LMFDB - Embedded newform 322.2.i.e.141.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.4
Character	$\chi$	$=$	322.141
Dual form			322.2.i.e.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.744281 - 1.62975i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.17446 - 1.35540i) q^{5} +(1.71908 + 0.504768i) q^{6} +(0.841254 - 0.540641i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.137541 - 0.158731i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.744281 - 1.62975i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.17446 - 1.35540i) q^{5} +(1.71908 + 0.504768i) q^{6} +(0.841254 - 0.540641i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.137541 - 0.158731i) q^{9} +(1.50875 + 0.969614i) q^{10} +(0.146791 - 1.02095i) q^{11} +(-0.254979 + 1.77342i) q^{12} +(-5.05493 - 3.24861i) q^{13} +(0.654861 + 0.755750i) q^{14} +(-1.33483 - 2.92288i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.82318 + 1.12259i) q^{17} +(0.137541 - 0.158731i) q^{18} +(5.25950 - 1.54433i) q^{19} +(-0.745027 + 1.63138i) q^{20} +(-0.254979 - 1.77342i) q^{21} +1.03145 q^{22} +(-4.74313 - 0.709021i) q^{23} -1.79166 q^{24} +(0.253822 + 1.76537i) q^{25} +(2.49615 - 5.46580i) q^{26} +(4.79618 - 1.40829i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(1.68215 + 0.493923i) q^{29} +(2.70316 - 1.73721i) q^{30} +(3.38105 + 7.40347i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.55464 - 0.999106i) q^{33} +(-0.567066 + 3.94403i) q^{34} +(0.255235 - 1.77520i) q^{35} +(0.176690 + 0.113552i) q^{36} +(-4.66017 - 5.37813i) q^{37} +(2.27711 + 4.98618i) q^{38} +(-9.05670 + 5.82038i) q^{39} +(-1.72081 - 0.505274i) q^{40} +(-5.81654 + 6.71265i) q^{41} +(1.71908 - 0.504768i) q^{42} +(-2.39625 + 5.24707i) q^{43} +(0.146791 + 1.02095i) q^{44} -0.376682 q^{45} +(0.0267858 - 4.79576i) q^{46} +3.84955 q^{47} +(-0.254979 - 1.77342i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-1.71128 + 0.502478i) q^{50} +(4.67506 - 5.39530i) q^{51} +(5.76541 + 1.69288i) q^{52} +(-6.93946 + 4.45972i) q^{53} +(2.07652 + 4.54694i) q^{54} +(-1.21140 - 1.39803i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(1.39768 - 9.72106i) q^{57} +(-0.249501 + 1.73532i) q^{58} +(-0.0787201 - 0.0505904i) q^{59} +(2.10423 + 2.42841i) q^{60} +(2.30839 + 5.05467i) q^{61} +(-6.84694 + 4.40026i) q^{62} +(-0.201524 - 0.0591728i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-10.3400 + 3.03609i) q^{65} +(0.767688 - 1.68100i) q^{66} +(1.33255 + 9.26810i) q^{67} -3.98459 q^{68} +(-4.68575 + 7.20240i) q^{69} +1.79345 q^{70} +(-1.50350 - 10.4570i) q^{71} +(-0.0872503 + 0.191051i) q^{72} +(-6.45114 + 1.89422i) q^{73} +(4.66017 - 5.37813i) q^{74} +(3.06603 + 0.900268i) q^{75} +(-4.61136 + 2.96354i) q^{76} +(-0.428480 - 0.938240i) q^{77} +(-7.05004 - 8.13618i) q^{78} +(9.93614 + 6.38557i) q^{79} +(0.255235 - 1.77520i) q^{80} +(1.36423 - 9.48841i) q^{81} +(-7.47211 - 4.80203i) q^{82} +(-0.824618 - 0.951659i) q^{83} +(0.744281 + 1.62975i) q^{84} +(6.01174 - 3.86351i) q^{85} +(-5.53468 - 1.62513i) q^{86} +(2.05696 - 2.37386i) q^{87} +(-0.989669 + 0.290593i) q^{88} +(1.83548 - 4.01914i) q^{89} +(-0.0536074 - 0.372848i) q^{90} -6.00881 q^{91} +(4.75075 - 0.655994i) q^{92} +14.5822 q^{93} +(0.547848 + 3.81037i) q^{94} +(4.08389 - 8.94248i) q^{95} +(1.71908 - 0.504768i) q^{96} +(-9.65569 + 11.1433i) q^{97} +(0.959493 + 0.281733i) q^{98} +(-0.182247 + 0.117123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	$ 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	0.744281	−	1.62975i	0.429711	−	0.940935i	−0.563663	−	0.826005i	$-0.690608\pi$
