LMFDB - Embedded newform 43.2.g.a.40.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			40.3
Character	$\chi$	$=$	43.40
Dual form			43.2.g.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.993512 + 0.478450i) q^{2} +(-0.0482746 + 0.644179i) q^{3} +(-0.488828 - 0.612971i) q^{4} +(-3.17479 - 0.979294i) q^{5} +(-0.356169 + 0.616903i) q^{6} +(1.23273 + 2.13515i) q^{7} +(-0.683135 - 2.99301i) q^{8} +(2.55386 + 0.384932i) q^{9} +O(q^{10})$	\(q+(0.993512 + 0.478450i) q^{2} +(-0.0482746 + 0.644179i) q^{3} +(-0.488828 - 0.612971i) q^{4} +(-3.17479 - 0.979294i) q^{5} +(-0.356169 + 0.616903i) q^{6} +(1.23273 + 2.13515i) q^{7} +(-0.683135 - 2.99301i) q^{8} +(2.55386 + 0.384932i) q^{9} +(-2.68565 - 2.49192i) q^{10} +(0.748014 - 0.937980i) q^{11} +(0.418461 - 0.285302i) q^{12} +(-4.22417 + 3.91945i) q^{13} +(0.203169 + 2.71110i) q^{14} +(0.784103 - 1.99786i) q^{15} +(0.404382 - 1.77171i) q^{16} +(1.02040 - 0.314752i) q^{17} +(2.35312 + 1.60433i) q^{18} +(2.13226 - 0.321387i) q^{19} +(0.951649 + 2.42476i) q^{20} +(-1.43493 + 0.691027i) q^{21} +(1.19194 - 0.574007i) q^{22} +(-2.16225 - 5.50933i) q^{23} +(1.96101 - 0.295575i) q^{24} +(4.98911 + 3.40152i) q^{25} +(-6.07203 + 1.87297i) q^{26} +(-0.802487 + 3.51593i) q^{27} +(0.706193 - 1.79935i) q^{28} +(0.177883 + 2.37368i) q^{29} +(1.73489 - 1.60975i) q^{30} +(6.31519 - 4.30562i) q^{31} +(-2.57877 + 3.23367i) q^{32} +(0.568117 + 0.527136i) q^{33} +(1.16437 + 0.175501i) q^{34} +(-1.82273 - 7.98588i) q^{35} +(-1.01244 - 1.75360i) q^{36} +(-2.83033 + 4.90228i) q^{37} +(2.27220 + 0.700880i) q^{38} +(-2.32091 - 2.91033i) q^{39} +(-0.762225 + 10.1712i) q^{40} +(-8.77658 - 4.22658i) q^{41} -1.75624 q^{42} +(-2.45449 - 6.08075i) q^{43} -0.940604 q^{44} +(-7.73101 - 3.72306i) q^{45} +(0.487716 - 6.50812i) q^{46} +(3.30437 + 4.14355i) q^{47} +(1.12178 + 0.346023i) q^{48} +(0.460743 - 0.798031i) q^{49} +(3.32928 + 5.76649i) q^{50} +(0.153497 + 0.672515i) q^{51} +(4.46740 + 0.673352i) q^{52} +(2.69519 + 2.50077i) q^{53} +(-2.47948 + 3.10917i) q^{54} +(-3.29335 + 2.24537i) q^{55} +(5.54842 - 5.14818i) q^{56} +(0.104097 + 1.38907i) q^{57} +(-0.958961 + 2.44339i) q^{58} +(0.208748 - 0.914583i) q^{59} +(-1.60792 + 0.495978i) q^{60} +(-2.31407 - 1.57771i) q^{61} +(8.33425 - 1.25619i) q^{62} +(2.32633 + 5.92739i) q^{63} +(-7.38381 + 3.55585i) q^{64} +(17.2492 - 8.30676i) q^{65} +(0.312223 + 0.795532i) q^{66} +(11.8546 - 1.78679i) q^{67} +(-0.691734 - 0.471616i) q^{68} +(3.65338 - 1.12692i) q^{69} +(2.00995 - 8.80616i) q^{70} +(-5.54884 + 14.1382i) q^{71} +(-0.592523 - 7.90668i) q^{72} +(-4.99699 + 4.63653i) q^{73} +(-5.15747 + 3.51630i) q^{74} +(-2.43203 + 3.04967i) q^{75} +(-1.23931 - 1.14991i) q^{76} +(2.92483 + 0.440848i) q^{77} +(-0.913405 - 4.00189i) q^{78} +(-1.18802 - 2.05771i) q^{79} +(-3.01886 + 5.22882i) q^{80} +(5.17773 + 1.59712i) q^{81} +(-6.69743 - 8.39832i) q^{82} +(-0.533459 + 7.11852i) q^{83} +(1.12501 + 0.541778i) q^{84} -3.54780 q^{85} +(0.470767 - 7.21565i) q^{86} -1.53767 q^{87} +(-3.31838 - 1.59805i) q^{88} +(-0.113343 + 1.51246i) q^{89} +(-5.89955 - 7.39780i) q^{90} +(-13.5759 - 4.18761i) q^{91} +(-2.32009 + 4.01851i) q^{92} +(2.46873 + 4.27597i) q^{93} +(1.30045 + 5.69764i) q^{94} +(-7.08423 - 1.06778i) q^{95} +(-1.95858 - 1.81729i) q^{96} +(-6.73777 + 8.44890i) q^{97} +(0.839572 - 0.572410i) q^{98} +(2.27138 - 2.10753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

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 $

$2$	0.993512	+	0.478450i	0.702519	+	0.338315i	0.750810	−	0.660518i	$-0.229663\pi$
$2$	0.993512	+	0.478450i	0.702519	+	0.338315i	−0.0482911	+	0.998833i	$0.515378\pi$
$3$	−0.0482746	+	0.644179i	−0.0278713	+	0.371917i	0.965776	+	0.259378i	$0.0835175\pi$
$3$	−0.0482746	+	0.644179i	−0.0278713	+	0.371917i	−0.993647	+	0.112539i	$0.964102\pi$
$4$	−0.488828	−	0.612971i	−0.244414	−	0.306485i
$5$	−3.17479	−	0.979294i	−1.41981	−	0.437954i	−0.512599	−	0.858628i	$-0.671317\pi$
$5$	−3.17479	−	0.979294i	−1.41981	−	0.437954i	−0.907212	+	0.420674i	$0.861794\pi$
$6$	−0.356169	+	0.616903i	−0.145405	+	0.251850i
$7$	1.23273	+	2.13515i	0.465929	+	0.807013i	0.999243	−	0.0389048i	$-0.0123869\pi$
$7$	1.23273	+	2.13515i	0.465929	+	0.807013i	−0.533314	+	0.845917i	$0.679054\pi$
$8$	−0.683135	−	2.99301i	−0.241525	−	1.05819i
$9$	2.55386	+	0.384932i	0.851285	+	0.128311i
$10$	−2.68565	−	2.49192i	−0.849278	−	0.788015i
$11$	0.748014	−	0.937980i	0.225535	−	0.282812i	−0.656170	−	0.754613i	$-0.727825\pi$
$11$	0.748014	−	0.937980i	0.225535	−	0.282812i	0.881705	+	0.471801i	$0.156396\pi$
$12$	0.418461	−	0.285302i	0.120799	−	0.0823596i
$13$	−4.22417	+	3.91945i	−1.17157	+	1.08706i	−0.176874	+	0.984233i	$0.556599\pi$
$13$	−4.22417	+	3.91945i	−1.17157	+	1.08706i	−0.994699	+	0.102828i	$0.967211\pi$
$14$	0.203169	+	2.71110i	0.0542992	+	0.724573i
$15$	0.784103	−	1.99786i	0.202455	−	0.515846i
$16$	0.404382	−	1.77171i	0.101096	−	0.442928i
$17$	1.02040	−	0.314752i	0.247483	−	0.0763385i	−0.168532	−	0.985696i	$-0.553903\pi$
$17$	1.02040	−	0.314752i	0.247483	−	0.0763385i	0.416015	+	0.909358i	$0.363426\pi$
$18$	2.35312	+	1.60433i	0.554635	+	0.378144i
$19$	2.13226	−	0.321387i	0.489175	−	0.0737312i	0.100176	−	0.994970i	$-0.468059\pi$
$19$	2.13226	−	0.321387i	0.489175	−	0.0737312i	0.388998	+	0.921238i	$0.372821\pi$
$20$	0.951649	+	2.42476i	0.212795	+	0.542193i
$21$	−1.43493	+	0.691027i	−0.313128	+	0.150794i
$22$	1.19194	−	0.574007i	0.254122	−	0.122379i
$23$	−2.16225	−	5.50933i	−0.450861	−	1.14877i	−0.957964	−	0.286889i	$-0.907379\pi$
$23$	−2.16225	−	5.50933i	−0.450861	−	1.14877i	0.507103	−	0.861886i	$-0.330716\pi$
$24$	1.96101	−	0.295575i	0.400290	−	0.0603340i
$25$	4.98911	+	3.40152i	0.997821	+	0.680303i
$26$	−6.07203	+	1.87297i	−1.19082	+	0.367320i
$27$	−0.802487	+	3.51593i	−0.154439	+	0.676641i
$28$	0.706193	−	1.79935i	0.133458	−	0.340045i
$29$	0.177883	+	2.37368i	0.0330320	+	0.440782i	0.989061	+	0.147509i	$0.0471255\pi$
$29$	0.177883	+	2.37368i	0.0330320	+	0.440782i	−0.956029	+	0.293273i	$0.905255\pi$
$30$	1.73489	−	1.60975i	0.316747	−	0.293898i
$31$	6.31519	−	4.30562i	1.13424	−	0.773313i	0.157455	−	0.987526i	$-0.449671\pi$
$31$	6.31519	−	4.30562i	1.13424	−	0.773313i	0.976787	+	0.214213i	$0.0687188\pi$
$32$	−2.57877	+	3.23367i	−0.455866	+	0.571638i
$33$	0.568117	+	0.527136i	0.0988965	+	0.0917626i
$34$	1.16437	+	0.175501i	0.199688	+	0.0300982i
$35$	−1.82273	−	7.98588i	−0.308097	−	1.34986i
$36$	−1.01244	−	1.75360i	−0.168741	−	0.292267i
$37$	−2.83033	+	4.90228i	−0.465304	+	0.805930i	−0.999215	−	0.0396104i	$-0.987388\pi$
$37$	−2.83033	+	4.90228i	−0.465304	+	0.805930i	0.533911	+	0.845541i	$0.320722\pi$
$38$	2.27220	+	0.700880i	0.368599	+	0.113698i
$39$	−2.32091	−	2.91033i	−0.371643	−	0.466026i
$40$	−0.762225	+	10.1712i	−0.120518	+	1.60820i
$41$	−8.77658	−	4.22658i	−1.37067	−	0.660081i	−0.403683	−	0.914899i	$-0.632270\pi$
$41$	−8.77658	−	4.22658i	−1.37067	−	0.660081i	−0.966989	+	0.254818i	$0.917984\pi$
$42$	−1.75624			−0.270994
$43$	−2.45449	−	6.08075i	−0.374306	−	0.927305i
$43$	−2.45449	−	6.08075i	−0.374306	−	0.927305i
$44$	−0.940604			−0.141801
$45$	−7.73101	−	3.72306i	−1.15247	−	0.555000i
$46$	0.487716	−	6.50812i	0.0719098	−	0.959570i
$47$	3.30437	+	4.14355i	0.481992	+	0.604398i	0.962062	−	0.272832i	$-0.0879602\pi$
$47$	3.30437	+	4.14355i	0.481992	+	0.604398i	−0.480070	+	0.877230i	$0.659389\pi$
$48$	1.12178	+	0.346023i	0.161915	+	0.0499442i
$49$	0.460743	−	0.798031i	0.0658205	−	0.114004i
$50$	3.32928	+	5.76649i	0.470832	+	0.815504i
$51$	0.153497	+	0.672515i	0.0214939	+	0.0941710i
$52$	4.46740	+	0.673352i	0.619517	+	0.0933772i
$53$	2.69519	+	2.50077i	0.370212	+	0.343507i	0.843237	−	0.537542i	$-0.180647\pi$
$53$	2.69519	+	2.50077i	0.370212	+	0.343507i	−0.473024	+	0.881049i	$0.656838\pi$
$54$	−2.47948	+	3.10917i	−0.337414	+	0.423104i
$55$	−3.29335	+	2.24537i	−0.444075	+	0.302765i
$56$	5.54842	−	5.14818i	0.741438	−	0.687954i
$57$	0.104097	+	1.38907i	0.0137880	+	0.183987i
$58$	−0.958961	+	2.44339i	−0.125918	+	0.320833i
$59$	0.208748	−	0.914583i	0.0271766	−	0.119069i	−0.959520	−	0.281640i	$-0.909122\pi$
$59$	0.208748	−	0.914583i	0.0271766	−	0.119069i	0.986697	+	0.162571i	$0.0519788\pi$
$60$	−1.60792	+	0.495978i	−0.207582	+	0.0640305i
$61$	−2.31407	−	1.57771i	−0.296287	−	0.202005i	0.406048	−	0.913852i	$-0.366907\pi$
$61$	−2.31407	−	1.57771i	−0.296287	−	0.202005i	−0.702335	+	0.711847i	$0.747859\pi$
$62$	8.33425	−	1.25619i	1.05845	−	0.159536i
$63$	2.32633	+	5.92739i	0.293090	+	0.746782i
$64$	−7.38381	+	3.55585i	−0.922976	+	0.444482i
$65$	17.2492	−	8.30676i	2.13950	−	1.03033i
$66$	0.312223	+	0.795532i	0.0384320	+	0.0979232i
$67$	11.8546	−	1.78679i	1.44827	−	0.218291i	0.622642	−	0.782507i	$-0.286059\pi$
$67$	11.8546	−	1.78679i	1.44827	−	0.218291i	0.825628	+	0.564216i	$0.190821\pi$
$68$	−0.691734	−	0.471616i	−0.0838850	−	0.0571919i
$69$	3.65338	−	1.12692i	0.439815	−	0.135665i
$70$	2.00995	−	8.80616i	0.240235	−	1.05254i
$71$	−5.54884	+	14.1382i	−0.658527	+	1.67790i	0.0740851	+	0.997252i	$0.476396\pi$
$71$	−5.54884	+	14.1382i	−0.658527	+	1.67790i	−0.732612	+	0.680647i	$0.761699\pi$
$72$	−0.592523	−	7.90668i	−0.0698296	−	0.931811i
$73$	−4.99699	+	4.63653i	−0.584853	+	0.542664i	−0.916136	−	0.400867i	$-0.868709\pi$
$73$	−4.99699	+	4.63653i	−0.584853	+	0.542664i	0.331283	+	0.943531i	$0.392518\pi$
$74$	−5.15747	+	3.51630i	−0.599544	+	0.408762i
