LMFDB - Embedded newform 187.2.g.f.69.5

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			69.5
Character	$\chi$	$=$	187.69
Dual form			187.2.g.f.103.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415893 + 0.302164i) q^{2} +(0.814643 + 2.50721i) q^{3} +(-0.536370 + 1.65078i) q^{4} +(-3.29479 - 2.39381i) q^{5} +(-1.09640 - 0.796578i) q^{6} +(-0.581623 + 1.79005i) q^{7} +(-0.593447 - 1.82644i) q^{8} +(-3.19543 + 2.32161i) q^{9} +O(q^{10})$	\(q+(-0.415893 + 0.302164i) q^{2} +(0.814643 + 2.50721i) q^{3} +(-0.536370 + 1.65078i) q^{4} +(-3.29479 - 2.39381i) q^{5} +(-1.09640 - 0.796578i) q^{6} +(-0.581623 + 1.79005i) q^{7} +(-0.593447 - 1.82644i) q^{8} +(-3.19543 + 2.32161i) q^{9} +2.09360 q^{10} +(3.19252 + 0.898776i) q^{11} -4.57580 q^{12} +(-1.18726 + 0.862592i) q^{13} +(-0.298997 - 0.920217i) q^{14} +(3.31771 - 10.2108i) q^{15} +(-2.00977 - 1.46019i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.627448 - 1.93109i) q^{18} +(1.72318 + 5.30339i) q^{19} +(5.71887 - 4.15500i) q^{20} -4.96186 q^{21} +(-1.59933 + 0.590871i) q^{22} +0.385329 q^{23} +(4.09584 - 2.97580i) q^{24} +(3.58026 + 11.0189i) q^{25} +(0.233127 - 0.717492i) q^{26} +(-2.02562 - 1.47170i) q^{27} +(-2.64301 - 1.92026i) q^{28} +(-3.10949 + 9.57003i) q^{29} +(1.70554 + 5.24912i) q^{30} +(-1.13698 + 0.826065i) q^{31} +5.11794 q^{32} +(0.347343 + 8.73652i) q^{33} +0.514072 q^{34} +(6.20137 - 4.50556i) q^{35} +(-2.11854 - 6.52018i) q^{36} +(2.02914 - 6.24505i) q^{37} +(-2.31915 - 1.68496i) q^{38} +(-3.12989 - 2.27400i) q^{39} +(-2.41687 + 7.43835i) q^{40} +(-0.619399 - 1.90631i) q^{41} +(2.06360 - 1.49930i) q^{42} +3.33783 q^{43} +(-3.19605 + 4.78807i) q^{44} +16.0858 q^{45} +(-0.160256 + 0.116433i) q^{46} +(0.528459 + 1.62643i) q^{47} +(2.02375 - 6.22846i) q^{48} +(2.79712 + 2.03222i) q^{49} +(-4.81853 - 3.50086i) q^{50} +(0.814643 - 2.50721i) q^{51} +(-0.787138 - 2.42256i) q^{52} +(8.14017 - 5.91418i) q^{53} +1.28714 q^{54} +(-8.36720 - 10.6036i) q^{55} +3.61459 q^{56} +(-11.8930 + 8.64075i) q^{57} +(-1.59850 - 4.91969i) q^{58} +(2.22041 - 6.83372i) q^{59} +(15.0763 + 10.9536i) q^{60} +(-8.92510 - 6.48447i) q^{61} +(0.223256 - 0.687110i) q^{62} +(-2.29728 - 7.07029i) q^{63} +(1.89103 - 1.37391i) q^{64} +5.97664 q^{65} +(-2.78432 - 3.52851i) q^{66} +7.28195 q^{67} +(1.40423 - 1.02024i) q^{68} +(0.313905 + 0.966102i) q^{69} +(-1.21769 + 3.74766i) q^{70} +(1.81705 + 1.32017i) q^{71} +(6.13661 + 4.45851i) q^{72} +(1.46468 - 4.50783i) q^{73} +(1.04312 + 3.21041i) q^{74} +(-24.7101 + 17.9530i) q^{75} -9.67898 q^{76} +(-3.46570 + 5.19203i) q^{77} +1.98882 q^{78} +(-5.36702 + 3.89937i) q^{79} +(3.12638 + 9.62202i) q^{80} +(-1.62192 + 4.99176i) q^{81} +(0.833624 + 0.605663i) q^{82} +(11.9874 + 8.70933i) q^{83} +(2.66139 - 8.19092i) q^{84} +(1.25850 + 3.87326i) q^{85} +(-1.38818 + 1.00857i) q^{86} -26.5272 q^{87} +(-0.253031 - 6.36434i) q^{88} -9.20456 q^{89} +(-6.68996 + 4.86054i) q^{90} +(-0.853549 - 2.62695i) q^{91} +(-0.206679 + 0.636092i) q^{92} +(-2.99736 - 2.17771i) q^{93} +(-0.711231 - 0.516740i) q^{94} +(7.01779 - 21.5985i) q^{95} +(4.16929 + 12.8318i) q^{96} +(7.32314 - 5.32057i) q^{97} -1.77737 q^{98} +(-12.2881 + 4.53983i) 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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.415893	+	0.302164i	−0.294081	+	0.213662i	−0.725036	−	0.688711i	$-0.758177\pi$
$2$	−0.415893	+	0.302164i	−0.294081	+	0.213662i	0.430955	+	0.902374i	$0.358177\pi$
$3$	0.814643	+	2.50721i	0.470334	+	1.44754i	0.852148	+	0.523301i	$0.175300\pi$
$3$	0.814643	+	2.50721i	0.470334	+	1.44754i	−0.381813	+	0.924239i	$0.624700\pi$
$4$	−0.536370	+	1.65078i	−0.268185	+	0.825388i
$5$	−3.29479	−	2.39381i	−1.47348	−	1.07054i	−0.979588	−	0.201017i	$-0.935575\pi$
$5$	−3.29479	−	2.39381i	−1.47348	−	1.07054i	−0.493888	−	0.869525i	$-0.664425\pi$
$6$	−1.09640	−	0.796578i	−0.447601	−	0.325201i
$7$	−0.581623	+	1.79005i	−0.219833	+	0.676576i	0.778942	+	0.627096i	$0.215757\pi$
$7$	−0.581623	+	1.79005i	−0.219833	+	0.676576i	−0.998775	+	0.0494805i	$0.984243\pi$
$8$	−0.593447	−	1.82644i	−0.209815	−	0.645745i
$9$	−3.19543	+	2.32161i	−1.06514	+	0.773871i
$10$	2.09360			0.662056
$11$	3.19252	+	0.898776i	0.962582	+	0.270991i
$11$	3.19252	+	0.898776i	0.962582	+	0.270991i
$12$	−4.57580			−1.32092
$13$	−1.18726	+	0.862592i	−0.329285	+	0.239240i	−0.740127	−	0.672467i	$-0.765235\pi$
$13$	−1.18726	+	0.862592i	−0.329285	+	0.239240i	0.410842	+	0.911707i	$0.365235\pi$
$14$	−0.298997	−	0.920217i	−0.0799102	−	0.245938i
$15$	3.31771	−	10.2108i	0.856628	−	2.63643i
$16$	−2.00977	−	1.46019i	−0.502443	−	0.365046i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	0.627448	−	1.93109i	0.147891	−	0.455162i
$19$	1.72318	+	5.30339i	0.395324	+	1.21668i	0.928709	+	0.370809i	$0.120920\pi$
$19$	1.72318	+	5.30339i	0.395324	+	1.21668i	−0.533385	+	0.845873i	$0.679080\pi$
$20$	5.71887	−	4.15500i	1.27878	−	0.929086i
$21$	−4.96186			−1.08277
$22$	−1.59933	+	0.590871i	−0.340978	+	0.125974i
$23$	0.385329			0.0803466			0.0401733	−	0.999193i	$-0.487209\pi$
$23$	0.385329			0.0803466			0.0401733	+	0.999193i	$0.487209\pi$
$24$	4.09584	−	2.97580i	0.836059	−	0.607432i
$25$	3.58026	+	11.0189i	0.716052	+	2.20378i
$26$	0.233127	−	0.717492i	0.0457200	−	0.140712i
$27$	−2.02562	−	1.47170i	−0.389832	−	0.283229i
$28$	−2.64301	−	1.92026i	−0.499482	−	0.362895i
$29$	−3.10949	+	9.57003i	−0.577418	+	1.77711i	0.0503753	+	0.998730i	$0.483958\pi$
$29$	−3.10949	+	9.57003i	−0.577418	+	1.77711i	−0.627793	+	0.778380i	$0.716042\pi$
$30$	1.70554	+	5.24912i	0.311388	+	0.958353i
$31$	−1.13698	+	0.826065i	−0.204208	+	0.148366i	−0.685189	−	0.728365i	$-0.740280\pi$
$31$	−1.13698	+	0.826065i	−0.204208	+	0.148366i	0.480981	+	0.876731i	$0.340280\pi$
$32$	5.11794			0.904732
$33$	0.347343	+	8.73652i	0.0604647	+	1.52083i
$34$	0.514072			0.0881627
$35$	6.20137	−	4.50556i	1.04822	−	0.761578i
$36$	−2.11854	−	6.52018i	−0.353089	−	1.08670i
$37$	2.02914	−	6.24505i	0.333588	−	1.02668i	−0.633825	−	0.773477i	$-0.718516\pi$
$37$	2.02914	−	6.24505i	0.333588	−	1.02668i	0.967413	−	0.253203i	$-0.0814840\pi$
$38$	−2.31915	−	1.68496i	−0.376216	−	0.273337i
$39$	−3.12989	−	2.27400i	−0.501184	−	0.364131i
$40$	−2.41687	+	7.43835i	−0.382140	+	1.17611i
$41$	−0.619399	−	1.90631i	−0.0967339	−	0.297716i	0.890968	−	0.454067i	$-0.150027\pi$
$41$	−0.619399	−	1.90631i	−0.0967339	−	0.297716i	−0.987702	+	0.156350i	$0.950027\pi$
$42$	2.06360	−	1.49930i	0.318421	−	0.231346i
$43$	3.33783			0.509014			0.254507	−	0.967071i	$-0.418087\pi$
$43$	3.33783			0.509014			0.254507	+	0.967071i	$0.418087\pi$
$44$	−3.19605	+	4.78807i	−0.481823	+	0.721828i
$45$	16.0858			2.39792
$46$	−0.160256	+	0.116433i	−0.0236284	+	0.0171670i
$47$	0.528459	+	1.62643i	0.0770837	+	0.237239i	0.982172	−	0.187984i	$-0.0601955\pi$
$47$	0.528459	+	1.62643i	0.0770837	+	0.237239i	−0.905088	+	0.425224i	$0.860195\pi$
$48$	2.02375	−	6.22846i	0.292103	−	0.899001i
$49$	2.79712	+	2.03222i	0.399588	+	0.290318i
$50$	−4.81853	−	3.50086i	−0.681443	−	0.495097i
$51$	0.814643	−	2.50721i	0.114073	−	0.351080i
$52$	−0.787138	−	2.42256i	−0.109156	−	0.335949i
$53$	8.14017	−	5.91418i	1.11814	−	0.812375i	0.134213	−	0.990953i	$-0.457150\pi$
$53$	8.14017	−	5.91418i	1.11814	−	0.812375i	0.983926	+	0.178577i	$0.0571495\pi$
$54$	1.28714			0.175157
$55$	−8.36720	−	10.6036i	−1.12823	−	1.42978i
$56$	3.61459			0.483020
$57$	−11.8930	+	8.64075i	−1.57526	+	1.14449i
$58$	−1.59850	−	4.91969i	−0.209894	−	0.645987i
$59$	2.22041	−	6.83372i	0.289073	−	0.889675i	−0.696075	−	0.717969i	$-0.745072\pi$
$59$	2.22041	−	6.83372i	0.289073	−	0.889675i	0.985148	−	0.171706i	$-0.0549280\pi$
$60$	15.0763	+	10.9536i	1.94634	+	1.41410i
$61$	−8.92510	−	6.48447i	−1.14274	−	0.830251i	−0.155244	−	0.987876i	$-0.549616\pi$
$61$	−8.92510	−	6.48447i	−1.14274	−	0.830251i	−0.987499	+	0.157625i	$0.949616\pi$
$62$	0.223256	−	0.687110i	0.0283535	−	0.0872631i
$63$	−2.29728	−	7.07029i	−0.289430	−	0.890772i
$64$	1.89103	−	1.37391i	0.236379	−	0.171739i
$65$	5.97664			0.741311
$66$	−2.78432	−	3.52851i	−0.342726	−	0.434329i
$67$	7.28195			0.889632			0.444816	−	0.895622i	$-0.353269\pi$
$67$	7.28195			0.889632			0.444816	+	0.895622i	$0.353269\pi$
$68$	1.40423	−	1.02024i	0.170288	−	0.123722i
$69$	0.313905	+	0.966102i	0.0377898	+	0.116305i
$70$	−1.21769	+	3.74766i	−0.145542	+	0.447931i
$71$	1.81705	+	1.32017i	0.215645	+	0.156675i	0.690364	−	0.723462i	$-0.257450\pi$
$71$	1.81705	+	1.32017i	0.215645	+	0.156675i	−0.474719	+	0.880137i	$0.657450\pi$
$72$	6.13661	+	4.45851i	0.723207	+	0.525440i
$73$	1.46468	−	4.50783i	0.171428	−	0.527602i	−0.828024	−	0.560692i	$-0.810535\pi$
$73$	1.46468	−	4.50783i	0.171428	−	0.527602i	0.999452	+	0.0330908i	$0.0105350\pi$
$74$	1.04312	+	3.21041i	0.121261	+	0.373202i
$75$	−24.7101	+	17.9530i	−2.85328	+	2.07303i
