LMFDB - Embedded newform 722.2.i.a.505.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$16$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			505.13
Character	$\chi$	$=$	722.505
Dual form			722.2.i.a.539.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.851919 + 0.523673i) q^{2} +(0.655642 - 1.75114i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.237058 + 0.322529i) q^{5} +(0.358471 + 1.83517i) q^{6} +(-1.22782 + 1.87932i) q^{7} +(0.0825793 + 0.996584i) q^{8} +(-0.374312 - 0.325989i) q^{9} +O(q^{10})$	\(q+(-0.851919 + 0.523673i) q^{2} +(0.655642 - 1.75114i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.237058 + 0.322529i) q^{5} +(0.358471 + 1.83517i) q^{6} +(-1.22782 + 1.87932i) q^{7} +(0.0825793 + 0.996584i) q^{8} +(-0.374312 - 0.325989i) q^{9} +(-0.370854 - 0.150628i) q^{10} +(-3.25518 - 1.11750i) q^{11} +(-1.26642 - 1.37570i) q^{12} +(-3.48527 - 4.23194i) q^{13} +(0.0618556 - 2.24401i) q^{14} +(0.720219 - 0.203659i) q^{15} +(-0.592235 - 0.805765i) q^{16} +(-1.59462 - 3.15106i) q^{17} +(0.489595 + 0.0816990i) q^{18} +(-3.63045 + 2.41243i) q^{19} +(0.394818 - 0.0658834i) q^{20} +(2.48595 + 3.38225i) q^{21} +(3.35835 - 0.752625i) q^{22} +(-1.85213 - 4.94682i) q^{23} +(1.79930 + 0.508795i) q^{24} +(1.44475 - 4.61911i) q^{25} +(5.18532 + 1.78012i) q^{26} +(4.11720 - 2.22812i) q^{27} +(1.12243 + 1.94411i) q^{28} +(1.69248 + 0.0933769i) q^{29} +(-0.506918 + 0.550660i) q^{30} +(-0.225686 + 0.122135i) q^{31} +(0.926494 + 0.376309i) q^{32} +(-4.09114 + 4.96759i) q^{33} +(3.00861 + 1.84939i) q^{34} +(-0.897201 + 0.0494999i) q^{35} +(-0.459879 + 0.186787i) q^{36} +(-3.71828 - 1.27649i) q^{37} +(1.82953 - 3.95636i) q^{38} +(-9.69581 + 3.32858i) q^{39} +(-0.301851 + 0.262883i) q^{40} +(-5.44433 - 5.29633i) q^{41} +(-3.88902 - 1.57958i) q^{42} +(-1.01978 + 0.414200i) q^{43} +(-2.46692 + 2.39986i) q^{44} +(0.0164071 - 0.198005i) q^{45} +(4.16838 + 3.24438i) q^{46} +(0.434335 + 2.22355i) q^{47} +(-1.79930 + 0.508795i) q^{48} +(0.787566 + 1.79547i) q^{49} +(1.18810 + 4.69168i) q^{50} +(-6.56345 + 0.726442i) q^{51} +(-5.34968 + 1.19889i) q^{52} +(-1.19118 - 6.09817i) q^{53} +(-2.34072 + 4.05425i) q^{54} +(-0.411238 - 1.31480i) q^{55} +(-1.97429 - 1.06844i) q^{56} +(1.84422 + 7.93913i) q^{57} +(-1.49076 + 0.806758i) q^{58} +(7.34928 + 7.14949i) q^{59} +(0.143488 - 0.734578i) q^{60} +(-8.86482 + 4.18341i) q^{61} +(0.128308 - 0.222235i) q^{62} +(1.07223 - 0.303197i) q^{63} +(-0.986361 + 0.164595i) q^{64} +(0.538710 - 2.12732i) q^{65} +(0.883926 - 6.37441i) q^{66} +(-2.66338 + 1.84675i) q^{67} -3.53157 q^{68} -9.87691 q^{69} +(0.738421 - 0.512010i) q^{70} +(2.75422 + 1.29975i) q^{71} +(0.293965 - 0.399954i) q^{72} +(-1.03979 - 2.05468i) q^{73} +(3.83614 - 0.859698i) q^{74} +(-7.14148 - 5.55844i) q^{75} +(0.513228 + 4.32858i) q^{76} +(6.09693 - 4.74543i) q^{77} +(6.51697 - 7.91311i) q^{78} +(-1.92248 + 0.780843i) q^{79} +(0.119489 - 0.382026i) q^{80} +(-1.40687 - 10.1456i) q^{81} +(7.41168 + 1.66100i) q^{82} +(-1.52077 - 3.46700i) q^{83} +(4.14032 - 0.690897i) q^{84} +(0.638290 - 1.26129i) q^{85} +(0.651868 - 0.886898i) q^{86} +(1.27318 - 2.90256i) q^{87} +(0.844876 - 3.33634i) q^{88} +(5.46934 - 10.8077i) q^{89} +(0.0897122 + 0.177276i) q^{90} +(12.2325 - 1.35389i) q^{91} +(-5.25012 - 0.581083i) q^{92} +(0.0659068 + 0.475286i) q^{93} +(-1.53443 - 1.66684i) q^{94} +(-1.63871 - 0.599042i) q^{95} +(1.26642 - 1.37570i) q^{96} +(10.0423 + 6.96321i) q^{97} +(-1.61118 - 1.11717i) q^{98} +(0.854159 + 1.47945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) $ 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{47}{57}\right)$

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 $

$2$	−0.851919	+	0.523673i	−0.602398	+	0.370293i
$2$	−0.851919	+	0.523673i	−0.602398	+	0.370293i
$3$	0.655642	−	1.75114i	0.378535	−	1.01102i	−0.599093	−	0.800680i	$-0.704472\pi$
$3$	0.655642	−	1.75114i	0.378535	−	1.01102i	0.977628	−	0.210343i	$-0.0674579\pi$
$4$	0.451533	−	0.892254i	0.225767	−	0.446127i
$5$	0.237058	+	0.322529i	0.106016	+	0.144239i	0.855539	−	0.517739i	$-0.173226\pi$
$5$	0.237058	+	0.322529i	0.106016	+	0.144239i	−0.749523	+	0.661978i	$0.769717\pi$
$6$	0.358471	+	1.83517i	0.146345	+	0.749207i
$7$	−1.22782	+	1.87932i	−0.464073	+	0.710317i	−0.990133	−	0.140131i	$-0.955248\pi$
$7$	−1.22782	+	1.87932i	−0.464073	+	0.710317i	0.526060	+	0.850447i	$0.323669\pi$
$8$	0.0825793	+	0.996584i	0.0291962	+	0.352346i
$9$	−0.374312	−	0.325989i	−0.124771	−	0.108663i
$10$	−0.370854	−	0.150628i	−0.117274	−	0.0476327i
$11$	−3.25518	−	1.11750i	−0.981473	−	0.336940i	−0.213162	−	0.977017i	$-0.568376\pi$
$11$	−3.25518	−	1.11750i	−0.981473	−	0.336940i	−0.768311	+	0.640077i	$0.778903\pi$
$12$	−1.26642	−	1.37570i	−0.365584	−	0.397130i
$13$	−3.48527	−	4.23194i	−0.966641	−	1.17373i	−0.984765	−	0.173892i	$-0.944366\pi$
$13$	−3.48527	−	4.23194i	−0.966641	−	1.17373i	0.0181234	−	0.999836i	$-0.494231\pi$
$14$	0.0618556	−	2.24401i	0.0165316	−	0.599736i
$15$	0.720219	−	0.203659i	0.185960	−	0.0525844i
$16$	−0.592235	−	0.805765i	−0.148059	−	0.201441i
$17$	−1.59462	−	3.15106i	−0.386752	−	0.764243i	0.612912	−	0.790151i	$-0.289998\pi$
$17$	−1.59462	−	3.15106i	−0.386752	−	0.764243i	−0.999664	+	0.0259078i	$0.991752\pi$
$18$	0.489595	+	0.0816990i	0.115399	+	0.0192566i
$19$	−3.63045	+	2.41243i	−0.832883	+	0.553449i
$19$	−3.63045	+	2.41243i	−0.832883	+	0.553449i
$20$	0.394818	−	0.0658834i	0.0882839	−	0.0147320i
$21$	2.48595	+	3.38225i	0.542478	+	0.738068i
$22$	3.35835	−	0.752625i	0.716004	−	0.160460i
$23$	−1.85213	−	4.94682i	−0.386196	−	1.03148i	−0.974804	−	0.223064i	$-0.928394\pi$
$23$	−1.85213	−	4.94682i	−0.386196	−	1.03148i	0.588608	−	0.808418i	$-0.299676\pi$
$24$	1.79930	+	0.508795i	0.367281	+	0.103857i
$25$	1.44475	−	4.61911i	0.288949	−	0.923822i
$26$	5.18532	+	1.78012i	1.01693	+	0.349111i
$27$	4.11720	−	2.22812i	0.792356	−	0.428802i
$28$	1.12243	+	1.94411i	0.212119	+	0.367401i
$29$	1.69248	+	0.0933769i	0.314286	+	0.0173397i	0.211544	−	0.977368i	$-0.432151\pi$
$29$	1.69248	+	0.0933769i	0.314286	+	0.0173397i	0.102742	+	0.994708i	$0.467238\pi$
$30$	−0.506918	+	0.550660i	−0.0925502	+	0.100536i
$31$	−0.225686	+	0.122135i	−0.0405344	+	0.0219361i	−0.496088	−	0.868272i	$-0.665231\pi$
$31$	−0.225686	+	0.122135i	−0.0405344	+	0.0219361i	0.455554	+	0.890208i	$0.349441\pi$
$32$	0.926494	+	0.376309i	0.163783	+	0.0665227i
$33$	−4.09114	+	4.96759i	−0.712176	+	0.864747i
$34$	3.00861	+	1.84939i	0.515973	+	0.317167i
$35$	−0.897201	+	0.0494999i	−0.151655	+	0.00836702i
$36$	−0.459879	+	0.186787i	−0.0766465	+	0.0311311i
$37$	−3.71828	−	1.27649i	−0.611281	−	0.209853i	0.00163798	−	0.999999i	$-0.499479\pi$
$37$	−3.71828	−	1.27649i	−0.611281	−	0.209853i	−0.612919	+	0.790146i	$0.710005\pi$
$38$	1.82953	−	3.95636i	0.296789	−	0.641807i
$39$	−9.69581	+	3.32858i	−1.55257	+	0.532999i
$40$	−0.301851	+	0.262883i	−0.0477269	+	0.0415654i
$41$	−5.44433	−	5.29633i	−0.850262	−	0.827148i	0.136278	−	0.990671i	$-0.456486\pi$
$41$	−5.44433	−	5.29633i	−0.850262	−	0.827148i	−0.986539	+	0.163523i	$0.947714\pi$
$42$	−3.88902	−	1.57958i	−0.600089	−	0.243735i
$43$	−1.01978	+	0.414200i	−0.155516	+	0.0631650i	−0.452739	−	0.891643i	$-0.649553\pi$
$43$	−1.01978	+	0.414200i	−0.155516	+	0.0631650i	0.297224	+	0.954808i	$0.403939\pi$
$44$	−2.46692	+	2.39986i	−0.371902	+	0.361792i
$45$	0.0164071	−	0.198005i	0.00244583	−	0.0295168i
$46$	4.16838	+	3.24438i	0.614594	+	0.478358i
$47$	0.434335	+	2.22355i	0.0633543	+	0.324339i	0.999638	−	0.0269062i	$-0.00856554\pi$
$47$	0.434335	+	2.22355i	0.0633543	+	0.324339i	−0.936284	+	0.351245i	$0.885759\pi$
$48$	−1.79930	+	0.508795i	−0.259707	+	0.0734382i
$49$	0.787566	+	1.79547i	0.112509	+	0.256496i
$50$	1.18810	+	4.69168i	0.168022	+	0.663504i
$51$	−6.56345	+	0.726442i	−0.919066	+	0.101722i
$52$	−5.34968	+	1.19889i	−0.741867	+	0.166256i
$53$	−1.19118	−	6.09817i	−0.163621	−	0.837649i	−0.969410	−	0.245446i	$-0.921066\pi$
$53$	−1.19118	−	6.09817i	−0.163621	−	0.837649i	0.805789	−	0.592203i	$-0.201741\pi$
$54$	−2.34072	+	4.05425i	−0.318532	+	0.551713i
$55$	−0.411238	−	1.31480i	−0.0554514	−	0.177288i
$56$	−1.97429	−	1.06844i	−0.263826	−	0.142776i
$57$	1.84422	+	7.93913i	0.244274	+	1.05156i
$58$	−1.49076	+	0.806758i	−0.195746	+	0.105933i
$59$	7.34928	+	7.14949i	0.956794	+	0.930784i	0.997659	−	0.0683807i	$-0.0217833\pi$
$59$	7.34928	+	7.14949i	0.956794	+	0.930784i	−0.0408649	+	0.999165i	$0.513011\pi$
$60$	0.143488	−	0.734578i	0.0185242	−	0.0948336i
$61$	−8.86482	+	4.18341i	−1.13502	+	0.535631i	−0.899797	−	0.436310i	$-0.856285\pi$
$61$	−8.86482	+	4.18341i	−1.13502	+	0.535631i	−0.235227	+	0.971940i	$0.575583\pi$
$62$	0.128308	−	0.222235i	0.0162951	−	0.0282239i
$63$	1.07223	−	0.303197i	0.135088	−	0.0381992i
$64$	−0.986361	+	0.164595i	−0.123295	+	0.0205743i
$65$	0.538710	−	2.12732i	0.0668187	−	0.263861i
$66$	0.883926	−	6.37441i	0.108804	−	0.784636i
$67$	−2.66338	+	1.84675i	−0.325384	+	0.225616i	−0.721222	−	0.692704i	$-0.756419\pi$
$67$	−2.66338	+	1.84675i	−0.325384	+	0.225616i	0.395838	+	0.918320i	$0.370454\pi$
$68$	−3.53157			−0.428265
$69$	−9.87691			−1.18904
$70$	0.738421	−	0.512010i	0.0882582	−	0.0611969i
$71$	2.75422	+	1.29975i	0.326865	+	0.154251i	0.583182	−	0.812341i	$-0.301807\pi$
$71$	2.75422	+	1.29975i	0.326865	+	0.154251i	−0.256317	+	0.966593i	$0.582509\pi$
$72$	0.293965	−	0.399954i	0.0346441	−	0.0471350i
$73$	−1.03979	−	2.05468i	−0.121698	−	0.240482i	0.823266	−	0.567655i	$-0.192149\pi$
$73$	−1.03979	−	2.05468i	−0.121698	−	0.240482i	−0.944964	+	0.327174i	$0.893904\pi$
