LMFDB - Embedded newform 43.2.g.a.9.2

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			9.2
Character	$\chi$	$=$	43.9
Dual form			43.2.g.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11243 - 1.39495i) q^{2} +(-2.93359 - 0.442167i) q^{3} +(-0.263330 + 1.15372i) q^{4} +(-0.492700 - 0.335917i) q^{5} +(2.64662 + 4.58409i) q^{6} +(2.18154 - 3.77854i) q^{7} +(-1.31271 + 0.632167i) q^{8} +(5.54371 + 1.71001i) q^{9} +O(q^{10})$	\(q+(-1.11243 - 1.39495i) q^{2} +(-2.93359 - 0.442167i) q^{3} +(-0.263330 + 1.15372i) q^{4} +(-0.492700 - 0.335917i) q^{5} +(2.64662 + 4.58409i) q^{6} +(2.18154 - 3.77854i) q^{7} +(-1.31271 + 0.632167i) q^{8} +(5.54371 + 1.71001i) q^{9} +(0.0795092 + 1.06098i) q^{10} +(-0.452993 - 1.98469i) q^{11} +(1.28264 - 3.26811i) q^{12} +(-0.130264 + 1.73826i) q^{13} +(-7.69769 + 1.16024i) q^{14} +(1.29685 + 1.20330i) q^{15} +(4.47454 + 2.15483i) q^{16} +(1.21261 - 0.826746i) q^{17} +(-3.78164 - 9.63546i) q^{18} +(-2.07906 + 0.641305i) q^{19} +(0.517297 - 0.479982i) q^{20} +(-8.07048 + 10.1201i) q^{21} +(-2.26462 + 2.83974i) q^{22} +(1.99563 - 1.85167i) q^{23} +(4.13047 - 1.27408i) q^{24} +(-1.69679 - 4.32336i) q^{25} +(2.56969 - 1.75199i) q^{26} +(-7.48807 - 3.60606i) q^{27} +(3.78492 + 3.51189i) q^{28} +(7.48963 - 1.12888i) q^{29} +(0.235882 - 3.14762i) q^{30} +(-0.208229 + 0.530558i) q^{31} +(-1.32334 - 5.79793i) q^{32} +(0.451329 + 6.02256i) q^{33} +(-2.50222 - 0.771833i) q^{34} +(-2.34412 + 1.12887i) q^{35} +(-3.43270 + 5.94561i) q^{36} +(1.98083 + 3.43090i) q^{37} +(3.20740 + 2.18677i) q^{38} +(1.15074 - 5.04173i) q^{39} +(0.859126 + 0.129492i) q^{40} +(1.32534 + 1.66193i) q^{41} +23.0949 q^{42} +(3.81986 + 5.32998i) q^{43} +2.40907 q^{44} +(-2.15696 - 2.70475i) q^{45} +(-4.80299 - 0.723935i) q^{46} +(-2.08348 + 9.12834i) q^{47} +(-12.1737 - 8.29987i) q^{48} +(-6.01823 - 10.4239i) q^{49} +(-4.14329 + 7.17639i) q^{50} +(-3.92287 + 1.88915i) q^{51} +(-1.97117 - 0.608024i) q^{52} +(-0.441351 - 5.88942i) q^{53} +(3.29971 + 14.4570i) q^{54} +(-0.443502 + 1.13002i) q^{55} +(-0.475058 + 6.33921i) q^{56} +(6.38267 - 0.962032i) q^{57} +(-9.90645 - 9.19184i) q^{58} +(-4.60418 - 2.21726i) q^{59} +(-1.72977 + 1.17934i) q^{60} +(-3.57526 - 9.10961i) q^{61} +(0.971743 - 0.299743i) q^{62} +(18.5551 - 17.2167i) q^{63} +(-0.422726 + 0.530082i) q^{64} +(0.648092 - 0.812681i) q^{65} +(7.89909 - 7.32929i) q^{66} +(-0.506577 + 0.156258i) q^{67} +(0.634519 + 1.61673i) q^{68} +(-6.67310 + 4.54964i) q^{69} +(4.18239 + 2.01413i) q^{70} +(3.91319 + 3.63091i) q^{71} +(-8.35828 + 1.25981i) q^{72} +(-1.05058 + 14.0191i) q^{73} +(2.58239 - 6.57982i) q^{74} +(3.06604 + 13.4332i) q^{75} +(-0.192410 - 2.56753i) q^{76} +(-8.48745 - 2.61803i) q^{77} +(-8.31309 + 4.00337i) q^{78} +(-1.82633 + 3.16330i) q^{79} +(-1.48076 - 2.56476i) q^{80} +(5.99228 + 4.08546i) q^{81} +(0.843946 - 3.69757i) q^{82} +(10.2305 + 1.54199i) q^{83} +(-9.55055 - 11.9760i) q^{84} -0.875173 q^{85} +(3.18571 - 11.2578i) q^{86} -22.4706 q^{87} +(1.84930 + 2.31895i) q^{88} +(5.97021 + 0.899865i) q^{89} +(-1.37350 + 6.01770i) q^{90} +(6.28390 + 4.28429i) q^{91} +(1.61081 + 2.79000i) q^{92} +(0.845453 - 1.46437i) q^{93} +(15.0513 - 7.24833i) q^{94} +(1.23978 + 0.382420i) q^{95} +(1.31848 + 17.5939i) q^{96} +(-2.28198 - 9.99799i) q^{97} +(-7.84589 + 19.9910i) q^{98} +(0.882576 - 11.7772i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−1.11243	−	1.39495i	−0.786610	−	0.986378i	−0.999956	−	0.00940101i	$-0.997008\pi$
$2$	−1.11243	−	1.39495i	−0.786610	−	0.986378i	0.213346	−	0.976977i	$-0.431564\pi$
$3$	−2.93359	−	0.442167i	−1.69371	−	0.255285i	−0.769906	−	0.638157i	$-0.779697\pi$
$3$	−2.93359	−	0.442167i	−1.69371	−	0.255285i	−0.923802	+	0.382872i	$0.874935\pi$
$4$	−0.263330	+	1.15372i	−0.131665	+	0.576861i
$5$	−0.492700	−	0.335917i	−0.220342	−	0.150227i	0.448119	−	0.893974i	$-0.352094\pi$
$5$	−0.492700	−	0.335917i	−0.220342	−	0.150227i	−0.668461	+	0.743747i	$0.733047\pi$
$6$	2.64662	+	4.58409i	1.08048	+	1.87145i
$7$	2.18154	−	3.77854i	0.824544	−	1.42815i	−0.0777227	−	0.996975i	$-0.524765\pi$
$7$	2.18154	−	3.77854i	0.824544	−	1.42815i	0.902267	−	0.431178i	$-0.141902\pi$
$8$	−1.31271	+	0.632167i	−0.464112	+	0.223505i
$9$	5.54371	+	1.71001i	1.84790	+	0.570003i
$10$	0.0795092	+	1.06098i	0.0251430	+	0.335510i
$11$	−0.452993	−	1.98469i	−0.136582	−	0.598407i	−0.996171	−	0.0874207i	$-0.972138\pi$
$11$	−0.452993	−	1.98469i	−0.136582	−	0.598407i	0.859589	−	0.510986i	$-0.170720\pi$
$12$	1.28264	−	3.26811i	0.370266	−	0.943422i
$13$	−0.130264	+	1.73826i	−0.0361289	+	0.482106i	0.949566	+	0.313567i	$0.101524\pi$
$13$	−0.130264	+	1.73826i	−0.0361289	+	0.482106i	−0.985695	+	0.168539i	$0.946095\pi$
$14$	−7.69769	+	1.16024i	−2.05729	+	0.310087i
$15$	1.29685	+	1.20330i	0.334844	+	0.310690i
$16$	4.47454	+	2.15483i	1.11864	+	0.538706i
$17$	1.21261	−	0.826746i	0.294102	−	0.200515i	−0.407275	−	0.913305i	$-0.633521\pi$
$17$	1.21261	−	0.826746i	0.294102	−	0.200515i	0.701378	+	0.712790i	$0.252569\pi$
$18$	−3.78164	−	9.63546i	−0.891341	−	2.27110i
$19$	−2.07906	+	0.641305i	−0.476969	+	0.147125i	−0.523912	−	0.851772i	$-0.675528\pi$
$19$	−2.07906	+	0.641305i	−0.476969	+	0.147125i	0.0469436	+	0.998898i	$0.485052\pi$
$20$	0.517297	−	0.479982i	0.115671	−	0.107327i
$21$	−8.07048	+	10.1201i	−1.76112	+	2.20838i
$22$	−2.26462	+	2.83974i	−0.482818	+	0.605434i
$23$	1.99563	−	1.85167i	0.416117	−	0.386100i	−0.444143	−	0.895956i	$-0.646492\pi$
$23$	1.99563	−	1.85167i	0.416117	−	0.386100i	0.860260	+	0.509856i	$0.170301\pi$
$24$	4.13047	−	1.27408i	0.843128	−	0.260071i
$25$	−1.69679	−	4.32336i	−0.339358	−	0.864671i
$26$	2.56969	−	1.75199i	0.503958	−	0.343593i
$27$	−7.48807	−	3.60606i	−1.44108	−	0.693987i
$28$	3.78492	+	3.51189i	0.715283	+	0.663685i
$29$	7.48963	−	1.12888i	1.39079	−	0.209628i	0.589434	−	0.807817i	$-0.299351\pi$
$29$	7.48963	−	1.12888i	1.39079	−	0.209628i	0.801355	+	0.598189i	$0.204113\pi$
$30$	0.235882	−	3.14762i	0.0430659	−	0.574675i
$31$	−0.208229	+	0.530558i	−0.0373990	+	0.0952911i	−0.948353	−	0.317217i	$-0.897252\pi$
$31$	−0.208229	+	0.530558i	−0.0373990	+	0.0952911i	0.910954	+	0.412508i	$0.135347\pi$
$32$	−1.32334	−	5.79793i	−0.233936	−	1.02494i
$33$	0.451329	+	6.02256i	0.0785662	+	1.04839i
$34$	−2.50222	−	0.771833i	−0.429128	−	0.132368i
$35$	−2.34412	+	1.12887i	−0.396228	+	0.190813i
$36$	−3.43270	+	5.94561i	−0.572116	+	0.990934i
$37$	1.98083	+	3.43090i	0.325647	+	0.564037i	0.981643	−	0.190727i	$-0.0610846\pi$
$37$	1.98083	+	3.43090i	0.325647	+	0.564037i	−0.655996	+	0.754764i	$0.727751\pi$
$38$	3.20740	+	2.18677i	0.520310	+	0.354741i
$39$	1.15074	−	5.04173i	0.184266	−	0.807324i
$40$	0.859126	+	0.129492i	0.135840	+	0.0204746i
$41$	1.32534	+	1.66193i	0.206984	+	0.259549i	0.874478	−	0.485066i	$-0.161204\pi$
$41$	1.32534	+	1.66193i	0.206984	+	0.259549i	−0.667494	+	0.744615i	$0.732633\pi$
$42$	23.0949			3.56361
$43$	3.81986	+	5.32998i	0.582523	+	0.812814i
$43$	3.81986	+	5.32998i	0.582523	+	0.812814i
$44$	2.40907			0.363181
$45$	−2.15696	−	2.70475i	−0.321541	−	0.403200i
$46$	−4.80299	−	0.723935i	−0.708163	−	0.106738i
$47$	−2.08348	+	9.12834i	−0.303907	+	1.33151i	0.560266	+	0.828312i	$0.310699\pi$
$47$	−2.08348	+	9.12834i	−0.303907	+	1.33151i	−0.864174	+	0.503193i	$0.832158\pi$
$48$	−12.1737	−	8.29987i	−1.75712	−	1.19798i
$49$	−6.01823	−	10.4239i	−0.859747	−	1.48913i
$50$	−4.14329	+	7.17639i	−0.585950	+	1.01489i
$51$	−3.92287	+	1.88915i	−0.549312	+	0.264535i
$52$	−1.97117	−	0.608024i	−0.273351	−	0.0843178i
$53$	−0.441351	−	5.88942i	−0.0606242	−	0.808974i	−0.941797	−	0.336181i	$-0.890865\pi$
$53$	−0.441351	−	5.88942i	−0.0606242	−	0.808974i	0.881173	−	0.472794i	$-0.156754\pi$
$54$	3.29971	+	14.4570i	0.449034	+	1.96735i
$55$	−0.443502	+	1.13002i	−0.0598017	+	0.152372i
$56$	−0.475058	+	6.33921i	−0.0634823	+	0.847113i
$57$	6.38267	−	0.962032i	0.845405	−	0.127424i
$58$	−9.90645	−	9.19184i	−1.30078	−	1.20695i
$59$	−4.60418	−	2.21726i	−0.599413	−	0.288662i	0.109468	−	0.993990i	$-0.465085\pi$
$59$	−4.60418	−	2.21726i	−0.599413	−	0.288662i	−0.708881	+	0.705328i	$0.750800\pi$
$60$	−1.72977	+	1.17934i	−0.223312	+	0.152252i
$61$	−3.57526	−	9.10961i	−0.457765	−	1.16637i	−0.954433	−	0.298426i	$-0.903539\pi$
$61$	−3.57526	−	9.10961i	−0.457765	−	1.16637i	0.496668	−	0.867941i	$-0.334557\pi$
$62$	0.971743	−	0.299743i	0.123411	−	0.0380674i
$63$	18.5551	−	17.2167i	2.33773	−	2.16910i
$64$	−0.422726	+	0.530082i	−0.0528407	+	0.0662602i
$65$	0.648092	−	0.812681i	0.0803859	−	0.100801i
$66$	7.89909	−	7.32929i	0.972311	−	0.902173i
$67$	−0.506577	+	0.156258i	−0.0618882	+	0.0190900i	−0.325545	−	0.945527i	$-0.605548\pi$
$67$	−0.506577	+	0.156258i	−0.0618882	+	0.0190900i	0.263656	+	0.964617i	$0.415071\pi$
$68$	0.634519	+	1.61673i	0.0769467	+	0.196057i
$69$	−6.67310	+	4.54964i	−0.803347	+	0.547712i
$70$	4.18239	+	2.01413i	0.499891	+	0.240735i
$71$	3.91319	+	3.63091i	0.464410	+	0.430910i	0.877352	−	0.479848i	$-0.159308\pi$
$71$	3.91319	+	3.63091i	0.464410	+	0.430910i	−0.412941	+	0.910758i	$0.635499\pi$
$72$	−8.35828	+	1.25981i	−0.985033	+	0.148470i
$73$	−1.05058	+	14.0191i	−0.122961	+	1.64081i	0.505401	+	0.862885i	$0.331345\pi$
$73$	−1.05058	+	14.0191i	−0.122961	+	1.64081i	−0.628362	+	0.777921i	$0.716274\pi$
$74$	2.58239	−	6.57982i	0.300196	−	0.764888i
$75$	3.06604	+	13.4332i	0.354036	+	1.55113i