$76$	−9.67898			−1.11026
$77$	−3.46570	+	5.19203i	−0.394953	+	0.591687i
$78$	1.98882			0.225190
$79$	−5.36702	+	3.89937i	−0.603837	+	0.438713i	−0.847239	−	0.531213i	$-0.821737\pi$
$79$	−5.36702	+	3.89937i	−0.603837	+	0.438713i	0.243402	+	0.969925i	$0.421737\pi$
$80$	3.12638	+	9.62202i	0.349540	+	1.07577i
$81$	−1.62192	+	4.99176i	−0.180214	+	0.554640i
$82$	0.833624	+	0.605663i	0.0920584	+	0.0668843i
$83$	11.9874	+	8.70933i	1.31578	+	0.955973i	0.999974	+	0.00715024i	$0.00227601\pi$
$83$	11.9874	+	8.70933i	1.31578	+	0.955973i	0.315809	+	0.948823i	$0.397724\pi$
$84$	2.66139	−	8.19092i	0.290382	−	0.893703i
$85$	1.25850	+	3.87326i	0.136503	+	0.420114i
$86$	−1.38818	+	1.00857i	−0.149691	+	0.108757i
$87$	−26.5272			−2.84402
$88$	−0.253031	−	6.36434i	−0.0269732	−	0.678441i
$89$	−9.20456			−0.975681			−0.487841	−	0.872933i	$-0.662215\pi$
$89$	−9.20456			−0.975681			−0.487841	+	0.872933i	$0.662215\pi$
$90$	−6.68996	+	4.86054i	−0.705184	+	0.512346i
$91$	−0.853549	−	2.62695i	−0.0894762	−	0.275380i
$92$	−0.206679	+	0.636092i	−0.0215478	+	0.0663172i
$93$	−2.99736	−	2.17771i	−0.310811	−	0.225818i
$94$	−0.711231	−	0.516740i	−0.0733579	−	0.0532976i
$95$	7.01779	−	21.5985i	0.720010	−	2.21596i
$96$	4.16929	+	12.8318i	0.425527	+	1.30964i
$97$	7.32314	−	5.32057i	0.743552	−	0.540222i	−0.150270	−	0.988645i	$-0.548014\pi$
$97$	7.32314	−	5.32057i	0.743552	−	0.540222i	0.893821	+	0.448423i	$0.148014\pi$
$98$	−1.77737			−0.179541
$99$	−12.2881	+	4.53983i	−1.23500	+	0.456270i
$100$	−20.1101			−2.01101
$101$	−3.26711	+	2.37369i	−0.325089	+	0.236191i	−0.738344	−	0.674424i	$-0.764392\pi$
$101$	−3.26711	+	2.37369i	−0.325089	+	0.236191i	0.413255	+	0.910615i	$0.364392\pi$
$102$	0.418786	+	1.28889i	0.0414660	+	0.127619i
$103$	−2.29123	+	7.05168i	−0.225762	+	0.694823i	0.772452	+	0.635073i	$0.219030\pi$
$103$	−2.29123	+	7.05168i	−0.225762	+	0.694823i	−0.998213	+	0.0597493i	$0.980970\pi$
$104$	2.28005	+	1.65655i	0.223577	+	0.162438i
$105$	16.3483	+	11.8777i	1.59543	+	1.15915i
$106$	−1.59839	+	4.91934i	−0.155249	+	0.477808i
$107$	−3.61364	−	11.1216i	−0.349344	−	1.07517i	−0.959217	−	0.282671i	$-0.908780\pi$
$107$	−3.61364	−	11.1216i	−0.349344	−	1.07517i	0.609873	−	0.792499i	$-0.291220\pi$
$108$	3.51594	−	2.55448i	0.338321	−	0.245805i
$109$	9.52166			0.912009			0.456005	−	0.889977i	$-0.349280\pi$
$109$	9.52166			0.912009			0.456005	+	0.889977i	$0.349280\pi$
$110$	6.68388	+	1.88168i	0.637283	+	0.179411i
$111$	17.3107			1.64306
$112$	3.78274	−	2.74832i	0.357435	−	0.259692i
$113$	−3.83437	−	11.8010i	−0.360708	−	1.11014i	−0.952626	−	0.304145i	$-0.901629\pi$
$113$	−3.83437	−	11.8010i	−0.360708	−	1.11014i	0.591918	−	0.805998i	$-0.298371\pi$
$114$	2.33528	−	7.18726i	0.218719	−	0.673148i
$115$	−1.26958	−	0.922403i	−0.118389	−	0.0860145i
$116$	−14.1301	−	10.2662i	−1.31195	−	0.953189i
$117$	1.79118	−	5.51270i	0.165595	−	0.509649i
$118$	1.14145	+	3.51303i	0.105079	+	0.323401i
$119$	1.52271	−	1.10631i	0.139587	−	0.101416i
$120$	−20.6184			−1.88219
$121$	9.38440	+	5.73873i	0.853128	+	0.521702i
$122$	5.67127			0.513452
$123$	4.27495	−	3.10593i	0.385459	−	0.280052i
$124$	−0.753807	−	2.31998i	−0.0676938	−	0.208340i
$125$	8.28843	−	25.5092i	0.741340	−	2.28161i
$126$	3.09181	+	2.24633i	0.275440	+	0.200119i
$127$	1.91225	+	1.38933i	0.169684	+	0.123283i	0.669386	−	0.742915i	$-0.266557\pi$
$127$	1.91225	+	1.38933i	0.169684	+	0.123283i	−0.499702	+	0.866197i	$0.666557\pi$
$128$	−3.53438	+	10.8777i	−0.312398	+	0.961462i
$129$	2.71914	+	8.36865i	0.239407	+	0.736818i
$130$	−2.48564	+	1.80593i	−0.218005	+	0.158390i
$131$	−14.5468			−1.27096			−0.635480	−	0.772117i	$-0.719198\pi$
$131$	−14.5468			−1.27096			−0.635480	+	0.772117i	$0.719198\pi$
$132$	−14.6083	−	4.11262i	−1.27149	−	0.357958i
$133$	−10.4956			−0.910083
$134$	−3.02851	+	2.20034i	−0.261624	+	0.190081i
$135$	3.15104	+	9.69790i	0.271198	+	0.834663i
$136$	−0.593447	+	1.82644i	−0.0508877	+	0.156616i
$137$	−8.78995	−	6.38627i	−0.750976	−	0.545616i	0.145153	−	0.989409i	$-0.453633\pi$
$137$	−8.78995	−	6.38627i	−0.750976	−	0.545616i	−0.896129	+	0.443793i	$0.853633\pi$
$138$	−0.422473	−	0.306944i	−0.0359633	−	0.0261288i
$139$	−4.50124	+	13.8534i	−0.381790	+	1.17503i	0.556992	+	0.830518i	$0.311955\pi$
$139$	−4.50124	+	13.8534i	−0.381790	+	1.17503i	−0.938782	+	0.344511i	$0.888045\pi$
$140$	4.11144	+	12.6537i	0.347480	+	1.06943i
$141$	−3.64730	+	2.64992i	−0.307158	+	0.223163i
$142$	−1.15461			−0.0968926
$143$	−4.56562	+	1.68677i	−0.381796	+	0.141055i
$144$	9.81207			0.817672
$145$	33.1539	−	24.0877i	2.75328	−	2.00038i
$146$	0.752953	+	2.31735i	0.0623148	+	0.191785i
$147$	−2.81657	+	8.66851i	−0.232307	+	0.714966i
$148$	9.22081	+	6.69931i	0.757946	+	0.550680i
$149$	12.4237	+	9.02635i	1.01779	+	0.739467i	0.965829	−	0.259182i	$-0.0834529\pi$
$149$	12.4237	+	9.02635i	1.01779	+	0.739467i	0.0519608	+	0.998649i	$0.483453\pi$
$150$	4.85204	−	14.9330i	0.396167	−	1.21928i
$151$	3.31981	+	10.2173i	0.270163	+	0.831475i	0.990459	+	0.137808i	$0.0440058\pi$
$151$	3.31981	+	10.2173i	0.270163	+	0.831475i	−0.720296	+	0.693666i	$0.755994\pi$
$152$	8.66373	−	6.29457i	0.702721	−	0.510557i
$153$	3.94976			0.319320
$154$	−0.127485	−	3.20654i	−0.0102730	−	0.258391i
$155$	5.72356			0.459727
$156$	5.43264	−	3.94705i	0.434960	−	0.316017i
$157$	−0.425953	−	1.31095i	−0.0339948	−	0.104625i	0.932619	−	0.360862i	$-0.117517\pi$
$157$	−0.425953	−	1.31095i	−0.0339948	−	0.104625i	−0.966614	+	0.256237i	$0.917517\pi$
$158$	1.05386	−	3.24344i	0.0838404	−	0.258034i
$159$	21.4594	+	15.5912i	1.70185	+	1.23646i
$160$	−16.8625	−	12.2514i	−1.33310	−	0.968555i
$161$	−0.224116	+	0.689759i	−0.0176628	+	0.0543606i
$162$	−0.833786	−	2.56613i	−0.0655084	−	0.201614i
$163$	−1.93909	+	1.40883i	−0.151881	+	0.110348i	−0.661130	−	0.750271i	$-0.729923\pi$
$163$	−1.93909	+	1.40883i	−0.151881	+	0.110348i	0.509250	+	0.860619i	$0.329923\pi$
$164$	3.47913			0.271674
$165$	19.7691	−	29.6165i	1.53902	−	2.30564i
$166$	−7.61711			−0.591202
$167$	−10.9219	+	7.93520i	−0.845159	+	0.614044i	−0.923807	−	0.382858i	$-0.874940\pi$
$167$	−10.9219	+	7.93520i	−0.845159	+	0.614044i	0.0786479	+	0.996902i	$0.474940\pi$
$168$	2.94460	+	9.06255i	0.227181	+	0.699191i
$169$	−3.35171	+	10.3155i	−0.257824	+	0.793500i
$170$	−1.69376	−	1.23059i	−0.129906	−	0.0943820i
$171$	−17.8187	−	12.9461i	−1.36263	−	0.990010i
$172$	−1.79031	+	5.51001i	−0.136510	+	0.420134i
$173$	−3.51950	−	10.8319i	−0.267582	−	0.823534i	−0.991087	−	0.133214i	$-0.957470\pi$
$173$	−3.51950	−	10.8319i	−0.267582	−	0.823534i	0.723505	−	0.690319i	$-0.242530\pi$
$174$	11.0325	−	8.01558i	0.836372	−	0.607660i
$175$	−21.8068			−1.64844
$176$	−5.10387	−	6.46801i	−0.384718	−	0.487545i
$177$	18.9424			1.42380
$178$	3.82811	−	2.78129i	0.286929	−	0.208466i
$179$	−1.40831	−	4.33433i	−0.105262	−	0.323963i	0.884530	−	0.466484i	$-0.154479\pi$
$179$	−1.40831	−	4.33433i	−0.105262	−	0.323963i	−0.989792	+	0.142520i	$0.954479\pi$
$180$	−8.62792	+	26.5540i	−0.643087	+	1.97922i
$181$	7.52048	+	5.46395i	0.558993	+	0.406132i	0.831090	−	0.556138i	$-0.187717\pi$
$181$	7.52048	+	5.46395i	0.558993	+	0.406132i	−0.272097	+	0.962270i	$0.587717\pi$
$182$	1.14876	+	0.834621i	0.0851515	+	0.0618662i
$183$	8.98717	−	27.6597i	0.664351	−	2.04466i
$184$	−0.228672	−	0.703781i	−0.0168579	−	0.0518834i
$185$	−21.6350	+	15.7188i	−1.59064	+	1.15567i
$186$	1.90461			0.139652
$187$	−2.05452	−	2.60364i	−0.150241	−	0.190397i
$188$	−2.96832			−0.216487
$189$	3.81257	−	2.77000i	0.277324	−	0.201488i
$190$	3.60765	+	11.1032i	0.261727	+	0.805512i
$191$	4.93749	−	15.1960i	0.357264	−	1.09955i	−0.597421	−	0.801928i	$-0.703808\pi$
$191$	4.93749	−	15.1960i	0.357264	−	1.09955i	0.954685	−	0.297618i	$-0.0961923\pi$
$192$	4.98521	+	3.62197i	0.359776	+	0.261393i
$193$	−0.417375	−	0.303240i	−0.0300433	−	0.0218277i	0.572662	−	0.819791i	$-0.305911\pi$
$193$	−0.417375	−	0.303240i	−0.0300433	−	0.0218277i	−0.602706	+	0.797964i	$0.705911\pi$
$194$	−1.43796	+	4.42558i	−0.103239	+	0.317738i
$195$	4.86883	+	14.9847i	0.348664	+	1.07308i
$196$	−4.85504	+	3.52739i	−0.346788	+	0.251956i
$197$	16.3723			1.16648			0.583240	−	0.812300i	$-0.301785\pi$
$197$	16.3723			1.16648			0.583240	+	0.812300i	$0.301785\pi$
$198$	3.73876	−	5.60110i	0.265702	−	0.398053i
$199$	0.457479			0.0324299			0.0162149	−	0.999869i	$-0.494838\pi$
$199$	0.457479			0.0324299			0.0162149	+	0.999869i	$0.494838\pi$
$200$	18.0007	−	13.0783i	1.27284	−	0.924774i
$201$	5.93219	+	18.2574i	0.418424	+	1.28778i
$202$	0.641523	−	1.97441i	0.0451374	−	0.138919i
$203$	−15.3223	−	11.1323i	−1.07542	−	0.781335i
$204$	3.70190	+	2.68959i	0.259185	+	0.188309i
$205$	−2.52256	+	7.76363i	−0.176183	+	0.542236i
$206$	−1.17786	−	3.62507i	−0.0820653	−	0.252571i
$207$	−1.23129	+	0.894585i	−0.0855806	+	0.0621779i
$208$	3.64566			0.252781
$209$	0.734719	+	18.4800i	0.0508216	+	1.27829i