$74$	3.83614	−	0.859698i	0.445942	−	0.0999379i
$75$	−7.14148	−	5.55844i	−0.824627	−	0.641833i
$76$	0.513228	+	4.32858i	0.0588712	+	0.496522i
$77$	6.09693	−	4.74543i	0.694809	−	0.540792i
$78$	6.51697	−	7.91311i	0.737901	−	0.895984i
$79$	−1.92248	+	0.780843i	−0.216296	+	0.0878517i	−0.481885	−	0.876235i	$-0.660048\pi$
$79$	−1.92248	+	0.780843i	−0.216296	+	0.0878517i	0.265589	+	0.964086i	$0.414434\pi$
$80$	0.119489	−	0.382026i	0.0133592	−	0.0427118i
$81$	−1.40687	−	10.1456i	−0.156319	−	1.12729i
$82$	7.41168	+	1.66100i	0.818483	+	0.183426i
$83$	−1.52077	−	3.46700i	−0.166926	−	0.380552i	0.812325	−	0.583205i	$-0.198202\pi$
$83$	−1.52077	−	3.46700i	−0.166926	−	0.380552i	−0.979251	+	0.202653i	$0.935044\pi$
$84$	4.14032	−	0.690897i	0.451746	−	0.0753830i
$85$	0.638290	−	1.26129i	0.0692322	−	0.136807i
$86$	0.651868	−	0.886898i	0.0702927	−	0.0956367i
$87$	1.27318	−	2.90256i	0.136499	−	0.311187i
$88$	0.844876	−	3.33634i	0.0900641	−	0.355655i
$89$	5.46934	−	10.8077i	0.579749	−	1.14562i	−0.394237	−	0.919009i	$-0.628991\pi$
$89$	5.46934	−	10.8077i	0.579749	−	1.14562i	0.973986	−	0.226607i	$-0.0727633\pi$
$90$	0.0897122	+	0.177276i	0.00945649	+	0.0186865i
$91$	12.2325	−	1.35389i	1.28231	−	0.141926i
$92$	−5.25012	−	0.581083i	−0.547362	−	0.0605820i
$93$	0.0659068	+	0.475286i	0.00683422	+	0.0492848i
$94$	−1.53443	−	1.66684i	−0.158265	−	0.171921i
$95$	−1.63871	−	0.599042i	−0.168128	−	0.0614604i
$96$	1.26642	−	1.37570i	0.129253	−	0.140407i
$97$	10.0423	+	6.96321i	1.01965	+	0.707007i	0.956720	−	0.291011i	$-0.0939918\pi$
$97$	10.0423	+	6.96321i	1.01965	+	0.707007i	0.0629264	+	0.998018i	$0.479957\pi$
$98$	−1.61118	−	1.11717i	−0.162754	−	0.112851i
$99$	0.854159	+	1.47945i	0.0858462	+	0.148690i
$100$	−3.46907	−	3.37476i	−0.346907	−	0.337476i
$101$	−11.6964	−	10.1864i	−1.16384	−	1.01358i	−0.999631	−	0.0271586i	$-0.991354\pi$
$101$	−11.6964	−	10.1864i	−1.16384	−	1.01358i	−0.164204	−	0.986426i	$-0.552506\pi$
$102$	5.21111	−	4.05597i	0.515977	−	0.401601i
$103$	8.15908	+	12.4884i	0.803938	+	1.23052i	0.969687	+	0.244351i	$0.0785749\pi$
$103$	8.15908	+	12.4884i	0.803938	+	1.23052i	−0.165749	+	0.986168i	$0.553004\pi$
$104$	3.92967	−	3.82284i	0.385336	−	0.374860i
$105$	−0.501561	+	1.60358i	−0.0489474	+	0.156493i
$106$	4.20824	+	4.57136i	0.408740	+	0.444010i
$107$	14.3767	+	7.78028i	1.38985	+	0.752148i	0.986633	−	0.162957i	$-0.0521032\pi$
$107$	14.3767	+	7.78028i	1.38985	+	0.752148i	0.403215	+	0.915105i	$0.367893\pi$
$108$	−0.128994	−	4.67966i	−0.0124125	−	0.450301i
$109$	−2.97658	+	15.2384i	−0.285105	+	1.45958i	0.513692	+	0.857975i	$0.328278\pi$
$109$	−2.97658	+	15.2384i	−0.285105	+	1.45958i	−0.798796	+	0.601602i	$0.794529\pi$
$110$	1.03887	+	0.904751i	0.0990522	+	0.0862647i
$111$	−4.67317	+	5.67432i	−0.443558	+	0.538582i
$112$	2.24145	−	0.123664i	0.211797	−	0.0116852i
$113$	−6.60570	−	10.1108i	−0.621412	−	0.951141i	−0.999676	−	0.0254439i	$-0.991900\pi$
$113$	−6.60570	−	10.1108i	−0.621412	−	0.951141i	0.378265	−	0.925698i	$-0.376521\pi$
$114$	−5.72864	−	5.79773i	−0.536536	−	0.543007i
$115$	1.15643	−	1.77005i	0.107838	−	0.165058i
$116$	0.847529	−	1.46796i	0.0786911	−	0.136297i
$117$	−0.0749825	+	2.72022i	−0.00693213	+	0.251485i
$118$	−10.0050	−	2.24217i	−0.921034	−	0.206408i
$119$	7.87976	+	0.872131i	0.722336	+	0.0799481i
$120$	0.262438	+	0.700942i	0.0239572	+	0.0639869i
$121$	0.666818	+	0.519005i	0.0606198	+	0.0471823i
$122$	5.36137	−	8.20619i	0.485396	−	0.742954i
$123$	−12.8442	+	6.06130i	−1.15812	+	0.546529i
$124$	0.00707086	+	0.256518i	0.000634982	+	0.0230360i
$125$	3.72523	−	1.27887i	0.333195	−	0.114386i
$126$	−0.754674	+	0.819795i	−0.0672317	+	0.0730331i
$127$	3.32862	+	5.76533i	0.295367	+	0.511590i	0.975070	−	0.221897i	$-0.0712248\pi$
$127$	3.32862	+	5.76533i	0.295367	+	0.511590i	−0.679703	+	0.733487i	$0.737891\pi$
$128$	0.754107	−	0.656752i	0.0666542	−	0.0580492i
$129$	0.0567105	+	2.05735i	0.00499308	+	0.181140i
$130$	0.655081	+	2.09441i	0.0574544	+	0.183692i
$131$	−0.166076	+	6.02492i	−0.0145101	+	0.526400i	0.957093	+	0.289782i	$0.0935828\pi$
$131$	−0.166076	+	6.02492i	−0.0145101	+	0.526400i	−0.971603	+	0.236618i	$0.923961\pi$
$132$	2.58507	+	5.89337i	0.225002	+	0.512952i
$133$	−0.0761756	−	9.78482i	−0.00660526	−	0.848451i
$134$	1.30189	−	2.96802i	0.112467	−	0.256398i
$135$	1.69465	+	0.799724i	0.145852	+	0.0688293i
$136$	3.00861	−	1.84939i	0.257986	−	0.158584i
$137$	6.25630	−	4.33802i	0.534512	−	0.370622i	−0.271577	−	0.962417i	$-0.587545\pi$
$137$	6.25630	−	4.33802i	0.534512	−	0.370622i	0.806089	+	0.591795i	$0.201580\pi$
$138$	8.41433	−	5.17227i	0.716275	−	0.440293i
$139$	2.12443	−	15.3202i	0.180191	−	1.29945i	−0.657563	−	0.753399i	$-0.728413\pi$
$139$	2.12443	−	15.3202i	0.180191	−	1.29945i	0.837755	−	0.546047i	$-0.183868\pi$
$140$	−0.360950	+	0.822882i	−0.0305058	+	0.0695462i
$141$	4.17852	+	0.697272i	0.351895	+	0.0587209i
$142$	−3.02701	+	0.335030i	−0.254021	+	0.0281151i
$143$	6.61598	+	17.6705i	0.553256	+	1.47768i
$144$	−0.0409895	+	0.494670i	−0.00341579	+	0.0412225i
$145$	0.371100	+	0.568011i	0.0308182	+	0.0471707i
$146$	1.96179	+	1.20591i	0.162359	+	0.0998018i
$147$	3.66049	−	0.201955i	0.301912	−	0.0166569i
$148$	−2.81788	+	2.74127i	−0.231628	+	0.225331i
$149$	−4.05842	−	1.14761i	−0.332479	−	0.0940160i	0.101773	−	0.994808i	$-0.467549\pi$
$149$	−4.05842	−	1.14761i	−0.332479	−	0.0940160i	−0.434252	+	0.900792i	$0.642987\pi$
$150$	8.99477	+	0.995541i	0.734420	+	0.0812856i
$151$	−1.67124	−	6.59956i	−0.136003	−	0.537065i	−0.999467	−	0.0326535i	$-0.989604\pi$
$151$	−1.67124	−	6.59956i	−0.136003	−	0.537065i	0.863463	−	0.504411i	$-0.168291\pi$
$152$	−2.70399	−	3.41884i	−0.219322	−	0.277304i
$153$	−0.430323	+	1.69931i	−0.0347895	+	0.137381i
$154$	−2.70904	+	7.23552i	−0.218300	+	0.583055i
$155$	−0.0928929	−	0.0438372i	−0.00746134	−	0.00352109i
$156$	−1.40805	+	10.1541i	−0.112734	+	0.812978i
$157$	−2.59358	+	6.92716i	−0.206991	+	0.552847i	−0.998282	−	0.0585919i	$-0.981339\pi$
$157$	−2.59358	+	6.92716i	−0.206991	+	0.552847i	0.791291	+	0.611439i	$0.209409\pi$
$158$	1.22889	−	1.67196i	0.0977652	−	0.133014i
$159$	−11.4598	−	1.91230i	−0.908818	−	0.151655i
$160$	0.0982622	+	0.388028i	0.00776831	+	0.0306763i
$161$	11.5707	+	2.59306i	0.911902	+	0.204362i
$162$	6.51154	+	7.90652i	0.511595	+	0.621195i
$163$	−5.24684	−	2.83945i	−0.410964	−	0.222403i	0.257292	−	0.966334i	$-0.417170\pi$
$163$	−5.24684	−	2.83945i	−0.410964	−	0.222403i	−0.668257	+	0.743931i	$0.732959\pi$
$164$	−7.18397	+	2.46626i	−0.560974	+	0.192583i
$165$	−2.57203	−	0.141903i	−0.200232	−	0.0110471i
$166$	3.11114	+	2.15722i	0.241471	+	0.167433i
$167$	16.4053	+	0.905105i	1.26948	+	0.0700391i	0.677264	−	0.735740i	$-0.263166\pi$
$167$	16.4053	+	0.905105i	1.26948	+	0.0700391i	0.592216	+	0.805780i	$0.298253\pi$
$168$	−3.16541	+	2.75676i	−0.244217	+	0.212689i
$169$	−3.26990	+	16.7400i	−0.251530	+	1.28770i
$170$	0.116735	+	1.40878i	0.00895313	+	0.108048i
$171$	2.14535	+	0.280486i	0.164059	+	0.0214493i
$172$	−0.0908943	+	1.09693i	−0.00693063	+	0.0836402i
$173$	−18.8896	−	5.34148i	−1.43615	−	0.406105i	−0.536941	−	0.843620i	$-0.680420\pi$
$173$	−18.8896	−	5.34148i	−1.43615	−	0.406105i	−0.899211	+	0.437515i	$0.855859\pi$
$174$	0.435344	+	3.13947i	0.0330034	+	0.238003i
$175$	6.90690	+	8.38658i	0.522112	+	0.633966i
$176$	1.02739	+	3.28473i	0.0774421	+	0.247596i
$177$	17.3383	−	8.18212i	1.30322	−	0.615006i
$178$	1.00027	+	12.0715i	0.0749733	+	0.904794i
$179$	−2.68625	+	2.09079i	−0.200780	+	0.156273i	−0.709612	−	0.704592i	$-0.751130\pi$
$179$	−2.68625	+	2.09079i	−0.200780	+	0.156273i	0.508833	+	0.860866i	$0.330077\pi$
$180$	−0.169262	−	0.104045i	−0.0126161	−	0.00775506i
$181$	18.2416	+	11.2130i	1.35588	+	0.833459i	0.995070	−	0.0991779i	$-0.0316213\pi$
$181$	18.2416	+	11.2130i	1.35588	+	0.833459i	0.360815	+	0.932637i	$0.382498\pi$
$182$	−9.71208	+	7.55921i	−0.719907	+	0.560326i
$183$	1.51360	+	18.2664i	0.111888	+	1.35029i
$184$	4.77697	−	2.25431i	0.352163	−	0.166190i
$185$	−0.469744	−	1.50185i	−0.0345363	−	0.110419i
$186$	−0.305041	−	0.370391i	−0.0223667	−	0.0271584i
$187$	1.66946	+	12.0392i	0.122083	+	0.880396i
$188$	2.18009	+	0.616471i	0.158999	+	0.0449608i
$189$	−0.867841	+	10.4733i	−0.0631261	+	0.761819i
$190$	1.70975	−	0.347811i	0.124038	−	0.0252329i
$191$	−0.874174	−	10.5497i	−0.0632530	−	0.763350i	−0.952227	−	0.305392i	$-0.901213\pi$
$191$	−0.874174	−	10.5497i	−0.0632530	−	0.763350i	0.888974	−	0.457958i	$-0.151419\pi$
$192$	−0.358471	+	1.83517i	−0.0258704	+	0.132442i
$193$	8.84819	−	7.70590i	0.636907	−	0.554683i	−0.276866	−	0.960909i	$-0.589296\pi$
$193$	8.84819	−	7.70590i	0.636907	−	0.554683i	0.913773	+	0.406226i	$0.133155\pi$
$194$	−12.2017	−	0.673187i	−0.876032	−	0.0483320i
$195$	−3.37203	−	2.33812i	−0.241476	−	0.167436i
$196$	1.95763	+	0.108005i	0.139831	+	0.00771467i
$197$	15.8185	−	5.43050i	1.12702	−	0.386907i	0.302733	−	0.953076i	$-0.402101\pi$
$197$	15.8185	−	5.43050i	1.12702	−	0.386907i	0.824290	+	0.566168i	$0.191575\pi$
$198$	−1.50242	−	0.813069i	−0.106772	−	0.0577823i
$199$	9.10836	+	11.0597i	0.645674	+	0.783999i	0.987812	−	0.155651i	$-0.0497475\pi$
$199$	9.10836	+	11.0597i	0.645674	+	0.783999i	−0.342138	+	0.939650i	$0.611151\pi$
$200$	4.72264	+	1.05837i	0.333941	+	0.0748379i
$201$	1.48769	+	5.87476i	0.104934	+	0.414374i
$202$	15.2987	+	2.55291i	1.07642	+	0.179622i
$203$	−2.25355	+	3.06607i	−0.158168	+	0.215196i
$204$	−2.31544	+	6.18428i	−0.162114	+	0.432986i
$205$	0.417597	−	3.01149i	0.0291663	−	0.210332i
