LMFDB - Embedded newform 115.2.g.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.1
Root			$1.58773 - 1.83233i$ of defining polynomial
Character	$\chi$	$=$	115.16
Dual form			115.2.g.b.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.186393 - 0.215109i) q^{2} +(-2.03964 + 1.31080i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.0982103 + 0.683068i) q^{6} +(-4.87354 + 1.43100i) q^{7} +(0.938384 + 0.603063i) q^{8} +(1.19570 - 2.61822i) q^{9} +O(q^{10})$	\(q+(0.186393 - 0.215109i) q^{2} +(-2.03964 + 1.31080i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.0982103 + 0.683068i) q^{6} +(-4.87354 + 1.43100i) q^{7} +(0.938384 + 0.603063i) q^{8} +(1.19570 - 2.61822i) q^{9} +(-0.273100 - 0.0801894i) q^{10} +(2.39693 + 2.76621i) q^{11} +(-3.04683 - 3.51622i) q^{12} +(4.71898 + 1.38562i) q^{13} +(-0.600571 + 1.31507i) q^{14} +(2.03964 + 1.31080i) q^{15} +(-3.37787 + 0.991834i) q^{16} +(0.237653 - 1.65292i) q^{17} +(-0.340332 - 0.745222i) q^{18} +(-0.314321 - 2.18615i) q^{19} +(1.61435 - 1.03748i) q^{20} +(8.06451 - 9.30694i) q^{21} +1.04181 q^{22} +(3.82485 + 2.89319i) q^{23} -2.70446 q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.17764 - 0.756824i) q^{26} +(-0.0419833 - 0.292000i) q^{27} +(-4.04908 - 8.86625i) q^{28} +(-0.240417 + 1.67214i) q^{29} +(0.662138 - 0.194421i) q^{30} +(-1.04163 - 0.669418i) q^{31} +(-1.34302 + 2.94080i) q^{32} +(-8.51482 - 2.50018i) q^{33} +(-0.311260 - 0.359213i) q^{34} +(3.32622 + 3.83867i) q^{35} +(5.29973 + 1.55614i) q^{36} +(-1.32998 + 2.91224i) q^{37} +(-0.528847 - 0.339869i) q^{38} +(-11.4413 + 3.35946i) q^{39} +(0.158746 - 1.10411i) q^{40} +(3.16340 + 6.92687i) q^{41} +(-0.498838 - 3.46949i) q^{42} +(-1.68924 + 1.08561i) q^{43} +(-4.59968 + 5.30831i) q^{44} -2.87833 q^{45} +(1.33527 - 0.283488i) q^{46} +8.67911 q^{47} +(5.58956 - 6.45069i) q^{48} +(15.8148 - 10.1636i) q^{49} +(0.0405070 + 0.281733i) q^{50} +(1.68191 + 3.68287i) q^{51} +(-1.34316 + 9.34189i) q^{52} +(-5.20829 + 1.52929i) q^{53} +(-0.0706372 - 0.0453958i) q^{54} +(1.52051 - 3.32945i) q^{55} +(-5.43623 - 1.59622i) q^{56} +(3.50670 + 4.04695i) q^{57} +(0.314880 + 0.363391i) q^{58} +(-1.56713 - 0.460150i) q^{59} +(-1.93277 + 4.23218i) q^{60} +(-6.36917 - 4.09322i) q^{61} +(-0.338151 + 0.0992900i) q^{62} +(-2.08062 + 14.4710i) q^{63} +(-2.54266 - 5.56764i) q^{64} +(-0.699932 - 4.86814i) q^{65} +(-2.12491 + 1.36560i) q^{66} +(0.0752564 - 0.0868505i) q^{67} +3.20454 q^{68} +(-11.5937 - 0.887472i) q^{69} +1.44571 q^{70} +(-1.26600 + 1.46104i) q^{71} +(2.70098 - 1.73581i) q^{72} +(1.48784 + 10.3482i) q^{73} +(0.378550 + 0.828910i) q^{74} +(0.345046 - 2.39985i) q^{75} +(4.06665 - 1.19408i) q^{76} +(-15.6400 - 10.0512i) q^{77} +(-1.40992 + 3.08730i) q^{78} +(-0.948139 - 0.278399i) q^{79} +(2.30542 + 2.66060i) q^{80} +(6.12309 + 7.06642i) q^{81} +(2.07967 + 0.610645i) q^{82} +(6.48492 - 14.2000i) q^{83} +(19.8805 + 12.7764i) q^{84} +(-1.60227 + 0.470469i) q^{85} +(-0.0813383 + 0.565720i) q^{86} +(-1.70147 - 3.72570i) q^{87} +(0.581046 + 4.04127i) q^{88} +(2.51564 - 1.61670i) q^{89} +(-0.536499 + 0.619153i) q^{90} -24.9809 q^{91} +(-4.45092 + 8.05525i) q^{92} +3.00203 q^{93} +(1.61772 - 1.86695i) q^{94} +(-1.85802 + 1.19408i) q^{95} +(-1.11552 - 7.75859i) q^{96} +(-4.59160 - 10.0542i) q^{97} +(0.761496 - 5.29632i) q^{98} +(10.1085 - 2.96813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.186393	−	0.215109i	0.131800	−	0.152105i	−0.686013	−	0.727589i	$-0.740641\pi$
$2$	0.186393	−	0.215109i	0.131800	−	0.152105i	0.817813	+	0.575484i	$0.195186\pi$
$3$	−2.03964	+	1.31080i	−1.17759	+	0.756789i	−0.974941	−	0.222463i	$-0.928590\pi$
$3$	−2.03964	+	1.31080i	−1.17759	+	0.756789i	−0.202646	+	0.979252i	$0.564954\pi$
$4$	0.273100	+	1.89945i	0.136550	+	0.949727i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	−0.0982103	+	0.683068i	−0.0400942	+	0.278861i
$7$	−4.87354	+	1.43100i	−1.84202	+	0.540867i	−0.842024	+	0.539440i	$0.818636\pi$
$7$	−4.87354	+	1.43100i	−1.84202	+	0.540867i	−0.999999	+	0.00142704i	$0.999546\pi$
$8$	0.938384	+	0.603063i	0.331769	+	0.213215i
$9$	1.19570	−	2.61822i	0.398567	−	0.872739i
$10$	−0.273100	−	0.0801894i	−0.0863619	−	0.0253581i
$11$	2.39693	+	2.76621i	0.722702	+	0.834043i	0.991629	−	0.129118i	$-0.0412145\pi$
$11$	2.39693	+	2.76621i	0.722702	+	0.834043i	−0.268927	+	0.963161i	$0.586669\pi$
$12$	−3.04683	−	3.51622i	−0.879543	−	1.01505i
$13$	4.71898	+	1.38562i	1.30881	+	0.384301i	0.860442	−	0.509549i	$-0.170188\pi$
$13$	4.71898	+	1.38562i	1.30881	+	0.384301i	0.448367	+	0.893850i	$0.352006\pi$
$14$	−0.600571	+	1.31507i	−0.160509	+	0.351467i
$15$	2.03964	+	1.31080i	0.526633	+	0.338446i
$16$	−3.37787	+	0.991834i	−0.844469	+	0.247958i
$17$	0.237653	−	1.65292i	0.0576394	−	0.400891i	−0.940493	−	0.339812i	$-0.889637\pi$
$17$	0.237653	−	1.65292i	0.0576394	−	0.400891i	0.998133	−	0.0610794i	$-0.0194543\pi$
$18$	−0.340332	−	0.745222i	−0.0802169	−	0.175651i
$19$	−0.314321	−	2.18615i	−0.0721102	−	0.501537i	−0.993584	−	0.113097i	$-0.963923\pi$
$19$	−0.314321	−	2.18615i	−0.0721102	−	0.501537i	0.921474	−	0.388440i	$-0.126986\pi$
$20$	1.61435	−	1.03748i	0.360980	−	0.231988i
$21$	8.06451	−	9.30694i	1.75982	−	2.03094i
$22$	1.04181			0.222114
$23$	3.82485	+	2.89319i	0.797535	+	0.603272i
$23$	3.82485	+	2.89319i	0.797535	+	0.603272i
$24$	−2.70446			−0.552046
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	1.17764	−	0.756824i	0.230954	−	0.148425i
$27$	−0.0419833	−	0.292000i	−0.00807969	−	0.0561955i
$28$	−4.04908	−	8.86625i	−0.765204	−	1.67556i
$29$	−0.240417	+	1.67214i	−0.0446444	+	0.310509i	0.955248	+	0.295808i	$0.0955887\pi$
$29$	−0.240417	+	1.67214i	−0.0446444	+	0.310509i	−0.999892	+	0.0147010i	$0.995320\pi$
$30$	0.662138	−	0.194421i	0.120889	−	0.0354963i
$31$	−1.04163	−	0.669418i	−0.187083	−	0.120231i	0.443747	−	0.896152i	$-0.353649\pi$
$31$	−1.04163	−	0.669418i	−0.187083	−	0.120231i	−0.630830	+	0.775921i	$0.717285\pi$
$32$	−1.34302	+	2.94080i	−0.237414	+	0.519864i
$33$	−8.51482	−	2.50018i	−1.48224	−	0.435225i
$34$	−0.311260	−	0.359213i	−0.0533806	−	0.0616045i
$35$	3.32622	+	3.83867i	0.562234	+	0.648853i
$36$	5.29973	+	1.55614i	0.883288	+	0.259357i
$37$	−1.32998	+	2.91224i	−0.218647	+	0.478769i	−0.986891	−	0.161387i	$-0.948403\pi$
$37$	−1.32998	+	2.91224i	−0.218647	+	0.478769i	0.768245	+	0.640156i	$0.221130\pi$
$38$	−0.528847	−	0.339869i	−0.0857903	−	0.0551341i
$39$	−11.4413	+	3.35946i	−1.83207	+	0.537945i
$40$	0.158746	−	1.10411i	0.0251000	−	0.174574i
$41$	3.16340	+	6.92687i	0.494040	+	1.08180i	0.978361	+	0.206906i	$0.0663393\pi$
$41$	3.16340	+	6.92687i	0.494040	+	1.08180i	−0.484321	+	0.874890i	$0.660933\pi$
$42$	−0.498838	−	3.46949i	−0.0769724	−	0.535355i
$43$	−1.68924	+	1.08561i	−0.257607	+	0.165554i	−0.663070	−	0.748558i	$-0.730747\pi$
$43$	−1.68924	+	1.08561i	−0.257607	+	0.165554i	0.405463	+	0.914112i	$0.367110\pi$
$44$	−4.59968	+	5.30831i	−0.693428	+	0.800258i
$45$	−2.87833			−0.429075
$46$	1.33527	−	0.283488i	0.196875	−	0.0417980i
$47$	8.67911			1.26598			0.632989	−	0.774161i	$-0.281828\pi$
$47$	8.67911			1.26598			0.632989	+	0.774161i	$0.281828\pi$
$48$	5.58956	−	6.45069i	0.806783	−	0.931078i
$49$	15.8148	−	10.1636i	2.25926	−	1.45194i
$50$	0.0405070	+	0.281733i	0.00572856	+	0.0398430i
$51$	1.68191	+	3.68287i	0.235515	+	0.515705i
$52$	−1.34316	+	9.34189i	−0.186263	+	1.29549i
$53$	−5.20829	+	1.52929i	−0.715414	+	0.210065i	−0.619129	−	0.785289i	$-0.712514\pi$
$53$	−5.20829	+	1.52929i	−0.715414	+	0.210065i	−0.0962850	+	0.995354i	$0.530696\pi$
$54$	−0.0706372	−	0.0453958i	−0.00961251	−	0.00617758i
$55$	1.52051	−	3.32945i	0.205025	−	0.448943i
$56$	−5.43623	−	1.59622i	−0.726447	−	0.213304i
$57$	3.50670	+	4.04695i	0.464474	+	0.536032i
$58$	0.314880	+	0.363391i	0.0413458	+	0.0477155i
$59$	−1.56713	−	0.460150i	−0.204023	−	0.0599064i	0.178124	−	0.984008i	$-0.442997\pi$
$59$	−1.56713	−	0.460150i	−0.204023	−	0.0599064i	−0.382147	+	0.924102i	$0.624815\pi$
$60$	−1.93277	+	4.23218i	−0.249520	+	0.546372i
$61$	−6.36917	−	4.09322i	−0.815488	−	0.524083i	0.0651478	−	0.997876i	$-0.479248\pi$
$61$	−6.36917	−	4.09322i	−0.815488	−	0.524083i	−0.880636	+	0.473793i	$0.842884\pi$
$62$	−0.338151	+	0.0992900i	−0.0429452	+	0.0126098i
$63$	−2.08062	+	14.4710i	−0.262133	+	1.82318i
$64$	−2.54266	−	5.56764i	−0.317832	−	0.695955i
$65$	−0.699932	−	4.86814i	−0.0868159	−	0.603818i
$66$	−2.12491	+	1.36560i	−0.261558	+	0.168093i
$67$	0.0752564	−	0.0868505i	0.00919404	−	0.0106105i	−0.751134	−	0.660150i	$-0.770493\pi$
$67$	0.0752564	−	0.0868505i	0.00919404	−	0.0106105i	0.760328	+	0.649539i	$0.225038\pi$
$68$	3.20454			0.388608
$69$	−11.5937	−	0.887472i	−1.39572	−	0.106839i
$70$	1.44571			0.172796
$71$	−1.26600	+	1.46104i	−0.150246	+	0.173394i	−0.825884	−	0.563841i	$-0.809323\pi$
$71$	−1.26600	+	1.46104i	−0.150246	+	0.173394i	0.675637	+	0.737234i	$0.263869\pi$
$72$	2.70098	−	1.73581i	0.318313	−	0.204567i
$73$	1.48784	+	10.3482i	0.174139	+	1.21116i	0.870024	+	0.493009i	$0.164103\pi$
$73$	1.48784	+	10.3482i	0.174139	+	1.21116i	−0.695885	+	0.718153i	$0.744988\pi$
$74$	0.378550	+	0.828910i	0.0440056	+	0.0963588i
$75$	0.345046	−	2.39985i	0.0398425	−	0.277111i
$76$	4.06665	−	1.19408i	0.466477	−	0.136970i
$77$	−15.6400	−	10.0512i	−1.78234	−	1.14544i
