LMFDB - Embedded newform 187.2.g.f.103.7

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			103.7
Character	$\chi$	$=$	187.103
Dual form			187.2.g.f.69.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31285 + 0.953841i) q^{2} +(-0.637980 + 1.96350i) q^{3} +(0.195728 + 0.602389i) q^{4} +(-2.95777 + 2.14895i) q^{5} +(-2.71044 + 1.96925i) q^{6} +(-0.195368 - 0.601281i) q^{7} +(0.685306 - 2.10916i) q^{8} +(-1.02126 - 0.741992i) q^{9} +O(q^{10})$	\(q+(1.31285 + 0.953841i) q^{2} +(-0.637980 + 1.96350i) q^{3} +(0.195728 + 0.602389i) q^{4} +(-2.95777 + 2.14895i) q^{5} +(-2.71044 + 1.96925i) q^{6} +(-0.195368 - 0.601281i) q^{7} +(0.685306 - 2.10916i) q^{8} +(-1.02126 - 0.741992i) q^{9} -5.93286 q^{10} +(2.30503 + 2.38471i) q^{11} -1.30766 q^{12} +(2.34407 + 1.70307i) q^{13} +(0.317038 - 0.975742i) q^{14} +(-2.33246 - 7.17857i) q^{15} +(3.93635 - 2.85993i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(-0.633025 - 1.94825i) q^{18} +(-0.402129 + 1.23762i) q^{19} +(-1.87342 - 1.36112i) q^{20} +1.30526 q^{21} +(0.751525 + 5.32940i) q^{22} +7.02655 q^{23} +(3.70412 + 2.69120i) q^{24} +(2.58535 - 7.95689i) q^{25} +(1.45296 + 4.47175i) q^{26} +(-2.90231 + 2.10865i) q^{27} +(0.323966 - 0.235375i) q^{28} +(0.765286 + 2.35531i) q^{29} +(3.78505 - 11.6492i) q^{30} +(-4.76789 - 3.46408i) q^{31} +3.46036 q^{32} +(-6.15294 + 3.00453i) q^{33} -1.62277 q^{34} +(1.86997 + 1.35862i) q^{35} +(0.247078 - 0.760427i) q^{36} +(-2.36020 - 7.26393i) q^{37} +(-1.70843 + 1.24125i) q^{38} +(-4.83945 + 3.51606i) q^{39} +(2.50548 + 7.71108i) q^{40} +(0.293175 - 0.902299i) q^{41} +(1.71361 + 1.24501i) q^{42} -4.42018 q^{43} +(-0.985363 + 1.85528i) q^{44} +4.61517 q^{45} +(9.22481 + 6.70221i) q^{46} +(3.13069 - 9.63528i) q^{47} +(3.10415 + 9.55360i) q^{48} +(5.33975 - 3.87955i) q^{49} +(10.9838 - 7.98019i) q^{50} +(-0.637980 - 1.96350i) q^{51} +(-0.567109 + 1.74538i) q^{52} +(5.04208 + 3.66329i) q^{53} -5.82162 q^{54} +(-11.9424 - 2.10004i) q^{55} -1.40208 q^{56} +(-2.17353 - 1.57916i) q^{57} +(-1.24189 + 3.82213i) q^{58} +(2.04423 + 6.29149i) q^{59} +(3.86776 - 2.81009i) q^{60} +(10.5010 - 7.62941i) q^{61} +(-2.95535 - 9.09562i) q^{62} +(-0.246623 + 0.759028i) q^{63} +(-3.32977 - 2.41922i) q^{64} -10.5930 q^{65} +(-10.9437 - 1.92443i) q^{66} -5.11549 q^{67} +(-0.512423 - 0.372297i) q^{68} +(-4.48280 + 13.7966i) q^{69} +(1.15909 + 3.56732i) q^{70} +(-2.70418 + 1.96470i) q^{71} +(-2.26486 + 1.64551i) q^{72} +(-1.64861 - 5.07389i) q^{73} +(3.83006 - 11.7877i) q^{74} +(13.9740 + 10.1527i) q^{75} -0.824239 q^{76} +(0.983551 - 1.85187i) q^{77} -9.70724 q^{78} +(5.38886 + 3.91524i) q^{79} +(-5.49699 + 16.9180i) q^{80} +(-3.45899 - 10.6457i) q^{81} +(1.24554 - 0.904941i) q^{82} +(-13.5587 + 9.85095i) q^{83} +(0.255475 + 0.786272i) q^{84} +(1.12977 - 3.47707i) q^{85} +(-5.80304 - 4.21615i) q^{86} -5.11289 q^{87} +(6.60937 - 3.22741i) q^{88} +10.2267 q^{89} +(6.05902 + 4.40214i) q^{90} +(0.566066 - 1.74217i) q^{91} +(1.37529 + 4.23272i) q^{92} +(9.84353 - 7.15175i) q^{93} +(13.3007 - 9.66350i) q^{94} +(-1.47018 - 4.52476i) q^{95} +(-2.20764 + 6.79442i) q^{96} +(-9.57447 - 6.95626i) q^{97} +10.7108 q^{98} +(-0.584610 - 4.14573i) 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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.31285	+	0.953841i	0.928325	+	0.674468i	0.945582	−	0.325383i	$-0.105493\pi$
$2$	1.31285	+	0.953841i	0.928325	+	0.674468i	−0.0172569	+	0.999851i	$0.505493\pi$
$3$	−0.637980	+	1.96350i	−0.368338	+	1.13363i	0.579526	+	0.814953i	$0.303238\pi$
$3$	−0.637980	+	1.96350i	−0.368338	+	1.13363i	−0.947864	+	0.318674i	$0.896762\pi$
$4$	0.195728	+	0.602389i	0.0978640	+	0.301194i
$5$	−2.95777	+	2.14895i	−1.32275	+	0.961038i	−0.322861	+	0.946446i	$0.604645\pi$
$5$	−2.95777	+	2.14895i	−1.32275	+	0.961038i	−0.999894	+	0.0145913i	$0.995355\pi$
$6$	−2.71044	+	1.96925i	−1.10653	+	0.803943i
$7$	−0.195368	−	0.601281i	−0.0738422	−	0.227263i	0.907323	−	0.420435i	$-0.138122\pi$
$7$	−0.195368	−	0.601281i	−0.0738422	−	0.227263i	−0.981165	+	0.193172i	$0.938122\pi$
$8$	0.685306	−	2.10916i	0.242292	−	0.745699i
$9$	−1.02126	−	0.741992i	−0.340422	−	0.247331i
$10$	−5.93286			−1.87614
$11$	2.30503	+	2.38471i	0.694993	+	0.719017i
$11$	2.30503	+	2.38471i	0.694993	+	0.719017i
$12$	−1.30766			−0.377489
$13$	2.34407	+	1.70307i	0.650129	+	0.472346i	0.863315	−	0.504665i	$-0.168384\pi$
$13$	2.34407	+	1.70307i	0.650129	+	0.472346i	−0.213186	+	0.977012i	$0.568384\pi$
$14$	0.317038	−	0.975742i	0.0847319	−	0.260778i
$15$	−2.33246	−	7.17857i	−0.602238	−	1.85350i
$16$	3.93635	−	2.85993i	0.984088	−	0.714981i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$18$	−0.633025	−	1.94825i	−0.149205	−	0.459207i
$19$	−0.402129	+	1.23762i	−0.0922546	+	0.283931i	−0.986528	−	0.163590i	$-0.947693\pi$
$19$	−0.402129	+	1.23762i	−0.0922546	+	0.283931i	0.894274	+	0.447520i	$0.147693\pi$
$20$	−1.87342	−	1.36112i	−0.418909	−	0.304355i
$21$	1.30526			0.284830
$22$	0.751525	+	5.32940i	0.160226	+	1.13623i
$23$	7.02655			1.46514			0.732568	−	0.680693i	$-0.238321\pi$
$23$	7.02655			1.46514			0.732568	+	0.680693i	$0.238321\pi$
$24$	3.70412	+	2.69120i	0.756100	+	0.549339i
$25$	2.58535	−	7.95689i	0.517070	−	1.59138i
$26$	1.45296	+	4.47175i	0.284949	+	0.876982i
$27$	−2.90231	+	2.10865i	−0.558550	+	0.405810i
$28$	0.323966	−	0.235375i	0.0612238	−	0.0444817i
$29$	0.765286	+	2.35531i	0.142110	+	0.437370i	0.996628	−	0.0820519i	$-0.0261473\pi$
$29$	0.765286	+	2.35531i	0.142110	+	0.437370i	−0.854518	+	0.519422i	$0.826147\pi$
$30$	3.78505	−	11.6492i	0.691052	−	2.12684i
$31$	−4.76789	−	3.46408i	−0.856338	−	0.622166i	0.0705479	−	0.997508i	$-0.477525\pi$
$31$	−4.76789	−	3.46408i	−0.856338	−	0.622166i	−0.926886	+	0.375342i	$0.877525\pi$
$32$	3.46036			0.611711
$33$	−6.15294	+	3.00453i	−1.07109	+	0.523022i
$34$	−1.62277			−0.278303
$35$	1.86997	+	1.35862i	0.316083	+	0.229648i
$36$	0.247078	−	0.760427i	0.0411796	−	0.126738i
$37$	−2.36020	−	7.26393i	−0.388014	−	1.19418i	−0.934270	−	0.356566i	$-0.883948\pi$
$37$	−2.36020	−	7.26393i	−0.388014	−	1.19418i	0.546257	−	0.837618i	$-0.316052\pi$
$38$	−1.70843	+	1.24125i	−0.277144	+	0.201357i
$39$	−4.83945	+	3.51606i	−0.774932	+	0.563021i
$40$	2.50548	+	7.71108i	0.396152	+	1.21923i
$41$	0.293175	−	0.902299i	0.0457862	−	0.140915i	−0.925550	−	0.378626i	$-0.876397\pi$
$41$	0.293175	−	0.902299i	0.0457862	−	0.140915i	0.971336	+	0.237710i	$0.0763968\pi$
$42$	1.71361	+	1.24501i	0.264415	+	0.192109i
$43$	−4.42018			−0.674071			−0.337036	−	0.941492i	$-0.609424\pi$
$43$	−4.42018			−0.674071			−0.337036	+	0.941492i	$0.609424\pi$
$44$	−0.985363	+	1.85528i	−0.148549	+	0.279694i
$45$	4.61517			0.687988
$46$	9.22481	+	6.70221i	1.36012	+	0.988188i
$47$	3.13069	−	9.63528i	0.456658	−	1.40545i	−0.412519	−	0.910949i	$-0.635351\pi$
$47$	3.13069	−	9.63528i	0.456658	−	1.40545i	0.869177	−	0.494501i	$-0.164649\pi$
$48$	3.10415	+	9.55360i	0.448046	+	1.37894i
$49$	5.33975	−	3.87955i	0.762821	−	0.554222i
$50$	10.9838	−	7.98019i	1.55334	−	1.12857i
$51$	−0.637980	−	1.96350i	−0.0893351	−	0.274945i
$52$	−0.567109	+	1.74538i	−0.0786438	+	0.242041i
$53$	5.04208	+	3.66329i	0.692583	+	0.503191i	0.877508	−	0.479562i	$-0.159204\pi$
$53$	5.04208	+	3.66329i	0.692583	+	0.503191i	−0.184925	+	0.982753i	$0.559204\pi$
$54$	−5.82162			−0.792222
$55$	−11.9424	−	2.10004i	−1.61031	−	0.283169i
$56$	−1.40208			−0.187361
$57$	−2.17353	−	1.57916i	−0.287891	−	0.209165i
$58$	−1.24189	+	3.82213i	−0.163068	+	0.501870i
$59$	2.04423	+	6.29149i	0.266136	+	0.819082i	0.991430	+	0.130642i	$0.0417039\pi$
$59$	2.04423	+	6.29149i	0.266136	+	0.819082i	−0.725294	+	0.688440i	$0.758296\pi$
$60$	3.86776	−	2.81009i	0.499326	−	0.362781i
$61$	10.5010	−	7.62941i	1.34451	−	0.976846i	0.345248	−	0.938511i	$-0.387795\pi$
$61$	10.5010	−	7.62941i	1.34451	−	0.976846i	0.999265	−	0.0383348i	$-0.0122053\pi$
$62$	−2.95535	−	9.09562i	−0.375329	−	1.15515i
$63$	−0.246623	+	0.759028i	−0.0310716	+	0.0956286i
$64$	−3.32977	−	2.41922i	−0.416221	−	0.302402i
$65$	−10.5930			−1.31390
$66$	−10.9437	−	1.92443i	−1.34708	−	0.236881i
$67$	−5.11549			−0.624956			−0.312478	−	0.949925i	$-0.601159\pi$
$67$	−5.11549			−0.624956			−0.312478	+	0.949925i	$0.601159\pi$
$68$	−0.512423	−	0.372297i	−0.0621404	−	0.0451476i
$69$	−4.48280	+	13.7966i	−0.539665	+	1.66092i
$70$	1.15909	+	3.56732i	0.138538	+	0.426376i
$71$	−2.70418	+	1.96470i	−0.320927	+	0.233167i	−0.736571	−	0.676360i	$-0.763556\pi$
$71$	−2.70418	+	1.96470i	−0.320927	+	0.233167i	0.415644	+	0.909527i	$0.363556\pi$
$72$	−2.26486	+	1.64551i	−0.266916	+	0.193926i
$73$	−1.64861	−	5.07389i	−0.192955	−	0.593854i	−0.999994	−	0.00335662i	$-0.998932\pi$
$73$	−1.64861	−	5.07389i	−0.192955	−	0.593854i	0.807039	−	0.590498i	$-0.201068\pi$
$74$	3.83006	−	11.7877i	0.445235	−	1.37029i