$3$	0.744281	−	1.62975i	0.429711	−	0.940935i	0.993374	−	0.114930i	$-0.0366645\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	1.17446	−	1.35540i	0.525235	−	0.606154i	−0.429699	−	0.902972i	$-0.641380\pi$
$5$	1.17446	−	1.35540i	0.525235	−	0.606154i	0.954934	+	0.296819i	$0.0959257\pi$
$6$	1.71908	+	0.504768i	0.701812	+	0.206071i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−0.137541	−	0.158731i	−0.0458472	−	0.0529104i
$10$	1.50875	+	0.969614i	0.477108	+	0.306619i
$11$	0.146791	−	1.02095i	0.0442590	−	0.307828i	−0.955652	−	0.294498i	$-0.904848\pi$
$11$	0.146791	−	1.02095i	0.0442590	−	0.307828i	0.999911	−	0.0133304i	$-0.00424333\pi$
$12$	−0.254979	+	1.77342i	−0.0736062	+	0.511942i
$13$	−5.05493	−	3.24861i	−1.40199	−	0.901001i	−0.402092	−	0.915599i	$-0.631717\pi$
$13$	−5.05493	−	3.24861i	−1.40199	−	0.901001i	−0.999893	+	0.0145982i	$0.995353\pi$
$14$	0.654861	+	0.755750i	0.175019	+	0.201983i
$15$	−1.33483	−	2.92288i	−0.344652	−	0.754683i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	3.82318	+	1.12259i	0.927258	+	0.272268i	0.710288	−	0.703911i	$-0.248564\pi$
$17$	3.82318	+	1.12259i	0.927258	+	0.272268i	0.216970	+	0.976178i	$0.430383\pi$
$18$	0.137541	−	0.158731i	0.0324188	−	0.0374133i
$19$	5.25950	−	1.54433i	1.20661	−	0.354293i	0.384234	−	0.923236i	$-0.374466\pi$
$19$	5.25950	−	1.54433i	1.20661	−	0.354293i	0.822377	+	0.568943i	$0.192647\pi$
$20$	−0.745027	+	1.63138i	−0.166593	+	0.364788i
$21$	−0.254979	−	1.77342i	−0.0556410	−	0.386992i
$22$	1.03145			0.219906
$23$	−4.74313	−	0.709021i	−0.989011	−	0.147841i
$23$	−4.74313	−	0.709021i	−0.989011	−	0.147841i
$24$	−1.79166			−0.365720
$25$	0.253822	+	1.76537i	0.0507645	+	0.353075i
$26$	2.49615	−	5.46580i	0.489535	−	1.07193i
$27$	4.79618	−	1.40829i	0.923026	−	0.271025i
$28$	−0.654861	+	0.755750i	−0.123757	+	0.142823i
$29$	1.68215	+	0.493923i	0.312367	+	0.0917192i	0.434159	−	0.900836i	$-0.357046\pi$
$29$	1.68215	+	0.493923i	0.312367	+	0.0917192i	−0.121792	+	0.992556i	$0.538864\pi$
$30$	2.70316	−	1.73721i	0.493527	−	0.317170i
$31$	3.38105	+	7.40347i	0.607255	+	1.32970i	0.924436	+	0.381338i	$0.124537\pi$
$31$	3.38105	+	7.40347i	0.607255	+	1.32970i	−0.317181	+	0.948365i	$0.602736\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−1.55464	−	0.999106i	−0.270628	−	0.173922i
$34$	−0.567066	+	3.94403i	−0.0972510	+	0.676396i
$35$	0.255235	−	1.77520i	0.0431426	−	0.300063i
$36$	0.176690	+	0.113552i	0.0294483	+	0.0189253i
$37$	−4.66017	−	5.37813i	−0.766128	−	0.884158i	0.229899	−	0.973214i	$-0.426160\pi$
$37$	−4.66017	−	5.37813i	−0.766128	−	0.884158i	−0.996027	+	0.0890561i	$0.971615\pi$
$38$	2.27711	+	4.98618i	0.369396	+	0.808865i
$39$	−9.05670	+	5.82038i	−1.45023	+	0.932007i
$40$	−1.72081	−	0.505274i	−0.272083	−	0.0798908i
$41$	−5.81654	+	6.71265i	−0.908392	+	1.04834i	0.0902336	+	0.995921i	$0.471239\pi$
$41$	−5.81654	+	6.71265i	−0.908392	+	1.04834i	−0.998625	+	0.0524191i	$0.983307\pi$
$42$	1.71908	−	0.504768i	0.265260	−	0.0778874i
$43$	−2.39625	+	5.24707i	−0.365425	+	0.800170i	0.634210	+	0.773161i	$0.281326\pi$
$43$	−2.39625	+	5.24707i	−0.365425	+	0.800170i	−0.999635	+	0.0270090i	$0.991402\pi$
$44$	0.146791	+	1.02095i	0.0221295	+	0.153914i
$45$	−0.376682			−0.0561524
$46$	0.0267858	−	4.79576i	0.00394935	−	0.707096i
$47$	3.84955			0.561515			0.280757	−	0.959779i	$-0.409414\pi$
$47$	3.84955			0.561515			0.280757	+	0.959779i	$0.409414\pi$
$48$	−0.254979	−	1.77342i	−0.0368031	−	0.255971i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	−1.71128	+	0.502478i	−0.242012	+	0.0710611i
$51$	4.67506	−	5.39530i	0.654639	−	0.755494i
$52$	5.76541	+	1.69288i	0.799518	+	0.234760i
