409$	−8.11062	+	24.9619i	−0.401044	+	1.23429i	0.523109	+	0.852266i	$0.324772\pi$
$409$	−8.11062	+	24.9619i	−0.401044	+	1.23429i	−0.924153	+	0.382022i	$0.875228\pi$
$410$	38.2136	−	27.7638i	1.88724	−	1.37116i
$411$	24.5183	+	17.8136i	1.20940	+	0.878678i
$412$	3.41123	+	10.4987i	0.168059	+	0.517234i
$413$	2.27675	+	7.00713i	0.112032	+	0.344798i
$414$	−20.3301	−	14.7706i	−0.999168	−	0.725938i
$415$	−7.53701	+	5.47596i	−0.369977	+	0.268804i
$416$	−1.20302	+	3.70253i	−0.0589831	+	0.181531i
$417$	3.34863			0.163983
$418$	−29.7452	−	32.2754i	−1.45489	−	1.57864i
$419$	9.22578			0.450709			0.225354	−	0.974277i	$-0.427646\pi$
$419$	9.22578			0.450709			0.225354	+	0.974277i	$0.427646\pi$
$420$	7.49719	−	23.0740i	0.365826	−	1.12590i
$421$	3.28289	−	2.38516i	0.159998	−	0.116246i	−0.504905	−	0.863175i	$-0.668473\pi$
$421$	3.28289	−	2.38516i	0.159998	−	0.116246i	0.664904	+	0.746929i	$0.268473\pi$
$422$	23.5349	+	17.0991i	1.14566	+	0.832370i
$423$	−1.74865	−	5.38180i	−0.0850224	−	0.261672i
$424$	−18.9573	−	58.3446i	−0.920648	−	2.83346i
$425$	0.148835	+	0.108135i	0.00721955	+	0.00524531i
$426$	64.9073	−	47.1579i	3.14477	−	2.28481i
$427$	0.724680	−	2.23034i	0.0350697	−	0.107933i
$428$	54.2259			2.62111
$429$	−4.59570	−	4.98662i	−0.221882	−	0.240756i
$430$	−14.8115			−0.714276
$431$	10.2948	−	31.6842i	0.495884	−	1.52617i	−0.319691	−	0.947522i	$-0.603579\pi$
$431$	10.2948	−	31.6842i	0.495884	−	1.52617i	0.815575	−	0.578652i	$-0.196421\pi$
$432$	−13.6103	+	9.88849i	−0.654828	+	0.475760i
$433$	9.95240	+	7.23084i	0.478282	+	0.347492i	0.800660	−	0.599119i	$-0.204482\pi$
$433$	9.95240	+	7.23084i	0.478282	+	0.347492i	−0.322378	+	0.946611i	$0.604482\pi$
$434$	−6.39482	−	19.6812i	−0.306961	−	0.944729i
$435$	−12.1363	−	37.3516i	−0.581889	−	1.79087i
$436$	46.2895	+	33.6313i	2.21686	+	1.61065i
$437$	−23.4149	+	17.0119i	−1.12009	+	0.813791i
$438$	1.47990	−	4.55467i	0.0707125	−	0.217631i
$439$	−8.90812			−0.425161			−0.212581	−	0.977144i	$-0.568187\pi$
$439$	−8.90812			−0.425161			−0.212581	+	0.977144i	$0.568187\pi$
$440$	42.8463	+	8.58964i	2.04262	+	0.409495i
$441$	−10.2187			−0.486606
$442$	−0.728160	+	2.24105i	−0.0346350	+	0.106596i
$443$	−18.1573	+	13.1920i	−0.862678	+	0.626772i	−0.928612	−	0.371052i	$-0.878997\pi$
$443$	−18.1573	+	13.1920i	−0.862678	+	0.626772i	0.0659340	+	0.997824i	$0.478997\pi$
$444$	84.5666	+	61.4412i	4.01335	+	2.91587i
$445$	−4.70648	−	14.4851i	−0.223109	−	0.686658i
$446$	1.71839	+	5.28865i	0.0813680	+	0.250425i
$447$	1.03226	+	0.749981i	0.0488243	+	0.0354729i
$448$	−2.12365	+	1.54292i	−0.100333	+	0.0728963i
$449$	8.20433	−	25.2503i	0.387186	−	1.19164i	−0.547695	−	0.836678i	$-0.684495\pi$
$449$	8.20433	−	25.2503i	0.387186	−	1.19164i	0.934882	−	0.354960i	$-0.115505\pi$
$450$	−0.837060			−0.0394594
$451$	−13.8492	+	24.6426i	−0.652135	+	1.16038i
$452$	−40.0832			−1.88535
$453$	0.558486	−	1.71884i	0.0262399	−	0.0807583i
$454$	22.9156	−	16.6492i	1.07548	−	0.781385i
$455$	−1.90932	−	1.38720i	−0.0895104	−	0.0650331i
$456$	−21.3046	−	65.5688i	−0.997679	−	3.07054i
$457$	10.9060	+	33.5652i	0.510161	+	1.57011i	0.791918	+	0.610628i	$0.209083\pi$
$457$	10.9060	+	33.5652i	0.510161	+	1.57011i	−0.281757	+	0.959486i	$0.590917\pi$
$458$	−18.1525	−	13.1886i	−0.848211	−	0.616262i
$459$	−2.12430	+	1.54339i	−0.0991536	+	0.0720393i
$460$	16.3952	−	50.4593i	0.764430	−	2.35267i
$461$	−39.0705			−1.81969			−0.909846	−	0.414945i	$-0.863801\pi$
$461$	−39.0705			−1.81969			−0.909846	+	0.414945i	$0.863801\pi$
$462$	2.45469	+	21.0101i	0.114203	+	0.977478i
$463$	29.8272			1.38619			0.693094	−	0.720847i	$-0.256247\pi$
$463$	29.8272			1.38619			0.693094	+	0.720847i	$0.256247\pi$
$464$	16.1695	−	49.7645i	0.750649	−	2.31026i
$465$	27.6611	−	20.0969i	1.28275	−	0.931973i
$466$	−11.8663	−	8.62136i	−0.549695	−	0.399377i
$467$	−2.44159	−	7.51444i	−0.112983	−	0.347727i	0.878538	−	0.477673i	$-0.158520\pi$
$467$	−2.44159	−	7.51444i	−0.112983	−	0.347727i	−0.991521	+	0.129946i	$0.958520\pi$
$468$	−2.27410	−	6.99896i	−0.105120	−	0.323527i
$469$	11.5130	+	8.36470i	0.531622	+	0.386246i
$470$	14.0818	−	10.2310i	0.649546	−	0.471923i
$471$	−0.787920	+	2.42497i	−0.0363054	+	0.111737i
$472$	−38.3803			−1.76659
$473$	8.05535	−	3.69889i	0.370385	−	0.170075i
$474$	19.1397			0.879116
$475$	−0.297915	+	0.916889i	−0.0136693	+	0.0420698i
$476$	4.08161	−	2.96546i	0.187080	−	0.135922i
$477$	14.8939	+	10.8211i	0.681947	+	0.495463i
$478$	−8.72550	−	26.8543i	−0.399095	−	1.22829i
$479$	−7.47025	−	22.9911i	−0.341324	−	1.05049i	−0.963522	−	0.267628i	$-0.913760\pi$
$479$	−7.47025	−	22.9911i	−0.341324	−	1.05049i	0.622198	−	0.782860i	$-0.286240\pi$
$480$	16.2320	+	11.7932i	0.740884	+	0.538284i
$481$	8.22628	−	5.97675i	0.375086	−	0.272516i
$482$	−8.55885	+	26.3414i	−0.389845	+	1.19982i
$483$	13.9484			0.634675
$484$	−46.8548	+	11.1000i	−2.12976	+	0.504544i
$485$	1.26234			0.0573200
$486$	12.9349	−	39.8094i	0.586737	−	1.80579i
$487$	13.7179	−	9.96663i	0.621617	−	0.451631i	−0.231869	−	0.972747i	$-0.574484\pi$