$75$	−2.43203	+	3.04967i	−0.280827	+	0.352146i
$76$	−1.23931	−	1.14991i	−0.142159	−	0.131904i
$77$	2.92483	+	0.440848i	0.333316	+	0.0502393i
$78$	−0.913405	−	4.00189i	−0.103423	−	0.453125i
$79$	−1.18802	−	2.05771i	−0.133662	−	0.231510i	0.791423	−	0.611268i	$-0.209340\pi$
$79$	−1.18802	−	2.05771i	−0.133662	−	0.231510i	−0.925086	+	0.379759i	$0.876007\pi$
$80$	−3.01886	+	5.22882i	−0.337519	+	0.584599i
$81$	5.17773	+	1.59712i	0.575304	+	0.177458i
$82$	−6.69743	−	8.39832i	−0.739608	−	0.927439i
$83$	−0.533459	+	7.11852i	−0.0585548	+	0.781359i	0.888211	+	0.459436i	$0.151948\pi$
$83$	−0.533459	+	7.11852i	−0.0585548	+	0.781359i	−0.946766	+	0.321923i	$0.895671\pi$
$84$	1.12501	+	0.541778i	0.122749	+	0.0591128i
$85$	−3.54780			−0.384813
$86$	0.470767	−	7.21565i	0.0507642	−	0.778083i
$87$	−1.53767			−0.164855
$88$	−3.31838	−	1.59805i	−0.353740	−	0.170352i
$89$	−0.113343	+	1.51246i	−0.0120143	+	0.160320i	0.987970	+	0.154648i	$0.0494245\pi$
$89$	−0.113343	+	1.51246i	−0.0120143	+	0.160320i	−0.999984	+	0.00567185i	$0.998195\pi$
$90$	−5.89955	−	7.39780i	−0.621867	−	0.779797i
$91$	−13.5759	−	4.18761i	−1.42314	−	0.438981i
$92$	−2.32009	+	4.01851i	−0.241886	+	0.418959i
$93$	2.46873	+	4.27597i	0.255995	+	0.443397i
$94$	1.30045	+	5.69764i	0.134131	+	0.587667i
$95$	−7.08423	−	1.06778i	−0.726827	−	0.109551i
$96$	−1.95858	−	1.81729i	−0.199896	−	0.185477i
$97$	−6.73777	+	8.44890i	−0.684117	+	0.857856i	−0.995726	−	0.0923546i	$-0.970561\pi$
$97$	−6.73777	+	8.44890i	−0.684117	+	0.857856i	0.311609	+	0.950210i	$0.399132\pi$
$98$	0.839572	−	0.572410i	0.0848096	−	0.0578222i
$99$	2.27138	−	2.10753i	0.228282	−	0.211815i
$100$	−0.353785	−	4.72093i	−0.0353785	−	0.472093i
$101$	4.38155	−	11.1640i	0.435981	−	1.11086i	−0.529019	−	0.848610i	$-0.677440\pi$
$101$	4.38155	−	11.1640i	0.435981	−	1.11086i	0.965000	−	0.262251i	$-0.0844647\pi$
$102$	−0.169264	+	0.741593i	−0.0167596	+	0.0734287i
$103$	10.0219	−	3.09135i	0.987489	−	0.304600i	0.241385	−	0.970429i	$-0.422398\pi$
$103$	10.0219	−	3.09135i	0.987489	−	0.304600i	0.746104	+	0.665829i	$0.231922\pi$
$104$	14.6166	+	9.96546i	1.43328	+	0.977193i
$105$	5.23233	−	0.788647i	0.510623	−	0.0769641i
$106$	1.48121	+	3.77406i	0.143868	+	0.366569i
$107$	8.45359	−	4.07104i	0.817240	−	0.393562i	0.0219258	−	0.999760i	$-0.493020\pi$
$107$	8.45359	−	4.07104i	0.817240	−	0.393562i	0.795314	+	0.606198i	$0.207306\pi$
$108$	2.54744	−	1.22678i	0.245127	−	0.118047i
$109$	−5.33036	−	13.5815i	−0.510556	−	1.30087i	−0.921204	−	0.389080i	$-0.872793\pi$
$109$	−5.33036	−	13.5815i	−0.510556	−	1.30087i	0.410648	−	0.911794i	$-0.365302\pi$
$110$	−4.34628	+	0.655096i	−0.414401	+	0.0624610i
$111$	−3.02132	−	2.05990i	−0.286771	−	0.195517i
$112$	4.28138	−	1.32063i	0.404552	−	0.124788i
$113$	0.492626	−	2.15834i	0.0463424	−	0.203039i	−0.946457	−	0.322831i	$-0.895365\pi$
$113$	0.492626	−	2.15834i	0.0463424	−	0.203039i	0.992799	+	0.119792i	$0.0382226\pi$
$114$	−0.561182	+	1.42987i	−0.0525595	+	0.133919i
$115$	1.46945	+	19.6085i	0.137027	+	1.82850i
$116$	1.36804	−	1.26936i	0.127020	−	0.117857i
$117$	−12.2966	+	8.38371i	−1.13682	+	0.775074i
$118$	0.644976	−	0.808774i	0.0593748	−	0.0744537i
$119$	1.92992	+	1.79071i	0.176916	+	0.164154i
$120$	−6.51527	−	0.982019i	−0.594760	−	0.0896456i
$121$	2.12745	+	9.32096i	0.193404	+	0.847360i
$122$	−1.54420	−	2.67464i	−0.139806	−	0.242150i
$123$	3.14636	−	5.44966i	0.283698	−	0.491379i
$124$	−5.72626	−	1.76632i	−0.514234	−	0.158620i
$125$	−2.15089	−	2.69713i	−0.192382	−	0.241239i
$126$	−0.524725	+	7.00197i	−0.0467462	+	0.623785i
$127$	−0.116462	−	0.0560852i	−0.0103343	−	0.00497676i	0.428709	−	0.903442i	$-0.358968\pi$
$127$	−0.116462	−	0.0560852i	−0.0103343	−	0.00497676i	−0.439044	+	0.898466i	$0.644683\pi$
$128$	−0.765157			−0.0676310
$129$	4.03558	−	1.28759i	0.355313	−	0.113366i
$130$	21.1116			1.85161
$131$	1.92224	+	0.925700i	0.167946	+	0.0808788i	0.515968	−	0.856608i	$-0.327432\pi$
$131$	1.92224	+	0.925700i	0.167946	+	0.0808788i	−0.348022	+	0.937486i	$0.613147\pi$
$132$	0.0454073	−	0.605918i	0.00395220	−	0.0527384i
$133$	3.31472	+	4.15653i	0.287423	+	0.360417i
$134$	12.6326	+	3.89663i	1.09129	+	0.336618i
$135$	5.99086	−	10.3765i	0.515611	−	0.893065i
$136$	−1.63913	−	2.83905i	−0.140554	−	0.243447i
$137$	−0.137699	−	0.603299i	−0.0117644	−	0.0515433i	0.968705	−	0.248215i	$-0.0798439\pi$
$137$	−0.137699	−	0.603299i	−0.0117644	−	0.0515433i	−0.980469	+	0.196672i	$0.936987\pi$
$138$	4.16885	+	0.628353i	0.354876	+	0.0534890i
$139$	−6.96371	−	6.46138i	−0.590654	−	0.548047i	0.327205	−	0.944953i	$-0.393893\pi$
$139$	−6.96371	−	6.46138i	−0.590654	−	0.548047i	−0.917859	+	0.396906i	$0.870084\pi$
$140$	−4.00411	+	5.02100i	−0.338409	+	0.424352i
$141$	−2.82870	+	1.92858i	−0.238220	+	0.162416i
$142$	−12.2773	+	11.3917i	−1.03029	+	0.955966i
$143$	0.516633	+	6.89399i	0.0432030	+	0.576505i
$144$	1.71472	−	4.36904i	0.142894	−	0.364087i
$145$	1.75979	−	7.71016i	0.146143	−	0.640294i
$146$	−7.18292	+	2.21564i	−0.594462	+	0.183367i
$147$	0.491833	+	0.335326i	0.0405657	+	0.0276572i
$148$	4.38850	−	0.661460i	0.360733	−	0.0543717i
$149$	−1.57707	−	4.01830i	−0.129198	−	0.329192i	0.851607	−	0.524180i	$-0.175628\pi$
$149$	−1.57707	−	4.01830i	−0.129198	−	0.329192i	−0.980806	+	0.194989i	$0.937533\pi$
$150$	−3.87537	+	1.86628i	−0.316423	+	0.152381i
$151$	−4.00622	+	1.92929i	−0.326022	+	0.157004i	−0.589734	−	0.807598i	$-0.700767\pi$
$151$	−4.00622	+	1.92929i	−0.326022	+	0.157004i	0.263712	+	0.964601i	$0.415053\pi$
$152$	−2.41854	−	6.16233i	−0.196169	−	0.499831i
$153$	2.72711	−	0.411046i	0.220474	−	0.0332311i
$154$	2.69493	+	1.83737i	0.217164	+	0.148060i
$155$	−24.2659	+	7.48504i	−1.94908	+	0.601213i
$156$	−0.649422	+	2.84530i	−0.0519953	+	0.227806i
$157$	5.11902	−	13.0430i	0.408542	−	1.04095i	−0.567502	−	0.823372i	$-0.692090\pi$
$157$	5.11902	−	13.0430i	0.408542	−	1.04095i	0.976043	−	0.217576i	$-0.0698149\pi$
$158$	−0.195799	−	2.61276i	−0.0155770	−	0.207860i
$159$	−1.74105	+	1.61546i	−0.138074	+	0.128114i
$160$	11.3538	−	7.74087i	0.897595	−	0.611970i
$161$	9.09779	−	11.4083i	0.717007	−	0.899098i
$162$	4.38000	+	4.06404i	0.344125	+	0.319302i
$163$	1.88482	+	0.284091i	0.147630	+	0.0222517i	0.222442	−	0.974946i	$-0.428597\pi$
$163$	1.88482	+	0.284091i	0.147630	+	0.0222517i	−0.0748113	+	0.997198i	$0.523835\pi$
$164$	1.69947	+	7.44586i	0.132706	+	0.581424i
$165$	−1.28743	−	2.22990i	−0.100227	−	0.173598i
$166$	−3.93586	+	6.81710i	−0.305482	+	0.529110i
$167$	−13.2910	−	4.09972i	−1.02849	−	0.317246i	−0.265809	−	0.964026i	$-0.585639\pi$
$167$	−13.2910	−	4.09972i	−1.02849	−	0.317246i	−0.762677	+	0.646780i	$0.776115\pi$
$168$	3.04850	+	3.82270i	0.235197	+	0.294928i
$169$	1.50997	−	20.1492i	0.116152	−	1.54994i
$170$	−3.52478	−	1.69744i	−0.270338	−	0.130188i
$171$	5.56920			0.425888
$172$	−2.52750	+	4.47697i	−0.192720	+	0.341366i
$173$	−9.52832			−0.724424			−0.362212	−	0.932096i	$-0.617978\pi$
$173$	−9.52832			−0.724424			−0.362212	+	0.932096i	$0.617978\pi$
$174$	−1.52769	−	0.735696i	−0.115814	−	0.0557730i
$175$	−1.11253	+	14.8457i	−0.0840993	+	1.12223i
$176$	−1.35935	−	1.70457i	−0.102465	−	0.128487i
$177$	0.579078	+	0.178622i	0.0435262	+	0.0134260i
$178$	−0.836244	+	1.44842i	−0.0626791	+	0.108563i
$179$	3.21069	+	5.56108i	0.239978	+	0.415655i	0.960708	−	0.277562i	$-0.0895263\pi$
$179$	3.21069	+	5.56108i	0.239978	+	0.415655i	−0.720729	+	0.693216i	$0.756193\pi$
$180$	1.49701	+	6.55881i	0.111580	+	0.488865i
$181$	8.53898	+	1.28704i	0.634697	+	0.0956652i	0.458507	−	0.888691i	$-0.348384\pi$
$181$	8.53898	+	1.28704i	0.634697	+	0.0956652i	0.176191	+	0.984356i	$0.443623\pi$
$182$	−11.4843	−	10.6558i	−0.851270	−	0.789863i
$183$	1.12804	−	1.41451i	0.0833869	−	0.104564i
$184$	−15.0124	+	10.2353i	−1.10673	+	0.754553i
$185$	13.7865	−	12.7920i	1.01360	−	0.940487i
$186$	0.406877	+	5.42939i	0.0298336	+	0.398102i
$187$	0.468043	−	1.19255i	0.0342267	−	0.0872082i
$188$	0.924605	−	4.05096i	0.0674338	−	0.295447i
$189$	−8.49630	+	2.62076i	−0.618015	+	0.190632i
$190$	−6.52739	−	4.45030i	−0.473547	−	0.322859i
$191$	−2.21966	+	0.334559i	−0.160609	+	0.0242079i	−0.228854	−	0.973461i	$-0.573498\pi$
$191$	−2.21966	+	0.334559i	−0.160609	+	0.0242079i	0.0682457	+	0.997669i	$0.478260\pi$
$192$	−1.93416	−	4.92815i	−0.139586	−	0.355659i
$193$	−15.2825	+	7.35968i	−1.10006	+	0.529761i	−0.893678	−	0.448710i	$-0.851884\pi$
$193$	−15.2825	+	7.35968i	−1.10006	+	0.529761i	−0.206383	+	0.978471i	$0.566169\pi$
$194$	−10.7364	+	5.17040i	−0.770831	+	0.371213i
$195$	4.51835	+	11.5126i	0.323566	+	0.824431i
$196$	−0.714394	+	0.107677i	−0.0510281	+	0.00769125i
$197$	−4.64209	−	3.16493i	−0.330736	−	0.225492i	0.386554	−	0.922267i	$-0.373665\pi$
$197$	−4.64209	−	3.16493i	−0.330736	−	0.225492i	−0.717290	+	0.696775i	$0.754618\pi$
$198$	3.26499	−	1.00712i	0.232033	−	0.0715726i
$199$	4.08945	−	17.9170i	0.289893	−	1.27011i	−0.594778	−	0.803890i	$-0.702760\pi$
$199$	4.08945	−	17.9170i	0.289893	−	1.27011i	0.884671	−	0.466216i	$-0.154383\pi$
$200$	6.77254	−	17.2561i	0.478891	−	1.22019i
$201$	0.578740	+	7.72274i	0.0408211	+	0.544720i
$202$	9.69455	−	8.99523i	0.682106	−	0.632902i
$203$	−4.84890	+	3.30592i	−0.340326	+	0.232030i
$204$	0.337199	−	0.422834i	0.0236086	−	0.0296043i
$205$	23.7248	+	22.0134i	1.65701	+	1.53748i
$206$	11.4360	+	1.72369i	0.796781	+	0.120095i
$207$	−3.40137	−	14.9024i	−0.236411	−	1.03579i