$75$	13.9740	+	10.1527i	1.61357	+	1.17233i
$76$	−0.824239			−0.0945467
$77$	0.983551	−	1.85187i	0.112086	−	0.211040i
$78$	−9.70724			−1.09913
$79$	5.38886	+	3.91524i	0.606295	+	0.440499i	0.848108	−	0.529824i	$-0.177742\pi$
$79$	5.38886	+	3.91524i	0.606295	+	0.440499i	−0.241813	+	0.970323i	$0.577742\pi$
$80$	−5.49699	+	16.9180i	−0.614582	+	1.89149i
$81$	−3.45899	−	10.6457i	−0.384332	−	1.18285i
$82$	1.24554	−	0.904941i	0.137547	−	0.0999341i
$83$	−13.5587	+	9.85095i	−1.48826	+	1.08128i	−0.513480	+	0.858102i	$0.671644\pi$
$83$	−13.5587	+	9.85095i	−1.48826	+	1.08128i	−0.974777	+	0.223180i	$0.928356\pi$
$84$	0.255475	+	0.786272i	0.0278746	+	0.0857893i
$85$	1.12977	−	3.47707i	0.122540	−	0.377141i
$86$	−5.80304	−	4.21615i	−0.625758	−	0.454640i
$87$	−5.11289			−0.548159
$88$	6.60937	−	3.22741i	0.704562	−	0.344043i
$89$	10.2267			1.08403			0.542016	−	0.840368i	$-0.317661\pi$
$89$	10.2267			1.08403			0.542016	+	0.840368i	$0.317661\pi$
$90$	6.05902	+	4.40214i	0.638677	+	0.464026i
$91$	0.566066	−	1.74217i	0.0593398	−	0.182629i
$92$	1.37529	+	4.23272i	0.143384	+	0.441291i
$93$	9.84353	−	7.15175i	1.02073	−	0.741601i
$94$	13.3007	−	9.66350i	1.37186	−	0.996714i
$95$	−1.47018	−	4.52476i	−0.150838	−	0.464231i
$96$	−2.20764	+	6.79442i	−0.225316	+	0.693452i
$97$	−9.57447	−	6.95626i	−0.972140	−	0.706301i	−0.0162019	−	0.999869i	$-0.505157\pi$
$97$	−9.57447	−	6.95626i	−0.972140	−	0.706301i	−0.955938	+	0.293568i	$0.905157\pi$
$98$	10.7108			1.08195
$99$	−0.584610	−	4.14573i	−0.0587556	−	0.416662i
$100$	5.29917			0.529917
$101$	−8.01087	−	5.82024i	−0.797111	−	0.579135i	0.112954	−	0.993600i	$-0.463969\pi$
$101$	−8.01087	−	5.82024i	−0.797111	−	0.579135i	−0.910065	+	0.414465i	$0.863969\pi$
$102$	1.03530	−	3.18631i	0.102510	−	0.315492i
$103$	5.85965	+	18.0341i	0.577368	+	1.77696i	0.627969	+	0.778238i	$0.283886\pi$
$103$	5.85965	+	18.0341i	0.577368	+	1.77696i	−0.0506005	+	0.998719i	$0.516114\pi$
$104$	5.19844	−	3.77689i	0.509749	−	0.370355i
$105$	−3.86065	+	2.80492i	−0.376761	+	0.273733i
$106$	3.12530	+	9.61869i	0.303556	+	0.934250i
$107$	−3.52924	+	10.8619i	−0.341185	+	1.05006i	0.622410	+	0.782691i	$0.286154\pi$
$107$	−3.52924	+	10.8619i	−0.341185	+	1.05006i	−0.963595	+	0.267367i	$0.913846\pi$
$108$	−1.83829	−	1.33560i	−0.176890	−	0.128518i
$109$	−3.22026			−0.308445			−0.154222	−	0.988036i	$-0.549287\pi$
$109$	−3.22026			−0.308445			−0.154222	+	0.988036i	$0.549287\pi$
$110$	−13.6754	−	14.1481i	−1.30390	−	1.34897i
$111$	15.7685			1.49668
$112$	−2.48866	−	1.80811i	−0.235156	−	0.170851i
$113$	−1.58367	+	4.87404i	−0.148979	+	0.458511i	−0.997501	−	0.0706489i	$-0.977493\pi$
$113$	−1.58367	+	4.87404i	−0.148979	+	0.458511i	0.848522	+	0.529160i	$0.177493\pi$
$114$	−1.34725	−	4.14640i	−0.126181	−	0.388346i
$115$	−20.7829	+	15.0997i	−1.93802	+	1.40805i
$116$	−1.26902	+	0.922000i	−0.117826	+	0.0856056i
$117$	−1.13026	−	3.47857i	−0.104492	−	0.321594i
$118$	−3.31732	+	10.2096i	−0.305384	+	0.939874i
$119$	0.511480	+	0.371612i	0.0468873	+	0.0340656i
$120$	−16.7392			−1.52807
$121$	−0.373673	+	10.9937i	−0.0339703	+	0.999423i
$122$	21.0635			1.90700
$123$	1.58463	+	1.15130i	0.142881	+	0.103809i
$124$	1.15351	−	3.55014i	0.103588	−	0.318812i
$125$	3.80321	+	11.7051i	0.340170	+	1.04693i
$126$	−1.04777	+	0.761251i	−0.0933430	+	0.0678176i
$127$	−11.3846	+	8.27139i	−1.01022	+	0.733968i	−0.964255	−	0.264976i	$-0.914636\pi$
$127$	−11.3846	+	8.27139i	−1.01022	+	0.733968i	−0.0459645	+	0.998943i	$0.514636\pi$
$128$	−4.20256	−	12.9341i	−0.371457	−	1.14323i
$129$	2.81999	−	8.67903i	0.248286	−	0.764146i
$130$	−13.9071	−	10.1041i	−1.21973	−	0.886185i
$131$	10.0036			0.874020			0.437010	−	0.899457i	$-0.356037\pi$
$131$	10.0036			0.874020			0.437010	+	0.899457i	$0.356037\pi$
$132$	−3.01420	−	3.11839i	−0.262352	−	0.271421i
$133$	0.822723			0.0713391
$134$	−6.71587	−	4.87936i	−0.580163	−	0.421513i
$135$	4.05299	−	12.4738i	0.348826	−	1.07358i
$136$	0.685306	+	2.10916i	0.0587645	+	0.180859i
$137$	−2.86510	+	2.08162i	−0.244782	+	0.177845i	−0.703411	−	0.710783i	$-0.748341\pi$
$137$	−2.86510	+	2.08162i	−0.244782	+	0.177845i	0.458629	+	0.888628i	$0.348341\pi$
$138$	−19.0450	+	13.8370i	−1.62122	+	1.17789i
$139$	−4.07184	−	12.5318i	−0.345369	−	1.06294i	−0.961386	−	0.275203i	$-0.911255\pi$
$139$	−4.07184	−	12.5318i	−0.345369	−	1.06294i	0.616017	−	0.787733i	$-0.288745\pi$
$140$	−0.452408	+	1.39237i	−0.0382355	+	0.117677i
$141$	16.9216	+	12.2942i	1.42505	+	1.03536i
$142$	−5.42419			−0.455188
$143$	1.34184	+	9.51555i	0.112210	+	0.795731i
$144$	−6.14210			−0.511842
$145$	−7.32497	−	5.32190i	−0.608306	−	0.441960i
$146$	2.67531	−	8.23377i	0.221411	−	0.681432i
$147$	4.21085	+	12.9597i	0.347305	+	1.06890i
$148$	3.91376	−	2.84351i	0.321709	−	0.233735i
$149$	16.7008	−	12.1339i	1.36818	−	0.994044i	0.370307	−	0.928909i	$-0.379252\pi$
$149$	16.7008	−	12.1339i	1.36818	−	0.994044i	0.997876	−	0.0651345i	$-0.0207476\pi$
$150$	8.66167	+	26.6579i	0.707222	+	2.17661i
$151$	1.45704	−	4.48430i	0.118572	−	0.364927i	−0.874103	−	0.485740i	$-0.838550\pi$
$151$	1.45704	−	4.48430i	0.118572	−	0.364927i	0.992675	+	0.120813i	$0.0385501\pi$
$152$	2.33476	+	1.69630i	0.189374	+	0.137588i
$153$	1.26235			0.102055
$154$	3.05764	−	1.49307i	0.246392	−	0.120315i
$155$	21.5464			1.73065
$156$	−3.06525	−	2.22704i	−0.245417	−	0.178306i
$157$	1.38075	−	4.24951i	0.110196	−	0.339147i	−0.880719	−	0.473639i	$-0.842940\pi$
$157$	1.38075	−	4.24951i	0.110196	−	0.339147i	0.990915	+	0.134492i	$0.0429401\pi$
$158$	3.34025	+	10.2802i	0.265736	+	0.817852i
$159$	−10.4096	+	7.56302i	−0.825536	+	0.599787i
$160$	−10.2349	+	7.43612i	−0.809143	+	0.587877i
$161$	−1.37276	−	4.22493i	−0.108189	−	0.332971i
$162$	5.61315	−	17.2755i	0.441011	−	1.35729i
$163$	10.3211	+	7.49874i	0.808413	+	0.587347i	0.913370	−	0.407130i	$-0.133470\pi$
$163$	10.3211	+	7.49874i	0.808413	+	0.587347i	−0.104957	+	0.994477i	$0.533470\pi$
$164$	0.600917			0.0469238
$165$	11.7424	−	22.1090i	0.914145	−	1.72119i
$166$	−27.1967			−2.11088
$167$	−10.1987	−	7.40977i	−0.789197	−	0.573385i	0.118528	−	0.992951i	$-0.462182\pi$
$167$	−10.1987	−	7.40977i	−0.789197	−	0.573385i	−0.907725	+	0.419565i	$0.862182\pi$
$168$	0.894500	−	2.75299i	0.0690122	−	0.212398i
$169$	−1.42299	−	4.37950i	−0.109461	−	0.336885i
$170$	4.79979	−	3.48725i	0.368127	−	0.267460i
$171$	1.32899	−	0.965566i	0.101630	−	0.0738387i
$172$	−0.865154	−	2.66267i	−0.0659673	−	0.203027i
$173$	1.25296	−	3.85623i	0.0952611	−	0.293183i	−0.892061	−	0.451916i	$-0.850741\pi$
$173$	1.25296	−	3.85623i	0.0952611	−	0.293183i	0.987322	+	0.158732i	$0.0507407\pi$
$174$	−6.71246	−	4.87689i	−0.508870	−	0.369716i
$175$	−5.28942			−0.399842
$176$	15.8935	+	2.79483i	1.19802	+	0.210669i
$177$	−13.6575			−1.02656
$178$	13.4262	+	9.75469i	1.00633	+	0.731145i
$179$	4.50313	−	13.8592i	0.336579	−	1.03588i	−0.629359	−	0.777114i	$-0.716683\pi$
$179$	4.50313	−	13.8592i	0.336579	−	1.03588i	0.965939	−	0.258770i	$-0.0833173\pi$
$180$	0.903317	+	2.78013i	0.0673293	+	0.207218i
$181$	7.90480	−	5.74318i	0.587559	−	0.426887i	−0.253882	−	0.967235i	$-0.581708\pi$
$181$	7.90480	−	5.74318i	0.587559	−	0.426887i	0.841441	+	0.540348i	$0.181708\pi$
$182$	2.40491	−	1.74727i	0.178264	−	0.129516i
$183$	8.28094	+	25.4861i	0.612144	+	1.88399i
$184$	4.81534	−	14.8201i	0.354991	−	1.09255i
$185$	22.5907	+	16.4131i	1.66090	+	1.20672i
$186$	19.7447			1.44775
$187$	−3.26651	−	0.574407i	−0.238871	−	0.0420048i
$188$	6.41695			0.468004
$189$	1.83491	+	1.33314i	0.133470	+	0.0969717i
$190$	2.38577	−	7.34266i	0.173082	−	0.532692i
$191$	−0.403828	−	1.24285i	−0.0292200	−	0.0899298i	0.935383	−	0.353636i	$-0.115055\pi$
$191$	−0.403828	−	1.24285i	−0.0292200	−	0.0899298i	−0.964603	+	0.263707i	$0.915055\pi$
$192$	6.87446	−	4.99459i	0.496122	−	0.360453i
$193$	−16.9482	+	12.3136i	−1.21996	+	0.886350i	−0.996096	−	0.0882716i	$-0.971866\pi$
$193$	−16.9482	+	12.3136i	−1.21996	+	0.886350i	−0.223859	+	0.974621i	$0.571866\pi$
$194$	−5.93468	−	18.2651i	−0.426085	−	1.31135i
$195$	6.75814	−	20.7994i	0.483960	−	1.48948i
$196$	3.38214	+	2.45727i	0.241581	+	0.175519i
$197$	21.0368			1.49881			0.749407	−	0.662110i	$-0.230339\pi$
$197$	21.0368			1.49881			0.749407	+	0.662110i	$0.230339\pi$
$198$	3.18687	−	6.00035i	0.226481	−	0.426427i
$199$	−0.377720			−0.0267759			−0.0133879	−	0.999910i	$-0.504262\pi$
$199$	−0.377720			−0.0267759			−0.0133879	+	0.999910i	$0.504262\pi$
$200$	−15.0106	−	10.9058i	−1.06141	−	0.771157i
$201$	3.26358	−	10.0443i	0.230195	−	0.708468i
$202$	−4.96549	−	15.2822i	−0.349371	−	1.07525i
$203$	1.26669	−	0.920304i	0.0889042	−	0.0645927i
$204$	1.05792	−	0.768624i	0.0740692	−	0.0538145i
$205$	1.07185	+	3.29881i	0.0748611	+	0.230399i
$206$	−9.50888	+	29.2653i	−0.662515	+	2.03901i
$207$	−7.17597	−	5.21365i	−0.498764	−	0.362373i
$208$	14.0977			0.977502