$76$	−0.192410	−	2.56753i	−0.0220709	−	0.294516i
$77$	−8.48745	−	2.61803i	−0.967234	−	0.298352i
$78$	−8.31309	+	4.00337i	−0.941272	+	0.453293i
$79$	−1.82633	+	3.16330i	−0.205478	+	0.355899i	−0.950285	−	0.311381i	$-0.899208\pi$
$79$	−1.82633	+	3.16330i	−0.205478	+	0.355899i	0.744807	+	0.667280i	$0.232542\pi$
$80$	−1.48076	−	2.56476i	−0.165554	−	0.286748i
$81$	5.99228	+	4.08546i	0.665809	+	0.453941i
$82$	0.843946	−	3.69757i	0.0931983	−	0.408328i
$83$	10.2305	+	1.54199i	1.12294	+	0.169256i	0.684155	−	0.729337i	$-0.260171\pi$
$83$	10.2305	+	1.54199i	1.12294	+	0.169256i	0.438784	+	0.898592i	$0.355409\pi$
$84$	−9.55055	−	11.9760i	−1.04205	−	1.30669i
$85$	−0.875173			−0.0949258
$86$	3.18571	−	11.2578i	0.343524	−	1.21396i
$87$	−22.4706			−2.40910
$88$	1.84930	+	2.31895i	0.197136	+	0.247201i
$89$	5.97021	+	0.899865i	0.632841	+	0.0953855i	0.457626	−	0.889145i	$-0.348700\pi$
$89$	5.97021	+	0.899865i	0.632841	+	0.0953855i	0.175215	+	0.984530i	$0.443938\pi$
$90$	−1.37350	+	6.01770i	−0.144780	+	0.634322i
$91$	6.28390	+	4.28429i	0.658731	+	0.449115i
$92$	1.61081	+	2.79000i	0.167938	+	0.290878i
$93$	0.845453	−	1.46437i	0.0876694	−	0.151848i
$94$	15.0513	−	7.24833i	1.55242	−	0.747608i
$95$	1.23978	+	0.382420i	0.127198	+	0.0392355i
$96$	1.31848	+	17.5939i	0.134567	+	1.79567i
$97$	−2.28198	−	9.99799i	−0.231700	−	1.01514i	−0.948230	−	0.317586i	$-0.897128\pi$
$97$	−2.28198	−	9.99799i	−0.231700	−	1.01514i	0.716530	−	0.697556i	$-0.245729\pi$
$98$	−7.84589	+	19.9910i	−0.792554	+	2.01940i
$99$	0.882576	−	11.7772i	0.0887023	−	1.18365i
$100$	5.43477	−	0.819160i	0.543477	−	0.0819160i
$101$	8.19564	+	7.60445i	0.815497	+	0.756671i	0.972989	−	0.230849i	$-0.0741505\pi$
$101$	8.19564	+	7.60445i	0.815497	+	0.756671i	−0.157492	+	0.987520i	$0.550341\pi$
$102$	6.99921	+	3.37064i	0.693025	+	0.333743i
$103$	−0.115290	+	0.0786031i	−0.0113598	+	0.00774499i	−0.568987	−	0.822347i	$-0.692664\pi$
$103$	−0.115290	+	0.0786031i	−0.0113598	+	0.00774499i	0.557627	+	0.830092i	$0.311712\pi$
$104$	−0.927870	−	2.36417i	−0.0909851	−	0.231826i
$105$	7.37582	−	2.27514i	0.719807	−	0.222031i
$106$	−7.72447	+	7.16726i	−0.750267	+	0.696146i
$107$	3.64662	−	4.57272i	0.352533	−	0.442062i	−0.573671	−	0.819086i	$-0.694481\pi$
$107$	3.64662	−	4.57272i	0.352533	−	0.442062i	0.926203	+	0.377024i	$0.123053\pi$
$108$	6.13223	−	7.68957i	0.590074	−	0.739929i
$109$	−0.578145	+	0.536440i	−0.0553762	+	0.0513816i	−0.707375	−	0.706838i	$-0.750121\pi$
$109$	−0.578145	+	0.536440i	−0.0553762	+	0.0513816i	0.651999	+	0.758220i	$0.273931\pi$
$110$	2.06969	−	0.638415i	0.197337	−	0.0608705i
$111$	−4.29392	−	10.9407i	−0.407560	−	1.03845i
$112$	17.9035	−	12.2064i	1.69172	−	1.15340i
$113$	5.42511	+	2.61260i	0.510352	+	0.245772i	0.671294	−	0.741191i	$-0.265739\pi$
$113$	5.42511	+	2.61260i	0.510352	+	0.245772i	−0.160942	+	0.986964i	$0.551453\pi$
$114$	−8.44228	−	7.83329i	−0.790692	−	0.733655i
$115$	−1.60525	+	0.241953i	−0.149691	+	0.0225622i
$116$	−0.669827	+	8.93822i	−0.0621919	+	0.829893i
$117$	−3.69458	+	9.41364i	−0.341564	+	0.870292i
$118$	2.02889	+	8.88915i	0.186775	+	0.818313i
$119$	−0.478526	−	6.38549i	−0.0438664	−	0.585357i
$120$	−2.46306	−	0.759755i	−0.224846	−	0.0693558i
$121$	6.17687	−	2.97462i	0.561533	−	0.270420i
$122$	−8.73020	+	15.1211i	−0.790395	+	1.36900i
$123$	−3.15316	−	5.46143i	−0.284311	−	0.492441i
$124$	−0.557284	−	0.379950i	−0.0500456	−	0.0341205i
$125$	−1.27974	+	5.60692i	−0.114464	+	0.501498i
$126$	−44.6577	−	6.73107i	−3.97843	−	0.599651i
$127$	−2.35751	−	2.95623i	−0.209195	−	0.262323i	0.666153	−	0.745815i	$-0.267940\pi$
$127$	−2.35751	−	2.95623i	−0.209195	−	0.262323i	−0.875349	+	0.483492i	$0.839368\pi$
$128$	−10.6844			−0.944374
$129$	−8.84914	−	17.3250i	−0.779124	−	1.52538i
$130$	−1.85461			−0.162660
$131$	−10.8237	−	13.5725i	−0.945669	−	1.18583i	−0.982453	−	0.186508i	$-0.940283\pi$
$131$	−10.8237	−	13.5725i	−0.945669	−	1.18583i	0.0367848	−	0.999323i	$-0.488288\pi$
$132$	−7.06721	−	1.06521i	−0.615122	−	0.0927147i
$133$	−2.11235	+	9.25483i	−0.183164	+	0.802496i
$134$	0.781506	+	0.532822i	0.0675118	+	0.0460288i
$135$	2.47803	+	4.29207i	0.213275	+	0.369403i
$136$	−1.06917	+	1.85185i	−0.0916803	+	0.158795i
$137$	−2.80268	+	1.34970i	−0.239449	+	0.115312i	−0.549760	−	0.835322i	$-0.685281\pi$
$137$	−2.80268	+	1.34970i	−0.239449	+	0.115312i	0.310311	+	0.950635i	$0.399567\pi$
$138$	13.7699	+	4.24745i	1.17217	+	0.361567i
$139$	0.390211	+	5.20700i	0.0330973	+	0.441652i	0.988995	+	0.147951i	$0.0472679\pi$
$139$	0.390211	+	5.20700i	0.0330973	+	0.441652i	−0.955897	+	0.293701i	$0.905113\pi$
$140$	−0.685124	−	3.00173i	−0.0579036	−	0.253692i
$141$	10.1483	−	25.8575i	0.854644	−	2.17760i
$142$	0.711766	−	9.49785i	0.0597301	−	0.797042i
$143$	3.50891	−	0.528883i	0.293430	−	0.0442275i
$144$	21.1208	+	19.5972i	1.76007	+	1.63310i
$145$	−4.06935	−	1.95969i	−0.337941	−	0.162744i
$146$	20.7246	−	14.1298i	1.71518	−	1.16939i
$147$	13.0459	+	33.2404i	1.07601	+	2.74162i
$148$	−4.47992	+	1.38187i	−0.368247	+	0.113589i
$149$	−14.9269	+	13.8502i	−1.22286	+	1.13465i	−0.236229	+	0.971698i	$0.575911\pi$
$149$	−14.9269	+	13.8502i	−1.22286	+	1.13465i	−0.986634	+	0.162953i	$0.947898\pi$
$150$	15.3279	−	19.2205i	1.25152	−	1.56935i
$151$	−12.4488	+	15.6103i	−1.01307	+	1.27035i	−0.0506675	+	0.998716i	$0.516135\pi$
$151$	−12.4488	+	15.6103i	−1.01307	+	1.27035i	−0.962401	+	0.271632i	$0.912437\pi$
$152$	2.32379	−	2.15616i	0.188484	−	0.174887i
$153$	8.13612	−	2.50966i	0.657766	−	0.202894i
$154$	5.78971	+	14.7519i	0.466548	+	1.18875i
$155$	0.280818	−	0.191458i	0.0225558	−	0.0153783i
$156$	5.51374	+	2.65528i	0.441452	+	0.212592i
$157$	−12.6185	−	11.7083i	−1.00707	−	0.934423i	−0.00921861	−	0.999958i	$-0.502934\pi$
$157$	−12.6185	−	11.7083i	−1.00707	−	0.934423i	−0.997850	+	0.0655341i	$0.979125\pi$
$158$	6.44432	−	0.971325i	0.512682	−	0.0772744i
$159$	−1.30937	+	17.4723i	−0.103840	+	1.38564i
$160$	−1.29561	+	3.30117i	−0.102427	+	0.260980i
$161$	−2.64307	−	11.5800i	−0.208303	−	0.912636i
$162$	−0.967001	−	12.9037i	−0.0759748	−	1.01381i
$163$	20.8543	+	6.43270i	1.63344	+	0.503848i	0.969737	−	0.244152i	$-0.0785095\pi$
$163$	20.8543	+	6.43270i	1.63344	+	0.503848i	0.663699	+	0.748000i	$0.268986\pi$
$164$	−2.26641	+	1.09144i	−0.176977	+	0.0852274i
$165$	1.80071	−	3.11892i	0.140185	−	0.242808i
$166$	−9.22972	−	15.9863i	−0.716365	−	1.24078i
$167$	7.00644	+	4.77691i	0.542175	+	0.369649i	0.803224	−	0.595677i	$-0.203116\pi$
$167$	7.00644	+	4.77691i	0.542175	+	0.369649i	−0.261049	+	0.965325i	$0.584069\pi$
$168$	4.19662	−	18.3866i	0.323776	−	1.41856i
$169$	9.85023	+	1.48468i	0.757710	+	0.114206i
$170$	0.973572	+	1.22082i	0.0746696	+	0.0936327i
$171$	−12.6223			−0.965254
$172$	−7.15520	+	3.00351i	−0.545579	+	0.229016i
$173$	−11.0837			−0.842677			−0.421338	−	0.906904i	$-0.638439\pi$
$173$	−11.0837			−0.842677			−0.421338	+	0.906904i	$0.638439\pi$
$174$	24.9971	+	31.3454i	1.89503	+	2.37629i
$175$	−20.0376	−	3.02018i	−1.51470	−	0.228304i
$176$	2.24973	−	9.85670i	0.169580	−	0.742977i
$177$	12.5264	+	8.54034i	0.941540	+	0.641931i
$178$	−5.38621	−	9.32918i	−0.403713	−	0.699252i
$179$	7.70817	−	13.3509i	0.576135	−	0.997896i	−0.419782	−	0.907625i	$-0.637893\pi$
$179$	7.70817	−	13.3509i	0.576135	−	0.997896i	0.995917	−	0.0902708i	$-0.0287733\pi$
$180$	3.68852	−	1.77630i	0.274926	−	0.132397i
$181$	−3.06551	−	0.945583i	−0.227857	−	0.0702847i	0.178724	−	0.983899i	$-0.442803\pi$
$181$	−3.06551	−	0.945583i	−0.227857	−	0.0702847i	−0.406581	+	0.913615i	$0.633279\pi$
$182$	−1.01406	−	13.5317i	−0.0751672	−	1.00304i
$183$	6.46036	+	28.3047i	0.477564	+	2.09234i
$184$	−1.44911	+	3.69227i	−0.106830	+	0.272198i
$185$	0.176543	−	2.35580i	0.0129797	−	0.173202i
$186$	−2.98323	+	0.449649i	−0.218741	+	0.0329699i
$187$	−2.19014	−	2.03215i	−0.160159	−	0.148606i
$188$	−9.98293	−	4.80753i	−0.728080	−	0.350625i
$189$	−29.9612	+	20.4272i	−2.17935	+	1.48586i
$190$	−0.845713	−	2.15484i	−0.0613545	−	0.156329i
$191$	−5.09606	+	1.57193i	−0.368738	+	0.113741i	−0.473586	−	0.880748i	$-0.657041\pi$
$191$	−5.09606	+	1.57193i	−0.368738	+	0.113741i	0.104848	+	0.994488i	$0.466564\pi$
$192$	1.47449	−	1.36813i	0.106412	−	0.0987360i
$193$	−4.19096	+	5.25530i	−0.301672	+	0.378285i	−0.909444	−	0.415827i	$-0.863492\pi$
$193$	−4.19096	+	5.25530i	−0.301672	+	0.378285i	0.607772	+	0.794112i	$0.292064\pi$
$194$	−11.4081	+	14.3054i	−0.819057	+	1.02706i
$195$	−2.26057	+	2.09751i	−0.161883	+	0.150206i
$196$	13.6110	−	4.19845i	0.972217	−	0.299889i
$197$	−1.77600	−	4.52518i	−0.126535	−	0.322406i	0.853542	−	0.521024i	$-0.174450\pi$
$197$	−1.77600	−	4.52518i	−0.126535	−	0.322406i	−0.980077	+	0.198618i	$0.936355\pi$
$198$	−17.4103	+	11.8702i	−1.23730	+	0.843577i
$199$	20.4216	+	9.83452i	1.44765	+	0.697151i	0.982185	−	0.187916i	$-0.0601734\pi$
$199$	20.4216	+	9.83452i	1.44765	+	0.697151i	0.465463	+	0.885067i	$0.345888\pi$
$200$	4.96048	+	4.60265i	0.350759	+	0.325456i
$201$	1.55518	−	0.234406i	0.109694	−	0.0165337i
$202$	1.49070	−	19.8920i	0.104885	−	1.39959i
$203$	12.0734	−	30.7625i	0.847387	−	2.15911i
$204$	−1.14655	−	5.02338i	−0.0802747	−	0.351707i
$205$	−0.0947264	−	1.26404i	−0.00661598	−	0.0882841i
$206$	0.237899	+	0.0733822i	0.0165752	+	0.00511278i
$207$	14.2295	−	6.85259i	0.989022	−	0.476288i
$208$	−4.32852	+	7.49721i	−0.300129	+	0.519838i
$209$	2.21459	+	3.83578i	0.153186	+	0.265327i