$208$	5.23597	+	9.06897i	0.363049	+	0.628820i
$209$	1.29351	−	2.24042i	0.0894738	−	0.154973i
$210$	5.57571	+	1.71988i	0.384761	+	0.118683i
$211$	16.5493	+	20.7522i	1.13930	+	1.42864i	0.887470	+	0.460865i	$0.152461\pi$
$211$	16.5493	+	20.7522i	1.13930	+	1.42864i	0.251830	+	0.967771i	$0.418968\pi$
$212$	0.215415	−	2.87452i	0.0147948	−	0.197423i
$213$	−8.83968	−	4.25697i	−0.605685	−	0.291683i
$214$	10.3465			0.707275
$215$	1.83766	+	21.7088i	0.125328	+	1.48053i
$216$	11.0714			0.753314
$217$	16.9781	+	8.17623i	1.15255	+	0.555038i
$218$	1.20231	−	16.0437i	0.0814308	−	1.08662i
$219$	−2.74553	−	3.44278i	−0.185526	−	0.232642i
$220$	2.98623	+	0.921128i	0.201331	+	0.0621025i
$221$	−3.07669	+	5.32898i	−0.206960	+	0.358466i
$222$	−2.01616	−	3.49208i	−0.135315	−	0.234373i
$223$	−4.19133	−	18.3634i	−0.280672	−	1.22970i	−0.896934	−	0.442164i	$-0.854211\pi$
$223$	−4.19133	−	18.3634i	−0.280672	−	1.22970i	0.616262	−	0.787541i	$-0.288646\pi$
$224$	−10.0833	−	1.51982i	−0.673720	−	0.101547i
$225$	11.4321	+	10.6074i	0.762141	+	0.707163i
$226$	1.52209	−	1.90864i	0.101248	−	0.126961i
$227$	−2.52166	+	1.71924i	−0.167369	+	0.114110i	−0.644108	−	0.764935i	$-0.722771\pi$
$227$	−2.52166	+	1.71924i	−0.167369	+	0.114110i	0.476739	+	0.879045i	$0.341819\pi$
$228$	0.800577	−	0.742827i	0.0530195	−	0.0491949i
$229$	−0.742392	−	9.90653i	−0.0490586	−	0.654642i	−0.966483	−	0.256731i	$-0.917354\pi$
$229$	−0.742392	−	9.90653i	−0.0490586	−	0.654642i	0.917424	−	0.397911i	$-0.130265\pi$
$230$	−7.92176	+	20.1843i	−0.522345	+	1.33091i
$231$	−0.425180	+	1.86284i	−0.0279748	+	0.122566i
$232$	6.98294	−	2.15395i	0.458452	−	0.141414i
$233$	−6.09982	−	4.15878i	−0.399612	−	0.272451i	0.346794	−	0.937941i	$-0.387270\pi$
$233$	−6.09982	−	4.15878i	−0.399612	−	0.272451i	−0.746407	+	0.665490i	$0.768223\pi$
$234$	−16.2280	+	2.44598i	−1.06086	+	0.159899i
$235$	−6.43294	−	16.3909i	−0.419638	−	1.06922i
$236$	−0.662654	+	0.319117i	−0.0431351	+	0.0207728i
$237$	1.38288	−	0.665961i	0.0898278	−	0.0432588i
$238$	1.06064	+	2.70246i	0.0687510	+	0.175175i
$239$	14.7596	−	2.22464i	0.954716	−	0.143900i	0.346833	−	0.937927i	$-0.387257\pi$
$239$	14.7596	−	2.22464i	0.954716	−	0.143900i	0.607883	+	0.794027i	$0.292019\pi$
$240$	−3.22256	−	2.19711i	−0.208015	−	0.141823i
$241$	3.67789	−	1.13448i	0.236914	−	0.0730781i	−0.174025	−	0.984741i	$-0.555677\pi$
$241$	3.67789	−	1.13448i	0.236914	−	0.0730781i	0.410938	+	0.911663i	$0.365201\pi$
$242$	−2.34597	+	10.2784i	−0.150805	+	0.660719i
$243$	−5.23142	+	13.3294i	−0.335596	+	0.855084i
$244$	0.164094	+	2.18969i	0.0105051	+	0.140180i
$245$	−2.24427	+	2.08238i	−0.143381	+	0.133038i
$246$	5.73334	−	3.90892i	0.365544	−	0.249224i
$247$	−7.74737	+	9.71490i	−0.492954	+	0.618144i
$248$	−17.2009	−	15.9601i	−1.09226	−	1.01347i
$249$	−4.55985	−	0.687287i	−0.288969	−	0.0435550i
$250$	−0.846494	−	3.70873i	−0.0535370	−	0.234561i
$251$	−7.11768	−	12.3282i	−0.449264	−	0.778148i	0.549075	−	0.835773i	$-0.314980\pi$
$251$	−7.11768	−	12.3282i	−0.449264	−	0.778148i	−0.998338	+	0.0576258i	$0.981647\pi$
$252$	2.49614	−	4.32345i	0.157242	−	0.272352i
$253$	−6.78504	−	2.09291i	−0.426572	−	0.131580i
$254$	−0.0888726	−	0.111443i	−0.00557636	−	0.00699254i
$255$	0.171268	−	2.28542i	0.0107252	−	0.143118i
$256$	14.0074	+	6.74562i	0.875464	+	0.421601i
$257$	−6.95341			−0.433742			−0.216871	−	0.976200i	$-0.569585\pi$
$257$	−6.95341			−0.433742			−0.216871	+	0.976200i	$0.569585\pi$
$258$	4.62544	+	0.651591i	0.287968	+	0.0405663i
$259$	−13.9562			−0.867194
$260$	−13.5237	−	6.51266i	−0.838702	−	0.403898i
$261$	−0.459419	+	6.13052i	−0.0284373	+	0.379470i
$262$	1.46686	+	1.83939i	0.0906231	+	0.113638i
$263$	6.90646	+	2.13036i	0.425871	+	0.131364i	0.500279	−	0.865864i	$-0.333231\pi$
$263$	6.90646	+	2.13036i	0.425871	+	0.131364i	−0.0744085	+	0.997228i	$0.523707\pi$
$264$	1.18962	−	2.06049i	0.0732162	−	0.126814i
$265$	−6.10768	−	10.5788i	−0.375192	−	0.649851i
$266$	1.30452	+	5.71549i	0.0799854	+	0.350439i
$267$	−0.968823	−	0.146027i	−0.0592910	−	0.00893668i
$268$	−6.89011	−	6.39309i	−0.420880	−	0.390520i
$269$	−2.32631	+	2.91711i	−0.141838	+	0.177859i	−0.847676	−	0.530514i	$-0.821999\pi$
$269$	−2.32631	+	2.91711i	−0.141838	+	0.177859i	0.705838	+	0.708373i	$0.250570\pi$
$270$	10.9166	−	7.44282i	0.664364	−	0.452956i
$271$	−10.5145	+	9.75608i	−0.638713	+	0.592639i	−0.931590	−	0.363511i	$-0.881578\pi$
$271$	−10.5145	+	9.75608i	−0.638713	+	0.592639i	0.292877	+	0.956150i	$0.405387\pi$
$272$	−0.145018	−	1.93514i	−0.00879304	−	0.117335i
$273$	3.35294	−	8.54316i	0.202929	−	0.517056i
$274$	0.151843	−	0.665267i	0.00917317	−	0.0401903i
$275$	6.92248	−	2.13530i	0.417441	−	0.128763i
$276$	−2.47664	−	1.68855i	−0.149076	−	0.101638i
$277$	−25.3438	+	3.81996i	−1.52276	+	0.229519i	−0.856479	−	0.516182i	$-0.827353\pi$
$277$	−25.3438	+	3.81996i	−1.52276	+	0.229519i	−0.666281	+	0.745701i	$0.732115\pi$
$278$	−3.82708	−	9.75125i	−0.229533	−	0.584841i
$279$	17.7855	−	8.56503i	1.06479	−	0.512775i
$280$	−22.6567	+	10.9109i	−1.35399	+	0.652049i
$281$	7.49491	+	19.0967i	0.447109	+	1.13921i	0.959811	+	0.280648i	$0.0905494\pi$
$281$	7.49491	+	19.0967i	0.447109	+	1.13921i	−0.512702	+	0.858567i	$0.671355\pi$
$282$	−3.73308	+	0.562671i	−0.222302	+	0.0335066i
$283$	−0.291221	−	0.198551i	−0.0173113	−	0.0118027i	0.554633	−	0.832095i	$-0.312858\pi$
$283$	−0.291221	−	0.198551i	−0.0173113	−	0.0118027i	−0.571945	+	0.820292i	$0.693811\pi$
$284$	11.3787	−	3.50988i	0.675204	−	0.208273i
$285$	1.02983	−	4.51197i	0.0610017	−	0.267266i
$286$	−2.78515	+	7.09645i	−0.164689	+	0.419622i
$287$	−1.79477	−	23.9496i	−0.105942	−	1.41370i
$288$	−7.83054	+	7.26568i	−0.461419	+	0.428134i
$289$	−13.1039	+	8.93410i	−0.770818	+	0.525535i
$290$	5.43730	−	6.81816i	0.319289	−	0.400376i
$291$	−5.11734	−	4.74820i	−0.299984	−	0.278344i
$292$	5.28472	+	0.796544i	0.309265	+	0.0466142i
$293$	5.80931	+	25.4523i	0.339384	+	1.48694i	0.800357	+	0.599523i	$0.204643\pi$
$293$	5.80931	+	25.4523i	0.339384	+	1.48694i	−0.460974	+	0.887414i	$0.652500\pi$
$294$	0.328205	+	0.568468i	0.0191413	+	0.0331537i
$295$	−1.55838	+	2.69919i	−0.0907322	+	0.157153i
$296$	16.6061	+	5.12230i	0.965209	+	0.297727i
$297$	2.69760	+	3.38268i	0.156530	+	0.196283i
$298$	0.355722	−	4.74678i	0.0206064	−	0.274973i
$299$	30.7273	+	14.7975i	1.77700	+	0.855760i
$300$	3.05821			0.176566
$301$	9.95760	−	12.7366i	0.573947	−	0.734128i
$302$	−4.90330			−0.282153
$303$	6.98011	+	3.36144i	0.400997	+	0.193110i
$304$	0.292843	−	3.90772i	0.0167957	−	0.224123i
$305$	5.80166	+	7.27505i	0.332202	+	0.416568i
$306$	2.90609	+	0.896409i	0.166130	+	0.0512443i
$307$	7.67349	−	13.2909i	0.437949	−	0.758551i	−0.559582	−	0.828775i	$-0.689038\pi$
$307$	7.67349	−	13.2909i	0.437949	−	0.758551i	0.997531	+	0.0702244i	$0.0223715\pi$
$308$	−1.15951	−	2.00834i	−0.0660694	−	0.114436i
$309$	1.50758	+	6.60515i	0.0857634	+	0.375754i
$310$	−27.6897	−	4.17355i	−1.57267	−	0.237042i
$311$	23.6164	+	21.9128i	1.33916	+	1.24256i	0.946431	+	0.322905i	$0.104659\pi$
$311$	23.6164	+	21.9128i	1.33916	+	1.24256i	0.392729	+	0.919654i	$0.371531\pi$
$312$	−7.12515	+	8.93466i	−0.403382	+	0.505826i
$313$	21.6774	−	14.7794i	1.22528	−	0.835380i	0.234665	−	0.972076i	$-0.424601\pi$
$313$	21.6774	−	14.7794i	1.22528	−	0.835380i	0.990613	+	0.136696i	$0.0436484\pi$
$314$	11.3263	−	10.5092i	0.639177	−	0.593070i
$315$	−1.58096	−	21.0964i	−0.0890769	−	1.18865i
$316$	−0.680577	+	1.73408i	−0.0382855	+	0.0975498i
$317$	0.463392	−	2.03025i	0.0260267	−	0.114030i	−0.960246	−	0.279155i	$-0.909946\pi$
$317$	0.463392	−	2.03025i	0.0260267	−	0.114030i	0.986273	+	0.165125i	$0.0528027\pi$
$318$	−2.50267	+	0.771973i	−0.140343	+	0.0432901i
$319$	2.35953	+	1.60870i	0.132108	+	0.0900698i
$320$	26.9243	−	4.05818i	1.50511	−	0.226859i
$321$	2.21438	+	5.64216i	0.123595	+	0.314915i
$322$	14.4971	−	6.98142i	0.807890	−	0.389059i
$323$	2.07461	−	0.999077i	0.115434	−	0.0555901i
$324$	−1.55203	−	3.95451i	−0.0862240	−	0.219695i
$325$	−34.4069	+	5.18601i	−1.90855	+	0.287668i
$326$	1.73667	+	1.18404i	0.0961850	+	0.0655778i
$327$	9.00626	−	2.77806i	0.498047	−	0.153627i
$328$	−6.65460	+	29.1557i	−0.367439	+	1.60986i
$329$	−4.77371	+	12.1632i	−0.263183	+	0.670580i
$330$	−0.212185	−	2.83141i	−0.0116804	−	0.155864i
$331$	−3.94165	+	3.65732i	−0.216653	+	0.201024i	−0.781032	−	0.624492i	$-0.785306\pi$
$331$	−3.94165	+	3.65732i	−0.216653	+	0.201024i	0.564379	+	0.825516i	$0.309116\pi$
$332$	4.62421	−	3.15274i	0.253787	−	0.173029i
$333$	−9.11531	+	11.4302i	−0.499516	+	0.626373i
$334$	−11.2432	−	10.4322i	−0.615202	−	0.570824i
$335$	−39.3857	−	5.93644i	−2.15187	−	0.324342i
$336$	0.644041	+	2.82173i	0.0351353	+	0.153938i
$337$	6.11409	+	10.5899i	0.333055	+	0.576869i	0.983109	−	0.183019i	$-0.0585870\pi$
$337$	6.11409	+	10.5899i	0.333055	+	0.576869i	−0.650054	+	0.759888i	$0.725254\pi$
$338$	11.1406	−	19.2960i	0.605967	−	1.04957i
$339$	1.36658	+	0.421533i	0.0742222	+	0.0228945i
$340$	1.73426	+	2.17470i	0.0940535	+	0.117939i
$341$	0.685262	−	9.14419i	0.0371090	−	0.495186i
$342$	5.53307	+	2.66459i	0.299194	+	0.144084i
$343$	19.5301			1.05453
$344$	−16.5230	+	11.5003i	−0.890859	+	0.620054i
$345$	−12.7023			−0.683869
$346$	−9.46650	−	4.55882i	−0.508922	−	0.245084i
$347$	0.201738	−	2.69200i	0.0108299	−	0.144514i	−0.989168	−	0.146791i	$-0.953106\pi$
$347$	0.201738	−	2.69200i	0.0108299	−	0.144514i	0.999997	+	0.00227647i	$0.000724624\pi$