$53$	−6.93946	+	4.45972i	−0.953209	+	0.612590i	−0.922111	−	0.386926i	$-0.873537\pi$
$53$	−6.93946	+	4.45972i	−0.953209	+	0.612590i	−0.0310981	+	0.999516i	$0.509900\pi$
$54$	2.07652	+	4.54694i	0.282579	+	0.618761i
$55$	−1.21140	−	1.39803i	−0.163345	−	0.188510i
$56$	−0.841254	−	0.540641i	−0.112417	−	0.0722462i
$57$	1.39768	−	9.72106i	0.185127	−	1.28759i
$58$	−0.249501	+	1.73532i	−0.0327611	+	0.227859i
$59$	−0.0787201	−	0.0505904i	−0.0102485	−	0.00658630i	0.535507	−	0.844531i	$-0.320121\pi$
$59$	−0.0787201	−	0.0505904i	−0.0102485	−	0.00658630i	−0.545755	+	0.837945i	$0.683757\pi$
$60$	2.10423	+	2.42841i	0.271655	+	0.313507i
$61$	2.30839	+	5.05467i	0.295559	+	0.647185i	0.997908	−	0.0646483i	$-0.0205926\pi$
$61$	2.30839	+	5.05467i	0.295559	+	0.647185i	−0.702349	+	0.711833i	$0.747865\pi$
$62$	−6.84694	+	4.40026i	−0.869563	+	0.558834i
$63$	−0.201524	−	0.0591728i	−0.0253896	−	0.00745507i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−10.3400	+	3.03609i	−1.28252	+	0.376581i
$66$	0.767688	−	1.68100i	0.0944959	−	0.206917i
$67$	1.33255	+	9.26810i	0.162797	+	1.13228i	0.893330	+	0.449401i	$0.148363\pi$
$67$	1.33255	+	9.26810i	0.162797	+	1.13228i	−0.730533	+	0.682877i	$0.760728\pi$
$68$	−3.98459			−0.483202
$69$	−4.68575	+	7.20240i	−0.564098	+	0.867067i
$70$	1.79345			0.214359
$71$	−1.50350	−	10.4570i	−0.178432	−	1.24102i	−0.860392	−	0.509633i	$-0.829781\pi$
$71$	−1.50350	−	10.4570i	−0.178432	−	1.24102i	0.681960	−	0.731390i	$-0.261128\pi$
$72$	−0.0872503	+	0.191051i	−0.0102825	+	0.0225156i
$73$	−6.45114	+	1.89422i	−0.755048	+	0.221702i	−0.636532	−	0.771250i	$-0.719632\pi$
$73$	−6.45114	+	1.89422i	−0.755048	+	0.221702i	−0.118516	+	0.992952i	$0.537814\pi$
$74$	4.66017	−	5.37813i	0.541734	−	0.625194i
$75$	3.06603	+	0.900268i	0.354035	+	0.103954i
$76$	−4.61136	+	2.96354i	−0.528959	+	0.339942i
$77$	−0.428480	−	0.938240i	−0.0488298	−	0.106922i
$78$	−7.05004	−	8.13618i	−0.798260	−	0.921241i
$79$	9.93614	+	6.38557i	1.11790	+	0.718433i	0.963001	−	0.269497i	$-0.0868573\pi$
$79$	9.93614	+	6.38557i	1.11790	+	0.718433i	0.154902	+	0.987930i	$0.450494\pi$
$80$	0.255235	−	1.77520i	0.0285361	−	0.198473i
$81$	1.36423	−	9.48841i	0.151581	−	1.05427i
$82$	−7.47211	−	4.80203i	−0.825156	−	0.530296i
$83$	−0.824618	−	0.951659i	−0.0905135	−	0.104458i	0.708686	−	0.705524i	$-0.249288\pi$
$83$	−0.824618	−	0.951659i	−0.0905135	−	0.104458i	−0.799199	+	0.601066i	$0.794743\pi$
$84$	0.744281	+	1.62975i	0.0812077	+	0.177820i
$85$	6.01174	−	3.86351i	0.652065	−	0.419057i
$86$	−5.53468	−	1.62513i	−0.596820	−	0.175242i
$87$	2.05696	−	2.37386i	0.220529	−	0.254504i
$88$	−0.989669	+	0.290593i	−0.105499	+	0.0309773i
$89$	1.83548	−	4.01914i	0.194560	−	0.426028i	−0.787059	−	0.616878i	$-0.788397\pi$
$89$	1.83548	−	4.01914i	0.194560	−	0.426028i	0.981619	+	0.190850i	$0.0611245\pi$
$90$	−0.0536074	−	0.372848i	−0.00565072	−	0.0393016i
$91$	−6.00881			−0.629894
$92$	4.75075	−	0.655994i	0.495300	−	0.0683921i
$93$	14.5822			1.51211
$94$	0.547848	+	3.81037i	0.0565063	+	0.393010i
$95$	4.08389	−	8.94248i	0.418999	−	0.917479i
$96$	1.71908	−	0.504768i	0.175453	−	0.0515177i
$97$	−9.65569	+	11.1433i	−0.980387	+	1.13143i	0.0109310	+	0.999940i	$0.496520\pi$
$97$	−9.65569	+	11.1433i	−0.980387	+	1.13143i	−0.991318	+	0.131487i	$0.958025\pi$
$98$	0.959493	+	0.281733i	0.0969234	+	0.0284593i
$99$	−0.182247	+	0.117123i	−0.0183165	+	0.0117713i
$100$	−0.740904	−	1.62235i	−0.0740904	−	0.162235i
$101$	−13.0138	−	15.0187i	−1.29492	−	1.49442i	−0.760752	−	0.649042i	$-0.775170\pi$
$101$	−13.0138	−	15.0187i	−1.29492	−	1.49442i	−0.534170	−	0.845377i	$-0.679376\pi$