$487$	13.7179	−	9.96663i	0.621617	−	0.451631i	0.853486	+	0.521116i	$0.174484\pi$
$488$	9.88316	+	7.18053i	0.447390	+	0.325048i
$489$	−12.2712	−	37.7667i	−0.554921	−	1.70787i
$490$	−9.71314	−	29.8940i	−0.438795	−	1.35047i
$491$	26.9983	+	19.6154i	1.21841	+	0.885230i	0.995968	−	0.0897148i	$-0.0285955\pi$
$491$	26.9983	+	19.6154i	1.21841	+	0.885230i	0.222447	+	0.974945i	$0.428596\pi$
$492$	−66.1406	+	48.0540i	−2.98185	+	2.16644i
$493$	2.52372	−	7.76722i	0.113663	−	0.349818i
$494$	−12.3483			−0.555577
$495$	−11.9174	+	5.47230i	−0.535648	+	0.245962i
$496$	45.5536			2.04542
$497$	−5.16359	+	15.8919i	−0.231619	+	0.712850i
$498$	19.0053	−	13.8082i	0.851649	−	0.618759i
$499$	−27.3623	−	19.8799i	−1.22490	−	0.889945i	−0.228407	−	0.973566i	$-0.573352\pi$
$499$	−27.3623	−	19.8799i	−1.22490	−	0.889945i	−0.996498	+	0.0836209i	$0.973352\pi$
$500$	−15.3889	−	47.3622i	−0.688213	−	2.11810i
$501$	12.8552	+	39.5644i	0.574330	+	1.76761i
$502$	11.6374	+	8.45507i	0.519403	+	0.377368i
$503$	−1.58958	+	1.15490i	−0.0708759	+	0.0514944i	−0.622659	−	0.782493i	$-0.713948\pi$
$503$	−1.58958	+	1.15490i	−0.0708759	+	0.0514944i	0.551783	+	0.833988i	$0.313948\pi$
$504$	−3.85259	+	11.8571i	−0.171608	+	0.528156i
$505$	22.2817			0.991523
$506$	5.36803	+	45.9459i	0.238638	+	2.04254i
$507$	26.5788			1.18041
$508$	−12.8468	+	39.5383i	−0.569983	+	1.75423i
$509$	−25.7598	+	18.7156i	−1.14178	+	0.829553i	−0.987366	−	0.158453i	$-0.949349\pi$
$509$	−25.7598	+	18.7156i	−1.14178	+	0.829553i	−0.154415	+	0.988006i	$0.549349\pi$
$510$	9.82479	+	7.13813i	0.435049	+	0.316082i
$511$	0.308224	+	0.948617i	0.0136350	+	0.0419644i
$512$	−15.5131	−	47.7445i	−0.685590	−	2.11003i
$513$	−11.1321	−	8.08797i	−0.491496	−	0.357093i
$514$	−57.6792	+	41.9064i	−2.54412	+	1.84841i
$515$	1.71016	−	5.26334i	0.0753588	−	0.231930i
$516$	25.6360			1.12856
$517$	−5.10348	+	9.08088i	−0.224451	+	0.399376i
$518$	−31.7177			−1.39360
$519$	9.20368	−	28.3260i	0.403997	−	1.24337i
$520$	9.94611	−	7.22627i	0.436166	−	0.316893i
$521$	−3.52738	−	2.56279i	−0.154537	−	0.112278i	0.507830	−	0.861458i	$-0.330448\pi$
$521$	−3.52738	−	2.56279i	−0.154537	−	0.112278i	−0.662367	+	0.749180i	$0.730448\pi$
$522$	11.4829	+	35.3407i	0.502592	+	1.54682i
$523$	−4.54454	−	13.9866i	−0.198719	−	0.611593i	−0.999913	−	0.0131891i	$-0.995802\pi$
$523$	−4.54454	−	13.9866i	−0.198719	−	0.611593i	0.801194	−	0.598404i	$-0.204198\pi$
$524$	5.44315	+	3.95468i	0.237785	+	0.172761i
$525$	0.375888	−	0.273098i	0.0164051	−	0.0119190i
$526$	−10.9207	+	33.6105i	−0.476166	+	1.46549i
$527$	7.10998			0.309716
$528$	−45.6554	−	9.15279i	−1.98690	−	0.398324i
$529$	7.50301			0.326218
$530$	−17.4991	+	53.8566i	−0.760110	+	2.33938i
$531$	9.31801	−	6.76993i	0.404367	−	0.293790i
$532$	21.3892	+	15.5402i	0.927340	+	0.673752i
$533$	2.45752	+	7.56348i	0.106447	+	0.327611i
$534$	11.8679	+	36.5255i	0.513573	+	1.58061i
$535$	−21.9933	−	15.9791i	−0.950853	−	0.690835i
$536$	−59.9741	+	43.5737i	−2.59049	+	1.88210i
$537$	2.66798	−	8.21119i	0.115132	−	0.354339i
$538$	−69.4105			−2.99250
$539$	12.7480	+	13.8323i	0.549094	+	0.595801i
$540$	25.2244			1.08548
$541$	−0.0751054	+	0.231151i	−0.00322903	+	0.00993794i	−0.952658	−	0.304044i	$-0.901663\pi$
$541$	−0.0751054	+	0.231151i	−0.00322903	+	0.00993794i	0.949429	+	0.313982i	$0.101663\pi$
$542$	54.1714	−	39.3578i	2.32686	−	1.69056i
$543$	−5.04971	−	3.66883i	−0.216704	−	0.157444i
$544$	1.28930	+	3.96804i	0.0552781	+	0.170129i
$545$	−8.86407	−	27.2808i	−0.379695	−	1.16858i
$546$	4.81455	+	3.49797i	0.206044	+	0.149699i
$547$	22.1628	−	16.1022i	0.947613	−	0.688481i	−0.00262832	−	0.999997i	$-0.500837\pi$
$547$	22.1628	−	16.1022i	0.947613	−	0.688481i	0.950241	+	0.311516i	$0.100837\pi$
$548$	18.7083	−	57.5783i	0.799180	−	2.45962i
$549$	−3.66603			−0.156462
$550$	1.04424	+	1.13307i	0.0445266	+	0.0483141i
$551$	42.7979			1.82325
$552$	−22.4534	+	69.1043i	−0.955678	+	2.94128i
$553$	−3.22498	+	2.34309i	−0.137140	+	0.0996381i
$554$	−21.3641	−	15.5219i	−0.907673	−	0.659463i
$555$	−16.1938	−	49.8395i	−0.687390	−	2.11557i
$556$	−2.06714	−	6.36201i	−0.0876663	−	0.269809i
$557$	7.79635	+	5.66438i	0.330342	+	0.240007i	0.740576	−	0.671973i	$-0.234553\pi$
$557$	7.79635	+	5.66438i	0.330342	+	0.240007i	−0.410234	+	0.911980i	$0.634553\pi$
$558$	−26.1719	+	19.0150i	−1.10795	+	0.804969i
$559$	0.770615	−	2.37171i	0.0325935	−	0.100313i
$560$	−16.2052			−0.684793
$561$	−7.12588	−	1.42856i	−0.300855	−	0.0603140i
$562$	70.5434			2.97569
$563$	10.3844	−	31.9598i	0.437649	−	1.34695i	−0.452698	−	0.891664i	$-0.649538\pi$
$563$	10.3844	−	31.9598i	0.437649	−	1.34695i	0.890347	−	0.455282i	$-0.150462\pi$
$564$	−24.3730	+	17.7080i	−1.02629	+	0.745642i
$565$	16.2572	+	11.8115i	0.683946	+	0.496915i
$566$	−11.7156	−	36.0568i	−0.492442	−	1.51558i
$567$	3.97431	+	12.2317i	0.166905	+	0.513681i
$568$	−70.4209	−	51.1638i	−2.95480	−	2.14679i
$569$	37.1815	−	27.0140i	1.55873	−	1.13248i	0.621691	−	0.783262i	$-0.286446\pi$