$209$	−3.87829	+	1.89380i	−0.268267	+	0.130997i
$210$	−7.74390			−0.534380
$211$	−14.2266	−	10.3362i	−0.979400	−	0.711575i	−0.0218252	−	0.999762i	$-0.506948\pi$
$211$	−14.2266	−	10.3362i	−0.979400	−	0.711575i	−0.957574	+	0.288186i	$0.906948\pi$
$212$	−1.21985	+	3.75430i	−0.0837794	+	0.257846i
$213$	−2.13248	−	6.56310i	−0.146115	−	0.449696i
$214$	−14.9939	+	10.8937i	−1.02496	+	0.744678i
$215$	13.0739	−	9.49873i	0.891631	−	0.647808i
$216$	2.45850	+	7.56650i	0.167280	+	0.514835i
$217$	−1.15139	+	3.54361i	−0.0781614	+	0.240556i
$218$	−4.22772	−	3.07162i	−0.286337	−	0.208036i
$219$	11.0144			0.744282
$220$	−1.07242	−	7.60498i	−0.0723023	−	0.512728i
$221$	−2.89743			−0.194902
$222$	20.7017	+	15.0406i	1.38941	+	1.00946i
$223$	7.22984	−	22.2511i	0.484146	−	1.49005i	−0.349069	−	0.937097i	$-0.613502\pi$
$223$	7.22984	−	22.2511i	0.484146	−	1.49005i	0.833214	−	0.552950i	$-0.186498\pi$
$224$	−0.676043	−	2.08065i	−0.0451700	−	0.139019i
$225$	−8.54428	+	6.20778i	−0.569618	+	0.413852i
$226$	−6.72819	+	4.88832i	−0.447553	+	0.325166i
$227$	−3.14362	−	9.67508i	−0.208650	−	0.642158i	−0.999544	−	0.0302046i	$-0.990384\pi$
$227$	−3.14362	−	9.67508i	−0.208650	−	0.642158i	0.790894	−	0.611953i	$-0.209616\pi$
$228$	0.525848	−	1.61839i	0.0348251	−	0.107181i
$229$	2.38387	+	1.73198i	0.157530	+	0.114453i	0.663758	−	0.747947i	$-0.268960\pi$
$229$	2.38387	+	1.73198i	0.157530	+	0.114453i	−0.506228	+	0.862400i	$0.668960\pi$
$230$	−41.6875			−2.74880
$231$	3.00865	+	3.11266i	0.197955	+	0.204798i
$232$	5.49217			0.360579
$233$	−19.0835	−	13.8650i	−1.25020	−	0.908327i	−0.251970	−	0.967735i	$-0.581079\pi$
$233$	−19.0835	−	13.8650i	−1.25020	−	0.908327i	−0.998234	+	0.0594084i	$0.981079\pi$
$234$	1.83415	−	5.64492i	0.119902	−	0.369020i
$235$	11.4458	+	35.2266i	0.746643	+	2.29793i
$236$	−3.38981	+	2.46284i	−0.220658	+	0.160317i
$237$	−11.1256	+	8.08319i	−0.722683	+	0.525060i
$238$	0.317038	+	0.975742i	0.0205505	+	0.0632479i
$239$	−0.533501	+	1.64195i	−0.0345093	+	0.106209i	−0.966827	−	0.255431i	$-0.917783\pi$
$239$	−0.533501	+	1.64195i	−0.0345093	+	0.106209i	0.932318	+	0.361639i	$0.117783\pi$
$240$	−29.7115	−	21.5867i	−1.91787	−	1.39342i
$241$	23.9463			1.54252			0.771258	−	0.636523i	$-0.219628\pi$
$241$	23.9463			1.54252			0.771258	+	0.636523i	$0.219628\pi$
$242$	−10.9768	+	14.0766i	−0.705614	+	0.904878i
$243$	12.3472			0.792073
$244$	6.65121	+	4.83239i	0.425800	+	0.309362i
$245$	−7.45680	+	22.9497i	−0.476397	+	1.46620i
$246$	0.982220	+	3.02296i	0.0626241	+	0.192737i
$247$	−3.05038	+	2.21623i	−0.194091	+	0.141015i
$248$	−10.5737	+	7.68227i	−0.671433	+	0.487825i
$249$	−10.6922	−	32.9072i	−0.677590	−	2.08541i
$250$	−6.17175	+	18.9947i	−0.390336	+	1.20133i
$251$	3.36350	+	2.44372i	0.212302	+	0.154247i	0.688855	−	0.724899i	$-0.258114\pi$
$251$	3.36350	+	2.44372i	0.212302	+	0.154247i	−0.476553	+	0.879146i	$0.658114\pi$
$252$	−0.505501			−0.0318436
$253$	16.1964	+	16.7563i	1.01826	+	1.05346i
$254$	−22.8359			−1.43285
$255$	6.10645	+	4.43660i	0.382401	+	0.277831i
$256$	4.27607	−	13.1604i	0.267255	−	0.822525i
$257$	−1.44687	−	4.45300i	−0.0902530	−	0.277770i	0.895734	−	0.444589i	$-0.146650\pi$
$257$	−1.44687	−	4.45300i	−0.0902530	−	0.277770i	−0.985988	+	0.166819i	$0.946650\pi$
$258$	11.9806	−	8.70444i	0.745882	−	0.541915i
$259$	−3.90656	+	2.83828i	−0.242742	+	0.176362i
$260$	−2.07335	−	6.38112i	−0.128584	−	0.395740i
$261$	0.966061	−	2.97323i	0.0597977	−	0.184038i
$262$	13.1333	+	9.54187i	0.811375	+	0.589498i
$263$	−8.16857			−0.503695			−0.251848	−	0.967767i	$-0.581038\pi$
$263$	−8.16857			−0.503695			−0.251848	+	0.967767i	$0.581038\pi$
$264$	2.12038	+	15.0365i	0.130500	+	0.925435i
$265$	−22.7855			−1.39970
$266$	1.08011	+	0.784747i	0.0662259	+	0.0481160i
$267$	−6.52446	+	20.0802i	−0.399290	+	1.22889i
$268$	−1.00124	−	3.08151i	−0.0611607	−	0.188233i
$269$	−6.14815	+	4.46689i	−0.374859	+	0.272351i	−0.759223	−	0.650831i	$-0.774421\pi$
$269$	−6.14815	+	4.46689i	−0.374859	+	0.272351i	0.384364	+	0.923182i	$0.374421\pi$
$270$	17.2190	−	12.5103i	1.04792	−	0.761355i
$271$	3.55444	+	10.9394i	0.215917	+	0.664524i	0.999087	+	0.0427167i	$0.0136013\pi$
$271$	3.55444	+	10.9394i	0.215917	+	0.664524i	−0.783170	+	0.621807i	$0.786399\pi$
$272$	−1.50355	+	4.62746i	−0.0911662	+	0.280581i
$273$	3.05961	+	2.22294i	0.185176	+	0.134538i
$274$	−5.74699			−0.347188
$275$	24.9342	−	12.1756i	1.50359	−	0.734214i
$276$	−9.18835			−0.553074
$277$	−21.3519	−	15.5131i	−1.28291	−	0.932091i	−0.283276	−	0.959038i	$-0.591421\pi$
$277$	−21.3519	−	15.5131i	−1.28291	−	0.932091i	−0.999637	+	0.0269473i	$0.991421\pi$
$278$	6.60767	−	20.3363i	0.396301	−	1.21969i
$279$	2.29896	+	7.07548i	0.137635	+	0.423598i
$280$	4.14704	−	3.01300i	0.247833	−	0.180061i
$281$	−20.7822	+	15.0991i	−1.23976	+	0.900738i	−0.997582	−	0.0694937i	$-0.977862\pi$
$281$	−20.7822	+	15.0991i	−1.23976	+	0.900738i	−0.242177	+	0.970232i	$0.577862\pi$
$282$	10.4887	+	32.2810i	0.624594	+	1.92230i
$283$	−2.80321	+	8.62739i	−0.166633	+	0.512845i	−0.999153	−	0.0411506i	$-0.986898\pi$
$283$	−2.80321	+	8.62739i	−0.166633	+	0.512845i	0.832519	+	0.553996i	$0.186898\pi$
$284$	−1.71280	−	1.24442i	−0.101636	−	0.0738428i
$285$	9.82232			0.581824
$286$	−7.31470	+	13.7724i	−0.432527	+	0.814379i
$287$	−0.599812			−0.0354058
$288$	−3.53394	−	2.56756i	−0.208240	−	0.151295i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	−4.54034	−	13.9737i	−0.266618	−	0.820565i
$291$	19.7669	−	14.3615i	1.15876	−	0.841887i
$292$	2.73378	−	1.98621i	0.159982	−	0.116234i
$293$	1.92761	+	5.93259i	0.112612	+	0.346585i	0.991442	−	0.130551i	$-0.0416747\pi$
$293$	1.92761	+	5.93259i	0.112612	+	0.346585i	−0.878829	+	0.477137i	$0.841675\pi$
$294$	−6.83326	+	21.0306i	−0.398524	+	1.22653i
$295$	−19.5664	−	14.2158i	−1.13920	−	0.827678i
$296$	−16.9382			−0.984514
$297$	−11.7184	−	2.06066i	−0.679973	−	0.119572i
$298$	33.4994			1.94057
$299$	16.4707	+	11.9667i	0.952527	+	0.692052i
$300$	−3.38076	+	10.4049i	−0.195188	+	0.600728i
$301$	0.863562	+	2.65777i	0.0497749	+	0.153191i
$302$	6.19019	−	4.49744i	0.356205	−	0.258798i
$303$	16.5388	−	12.0162i	0.950130	−	0.690310i
$304$	1.95660	+	6.02178i	0.112218	+	0.345373i
$305$	−14.6643	+	45.1321i	−0.839676	+	2.58426i
$306$	1.65728	+	1.20408i	0.0947404	+	0.0688329i
$307$	8.42949			0.481096			0.240548	−	0.970637i	$-0.422673\pi$
$307$	8.42949			0.481096			0.240548	+	0.970637i	$0.422673\pi$
$308$	1.30805	+	0.230018i	0.0745332	+	0.0131065i
$309$	−39.1484			−2.22707
$310$	28.2872	+	20.5519i	1.60661	+	1.16727i
$311$	−10.4964	+	32.3046i	−0.595196	+	1.83183i	−0.0414492	+	0.999141i	$0.513197\pi$
$311$	−10.4964	+	32.3046i	−0.595196	+	1.83183i	−0.553747	+	0.832685i	$0.686803\pi$
$312$	4.09942	+	12.6167i	0.232084	+	0.714282i
$313$	7.82969	−	5.68860i	0.442560	−	0.321539i	−0.344091	−	0.938936i	$-0.611813\pi$
$313$	7.82969	−	5.68860i	0.442560	−	0.321539i	0.786651	+	0.617397i	$0.211813\pi$
$314$	5.86607	−	4.26195i	0.331042	−	0.240516i
$315$	−0.901656	−	2.77501i	−0.0508025	−	0.156354i
$316$	−1.30374	+	4.01251i	−0.0733414	+	0.225722i
$317$	−20.6983	−	15.0382i	−1.16253	−	0.844629i	−0.172436	−	0.985021i	$-0.555164\pi$
$317$	−20.6983	−	15.0382i	−1.16253	−	0.844629i	−0.990096	+	0.140392i	$0.955164\pi$
$318$	−20.8802			−1.17090
$319$	−3.85272	+	7.25404i	−0.215711	+	0.406149i
$320$	15.0475			0.841178
$321$	−19.0757	−	13.8593i	−1.06470	−	0.773553i
$322$	2.22768	−	6.85610i	0.124144	−	0.382075i
$323$	−0.402129	−	1.23762i	−0.0223750	−	0.0688633i
$324$	5.73581	−	4.16731i	0.318656	−	0.231517i
$325$	19.6114	−	14.2485i	1.08784	−	0.790364i
$326$	6.39749	+	19.6894i	0.354324	+	1.09050i
$327$	2.05446	−	6.32298i	0.113612	−	0.349661i
$328$	−1.70218	−	1.23670i	−0.0939869	−	0.0682855i
$329$	−6.40515			−0.353127
$330$	36.5045	−	17.8255i	2.00951	−	0.981260i
$331$	−1.49552			−0.0822012			−0.0411006	−	0.999155i	$-0.513086\pi$
$331$	−1.49552			−0.0822012			−0.0411006	+	0.999155i	$0.513086\pi$
$332$	−8.58791	−	6.23948i	−0.471323	−	0.342436i
$333$	−2.97940	+	9.16965i	−0.163270	+	0.502494i
$334$	−6.32158	−	19.4558i	−0.345902	−	1.06458i
$335$	15.1304	−	10.9929i	0.826664	−	0.600606i
$336$	5.13794	−	3.73294i	0.280298	−	0.203648i
$337$	7.04130	+	21.6709i	0.383564	+	1.18049i	0.937516	+	0.347941i	$0.113119\pi$
$337$	7.04130	+	21.6709i	0.383564	+	1.18049i	−0.553952	+	0.832549i	$0.686881\pi$
$338$	2.30918	−	7.10694i	0.125603	−	0.386566i
$339$	−8.55984	−	6.21908i	−0.464906	−	0.337774i
$340$	2.31567			0.125585
$341$	−2.72932	−	19.3548i	−0.147801	−	1.04812i
$342$	2.66576			0.144148
$343$	−6.95628	−	5.05403i	−0.375604	−	0.272892i
$344$	−3.02918	+	9.32285i	−0.163322	+	0.502655i
$345$	−16.3891	−	50.4405i	−0.882361	−	2.71563i
$346$	5.32318	−	3.86752i	0.286176	−	0.207919i
$347$	−17.3064	+	12.5738i	−0.929056	+	0.674999i	−0.945761	−	0.324862i	$-0.894682\pi$