$348$	0.751654	+	0.942544i	0.0402929	+	0.0505257i
$349$	−7.19519	−	2.21942i	−0.385150	−	0.118803i	0.0961326	−	0.995369i	$-0.469353\pi$
$349$	−7.19519	−	2.21942i	−0.385150	−	0.118803i	−0.481283	+	0.876566i	$0.659829\pi$
$350$	−8.20823	+	14.2171i	−0.438748	+	0.759934i
$351$	−10.3907	−	17.9972i	−0.554613	−	0.960618i
$352$	1.10417	+	4.83766i	0.0588522	+	0.257848i
$353$	5.44003	+	0.819952i	0.289543	+	0.0436416i	0.292208	−	0.956355i	$-0.405610\pi$
$353$	5.44003	+	0.819952i	0.289543	+	0.0436416i	−0.00266456	+	0.999996i	$0.500848\pi$
$354$	0.489859	+	0.454523i	0.0260357	+	0.0241576i
$355$	31.4619	−	39.4520i	1.66983	−	2.09389i
$356$	0.982498	−	0.669855i	0.0520723	−	0.0355023i
$357$	−1.24670	+	1.15677i	−0.0659825	+	0.0612229i
$358$	0.529161	+	7.06116i	0.0279670	+	0.373194i
$359$	−7.75539	+	19.7604i	−0.409314	+	1.04292i	0.566451	+	0.824095i	$0.308316\pi$
$359$	−7.75539	+	19.7604i	−0.409314	+	1.04292i	−0.975765	+	0.218820i	$0.929779\pi$
$360$	−5.86182	+	25.6823i	−0.308945	+	1.35358i
$361$	−13.7126	+	4.22979i	−0.721717	+	0.222620i
$362$	7.86779	+	5.36417i	0.413522	+	0.281935i
$363$	−6.10707	+	0.920493i	−0.320538	+	0.0483134i
$364$	4.06940	+	10.3687i	0.213294	+	0.543465i
$365$	20.4049	−	9.82650i	1.06804	−	0.514342i
$366$	1.79749	−	0.865627i	0.0939565	−	0.0452471i
$367$	4.40104	+	11.2137i	0.229733	+	0.585349i	0.998533	−	0.0541392i	$-0.0172415\pi$
$367$	4.40104	+	11.2137i	0.229733	+	0.585349i	−0.768801	+	0.639488i	$0.779146\pi$
$368$	−10.6353	+	1.60302i	−0.554405	+	0.0835631i
$369$	−20.7872	−	14.1725i	−1.08214	−	0.737789i
$370$	19.8174	−	6.11286i	1.03026	−	0.317792i
$371$	−2.01708	+	8.83742i	−0.104722	+	0.458816i
$372$	1.41426	−	3.60347i	0.0733259	−	0.186831i
$373$	−0.440427	−	5.87708i	−0.0228044	−	0.304304i	−0.996930	−	0.0782968i	$-0.975052\pi$
$373$	−0.440427	−	5.87708i	−0.0228044	−	0.304304i	0.974126	−	0.226007i	$-0.0725672\pi$
$374$	1.03558	−	0.960882i	0.0535488	−	0.0496860i
$375$	1.84127	−	1.25536i	0.0950829	−	0.0648264i
$376$	10.1443	−	12.7206i	0.523155	−	0.656015i
$377$	−10.0550	−	9.32963i	−0.517856	−	0.480501i
$378$	−9.69508	−	1.46130i	−0.498661	−	0.0751611i
$379$	−4.00235	−	17.5354i	−0.205587	−	0.900734i	−0.967463	−	0.253012i	$-0.918579\pi$
$379$	−4.00235	−	17.5354i	−0.205587	−	0.900734i	0.761876	−	0.647722i	$-0.224278\pi$
$380$	2.80845	+	4.86438i	0.144071	+	0.249538i
$381$	0.0417511	−	0.0723150i	0.00213897	−	0.00370481i
$382$	−2.36532	−	0.729606i	−0.121021	−	0.0373299i
$383$	−22.5411	−	28.2656i	−1.15180	−	1.44431i	−0.875489	−	0.483238i	$-0.839461\pi$
$383$	−22.5411	−	28.2656i	−1.15180	−	1.44431i	−0.276308	−	0.961069i	$-0.589111\pi$
$384$	0.0369376	−	0.492899i	0.00188497	−	0.0251531i
$385$	−8.85402	−	4.26387i	−0.451243	−	0.217307i
$386$	−18.7046			−0.952040
$387$	−3.92774	−	16.4742i	−0.199658	−	0.837429i
$388$	8.47254			0.430128
$389$	21.0115	+	10.1186i	1.06532	+	0.513032i	0.882596	−	0.470131i	$-0.155793\pi$
$389$	21.0115	+	10.1186i	1.06532	+	0.513032i	0.182726	+	0.983164i	$0.441508\pi$
$390$	−1.01915	+	13.5997i	−0.0516069	+	0.688646i
$391$	−3.94044	−	4.94115i	−0.199276	−	0.249885i
$392$	−2.70326	−	0.833846i	−0.136535	−	0.0421156i
$393$	−0.689112	+	1.19358i	−0.0347611	+	0.0602080i
$394$	−3.09772	−	5.36540i	−0.156061	−	0.270305i
$395$	1.75661	+	7.69621i	0.0883846	+	0.387238i
$396$	−2.40217	−	0.362069i	−0.120713	−	0.0181946i
$397$	9.30669	+	8.63535i	0.467089	+	0.433396i	0.878275	−	0.478156i	$-0.158695\pi$
$397$	9.30669	+	8.63535i	0.467089	+	0.433396i	−0.411185	+	0.911552i	$0.634885\pi$
$398$	12.6353	−	15.8442i	0.633352	−	0.794198i
$399$	−2.83757	+	1.93462i	−0.142056	+	0.0968521i
$400$	8.04402	−	7.46376i	0.402201	−	0.373188i
$401$	0.288681	+	3.85218i	0.0144160	+	0.192369i	0.999762	+	0.0218027i	$0.00694057\pi$
$401$	0.288681	+	3.85218i	0.0144160	+	0.192369i	−0.985346	+	0.170566i	$0.945440\pi$
$402$	−3.11996	+	7.94954i	−0.155610	+	0.396487i
$403$	−9.80072	+	42.9398i	−0.488209	+	2.13898i
$404$	−8.98503	+	2.77152i	−0.447022	+	0.137888i
$405$	−14.8742	−	10.1410i	−0.739104	−	0.503913i
$406$	−6.39916	+	0.964518i	−0.317585	+	0.0478682i
$407$	2.48111	+	6.32177i	0.122984	+	0.313359i
$408$	1.90799	−	0.918838i	0.0944594	−	0.0454892i
$409$	−11.8839	+	5.72298i	−0.587621	+	0.282983i	−0.703975	−	0.710225i	$-0.748593\pi$
$409$	−11.8839	+	5.72298i	−0.587621	+	0.282983i	0.116355	+	0.993208i	$0.462879\pi$
$410$	13.0386	+	33.2217i	0.643928	+	1.64070i
$411$	0.395280	−	0.0595789i	0.0194977	−	0.00293881i
$412$	−6.79390	−	4.63201i	−0.334712	−	0.228203i
$413$	2.21011	−	0.681727i	0.108752	−	0.0335456i
$414$	3.75074	−	16.4331i	0.184339	−	0.807641i
$415$	8.66475	−	22.0774i	0.425336	−	1.08374i
$416$	−1.78109	−	23.7669i	−0.0873249	−	1.16527i
$417$	4.49846	−	4.17396i	0.220290	−	0.204400i
$418$	2.35705	−	1.60701i	0.115287	−	0.0786013i
$419$	11.9422	−	14.9750i	0.583414	−	0.731578i	−0.399277	−	0.916830i	$-0.630739\pi$
$419$	11.9422	−	14.9750i	0.583414	−	0.731578i	0.982691	+	0.185253i	$0.0593104\pi$
$420$	−3.04113	−	2.82175i	−0.148392	−	0.137687i
$421$	30.1408	+	4.54299i	1.46897	+	0.221412i	0.834275	−	0.551348i	$-0.185887\pi$
$421$	30.1408	+	4.54299i	1.46897	+	0.221412i	0.634698	+	0.772761i	$0.281125\pi$
$422$	6.51305	+	28.5355i	0.317050	+	1.38909i
$423$	6.84390	+	11.8540i	0.332762	+	0.576360i
$424$	5.64365	−	9.77508i	0.274080	−	0.474720i
$425$	6.16152	+	1.90058i	0.298878	+	0.0921915i
$426$	−6.74559	−	8.45870i	−0.326825	−	0.409825i
$427$	0.516019	−	6.88579i	0.0249719	−	0.333227i
$428$	−6.62778	−	3.19177i	−0.320366	−	0.154280i
$429$	−4.46591			−0.215616
$430$	−8.56083	+	22.4472i	−0.412840	+	1.08250i
$431$	−35.9315			−1.73076			−0.865380	−	0.501117i	$-0.832923\pi$
$431$	−35.9315			−1.73076			−0.865380	+	0.501117i	$0.832923\pi$
$432$	5.90470	+	2.84356i	0.284090	+	0.136811i
$433$	−0.437619	+	5.83962i	−0.0210306	+	0.280634i	0.976767	+	0.214304i	$0.0687482\pi$
$433$	−0.437619	+	5.83962i	−0.0210306	+	0.280634i	−0.997798	+	0.0663305i	$0.978871\pi$
$434$	12.9560	+	16.2464i	0.621910	+	0.779850i
$435$	4.88177	+	1.50583i	0.234063	+	0.0721989i
$436$	−5.71945	+	9.90638i	−0.273912	+	0.474430i
$437$	−6.38112	−	11.0524i	−0.305250	−	0.528709i
$438$	−1.08051	−	4.73404i	−0.0516290	−	0.226201i
$439$	19.2178	+	2.89662i	0.917217	+	0.138248i	0.590652	−	0.806927i	$-0.298871\pi$
$439$	19.2178	+	2.89662i	0.917217	+	0.138248i	0.326565	+	0.945175i	$0.394109\pi$
$440$	8.97021	+	8.32314i	0.427638	+	0.396790i
$441$	1.48386	−	1.86070i	0.0706600	−	0.0886048i
$442$	−5.60638	+	3.82236i	−0.266668	+	0.181811i
$443$	−7.50104	+	6.95994i	−0.356385	+	0.330677i	−0.837964	−	0.545726i	$-0.816254\pi$
$443$	−7.50104	+	6.95994i	−0.356385	+	0.330677i	0.481579	+	0.876403i	$0.340064\pi$
$444$	0.214246	+	2.85891i	0.0101677	+	0.135678i
$445$	1.84098	−	4.69075i	0.0872709	−	0.222363i
$446$	4.62184	−	20.2496i	0.218851	−	0.958847i
$447$	2.66464	−	0.821932i	0.126033	−	0.0388760i
$448$	−16.6946	−	11.3822i	−0.788744	−	0.537756i
$449$	−13.5432	+	2.04130i	−0.639142	+	0.0963351i	−0.460615	−	0.887600i	$-0.652371\pi$
$449$	−13.5432	+	2.04130i	−0.639142	+	0.0963351i	−0.178527	+	0.983935i	$0.557133\pi$
$450$	6.28280	+	16.0083i	0.296174	+	0.754640i
$451$	−10.5295	+	5.07072i	−0.495813	+	0.238771i
$452$	−1.56381	+	0.753090i	−0.0735553	+	0.0354224i
$453$	−1.04941	−	2.67386i	−0.0493057	−	0.125629i
$454$	−3.32787	+	0.501596i	−0.156185	+	0.0235411i
$455$	38.9998	+	26.5896i	1.82834	+	1.24654i
$456$	4.08640	−	1.26049i	0.191363	−	0.0590278i
$457$	−2.14851	+	9.41322i	−0.100503	+	0.440332i	0.899491	+	0.436939i	$0.143937\pi$
$457$	−2.14851	+	9.41322i	−0.100503	+	0.440332i	−0.999994	+	0.00339341i	$0.998920\pi$
$458$	4.00221	−	10.1975i	0.187011	−	0.476496i
$459$	0.287786	+	3.84024i	0.0134327	+	0.179247i
$460$	11.3011	−	10.4859i	0.526917	−	0.488908i
$461$	5.55916	−	3.79017i	0.258916	−	0.176526i	−0.426904	−	0.904297i	$-0.640396\pi$
$461$	5.55916	−	3.79017i	0.258916	−	0.176526i	0.685820	+	0.727771i	$0.259444\pi$
$462$	−1.31370	+	1.64732i	−0.0611187	+	0.0766404i
$463$	−4.14568	−	3.84663i	−0.192666	−	0.178768i	0.577941	−	0.816079i	$-0.303856\pi$
$463$	−4.14568	−	3.84663i	−0.192666	−	0.178768i	−0.770607	+	0.637311i	$0.780047\pi$
$464$	4.27742	+	0.644717i	0.198574	+	0.0299303i
$465$	−3.65028	−	15.9929i	−0.169278	−	0.741654i
$466$	−4.07047	−	7.05026i	−0.188561	−	0.326597i
$467$	5.33101	−	9.23357i	0.246690	−	0.427279i	−0.715916	−	0.698187i	$-0.753991\pi$
$467$	5.33101	−	9.23357i	0.246690	−	0.427279i	0.962605	+	0.270908i	$0.0873239\pi$
$468$	11.1499	+	3.43929i	0.515404	+	0.158981i
$469$	18.4286	+	23.1088i	0.850955	+	1.06706i
$470$	1.45101	−	19.3624i	0.0669300	−	0.893119i
$471$	8.15494	+	3.92721i	0.375760	+	0.180956i
$472$	−2.87996			−0.132561
$473$	−7.53961	−	2.24622i	−0.346672	−	0.103281i
$474$	1.69254			0.0777409
$475$	11.7313	+	5.64949i	0.538269	+	0.259216i
$476$	0.154251	−	2.05833i	0.00707008	−	0.0943436i
$477$	5.92050	+	7.42407i	0.271081	+	0.339925i
$478$	15.7282	+	4.85150i	0.719390	+	0.221902i
$479$	5.41065	−	9.37152i	0.247219	−	0.428196i	−0.715534	−	0.698578i	$-0.753817\pi$
$479$	5.41065	−	9.37152i	0.247219	−	0.428196i	0.962753	+	0.270382i	$0.0871500\pi$
$480$	4.43841	+	7.68755i	0.202585	+	0.350887i
$481$	−7.25847	−	31.8014i	−0.330958	−	1.45002i
$482$	4.19682	+	0.632568i	0.191160	+	0.0288127i
$483$	6.90978	+	6.41134i	0.314406	+	0.291726i
$484$	4.67352	−	5.86041i	0.212433	−	0.266382i
$485$	29.6650	−	20.2253i	1.34702	−	0.918382i
$486$	−11.5750	+	10.7400i	−0.525051	+	0.487176i