$569$	37.1815	−	27.0140i	1.55873	−	1.13248i	0.937040	−	0.349222i	$-0.113554\pi$
$570$	−19.6658	+	60.5251i	−0.823709	+	2.53512i
$571$	−27.5033			−1.15098			−0.575488	−	0.817810i	$-0.695188\pi$
$571$	−27.5033			−1.15098			−0.575488	+	0.817810i	$0.695188\pi$
$572$	−6.63701	+	11.8096i	−0.277507	+	0.493783i
$573$	−13.6328			−0.569519
$574$	7.66573	−	23.5927i	0.319961	−	0.984740i
$575$	0.822008	−	0.597224i	0.0342801	−	0.0249060i
$576$	3.31983	+	2.41199i	0.138326	+	0.100500i
$577$	8.16678	+	25.1348i	0.339988	+	1.04637i	0.964213	+	0.265130i	$0.0854148\pi$
$577$	8.16678	+	25.1348i	0.339988	+	1.04637i	−0.624225	+	0.781244i	$0.714585\pi$
$578$	0.780378	+	2.40176i	0.0324594	+	0.0998999i
$579$	−37.8607	−	27.5074i	−1.57344	−	1.14317i
$580$	−63.4717	+	46.1149i	−2.63552	+	1.91482i
$581$	−1.51194	+	4.65327i	−0.0627258	+	0.193050i
$582$	−3.18312			−0.131945
$583$	−3.93266	−	33.6603i	−0.162874	−	1.39407i
$584$	−5.19588			−0.215007
$585$	−1.14008	+	3.50881i	−0.0471365	+	0.145071i
$586$	44.2213	−	32.1287i	1.82676	−	1.32722i
$587$	8.81002	+	6.40086i	0.363629	+	0.264192i	0.754564	−	0.656227i	$-0.227848\pi$
$587$	8.81002	+	6.40086i	0.363629	+	0.264192i	−0.390935	+	0.920418i	$0.627848\pi$
$588$	16.8116	+	51.7408i	0.693299	+	2.13376i
$589$	11.5137	+	35.4355i	0.474413	+	1.46009i
$590$	28.6618	+	20.8240i	1.17999	+	0.857312i
$591$	−3.77526	+	2.74289i	−0.155293	+	0.112827i
$592$	21.5755	−	66.4025i	0.886747	−	2.72913i
$593$	−33.9595			−1.39455			−0.697274	−	0.716804i	$-0.745604\pi$
$593$	−33.9595			−1.39455			−0.697274	+	0.716804i	$0.745604\pi$
$594$	−19.9862	+	9.17738i	−0.820045	+	0.376552i
$595$	−2.52930			−0.103691
$596$	0.787652	−	2.42414i	0.0322635	−	0.0992968i
$597$	−39.2008	+	28.4811i	−1.60438	+	1.16565i
$598$	10.5287	+	7.64953i	0.430549	+	0.312812i
$599$	2.22194	+	6.83842i	0.0907859	+	0.279410i	0.986133	−	0.165960i	$-0.0530722\pi$
$599$	2.22194	+	6.83842i	0.0907859	+	0.279410i	−0.895347	+	0.445370i	$0.853072\pi$
$600$	0.747923	+	2.30187i	0.0305338	+	0.0939735i
$601$	31.7058	+	23.0356i	1.29331	+	0.939641i	0.999867	−	0.0163364i	$-0.00520027\pi$
$601$	31.7058	+	23.0356i	1.29331	+	0.939641i	0.293439	+	0.955978i	$0.405200\pi$
$602$	−6.29316	+	4.57225i	−0.256490	+	0.186351i
$603$	6.87458	−	21.1578i	0.279955	−	0.861611i
$604$	−3.61036			−0.146903
$605$	22.2746	+	9.30498i	0.905590	+	0.378301i
$606$	−56.1856			−2.28238
$607$	4.67468	−	14.3872i	0.189739	−	0.583958i	−0.810258	−	0.586073i	$-0.800673\pi$
$607$	4.67468	−	14.3872i	0.189739	−	0.583958i	0.999998	+	0.00211516i	$0.000673277\pi$
$608$	−17.6885	+	12.8515i	−0.717364	+	0.521195i
$609$	−16.6867	−	12.1236i	−0.676179	−	0.491273i
$610$	−3.48464	−	10.7246i	−0.141089	−	0.434228i
$611$	0.905604	+	2.78716i	0.0366368	+	0.112757i
$612$	−6.38062	−	4.63579i	−0.257921	−	0.187391i
$613$	−20.1888	+	14.6680i	−0.815417	+	0.592435i	−0.915396	−	0.402554i	$-0.868123\pi$
$613$	−20.1888	+	14.6680i	−0.815417	+	0.592435i	0.0999787	+	0.994990i	$0.468123\pi$
$614$	4.38511	−	13.4960i	0.176969	−	0.544654i
$615$	40.9861			1.65272
$616$	20.8562	−	9.57685i	0.840320	−	0.385862i
$617$	2.44656			0.0984949			0.0492475	−	0.998787i	$-0.484318\pi$
$617$	2.44656			0.0984949			0.0492475	+	0.998787i	$0.484318\pi$
$618$	−4.31235	+	13.2720i	−0.173468	+	0.533880i
$619$	7.52094	−	5.46428i	0.302292	−	0.219628i	−0.426290	−	0.904587i	$-0.640180\pi$
$619$	7.52094	−	5.46428i	0.302292	−	0.219628i	0.728582	+	0.684958i	$0.240180\pi$
$620$	−55.2572	−	40.1467i	−2.21918	−	1.61233i
$621$	4.48137	+	13.7922i	0.179831	+	0.553464i
$622$	6.64055	+	20.4375i	0.266262	+	0.819470i
$623$	−6.47116	−	4.70157i	−0.259261	−	0.188364i
$624$	−10.5982	+	7.70004i	−0.424267	+	0.308248i
$625$	−7.43072	+	22.8694i	−0.297229	+	0.914776i
$626$	11.6581			0.465950
$627$	−4.41960	−	37.8281i	−0.176502	−	1.51071i
$628$	5.09354			0.203255
$629$	3.36749	−	10.3641i	0.134271	−	0.413243i
$630$	9.31036	−	6.76437i	0.370934	−	0.269499i
$631$	24.1508	+	17.5466i	0.961426	+	0.698517i	0.953482	−	0.301451i	$-0.0974711\pi$
$631$	24.1508	+	17.5466i	0.961426	+	0.698517i	0.00794481	+	0.999968i	$0.497471\pi$
$632$	−6.41691	−	19.7492i	−0.255251	−	0.785582i
$633$	7.80032	+	24.0069i	0.310035	+	0.954189i
$634$	2.41391	+	1.75380i	0.0958684	+	0.0696525i
$635$	16.8615	−	12.2506i	0.669127	−	0.486149i
$636$	30.2876	−	93.2155i	1.20098	−	3.69624i
$637$	5.29215			0.209682
$638$	33.5131	−	59.6315i	1.32680	−	2.36083i
$639$	26.1217			1.03336
$640$	−9.55934	+	29.4206i	−0.377866	+	1.16295i
$641$	−8.40805	+	6.10880i	−0.332098	+	0.241283i	−0.741320	−	0.671151i	$-0.765800\pi$
$641$	−8.40805	+	6.10880i	−0.332098	+	0.241283i	0.409222	+	0.912435i	$0.365800\pi$
$642$	55.4583	+	40.2928i	2.18876	+	1.59023i
$643$	7.32875	+	22.5556i	0.289018	+	0.889505i	0.985166	+	0.171607i	$0.0548958\pi$
$643$	7.32875	+	22.5556i	0.289018	+	0.889505i	−0.696148	+	0.717898i	$0.745104\pi$
$644$	−8.61048	−	26.5003i	−0.339300	−	1.04426i
$645$	−10.3976	−	7.55431i	−0.409406	−	0.297451i
$646$	−10.7064	+	7.77866i	−0.421238	+	0.306047i