$78$	−1.40992	+	3.08730i	−0.159642	+	0.349568i
$79$	−0.948139	−	0.278399i	−0.106674	−	0.0313223i	0.227960	−	0.973671i	$-0.426794\pi$
$79$	−0.948139	−	0.278399i	−0.106674	−	0.0313223i	−0.334634	+	0.942348i	$0.608613\pi$
$80$	2.30542	+	2.66060i	0.257754	+	0.297464i
$81$	6.12309	+	7.06642i	0.680343	+	0.785158i
$82$	2.07967	+	0.610645i	0.229661	+	0.0674344i
$83$	6.48492	−	14.2000i	0.711812	−	1.55865i	−0.113222	−	0.993570i	$-0.536117\pi$
$83$	6.48492	−	14.2000i	0.711812	−	1.55865i	0.825035	−	0.565082i	$-0.191155\pi$
$84$	19.8805	+	12.7764i	2.16914	+	1.39402i
$85$	−1.60227	+	0.470469i	−0.173791	+	0.0510295i
$86$	−0.0813383	+	0.565720i	−0.00877093	+	0.0610032i
$87$	−1.70147	−	3.72570i	−0.182417	−	0.399437i
$88$	0.581046	+	4.04127i	0.0619397	+	0.430800i
$89$	2.51564	−	1.61670i	0.266657	−	0.171370i	−0.400479	−	0.916306i	$-0.631156\pi$
$89$	2.51564	−	1.61670i	0.266657	−	0.171370i	0.667136	+	0.744936i	$0.267520\pi$
$90$	−0.536499	+	0.619153i	−0.0565520	+	0.0652645i
$91$	−24.9809			−2.61871
$92$	−4.45092	+	8.05525i	−0.464040	+	0.839818i
$93$	3.00203			0.311296
$94$	1.61772	−	1.86695i	0.166855	−	0.192561i
$95$	−1.85802	+	1.19408i	−0.190629	+	0.122510i
$96$	−1.11552	−	7.75859i	−0.113852	−	0.791858i
$97$	−4.59160	−	10.0542i	−0.466206	−	1.02085i	−0.986029	−	0.166575i	$-0.946729\pi$
$97$	−4.59160	−	10.0542i	−0.466206	−	1.02085i	0.519823	−	0.854274i	$-0.325998\pi$
$98$	0.761496	−	5.29632i	0.0769227	−	0.535009i
$99$	10.1085	−	2.96813i	1.01595	−	0.298309i
$100$	−1.61435	−	1.03748i	−0.161435	−	0.103748i
$101$	0.686642	−	1.50354i	0.0683234	−	0.149607i	−0.872389	−	0.488812i	$-0.837431\pi$
$101$	0.686642	−	1.50354i	0.0683234	−	0.149607i	0.940713	+	0.339204i	$0.110158\pi$
$102$	1.10571	+	0.324667i	0.109482	+	0.0321468i
$103$	1.76754	+	2.03985i	0.174160	+	0.200992i	0.836118	−	0.548549i	$-0.184820\pi$
$103$	1.76754	+	2.03985i	0.174160	+	0.200992i	−0.661958	+	0.749541i	$0.730274\pi$
$104$	3.59260	+	4.14608i	0.352283	+	0.406557i
$105$	−11.8160	−	3.46949i	−1.15312	−	0.338588i
$106$	−0.641824	+	1.40540i	−0.0623395	+	0.136504i
$107$	12.0243	+	7.72758i	1.16244	+	0.747053i	0.972077	−	0.234661i	$-0.0753980\pi$
$107$	12.0243	+	7.72758i	1.16244	+	0.747053i	0.190360	+	0.981714i	$0.439034\pi$
$108$	0.543175	−	0.159491i	0.0522671	−	0.0153470i
$109$	0.479482	−	3.33487i	0.0459260	−	0.319423i	−0.953888	−	0.300161i	$-0.902959\pi$
$109$	0.479482	−	3.33487i	0.0459260	−	0.319423i	0.999814	−	0.0192613i	$-0.00613143\pi$
$110$	−0.432782	−	0.947660i	−0.0412641	−	0.0903558i
$111$	−1.10468	−	7.68325i	−0.104852	−	0.729262i
$112$	15.0429	−	9.66747i	1.42142	−	0.913490i
$113$	11.4219	−	13.1816i	1.07449	−	1.24002i	0.105106	−	0.994461i	$-0.466482\pi$
$113$	11.4219	−	13.1816i	1.07449	−	1.24002i	0.969381	−	0.245563i	$-0.0789727\pi$
$114$	1.52416			0.142751
$115$	1.04284	−	4.68108i	0.0972454	−	0.436513i
$116$	−3.24181			−0.300995
$117$	9.27032	−	10.6985i	0.857042	−	0.989079i
$118$	−0.391083	+	0.251334i	−0.0360021	+	0.0231372i
$119$	1.20711	+	8.39563i	0.110656	+	0.769626i
$120$	1.12347	+	2.46006i	0.102559	+	0.224572i
$121$	−0.341154	+	2.37278i	−0.0310140	+	0.215707i
$122$	−2.06765	+	0.607118i	−0.187197	+	0.0549659i
$123$	−15.5319	−	9.98176i	−1.40047	−	0.900025i
$124$	0.987057	−	2.16135i	0.0886403	−	0.194095i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	2.72503	+	3.14485i	0.242765	+	0.280166i
$127$	0.728093	+	0.840265i	0.0646078	+	0.0745614i	0.787133	−	0.616783i	$-0.211564\pi$
$127$	0.728093	+	0.840265i	0.0646078	+	0.0745614i	−0.722526	+	0.691344i	$0.757019\pi$
$128$	−7.87557	−	2.31248i	−0.696109	−	0.204396i
$129$	2.02243	−	4.42851i	0.178065	−	0.389908i
$130$	−1.17764	−	0.756824i	−0.103286	−	0.0663779i
$131$	10.9641	−	3.21936i	0.957942	−	0.281277i	0.234852	−	0.972031i	$-0.424539\pi$
$131$	10.9641	−	3.21936i	0.957942	−	0.281277i	0.723090	+	0.690754i	$0.242721\pi$
$132$	2.42357	−	16.8563i	0.210945	−	1.46715i
$133$	4.66023	+	10.2045i	0.404093	+	0.884841i
$134$	−0.00465506	−	0.0323766i	−0.000402136	−	0.00279692i
$135$	−0.248172	+	0.159491i	−0.0213593	+	0.0137268i
$136$	1.21982	−	1.40775i	0.104599	−	0.120714i
$137$	15.4553			1.32044			0.660219	−	0.751073i	$-0.270463\pi$
$137$	15.4553			1.32044			0.660219	+	0.751073i	$0.270463\pi$
$138$	−2.35189	+	2.32849i	−0.200206	+	0.198214i
$139$	−15.1758			−1.28719			−0.643595	−	0.765366i	$-0.722558\pi$
$139$	−15.1758			−1.28719			−0.643595	+	0.765366i	$0.722558\pi$
$140$	−6.38297	+	7.36634i	−0.539460	+	0.622570i
$141$	−17.7023	+	11.3766i	−1.49080	+	0.958079i
$142$	0.0783095	+	0.544655i	0.00657159	+	0.0457064i
$143$	7.47816	+	16.3749i	0.625355	+	1.36934i
$144$	−1.44209	+	10.0299i	−0.120174	+	0.835829i
$145$	1.62091	−	0.475941i	0.134609	−	0.0395247i
$146$	2.50331	+	1.60878i	0.207175	+	0.133143i
$147$	−18.9342	+	41.4600i	−1.56166	+	3.41957i
$148$	−5.89488	−	1.73089i	−0.484556	−	0.142279i
$149$	2.14523	+	2.47572i	0.175744	+	0.202819i	0.836787	−	0.547529i	$-0.184431\pi$
$149$	2.14523	+	2.47572i	0.175744	+	0.202819i	−0.661043	+	0.750348i	$0.729886\pi$
$150$	−0.451914	−	0.521537i	−0.0368986	−	0.0425833i
$151$	17.7952	+	5.22516i	1.44816	+	0.425217i	0.908932	−	0.416945i	$-0.136899\pi$
$151$	17.7952	+	5.22516i	1.44816	+	0.425217i	0.539225	+	0.842162i	$0.318717\pi$
$152$	1.02343	−	2.24100i	0.0830113	−	0.181769i
$153$	−4.04353	−	2.59862i	−0.326900	−	0.210086i
$154$	−5.07728	+	1.49082i	−0.409139	+	0.120134i
$155$	−0.176213	+	1.22559i	−0.0141538	+	0.0984417i
$156$	−9.50576	−	20.8147i	−0.761070	−	1.66651i
$157$	1.97543	+	13.7394i	0.157657	+	1.09653i	0.902936	+	0.429774i	$0.141407\pi$
$157$	1.97543	+	13.7394i	0.157657	+	1.09653i	−0.745280	+	0.666752i	$0.767684\pi$
$158$	−0.236612	+	0.152061i	−0.0188239	+	0.0120974i
$159$	8.61845	−	9.94623i	0.683488	−	0.788787i
$160$	3.23295			0.255587
$161$	−22.7807	−	8.62672i	−1.79537	−	0.679881i
$162$	2.66135			0.209095
$163$	−0.208950	+	0.241141i	−0.0163662	+	0.0188876i	−0.763874	−	0.645366i	$-0.776705\pi$
$163$	−0.208950	+	0.241141i	−0.0163662	+	0.0188876i	0.747507	+	0.664253i	$0.231250\pi$
$164$	−12.2933	+	7.90046i	−0.959949	+	0.616922i
$165$	1.26294	+	8.78396i	0.0983200	+	0.683830i
$166$	−1.84580	−	4.04174i	−0.143262	−	0.313700i
$167$	0.762375	−	5.30243i	0.0589943	−	0.410315i	−0.938830	−	0.344382i	$-0.888089\pi$
$167$	0.762375	−	5.30243i	0.0589943	−	0.410315i	0.997824	−	0.0659329i	$-0.0210023\pi$
$168$	13.1803	−	3.87008i	1.01688	−	0.298583i
$169$	9.41250	+	6.04905i	0.724039	+	0.465311i
$170$	−0.197450	+	0.432354i	−0.0151437	+	0.0331601i
$171$	−6.09965	−	1.79102i	−0.466452	−	0.136963i
$172$	−2.52340	−	2.91215i	−0.192407	−	0.222050i
$173$	−5.24596	−	6.05416i	−0.398843	−	0.460289i	0.520433	−	0.853902i	$-0.325770\pi$
$173$	−5.24596	−	6.05416i	−0.398843	−	0.460289i	−0.919276	+	0.393613i	$0.871225\pi$
$174$	−1.11857	−	0.328443i	−0.0847989	−	0.0248992i
$175$	2.11001	−	4.62028i	0.159502	−	0.349260i
$176$	−10.8402	−	6.96654i	−0.817107	−	0.525123i
$177$	3.79954	−	1.11565i	0.285591	−	0.0838570i
$178$	0.121130	−	0.842478i	0.00907908	−	0.0631464i
$179$	−9.85285	−	21.5747i	−0.736437	−	1.61257i	−0.789328	−	0.613972i	$-0.789571\pi$
$179$	−9.85285	−	21.5747i	−0.736437	−	1.61257i	0.0528912	−	0.998600i	$-0.483156\pi$
$180$	−0.786071	−	5.46725i	−0.0585903	−	0.407504i
$181$	−20.9024	+	13.4331i	−1.55366	+	0.998478i	−0.569339	+	0.822103i	$0.692801\pi$
$181$	−20.9024	+	13.4331i	−1.55366	+	0.998478i	−0.984323	+	0.176376i	$0.943563\pi$
$182$	−4.65626	+	5.37361i	−0.345145	+	0.398319i
$183$	18.3562			1.35693
$184$	1.84440	+	5.02155i	0.135971	+	0.370193i
$185$	3.20156			0.235383
$186$	0.559557	−	0.645763i	0.0410287	−	0.0473496i
$187$	5.14195	−	3.30453i	0.376016	−	0.241651i
$188$	2.37027	+	16.4856i	0.172869	+	1.20233i
$189$	0.622459	+	1.36300i	0.0452773	+	0.0991434i
$190$	−0.0894651	+	0.622243i	−0.00649048	+	0.0451423i
$191$	−0.0202307	+	0.00594027i	−0.00146384	+	0.000429823i	−0.282464	−	0.959278i	$-0.591152\pi$
$191$	−0.0202307	+	0.00594027i	−0.00146384	+	0.000429823i	0.281001	+	0.959708i	$0.409334\pi$
$192$	12.4842	+	8.02308i	0.900967	+	0.579016i
$193$	−1.99651	+	4.37175i	−0.143712	+	0.314685i	−0.967777	−	0.251811i	$-0.918974\pi$
$193$	−1.99651	+	4.37175i	−0.143712	+	0.314685i	0.824065	+	0.566496i	$0.191701\pi$
$194$	−3.01859	−	0.886337i	−0.216722	−	0.0636353i
$195$	7.80875	+	9.01178i	0.559196	+	0.645347i
$196$	23.6242	+	27.2638i	1.68745	+	1.94742i
$197$	−3.60855	−	1.05957i	−0.257099	−	0.0754909i	0.150643	−	0.988588i	$-0.451865\pi$
$197$	−3.60855	−	1.05957i	−0.257099	−	0.0754909i	−0.407742	+	0.913097i	$0.633684\pi$
$198$	1.24569	−	2.72767i	0.0885271	−	0.193847i
$199$	−1.31836	−	0.847258i	−0.0934560	−	0.0600605i	0.493078	−	0.869985i	$-0.335872\pi$
$199$	−1.31836	−	0.847258i	−0.0934560	−	0.0600605i	−0.586534	+	0.809924i	$0.699508\pi$
$200$	−1.07028	+	0.314261i	−0.0756799	+	0.0222216i
$201$	−0.0396526	+	0.275790i	−0.00279688	+	0.0194527i
$202$	−0.195439	−	0.427951i	−0.0137510	−	0.0301105i
$203$	−1.22115	−	8.49327i	−0.0857078	−	0.596111i
$204$	−6.53611	+	4.20050i	−0.457619	+	0.294094i
$205$	4.98678	−	5.75505i	0.348292	−	0.401950i
$206$	0.768245			0.0535261
$207$	12.1484	−	6.55489i	0.844370	−	0.455596i
$208$	−17.3144			−1.20054
$209$	5.29394	−	6.10953i	0.366189	−	0.422605i
$210$	−2.94874	+	1.89504i	−0.203482	+	0.130770i