$210$	−11.3788	−	7.75795i	−0.785214	−	0.535350i
$211$	−4.22277	+	18.5012i	−0.290707	+	1.27367i	0.592836	+	0.805323i	$0.298008\pi$
$211$	−4.22277	+	18.5012i	−0.290707	+	1.27367i	−0.883543	+	0.468349i	$0.844849\pi$
$212$	6.91098	+	1.04166i	0.474648	+	0.0715417i
$213$	−9.87422	−	12.3819i	−0.676571	−	0.848393i
$214$	−10.4353			−0.713346
$215$	−0.0916113	−	3.90923i	−0.00624784	−	0.266608i
$216$	12.1093			0.823932
$217$	1.55047	+	1.94423i	0.105253	+	0.131983i
$218$	1.39145	+	0.209728i	0.0942412	+	0.0142046i
$219$	9.28074	−	40.6616i	0.627134	−	2.74766i
$220$	−1.18695	−	0.809247i	−0.0800239	−	0.0545594i
$221$	1.27914	+	2.21553i	0.0860441	+	0.149033i
$222$	−10.4850	+	18.1606i	−0.703710	+	1.21886i
$223$	−8.70607	+	4.19262i	−0.583002	+	0.280759i	−0.702048	−	0.712130i	$-0.747731\pi$
$223$	−8.70607	+	4.19262i	−0.583002	+	0.280759i	0.119046	+	0.992889i	$0.462016\pi$
$224$	−24.7946	−	7.64812i	−1.65666	−	0.511012i
$225$	−2.01355	−	26.8690i	−0.134237	−	1.79126i
$226$	−2.39064	−	10.4741i	−0.159023	−	0.696727i
$227$	−6.45065	+	16.4360i	−0.428144	+	1.09089i	0.540258	+	0.841500i	$0.318327\pi$
$227$	−6.45065	+	16.4360i	−0.428144	+	1.09089i	−0.968402	+	0.249394i	$0.919768\pi$
$228$	−0.570827	+	7.61716i	−0.0378039	+	0.504459i
$229$	0.234167	−	0.0352950i	0.0154742	−	0.00233236i	−0.141301	−	0.989967i	$-0.545128\pi$
$229$	0.234167	−	0.0352950i	0.0154742	−	0.00233236i	0.156775	+	0.987634i	$0.449890\pi$
$230$	2.12325	+	1.97009i	0.140003	+	0.129904i
$231$	23.7411	+	11.4331i	1.56205	+	0.752242i
$232$	−9.11805	+	6.21658i	−0.598629	+	0.408139i
$233$	2.54575	+	6.48646i	0.166777	+	0.424942i	0.989690	−	0.143226i	$-0.0457476\pi$
$233$	2.54575	+	6.48646i	0.166777	+	0.424942i	−0.822913	+	0.568168i	$0.807652\pi$
$234$	17.2415	−	5.31831i	1.12711	−	0.347669i
$235$	4.09290	−	3.79765i	0.266991	−	0.247732i
$236$	3.77052	−	4.72808i	0.245440	−	0.307772i
$237$	6.75641	−	8.47228i	0.438876	−	0.550333i
$238$	−8.37510	+	7.77096i	−0.542877	+	0.503716i
$239$	−28.2108	+	8.70187i	−1.82480	+	0.562877i	−0.999997	−	0.00253697i	$-0.999192\pi$
$239$	−28.2108	+	8.70187i	−1.82480	+	0.562877i	−0.824807	+	0.565414i	$0.808716\pi$
$240$	3.20990	+	8.17868i	0.207198	+	0.527932i
$241$	14.3617	−	9.79162i	0.925117	−	0.630734i	−0.00421050	−	0.999991i	$-0.501340\pi$
$241$	14.3617	−	9.79162i	0.925117	−	0.630734i	0.929327	+	0.369257i	$0.120388\pi$
$242$	−11.0208	−	5.30734i	−0.708444	−	0.341169i
$243$	2.50506	+	2.32435i	0.160699	+	0.149107i
$244$	11.4514	−	1.72603i	0.733103	−	0.110498i
$245$	−0.536378	+	7.15746i	−0.0342679	+	0.457274i
$246$	−4.11074	+	10.4740i	−0.262091	+	0.667797i
$247$	−0.843926	−	3.69748i	−0.0536977	−	0.235265i
$248$	−0.0620578	−	0.828103i	−0.00394067	−	0.0525846i
$249$	−29.3301	−	9.04715i	−1.85872	−	0.573340i
$250$	9.24500	−	4.45216i	0.584705	−	0.281579i
$251$	9.78186	−	16.9427i	0.617426	−	1.06941i	−0.372528	−	0.928021i	$-0.621509\pi$
$251$	9.78186	−	16.9427i	0.617426	−	1.06941i	0.989954	−	0.141392i	$-0.0451576\pi$
$252$	14.9771	+	25.9411i	0.943470	+	1.63414i
$253$	−4.57900	−	3.12191i	−0.287879	−	0.196273i
$254$	−1.50121	+	6.57722i	−0.0941941	+	0.412691i
$255$	2.56740	+	0.386973i	0.160777	+	0.0242332i
$256$	12.7311	+	15.9643i	0.795695	+	0.997770i
$257$	21.9755			1.37080			0.685398	−	0.728168i	$-0.259628\pi$
$257$	21.9755			1.37080			0.685398	+	0.728168i	$0.259628\pi$
$258$	−14.3234	+	31.6170i	−0.891734	+	1.96839i
$259$	17.2851			1.07404
$260$	0.766947	+	0.961721i	0.0475640	+	0.0596434i
$261$	43.4507	+	6.54914i	2.68953	+	0.405382i
$262$	−6.89225	+	30.1969i	−0.425805	+	1.86557i
$263$	−17.5044	−	11.9343i	−1.07937	−	0.735900i	−0.113137	−	0.993579i	$-0.536090\pi$
$263$	−17.5044	−	11.9343i	−1.07937	−	0.735900i	−0.966230	+	0.257679i	$0.917042\pi$
$264$	−4.39973	−	7.62055i	−0.270784	−	0.469012i
$265$	−1.76090	+	3.04997i	−0.108171	+	0.187358i
$266$	15.2599	−	7.34877i	0.935643	−	0.450582i
$267$	−17.1163	−	5.27967i	−1.04750	−	0.323110i
$268$	−0.0468820	−	0.625596i	−0.00286377	−	0.0382144i
$269$	0.540806	+	2.36943i	0.0329735	+	0.144466i	0.988735	−	0.149676i	$-0.0478231\pi$
$269$	0.540806	+	2.36943i	0.0329735	+	0.144466i	−0.955762	+	0.294143i	$0.904966\pi$
$270$	3.23058	−	8.23138i	0.196607	−	0.500946i
$271$	1.48929	−	19.8731i	0.0904677	−	1.20721i	−0.748541	−	0.663089i	$-0.769245\pi$
$271$	1.48929	−	19.8731i	0.0904677	−	1.20721i	0.839008	−	0.544118i	$-0.183136\pi$
$272$	7.20739	−	1.08634i	0.437012	−	0.0658690i
$273$	−16.5400	−	15.3469i	−1.00105	−	0.928835i
$274$	5.00055	+	2.40814i	0.302094	+	0.145481i
$275$	−7.81189	+	5.32606i	−0.471075	+	0.321173i
$276$	−3.49180	−	8.89696i	−0.210182	−	0.535534i
$277$	14.3542	−	4.42768i	0.862460	−	0.266034i	0.168196	−	0.985754i	$-0.446206\pi$
$277$	14.3542	−	4.42768i	0.862460	−	0.266034i	0.694265	+	0.719720i	$0.255730\pi$
$278$	6.82942	−	6.33677i	0.409601	−	0.380054i
$279$	−2.06162	+	2.58519i	−0.123426	+	0.154771i
$280$	2.36351	−	2.96375i	0.141247	−	0.177118i
$281$	−24.0279	+	22.2946i	−1.43338	+	1.32998i	−0.573793	+	0.819000i	$0.694529\pi$
$281$	−24.0279	+	22.2946i	−1.43338	+	1.32998i	−0.859590	+	0.510985i	$0.829281\pi$
$282$	−47.3593	+	14.6084i	−2.82021	+	0.869918i
$283$	4.57856	+	11.6660i	0.272167	+	0.693470i	0.999970	+	0.00768433i	$0.00244602\pi$
$283$	4.57856	+	11.6660i	0.272167	+	0.693470i	−0.727804	+	0.685786i	$0.759459\pi$
$284$	−5.21952	+	3.55861i	−0.309722	+	0.211165i
$285$	−3.46790	−	1.67005i	−0.205421	−	0.0989254i
$286$	−4.64120	−	4.30641i	−0.274440	−	0.254643i
$287$	9.17094	−	1.38230i	0.541344	−	0.0815944i
$288$	2.57829	−	34.4049i	0.151927	−	2.02733i
$289$	−5.42387	+	13.8198i	−0.319051	+	0.812930i
$290$	1.79321	+	7.85656i	0.105301	+	0.461353i
$291$	2.27359	+	30.3390i	0.133280	+	1.77850i
$292$	−15.8974	−	4.90371i	−0.930328	−	0.286968i
$293$	6.61965	−	3.18786i	0.386724	−	0.186237i	−0.230411	−	0.973093i	$-0.574007\pi$
$293$	6.61965	−	3.18786i	0.386724	−	0.186237i	0.617136	+	0.786857i	$0.288293\pi$
$294$	31.8560	−	55.1762i	1.85788	−	3.21794i
$295$	1.52366	+	2.63906i	0.0887112	+	0.153652i
$296$	−4.76916	−	3.25156i	−0.277202	−	0.188993i
$297$	−3.76488	+	16.4950i	−0.218460	+	0.957138i
$298$	35.9255	+	5.41490i	2.08111	+	0.313677i
$299$	2.95872	+	3.71012i	0.171107	+	0.214562i
$300$	−16.3056			−0.941403
$301$	28.4727	−	2.80591i	1.64114	−	0.161730i
$302$	35.6240			2.04993
$303$	−20.6802	−	25.9322i	−1.18805	−	1.48976i
$304$	−10.6847	−	1.61046i	−0.612812	−	0.0923665i
$305$	−1.29854	+	5.68929i	−0.0743544	+	0.325768i
$306$	−12.5518	−	8.55764i	−0.717536	−	0.489208i
$307$	−5.68990	−	9.85520i	−0.324740	−	0.562466i	0.656720	−	0.754135i	$-0.271943\pi$
$307$	−5.68990	−	9.85520i	−0.324740	−	0.562466i	−0.981460	+	0.191669i	$0.938610\pi$
$308$	5.25548	−	9.10275i	0.299459	−	0.518678i
$309$	0.372968	−	0.179612i	0.0212174	−	0.0102178i
$310$	−0.579466	−	0.178742i	−0.0329114	−	0.0101518i
$311$	1.85648	+	24.7730i	0.105271	+	1.40475i	0.760511	+	0.649325i	$0.224948\pi$
$311$	1.85648	+	24.7730i	0.105271	+	1.40475i	−0.655240	+	0.755421i	$0.727433\pi$
$312$	1.67663	+	7.34579i	0.0949204	+	0.415873i
$313$	6.18554	−	15.7605i	0.349627	−	0.890836i	−0.642578	−	0.766221i	$-0.722135\pi$
$313$	6.18554	−	15.7605i	0.349627	−	0.890836i	0.992205	−	0.124616i	$-0.0397698\pi$
$314$	−2.29517	+	30.6269i	−0.129524	+	1.72838i
$315$	−14.9255	+	2.24965i	−0.840955	+	0.126754i
$316$	−3.16864	−	2.94007i	−0.178250	−	0.165392i
$317$	−21.3116	−	10.2631i	−1.19698	−	0.576435i	−0.274166	−	0.961682i	$-0.588402\pi$
$317$	−21.3116	−	10.2631i	−1.19698	−	0.576435i	−0.922813	+	0.385247i	$0.874116\pi$
$318$	25.8295	−	17.6103i	1.44845	−	0.987535i
$319$	−5.63322	−	14.3532i	−0.315400	−	0.803626i
$320$	0.386340	−	0.119170i	0.0215971	−	0.00666182i
$321$	−12.7196	+	11.8021i	−0.709939	+	0.658727i
$322$	−13.2133	+	16.5690i	−0.736350	+	0.923354i
$323$	−1.99090	+	2.49651i	−0.110777	+	0.138909i
$324$	−6.29144	+	5.83760i	−0.349524	+	0.324311i
$325$	7.73614	−	2.38628i	0.429124	−	0.132367i
$326$	−14.2258	−	36.2467i	−0.787892	−	2.00752i
$327$	1.93323	−	1.31806i	0.106908	−	0.0728887i
$328$	−2.79040	−	1.34379i	−0.154074	−	0.0741982i
$329$	29.9466	+	27.7864i	1.65101	+	1.53191i
$330$	−6.35391	+	0.957698i	−0.349771	+	0.0527195i
$331$	1.80682	−	24.1103i	0.0993117	−	1.32522i	−0.695570	−	0.718458i	$-0.744848\pi$
$331$	1.80682	−	24.1103i	0.0993117	−	1.32522i	0.794882	−	0.606764i	$-0.207533\pi$
$332$	−4.47302	+	11.3971i	−0.245489	+	0.625495i
$333$	5.11429	+	22.4072i	0.280261	+	1.22791i
$334$	−1.13066	−	15.0876i	−0.0618671	−	0.825558i
$335$	0.302080	+	0.0931793i	0.0165044	+	0.00509093i
$336$	−57.9187	+	27.8922i	−3.15972	+	1.52164i
$337$	7.76921	−	13.4567i	0.423216	−	0.733031i	−0.573036	−	0.819530i	$-0.694235\pi$
$337$	7.76921	−	13.4567i	0.423216	−	0.733031i	0.996252	+	0.0864989i	$0.0275679\pi$
$338$	−8.88668	−	15.3922i	−0.483372	−	0.837224i
$339$	−14.7598	−	10.0631i	−0.801645	−	0.546552i
$340$	0.230459	−	1.00971i	0.0124984	−	0.0547590i
$341$	1.14732	+	0.172931i	0.0621309	+	0.00936472i
$342$	14.0415	+	17.6075i	0.759278	+	0.952105i
$343$	−21.9745			−1.18651
$344$	−8.38379	−	4.58192i	−0.452024	−	0.247041i
$345$	4.81613			0.259292
$346$	12.3299	+	15.4612i	0.662858	+	0.831197i
$347$	13.6421	+	2.05621i	0.732346	+	0.110383i	0.504620	−	0.863342i	$-0.331633\pi$
$347$	13.6421	+	2.05621i	0.732346	+	0.110383i	0.227726	+	0.973725i	$0.426871\pi$
$348$	5.91718	−	25.9249i	0.317194	−	1.38972i