$487$	1.44501	+	19.2824i	0.0654799	+	0.873768i	0.929148	+	0.369708i	$0.120542\pi$
$487$	1.44501	+	19.2824i	0.0654799	+	0.873768i	−0.863668	+	0.504061i	$0.831839\pi$
$488$	−3.14127	+	8.00383i	−0.142199	+	0.362316i
$489$	−0.273994	+	1.20045i	−0.0123904	+	0.0542861i
$490$	−3.22603	+	0.995097i	−0.145737	+	0.0449539i
$491$	−26.1499	−	17.8287i	−1.18013	−	0.804599i	−0.195750	−	0.980654i	$-0.562714\pi$
$491$	−26.1499	−	17.8287i	−1.18013	−	0.804599i	−0.984380	+	0.176054i	$0.943667\pi$
$492$	−4.87851	+	0.735317i	−0.219940	+	0.0331506i
$493$	0.928633	+	2.36612i	0.0418235	+	0.106565i
$494$	−12.3452	+	5.94514i	−0.555437	+	0.267484i
$495$	−9.27505	+	4.46663i	−0.416883	+	0.200760i
$496$	−5.07458	−	12.9298i	−0.227855	−	0.580566i
$497$	−37.0275	+	5.58100i	−1.66091	+	0.250342i
$498$	−4.20143	−	2.86449i	−0.188271	−	0.128361i
$499$	−9.47408	+	2.92237i	−0.424118	+	0.130823i	−0.499464	−	0.866334i	$-0.666470\pi$
$499$	−9.47408	+	2.92237i	−0.424118	+	0.130823i	0.0753466	+	0.997157i	$0.475994\pi$
$500$	−0.601848	+	2.63687i	−0.0269155	+	0.117924i
$501$	3.28257	−	8.36386i	0.146654	−	0.373670i
$502$	−1.17308	−	15.6536i	−0.0523571	−	0.698656i
$503$	−5.65458	+	5.24668i	−0.252125	+	0.233938i	−0.796102	−	0.605162i	$-0.793108\pi$
$503$	−5.65458	+	5.24668i	−0.252125	+	0.233938i	0.543977	+	0.839100i	$0.316918\pi$
$504$	16.1516	−	11.0119i	0.719447	−	0.490511i
$505$	−24.8434	+	31.1526i	−1.10552	+	1.38627i
$506$	−5.73967	−	5.32563i	−0.255159	−	0.236753i
$507$	12.9068	+	1.94539i	0.573212	+	0.0863978i
$508$	0.0225513	+	0.0988039i	0.00100055	+	0.00438371i
$509$	18.6174	+	32.2464i	0.825204	+	1.42929i	0.901764	+	0.432229i	$0.142273\pi$
$509$	18.6174	+	32.2464i	0.825204	+	1.42929i	−0.0765602	+	0.997065i	$0.524394\pi$
$510$	1.26362	−	2.18865i	0.0559538	−	0.0969149i
$511$	−16.0596	−	4.95375i	−0.710437	−	0.219141i
$512$	11.6432	+	14.6002i	0.514563	+	0.645242i
$513$	−0.581141	+	7.75479i	−0.0256580	+	0.342382i
$514$	−6.90829	−	3.32686i	−0.304712	−	0.146741i
$515$	−34.8449			−1.53545
$516$	−2.76196	−	1.84428i	−0.121588	−	0.0811901i
$517$	6.35828			0.279637
$518$	−13.8656	−	6.67733i	−0.609221	−	0.293385i
$519$	0.459975	−	6.13794i	0.0201907	−	0.269426i
$520$	−36.6457	−	45.9523i	−1.60702	−	2.01514i
$521$	−4.65069	−	1.43455i	−0.203751	−	0.0628487i	0.191200	−	0.981551i	$-0.438762\pi$
$521$	−4.65069	−	1.43455i	−0.203751	−	0.0628487i	−0.394951	+	0.918702i	$0.629238\pi$
$522$	−3.38959	+	5.87094i	−0.148358	+	0.256964i
$523$	4.05474	+	7.02302i	0.177301	+	0.307095i	0.940955	−	0.338531i	$-0.109930\pi$
$523$	4.05474	+	7.02302i	0.177301	+	0.307095i	−0.763654	+	0.645626i	$0.776597\pi$
$524$	−0.372215	−	1.63078i	−0.0162603	−	0.0712410i
$525$	−9.50957	−	1.43334i	−0.415032	−	0.0625559i
$526$	5.84238	+	5.42094i	0.254740	+	0.236364i
$527$	5.08882	−	6.38118i	0.221673	−	0.277969i
$528$	1.16367	−	0.793377i	0.0506422	−	0.0345273i
$529$	−8.81719	+	8.18116i	−0.383356	+	0.355703i
$530$	−1.00662	−	13.4324i	−0.0437247	−	0.583466i
$531$	0.885163	−	2.25536i	0.0384128	−	0.0978742i
$532$	0.927502	−	4.06365i	0.0402123	−	0.176182i
$533$	53.6396	−	16.5456i	2.32339	−	0.716671i
$534$	−0.892671	−	0.608612i	−0.0386296	−	0.0263372i
$535$	−30.8252	+	4.64615i	−1.33269	+	0.200870i
$536$	−13.4462	−	34.2603i	−0.580786	−	1.47982i
$537$	−3.73733	+	1.79980i	−0.161278	+	0.0776672i
$538$	−3.70691	+	1.78515i	−0.159816	+	0.0769635i
$539$	−0.403894	−	1.02911i	−0.0173970	−	0.0443267i
$540$	−9.28897	+	1.40009i	−0.399734	+	0.0602502i
$541$	13.4980	+	9.20276i	0.580323	+	0.395657i	0.817602	−	0.575784i	$-0.195303\pi$
$541$	13.4980	+	9.20276i	0.580323	+	0.395657i	−0.237279	+	0.971442i	$0.576256\pi$
$542$	−15.1141	+	4.66209i	−0.649207	+	0.200254i
$543$	−1.24130	+	5.43850i	−0.0532694	+	0.233389i
$544$	−1.61357	+	4.11131i	−0.0691813	+	0.176271i
$545$	3.62247	+	48.3385i	0.155170	+	2.07060i
$546$	7.41867	−	6.88352i	0.317490	−	0.294587i
$547$	22.1302	−	15.0881i	0.946220	−	0.645122i	0.0112835	−	0.999936i	$-0.496408\pi$
$547$	22.1302	−	15.0881i	0.946220	−	0.645122i	0.934937	+	0.354814i	$0.115456\pi$
$548$	−0.302494	+	0.379315i	−0.0129219	+	0.0162035i
$549$	−5.30250	−	4.92000i	−0.226305	−	0.209980i
$550$	7.89920	+	1.19061i	0.336823	+	0.0507679i
$551$	1.14216	+	5.00415i	0.0486578	+	0.213184i
$552$	−5.86863	−	10.1648i	−0.249785	−	0.432641i
$553$	2.92901	−	5.07320i	0.124554	−	0.215734i
$554$	−27.0070	−	8.33056i	−1.14742	−	0.353932i
$555$	7.57481	+	9.49851i	0.321533	+	0.403189i
$556$	−0.556581	+	7.42705i	−0.0236043	+	0.314977i
$557$	−14.4359	−	6.95199i	−0.611671	−	0.294565i	0.102286	−	0.994755i	$-0.467384\pi$
$557$	−14.4359	−	6.95199i	−0.611671	−	0.294565i	−0.713957	+	0.700190i	$0.753099\pi$
$558$	21.7680			0.921513
$559$	34.2014	+	16.0658i	1.44656	+	0.679512i
$560$	−14.8858			−0.629039
$561$	0.745624	+	0.359074i	0.0314803	+	0.0151601i
$562$	−1.69055	+	22.5588i	−0.0713114	+	0.951584i
$563$	3.02373	+	3.79164i	0.127435	+	0.159799i	0.841456	−	0.540326i	$-0.181699\pi$
$563$	3.02373	+	3.79164i	0.127435	+	0.159799i	−0.714021	+	0.700125i	$0.753128\pi$
$564$	2.56491	+	0.791170i	0.108002	+	0.0333143i
$565$	−3.67764	+	6.36985i	−0.154719	+	0.267982i
$566$	−0.194335	−	0.336598i	−0.00816851	−	0.0141483i
$567$	2.97266	+	13.0241i	0.124840	+	0.546960i
$568$	46.1065	+	6.94943i	1.93458	+	0.291592i
$569$	−20.5386	−	19.0571i	−0.861024	−	0.798913i	0.120006	−	0.992773i	$-0.461709\pi$
$569$	−20.5386	−	19.0571i	−0.861024	−	0.798913i	−0.981029	+	0.193860i	$0.937899\pi$
$570$	3.18190	−	3.98997i	0.133275	−	0.167122i
$571$	4.39256	−	2.99480i	0.183823	−	0.125328i	−0.467912	−	0.883775i	$-0.654994\pi$
$571$	4.39256	−	2.99480i	0.183823	−	0.125328i	0.651735	+	0.758447i	$0.274041\pi$
$572$	3.97327	−	3.68666i	0.166131	−	0.154147i
$573$	−0.108363	−	1.44601i	−0.00452694	−	0.0604078i
$574$	9.67556	−	24.6529i	0.403850	−	1.02899i
$575$	7.95236	−	34.8416i	0.331636	−	1.45299i
$576$	−20.2259	+	6.23888i	−0.842748	+	0.259953i
$577$	0.478277	+	0.326083i	0.0199109	+	0.0135750i	0.573235	−	0.819391i	$-0.305688\pi$
$577$	0.478277	+	0.326083i	0.0199109	+	0.0135750i	−0.553324	+	0.832966i	$0.686641\pi$
$578$	−17.2934	+	2.60656i	−0.719311	+	0.108419i
$579$	−4.00320	−	10.2000i	−0.166367	−	0.423897i
$580$	−5.58634	+	2.69024i	−0.231960	+	0.111706i
$581$	−15.8568	+	7.63621i	−0.657849	+	0.316803i
$582$	−2.81237	−	7.16579i	−0.116576	−	0.297032i
$583$	4.36171	−	0.657422i	0.180644	−	0.0272276i
$584$	17.2908	+	11.7887i	0.715498	+	0.487818i
$585$	47.2494	−	14.5745i	1.95352	−	0.602582i
$586$	−6.40602	+	28.0666i	−0.264630	+	1.15942i
$587$	−12.9290	+	32.9425i	−0.533636	+	1.35968i	0.369060	+	0.929406i	$0.379680\pi$
$587$	−12.9290	+	32.9425i	−0.533636	+	1.35968i	−0.902697	+	0.430278i	$0.858416\pi$
$588$	−0.0348766	−	0.465396i	−0.00143829	−	0.0191926i
$589$	12.0819	−	11.2103i	0.497825	−	0.461914i
$590$	−2.83969	+	1.93607i	−0.116908	+	0.0797067i
$591$	2.26288	−	2.83756i	0.0930823	−	0.116721i
$592$	7.54090	+	6.99694i	0.309929	+	0.287572i
$593$	13.8979	+	2.09477i	0.570719	+	0.0860221i	0.428061	−	0.903750i	$-0.359197\pi$
$593$	13.8979	+	2.09477i	0.570719	+	0.0860221i	0.142658	+	0.989772i	$0.454435\pi$
$594$	1.06165	+	4.65140i	0.0435601	+	0.190849i
$595$	−4.37348	−	7.57509i	−0.179295	−	0.310549i
$596$	−1.69219	+	2.93095i	−0.0693146	+	0.120056i
$597$	11.3444	+	3.49928i	0.464294	+	0.143216i
$598$	23.4481	+	29.4030i	0.958863	+	1.20238i
$599$	0.831581	−	11.0967i	0.0339775	−	0.453398i	−0.954105	−	0.299472i	$-0.903189\pi$
$599$	0.831581	−	11.0967i	0.0339775	−	0.453398i	0.988082	−	0.153925i	$-0.0491916\pi$
$600$	10.7891	+	5.19576i	0.440463	+	0.212116i
$601$	0.417393			0.0170258			0.00851291	−	0.999964i	$-0.497290\pi$
$601$	0.417393			0.0170258			0.00851291	+	0.999964i	$0.497290\pi$
$602$	15.9869	−	7.88980i	0.651575	−	0.321564i
$603$	30.9627			1.26090
$604$	3.14095	+	1.51260i	0.127804	+	0.0615469i
$605$	2.37375	−	31.6755i	0.0965068	−	1.28779i
$606$	5.32654	+	6.67927i	0.216376	+	0.271327i
$607$	−0.457176	−	0.141020i	−0.0185562	−	0.00572383i	0.285463	−	0.958390i	$-0.407853\pi$
$607$	−0.457176	−	0.141020i	−0.0185562	−	0.00572383i	−0.304019	+	0.952666i	$0.598329\pi$
$608$	−4.45935	+	7.72382i	−0.180851	+	0.313242i
$609$	−1.89553	−	3.28315i	−0.0768107	−	0.133040i
$610$	2.28327	+	10.0037i	0.0924469	+	0.405036i
$611$	−30.1986	−	4.55171i	−1.22171	−	0.184143i
$612$	−1.58505	−	1.47071i	−0.0640718	−	0.0594499i
$613$	3.59411	−	4.50687i	0.145165	−	0.182031i	−0.703933	−	0.710266i	$-0.748575\pi$
$613$	3.59411	−	4.50687i	0.145165	−	0.182031i	0.849098	+	0.528235i	$0.177146\pi$
$614$	13.9827	−	9.53327i	0.564297	−	0.384731i
$615$	−15.3259	+	14.2203i	−0.617999	+	0.573419i
$616$	−0.678594	−	9.05521i	−0.0273413	−	0.364845i
$617$	−5.05717	+	12.8854i	−0.203594	+	0.518749i	−0.995805	−	0.0914981i	$-0.970834\pi$
$617$	−5.05717	+	12.8854i	−0.203594	+	0.518749i	0.792211	+	0.610247i	$0.208930\pi$
$618$	−1.66243	+	7.28360i	−0.0668729	+	0.292989i
$619$	−30.6878	+	9.46594i	−1.23345	+	0.380468i	−0.841872	−	0.539678i	$-0.818546\pi$
$619$	−30.6878	+	9.46594i	−1.23345	+	0.380468i	−0.391576	+	0.920146i	$0.628070\pi$
$620$	16.4500	+	11.2154i	0.660646	+	0.450421i
$621$	21.1056	−	3.18116i	0.846938	−	0.127655i
$622$	12.9790	+	33.0699i	0.520409	+	1.32598i
$623$	−3.36905	+	1.62245i	−0.134978	+	0.0650021i
$624$	−6.09481	+	2.93511i	−0.243988	+	0.117498i
$625$	−6.84290	−	17.4354i	−0.273716	−	0.697417i
$626$	28.6079	−	4.31195i	1.14340	−	0.172340i
$627$	1.38079	+	0.941407i	0.0551434	+	0.0375962i