$206$	−13.4907	−	6.36642i	−0.939943	−	0.443570i
$207$	−0.919332	+	2.45543i	−0.0638980	+	0.170664i
$208$	−1.34584	+	5.31461i	−0.0933174	+	0.368502i
$209$	14.5137	−	3.79583i	1.00393	−	0.262563i
$210$	−0.412462	−	1.62878i	−0.0284626	−	0.112396i
$211$	−27.4477	−	3.03791i	−1.88958	−	0.209139i	−0.910627	−	0.413229i	$-0.864401\pi$
$211$	−27.4477	−	3.03791i	−1.88958	−	0.209139i	−0.978952	+	0.204091i	$0.934576\pi$
$212$	−5.97898	−	1.69069i	−0.410638	−	0.116117i
$213$	4.08182	−	3.97086i	0.279682	−	0.272079i
$214$	−16.3221	+	0.900516i	−1.11576	+	0.0615580i
$215$	−0.375340	−	0.230720i	−0.0255979	−	0.0157350i
$216$	2.56050	+	3.91914i	0.174220	+	0.266664i
$217$	0.0475710	−	0.574097i	0.00322933	−	0.0389723i
$218$	−5.44415	−	14.5407i	−0.368724	−	0.984818i
$219$	−4.27976	+	0.473683i	−0.289199	+	0.0320085i
$220$	−1.35883	−	0.226748i	−0.0916120	−	0.0152873i
$221$	−7.77737	+	17.7306i	−0.523163	+	1.19269i
$222$	1.00968	−	7.28127i	0.0677652	−	0.488687i
$223$	−10.5889	+	6.50899i	−0.709087	+	0.435874i	−0.830712	−	0.556702i	$-0.812067\pi$
$223$	−10.5889	+	6.50899i	−0.709087	+	0.435874i	0.121625	+	0.992576i	$0.461189\pi$
$224$	−1.84478	+	1.27914i	−0.123259	+	0.0854661i
$225$	−2.04656	+	1.25802i	−0.136438	+	0.0838678i
$226$	10.9223	+	5.15434i	0.726538	+	0.342861i
$227$	−2.45228	+	5.59064i	−0.162764	+	0.371064i	−0.978164	−	0.207833i	$-0.933359\pi$
$227$	−2.45228	+	5.59064i	−0.162764	+	0.371064i	0.815401	+	0.578897i	$0.196517\pi$
$228$	7.91645	+	1.93926i	0.524280	+	0.128431i
$229$	−0.964355	−	2.19851i	−0.0637264	−	0.145282i	0.881025	−	0.473070i	$-0.156854\pi$
$229$	−0.964355	−	2.19851i	−0.0637264	−	0.145282i	−0.944751	+	0.327789i	$0.893697\pi$
$230$	−0.0582590	+	2.11353i	−0.00384149	+	0.139362i
$231$	−4.31252	−	13.7879i	−0.283743	−	0.907176i
$232$	0.0467062	+	1.69441i	0.00306641	+	0.111244i
$233$	12.3880	−	10.7887i	0.811567	−	0.706794i	−0.147781	−	0.989020i	$-0.547213\pi$
$233$	12.3880	−	10.7887i	0.811567	−	0.706794i	0.959348	+	0.282226i	$0.0910728\pi$
$234$	−1.36063	−	2.35668i	−0.0889471	−	0.154061i
$235$	−0.614198	+	0.667197i	−0.0400659	+	0.0435231i
$236$	9.69760	−	3.32919i	0.631260	−	0.216712i
$237$	0.106910	+	3.87848i	0.00694453	+	0.251935i
$238$	−7.16963	+	3.38343i	−0.464738	+	0.219315i
$239$	12.3957	−	18.9731i	0.801812	−	1.22727i	−0.168570	−	0.985690i	$-0.553915\pi$
$239$	12.3957	−	18.9731i	0.801812	−	1.22727i	0.970382	−	0.241575i	$-0.0776641\pi$
$240$	−0.590640	−	0.459714i	−0.0381257	−	0.0296744i
$241$	−1.63367	−	4.36333i	−0.105234	−	0.281067i	0.873290	−	0.487200i	$-0.161982\pi$
$241$	−1.63367	−	4.36333i	−0.105234	−	0.281067i	−0.978524	+	0.206134i	$0.933912\pi$
$242$	−0.839864	−	0.0929561i	−0.0539885	−	0.00597545i
$243$	−4.98446	−	1.11704i	−0.319753	−	0.0716584i
$244$	−0.270097	+	9.79862i	−0.0172912	+	0.627292i
$245$	−0.392393	+	0.679644i	−0.0250690	+	0.0434209i
$246$	7.76805	−	11.8899i	0.495272	−	0.758071i
$247$	22.8624	+	6.95587i	1.45470	+	0.442592i
$248$	−0.140355	−	0.214829i	−0.00891256	−	0.0136417i
$249$	−7.06828	+	0.389968i	−0.447934	+	0.0247132i
$250$	−2.50388	+	3.04030i	−0.158360	+	0.192285i
$251$	5.82511	+	5.07309i	0.367678	+	0.320211i	0.820776	−	0.571250i	$-0.193541\pi$
$251$	5.82511	+	5.07309i	0.367678	+	0.320211i	−0.453099	+	0.891460i	$0.649682\pi$
$252$	0.213617	−	1.09360i	0.0134566	−	0.0688904i
$253$	0.500922	+	18.1725i	0.0314927	+	1.14250i
$254$	−5.85486	−	3.16849i	−0.367367	−	0.198809i
$255$	−1.79022	−	1.94469i	−0.112108	−	0.121781i
$256$	−0.298515	+	0.954405i	−0.0186572	+	0.0596503i
$257$	−0.882920	+	0.858918i	−0.0550751	+	0.0535779i	−0.724320	−	0.689464i	$-0.757846\pi$
$257$	−0.882920	+	0.858918i	−0.0550751	+	0.0535779i	0.669244	+	0.743042i	$0.266618\pi$
$258$	−1.12569	−	1.72300i	−0.0700826	−	0.107269i
$259$	6.96431	−	5.42054i	0.432741	−	0.336816i
$260$	−1.65486	−	1.44122i	−0.102630	−	0.0893807i
$261$	−0.603077	−	0.586683i	−0.0373295	−	0.0363147i
$262$	−3.01360	−	5.21972i	−0.186181	−	0.322475i
$263$	−18.0591	−	12.5219i	−1.11357	−	0.772135i	−0.137701	−	0.990474i	$-0.543971\pi$
$263$	−18.0591	−	12.5219i	−1.11357	−	0.772135i	−0.975873	+	0.218339i	$0.929936\pi$
$264$	−5.28847	−	3.66694i	−0.325483	−	0.225685i
$265$	1.68446	−	1.82981i	0.103476	−	0.112404i
$266$	5.18894	+	8.29599i	0.318154	+	0.508660i
$267$	−15.3399	−	16.6636i	−0.938788	−	1.01980i
$268$	0.445163	+	3.21028i	0.0271926	+	0.196099i
$269$	−24.9150	−	2.75759i	−1.51910	−	0.168133i	−0.688593	−	0.725148i	$-0.741771\pi$
$269$	−24.9150	−	2.75759i	−1.51910	−	0.168133i	−0.830503	+	0.557015i	$0.811947\pi$
$270$	−1.86250	+	0.206141i	−0.113348	+	0.0125454i
$271$	3.43237	+	6.78256i	0.208502	+	0.412011i	0.972398	−	0.233328i	$-0.0749617\pi$
$271$	3.43237	+	6.78256i	0.208502	+	0.412011i	−0.763896	+	0.645339i	$0.776716\pi$
$272$	−1.59462	+	3.15106i	−0.0966881	+	0.191061i
$273$	5.64927	−	22.3084i	0.341909	−	1.35017i
$274$	−3.05816	+	6.97190i	−0.184750	+	0.421188i
$275$	−9.86477	+	13.4215i	−0.594868	+	0.809347i
$276$	−4.45975	+	8.81271i	−0.268446	+	0.530463i
$277$	−6.87370	+	1.14702i	−0.413001	+	0.0689176i	−0.367447	−	0.930044i	$-0.619768\pi$
$277$	−6.87370	+	1.14702i	−0.413001	+	0.0689176i	−0.0455532	+	0.998962i	$0.514505\pi$
$278$	6.21296	+	14.1641i	0.372629	+	0.849507i
$279$	0.124292	+	0.0278544i	0.00744115	+	0.00166760i
$280$	−0.123421	−	0.890049i	−0.00737582	−	0.0531906i
$281$	3.21402	−	10.2758i	0.191732	−	0.613003i	−0.807984	−	0.589204i	$-0.799441\pi$
$281$	3.21402	−	10.2758i	0.191732	−	0.613003i	0.999717	−	0.0237987i	$-0.00757607\pi$
$282$	−3.92491	+	1.59416i	−0.233725	+	0.0949309i
$283$	17.3745	−	21.0967i	1.03281	−	1.25407i	0.0661983	−	0.997806i	$-0.478913\pi$
$283$	17.3745	−	21.0967i	1.03281	−	1.25407i	0.966608	−	0.256260i	$-0.0824905\pi$
$284$	2.40332	−	1.87058i	0.142611	−	0.110999i
$285$	−2.12341	+	2.47685i	−0.125780	+	0.146716i
$286$	−14.8899	−	11.5892i	−0.880455	−	0.685286i
$287$	16.6382	−	3.72870i	0.982120	−	0.220098i
$288$	−0.224125	−	0.442884i	−0.0132067	−	0.0260972i
$289$	2.68166	−	3.64853i	0.157745	−	0.214619i
$290$	−0.613599	−	0.289564i	−0.0360318	−	0.0170038i
$291$	18.7778	−	13.0202i	1.10077	−	0.763258i
$292$	−2.30279			−0.134761
$293$	17.4161			1.01746			0.508729	−	0.860927i	$-0.330116\pi$
$293$	17.4161			1.01746			0.508729	+	0.860927i	$0.330116\pi$
$294$	−3.01268	+	2.08895i	−0.175703	+	0.121830i
$295$	−0.563712	+	4.06520i	−0.0328206	+	0.236685i
$296$	0.965074	−	3.81099i	0.0560938	−	0.221509i
$297$	−15.8922	+	2.65193i	−0.922156	+	0.153881i
$298$	4.05842	−	1.14761i	0.235098	−	0.0664794i
$299$	−14.4794	+	25.0791i	−0.837367	+	1.45036i
$300$	−8.18415	+	3.86220i	−0.472512	+	0.222984i
$301$	0.473697	−	2.42506i	0.0273034	−	0.139778i
$302$	4.87977	+	4.74712i	0.280799	+	0.273166i
$303$	−25.5065	+	13.8034i	−1.46531	+	0.792986i
$304$	4.09393	+	1.49657i	0.234803	+	0.0858341i
$305$	−3.45075	−	1.86745i	−0.197589	−	0.106930i
$306$	−0.523280	−	1.67302i	−0.0299140	−	0.0956402i
$307$	11.6420	−	20.1645i	0.664443	−	1.15085i	−0.314993	−	0.949094i	$-0.602002\pi$
$307$	11.6420	−	20.1645i	0.664443	−	1.15085i	0.979436	−	0.201755i	$-0.0646646\pi$
$308$	−1.48116	−	7.58273i	−0.0843971	−	0.432066i
$309$	27.2184	−	6.09979i	1.54840	−	0.347005i
$310$	0.102094	−	0.0112997i	0.00579853	−	0.000641781i
$311$	−4.23856	−	16.7377i	−0.240347	−	0.949107i	−0.965475	−	0.260494i	$-0.916115\pi$
$311$	−4.23856	−	16.7377i	−0.240347	−	0.949107i	0.725129	−	0.688613i	$-0.241780\pi$
$312$	−4.11788	−	9.38782i	−0.233129	−	0.531481i
$313$	18.5640	−	5.24940i	1.04930	−	0.296714i	0.296548	−	0.955018i	$-0.404165\pi$
$313$	18.5640	−	5.24940i	1.04930	−	0.296714i	0.752752	+	0.658304i	$0.228726\pi$
$314$	−1.41804	−	7.25957i	−0.0800246	−	0.409681i
$315$	0.351970	+	0.273949i	0.0198312	+	0.0154353i
$316$	−0.171352	+	2.06792i	−0.00963932	+	0.116329i
$317$	10.1474	−	9.87157i	0.569936	−	0.554442i	−0.354853	−	0.934922i	$-0.615469\pi$
$317$	10.1474	−	9.87157i	0.569936	−	0.554442i	0.924789	+	0.380480i	$0.124241\pi$
$318$	10.7642	−	4.37204i	0.603627	−	0.245172i
$319$	−5.40498	−	2.19531i	−0.302621	−	0.122914i
$320$	−0.286911	−	0.279112i	−0.0160388	−	0.0156028i
$321$	23.0503	−	20.0746i	1.28655	−	1.12045i
$322$	−11.2153	+	3.85020i	−0.625002	+	0.214563i
$323$	13.3909	+	7.59286i	0.745089	+	0.422478i
$324$	−9.68774	−	3.32580i	−0.538208	−	0.184767i
$325$	−24.5831	+	9.98479i	−1.36363	+	0.553857i
$326$	5.95683	−	0.328647i	0.329918	−	0.0182021i
$327$	24.7331	+	15.2034i	1.36774	+	0.840748i
$328$	4.82865	−	5.86310i	0.266618	−	0.323736i
$329$	−4.71206	−	1.91387i	−0.259784	−	0.105515i
$330$	2.26547	−	1.22601i	0.124710	−	0.0674898i
$331$	−21.4497	+	23.3006i	−1.17898	+	1.28071i	−0.227231	+	0.973841i	$0.572967\pi$
$331$	−21.4497	+	23.3006i	−1.17898	+	1.28071i	−0.951750	+	0.306874i	$0.900717\pi$
$332$	−3.78012	−	0.208555i	−0.207461	−	0.0114459i
$333$	0.975677	+	1.68992i	0.0534667	+	0.0926071i
$334$	−14.4500	+	7.81993i	−0.790667	+	0.427887i
$335$	−1.22701	−	0.421232i	−0.0670385	−	0.0230143i
$336$	1.25304	−	4.00618i	0.0683587	−	0.218555i
$337$	−19.9480	−	5.64076i	−1.08664	−	0.307272i	−0.318739	−	0.947843i	$-0.603259\pi$
$337$	−19.9480	−	5.64076i	−1.08664	−	0.307272i	−0.767899	+	0.640571i	$0.778698\pi$
$338$	−5.98062	−	15.9735i	−0.325303	−	0.868845i
$339$	−22.0364	+	4.93847i	−1.19685	+	0.268221i
$340$	−0.837187	−	1.13903i	−0.0454028	−	0.0617728i
$341$	0.871135	−	0.145367i	0.0471746	−	0.00787205i
$342$	−1.97455	+	0.884508i	−0.106771	+	0.0478287i
$343$	−19.8410	−	3.31087i	−1.07131	−	0.178770i
$344$	−0.496999	−	0.982096i	−0.0267964	−	0.0529511i
$345$	−2.34140	−	3.18559i	−0.126057	−	0.171506i
$346$	18.8896	−	5.34148i	1.01551	−	0.287160i