$211$	1.89440	+	13.1759i	0.130416	+	0.907063i	0.945012	+	0.327035i	$0.106049\pi$
$211$	1.89440	+	13.1759i	0.130416	+	0.907063i	−0.814596	+	0.580028i	$0.803041\pi$
$212$	−4.32721	−	9.47526i	−0.297194	−	0.650763i
$213$	0.667054	−	4.63947i	0.0457058	−	0.317891i
$214$	3.90352	−	1.14618i	0.266839	−	0.0783511i
$215$	1.68924	+	1.08561i	0.115205	+	0.0740379i
$216$	0.136698	−	0.299327i	0.00930113	−	0.0203666i
$217$	6.03438	+	1.77185i	0.409640	+	0.120281i
$218$	−0.627988	−	0.724736i	−0.0425327	−	0.0490853i
$219$	−16.5990	−	19.1563i	−1.12166	−	1.29446i
$220$	6.73939	+	1.97886i	0.454369	+	0.133415i
$221$	3.41179	−	7.47078i	0.229502	−	0.502539i
$222$	−1.85864	−	1.19448i	−0.124744	−	0.0801680i
$223$	−3.85293	+	1.13132i	−0.258011	+	0.0757589i	−0.408180	−	0.912901i	$-0.633836\pi$
$223$	−3.85293	+	1.13132i	−0.258011	+	0.0757589i	0.150169	+	0.988660i	$0.452018\pi$
$224$	2.33696	−	16.2539i	0.156145	−	1.08601i
$225$	1.19570	+	2.61822i	0.0797133	+	0.174548i
$226$	−0.706515	−	4.91392i	−0.0469967	−	0.326869i
$227$	−9.60256	+	6.17119i	−0.637344	+	0.409596i	−0.819022	−	0.573762i	$-0.805483\pi$
$227$	−9.60256	+	6.17119i	−0.637344	+	0.409596i	0.181678	+	0.983358i	$0.441847\pi$
$228$	−6.72931	+	7.76604i	−0.445660	+	0.514319i
$229$	9.08755			0.600522			0.300261	−	0.953857i	$-0.402926\pi$
$229$	9.08755			0.600522			0.300261	+	0.953857i	$0.402926\pi$
$230$	−0.812563	−	1.09684i	−0.0535788	−	0.0723237i
$231$	45.0750			2.96572
$232$	−1.23401	+	1.42412i	−0.0810167	+	0.0934983i
$233$	−3.86058	+	2.48105i	−0.252915	+	0.162539i	−0.660955	−	0.750425i	$-0.729849\pi$
$233$	−3.86058	+	2.48105i	−0.252915	+	0.162539i	0.408040	+	0.912964i	$0.366212\pi$
$234$	−0.573424	−	3.98825i	−0.0374859	−	0.260720i
$235$	−3.60543	−	7.89479i	−0.235192	−	0.515000i
$236$	0.446051	−	3.10235i	0.0290354	−	0.201946i
$237$	2.29879	−	0.674985i	0.149322	−	0.0438450i
$238$	2.03097	+	1.30522i	0.131648	+	0.0846052i
$239$	−9.42045	+	20.6279i	−0.609358	+	1.33431i	0.313654	+	0.949537i	$0.398447\pi$
$239$	−9.42045	+	20.6279i	−0.609358	+	1.33431i	−0.923012	+	0.384771i	$0.874281\pi$
$240$	−8.18974	−	2.40473i	−0.528646	−	0.155224i
$241$	−4.54725	−	5.24781i	−0.292914	−	0.338041i	0.590150	−	0.807294i	$-0.299069\pi$
$241$	−4.54725	−	5.24781i	−0.292914	−	0.338041i	−0.883064	+	0.469253i	$0.844523\pi$
$242$	0.446817	+	0.515655i	0.0287225	+	0.0331475i
$243$	−20.9024	−	6.13750i	−1.34089	−	0.393721i
$244$	6.03545	−	13.2158i	0.386380	−	0.846055i
$245$	−15.8148	−	10.1636i	−1.01037	−	0.649326i
$246$	−5.04220	+	1.48052i	−0.321479	+	0.0943948i
$247$	1.54589	−	10.7519i	0.0983628	−	0.684128i
$248$	−0.573752	−	1.25634i	−0.0364333	−	0.0797778i
$249$	5.38641	+	37.4633i	0.341350	+	2.37414i
$250$	0.239446	−	0.153882i	0.0151439	−	0.00973238i
$251$	13.6142	−	15.7117i	0.859324	−	0.991712i	−0.140675	−	0.990056i	$-0.544927\pi$
$251$	13.6142	−	15.7117i	0.859324	−	0.991712i	0.999999	−	0.00165649i	$-0.000527277\pi$
$252$	−28.0552			−1.76731
$253$	1.16473	+	17.5151i	0.0732260	+	1.10116i
$254$	0.316460			0.0198564
$255$	2.65137	−	3.05984i	0.166035	−	0.191615i
$256$	8.33284	−	5.35519i	0.520803	−	0.334700i
$257$	−1.12098	−	7.79657i	−0.0699246	−	0.486336i	−0.994450	−	0.105215i	$-0.966447\pi$
$257$	−1.12098	−	7.79657i	−0.0699246	−	0.486336i	0.924525	−	0.381122i	$-0.124462\pi$
$258$	−0.575644	−	1.26048i	−0.0358380	−	0.0784743i
$259$	2.31427	−	16.0961i	0.143802	−	1.00016i
$260$	9.05565	−	2.65898i	0.561607	−	0.164903i
$261$	4.09056	+	2.62884i	0.253199	+	0.162721i
$262$	1.35112	−	2.95855i	0.0834727	−	0.182780i
$263$	−20.3735	−	5.98221i	−1.25629	−	0.368879i	−0.415174	−	0.909742i	$-0.636279\pi$
$263$	−20.3735	−	5.98221i	−1.25629	−	0.368879i	−0.841111	+	0.540863i	$0.818098\pi$
$264$	−6.48241	−	7.48110i	−0.398965	−	0.460430i
$265$	3.55470	+	4.10234i	0.218363	+	0.252005i
$266$	3.06371	+	0.899586i	0.187848	+	0.0551571i
$267$	−3.01183	+	6.59499i	−0.184321	+	0.403607i
$268$	0.185521	+	0.119227i	0.0113325	+	0.00728296i
$269$	11.2591	−	3.30596i	0.686477	−	0.201568i	0.0801494	−	0.996783i	$-0.474460\pi$
$269$	11.2591	−	3.30596i	0.686477	−	0.201568i	0.606327	+	0.795215i	$0.292642\pi$
$270$	−0.0119497	+	0.0831120i	−0.000727235	+	0.00505803i
$271$	4.85466	+	10.6302i	0.294899	+	0.645740i	0.997853	−	0.0654962i	$-0.0208630\pi$
$271$	4.85466	+	10.6302i	0.294899	+	0.645740i	−0.702953	+	0.711236i	$0.748136\pi$
$272$	0.836654	+	5.81906i	0.0507296	+	0.352832i
$273$	50.9521	−	32.7449i	3.08376	−	1.98181i
$274$	2.88076	−	3.32458i	0.174033	−	0.200845i
$275$	−3.66022			−0.220719
$276$	−1.48053	−	22.2641i	−0.0891174	−	1.34014i
$277$	−17.7150			−1.06439			−0.532195	−	0.846622i	$-0.678633\pi$
$277$	−17.7150			−1.06439			−0.532195	+	0.846622i	$0.678633\pi$
$278$	−2.82865	+	3.26444i	−0.169651	+	0.195788i
$279$	−2.99816	+	1.92680i	−0.179495	+	0.115355i
$280$	0.806318	+	5.60807i	0.0481867	+	0.335146i
$281$	11.0858	+	24.2745i	0.661323	+	1.44810i	0.881284	+	0.472587i	$0.156680\pi$
$281$	11.0858	+	24.2745i	0.661323	+	1.44810i	−0.219961	+	0.975509i	$0.570593\pi$
$282$	−0.852378	+	5.92842i	−0.0507584	+	0.353032i
$283$	8.37302	−	2.45854i	0.497724	−	0.146145i	−0.0232291	−	0.999730i	$-0.507395\pi$
$283$	8.37302	−	2.45854i	0.497724	−	0.146145i	0.520953	+	0.853585i	$0.325577\pi$
$284$	−3.12092	−	2.00569i	−0.185193	−	0.119016i
$285$	2.22450	−	4.87097i	0.131768	−	0.288531i
$286$	4.91626	+	1.44354i	0.290704	+	0.0853585i
$287$	−25.3293	−	29.2315i	−1.49514	−	1.72548i
$288$	6.09380	+	7.03262i	0.359081	+	0.414401i
$289$	13.6357	+	4.00381i	0.802102	+	0.235518i
$290$	0.199746	−	0.437383i	0.0117295	−	0.0256840i
$291$	22.5442	+	14.4883i	1.32157	+	0.849319i
$292$	−19.2495	+	5.65217i	−1.12649	+	0.330769i
$293$	−0.727926	+	5.06284i	−0.0425259	+	0.295774i	0.957448	+	0.288604i	$0.0931913\pi$
$293$	−0.727926	+	5.06284i	−0.0425259	+	0.295774i	−0.999974	+	0.00716959i	$0.997718\pi$
$294$	5.38923	+	11.8008i	0.314306	+	0.688234i
$295$	0.232441	+	1.61666i	0.0135332	+	0.0941257i
$296$	−3.00429	+	1.93074i	−0.174621	+	0.112222i
$297$	0.707102	−	0.816039i	0.0410302	−	0.0473514i
$298$	0.932405			0.0540128
$299$	14.0405	+	18.9527i	0.811983	+	1.09606i
$300$	4.65263			0.268620
$301$	6.67907	−	7.70806i	0.384975	−	0.444285i
$302$	4.44088	−	2.85398i	0.255544	−	0.164228i
$303$	0.570329	+	3.96672i	0.0327645	+	0.227882i
$304$	3.23003	+	7.07279i	0.185255	+	0.405652i
$305$	−1.07747	+	7.49398i	−0.0616959	+	0.429104i
$306$	−1.31267	+	0.385435i	−0.0750404	+	0.0220339i
$307$	−14.6101	−	9.38936i	−0.833844	−	0.535879i	0.0526533	−	0.998613i	$-0.483232\pi$
$307$	−14.6101	−	9.38936i	−0.833844	−	0.535879i	−0.886497	+	0.462734i	$0.846869\pi$
$308$	14.8205	−	32.4524i	0.844477	−	1.84915i
$309$	−6.27896	−	1.84367i	−0.357198	−	0.104883i
$310$	0.230790	+	0.266346i	0.0131080	+	0.0151274i
$311$	−10.3234	−	11.9138i	−0.585385	−	0.675570i	0.383369	−	0.923595i	$-0.374764\pi$
$311$	−10.3234	−	11.9138i	−0.585385	−	0.675570i	−0.968754	+	0.248025i	$0.920218\pi$
$312$	−12.7623	−	3.74734i	−0.722522	−	0.212152i
$313$	−2.06177	+	4.51465i	−0.116538	+	0.255183i	−0.958908	−	0.283717i	$-0.908432\pi$
$313$	−2.06177	+	4.51465i	−0.116538	+	0.255183i	0.842370	+	0.538900i	$0.181160\pi$
$314$	3.32368	+	2.13600i	0.187566	+	0.120541i
$315$	14.0276	−	4.11888i	0.790367	−	0.232073i
$316$	0.269868	−	1.87698i	0.0151813	−	0.105588i
$317$	2.29177	+	5.01828i	0.128719	+	0.281854i	0.963008	−	0.269472i	$-0.0868492\pi$
$317$	2.29177	+	5.01828i	0.128719	+	0.281854i	−0.834290	+	0.551326i	$0.814122\pi$
$318$	−0.533103	−	3.70781i	−0.0298949	−	0.207924i
$319$	−5.20175	+	3.34296i	−0.291242	+	0.187170i
$320$	−4.00825	+	4.62576i	−0.224068	+	0.258588i
$321$	−34.6546			−1.93423
$322$	−6.10184	+	3.29236i	−0.340042	+	0.183476i
$323$	−3.68822			−0.205218
$324$	−11.7501	+	13.5604i	−0.652785	+	0.753354i
$325$	−4.13745	+	2.65898i	−0.229504	+	0.147494i
$326$	0.0129248	+	0.0898938i	0.000715837	+	0.00497876i
$327$	3.39337	+	7.43044i	0.187654	+	0.410904i
$328$	−1.20886	+	8.40780i	−0.0667481	+	0.464243i
$329$	−42.2979	+	12.4198i	−2.33196	+	0.684725i
$330$	2.12491	+	1.36560i	0.116972	+	0.0751736i
$331$	9.48439	−	20.7679i	0.521309	−	1.14151i	−0.447632	−	0.894218i	$-0.647733\pi$
$331$	9.48439	−	20.7679i	0.521309	−	1.14151i	0.968941	−	0.247290i	$-0.0795401\pi$
$332$	28.7433	+	8.43978i	1.57749	+	0.463193i
$333$	6.03463	+	6.96433i	0.330695	+	0.381643i
$334$	−0.998499	−	1.15233i	−0.0546354	−	0.0630526i
$335$	−0.110265	−	0.0323766i	−0.00602440	−	0.00176892i
$336$	−18.0100	+	39.4363i	−0.982525	+	2.15143i
$337$	−4.05113	−	2.60350i	−0.220679	−	0.141822i	0.425631	−	0.904897i	$-0.360052\pi$
$337$	−4.05113	−	2.60350i	−0.220679	−	0.141822i	−0.646310	+	0.763075i	$0.723689\pi$
$338$	3.05563	−	0.897213i	0.166204	−	0.0488019i
$339$	−6.01822	+	41.8577i	−0.326865	+	2.27340i
$340$	−1.33121	−	2.91495i	−0.0721952	−	0.158086i
$341$	−0.644978	−	4.48592i	−0.0349275	−	0.242926i
$342$	−1.52219	+	0.978255i	−0.0823108	+	0.0528980i
$343$	−39.2464	+	45.2928i	−2.11911	+	2.44558i
$344$	−2.23985			−0.120765
$345$	4.00892	+	10.9147i	0.215833	+	0.587626i
$346$	−2.28011			−0.122580
$347$	5.61462	−	6.47961i	0.301408	−	0.347844i	−0.584761	−	0.811206i	$-0.698812\pi$
$347$	5.61462	−	6.47961i	0.301408	−	0.347844i	0.886169	+	0.463362i	$0.153357\pi$
$348$	6.61213	−	4.24936i	0.354447	−	0.227789i
$349$	−3.94020	−	27.4047i	−0.210914	−	1.46694i	−0.770114	−	0.637906i	$-0.779801\pi$