$628$	−10.4973	+	3.23799i	−0.418889	+	0.129210i
$629$	−1.34507	+	5.89314i	−0.0536315	+	0.234975i
$630$	8.52289	−	21.7160i	0.339560	−	0.865185i
$631$	−3.64187	−	48.5974i	−0.144981	−	1.93463i	−0.314804	−	0.949157i	$-0.601939\pi$
$631$	−3.64187	−	48.5974i	−0.144981	−	1.93463i	0.169824	−	0.985474i	$-0.445680\pi$
$632$	−5.34716	+	4.96143i	−0.212698	+	0.197355i
$633$	−14.1670	+	9.65891i	−0.563088	+	0.383907i
$634$	1.43176	−	1.79537i	0.0568624	−	0.0713032i
$635$	0.314819	+	0.292110i	0.0124932	+	0.0115920i
$636$	1.84130	+	0.277532i	0.0730125	+	0.0110049i
$637$	1.18159	+	5.17688i	0.0468162	+	0.205115i
$638$	1.57454	+	2.72718i	0.0623365	+	0.107970i
$639$	−19.6132	+	33.9711i	−0.775886	+	1.34387i
$640$	2.42922	+	0.749314i	0.0960232	+	0.0296192i
$641$	−24.6012	−	30.8490i	−0.971690	−	1.21846i	−0.975844	−	0.218469i	$-0.929894\pi$
$641$	−24.6012	−	30.8490i	−0.971690	−	1.21846i	0.00415371	−	0.999991i	$-0.498678\pi$
$642$	−0.499475	+	6.66503i	−0.0197127	+	0.263048i
$643$	−28.5864	−	13.7665i	−1.12734	−	0.542897i	−0.225186	−	0.974316i	$-0.572299\pi$
$643$	−28.5864	−	13.7665i	−1.12734	−	0.542897i	−0.902152	+	0.431418i	$0.858013\pi$
$644$	−11.4402			−0.450807
$645$	−14.0731	+	0.135803i	−0.554126	+	0.00534726i
$646$	2.53915			0.0999017
$647$	30.3021	+	14.5927i	1.19130	+	0.573699i	0.921183	−	0.389130i	$-0.127224\pi$
$647$	30.3021	+	14.5927i	1.19130	+	0.573699i	0.270114	+	0.962828i	$0.412939\pi$
$648$	1.24310	−	16.5881i	0.0488337	−	0.651640i
$649$	−0.701714	−	0.879922i	−0.0275447	−	0.0345400i
$650$	−36.6649	−	11.3096i	−1.43812	−	0.443600i
$651$	−6.08657	+	10.5422i	−0.238551	+	0.413183i
$652$	−0.747212	−	1.29421i	−0.0292631	−	0.0506851i
$653$	−7.70936	−	33.7769i	−0.301691	−	1.32179i	−0.867574	−	0.497308i	$-0.834322\pi$
$653$	−7.70936	−	33.7769i	−0.301691	−	1.32179i	0.565884	−	0.824485i	$-0.308535\pi$
$654$	10.2770	+	1.54901i	0.401862	+	0.0605710i
$655$	−5.19617	−	4.82134i	−0.203031	−	0.188385i
$656$	−11.0374	+	13.8404i	−0.430937	+	0.540378i
$657$	−14.5463	+	9.91752i	−0.567506	+	0.386919i
$658$	−10.5622	+	9.80032i	−0.411759	+	0.382056i
$659$	1.66762	+	22.2529i	0.0649613	+	0.866849i	0.930567	+	0.366122i	$0.119315\pi$
$659$	1.66762	+	22.2529i	0.0649613	+	0.866849i	−0.865605	+	0.500727i	$0.833066\pi$
$660$	−0.737531	+	1.87920i	−0.0287083	+	0.0731477i
$661$	4.38980	−	19.2330i	0.170744	−	0.748077i	−0.814950	−	0.579531i	$-0.803236\pi$
$661$	4.38980	−	19.2330i	0.170744	−	0.748077i	0.985694	−	0.168546i	$-0.0539071\pi$
$662$	−5.66592	+	1.74771i	−0.220212	+	0.0679265i
$663$	−3.28429	−	2.23919i	−0.127551	−	0.0869630i
$664$	21.6702	−	3.26626i	0.840968	−	0.126755i
$665$	−6.45309	−	16.4422i	−0.250240	−	0.637601i
$666$	−14.5250	+	6.99486i	−0.562831	+	0.271045i
$667$	12.6928	−	6.11252i	0.491466	−	0.236678i
$668$	3.98399	+	10.1510i	0.154145	+	0.392755i
$669$	12.0317	−	1.81348i	0.465171	−	0.0701132i
$670$	−36.2899	−	24.7420i	−1.40200	−	0.955868i
$671$	−3.21082	+	0.990406i	−0.123952	+	0.0382342i
$672$	1.46580	−	6.42210i	0.0565445	−	0.247738i
$673$	6.29767	−	16.0462i	0.242757	−	0.618535i	−0.756619	−	0.653856i	$-0.773150\pi$
$673$	6.29767	−	16.0462i	0.242757	−	0.618535i	0.999376	+	0.0353210i	$0.0112454\pi$
$674$	1.00767	+	13.4465i	0.0388142	+	0.517939i
$675$	−15.9632	+	14.8117i	−0.614423	+	0.570101i
$676$	−13.0890	+	8.92393i	−0.503423	+	0.343228i
$677$	25.8174	−	32.3740i	0.992242	−	1.24423i	0.0225900	−	0.999745i	$-0.492809\pi$
$677$	25.8174	−	32.3740i	0.992242	−	1.24423i	0.969652	−	0.244488i	$-0.0786198\pi$
$678$	1.15603	+	1.07264i	0.0443969	+	0.0411943i
$679$	−26.3456	−	3.97096i	−1.01105	−	0.152391i
$680$	2.42362	+	10.6186i	0.0929417	+	0.407204i
$681$	−0.985767	−	1.70740i	−0.0377747	−	0.0654277i
$682$	5.05586	−	8.75700i	0.193599	−	0.335323i
$683$	3.52745	+	1.08807i	0.134974	+	0.0416339i	0.361506	−	0.932370i	$-0.382263\pi$
$683$	3.52745	+	1.08807i	0.134974	+	0.0416339i	−0.226532	+	0.974004i	$0.572739\pi$
$684$	−2.72238	−	3.41376i	−0.104093	−	0.130528i
$685$	−0.153641	+	2.05020i	−0.00587033	+	0.0783341i
$686$	19.4034	+	9.34420i	0.740827	+	0.356763i
$687$	6.41742			0.244840
$688$	−11.7659	+	1.88971i	−0.448570	+	0.0720446i
$689$	−21.1866			−0.807144
$690$	−12.6199	−	6.07742i	−0.480431	−	0.231364i
$691$	−3.62927	+	48.4292i	−0.138064	+	1.84233i	0.312894	+	0.949788i	$0.398702\pi$
$691$	−3.62927	+	48.4292i	−0.138064	+	1.84233i	−0.450958	+	0.892545i	$0.648918\pi$
$692$	4.65771	+	5.84058i	0.177059	+	0.222025i
$693$	7.29991	+	2.25172i	0.277301	+	0.0855359i
$694$	1.48842	−	2.57802i	0.0564996	−	0.0978602i
$695$	15.7808	+	27.3331i	0.598598	+	1.03680i
$696$	1.05043	+	4.60225i	0.0398166	+	0.174448i
$697$	−10.2860	−	1.55036i	−0.389608	−	0.0587240i
$698$	−6.08663	−	5.64757i	−0.230382	−	0.213764i
$699$	2.97347	−	3.72861i	0.112467	−	0.141029i
$700$	9.64380	−	6.57503i	0.364501	−	0.248513i
$701$	30.4753	−	28.2769i	1.15104	−	1.06801i	0.154239	−	0.988034i	$-0.450707\pi$
$701$	30.4753	−	28.2769i	1.15104	−	1.06801i	0.996797	−	0.0799718i	$-0.0254830\pi$
$702$	−1.71251	−	22.8518i	−0.0646345	−	0.862487i
$703$	−4.45949	+	11.3626i	−0.168193	+	0.428548i
$704$	−2.18787	+	9.58569i	−0.0824585	+	0.361274i
$705$	10.8692	−	3.35270i	0.409358	−	0.126270i
$706$	5.01243	+	3.41741i	0.188645	+	0.128616i
$707$	29.2382	−	4.40694i	1.09961	−	0.165740i
$708$	−0.173579	−	0.442273i	−0.00652352	−	0.0166216i
$709$	20.0646	−	9.66260i	0.753542	−	0.362887i	−0.0173527	−	0.999849i	$-0.505524\pi$
$709$	20.0646	−	9.66260i	0.753542	−	0.362887i	0.770895	+	0.636963i	$0.219810\pi$
$710$	50.1336	−	24.1431i	1.88148	−	0.906074i
$711$	−2.24195	−	5.71239i	−0.0840796	−	0.214231i
$712$	4.60423	−	0.693976i	0.172551	−	0.0260078i
$713$	−37.3761	−	25.4826i	−1.39975	−	0.954332i
$714$	−1.79207	+	0.552781i	−0.0670666	+	0.0206873i
$715$	5.11104	−	22.3929i	0.191142	−	0.837449i
$716$	1.83930	−	4.68647i	0.0687380	−	0.175142i
$717$	0.720559	+	9.61519i	0.0269098	+	0.359086i
$718$	−17.1595	+	15.9216i	−0.640385	+	0.594191i
$719$	−11.2918	+	7.69860i	−0.421112	+	0.287109i	−0.755278	−	0.655405i	$-0.772498\pi$
$719$	−11.2918	+	7.69860i	−0.421112	+	0.287109i	0.334166	+	0.942514i	$0.391546\pi$
$720$	−9.72247	+	12.1916i	−0.362335	+	0.454354i
$721$	18.9549	+	17.5875i	0.705916	+	0.654994i
$722$	−15.6474	−	2.35847i	−0.582336	−	0.0877730i
$723$	0.553259	+	2.42399i	0.0205759	+	0.0901490i
$724$	−3.38517	−	5.86329i	−0.125809	−	0.217907i
$725$	−7.18665	+	12.4476i	−0.266905	+	0.462294i
$726$	−6.50786	−	2.00741i	−0.241529	−	0.0745020i
$727$	−17.9410	−	22.4973i	−0.665393	−	0.834377i	0.328525	−	0.944495i	$-0.393448\pi$
$727$	−17.9410	−	22.4973i	−0.665393	−	0.834377i	−0.993918	+	0.110118i	$0.964877\pi$
$728$	−3.25939	+	43.4935i	−0.120801	+	1.61198i
$729$	6.31158	+	3.03950i	0.233762	+	0.112574i
$730$	24.9740			0.924331
$731$	−4.41849	−	5.43224i	−0.163424	−	0.200919i
$732$	−1.41847			−0.0524282
$733$	−37.8550	−	18.2300i	−1.39821	−	0.673342i	−0.425411	−	0.905000i	$-0.639870\pi$
$733$	−37.8550	−	18.2300i	−1.39821	−	0.673342i	−0.972797	+	0.231659i	$0.925585\pi$
$734$	−0.992696	+	13.2466i	−0.0366411	+	0.488941i
$735$	−1.23308	−	1.54624i	−0.0454830	−	0.0570339i
$736$	23.3913	+	7.21527i	0.862215	+	0.265958i
$737$	7.19143	−	12.4559i	0.264900	−	0.458820i
$738$	−13.8715	−	24.0261i	−0.510617	−	0.884415i
$739$	10.5095	+	46.0449i	0.386597	+	1.69379i	0.676261	+	0.736662i	$0.263599\pi$
$739$	10.5095	+	46.0449i	0.386597	+	1.69379i	−0.289665	+	0.957128i	$0.593544\pi$
$740$	−14.5804	−	2.19763i	−0.535984	−	0.0807867i
$741$	−5.88414	−	5.45968i	−0.216159	−	0.200566i
$742$	−6.23226	+	7.81501i	−0.228794	+	0.286898i
$743$	−34.5776	+	23.5746i	−1.26853	+	0.864870i	−0.995277	−	0.0970725i	$-0.969052\pi$
$743$	−34.5776	+	23.5746i	−1.26853	+	0.864870i	−0.273253	+	0.961942i	$0.588100\pi$
$744$	11.1115	−	10.3100i	0.407369	−	0.377983i
$745$	1.07176	+	14.3017i	0.0392664	+	0.523973i
$746$	2.37432	−	6.04968i	0.0869302	−	0.221494i
$747$	−4.10252	+	17.9743i	−0.150103	+	0.657646i
$748$	−0.959793	+	0.296057i	−0.0350935	+	0.0108249i
$749$	19.1133	+	13.0312i	0.698385	+	0.476151i
$750$	2.42995	−	0.366256i	0.0887293	−	0.0133738i
$751$	0.465270	+	1.18549i	0.0169779	+	0.0432591i	0.939111	−	0.343613i	$-0.111651\pi$
$751$	0.465270	+	1.18549i	0.0169779	+	0.0432591i	−0.922133	+	0.386872i	$0.873556\pi$
$752$	8.67740	−	4.17882i	0.316432	−	0.152386i
$753$	8.28516	−	3.98992i	0.301928	−	0.145401i
$754$	−5.52595	−	14.0799i	−0.201243	−	0.512760i
$755$	14.6083	−	2.20184i	0.531649	−	0.0801333i
$756$	5.75968	+	3.92688i	0.209477	+	0.142819i
$757$	−27.2359	+	8.40115i	−0.989905	+	0.305345i	−0.747087	−	0.664727i	$-0.768548\pi$
$757$	−27.2359	+	8.40115i	−0.989905	+	0.305345i	−0.242818	+	0.970072i	$0.578072\pi$
$758$	4.41345	−	19.3366i	0.160304	−	0.702336i
$759$	1.67575	−	4.26975i	0.0608260	−	0.154982i
$760$	1.64362	+	21.9326i	0.0596204	+	0.795579i
$761$	17.4707	−	16.2105i	0.633313	−	0.587629i	−0.296783	−	0.954945i	$-0.595914\pi$
$761$	17.4707	−	16.2105i	0.633313	−	0.587629i	0.930096	+	0.367316i	$0.119723\pi$
$762$	0.0760794	−	0.0518700i	0.00275606	−	0.00187905i
$763$	22.4278	−	28.1235i	0.811939	−	1.01814i
$764$	1.29010	+	1.19704i	0.0466743	+	0.0433075i
$765$	−9.06056	−	1.36566i	−0.327585	−	0.0493755i
$766$	−8.87115	−	38.8671i	−0.320528	−	1.40432i
$767$	2.70288	+	4.68153i	0.0975954	+	0.169040i
$768$	−5.02159	+	8.69765i	−0.181201	+	0.313849i
$769$	43.8886	+	13.5379i	1.58266	+	0.488187i	0.956556	−	0.291548i	$-0.0941705\pi$