$210$	−10.3882			−0.716852
$211$	3.67508	−	2.67010i	0.253003	−	0.183818i	−0.454054	−	0.890974i	$-0.650023\pi$
$211$	3.67508	−	2.67010i	0.253003	−	0.183818i	0.707057	+	0.707157i	$0.250023\pi$
$212$	5.39685	+	16.6098i	0.370657	+	1.14077i
$213$	−1.82969	+	5.63121i	−0.125368	+	0.385844i
$214$	4.86345	+	3.53350i	0.332459	+	0.241545i
$215$	−10.9975	−	7.99012i	−0.750020	−	0.544921i
$216$	−1.48588	+	4.57306i	−0.101101	+	0.311158i
$217$	−0.817405	−	2.51571i	−0.0554891	−	0.170778i
$218$	−3.95999	+	2.87710i	−0.268205	+	0.194862i
$219$	12.4953			0.844353
$220$	21.9920	−	8.12495i	1.48270	−	0.547784i
$221$	1.46753			0.0987167
$222$	−7.19940	+	5.23067i	−0.483192	+	0.351060i
$223$	−2.09294	−	6.44141i	−0.140154	−	0.431349i	0.856202	−	0.516641i	$-0.172818\pi$
$223$	−2.09294	−	6.44141i	−0.140154	−	0.431349i	−0.996356	+	0.0852919i	$0.972818\pi$
$224$	−2.97671	+	9.16138i	−0.198890	+	0.612120i
$225$	−37.0221	−	26.8981i	−2.46814	−	1.79321i
$226$	5.16053	+	3.74934i	0.343273	+	0.249403i
$227$	1.38787	−	4.27142i	0.0921162	−	0.283504i	−0.894375	−	0.447317i	$-0.852379\pi$
$227$	1.38787	−	4.27142i	0.0921162	−	0.283504i	0.986491	+	0.163813i	$0.0523794\pi$
$228$	−7.88491	−	24.2673i	−0.522191	−	1.60714i
$229$	18.3627	−	13.3413i	1.21344	−	0.881616i	0.217901	−	0.975971i	$-0.430079\pi$
$229$	18.3627	−	13.3413i	1.21344	−	0.881616i	0.995539	+	0.0943551i	$0.0300789\pi$
$230$	0.806726			0.0531940
$231$	−15.8409	−	4.45960i	−1.04225	−	0.293420i
$232$	19.3244			1.26871
$233$	−15.8169	+	11.4916i	−1.03620	+	0.752841i	−0.969540	−	0.244935i	$-0.921233\pi$
$233$	−15.8169	+	11.4916i	−1.03620	+	0.752841i	−0.0666575	+	0.997776i	$0.521233\pi$
$234$	0.920798	+	2.83393i	0.0601945	+	0.185260i
$235$	2.15220	−	6.62378i	0.140394	−	0.432088i
$236$	10.0900	+	7.33081i	0.656802	+	0.477195i
$237$	−14.1487	−	10.2797i	−0.919060	−	0.667736i
$238$	−0.298997	+	0.920217i	−0.0193811	+	0.0596488i
$239$	4.86733	+	14.9801i	0.314841	+	0.968982i	0.975820	+	0.218577i	$0.0701415\pi$
$239$	4.86733	+	14.9801i	0.314841	+	0.968982i	−0.660978	+	0.750405i	$0.729859\pi$
$240$	−21.5776	+	15.6770i	−1.39283	+	1.01195i
$241$	−5.21997			−0.336248			−0.168124	−	0.985766i	$-0.553771\pi$
$241$	−5.21997			−0.336248			−0.168124	+	0.985766i	$0.553771\pi$
$242$	−5.63695	+	0.448933i	−0.362357	+	0.0288585i
$243$	−21.3481			−1.36948
$244$	15.4916	−	11.2553i	0.991746	−	0.720546i
$245$	−4.35117	−	13.3915i	−0.277986	−	0.855552i
$246$	−0.839421	+	2.58347i	−0.0535195	+	0.164716i
$247$	−6.62051	−	4.81008i	−0.421253	−	0.306058i
$248$	2.18350	+	1.58641i	0.138652	+	0.100737i
$249$	−12.0707	+	37.1499i	−0.764951	+	2.35428i
$250$	4.26085	+	13.1136i	0.269480	+	0.829374i
$251$	15.3386	−	11.1442i	0.968164	−	0.703413i	0.0131319	−	0.999914i	$-0.495820\pi$
$251$	15.3386	−	11.1442i	0.968164	−	0.703413i	0.955032	+	0.296501i	$0.0958199\pi$
$252$	12.9037			0.812854
$253$	1.23017	+	0.346324i	0.0773402	+	0.0217732i
$254$	−1.21510			−0.0762419
$255$	−8.68587	+	6.31065i	−0.543930	+	0.395188i
$256$	−0.372309	−	1.14585i	−0.0232693	−	0.0716156i
$257$	4.68412	−	14.4162i	0.292187	−	0.899260i	−0.691964	−	0.721932i	$-0.743254\pi$
$257$	4.68412	−	14.4162i	0.292187	−	0.899260i	0.984152	−	0.177329i	$-0.0567455\pi$
$258$	−3.65958	−	2.65884i	−0.227835	−	0.165532i
$259$	9.99877	+	7.26453i	0.621293	+	0.451396i
$260$	−3.20569	+	9.86610i	−0.198808	+	0.611869i
$261$	−12.2818	−	37.7994i	−0.760222	−	2.33972i
$262$	6.04992	−	4.39552i	0.373765	−	0.271556i
$263$	−6.32436			−0.389977			−0.194988	−	0.980806i	$-0.562467\pi$
$263$	−6.32436			−0.389977			−0.194988	+	0.980806i	$0.562467\pi$
$264$	15.7506	−	5.81907i	0.969384	−	0.358139i
$265$	−40.9776			−2.51723
$266$	4.36505	−	3.17139i	0.267638	−	0.194451i
$267$	−7.49843	−	23.0778i	−0.458897	−	1.41234i
$268$	−3.90582	+	12.0209i	−0.238586	+	0.734292i
$269$	−1.13263	−	0.822907i	−0.0690579	−	0.0501735i	0.552721	−	0.833367i	$-0.313590\pi$
$269$	−1.13263	−	0.822907i	−0.0690579	−	0.0501735i	−0.621779	+	0.783193i	$0.713590\pi$
$270$	−4.24086	−	3.08116i	−0.258090	−	0.187514i
$271$	3.71613	−	11.4371i	0.225739	−	0.694753i	−0.772477	−	0.635043i	$-0.780982\pi$
$271$	3.71613	−	11.4371i	0.225739	−	0.694753i	0.998216	−	0.0597101i	$-0.0190176\pi$
$272$	0.767665	+	2.36263i	0.0465465	+	0.143255i
$273$	5.89100	−	4.28006i	0.356539	−	0.259041i
$274$	5.58539			0.337425
$275$	1.52653	+	38.3960i	0.0920533	+	2.31536i
$276$	−1.76319			−0.106131
$277$	10.3593	−	7.52651i	0.622433	−	0.452224i	−0.231338	−	0.972874i	$-0.574310\pi$
$277$	10.3593	−	7.52651i	0.622433	−	0.452224i	0.853770	+	0.520650i	$0.174310\pi$
$278$	−2.31396	−	7.12164i	−0.138782	−	0.427128i
$279$	1.71534	−	5.27926i	0.102694	−	0.316061i
$280$	−11.9093	−	8.65263i	−0.711719	−	0.517094i
$281$	10.8879	+	7.91050i	0.649516	+	0.471901i	0.863106	−	0.505022i	$-0.168516\pi$
$281$	10.8879	+	7.91050i	0.649516	+	0.471901i	−0.213590	+	0.976923i	$0.568516\pi$
$282$	0.716178	−	2.20417i	0.0426478	−	0.131256i
$283$	0.726516	+	2.23599i	0.0431869	+	0.132916i	0.970325	−	0.241804i	$-0.0777390\pi$
$283$	0.726516	+	2.23599i	0.0431869	+	0.132916i	−0.927138	+	0.374719i	$0.877739\pi$
$284$	−3.15392	+	2.29145i	−0.187150	+	0.135973i
$285$	59.8691			3.54634
$286$	1.38913	−	2.08108i	0.0821409	−	0.123057i
$287$	3.77266			0.222693
$288$	−16.3540	+	11.8819i	−0.963669	+	0.700146i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−6.51005	+	20.0359i	−0.382283	+	1.17655i
$291$	19.3055	+	14.0263i	1.13171	+	0.822236i
$292$	6.65581	+	4.83573i	0.389502	+	0.282990i
$293$	−8.54529	+	26.2997i	−0.499221	+	1.53645i	0.311052	+	0.950393i	$0.399319\pi$
$293$	−8.54529	+	26.2997i	−0.499221	+	1.53645i	−0.810273	+	0.586052i	$0.800681\pi$
$294$	−1.44792	−	4.45624i	−0.0844444	−	0.259893i
$295$	−23.6744	+	17.2005i	−1.37838	+	1.00145i
$296$	−12.6104			−0.732965
$297$	−5.14412	−	6.51902i	−0.298492	−	0.378272i
$298$	−7.89437			−0.457309
$299$	−0.457484	+	0.332381i	−0.0264570	+	0.0192221i
$300$	−16.3826	−	50.4203i	−0.945847	−	2.91102i
$301$	−1.94136	+	5.97489i	−0.111898	+	0.344387i
$302$	−4.46800	−	3.24619i	−0.257105	−	0.186797i
$303$	−8.61288	−	6.25762i	−0.494797	−	0.359491i
$304$	4.28074	−	13.1748i	0.245517	−	0.755625i
$305$	13.8838	+	42.7299i	0.794984	+	2.44671i
$306$	−1.64268	+	1.19348i	−0.0939058	+	0.0682266i
$307$	13.7602			0.785335			0.392667	−	0.919681i	$-0.371552\pi$
$307$	13.7602			0.785335			0.392667	+	0.919681i	$0.371552\pi$
$308$	−6.71199	−	8.50595i	−0.382451	−	0.484672i
$309$	−19.5466			−1.11197
$310$	−2.38039	+	1.72945i	−0.135197	+	0.0982264i
$311$	−0.712279	−	2.19217i	−0.0403896	−	0.124306i	0.928829	−	0.370510i	$-0.120817\pi$
$311$	−0.712279	−	2.19217i	−0.0403896	−	0.124306i	−0.969218	+	0.246203i	$0.920817\pi$
$312$	−2.29590	+	7.06607i	−0.129980	+	0.400037i
$313$	9.00518	+	6.54264i	0.509003	+	0.369812i	0.812445	−	0.583038i	$-0.198136\pi$
$313$	9.00518	+	6.54264i	0.509003	+	0.369812i	−0.303442	+	0.952850i	$0.598136\pi$
$314$	0.573273	+	0.416507i	0.0323517	+	0.0235049i
$315$	−9.35586	+	28.7944i	−0.527143	+	1.62238i
$316$	−3.55828	−	10.9513i	−0.200169	−	0.616056i
$317$	4.86682	−	3.53595i	0.273348	−	0.198599i	−0.442663	−	0.896688i	$-0.645966\pi$
$317$	4.86682	−	3.53595i	0.273348	−	0.198599i	0.716011	+	0.698089i	$0.245966\pi$
$318$	−13.6359			−0.764666
$319$	−18.5284	+	27.7578i	−1.03739	+	1.55414i
$320$	−9.51943			−0.532152
$321$	24.9405	−	18.1203i	1.39204	−	1.01138i
$322$	−0.115212	−	0.354586i	−0.00642051	−	0.0197603i
$323$	1.72318	−	5.30339i	0.0958801	−	0.295089i
$324$	−7.37034	−	5.35486i	−0.409463	−	0.297492i
$325$	−13.7555	−	9.99396i	−0.763018	−	0.554365i
$326$	0.380755	−	1.17184i	0.0210881	−	0.0649025i
$327$	7.75675	+	23.8728i	0.428949	+	1.32017i
$328$	−3.11419	+	2.26259i	−0.171953	+	0.124931i
$329$	−3.21876			−0.177456
$330$	0.727199	+	18.2908i	0.0400310	+	1.00688i
$331$	18.2657			1.00397			0.501986	−	0.864876i	$-0.332603\pi$
$331$	18.2657			1.00397			0.501986	+	0.864876i	$0.332603\pi$
$332$	−20.8068	+	15.1170i	−1.14192	+	0.829655i
$333$	8.01462	+	24.6665i	0.439199	+	1.35171i
$334$	2.14460	−	6.60039i	0.117347	−	0.361157i
$335$	−23.9925	−	17.4316i	−1.31085	−	0.952389i
$336$	9.97221	+	7.24524i	0.544029	+	0.395260i
$337$	−1.27276	+	3.91715i	−0.0693317	+	0.213381i	−0.979719	−	0.200376i	$-0.935784\pi$
$337$	−1.27276	+	3.91715i	−0.0693317	+	0.213381i	0.910387	+	0.413757i	$0.135784\pi$
$338$	−1.72302	−	5.30292i	−0.0937200	−	0.288441i
$339$	26.4640	−	19.2272i	1.43732	−	1.04428i
$340$	−7.06891			−0.383365
$341$	−4.37229	+	1.61534i	−0.236773	+	0.0874756i
$342$	11.3225			0.612252
$343$	−15.9236	+	11.5692i	−0.859795	+	0.624678i
$344$	−1.98082	−	6.09635i	−0.106799	−	0.328693i
$345$	1.27841	−	3.93453i	0.0688271	−	0.211828i
$346$	4.73675	+	3.44145i	0.254649	+	0.185013i
$347$	27.1627	+	19.7348i	1.45817	+	1.05942i	0.983835	+	0.179078i	$0.0573113\pi$
$347$	27.1627	+	19.7348i	1.45817	+	1.05942i	0.474335	+	0.880345i	$0.342689\pi$