$349$	−3.94020	−	27.4047i	−0.210914	−	1.46694i	0.559200	−	0.829033i	$-0.311108\pi$
$350$	−0.600571	−	1.31507i	−0.0321019	−	0.0702933i
$351$	0.206482	−	1.43612i	0.0110212	−	0.0766542i
$352$	−11.3540	+	3.33383i	−0.605169	+	0.177694i
$353$	10.0746	+	6.47457i	0.536218	+	0.344607i	0.780558	−	0.625083i	$-0.214935\pi$
$353$	10.0746	+	6.47457i	0.536218	+	0.344607i	−0.244340	+	0.969690i	$0.578571\pi$
$354$	0.468222	−	1.02526i	0.0248857	−	0.0544921i
$355$	1.85492	+	0.544655i	0.0984491	+	0.0289073i
$356$	3.75787	+	4.33682i	0.199167	+	0.229851i
$357$	−13.4670	−	15.5418i	−0.712751	−	0.822559i
$358$	−6.47742	−	1.90194i	−0.342342	−	0.100521i
$359$	−5.06012	+	11.0801i	−0.267063	+	0.584786i	−0.994889	−	0.100976i	$-0.967804\pi$
$359$	−5.06012	+	11.0801i	−0.267063	+	0.584786i	0.727826	+	0.685762i	$0.240531\pi$
$360$	−2.70098	−	1.73581i	−0.142354	−	0.0914853i
$361$	13.5499	−	3.97861i	0.713153	−	0.209401i
$362$	−1.00647	+	7.00013i	−0.0528987	+	0.367919i
$363$	−2.41440	−	5.28681i	−0.126723	−	0.277485i
$364$	−6.82229	−	47.4501i	−0.357585	−	2.48706i
$365$	8.79496	−	5.65217i	0.460349	−	0.295848i
$366$	3.42146	−	3.94858i	0.178843	−	0.206395i
$367$	13.9795			0.729724			0.364862	−	0.931062i	$-0.381116\pi$
$367$	13.9795			0.729724			0.364862	+	0.931062i	$0.381116\pi$
$368$	−15.7894	−	5.97923i	−0.823080	−	0.311689i
$369$	21.9185			1.14103
$370$	0.596747	−	0.688683i	0.0310234	−	0.0358029i
$371$	23.1944	−	14.9061i	1.20419	−	0.773887i
$372$	0.819855	+	5.70222i	0.0425075	+	0.295646i
$373$	−5.52878	−	12.1063i	−0.286269	−	0.626842i	0.710796	−	0.703398i	$-0.248335\pi$
$373$	−5.52878	−	12.1063i	−0.286269	−	0.626842i	−0.997065	+	0.0765558i	$0.975608\pi$
$374$	0.247589	−	1.72202i	0.0128025	−	0.0890434i
$375$	−2.32632	+	0.683068i	−0.120130	+	0.0352735i
$376$	8.14434	+	5.23405i	0.420012	+	0.269925i
$377$	−3.45147	+	7.55766i	−0.177760	+	0.389239i
$378$	0.409214	+	0.120156i	0.0210477	+	0.00618017i
$379$	−1.84680	−	2.13132i	−0.0948637	−	0.109479i	0.706333	−	0.707880i	$-0.250348\pi$
$379$	−1.84680	−	2.13132i	−0.0948637	−	0.109479i	−0.801196	+	0.598401i	$0.795803\pi$
$380$	−2.77552	−	3.20312i	−0.142381	−	0.164316i
$381$	−2.58647	−	0.759455i	−0.132509	−	0.0389081i
$382$	−0.00249305	+	0.00545902i	−0.000127556	+	0.000279308i
$383$	4.54318	+	2.91973i	0.232146	+	0.149191i	0.651543	−	0.758612i	$-0.274122\pi$
$383$	4.54318	+	2.91973i	0.232146	+	0.149191i	−0.419397	+	0.907803i	$0.637758\pi$
$384$	19.0945	−	5.60666i	0.974413	−	0.286114i
$385$	−2.64581	+	18.4020i	−0.134843	+	0.937855i
$386$	0.568266	+	1.24433i	0.0289240	+	0.0633347i
$387$	0.822536	+	5.72086i	0.0418118	+	0.290808i
$388$	17.8435	−	11.4673i	0.905867	−	0.582165i
$389$	8.80117	−	10.1571i	0.446237	−	0.514985i	−0.487413	−	0.873172i	$-0.662059\pi$
$389$	8.80117	−	10.1571i	0.446237	−	0.514985i	0.933650	+	0.358187i	$0.116605\pi$
$390$	3.39401			0.171862
$391$	5.69119	−	5.63457i	0.287816	−	0.284953i
$392$	20.9696			1.05913
$393$	−18.1430	+	20.9381i	−0.915192	+	1.05619i
$394$	−0.900530	+	0.578735i	−0.0453680	+	0.0291563i
$395$	0.140631	+	0.978108i	0.00707590	+	0.0492140i
$396$	8.39848	+	18.3901i	0.422039	+	0.924137i
$397$	−3.88391	+	27.0132i	−0.194928	+	1.35575i	0.623806	+	0.781580i	$0.285586\pi$
$397$	−3.88391	+	27.0132i	−0.194928	+	1.35575i	−0.818733	+	0.574174i	$0.805323\pi$
$398$	−0.427985	+	0.125668i	−0.0214530	+	0.00629916i
$399$	−22.8812	−	14.7049i	−1.14549	−	0.736164i
$400$	1.46246	−	3.20234i	0.0731230	−	0.160117i
$401$	32.1671	+	9.44510i	1.60635	+	0.471666i	0.957303	−	0.289086i	$-0.0933512\pi$
$401$	32.1671	+	9.44510i	1.60635	+	0.471666i	0.649043	+	0.760751i	$0.275169\pi$
$402$	0.0519339	+	0.0599349i	0.00259023	+	0.00298928i
$403$	−3.98789	−	4.60227i	−0.198651	−	0.229255i
$404$	3.04342	+	0.893629i	0.151416	+	0.0444597i
$405$	3.88422	−	8.50526i	0.193009	−	0.422630i
$406$	−2.05459	−	1.32040i	−0.101968	−	0.0655306i
$407$	−11.2437	+	3.30145i	−0.557330	+	0.163647i
$408$	−0.642725	+	4.47025i	−0.0318196	+	0.221310i
$409$	5.39614	+	11.8159i	0.266822	+	0.584258i	0.994858	−	0.101280i	$-0.0322939\pi$
$409$	5.39614	+	11.8159i	0.266822	+	0.584258i	−0.728036	+	0.685539i	$0.759567\pi$
$410$	−0.308462	−	2.14540i	−0.0152339	−	0.105954i
$411$	−31.5233	+	20.2588i	−1.55493	+	0.999294i
$412$	−3.39188	+	3.91443i	−0.167106	+	0.192850i
$413$	8.29592			0.408216
$414$	0.854354	−	3.83500i	0.0419892	−	0.188480i
$415$	−15.6107			−0.766299
$416$	−10.4125	+	12.0166i	−0.510514	+	0.589164i
$417$	30.9531	−	19.8923i	1.51578	−	0.974132i
$418$	−0.327461	−	2.27754i	−0.0160167	−	0.111398i
$419$	−6.65752	−	14.5779i	−0.325241	−	0.712178i	0.674417	−	0.738351i	$-0.264395\pi$
$419$	−6.65752	−	14.5779i	−0.325241	−	0.712178i	−0.999657	+	0.0261729i	$0.991668\pi$
$420$	3.36319	−	23.3915i	0.164107	−	1.14139i
$421$	−5.00024	+	1.46820i	−0.243697	+	0.0715559i	−0.401300	−	0.915947i	$-0.631442\pi$
$421$	−5.00024	+	1.46820i	−0.243697	+	0.0715559i	0.157603	+	0.987503i	$0.449623\pi$
$422$	3.18734	+	2.04838i	0.155158	+	0.0997137i
$423$	10.3776	−	22.7238i	0.504576	−	1.10487i
$424$	−5.80964	−	1.70586i	−0.282141	−	0.0828441i
$425$	1.09356	+	1.26204i	0.0530455	+	0.0612178i
$426$	−0.873655	−	1.00825i	−0.0423287	−	0.0488500i
$427$	36.8978	+	10.8342i	1.78561	+	0.524302i
$428$	−11.3943	+	24.9501i	−0.550765	+	1.20601i
$429$	−36.7169	−	23.5965i	−1.77271	−	1.13925i
$430$	0.548386	−	0.161021i	0.0264455	−	0.00776511i
$431$	4.64931	−	32.3367i	0.223949	−	1.55760i	−0.498939	−	0.866637i	$-0.666277\pi$
$431$	4.64931	−	32.3367i	0.223949	−	1.55760i	0.722888	−	0.690965i	$-0.242814\pi$
$432$	0.431430	+	0.944700i	0.0207572	+	0.0454519i
$433$	−4.38440	−	30.4942i	−0.210701	−	1.46546i	−0.770824	−	0.637048i	$-0.780155\pi$
$433$	−4.38440	−	30.4942i	−0.210701	−	1.46546i	0.560123	−	0.828410i	$-0.310754\pi$
$434$	1.50591	−	0.967787i	0.0722858	−	0.0464552i
$435$	−2.68220	+	3.09543i	−0.128602	+	0.148414i
$436$	6.46538			0.309635
$437$	5.12272	−	9.27108i	0.245053	−	0.443496i
$438$	−7.21462			−0.344728
$439$	16.4208	−	18.9506i	0.783723	−	0.904465i	−0.213649	−	0.976910i	$-0.568535\pi$
$439$	16.4208	−	18.9506i	0.783723	−	0.904465i	0.997372	+	0.0724458i	$0.0230804\pi$
$440$	3.43469	−	2.20734i	0.163742	−	0.105231i
$441$	−7.70065	−	53.5592i	−0.366697	−	2.55044i
$442$	−0.971096	−	2.12640i	−0.0461903	−	0.101143i
$443$	5.11034	−	35.5432i	0.242799	−	1.68871i	−0.395140	−	0.918621i	$-0.629304\pi$
$443$	5.11034	−	35.5432i	0.242799	−	1.68871i	0.637940	−	0.770086i	$-0.279787\pi$
$444$	14.2923	−	4.19660i	0.678282	−	0.199162i
$445$	−2.51564	−	1.61670i	−0.119253	−	0.0766391i
$446$	−0.474801	+	1.03967i	−0.0224825	+	0.0492298i
$447$	−7.62067	−	2.23763i	−0.360445	−	0.105836i
$448$	20.3590	+	23.4956i	0.961873	+	1.11006i
$449$	11.0868	+	12.7949i	0.523219	+	0.603826i	0.954434	−	0.298423i	$-0.0964605\pi$
$449$	11.0868	+	12.7949i	0.523219	+	0.603826i	−0.431215	+	0.902249i	$0.641915\pi$
$450$	0.786071	+	0.230811i	0.0370558	+	0.0108806i
$451$	−11.5787	+	25.3538i	−0.545220	+	1.19387i
$452$	28.1572	+	18.0956i	1.32440	+	0.851143i
$453$	−43.1450	+	12.6685i	−2.02713	+	0.595219i
$454$	−0.462371	+	3.21586i	−0.0217001	+	0.150928i
$455$	10.3774	+	22.7234i	0.486502	+	1.06529i
$456$	0.850069	+	5.91236i	0.0398081	+	0.276871i
$457$	0.601197	−	0.386366i	0.0281228	−	0.0180734i	−0.526504	−	0.850173i	$-0.676497\pi$
$457$	0.601197	−	0.386366i	0.0281228	−	0.0180734i	0.554627	+	0.832099i	$0.312861\pi$
$458$	1.69385	−	1.95481i	0.0791486	−	0.0913423i
$459$	−0.492630			−0.0229940
$460$	9.17629	+	0.702424i	0.427847	+	0.0327507i
$461$	−42.3458			−1.97224			−0.986121	−	0.166030i	$-0.946905\pi$
$461$	−42.3458			−1.97224			−0.986121	+	0.166030i	$0.946905\pi$
$462$	8.40166	−	9.69603i	0.390880	−	0.451100i
$463$	−15.1562	+	9.74027i	−0.704366	+	0.452669i	−0.843167	−	0.537652i	$-0.819312\pi$
$463$	−15.1562	+	9.74027i	−0.704366	+	0.452669i	0.138801	+	0.990320i	$0.455675\pi$
$464$	−0.846385	−	5.88673i	−0.0392924	−	0.273285i
$465$	−1.24709	−	2.73074i	−0.0578323	−	0.126635i
$466$	−0.185890	+	1.29289i	−0.00861120	+	0.0598922i
$467$	−14.7356	+	4.32677i	−0.681883	+	0.200219i	−0.604288	−	0.796766i	$-0.706542\pi$
$467$	−14.7356	+	4.32677i	−0.681883	+	0.200219i	−0.0775949	+	0.996985i	$0.524724\pi$
$468$	22.8531	+	14.6868i	1.05638	+	0.678896i
$469$	−0.242482	+	0.530961i	−0.0111968	+	0.0245175i
$470$	−2.37027	−	0.695973i	−0.109332	−	0.0321028i
$471$	−22.0388	−	25.4341i	−1.01549	−	1.17194i
$472$	−1.19307	−	1.37687i	−0.0549154	−	0.0633758i
$473$	−7.05202	−	2.07066i	−0.324252	−	0.0952090i
$474$	0.283282	−	0.620302i	0.0130116	−	0.0284914i
$475$	1.85802	+	1.19408i	0.0852517	+	0.0547880i
$476$	−15.6174	+	4.58569i	−0.715824	+	0.210185i
$477$	−2.22353	+	15.4650i	−0.101809	+	0.708094i
$478$	2.68134	+	5.87131i	0.122642	+	0.268548i
$479$	2.23149	+	15.5203i	0.101959	+	0.709142i	0.975115	+	0.221700i	$0.0711607\pi$
$479$	2.23149	+	15.5203i	0.101959	+	0.709142i	−0.873156	+	0.487442i	$0.837930\pi$
$480$	−6.59406	+	4.23775i	−0.300976	+	0.193426i
$481$	−10.3114	+	11.9000i	−0.470158	+	0.542591i
$482$	−1.97642			−0.0900237
$483$	57.7723	−	12.2654i	2.62873	−	0.558097i
$484$	−4.60016			−0.209098
$485$	−7.23820	+	8.35333i	−0.328670	+	0.379305i
$486$	−5.21629	+	3.35230i	−0.236616	+	0.152064i
$487$	−2.90971	−	20.2375i	−0.131851	−	0.917047i	−0.943139	−	0.332399i	$-0.892142\pi$