$349$	11.1033	+	7.57012i	0.594348	+	0.405219i	0.822796	−	0.568337i	$-0.192413\pi$
$349$	11.1033	+	7.57012i	0.594348	+	0.405219i	−0.228449	+	0.973556i	$0.573365\pi$
$350$	18.0775	+	31.3112i	0.966283	+	1.67365i
$351$	7.24370	−	12.5465i	0.386640	−	0.669680i
$352$	−10.9076	+	5.25284i	−0.581378	+	0.279977i
$353$	7.28752	+	2.24790i	0.387876	+	0.119644i	0.482559	−	0.875864i	$-0.339708\pi$
$353$	7.28752	+	2.24790i	0.387876	+	0.119644i	−0.0946829	+	0.995507i	$0.530184\pi$
$354$	−2.02144	−	26.9742i	−0.107438	−	1.43366i
$355$	−0.708343	−	3.10346i	−0.0375950	−	0.164714i
$356$	−2.61033	+	6.65101i	−0.138347	+	0.352503i
$357$	−1.41965	+	18.9440i	−0.0751361	+	1.00262i
$358$	−27.1987	+	4.09954i	−1.43750	+	0.216668i
$359$	−12.3345	−	11.4447i	−0.650989	−	0.604029i	0.283950	−	0.958839i	$-0.408355\pi$
$359$	−12.3345	−	11.4447i	−0.650989	−	0.604029i	−0.934939	+	0.354810i	$0.884546\pi$
$360$	4.54131	+	2.18698i	0.239348	+	0.115264i
$361$	−11.7873	+	8.03646i	−0.620385	+	0.422972i
$362$	2.09113	+	5.32812i	0.109908	+	0.280040i
$363$	−19.4357	+	5.99511i	−1.02011	+	0.314661i
$364$	−6.59762	+	6.12169i	−0.345809	+	0.320864i
$365$	5.22686	−	6.55427i	0.273586	−	0.343066i
$366$	32.2969	−	40.4990i	1.68819	−	2.11692i
$367$	−0.0534689	+	0.0496119i	−0.00279105	+	0.00258972i	−0.681567	−	0.731756i	$-0.738701\pi$
$367$	−0.0534689	+	0.0496119i	−0.00279105	+	0.00258972i	0.678776	+	0.734345i	$0.262511\pi$
$368$	12.9195	−	3.98515i	0.673478	−	0.207740i
$369$	4.50541	+	11.4796i	0.234542	+	0.597603i
$370$	−3.48261	+	2.37441i	−0.181052	+	0.123439i
$371$	−23.2162	−	11.1803i	−1.20533	−	0.580455i
$372$	1.46684	+	1.36103i	0.0760522	+	0.0705661i
$373$	−25.4691	+	3.83884i	−1.31874	+	0.198768i	−0.770438	−	0.637514i	$-0.779963\pi$
$373$	−25.4691	+	3.83884i	−1.31874	+	0.198768i	−0.548299	+	0.836282i	$0.684725\pi$
$374$	−0.398362	+	5.31577i	−0.0205988	+	0.274872i
$375$	6.23344	−	15.8825i	0.321893	−	0.820171i
$376$	−3.03563	−	13.3000i	−0.156551	−	0.685893i
$377$	0.986652	+	13.1660i	0.0508152	+	0.678081i
$378$	61.8247	+	19.0704i	3.17992	+	0.980875i
$379$	14.4579	−	6.96257i	0.742654	−	0.357643i	−0.0239929	−	0.999712i	$-0.507638\pi$
$379$	14.4579	−	6.96257i	0.742654	−	0.357643i	0.766647	+	0.642069i	$0.221924\pi$
$380$	−0.767677	+	1.32966i	−0.0393810	+	0.0682099i
$381$	5.60882	+	9.71477i	0.287349	+	0.497703i
$382$	7.86178	+	5.36007i	0.402244	+	0.274245i
$383$	5.36944	−	23.5250i	0.274365	−	1.20207i	−0.630437	−	0.776241i	$-0.717124\pi$
$383$	5.36944	−	23.5250i	0.274365	−	1.20207i	0.904802	−	0.425833i	$-0.140019\pi$
$384$	31.3435	+	4.72428i	1.59949	+	0.241085i
$385$	3.30232	+	4.14098i	0.168302	+	0.211044i
$386$	11.9930			0.610430
$387$	12.0619	+	36.0798i	0.613139	+	1.83404i
$388$	12.1358			0.616103
$389$	10.2266	+	12.8237i	0.518507	+	0.650187i	0.970291	−	0.241940i	$-0.0777837\pi$
$389$	10.2266	+	12.8237i	0.518507	+	0.650187i	−0.451784	+	0.892127i	$0.649212\pi$
$390$	5.44066	+	0.820047i	0.275498	+	0.0415247i
$391$	0.889063	−	3.89524i	0.0449619	−	0.196991i
$392$	14.4898	+	9.87898i	0.731846	+	0.498964i
$393$	25.7509	+	44.6019i	1.29896	+	2.24987i
$394$	−4.33671	+	7.51140i	−0.218480	+	0.378419i
$395$	1.96244	−	0.945061i	0.0987410	−	0.0475512i
$396$	13.3552	+	4.11952i	0.671123	+	0.207014i
$397$	−0.575635	−	7.68131i	−0.0288903	−	0.385514i	−0.992842	−	0.119436i	$-0.961891\pi$
$397$	−0.575635	−	7.68131i	−0.0288903	−	0.385514i	0.963952	−	0.266078i	$-0.0857278\pi$
$398$	−8.99903	−	39.4273i	−0.451081	−	1.97631i
$399$	10.2890	−	26.2158i	0.515092	−	1.31243i
$400$	1.72371	−	23.0013i	0.0861856	−	1.15007i
$401$	−1.39718	+	0.210591i	−0.0697719	+	0.0105164i	−0.183835	−	0.982957i	$-0.558851\pi$
$401$	−1.39718	+	0.210591i	−0.0697719	+	0.0105164i	0.114064	+	0.993473i	$0.463613\pi$
$402$	−2.05702	−	1.90864i	−0.102595	−	0.0951941i
$403$	−0.895123	−	0.431068i	−0.0445892	−	0.0214730i
$404$	−10.9316	+	7.45302i	−0.543866	+	0.370802i
$405$	−1.58002	−	4.02581i	−0.0785116	−	0.200044i
$406$	−56.3430	+	17.3795i	−2.79626	+	0.862531i
$407$	5.91198	−	5.48551i	0.293046	−	0.271907i
$408$	3.95532	−	4.95982i	0.195818	−	0.245548i
$409$	−4.44166	+	5.56967i	−0.219626	+	0.275402i	−0.879423	−	0.476042i	$-0.842071\pi$
$409$	−4.44166	+	5.56967i	−0.219626	+	0.275402i	0.659796	+	0.751444i	$0.270642\pi$
$410$	−1.65789	+	1.53830i	−0.0818773	+	0.0759710i
$411$	8.81869	−	2.72021i	0.434994	−	0.134178i
$412$	−0.0603270	−	0.153711i	−0.00297210	−	0.00757278i
$413$	−18.4222	+	12.5600i	−0.906497	+	0.618039i
$414$	−25.3885	−	12.2264i	−1.24777	−	0.600896i
$415$	−4.52256	−	4.19632i	−0.222004	−	0.205989i
$416$	10.2507	−	1.54504i	0.502581	−	0.0757519i
$417$	1.15765	−	15.4477i	0.0566903	−	0.756479i
$418$	2.88713	−	7.35629i	0.141214	−	0.359808i
$419$	−3.05031	−	13.3643i	−0.149018	−	0.652889i	−0.993159	−	0.116769i	$-0.962746\pi$
$419$	−3.05031	−	13.3643i	−0.149018	−	0.652889i	0.844142	−	0.536120i	$-0.180111\pi$
$420$	0.682608	+	9.10877i	0.0333078	+	0.444462i
$421$	−1.78387	−	0.550250i	−0.0869404	−	0.0268176i	0.250980	−	0.967992i	$-0.419247\pi$
$421$	−1.78387	−	0.550250i	−0.0869404	−	0.0268176i	−0.337920	+	0.941175i	$0.609723\pi$
$422$	30.5057	−	14.6908i	1.48500	−	0.715136i
$423$	−27.1598	+	47.0421i	−1.32055	+	2.28726i
$424$	4.30246	+	7.45208i	0.208946	+	0.361905i
$425$	−5.63187	−	3.83975i	−0.273186	−	0.186255i
$426$	−6.28767	+	27.5481i	−0.304638	+	1.33471i
$427$	−42.2206	−	6.36373i	−2.04320	−	0.307962i
$428$	4.31539	+	5.41133i	0.208592	+	0.261566i
$429$	−10.5276			−0.508275
$430$	−5.35127	+	4.47656i	−0.258061	+	0.215879i
$431$	−23.8277			−1.14774			−0.573871	−	0.818946i	$-0.694559\pi$
$431$	−23.8277			−1.14774			−0.573871	+	0.818946i	$0.694559\pi$
$432$	−25.7352	−	32.2710i	−1.23819	−	1.55264i
$433$	−39.6397	−	5.97472i	−1.90496	−	0.287127i	−0.912442	−	0.409206i	$-0.865806\pi$
$433$	−39.6397	−	5.97472i	−1.90496	−	0.287127i	−0.992520	+	0.122079i	$0.961044\pi$
$434$	0.987305	−	4.32567i	0.0473922	−	0.207639i
$435$	11.0713	+	7.54826i	0.530827	+	0.361912i
$436$	−0.466660	−	0.808279i	−0.0223490	−	0.0387096i
$437$	−2.96154	+	5.12954i	−0.141670	+	0.245379i
$438$	−67.0450	+	32.2872i	−3.20354	+	1.54274i
$439$	7.92185	+	2.44357i	0.378089	+	0.116625i	0.477974	−	0.878374i	$-0.341371\pi$
$439$	7.92185	+	2.44357i	0.378089	+	0.116625i	−0.0998848	+	0.994999i	$0.531847\pi$
$440$	−0.132175	−	1.76376i	−0.00630121	−	0.0840839i
$441$	−15.5384	−	68.0781i	−0.739923	−	3.24182i
$442$	1.66760	−	4.24897i	0.0793195	−	0.202103i
$443$	−2.35373	+	31.4083i	−0.111829	+	1.49225i	0.605682	+	0.795706i	$0.292900\pi$
$443$	−2.35373	+	31.4083i	−0.111829	+	1.49225i	−0.717511	+	0.696547i	$0.754719\pi$
$444$	13.7533	−	2.07297i	0.652701	−	0.0983789i
$445$	−2.63924	−	2.44886i	−0.125112	−	0.116087i
$446$	15.5334	+	7.48050i	0.735529	+	0.354212i
$447$	49.9136	−	34.0305i	2.36083	−	1.60959i
$448$	1.08074	+	2.75368i	0.0510601	+	0.130099i
$449$	14.7459	−	4.54851i	0.695903	−	0.214658i	0.0734316	−	0.997300i	$-0.476605\pi$
$449$	14.7459	−	4.54851i	0.695903	−	0.214658i	0.622471	+	0.782643i	$0.286129\pi$
$450$	−35.2409	+	32.6988i	−1.66127	+	1.54143i
$451$	2.69804	−	3.38324i	0.127046	−	0.159310i
$452$	−4.44281	+	5.57110i	−0.208972	+	0.262043i
$453$	43.4220	−	40.2897i	2.04014	−	1.89298i
$454$	30.1033	−	9.28563i	1.41282	−	0.435796i
$455$	−1.65691	−	4.22173i	−0.0776771	−	0.197918i
$456$	−7.77041	+	5.29778i	−0.363883	+	0.248091i
$457$	8.36585	+	4.02878i	0.391338	+	0.188458i	0.619197	−	0.785236i	$-0.287458\pi$
$457$	8.36585	+	4.02878i	0.391338	+	0.188458i	−0.227859	+	0.973694i	$0.573173\pi$
$458$	−0.309730	−	0.287387i	−0.0144727	−	0.0134287i
$459$	−12.0614	+	1.81797i	−0.562980	+	0.0848555i
$460$	0.143564	−	1.91573i	0.00669371	−	0.0893214i
$461$	−7.64092	+	19.4688i	−0.355873	+	0.906750i	0.635068	+	0.772456i	$0.280972\pi$
$461$	−7.64092	+	19.4688i	−0.355873	+	0.906750i	−0.990942	+	0.134294i	$0.957123\pi$
$462$	−10.4618	−	45.8361i	−0.486727	−	2.13249i
$463$	0.163595	+	2.18303i	0.00760292	+	0.101454i	0.999714	−	0.0239064i	$-0.00761037\pi$
$463$	0.163595	+	2.18303i	0.00760292	+	0.101454i	−0.992111	+	0.125360i	$0.959991\pi$
$464$	35.9452	+	11.0876i	1.66871	+	0.514730i
$465$	−0.908460	+	0.437491i	−0.0421288	+	0.0202882i
$466$	6.21630	−	10.7669i	0.287965	−	0.498769i
$467$	0.115483	+	0.200022i	0.00534391	+	0.00925593i	0.868685	−	0.495365i	$-0.164966\pi$
$467$	0.115483	+	0.200022i	0.00534391	+	0.00925593i	−0.863341	+	0.504621i	$0.831632\pi$
$468$	−9.88784	−	6.74142i	−0.457066	−	0.311622i
$469$	−0.514690	+	2.25500i	−0.0237662	+	0.104126i
$470$	−9.85061	−	1.48474i	−0.454375	−	0.0684860i
$471$	31.8406	+	39.9268i	1.46714	+	1.83973i
$472$	7.44562			0.342713
$473$	8.84799	−	9.99567i	0.406831	−	0.459602i
$474$	−19.3345			−0.888061
$475$	6.30032	+	7.90035i	0.289079	+	0.362493i
$476$	7.49309	+	1.12940i	0.343445	+	0.0517660i
$477$	7.62423	−	33.4040i	0.349090	−	1.52946i
$478$	43.5213	+	29.6723i	1.99062	+	1.35718i
$479$	−2.50477	−	4.33839i	−0.114446	−	0.198226i	0.803112	−	0.595828i	$-0.203176\pi$
$479$	−2.50477	−	4.33839i	−0.114446	−	0.198226i	−0.917558	+	0.397602i	$0.869843\pi$
$480$	5.26046	−	9.11139i	0.240106	−	0.415876i
$481$	−6.22183	+	2.99627i	−0.283691	+	0.136618i
$482$	−29.6352	−	9.14126i	−1.34985	−	0.416373i
$483$	2.63336	+	35.1398i	0.119822	+	1.59891i
$484$	1.80534	+	7.90970i	0.0820607	+	0.359532i
$485$	−2.23417	+	5.69256i	−0.101448	+	0.258486i
$486$	0.455642	−	6.08011i	0.0206683	−	0.275800i