$647$	−10.0523	+	30.9378i	−0.395196	+	1.21629i	0.533612	+	0.845729i	$0.320834\pi$
$647$	−10.0523	+	30.9378i	−0.395196	+	1.21629i	−0.928809	+	0.370560i	$0.879166\pi$
$648$	−66.9967			−2.63188
$649$	−20.7883	−	4.16754i	−0.816012	−	0.163590i
$650$	0.433502			0.0170034
$651$	5.54886	−	17.0776i	0.217477	−	0.669325i
$652$	−64.1772	+	46.6275i	−2.51337	+	1.82607i
$653$	−25.9313	−	18.8402i	−1.01477	−	0.737273i	−0.0495648	−	0.998771i	$-0.515783\pi$
$653$	−25.9313	−	18.8402i	−1.01477	−	0.737273i	−0.965204	+	0.261498i	$0.915783\pi$
$654$	22.3516	+	68.7913i	0.874018	+	2.68995i
$655$	−1.04232	−	3.20793i	−0.0407268	−	0.125344i
$656$	44.1779	+	32.0971i	1.72486	+	1.25318i
$657$	1.26146	−	0.916506i	0.0492143	−	0.0357563i
$658$	2.82484	−	8.69397i	0.110124	−	0.338926i
$659$	23.6624			0.921758			0.460879	−	0.887463i	$-0.347534\pi$
$659$	23.6624			0.921758			0.460879	+	0.887463i	$0.347534\pi$
$660$	47.3144	+	51.3390i	1.84171	+	1.99837i
$661$	16.3152			0.634587			0.317293	−	0.948327i	$-0.397226\pi$
$661$	16.3152			0.634587			0.317293	+	0.948327i	$0.397226\pi$
$662$	−5.45554	+	16.7904i	−0.212035	+	0.652578i
$663$	−1.65416	+	1.20182i	−0.0642423	+	0.0466748i
$664$	−20.6198	−	14.9811i	−0.800202	−	0.581381i
$665$	−4.09586	−	12.6058i	−0.158831	−	0.488831i
$666$	15.3220	+	47.1563i	0.593716	+	1.82727i
$667$	−36.4912	−	26.5124i	−1.41295	−	1.02657i
$668$	67.2320	−	48.8469i	2.60128	−	1.88994i
$669$	−1.49107	+	4.58903i	−0.0576479	+	0.177422i
$670$	68.4296			2.64367
$671$	4.57341	+	4.96243i	0.176555	+	0.191573i
$672$	10.5372			0.406480
$673$	−5.31716	+	16.3645i	−0.204962	+	0.630807i	0.794753	+	0.606932i	$0.207600\pi$
$673$	−5.31716	+	16.3645i	−0.204962	+	0.630807i	−0.999715	+	0.0238743i	$0.992400\pi$
$674$	−16.4671	+	11.9640i	−0.634288	+	0.460837i
$675$	0.390807	+	0.283938i	0.0150422	+	0.0109288i
$676$	−16.4074	−	50.4966i	−0.631052	−	1.94218i
$677$	−9.20760	−	28.3381i	−0.353877	−	1.08912i	−0.956658	−	0.291214i	$-0.905941\pi$
$677$	−9.20760	−	28.3381i	−0.353877	−	1.08912i	0.602781	−	0.797907i	$-0.294059\pi$
$678$	−40.9942	−	29.7840i	−1.57437	−	1.14385i
$679$	0.536346	−	0.389678i	0.0205831	−	0.0149545i
$680$	4.07152	−	12.5308i	0.156136	−	0.480536i
$681$	24.5782			0.941838
$682$	58.3890	+	11.7056i	2.23583	+	0.448229i
$683$	3.73978			0.143099			0.0715494	−	0.997437i	$-0.477206\pi$
$683$	3.73978			0.143099			0.0715494	+	0.997437i	$0.477206\pi$
$684$	12.7718	−	39.3075i	0.488341	−	1.50296i
$685$	−24.5548	+	17.8401i	−0.938190	+	0.681635i
$686$	−29.8379	−	21.6785i	−1.13922	−	0.827690i
$687$	−6.01641	−	18.5166i	−0.229540	−	0.706452i
$688$	−5.29139	−	16.2852i	−0.201732	−	0.620868i
$689$	−7.71338	−	5.60410i	−0.293856	−	0.213499i
$690$	54.2618	−	39.4235i	2.06571	−	1.50083i
$691$	−3.64059	+	11.2046i	−0.138494	+	0.426242i	−0.996117	−	0.0880373i	$-0.971941\pi$
$691$	−3.64059	+	11.2046i	−0.138494	+	0.426242i	0.857623	+	0.514279i	$0.171941\pi$
$692$	−59.4976			−2.26176
$693$	−3.37423	+	6.00393i	−0.128176	+	0.228070i
$694$	77.0073			2.92316
$695$	−1.03633	+	3.18948i	−0.0393101	+	0.120984i
$696$	86.9250	−	63.1547i	3.29488	−	2.39387i
$697$	6.89527	+	5.00971i	0.261177	+	0.189756i
$698$	6.18043	+	19.0214i	0.233933	+	0.719971i
$699$	−3.93292	−	12.1043i	−0.148757	−	0.457826i
$700$	−0.750893	−	0.545556i	−0.0283811	−	0.0206201i
$701$	8.50069	−	6.17611i	0.321067	−	0.233269i	−0.415564	−	0.909564i	$-0.636416\pi$
$701$	8.50069	−	6.17611i	0.321067	−	0.233269i	0.736631	+	0.676295i	$0.236416\pi$
$702$	−1.91198	+	5.88448i	−0.0721632	+	0.222095i
$703$	57.1068			2.15382
$704$	−0.876581	−	7.50279i	−0.0330374	−	0.282772i
$705$	15.1035			0.568830
$706$	−2.38033	+	7.32590i	−0.0895849	+	0.275714i
$707$	9.46709	−	6.87824i	0.356047	−	0.258683i
$708$	−49.6082	−	36.0425i	−1.86439	−	1.35456i
$709$	−1.27110	−	3.91205i	−0.0477373	−	0.146920i	0.924347	−	0.381554i	$-0.124611\pi$
$709$	−1.27110	−	3.91205i	−0.0477373	−	0.146920i	−0.972084	+	0.234634i	$0.924611\pi$
$710$	24.8293	+	76.4167i	0.931827	+	2.86787i
$711$	5.04149	+	3.66286i	0.189071	+	0.137368i
$712$	33.7098	−	24.4916i	1.26333	−	0.917862i
$713$	12.1345	−	37.3462i	0.454441	−	1.39862i
$714$	6.37787			0.238686
$715$	6.17188	−	2.83403i	0.230815	−	0.105987i
$716$	−17.2472			−0.644560
$717$	7.57122	−	23.3018i	0.282752	−	0.870223i
$718$	−3.77456	+	2.74238i	−0.140865	+	0.102345i
$719$	−5.27214	−	3.83043i	−0.196618	−	0.142851i	0.485121	−	0.874447i	$-0.338776\pi$
$719$	−5.27214	−	3.83043i	−0.196618	−	0.142851i	−0.681738	+	0.731596i	$0.738776\pi$
$720$	7.82831	+	24.0931i	0.291744	+	0.897895i
$721$	−0.898148	−	2.76421i	−0.0334488	−	0.102945i
$722$	−17.2877	−	12.5602i	−0.643380	−	0.467443i
$723$	−19.4431	+	14.1263i	−0.723098	+	0.525362i
$724$	−3.85311	+	11.8586i	−0.143200	+	0.440723i
$725$	−1.50247			−0.0558004
$726$	−56.1676	−	23.4635i	−2.08458	−	0.870811i
$727$	−37.6288			−1.39558			−0.697788	−	0.716304i	$-0.745832\pi$
$727$	−37.6288			−1.39558			−0.697788	+	0.716304i	$0.745832\pi$
$728$	1.99521	−	6.14062i	0.0739473	−	0.227587i
$729$	2.30074	−	1.67159i	0.0852127	−	0.0619107i