$348$	14.2284	−	43.7906i	0.762723	−	2.34742i
$349$	−8.54929	−	26.3120i	−0.457633	−	1.40845i	−0.868016	−	0.496536i	$-0.834605\pi$
$349$	−8.54929	−	26.3120i	−0.457633	−	1.40845i	0.410383	−	0.911913i	$-0.365395\pi$
$350$	9.06930	−	6.58923i	0.484774	−	0.352209i
$351$	3.67441			0.196126
$352$	16.3391	+	4.59988i	0.870879	+	0.245174i
$353$	−28.4246			−1.51289			−0.756443	−	0.654059i	$-0.773065\pi$
$353$	−28.4246			−1.51289			−0.756443	+	0.654059i	$0.773065\pi$
$354$	−7.87804	+	5.72373i	−0.418713	+	0.304213i
$355$	−2.82659	−	8.69936i	−0.150020	−	0.461714i
$356$	4.93705	−	15.1947i	0.261663	−	0.805316i
$357$	4.01423	+	2.91651i	0.212456	+	0.154358i
$358$	1.89539	+	1.37708i	0.100174	+	0.0727809i
$359$	0.572814	−	1.76294i	0.0302320	−	0.0930444i	−0.934802	−	0.355169i	$-0.884423\pi$
$359$	0.572814	−	1.76294i	0.0302320	−	0.0930444i	0.965034	+	0.262125i	$0.0844232\pi$
$360$	−9.54605	−	29.3797i	−0.503121	−	1.54845i
$361$	−9.78532	+	7.10945i	−0.515017	+	0.374182i
$362$	−4.77873			−0.251164
$363$	−6.74327	+	28.2037i	−0.353930	+	1.48031i
$364$	4.79433			0.251291
$365$	−15.6167	+	11.3462i	−0.817415	+	0.593887i
$366$	4.62006	+	14.2191i	0.241494	+	0.743243i
$367$	8.02325	−	24.6930i	0.418810	−	1.28896i	−0.489988	−	0.871729i	$-0.662999\pi$
$367$	8.02325	−	24.6930i	0.418810	−	1.28896i	0.908798	−	0.417236i	$-0.137001\pi$
$368$	−0.774423	−	0.562652i	−0.0403696	−	0.0293302i
$369$	6.40497	+	4.65348i	0.333429	+	0.242251i
$370$	4.24821	−	13.0747i	0.220854	−	0.679719i
$371$	5.85218	+	18.0112i	0.303830	+	0.935093i
$372$	5.20260	−	3.77991i	0.269742	−	0.195979i
$373$	32.3001			1.67244			0.836218	−	0.548397i	$-0.184762\pi$
$373$	32.3001			1.67244			0.836218	+	0.548397i	$0.184762\pi$
$374$	1.64119	+	0.462036i	0.0848638	+	0.0238913i
$375$	70.7090			3.65140
$376$	2.65697	−	1.93040i	0.137023	−	0.0995528i
$377$	−4.56327	−	14.0443i	−0.235020	−	0.723318i
$378$	−0.748630	+	2.30405i	−0.0385054	+	0.118507i
$379$	−19.3676	−	14.0713i	−0.994844	−	0.722797i	−0.0338677	−	0.999426i	$-0.510782\pi$
$379$	−19.3676	−	14.0713i	−0.994844	−	0.722797i	−0.960977	+	0.276630i	$0.910782\pi$
$380$	31.8902	+	23.1696i	1.63593	+	1.18858i
$381$	−1.92554	+	5.92622i	−0.0986486	+	0.303609i
$382$	2.53823	+	7.81186i	0.129867	+	0.399690i
$383$	4.22677	−	3.07093i	0.215978	−	0.156917i	−0.474536	−	0.880236i	$-0.657384\pi$
$383$	4.22677	−	3.07093i	0.215978	−	0.156917i	0.690514	+	0.723319i	$0.257384\pi$
$384$	−30.1520			−1.53869
$385$	23.8475	−	8.81045i	1.21538	−	0.449022i
$386$	0.265212			0.0134989
$387$	−10.6658	+	7.74915i	−0.542172	+	0.393911i
$388$	4.85516	+	14.9427i	0.246484	+	0.758598i
$389$	−11.3627	+	34.9707i	−0.576111	+	1.77309i	0.0562540	+	0.998416i	$0.482084\pi$
$389$	−11.3627	+	34.9707i	−0.576111	+	1.77309i	−0.632365	+	0.774671i	$0.717916\pi$
$390$	−6.55276	−	4.76086i	−0.331812	−	0.241075i
$391$	−0.311738	−	0.226491i	−0.0157652	−	0.0114541i
$392$	2.05180	−	6.31479i	0.103632	−	0.318945i
$393$	−11.8505	−	36.4720i	−0.597776	−	1.83977i
$394$	−6.80914	+	4.94713i	−0.343040	+	0.249233i
$395$	27.0175			1.35940
$396$	−0.903289	−	22.7199i	−0.0453920	−	1.14172i
$397$	−0.124162			−0.00623151			−0.00311575	−	0.999995i	$-0.500992\pi$
$397$	−0.124162			−0.00623151			−0.00311575	+	0.999995i	$0.500992\pi$
$398$	−0.190263	+	0.138234i	−0.00953701	+	0.00692904i
$399$	−8.55016	−	26.3147i	−0.428044	−	1.31738i
$400$	8.89414	−	27.3733i	0.444707	−	1.36867i
$401$	−19.3692	−	14.0725i	−0.967250	−	0.702748i	−0.0124266	−	0.999923i	$-0.503956\pi$
$401$	−19.3692	−	14.0725i	−0.967250	−	0.702748i	−0.954823	+	0.297175i	$0.903956\pi$
$402$	−7.98389	−	5.80064i	−0.398200	−	0.289310i
$403$	0.637330	−	1.96150i	0.0317477	−	0.0977093i
$404$	−2.16606	−	6.66644i	−0.107765	−	0.331668i
$405$	17.2932	−	12.5643i	0.859307	−	0.624323i
$406$	9.73623			0.483201
$407$	12.0910	−	18.1137i	0.599327	−	0.897863i
$408$	−5.06273			−0.250643
$409$	10.3698	−	7.53413i	0.512756	−	0.372539i	−0.301112	−	0.953589i	$-0.597358\pi$
$409$	10.3698	−	7.53413i	0.512756	−	0.372539i	0.813868	+	0.581050i	$0.197358\pi$
$410$	−1.29678	−	3.99107i	−0.0640433	−	0.197105i
$411$	8.85108	−	27.2408i	0.436592	−	1.34369i
$412$	−10.4118	−	7.56462i	−0.512953	−	0.372682i
$413$	10.9413	+	7.94931i	0.538385	+	0.391160i
$414$	0.241774	−	0.744104i	0.0118825	−	0.0365707i
$415$	−18.6474	−	57.3908i	−0.915366	−	2.81721i
$416$	−6.07630	+	4.41469i	−0.297915	+	0.216448i
$417$	−38.4003			−1.88047
$418$	−5.88955	−	7.46368i	−0.288067	−	0.365061i
$419$	16.9549			0.828299			0.414150	−	0.910209i	$-0.364079\pi$
$419$	16.9549			0.828299			0.414150	+	0.910209i	$0.364079\pi$
$420$	−28.3762	+	20.6165i	−1.38462	+	1.00598i
$421$	7.94666	+	24.4573i	0.387296	+	1.19198i	0.934801	+	0.355173i	$0.115578\pi$
$421$	7.94666	+	24.4573i	0.387296	+	1.19198i	−0.547504	+	0.836803i	$0.684422\pi$
$422$	−0.721633	+	2.22096i	−0.0351285	+	0.108115i
$423$	−5.46459	−	3.97026i	−0.265698	−	0.193041i
$424$	−15.6327	−	11.3578i	−0.759190	−	0.551584i
$425$	3.58026	−	11.0189i	0.173668	−	0.534496i
$426$	−0.940594	−	2.89485i	−0.0455719	−	0.140256i
$427$	16.7986	−	12.2049i	0.812941	−	0.590636i
$428$	20.2976			0.981121
$429$	−7.94843	−	10.0729i	−0.383754	−	0.486323i
$430$	6.98809			0.336996
$431$	−3.82618	+	2.77988i	−0.184301	+	0.133902i	−0.676110	−	0.736801i	$-0.736336\pi$
$431$	−3.82618	+	2.77988i	−0.184301	+	0.133902i	0.491809	+	0.870703i	$0.336336\pi$
$432$	1.92209	+	5.91557i	0.0924764	+	0.284613i
$433$	−9.84843	+	30.3104i	−0.473286	+	1.45662i	0.374970	+	0.927037i	$0.377653\pi$
$433$	−9.84843	+	30.3104i	−0.473286	+	1.45662i	−0.848256	+	0.529586i	$0.822347\pi$
$434$	1.10011	+	0.799279i	0.0528071	+	0.0383666i
$435$	87.4018	+	63.5011i	4.19059	+	3.04464i
$436$	−5.10713	+	15.7181i	−0.244587	+	0.752762i
$437$	0.663990	+	2.04355i	0.0317629	+	0.0977563i
$438$	−5.19671	+	3.77563i	−0.248308	+	0.180407i
$439$	3.43096			0.163751			0.0818754	−	0.996643i	$-0.473909\pi$
$439$	3.43096			0.163751			0.0818754	+	0.996643i	$0.473909\pi$
$440$	−14.4013	+	21.5749i	−0.686555	+	1.02854i
$441$	−13.6560			−0.650287
$442$	−0.610335	+	0.443435i	−0.0290307	+	0.0210920i
$443$	−11.0646	−	34.0535i	−0.525697	−	1.61793i	−0.762934	−	0.646477i	$-0.776242\pi$
$443$	−11.0646	−	34.0535i	−0.525697	−	1.61793i	0.237237	−	0.971452i	$-0.423758\pi$
$444$	−9.28493	+	28.5761i	−0.440643	+	1.35616i
$445$	30.3271	+	22.0339i	1.43764	+	1.04451i
$446$	2.81681	+	2.04653i	0.133380	+	0.0969059i
$447$	−12.5101	+	38.5021i	−0.591707	+	1.82109i
$448$	1.35951	+	4.18414i	0.0642308	+	0.197682i
$449$	−4.39979	+	3.19664i	−0.207639	+	0.150859i	−0.686745	−	0.726899i	$-0.740961\pi$
$449$	−4.39979	+	3.19664i	−0.207639	+	0.150859i	0.479106	+	0.877757i	$0.340961\pi$
$450$	23.5249			1.10897
$451$	−0.264096	−	6.64265i	−0.0124358	−	0.312790i
$452$	21.5374			1.01304
$453$	−22.9126	+	16.6470i	−1.07653	+	0.782142i
$454$	0.713466	+	2.19582i	0.0334846	+	0.103055i
$455$	−3.47615	+	10.6985i	−0.162965	+	0.501553i
$456$	22.8397	+	16.5940i	1.06957	+	0.777085i
$457$	−18.7113	−	13.5945i	−0.875277	−	0.635926i	0.0567208	−	0.998390i	$-0.481936\pi$
$457$	−18.7113	−	13.5945i	−0.875277	−	0.635926i	−0.931998	+	0.362464i	$0.881936\pi$
$458$	−3.60566	+	11.0971i	−0.168482	+	0.518533i
$459$	0.773720	+	2.38126i	0.0361141	+	0.111148i
$460$	2.20364	−	1.60104i	0.102745	−	0.0746489i
$461$	−7.27333			−0.338753			−0.169376	−	0.985551i	$-0.554175\pi$
$461$	−7.27333			−0.338753			−0.169376	+	0.985551i	$0.554175\pi$
$462$	7.93564	−	2.93182i	0.369199	−	0.136401i
$463$	7.16738			0.333097			0.166548	−	0.986033i	$-0.446738\pi$
$463$	7.16738			0.333097			0.166548	+	0.986033i	$0.446738\pi$
$464$	20.2234	−	14.6932i	0.938848	−	0.682113i
$465$	4.66266	+	14.3502i	0.216226	+	0.665474i
$466$	3.10577	−	9.55858i	0.143872	−	0.442793i
$467$	3.75975	+	2.73162i	0.173981	+	0.126404i	0.671368	−	0.741124i	$-0.265707\pi$
$467$	3.75975	+	2.73162i	0.173981	+	0.126404i	−0.497387	+	0.867529i	$0.665707\pi$
$468$	8.13950	+	5.91369i	0.376248	+	0.273360i
$469$	−4.23535	+	13.0351i	−0.195570	+	0.601904i
$470$	1.10638	+	3.40510i	0.0510337	+	0.157066i
$471$	2.93983	−	2.13591i	0.135460	−	0.0984176i
$472$	−13.7991			−0.635155
$473$	10.6561	+	2.99996i	0.489968	+	0.137938i
$474$	8.99052			0.412948
$475$	−52.2682	+	37.9751i	−2.39823	+	1.74242i
$476$	1.00954	+	3.10705i	0.0462722	+	0.142411i
$477$	−12.2809	+	37.7967i	−0.562303	+	1.73059i
$478$	−6.55074	−	4.75939i	−0.299624	−	0.217689i
$479$	−29.6053	−	21.5095i	−1.35270	−	0.982793i	−0.998872	−	0.0474822i	$-0.984880\pi$
$479$	−29.6053	−	21.5095i	−1.35270	−	0.982793i	−0.353827	−	0.935311i	$-0.615120\pi$
$480$	16.9798	−	52.2585i	0.775019	−	2.38526i
$481$	2.97782	+	9.16478i	0.135777	+	0.417878i
$482$	2.17095	−	1.57729i	0.0988841	−	0.0718435i
$483$	−1.91195			−0.0869966
$484$	−14.5069	+	12.4135i	−0.659403	+	0.564249i
$485$	−36.8646			−1.67394