$487$	12.8944	−	1.94351i	0.584299	−	0.0880689i	0.149761	−	0.988722i	$-0.452150\pi$
$487$	12.8944	−	1.94351i	0.584299	−	0.0880689i	0.434538	+	0.900653i	$0.356912\pi$
$488$	10.4521	+	9.69810i	0.473143	+	0.439012i
$489$	−58.3336	−	28.0920i	−2.63794	−	1.27036i
$490$	10.5810	−	7.21399i	0.478000	−	0.325895i
$491$	9.25153	+	23.5725i	0.417516	+	1.06381i	0.972696	+	0.232083i	$0.0745541\pi$
$491$	9.25153	+	23.5725i	0.417516	+	1.06381i	−0.555180	+	0.831730i	$0.687351\pi$
$492$	7.13130	−	2.19971i	0.321504	−	0.0991708i
$493$	8.14873	−	7.56092i	0.367000	−	0.340527i
$494$	−4.21898	+	5.29044i	−0.189821	+	0.238028i
$495$	−4.39099	+	5.50613i	−0.197360	+	0.247482i
$496$	−2.07499	+	1.92531i	−0.0931698	+	0.0864489i
$497$	22.2563	−	6.86516i	0.998332	−	0.307945i
$498$	20.0076	+	50.9784i	0.896560	+	2.28440i
$499$	7.17570	−	4.89231i	0.321228	−	0.219010i	−0.391960	−	0.919982i	$-0.628203\pi$
$499$	7.17570	−	4.89231i	0.321228	−	0.219010i	0.713188	+	0.700973i	$0.247250\pi$
$500$	−6.13184	−	2.95294i	−0.274224	−	0.132059i
$501$	−18.4418	−	17.1115i	−0.823920	−	0.764486i
$502$	−34.5158	+	5.20243i	−1.54052	+	0.232196i
$503$	2.14991	−	28.6886i	0.0958599	−	1.27916i	−0.717153	−	0.696916i	$-0.754555\pi$
$503$	2.14991	−	28.6886i	0.0958599	−	1.27916i	0.813013	−	0.582246i	$-0.197826\pi$
$504$	−13.4737	+	34.3304i	−0.600166	+	1.52920i
$505$	−1.48353	−	6.49976i	−0.0660162	−	0.289236i
$506$	0.738934	+	9.86039i	0.0328496	+	0.438348i
$507$	−28.2400	−	8.71090i	−1.25418	−	0.386864i
$508$	4.03147	−	1.94145i	0.178867	−	0.0861380i
$509$	−13.2695	+	22.9835i	−0.588162	+	1.01873i	0.406311	+	0.913735i	$0.366815\pi$
$509$	−13.2695	+	22.9835i	−0.588162	+	1.01873i	−0.994473	+	0.104992i	$0.966518\pi$
$510$	−2.31625	−	4.01187i	−0.102565	−	0.177648i
$511$	50.6796	+	34.5528i	2.24193	+	1.52852i
$512$	3.35188	−	14.6855i	0.148133	−	0.649015i
$513$	17.8807	+	2.69509i	0.789453	+	0.118991i
$514$	−24.4464	−	30.6548i	−1.07828	−	1.35212i
$515$	0.0832072			0.00366655
$516$	22.3185	−	5.64728i	0.982516	−	0.248607i
$517$	19.0607			0.838290
$518$	−19.2285	−	24.1118i	−0.844852	−	1.05941i
$519$	32.5149	+	4.90084i	1.42725	+	0.215123i
$520$	−0.337005	+	1.47651i	−0.0147786	+	0.0647495i
$521$	−29.4870	−	20.1039i	−1.29185	−	0.880769i	−0.294654	−	0.955604i	$-0.595205\pi$
$521$	−29.4870	−	20.1039i	−1.29185	−	0.880769i	−0.997196	+	0.0748353i	$0.976157\pi$
$522$	−39.2003	−	67.8970i	−1.71575	−	2.97177i
$523$	19.4445	−	33.6789i	0.850249	−	1.47267i	−0.0307344	−	0.999528i	$-0.509785\pi$
$523$	19.4445	−	33.6789i	0.850249	−	1.47267i	0.880983	−	0.473147i	$-0.156882\pi$
$524$	18.5090	−	8.91349i	0.808571	−	0.389387i
$525$	57.4466	+	17.7199i	2.50717	+	0.773361i
$526$	2.82476	+	37.6939i	0.123166	+	1.64353i
$527$	0.186136	+	0.815515i	0.00810821	+	0.0355244i
$528$	−10.9581	+	27.9207i	−0.476889	+	1.21509i
$529$	−1.16495	+	15.5452i	−0.0506501	+	0.675878i
$530$	6.21344	−	0.936526i	0.269895	−	0.0406801i
$531$	−21.7327	−	20.1650i	−0.943120	−	0.875087i
$532$	−10.1213	−	4.87414i	−0.438812	−	0.211321i
$533$	−3.06150	+	2.08730i	−0.132608	+	0.0904109i
$534$	11.6759	+	29.7496i	0.505264	+	1.28739i
$535$	−3.33275	+	1.02802i	−0.144087	+	0.0444450i
$536$	0.566206	−	0.525362i	0.0244564	−	0.0226922i
$537$	−28.5159	+	35.7578i	−1.23055	+	1.54307i
$538$	2.70362	−	3.39023i	0.116561	−	0.146163i
$539$	−17.9620	+	16.6663i	−0.773676	+	0.717866i
$540$	−5.60440	+	1.72873i	−0.241175	+	0.0743927i
$541$	6.99876	+	17.8325i	0.300900	+	0.766681i	0.998728	+	0.0504159i	$0.0160547\pi$
$541$	6.99876	+	17.8325i	0.300900	+	0.766681i	−0.697828	+	0.716265i	$0.745850\pi$
$542$	−29.3787	+	20.0301i	−1.26192	+	0.860366i
$543$	8.57483	+	4.12942i	0.367981	+	0.177210i
$544$	−6.39812	−	5.93658i	−0.274317	−	0.254529i
$545$	0.465051	−	0.0700951i	0.0199206	−	0.00300255i
$546$	−3.00844	+	40.1448i	−0.128749	+	1.71804i
$547$	−0.882978	+	2.24979i	−0.0377534	+	0.0961942i	−0.948507	−	0.316756i	$-0.897406\pi$
$547$	−0.882978	+	2.24979i	−0.0377534	+	0.0961942i	0.910754	+	0.412950i	$0.135502\pi$
$548$	−0.819149	−	3.58893i	−0.0349923	−	0.153311i
$549$	−4.24269	−	56.6147i	−0.181074	−	2.41626i
$550$	16.1198	+	4.97230i	0.687350	+	0.212019i
$551$	−14.8474	+	7.15014i	−0.632521	+	0.304606i
$552$	5.88370	−	10.1909i	0.250427	−	0.433752i
$553$	7.96843	+	13.8017i	0.338852	+	0.586909i
$554$	−22.1445	−	15.0979i	−0.940830	−	0.641447i
$555$	−1.55956	+	6.83289i	−0.0661997	+	0.290040i
$556$	−6.11019	−	0.920963i	−0.259130	−	0.0390575i
$557$	1.65271	+	2.07243i	0.0700274	+	0.0878116i	0.815611	−	0.578600i	$-0.196401\pi$
$557$	1.65271	+	2.07243i	0.0700274	+	0.0878116i	−0.745584	+	0.666412i	$0.767829\pi$
$558$	5.89962			0.249751
$559$	−9.76247	+	5.94559i	−0.412909	+	0.251472i
$560$	−12.9214			−0.546027
$561$	5.52642	+	6.92991i	0.233326	+	0.292581i
$562$	57.8293	+	8.71636i	2.43938	+	0.367678i
$563$	−1.07396	+	4.70535i	−0.0452622	+	0.198307i	−0.992504	−	0.122214i	$-0.961001\pi$
$563$	−1.07396	+	4.70535i	−0.0452622	+	0.198307i	0.947242	+	0.320520i	$0.103858\pi$
$564$	27.1601	+	18.5174i	1.14365	+	0.779724i
$565$	−1.79534	−	3.10961i	−0.0755303	−	0.130822i
$566$	11.1801	−	19.3645i	0.469934	−	0.813950i
$567$	28.5095	−	13.7294i	1.19729	−	0.576582i
$568$	−7.43222	−	2.29254i	−0.311849	−	0.0961927i
$569$	0.904422	+	12.0687i	0.0379153	+	0.505945i	0.983541	+	0.180687i	$0.0578321\pi$
$569$	0.904422	+	12.0687i	0.0379153	+	0.505945i	−0.945625	+	0.325258i	$0.894549\pi$
$570$	1.52817	+	6.69537i	0.0640081	+	0.280438i
$571$	−10.2678	+	26.1619i	−0.429694	+	1.09484i	0.538052	+	0.842912i	$0.319160\pi$
$571$	−10.2678	+	26.1619i	−0.429694	+	1.09484i	−0.967746	+	0.251930i	$0.918935\pi$
$572$	−0.313816	+	4.18758i	−0.0131213	+	0.175092i
$573$	15.6448	−	2.35807i	0.653570	−	0.0985099i
$574$	−12.1303	−	11.2553i	−0.506309	−	0.469786i
$575$	−11.3916	−	5.48591i	−0.475063	−	0.228778i
$576$	−3.24991	+	2.21575i	−0.135413	+	0.0923231i
$577$	−8.48151	−	21.6105i	−0.353090	−	0.899659i	−0.991517	−	0.129976i	$-0.958510\pi$
$577$	−8.48151	−	21.6105i	−0.353090	−	0.899659i	0.638427	−	0.769682i	$-0.279585\pi$
$578$	25.3116	−	7.80760i	1.05282	−	0.324753i
$579$	14.6183	−	13.5638i	0.607515	−	0.563691i
$580$	3.33252	−	4.17885i	0.138375	−	0.173517i
$581$	28.1446	−	35.2923i	1.16764	−	1.46417i
$582$	39.7921	−	36.9217i	1.64944	−	1.53045i
$583$	−11.4887	+	3.54381i	−0.475815	+	0.146770i
$584$	−7.48327	−	19.0671i	−0.309660	−	0.789001i
$585$	4.98252	−	3.39703i	0.206002	−	0.140450i
$586$	−11.8108	−	5.68780i	−0.487901	−	0.234961i
$587$	−25.3059	−	23.4805i	−1.04449	−	0.969143i	−0.0449330	−	0.998990i	$-0.514307\pi$
$587$	−25.3059	−	23.4805i	−1.04449	−	0.969143i	−0.999554	+	0.0298472i	$0.990498\pi$
$588$	−41.7856	+	6.29817i	−1.72321	+	0.259732i
$589$	0.0926704	−	1.23660i	0.00381842	−	0.0509532i
$590$	1.98638	−	5.06122i	0.0817781	−	0.208367i
$591$	3.20917	+	14.0603i	0.132008	+	0.578364i
$592$	1.47032	+	19.6201i	0.0604298	+	0.806380i
$593$	25.9112	+	7.99254i	1.06404	+	0.328214i	0.776868	−	0.629663i	$-0.216807\pi$
$593$	25.9112	+	7.99254i	1.06404	+	0.328214i	0.287177	+	0.957878i	$0.407283\pi$
$594$	27.1979	−	13.0978i	1.11594	−	0.537410i
$595$	−1.90922	+	3.30687i	−0.0782705	+	0.135569i
$596$	−12.0486	−	20.8687i	−0.493528	−	0.854816i
$597$	−55.5600	−	37.8802i	−2.27392	−	1.55033i
$598$	1.88404	−	8.25454i	0.0770443	−	0.337553i
$599$	−7.61082	−	1.14715i	−0.310970	−	0.0468711i	−0.00829658	−	0.999966i	$-0.502641\pi$
$599$	−7.61082	−	1.14715i	−0.310970	−	0.0468711i	−0.302673	+	0.953094i	$0.597879\pi$
$600$	−12.5169	−	15.6956i	−0.510998	−	0.640772i
$601$	−31.0119			−1.26500			−0.632500	−	0.774560i	$-0.717971\pi$
$601$	−31.0119			−1.26500			−0.632500	+	0.774560i	$0.717971\pi$
$602$	−35.5881	−	36.5966i	−1.45046	−	1.49156i
$603$	−3.07552			−0.125245
$604$	−14.7318	−	18.4731i	−0.599429	−	0.751660i
$605$	−4.04256	−	0.609319i	−0.164354	−	0.0247723i
$606$	−13.1687	+	57.6957i	−0.534940	+	2.34373i
$607$	3.94082	+	2.68680i	0.159953	+	0.109054i	0.640651	−	0.767832i	$-0.278664\pi$
$607$	3.94082	+	2.68680i	0.159953	+	0.109054i	−0.480698	+	0.876886i	$0.659617\pi$
$608$	6.46954	+	11.2056i	0.262374	+	0.454446i
$609$	−49.0206	+	84.9061i	−1.98641	+	3.44057i
$610$	9.38081	−	4.51756i	0.379818	−	0.182911i
$611$	−15.5960	−	4.81073i	−0.630947	−	0.194621i
$612$	0.752971	+	10.0477i	0.0304370	+	0.406154i
$613$	7.62154	+	33.3922i	0.307831	+	1.34870i	0.858003	+	0.513645i	$0.171705\pi$
$613$	7.62154	+	33.3922i	0.307831	+	1.34870i	−0.550171	+	0.835052i	$0.685438\pi$
$614$	−7.41786	+	18.9004i	−0.299360	+	0.762758i
$615$	−0.281027	+	3.75005i	−0.0113321	+	0.151216i
$616$	12.7966	−	1.92877i	0.515588	−	0.0777125i
$617$	−16.7395	−	15.5320i	−0.673908	−	0.625295i	0.267104	−	0.963668i	$-0.413933\pi$
$617$	−16.7395	−	15.5320i	−0.673908	−	0.625295i	−0.941012	+	0.338372i	$0.890124\pi$
$618$	−0.665452	−	0.320465i	−0.0267684	−	0.0128910i
$619$	13.4359	−	9.16045i	0.540035	−	0.368190i	−0.262372	−	0.964967i	$-0.584505\pi$
$619$	13.4359	−	9.16045i	0.540035	−	0.368190i	0.802407	+	0.596777i	$0.203552\pi$
$620$	0.146942	+	0.374402i	0.00590134	+	0.0150364i
$621$	−21.6206	+	6.66909i	−0.867607	+	0.267621i
$622$	32.4918	−	30.1480i	1.30280	−	1.20882i
$623$	16.4244	−	20.5956i	0.658031	−	0.825145i
$624$	16.0131	−	20.0798i	0.641037	−	0.803835i
$625$	−14.5090	+	13.4624i	−0.580359	+	0.538494i
$626$	−28.8661	+	8.90401i	−1.15372	+	0.355876i
$627$	−4.80064	−	12.2318i	−0.191719	−	0.488492i
$628$	16.8310	−	11.4752i	0.671628	−	0.457908i