$347$	−17.3064	+	12.5738i	−0.929056	+	0.674999i	0.0167057	+	0.999860i	$0.494682\pi$
$348$	−1.00074	−	3.07995i	−0.0536451	−	0.165103i
$349$	2.14489	−	6.60131i	0.114814	−	0.353360i	−0.877095	−	0.480318i	$-0.840521\pi$
$349$	2.14489	−	6.60131i	0.114814	−	0.353360i	0.991908	+	0.126958i	$0.0405213\pi$
$350$	−6.94421	−	5.04527i	−0.371184	−	0.269681i
$351$	−10.3944			−0.554812
$352$	7.97623	+	8.25195i	0.425134	+	0.439830i
$353$	14.1565			0.753472			0.376736	−	0.926321i	$-0.377046\pi$
$353$	14.1565			0.753472			0.376736	+	0.926321i	$0.377046\pi$
$354$	−17.9303	−	13.0271i	−0.952983	−	0.692383i
$355$	3.77630	−	11.6223i	0.200425	−	0.616846i
$356$	2.00166	+	6.16048i	0.106088	+	0.326505i
$357$	−1.05597	+	0.767210i	−0.0558881	+	0.0406051i
$358$	19.1314	−	13.8998i	1.01113	−	0.734626i
$359$	−4.76678	−	14.6707i	−0.251581	−	0.774288i	−0.994484	−	0.104888i	$-0.966552\pi$
$359$	−4.76678	−	14.6707i	−0.251581	−	0.774288i	0.742903	−	0.669399i	$-0.233448\pi$
$360$	3.16280	−	9.73411i	0.166694	−	0.513032i
$361$	14.0013	+	10.1726i	0.736911	+	0.535397i
$362$	15.8559			0.833368
$363$	−21.3476	−	7.74744i	−1.12046	−	0.406635i
$364$	1.16026			0.0608141
$365$	15.7797	+	11.4646i	0.825948	+	0.600086i
$366$	−13.4381	+	41.3581i	−0.702419	+	2.16182i
$367$	−7.48678	−	23.0420i	−0.390807	−	1.20278i	−0.932179	−	0.361997i	$-0.882095\pi$
$367$	−7.48678	−	23.0420i	−0.390807	−	1.20278i	0.541372	−	0.840783i	$-0.317905\pi$
$368$	27.6590	−	20.0954i	1.44182	−	1.04755i
$369$	−0.968908	+	0.703953i	−0.0504393	+	0.0366463i
$370$	14.0027	+	43.0959i	0.727966	+	2.24045i
$371$	1.21760	−	3.74739i	0.0632148	−	0.194555i
$372$	6.23479	+	4.52984i	0.323259	+	0.234861i
$373$	3.97837			0.205992			0.102996	−	0.994682i	$-0.467157\pi$
$373$	3.97837			0.205992			0.102996	+	0.994682i	$0.467157\pi$
$374$	−3.74054	−	3.86984i	−0.193419	−	0.200105i
$375$	−25.4093			−1.31213
$376$	−18.1768	−	13.2062i	−0.937398	−	0.681060i
$377$	−2.21737	+	6.82435i	−0.114200	+	0.351472i
$378$	1.13736	+	3.50043i	0.0584994	+	0.180043i
$379$	−9.94589	+	7.22611i	−0.510886	+	0.371181i	−0.813160	−	0.582041i	$-0.802254\pi$
$379$	−9.94589	+	7.22611i	−0.510886	+	0.371181i	0.302273	+	0.953221i	$0.402254\pi$
$380$	2.43791	−	1.77125i	0.125062	−	0.0908630i
$381$	−8.97774	−	27.6306i	−0.459944	−	1.41556i
$382$	0.655321	−	2.01687i	0.0335291	−	0.103192i
$383$	−19.8755	−	14.4404i	−1.01559	−	0.737870i	−0.0502171	−	0.998738i	$-0.515991\pi$
$383$	−19.8755	−	14.4404i	−1.01559	−	0.737870i	−0.965375	+	0.260868i	$0.915991\pi$
$384$	28.0773			1.43282
$385$	1.07044	+	7.59099i	0.0545548	+	0.386873i
$386$	−33.9956			−1.73033
$387$	4.51418	+	3.27974i	0.229468	+	0.166719i
$388$	2.31638	−	7.12909i	0.117596	−	0.361925i
$389$	2.23100	+	6.86632i	0.113116	+	0.348136i	0.991549	−	0.129729i	$-0.0414108\pi$
$389$	2.23100	+	6.86632i	0.113116	+	0.348136i	−0.878433	+	0.477865i	$0.841411\pi$
$390$	28.7118	−	20.8603i	1.45388	−	1.05630i
$391$	−5.68460	+	4.13010i	−0.287482	+	0.208868i
$392$	−4.52322	−	13.9210i	−0.228457	−	0.703119i
$393$	−6.38211	+	19.6421i	−0.321935	+	0.990813i
$394$	27.6182	+	20.0658i	1.39139	+	1.01090i
$395$	−24.3527			−1.22531
$396$	2.38292	−	1.16360i	0.119746	−	0.0584731i
$397$	15.9590			0.800959			0.400480	−	0.916306i	$-0.368844\pi$
$397$	15.9590			0.800959			0.400480	+	0.916306i	$0.368844\pi$
$398$	−0.495890	−	0.360285i	−0.0248567	−	0.0180595i
$399$	−0.524881	+	1.61542i	−0.0262769	+	0.0808720i
$400$	−12.5793	−	38.7150i	−0.628963	−	1.93575i
$401$	−3.87890	+	2.81818i	−0.193703	+	0.140733i	−0.680410	−	0.732832i	$-0.738198\pi$
$401$	−3.87890	+	2.81818i	−0.193703	+	0.140733i	0.486707	+	0.873566i	$0.338198\pi$
$402$	13.8652	−	10.0737i	0.691534	−	0.502429i
$403$	−5.27672	−	16.2401i	−0.262852	−	0.808976i
$404$	1.93810	−	5.96484i	0.0964238	−	0.296762i
$405$	33.1079	+	24.0543i	1.64514	+	1.19527i
$406$	2.54080			0.126098
$407$	11.8820	−	22.3720i	0.588971	−	1.10894i
$408$	−4.57854			−0.226672
$409$	12.3986	+	9.00815i	0.613074	+	0.445424i	0.850495	−	0.525983i	$-0.176302\pi$
$409$	12.3986	+	9.00815i	0.613074	+	0.445424i	−0.237422	+	0.971407i	$0.576302\pi$
$410$	−1.73937	+	5.35322i	−0.0859011	+	0.264376i
$411$	−2.25938	−	6.95367i	−0.111447	−	0.342999i
$412$	−9.71667	+	7.05958i	−0.478706	+	0.347800i
$413$	3.38357	−	2.45831i	0.166495	−	0.120966i
$414$	−4.44798	−	13.6895i	−0.218606	−	0.672801i
$415$	18.9343	−	58.2737i	0.929446	−	2.86054i
$416$	8.11133	+	5.89323i	0.397691	+	0.288939i
$417$	27.2040			1.33219
$418$	−6.89801	−	1.21300i	−0.337392	−	0.0593297i
$419$	−12.7816			−0.624421			−0.312210	−	0.950013i	$-0.601069\pi$
$419$	−12.7816			−0.624421			−0.312210	+	0.950013i	$0.601069\pi$
$420$	−2.44529	−	1.77661i	−0.119318	−	0.0866896i
$421$	3.27924	−	10.0925i	0.159821	−	0.491877i	−0.838797	−	0.544445i	$-0.816740\pi$
$421$	3.27924	−	10.0925i	0.159821	−	0.491877i	0.998617	+	0.0525674i	$0.0167404\pi$
$422$	−8.81827	−	27.1398i	−0.429267	−	1.32115i
$423$	−10.3466	+	7.51722i	−0.503067	+	0.365500i
$424$	11.1818	−	8.12406i	0.543037	−	0.394539i
$425$	2.58535	+	7.95689i	0.125408	+	0.385966i
$426$	3.46053	−	10.6504i	0.167663	−	0.516014i
$427$	−6.63898	−	4.82350i	−0.321283	−	0.233425i
$428$	−7.23385			−0.349661
$429$	−19.5399	−	3.43604i	−0.943393	−	0.165894i
$430$	26.2243			1.26465
$431$	17.8950	+	13.0015i	0.861970	+	0.626258i	0.928420	−	0.371532i	$-0.121167\pi$
$431$	17.8950	+	13.0015i	0.861970	+	0.626258i	−0.0664499	+	0.997790i	$0.521167\pi$
$432$	−5.39392	+	16.6008i	−0.259515	+	0.798706i
$433$	9.38859	+	28.8951i	0.451187	+	1.38861i	0.875554	+	0.483120i	$0.160497\pi$
$433$	9.38859	+	28.8951i	0.451187	+	1.38861i	−0.424367	+	0.905490i	$0.639503\pi$
$434$	−4.89164	+	3.55399i	−0.234806	+	0.170597i
$435$	15.1227	−	10.9873i	0.725080	−	0.526802i
$436$	−0.630295	−	1.93985i	−0.0301856	−	0.0929018i
$437$	−2.82558	+	8.69623i	−0.135166	+	0.415997i
$438$	14.4602	+	10.5060i	0.690936	+	0.501994i
$439$	16.6236			0.793402			0.396701	−	0.917948i	$-0.370155\pi$
$439$	16.6236			0.793402			0.396701	+	0.917948i	$0.370155\pi$
$440$	−12.6135	+	23.7491i	−0.601324	+	1.13220i
$441$	−8.33190			−0.396757
$442$	−3.80390	−	2.76369i	−0.180933	−	0.131455i
$443$	−9.50244	+	29.2455i	−0.451474	+	1.38950i	0.423750	+	0.905779i	$0.360713\pi$
$443$	−9.50244	+	29.2455i	−0.451474	+	1.38950i	−0.875225	+	0.483717i	$0.839287\pi$
$444$	3.08634	+	9.49877i	0.146471	+	0.450792i
$445$	−30.2483	+	21.9767i	−1.43391	+	1.04180i
$446$	30.7158	−	22.3163i	1.45443	−	1.05671i
$447$	13.1700	+	40.5332i	0.622921	+	1.91715i
$448$	−0.804099	+	2.47476i	−0.0379901	+	0.116922i
$449$	5.13246	+	3.72895i	0.242216	+	0.175980i	0.702270	−	0.711911i	$-0.252170\pi$
$449$	5.13246	+	3.72895i	0.242216	+	0.175980i	−0.460054	+	0.887891i	$0.652170\pi$
$450$	−17.1386			−0.807921
$451$	2.82750	−	1.38069i	0.133142	−	0.0650142i
$452$	−3.24604			−0.152681
$453$	7.87537	+	5.72179i	0.370017	+	0.268833i
$454$	5.10139	−	15.7005i	0.239420	−	0.736859i
$455$	2.06954	+	6.36938i	0.0970214	+	0.298601i
$456$	−4.82023	+	3.50210i	−0.225728	+	0.164001i
$457$	9.68136	−	7.03392i	0.452875	−	0.329033i	−0.337855	−	0.941198i	$-0.609701\pi$
$457$	9.68136	−	7.03392i	0.452875	−	0.329033i	0.790730	+	0.612165i	$0.209701\pi$
$458$	1.47763	+	4.54766i	0.0690449	+	0.212498i
$459$	1.10858	−	3.41187i	0.0517443	−	0.159253i
$460$	−13.1637	−	9.56397i	−0.613759	−	0.445922i
$461$	−10.4704			−0.487653			−0.243827	−	0.969819i	$-0.578403\pi$
$461$	−10.4704			−0.487653			−0.243827	+	0.969819i	$0.578403\pi$
$462$	0.980932	+	6.95623i	0.0456371	+	0.323633i
$463$	−16.4699			−0.765420			−0.382710	−	0.923869i	$-0.625009\pi$
$463$	−16.4699			−0.765420			−0.382710	+	0.923869i	$0.625009\pi$
$464$	9.74845	+	7.08266i	0.452560	+	0.328804i
$465$	−13.7462	+	42.3064i	−0.637464	+	1.96191i
$466$	−11.8288	−	36.4053i	−0.547959	−	1.68644i
$467$	−22.7082	+	16.4985i	−1.05081	+	0.763459i	−0.972366	−	0.233460i	$-0.924995\pi$
$467$	−22.7082	+	16.4985i	−1.05081	+	0.763459i	−0.0784444	+	0.996918i	$0.524995\pi$
$468$	1.87423	−	1.36171i	0.0866362	−	0.0629449i
$469$	0.999402	+	3.07584i	0.0461481	+	0.142029i
$470$	−18.5740	+	57.1648i	−0.856753	+	2.63682i
$471$	7.46302	+	5.42220i	0.343878	+	0.249842i
$472$	14.6706			0.675271
$473$	−10.1887	−	10.5408i	−0.468475	−	0.484669i
$474$	−22.3163			−1.02502
$475$	8.80800	+	6.39939i	0.404139	+	0.293624i
$476$	−0.123744	+	0.380845i	−0.00567180	+	0.0174560i
$477$	−2.43117	−	7.48237i	−0.111316	−	0.342594i
$478$	−2.26656	+	1.64676i	−0.103670	+	0.0753208i
$479$	−18.0236	+	13.0949i	−0.823519	+	0.598322i	−0.917718	−	0.397232i	$-0.869971\pi$
$479$	−18.0236	+	13.0949i	−0.823519	+	0.598322i	0.0941992	+	0.995553i	$0.469971\pi$
$480$	−8.07114	−	24.8404i	−0.368395	−	1.13380i
$481$	6.83851	−	21.0468i	0.311809	−	0.959650i
$482$	31.4379	+	22.8410i	1.43196	+	1.04038i
$483$	9.17145			0.417315
$484$	−6.69559	+	1.92667i	−0.304345	+	0.0875759i
$485$	43.2677			1.96469
$486$	16.2100	+	11.7773i	0.735301	+	0.534227i