$102$	6.00572	+	3.85964i	0.594655	+	0.382161i
$103$	−1.49238	+	10.3797i	−0.147049	+	1.02275i	0.773969	+	0.633224i	$0.218269\pi$
$103$	−1.49238	+	10.3797i	−0.147049	+	1.02275i	−0.921017	+	0.389522i	$0.872640\pi$
$104$	−0.855142	+	5.94765i	−0.0838536	+	0.583215i
$105$	−2.70316	−	1.73721i	−0.263801	−	0.169535i
$106$	−5.40192	−	6.23415i	−0.524681	−	0.605514i
$107$	−3.37265	−	7.38507i	−0.326046	−	0.713942i	0.673638	−	0.739061i	$-0.264731\pi$
$107$	−3.37265	−	7.38507i	−0.326046	−	0.713942i	−0.999684	+	0.0251196i	$0.992003\pi$
$108$	−4.20514	+	2.70248i	−0.404640	+	0.260046i
$109$	−7.26418	−	2.13296i	−0.695782	−	0.204300i	−0.0853295	−	0.996353i	$-0.527194\pi$
$109$	−7.26418	−	2.13296i	−0.695782	−	0.204300i	−0.610453	+	0.792053i	$0.709012\pi$
$110$	1.21140	−	1.39803i	0.115502	−	0.133297i
$111$	−12.2335	+	3.59207i	−1.16115	+	0.340944i
$112$	0.415415	−	0.909632i	0.0392530	−	0.0859521i
$113$	0.353815	+	2.46084i	0.0332841	+	0.231496i	0.999673	−	0.0255903i	$-0.00814654\pi$
$113$	0.353815	+	2.46084i	0.0332841	+	0.231496i	−0.966388	+	0.257087i	$0.917237\pi$
$114$	9.82103			0.919824
$115$	−6.53163	+	5.59613i	−0.609078	+	0.521842i
$116$	−1.75316			−0.162777
$117$	0.179607	+	1.24919i	0.0166047	+	0.115488i
$118$	0.0388724	−	0.0851186i	0.00357849	−	0.00783580i
$119$	3.82318	−	1.12259i	0.350471	−	0.102907i
$120$	−2.10423	+	2.42841i	−0.192089	+	0.221683i
$121$	9.53363	+	2.79933i	0.866694	+	0.254484i
$122$	−4.67471	+	3.00425i	−0.423228	+	0.271992i
$123$	6.61078	+	14.4756i	0.596074	+	1.30522i
$124$	−5.32990	−	6.15103i	−0.478639	−	0.552379i
$125$	10.2346	+	6.57740i	0.915414	+	0.588301i
$126$	0.0298906	−	0.207894i	0.00266287	−	0.0185207i
$127$	−0.615478	+	4.28074i	−0.0546148	+	0.379854i	0.944122	+	0.329598i	$0.106913\pi$
$127$	−0.615478	+	4.28074i	−0.0546148	+	0.379854i	−0.998736	+	0.0502568i	$0.983996\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	6.76791	+	7.81058i	0.595881	+	0.687683i
$130$	−4.47672	−	9.80266i	−0.392635	−	0.859750i
$131$	5.18633	−	3.33305i	0.453131	−	0.291210i	−0.294099	−	0.955775i	$-0.595020\pi$
$131$	5.18633	−	3.33305i	0.453131	−	0.291210i	0.747230	+	0.664565i	$0.231383\pi$
$132$	1.77315	+	0.520643i	0.154333	+	0.0453161i
$133$	3.58964	−	4.14267i	0.311262	−	0.359215i
$134$	−8.98412	+	2.63798i	−0.776110	+	0.227886i
$135$	3.72414	−	8.15473i	0.320523	−	0.701847i
$136$	−0.567066	−	3.94403i	−0.0486255	−	0.338198i
$137$	−9.42984			−0.805646			−0.402823	−	0.915278i	$-0.631971\pi$
$137$	−9.42984			−0.805646			−0.402823	+	0.915278i	$0.631971\pi$
$138$	−7.79594	−	3.61304i	−0.663634	−	0.307563i
$139$	14.1236			1.19794			0.598972	−	0.800770i	$-0.295576\pi$
$139$	14.1236			1.19794			0.598972	+	0.800770i	$0.295576\pi$
$140$	0.255235	+	1.77520i	0.0215713	+	0.150032i
$141$	2.86515	−	6.27380i	0.241289	−	0.528349i
$142$	10.1366	−	2.97638i	0.850648	−	0.249773i
$143$	−4.05868	+	4.68397i	−0.339404	+	0.391693i
$144$	−0.201524	−	0.0591728i	−0.0167937	−	0.00493106i
$145$	2.64508	−	1.69989i	0.219662	−	0.141168i
$146$	−2.79304	−	6.11590i	−0.231153	−	0.506155i
$147$	−1.17329	−	1.35404i	−0.0967709	−	0.111680i
$148$	5.98660	+	3.84735i	0.492095	+	0.316250i
$149$	0.304991	−	2.12126i	0.0249858	−	0.173780i	−0.973507	−	0.228656i	$-0.926567\pi$
$149$	0.304991	−	2.12126i	0.0249858	−	0.173780i	0.998493	+	0.0548753i	$0.0174761\pi$
$150$	−0.454763	+	3.16294i	−0.0371312	+	0.258253i
$151$	17.7853	+	11.4299i	1.44734	+	0.930152i	0.999348	+	0.0361163i	$0.0114987\pi$
$151$	17.7853	+	11.4299i	1.44734	+	0.930152i	0.447997	+	0.894035i	$0.352138\pi$
$152$	−3.58964	−	4.14267i	−0.291158	−	0.336015i
$153$	−0.347656	−	0.761261i	−0.0281064	−	0.0615443i