$629$	5.23847	+	2.52272i	0.208872	+	0.100587i
$630$	19.7418	+	18.3177i	0.786531	+	0.729794i
$631$	1.89851	−	0.286155i	0.0755786	−	0.0113916i	−0.111144	−	0.993804i	$-0.535452\pi$
$631$	1.89851	−	0.286155i	0.0755786	−	0.0113916i	0.186723	+	0.982413i	$0.440213\pi$
$632$	0.397707	−	5.30704i	0.0158200	−	0.211103i
$633$	20.5685	−	52.4076i	0.817523	−	2.08302i
$634$	9.39123	+	41.1457i	0.372973	+	1.63410i
$635$	0.168499	+	2.24846i	0.00668667	+	0.0892274i
$636$	−19.8134	−	6.11162i	−0.785652	−	0.242341i
$637$	18.9034	−	9.10337i	0.748978	−	0.360689i
$638$	−13.7554	+	23.8251i	−0.544582	+	0.943243i
$639$	15.4847	+	26.8203i	0.612566	+	1.06099i
$640$	5.26419	+	3.58906i	0.208085	+	0.141870i
$641$	6.59005	−	28.8729i	0.260291	−	1.14041i	−0.660645	−	0.750698i	$-0.729717\pi$
$641$	6.59005	−	28.8729i	0.260291	−	1.14041i	0.920937	−	0.389712i	$-0.127426\pi$
$642$	30.6130	+	4.61417i	1.20820	+	0.182107i
$643$	−6.44594	−	8.08296i	−0.254203	−	0.318761i	0.638312	−	0.769778i	$-0.279633\pi$
$643$	−6.44594	−	8.08296i	−0.254203	−	0.318761i	−0.892515	+	0.451017i	$0.851061\pi$
$644$	14.0562			0.553890
$645$	−1.45979	+	11.5086i	−0.0574790	+	0.453150i
$646$	5.69725			0.224155
$647$	9.51303	+	11.9290i	0.373996	+	0.468976i	0.932837	−	0.360299i	$-0.117325\pi$
$647$	9.51303	+	11.9290i	0.373996	+	0.468976i	−0.558841	+	0.829275i	$0.688754\pi$
$648$	−10.4488	−	1.57490i	−0.410468	−	0.0618681i
$649$	−2.31491	+	10.1423i	−0.0908681	+	0.398119i
$650$	−11.9347	−	8.13694i	−0.468117	−	0.319157i
$651$	−3.68878	−	6.38915i	−0.144575	−	0.250411i
$652$	−12.9131	+	22.3662i	−0.505717	+	0.875927i
$653$	1.77106	−	0.852898i	0.0693070	−	0.0333765i	−0.398909	−	0.916990i	$-0.630611\pi$
$653$	1.77106	−	0.852898i	0.0693070	−	0.0333765i	0.468216	+	0.883614i	$0.344897\pi$
$654$	−3.98922	−	1.23051i	−0.155991	−	0.0481168i
$655$	0.773602	+	10.3230i	0.0302271	+	0.403353i
$656$	2.34914	+	10.2922i	0.0917184	+	0.401845i
$657$	−29.7968	+	75.9210i	−1.16248	+	2.96196i
$658$	5.44695	−	72.6844i	0.212344	−	2.83353i
$659$	29.3755	−	4.42764i	1.14431	−	0.172476i	0.450594	−	0.892729i	$-0.351212\pi$
$659$	29.3755	−	4.42764i	1.14431	−	0.172476i	0.693712	+	0.720252i	$0.255974\pi$
$660$	3.12419	+	2.89883i	0.121609	+	0.112837i
$661$	10.6317	+	5.11995i	0.413525	+	0.199143i	0.629066	−	0.777352i	$-0.283437\pi$
$661$	10.6317	+	5.11995i	0.413525	+	0.199143i	−0.215542	+	0.976495i	$0.569152\pi$
$662$	−35.6426	+	24.3007i	−1.38529	+	0.944474i
$663$	−2.77283	−	7.06505i	−0.107688	−	0.274384i
$664$	−14.4044	+	4.44317i	−0.558999	+	0.172428i
$665$	4.14961	−	3.85028i	0.160915	−	0.149307i
$666$	25.5675	−	32.0607i	0.990722	−	1.24233i
$667$	12.8562	−	16.1212i	0.497794	−	0.624214i
$668$	−7.35624	+	6.82559i	−0.284621	+	0.264090i
$669$	27.3939	−	8.44989i	1.05911	−	0.326692i
$670$	−0.206064	−	0.525042i	−0.00796094	−	0.0202841i
$671$	−16.4602	+	11.2224i	−0.635439	+	0.433235i
$672$	69.3554	+	33.3998i	2.67544	+	1.28843i
$673$	−14.9166	−	13.8406i	−0.574993	−	0.533516i	0.338183	−	0.941080i	$-0.390188\pi$
$673$	−14.9166	−	13.8406i	−0.574993	−	0.533516i	−0.913176	+	0.407565i	$0.866378\pi$
$674$	−27.4141	+	4.13201i	−1.05595	+	0.159159i
$675$	−2.88460	+	38.4923i	−0.111028	+	1.48157i
$676$	−4.30677	+	10.9735i	−0.165645	+	0.422057i
$677$	5.30533	+	23.2442i	0.203900	+	0.893346i	0.968534	+	0.248881i	$0.0800628\pi$
$677$	5.30533	+	23.2442i	0.203900	+	0.893346i	−0.764634	+	0.644465i	$0.777080\pi$
$678$	2.38186	+	31.7838i	0.0914749	+	1.22065i
$679$	−42.7560	−	13.1885i	−1.64082	−	0.506127i
$680$	1.14885	−	0.553255i	0.0440562	−	0.0212164i
$681$	26.1910	−	45.3641i	1.00364	−	1.73836i
$682$	−1.03509	−	1.79283i	−0.0396356	−	0.0686509i
$683$	29.2625	+	19.9508i	1.11970	+	0.763398i	0.974138	−	0.225952i	$-0.0725492\pi$
$683$	29.2625	+	19.9508i	1.11970	+	0.763398i	0.145560	+	0.989349i	$0.453502\pi$
$684$	3.32383	−	14.5627i	0.127090	−	0.556818i
$685$	1.83426	+	0.276471i	0.0700836	+	0.0105634i
$686$	24.4451	+	30.6532i	0.933320	+	1.17035i
$687$	−0.702556			−0.0268042
$688$	5.60693	+	32.0803i	0.213762	+	1.22305i
$689$	10.2948			0.392202
$690$	−5.35763	−	6.71826i	−0.203962	−	0.255760i
$691$	−15.4237	−	2.32475i	−0.586746	−	0.0884377i	−0.151041	−	0.988527i	$-0.548263\pi$
$691$	−15.4237	−	2.32475i	−0.586746	−	0.0884377i	−0.435704	+	0.900090i	$0.643501\pi$
$692$	2.91866	−	12.7875i	0.110951	−	0.486107i
$693$	−42.5751	−	29.0272i	−1.61729	−	1.10265i
$694$	−12.3076	−	21.3174i	−0.467191	−	0.809198i
$695$	1.55686	−	2.69657i	0.0590552	−	0.102287i
$696$	29.4974	−	14.2052i	1.11810	−	0.538446i
$697$	2.98112	+	0.919554i	0.112918	+	0.0348306i
$698$	−1.79179	−	23.9098i	−0.0678204	−	0.905001i
$699$	−4.60007	−	20.1542i	−0.173991	−	0.762304i
$700$	8.76094	−	22.3225i	0.331132	−	0.843712i
$701$	0.820522	−	10.9491i	0.0309907	−	0.413542i	−0.960036	−	0.279877i	$-0.909706\pi$
$701$	0.820522	−	10.9491i	0.0309907	−	0.413542i	0.991027	−	0.133665i	$-0.0426746\pi$
$702$	−25.5598	+	3.85252i	−0.964693	+	0.145404i
$703$	−6.31852	−	5.86273i	−0.238308	−	0.221117i
$704$	1.24354	+	0.598857i	0.0468677	+	0.0225703i
$705$	−13.6861	+	9.33100i	−0.515447	+	0.351426i
$706$	−4.97118	−	12.6664i	−0.187093	−	0.476705i
$707$	46.6128	−	14.3781i	1.75305	−	0.540746i
$708$	−13.1517	+	12.2030i	−0.494273	+	0.458618i
$709$	20.7337	−	25.9992i	0.778670	−	0.976421i	−0.221329	−	0.975199i	$-0.571040\pi$
$709$	20.7337	−	25.9992i	0.778670	−	0.976421i	0.999999	−	0.00122191i	$-0.000388946\pi$
$710$	−3.54118	+	4.44049i	−0.132898	+	0.166649i
$711$	−15.5339	+	14.4134i	−0.582568	+	0.540544i
$712$	−8.40601	+	2.59291i	−0.315029	+	0.0971735i
$713$	0.566873	+	1.44437i	0.0212295	+	0.0540920i
$714$	28.0052	−	19.0936i	1.04807	−	0.714560i
$715$	−1.90650	−	0.918122i	−0.0712991	−	0.0343358i
$716$	13.3735	+	12.4088i	0.499791	+	0.463738i
$717$	86.6065	−	13.0538i	3.23438	−	0.487504i
$718$	−2.24350	+	29.9375i	−0.0837268	+	1.11726i
$719$	−8.42223	+	21.4595i	−0.314096	+	0.800304i	0.683431	+	0.730015i	$0.260487\pi$
$719$	−8.42223	+	21.4595i	−0.314096	+	0.800304i	−0.997527	+	0.0702882i	$0.977608\pi$
$720$	−3.82316	−	16.7504i	−0.142481	−	0.624250i
$721$	0.0454960	+	0.607102i	0.00169436	+	0.0226096i
$722$	24.3231	+	7.50268i	0.905211	+	0.279221i
$723$	−46.4608	+	22.3743i	−1.72789	+	0.832110i
$724$	1.89818	−	3.28774i	0.0705453	−	0.122188i
$725$	−17.5889	−	30.4649i	−0.653235	−	1.13144i
$726$	29.9838	+	20.4426i	1.11280	+	0.758695i
$727$	−6.21668	+	27.2370i	−0.230564	+	1.01017i	0.718610	+	0.695413i	$0.244779\pi$
$727$	−6.21668	+	27.2370i	−0.230564	+	1.01017i	−0.949174	+	0.314753i	$0.898078\pi$
$728$	−10.9573	−	1.65155i	−0.406105	−	0.0612104i
$729$	−19.8866	−	24.9370i	−0.736540	−	0.923592i
$730$	−14.9574			−0.553599
$731$	9.03855	+	3.30516i	0.334303	+	0.122246i
$732$	−34.3570			−1.26987
$733$	4.22218	+	5.29445i	0.155950	+	0.195555i	0.853668	−	0.520817i	$-0.174373\pi$
$733$	4.22218	+	5.29445i	0.155950	+	0.195555i	−0.697718	+	0.716372i	$0.745801\pi$
$734$	0.128687	+	0.0193964i	0.00474991	+	0.000715934i
$735$	4.73831	−	20.7599i	0.174775	−	0.765740i
$736$	−13.3768	−	9.12011i	−0.493074	−	0.336172i
$737$	0.539600	+	0.934614i	0.0198764	+	0.0344269i
$738$	11.0015	−	19.0551i	0.404970	−	0.701428i
$739$	−13.6045	+	6.55159i	−0.500450	+	0.241004i	−0.667040	−	0.745022i	$-0.732439\pi$
$739$	−13.6045	+	6.55159i	−0.500450	+	0.241004i	0.166590	+	0.986026i	$0.446725\pi$
$740$	2.67145	+	0.824033i	0.0982045	+	0.0302921i
$741$	0.840826	+	11.2200i	0.0308885	+	0.412178i
$742$	10.2305	+	44.8228i	0.375574	+	1.64550i
$743$	9.34603	−	23.8133i	0.342873	−	0.873626i	−0.650586	−	0.759433i	$-0.725477\pi$
$743$	9.34603	−	23.8133i	0.342873	−	0.873626i	0.993459	−	0.114193i	$-0.0364282\pi$
$744$	−0.184108	+	2.45675i	−0.00674974	+	0.0900690i
$745$	12.0070	−	1.80976i	0.439903	−	0.0663046i
$746$	33.6876	+	31.2576i	1.23339	+	1.14442i
$747$	54.0779	+	26.0425i	1.97861	+	0.952847i
$748$	2.92127	−	1.99169i	0.106812	−	0.0728233i
$749$	−9.32295	−	23.7545i	−0.340653	−	0.867970i
$750$	−29.0896	+	8.97296i	−1.06220	+	0.327646i
$751$	−19.4680	+	18.0637i	−0.710398	+	0.659153i	−0.950190	−	0.311671i	$-0.899111\pi$
$751$	−19.4680	+	18.0637i	−0.710398	+	0.659153i	0.239792	+	0.970824i	$0.422921\pi$
$752$	−28.9926	+	36.3556i	−1.05725	+	1.32575i
$753$	−36.1874	+	45.3776i	−1.31874	+	1.65365i
$754$	17.2683	−	16.0226i	0.628873	−	0.583509i
$755$	11.3773	−	3.50943i	0.414062	−	0.127721i
$756$	−15.6776	−	39.9460i	−0.570190	−	1.45282i
$757$	−35.7878	+	24.3997i	−1.30073	+	0.886824i	−0.997807	−	0.0661909i	$-0.978915\pi$
$757$	−35.7878	+	24.3997i	−1.30073	+	0.886824i	−0.302924	+	0.953015i	$0.597963\pi$
$758$	−25.7959	−	12.4227i	−0.936951	−	0.451212i
$759$	12.0525	+	11.1831i	0.437478	+	0.405920i
$760$	−1.86922	+	0.281739i	−0.0678037	+	0.0102198i
$761$	−2.59319	+	34.6036i	−0.0940029	+	1.25438i	0.728271	+	0.685289i	$0.240324\pi$
$761$	−2.59319	+	34.6036i	−0.0940029	+	1.25438i	−0.822274	+	0.569092i	$0.807295\pi$
$762$	7.31215	−	18.6311i	0.264891	−	0.674932i
$763$	0.765713	+	3.35481i	0.0277207	+	0.121452i
$764$	−0.471623	−	6.29337i	−0.0170627	−	0.227686i
$765$	−4.85170	−	1.49655i	−0.175414	−	0.0541079i
$766$	−38.7894	+	18.6800i	−1.40152	+	0.674935i
$767$	4.45393	−	7.71443i	0.160822	−	0.278552i
$768$	−30.2890	−	52.4620i	−1.09296	−	1.89306i
$769$	−12.9224	−	8.81031i	−0.465992	−	0.317708i	0.307462	−	0.951560i	$-0.400520\pi$
$769$	−12.9224	−	8.81031i	−0.465992	−	0.317708i	−0.773454	+	0.633852i	$0.781473\pi$