$487$	2.82018	−	8.67962i	0.127795	−	0.393311i	−0.866605	−	0.498994i	$-0.833703\pi$
$487$	2.82018	−	8.67962i	0.127795	−	0.393311i	0.994400	+	0.105683i	$0.0337029\pi$
$488$	−8.89523	−	27.3767i	−0.402668	−	1.23929i
$489$	−21.3085	+	15.4815i	−0.963602	+	0.700098i
$490$	−31.6800	+	23.0169i	−1.43116	+	1.03980i
$491$	10.2607	+	31.5793i	0.463061	+	1.42515i	0.861405	+	0.507918i	$0.169585\pi$
$491$	10.2607	+	31.5793i	0.463061	+	1.42515i	−0.398345	+	0.917236i	$0.630415\pi$
$492$	−0.383373	+	1.17990i	−0.0172838	+	0.0531941i
$493$	−2.00355	−	1.45566i	−0.0902352	−	0.0655597i
$494$	−6.11862			−0.275290
$495$	10.6381	+	11.0058i	0.478147	+	0.494675i
$496$	−28.6751			−1.28755
$497$	1.70965	+	1.24213i	0.0766881	+	0.0557172i
$498$	17.3510	−	53.4008i	0.777516	−	2.39295i
$499$	−6.93607	−	21.3470i	−0.310501	−	0.955624i	−0.977567	−	0.210625i	$-0.932450\pi$
$499$	−6.93607	−	21.3470i	−0.310501	−	0.955624i	0.667066	−	0.744999i	$-0.267550\pi$
$500$	−6.30662	+	4.58203i	−0.282041	+	0.204914i
$501$	21.0556	−	15.2978i	0.940697	−	0.683456i
$502$	2.08484	+	6.41649i	0.0930511	+	0.286382i
$503$	8.78349	−	27.0328i	0.391636	−	1.20533i	−0.539914	−	0.841720i	$-0.681543\pi$
$503$	8.78349	−	27.0328i	0.391636	−	1.20533i	0.931550	−	0.363613i	$-0.118457\pi$
$504$	1.43190	+	1.04033i	0.0637818	+	0.0463402i
$505$	36.2017			1.61095
$506$	5.28063	+	37.4473i	0.234752	+	1.66473i
$507$	9.50700			0.422221
$508$	−7.21088	−	5.23901i	−0.319931	−	0.232444i
$509$	−5.90713	+	18.1803i	−0.261829	+	0.805827i	0.730578	+	0.682829i	$0.239251\pi$
$509$	−5.90713	+	18.1803i	−0.261829	+	0.805827i	−0.992407	+	0.122998i	$0.960749\pi$
$510$	3.78505	+	11.6492i	0.167605	+	0.515834i
$511$	−2.72875	+	1.98255i	−0.120713	+	0.0877029i
$512$	−3.83809	+	2.78854i	−0.169621	+	0.123237i
$513$	−1.44262	−	4.43992i	−0.0636931	−	0.196027i
$514$	2.34793	−	7.22620i	0.103563	−	0.318734i
$515$	−56.0859	−	40.7488i	−2.47144	−	1.79561i
$516$	5.78010			0.254455
$517$	30.1937	−	14.7438i	1.32792	−	0.648433i
$518$	−7.83599			−0.344294
$519$	6.77233	+	4.92039i	0.297272	+	0.215981i
$520$	−7.25947	+	22.3423i	−0.318349	+	0.979777i
$521$	−4.82137	−	14.8386i	−0.211228	−	0.650092i	−0.999400	−	0.0346375i	$-0.988972\pi$
$521$	−4.82137	−	14.8386i	−0.211228	−	0.650092i	0.788172	−	0.615455i	$-0.211028\pi$
$522$	4.10429	−	2.98194i	0.179640	−	0.130516i
$523$	−2.17748	+	1.58203i	−0.0952146	+	0.0691775i	−0.634374	−	0.773026i	$-0.718742\pi$
$523$	−2.17748	+	1.58203i	−0.0952146	+	0.0691775i	0.539159	+	0.842204i	$0.318742\pi$
$524$	1.95799	+	6.02607i	0.0855351	+	0.263250i
$525$	3.37454	−	10.3858i	0.147277	−	0.453272i
$526$	−10.7241	−	7.79152i	−0.467593	−	0.339726i
$527$	5.89344			0.256722
$528$	−15.6274	+	29.4238i	−0.680095	+	1.28051i
$529$	26.3724			1.14663
$530$	−29.9140	−	21.7338i	−1.29938	−	0.944054i
$531$	2.58054	−	7.94208i	0.111986	−	0.344657i
$532$	0.161030	+	0.495599i	0.00698153	+	0.0214870i
$533$	2.22390	−	1.61576i	0.0963278	−	0.0699862i
$534$	−27.7190	+	20.1390i	−1.19952	+	0.871500i
$535$	−12.9029	−	39.7111i	−0.557842	−	1.71686i
$536$	−3.50568	+	10.7894i	−0.151422	+	0.466029i
$537$	24.3396	+	17.6838i	1.05033	+	0.763111i
$538$	−12.3323			−0.531683
$539$	21.5599	+	3.79126i	0.928650	+	0.163301i
$540$	8.30737			0.357492
$541$	−33.0632	−	24.0218i	−1.42150	−	1.03278i	−0.991522	−	0.129939i	$-0.958522\pi$
$541$	−33.0632	−	24.0218i	−1.42150	−	1.03278i	−0.429977	−	0.902840i	$-0.641478\pi$
$542$	−5.76805	+	17.7522i	−0.247759	+	0.762523i
$543$	6.23362	+	19.1851i	0.267510	+	0.823312i
$544$	−2.79949	+	2.03395i	−0.120027	+	0.0872048i
$545$	9.52478	−	6.92016i	0.407997	−	0.296427i
$546$	1.89648	+	5.83677i	0.0811620	+	0.249791i
$547$	−7.50890	+	23.1100i	−0.321058	+	0.988113i	0.652131	+	0.758106i	$0.273875\pi$
$547$	−7.50890	+	23.1100i	−0.321058	+	0.988113i	−0.973189	+	0.230007i	$0.926125\pi$
$548$	−1.81473	−	1.31848i	−0.0775213	−	0.0563225i
$549$	−16.3853			−0.699305
$550$	44.3484	+	7.79856i	1.89102	+	0.332532i
$551$	−3.22273			−0.137293
$552$	26.0272	+	18.9098i	1.10779	+	0.804856i
$553$	1.30135	−	4.00513i	0.0553389	−	0.170316i
$554$	−13.2349	−	40.7327i	−0.562295	−	1.73057i
$555$	−46.6396	+	33.8856i	−1.97974	+	1.43837i
$556$	6.75206	−	4.90566i	0.286351	−	0.208046i
$557$	−11.5714	−	35.6130i	−0.490294	−	1.50897i	−0.824165	−	0.566350i	$-0.808355\pi$
$557$	−11.5714	−	35.6130i	−0.490294	−	1.50897i	0.333871	−	0.942619i	$-0.391645\pi$
$558$	−3.73069	+	11.4819i	−0.157933	+	0.486067i
$559$	−10.3612	−	7.52787i	−0.438233	−	0.318395i
$560$	11.2464			0.475247
$561$	3.21181	−	6.04732i	0.135603	−	0.255318i
$562$	−41.6860			−1.75842
$563$	−18.2424	−	13.2539i	−0.768824	−	0.558583i	0.132780	−	0.991146i	$-0.457610\pi$
$563$	−18.2424	−	13.2539i	−0.768824	−	0.558583i	−0.901604	+	0.432562i	$0.857610\pi$
$564$	−4.09389	+	12.5997i	−0.172384	+	0.530542i
$565$	−5.78991	−	17.8195i	−0.243584	−	0.749673i
$566$	−11.9094	+	8.65265i	−0.500588	+	0.363698i
$567$	−5.72526	+	4.15965i	−0.240438	+	0.174689i
$568$	2.29067	+	7.04996i	0.0961144	+	0.295810i
$569$	−3.53733	+	10.8868i	−0.148293	+	0.456398i	−0.997420	−	0.0717907i	$-0.977129\pi$
$569$	−3.53733	+	10.8868i	−0.148293	+	0.456398i	0.849127	+	0.528189i	$0.177129\pi$
$570$	12.8952	+	9.36894i	0.540122	+	0.392422i
$571$	−8.54691			−0.357677			−0.178839	−	0.983878i	$-0.557234\pi$
$571$	−8.54691			−0.357677			−0.178839	+	0.983878i	$0.557234\pi$
$572$	−5.46943	+	2.67077i	−0.228688	+	0.111670i
$573$	2.69798			0.112710
$574$	−0.787463	−	0.572126i	−0.0328681	−	0.0238801i
$575$	18.1661	−	55.9095i	0.757578	−	2.33159i
$576$	1.60553	+	4.94133i	0.0668972	+	0.205889i
$577$	5.18606	−	3.76789i	0.215898	−	0.156859i	−0.474580	−	0.880212i	$-0.657400\pi$
$577$	5.18606	−	3.76789i	0.215898	−	0.156859i	0.690478	+	0.723353i	$0.257400\pi$
$578$	1.31285	−	0.953841i	0.0546074	−	0.0396746i
$579$	−13.3651	−	41.1335i	−0.555435	−	1.70945i
$580$	1.77215	−	5.45413i	0.0735847	−	0.226470i
$581$	8.57211	+	6.22801i	0.355631	+	0.258381i
$582$	39.6496			1.64353
$583$	2.88628	+	20.4679i	0.119537	+	0.847693i
$584$	−11.8314			−0.489588
$585$	10.8183	+	7.85994i	0.447281	+	0.324969i
$586$	−3.12808	+	9.62723i	−0.129220	+	0.397697i
$587$	3.39417	+	10.4462i	0.140092	+	0.431159i	0.996347	−	0.0853938i	$-0.0272148\pi$
$587$	3.39417	+	10.4462i	0.140092	+	0.431159i	−0.856255	+	0.516553i	$0.827215\pi$
$588$	−6.98258	+	5.07314i	−0.287957	+	0.209213i
$589$	6.20453	−	4.50786i	0.255653	−	0.185743i
$590$	−12.1281	−	37.3265i	−0.499307	−	1.53671i
$591$	−13.4211	+	41.3059i	−0.552070	+	1.69910i
$592$	−30.0649	−	21.8434i	−1.23566	−	0.897758i
$593$	−40.2318			−1.65212			−0.826062	−	0.563580i	$-0.809424\pi$
$593$	−40.2318			−1.65212			−0.826062	+	0.563580i	$0.809424\pi$
$594$	−13.4190	−	13.8829i	−0.550589	−	0.569621i
$595$	−2.31141			−0.0947587
$596$	10.5781	+	7.68545i	0.433296	+	0.314808i
$597$	0.240978	−	0.741654i	0.00986257	−	0.0303539i
$598$	10.2093	+	31.4209i	0.417489	+	1.28490i
$599$	17.1101	−	12.4312i	0.699099	−	0.507925i	−0.180540	−	0.983568i	$-0.557784\pi$
$599$	17.1101	−	12.4312i	0.699099	−	0.507925i	0.879639	+	0.475643i	$0.157784\pi$
$600$	30.9900	−	22.5156i	1.26516	−	0.919194i
$601$	−8.21234	−	25.2750i	−0.334988	−	1.03099i	−0.966728	−	0.255808i	$-0.917659\pi$
$601$	−8.21234	−	25.2750i	−0.334988	−	1.03099i	0.631739	−	0.775181i	$-0.282341\pi$
$602$	−1.40136	+	4.31296i	−0.0571153	+	0.175783i
$603$	5.22427	+	3.79565i	0.212749	+	0.154571i
$604$	2.98648			0.121518
$605$	−22.5195	−	33.3197i	−0.915549	−	1.35464i
$606$	33.1745			1.34762
$607$	32.2890	+	23.4593i	1.31057	+	0.952184i	0.999999	+	0.00163306i	$0.000519818\pi$
$607$	32.2890	+	23.4593i	1.31057	+	0.952184i	0.310570	+	0.950551i	$0.399480\pi$
$608$	−1.39151	+	4.28263i	−0.0564332	+	0.173683i
$609$	0.998895	+	3.07428i	0.0404773	+	0.124576i
$610$	−62.3009	+	45.2642i	−2.52249	+	1.83270i
$611$	23.7481	−	17.2540i	0.960746	−	0.698023i
$612$	0.247078	+	0.760427i	0.00998753	+	0.0307384i
$613$	−7.37905	+	22.7104i	−0.298037	+	0.917264i	0.684147	+	0.729344i	$0.260175\pi$
$613$	−7.37905	+	22.7104i	−0.298037	+	0.917264i	−0.982184	+	0.187920i	$0.939825\pi$
$614$	11.0667	+	8.04040i	0.446614	+	0.324484i
$615$	−7.16103			−0.288761
$616$	−3.23184	−	3.34356i	−0.130215	−	0.134716i
$617$	28.2081			1.13562			0.567809	−	0.823161i	$-0.307791\pi$
$617$	28.2081			1.13562			0.567809	+	0.823161i	$0.307791\pi$
$618$	−51.3960	−	37.3414i	−2.06745	−	1.50209i
$619$	−4.30674	+	13.2548i	−0.173103	+	0.532755i	−0.999542	−	0.0302710i	$-0.990363\pi$
$619$	−4.30674	+	13.2548i	−0.173103	+	0.532755i	0.826439	+	0.563026i	$0.190363\pi$
$620$	4.21724	+	12.9793i	0.169368	+	0.521262i
$621$	−20.3932	+	14.8166i	−0.818352	+	0.594568i
$622$	−44.5937	+	32.3992i	−1.78804	+	1.29909i
$623$	−1.99798	−	6.14914i	−0.0800473	−	0.246360i
$624$	−8.99408	+	27.6809i	−0.360051	+	1.10812i
$625$	−2.55995	−	1.85991i	−0.102398	−	0.0743965i