$486$	8.87855	−	6.45064i	0.402739	−	0.292607i
$487$	3.92773	+	12.0883i	0.177982	+	0.547774i	0.999757	−	0.0220389i	$-0.00701577\pi$
$487$	3.92773	+	12.0883i	0.177982	+	0.547774i	−0.821775	+	0.569813i	$0.807016\pi$
$488$	−6.54693	+	20.1494i	−0.296366	+	0.912120i
$489$	−5.11190	−	3.71401i	−0.231168	−	0.167953i
$490$	5.85606	+	4.25467i	0.264550	+	0.192207i
$491$	6.68183	−	20.5646i	0.301547	−	0.928066i	−0.679396	−	0.733771i	$-0.737758\pi$
$491$	6.68183	−	20.5646i	0.301547	−	0.928066i	0.980943	−	0.194294i	$-0.0622417\pi$
$492$	2.83425	+	8.72291i	0.127778	+	0.393259i
$493$	8.14076	−	5.91461i	0.366641	−	0.266380i
$494$	4.20686			0.189276
$495$	51.3542	+	14.4575i	2.30820	+	0.649816i
$496$	3.49128			0.156763
$497$	−3.42001	+	2.48478i	−0.153408	+	0.111458i
$498$	−6.20523	−	19.0977i	−0.278063	−	0.855790i
$499$	−1.88344	+	5.79664i	−0.0843144	+	0.259493i	−0.984322	−	0.176381i	$-0.943561\pi$
$499$	−1.88344	+	5.79664i	−0.0843144	+	0.259493i	0.900008	+	0.435874i	$0.143561\pi$
$500$	37.6643	+	27.3647i	1.68440	+	1.22379i
$501$	−28.7927	−	20.9191i	−1.28636	−	0.934596i
$502$	−3.01186	+	9.26956i	−0.134426	+	0.413721i
$503$	−3.32449	−	10.2317i	−0.148232	−	0.456210i	0.849181	−	0.528102i	$-0.177096\pi$
$503$	−3.32449	−	10.2317i	−0.148232	−	0.456210i	−0.997412	+	0.0718921i	$0.977096\pi$
$504$	−11.5502	+	8.39169i	−0.514485	+	0.373795i
$505$	16.4466			0.731864
$506$	−0.616267	+	0.227680i	−0.0273964	+	0.0101216i
$507$	−28.5936			−1.26989
$508$	−3.31914	+	2.41150i	−0.147263	+	0.106993i
$509$	−5.15397	−	15.8623i	−0.228446	−	0.703084i	−0.997924	−	0.0644103i	$-0.979483\pi$
$509$	−5.15397	−	15.8623i	−0.228446	−	0.703084i	0.769478	−	0.638674i	$-0.220517\pi$
$510$	1.70554	−	5.24912i	0.0755226	−	0.232435i
$511$	7.21736	+	5.24372i	0.319277	+	0.231968i
$512$	−18.0052	−	13.0815i	−0.795724	−	0.578127i
$513$	4.31451	−	13.2787i	0.190490	−	0.586268i
$514$	2.40798	+	7.41099i	0.106211	+	0.326885i
$515$	24.4295	−	17.7491i	1.07649	−	0.782117i
$516$	−15.2732			−0.672367
$517$	0.225321	+	5.66738i	0.00990963	+	0.249251i
$518$	−6.35350			−0.279157
$519$	24.2907	−	17.6483i	1.06625	−	0.774672i
$520$	−3.54682	−	10.9160i	−0.155538	−	0.478698i
$521$	−10.2929	+	31.6782i	−0.450939	+	1.38785i	0.424899	+	0.905241i	$0.360310\pi$
$521$	−10.2929	+	31.6782i	−0.450939	+	1.38785i	−0.875838	+	0.482606i	$0.839690\pi$
$522$	16.5295	+	12.0094i	0.723478	+	0.525637i
$523$	−34.7726	−	25.2638i	−1.52050	−	1.10471i	−0.961239	−	0.275718i	$-0.911085\pi$
$523$	−34.7726	−	25.2638i	−1.52050	−	1.10471i	−0.559262	−	0.828991i	$-0.688915\pi$
$524$	7.80247	−	24.0135i	0.340852	−	1.04904i
$525$	−17.7648	−	54.6743i	−0.775317	−	2.38618i
$526$	2.63026	−	1.91100i	0.114685	−	0.0833234i
$527$	1.40539			0.0612196
$528$	12.0589	−	18.0656i	0.524794	−	0.786205i
$529$	−22.8515			−0.993544
$530$	17.0423	−	12.3820i	0.740270	−	0.537838i
$531$	8.77010	+	26.9916i	0.380590	+	1.17134i
$532$	5.62952	−	17.3259i	0.244071	−	0.751172i
$533$	2.37976	+	1.72899i	0.103079	+	0.0748910i
$534$	10.0918	+	7.33215i	0.436716	+	0.317293i
$535$	−14.7169	+	45.2938i	−0.636265	+	1.95822i
$536$	−4.32145	−	13.3001i	−0.186658	−	0.574475i
$537$	9.71983	−	7.06187i	0.419442	−	0.304742i
$538$	0.719708			0.0310288
$539$	7.10334	+	9.00190i	0.305963	+	0.387739i
$540$	−17.6992			−0.761652
$541$	22.4649	−	16.3217i	0.965841	−	0.701725i	0.0113413	−	0.999936i	$-0.496390\pi$
$541$	22.4649	−	16.3217i	0.965841	−	0.701725i	0.954500	+	0.298211i	$0.0963899\pi$
$542$	1.91036	+	5.87949i	0.0820570	+	0.252546i
$543$	−7.57278	+	23.3066i	−0.324979	+	1.00018i
$544$	−4.14050	−	3.00825i	−0.177522	−	0.128978i
$545$	−31.3719	−	22.7930i	−1.34382	−	0.976345i
$546$	−1.15675	+	3.56010i	−0.0495041	+	0.152358i
$547$	−11.4878	−	35.3557i	−0.491181	−	1.51170i	−0.822825	−	0.568294i	$-0.807603\pi$
$547$	−11.4878	−	35.3557i	−0.491181	−	1.51170i	0.331645	−	0.943404i	$-0.392397\pi$
$548$	15.2570	−	11.0848i	0.651746	−	0.473521i
$549$	43.5739			1.85969
$550$	−12.2368	−	15.5074i	−0.521777	−	0.661236i
$551$	−56.1118			−2.39045
$552$	1.57824	−	1.14666i	0.0671745	−	0.0488051i
$553$	−3.85849	−	11.8752i	−0.164080	−	0.504985i
$554$	−2.03414	+	6.26045i	−0.0864224	+	0.265981i
$555$	−57.0351	−	41.4384i	−2.42101	−	1.75896i
$556$	−20.4545	−	14.8611i	−0.867465	−	0.630250i
$557$	4.46846	−	13.7525i	0.189335	−	0.582713i	−0.810661	−	0.585515i	$-0.800892\pi$
$557$	4.46846	−	13.7525i	0.189335	−	0.582713i	0.999996	+	0.00280279i	$0.000892156\pi$
$558$	0.881807	+	2.71392i	0.0373299	+	0.114890i
$559$	−3.96285	+	2.87918i	−0.167611	+	0.121776i
$560$	−19.0423			−0.804684
$561$	4.85419	−	7.27216i	0.204944	−	0.307031i
$562$	−6.91847			−0.291838
$563$	−18.8940	+	13.7273i	−0.796287	+	0.578536i	−0.909822	−	0.414998i	$-0.863782\pi$
$563$	−18.8940	+	13.7273i	−0.796287	+	0.578536i	0.113536	+	0.993534i	$0.463782\pi$
$564$	−2.41812	−	7.44222i	−0.101821	−	0.313374i
$565$	−15.6158	+	48.0606i	−0.656962	+	2.02192i
$566$	−0.977788	−	0.710405i	−0.0410995	−	0.0298605i
$567$	−7.99217	−	5.80665i	−0.335640	−	0.243857i
$568$	1.33288	−	4.10220i	0.0559266	−	0.172124i
$569$	2.56857	+	7.90526i	0.107680	+	0.331406i	0.990350	−	0.138588i	$-0.0442563\pi$
$569$	2.56857	+	7.90526i	0.107680	+	0.331406i	−0.882670	+	0.469993i	$0.844256\pi$
$570$	−24.8992	+	18.0903i	−1.04291	+	0.757720i
$571$	25.6196			1.07215			0.536073	−	0.844171i	$-0.319907\pi$
$571$	25.6196			1.07215			0.536073	+	0.844171i	$0.319907\pi$
$572$	−0.335616	−	8.44155i	−0.0140328	−	0.352959i
$573$	42.1220			1.75967
$574$	−1.56902	+	1.13996i	−0.0654898	+	0.0475811i
$575$	1.37958	+	4.24590i	0.0575324	+	0.177066i
$576$	−2.85295	+	8.78048i	−0.118873	+	0.365853i
$577$	−16.9363	−	12.3049i	−0.705067	−	0.512261i	0.176511	−	0.984299i	$-0.443519\pi$
$577$	−16.9363	−	12.3049i	−0.705067	−	0.512261i	−0.881579	+	0.472037i	$0.843519\pi$
$578$	−0.415893	−	0.302164i	−0.0172989	−	0.0125684i
$579$	0.420277	−	1.29348i	0.0174661	−	0.0537552i
$580$	21.9807	+	67.6497i	0.912700	+	2.80900i
$581$	−22.5623	+	16.3925i	−0.936041	+	0.680074i
$582$	−12.2673			−0.508496
$583$	31.3032	−	11.5650i	1.29645	−	0.478972i
$584$	−9.10251			−0.376664
$585$	−19.0979	+	13.8754i	−0.789601	+	0.573679i
$586$	−4.39290	−	13.5200i	−0.181469	−	0.558504i
$587$	4.22995	−	13.0184i	0.174589	−	0.537329i	−0.825026	−	0.565095i	$-0.808839\pi$
$587$	4.22995	−	13.0184i	0.174589	−	0.537329i	0.999614	+	0.0277664i	$0.00883945\pi$
$588$	−12.7990	−	9.29905i	−0.527824	−	0.383486i
$589$	−6.34017	−	4.60640i	−0.261242	−	0.189803i
$590$	4.64866	−	14.3071i	0.191382	−	0.589015i
$591$	13.3376	+	41.0489i	0.548636	+	1.68853i
$592$	−13.1970	+	9.58821i	−0.542395	+	0.394073i
$593$	34.8619			1.43161			0.715803	−	0.698302i	$-0.246061\pi$
$593$	34.8619			1.43161			0.715803	+	0.698302i	$0.246061\pi$
$594$	4.10922	+	1.15685i	0.168603	+	0.0474661i
$595$	−7.66531			−0.314247
$596$	−21.5642	+	15.6673i	−0.883303	+	0.641758i
$597$	0.372683	+	1.14700i	0.0152529	+	0.0469435i
$598$	0.0898307	−	0.276470i	0.00367345	−	0.0113057i
$599$	26.1989	+	19.0346i	1.07046	+	0.777733i	0.975994	−	0.217795i	$-0.0698865\pi$
$599$	26.1989	+	19.0346i	1.07046	+	0.777733i	0.0944632	+	0.995528i	$0.469887\pi$
$600$	47.4542	+	34.4775i	1.93731	+	1.40754i
$601$	−1.76231	+	5.42383i	−0.0718860	+	0.221242i	−0.980544	−	0.196298i	$-0.937108\pi$
$601$	−1.76231	+	5.42383i	−0.0718860	+	0.221242i	0.908658	+	0.417541i	$0.137108\pi$
$602$	−0.997999	−	3.07153i	−0.0406754	−	0.125186i
$603$	−23.2689	+	16.9059i	−0.947585	+	0.688460i
$604$	−18.6472			−0.758743
$605$	−17.1823	−	41.3724i	−0.698558	−	1.68203i
$606$	5.47287			0.222320
$607$	22.7589	−	16.5353i	0.923755	−	0.671147i	−0.0207011	−	0.999786i	$-0.506590\pi$
$607$	22.7589	−	16.5353i	0.923755	−	0.671147i	0.944456	+	0.328639i	$0.106590\pi$
$608$	8.81911	+	27.1424i	0.357662	+	1.10077i
$609$	15.4289	−	47.4852i	0.625209	−	1.92420i
$610$	−18.6856	−	13.5759i	−0.756560	−	0.549673i
$611$	−2.03036	−	1.47514i	−0.0821396	−	0.0596779i
$612$	−2.11854	+	6.52018i	−0.0856367	+	0.263563i
$613$	2.52190	+	7.76160i	0.101858	+	0.313488i	0.988980	−	0.148047i	$-0.0472987\pi$
$613$	2.52190	+	7.76160i	0.101858	+	0.313488i	−0.887122	+	0.461535i	$0.847299\pi$
$614$	−5.72277	+	4.15783i	−0.230952	+	0.167797i
$615$	−21.5201			−0.867773
$616$	11.5397	+	3.24871i	0.464946	+	0.130894i
$617$	−0.967413			−0.0389466			−0.0194733	−	0.999810i	$-0.506199\pi$
$617$	−0.967413			−0.0389466			−0.0194733	+	0.999810i	$0.506199\pi$
$618$	8.12930	−	5.90628i	0.327009	−	0.237586i
$619$	14.1219	+	43.4626i	0.567605	+	1.74691i	0.660081	+	0.751194i	$0.270522\pi$
$619$	14.1219	+	43.4626i	0.567605	+	1.74691i	−0.0924760	+	0.995715i	$0.529478\pi$
$620$	−3.06994	+	9.44832i	−0.123292	+	0.379453i
$621$	−0.780531	−	0.567089i	−0.0313216	−	0.0227565i
$622$	0.958627	+	0.696483i	0.0384374	+	0.0279264i
$623$	5.35359	−	16.4766i	0.214487	−	0.660123i
$624$	2.96991	+	9.14044i	0.118892	+	0.365911i
$625$	−41.5064	+	30.1562i	−1.66026	+	1.20625i