$770$	2.10284	−	9.21314i	0.0757810	−	0.332018i
$771$	−64.4672	−	9.71687i	−2.32173	−	0.349944i
$772$	−4.95955	−	6.21908i	−0.178498	−	0.223830i
$773$	36.9024			1.32729			0.663643	−	0.748049i	$-0.269009\pi$
$773$	36.9024			1.32729			0.663643	+	0.748049i	$0.269009\pi$
$774$	36.9115	−	56.9621i	1.32676	−	2.04746i
$775$	2.64711			0.0950871
$776$	9.31597	+	11.6819i	0.334424	+	0.419354i
$777$	−50.7073	−	7.64289i	−1.81911	−	0.274187i
$778$	6.51203	−	28.5310i	0.233467	−	1.02289i
$779$	−3.82127	−	2.60530i	−0.136911	−	0.0933444i
$780$	−1.82466	−	3.16041i	−0.0653335	−	0.113161i
$781$	5.43359	−	9.41125i	0.194429	−	0.336761i
$782$	−6.42269	+	3.09300i	−0.229675	+	0.110606i
$783$	−60.1537	−	18.5549i	−2.14972	−	0.663100i
$784$	−4.46717	−	59.6103i	−0.159542	−	2.12894i
$785$	2.28414	+	10.0074i	0.0815243	+	0.357181i
$786$	33.5711	−	85.5378i	1.19744	−	3.05103i
$787$	−2.89420	+	38.6204i	−0.103167	+	1.37667i	0.669950	+	0.742406i	$0.266316\pi$
$787$	−2.89420	+	38.6204i	−0.103167	+	1.37667i	−0.773117	+	0.634263i	$0.781304\pi$
$788$	5.68848	−	0.857400i	0.202644	−	0.0305436i
$789$	46.0737	+	42.7502i	1.64027	+	1.52195i
$790$	−3.50140	−	1.68618i	−0.124574	−	0.0599917i
$791$	21.7069	−	14.7995i	0.771808	−	0.526210i
$792$	6.28657	+	16.0179i	0.223383	+	0.569172i
$793$	16.3006	−	5.02806i	0.578851	−	0.178552i
$794$	−10.0747	+	9.34794i	−0.357537	+	0.331746i
$795$	6.51436	−	8.16875i	0.231041	−	0.289716i
$796$	−16.7239	+	20.9711i	−0.592764	+	0.743302i
$797$	−28.3808	+	26.3335i	−1.00530	+	0.932782i	−0.997740	−	0.0671893i	$-0.978597\pi$
$797$	−28.3808	+	26.3335i	−1.00530	+	0.932782i	−0.00755980	+	0.999971i	$0.502406\pi$
$798$	−48.0156	+	14.8108i	−1.69973	+	0.524298i
$799$	5.02036	+	12.7917i	0.177608	+	0.452537i
$800$	−22.8211	+	15.5591i	−0.806847	+	0.550099i
$801$	31.5583	+	15.1977i	1.11506	+	0.536984i
$802$	1.84804	+	1.71473i	0.0652565	+	0.0605492i
$803$	28.2994	−	4.26544i	0.998663	−	0.150524i
$804$	−0.139086	+	1.85597i	−0.00490518	+	0.0654551i
$805$	−2.58769	+	6.59334i	−0.0912042	+	0.232385i
$806$	0.394447	+	1.72819i	0.0138938	+	0.0608727i
$807$	−0.538819	−	7.19005i	−0.0189673	−	0.253102i
$808$	−15.5658	−	4.80140i	−0.547602	−	0.168913i
$809$	23.3522	−	11.2458i	0.821018	−	0.395382i	0.0242795	−	0.999705i	$-0.492271\pi$
$809$	23.3522	−	11.2458i	0.821018	−	0.395382i	0.796739	+	0.604324i	$0.206557\pi$
$810$	−3.85814	+	6.68249i	−0.135561	+	0.234799i
$811$	−5.83095	−	10.0995i	−0.204752	−	0.354641i	0.745302	−	0.666728i	$-0.232306\pi$
$811$	−5.83095	−	10.0995i	−0.204752	−	0.354641i	−0.950054	+	0.312086i	$0.898972\pi$
$812$	32.3121	+	22.0300i	1.13393	+	0.773103i
$813$	−13.1562	+	57.6411i	−0.461408	+	2.02156i
$814$	−14.2287	−	2.14463i	−0.498716	−	0.0751693i
$815$	−8.11406	−	10.1747i	−0.284223	−	0.356404i
$816$	−21.6238			−0.756986
$817$	−11.3598	−	8.63165i	−0.397431	−	0.301983i
$818$	12.7105			0.444411
$819$	27.5099	+	34.4964i	0.961274	+	1.20540i
$820$	1.48329	+	0.223570i	0.0517988	+	0.00780741i
$821$	1.54182	−	6.75515i	0.0538099	−	0.235756i	−0.940870	−	0.338767i	$-0.889990\pi$
$821$	1.54182	−	6.75515i	0.0538099	−	0.235756i	0.994680	+	0.103010i	$0.0328474\pi$
$822$	−13.6048	−	9.27557i	−0.474521	−	0.323523i
$823$	−1.10308	−	1.91060i	−0.0384511	−	0.0665993i	0.846159	−	0.532930i	$-0.178909\pi$
$823$	−1.10308	−	1.91060i	−0.0384511	−	0.0665993i	−0.884611	+	0.466331i	$0.845576\pi$
$824$	0.101651	−	0.176065i	0.00354119	−	0.00613352i
$825$	25.2719	−	12.1703i	0.879854	−	0.423715i
$826$	38.0141	+	11.7258i	1.32268	+	0.407993i
$827$	−0.862574	−	11.5102i	−0.0299946	−	0.400250i	−0.991914	−	0.126915i	$-0.959492\pi$
$827$	−0.862574	−	11.5102i	−0.0299946	−	0.400250i	0.961919	−	0.273335i	$-0.0881267\pi$
$828$	4.15893	+	18.2214i	0.144533	+	0.633239i
$829$	17.7959	−	45.3432i	0.618077	−	1.57483i	−0.187450	−	0.982274i	$-0.560022\pi$
$829$	17.7959	−	45.3432i	0.618077	−	1.57483i	0.805527	−	0.592559i	$-0.201882\pi$
$830$	−0.822603	+	10.9769i	−0.0285530	+	0.381013i
$831$	−44.0671	+	6.64204i	−1.52867	+	0.230410i
$832$	−0.866353	−	0.803858i	−0.0300354	−	0.0278688i
$833$	−15.9157	−	7.66459i	−0.551446	−	0.265562i
$834$	−22.8366	+	15.5697i	−0.790767	+	0.539136i
$835$	−1.84743	−	4.70716i	−0.0639328	−	0.162898i
$836$	−5.00859	+	1.54495i	−0.173226	+	0.0534331i
$837$	3.47246	−	3.22197i	0.120026	−	0.111368i
$838$	−15.2492	+	19.1219i	−0.526776	+	0.660557i
$839$	−3.63297	+	4.55560i	−0.125424	+	0.157277i	−0.840579	−	0.541690i	$-0.817785\pi$
$839$	−3.63297	+	4.55560i	−0.125424	+	0.157277i	0.715155	+	0.698966i	$0.246356\pi$
$840$	−8.24403	+	7.64935i	−0.284446	+	0.263928i
$841$	27.1085	−	8.36187i	0.934777	−	0.288340i
$842$	1.21687	+	3.10052i	0.0419359	+	0.106851i
$843$	80.3458	−	54.7789i	2.76726	−	1.88668i
$844$	−20.2332	−	9.74381i	−0.696456	−	0.335396i
$845$	−4.35447	−	4.04036i	−0.149798	−	0.138993i
$846$	95.8348	−	14.4448i	3.29487	−	0.496621i
$847$	2.23536	−	29.8288i	0.0768078	−	1.02493i
$848$	10.7158	−	27.3035i	0.367983	−	0.937606i
$849$	−8.27329	−	36.2476i	−0.283938	−	1.24402i
$850$	0.908841	+	12.1276i	0.0311730	+	0.415975i
$851$	10.3059	+	3.17895i	0.353282	+	0.108973i
$852$	16.8854	−	8.13160i	0.578485	−	0.278584i
$853$	−6.61073	+	11.4501i	−0.226347	+	0.392045i	−0.956723	−	0.291001i	$-0.906012\pi$
$853$	−6.61073	+	11.4501i	−0.226347	+	0.392045i	0.730376	+	0.683046i	$0.239345\pi$
$854$	38.0905	+	65.9748i	1.30343	+	2.25761i
$855$	6.21902	+	4.24005i	0.212686	+	0.145007i
$856$	−1.89623	+	8.30793i	−0.0648118	+	0.283959i
$857$	−0.650028	−	0.0979759i	−0.0222045	−	0.00334679i	0.137931	−	0.990442i	$-0.455955\pi$
$857$	−0.650028	−	0.0979759i	−0.0222045	−	0.00334679i	−0.160135	+	0.987095i	$0.551193\pi$
$858$	11.7112	+	14.6854i	0.399814	+	0.501351i
$859$	38.6154			1.31754			0.658771	−	0.752344i	$-0.271077\pi$
$859$	38.6154			1.31754			0.658771	+	0.752344i	$0.271077\pi$
$860$	4.53430	+	0.923723i	0.154618	+	0.0314987i
$861$	−27.5150			−0.937708
$862$	26.5068	+	33.2385i	0.902825	+	1.13211i
$863$	16.3367	+	2.46236i	0.556108	+	0.0838198i	0.421083	−	0.907022i	$-0.361650\pi$
$863$	16.3367	+	2.46236i	0.556108	+	0.0838198i	0.135026	+	0.990842i	$0.456888\pi$
$864$	−10.9984	+	48.1873i	−0.374175	+	1.63937i
$865$	5.46092	+	3.72319i	0.185677	+	0.126592i
$866$	35.7621	+	61.9418i	1.21525	+	2.10487i
$867$	22.0221	−	38.1434i	0.747909	−	1.29542i
$868$	−2.65139	+	1.27684i	−0.0899941	+	0.0433389i
$869$	7.10549	+	2.19175i	0.241037	+	0.0743501i
$870$	−1.78662	−	23.8408i	−0.0605721	−	0.808279i
$871$	−0.205628	−	0.900916i	−0.00696745	−	0.0305264i
$872$	0.419816	−	1.06967i	0.0142168	−	0.0362237i
$873$	4.44603	−	59.3281i	0.150475	−	2.00795i
$874$	10.4500	−	1.57508i	0.353475	−	0.0532778i
$875$	18.3942	+	17.0673i	0.621836	+	0.576979i
$876$	44.4683	+	21.4148i	1.50244	+	0.723539i
$877$	−38.9124	+	26.5300i	−1.31398	+	0.895855i	−0.998589	−	0.0531078i	$-0.983087\pi$
$877$	−38.9124	+	26.5300i	−1.31398	+	0.895855i	−0.315389	+	0.948963i	$0.602135\pi$
$878$	−5.40389	−	13.7689i	−0.182372	−	0.464677i
$879$	−20.8289	+	6.42487i	−0.702542	+	0.216705i
$880$	−4.41947	+	4.10067i	−0.148980	+	0.138234i
$881$	16.0354	−	20.1078i	0.540246	−	0.677447i	−0.434523	−	0.900661i	$-0.643083\pi$
$881$	16.0354	−	20.1078i	0.540246	−	0.677447i	0.974770	+	0.223213i	$0.0716546\pi$
$882$	−77.6801	+	97.4077i	−2.61562	+	3.27989i
$883$	5.99913	−	5.56638i	0.201887	−	0.187324i	−0.572750	−	0.819730i	$-0.694123\pi$
$883$	5.99913	−	5.56638i	0.201887	−	0.187324i	0.774637	+	0.632407i	$0.217933\pi$
$884$	−2.89294	+	0.892355i	−0.0973003	+	0.0300132i
$885$	−3.30290	−	8.41564i	−0.111026	−	0.282889i
$886$	46.4313	−	31.6563i	1.55989	−	1.06352i
$887$	−25.8411	−	12.4444i	−0.867658	−	0.417842i	−0.0535564	−	0.998565i	$-0.517056\pi$
$887$	−25.8411	−	12.4444i	−0.867658	−	0.417842i	−0.814101	+	0.580723i	$0.802770\pi$
$888$	12.5530	+	11.6475i	0.421252	+	0.390864i
$889$	−16.3132	+	2.45882i	−0.547128	+	0.0824662i
$890$	−0.480049	+	6.40580i	−0.0160913	+	0.214723i
$891$	5.39392	−	13.7435i	0.180703	−	0.460424i
$892$	−2.54456	−	11.1484i	−0.0851981	−	0.373277i
$893$	−1.52236	−	20.3145i	−0.0509439	−	0.679799i
$894$	−102.996	−	31.7702i	−3.44471	−	1.06255i
$895$	−8.28261	+	3.98870i	−0.276857	+	0.133327i
$896$	−23.3084	+	40.3713i	−0.778678	+	1.34871i
$897$	−7.03918	−	12.1922i	−0.235031	−	0.407086i
$898$	−22.7488	−	15.5099i	−0.759138	−	0.517571i
$899$	−0.960619	+	4.20875i	−0.0320385	+	0.140370i
$900$	31.5295	+	4.75231i	1.05098	+	0.158410i
$901$	−5.40425	−	6.77671i	−0.180042	−	0.225765i
$902$	−7.72083			−0.257076
$903$	−84.7678	−	4.35832i	−2.82090	−	0.145036i
$904$	−8.77319			−0.291792
$905$	1.19274	+	1.49564i	0.0396479	+	0.0497169i
$906$	−104.506	−	15.7518i	−3.47199	−	0.523318i
$907$	−2.08244	+	9.12375i	−0.0691461	+	0.302949i	−0.997662	−	0.0683442i	$-0.978228\pi$
$907$	−2.08244	+	9.12375i	−0.0691461	+	0.302949i	0.928516	+	0.371293i	$0.121086\pi$
$908$	−17.2639	−	11.7703i	−0.572923	−	0.390612i
$909$	32.4306	+	56.1714i	1.07566	+	1.86309i
$910$	−4.04590	+	7.00770i	−0.134120	+	0.232303i
$911$	15.5906	−	7.50806i	0.516541	−	0.248753i	−0.157404	−	0.987534i	$-0.550313\pi$
$911$	15.5906	−	7.50806i	0.516541	−	0.248753i	0.673945	+	0.738781i	$0.264598\pi$
$912$	30.6325	+	9.44888i	1.01434	+	0.312884i
$913$	−1.57394	−	21.0028i	−0.0520899	−	0.695092i
$914$	−3.68652	−	16.1517i	−0.121939	−	0.534250i
$915$	6.32501	−	16.1159i	0.209098	−	0.532774i
$916$	−0.0209425	+	0.279458i	−0.000691959	+	0.00923355i