$626$	15.7052			0.627708
$627$	−1.24421	−	8.82324i	−0.0496889	−	0.352366i
$628$	2.83011			0.112934
$629$	6.17907	+	4.48936i	0.246376	+	0.179002i
$630$	1.46318	−	4.50321i	0.0582946	−	0.179412i
$631$	0.466954	+	1.43714i	0.0185891	+	0.0572115i	0.959921	−	0.280271i	$-0.0904245\pi$
$631$	0.466954	+	1.43714i	0.0185891	+	0.0572115i	−0.941332	+	0.337483i	$0.890424\pi$
$632$	11.9509	−	8.68282i	0.475380	−	0.345384i
$633$	29.3715	−	21.3396i	1.16741	−	0.848174i
$634$	−12.8297	−	39.4858i	−0.509533	−	1.56818i
$635$	15.8982	−	48.9298i	0.630902	−	1.94172i
$636$	−6.59333	−	4.79034i	−0.261443	−	0.189949i
$637$	19.1239			0.757717
$638$	−11.9773	+	5.84859i	−0.474184	+	0.231548i
$639$	4.21948			0.166920
$640$	40.2249	+	29.2251i	1.59003	+	1.15522i
$641$	1.21668	−	3.74456i	0.0480561	−	0.147901i	−0.924149	−	0.382032i	$-0.875224\pi$
$641$	1.21668	−	3.74456i	0.0480561	−	0.147901i	0.972205	+	0.234131i	$0.0752244\pi$
$642$	−11.8240	−	36.3905i	−0.466655	−	1.43622i
$643$	17.9453	−	13.0381i	0.707695	−	0.514171i	−0.174734	−	0.984616i	$-0.555907\pi$
$643$	17.9453	−	13.0381i	0.707695	−	0.514171i	0.882429	+	0.470445i	$0.155907\pi$
$644$	2.27636	−	1.65387i	0.0897012	−	0.0651718i
$645$	10.3099	+	31.7306i	0.405951	+	1.24939i
$646$	0.652563	−	2.00838i	0.0256748	−	0.0790188i
$647$	10.4276	+	7.57608i	0.409950	+	0.297846i	0.773582	−	0.633697i	$-0.218463\pi$
$647$	10.4276	+	7.57608i	0.409950	+	0.297846i	−0.363631	+	0.931543i	$0.618463\pi$
$648$	−24.8239			−0.975173
$649$	−10.2914	+	19.3770i	−0.403971	+	0.760612i
$650$	39.3376			1.54295
$651$	−6.22332	−	4.52151i	−0.243911	−	0.177212i
$652$	−2.49702	+	7.68505i	−0.0977910	+	0.300970i
$653$	15.0201	+	46.2271i	0.587782	+	1.80901i	0.587799	+	0.809007i	$0.299995\pi$
$653$	15.0201	+	46.2271i	0.587782	+	1.80901i	−1.69700e−5		1.00000i	$0.500005\pi$
$654$	8.72832	−	6.34149i	0.341304	−	0.247972i
$655$	−29.5884	+	21.4972i	−1.15611	+	0.839966i
$656$	−1.42647	−	4.39022i	−0.0556943	−	0.171409i
$657$	−2.08112	+	6.40504i	−0.0811924	+	0.249884i
$658$	−8.40900	−	6.10949i	−0.327817	−	0.238173i
$659$	−0.655855			−0.0255485			−0.0127742	−	0.999918i	$-0.504066\pi$
$659$	−0.655855			−0.0255485			−0.0127742	+	0.999918i	$0.504066\pi$
$660$	15.6166	+	2.74614i	0.607874	+	0.106893i
$661$	2.10351			0.0818172			0.0409086	−	0.999163i	$-0.486975\pi$
$661$	2.10351			0.0818172			0.0409086	+	0.999163i	$0.486975\pi$
$662$	−1.96339	−	1.42649i	−0.0763094	−	0.0554420i
$663$	1.84850	−	5.68911i	0.0717900	−	0.220947i
$664$	11.4853	+	35.3483i	0.445718	+	1.37178i
$665$	−2.43343	+	1.76799i	−0.0943642	+	0.0685596i
$666$	−12.6579	+	9.19650i	−0.490483	+	0.356357i
$667$	5.37732	+	16.5497i	0.208211	+	0.640807i
$668$	2.46740	−	7.59387i	0.0954665	−	0.293816i
$669$	39.0776	+	28.3916i	1.51083	+	1.09768i
$670$	30.3495			1.17250
$671$	42.3990	+	7.45577i	1.63680	+	0.287827i
$672$	4.51665			0.174234
$673$	11.8313	+	8.59592i	0.456062	+	0.331348i	0.791984	−	0.610541i	$-0.209048\pi$
$673$	11.8313	+	8.59592i	0.456062	+	0.331348i	−0.335923	+	0.941890i	$0.609048\pi$
$674$	−11.4264	+	35.1669i	−0.440130	+	1.35458i
$675$	9.27482	+	28.5450i	0.356988	+	1.09870i
$676$	2.35965	−	1.71438i	0.0907556	−	0.0659378i
$677$	−24.6922	+	17.9399i	−0.948998	+	0.689487i	−0.950570	−	0.310512i	$-0.899500\pi$
$677$	−24.6922	+	17.9399i	−0.948998	+	0.689487i	0.00157184	+	0.999999i	$0.499500\pi$
$678$	−5.30576	−	16.3295i	−0.203767	−	0.627129i
$679$	−2.31212	+	7.11598i	−0.0887310	+	0.273086i
$680$	−6.55944	−	4.76571i	−0.251543	−	0.182757i
$681$	21.0026			0.804821
$682$	14.8783	−	28.0133i	0.569718	−	1.07269i
$683$	23.1910			0.887380			0.443690	−	0.896180i	$-0.353669\pi$
$683$	23.1910			0.887380			0.443690	+	0.896180i	$0.353669\pi$
$684$	0.841767	+	0.611579i	0.0321857	+	0.0233843i
$685$	4.00103	−	12.3139i	0.152872	−	0.470490i
$686$	−4.31181	−	13.2704i	−0.164625	−	0.506665i
$687$	−4.92160	+	3.57576i	−0.187771	+	0.136424i
$688$	−17.3994	+	12.6414i	−0.663345	+	0.481949i
$689$	5.58017	+	17.1740i	0.212588	+	0.654278i
$690$	26.5958	−	81.8535i	1.01249	−	3.11611i
$691$	−15.5610	−	11.3057i	−0.591969	−	0.430090i	0.251050	−	0.967974i	$-0.419224\pi$
$691$	−15.5610	−	11.3057i	−0.591969	−	0.430090i	−0.843019	+	0.537884i	$0.819224\pi$
$692$	2.56819			0.0976278
$693$	−2.37854	+	1.16146i	−0.0903531	+	0.0441202i
$694$	−34.7141			−1.31773
$695$	38.9738	+	28.3161i	1.47836	+	1.07409i
$696$	−3.50390	+	10.7839i	−0.132815	+	0.408762i
$697$	0.293175	+	0.902299i	0.0111048	+	0.0341770i
$698$	9.11253	−	6.62064i	0.344914	−	0.250595i
$699$	39.3989	−	28.6249i	1.49020	−	1.08269i
$700$	−1.03529	−	3.18629i	−0.0391302	−	0.120430i
$701$	−5.05123	+	15.5461i	−0.190782	+	0.587167i	−1.00000		0.000341682i	$-0.999891\pi$
$701$	−5.05123	+	15.5461i	−0.190782	+	0.587167i	0.809218	+	0.587509i	$0.199891\pi$
$702$	−13.6463	−	9.91462i	−0.515046	−	0.374203i
$703$	9.93913			0.374861
$704$	−1.90608	−	13.5169i	−0.0718383	−	0.509437i
$705$	−76.4697			−2.88002
$706$	18.5853	+	13.5030i	0.699467	+	0.508193i
$707$	−1.93453	+	5.95387i	−0.0727555	+	0.223918i
$708$	−2.67316	−	8.22713i	−0.100463	−	0.309195i
$709$	30.1231	−	21.8857i	1.13130	−	0.821935i	0.145413	−	0.989371i	$-0.453549\pi$
$709$	30.1231	−	21.8857i	1.13130	−	0.821935i	0.985883	+	0.167437i	$0.0535489\pi$
$710$	16.0435	−	11.6563i	0.602103	−	0.437453i
$711$	−2.59838	−	7.99699i	−0.0974469	−	0.299911i
$712$	7.00845	−	21.5698i	0.262653	−	0.808362i
$713$	−33.5018	−	24.3405i	−1.25465	−	0.911559i
$714$	−2.11813			−0.0792691
$715$	−24.4172	−	25.2613i	−0.913153	−	0.944719i
$716$	9.23001			0.344942
$717$	−2.88360	−	2.09506i	−0.107690	−	0.0782414i
$718$	7.73540	−	23.8071i	0.288683	−	0.888474i
$719$	−0.472748	−	1.45497i	−0.0176305	−	0.0542612i	0.941854	−	0.336022i	$-0.109082\pi$
$719$	−0.472748	−	1.45497i	−0.0176305	−	0.0542612i	−0.959485	+	0.281761i	$0.909082\pi$
$720$	18.1669	−	13.1990i	0.677041	−	0.491899i
$721$	9.69880	−	7.04659i	0.361202	−	0.262429i
$722$	8.67863	+	26.7101i	0.322985	+	0.994046i
$723$	−15.2772	+	47.0185i	−0.568167	+	1.74864i
$724$	5.00682	+	3.63767i	0.186077	+	0.135193i
$725$	20.7195			0.769502
$726$	−20.6364	−	30.5335i	−0.765890	−	1.13320i
$727$	19.2169			0.712717			0.356358	−	0.934349i	$-0.384018\pi$
$727$	19.2169			0.712717			0.356358	+	0.934349i	$0.384018\pi$
$728$	−3.28658	−	2.38784i	−0.121809	−	0.0884993i
$729$	2.49971	−	7.69331i	0.0925818	−	0.284937i
$730$	9.78096	+	30.1027i	0.362010	+	1.11415i
$731$	3.57600	−	2.59812i	0.132263	−	0.0960949i
$732$	−13.7317	+	9.97669i	−0.507539	+	0.368749i
$733$	12.7777	+	39.3257i	0.471954	+	1.45253i	0.850021	+	0.526748i	$0.176589\pi$
$733$	12.7777	+	39.3257i	0.471954	+	1.45253i	−0.378067	+	0.925778i	$0.623411\pi$
$734$	12.1493	−	37.3918i	0.448440	−	1.38016i
$735$	−40.3044	−	29.2828i	−1.48665	−	1.08011i
$736$	24.3144			0.896240
$737$	−11.7914	−	12.1989i	−0.434340	−	0.449354i
$738$	−1.94349			−0.0715409
$739$	7.15179	+	5.19608i	0.263083	+	0.191141i	0.711505	−	0.702681i	$-0.248014\pi$
$739$	7.15179	+	5.19608i	0.263083	+	0.191141i	−0.448422	+	0.893822i	$0.648014\pi$
$740$	−5.46544	+	16.8209i	−0.200914	+	0.618349i
$741$	−2.40549	−	7.40333i	−0.0883678	−	0.271968i
$742$	5.17295	−	3.75837i	0.189905	−	0.137974i
$743$	0.0885128	−	0.0643083i	0.00324722	−	0.00235924i	−0.586160	−	0.810195i	$-0.699361\pi$
$743$	0.0885128	−	0.0643083i	0.00324722	−	0.00235924i	0.589408	+	0.807836i	$0.299361\pi$
$744$	−8.33831	−	25.6627i	−0.305697	−	0.940840i
$745$	−23.3222	+	71.7783i	−0.854458	+	2.62975i
$746$	5.22301	+	3.79474i	0.191228	+	0.138935i
$747$	21.1563			0.774069
$748$	−0.293330	−	2.08013i	−0.0107252	−	0.0760572i
$749$	7.22055			0.263833
$750$	−33.3586	−	24.2365i	−1.21808	−	0.884990i
$751$	0.622431	−	1.91565i	0.0227128	−	0.0699029i	−0.939058	−	0.343760i	$-0.888299\pi$
$751$	0.622431	−	1.91565i	0.0227128	−	0.0699029i	0.961770	+	0.273857i	$0.0882994\pi$
$752$	−15.2327	−	46.8814i	−0.555479	−	1.70959i
$753$	−6.94410	+	5.04518i	−0.253057	+	0.183857i
$754$	−9.42042	+	6.84433i	−0.343071	+	0.249256i
$755$	5.32694	+	16.3946i	0.193867	+	0.596662i
$756$	−0.443926	+	1.36626i	−0.0161454	+	0.0496905i
$757$	−2.25702	−	1.63982i	−0.0820328	−	0.0596003i	0.546013	−	0.837777i	$-0.316145\pi$
$757$	−2.25702	−	1.63982i	−0.0820328	−	0.0596003i	−0.628046	+	0.778176i	$0.716145\pi$
$758$	−19.9500			−0.724618
$759$	−43.2339	+	21.1115i	−1.56929	+	0.766298i
$760$	−10.5510			−0.382723
$761$	−34.1431	−	24.8064i	−1.23769	−	0.899231i	−0.240243	−	0.970713i	$-0.577227\pi$
$761$	−34.1431	−	24.8064i	−1.23769	−	0.899231i	−0.997442	+	0.0714819i	$0.977227\pi$
$762$	14.5688	−	44.8382i	0.527773	−	1.62432i
$763$	0.629135	+	1.93628i	0.0227762	+	0.0700980i
$764$	0.669641	−	0.486523i	0.0242268	−	0.0176018i
$765$	−3.73375	+	2.71273i	−0.134994	+	0.0980789i
$766$	−12.3197	−	37.9162i	−0.445129	−	1.36997i
$767$	−5.92301	+	18.2292i	−0.213868	+	0.658217i
$768$	23.1124	+	16.7921i	0.833997	+	0.605934i