$626$	−5.72215			−0.228703
$627$	−45.7347	+	16.8967i	−1.82647	+	0.674788i
$628$	2.39255			0.0954733
$629$	−5.31235	+	3.85965i	−0.211817	+	0.153894i
$630$	−4.80959	−	14.8024i	−0.191619	−	0.589741i
$631$	9.29694	−	28.6130i	0.370105	−	1.13907i	−0.576617	−	0.817015i	$-0.695627\pi$
$631$	9.29694	−	28.6130i	0.370105	−	1.13907i	0.946722	−	0.322052i	$-0.104373\pi$
$632$	10.3070	+	7.48848i	0.409991	+	0.297876i
$633$	9.68841	+	7.03904i	0.385080	+	0.279777i
$634$	−0.955639	+	2.94116i	−0.0379533	+	0.116808i
$635$	−2.97467	−	9.15509i	−0.118046	−	0.363309i
$636$	−37.2478	+	27.0621i	−1.47697	+	1.07308i
$637$	−5.07387			−0.201034
$638$	−0.681561	−	17.1429i	−0.0269833	−	0.678695i
$639$	−8.87119			−0.350939
$640$	37.6842	−	27.3791i	1.48960	−	1.08226i
$641$	1.32359	+	4.07360i	0.0522788	+	0.160897i	0.973787	−	0.227461i	$-0.0730423\pi$
$641$	1.32359	+	4.07360i	0.0522788	+	0.160897i	−0.921509	+	0.388358i	$0.873042\pi$
$642$	−4.89727	+	15.0723i	−0.193280	+	0.594854i
$643$	6.79438	+	4.93640i	0.267944	+	0.194673i	0.713642	−	0.700511i	$-0.247044\pi$
$643$	6.79438	+	4.93640i	0.267944	+	0.194673i	−0.445698	+	0.895183i	$0.647044\pi$
$644$	−1.01843	−	0.739932i	−0.0401317	−	0.0291574i
$645$	11.0739	−	34.0821i	0.436036	−	1.34198i
$646$	0.885838	+	2.72633i	0.0348528	+	0.107266i
$647$	−17.6378	+	12.8146i	−0.693414	+	0.503795i	−0.877781	−	0.479063i	$-0.840977\pi$
$647$	−17.6378	+	12.8146i	−0.693414	+	0.503795i	0.184367	+	0.982858i	$0.440977\pi$
$648$	10.0797			0.395968
$649$	13.2307	−	19.8212i	0.519350	−	0.778049i
$650$	8.74064			0.342836
$651$	5.64154	−	4.09882i	0.221109	−	0.160645i
$652$	−1.28559	−	3.95665i	−0.0503477	−	0.154954i
$653$	−0.616274	+	1.89670i	−0.0241167	+	0.0742235i	−0.962390	−	0.271670i	$-0.912424\pi$
$653$	−0.616274	+	1.89670i	−0.0241167	+	0.0742235i	0.938274	+	0.345893i	$0.112424\pi$
$654$	−10.4395	−	7.58474i	−0.408217	−	0.296587i
$655$	47.9287	+	34.8222i	1.87273	+	1.36062i
$656$	−1.53872	+	4.73570i	−0.0600770	+	0.184898i
$657$	5.78515	+	17.8049i	0.225700	+	0.694634i
$658$	1.33866	−	0.972594i	0.0521864	−	0.0379157i
$659$	−18.5217			−0.721503			−0.360752	−	0.932662i	$-0.617480\pi$
$659$	−18.5217			−0.721503			−0.360752	+	0.932662i	$0.617480\pi$
$660$	38.2867	+	48.5198i	1.49031	+	1.88863i
$661$	1.89916			0.0738687			0.0369344	−	0.999318i	$-0.488241\pi$
$661$	1.89916			0.0738687			0.0369344	+	0.999318i	$0.488241\pi$
$662$	−7.59657	+	5.51923i	−0.295249	+	0.214511i
$663$	1.19551	+	3.67941i	0.0464298	+	0.142896i
$664$	8.79322	−	27.0628i	0.341243	−	1.05024i
$665$	34.5808	+	25.1244i	1.34099	+	0.974283i
$666$	−10.7866	−	7.83689i	−0.417970	−	0.303673i
$667$	−1.19818	+	3.68761i	−0.0463936	+	0.142785i
$668$	−7.24108	−	22.2858i	−0.280166	−	0.862262i
$669$	14.4450	−	10.4949i	0.558476	−	0.405756i
$670$	15.2455			0.588986
$671$	−22.6655	−	28.7235i	−0.874992	−	1.10886i
$672$	−25.3945			−0.979614
$673$	1.32509	−	0.962736i	0.0510786	−	0.0371108i	−0.561953	−	0.827169i	$-0.689950\pi$
$673$	1.32509	−	0.962736i	0.0510786	−	0.0371108i	0.613032	+	0.790058i	$0.289950\pi$
$674$	−0.654291	−	2.01370i	−0.0252023	−	0.0775648i
$675$	8.96429	−	27.5892i	0.345036	−	1.06191i
$676$	−15.2308	−	11.0658i	−0.585801	−	0.425610i
$677$	1.95862	+	1.42302i	0.0752760	+	0.0546912i	0.624787	−	0.780795i	$-0.285186\pi$
$677$	1.95862	+	1.42302i	0.0752760	+	0.0546912i	−0.549511	+	0.835487i	$0.685186\pi$
$678$	−5.19641	+	15.9929i	−0.199567	+	0.614204i
$679$	5.26479	+	16.2034i	0.202044	+	0.621828i
$680$	6.32744	−	4.59715i	0.242646	−	0.176293i
$681$	11.8400			0.453710
$682$	1.33031	−	1.99296i	0.0509401	−	0.0763143i
$683$	13.1100			0.501641			0.250821	−	0.968034i	$-0.419300\pi$
$683$	13.1100			0.501641			0.250821	+	0.968034i	$0.419300\pi$
$684$	30.9285	−	22.4708i	1.18258	−	0.859194i
$685$	13.6736	+	42.0829i	0.522440	+	1.60790i
$686$	3.12673	−	9.62310i	0.119379	−	0.367412i
$687$	48.4084	+	35.1708i	1.84690	+	1.34185i
$688$	−6.70828	−	4.87385i	−0.255751	−	0.185814i
$689$	−4.56294	+	14.0433i	−0.173834	+	0.535007i
$690$	0.657194	+	2.02264i	0.0250190	+	0.0770004i
$691$	41.8009	−	30.3701i	1.59018	−	1.15533i	0.686498	−	0.727132i	$-0.259147\pi$
$691$	41.8009	−	30.3701i	1.59018	−	1.15533i	0.903683	−	0.428202i	$-0.140853\pi$
$692$	19.7688			0.751497
$693$	−0.979500	−	24.6368i	−0.0372081	−	0.935874i
$694$	−17.2599			−0.655179
$695$	47.9930	−	34.8689i	1.82048	−	1.32265i
$696$	15.7425	+	48.4505i	0.596719	+	1.83651i
$697$	−0.619399	+	1.90631i	−0.0234614	+	0.0722068i
$698$	11.5061	+	8.35970i	0.435514	+	0.316419i
$699$	−41.6971	−	30.2947i	−1.57713	−	1.14585i
$700$	11.6965	−	35.9981i	0.442086	−	1.36060i
$701$	−1.03359	−	3.18106i	−0.0390382	−	0.120147i	0.929638	−	0.368473i	$-0.120119\pi$
$701$	−1.03359	−	3.18106i	−0.0390382	−	0.120147i	−0.968676	+	0.248326i	$0.920119\pi$
$702$	−1.52816	+	1.11028i	−0.0576768	+	0.0419047i
$703$	36.6165			1.38102
$704$	7.27199	−	2.68664i	0.274074	−	0.101256i
$705$	18.3605			0.691496
$706$	11.8216	−	8.58888i	0.444911	−	0.323247i
$707$	−2.34881	−	7.22889i	−0.0883360	−	0.271870i
$708$	−10.1602	+	31.2698i	−0.381842	+	1.17519i
$709$	11.5630	+	8.40099i	0.434257	+	0.315506i	0.783349	−	0.621583i	$-0.213510\pi$
$709$	11.5630	+	8.40099i	0.434257	+	0.315506i	−0.349092	+	0.937088i	$0.613510\pi$
$710$	3.80420	+	2.76391i	0.142769	+	0.103728i
$711$	8.09709	−	24.9203i	0.303665	−	0.934584i
$712$	5.46242	+	16.8116i	0.204713	+	0.630041i
$713$	−0.438112	+	0.318307i	−0.0164074	+	0.0119207i
$714$	−2.55076			−0.0954596
$715$	19.0806	+	5.37166i	0.713572	+	0.200889i
$716$	7.91039			0.295625
$717$	−33.5932	+	24.4069i	−1.25456	+	0.911491i
$718$	0.294468	+	0.906279i	0.0109894	+	0.0338220i
$719$	−8.07454	+	24.8509i	−0.301129	+	0.926781i	0.679964	+	0.733246i	$0.261995\pi$
$719$	−8.07454	+	24.8509i	−0.301129	+	0.926781i	−0.981093	+	0.193535i	$0.938005\pi$
$720$	−32.3287	−	23.4882i	−1.20482	−	0.875353i
$721$	−11.2902	−	8.20284i	−0.420471	−	0.305490i
$722$	1.92143	−	5.91355i	0.0715081	−	0.220079i
$723$	−4.25241	−	13.0876i	−0.158149	−	0.486732i
$724$	−13.0535	+	9.48394i	−0.485130	+	0.352468i
$725$	−116.584			−4.32982
$726$	−5.71767	−	13.7673i	−0.212203	−	0.510953i
$727$	−9.90164			−0.367232			−0.183616	−	0.982998i	$-0.558780\pi$
$727$	−9.90164			−0.367232			−0.183616	+	0.982998i	$0.558780\pi$
$728$	−4.29144	+	3.11792i	−0.159051	+	0.115558i
$729$	−12.5253	−	38.5491i	−0.463902	−	1.42774i
$730$	3.06647	−	9.43762i	0.113495	−	0.349302i
$731$	−2.70036	−	1.96193i	−0.0998764	−	0.0725645i
$732$	40.8395	+	29.6716i	1.50947	+	1.09670i
$733$	1.06542	−	3.27904i	0.0393524	−	0.121114i	−0.929450	−	0.368947i	$-0.879718\pi$
$733$	1.06542	−	3.27904i	0.0393524	−	0.121114i	0.968803	+	0.247833i	$0.0797184\pi$
$734$	4.12453	+	12.6940i	0.152239	+	0.468544i
$735$	30.0307	−	21.8186i	1.10770	−	0.804791i
$736$	1.97209			0.0726922
$737$	23.2478	+	6.54484i	0.856343	+	0.241082i
$738$	−4.06990			−0.149815
$739$	7.55598	−	5.48974i	0.277951	−	0.201943i	−0.440072	−	0.897962i	$-0.645047\pi$
$739$	7.55598	−	5.48974i	0.277951	−	0.201943i	0.718023	+	0.696019i	$0.245047\pi$
$740$	−14.3438	−	44.1457i	−0.527288	−	1.62283i
$741$	6.66656	−	20.5175i	0.244902	−	0.753731i
$742$	−7.87621	−	5.72240i	−0.289145	−	0.210076i
$743$	13.3968	+	9.73335i	0.491481	+	0.357082i	0.805754	−	0.592251i	$-0.201761\pi$
$743$	13.3968	+	9.73335i	0.491481	+	0.357082i	−0.314273	+	0.949333i	$0.601761\pi$
$744$	−2.19868	+	6.76685i	−0.0806077	+	0.248085i
$745$	−19.3262	−	59.4799i	−0.708057	−	2.17917i
$746$	−13.4334	+	9.75994i	−0.491832	+	0.357337i
$747$	−58.5244			−2.14130
$748$	5.40001	−	1.99503i	0.197444	−	0.0729457i
$749$	22.0101			0.804231
$750$	−29.4074	+	21.3657i	−1.07381	+	0.780167i
$751$	2.44083	+	7.51210i	0.0890671	+	0.274120i	0.985662	−	0.168731i	$-0.0539669\pi$
$751$	2.44083	+	7.51210i	0.0890671	+	0.274120i	−0.896595	+	0.442851i	$0.853967\pi$
$752$	1.31281	−	4.04040i	0.0478731	−	0.147338i
$753$	40.4363	+	29.3787i	1.47358	+	1.07062i
$754$	6.14152	+	4.46207i	0.223661	+	0.162499i
$755$	13.5202	−	41.6110i	0.492051	−	1.51438i
$756$	2.52770	+	7.77945i	0.0919315	+	0.282936i
$757$	−8.00798	+	5.81814i	−0.291055	+	0.211464i	−0.723725	−	0.690089i	$-0.757572\pi$
$757$	−8.00798	+	5.81814i	−0.291055	+	0.211464i	0.432670	+	0.901552i	$0.357572\pi$
$758$	12.3067			0.446999
$759$	0.133841	+	3.36643i	0.00485813	+	0.122194i
$760$	−43.6132			−1.58202
$761$	17.6475	−	12.8217i	0.639723	−	0.464786i	−0.220032	−	0.975493i	$-0.570616\pi$
$761$	17.6475	−	12.8217i	0.639723	−	0.464786i	0.859755	+	0.510707i	$0.170616\pi$
$762$	−0.989869	−	3.04650i	−0.0358592	−	0.110363i
$763$	−5.53802	+	17.0443i	−0.200490	+	0.617044i
$764$	22.4369	+	16.3014i	0.811740	+	0.589764i
$765$	−13.0137	−	9.45497i	−0.470510	−	0.341845i
$766$	−0.829961	+	2.55436i	−0.0299877	+	0.0922926i
$767$	3.25852	+	10.0287i	0.117658	+	0.362115i
$768$	2.56959	−	1.86692i	0.0927221	−	0.0673666i