$347$	0.249534	−	9.05264i	0.0133957	−	0.485971i	−0.962941	−	0.269713i	$-0.913071\pi$
$347$	0.249534	−	9.05264i	0.0133957	−	0.485971i	0.976336	−	0.216258i	$-0.0693851\pi$
$348$	−2.01494	−	2.44660i	−0.108012	−	0.131152i
$349$	13.1127	+	14.2442i	0.701907	+	0.762474i	0.980197	−	0.198023i	$-0.0634520\pi$
$349$	13.1127	+	14.2442i	0.701907	+	0.762474i	−0.278291	+	0.960497i	$0.589768\pi$
$350$	−10.2759	−	3.52774i	−0.549272	−	0.188565i
$351$	−23.7788	−	9.65813i	−1.26922	−	0.515513i
$352$	−2.59538	−	2.26031i	−0.138334	−	0.120475i
$353$	−2.90611	−	35.0716i	−0.154677	−	1.86667i	−0.426716	−	0.904386i	$-0.640330\pi$
$353$	−2.90611	−	35.0716i	−0.154677	−	1.86667i	0.272039	−	0.962286i	$-0.412302\pi$
$354$	−10.4860	+	16.0501i	−0.557327	+	0.853053i
$355$	0.233703	+	1.19643i	0.0124037	+	0.0634999i
$356$	−7.17364	−	9.76009i	−0.380202	−	0.517284i
$357$	6.69353	−	13.2268i	0.354259	−	0.700035i
$358$	1.19358	−	3.18790i	0.0630825	−	0.168486i
$359$	−15.3836	+	9.45629i	−0.811917	+	0.499084i	−0.866352	−	0.499434i	$-0.833541\pi$
$359$	−15.3836	+	9.45629i	−0.811917	+	0.499084i	0.0544349	+	0.998517i	$0.482664\pi$
$360$	0.198683			0.0104715
$361$	7.36039	−	17.5164i	0.387389	−	0.921916i
$362$	−21.4123			−1.12541
$363$	1.34605	−	0.827411i	0.0706491	−	0.0434278i
$364$	4.31535	−	11.5258i	0.226186	−	0.604116i
$365$	0.416203	−	0.822439i	0.0217850	−	0.0430484i
$366$	−10.8551	−	14.7689i	−0.567403	−	0.771980i
$367$	3.46131	+	17.7200i	0.180679	+	0.924976i	0.955991	+	0.293397i	$0.0947859\pi$
$367$	3.46131	+	17.7200i	0.180679	+	0.924976i	−0.775312	+	0.631579i	$0.782407\pi$
$368$	−2.88908	+	4.42206i	−0.150603	+	0.230516i
$369$	0.311336	+	3.75727i	0.0162075	+	0.195596i
$370$	1.18666	+	1.03347i	0.0616917	+	0.0537274i
$371$	12.9230	+	5.24886i	0.670928	+	0.272507i
$372$	0.453835	+	0.155802i	0.0235302	+	0.00807794i
$373$	−12.1668	−	13.2167i	−0.629973	−	0.684333i	0.336329	−	0.941745i	$-0.390815\pi$
$373$	−12.1668	−	13.2167i	−0.629973	−	0.684333i	−0.966302	+	0.257412i	$0.917130\pi$
$374$	−7.72687	−	9.38221i	−0.399547	−	0.485143i
$375$	0.202929	−	7.36189i	0.0104792	−	0.380166i
$376$	−2.18009	+	0.616471i	−0.112430	+	0.0317921i
$377$	−5.50360	−	7.48792i	−0.283450	−	0.385648i
$378$	−4.74524	−	9.37685i	−0.244069	−	0.482293i
$379$	−25.3247	−	4.22595i	−1.30084	−	0.217073i	−0.526684	−	0.850061i	$-0.676565\pi$
$379$	−25.3247	−	4.22595i	−1.30084	−	0.217073i	−0.774161	+	0.632989i	$0.781828\pi$
$380$	−1.27443	+	1.19166i	−0.0653768	+	0.0611306i
$381$	12.2783	−	2.04889i	0.629036	−	0.104968i
$382$	6.26932	+	8.52972i	0.320766	+	0.436418i
$383$	10.4430	−	2.34032i	0.533611	−	0.119585i	0.0564573	−	0.998405i	$-0.482020\pi$
$383$	10.4430	−	2.34032i	0.533611	−	0.119585i	0.477153	+	0.878820i	$0.341669\pi$
$384$	−0.655642	−	1.75114i	−0.0334581	−	0.0893626i
$385$	2.97586	+	0.841494i	0.151664	+	0.0428865i
$386$	−3.50258	+	11.1984i	−0.178276	+	0.569982i
$387$	0.516742	+	0.177398i	0.0262675	+	0.00901763i
$388$	10.7474	−	5.81621i	0.545617	−	0.295273i
$389$	7.77562	+	13.4678i	0.394240	+	0.682843i	0.993004	−	0.118082i	$-0.0376746\pi$
$389$	7.77562	+	13.4678i	0.394240	+	0.682843i	−0.598764	+	0.800925i	$0.704341\pi$
$390$	4.09711	+	0.226044i	0.207465	+	0.0114462i
$391$	−12.6343	+	13.7245i	−0.638942	+	0.694076i
$392$	−1.72430	+	0.933145i	−0.0870904	+	0.0471310i
$393$	10.4416	+	4.24101i	0.526709	+	0.213931i
$394$	−10.6323	+	12.9101i	−0.535647	+	0.650400i
$395$	−0.707583	−	0.434950i	−0.0356024	−	0.0218847i
$396$	1.70572	−	0.0941074i	0.0857158	−	0.00472907i
$397$	−4.18468	+	1.69967i	−0.210023	+	0.0853039i	−0.478896	−	0.877872i	$-0.658963\pi$
$397$	−4.18468	+	1.69967i	−0.210023	+	0.0853039i	0.268873	+	0.963176i	$0.413349\pi$
$398$	−13.5512	−	4.65214i	−0.679262	−	0.233191i
$399$	−17.1846	−	6.28194i	−0.860304	−	0.314491i
$400$	−4.57755	+	1.57147i	−0.228877	+	0.0785737i
$401$	21.1782	−	18.4441i	1.05759	−	0.921054i	0.0605653	−	0.998164i	$-0.480710\pi$
$401$	21.1782	−	18.4441i	1.05759	−	0.921054i	0.997023	+	0.0771101i	$0.0245693\pi$
$402$	−4.34385	−	4.22576i	−0.216652	−	0.210762i
$403$	1.30345	+	0.529414i	0.0649293	+	0.0263720i
$404$	−14.3702	+	5.83666i	−0.714943	+	0.290385i
$405$	2.93875	−	2.85886i	0.146028	−	0.142058i
$406$	0.314228	−	3.79217i	0.0155949	−	0.188202i
$407$	10.6772	+	8.31038i	0.529248	+	0.411930i
$408$	−1.26597	−	6.48104i	−0.0626747	−	0.320859i
$409$	25.5410	−	7.22231i	1.26292	−	0.357120i	0.426141	−	0.904657i	$-0.359873\pi$
$409$	25.5410	−	7.22231i	1.26292	−	0.357120i	0.836782	+	0.547537i	$0.184434\pi$
$410$	1.22128	+	2.78423i	0.0603146	+	0.137503i
$411$	−3.49460	−	13.7999i	−0.172376	−	0.680697i
$412$	14.8269	−	1.64104i	0.730470	−	0.0808484i
$413$	−22.4598	+	5.03336i	−1.10517	+	0.247675i
$414$	−0.502643	−	2.57325i	−0.0247036	−	0.126469i
$415$	0.757698	−	1.31237i	0.0371939	−	0.0644217i
$416$	−1.63657	−	5.23240i	−0.0802394	−	0.256540i
$417$	−25.4351	−	13.7648i	−1.24556	−	0.674064i
$418$	−10.3767	+	10.8342i	−0.507541	+	0.529916i
$419$	20.2488	−	10.9581i	0.989219	−	0.535339i	0.101063	−	0.994880i	$-0.467776\pi$
$419$	20.2488	−	10.9581i	0.989219	−	0.535339i	0.888156	+	0.459542i	$0.151986\pi$
$420$	1.20433	+	1.17159i	0.0587653	+	0.0571677i
$421$	−3.06781	+	15.7055i	−0.149516	+	0.765437i	0.828997	+	0.559252i	$0.188912\pi$
$421$	−3.06781	+	15.7055i	−0.149516	+	0.765437i	−0.978513	+	0.206185i	$0.933895\pi$
$422$	24.9741	−	11.7856i	1.21572	−	0.573713i
$423$	0.562276	−	0.973891i	0.0273388	−	0.0473522i
$424$	5.97898	−	1.69069i	0.290365	−	0.0821074i
$425$	−16.8589	+	2.81325i	−0.817776	+	0.136463i
$426$	−1.39795	+	5.52039i	−0.0677310	+	0.267464i
$427$	3.02245	−	21.7963i	0.146267	−	1.05480i
$428$	13.4336	−	9.31462i	0.649335	−	0.450239i
$429$	35.2813			1.70340
$430$	0.440581			0.0212467
$431$	−33.1595	+	22.9923i	−1.59724	+	1.10750i	−0.664297	+	0.747469i	$0.731269\pi$
$431$	−33.1595	+	22.9923i	−1.59724	+	1.10750i	−0.932940	+	0.360031i	$0.882766\pi$
$432$	−4.23369	−	1.99793i	−0.203694	−	0.0961254i
$433$	20.9451	−	28.4969i	1.00656	−	1.36947i	0.0785522	−	0.996910i	$-0.474970\pi$
$433$	20.9451	−	28.4969i	1.00656	−	1.36947i	0.928007	−	0.372563i	$-0.121521\pi$
$434$	0.260112	+	0.513996i	0.0124858	+	0.0246726i
$435$	1.23798	−	0.277437i	0.0593564	−	0.0133021i
$436$	12.2525	+	9.53652i	0.586790	+	0.456717i
$437$	18.6579	+	13.4911i	0.892528	+	0.645365i
$438$	3.39795	−	2.64473i	0.162360	−	0.126370i
$439$	11.2875	−	13.7056i	0.538721	−	0.654133i	−0.429841	−	0.902904i	$-0.641430\pi$
$439$	11.2875	−	13.7056i	0.538721	−	0.654133i	0.968562	+	0.248772i	$0.0800270\pi$
$440$	1.27635	−	0.518409i	0.0608477	−	0.0247142i
$441$	0.290507	−	0.928804i	0.0138337	−	0.0442288i
$442$	−2.65935	−	19.1779i	−0.126493	−	0.912198i
$443$	−24.6540	−	5.52510i	−1.17135	−	0.262505i	−0.410762	−	0.911742i	$-0.634737\pi$
$443$	−24.6540	−	5.52510i	−1.17135	−	0.262505i	−0.760586	+	0.649237i	$0.775088\pi$
$444$	2.95284	+	6.73180i	0.140136	+	0.319477i
$445$	4.78236	−	0.798034i	0.226705	−	0.0378304i
$446$	5.61233	−	11.0903i	0.265752	−	0.525139i
$447$	−4.67050	+	6.35445i	−0.220907	+	0.300555i
$448$	0.901750	−	2.05578i	0.0426037	−	0.0971266i
$449$	−9.08288	+	35.8675i	−0.428648	+	1.69269i	0.258366	+	0.966047i	$0.416816\pi$
$449$	−9.08288	+	35.8675i	−0.428648	+	1.69269i	−0.687014	+	0.726645i	$0.741079\pi$
$450$	1.08472	−	2.14346i	0.0511340	−	0.101044i
$451$	11.8036	+	23.3245i	0.555810	+	1.09831i
$452$	−12.0041	+	1.32861i	−0.564624	+	0.0624926i
$453$	−12.6525	−	1.40038i	−0.594467	−	0.0657956i
$454$	−0.838520	−	6.04697i	−0.0393537	−	0.283798i
$455$	3.33647	+	3.62437i	0.156416	+	0.169913i
$456$	−7.75972	+	2.49353i	−0.363382	+	0.116770i
$457$	−9.17664	+	9.96849i	−0.429265	+	0.466306i	−0.912436	−	0.409220i	$-0.865801\pi$
$457$	−9.17664	+	9.96849i	−0.429265	+	0.466306i	0.483171	+	0.875526i	$0.339485\pi$
$458$	1.97285	+	1.36795i	0.0921853	+	0.0639199i
$459$	−13.5863	−	9.42053i	−0.634154	−	0.439713i
$460$	−1.05717	−	1.83107i	−0.0492906	−	0.0853739i
$461$	−3.41996	−	3.32698i	−0.159283	−	0.154953i	0.613338	−	0.789821i	$-0.289827\pi$
$461$	−3.41996	−	3.32698i	−0.159283	−	0.154953i	−0.772621	+	0.634868i	$0.781055\pi$
$462$	10.8943	+	9.48782i	0.506847	+	0.441413i
$463$	−0.0457251	+	0.0355893i	−0.00212503	+	0.00165397i	−0.615275	−	0.788313i	$-0.710955\pi$
$463$	−0.0457251	+	0.0355893i	−0.00212503	+	0.00165397i	0.613150	+	0.789967i	$0.289902\pi$
$464$	−0.927108	−	1.41905i	−0.0430399	−	0.0658775i
$465$	−0.137670	+	0.133927i	−0.00638428	+	0.00621072i
$466$	−4.90383	+	15.6784i	−0.227166	+	0.726289i
$467$	−19.7863	−	21.4937i	−0.915603	−	0.994610i	0.0843953	−	0.996432i	$-0.473104\pi$
$467$	−19.7863	−	21.4937i	−0.915603	−	0.994610i	−0.999998	+	0.00182234i	$0.999420\pi$
$468$	2.39327	+	1.29518i	0.110629	+	0.0598695i
$469$	−0.200474	−	7.27283i	−0.00925703	−	0.335828i
$470$	0.173854	−	0.890037i	0.00801930	−	0.0410543i
$471$	10.4300	+	9.08347i	0.480588	+	0.418544i
$472$	−6.51817	+	7.91458i	−0.300023	+	0.364298i
$473$	3.78245	−	0.208683i	0.173917	−	0.00959527i
$474$	−2.12214	−	3.24817i	−0.0974729	−	0.149193i
$475$	5.89818	+	20.2548i	0.270627	+	0.929354i
$476$	4.33614	−	6.63695i	0.198746	−	0.304204i
$477$	−1.54206	+	2.67093i	−0.0706062	+	0.122294i
$478$	−0.624476	+	22.6548i	−0.0285629	+	1.03621i
$479$	−16.4273	−	3.68145i	−0.750584	−	0.168210i	−0.173431	−	0.984846i	$-0.555485\pi$
$479$	−16.4273	−	3.68145i	−0.750584	−	0.168210i	−0.577153	+	0.816636i	$0.695836\pi$
$480$	0.743918	+	0.0823368i	0.0339550	+	0.00375814i
$481$	7.55721	+	20.1844i	0.344579	+	0.920330i
$482$	3.67671	+	2.86170i	0.167469	+	0.130347i
$483$	12.1271	−	18.5619i	0.551801	−	0.844595i