$769$	−37.8018			−1.36317			−0.681584	−	0.731740i	$-0.738709\pi$
$769$	−37.8018			−1.36317			−0.681584	+	0.731740i	$0.738709\pi$
$770$	−5.83527	+	10.9869i	−0.210289	+	0.395939i
$771$	9.66653			0.348132
$772$	−10.7348	−	7.79928i	−0.386353	−	0.280702i
$773$	−5.35901	+	16.4933i	−0.192750	+	0.593224i	0.807245	+	0.590216i	$0.200958\pi$
$773$	−5.35901	+	16.4933i	−0.192750	+	0.593224i	−0.999995	+	0.00300808i	$0.999042\pi$
$774$	2.79808	+	8.61162i	0.100575	+	0.309538i
$775$	−39.8899	+	28.9817i	−1.43289	+	1.04105i
$776$	−21.2333	+	15.4269i	−0.762230	+	0.553793i
$777$	−3.08066	−	9.48129i	−0.110518	−	0.340140i
$778$	−3.62041	+	11.1425i	−0.129798	+	0.399477i
$779$	0.998814	+	0.725681i	0.0357862	+	0.0260002i
$780$	13.8521			0.495984
$781$	−10.9185	−	1.91998i	−0.390693	−	0.0687024i
$782$	−11.4025			−0.407752
$783$	−7.18763	−	5.22212i	−0.256865	−	0.186623i
$784$	9.92388	−	30.5426i	0.354424	−	1.09081i
$785$	5.04802	+	15.5362i	0.180172	+	0.554511i
$786$	−27.1142	+	19.6996i	−0.967132	+	0.702662i
$787$	17.8573	−	12.9741i	0.636544	−	0.462476i	−0.222117	−	0.975020i	$-0.571297\pi$
$787$	17.8573	−	12.9741i	0.636544	−	0.462476i	0.858661	+	0.512544i	$0.171297\pi$
$788$	4.11750	+	12.6724i	0.146680	+	0.451434i
$789$	5.21138	−	16.0390i	0.185530	−	0.571003i
$790$	−31.9714	−	23.2286i	−1.13749	−	0.826435i
$791$	3.24007			0.115204
$792$	−9.14464	−	1.60806i	−0.324941	−	0.0571400i
$793$	37.6085			1.33552
$794$	20.9518	+	15.2224i	0.743551	+	0.540221i
$795$	14.5367	−	44.7394i	0.515564	−	1.58674i
$796$	−0.0739304	−	0.227534i	−0.00262039	−	0.00806475i
$797$	15.3263	−	11.1352i	0.542885	−	0.394429i	−0.282271	−	0.959335i	$-0.591088\pi$
$797$	15.3263	−	11.1352i	0.542885	−	0.394429i	0.825155	+	0.564906i	$0.191088\pi$
$798$	−2.22994	+	1.62015i	−0.0789391	+	0.0573526i
$799$	3.13069	+	9.63528i	0.110756	+	0.340872i
$800$	8.94624	−	27.5337i	0.316297	−	0.973463i
$801$	−10.4442	−	7.58816i	−0.369028	−	0.268115i
$802$	−7.78051			−0.274740
$803$	8.29967	−	15.6269i	0.292889	−	0.551462i
$804$	6.68932			0.235914
$805$	13.1395	+	9.54637i	0.463105	+	0.336466i
$806$	8.56292	−	26.3540i	0.301616	−	0.928279i
$807$	−4.84835	−	14.9217i	−0.170670	−	0.525268i
$808$	−17.7657	+	12.9075i	−0.624995	+	0.454085i
$809$	35.7749	−	25.9920i	1.25778	−	0.913829i	0.259131	−	0.965842i	$-0.416564\pi$
$809$	35.7749	−	25.9920i	1.25778	−	0.913829i	0.998646	+	0.0520136i	$0.0165639\pi$
$810$	20.5217	+	63.1593i	0.721059	+	2.21919i
$811$	2.47382	−	7.61363i	0.0868676	−	0.267351i	−0.898182	−	0.439625i	$-0.855111\pi$
$811$	2.47382	−	7.61363i	0.0868676	−	0.267351i	0.985049	+	0.172274i	$0.0551114\pi$
$812$	0.802308	+	0.582911i	0.0281555	+	0.0204562i
$813$	−23.7473			−0.832853
$814$	36.9387	−	18.0374i	1.29470	−	0.632212i
$815$	−46.6419			−1.63379
$816$	−8.12678	−	5.90445i	−0.284494	−	0.206697i
$817$	1.77748	−	5.47053i	0.0621862	−	0.191390i
$818$	7.68523	+	23.6527i	0.268708	+	0.826997i
$819$	−1.87078	+	1.35920i	−0.0653703	+	0.0474943i
$820$	−1.77738	+	1.29134i	−0.0620686	+	0.0450955i
$821$	13.8700	+	42.6874i	0.484065	+	1.48980i	0.833330	+	0.552776i	$0.186432\pi$
$821$	13.8700	+	42.6874i	0.484065	+	1.48980i	−0.349264	+	0.937024i	$0.613568\pi$
$822$	3.66646	−	11.2842i	0.127883	−	0.393582i
$823$	18.0518	+	13.1154i	0.629247	+	0.457175i	0.856139	−	0.516745i	$-0.172857\pi$
$823$	18.0518	+	13.1154i	0.629247	+	0.457175i	−0.226892	+	0.973920i	$0.572857\pi$
$824$	42.0525			1.46497
$825$	7.99922	+	56.7260i	0.278497	+	1.97495i
$826$	6.78696			0.236149
$827$	0.740741	+	0.538180i	0.0257581	+	0.0187143i	0.600590	−	0.799557i	$-0.294932\pi$
$827$	0.740741	+	0.538180i	0.0257581	+	0.0187143i	−0.574832	+	0.818272i	$0.694932\pi$
$828$	1.73610	−	5.34318i	0.0603338	−	0.185688i
$829$	−4.38063	−	13.4822i	−0.152145	−	0.468256i	0.845715	−	0.533635i	$-0.179174\pi$
$829$	−4.38063	−	13.4822i	−0.152145	−	0.468256i	−0.997860	+	0.0653792i	$0.979174\pi$
$830$	80.4417	−	58.4443i	2.79217	−	2.02863i
$831$	44.0821	−	32.0275i	1.52919	−	1.11102i
$832$	−3.68512	−	11.3416i	−0.127759	−	0.393201i
$833$	−2.03960	+	6.27725i	−0.0706680	+	0.217494i
$834$	35.7148	+	25.9483i	1.23670	+	0.898516i
$835$	46.0885			1.59496
$836$	−1.89990	−	1.96557i	−0.0657093	−	0.0679807i
$837$	21.1424			0.730789
$838$	−16.7803	−	12.1916i	−0.579666	−	0.421152i
$839$	−0.281080	+	0.865075i	−0.00970396	+	0.0298657i	−0.955791	−	0.294046i	$-0.904998\pi$
$839$	−0.281080	+	0.865075i	−0.00970396	+	0.0298657i	0.946087	+	0.323912i	$0.104998\pi$
$840$	3.27030	+	10.0649i	0.112836	+	0.347273i
$841$	18.4997	−	13.4408i	0.637920	−	0.463476i
$842$	13.9318	−	10.1220i	0.480121	−	0.348828i
$843$	−16.3885	−	50.4387i	−0.564451	−	1.73720i
$844$	3.44189	−	10.5930i	0.118475	−	0.364627i
$845$	13.6202	+	9.89564i	0.468549	+	0.340420i
$846$	−20.7537			−0.713528
$847$	6.68328	−	1.92313i	0.229640	−	0.0660794i
$848$	30.3241			1.04133
$849$	−15.1515	−	11.0082i	−0.519998	−	0.377801i
$850$	−4.19543	+	12.9122i	−0.143902	+	0.442885i
$851$	−16.5840	−	51.0404i	−0.568493	−	1.74964i
$852$	3.53615	−	2.56916i	0.121147	−	0.0880181i
$853$	4.43016	−	3.21870i	0.151686	−	0.110206i	−0.509354	−	0.860557i	$-0.670115\pi$
$853$	4.43016	−	3.21870i	0.151686	−	0.110206i	0.661040	+	0.750351i	$0.270115\pi$
$854$	−4.11513	−	12.6651i	−0.140817	−	0.433389i
$855$	−1.85589	+	5.71184i	−0.0634701	+	0.195341i
$856$	20.4908	+	14.8874i	0.700361	+	0.508842i
$857$	−58.2602			−1.99013			−0.995066	−	0.0992194i	$-0.968365\pi$
$857$	−58.2602			−1.99013			−0.995066	+	0.0992194i	$0.968365\pi$
$858$	−22.3755	−	23.1489i	−0.763886	−	0.790291i
$859$	−27.2189			−0.928698			−0.464349	−	0.885652i	$-0.653712\pi$
$859$	−27.2189			−0.928698			−0.464349	+	0.885652i	$0.653712\pi$
$860$	8.28085	+	6.01639i	0.282375	+	0.205157i
$861$	0.382668	−	1.17773i	0.0130413	−	0.0401370i
$862$	11.0921	+	34.1379i	0.377798	+	1.16274i
$863$	−1.19105	+	0.865351i	−0.0405439	+	0.0294569i	−0.607873	−	0.794035i	$-0.707977\pi$
$863$	−1.19105	+	0.865351i	−0.0405439	+	0.0294569i	0.567329	+	0.823491i	$0.307977\pi$
$864$	−10.0430	+	7.29669i	−0.341671	+	0.248239i
$865$	4.58084	+	14.0984i	0.155753	+	0.479359i
$866$	−15.2355	+	46.8902i	−0.517725	+	1.59339i
$867$	1.67025	+	1.21351i	0.0567248	+	0.0412130i
$868$	−2.35999			−0.0801033
$869$	3.08479	+	21.8756i	0.104644	+	0.742079i
$870$	30.3341			1.02842
$871$	−11.9911	−	8.71202i	−0.406302	−	0.295196i
$872$	−2.20686	+	6.79203i	−0.0747338	+	0.230007i
$873$	4.61658	+	14.2084i	0.156247	+	0.480880i
$874$	−12.0044	+	8.72170i	−0.406054	+	0.295016i
$875$	6.29502	−	4.57360i	0.212810	−	0.154616i
$876$	2.15582	+	6.63493i	0.0728384	+	0.224174i
$877$	−12.8959	+	39.6896i	−0.435465	+	1.34022i	0.457144	+	0.889393i	$0.348872\pi$
$877$	−12.8959	+	39.6896i	−0.435465	+	1.34022i	−0.892609	+	0.450831i	$0.851128\pi$
$878$	21.8243	+	15.8563i	0.736535	+	0.535124i
$879$	−12.8784			−0.434378
$880$	−53.0152	+	25.8878i	−1.78714	+	0.872677i
$881$	35.5985			1.19934			0.599672	−	0.800246i	$-0.295298\pi$
$881$	35.5985			1.19934			0.599672	+	0.800246i	$0.295298\pi$
$882$	−10.9385	−	7.94731i	−0.368320	−	0.267600i
$883$	14.5308	−	44.7212i	0.489000	−	1.50499i	−0.337102	−	0.941468i	$-0.609447\pi$
$883$	14.5308	−	44.7212i	0.489000	−	1.50499i	0.826102	−	0.563520i	$-0.190553\pi$
$884$	−0.567109	−	1.74538i	−0.0190739	−	0.0587035i
$885$	40.3958	−	29.3493i	1.35789	−	0.986564i
$886$	−40.3708	+	29.3311i	−1.35629	+	0.985399i
$887$	6.20205	+	19.0879i	0.208244	+	0.640911i	0.999565	+	0.0295084i	$0.00939419\pi$
$887$	6.20205	+	19.0879i	0.208244	+	0.640911i	−0.791320	+	0.611402i	$0.790606\pi$
$888$	10.8063	−	33.2582i	0.362634	−	1.11607i
$889$	7.19762	+	5.22937i	0.241400	+	0.175388i
$890$	−60.6738			−2.03379
$891$	17.4138	−	32.7873i	0.583383	−	1.09842i
$892$	14.8189			0.496174
$893$	10.6659	+	7.74925i	0.356921	+	0.259319i
$894$	−21.3720	+	65.7762i	−0.714786	+	2.19988i
$895$	16.4634	+	50.6693i	0.550312	+	1.69369i
$896$	−6.95600	+	5.05383i	−0.232384	+	0.168837i
$897$	−34.0046	+	24.7058i	−1.13538	+	0.824902i
$898$	3.18132	+	9.79110i	0.106162	+	0.326733i
$899$	4.51017	−	13.8809i	0.150423	−	0.462953i
$900$	−5.41185	−	3.93194i	−0.180395	−	0.131065i
$901$	−6.23235			−0.207630
$902$	5.02904	+	0.884345i	0.167449	+	0.0294455i
$903$	−5.76947			−0.191996
$904$	9.19482	+	6.68043i	0.305815	+	0.222188i
$905$	−11.0388	+	33.9740i	−0.366943	+	1.12933i
$906$	4.88150	+	15.0237i	0.162177	+	0.499129i
$907$	4.68758	−	3.40572i	0.155648	−	0.113085i	−0.507235	−	0.861808i	$-0.669332\pi$
$907$	4.68758	−	3.40572i	0.155648	−	0.113085i	0.662884	+	0.748722i	$0.269332\pi$
$908$	5.21287	−	3.78737i	0.172995	−	0.125688i
$909$	3.86265	+	11.8880i	0.128116	+	0.394300i
$910$	−3.35839	+	10.3361i	−0.111330	+	0.342637i
$911$	7.94559	+	5.77281i	0.263249	+	0.191262i	0.711578	−	0.702607i	$-0.247981\pi$
$911$	7.94559	+	5.77281i	0.263249	+	0.191262i	−0.448329	+	0.893869i	$0.647981\pi$
$912$	−13.0720			−0.432859