$487$	−2.90971	−	20.2375i	−0.131851	−	0.917047i	0.811287	−	0.584648i	$-0.198767\pi$
$488$	−3.50826	−	7.68202i	−0.158812	−	0.347749i
$489$	0.110096	−	0.765731i	0.00497869	−	0.0346276i
$490$	−5.13404	+	1.50749i	−0.231932	+	0.0681014i
$491$	15.7909	+	10.1482i	0.712634	+	0.457982i	0.846068	−	0.533076i	$-0.178964\pi$
$491$	15.7909	+	10.1482i	0.712634	+	0.457982i	−0.133433	+	0.991058i	$0.542600\pi$
$492$	14.7181	−	32.2282i	0.663544	−	1.45296i
$493$	2.70677	+	0.794780i	0.121907	+	0.0357951i
$494$	−2.02469	−	2.33661i	−0.0910950	−	0.105129i
$495$	−6.89915	−	7.96204i	−0.310094	−	0.357867i
$496$	4.18246	+	1.22808i	0.187798	+	0.0551425i
$497$	4.07914	−	8.93207i	0.182974	−	0.400658i
$498$	9.06267	+	5.82423i	0.406108	+	0.260990i
$499$	23.8179	−	6.99356i	1.06623	−	0.313075i	0.298875	−	0.954292i	$-0.403389\pi$
$499$	23.8179	−	6.99356i	1.06623	−	0.313075i	0.767359	+	0.641218i	$0.221570\pi$
$500$	−0.273100	+	1.89945i	−0.0122134	+	0.0849461i
$501$	5.39545	+	11.8144i	0.241051	+	0.527828i
$502$	−0.842122	−	5.85709i	−0.0375857	−	0.261415i
$503$	−27.5914	+	17.7319i	−1.23024	+	0.790627i	−0.983928	−	0.178564i	$-0.942855\pi$
$503$	−27.5914	+	17.7319i	−1.23024	+	0.790627i	−0.246311	+	0.969191i	$0.579218\pi$
$504$	−10.6794	+	12.3246i	−0.475696	+	0.548983i
$505$	−1.65291			−0.0735534
$506$	3.98475	+	3.01414i	0.177144	+	0.133995i
$507$	−27.1272			−1.20476
$508$	−1.39720	+	1.61246i	−0.0619908	+	0.0715412i
$509$	−3.21393	+	2.06547i	−0.142455	+	0.0915503i	−0.609927	−	0.792458i	$-0.708801\pi$
$509$	−3.21393	+	2.06547i	−0.142455	+	0.0915503i	0.467472	+	0.884008i	$0.345165\pi$
$510$	−0.164003	−	1.14066i	−0.00726216	−	0.0505095i
$511$	−22.0593	−	48.3031i	−0.975845	−	2.13680i
$512$	2.73749	−	19.0397i	0.120981	−	0.841442i
$513$	−0.625160	+	0.183564i	−0.0276015	+	0.00810453i
$514$	−1.88605	−	1.21209i	−0.0831902	−	0.0534631i
$515$	1.12125	−	2.45519i	0.0494081	−	0.108189i
$516$	8.96407	+	2.63209i	0.394621	+	0.115871i
$517$	20.8032	+	24.0082i	0.914925	+	1.05588i
$518$	−3.03105	−	3.49802i	−0.133177	−	0.153694i
$519$	18.6357	+	5.47192i	0.818015	+	0.240191i
$520$	2.27899	−	4.99029i	0.0999402	−	0.218839i
$521$	−16.0733	−	10.3297i	−0.704182	−	0.452551i	0.138920	−	0.990304i	$-0.455637\pi$
$521$	−16.0733	−	10.3297i	−0.704182	−	0.452551i	−0.843102	+	0.537753i	$0.819273\pi$
$522$	1.32794	−	0.389918i	0.0581223	−	0.0170662i
$523$	2.63265	−	18.3105i	0.115118	−	0.800662i	−0.847693	−	0.530486i	$-0.822009\pi$
$523$	2.63265	−	18.3105i	0.115118	−	0.800662i	0.962811	−	0.270175i	$-0.0870816\pi$
$524$	9.10934	+	19.9467i	0.397943	+	0.871374i
$525$	1.75259	+	12.1895i	0.0764891	+	0.531994i
$526$	−5.08430	+	3.26748i	−0.221686	+	0.142469i
$527$	−1.35404	+	1.56264i	−0.0589829	+	0.0680699i
$528$	31.2417			1.35962
$529$	6.25889	+	22.1320i	0.272126	+	0.962262i
$530$	1.54502			0.0671113
$531$	−3.07859	+	3.55288i	−0.133599	+	0.154182i
$532$	−18.1102	+	11.6387i	−0.785178	+	0.504603i
$533$	5.33000	+	37.0710i	0.230868	+	1.60572i
$534$	0.857256	+	1.87713i	0.0370971	+	0.0812313i
$535$	2.03416	−	14.1479i	0.0879443	−	0.611666i
$536$	0.122996	−	0.0361148i	0.00531261	−	0.00155992i
$537$	48.3764	+	31.0896i	2.08760	+	1.34162i
$538$	1.38747	−	3.03813i	0.0598179	−	0.130983i
$539$	66.0215	+	19.3857i	2.84375	+	0.835000i
$540$	−0.370721	−	0.427835i	−0.0159533	−	0.0184111i
$541$	−4.26027	−	4.91661i	−0.183163	−	0.211382i	0.656741	−	0.754116i	$-0.271934\pi$
$541$	−4.26027	−	4.91661i	−0.183163	−	0.211382i	−0.839904	+	0.542734i	$0.817389\pi$
$542$	3.19153	+	0.937117i	0.137088	+	0.0402526i
$543$	25.0252	−	54.7976i	1.07394	−	2.35159i
$544$	4.54172	+	2.91879i	0.194725	+	0.125142i
$545$	−3.23269	+	0.949203i	−0.138473	+	0.0406594i
$546$	2.45338	−	17.0637i	0.104995	−	0.730257i
$547$	−12.7220	−	27.8573i	−0.543954	−	1.19109i	−0.959549	−	0.281543i	$-0.909154\pi$
$547$	−12.7220	−	27.8573i	−0.543954	−	1.19109i	0.415595	−	0.909550i	$-0.363573\pi$
$548$	4.22085	+	29.3567i	0.180306	+	1.25406i
$549$	−18.3325	+	11.7816i	−0.782414	+	0.502827i
$550$	−0.682238	+	0.787344i	−0.0290907	+	0.0335725i
$551$	3.73112			0.158951
$552$	−10.3441	−	7.82452i	−0.440276	−	0.333034i
$553$	5.01918			0.213437
$554$	−3.30194	+	3.81065i	−0.140286	+	0.161899i
$555$	−6.53003	+	4.19660i	−0.277184	+	0.178136i
$556$	−4.14450	−	28.8256i	−0.175766	−	1.22248i
$557$	7.20819	+	15.7837i	0.305421	+	0.668778i	0.998650	−	0.0519386i	$-0.0165400\pi$
$557$	7.20819	+	15.7837i	0.305421	+	0.668778i	−0.693229	+	0.720717i	$0.743813\pi$
$558$	−0.144364	+	1.00407i	−0.00611141	+	0.0425058i
$559$	−9.47573	+	2.78232i	−0.400780	+	0.117680i
$560$	−15.0429	−	9.66747i	−0.635678	−	0.408525i
$561$	−6.15616	+	13.4801i	−0.259913	+	0.569130i
$562$	7.28797	+	2.13994i	0.307424	+	0.0902679i
$563$	12.3632	+	14.2679i	0.521046	+	0.601319i	0.953892	−	0.300149i	$-0.0970363\pi$
$563$	12.3632	+	14.2679i	0.521046	+	0.601319i	−0.432847	+	0.901468i	$0.642491\pi$
$564$	−26.4437	−	30.5177i	−1.11348	−	1.28503i
$565$	−16.7353	−	4.91392i	−0.704059	−	0.206730i
$566$	1.03182	−	2.25936i	0.0433705	−	0.0949681i
$567$	−39.9531	−	25.6763i	−1.67787	−	1.07830i
$568$	−2.06909	+	0.607540i	−0.0868172	+	0.0254918i
$569$	−0.747143	+	5.19649i	−0.0313218	+	0.217848i	−0.999471	−	0.0325264i	$-0.989645\pi$
$569$	−0.747143	+	5.19649i	−0.0313218	+	0.217848i	0.968149	+	0.250375i	$0.0805538\pi$
$570$	−0.633158	−	1.38642i	−0.0265201	−	0.0580709i
$571$	3.96094	+	27.5489i	0.165760	+	1.15289i	0.887529	+	0.460752i	$0.152420\pi$
$571$	3.96094	+	27.5489i	0.165760	+	1.15289i	−0.721769	+	0.692134i	$0.756671\pi$
$572$	−29.0611	+	18.6764i	−1.21510	+	0.780900i
$573$	0.0334769	−	0.0386344i	0.00139852	−	0.00161397i
$574$	−11.0092			−0.459513
$575$	−4.69127	+	0.995988i	−0.195639	+	0.0415356i
$576$	−17.6176			−0.734065
$577$	−24.0230	+	27.7240i	−1.00009	+	1.15416i	−0.0120547	+	0.999927i	$0.503837\pi$
$577$	−24.0230	+	27.7240i	−1.00009	+	1.15416i	−0.988034	+	0.154236i	$0.950708\pi$
$578$	3.40286	−	2.18688i	0.141540	−	0.0909623i
$579$	−1.65831	−	11.5338i	−0.0689171	−	0.479329i
$580$	1.34670	+	2.94885i	0.0559185	+	0.122445i
$581$	−11.2843	+	78.4841i	−0.468152	+	3.25607i
$582$	7.31864	−	2.14895i	0.303367	−	0.0890767i
$583$	−16.7143	−	10.7416i	−0.692234	−	0.444872i
$584$	−4.84443	+	10.6078i	−0.200464	+	0.438955i
$585$	−13.5827	−	3.98825i	−0.561578	−	0.164894i
$586$	0.953380	+	1.10026i	0.0393838	+	0.0454513i
$587$	12.8194	+	14.7944i	0.529114	+	0.610630i	0.955889	−	0.293728i	$-0.0948958\pi$
$587$	12.8194	+	14.7944i	0.529114	+	0.610630i	−0.426775	+	0.904358i	$0.640350\pi$
$588$	−83.9223	−	24.6418i	−3.46090	−	1.01621i
$589$	−1.13604	+	2.48758i	−0.0468097	+	0.102499i
$590$	0.391083	+	0.251334i	0.0161006	+	0.0103473i
$591$	8.74902	−	2.56894i	0.359887	−	0.105672i
$592$	1.60403	−	11.1563i	0.0659254	−	0.458521i
$593$	8.78116	+	19.2281i	0.360599	+	0.789602i	0.999789	+	0.0205529i	$0.00654265\pi$
$593$	8.78116	+	19.2281i	0.360599	+	0.789602i	−0.639190	+	0.769049i	$0.720730\pi$
$594$	−0.0437385	−	0.304208i	−0.00179461	−	0.0124818i
$595$	7.13548	−	4.58569i	0.292526	−	0.187995i
$596$	−4.11666	+	4.75088i	−0.168625	+	0.194604i
$597$	3.79956			0.155506
$598$	6.69393	+	0.512406i	0.273735	+	0.0209538i
$599$	18.6754			0.763055			0.381527	−	0.924358i	$-0.375398\pi$
$599$	18.6754			0.763055			0.381527	+	0.924358i	$0.375398\pi$
$600$	1.77105	−	2.04390i	0.0723026	−	0.0834417i
$601$	−32.4316	+	20.8425i	−1.32291	+	0.850185i	−0.995506	−	0.0946982i	$-0.969811\pi$
$601$	−32.4316	+	20.8425i	−1.32291	+	0.850185i	−0.327408	+	0.944883i	$0.606175\pi$
$602$	−0.413140	−	2.87345i	−0.0168383	−	0.117113i
$603$	−0.137409	−	0.300885i	−0.00559575	−	0.0122530i
$604$	−5.06506	+	35.2282i	−0.206094	+	1.43342i
$605$	2.30008	−	0.675364i	0.0935115	−	0.0274574i
$606$	0.959582	+	0.616686i	0.0389804	+	0.0250512i
$607$	18.0545	−	39.5337i	0.732808	−	1.60462i	−0.0622281	−	0.998062i	$-0.519821\pi$
$607$	18.0545	−	39.5337i	0.732808	−	1.60462i	0.795036	−	0.606563i	$-0.207452\pi$
$608$	6.85116	+	2.01168i	0.277851	+	0.0815845i
$609$	13.6237	+	15.7225i	0.552059	+	0.637110i
$610$	1.41119	+	1.62860i	0.0571373	+	0.0659400i
$611$	40.9565	+	12.0259i	1.65692	+	0.486516i
$612$	3.83167	−	8.39018i	0.154886	−	0.339153i
$613$	−8.22509	−	5.28594i	−0.332208	−	0.213497i	0.363893	−	0.931441i	$-0.381447\pi$
$613$	−8.22509	−	5.28594i	−0.332208	−	0.213497i	−0.696101	+	0.717943i	$0.745084\pi$
$614$	−4.74296	+	1.39266i	−0.191410	+	0.0562031i
$615$	−2.62753	+	18.2749i	−0.105952	+	0.736915i
$616$	−8.61480	−	18.8638i	−0.347100	−	0.760043i
$617$	−3.32889	−	23.1530i	−0.134016	−	0.932103i	−0.940245	−	0.340499i	$-0.889404\pi$
$617$	−3.32889	−	23.1530i	−0.134016	−	0.932103i	0.806229	−	0.591604i	$-0.201505\pi$
$618$	−1.56694	+	1.00701i	−0.0630317	+	0.0405080i
$619$	−22.5692	+	26.0462i	−0.907131	+	1.04688i	0.0915634	+	0.995799i	$0.470814\pi$
$619$	−22.5692	+	26.0462i	−0.907131	+	1.04688i	−0.998694	+	0.0510856i	$0.983732\pi$
$620$	−2.37607			−0.0954255
$621$	0.684233	−	1.23832i	0.0274573	−	0.0496921i
$622$	−4.48697			−0.179911
$623$	−9.94656	+	11.4789i	−0.398500	+	0.459894i
$624$	35.3152	−	22.6957i	1.41374	−	0.908555i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	0.586841	+	1.28500i	0.0234549	+	0.0513590i
$627$	−2.78937	+	19.4005i	−0.111397	+	0.774782i
$628$	−25.5579	+	7.50448i	−1.01987	+	0.299461i
$629$	4.49762	+	2.89044i	0.179332	+	0.115249i