$154$	0.867711	−	0.557644i	0.0699221	−	0.0449362i
$155$	14.0056	+	4.11241i	1.12496	+	0.330317i
$156$	7.05004	−	8.13618i	0.564455	−	0.651416i
$157$	19.2009	−	5.63789i	1.53240	−	0.449952i	0.596614	−	0.802528i	$-0.296512\pi$
$157$	19.2009	−	5.63789i	1.53240	−	0.449952i	0.935783	+	0.352576i	$0.114694\pi$
$158$	−4.90652	+	10.7438i	−0.390341	+	0.854729i
$159$	2.10331	+	14.6289i	0.166804	+	1.16014i
$160$	1.79345			0.141785
$161$	−4.37350	+	1.96786i	−0.344680	+	0.155089i
$162$	9.58598			0.753146
$163$	−2.37073	−	16.4888i	−0.185690	−	1.29150i	−0.843014	−	0.537892i	$-0.819221\pi$
$163$	−2.37073	−	16.4888i	−0.185690	−	1.29150i	0.657325	−	0.753608i	$-0.271688\pi$
$164$	3.68976	−	8.07945i	0.288122	−	0.630899i
$165$	−3.18005	+	0.933748i	−0.247567	+	0.0726922i
$166$	0.824618	−	0.951659i	0.0640027	−	0.0738631i
$167$	8.59536	+	2.52383i	0.665129	+	0.195300i	0.596833	−	0.802366i	$-0.296426\pi$
$167$	8.59536	+	2.52383i	0.665129	+	0.195300i	0.0682963	+	0.997665i	$0.478244\pi$
$168$	−1.50724	+	0.968642i	−0.116286	+	0.0747324i
$169$	9.59848	+	21.0177i	0.738344	+	1.61675i
$170$	4.67975	+	5.40071i	0.358920	+	0.414216i
$171$	−0.968532	−	0.622438i	−0.0740655	−	0.0475990i
$172$	0.820920	−	5.70963i	0.0625946	−	0.435355i
$173$	2.57575	−	17.9147i	0.195831	−	1.36203i	−0.620390	−	0.784293i	$-0.713026\pi$
$173$	2.57575	−	17.9147i	0.195831	−	1.36203i	0.816221	−	0.577740i	$-0.196065\pi$
$174$	2.64243	+	1.69819i	0.200322	+	0.128739i
$175$	1.16796	+	1.34790i	0.0882897	+	0.101892i
$176$	−0.428480	−	0.938240i	−0.0322979	−	0.0707225i
$177$	−0.141039	+	0.0906405i	−0.0106012	+	0.00681296i
$178$	4.23944	+	1.24481i	0.317760	+	0.0933027i
$179$	−4.37547	+	5.04957i	−0.327038	+	0.377422i	−0.895329	−	0.445406i	$-0.853059\pi$
$179$	−4.37547	+	5.04957i	−0.327038	+	0.377422i	0.568291	+	0.822828i	$0.307605\pi$
$180$	0.361424	−	0.106124i	0.0269389	−	0.00790998i
$181$	1.50598	−	3.29764i	0.111939	−	0.245112i	−0.845369	−	0.534183i	$-0.820619\pi$
$181$	1.50598	−	3.29764i	0.111939	−	0.245112i	0.957308	+	0.289071i	$0.0933465\pi$
$182$	−0.855142	−	5.94765i	−0.0633874	−	0.440869i
$183$	9.95593			0.735964
$184$	1.32542	+	4.60904i	0.0977113	+	0.339783i
$185$	−12.7627			−0.938333
$186$	2.07527	+	14.4338i	0.152166	+	1.05834i
$187$	1.70732	−	3.73850i	0.124851	−	0.273386i
$188$	−3.69362	+	1.08454i	−0.269385	+	0.0790985i
$189$	3.27343	−	3.77774i	0.238107	−	0.274790i
$190$	9.43266	+	2.76968i	0.684317	+	0.200934i
$191$	−2.48269	+	1.59553i	−0.179641	+	0.115448i	−0.627371	−	0.778721i	$-0.715869\pi$
$191$	−2.48269	+	1.59553i	−0.179641	+	0.115448i	0.447730	+	0.894169i	$0.352233\pi$
$192$	0.744281	+	1.62975i	0.0537138	+	0.117617i
$193$	−10.4531	−	12.0635i	−0.752432	−	0.868353i	0.242370	−	0.970184i	$-0.422075\pi$
$193$	−10.4531	−	12.0635i	−0.752432	−	0.868353i	−0.994802	+	0.101831i	$0.967530\pi$
$194$	−12.4040	−	7.97156i	−0.890554	−	0.572325i
$195$	−2.74779	+	19.1113i	−0.196773	+	1.36859i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	−6.47748	−	4.16282i	−0.461501	−	0.296589i	0.289154	−	0.957282i	$-0.406626\pi$
$197$	−6.47748	−	4.16282i	−0.461501	−	0.296589i	−0.750656	+	0.660694i	$0.770262\pi$
$198$	−0.141867	−	0.163723i	−0.0100821	−	0.0116353i
$199$	−2.92308	−	6.40066i	−0.207212	−	0.453731i	0.777281	−	0.629153i	$-0.216598\pi$
$199$	−2.92308	−	6.40066i	−0.207212	−	0.453731i	−0.984493	+	0.175422i	$0.943871\pi$
$200$	1.50040	−	0.964248i	0.106094	−	0.0681826i
$201$	16.0965	+	4.72635i	1.13536	+	0.333371i
$202$	13.0138	−	15.0187i	0.915648	−	1.05671i
$203$	1.68215	−	0.493923i	0.118064	−	0.0346666i
$204$	−2.96565	+	6.49387i	−0.207637	+	0.454662i