$484$	0.764175	−	0.360623i	0.0347352	−	0.0163919i
$485$	0.134782	+	4.88963i	0.00612013	+	0.222027i
$486$	4.83133	−	1.65860i	0.219153	−	0.0752355i
$487$	−15.7118	+	17.0676i	−0.711971	+	0.773406i	−0.981885	−	0.189478i	$-0.939320\pi$
$487$	−15.7118	+	17.0676i	−0.711971	+	0.773406i	0.269914	+	0.962884i	$0.413005\pi$
$488$	−4.90117	−	8.48908i	−0.221866	−	0.384282i
$489$	−8.41232	+	7.32630i	−0.380418	+	0.331307i
$490$	−0.0216242	−	0.784487i	−0.000976884	−	0.0354395i
$491$	8.20666	+	26.2382i	0.370361	+	1.18411i	0.933752	+	0.357921i	$0.116514\pi$
$491$	8.20666	+	26.2382i	0.370361	+	1.18411i	−0.563390	+	0.826191i	$0.690503\pi$
$492$	−0.391341	+	14.1971i	−0.0176430	+	0.640056i
$493$	−2.40463	−	5.48201i	−0.108299	−	0.246897i
$494$	−23.1195	+	6.04656i	−1.04020	+	0.272048i
$495$	−0.274679	+	0.626206i	−0.0123459	+	0.0281458i
$496$	0.232072	+	0.109517i	0.0104203	+	0.00491747i
$497$	−5.82433	+	3.58020i	−0.261257	+	0.160594i
$498$	5.81739	−	4.03369i	0.260684	−	0.180754i
$499$	−18.6620	+	11.4715i	−0.835426	+	0.513535i	−0.874116	−	0.485717i	$-0.838559\pi$
$499$	−18.6620	+	11.4715i	−0.835426	+	0.513535i	0.0386900	+	0.999251i	$0.487682\pi$
$500$	0.540986	−	3.90131i	0.0241936	−	0.174472i
$501$	12.3410	−	28.1346i	0.551354	−	1.25696i
$502$	−7.61916	−	1.27141i	−0.340060	−	0.0567460i
$503$	0.831752	−	0.0920582i	0.0370860	−	0.00410467i	−0.0914461	−	0.995810i	$-0.529149\pi$
$503$	0.831752	−	0.0920582i	0.0370860	−	0.00410467i	0.128532	+	0.991705i	$0.458973\pi$
$504$	0.390705	+	1.04353i	0.0174034	+	0.0464823i
$505$	0.512686	−	6.18720i	0.0228142	−	0.275327i
$506$	−9.94320	−	15.2192i	−0.442029	−	0.676576i
$507$	27.1703	+	16.7015i	1.20668	+	0.741741i
$508$	6.64712	−	0.366732i	0.294918	−	0.0162711i
$509$	−9.35660	+	9.10224i	−0.414724	+	0.403450i	−0.874842	−	0.484408i	$-0.839035\pi$
$509$	−9.35660	+	9.10224i	−0.414724	+	0.403450i	0.460118	+	0.887858i	$0.347807\pi$
$510$	2.54350	+	0.719234i	0.112628	+	0.0318482i
$511$	5.13807	+	0.568681i	0.227295	+	0.0251570i
$512$	−0.245485	−	0.969400i	−0.0108490	−	0.0428418i
$513$	−9.57214	+	18.0215i	−0.422620	+	0.795670i
$514$	0.302385	−	1.19409i	0.0133376	−	0.0526691i
$515$	−2.09370	+	5.59202i	−0.0922593	+	0.246414i
$516$	1.86129	+	0.878363i	0.0819387	+	0.0386678i
$517$	1.07099	−	7.72343i	0.0471021	−	0.339676i
$518$	−3.09444	+	8.26489i	−0.135962	+	0.363138i
$519$	−21.7385	+	29.5763i	−0.954215	+	1.29826i
$520$	2.16454	+	0.361197i	0.0949212	+	0.0158396i
$521$	7.33510	+	28.9657i	0.321357	+	1.26901i	0.893577	+	0.448909i	$0.148187\pi$
$521$	7.33510	+	28.9657i	0.321357	+	1.26901i	−0.572221	+	0.820100i	$0.693918\pi$
$522$	0.821003	+	0.183991i	0.0359343	+	0.00805307i
$523$	−13.2770	−	16.1214i	−0.580562	−	0.704938i	0.396465	−	0.918050i	$-0.370237\pi$
$523$	−13.2770	−	16.1214i	−0.580562	−	0.704938i	−0.977028	+	0.213112i	$0.931640\pi$
$524$	5.30077	+	2.86863i	0.231565	+	0.125317i
$525$	19.2146	−	6.59636i	0.838592	−	0.287889i
$526$	21.9423	+	1.21059i	0.956731	+	0.0527843i
$527$	0.744739	+	0.516390i	0.0324413	+	0.0224943i
$528$	6.42563	+	0.354512i	0.279640	+	0.0154282i
$529$	−3.69615	+	3.21898i	−0.160702	+	0.139956i
$530$	−0.476802	+	2.44096i	−0.0207109	+	0.106028i
$531$	−0.420271	−	5.07192i	−0.0182382	−	0.220103i
$532$	−8.76494	−	4.35020i	−0.380008	−	0.188605i
$533$	−3.43872	+	41.4992i	−0.148948	+	1.79753i
$534$	21.7946	+	6.16294i	0.943147	+	0.266696i
$535$	0.898746	+	6.48128i	0.0388562	+	0.280210i
$536$	−2.06038	−	2.50178i	−0.0889949	−	0.108061i
$537$	1.90006	+	6.07482i	0.0819934	+	0.262148i
$538$	22.6697	−	10.6981i	0.977359	−	0.461227i
$539$	−0.557223	−	6.72468i	−0.0240013	−	0.289653i
$540$	1.47875	−	1.15096i	0.0636352	−	0.0495293i
$541$	12.1821	+	7.48829i	0.523748	+	0.321947i	0.760192	−	0.649698i	$-0.225105\pi$
$541$	12.1821	+	7.48829i	0.523748	+	0.321947i	−0.236444	+	0.971645i	$0.575982\pi$
$542$	−6.47595	−	3.98075i	−0.278166	−	0.170988i
$543$	31.5956	−	24.5918i	1.35590	−	1.05534i
$544$	−0.291635	−	3.51951i	−0.0125037	−	0.150898i
$545$	−5.62046	+	2.65236i	−0.240754	+	0.113615i
$546$	6.86961	+	21.9634i	0.293992	+	0.939945i
$547$	9.05802	+	10.9985i	0.387293	+	0.470264i	0.928880	−	0.370381i	$-0.120773\pi$
$547$	9.05802	+	10.9985i	0.387293	+	0.470264i	−0.541587	+	0.840645i	$0.682176\pi$
$548$	−1.04569	−	7.54097i	−0.0446697	−	0.322134i
$549$	4.68195	+	1.32393i	0.199821	+	0.0565040i
$550$	1.37551	−	16.6000i	0.0586520	−	0.707825i
$551$	−6.36975	+	3.74399i	−0.271360	+	0.159499i
$552$	−0.815629	−	9.84318i	−0.0347155	−	0.418953i
$553$	0.893005	−	4.57169i	0.0379744	−	0.194408i
$554$	5.25518	−	4.57674i	0.223271	−	0.194447i
$555$	−2.93794	−	0.162091i	−0.124709	−	0.00688038i
$556$	−12.7103	−	8.81313i	−0.539037	−	0.373760i
$557$	0.537331	+	0.0296454i	0.0227674	+	0.00125611i	0.0664679	−	0.997789i	$-0.478827\pi$
$557$	0.537331	+	0.0296454i	0.0227674	+	0.00125611i	−0.0437005	+	0.999045i	$0.513915\pi$
$558$	−0.120473	+	0.0413585i	−0.00510004	+	0.00175084i
$559$	5.30709	+	2.87206i	0.224466	+	0.121475i
$560$	0.571239	+	0.693617i	0.0241393	+	0.0293107i
$561$	22.1770	+	4.96998i	0.936313	+	0.209833i
$562$	2.64307	+	10.4372i	0.111491	+	0.440269i
$563$	17.8007	+	2.97042i	0.750212	+	0.125188i	0.527334	−	0.849658i	$-0.323192\pi$
$563$	17.8007	+	2.97042i	0.750212	+	0.125188i	0.222878	+	0.974846i	$0.428455\pi$
$564$	2.50889	−	3.41346i	0.105643	−	0.143733i
$565$	1.69508	−	4.52737i	0.0713127	−	0.190468i
$566$	−3.75391	+	27.0712i	−0.157788	+	1.13789i
$567$	20.7943	+	9.81307i	0.873279	+	0.412110i
$568$	−1.06787	+	2.85214i	−0.0448066	+	0.119673i
$569$	−6.74745	+	26.6451i	−0.282868	+	1.11702i	0.650907	+	0.759158i	$0.274389\pi$
$569$	−6.74745	+	26.6451i	−0.282868	+	1.11702i	−0.933775	+	0.357862i	$0.883506\pi$
$570$	0.511916	−	3.22205i	0.0214418	−	0.134957i
$571$	−6.02654	−	23.7983i	−0.252203	−	0.995927i	−0.957828	−	0.287342i	$-0.907228\pi$
$571$	−6.02654	−	23.7983i	−0.252203	−	0.995927i	0.705625	−	0.708585i	$-0.250666\pi$
$572$	18.7539	+	2.07568i	0.784141	+	0.0867887i
$573$	−19.0472	−	5.38603i	−0.795708	−	0.225005i
$574$	−12.2218	+	11.8895i	−0.510126	+	0.496259i
$575$	−25.5257	+	1.40829i	−1.06450	+	0.0587299i
$576$	0.422863	+	0.259933i	0.0176193	+	0.0108305i
$577$	−12.3800	−	18.9490i	−0.515386	−	0.788858i	0.480733	−	0.876867i	$-0.340371\pi$
$577$	−12.3800	−	18.9490i	−0.515386	−	0.788858i	−0.996120	+	0.0880092i	$0.971950\pi$
$578$	−0.373922	+	4.51256i	−0.0155531	+	0.187698i
$579$	−7.69287	−	20.5467i	−0.319705	−	0.853894i
$580$	0.674374	−	0.0746397i	0.0280019	−	0.00309925i
$581$	8.38283	+	1.39885i	0.347778	+	0.0580339i
$582$	−9.17880	+	20.9256i	−0.380474	+	0.867393i
$583$	−2.93723	+	21.1818i	−0.121648	+	0.877260i
$584$	1.96179	−	1.20591i	0.0811795	−	0.0499009i
$585$	−0.895127	+	0.620667i	−0.0370089	+	0.0256614i
$586$	−14.8371	+	9.12033i	−0.612915	+	0.376757i
$587$	−0.577760	−	0.272651i	−0.0238467	−	0.0112535i	0.414816	−	0.909905i	$-0.363846\pi$
$587$	−0.577760	−	0.272651i	−0.0238467	−	0.0112535i	−0.438663	+	0.898652i	$0.644548\pi$
$588$	1.47264	−	3.35727i	0.0607305	−	0.138452i
$589$	0.524701	−	0.987858i	0.0216199	−	0.0407040i
$590$	−1.64860	−	3.75842i	−0.0678717	−	0.154732i
$591$	0.861702	−	31.2609i	0.0354457	−	1.28590i
$592$	1.17355	+	3.75204i	0.0482325	+	0.154208i
$593$	0.547427	+	19.8596i	0.0224801	+	0.815537i	0.923910	+	0.382611i	$0.124975\pi$
$593$	0.547427	+	19.8596i	0.0224801	+	0.815537i	−0.901429	+	0.432926i	$0.857481\pi$
$594$	12.1501	−	10.5815i	0.498524	−	0.434165i
$595$	1.58667	+	2.74820i	0.0650472	+	0.112665i
$596$	−2.85647	+	3.10296i	−0.117006	+	0.127102i
$597$	25.3389	−	8.69884i	1.03705	−	0.356020i
$598$	−0.797942	−	28.9479i	−0.0326303	−	1.18377i
$599$	−11.9898	+	5.65810i	−0.489888	+	0.231184i	−0.655768	−	0.754962i	$-0.727655\pi$
$599$	−11.9898	+	5.65810i	−0.489888	+	0.231184i	0.165880	+	0.986146i	$0.446953\pi$
$600$	4.94971	−	7.57610i	0.202071	−	0.309293i
$601$	27.5149	+	21.4157i	1.12236	+	0.873565i	0.993010	−	0.118034i	$-0.0376592\pi$
$601$	27.5149	+	21.4157i	1.12236	+	0.873565i	0.129347	+	0.991599i	$0.458712\pi$
$602$	0.866389	+	2.31402i	0.0353114	+	0.0943125i
$603$	1.59895	+	0.176972i	0.0651145	+	0.00720687i
$604$	−6.64311	−	1.48876i	−0.270304	−	0.0605766i
$605$	−0.00931973	+	0.338102i	−0.000378901	+	0.0137458i
$606$	14.5010	−	25.1165i	0.589063	−	1.02029i
$607$	2.41806	−	3.70112i	0.0981462	−	0.150224i	−0.784717	−	0.619854i	$-0.787192\pi$
$607$	2.41806	−	3.70112i	0.0981462	−	0.150224i	0.882863	+	0.469630i	$0.155613\pi$
$608$	−4.27141	+	0.868926i	−0.173229	+	0.0352396i
$609$	3.89160	+	5.95654i	0.157696	+	0.241371i
$610$	3.91769	−	0.216145i	0.158623	−	0.00875146i
$611$	7.89615	−	9.58777i	0.319444	−	0.387880i
$612$	1.32191	+	1.15125i	0.0534350	+	0.0465366i
$613$	0.179891	−	0.920941i	0.00726573	−	0.0371965i	−0.977642	−	0.210274i	$-0.932564\pi$
$613$	0.179891	−	0.920941i	0.00726573	−	0.0371965i	0.984908	+	0.173078i	$0.0553713\pi$
$614$	0.641575	+	23.2751i	0.0258918	+	0.939308i
$615$	−4.99976	−	2.70573i	−0.201610	−	0.109106i
$616$	5.23270	+	5.68423i	0.210831	+	0.229024i
$617$	7.74028	−	24.7471i	0.311612	−	0.996279i	−0.658286	−	0.752768i	$-0.728718\pi$
$617$	7.74028	−	24.7471i	0.311612	−	0.996279i	0.969898	−	0.243511i	$-0.0782992\pi$
$618$	−19.9936	+	19.4501i	−0.804260	+	0.782396i
$619$	−7.65851	−	11.7222i	−0.307821	−	0.471156i	0.649427	−	0.760424i	$-0.275009\pi$
$619$	−7.65851	−	11.7222i	−0.307821	−	0.471156i	−0.957248	+	0.289269i	$0.906588\pi$
$620$	−0.0810582	+	0.0630901i	−0.00325537	+	0.00253376i
$621$	−18.6477	−	16.2403i	−0.748306	−	0.651700i
$622$	12.3760	+	12.0395i	0.496232	+	0.482742i