$630$	1.72864	−	3.78519i	0.0688707	−	0.150806i
$631$	−11.8886	−	3.49081i	−0.473279	−	0.138967i	0.0363905	−	0.999338i	$-0.488414\pi$
$631$	−11.8886	−	3.49081i	−0.473279	−	0.138967i	−0.509669	+	0.860370i	$0.670232\pi$
$632$	−0.721827	−	0.833032i	−0.0287127	−	0.0331363i
$633$	−21.1348	−	24.3908i	−0.840032	−	0.969449i
$634$	1.50664	+	0.442391i	0.0598365	+	0.0175696i
$635$	0.461871	−	1.01136i	0.0183288	−	0.0401344i
$636$	21.2461	+	13.6540i	0.842462	+	0.541418i
$637$	88.7125	−	26.0483i	3.51492	−	1.03207i
$638$	−0.250468	+	1.74205i	−0.00991614	+	0.0689683i
$639$	2.31157	+	5.06162i	0.0914441	+	0.200235i
$640$	1.16813	+	8.12451i	0.0461743	+	0.321149i
$641$	27.2653	−	17.5223i	1.07691	−	0.692091i	0.123072	−	0.992398i	$-0.460725\pi$
$641$	27.2653	−	17.5223i	1.07691	−	0.692091i	0.953843	+	0.300307i	$0.0970890\pi$
$642$	−6.45938	+	7.45452i	−0.254931	+	0.294206i
$643$	30.7602			1.21306			0.606532	−	0.795059i	$-0.292560\pi$
$643$	30.7602			1.21306			0.606532	+	0.795059i	$0.292560\pi$
$644$	10.1646	−	45.6268i	0.400543	−	1.79795i
$645$	−4.86846			−0.191695
$646$	−0.687458	+	0.793369i	−0.0270477	+	0.0312147i
$647$	−29.6696	+	19.0675i	−1.16643	+	0.749622i	−0.972844	−	0.231461i	$-0.925650\pi$
$647$	−29.6696	+	19.0675i	−1.16643	+	0.749622i	−0.193590	+	0.981083i	$0.562013\pi$
$648$	1.48431	+	10.3236i	0.0583094	+	0.405551i
$649$	−2.48343	−	5.43794i	−0.0974830	−	0.213458i
$650$	−0.199222	+	1.38562i	−0.00781411	+	0.0543483i
$651$	−14.6305	+	4.29590i	−0.573415	+	0.168370i
$652$	−0.515100	−	0.331035i	−0.0201729	−	0.0129643i
$653$	14.7214	−	32.2355i	0.576094	−	1.26147i	−0.367394	−	0.930065i	$-0.619750\pi$
$653$	14.7214	−	32.2355i	0.576094	−	1.26147i	0.943488	−	0.331405i	$-0.107523\pi$
$654$	2.23085	+	0.655037i	0.0872332	+	0.0256140i
$655$	−7.48311	−	8.63596i	−0.292389	−	0.337435i
$656$	−17.5559	−	20.2605i	−0.685441	−	0.791041i
$657$	28.8728	+	8.47781i	1.12643	+	0.330751i
$658$	−5.21242	+	11.4136i	−0.203201	+	0.444949i
$659$	−21.6958	−	13.9431i	−0.845149	−	0.543144i	0.0449092	−	0.998991i	$-0.485700\pi$
$659$	−21.6958	−	13.9431i	−0.845149	−	0.543144i	−0.890058	+	0.455847i	$0.849337\pi$
$660$	−16.3398	+	4.79780i	−0.636026	+	0.186754i
$661$	2.88193	−	20.0443i	0.112094	−	0.779633i	−0.853782	−	0.520630i	$-0.825697\pi$
$661$	2.88193	−	20.0443i	0.112094	−	0.779633i	0.965877	−	0.259003i	$-0.0833938\pi$
$662$	−2.69954	−	5.91117i	−0.104921	−	0.229744i
$663$	2.83385	+	19.7099i	0.110058	+	0.765468i
$664$	14.6488	−	9.41424i	0.568485	−	0.365343i
$665$	7.34640	−	8.47819i	0.284881	−	0.328770i
$666$	2.62290			0.101635
$667$	−5.75738	+	5.70010i	−0.222927	+	0.220709i
$668$	10.2799			0.397742
$669$	6.37566	−	7.35790i	0.246497	−	0.284473i
$670$	−0.0275170	+	0.0176841i	−0.00106308	+	0.000683197i
$671$	−3.94378	−	27.4296i	−0.152248	−	1.05891i
$672$	16.5391	+	36.2155i	0.638008	+	1.39704i
$673$	5.95276	−	41.4024i	0.229462	−	1.59594i	−0.470920	−	0.882176i	$-0.656078\pi$
$673$	5.95276	−	41.4024i	0.229462	−	1.59594i	0.700382	−	0.713768i	$-0.253013\pi$
$674$	−1.31514	+	0.386159i	−0.0506572	+	0.0148743i
$675$	0.248172	+	0.159491i	0.00955216	+	0.00613880i
$676$	−8.91933	+	19.5306i	−0.343051	+	0.751177i
$677$	−19.8194	−	5.81951i	−0.761723	−	0.223662i	−0.122275	−	0.992496i	$-0.539019\pi$
$677$	−19.8194	−	5.81951i	−0.761723	−	0.223662i	−0.639448	+	0.768834i	$0.720837\pi$
$678$	7.88220	+	9.09654i	0.302714	+	0.349350i
$679$	36.7649	+	42.4289i	1.41091	+	1.62827i
$680$	−1.78727	−	0.524789i	−0.0685386	−	0.0201247i
$681$	11.4966	−	25.1740i	0.440550	−	0.964670i
$682$	−1.08518	−	0.697403i	−0.0415537	−	0.0267050i
$683$	29.5940	−	8.68957i	1.13238	−	0.332497i	0.338738	−	0.940881i	$-0.390000\pi$
$683$	29.5940	−	8.68957i	1.13238	−	0.332497i	0.793643	+	0.608383i	$0.208182\pi$
$684$	1.73614	−	12.0751i	0.0663830	−	0.461704i
$685$	−6.42038	−	14.0587i	−0.245310	−	0.537154i
$686$	2.42763	+	16.8845i	0.0926872	+	0.644653i
$687$	−18.5353	+	11.9119i	−0.707167	+	0.454469i
$688$	4.62930	−	5.34250i	0.176490	−	0.203681i
$689$	−26.6968			−1.01707
$690$	3.09508	+	1.17206i	0.117828	+	0.0446196i
$691$	14.6734			0.558202			0.279101	−	0.960262i	$-0.409964\pi$
$691$	14.6734			0.558202			0.279101	+	0.960262i	$0.409964\pi$
$692$	10.0669	−	11.6179i	0.382687	−	0.441644i
$693$	−45.0169	+	28.9306i	−1.71005	+	1.09898i
$694$	−0.347297	−	2.41551i	−0.0131832	−	0.0916914i
$695$	6.30424	+	13.8044i	0.239133	+	0.523629i
$696$	0.650200	−	4.52224i	0.0246458	−	0.171415i
$697$	12.2013	−	3.58263i	0.462158	−	0.135702i
$698$	−6.62941	−	4.26046i	−0.250927	−	0.161261i
$699$	4.62205	−	10.1209i	0.174822	−	0.382807i
$700$	9.35225	+	2.74607i	0.353482	+	0.103792i
$701$	−19.7005	−	22.7356i	−0.744079	−	0.858713i	0.249901	−	0.968271i	$-0.419602\pi$
$701$	−19.7005	−	22.7356i	−0.744079	−	0.858713i	−0.993980	+	0.109558i	$0.965056\pi$
$702$	−0.270434	−	0.312098i	−0.0102069	−	0.0117794i
$703$	6.78463	+	1.99215i	0.255887	+	0.0751353i
$704$	9.30667	−	20.3788i	0.350758	−	0.768054i
$705$	17.7023	+	11.3766i	0.666706	+	0.428466i
$706$	3.27058	−	0.960328i	0.123090	−	0.0361424i
$707$	−1.19482	+	8.31012i	−0.0449356	+	0.312534i
$708$	3.15677	+	6.91237i	0.118639	+	0.259783i
$709$	0.234245	+	1.62921i	0.00879724	+	0.0611862i	0.993747	−	0.111654i	$-0.0356148\pi$
$709$	0.234245	+	1.62921i	0.00879724	+	0.0611862i	−0.984950	+	0.172840i	$0.944706\pi$
$710$	0.462904	−	0.297491i	0.0173725	−	0.0111646i
$711$	−1.86260	+	2.14955i	−0.0698529	+	0.0806145i
$712$	3.33561			0.125007
$713$	−2.04734	−	5.57407i	−0.0766734	−	0.208750i
$714$	−5.85333			−0.219056
$715$	11.7886	−	13.6047i	0.440868	−	0.508789i
$716$	38.2894	−	24.6071i	1.43094	−	0.919611i
$717$	−7.82467	−	54.4218i	−0.292218	−	2.03242i
$718$	1.44026	+	3.15373i	0.0537501	+	0.117696i
$719$	5.93249	−	41.2614i	0.221244	−	1.53879i	−0.512096	−	0.858928i	$-0.671131\pi$
$719$	5.93249	−	41.2614i	0.221244	−	1.53879i	0.733341	−	0.679861i	$-0.237960\pi$
$720$	9.72262	−	2.85482i	0.362341	−	0.106393i
$721$	−11.5332	−	7.41191i	−0.429517	−	0.276034i
$722$	1.66977	−	3.65629i	0.0621425	−	0.136073i
$723$	16.1536	+	4.74312i	0.600758	+	0.176398i
$724$	−31.2241	−	36.0345i	−1.16043	−	1.33921i
$725$	−1.10628	−	1.27671i	−0.0410862	−	0.0474160i
$726$	−1.58727	−	0.466063i	−0.0589089	−	0.0172972i
$727$	−19.2577	+	42.1684i	−0.714228	+	1.56394i	0.107593	+	0.994195i	$0.465686\pi$
$727$	−19.2577	+	42.1684i	−0.714228	+	1.56394i	−0.821821	+	0.569746i	$0.807042\pi$
$728$	−23.4417	−	15.0651i	−0.868807	−	0.558348i
$729$	23.7640	−	6.97774i	0.880148	−	0.258435i
$730$	0.423484	−	2.94540i	0.0156739	−	0.109014i
$731$	1.39297	+	3.05017i	0.0515208	+	0.112815i
$732$	5.01308	+	34.8667i	0.185289	+	1.28871i
$733$	17.0597	−	10.9636i	0.630113	−	0.404949i	−0.186238	−	0.982505i	$-0.559630\pi$
$733$	17.0597	−	10.9636i	0.630113	−	0.404949i	0.816351	+	0.577556i	$0.195993\pi$
$734$	2.60568	−	3.00711i	0.0961773	−	0.110995i
$735$	45.5789			1.68120
$736$	−13.6451	+	7.36249i	−0.502966	+	0.271385i
$737$	0.420631			0.0154941
$738$	4.08546	−	4.71487i	0.150388	−	0.173557i
$739$	−42.4555	+	27.2845i	−1.56175	+	1.00368i	−0.579753	+	0.814792i	$0.696851\pi$
$739$	−42.4555	+	27.2845i	−1.56175	+	1.00368i	−0.981999	+	0.188885i	$0.939513\pi$
$740$	0.874346	+	6.08121i	0.0321416	+	0.223550i
$741$	10.9405	+	23.9564i	0.401910	+	0.880060i
$742$	1.11683	−	7.76771i	0.0410000	−	0.285162i
$743$	41.0453	−	12.0520i	1.50581	−	0.442144i	0.578259	−	0.815853i	$-0.303732\pi$
$743$	41.0453	−	12.0520i	1.50581	−	0.442144i	0.927546	+	0.373709i	$0.121914\pi$
$744$	2.81706	+	1.81041i	0.103278	+	0.0663730i
$745$	1.36084	−	2.97982i	0.0498573	−	0.109172i
$746$	−3.63470	−	1.06725i	−0.133076	−	0.0390746i
$747$	−29.4246	−	33.9579i	−1.07659	−	1.24245i
$748$	7.68107	+	8.86442i	0.280848	+	0.324115i
$749$	−69.6592	−	20.4538i	−2.54529	−	0.747366i
$750$	−0.286675	+	0.627730i	−0.0104679	+	0.0229215i
$751$	20.3602	+	13.0847i	0.742956	+	0.477469i	0.856554	−	0.516058i	$-0.172601\pi$
$751$	20.3602	+	13.0847i	0.742956	+	0.477469i	−0.113598	+	0.993527i	$0.536237\pi$
$752$	−29.3169	+	8.60823i	−1.06908	+	0.313910i
$753$	−7.17334	+	49.8917i	−0.261411	+	1.81815i
$754$	0.982390	+	2.15113i	0.0357765	+	0.0783397i
$755$	−2.63944	−	18.3577i	−0.0960592	−	0.668106i
$756$	−2.41895	+	1.55457i	−0.0879765	+	0.0565391i
$757$	16.2196	−	18.7185i	0.589513	−	0.680334i	−0.380109	−	0.924942i	$-0.624114\pi$
$757$	16.2196	−	18.7185i	0.589513	−	0.680334i	0.969622	+	0.244607i	$0.0786591\pi$
$758$	−0.802695			−0.0291552
$759$	−25.3344	−	34.1978i	−0.919580	−	1.24130i
$760$	−2.46364			−0.0893656
$761$	5.09474	−	5.87964i	0.184684	−	0.213137i	−0.655856	−	0.754886i	$-0.727692\pi$
$761$	5.09474	−	5.87964i	0.184684	−	0.213137i	0.840540	+	0.541749i	$0.182238\pi$
$762$	−0.645464	+	0.414815i	−0.0233827	+	0.0150271i
$763$	2.43542	+	16.9387i	0.0881683	+	0.613224i
$764$	−0.0168083	−	0.0368050i	−0.000608102	−	0.00133156i
$765$	−0.684044	+	4.75763i	−0.0247317	+	0.172013i
$766$	1.47488	−	0.433062i	0.0532894	−	0.0156472i
$767$	−6.75764	−	4.34287i	−0.244004	−	0.156812i
$768$	−9.97644	+	21.8453i	−0.359994	+	0.788276i
$769$	−23.6692	−	6.94989i	−0.853531	−	0.250619i	−0.174435	−	0.984669i	$-0.555810\pi$
$769$	−23.6692	−	6.94989i	−0.853531	−	0.250619i	−0.679096	+	0.734049i	$0.737628\pi$
$770$	3.46528	+	3.99914i	0.124880	+	0.144119i
$771$	12.5061	+	14.4328i	0.450397	+	0.519785i