$205$	2.26702	+	15.7675i	0.158336	+	1.10125i
$206$	−10.4865			−0.730627
$207$	0.539833	+	0.850403i	0.0375210	+	0.0591071i
$208$	−6.00881			−0.416636
$209$	−0.804638	−	5.59638i	−0.0556580	−	0.387110i
$210$	1.33483	−	2.92288i	0.0921122	−	0.201698i
$211$	5.23116	−	1.53601i	0.360128	−	0.105743i	−0.0966632	−	0.995317i	$-0.530817\pi$
$211$	5.23116	−	1.53601i	0.360128	−	0.105743i	0.456791	+	0.889574i	$0.348999\pi$
$212$	5.40192	−	6.23415i	0.371005	−	0.428163i
$213$	−18.1614	−	5.33266i	−1.24440	−	0.365388i
$214$	6.82992	−	4.38932i	0.466884	−	0.300048i
$215$	4.29757	+	9.41036i	0.293092	+	0.641781i
$216$	−3.27343	−	3.77774i	−0.222729	−	0.257043i
$217$	6.84694	+	4.40026i	0.464801	+	0.298709i
$218$	1.07744	−	7.49379i	0.0729738	−	0.507544i
$219$	−1.71435	+	11.9236i	−0.115845	+	0.805719i
$220$	1.55620	+	1.00011i	0.104919	+	0.0674273i
$221$	−15.6791	−	18.0946i	−1.05469	−	1.21718i
$222$	−5.29651	−	11.5977i	−0.355479	−	0.778389i
$223$	4.96039	−	3.18785i	0.332172	−	0.213474i	−0.363914	−	0.931433i	$-0.618560\pi$
$223$	4.96039	−	3.18785i	0.332172	−	0.213474i	0.696086	+	0.717959i	$0.254923\pi$
$224$	0.959493	+	0.281733i	0.0641088	+	0.0188240i
$225$	0.245309	−	0.283102i	0.0163539	−	0.0188734i
$226$	−2.38544	+	0.700428i	−0.158677	+	0.0465918i
$227$	−7.10297	+	15.5533i	−0.471441	+	1.03231i	0.513288	+	0.858216i	$0.328427\pi$
$227$	−7.10297	+	15.5533i	−0.471441	+	1.03231i	−0.984729	+	0.174095i	$0.944300\pi$
$228$	1.39768	+	9.72106i	0.0925635	+	0.643793i
$229$	−20.9277			−1.38294			−0.691470	−	0.722405i	$-0.743037\pi$
$229$	−20.9277			−1.38294			−0.691470	+	0.722405i	$0.743037\pi$
$230$	−6.46871	−	5.66874i	−0.426534	−	0.373786i
$231$	−1.84800			−0.121590
$232$	−0.249501	−	1.73532i	−0.0163806	−	0.113929i
$233$	6.90776	−	15.1259i	0.452543	−	0.990930i	−0.536582	−	0.843848i	$-0.680285\pi$
$233$	6.90776	−	15.1259i	0.452543	−	0.990930i	0.989124	−	0.147082i	$-0.0469881\pi$
$234$	−1.21092	+	0.355558i	−0.0791602	+	0.0232435i
$235$	4.52115	−	5.21769i	0.294927	−	0.340364i
$236$	0.0897844	+	0.0263631i	0.00584446	+	0.00171609i
$237$	17.8022	−	11.4408i	1.15637	−	0.743157i
$238$	1.65526	+	3.62451i	0.107294	+	0.234942i
$239$	−13.1126	−	15.1328i	−0.848186	−	0.978859i	0.151769	−	0.988416i	$-0.451503\pi$
$239$	−13.1126	−	15.1328i	−0.848186	−	0.978859i	−0.999954	+	0.00955748i	$0.996958\pi$
$240$	−2.70316	−	1.73721i	−0.174488	−	0.112137i
$241$	1.58276	−	11.0083i	0.101954	−	0.709109i	−0.873164	−	0.487426i	$-0.837936\pi$
$241$	1.58276	−	11.0083i	0.101954	−	0.709109i	0.975119	−	0.221683i	$-0.0711550\pi$
$242$	−1.41406	+	9.83498i	−0.0908990	+	0.632216i
$243$	−1.83292	−	1.17794i	−0.117582	−	0.0755651i
$244$	−3.63895	−	4.19957i	−0.232960	−	0.268850i
$245$	−0.745027	−	1.63138i	−0.0475980	−	0.104225i
$246$	−13.3874	+	8.60359i	−0.853552	+	0.548545i
$247$	−31.6033	−	9.27956i	−2.01087	−	0.590444i
$248$	5.32990	−	6.15103i	0.338449	−	0.390591i
$249$	−2.16471	+	0.635617i	−0.137183	+	0.0402806i
$250$	−5.05391	+	11.0665i	−0.319637	+	0.699908i
$251$	1.93965	+	13.4906i	0.122430	+	0.851517i	0.954790	+	0.297282i	$0.0960800\pi$
$251$	1.93965	+	13.4906i	0.122430	+	0.851517i	−0.832360	+	0.554235i	$0.813011\pi$
$252$	0.210032			0.0132307
$253$	−1.42012	+	4.73843i	−0.0892823	+	0.297902i
$254$	−4.32476			−0.271360
$255$	−1.82212	−	12.6732i	−0.114106	−	0.793624i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	10.0191	−	2.94187i	0.624973	−	0.183509i	0.0461139	−	0.998936i	$-0.485316\pi$
$257$	10.0191	−	2.94187i	0.624973	−	0.183509i	0.578859	+	0.815428i	$0.303498\pi$
$258$	−6.76791	+	7.81058i	−0.421351	+	0.486265i
$259$	−6.82802	−	2.00489i	−0.424273	−	0.124578i