$730$	3.88020	+	2.81913i	0.143613	+	0.104341i
$731$	−0.825877	−	2.54179i	−0.0305462	−	0.0940115i
$732$	6.03126	+	18.5623i	0.222922	+	0.686083i
$733$	−37.2304	−	27.0495i	−1.37514	−	0.999096i	−0.997316	−	0.0732178i	$-0.976673\pi$
$733$	−37.2304	−	27.0495i	−1.37514	−	0.999096i	−0.377822	−	0.925878i	$-0.623327\pi$
$734$	−59.7961	+	43.4444i	−2.20711	+	1.60356i
$735$	8.42821	−	25.9394i	0.310879	−	0.956788i
$736$	23.0431			0.849381
$737$	−37.2159	+	17.0890i	−1.37086	+	0.629480i
$738$	−38.7796			−1.42750
$739$	−10.0687	+	30.9883i	−0.370383	+	1.13992i	0.576157	+	0.817339i	$0.304552\pi$
$739$	−10.0687	+	30.9883i	−0.370383	+	1.13992i	−0.946541	+	0.322584i	$0.895448\pi$
$740$	−84.6925	+	61.5327i	−3.11336	+	2.26199i
$741$	−8.66845	−	6.29799i	−0.318443	−	0.231363i
$742$	9.19020	+	28.2845i	0.337383	+	1.03836i
$743$	1.69619	+	5.22034i	0.0622273	+	0.191516i	0.977337	−	0.211689i	$-0.0678963\pi$
$743$	1.69619	+	5.22034i	0.0622273	+	0.191516i	−0.915110	+	0.403205i	$0.867896\pi$
$744$	75.6752	+	54.9812i	2.77439	+	2.01571i
$745$	−1.03380	+	0.751098i	−0.0378754	+	0.0275181i
$746$	−5.14750	+	15.8424i	−0.188464	+	0.580031i
$747$	7.64863			0.279849
$748$	1.68477	+	14.4202i	0.0616012	+	0.527254i
$749$	−14.2772			−0.521677
$750$	19.4541	−	59.8735i	0.710362	−	2.18627i
$751$	−29.1265	+	21.1617i	−1.06284	+	0.772200i	−0.974612	−	0.223900i	$-0.928121\pi$
$751$	−29.1265	+	21.1617i	−1.06284	+	0.772200i	−0.0882300	+	0.996100i	$0.528121\pi$
$752$	16.2797	+	11.8279i	0.593659	+	0.431318i
$753$	3.85706	+	11.8708i	0.140559	+	0.432597i
$754$	−5.94684	−	18.3025i	−0.216571	−	0.666537i
$755$	1.46431	+	1.06388i	0.0532918	+	0.0387187i
$756$	10.7174	−	7.78663i	0.389787	−	0.283197i
$757$	−5.86715	+	18.0572i	−0.213245	+	0.656302i	0.786028	+	0.618191i	$0.212134\pi$
$757$	−5.86715	+	18.0572i	−0.213245	+	0.656302i	−0.999274	+	0.0381109i	$0.987866\pi$
$758$	59.1061			2.14683
$759$	−19.6654	+	34.9916i	−0.713807	+	1.27011i
$760$	69.0458			2.50455
$761$	0.407462	−	1.25404i	0.0147705	−	0.0454589i	−0.943400	−	0.331658i	$-0.892392\pi$
$761$	0.407462	−	1.25404i	0.0147705	−	0.0454589i	0.958170	+	0.286199i	$0.0923919\pi$
$762$	−42.5179	+	30.8910i	−1.54026	+	1.11906i
$763$	−12.1876	−	8.85482i	−0.441221	−	0.320566i
$764$	8.41566	+	25.9007i	0.304468	+	0.937056i
$765$	1.22184	+	3.76043i	0.0441757	+	0.135959i
$766$	15.0665	+	10.9464i	0.544374	+	0.395511i
$767$	−4.82568	+	3.50606i	−0.174245	+	0.126596i
$768$	21.0204	−	64.6940i	0.758507	−	2.33444i
$769$	51.0730			1.84174			0.920870	−	0.389871i	$-0.127480\pi$
$769$	51.0730			1.84174			0.920870	+	0.389871i	$0.127480\pi$
$770$	−20.7712	−	4.16412i	−0.748543	−	0.150064i
$771$	−61.8640			−2.22798
$772$	−28.8891	+	88.9114i	−1.03974	+	3.19999i
$773$	8.31917	−	6.04423i	0.299220	−	0.217396i	−0.428037	−	0.903761i	$-0.640795\pi$
$773$	8.31917	−	6.04423i	0.299220	−	0.217396i	0.727257	+	0.686365i	$0.240795\pi$
$774$	9.83785	+	7.14762i	0.353614	+	0.256916i
$775$	−0.404201	−	1.24400i	−0.0145193	−	0.0446859i
$776$	1.06720	+	3.28449i	0.0383101	+	0.117906i
$777$	−22.2656	−	16.1769i	−0.798775	−	0.580344i
$778$	8.15638	−	5.92596i	0.292420	−	0.212456i
$779$	−13.8019	+	42.4779i	−0.494505	+	1.52193i
$780$	19.6419			0.703293
$781$	−32.5871	−	35.3590i	−1.16606	−	1.26525i
$782$	13.9474			0.498759
$783$	6.62673	−	20.3950i	0.236820	−	0.728857i
$784$	29.3983	−	21.3591i	1.04994	−	0.762825i
$785$	−2.06587	−	1.50094i	−0.0737342	−	0.0535710i
$786$	2.62832	+	8.08913i	0.0937489	+	0.288530i
$787$	9.98614	+	30.7342i	0.355968	+	1.09556i	0.955446	+	0.295165i	$0.0953745\pi$
$787$	9.98614	+	30.7342i	0.355968	+	1.09556i	−0.599479	+	0.800391i	$0.704625\pi$
$788$	7.54166	+	5.47934i	0.268661	+	0.195193i
$789$	−24.8086	+	18.0245i	−0.883210	+	0.641690i
$790$	−5.92330	+	18.2301i	−0.210742	+	0.648596i
$791$	10.5535			0.375241
$792$	−24.3135	−	26.3816i	−0.863942	−	0.937431i
$793$	1.89859			0.0674208
$794$	−2.97425	+	9.15380i	−0.105552	+	0.324856i
$795$	−39.7526	+	28.8820i	−1.40988	+	1.02434i
$796$	78.3097	+	56.8953i	2.77561	+	2.01660i
$797$	−15.7126	−	48.3585i	−0.556570	−	1.71295i	−0.691761	−	0.722127i	$-0.743165\pi$
$797$	−15.7126	−	48.3585i	−0.556570	−	1.71295i	0.135191	−	0.990820i	$-0.456835\pi$
$798$	10.3281	+	31.7867i	0.365612	+	1.12524i
$799$	2.54092	+	1.84609i	0.0898915	+	0.0653100i
$800$	0.620976	−	0.451166i	0.0219548	−	0.0159511i
$801$	−3.86401	+	11.8922i	−0.136528	+	0.420191i
$802$	−4.60377			−0.162565
$803$	−2.81430	−	0.564197i	−0.0993143	−	0.0199101i
$804$	−118.439			−4.17701
$805$	−4.31671	+	13.2855i	−0.152144	+	0.468252i
$806$	13.5541	−	9.84762i	0.477422	−	0.346868i
$807$	−48.7257	−	35.4013i	−1.71523	−	1.24619i
$808$	18.8372	+	57.9748i	0.662689	+	2.03955i
$809$	15.5615	+	47.8934i	0.547113	+	1.68384i	0.715911	+	0.698191i	$0.246012\pi$
$809$	15.5615	+	47.8934i	0.547113	+	1.68384i	−0.168798	+	0.985651i	$0.553988\pi$
$810$	50.0321	+	36.3505i	1.75795	+	1.27722i
$811$	9.60035	−	6.97506i	0.337114	−	0.244928i	−0.406329	−	0.913727i	$-0.633191\pi$
$811$	9.60035	−	6.97506i	0.337114	−	0.244928i	0.743443	+	0.668799i	$0.233191\pi$