$917$	−74.8963	+	11.2888i	−2.47329	+	0.372789i
$918$	15.9535	+	14.8027i	0.526545	+	0.488562i
$919$	32.5165	+	15.6591i	1.07262	+	0.516546i	0.884950	−	0.465686i	$-0.154192\pi$
$919$	32.5165	+	15.6591i	1.07262	+	0.516546i	0.187669	+	0.982232i	$0.439907\pi$
$920$	1.95427	−	1.33240i	0.0644305	−	0.0439280i
$921$	12.3342	+	31.4270i	0.406425	+	1.03555i
$922$	35.6579	−	10.9990i	1.17433	−	0.362233i
$923$	−6.82121	+	6.32916i	−0.224523	+	0.208327i
$924$	−19.4423	+	24.3799i	−0.639606	+	0.802041i
$925$	11.4720	−	14.3854i	0.377196	−	0.472988i
$926$	2.86322	−	2.65668i	0.0940913	−	0.0873040i
$927$	−0.773544	+	0.238607i	−0.0254065	+	0.00783687i
$928$	−16.4565	−	41.9304i	−0.540210	−	1.37643i
$929$	11.9724	−	8.16266i	0.392803	−	0.267808i	−0.350772	−	0.936461i	$-0.614081\pi$
$929$	11.9724	−	8.16266i	0.392803	−	0.267808i	0.743575	+	0.668652i	$0.233129\pi$
$930$	1.62088	+	0.780575i	0.0531508	+	0.0255961i
$931$	19.1971	+	17.8123i	0.629161	+	0.583776i
$932$	−8.15395	+	1.22901i	−0.267091	+	0.0402575i
$933$	5.50765	−	73.4945i	0.180312	−	2.40610i
$934$	0.150554	−	0.383605i	0.00492627	−	0.0125519i
$935$	0.396447	+	1.73695i	0.0129652	+	0.0568042i
$936$	−1.10108	−	14.6930i	−0.0359901	−	0.480254i
$937$	10.8335	+	3.34170i	0.353916	+	0.109169i	0.466615	−	0.884461i	$-0.345473\pi$
$937$	10.8335	+	3.34170i	0.353916	+	0.109169i	−0.112699	+	0.993629i	$0.535950\pi$
$938$	3.71817	−	1.79058i	0.121403	−	0.0584644i
$939$	−25.1146	+	43.4998i	−0.819584	+	1.41956i
$940$	3.30366	+	5.72210i	0.107753	+	0.186634i
$941$	−28.7723	−	19.6166i	−0.937949	−	0.639483i	−0.00519143	−	0.999987i	$-0.501652\pi$
$941$	−28.7723	−	19.6166i	−0.937949	−	0.639483i	−0.932758	+	0.360504i	$0.882605\pi$
$942$	20.2753	−	88.8319i	0.660605	−	2.89430i
$943$	5.72223	+	0.862488i	0.186342	+	0.0280865i
$944$	−15.8238	−	19.8424i	−0.515021	−	0.645816i
$945$	21.6237			0.703419
$946$	−23.7863	−	1.22296i	−0.773358	−	0.0397620i
$947$	34.7749			1.13003			0.565016	−	0.825080i	$-0.308870\pi$
$947$	34.7749			1.13003			0.565016	+	0.825080i	$0.308870\pi$
$948$	7.99549	+	10.0260i	0.259682	+	0.325630i
$949$	−24.2319	−	3.65237i	−0.786600	−	0.118561i
$950$	4.01189	−	17.5772i	0.130163	−	0.570281i
$951$	57.9815	+	39.5311i	1.88018	+	1.28188i
$952$	4.66486	+	8.07977i	0.151189	+	0.261867i
$953$	−3.94892	+	6.83974i	−0.127918	+	0.221561i	−0.922870	−	0.385112i	$-0.874163\pi$
$953$	−3.94892	+	6.83974i	−0.127918	+	0.221561i	0.794952	+	0.606673i	$0.207496\pi$
$954$	−55.0783	+	26.5243i	−1.78322	+	0.858756i
$955$	3.03886	+	0.937364i	0.0983352	+	0.0303324i
$956$	−2.61081	−	34.8389i	−0.0844397	−	1.12677i
$957$	10.1790	+	44.5972i	0.329041	+	1.44162i
$958$	−3.26544	+	8.32020i	−0.105502	+	0.268814i
$959$	−1.01427	+	13.5344i	−0.0327523	+	0.437050i
$960$	−1.18606	+	0.178769i	−0.0382798	+	0.00576975i
$961$	22.4865	+	20.8644i	0.725370	+	0.673045i
$962$	11.1010	+	5.34597i	0.357911	+	0.172361i
$963$	28.0352	−	19.1141i	0.903422	−	0.615943i
$964$	7.51496	+	19.1478i	0.242041	+	0.616710i
$965$	3.83023	−	1.18147i	0.123299	−	0.0380328i
$966$	46.0887	−	42.7641i	1.48288	−	1.37591i
$967$	−2.09656	+	2.62900i	−0.0674208	+	0.0845429i	−0.814398	−	0.580306i	$-0.802933\pi$
$967$	−2.09656	+	2.62900i	−0.0674208	+	0.0845429i	0.746978	+	0.664849i	$0.231504\pi$
$968$	−6.22796	+	7.80962i	−0.200174	+	0.251011i
$969$	6.94435	−	6.44342i	0.223085	−	0.206992i
$970$	10.4262	−	3.21605i	0.334765	−	0.103261i
$971$	−17.7430	−	45.2084i	−0.569400	−	1.45081i	−0.868065	−	0.496450i	$-0.834637\pi$
$971$	−17.7430	−	45.2084i	−0.569400	−	1.45081i	0.298665	−	0.954358i	$-0.403459\pi$
$972$	−3.34131	+	2.27807i	−0.107173	+	0.0730691i
$973$	20.5261	+	9.88485i	0.658037	+	0.316894i
$974$	−17.0552	−	15.8249i	−0.546485	−	0.507064i
$975$	−23.7498	+	3.57970i	−0.760602	+	0.114642i
$976$	3.63198	−	48.4654i	0.116257	−	1.55134i
$977$	0.376939	−	0.960425i	0.0120593	−	0.0307267i	−0.924717	−	0.380655i	$-0.875699\pi$
$977$	0.376939	−	0.960425i	0.0120593	−	0.0307267i	0.936777	+	0.349928i	$0.113794\pi$
$978$	25.7055	+	112.623i	0.821970	+	3.60128i
$979$	−0.918509	−	12.2567i	−0.0293557	−	0.391724i
$980$	−8.11648	−	2.50360i	−0.259272	−	0.0799747i
$981$	−4.12238	+	1.98523i	−0.131618	+	0.0633837i
$982$	22.5907	−	39.1283i	0.720899	−	1.24863i
$983$	27.8010	+	48.1527i	0.886713	+	1.53583i	0.843738	+	0.536756i	$0.180350\pi$
$983$	27.8010	+	48.1527i	0.886713	+	1.53583i	0.0429752	+	0.999076i	$0.486316\pi$
$984$	7.59171	+	5.17594i	0.242015	+	0.165003i
$985$	−0.645049	+	2.82614i	−0.0205530	+	0.0900484i
$986$	−19.6120	−	2.95604i	−0.624574	−	0.0941394i
$987$	−75.5647	−	94.7551i	−2.40525	−	3.01609i
$988$	4.48810			0.142785
$989$	17.4924	+	3.56354i	0.556226	+	0.113314i
$990$	12.5655			0.399357
$991$	−26.0171	−	32.6244i	−0.826461	−	1.03635i	−0.998684	−	0.0512909i	$-0.983666\pi$
$991$	−26.0171	−	32.6244i	−0.826461	−	1.03635i	0.172223	−	0.985058i	$-0.444905\pi$
$992$	3.35170	+	0.505187i	0.106416	+	0.0160397i
$993$	−15.9612	+	69.9308i	−0.506515	+	2.21919i
$994$	−34.3352	−	23.4094i	−1.08905	−	0.742500i
$995$	−6.75813	−	11.7054i	−0.214247	−	0.371087i
$996$	18.1614	−	31.4565i	0.575466	−	0.996736i
$997$	−15.0791	+	7.26169i	−0.477558	+	0.229980i	−0.657148	−	0.753762i	$-0.728237\pi$
$997$	−15.0791	+	7.26169i	−0.477558	+	0.229980i	0.179589	+	0.983742i	$0.442523\pi$
$998$	−14.8070	−	4.56736i	−0.468708	−	0.144577i
$999$	−2.46056	−	32.8339i	−0.0778486	−	1.03882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.9.2	✓	36
3.2	odd	2		387.2.y.c.181.2		36
4.3	odd	2		688.2.bg.c.353.3		36
43.14	even	21		1849.2.a.n.1.5		18
43.24	even	21	inner	43.2.g.a.24.2	yes	36
43.29	odd	42		1849.2.a.o.1.14		18
129.110	odd	42		387.2.y.c.325.2		36
172.67	odd	42		688.2.bg.c.497.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.9.2	✓	36	1.1	even	1	trivial
43.2.g.a.24.2	yes	36	43.24	even	21	inner
387.2.y.c.181.2		36	3.2	odd	2
387.2.y.c.325.2		36	129.110	odd	42
688.2.bg.c.353.3		36	4.3	odd	2
688.2.bg.c.497.3		36	172.67	odd	42
1849.2.a.n.1.5		18	43.14	even	21
1849.2.a.o.1.14		18	43.29	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)

\(f(q)\)	\(=\)	\(q+(-1.11243 - 1.39495i) q^{2} +(-2.93359 - 0.442167i) q^{3} +(-0.263330 + 1.15372i) q^{4} +(-0.492700 - 0.335917i) q^{5} +(2.64662 + 4.58409i) q^{6} +(2.18154 - 3.77854i) q^{7} +(-1.31271 + 0.632167i) q^{8} +(5.54371 + 1.71001i) q^{9} +O(q^{10})\)	\(q+(-1.11243 - 1.39495i) q^{2} +(-2.93359 - 0.442167i) q^{3} +(-0.263330 + 1.15372i) q^{4} +(-0.492700 - 0.335917i) q^{5} +(2.64662 + 4.58409i) q^{6} +(2.18154 - 3.77854i) q^{7} +(-1.31271 + 0.632167i) q^{8} +(5.54371 + 1.71001i) q^{9} +(0.0795092 + 1.06098i) q^{10} +(-0.452993 - 1.98469i) q^{11} +(1.28264 - 3.26811i) q^{12} +(-0.130264 + 1.73826i) q^{13} +(-7.69769 + 1.16024i) q^{14} +(1.29685 + 1.20330i) q^{15} +(4.47454 + 2.15483i) q^{16} +(1.21261 - 0.826746i) q^{17} +(-3.78164 - 9.63546i) q^{18} +(-2.07906 + 0.641305i) q^{19} +(0.517297 - 0.479982i) q^{20} +(-8.07048 + 10.1201i) q^{21} +(-2.26462 + 2.83974i) q^{22} +(1.99563 - 1.85167i) q^{23} +(4.13047 - 1.27408i) q^{24} +(-1.69679 - 4.32336i) q^{25} +(2.56969 - 1.75199i) q^{26} +(-7.48807 - 3.60606i) q^{27} +(3.78492 + 3.51189i) q^{28} +(7.48963 - 1.12888i) q^{29} +(0.235882 - 3.14762i) q^{30} +(-0.208229 + 0.530558i) q^{31} +(-1.32334 - 5.79793i) q^{32} +(0.451329 + 6.02256i) q^{33} +(-2.50222 - 0.771833i) q^{34} +(-2.34412 + 1.12887i) q^{35} +(-3.43270 + 5.94561i) q^{36} +(1.98083 + 3.43090i) q^{37} +(3.20740 + 2.18677i) q^{38} +(1.15074 - 5.04173i) q^{39} +(0.859126 + 0.129492i) q^{40} +(1.32534 + 1.66193i) q^{41} +23.0949 q^{42} +(3.81986 + 5.32998i) q^{43} +2.40907 q^{44} +(-2.15696 - 2.70475i) q^{45} +(-4.80299 - 0.723935i) q^{46} +(-2.08348 + 9.12834i) q^{47} +(-12.1737 - 8.29987i) q^{48} +(-6.01823 - 10.4239i) q^{49} +(-4.14329 + 7.17639i) q^{50} +(-3.92287 + 1.88915i) q^{51} +(-1.97117 - 0.608024i) q^{52} +(-0.441351 - 5.88942i) q^{53} +(3.29971 + 14.4570i) q^{54} +(-0.443502 + 1.13002i) q^{55} +(-0.475058 + 6.33921i) q^{56} +(6.38267 - 0.962032i) q^{57} +(-9.90645 - 9.19184i) q^{58} +(-4.60418 - 2.21726i) q^{59} +(-1.72977 + 1.17934i) q^{60} +(-3.57526 - 9.10961i) q^{61} +(0.971743 - 0.299743i) q^{62} +(18.5551 - 17.2167i) q^{63} +(-0.422726 + 0.530082i) q^{64} +(0.648092 - 0.812681i) q^{65} +(7.89909 - 7.32929i) q^{66} +(-0.506577 + 0.156258i) q^{67} +(0.634519 + 1.61673i) q^{68} +(-6.67310 + 4.54964i) q^{69} +(4.18239 + 2.01413i) q^{70} +(3.91319 + 3.63091i) q^{71} +(-8.35828 + 1.25981i) q^{72} +(-1.05058 + 14.0191i) q^{73} +(2.58239 - 6.57982i) q^{74} +(3.06604 + 13.4332i) q^{75} +(-0.192410 - 2.56753i) q^{76} +(-8.48745 - 2.61803i) q^{77} +(-8.31309 + 4.00337i) q^{78} +(-1.82633 + 3.16330i) q^{79} +(-1.48076 - 2.56476i) q^{80} +(5.99228 + 4.08546i) q^{81} +(0.843946 - 3.69757i) q^{82} +(10.2305 + 1.54199i) q^{83} +(-9.55055 - 11.9760i) q^{84} -0.875173 q^{85} +(3.18571 - 11.2578i) q^{86} -22.4706 q^{87} +(1.84930 + 2.31895i) q^{88} +(5.97021 + 0.899865i) q^{89} +(-1.37350 + 6.01770i) q^{90} +(6.28390 + 4.28429i) q^{91} +(1.61081 + 2.79000i) q^{92} +(0.845453 - 1.46437i) q^{93} +(15.0513 - 7.24833i) q^{94} +(1.23978 + 0.382420i) q^{95} +(1.31848 + 17.5939i) q^{96} +(-2.28198 - 9.99799i) q^{97} +(-7.84589 + 19.9910i) q^{98} +(0.882576 - 11.7772i) 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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