$769$	43.8886	+	13.5379i	1.58266	+	0.488187i	0.626109	+	0.779736i	$0.284647\pi$
$770$	−6.75653	−	8.47242i	−0.243488	−	0.305325i
$771$	0.335673	−	4.47924i	0.0120890	−	0.161316i
$772$	11.9818	+	5.77013i	0.431234	+	0.207671i
$773$	18.2262			0.655551			0.327776	−	0.944756i	$-0.393701\pi$
$773$	18.2262			0.655551			0.327776	+	0.944756i	$0.393701\pi$
$774$	3.97980	−	18.2465i	0.143051	−	0.655857i
$775$	46.1528			1.65786
$776$	29.8904	+	14.3945i	1.07300	+	0.516732i
$777$	0.673728	−	8.99028i	0.0241699	−	0.322524i
$778$	16.0339	+	20.1059i	0.574843	+	0.720830i
$779$	−20.0724	−	6.19150i	−0.719167	−	0.221834i
$780$	4.84817	−	8.39727i	0.173592	−	0.300671i
$781$	9.11076	+	15.7803i	0.326009	+	0.564663i
$782$	−1.55078	−	6.79440i	−0.0554557	−	0.242967i
$783$	−8.48845	−	1.27943i	−0.303352	−	0.0457230i
$784$	−1.22757	−	1.13901i	−0.0438416	−	0.0406791i
$785$	−29.0248	+	36.3959i	−1.03594	+	1.29903i
$786$	−1.25571	+	0.856127i	−0.0447896	+	0.0305370i
$787$	13.8717	−	12.8710i	0.494472	−	0.458803i	−0.393084	−	0.919502i	$-0.628592\pi$
$787$	13.8717	−	12.8710i	0.494472	−	0.458803i	0.887556	+	0.460700i	$0.152402\pi$
$788$	0.329178	+	4.39257i	0.0117265	+	0.156479i
$789$	−1.70574	+	4.34616i	−0.0607260	+	0.154727i
$790$	−1.93704	+	8.48673i	−0.0689168	+	0.301944i
$791$	5.21566	−	1.60882i	0.185448	−	0.0572030i
$792$	−7.85952	−	5.35853i	−0.279276	−	0.190407i
$793$	15.9588	−	2.40540i	0.566713	−	0.0854182i
$794$	5.11473	+	13.0321i	0.181515	+	0.462492i
$795$	7.10950	−	3.42375i	0.252148	−	0.121428i
$796$	−12.9817	+	6.25164i	−0.460123	+	0.221583i
$797$	8.31314	+	21.1815i	0.294466	+	0.750288i	0.999168	+	0.0407843i	$0.0129856\pi$
$797$	8.31314	+	21.1815i	0.294466	+	0.750288i	−0.704702	+	0.709504i	$0.748919\pi$
$798$	−3.74478	+	0.564434i	−0.132564	+	0.0199808i
$799$	4.67597	+	3.18802i	0.165424	+	0.112784i
$800$	−23.8651	+	7.36142i	−0.843760	+	0.260265i
$801$	−0.871655	+	3.81897i	−0.0307984	+	0.134937i
$802$	−1.55627	+	3.96531i	−0.0549538	+	0.140020i
$803$	0.611152	+	8.15526i	0.0215671	+	0.287793i
$804$	4.45091	−	4.12984i	0.156972	−	0.145648i
$805$	−40.0557	+	27.3095i	−1.41178	+	0.962533i
$806$	−30.2817	+	37.9720i	−1.06663	+	1.33751i
$807$	−1.76684	−	1.63939i	−0.0621956	−	0.0577091i
$808$	−36.4072	−	5.48750i	−1.28080	−	0.193050i
$809$	−4.00438	−	17.5443i	−0.140787	−	0.616826i	−0.995253	−	0.0973198i	$-0.968973\pi$
$809$	−4.00438	−	17.5443i	−0.140787	−	0.616826i	0.854467	−	0.519506i	$-0.173884\pi$
$810$	−9.92570	−	17.1918i	−0.348753	−	0.604059i
$811$	5.49259	−	9.51345i	0.192871	−	0.334062i	−0.753329	−	0.657643i	$-0.771553\pi$
$811$	5.49259	−	9.51345i	0.192871	−	0.334062i	0.946201	+	0.323581i	$0.104887\pi$
$812$	4.39671	+	1.35621i	0.154294	+	0.0475935i
$813$	−5.77708	−	7.24423i	−0.202611	−	0.254066i
$814$	−0.559638	+	7.46785i	−0.0196153	+	0.261748i
$815$	−5.70570	−	2.74772i	−0.199862	−	0.0962484i
$816$	1.25358			0.0438839
$817$	−7.18789	−	12.1769i	−0.251473	−	0.426016i
$818$	−14.5450			−0.508552
$819$	−33.0590	−	15.9204i	−1.15517	−	0.556302i
$820$	1.89622	−	25.3033i	0.0662190	−	0.883631i
$821$	25.8105	+	32.3653i	0.900791	+	1.12956i	0.991030	+	0.133636i	$0.0426653\pi$
$821$	25.8105	+	32.3653i	0.900791	+	1.12956i	−0.0902396	+	0.995920i	$0.528763\pi$
$822$	0.421221	+	0.129930i	0.0146918	+	0.00453181i
$823$	14.9966	−	25.9748i	0.522748	−	0.905426i	−0.476902	−	0.878957i	$-0.658240\pi$
$823$	14.9966	−	25.9748i	0.522748	−	0.905426i	0.999650	−	0.0264695i	$-0.00842650\pi$
$824$	−16.0988	−	27.8839i	−0.560827	−	0.971382i
$825$	1.04134	+	4.56240i	0.0362547	+	0.158842i
$826$	2.52194	+	0.380121i	0.0877495	+	0.0132261i
$827$	−5.08513	−	4.71831i	−0.176827	−	0.164072i	0.586794	−	0.809736i	$-0.300390\pi$
$827$	−5.08513	−	4.71831i	−0.176827	−	0.164072i	−0.763621	+	0.645665i	$0.776580\pi$
$828$	−7.47203	+	9.36962i	−0.259671	+	0.325617i
$829$	−23.9390	+	16.3213i	−0.831436	+	0.566863i	−0.902540	−	0.430605i	$-0.858300\pi$
$829$	−23.9390	+	16.3213i	−0.831436	+	0.566863i	0.0711043	+	0.997469i	$0.477348\pi$
$830$	19.1715	−	17.7885i	0.665452	−	0.617449i
$831$	−1.23728	−	16.5103i	−0.0429207	−	0.572738i
$832$	17.2534	−	43.9610i	0.598155	−	1.52407i
$833$	0.218961	−	0.959331i	0.00758655	−	0.0332388i
$834$	6.46631	−	1.99459i	0.223910	−	0.0690670i
$835$	38.1813	+	26.0315i	1.32132	+	0.900859i
$836$	−2.00562	+	0.302298i	−0.0693657	+	0.0104552i
$837$	10.0704	+	25.6590i	0.348084	+	0.886903i
$838$	19.0295	−	9.16413i	0.657363	−	0.316569i
$839$	45.4757	−	21.8999i	1.56999	−	0.756070i	0.572054	−	0.820216i	$-0.306147\pi$
$839$	45.4757	−	21.8999i	1.56999	−	0.756070i	0.997940	+	0.0641464i	$0.0204325\pi$
$840$	−5.93482	−	15.1217i	−0.204771	−	0.521747i
$841$	23.0734	−	3.47775i	0.795633	−	0.119922i
$842$	27.7717	+	18.9344i	0.957074	+	0.652522i
$843$	−12.6635	+	3.90618i	−0.436155	+	0.134536i
$844$	4.63071	−	20.2885i	0.159396	−	0.698357i
$845$	−24.5259	+	62.4909i	−0.843716	+	2.14975i
$846$	1.12796	+	15.0515i	0.0387799	+	0.517482i
$847$	−17.2791	+	16.0327i	−0.593718	+	0.550889i
$848$	5.52053	−	3.76383i	0.189576	−	0.129251i
$849$	0.141961	−	0.178014i	0.00487210	−	0.00610942i
$850$	5.21221	+	4.83623i	0.178777	+	0.165881i
$851$	33.1282	+	4.99327i	1.13562	+	0.171167i
$852$	1.71169	+	7.49939i	0.0586414	+	0.256925i
$853$	−11.4176	−	19.7759i	−0.390933	−	0.677115i	0.601640	−	0.798767i	$-0.294514\pi$
$853$	−11.4176	−	19.7759i	−0.390933	−	0.677115i	−0.992573	+	0.121652i	$0.961181\pi$
$854$	3.80718	−	6.59423i	0.130279	−	0.225650i
$855$	−17.6811	−	5.45389i	−0.604680	−	0.186519i
$856$	−17.9596	−	22.5206i	−0.613846	−	0.769739i
$857$	2.82440	−	37.6890i	0.0964796	−	1.28743i	−0.713368	−	0.700790i	$-0.752831\pi$
$857$	2.82440	−	37.6890i	0.0964796	−	1.28743i	0.809847	−	0.586641i	$-0.199550\pi$
$858$	−4.43693	−	2.13671i	−0.151474	−	0.0729462i
$859$	−33.4445			−1.14111			−0.570556	−	0.821258i	$-0.693272\pi$
$859$	−33.4445			−1.14111			−0.570556	+	0.821258i	$0.693272\pi$
$860$	12.4085	−	11.7383i	0.423128	−	0.400272i
$861$	15.5145			0.528732
$862$	−35.6984	−	17.1914i	−1.21589	−	0.585542i
$863$	2.89858	−	38.6788i	0.0986687	−	1.31664i	−0.699684	−	0.714452i	$-0.746676\pi$
$863$	2.89858	−	38.6788i	0.0986687	−	1.31664i	0.798353	−	0.602190i	$-0.205705\pi$
$864$	−9.29993	−	11.6617i	−0.316390	−	0.396740i
$865$	30.2504	+	9.33103i	1.02855	+	0.317264i
$866$	−3.22875	+	5.59235i	−0.109717	+	0.190036i
$867$	−5.12257	−	8.87256i	−0.173972	−	0.301328i
$868$	−3.28759	−	14.4039i	−0.111588	−	0.488899i
$869$	−2.81874	−	0.424857i	−0.0956192	−	0.0144123i
$870$	4.12964	+	3.83174i	0.140008	+	0.129908i
$871$	−43.0725	+	54.0113i	−1.45946	+	1.83010i
$872$	−37.0083	+	25.2318i	−1.25326	+	0.854457i
$873$	−20.4596	+	18.9837i	−0.692451	+	0.642501i
$874$	−1.05169	−	14.0338i	−0.0355738	−	0.474699i
$875$	3.10732	−	7.91733i	0.105047	−	0.267655i
$876$	−0.768235	+	3.36586i	−0.0259562	+	0.113722i
$877$	−32.7657	+	10.1069i	−1.10642	+	0.341285i	−0.793546	−	0.608510i	$-0.791767\pi$
$877$	−32.7657	+	10.1069i	−1.10642	+	0.341285i	−0.312873	+	0.949795i	$0.601291\pi$
$878$	17.7073	+	12.0726i	0.597591	+	0.407431i
$879$	−16.6763	+	2.51354i	−0.562477	+	0.0847797i
$880$	2.64638	+	6.74286i	0.0892093	+	0.227302i
$881$	−8.04747	+	3.87546i	−0.271126	+	0.130567i	−0.564507	−	0.825428i	$-0.690934\pi$
$881$	−8.04747	+	3.87546i	−0.271126	+	0.130567i	0.293381	+	0.955996i	$0.405220\pi$
$882$	2.36448	−	1.13868i	0.0796163	−	0.0383412i
$883$	−1.33505	−	3.40166i	−0.0449281	−	0.114475i	0.906648	−	0.421887i	$-0.138632\pi$
$883$	−1.33505	−	3.40166i	−0.0449281	−	0.114475i	−0.951576	+	0.307412i	$0.900537\pi$
$884$	4.77048	−	0.719034i	0.160449	−	0.0241837i
$885$	−1.66353	−	1.13418i	−0.0559190	−	0.0381249i
$886$	−10.7824	+	3.32592i	−0.362240	+	0.111736i
$887$	6.91531	−	30.2979i	0.232193	−	1.01731i	−0.715623	−	0.698487i	$-0.753857\pi$
$887$	6.91531	−	30.2979i	0.232193	−	1.01731i	0.947816	−	0.318818i	$-0.103286\pi$
$888$	−4.10133	+	10.4500i	−0.137632	+	0.350680i
$889$	−0.0238160	−	0.317803i	−0.000798764	−	0.0106588i
$890$	4.07333	−	3.77950i	0.136538	−	0.126689i
$891$	5.37108	−	3.66194i	0.179938	−	0.122680i
$892$	−9.20739	+	11.5457i	−0.308286	+	0.386579i
$893$	8.37746	+	7.77315i	0.280341	+	0.260119i
$894$	3.04060	+	0.458297i	0.101693	+	0.0153277i
$895$	−4.74735	−	20.7995i	−0.158686	−	0.695251i
$896$	−0.943234	−	1.63373i	−0.0315112	−	0.0545791i
$897$	−11.0156	+	19.0795i	−0.367799	+	0.637047i
$898$	−14.4320	−	4.45167i	−0.481601	−	0.148554i
$899$	11.3436	+	14.2244i	0.378329	+	0.474409i
$900$	0.913721	−	12.1928i	0.0304574	−	0.406425i
$901$	3.53729	+	1.70347i	0.117844	+	0.0567508i
$902$	−12.8872			−0.429098
$903$	7.72399	+	7.02934i	0.257038	+	0.233922i
$904$	−6.79645			−0.226047
$905$	−25.8491	−	12.4483i	−0.859254	−	0.413795i
$906$	0.236705	−	3.15860i	0.00786399	−	0.104938i
$907$	−36.4324	−	45.6848i	−1.20972	−	1.51694i	−0.794553	−	0.607194i	$-0.792295\pi$
$907$	−36.4324	−	45.6848i	−1.20972	−	1.51694i	−0.415166	−	0.909746i	$-0.636276\pi$
$908$	2.28650	+	0.705293i	0.0758803	+	0.0234060i
$909$	15.4872	−	26.8247i	0.513679	−	0.889718i
$910$	26.0250	+	45.0766i	0.862719	+	1.49427i
$911$	11.7728	+	51.5800i	0.390050	+	1.70892i	0.664473	+	0.747313i	$0.268656\pi$
$911$	11.7728	+	51.5800i	0.390050	+	1.70892i	−0.274422	+	0.961609i	$0.588487\pi$
$912$	2.50314	+	0.377287i	0.0828872	+	0.0124932i
$913$	6.27799	+	5.82513i	0.207771	+	0.192784i
$914$	−6.63833	+	8.32420i	−0.219576	+	0.275340i
$915$	−4.96651	+	3.38611i	−0.164188	+	0.111941i