$623$	13.5958	+	23.5486i	0.544704	+	0.943455i
$624$	8.42425	+	5.84125i	0.337240	+	0.233837i
$625$	−18.5905	−	12.8904i	−0.743622	−	0.515616i
$626$	−13.0661	+	14.1935i	−0.522225	+	0.567288i
$627$	2.86873	−	27.9042i	0.114566	−	1.11439i
$628$	5.00969	+	5.44198i	0.199909	+	0.217159i
$629$	1.90696	+	13.7520i	0.0760356	+	0.548329i
$630$	−0.443309	−	0.0490655i	−0.0176619	−	0.00195481i
$631$	33.3167	−	3.68749i	1.32632	−	0.146797i	0.581216	−	0.813750i	$-0.302577\pi$
$631$	33.3167	−	3.68749i	1.32632	−	0.146797i	0.745100	+	0.666953i	$0.232402\pi$
$632$	−0.936933	−	1.85143i	−0.0372692	−	0.0736459i
$633$	−23.3157	+	46.0731i	−0.926716	+	1.83124i
$634$	−3.47532	+	13.7237i	−0.138022	+	0.545038i
$635$	−1.07041	+	2.44029i	−0.0424780	+	0.0968401i
$636$	−6.88072	+	9.36155i	−0.272838	+	0.371210i
$637$	4.85343	−	9.59064i	0.192300	−	0.379995i
$638$	5.75424	−	0.960212i	0.227812	−	0.0380152i
$639$	−0.607234	−	1.38435i	−0.0240218	−	0.0547642i
$640$	0.390589	+	0.0875330i	0.0154394	+	0.00346004i
$641$	0.707562	+	5.10257i	0.0279470	+	0.201539i	0.999356	−	0.0358713i	$-0.0114206\pi$
$641$	0.707562	+	5.10257i	0.0279470	+	0.201539i	−0.971409	+	0.237411i	$0.923701\pi$
$642$	−9.12453	+	29.1728i	−0.360117	+	1.15136i
$643$	−7.80064	+	3.16834i	−0.307627	+	0.124947i	−0.524901	−	0.851163i	$-0.675898\pi$
$643$	−7.80064	+	3.16834i	−0.307627	+	0.124947i	0.217274	+	0.976111i	$0.430284\pi$
$644$	7.53825	−	9.15319i	0.297049	−	0.360686i
$645$	−0.650113	+	0.506003i	−0.0255982	+	0.0199238i
$646$	−15.3841	+	0.543944i	−0.605281	+	0.0214012i
$647$	5.65535	+	4.40174i	0.222335	+	0.173050i	0.719255	−	0.694746i	$-0.244483\pi$
$647$	5.65535	+	4.40174i	0.222335	+	0.173050i	−0.496920	+	0.867796i	$0.665536\pi$
$648$	9.99481	−	2.23989i	0.392633	−	0.0879911i
$649$	−15.9336	−	31.4857i	−0.625449	−	1.23592i
$650$	15.7141	−	21.3797i	0.616356	−	0.838583i
$651$	−0.974136	−	0.459706i	−0.0381794	−	0.0180173i
$652$	−4.90263	+	3.39941i	−0.192002	+	0.133131i
$653$	1.95827			0.0766329			0.0383164	−	0.999266i	$-0.487801\pi$
$653$	1.95827			0.0766329			0.0383164	+	0.999266i	$0.487801\pi$
$654$	−29.0322			−1.13525
$655$	−1.98258	+	1.37469i	−0.0774659	+	0.0537136i
$656$	−1.04327	+	7.52353i	−0.0407329	+	0.293744i
$657$	−0.280596	+	1.10805i	−0.0109471	+	0.0432291i
$658$	5.01653	−	0.837112i	0.195565	−	0.0326340i
$659$	6.00345	−	1.69762i	0.233861	−	0.0661297i	−0.153156	−	0.988202i	$-0.548944\pi$
$659$	6.00345	−	1.69762i	0.233861	−	0.0661297i	0.387018	+	0.922072i	$0.373505\pi$
$660$	−1.28797	+	2.23083i	−0.0501342	+	0.0868350i
$661$	16.4490	−	7.76245i	0.639790	−	0.301924i	−0.0792899	−	0.996852i	$-0.525265\pi$
$661$	16.4490	−	7.76245i	0.639790	−	0.301924i	0.719080	+	0.694927i	$0.244564\pi$
$662$	6.07152	−	31.0828i	0.235976	−	1.20807i
$663$	25.9497	+	25.2442i	1.00780	+	0.980405i
$664$	3.32957	−	1.80187i	0.129212	−	0.0699263i
$665$	3.13783	−	2.34414i	0.121680	−	0.0909018i
$666$	−1.71616	−	0.928741i	−0.0665000	−	0.0359880i
$667$	−2.67278	−	8.54535i	−0.103490	−	0.330877i
$668$	8.21512	−	14.2290i	0.317852	−	0.550537i
$669$	4.45562	+	22.8103i	0.172264	+	0.881896i
$670$	1.26590	−	0.283694i	0.0489059	−	0.0109601i
$671$	33.5315	−	3.71127i	1.29447	−	0.143272i
$672$	1.03044	+	4.06912i	0.0397501	+	0.156970i
$673$	−3.75240	−	8.55460i	−0.144644	−	0.329756i	0.828486	−	0.560009i	$-0.189202\pi$
$673$	−3.75240	−	8.55460i	−0.144644	−	0.329756i	−0.973131	+	0.230253i	$0.926044\pi$
$674$	19.9480	−	5.64076i	0.768369	−	0.217274i
$675$	−4.34361	−	22.2369i	−0.167186	−	0.855898i
$676$	13.4599	+	10.4763i	0.517689	+	0.402933i
$677$	−1.13339	+	13.6780i	−0.0435597	+	0.525688i	0.939518	+	0.342499i	$0.111273\pi$
$677$	−1.13339	+	13.6780i	−0.0435597	+	0.525688i	−0.983078	+	0.183189i	$0.941358\pi$
$678$	16.1871	−	15.7470i	0.621661	−	0.604761i
$679$	−25.4163	+	10.3232i	−0.975389	+	0.396169i
$680$	1.30970	+	0.531953i	0.0502246	+	0.0203995i
$681$	8.18219	+	7.95976i	0.313542	+	0.305019i
$682$	−0.666012	+	0.580031i	−0.0255029	+	0.0222105i
$683$	−9.92023	+	3.40562i	−0.379587	+	0.130312i	−0.507888	−	0.861423i	$-0.669574\pi$
$683$	−9.92023	+	3.40562i	−0.379587	+	0.130312i	0.128301	+	0.991735i	$0.459047\pi$
$684$	1.21896	−	1.78755i	0.0466081	−	0.0683485i
$685$	2.88224	+	0.989475i	0.110125	+	0.0378059i
$686$	18.6367	−	7.56958i	0.711553	−	0.289008i
$687$	−4.48217	+	0.247288i	−0.171006	+	0.00943464i
$688$	0.937700	+	0.576402i	0.0357495	+	0.0219751i
$689$	−21.6555	+	26.2948i	−0.825008	+	1.00175i
$690$	3.66289	+	1.48774i	0.139444	+	0.0566372i
$691$	−24.2536	+	13.1254i	−0.922652	+	0.499314i	−0.866539	−	0.499110i	$-0.833660\pi$
$691$	−24.2536	+	13.1254i	−0.922652	+	0.499314i	−0.0561136	+	0.998424i	$0.517871\pi$
$692$	−13.2953	+	14.4425i	−0.505410	+	0.549021i
$693$	−3.82911	−	0.211258i	−0.145456	−	0.00802502i
$694$	4.52804	+	7.84279i	0.171882	+	0.297708i
$695$	5.44484	−	2.94660i	0.206534	−	0.111771i
$696$	2.99778	+	1.02914i	0.113631	+	0.0390094i
$697$	−8.00738	+	25.6010i	−0.303301	+	0.969708i
$698$	−18.6303	−	5.26814i	−0.705166	−	0.199402i
$699$	−10.7705	−	28.7668i	−0.407378	−	1.08806i
$700$	10.6017	−	2.37589i	0.400705	−	0.0898001i
$701$	−19.7202	−	26.8303i	−0.744821	−	1.01337i	−0.998933	−	0.0461908i	$-0.985292\pi$
$701$	−19.7202	−	26.8303i	−0.744821	−	1.01337i	0.254111	−	0.967175i	$-0.418217\pi$
$702$	25.3154	−	4.22439i	0.955467	−	0.159439i
$703$	16.5785	−	4.33585i	0.625269	−	0.163530i
$704$	3.39472	+	0.566478i	0.127943	+	0.0213499i
$705$	0.765662	+	1.51299i	0.0288365	+	0.0569825i
$706$	20.8418	+	28.3563i	0.784392	+	1.06720i
$707$	33.5046	−	9.47420i	1.26007	−	0.356314i
$708$	0.528270	−	19.1646i	0.0198536	−	0.720251i
$709$	10.9433	+	13.2877i	0.410983	+	0.499029i	0.935969	−	0.352082i	$-0.114526\pi$
$709$	10.9433	+	13.2877i	0.410983	+	0.499029i	−0.524986	+	0.851111i	$0.675930\pi$
$710$	−0.825634	−	0.896878i	−0.0309855	−	0.0336592i
$711$	0.974152	+	0.334427i	0.0365336	+	0.0125420i
$712$	11.2225	+	4.55817i	0.420579	+	0.170825i
$713$	1.02218	+	0.890218i	0.0382810	+	0.0333389i
$714$	1.22416	+	14.7734i	0.0458129	+	0.552879i
$715$	−4.13088	+	6.32278i	−0.154486	+	0.236459i
$716$	0.652587	+	3.34088i	0.0243883	+	0.124855i
$717$	−25.0974	−	34.1462i	−0.937278	−	1.27521i
$718$	8.15362	−	16.1120i	0.304290	−	0.601294i
$719$	−4.89768	+	13.0811i	−0.182653	+	0.487843i	−0.995514	−	0.0946137i	$-0.969838\pi$
$719$	−4.89768	+	13.0811i	−0.182653	+	0.487843i	0.812861	+	0.582457i	$0.197909\pi$
$720$	−0.169262	+	0.104045i	−0.00630803	+	0.00387753i
$721$	−33.4876			−1.24714
$722$	2.90241	+	18.7770i	0.108017	+	0.698808i
$723$	−8.71190			−0.323999
$724$	18.2416	−	11.2130i	0.677942	−	0.416730i
$725$	2.87653	−	7.68286i	0.106831	−	0.285334i
$726$	−0.713429	+	1.40978i	−0.0264779	+	0.0523217i
$727$	−17.2835	−	23.5150i	−0.641008	−	0.872122i	0.357071	−	0.934077i	$-0.383775\pi$
$727$	−17.2835	−	23.5150i	−0.641008	−	0.872122i	−0.998079	+	0.0619547i	$0.980267\pi$
$728$	2.35941	+	12.0789i	0.0874457	+	0.447673i
$729$	11.5826	−	17.7285i	0.428984	−	0.656610i
$730$	0.0761178	+	0.918606i	0.00281725	+	0.0339991i
$731$	2.93134	+	2.55290i	0.108419	+	0.0944225i
$732$	16.9817	+	6.89737i	0.627661	+	0.254934i
$733$	11.1567	+	3.83011i	0.412084	+	0.141469i	0.522943	−	0.852368i	$-0.324834\pi$
$733$	11.1567	+	3.83011i	0.412084	+	0.141469i	−0.110859	+	0.993836i	$0.535360\pi$
$734$	−12.2282	−	13.2834i	−0.451353	−	0.490300i
$735$	0.932884	+	1.13274i	0.0344099	+	0.0417817i
$736$	0.145547	−	5.28017i	0.00536493	−	0.194630i
$737$	10.7335	−	3.03515i	0.395375	−	0.111801i
$738$	−2.23281	−	3.03785i	−0.0821910	−	0.111825i
$739$	−5.83500	−	11.5303i	−0.214644	−	0.424148i	0.759363	−	0.650668i	$-0.225511\pi$
$739$	−5.83500	−	11.5303i	−0.214644	−	0.424148i	−0.974007	+	0.226520i	$0.927265\pi$
$740$	−1.55214	−	0.259007i	−0.0570578	−	0.00952127i
$741$	27.1702	−	35.4747i	0.998124	−	1.30320i
$742$	−13.7580	+	2.29581i	−0.505073	+	0.0842818i
$743$	20.1999	+	27.4829i	0.741062	+	1.00825i	0.999113	+	0.0421199i	$0.0134111\pi$
$743$	20.1999	+	27.4829i	0.741062	+	1.00825i	−0.258050	+	0.966131i	$0.583080\pi$
$744$	−0.468220	+	0.104930i	−0.0171658	+	0.00384694i
$745$	−0.591943	−	1.58101i	−0.0216871	−	0.0579237i
$746$	17.2863	+	4.88811i	0.632898	+	0.178966i
$747$	−0.560961	+	1.79349i	−0.0205245	+	0.0656204i
$748$	11.4959	+	3.94654i	0.420331	+	0.144300i
$749$	−32.2737	+	17.4656i	−1.17925	+	0.638181i
$750$	3.68234	+	6.37800i	0.134460	+	0.232892i
$751$	−21.2588	−	1.17288i	−0.775744	−	0.0427990i	−0.337111	−	0.941465i	$-0.609450\pi$
$751$	−21.2588	−	1.17288i	−0.775744	−	0.0427990i	−0.438633	+	0.898666i	$0.644537\pi$
$752$	1.53443	−	1.66684i	0.0559550	−	0.0607833i
$753$	12.7029	−	6.87446i	0.462919	−	0.250519i
$754$	8.60985	+	3.49702i	0.313552	+	0.127354i
$755$	1.73237	−	2.10350i	0.0630475	−	0.0765543i
$756$	8.95297	+	5.50337i	0.325616	+	0.200156i
$757$	−22.3248	+	1.23169i	−0.811409	+	0.0447667i	−0.456040	−	0.889959i	$-0.650733\pi$
$757$	−22.3248	+	1.23169i	−0.811409	+	0.0447667i	−0.355369	+	0.934726i	$0.615645\pi$
$758$	23.7877	−	9.66171i	0.864007	−	0.350929i
$759$	32.1511	+	11.0375i	1.16701	+	0.400635i
$760$	0.461672	−	1.68258i	0.0167466	−	0.0610335i
$761$	−36.6620	+	12.5861i	−1.32900	+	0.456245i	−0.895561	−	0.444940i	$-0.853225\pi$
$761$	−36.6620	+	12.5861i	−1.32900	+	0.456245i	−0.433435	+	0.901185i	$0.642699\pi$
$762$	−9.38717	+	8.17530i	−0.340061	+	0.296160i
$763$	−24.9832	−	24.3040i	−0.904452	−	0.879865i
$764$	−9.80774	−	3.98356i	−0.354832	−	0.144120i
$765$	−0.650087	+	0.264043i	−0.0235040	+	0.00954648i
$766$	−7.67100	+	7.46246i	−0.277165	+	0.269630i
$767$	4.64192	−	56.0196i	0.167610	−	2.02275i