$812$	−12.7325	+	39.1867i	−0.446825	+	1.37519i
$813$	58.1016			2.03771
$814$	44.7177	−	79.5684i	1.56735	−	2.78887i
$815$	39.7694			1.39306
$816$	−4.33845	+	13.3524i	−0.151876	+	0.467427i
$817$	11.3306	−	8.23219i	0.396409	−	0.288008i
$818$	53.6231	+	38.9595i	1.87489	+	1.36219i
$819$	0.598751	+	1.84276i	0.0209220	+	0.0643914i
$820$	−25.3011	−	77.8687i	−0.883552	−	2.71929i
$821$	−17.1688	−	12.4739i	−0.599197	−	0.435342i	0.246397	−	0.969169i	$-0.420753\pi$
$821$	−17.1688	−	12.4739i	−0.599197	−	0.435342i	−0.845594	+	0.533827i	$0.820753\pi$
$822$	61.9173	−	44.9856i	2.15962	−	1.56905i
$823$	7.06709	−	21.7503i	0.246343	−	0.758167i	−0.749069	−	0.662492i	$-0.769499\pi$
$823$	7.06709	−	21.7503i	0.246343	−	0.758167i	0.995413	−	0.0956751i	$-0.0305010\pi$
$824$	15.1405			0.527444
$825$	0.155155	+	1.32800i	0.00540181	+	0.0462350i
$826$	18.6061			0.647390
$827$	−0.601301	+	1.85061i	−0.0209093	+	0.0643521i	−0.960967	−	0.276664i	$-0.910771\pi$
$827$	−0.601301	+	1.85061i	−0.0209093	+	0.0643521i	0.940057	+	0.341016i	$0.110771\pi$
$828$	−35.2399	+	25.6033i	−1.22467	+	0.889775i
$829$	−4.22266	−	3.06794i	−0.146659	−	0.106554i	0.512036	−	0.858964i	$-0.328891\pi$
$829$	−4.22266	−	3.06794i	−0.146659	−	0.106554i	−0.658695	+	0.752410i	$0.728891\pi$
$830$	7.27020	+	22.3754i	0.252352	+	0.776661i
$831$	−7.08084	−	21.7926i	−0.245632	−	0.755976i
$832$	−1.71929	−	1.24914i	−0.0596058	−	0.0433061i
$833$	4.58847	−	3.33372i	0.158981	−	0.115506i
$834$	2.61320	−	8.04260i	0.0904877	−	0.278493i
$835$	−41.6624			−1.44179
$836$	−69.1406	+	31.7483i	−2.39128	+	1.09804i
$837$	18.6692			0.645302
$838$	7.19960	−	22.1581i	0.248706	−	0.765438i
$839$	−8.43498	+	6.12837i	−0.291208	+	0.211575i	−0.723791	−	0.690019i	$-0.757602\pi$
$839$	−8.43498	+	6.12837i	−0.291208	+	0.211575i	0.432583	+	0.901594i	$0.357602\pi$
$840$	−26.9206	−	19.5590i	−0.928849	−	0.674848i
$841$	11.6496	+	35.8538i	0.401711	+	1.23634i
$842$	−3.16668	−	9.74604i	−0.109131	−	0.335871i
$843$	49.5210	+	35.9791i	1.70560	+	1.23919i
$844$	40.7951	−	29.6394i	1.40422	−	1.02023i
$845$	−8.22554	+	25.3156i	−0.282967	+	0.870884i
$846$	−14.2904			−0.491313
$847$	12.3365	−	2.92253i	0.423886	−	0.100419i
$848$	−65.4665			−2.24813
$849$	10.1657	−	31.2869i	0.348887	−	1.07377i
$850$	0.375861	−	0.273079i	0.0128919	−	0.00936654i
$851$	−48.6915	−	35.3765i	−1.66912	−	1.21269i
$852$	−42.9748	−	132.263i	−1.47229	−	4.53125i
$853$	6.02374	+	18.5392i	0.206249	+	0.634769i	0.999660	+	0.0260827i	$0.00830332\pi$
$853$	6.02374	+	18.5392i	0.206249	+	0.634769i	−0.793411	+	0.608687i	$0.791697\pi$
$854$	−4.79120	−	3.48101i	−0.163951	−	0.119118i
$855$	−16.7630	+	12.1791i	−0.573284	+	0.416515i
$856$	22.9826	−	70.7332i	0.785530	−	2.41761i
$857$	−7.84888			−0.268113			−0.134056	−	0.990974i	$-0.542800\pi$
$857$	−7.84888			−0.268113			−0.134056	+	0.990974i	$0.542800\pi$
$858$	−15.5630	+	7.14630i	−0.531313	+	0.243971i
$859$	0.0377652			0.00128853			0.000644266	−	1.00000i	$-0.499795\pi$
$859$	0.0377652			0.00128853			0.000644266		1.00000i	$0.499795\pi$
$860$	−7.93375	+	24.4176i	−0.270539	+	0.832633i
$861$	17.4142	−	12.6522i	0.593476	−	0.431185i
$862$	−68.0639	−	49.4513i	−2.31826	−	1.68432i
$863$	1.82031	+	5.60235i	0.0619642	+	0.190706i	0.977246	−	0.212107i	$-0.0680325\pi$
$863$	1.82031	+	5.60235i	0.0619642	+	0.190706i	−0.915282	+	0.402813i	$0.868032\pi$
$864$	3.38540	+	10.4192i	0.115174	+	0.354468i
$865$	24.1314	+	17.5325i	0.820493	+	0.596123i
$866$	25.1334	−	18.2605i	0.854066	−	0.620516i
$867$	−0.677143	+	2.08403i	−0.0229970	+	0.0707775i
$868$	−35.8709			−1.21754
$869$	−1.33118	−	11.3938i	−0.0451571	−	0.386507i
$870$	−99.1802			−3.36252
$871$	−3.56026	+	10.9573i	−0.120635	+	0.371275i
$872$	63.4882	−	46.1269i	2.14998	−	1.56205i
$873$	−0.838450	−	0.609169i	−0.0283772	−	0.0206173i
$874$	22.5860	+	69.5126i	0.763984	+	2.35130i
$875$	4.05177	+	12.4701i	0.136975	+	0.421565i
$876$	−6.71590	−	4.87939i	−0.226909	−	0.164859i
$877$	12.7675	−	9.27616i	0.431129	−	0.313234i	−0.350971	−	0.936386i	$-0.614148\pi$
$877$	12.7675	−	9.27616i	0.431129	−	0.313234i	0.782100	+	0.623153i	$0.214148\pi$
$878$	−6.95170	+	21.3951i	−0.234608	+	0.722051i
$879$	47.4296			1.59976
$880$	22.8471	−	40.6530i	0.770175	−	1.37041i
$881$	−47.0114			−1.58385			−0.791927	−	0.610616i	$-0.790922\pi$
$881$	−47.0114			−1.58385			−0.791927	+	0.610616i	$0.790922\pi$
$882$	−7.97447	+	24.5429i	−0.268514	+	0.826402i
$883$	27.6888	−	20.1171i	0.931803	−	0.676995i	−0.0146304	−	0.999893i	$-0.504657\pi$
$883$	27.6888	−	20.1171i	0.931803	−	0.676995i	0.946434	+	0.322898i	$0.104657\pi$
$884$	3.30444	+	2.40082i	0.111140	+	0.0807482i
$885$	9.49957	+	29.2367i	0.319325	+	0.982780i
$886$	17.5145	+	53.9041i	0.588412	+	1.81094i
$887$	24.1347	+	17.5349i	0.810364	+	0.588764i	0.913936	−	0.405858i	$-0.133027\pi$
$887$	24.1347	+	17.5349i	0.810364	+	0.588764i	−0.103572	+	0.994622i	$0.533027\pi$
$888$	115.987	−	84.2695i	3.89227	−	2.82790i
$889$	3.38244	−	10.4101i	0.113443	−	0.349143i