$916$	−5.70951	+	5.29765i	−0.188648	+	0.175039i
$917$	0.393089	+	5.24541i	0.0129809	+	0.173219i
$918$	−1.55144	+	3.95301i	−0.0512053	+	0.130469i
$919$	2.01670	−	8.83573i	0.0665247	−	0.291464i	−0.930712	−	0.365753i	$-0.880812\pi$
$919$	2.01670	−	8.83573i	0.0665247	−	0.291464i	0.997237	+	0.0742890i	$0.0236687\pi$
$920$	57.6845	−	17.7933i	1.90180	−	0.586628i
$921$	8.19128	+	5.58472i	0.269912	+	0.184023i
$922$	7.33650	−	1.10580i	0.241615	−	0.0364176i
$923$	−31.9749	−	81.4707i	−1.05247	−	2.68164i
$924$	1.34970	−	0.649983i	0.0444020	−	0.0213829i
$925$	−30.7960	+	14.8306i	−1.01257	+	0.487627i
$926$	−2.27836	−	5.80517i	−0.0748716	−	0.190770i
$927$	26.7845	−	4.03711i	0.879719	−	0.132596i
$928$	−8.13443	−	5.54596i	−0.267026	−	0.182055i
$929$	−15.6428	+	4.82516i	−0.513223	+	0.158308i	−0.540540	−	0.841318i	$-0.681780\pi$
$929$	−15.6428	+	4.82516i	−0.513223	+	0.158308i	0.0273167	+	0.999627i	$0.491304\pi$
$930$	4.02522	−	17.6357i	0.131992	−	0.578296i
$931$	0.725949	−	1.84969i	0.0237920	−	0.0606211i
$932$	0.432547	+	5.77194i	0.0141685	+	0.189066i
$933$	−15.2558	+	14.1553i	−0.499453	+	0.463425i
$934$	9.71423	−	6.62305i	0.317859	−	0.216713i
$935$	−2.65380	+	3.32776i	−0.0867886	+	0.108829i
$936$	33.4928	+	31.0768i	1.09475	+	1.01578i
$937$	−4.93971	−	0.744541i	−0.161373	−	0.0243231i	0.0678587	−	0.997695i	$-0.478383\pi$
$937$	−4.93971	−	0.744541i	−0.161373	−	0.0243231i	−0.229232	+	0.973372i	$0.573621\pi$
$938$	7.25267	+	31.7760i	0.236808	+	1.03752i
$939$	8.47411	+	14.6776i	0.276542	+	0.478985i
$940$	−6.90252	+	11.9555i	−0.225135	+	0.389946i
$941$	−1.96260	−	0.605383i	−0.0639790	−	0.0197349i	0.262600	−	0.964905i	$-0.415420\pi$
$941$	−1.96260	−	0.605383i	−0.0639790	−	0.0197349i	−0.326579	+	0.945170i	$0.605896\pi$
$942$	6.22306	+	7.80347i	0.202758	+	0.254251i
$943$	−4.30843	+	57.4920i	−0.140302	+	1.87220i
$944$	−1.53596	−	0.739682i	−0.0499914	−	0.0240746i
$945$	29.5405			0.960953
$946$	−6.41599	−	5.83898i	−0.208602	−	0.189841i
$947$	44.9310			1.46006			0.730031	−	0.683414i	$-0.239505\pi$
$947$	44.9310			1.46006			0.730031	+	0.683414i	$0.239505\pi$
$948$	−1.08421	−	0.522126i	−0.0352134	−	0.0169579i
$949$	2.93546	−	39.1709i	0.0952889	−	1.27154i
$950$	8.95218	+	11.2257i	0.290447	+	0.364209i
$951$	1.28548	+	0.396517i	0.0416844	+	0.0128579i
$952$	4.04121	−	6.99958i	0.130976	−	0.226858i
$953$	30.1466	+	52.2155i	0.976545	+	1.69143i	0.674740	+	0.738056i	$0.264256\pi$
$953$	30.1466	+	52.2155i	0.976545	+	1.69143i	0.301805	+	0.953370i	$0.402411\pi$
$954$	2.33004	+	10.2086i	0.0754378	+	0.330514i
$955$	7.37458	+	1.11154i	0.238636	+	0.0359686i
$956$	−8.57852	−	7.95970i	−0.277449	−	0.257435i
$957$	−1.15020	+	1.44230i	−0.0371805	+	0.0466229i
$958$	9.85935	−	6.72199i	0.318541	−	0.217178i
$959$	1.11839	−	1.03772i	0.0361147	−	0.0335096i
$960$	1.31444	+	17.5400i	0.0424234	+	0.566101i
$961$	10.0177	−	25.5246i	0.323150	−	0.823374i
$962$	8.00402	−	35.0679i	0.258060	−	1.13064i
$963$	23.1563	−	7.14278i	0.746202	−	0.230173i
$964$	−2.49326	−	1.69987i	−0.0803023	−	0.0547492i
$965$	55.7262	−	8.39937i	1.79389	−	0.270385i
$966$	3.79744	+	9.67573i	0.122181	+	0.311312i
$967$	−38.2384	+	18.4147i	−1.22966	+	0.592175i	−0.931987	−	0.362491i	$-0.881926\pi$
$967$	−38.2384	+	18.4147i	−1.22966	+	0.592175i	−0.297677	+	0.954667i	$0.596212\pi$
$968$	26.4444	−	12.7349i	0.849955	−	0.409317i
$969$	0.543434	+	1.38465i	0.0174576	+	0.0444813i
$970$	39.1493	−	5.90081i	1.25701	−	0.189464i
$971$	−2.07167	−	1.41244i	−0.0664832	−	0.0453275i	0.529622	−	0.848234i	$-0.322334\pi$
$971$	−2.07167	−	1.41244i	−0.0664832	−	0.0453275i	−0.596106	+	0.802906i	$0.703286\pi$
$972$	10.7278	−	3.30910i	0.344095	−	0.106139i
$973$	5.21166	−	22.8338i	0.167078	−	0.732017i
$974$	−7.79002	+	19.8487i	−0.249608	+	0.635992i
$975$	−1.67974	−	22.4146i	−0.0537947	−	0.717841i
$976$	−3.73101	+	3.46188i	−0.119427	+	0.110812i
$977$	13.1561	−	8.96965i	0.420900	−	0.286965i	−0.334291	−	0.942470i	$-0.608497\pi$
$977$	13.1561	−	8.96965i	0.420900	−	0.286965i	0.755190	+	0.655505i	$0.227544\pi$
$978$	−0.846570	+	1.06157i	−0.0270703	+	0.0339451i
$979$	1.33387	+	1.23765i	0.0426308	+	0.0395556i
$980$	2.37350	+	0.357748i	0.0758187	+	0.0114278i
$981$	−8.38500	−	36.7371i	−0.267712	−	1.17292i
$982$	−17.4501	−	30.2245i	−0.556856	−	0.964503i
$983$	18.2286	−	31.5728i	0.581402	−	1.00702i	−0.413912	−	0.910317i	$-0.635838\pi$
$983$	18.2286	−	31.5728i	0.581402	−	1.00702i	0.995314	−	0.0967001i	$-0.0308288\pi$
$984$	−18.4603	−	5.69424i	−0.588492	−	0.181526i
$985$	11.6383	+	14.5940i	0.370827	+	0.465002i
$986$	−0.209462	+	2.79507i	−0.00667062	+	0.0890133i
$987$	−7.60485	−	3.66230i	−0.242065	−	0.116572i
$988$	9.74208			0.309937
$989$	−28.1936	+	26.6707i	−0.896505	+	0.848079i
$990$	−11.3519			−0.360788
$991$	45.1912	+	21.7629i	1.43555	+	0.691322i	0.980020	−	0.198900i	$-0.0637369\pi$
$991$	45.1912	+	21.7629i	1.43555	+	0.691322i	0.455526	+	0.890222i	$0.349451\pi$
$992$	−2.36243	+	31.5245i	−0.0750073	+	1.00090i
$993$	−2.16569	−	2.71569i	−0.0687260	−	0.0861797i
$994$	−39.4575	−	12.1710i	−1.25152	−	0.386042i
$995$	−30.5292	+	52.8782i	−0.967841	+	1.67635i
$996$	1.80770	+	3.13102i	0.0572790	+	0.0992102i
$997$	−8.53399	−	37.3899i	−0.270274	−	1.18415i	−0.909690	−	0.415288i	$-0.863681\pi$
$997$	−8.53399	−	37.3899i	−0.270274	−	1.18415i	0.639416	−	0.768861i	$-0.279176\pi$
$998$	−10.8108	−	1.62947i	−0.342210	−	0.0515799i
$999$	−14.9648	−	13.8853i	−0.473464	−	0.439310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.40.3	yes	36
3.2	odd	2		387.2.y.c.298.1		36
4.3	odd	2		688.2.bg.c.513.2		36
43.10	even	21		1849.2.a.n.1.7		18
43.14	even	21	inner	43.2.g.a.14.3	✓	36
43.33	odd	42		1849.2.a.o.1.12		18
129.14	odd	42		387.2.y.c.100.1		36
172.143	odd	42		688.2.bg.c.401.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.14.3	✓	36	43.14	even	21	inner
43.2.g.a.40.3	yes	36	1.1	even	1	trivial
387.2.y.c.100.1		36	129.14	odd	42
387.2.y.c.298.1		36	3.2	odd	2
688.2.bg.c.401.2		36	172.143	odd	42
688.2.bg.c.513.2		36	4.3	odd	2
1849.2.a.n.1.7		18	43.10	even	21
1849.2.a.o.1.12		18	43.33	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.993512 + 0.478450i) q^{2} +(-0.0482746 + 0.644179i) q^{3} +(-0.488828 - 0.612971i) q^{4} +(-3.17479 - 0.979294i) q^{5} +(-0.356169 + 0.616903i) q^{6} +(1.23273 + 2.13515i) q^{7} +(-0.683135 - 2.99301i) q^{8} +(2.55386 + 0.384932i) q^{9} +O(q^{10})\)	\(q+(0.993512 + 0.478450i) q^{2} +(-0.0482746 + 0.644179i) q^{3} +(-0.488828 - 0.612971i) q^{4} +(-3.17479 - 0.979294i) q^{5} +(-0.356169 + 0.616903i) q^{6} +(1.23273 + 2.13515i) q^{7} +(-0.683135 - 2.99301i) q^{8} +(2.55386 + 0.384932i) q^{9} +(-2.68565 - 2.49192i) q^{10} +(0.748014 - 0.937980i) q^{11} +(0.418461 - 0.285302i) q^{12} +(-4.22417 + 3.91945i) q^{13} +(0.203169 + 2.71110i) q^{14} +(0.784103 - 1.99786i) q^{15} +(0.404382 - 1.77171i) q^{16} +(1.02040 - 0.314752i) q^{17} +(2.35312 + 1.60433i) q^{18} +(2.13226 - 0.321387i) q^{19} +(0.951649 + 2.42476i) q^{20} +(-1.43493 + 0.691027i) q^{21} +(1.19194 - 0.574007i) q^{22} +(-2.16225 - 5.50933i) q^{23} +(1.96101 - 0.295575i) q^{24} +(4.98911 + 3.40152i) q^{25} +(-6.07203 + 1.87297i) q^{26} +(-0.802487 + 3.51593i) q^{27} +(0.706193 - 1.79935i) q^{28} +(0.177883 + 2.37368i) q^{29} +(1.73489 - 1.60975i) q^{30} +(6.31519 - 4.30562i) q^{31} +(-2.57877 + 3.23367i) q^{32} +(0.568117 + 0.527136i) q^{33} +(1.16437 + 0.175501i) q^{34} +(-1.82273 - 7.98588i) q^{35} +(-1.01244 - 1.75360i) q^{36} +(-2.83033 + 4.90228i) q^{37} +(2.27220 + 0.700880i) q^{38} +(-2.32091 - 2.91033i) q^{39} +(-0.762225 + 10.1712i) q^{40} +(-8.77658 - 4.22658i) q^{41} -1.75624 q^{42} +(-2.45449 - 6.08075i) q^{43} -0.940604 q^{44} +(-7.73101 - 3.72306i) q^{45} +(0.487716 - 6.50812i) q^{46} +(3.30437 + 4.14355i) q^{47} +(1.12178 + 0.346023i) q^{48} +(0.460743 - 0.798031i) q^{49} +(3.32928 + 5.76649i) q^{50} +(0.153497 + 0.672515i) q^{51} +(4.46740 + 0.673352i) q^{52} +(2.69519 + 2.50077i) q^{53} +(-2.47948 + 3.10917i) q^{54} +(-3.29335 + 2.24537i) q^{55} +(5.54842 - 5.14818i) q^{56} +(0.104097 + 1.38907i) q^{57} +(-0.958961 + 2.44339i) q^{58} +(0.208748 - 0.914583i) q^{59} +(-1.60792 + 0.495978i) q^{60} +(-2.31407 - 1.57771i) q^{61} +(8.33425 - 1.25619i) q^{62} +(2.32633 + 5.92739i) q^{63} +(-7.38381 + 3.55585i) q^{64} +(17.2492 - 8.30676i) q^{65} +(0.312223 + 0.795532i) q^{66} +(11.8546 - 1.78679i) q^{67} +(-0.691734 - 0.471616i) q^{68} +(3.65338 - 1.12692i) q^{69} +(2.00995 - 8.80616i) q^{70} +(-5.54884 + 14.1382i) q^{71} +(-0.592523 - 7.90668i) q^{72} +(-4.99699 + 4.63653i) q^{73} +(-5.15747 + 3.51630i) q^{74} +(-2.43203 + 3.04967i) q^{75} +(-1.23931 - 1.14991i) q^{76} +(2.92483 + 0.440848i) q^{77} +(-0.913405 - 4.00189i) q^{78} +(-1.18802 - 2.05771i) q^{79} +(-3.01886 + 5.22882i) q^{80} +(5.17773 + 1.59712i) q^{81} +(-6.69743 - 8.39832i) q^{82} +(-0.533459 + 7.11852i) q^{83} +(1.12501 + 0.541778i) q^{84} -3.54780 q^{85} +(0.470767 - 7.21565i) q^{86} -1.53767 q^{87} +(-3.31838 - 1.59805i) q^{88} +(-0.113343 + 1.51246i) q^{89} +(-5.89955 - 7.39780i) q^{90} +(-13.5759 - 4.18761i) q^{91} +(-2.32009 + 4.01851i) q^{92} +(2.46873 + 4.27597i) q^{93} +(1.30045 + 5.69764i) q^{94} +(-7.08423 - 1.06778i) q^{95} +(-1.95858 - 1.81729i) q^{96} +(-6.73777 + 8.44890i) q^{97} +(0.839572 - 0.572410i) q^{98} +(2.27138 - 2.10753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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