$260$	9.06578	−	5.82622i	0.562236	−	0.361327i
$261$	−0.152964	−	0.334944i	−0.00946824	−	0.0207325i
$262$	4.03721	+	4.65919i	0.249420	+	0.287846i
$263$	−21.5219	−	13.8313i	−1.32710	−	0.852875i	−0.331219	−	0.943554i	$-0.607460\pi$
$263$	−21.5219	−	13.8313i	−1.32710	−	0.852875i	−0.995880	+	0.0906793i	$0.971096\pi$
$264$	−0.262998	+	1.82919i	−0.0161864	+	0.112579i
$265$	−2.10542	+	14.6435i	−0.129335	+	0.899545i
$266$	4.61136	+	2.96354i	0.282741	+	0.181706i
$267$	−5.18407	−	5.98273i	−0.317260	−	0.366137i
$268$	−3.88970	−	8.51725i	−0.237601	−	0.520274i
$269$	−21.8827	+	14.0632i	−1.33421	+	0.857445i	−0.996483	−	0.0837981i	$-0.973295\pi$
$269$	−21.8827	+	14.0632i	−1.33421	+	0.857445i	−0.337728	+	0.941244i	$0.609659\pi$
$270$	8.60173	+	2.52569i	0.523484	+	0.153709i
$271$	4.16173	−	4.80289i	0.252807	−	0.291755i	−0.615133	−	0.788423i	$-0.710898\pi$
$271$	4.16173	−	4.80289i	0.252807	−	0.291755i	0.867941	+	0.496668i	$0.165443\pi$
$272$	3.82318	−	1.12259i	0.231815	−	0.0680669i
$273$	−4.47224	+	9.79284i	−0.270672	+	0.592690i
$274$	−1.34201	−	9.33386i	−0.0810736	−	0.563879i
$275$	1.83962			0.110933
$276$	2.46679	−	8.23078i	0.148483	−	0.495434i
$277$	−14.7030			−0.883420			−0.441710	−	0.897158i	$-0.645628\pi$
$277$	−14.7030			−0.883420			−0.441710	+	0.897158i	$0.645628\pi$
$278$	2.00999	+	13.9798i	0.120551	+	0.838453i
$279$	0.710128	−	1.55496i	0.0425143	−	0.0930932i
$280$	−1.72081	+	0.505274i	−0.102838	+	0.0301959i
$281$	3.41124	−	3.93678i	0.203497	−	0.234848i	−0.644823	−	0.764332i	$-0.723069\pi$
$281$	3.41124	−	3.93678i	0.203497	−	0.234848i	0.848320	+	0.529484i	$0.177614\pi$
$282$	6.61769	+	1.94313i	0.394078	+	0.115712i
$283$	15.0377	−	9.66414i	0.893898	−	0.574473i	−0.0110768	−	0.999939i	$-0.503526\pi$
$283$	15.0377	−	9.66414i	0.893898	−	0.574473i	0.904975	+	0.425465i	$0.139890\pi$
$284$	4.38868	+	9.60988i	0.260420	+	0.570241i
$285$	−11.5344	−	13.3114i	−0.683240	−	0.788501i
$286$	−5.21391	−	3.35077i	−0.308305	−	0.198135i
$287$	−1.26406	+	8.79170i	−0.0746149	+	0.518958i
$288$	0.0298906	−	0.207894i	0.00176132	−	0.0122503i
$289$	−0.944778	−	0.607172i	−0.0555752	−	0.0357160i
$290$	2.05902	+	2.37624i	0.120910	+	0.139538i
$291$	10.9742	+	24.0301i	0.643317	+	1.40867i
$292$	5.65615	−	3.63499i	0.331001	−	0.212722i
$293$	6.79563	+	1.99538i	0.397005	+	0.116571i	0.474140	−	0.880450i	$-0.342759\pi$
$293$	6.79563	+	1.99538i	0.397005	+	0.116571i	−0.0771351	+	0.997021i	$0.524577\pi$
$294$	1.17329	−	1.35404i	0.0684274	−	0.0789694i
$295$	−0.161024	+	0.0472809i	−0.00937518	+	0.00275280i
$296$	−2.95621	+	6.47320i	−0.171826	+	0.376247i
$297$	−0.733757	−	5.10339i	−0.0425769	−	0.296129i
$298$	2.14307			0.124145
$299$	21.6729	+	18.9926i	1.25337	+	1.09837i
$300$	−3.19547			−0.184490
$301$	0.820920	+	5.70963i	0.0473171	+	0.329097i
$302$	−8.78245	+	19.2309i	−0.505373	+	1.10661i
$303$	−34.1627	+	10.0311i	−1.96259	+	0.576270i
$304$	3.58964	−	4.14267i	0.205880	−	0.237598i
$305$	9.56223	+	2.80772i	0.547532	+	0.160770i
$306$	0.704036	−	0.452457i	0.0402471	−	0.0258652i
$307$	−10.1453	−	22.2152i	−0.579024	−	1.26789i	−0.941851	−	0.336030i	$-0.890916\pi$
$307$	−10.1453	−	22.2152i	−0.579024	−	1.26789i	0.362827	−	0.931856i	$-0.381812\pi$
$308$	0.675456	+	0.779518i	0.0384877	+	0.0444172i
$309$	15.8056	+	10.1576i	0.899149	+	0.577848i
$310$	−2.07735	+	14.4483i	−0.117986	+	0.820608i
$311$	−1.04523	+	7.26973i	−0.0592696	+	0.412229i	0.938489	+	0.345310i	$0.112226\pi$
$311$	−1.04523	+	7.26973i	−0.0592696	+	0.412229i	−0.997758	+	0.0669192i	$0.978683\pi$
$312$	9.05670	+	5.82038i	0.512734	+	0.329514i
$313$	−5.73009	−	6.61288i	−0.323884	−	0.373782i	0.570335	−	0.821412i	$-0.306813\pi$