$769$	−24.2335			−0.873881			−0.436941	−	0.899490i	$-0.643938\pi$
$769$	−24.2335			−0.873881			−0.436941	+	0.899490i	$0.643938\pi$
$770$	−7.25581	+	10.8701i	−0.261481	+	0.391730i
$771$	39.9605			1.43914
$772$	0.724449	−	0.526343i	0.0260735	−	0.0189435i
$773$	3.68126	+	11.3297i	0.132406	+	0.407503i	0.995177	−	0.0980908i	$-0.0312736\pi$
$773$	3.68126	+	11.3297i	0.132406	+	0.407503i	−0.862772	+	0.505594i	$0.831274\pi$
$774$	2.09431	−	6.44564i	0.0752786	−	0.231684i
$775$	−13.1730	−	9.57076i	−0.473189	−	0.343792i
$776$	−14.0636	−	10.2178i	−0.504854	−	0.366798i
$777$	−10.0683	+	30.9870i	−0.361198	+	1.11165i
$778$	−5.84124	−	17.9775i	−0.209419	−	0.644524i
$779$	9.04260	−	6.56983i	0.323985	−	0.235389i
$780$	−27.3479			−0.979212
$781$	4.61445	+	5.84779i	0.165118	+	0.209250i
$782$	0.198087			0.00708357
$783$	20.3829	−	14.8090i	0.728425	−	0.529232i
$784$	−2.65414	−	8.16862i	−0.0947909	−	0.291736i
$785$	−1.73473	+	5.33896i	−0.0619152	+	0.190556i
$786$	15.9490	+	11.5877i	0.568884	+	0.413318i
$787$	−31.1965	−	22.6656i	−1.11204	−	0.807941i	−0.129052	−	0.991638i	$-0.541193\pi$
$787$	−31.1965	−	22.6656i	−1.11204	−	0.807941i	−0.982983	+	0.183697i	$0.941193\pi$
$788$	−8.78162	+	27.0270i	−0.312832	+	0.962799i
$789$	−5.15210	−	15.8565i	−0.183420	−	0.564507i
$790$	−11.2364	+	8.16373i	−0.399774	+	0.290453i
$791$	23.3546			0.830392
$792$	15.5841	+	19.7493i	0.553756	+	0.701762i
$793$	16.1898			0.574918
$794$	0.0516381	−	0.0375173i	0.00183257	−	0.00133144i
$795$	−33.3821	−	102.740i	−1.18394	−	3.64380i
$796$	−0.245378	+	0.755197i	−0.00869720	+	0.0267672i
$797$	36.6461	+	26.6250i	1.29807	+	0.943104i	0.999935	−	0.0114188i	$-0.00363479\pi$
$797$	36.6461	+	26.6250i	1.29807	+	0.943104i	0.298137	+	0.954523i	$0.403635\pi$
$798$	11.5073	+	8.36055i	0.407355	+	0.295960i
$799$	0.528459	−	1.62643i	0.0186955	−	0.0575389i
$800$	18.3236	+	56.3941i	0.647835	+	1.99383i
$801$	29.4125	−	21.3694i	1.03924	−	0.755052i
$802$	12.3077			0.434601
$803$	8.72756	−	13.0749i	0.307989	−	0.461404i
$804$	−33.3208			−1.17513
$805$	2.38957	−	1.73612i	0.0842211	−	0.0611902i
$806$	0.327634	+	1.00835i	0.0115404	+	0.0355177i
$807$	1.14051	−	3.51013i	0.0401479	−	0.123562i
$808$	6.27427	+	4.55852i	0.220728	+	0.160368i
$809$	−10.5109	−	7.63658i	−0.369542	−	0.268488i	0.387479	−	0.921879i	$-0.373346\pi$
$809$	−10.5109	−	7.63658i	−0.369542	−	0.268488i	−0.757021	+	0.653391i	$0.773346\pi$
$810$	−3.39567	+	10.4508i	−0.119312	+	0.367203i
$811$	−6.47871	−	19.9394i	−0.227498	−	0.700168i	−0.998028	−	0.0627641i	$-0.980008\pi$
$811$	−6.47871	−	19.9394i	−0.227498	−	0.700168i	0.770530	−	0.637404i	$-0.219992\pi$
$812$	26.5954	−	19.3227i	0.933315	−	0.678093i
$813$	31.7025			1.11186
$814$	0.444762	+	11.1868i	0.0155889	+	0.392098i
$815$	9.76135			0.341925
$816$	−5.29825	+	3.84940i	−0.185476	+	0.134756i
$817$	5.75167	+	17.7018i	0.201225	+	0.619308i
$818$	−2.03620	+	6.26679i	−0.0711942	+	0.219113i
$819$	8.82622	+	6.41263i	0.308413	+	0.224075i
$820$	−11.4630	−	8.32836i	−0.400305	−	0.290839i
$821$	−1.01112	+	3.11190i	−0.0352883	+	0.108606i	−0.967149	−	0.254210i	$-0.918185\pi$
$821$	−1.01112	+	3.11190i	−0.0352883	+	0.108606i	0.931861	+	0.362816i	$0.118185\pi$
$822$	4.55010	+	14.0038i	0.158703	+	0.488437i
$823$	2.28704	−	1.66163i	0.0797213	−	0.0579209i	−0.547211	−	0.836995i	$-0.684310\pi$
$823$	2.28704	−	1.66163i	0.0797213	−	0.0579209i	0.626932	+	0.779074i	$0.284310\pi$
$824$	14.2392			0.496047
$825$	−95.0233	+	35.1064i	−3.30829	+	1.22225i
$826$	−6.95240			−0.241905
$827$	19.8596	−	14.4288i	0.690585	−	0.501739i	−0.186267	−	0.982499i	$-0.559639\pi$
$827$	19.8596	−	14.4288i	0.690585	−	0.501739i	0.876852	+	0.480760i	$0.159639\pi$
$828$	−0.816333	−	2.51241i	−0.0283695	−	0.0873124i
$829$	16.7152	−	51.4441i	0.580543	−	1.78673i	−0.0359329	−	0.999354i	$-0.511440\pi$
$829$	16.7152	−	51.4441i	0.580543	−	1.78673i	0.616476	−	0.787374i	$-0.288560\pi$
$830$	25.0968	+	18.2339i	0.871123	+	0.632908i
$831$	27.3097	+	19.8417i	0.947364	+	0.688300i
$832$	−1.06001	+	3.26237i	−0.0367492	+	0.113102i
$833$	−1.06840	−	3.28821i	−0.0370180	−	0.113930i
$834$	15.9704	−	11.6032i	0.553011	−	0.401786i
$835$	54.9806			1.90268
$836$	−30.9004	−	8.69923i	−1.06871	−	0.300869i
$837$	3.51882			0.121628
$838$	−7.05141	+	5.12315i	−0.243587	+	0.176976i
$839$	8.44151	+	25.9803i	0.291433	+	0.896939i	0.984396	+	0.175966i	$0.0563048\pi$
$839$	8.44151	+	25.9803i	0.291433	+	0.896939i	−0.692963	+	0.720973i	$0.743695\pi$
$840$	11.9922	−	36.9080i	0.413768	−	1.27345i
$841$	−58.4551	−	42.4701i	−2.01569	−	1.46449i
$842$	−10.6951	−	7.77043i	−0.368577	−	0.267787i
$843$	−10.9636	+	33.7425i	−0.377606	+	1.16215i
$844$	2.43654	+	7.49891i	0.0838693	+	0.258123i
$845$	35.7365	−	25.9641i	1.22937	−	0.893192i
$846$	3.47236			0.119382
$847$	−15.7308	+	13.4608i	−0.540517	+	0.462519i
$848$	−24.9957			−0.858356
$849$	−5.01425	+	3.64306i	−0.172088	+	0.125030i
$850$	1.84051	+	5.66452i	0.0631291	+	0.194291i
$851$	0.781886	−	2.40640i	0.0268027	−	0.0824902i
$852$	−8.31448	−	6.04082i	−0.284849	−	0.206955i
$853$	−5.77938	−	4.19897i	−0.197882	−	0.143770i	0.484432	−	0.874829i	$-0.339026\pi$
$853$	−5.77938	−	4.19897i	−0.197882	−	0.143770i	−0.682314	+	0.731059i	$0.739026\pi$
$854$	−3.29854	+	10.1519i	−0.112874	+	0.347390i
$855$	27.7186	+	85.3091i	0.947957	+	2.91751i
$856$	−18.1685	+	13.2002i	−0.620988	+	0.451174i
$857$	2.89249			0.0988054			0.0494027	−	0.998779i	$-0.484268\pi$
$857$	2.89249			0.0988054			0.0494027	+	0.998779i	$0.484268\pi$
$858$	6.34936	+	1.78751i	0.216764	+	0.0610244i
$859$	−11.0236			−0.376119			−0.188059	−	0.982158i	$-0.560220\pi$
$859$	−11.0236			−0.376119			−0.188059	+	0.982158i	$0.560220\pi$
$860$	19.0886	−	13.8687i	0.650916	−	0.472918i
$861$	3.07337	+	9.45887i	0.104740	+	0.322357i
$862$	0.751302	−	2.31227i	0.0255895	−	0.0787563i
$863$	1.86543	+	1.35532i	0.0635001	+	0.0461355i	0.619082	−	0.785326i	$-0.287505\pi$
$863$	1.86543	+	1.35532i	0.0635001	+	0.0461355i	−0.555582	+	0.831461i	$0.687505\pi$
$864$	−10.3670	−	7.53208i	−0.352693	−	0.256247i
$865$	−14.3335	+	44.1138i	−0.487352	+	1.49992i
$866$	−5.06281	−	15.5817i	−0.172041	−	0.529489i
$867$	−2.13276	+	1.54954i	−0.0724324	+	0.0526253i
$868$	4.59132			0.155839
$869$	−20.6390	+	7.62507i	−0.700130	+	0.258663i
$870$	−55.5376			−1.88290
$871$	−8.64554	+	6.28135i	−0.292943	+	0.212835i
$872$	−5.65060	−	17.3908i	−0.191354	−	0.588926i
$873$	−11.0482	+	34.0030i	−0.373926	+	1.15083i
$874$	−0.893637	−	0.649265i	−0.0302277	−	0.0219617i
$875$	40.8420	+	29.6735i	1.38071	+	1.00315i
$876$	−6.70210	+	20.6269i	−0.226443	+	0.696919i
$877$	9.35041	+	28.7776i	0.315741	+	0.971751i	0.975448	+	0.220228i	$0.0706802\pi$
$877$	9.35041	+	28.7776i	0.315741	+	0.971751i	−0.659707	+	0.751522i	$0.729320\pi$
$878$	−1.42691	+	1.03671i	−0.0481560	+	0.0349874i
$879$	−72.9003			−2.45887
$880$	1.33301	+	33.5284i	0.0449357	+	1.13024i
$881$	23.5055			0.791920			0.395960	−	0.918268i	$-0.370412\pi$
$881$	23.5055			0.791920			0.395960	+	0.918268i	$0.370412\pi$
$882$	5.67945	−	4.12636i	0.191237	−	0.138942i
$883$	−5.38358	−	16.5690i	−0.181172	−	0.557590i	0.818689	−	0.574237i	$-0.194701\pi$
$883$	−5.38358	−	16.5690i	−0.181172	−	0.557590i	−0.999861	+	0.0166465i	$0.994701\pi$
$884$	−0.787138	+	2.42256i	−0.0264743	+	0.0814796i
$885$	−62.4114	−	45.3446i	−2.09794	−	1.52424i
$886$	14.8914	+	10.8193i	0.500288	+	0.363481i
$887$	−5.78820	+	17.8142i	−0.194349	+	0.598144i	0.805635	+	0.592412i	$0.201824\pi$
$887$	−5.78820	+	17.8142i	−0.194349	+	0.598144i	−0.999984	+	0.00573141i	$0.998176\pi$
$888$	−10.2730	−	31.6170i	−0.344739	−	1.06100i
$889$	−3.59918	+	2.61496i	−0.120713	+	0.0877028i
$890$	−19.2707			−0.645956
$891$	−9.66450	+	14.4786i	−0.323773	+	0.485051i
$892$	11.7559			0.393618
$893$	−7.71497	+	5.60525i	−0.258172	+	0.187573i
$894$	−6.43110	−	19.7929i	−0.215088	−	0.661973i
$895$	−5.73547	+	17.6519i	−0.191715	+	0.590040i
$896$	−17.4160	−	12.6534i	−0.581827	−	0.422722i
$897$	−1.20604	−	0.876237i	−0.0402684	−	0.0292567i
$898$	0.863935	−	2.65892i	0.0288299	−	0.0887293i
$899$	−4.37004	−	13.4496i	−0.145749	−	0.448569i
$900$	64.2604	−	46.6879i	2.14201	−	1.55626i
$901$	−10.0618			−0.335207
$902$	2.11701	+	2.68283i	0.0704886	+	0.0893286i
$903$	−16.5618			−0.551143
$904$	−19.2783	+	14.0065i	−0.641188	+	0.465850i
$905$	−11.6988	−	36.0052i	−0.388881	−	1.19685i
$906$	4.49907	−	13.8467i	0.149472	−	0.460026i
$907$	5.07854	+	3.68978i	0.168630	+	0.122517i	0.668899	−	0.743353i	$-0.266766\pi$
$907$	5.07854	+	3.68978i	0.168630	+	0.122517i	−0.500269	+	0.865870i	$0.666766\pi$
$908$	6.30676	+	4.58213i	0.209297	+	0.152063i
$909$	4.92901	−	15.1699i	0.163485	−	0.503155i
$910$	−1.78699	−	5.49980i	−0.0592383	−	0.182317i
$911$	−17.4424	+	12.6726i	−0.577892	+	0.419863i	−0.837964	−	0.545726i	$-0.816254\pi$
$911$	−17.4424	+	12.6726i	−0.577892	+	0.419863i	0.260071	+	0.965589i	$0.416254\pi$