$772$	−8.84918	−	2.59835i	−0.318489	−	0.0935168i
$773$	3.33244	−	7.29703i	0.119860	−	0.262456i	−0.840187	−	0.542297i	$-0.817555\pi$
$773$	3.33244	−	7.29703i	0.119860	−	0.262456i	0.960046	+	0.279841i	$0.0902819\pi$
$774$	1.38392	+	0.889393i	0.0497441	+	0.0319686i
$775$	1.18804	−	0.348839i	0.0426756	−	0.0125307i
$776$	1.75463	−	12.2037i	0.0629876	−	0.438088i
$777$	16.3784	+	35.8638i	0.587574	+	1.28661i
$778$	−0.544405	−	3.78642i	−0.0195179	−	0.135750i
$779$	14.1489	−	9.09292i	0.506936	−	0.325788i
$780$	−14.9849	+	17.2935i	−0.536545	+	0.619206i
$781$	−7.07605			−0.253201
$782$	−0.151249	−	2.27447i	−0.00540866	−	0.0813348i
$783$	0.498359			0.0178099
$784$	−43.3399	+	50.0169i	−1.54785	+	1.78632i
$785$	11.6772	−	7.50448i	0.416777	−	0.267846i
$786$	1.12225	+	7.80543i	0.0400294	+	0.278410i
$787$	14.2985	+	31.3093i	0.509686	+	1.11606i	0.973199	+	0.229966i	$0.0738615\pi$
$787$	14.2985	+	31.3093i	0.509686	+	1.11606i	−0.463513	+	0.886090i	$0.653411\pi$
$788$	1.02710	−	7.14364i	0.0365889	−	0.254482i
$789$	49.3961	−	14.5040i	1.75855	−	0.516356i
$790$	0.236612	+	0.152061i	0.00841829	+	0.00541010i
$791$	−36.8024	+	80.5859i	−1.30854	+	2.86531i
$792$	11.2757	+	3.31083i	0.400663	+	0.117645i
$793$	−24.3843	−	28.1410i	−0.865913	−	0.999317i
$794$	5.08684	+	5.87053i	0.180525	+	0.208337i
$795$	−12.6276	−	3.70781i	−0.447856	−	0.131502i
$796$	1.24928	−	2.73555i	0.0442797	−	0.0969589i
$797$	24.0181	+	15.4355i	0.850765	+	0.546754i	0.891813	−	0.452404i	$-0.149433\pi$
$797$	24.0181	+	15.4355i	0.850765	+	0.546754i	−0.0410482	+	0.999157i	$0.513070\pi$
$798$	−7.42804	+	2.18107i	−0.262950	+	0.0772090i
$799$	2.06262	−	14.3458i	0.0729703	−	0.507519i
$800$	−1.34302	−	2.94080i	−0.0474828	−	0.103973i
$801$	−1.22493	−	8.51958i	−0.0432808	−	0.301025i
$802$	8.02743	−	5.15892i	0.283459	−	0.182168i
$803$	−25.0589	+	28.9195i	−0.884310	+	1.02055i
$804$	−0.534679			−0.0188567
$805$	1.61630	+	24.3057i	0.0569670	+	0.856663i
$806$	−1.73330			−0.0610530
$807$	−18.6310	+	21.5013i	−0.655842	+	0.756882i
$808$	1.55106	−	0.996807i	0.0545661	−	0.0350675i
$809$	−0.711497	−	4.94857i	−0.0250149	−	0.173983i	0.973484	−	0.228755i	$-0.0734656\pi$
$809$	−0.711497	−	4.94857i	−0.0250149	−	0.173983i	−0.998499	+	0.0547729i	$0.982557\pi$
$810$	−1.10556	−	2.42085i	−0.0388456	−	0.0850600i
$811$	6.32913	−	44.0201i	0.222246	−	1.54575i	−0.507268	−	0.861788i	$-0.669345\pi$
$811$	6.32913	−	44.0201i	0.222246	−	1.54575i	0.729514	−	0.683966i	$-0.239746\pi$
$812$	15.7991	−	4.63903i	0.554439	−	0.162798i
$813$	−23.8358	−	15.3184i	−0.835959	−	0.537238i
$814$	−1.38558	+	3.03399i	−0.0485644	+	0.106341i
$815$	0.306150	+	0.0898938i	0.0107240	+	0.00314884i
$816$	−9.33408	−	10.7721i	−0.326758	−	0.377099i
$817$	2.90427	+	3.35170i	0.101607	+	0.117261i
$818$	3.54750	+	1.04164i	0.124036	+	0.0364201i
$819$	−29.8697	+	65.4054i	−1.04373	+	2.28545i
$820$	12.2933	+	7.90046i	0.429302	+	0.275896i
$821$	9.47535	−	2.78221i	0.330692	−	0.0970999i	−0.112172	−	0.993689i	$-0.535781\pi$
$821$	9.47535	−	2.78221i	0.330692	−	0.0970999i	0.442864	+	0.896589i	$0.353963\pi$
$822$	−1.51787	+	10.5570i	−0.0529419	+	0.368219i
$823$	−0.00349339	−	0.00764945i	−0.000121772	−	0.000266643i	0.909571	−	0.415548i	$-0.136410\pi$
$823$	−0.00349339	−	0.00764945i	−0.000121772	−	0.000266643i	−0.909693	+	0.415282i	$0.863683\pi$
$824$	0.428473	+	2.98009i	0.0149266	+	0.103817i
$825$	7.46553	−	4.79780i	0.259916	−	0.167038i
$826$	1.54630	−	1.78453i	0.0538027	−	0.0620916i
$827$	−21.6866			−0.754118			−0.377059	−	0.926189i	$-0.623065\pi$
$827$	−21.6866			−0.754118			−0.377059	+	0.926189i	$0.623065\pi$
$828$	15.7684	+	21.2851i	0.547991	+	0.739709i
$829$	9.43076			0.327544			0.163772	−	0.986498i	$-0.447634\pi$
$829$	9.43076			0.327544			0.163772	+	0.986498i	$0.447634\pi$
$830$	−2.90972	+	3.35800i	−0.100998	+	0.116558i
$831$	36.1322	−	23.2207i	1.25341	−	0.805519i
$832$	−4.28412	−	29.7967i	−0.148525	−	1.03302i
$833$	−13.0411	−	28.5560i	−0.451846	−	0.989406i
$834$	1.49042	−	10.3661i	0.0516089	−	0.358948i
$835$	−5.13997	+	1.50923i	−0.177876	+	0.0522291i
$836$	13.0505	+	8.38707i	0.451362	+	0.290073i
$837$	−0.151739	+	0.332262i	−0.00524486	+	0.0114847i
$838$	−4.37675	−	1.28513i	−0.151192	−	0.0443941i
$839$	21.4975	+	24.8094i	0.742175	+	0.856515i	0.993785	−	0.111313i	$-0.0355057\pi$
$839$	21.4975	+	24.8094i	0.742175	+	0.856515i	−0.251611	+	0.967829i	$0.580960\pi$
$840$	−8.99564	−	10.3815i	−0.310379	−	0.358196i
$841$	25.0870	+	7.36622i	0.865070	+	0.254008i
$842$	−0.616186	+	1.34926i	−0.0212352	+	0.0464985i
$843$	−54.4300	−	34.9800i	−1.87467	−	1.20478i
$844$	−24.5096	+	7.19666i	−0.843654	+	0.247719i
$845$	1.59231	−	11.0748i	0.0547772	−	0.380984i
$846$	−2.95377	−	6.46786i	−0.101553	−	0.222370i
$847$	−1.73282	−	12.0520i	−0.0595404	−	0.414112i
$848$	16.0762	−	10.3315i	0.552057	−	0.354786i
$849$	−13.8553	+	15.9899i	−0.475513	+	0.548771i
$850$	0.475307			0.0163029
$851$	−13.5126	+	7.29100i	−0.463207	+	0.249932i
$852$	8.99462			0.308151
$853$	11.9410	−	13.7806i	0.408852	−	0.471840i	−0.513557	−	0.858056i	$-0.671672\pi$
$853$	11.9410	−	13.7806i	0.408852	−	0.471840i	0.922409	+	0.386215i	$0.126218\pi$
$854$	9.20800	−	5.91762i	0.315091	−	0.202497i
$855$	0.904718	+	6.29245i	0.0309407	+	0.215197i
$856$	6.62324	+	14.5029i	0.226378	+	0.495698i
$857$	6.64425	−	46.2118i	0.226963	−	1.57856i	−0.483829	−	0.875162i	$-0.660754\pi$
$857$	6.64425	−	46.2118i	0.226963	−	1.57856i	0.710792	−	0.703402i	$-0.248336\pi$
$858$	−11.9196	+	3.49991i	−0.406928	+	0.119485i
$859$	35.3292	+	22.7047i	1.20542	+	0.774675i	0.979885	−	0.199561i	$-0.0639515\pi$
$859$	35.3292	+	22.7047i	1.20542	+	0.774675i	0.225532	+	0.974236i	$0.427588\pi$
$860$	−1.60073	+	3.50511i	−0.0545845	+	0.119523i
$861$	89.9793	+	26.4203i	3.06648	+	0.900401i
$862$	−6.08930	−	7.02743i	−0.207402	−	0.239355i
$863$	30.0578	+	34.6886i	1.02318	+	1.18081i	0.983371	+	0.181606i	$0.0581297\pi$
$863$	30.0578	+	34.6886i	1.02318	+	1.18081i	0.0398095	+	0.999207i	$0.487325\pi$
$864$	0.915098	+	0.268697i	0.0311323	+	0.00914126i
$865$	−3.32781	+	7.28688i	−0.113149	+	0.247761i
$866$	−7.37679	−	4.74078i	−0.250674	−	0.161098i
$867$	−33.0602	+	9.70734i	−1.12278	+	0.329679i
$868$	−1.71756	+	11.9459i	−0.0582979	+	0.405471i
$869$	−1.50252	−	3.29005i	−0.0509694	−	0.111607i
$870$	0.165910	+	1.15393i	0.00562488	+	0.0391219i
$871$	0.475475	−	0.305569i	0.0161108	−	0.0103538i
$872$	2.46108	−	2.84023i	0.0833425	−	0.0961824i
$873$	−31.8142			−1.07675
$874$	−1.03945	−	2.83000i	−0.0351600	−	0.0957263i
$875$	−5.07928			−0.171711
$876$	31.8533	−	36.7607i	1.07622	−	1.24203i
$877$	−19.3306	+	12.4230i	−0.652749	+	0.419496i	−0.824670	−	0.565614i	$-0.808639\pi$
$877$	−19.3306	+	12.4230i	−0.652749	+	0.419496i	0.171921	+	0.985111i	$0.445003\pi$
$878$	−1.01573	−	7.06453i	−0.0342791	−	0.238416i
$879$	−5.15165	−	11.2805i	−0.173761	−	0.380483i
$880$	−1.83383	+	12.7546i	−0.0618183	+	0.429956i
$881$	−16.9605	+	4.98006i	−0.571414	+	0.167782i	−0.554660	−	0.832077i	$-0.687152\pi$
$881$	−16.9605	+	4.98006i	−0.571414	+	0.167782i	−0.0167546	+	0.999860i	$0.505333\pi$
$882$	−12.9564	−	8.32657i	−0.436264	−	0.280370i
$883$	−2.38160	+	5.21497i	−0.0801472	+	0.175498i	−0.945463	−	0.325729i	$-0.894390\pi$
$883$	−2.38160	+	5.21497i	−0.0801472	+	0.175498i	0.865316	+	0.501227i	$0.167118\pi$
$884$	15.1221	+	4.44026i	0.508613	+	0.149342i
$885$	−2.59321	−	2.99273i	−0.0871699	−	0.100599i
$886$	−6.69312	−	7.72427i	−0.224860	−	0.259502i
$887$	−15.2256	−	4.47063i	−0.511225	−	0.150109i	0.0159387	−	0.999873i	$-0.494926\pi$
$887$	−15.2256	−	4.47063i	−0.511225	−	0.150109i	−0.527164	+	0.849764i	$0.676745\pi$
$888$	3.59687	−	7.87604i	0.120703	−	0.264303i
$889$	−4.75081	−	3.05316i	−0.159337	−	0.102400i
$890$	−0.816664	+	0.239794i	−0.0273746	+	0.00803792i
$891$	−4.87056	+	33.8755i	−0.163170	+	1.13487i
$892$	−3.20113	−	7.00949i	−0.107182	−	0.234695i
$893$	−2.72803	−	18.9738i	−0.0912899	−	0.634935i
$894$	−1.90177	+	1.22219i	−0.0636048	+	0.0408763i
$895$	−15.5321	+	17.9249i	−0.519179	+	0.599165i
$896$	41.6910			1.39280
$897$	−53.4807	−	20.2524i	−1.78567	−	0.676207i
$898$	4.81879			0.160805
$899$	1.36979	−	1.58082i	0.0456850	−	0.0527232i
$900$	−4.64664	+	2.98621i	−0.154888	+	0.0995404i
$901$	1.29002	+	8.97231i	0.0429769	+	0.298911i
$902$	3.29565	+	7.21646i	0.109733	+	0.240282i
$903$	−3.51920	+	24.4766i	−0.117112	+	0.814530i
$904$	18.6675	−	5.48128i	0.620873	−	0.182305i
$905$	20.9024	+	13.4331i	0.694819	+	0.446533i
$906$	−5.31681	+	11.6422i	−0.176639	+	0.386786i
$907$	−43.3982	−	12.7428i	−1.44101	−	0.423119i	−0.534453	−	0.845198i	$-0.679482\pi$
$907$	−43.3982	−	12.7428i	−1.44101	−	0.423119i	−0.906559	+	0.422079i	$0.861301\pi$
$908$	−14.3443	−	16.5543i	−0.476034	−	0.549372i
$909$	−3.11557	−	3.59556i	−0.103337	−	0.119257i
$910$	6.82229	+	2.00321i	0.226157	+	0.0664056i
$911$	8.06302	−	17.6555i	0.267140	−	0.584954i	−0.727759	−	0.685833i	$-0.759438\pi$
$911$	8.06302	−	17.6555i	0.267140	−	0.584954i	0.994899	+	0.100879i	$0.0321654\pi$
$912$	−15.8591	−	10.1920i	−0.525147	−	0.337492i
$913$	54.8240	−	16.0978i	1.81441	−	0.532759i
$914$	0.0289481	−	0.201339i	0.000957519	−	0.00665969i
$915$	−7.62544	−	16.6974i	−0.252089	−	0.551998i
$916$	2.48181	+	17.2614i	0.0820013	+	0.570332i
$917$	−48.8272	+	31.3794i	−1.61242	+	1.03624i