$768$	1.47558	+	1.14849i	0.0532454	+	0.0414426i
$769$	−9.55053	−	48.8934i	−0.344401	−	1.76314i	−0.603571	−	0.797309i	$-0.706256\pi$
$769$	−9.55053	−	48.8934i	−0.344401	−	1.76314i	0.259170	−	0.965832i	$-0.416551\pi$
$770$	−2.97586	+	0.841494i	−0.107243	+	0.0303253i
$771$	0.925208	+	2.10926i	0.0333206	+	0.0759632i
$772$	−2.88037	−	11.3743i	−0.103667	−	0.409370i
$773$	32.0788	−	3.55049i	1.15380	−	0.127702i	0.487316	−	0.873225i	$-0.337976\pi$
$773$	32.0788	−	3.55049i	1.15380	−	0.127702i	0.666480	+	0.745523i	$0.267800\pi$
$774$	−0.533121	+	0.119475i	−0.0191626	+	0.00429445i
$775$	0.238097	+	1.21892i	0.00855269	+	0.0437850i
$776$	−6.11014	+	10.5831i	−0.219341	+	0.379910i
$777$	−4.92604	−	15.7494i	−0.176721	−	0.565008i
$778$	−13.6769	−	7.40158i	−0.490341	−	0.265359i
$779$	32.5424	+	6.09402i	1.16595	+	0.218341i
$780$	−3.60878	+	1.95297i	−0.129215	+	0.0699277i
$781$	−7.51299	−	7.30875i	−0.268836	−	0.261528i
$782$	3.57624	−	18.3083i	0.127886	−	0.654705i
$783$	7.17635	−	3.38660i	0.256462	−	0.121027i
$784$	0.980303	−	1.69793i	0.0350108	−	0.0606405i
$785$	−2.84904	+	0.805632i	−0.101687	+	0.0287542i
$786$	−11.1163	+	1.85498i	−0.396506	+	0.0661651i
$787$	−3.68796	+	14.5634i	−0.131461	+	0.519130i	0.868273	+	0.496087i	$0.165230\pi$
$787$	−3.68796	+	14.5634i	−0.131461	+	0.519130i	−0.999734	+	0.0230430i	$0.992665\pi$
$788$	2.29720	−	16.5662i	0.0818343	−	0.590146i
$789$	−33.7680	+	23.4142i	−1.20217	+	0.833568i
$790$	0.830575			0.0295505
$791$	27.1120			0.963992
$792$	−1.40386	+	0.973413i	−0.0498839	+	0.0345887i
$793$	48.6002	+	22.9350i	1.72585	+	0.814446i
$794$	2.67494	−	3.63938i	0.0949300	−	0.129157i
$795$	−2.09986	−	4.14943i	−0.0744742	−	0.147165i
$796$	13.9808	−	3.13316i	0.495535	−	0.111052i
$797$	−9.53966	−	7.42502i	−0.337912	−	0.263008i	0.431014	−	0.902345i	$-0.358156\pi$
$797$	−9.53966	−	7.42502i	−0.337912	−	0.263008i	−0.768926	+	0.639338i	$0.779209\pi$
$798$	17.9295	−	3.64737i	0.634699	−	0.129116i
$799$	6.31394	−	4.91434i	0.223371	−	0.173857i
$800$	3.07676	−	3.73591i	0.108780	−	0.132084i
$801$	−5.57044	+	2.26252i	−0.196822	+	0.0799421i
$802$	−8.38343	+	26.8033i	−0.296029	+	0.946458i
$803$	1.08858	+	7.85030i	0.0384153	+	0.277031i
$804$	5.91353	+	1.32525i	0.208554	+	0.0467380i
$805$	1.90660	+	4.34661i	0.0671988	+	0.153198i
$806$	−1.38767	+	0.231561i	−0.0488786	+	0.00815640i
$807$	−21.1643	+	41.8218i	−0.745018	+	1.47220i
$808$	9.18573	−	12.4976i	0.323153	−	0.439665i
$809$	12.0082	−	27.3760i	0.422186	−	0.962488i	−0.568038	−	0.823002i	$-0.692297\pi$
$809$	12.0082	−	27.3760i	0.422186	−	0.962488i	0.990224	−	0.139485i	$-0.0445448\pi$
$810$	−1.00647	+	3.97447i	−0.0353638	+	0.139648i
$811$	0.943000	−	1.86342i	0.0331132	−	0.0654335i	−0.875098	−	0.483946i	$-0.839203\pi$
$811$	0.943000	−	1.86342i	0.0331132	−	0.0654335i	0.908211	+	0.418513i	$0.137449\pi$
$812$	1.71816	+	3.39517i	0.0602956	+	0.119147i
$813$	14.1276	−	1.56365i	0.495477	−	0.0548394i
$814$	−13.4480	−	1.48843i	−0.471353	−	0.0521693i
$815$	−0.328001	−	2.36537i	−0.0114894	−	0.0828554i
$816$	4.47245	+	4.85837i	0.156567	+	0.170077i
$817$	2.70305	−	3.96389i	0.0945677	−	0.138679i
$818$	−17.9768	+	19.5280i	−0.628543	+	0.682779i
$819$	−5.02011	−	3.48087i	−0.175417	−	0.121631i
$820$	−2.49846	−	1.73239i	−0.0872499	−	0.0604978i
$821$	−20.9213	−	36.2367i	−0.730158	−	1.26467i	−0.956816	−	0.290696i	$-0.906113\pi$
$821$	−20.9213	−	36.2367i	−0.730158	−	1.26467i	0.226658	−	0.973974i	$-0.427220\pi$
$822$	10.2037	+	9.92634i	0.355896	+	0.346221i
$823$	26.7240	+	23.2740i	0.931541	+	0.811280i	0.982278	−	0.187432i	$-0.0600164\pi$
$823$	26.7240	+	23.2740i	0.931541	+	0.811280i	−0.0507361	+	0.998712i	$0.516157\pi$
$824$	−11.7720	+	9.16250i	−0.410096	+	0.319191i
$825$	17.0352	+	26.0743i	0.593090	+	0.907791i
$826$	16.4981	−	16.0496i	0.574042	−	0.558437i
$827$	−7.13741	+	22.8196i	−0.248192	+	0.793515i	0.743932	+	0.668256i	$0.232959\pi$
$827$	−7.13741	+	22.8196i	−0.248192	+	0.793515i	−0.992124	+	0.125259i	$0.960024\pi$
$828$	1.77576	+	1.92898i	0.0617118	+	0.0670368i
$829$	−43.8734	−	23.7431i	−1.52379	−	0.824633i	−0.524152	−	0.851625i	$-0.675618\pi$
$829$	−43.8734	−	23.7431i	−1.52379	−	0.824633i	−0.999636	+	0.0269923i	$0.991407\pi$
$830$	0.0417557	+	1.51482i	0.00144936	+	0.0525802i
$831$	−2.49810	+	12.7889i	−0.0866580	+	0.443640i
$832$	4.13429	+	3.60056i	0.143331	+	0.124827i
$833$	4.40176	−	5.34476i	0.152512	−	0.185185i
$834$	28.8769	−	1.59318i	0.999924	−	0.0551673i
$835$	3.59708	+	5.50574i	0.124482	+	0.190534i
$836$	3.16656	−	14.6638i	0.109518	−	0.507159i
$837$	−0.657064	+	1.00571i	−0.0227115	+	0.0347625i
$838$	−11.5119	+	19.9392i	−0.397672	+	0.688787i
$839$	0.193162	−	7.00755i	0.00666868	−	0.241927i	−0.988940	−	0.148316i	$-0.952615\pi$
$839$	0.193162	−	7.00755i	0.00666868	−	0.241927i	0.995609	−	0.0936118i	$-0.0298413\pi$
$840$	−1.63952	−	0.367425i	−0.0565689	−	0.0126774i
$841$	−25.9682	−	2.87416i	−0.895455	−	0.0991090i
$842$	−5.61100	−	14.9863i	−0.193368	−	0.516462i
$843$	−15.8871	−	12.3655i	−0.547182	−	0.425889i
$844$	−15.1042	+	23.1186i	−0.519906	+	0.795776i
$845$	−6.17431	+	2.91373i	−0.212403	+	0.100235i
$846$	0.0309863	+	1.12413i	0.00106533	+	0.0386482i
$847$	−1.79411	+	0.615919i	−0.0616464	+	0.0211632i
$848$	−4.20824	+	4.57136i	−0.144511	+	0.156981i
$849$	−25.5518	−	44.2571i	−0.876936	−	1.51890i
$850$	12.8892	−	11.2252i	0.442096	−	0.385021i
$851$	0.572186	+	20.7579i	0.0196143	+	0.711570i
$852$	−1.69993	−	5.43499i	−0.0582388	−	0.186200i
$853$	−0.366662	+	13.3018i	−0.0125543	+	0.455445i	0.967059	+	0.254552i	$0.0819281\pi$
$853$	−0.366662	+	13.3018i	−0.0125543	+	0.455445i	−0.979613	+	0.200893i	$0.935616\pi$
$854$	8.83926	+	20.1515i	0.302473	+	0.689570i
$855$	0.418107	+	0.758428i	0.0142989	+	0.0259377i
$856$	−6.56649	+	14.9701i	−0.224438	+	0.511667i
$857$	33.7522	+	15.9280i	1.15295	+	0.544091i	0.905306	−	0.424759i	$-0.139641\pi$
$857$	33.7522	+	15.9280i	1.15295	+	0.544091i	0.247646	+	0.968851i	$0.420343\pi$
$858$	−30.0568	+	18.4759i	−1.02612	+	0.630755i
$859$	3.57763	−	2.48068i	0.122067	−	0.0846396i	−0.507201	−	0.861828i	$-0.669320\pi$
$859$	3.57763	−	2.48068i	0.122067	−	0.0846396i	0.629268	+	0.777188i	$0.283355\pi$
$860$	−0.375340	+	0.230720i	−0.0127990	+	0.00786750i
$861$	4.37920	−	31.5805i	0.149243	−	1.07626i
$862$	16.2088	−	36.9523i	0.552073	−	1.25860i
$863$	−31.1751	−	5.20220i	−1.06121	−	0.177085i	−0.391856	−	0.920027i	$-0.628167\pi$
$863$	−31.1751	−	5.20220i	−1.06121	−	0.177085i	−0.669356	+	0.742942i	$0.733430\pi$
$864$	4.65303	−	0.514997i	0.158299	−	0.0175205i
$865$	−2.75516	−	7.35869i	−0.0936781	−	0.250203i
$866$	−2.92052	+	35.2455i	−0.0992434	+	1.19769i
$867$	−4.63088	−	7.08810i	−0.157273	−	0.240724i
$868$	−0.490761	−	0.301669i	−0.0166575	−	0.0102393i
$869$	7.13060	−	0.393406i	0.241889	−	0.0133454i
$870$	−0.909370	+	0.884649i	−0.0308305	+	0.0299924i
$871$	17.0979	+	4.83483i	0.579341	+	0.163822i
$872$	−15.4322	−	1.70803i	−0.522600	−	0.0578413i
$873$	−1.48904	−	5.88010i	−0.0503965	−	0.199011i
$874$	−22.9599	−	1.72266i	−0.776631	−	0.0582698i
$875$	−2.17050	+	8.57113i	−0.0733765	+	0.289757i
$876$	−1.50981	+	4.03251i	−0.0510116	+	0.136246i
$877$	−41.0776	−	19.3850i	−1.38709	−	0.654584i	−0.419651	−	0.907685i	$-0.637848\pi$
$877$	−41.0776	−	19.3850i	−1.38709	−	0.654584i	−0.967440	+	0.253101i	$0.918549\pi$
$878$	−2.43875	+	17.5870i	−0.0823039	+	0.593532i
$879$	11.4187	−	30.4980i	0.385144	−	1.02867i
$880$	−0.815872	+	1.11003i	−0.0275030	+	0.0374192i
$881$	−38.4286	−	6.41259i	−1.29469	−	0.216046i	−0.523158	−	0.852236i	$-0.675246\pi$
$881$	−38.4286	−	6.41259i	−1.29469	−	0.216046i	−0.771533	+	0.636190i	$0.780510\pi$
$882$	0.238901	+	0.943397i	0.00804420	+	0.0317658i
$883$	21.9838	+	4.92668i	0.739813	+	0.165796i	0.572266	−	0.820068i	$-0.306064\pi$
$883$	21.9838	+	4.92668i	0.739813	+	0.165796i	0.167547	+	0.985864i	$0.446415\pi$
$884$	12.3085	+	14.9454i	0.413979	+	0.502667i
$885$	6.74915	+	3.65246i	0.226870	+	0.122776i
$886$	23.8966	−	8.20371i	0.802822	−	0.275609i
$887$	36.0323	+	1.98796i	1.20984	+	0.0667490i	0.648749	−	0.761002i	$-0.275292\pi$
$887$	36.0323	+	1.98796i	1.20984	+	0.0667490i	0.561095	+	0.827751i	$0.310380\pi$
$888$	−6.04084	−	4.18863i	−0.202717	−	0.140561i
$889$	−14.9219	−	0.823262i	−0.500463	−	0.0276113i
$890$	−3.65627	+	3.18425i	−0.122559	+	0.106736i
$891$	−6.75816	+	34.5980i	−0.226407	+	1.15908i
$892$	1.02642	+	12.3870i	0.0343671	+	0.414749i
$893$	−6.94099	−	7.02470i	−0.232271	−	0.235073i
$894$	0.651240	−	7.85929i	0.0217807	−	0.262854i
$895$	−1.31114	−	0.370755i	−0.0438265	−	0.0123930i
$896$	0.308339	+	2.22358i	0.0103009	+	0.0742847i
$897$	34.4237	+	41.7984i	1.14938	+	1.39561i
$898$	−11.0450	−	35.3127i	−0.368575	−	1.17840i
$899$	−0.393375	+	0.185638i	−0.0131198	+	0.00619137i
$900$	0.198380	+	2.39409i	0.00661267	+	0.0798030i
$901$	−17.3162	+	13.4777i	−0.576887	+	0.449009i
$902$	−22.2701	−	13.6894i	−0.741515	−	0.455807i
$903$	−3.93606	−	2.41949i	−0.130984	−	0.0805154i
$904$	9.53074	−	7.41808i	0.316988	−	0.246722i
$905$	0.707775	+	8.54158i	0.0235273	+	0.283932i
$906$	11.5123	−	5.43277i	0.382469	−	0.180492i
$907$	−9.31882	−	29.7939i	−0.309426	−	0.989291i	−0.970933	−	0.239352i	$-0.923065\pi$
$907$	−9.31882	−	29.7939i	−0.309426	−	0.989291i	0.661507	−	0.749939i	$-0.269917\pi$
$908$	3.88099	+	4.71242i	0.128795	+	0.156387i
$909$	1.05745	+	7.62579i	0.0350735	+	0.252931i
$910$	−4.74039	−	1.34046i	−0.157142	−	0.0444357i
$911$	2.81370	−	33.9563i	0.0932221	−	1.12502i	−0.776044	−	0.630679i	$-0.782776\pi$
$911$	2.81370	−	33.9563i	0.0932221	−	1.12502i	0.869266	−	0.494345i	$-0.164592\pi$