$890$	−38.4624			−1.28926
$891$	−36.2881	−	7.27487i	−1.21570	−	0.243717i
$892$	9.63906			0.322740
$893$	−5.08604	+	15.6532i	−0.170198	+	0.523815i
$894$	2.60683	−	1.89397i	0.0871853	−	0.0633438i
$895$	6.99525	+	5.08235i	0.233826	+	0.169884i
$896$	5.02040	+	15.4512i	0.167720	+	0.516188i
$897$	3.48959	+	10.7398i	0.116514	+	0.358593i
$898$	−54.2427	−	39.4096i	−1.81010	−	1.31512i
$899$	−46.9770	+	34.1308i	−1.56677	+	1.13833i
$900$	−0.448368	+	1.37994i	−0.0149456	+	0.0459979i
$901$	−10.2180			−0.340410
$902$	48.3780	+	52.4931i	1.61081	+	1.74783i
$903$	−6.74973			−0.224617
$904$	−16.9885	+	52.2852i	−0.565029	+	1.73898i
$905$	5.05723	−	3.67429i	0.168108	−	0.122138i
$906$	−3.69241	−	2.68269i	−0.122672	−	0.0891265i
$907$	−6.02576	−	18.5454i	−0.200082	−	0.615790i	−0.999880	−	0.0155195i	$-0.995060\pi$
$907$	−6.02576	−	18.5454i	−0.200082	−	0.615790i	0.799797	−	0.600270i	$-0.204940\pi$
$908$	−15.1723	−	46.6957i	−0.503512	−	1.54965i
$909$	−14.7995	−	10.7525i	−0.490870	−	0.356638i
$910$	−4.82172	+	3.50318i	−0.159838	+	0.116129i
$911$	−14.3767	+	44.2469i	−0.476321	+	1.46597i	0.367846	+	0.929887i	$0.380095\pi$
$911$	−14.3767	+	44.2469i	−0.476321	+	1.46597i	−0.844167	+	0.536080i	$0.819905\pi$
$912$	−73.5726			−2.43623
$913$	−9.54176	−	10.3534i	−0.315786	−	0.342647i
$914$	89.1262			2.94803
$915$	3.02367	−	9.30589i	0.0999594	−	0.307643i
$916$	−31.4654	+	22.8609i	−1.03964	+	0.755346i
$917$	−1.43313	−	1.04123i	−0.0473263	−	0.0343845i
$918$	2.04910	+	6.30647i	0.0676302	+	0.208145i
$919$	2.85110	+	8.77480i	0.0940493	+	0.289454i	0.987005	−	0.160691i	$-0.0513723\pi$
$919$	2.85110	+	8.77480i	0.0940493	+	0.289454i	−0.892955	+	0.450145i	$0.851372\pi$
$920$	−58.8712	−	42.7724i	−1.94093	−	1.41016i
$921$	9.96166	−	7.23757i	0.328248	−	0.238486i
$922$	−30.4897	+	93.8377i	−1.00413	+	3.09038i
$923$	−13.5281			−0.445283
$924$	35.9511	+	7.20731i	1.18270	+	0.237103i
$925$	−2.00480			−0.0659175
$926$	23.2765	−	71.6377i	0.764913	−	2.35416i
$927$	−3.67583	+	2.67064i	−0.120730	+	0.0877155i
$928$	−27.5669	−	20.0285i	−0.904927	−	0.657468i
$929$	−9.53845	−	29.3563i	−0.312947	−	0.963150i	−0.976591	−	0.215103i	$-0.930991\pi$
$929$	−9.53845	−	29.3563i	−0.312947	−	0.963150i	0.663645	−	0.748048i	$-0.269009\pi$
$930$	−26.6819	−	82.1183i	−0.874933	−	2.69277i
$931$	24.0454	+	17.4700i	0.788055	+	0.572555i
$932$	−20.5689	+	14.9442i	−0.673756	+	0.489512i
$933$	−5.76209	+	17.7339i	−0.188642	+	0.580581i
$934$	−19.9532			−0.652889
$935$	3.56596	−	6.34510i	0.116619	−	0.207507i
$936$	−10.0934			−0.329913
$937$	−0.398007	+	1.22494i	−0.0130023	+	0.0400170i	−0.957347	−	0.288940i	$-0.906697\pi$
$937$	−0.398007	+	1.22494i	−0.0130023	+	0.0400170i	0.944345	+	0.328957i	$0.106697\pi$
$938$	29.0745	−	21.1239i	0.949316	−	0.689718i
$939$	8.18390	+	5.94595i	0.267071	+	0.194039i
$940$	−9.32351	−	28.6948i	−0.304100	−	0.935922i
$941$	5.49943	+	16.9255i	0.179276	+	0.551756i	0.999803	−	0.0198527i	$-0.00631973\pi$
$941$	5.49943	+	16.9255i	0.179276	+	0.551756i	−0.820527	+	0.571608i	$0.806320\pi$
$942$	5.20931	+	3.78478i	0.169728	+	0.123315i
$943$	38.0822	−	27.6684i	1.24013	−	0.901006i
$944$	−12.6565	+	38.9528i	−0.411935	+	1.26781i
$945$	−6.64136			−0.216043
$946$	−2.59763	−	22.2335i	−0.0844562	−	0.722874i
$947$	53.3660			1.73416			0.867081	−	0.498168i	$-0.165994\pi$
$947$	53.3660			1.73416			0.867081	+	0.498168i	$0.165994\pi$
$948$	10.2521	−	31.5528i	0.332973	−	1.02479i
$949$	−0.653295	+	0.474646i	−0.0212068	+	0.0154077i
$950$	1.96966	+	1.43104i	0.0639042	+	0.0464291i
$951$	0.800057	+	2.46232i	0.0259436	+	0.0798462i
$952$	−2.13829	−	6.58098i	−0.0693024	−	0.213291i
$953$	−32.9166	−	23.9153i	−1.06627	−	0.774692i	−0.0910336	−	0.995848i	$-0.529017\pi$
$953$	−32.9166	−	23.9153i	−1.06627	−	0.774692i	−0.975238	+	0.221156i	$0.929017\pi$
$954$	37.6125	−	27.3271i	1.21775	−	0.884747i
$955$	4.21905	−	12.9849i	0.136525	−	0.420181i
$956$	−48.9445			−1.58298
$957$	53.9397	−	24.7683i	1.74362	−	0.800646i
$958$	−61.0485			−1.97239
$959$	−4.92574	+	15.1599i	−0.159060	+	0.489537i
$960$	−8.86077	+	6.43772i	−0.285980	+	0.207777i
$961$	−15.8177	−	11.4923i	−0.510249	−	0.370718i
$962$	−7.93508	−	24.4217i	−0.255837	−	0.787386i
$963$	6.89695	+	21.2266i	0.222251	+	0.684019i
$964$	38.8407	+	28.2194i	1.25097	+	0.908885i
$965$	37.9171	−	27.5484i	1.22059	−	0.886813i
$966$	10.8850	−	33.5007i	0.350220	−	1.07787i
$967$	−41.1474			−1.32321			−0.661606	−	0.749852i	$-0.730125\pi$
$967$	−41.1474			−1.32321			−0.661606	+	0.749852i	$0.730125\pi$
$968$	−5.37952	+	65.8228i	−0.172904	+	2.11562i
$969$	−11.4832			−0.368893
$970$	0.985104	−	3.03184i	0.0316298	−	0.0973465i
$971$	−6.61246	+	4.80423i	−0.212204	+	0.154175i	−0.688810	−	0.724942i	$-0.741867\pi$
$971$	−6.61246	+	4.80423i	−0.212204	+	0.154175i	0.476606	+	0.879117i	$0.341867\pi$
$972$	−58.6993	−	42.6475i	−1.88278	−	1.36792i
$973$	0.544260	+	1.67506i	0.0174482	+	0.0537000i
$974$	−13.2323	−	40.7248i	−0.423989	−	1.30491i
$975$	0.304316	+	0.221099i	0.00974592	+	0.00708082i