$918$	−0.0918226	+	0.105969i	−0.00303060	+	0.00349750i
$919$	0.705583			0.0232750			0.0116375	−	0.999932i	$-0.496296\pi$
$919$	0.705583			0.0232750			0.0116375	+	0.999932i	$0.496296\pi$
$920$	3.80157	−	3.76375i	0.125334	−	0.124087i
$921$	42.1070			1.38747
$922$	−7.89296	+	9.10896i	−0.259941	+	0.299987i
$923$	−7.99866	+	5.14043i	−0.263279	+	0.169199i
$924$	12.3100	+	85.6179i	0.404969	+	2.81662i
$925$	−1.32998	−	2.91224i	−0.0437293	−	0.0957539i
$926$	−0.729781	+	5.07574i	−0.0239821	+	0.166799i
$927$	7.45420	−	2.18875i	0.244828	−	0.0718880i
$928$	−4.59454	−	2.95273i	−0.150823	−	0.0969282i
$929$	18.3881	−	40.2643i	0.603294	−	1.32103i	−0.323774	−	0.946135i	$-0.604952\pi$
$929$	18.3881	−	40.2643i	0.603294	−	1.32103i	0.927068	−	0.374894i	$-0.122321\pi$
$930$	−0.819855	−	0.240731i	−0.0268841	−	0.00789389i
$931$	−27.1900	−	31.3789i	−0.891116	−	1.02840i
$932$	−5.76696	−	6.65542i	−0.188903	−	0.218006i
$933$	36.6726	+	10.7680i	1.20061	+	0.352530i
$934$	−1.81589	+	3.97624i	−0.0594176	+	0.130106i
$935$	−5.14195	−	3.30453i	−0.168160	−	0.108070i
$936$	15.1510	−	4.44874i	0.495226	−	0.145412i
$937$	−2.13160	+	14.8256i	−0.0696362	+	0.484331i	0.924923	+	0.380155i	$0.124129\pi$
$937$	−2.13160	+	14.8256i	−0.0696362	+	0.484331i	−0.994559	+	0.104175i	$0.966780\pi$
$938$	0.0690175	+	0.151127i	0.00225350	+	0.00493448i
$939$	−1.71252	−	11.9108i	−0.0558859	−	0.388695i
$940$	14.0111	−	9.00442i	0.456993	−	0.293692i
$941$	−19.6070	+	22.6277i	−0.639172	+	0.737643i	−0.979228	−	0.202762i	$-0.935008\pi$
$941$	−19.6070	+	22.6277i	−0.639172	+	0.737643i	0.340057	+	0.940405i	$0.389554\pi$
$942$	−9.57897			−0.312100
$943$	−7.94126	+	35.6465i	−0.258603	+	1.16081i
$944$	5.74995			0.187145
$945$	0.981246	−	1.13242i	0.0319199	−	0.0368376i
$946$	−1.75986	+	1.13099i	−0.0572180	+	0.0367718i
$947$	7.83099	+	54.4657i	0.254473	+	1.76990i	0.570646	+	0.821196i	$0.306693\pi$
$947$	7.83099	+	54.4657i	0.254473	+	1.76990i	−0.316173	+	0.948701i	$0.602398\pi$
$948$	1.90990	+	4.18210i	0.0620307	+	0.135828i
$949$	−7.31750	+	50.8943i	−0.237536	+	1.65210i
$950$	0.603177	−	0.177109i	0.0195697	−	0.00574617i
$951$	−11.2523	−	7.23143i	−0.364882	−	0.234495i
$952$	−3.93036	+	8.60629i	−0.127384	+	0.278931i
$953$	−38.9112	−	11.4254i	−1.26046	−	0.370104i	−0.417793	−	0.908542i	$-0.637196\pi$
$953$	−38.9112	−	11.4254i	−1.26046	−	0.370104i	−0.842665	+	0.538439i	$0.819014\pi$
$954$	2.91221	+	3.36087i	0.0942863	+	0.108812i
$955$	0.0138076	+	0.0159348i	0.000446803	+	0.000515638i
$956$	−41.7545	−	12.2602i	−1.35044	−	0.396524i
$957$	6.22775	−	13.6369i	0.201315	−	0.440818i
$958$	3.75449	+	2.41287i	0.121302	+	0.0779561i
$959$	−75.3221	+	22.1166i	−2.43228	+	0.714181i
$960$	2.11195	−	14.6889i	0.0681627	−	0.474082i
$961$	−12.2410	−	26.8040i	−0.394870	−	0.864646i
$962$	0.637819	+	4.43613i	0.0205641	+	0.143027i
$963$	34.6100	−	22.2425i	1.11529	−	0.716754i
$964$	8.72611	−	10.0705i	0.281049	−	0.324348i
$965$	4.80606			0.154713
$966$	8.12993	−	14.7135i	0.261576	−	0.473400i
$967$	15.0642			0.484433			0.242217	−	0.970222i	$-0.422125\pi$
$967$	15.0642			0.484433			0.242217	+	0.970222i	$0.422125\pi$
$968$	−1.75107	+	2.02084i	−0.0562815	+	0.0649524i
$969$	7.52265	−	4.83451i	0.241662	−	0.155307i
$970$	0.447726	+	3.11400i	0.0143756	+	0.0999845i
$971$	7.02203	+	15.3761i	0.225348	+	0.493442i	0.988207	−	0.153122i	$-0.0489326\pi$
$971$	7.02203	+	15.3761i	0.225348	+	0.493442i	−0.762860	+	0.646564i	$0.776205\pi$
$972$	5.94944	−	41.3793i	0.190828	−	1.32724i
$973$	73.9596	−	21.7165i	2.37104	−	0.696199i
$974$	−4.89561	−	3.14621i	−0.156865	−	0.100811i
$975$	4.95353	−	10.8467i	0.158640	−	0.347373i
$976$	25.5740	+	7.50922i	0.818605	+	0.240364i
$977$	−16.9016	−	19.5055i	−0.540730	−	0.624035i	0.417968	−	0.908462i	$-0.362742\pi$
$977$	−16.9016	−	19.5055i	−0.540730	−	0.624035i	−0.958698	+	0.284426i	$0.908197\pi$
$978$	−0.144195	−	0.166409i	−0.00461083	−	0.00532118i
$979$	10.5020	+	3.08365i	0.335644	+	0.0985539i
$980$	14.9862	−	32.8152i	0.478716	−	1.04824i
$981$	−8.15810	−	5.24289i	−0.260468	−	0.167393i
$982$	5.12628	−	1.50521i	0.163586	−	0.0480332i
$983$	−6.56810	+	45.6822i	−0.209490	+	1.45703i	0.565336	+	0.824860i	$0.308746\pi$
$983$	−6.56810	+	45.6822i	−0.209490	+	1.45703i	−0.774826	+	0.632174i	$0.782163\pi$
$984$	−8.55528	−	18.7335i	−0.272732	−	0.597201i
$985$	0.535231	+	3.72261i	0.0170539	+	0.118612i
$986$	0.675487	−	0.434109i	0.0215119	−	0.0138248i
$987$	69.9928	−	80.7760i	2.22789	−	2.57113i
$988$	20.8449			0.663166
$989$	−9.60196	−	0.735009i	−0.305325	−	0.0233719i
$990$	−2.99866			−0.0953036
$991$	16.9647	−	19.5783i	0.538901	−	0.621924i	−0.419360	−	0.907820i	$-0.637746\pi$
$991$	16.9647	−	19.5783i	0.538901	−	0.621924i	0.958261	+	0.285896i	$0.0922910\pi$
$992$	3.36755	−	2.16420i	0.106920	−	0.0687133i
$993$	7.87779	+	54.7912i	0.249994	+	1.73875i
$994$	−1.16104	−	2.54233i	−0.0368261	−	0.0806379i
$995$	−0.223027	+	1.55119i	−0.00707042	+	0.0491759i
$996$	−69.6888	+	20.4625i	−2.20817	+	0.648378i
$997$	45.9607	+	29.5371i	1.45559	+	0.935450i	0.998951	+	0.0457980i	$0.0145831\pi$
$997$	45.9607	+	29.5371i	1.45559	+	0.935450i	0.456638	+	0.889652i	$0.349053\pi$
$998$	2.93510	−	6.42698i	0.0929091	−	0.203443i
$999$	0.906212	+	0.266088i	0.0286713	+	0.00841865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.16.1	✓	20
5.2	odd	4		575.2.p.c.499.4		40
5.3	odd	4		575.2.p.c.499.1		40
5.4	even	2		575.2.k.c.476.2		20
23.6	even	11		2645.2.a.t.1.5		10
23.13	even	11	inner	115.2.g.b.36.1	yes	20
23.17	odd	22		2645.2.a.u.1.5		10
115.13	odd	44		575.2.p.c.174.4		40
115.59	even	22		575.2.k.c.151.2		20
115.82	odd	44		575.2.p.c.174.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.16.1	✓	20	1.1	even	1	trivial
115.2.g.b.36.1	yes	20	23.13	even	11	inner
575.2.k.c.151.2		20	115.59	even	22
575.2.k.c.476.2		20	5.4	even	2
575.2.p.c.174.1		40	115.82	odd	44
575.2.p.c.174.4		40	115.13	odd	44
575.2.p.c.499.1		40	5.3	odd	4
575.2.p.c.499.4		40	5.2	odd	4
2645.2.a.t.1.5		10	23.6	even	11
2645.2.a.u.1.5		10	23.17	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.186393 - 0.215109i) q^{2} +(-2.03964 + 1.31080i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.0982103 + 0.683068i) q^{6} +(-4.87354 + 1.43100i) q^{7} +(0.938384 + 0.603063i) q^{8} +(1.19570 - 2.61822i) q^{9} +O(q^{10})\)	\(q+(0.186393 - 0.215109i) q^{2} +(-2.03964 + 1.31080i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.0982103 + 0.683068i) q^{6} +(-4.87354 + 1.43100i) q^{7} +(0.938384 + 0.603063i) q^{8} +(1.19570 - 2.61822i) q^{9} +(-0.273100 - 0.0801894i) q^{10} +(2.39693 + 2.76621i) q^{11} +(-3.04683 - 3.51622i) q^{12} +(4.71898 + 1.38562i) q^{13} +(-0.600571 + 1.31507i) q^{14} +(2.03964 + 1.31080i) q^{15} +(-3.37787 + 0.991834i) q^{16} +(0.237653 - 1.65292i) q^{17} +(-0.340332 - 0.745222i) q^{18} +(-0.314321 - 2.18615i) q^{19} +(1.61435 - 1.03748i) q^{20} +(8.06451 - 9.30694i) q^{21} +1.04181 q^{22} +(3.82485 + 2.89319i) q^{23} -2.70446 q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.17764 - 0.756824i) q^{26} +(-0.0419833 - 0.292000i) q^{27} +(-4.04908 - 8.86625i) q^{28} +(-0.240417 + 1.67214i) q^{29} +(0.662138 - 0.194421i) q^{30} +(-1.04163 - 0.669418i) q^{31} +(-1.34302 + 2.94080i) q^{32} +(-8.51482 - 2.50018i) q^{33} +(-0.311260 - 0.359213i) q^{34} +(3.32622 + 3.83867i) q^{35} +(5.29973 + 1.55614i) q^{36} +(-1.32998 + 2.91224i) q^{37} +(-0.528847 - 0.339869i) q^{38} +(-11.4413 + 3.35946i) q^{39} +(0.158746 - 1.10411i) q^{40} +(3.16340 + 6.92687i) q^{41} +(-0.498838 - 3.46949i) q^{42} +(-1.68924 + 1.08561i) q^{43} +(-4.59968 + 5.30831i) q^{44} -2.87833 q^{45} +(1.33527 - 0.283488i) q^{46} +8.67911 q^{47} +(5.58956 - 6.45069i) q^{48} +(15.8148 - 10.1636i) q^{49} +(0.0405070 + 0.281733i) q^{50} +(1.68191 + 3.68287i) q^{51} +(-1.34316 + 9.34189i) q^{52} +(-5.20829 + 1.52929i) q^{53} +(-0.0706372 - 0.0453958i) q^{54} +(1.52051 - 3.32945i) q^{55} +(-5.43623 - 1.59622i) q^{56} +(3.50670 + 4.04695i) q^{57} +(0.314880 + 0.363391i) q^{58} +(-1.56713 - 0.460150i) q^{59} +(-1.93277 + 4.23218i) q^{60} +(-6.36917 - 4.09322i) q^{61} +(-0.338151 + 0.0992900i) q^{62} +(-2.08062 + 14.4710i) q^{63} +(-2.54266 - 5.56764i) q^{64} +(-0.699932 - 4.86814i) q^{65} +(-2.12491 + 1.36560i) q^{66} +(0.0752564 - 0.0868505i) q^{67} +3.20454 q^{68} +(-11.5937 - 0.887472i) q^{69} +1.44571 q^{70} +(-1.26600 + 1.46104i) q^{71} +(2.70098 - 1.73581i) q^{72} +(1.48784 + 10.3482i) q^{73} +(0.378550 + 0.828910i) q^{74} +(0.345046 - 2.39985i) q^{75} +(4.06665 - 1.19408i) q^{76} +(-15.6400 - 10.0512i) q^{77} +(-1.40992 + 3.08730i) q^{78} +(-0.948139 - 0.278399i) q^{79} +(2.30542 + 2.66060i) q^{80} +(6.12309 + 7.06642i) q^{81} +(2.07967 + 0.610645i) q^{82} +(6.48492 - 14.2000i) q^{83} +(19.8805 + 12.7764i) q^{84} +(-1.60227 + 0.470469i) q^{85} +(-0.0813383 + 0.565720i) q^{86} +(-1.70147 - 3.72570i) q^{87} +(0.581046 + 4.04127i) q^{88} +(2.51564 - 1.61670i) q^{89} +(-0.536499 + 0.619153i) q^{90} -24.9809 q^{91} +(-4.45092 + 8.05525i) q^{92} +3.00203 q^{93} +(1.61772 - 1.86695i) q^{94} +(-1.85802 + 1.19408i) q^{95} +(-1.11552 - 7.75859i) q^{96} +(-4.59160 - 10.0542i) q^{97} +(0.761496 - 5.29632i) q^{98} +(10.1085 - 2.96813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

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