$913$	−54.7448	−	9.62674i	−1.81179	−	0.318599i
$914$	19.4194			0.642337
$915$	−79.2613	−	57.5867i	−2.62030	−	1.90376i
$916$	−0.576736	+	1.77501i	−0.0190559	+	0.0586481i
$917$	−1.95439	−	6.01498i	−0.0645395	−	0.198632i
$918$	4.70979	−	3.42186i	0.155446	−	0.112938i
$919$	5.82874	−	4.23483i	0.192273	−	0.139694i	−0.487484	−	0.873132i	$-0.662085\pi$
$919$	5.82874	−	4.23483i	0.192273	−	0.139694i	0.679757	+	0.733438i	$0.262085\pi$
$920$	17.6049	+	54.1823i	0.580416	+	1.78634i
$921$	−5.37785	+	16.5513i	−0.177206	+	0.545384i
$922$	−13.7460	−	9.98706i	−0.452701	−	0.328906i
$923$	−9.68481			−0.318779
$924$	−1.28615	+	2.42161i	−0.0423113	+	0.0796652i
$925$	−63.9002			−2.10103
$926$	−21.6225	−	15.7097i	−0.710559	−	0.516251i
$927$	7.39694	−	22.7655i	0.242948	−	0.747716i
$928$	2.64817	+	8.15021i	0.0869303	+	0.267544i
$929$	10.8318	−	7.86974i	0.355379	−	0.258198i	−0.395743	−	0.918361i	$-0.629513\pi$
$929$	10.8318	−	7.86974i	0.355379	−	0.258198i	0.751122	+	0.660163i	$0.229513\pi$
$930$	−58.4003	+	42.4303i	−1.91502	+	1.39134i
$931$	2.65417	+	8.16869i	0.0869868	+	0.267718i
$932$	4.61694	−	14.2095i	0.151233	−	0.465447i
$933$	−56.7336	−	41.2194i	−1.85737	−	1.34946i
$934$	−45.5494			−1.49042
$935$	10.8959	−	5.32058i	0.356335	−	0.174001i
$936$	−8.11141			−0.265130
$937$	−23.1030	−	16.7853i	−0.754742	−	0.548352i	0.142551	−	0.989787i	$-0.454469\pi$
$937$	−23.1030	−	16.7853i	−0.754742	−	0.548352i	−0.897293	+	0.441435i	$0.854469\pi$
$938$	−1.62180	+	4.99139i	−0.0529537	+	0.162975i
$939$	6.17439	+	19.0028i	0.201494	+	0.620134i
$940$	−18.9799	+	13.7897i	−0.619055	+	0.449770i
$941$	−41.0633	+	29.8343i	−1.33863	+	0.972569i	−0.339133	+	0.940738i	$0.610134\pi$
$941$	−41.0633	+	29.8343i	−1.33863	+	0.972569i	−0.999493	+	0.0318305i	$0.989866\pi$
$942$	4.62590	+	14.2371i	0.150720	+	0.463869i
$943$	2.06001	−	6.34005i	0.0670831	−	0.206460i
$944$	26.0400	+	18.9192i	0.847529	+	0.615766i
$945$	−8.29209			−0.269742
$946$	−3.32188	−	23.5569i	−0.108004	−	0.765901i
$947$	2.64871			0.0860714			0.0430357	−	0.999074i	$-0.486297\pi$
$947$	2.64871			0.0860714			0.0430357	+	0.999074i	$0.486297\pi$
$948$	−7.04681	−	5.11981i	−0.228870	−	0.166284i
$949$	4.77673	−	14.7013i	0.155059	−	0.477223i
$950$	5.45958	+	16.8029i	0.177132	+	0.545157i
$951$	42.7326	−	31.0470i	1.38570	−	1.00677i
$952$	1.13431	−	0.824123i	0.0367631	−	0.0267100i
$953$	−0.341318	−	1.05047i	−0.0110564	−	0.0340280i	0.945376	−	0.325982i	$-0.105695\pi$
$953$	−0.341318	−	1.05047i	−0.0110564	−	0.0340280i	−0.956433	+	0.291954i	$0.905695\pi$
$954$	3.94523	−	12.1422i	0.127732	−	0.393118i
$955$	3.86526	+	2.80827i	0.125077	+	0.0908736i
$956$	−1.09351			−0.0353667
$957$	−11.7854	−	12.1928i	−0.380967	−	0.394136i
$958$	−36.1528			−1.16804
$959$	1.81139	+	1.31605i	0.0584928	+	0.0424975i
$960$	−9.59998	+	29.5457i	−0.309838	+	0.953583i
$961$	1.15344	+	3.54992i	0.0372077	+	0.114513i
$962$	29.0532	−	21.1084i	0.936713	−	0.680562i
$963$	11.6637	−	8.47419i	0.375858	−	0.273077i
$964$	4.68696	+	14.4250i	0.150957	+	0.464597i
$965$	23.6676	−	72.8414i	0.761887	−	2.34485i
$966$	12.0407	+	8.74811i	0.387404	+	0.281466i
$967$	−30.0816			−0.967360			−0.483680	−	0.875245i	$-0.660700\pi$
$967$	−30.0816			−0.967360			−0.483680	+	0.875245i	$0.660700\pi$
$968$	22.9312	+	8.32215i	0.737038	+	0.267484i
$969$	2.68663			0.0863069
$970$	56.8040	+	41.2705i	1.82387	+	1.32512i
$971$	−10.0936	+	31.0649i	−0.323919	+	0.996919i	0.648008	+	0.761634i	$0.275602\pi$
$971$	−10.0936	+	31.0649i	−0.323919	+	0.996919i	−0.971926	+	0.235285i	$0.924398\pi$
$972$	2.41669	+	7.43781i	0.0775154	+	0.238568i
$973$	−6.73964	+	4.89664i	−0.216063	+	0.156979i
$974$	11.9815	−	8.70504i	0.383911	−	0.278928i
$975$	15.4653	+	47.5972i	0.495285	+	1.52433i
$976$	19.5160	−	60.0641i	0.624692	−	1.92260i
$977$	10.1807	+	7.39673i	0.325710	+	0.236642i	0.738608	−	0.674135i	$-0.235483\pi$
$977$	10.1807	+	7.39673i	0.325710	+	0.236642i	−0.412898	+	0.910777i	$0.635483\pi$
$978$	−42.7417			−1.36673
$979$	23.5729	+	24.3878i	0.753395	+	0.779437i
$980$	−15.2841			−0.488233
$981$	3.28874	+	2.38941i	0.105001	+	0.0762879i
$982$	−16.6508	+	51.2460i	−0.531350	+	1.63533i
$983$	−8.56957	−	26.3744i	−0.273327	−	0.841213i	−0.989657	−	0.143452i	$-0.954180\pi$
$983$	−8.56957	−	26.3744i	−0.273327	−	0.841213i	0.716330	−	0.697761i	$-0.245820\pi$
$984$	3.51422	−	2.55323i	0.112029	−	0.0813940i
$985$	−62.2221	+	45.2070i	−1.98256	+	1.44042i
$986$	−1.24189	−	3.82213i	−0.0395497	−	0.121721i
$987$	4.08636	−	12.5765i	0.130070	−	0.400315i
$988$	−1.93208	−	1.40374i	−0.0614675	−	0.0446588i
$989$	−31.0586			−0.987607
$990$	3.46841	+	24.5961i	0.110233	+	0.781714i
$991$	37.2665			1.18381			0.591905	−	0.806007i	$-0.298376\pi$
$991$	37.2665			1.18381			0.591905	+	0.806007i	$0.298376\pi$
$992$	−16.4986	−	11.9869i	−0.523831	−	0.380586i
$993$	0.954111	−	2.93645i	0.0302778	−	0.0931855i
$994$	1.05971	+	3.26146i	0.0336121	+	0.103447i
$995$	1.11721	−	0.811700i	0.0354179	−	0.0257326i
$996$	17.7301	−	12.8817i	0.561801	−	0.408172i
$997$	−9.30581	−	28.6403i	−0.294718	−	0.907049i	−0.983316	−	0.181905i	$-0.941774\pi$
$997$	−9.30581	−	28.6403i	−0.294718	−	0.907049i	0.688598	−	0.725143i	$-0.258226\pi$
$998$	11.2557	−	34.6414i	0.356292	−	1.09655i
$999$	22.1671	+	16.1054i	0.701337	+	0.509551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.103.7	yes	36
11.3	even	5	inner	187.2.g.f.69.7	✓	36
11.5	even	5		2057.2.a.bd.1.6		18
11.6	odd	10		2057.2.a.be.1.13		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.7	✓	36	11.3	even	5	inner
187.2.g.f.103.7	yes	36	1.1	even	1	trivial
2057.2.a.bd.1.6		18	11.5	even	5
2057.2.a.be.1.13		18	11.6	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)

\(f(q)\)	\(=\)	\(q+(1.31285 + 0.953841i) q^{2} +(-0.637980 + 1.96350i) q^{3} +(0.195728 + 0.602389i) q^{4} +(-2.95777 + 2.14895i) q^{5} +(-2.71044 + 1.96925i) q^{6} +(-0.195368 - 0.601281i) q^{7} +(0.685306 - 2.10916i) q^{8} +(-1.02126 - 0.741992i) q^{9} +O(q^{10})\)	\(q+(1.31285 + 0.953841i) q^{2} +(-0.637980 + 1.96350i) q^{3} +(0.195728 + 0.602389i) q^{4} +(-2.95777 + 2.14895i) q^{5} +(-2.71044 + 1.96925i) q^{6} +(-0.195368 - 0.601281i) q^{7} +(0.685306 - 2.10916i) q^{8} +(-1.02126 - 0.741992i) q^{9} -5.93286 q^{10} +(2.30503 + 2.38471i) q^{11} -1.30766 q^{12} +(2.34407 + 1.70307i) q^{13} +(0.317038 - 0.975742i) q^{14} +(-2.33246 - 7.17857i) q^{15} +(3.93635 - 2.85993i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(-0.633025 - 1.94825i) q^{18} +(-0.402129 + 1.23762i) q^{19} +(-1.87342 - 1.36112i) q^{20} +1.30526 q^{21} +(0.751525 + 5.32940i) q^{22} +7.02655 q^{23} +(3.70412 + 2.69120i) q^{24} +(2.58535 - 7.95689i) q^{25} +(1.45296 + 4.47175i) q^{26} +(-2.90231 + 2.10865i) q^{27} +(0.323966 - 0.235375i) q^{28} +(0.765286 + 2.35531i) q^{29} +(3.78505 - 11.6492i) q^{30} +(-4.76789 - 3.46408i) q^{31} +3.46036 q^{32} +(-6.15294 + 3.00453i) q^{33} -1.62277 q^{34} +(1.86997 + 1.35862i) q^{35} +(0.247078 - 0.760427i) q^{36} +(-2.36020 - 7.26393i) q^{37} +(-1.70843 + 1.24125i) q^{38} +(-4.83945 + 3.51606i) q^{39} +(2.50548 + 7.71108i) q^{40} +(0.293175 - 0.902299i) q^{41} +(1.71361 + 1.24501i) q^{42} -4.42018 q^{43} +(-0.985363 + 1.85528i) q^{44} +4.61517 q^{45} +(9.22481 + 6.70221i) q^{46} +(3.13069 - 9.63528i) q^{47} +(3.10415 + 9.55360i) q^{48} +(5.33975 - 3.87955i) q^{49} +(10.9838 - 7.98019i) q^{50} +(-0.637980 - 1.96350i) q^{51} +(-0.567109 + 1.74538i) q^{52} +(5.04208 + 3.66329i) q^{53} -5.82162 q^{54} +(-11.9424 - 2.10004i) q^{55} -1.40208 q^{56} +(-2.17353 - 1.57916i) q^{57} +(-1.24189 + 3.82213i) q^{58} +(2.04423 + 6.29149i) q^{59} +(3.86776 - 2.81009i) q^{60} +(10.5010 - 7.62941i) q^{61} +(-2.95535 - 9.09562i) q^{62} +(-0.246623 + 0.759028i) q^{63} +(-3.32977 - 2.41922i) q^{64} -10.5930 q^{65} +(-10.9437 - 1.92443i) q^{66} -5.11549 q^{67} +(-0.512423 - 0.372297i) q^{68} +(-4.48280 + 13.7966i) q^{69} +(1.15909 + 3.56732i) q^{70} +(-2.70418 + 1.96470i) q^{71} +(-2.26486 + 1.64551i) q^{72} +(-1.64861 - 5.07389i) q^{73} +(3.83006 - 11.7877i) q^{74} +(13.9740 + 10.1527i) q^{75} -0.824239 q^{76} +(0.983551 - 1.85187i) q^{77} -9.70724 q^{78} +(5.38886 + 3.91524i) q^{79} +(-5.49699 + 16.9180i) q^{80} +(-3.45899 - 10.6457i) q^{81} +(1.24554 - 0.904941i) q^{82} +(-13.5587 + 9.85095i) q^{83} +(0.255475 + 0.786272i) q^{84} +(1.12977 - 3.47707i) q^{85} +(-5.80304 - 4.21615i) q^{86} -5.11289 q^{87} +(6.60937 - 3.22741i) q^{88} +10.2267 q^{89} +(6.05902 + 4.40214i) q^{90} +(0.566066 - 1.74217i) q^{91} +(1.37529 + 4.23272i) q^{92} +(9.84353 - 7.15175i) q^{93} +(13.3007 - 9.66350i) q^{94} +(-1.47018 - 4.52476i) q^{95} +(-2.20764 + 6.79442i) q^{96} +(-9.57447 - 6.95626i) q^{97} +10.7108 q^{98} +(-0.584610 - 4.14573i) 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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