$976$	10.5468	−	7.66270i	0.337595	−	0.245277i
$977$	17.4398	−	53.6742i	0.557949	−	1.71719i	−0.130077	−	0.991504i	$-0.541522\pi$
$977$	17.4398	−	53.6742i	0.557949	−	1.71719i	0.688026	−	0.725686i	$-0.258478\pi$
$978$	−100.283			−3.20668
$979$	20.9180	−	9.60524i	0.668543	−	0.306985i
$980$	−54.4845			−1.74044
$981$	−7.27738	+	22.3975i	−0.232349	+	0.715097i
$982$	68.1802	−	49.5358i	2.17572	−	1.58075i
$983$	−18.8536	−	13.6980i	−0.601338	−	0.436897i	0.245016	−	0.969519i	$-0.421207\pi$
$983$	−18.8536	−	13.6980i	−0.601338	−	0.436897i	−0.846353	+	0.532622i	$0.821207\pi$
$984$	34.6500	+	106.642i	1.10460	+	3.39962i
$985$	−1.44417	−	4.44469i	−0.0460150	−	0.141620i
$986$	−16.6855	−	12.1227i	−0.531375	−	0.386067i
$987$	6.41719	−	4.66236i	0.204261	−	0.148405i
$988$	−6.61434	+	20.3568i	−0.210430	+	0.647637i
$989$	−14.7606			−0.469360
$990$	3.84304	+	32.8932i	0.122140	+	1.04542i
$991$	50.2750			1.59704			0.798519	−	0.601970i	$-0.205617\pi$
$991$	50.2750			1.59704			0.798519	+	0.601970i	$0.205617\pi$
$992$	9.16687	−	28.2127i	0.291048	−	0.895754i
$993$	−12.3933	+	9.00429i	−0.393291	+	0.285742i
$994$	34.1389	+	24.8034i	1.08282	+	0.786716i
$995$	−14.9957	−	46.1520i	−0.475395	−	1.46312i
$996$	−12.5833	−	38.7276i	−0.398719	−	1.22713i
$997$	−30.8358	−	22.4035i	−0.976580	−	0.709527i	−0.0196385	−	0.999807i	$-0.506252\pi$
$997$	−30.8358	−	22.4035i	−0.976580	−	0.709527i	−0.956942	+	0.290280i	$0.906252\pi$
$998$	−69.0995	+	50.2037i	−2.18731	+	1.58917i
$999$	8.84227	−	27.2137i	0.279757	−	0.861004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.86.9	✓	36
11.4	even	5		2057.2.a.bd.1.17		18
11.5	even	5	inner	187.2.g.f.137.9	yes	36
11.7	odd	10		2057.2.a.be.1.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.86.9	✓	36	1.1	even	1	trivial
187.2.g.f.137.9	yes	36	11.5	even	5	inner
2057.2.a.bd.1.17		18	11.4	even	5
2057.2.a.be.1.2		18	11.7	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.780378 - 2.40176i) q^{2} +(1.77278 - 1.28800i) q^{3} +(-3.54141 - 2.57299i) q^{4} +(0.678152 + 2.08714i) q^{5} +(-1.71003 - 5.26293i) q^{6} +(0.932422 + 0.677444i) q^{7} +(-4.85721 + 3.52897i) q^{8} +(0.556762 - 1.71354i) q^{9} +O(q^{10})\)	\(q+(0.780378 - 2.40176i) q^{2} +(1.77278 - 1.28800i) q^{3} +(-3.54141 - 2.57299i) q^{4} +(0.678152 + 2.08714i) q^{5} +(-1.71003 - 5.26293i) q^{6} +(0.932422 + 0.677444i) q^{7} +(-4.85721 + 3.52897i) q^{8} +(0.556762 - 1.71354i) q^{9} +5.54201 q^{10} +(-3.01405 + 1.38401i) q^{11} -9.59217 q^{12} +(-0.288340 + 0.887418i) q^{13} +(2.35470 - 1.71079i) q^{14} +(3.89046 + 2.82658i) q^{15} +(1.97987 + 6.09341i) q^{16} +(0.309017 + 0.951057i) q^{17} +(-3.68101 - 2.67441i) q^{18} +(-4.23956 + 3.08022i) q^{19} +(2.96856 - 9.13628i) q^{20} +2.52553 q^{21} +(0.971950 + 8.31907i) q^{22} +5.52295 q^{23} +(-4.06546 + 12.5122i) q^{24} +(0.148835 - 0.108135i) q^{25} +(1.90635 + 1.38504i) q^{26} +(0.811409 + 2.49726i) q^{27} +(-1.55903 - 4.79822i) q^{28} +(-6.60719 - 4.80041i) q^{29} +(9.82479 - 7.13813i) q^{30} +(2.19710 - 6.76199i) q^{31} +4.17225 q^{32} +(-3.56066 + 6.33566i) q^{33} +2.52536 q^{34} +(-0.781595 + 2.40550i) q^{35} +(-6.38062 + 4.63579i) q^{36} +(-8.81621 - 6.40535i) q^{37} +(4.08948 + 12.5861i) q^{38} +(0.631833 + 1.94458i) q^{39} +(-10.6594 - 7.74448i) q^{40} +(6.89527 - 5.00971i) q^{41} +(1.97087 - 6.06572i) q^{42} -2.67260 q^{43} +(14.2350 + 2.85377i) q^{44} +3.95395 q^{45} +(4.30999 - 13.2648i) q^{46} +(2.54092 - 1.84609i) q^{47} +(11.3582 + 8.25223i) q^{48} +(-1.75264 - 5.39407i) q^{49} +(-0.143566 - 0.441851i) q^{50} +(1.77278 + 1.28800i) q^{51} +(3.30444 - 2.40082i) q^{52} +(-3.15753 + 9.71788i) q^{53} +6.63101 q^{54} +(-4.93260 - 5.35218i) q^{55} -6.91965 q^{56} +(-3.54849 + 10.9211i) q^{57} +(-16.6855 + 12.1227i) q^{58} +(5.17174 + 3.75749i) q^{59} +(-6.50495 - 20.0202i) q^{60} +(-0.628769 - 1.93515i) q^{61} +(-14.5261 - 10.5538i) q^{62} +(1.67996 - 1.22056i) q^{63} +(-0.703806 + 2.16609i) q^{64} -2.04770 q^{65} +(12.4381 + 13.4961i) q^{66} +12.3474 q^{67} +(1.35270 - 4.16318i) q^{68} +(9.79101 - 7.11358i) q^{69} +(5.16749 + 3.75440i) q^{70} +(4.48020 + 13.7886i) q^{71} +(3.34271 + 10.2878i) q^{72} +(0.700144 + 0.508684i) q^{73} +(-22.2641 + 16.1758i) q^{74} +(0.124574 - 0.383400i) q^{75} +22.9394 q^{76} +(-3.74796 - 0.751374i) q^{77} +5.16348 q^{78} +(-1.06880 + 3.28943i) q^{79} +(-11.3751 + 8.26451i) q^{80} +(9.02779 + 6.55908i) q^{81} +(-6.65118 - 20.4702i) q^{82} +(1.31184 + 4.03741i) q^{83} +(-8.94395 - 6.49816i) q^{84} +(-1.77542 + 1.28992i) q^{85} +(-2.08563 + 6.41892i) q^{86} -17.8961 q^{87} +(9.75577 - 17.3589i) q^{88} -6.94016 q^{89} +(3.08558 - 9.49643i) q^{90} +(-0.870030 + 0.632114i) q^{91} +(-19.5590 - 14.2105i) q^{92} +(-4.81448 - 14.8174i) q^{93} +(-2.45098 - 7.54333i) q^{94} +(-9.30391 - 6.75969i) q^{95} +(7.39650 - 5.37387i) q^{96} +(0.177752 - 0.547065i) q^{97} -14.3230 q^{98} +(0.693438 + 5.93525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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