$912$	5.30486	−	6.18784i	0.175661	−	0.204900i
$913$	1.07598	+	12.9851i	0.0356097	+	0.429746i
$914$	2.59753	−	13.2979i	0.0859187	−	0.439856i
$915$	−5.53263	+	4.81837i	−0.182903	+	0.159290i
$916$	−2.39707	−	0.132250i	−0.0792013	−	0.00436966i
$917$	−11.1188	−	7.70964i	−0.367177	−	0.254595i
$918$	16.5077	+	0.910756i	0.544836	+	0.0300594i
$919$	11.0319	−	3.78726i	0.363909	−	0.124930i	−0.136680	−	0.990615i	$-0.543643\pi$
$919$	11.0319	−	3.78726i	0.363909	−	0.124930i	0.500589	+	0.865685i	$0.333117\pi$
$920$	1.85950	+	1.00631i	0.0613059	+	0.0331771i
$921$	−27.6779	−	33.6075i	−0.912019	−	1.10740i
$922$	4.65578	+	1.04338i	0.153330	+	0.0343620i
$923$	−4.09876	−	16.1856i	−0.134912	−	0.532757i
$924$	−14.2495	−	2.37783i	−0.468776	−	0.0782248i
$925$	−11.2682	+	15.3309i	−0.370496	+	0.504078i
$926$	0.0203170	−	0.0542642i	0.000667657	−	0.00178323i
$927$	1.01704	−	7.33433i	0.0334038	−	0.240891i
$928$	1.53294	+	0.723411i	0.0503211	+	0.0237471i
$929$	−15.0129	+	40.0977i	−0.492557	+	1.31556i	0.420338	+	0.907368i	$0.361911\pi$
$929$	−15.0129	+	40.0977i	−0.492557	+	1.31556i	−0.912895	+	0.408194i	$0.866159\pi$
$930$	0.0471495	−	0.186189i	0.00154609	−	0.00610538i
$931$	−7.19067	−	4.61843i	−0.235665	−	0.151363i
$932$	−4.03269	−	15.9248i	−0.132095	−	0.521633i
$933$	−32.0890	−	3.55161i	−1.05055	−	0.116275i
$934$	28.1120	+	7.94933i	0.919854	+	0.260110i
$935$	−3.48725	+	3.39245i	−0.114045	+	0.110945i
$936$	−2.71713	+	0.149908i	−0.0888120	+	0.00489990i
$937$	17.9123	+	11.0107i	0.585171	+	0.359703i	0.784405	−	0.620249i	$-0.212968\pi$
$937$	17.9123	+	11.0107i	0.585171	+	0.359703i	−0.199235	+	0.979952i	$0.563846\pi$
$938$	3.97937	+	6.09088i	0.129931	+	0.198874i
$939$	2.97890	−	35.9500i	0.0972127	−	1.17318i
$940$	0.317978	+	0.849282i	0.0103713	+	0.0277005i
$941$	−50.8677	+	5.63004i	−1.65824	+	0.183534i	−0.889789	−	0.456373i	$-0.849148\pi$
$941$	−50.8677	+	5.63004i	−1.65824	+	0.183534i	−0.768452	+	0.639907i	$0.778973\pi$
$942$	−13.6423	−	2.27649i	−0.444489	−	0.0741721i
$943$	−16.1164	+	36.7416i	−0.524821	+	1.19647i
$944$	1.40831	−	10.1560i	0.0458365	−	0.330549i
$945$	−3.58367	+	2.20287i	−0.116577	+	0.0716594i
$946$	−3.11306	+	2.15855i	−0.101214	+	0.0701804i
$947$	37.3969	−	22.9878i	1.21524	−	0.747003i	0.240563	−	0.970634i	$-0.422668\pi$
$947$	37.3969	−	22.9878i	1.21524	−	0.747003i	0.974674	+	0.223630i	$0.0717909\pi$
$948$	3.50887	+	1.65587i	0.113963	+	0.0537803i
$949$	−5.07131	+	11.5614i	−0.164622	+	0.375300i
$950$	−15.6317	−	14.1667i	−0.507158	−	0.459630i
$951$	−10.6334	−	24.2418i	−0.344813	−	0.786094i
$952$	−0.218447	+	7.92486i	−0.00707992	+	0.256846i
$953$	9.53909	+	30.4982i	0.309001	+	0.987932i	0.971132	+	0.238544i	$0.0766700\pi$
$953$	9.53909	+	30.4982i	0.309001	+	0.987932i	−0.662130	+	0.749389i	$0.730348\pi$
$954$	−0.0849811	−	3.08295i	−0.00275136	−	0.0998143i
$955$	3.19536	−	2.78284i	0.103399	−	0.0900506i
$956$	−11.3317	−	19.6271i	−0.366494	−	0.634786i
$957$	−7.38804	+	8.02555i	−0.238822	+	0.259429i
$958$	15.9226	−	5.46625i	0.514437	−	0.176606i
$959$	0.470915	+	17.0839i	0.0152066	+	0.551668i
$960$	−0.676876	+	0.319425i	−0.0218461	+	0.0103094i
$961$	−16.9194	+	25.8970i	−0.545786	+	0.835388i
$962$	−17.0082	−	13.2380i	−0.548366	−	0.426810i
$963$	−2.84509	−	7.59890i	−0.0916817	−	0.244871i
$964$	−4.63085	−	0.512542i	−0.149150	−	0.0165079i
$965$	4.58291	+	1.02705i	0.147529	+	0.0330620i
$966$	−0.610942	+	22.1639i	−0.0196568	+	0.713110i
$967$	−6.23021	+	10.7910i	−0.200350	+	0.347016i	−0.948641	−	0.316354i	$-0.897541\pi$
$967$	−6.23021	+	10.7910i	−0.200350	+	0.347016i	0.748291	+	0.663370i	$0.230875\pi$
$968$	−0.462167	+	0.707399i	−0.0148546	+	0.0227367i
$969$	22.0758	−	18.4712i	0.709177	−	0.593379i
$970$	−2.67539	−	4.09499i	−0.0859017	−	0.131482i
$971$	24.3532	−	1.34360i	0.781531	−	0.0431183i	0.340072	−	0.940400i	$-0.389549\pi$
$971$	24.3532	−	1.34360i	0.781531	−	0.0431183i	0.441459	+	0.897281i	$0.354461\pi$
$972$	−3.24734	+	3.94302i	−0.104158	+	0.126473i
$973$	26.1832	+	22.8030i	0.839396	+	0.731031i
$974$	4.44737	−	22.7681i	0.142503	−	0.729536i
$975$	1.36708	+	49.5950i	0.0437815	+	1.58831i
$976$	8.62090	+	4.66540i	0.275948	+	0.149336i
$977$	8.51277	+	9.24733i	0.272348	+	0.295848i	0.856874	−	0.515527i	$-0.172404\pi$
$977$	8.51277	+	9.24733i	0.272348	+	0.295848i	−0.584526	+	0.811375i	$0.698719\pi$
$978$	3.33004	−	10.6467i	0.106483	−	0.340445i
$979$	−29.8814	+	29.0690i	−0.955012	+	0.929050i
$980$	0.429237	+	0.656996i	0.0137115	+	0.0209870i
$981$	6.08172	−	4.73360i	0.194175	−	0.151132i
$982$	−20.7316	−	18.0552i	−0.661573	−	0.576164i
$983$	9.85440	+	9.58651i	0.314307	+	0.305762i	0.837484	−	0.546461i	$-0.184025\pi$
$983$	9.85440	+	9.58651i	0.314307	+	0.305762i	−0.523178	+	0.852224i	$0.675254\pi$
$984$	−7.10126	−	12.2997i	−0.226380	−	0.392102i
$985$	5.50140	+	3.81459i	0.175289	+	0.121543i
$986$	4.91933	+	3.41099i	0.156664	+	0.108628i
$987$	−6.44088	+	6.99666i	−0.205016	+	0.222706i
$988$	16.5295	−	17.2582i	0.525874	−	0.549058i
$989$	3.93774	+	4.27753i	0.125213	+	0.136018i
$990$	−0.0939223	−	0.677319i	−0.00298505	−	0.0215266i
$991$	−6.88452	−	0.761979i	−0.218694	−	0.0242051i	−6.56248e−6	−	1.00000i	$-0.500002\pi$
$991$	−6.88452	−	0.761979i	−0.218694	−	0.0242051i	−0.218687	+	0.975795i	$0.570178\pi$
$992$	−0.255058	+	0.0282298i	−0.00809808	+	0.000896296i
$993$	26.7393	+	52.8383i	0.848546	+	1.67677i
$994$	3.08700	−	6.10008i	0.0979138	−	0.193483i
$995$	−1.40785	+	5.55949i	−0.0446320	+	0.176248i
$996$	−2.84361	+	6.48279i	−0.0901034	+	0.205415i
$997$	0.732841	−	0.997066i	0.0232093	−	0.0315774i	−0.794006	−	0.607910i	$-0.792008\pi$
$997$	0.732841	−	0.997066i	0.0232093	−	0.0315774i	0.817215	+	0.576333i	$0.195517\pi$
$998$	9.89122	−	19.5456i	0.313101	−	0.618704i
$999$	−18.1531	+	3.02921i	−0.574338	+	0.0958400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.a.505.13	✓	576
361.178	even	57	inner	722.2.i.a.539.13	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.a.505.13	✓	576	1.1	even	1	trivial
722.2.i.a.539.13	yes	576	361.178	even	57	inner

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.851919 + 0.523673i) q^{2} +(0.655642 - 1.75114i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.237058 + 0.322529i) q^{5} +(0.358471 + 1.83517i) q^{6} +(-1.22782 + 1.87932i) q^{7} +(0.0825793 + 0.996584i) q^{8} +(-0.374312 - 0.325989i) q^{9} +O(q^{10})\)	\(q+(-0.851919 + 0.523673i) q^{2} +(0.655642 - 1.75114i) q^{3} +(0.451533 - 0.892254i) q^{4} +(0.237058 + 0.322529i) q^{5} +(0.358471 + 1.83517i) q^{6} +(-1.22782 + 1.87932i) q^{7} +(0.0825793 + 0.996584i) q^{8} +(-0.374312 - 0.325989i) q^{9} +(-0.370854 - 0.150628i) q^{10} +(-3.25518 - 1.11750i) q^{11} +(-1.26642 - 1.37570i) q^{12} +(-3.48527 - 4.23194i) q^{13} +(0.0618556 - 2.24401i) q^{14} +(0.720219 - 0.203659i) q^{15} +(-0.592235 - 0.805765i) q^{16} +(-1.59462 - 3.15106i) q^{17} +(0.489595 + 0.0816990i) q^{18} +(-3.63045 + 2.41243i) q^{19} +(0.394818 - 0.0658834i) q^{20} +(2.48595 + 3.38225i) q^{21} +(3.35835 - 0.752625i) q^{22} +(-1.85213 - 4.94682i) q^{23} +(1.79930 + 0.508795i) q^{24} +(1.44475 - 4.61911i) q^{25} +(5.18532 + 1.78012i) q^{26} +(4.11720 - 2.22812i) q^{27} +(1.12243 + 1.94411i) q^{28} +(1.69248 + 0.0933769i) q^{29} +(-0.506918 + 0.550660i) q^{30} +(-0.225686 + 0.122135i) q^{31} +(0.926494 + 0.376309i) q^{32} +(-4.09114 + 4.96759i) q^{33} +(3.00861 + 1.84939i) q^{34} +(-0.897201 + 0.0494999i) q^{35} +(-0.459879 + 0.186787i) q^{36} +(-3.71828 - 1.27649i) q^{37} +(1.82953 - 3.95636i) q^{38} +(-9.69581 + 3.32858i) q^{39} +(-0.301851 + 0.262883i) q^{40} +(-5.44433 - 5.29633i) q^{41} +(-3.88902 - 1.57958i) q^{42} +(-1.01978 + 0.414200i) q^{43} +(-2.46692 + 2.39986i) q^{44} +(0.0164071 - 0.198005i) q^{45} +(4.16838 + 3.24438i) q^{46} +(0.434335 + 2.22355i) q^{47} +(-1.79930 + 0.508795i) q^{48} +(0.787566 + 1.79547i) q^{49} +(1.18810 + 4.69168i) q^{50} +(-6.56345 + 0.726442i) q^{51} +(-5.34968 + 1.19889i) q^{52} +(-1.19118 - 6.09817i) q^{53} +(-2.34072 + 4.05425i) q^{54} +(-0.411238 - 1.31480i) q^{55} +(-1.97429 - 1.06844i) q^{56} +(1.84422 + 7.93913i) q^{57} +(-1.49076 + 0.806758i) q^{58} +(7.34928 + 7.14949i) q^{59} +(0.143488 - 0.734578i) q^{60} +(-8.86482 + 4.18341i) q^{61} +(0.128308 - 0.222235i) q^{62} +(1.07223 - 0.303197i) q^{63} +(-0.986361 + 0.164595i) q^{64} +(0.538710 - 2.12732i) q^{65} +(0.883926 - 6.37441i) q^{66} +(-2.66338 + 1.84675i) q^{67} -3.53157 q^{68} -9.87691 q^{69} +(0.738421 - 0.512010i) q^{70} +(2.75422 + 1.29975i) q^{71} +(0.293965 - 0.399954i) q^{72} +(-1.03979 - 2.05468i) q^{73} +(3.83614 - 0.859698i) q^{74} +(-7.14148 - 5.55844i) q^{75} +(0.513228 + 4.32858i) q^{76} +(6.09693 - 4.74543i) q^{77} +(6.51697 - 7.91311i) q^{78} +(-1.92248 + 0.780843i) q^{79} +(0.119489 - 0.382026i) q^{80} +(-1.40687 - 10.1456i) q^{81} +(7.41168 + 1.66100i) q^{82} +(-1.52077 - 3.46700i) q^{83} +(4.14032 - 0.690897i) q^{84} +(0.638290 - 1.26129i) q^{85} +(0.651868 - 0.886898i) q^{86} +(1.27318 - 2.90256i) q^{87} +(0.844876 - 3.33634i) q^{88} +(5.46934 - 10.8077i) q^{89} +(0.0897122 + 0.177276i) q^{90} +(12.2325 - 1.35389i) q^{91} +(-5.25012 - 0.581083i) q^{92} +(0.0659068 + 0.475286i) q^{93} +(-1.53443 - 1.66684i) q^{94} +(-1.63871 - 0.599042i) q^{95} +(1.26642 - 1.37570i) q^{96} +(10.0423 + 6.96321i) q^{97} +(-1.61118 - 1.11717i) q^{98} +(0.854159 + 1.47945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

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Database

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