$912$	36.5193			1.20927
$913$	30.4422	+	38.5787i	1.00749	+	1.27677i
$914$	11.8897			0.393276
$915$	−95.8228	+	69.6193i	−3.16780	+	2.30154i
$916$	12.1743	+	37.4685i	0.402249	+	1.23800i
$917$	8.46076	−	26.0395i	0.279399	−	0.859902i
$918$	−1.04132	−	0.756561i	−0.0343686	−	0.0249703i
$919$	24.2343	+	17.6072i	0.799414	+	0.580809i	0.910742	−	0.412975i	$-0.135510\pi$
$919$	24.2343	+	17.6072i	0.799414	+	0.580809i	−0.111328	+	0.993784i	$0.535510\pi$
$920$	−0.931288	+	2.86621i	−0.0307037	+	0.0944961i
$921$	11.2096	+	34.4997i	0.369370	+	1.13680i
$922$	3.02493	−	2.19774i	0.0996207	−	0.0723787i
$923$	−3.29607			−0.108492
$924$	15.8584	−	23.7577i	0.521702	−	0.781571i
$925$	76.0784			2.50144
$926$	−2.98087	+	2.16573i	−0.0979574	+	0.0711702i
$927$	−9.04982	−	27.8525i	−0.297235	−	0.914795i
$928$	−15.9142	+	48.9788i	−0.522409	+	1.60781i
$929$	−29.8075	−	21.6564i	−0.977952	−	0.710523i	−0.0207017	−	0.999786i	$-0.506590\pi$
$929$	−29.8075	−	21.6564i	−0.977952	−	0.710523i	−0.957250	+	0.289262i	$0.906590\pi$
$930$	−6.27528	−	4.55926i	−0.205775	−	0.149504i
$931$	−5.95776	+	18.3361i	−0.195258	+	0.600941i
$932$	−10.4864	−	32.2739i	−0.343494	−	1.05717i
$933$	4.91598	−	3.57167i	0.160942	−	0.116931i
$934$	−2.38905			−0.0781722
$935$	0.536592	+	13.4966i	0.0175484	+	0.441385i
$936$	−11.1316			−0.363848
$937$	4.05497	−	2.94611i	0.132470	−	0.0962452i	−0.519577	−	0.854424i	$-0.673910\pi$
$937$	4.05497	−	2.94611i	0.132470	−	0.0962452i	0.652047	+	0.758178i	$0.273910\pi$
$938$	−2.17728	−	6.70097i	−0.0710906	−	0.218795i
$939$	−9.06780	+	27.9078i	−0.295916	+	0.910737i
$940$	9.78000	+	7.10559i	0.318989	+	0.231759i
$941$	−30.2909	−	22.0077i	−0.987457	−	0.717429i	−0.0280940	−	0.999605i	$-0.508944\pi$
$941$	−30.2909	−	22.0077i	−0.987457	−	0.717429i	−0.959363	+	0.282176i	$0.908944\pi$
$942$	−0.577260	+	1.77662i	−0.0188081	+	0.0578855i
$943$	−0.238672	−	0.734558i	−0.00777224	−	0.0239205i
$944$	−14.4410	+	10.4920i	−0.470015	+	0.341486i
$945$	−19.1925			−0.624331
$946$	−5.33828	+	1.97223i	−0.173562	+	0.0641226i
$947$	17.5846			0.571421			0.285711	−	0.958316i	$-0.407770\pi$
$947$	17.5846			0.571421			0.285711	+	0.958316i	$0.407770\pi$
$948$	24.5584	−	17.8427i	0.797620	−	0.579505i
$949$	2.14946	+	6.61537i	0.0697745	+	0.214744i
$950$	10.2633	−	31.5871i	0.332985	−	1.02482i
$951$	12.8301	+	9.32161i	0.416044	+	0.302274i
$952$	−2.92427	−	2.12460i	−0.0947760	−	0.0688588i
$953$	16.2520	−	50.0184i	0.526453	−	1.62026i	−0.234972	−	0.972002i	$-0.575500\pi$
$953$	16.2520	−	50.0184i	0.526453	−	1.62026i	0.761425	−	0.648253i	$-0.224500\pi$
$954$	−6.31326	−	19.4302i	−0.204399	−	0.629077i
$955$	−52.6444	+	38.2484i	−1.70353	+	1.23769i
$956$	−27.3395			−0.884222
$957$	−84.6888	−	23.8421i	−2.73760	−	0.770704i
$958$	18.8120			0.607789
$959$	16.5442	−	12.0201i	0.534240	−	0.388148i
$960$	−7.75494	−	23.8672i	−0.250290	−	0.770312i
$961$	−8.96918	+	27.6043i	−0.289329	+	0.890462i
$962$	−4.00772	−	2.91178i	−0.129214	−	0.0938796i
$963$	37.3673	+	27.1489i	1.20414	+	0.874861i
$964$	2.79983	−	8.61700i	0.0901766	−	0.277535i
$965$	0.649264	+	1.99823i	0.0209005	+	0.0643252i
$966$	0.795166	−	0.577722i	0.0255841	−	0.0185879i
$967$	−53.2519			−1.71246			−0.856232	−	0.516591i	$-0.827201\pi$
$967$	−53.2519			−1.71246			−0.856232	+	0.516591i	$0.827201\pi$
$968$	4.91231	−	20.5457i	0.157888	−	0.660364i
$969$	14.7005			0.472249
$970$	15.3318	−	11.1392i	0.492273	−	0.357657i
$971$	14.0645	+	43.2862i	0.451353	+	1.38912i	0.875364	+	0.483464i	$0.160621\pi$
$971$	14.0645	+	43.2862i	0.451353	+	1.38912i	−0.424012	+	0.905657i	$0.639379\pi$
$972$	11.4505	−	35.2410i	0.367275	−	1.13036i
$973$	−22.1803	−	16.1149i	−0.711067	−	0.516620i
$974$	−5.28617	−	3.84063i	−0.169380	−	0.123062i
$975$	13.8512	−	42.6295i	0.443592	−	1.36524i
$976$	8.46891	+	26.0646i	0.271083	+	0.834308i
$977$	44.2225	−	32.1295i	1.41480	−	1.02791i	0.422201	−	0.906502i	$-0.361258\pi$
$977$	44.2225	−	32.1295i	1.41480	−	1.02791i	0.992602	−	0.121412i	$-0.0387424\pi$
$978$	3.24825			0.103867
$979$	−29.3858	−	8.27284i	−0.939173	−	0.264401i
$980$	24.4402			0.780715
$981$	−30.4258	+	22.1056i	−0.971420	+	0.705778i
$982$	3.43495	+	10.5717i	0.109614	+	0.337356i
$983$	4.48578	−	13.8058i	0.143074	−	0.440337i	−0.853684	−	0.520791i	$-0.825637\pi$
$983$	4.48578	−	13.8058i	0.143074	−	0.440337i	0.996758	+	0.0804542i	$0.0256371\pi$
$984$	−8.20976	−	5.96474i	−0.261718	−	0.190149i
$985$	−53.9434	−	39.1922i	−1.71878	−	1.24877i
$986$	−1.59850	+	4.91969i	−0.0509067	+	0.156675i
$987$	−2.62214	−	8.07012i	−0.0834636	−	0.256875i
$988$	11.4914	−	8.34901i	0.365591	−	0.265617i
$989$	1.28616			0.0408976
$990$	−25.7264	+	9.50461i	−0.817638	+	0.302076i
$991$	56.4879			1.79440			0.897199	−	0.441626i	$-0.145598\pi$
$991$	56.4879			1.79440			0.897199	+	0.441626i	$0.145598\pi$
$992$	−5.81900	+	4.22775i	−0.184753	+	0.134231i
$993$	14.8800	+	45.7959i	0.472202	+	1.45329i
$994$	0.671547	−	2.06681i	0.0213002	−	0.0655552i
$995$	−1.50730	−	1.09512i	−0.0477846	−	0.0347176i
$996$	−54.8518	−	39.8521i	−1.73805	−	1.26276i
$997$	7.67734	−	23.6284i	0.243144	−	0.748319i	−0.752793	−	0.658258i	$-0.771294\pi$
$997$	7.67734	−	23.6284i	0.243144	−	0.748319i	0.995936	−	0.0900615i	$-0.0287064\pi$
$998$	−0.968225	−	2.97989i	−0.0306486	−	0.0943268i
$999$	−13.3011	+	9.66383i	−0.420829	+	0.305750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.69.5	✓	36
11.2	odd	10		2057.2.a.be.1.8		18
11.4	even	5	inner	187.2.g.f.103.5	yes	36
11.9	even	5		2057.2.a.bd.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.5	✓	36	1.1	even	1	trivial
187.2.g.f.103.5	yes	36	11.4	even	5	inner
2057.2.a.bd.1.11		18	11.9	even	5
2057.2.a.be.1.8		18	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415893 + 0.302164i) q^{2} +(0.814643 + 2.50721i) q^{3} +(-0.536370 + 1.65078i) q^{4} +(-3.29479 - 2.39381i) q^{5} +(-1.09640 - 0.796578i) q^{6} +(-0.581623 + 1.79005i) q^{7} +(-0.593447 - 1.82644i) q^{8} +(-3.19543 + 2.32161i) q^{9} +O(q^{10})\)	\(q+(-0.415893 + 0.302164i) q^{2} +(0.814643 + 2.50721i) q^{3} +(-0.536370 + 1.65078i) q^{4} +(-3.29479 - 2.39381i) q^{5} +(-1.09640 - 0.796578i) q^{6} +(-0.581623 + 1.79005i) q^{7} +(-0.593447 - 1.82644i) q^{8} +(-3.19543 + 2.32161i) q^{9} +2.09360 q^{10} +(3.19252 + 0.898776i) q^{11} -4.57580 q^{12} +(-1.18726 + 0.862592i) q^{13} +(-0.298997 - 0.920217i) q^{14} +(3.31771 - 10.2108i) q^{15} +(-2.00977 - 1.46019i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.627448 - 1.93109i) q^{18} +(1.72318 + 5.30339i) q^{19} +(5.71887 - 4.15500i) q^{20} -4.96186 q^{21} +(-1.59933 + 0.590871i) q^{22} +0.385329 q^{23} +(4.09584 - 2.97580i) q^{24} +(3.58026 + 11.0189i) q^{25} +(0.233127 - 0.717492i) q^{26} +(-2.02562 - 1.47170i) q^{27} +(-2.64301 - 1.92026i) q^{28} +(-3.10949 + 9.57003i) q^{29} +(1.70554 + 5.24912i) q^{30} +(-1.13698 + 0.826065i) q^{31} +5.11794 q^{32} +(0.347343 + 8.73652i) q^{33} +0.514072 q^{34} +(6.20137 - 4.50556i) q^{35} +(-2.11854 - 6.52018i) q^{36} +(2.02914 - 6.24505i) q^{37} +(-2.31915 - 1.68496i) q^{38} +(-3.12989 - 2.27400i) q^{39} +(-2.41687 + 7.43835i) q^{40} +(-0.619399 - 1.90631i) q^{41} +(2.06360 - 1.49930i) q^{42} +3.33783 q^{43} +(-3.19605 + 4.78807i) q^{44} +16.0858 q^{45} +(-0.160256 + 0.116433i) q^{46} +(0.528459 + 1.62643i) q^{47} +(2.02375 - 6.22846i) q^{48} +(2.79712 + 2.03222i) q^{49} +(-4.81853 - 3.50086i) q^{50} +(0.814643 - 2.50721i) q^{51} +(-0.787138 - 2.42256i) q^{52} +(8.14017 - 5.91418i) q^{53} +1.28714 q^{54} +(-8.36720 - 10.6036i) q^{55} +3.61459 q^{56} +(-11.8930 + 8.64075i) q^{57} +(-1.59850 - 4.91969i) q^{58} +(2.22041 - 6.83372i) q^{59} +(15.0763 + 10.9536i) q^{60} +(-8.92510 - 6.48447i) q^{61} +(0.223256 - 0.687110i) q^{62} +(-2.29728 - 7.07029i) q^{63} +(1.89103 - 1.37391i) q^{64} +5.97664 q^{65} +(-2.78432 - 3.52851i) q^{66} +7.28195 q^{67} +(1.40423 - 1.02024i) q^{68} +(0.313905 + 0.966102i) q^{69} +(-1.21769 + 3.74766i) q^{70} +(1.81705 + 1.32017i) q^{71} +(6.13661 + 4.45851i) q^{72} +(1.46468 - 4.50783i) q^{73} +(1.04312 + 3.21041i) q^{74} +(-24.7101 + 17.9530i) q^{75} -9.67898 q^{76} +(-3.46570 + 5.19203i) q^{77} +1.98882 q^{78} +(-5.36702 + 3.89937i) q^{79} +(3.12638 + 9.62202i) q^{80} +(-1.62192 + 4.99176i) q^{81} +(0.833624 + 0.605663i) q^{82} +(11.9874 + 8.70933i) q^{83} +(2.66139 - 8.19092i) q^{84} +(1.25850 + 3.87326i) q^{85} +(-1.38818 + 1.00857i) q^{86} -26.5272 q^{87} +(-0.253031 - 6.36434i) q^{88} -9.20456 q^{89} +(-6.68996 + 4.86054i) q^{90} +(-0.853549 - 2.62695i) q^{91} +(-0.206679 + 0.636092i) q^{92} +(-2.99736 - 2.17771i) q^{93} +(-0.711231 - 0.516740i) q^{94} +(7.01779 - 21.5985i) q^{95} +(4.16929 + 12.8318i) q^{96} +(7.32314 - 5.32057i) q^{97} -1.77737 q^{98} +(-12.2881 + 4.53983i) 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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