$313$	−5.73009	−	6.61288i	−0.323884	−	0.373782i	−0.894219	+	0.447630i	$0.852268\pi$
$314$	8.31307	+	18.2031i	0.469134	+	1.02726i
$315$	−0.316885	+	0.203650i	−0.0178544	+	0.0114744i
$316$	−11.3327	−	3.32758i	−0.637513	−	0.187191i
$317$	12.4020	−	14.3127i	0.696566	−	0.803880i	−0.291718	−	0.956504i	$-0.594227\pi$
$317$	12.4020	−	14.3127i	0.696566	−	0.803880i	0.988284	+	0.152624i	$0.0487725\pi$
$318$	−14.1806	+	4.16381i	−0.795210	+	0.233495i
$319$	0.751195	−	1.64489i	0.0420589	−	0.0920960i
$320$	0.255235	+	1.77520i	0.0142681	+	0.0992366i
$321$	−14.5460			−0.811878
$322$	−2.57025	−	4.04893i	−0.143234	−	0.225638i
$323$	21.8417			1.21530
$324$	1.36423	+	9.48841i	0.0757904	+	0.527134i
$325$	4.45195	−	9.74841i	0.246950	−	0.540745i
$326$	15.9835	−	4.69319i	0.885246	−	0.259932i
$327$	−8.88277	+	10.2513i	−0.491218	+	0.566896i
$328$	8.52232	+	2.50238i	0.470566	+	0.138171i
$329$	3.23845	−	2.08123i	0.178542	−	0.114742i
$330$	−1.37681	−	3.01480i	−0.0757911	−	0.165959i
$331$	5.53954	+	6.39297i	0.304481	+	0.351390i	0.887284	−	0.461224i	$-0.152590\pi$
$331$	5.53954	+	6.39297i	0.304481	+	0.351390i	−0.582803	+	0.812613i	$0.698044\pi$
$332$	1.05933	+	0.680789i	0.0581382	+	0.0373631i
$333$	−0.212710	+	1.47943i	−0.0116564	+	0.0810723i
$334$	−1.27489	+	8.86705i	−0.0697589	+	0.485184i
$335$	14.1270	+	9.07889i	0.771842	+	0.496033i
$336$	−1.17329	−	1.35404i	−0.0640080	−	0.0738691i
$337$	7.33165	+	16.0541i	0.399381	+	0.874521i	0.997333	+	0.0729896i	$0.0232540\pi$
$337$	7.33165	+	16.0541i	0.399381	+	0.874521i	−0.597952	+	0.801532i	$0.704019\pi$
$338$	−19.4378	+	12.4919i	−1.05728	+	0.679470i
$339$	4.27388	+	1.25493i	0.232126	+	0.0681582i
$340$	−4.67975	+	5.40071i	−0.253795	+	0.292895i
$341$	8.05489	−	2.36513i	0.436197	−	0.128079i
$342$	0.478266	−	1.04726i	0.0258616	−	0.0566291i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	5.76834			0.311008
$345$	4.25891	+	14.8100i	0.229292	+	0.797344i
$346$	18.0990			0.973007
$347$	−0.632502	−	4.39915i	−0.0339545	−	0.236159i	0.965776	−	0.259378i	$-0.0835175\pi$
$347$	−0.632502	−	4.39915i	−0.0339545	−	0.236159i	−0.999730	+	0.0232192i	$0.992608\pi$
$348$	−1.30485	+	2.85721i	−0.0699471	+	0.153163i
$349$	−5.03180	+	1.47747i	−0.269346	+	0.0790871i	−0.413617	−	0.910451i	$-0.635735\pi$
$349$	−5.03180	+	1.47747i	−0.269346	+	0.0790871i	0.144271	+	0.989538i	$0.453916\pi$
$350$	−1.16796	+	1.34790i	−0.0624302	+	0.0720483i
$351$	−28.8193	−	8.46212i	−1.53826	−	0.451675i
$352$	0.867711	−	0.557644i	0.0462492	−	0.0297225i
$353$	1.86896	+	4.09245i	0.0994747	+	0.217819i	0.952826	−	0.303517i	$-0.0981610\pi$
$353$	1.86896	+	4.09245i	0.0994747	+	0.217819i	−0.853351	+	0.521336i	$0.825434\pi$
$354$	−0.109790	−	0.126704i	−0.00583527	−	0.00673426i
$355$	−15.9393	−	10.2436i	−0.845969	−	0.543672i
$356$	−0.628807	+	4.37345i	−0.0333267	+	0.231792i
$357$	1.01599	−	7.06635i	0.0537717	−	0.373991i
$358$	−5.62086	−	3.61231i	−0.297072	−	0.190916i
$359$	−18.5767	−	21.4387i	−0.980443	−	1.13149i	−0.991309	−	0.131551i	$-0.958004\pi$
$359$	−18.5767	−	21.4387i	−0.980443	−	1.13149i	0.0108661	−	0.999941i	$-0.496541\pi$
$360$	0.156479	+	0.342642i	0.00824718	+	0.0180588i
$361$	9.29353	−	5.97259i	0.489133	−	0.314347i
$362$	3.47840	+	1.02135i	0.182821	+	0.0536810i
$363$	11.6579	−	13.4539i	0.611881	−	0.706148i
$364$	5.76541	−	1.69288i	0.302189	−	0.0887308i
$365$	−5.00918	+	10.9686i	−0.262192	+	0.574121i
$366$	1.41688	+	9.85460i	0.0740614	+	0.515108i
$367$	−12.9875			−0.677942			−0.338971	−	0.940797i	$-0.610079\pi$
$367$	−12.9875			−0.677942			−0.338971	+	0.940797i	$0.610079\pi$
$368$	−4.37350	+	1.96786i	−0.227984	+	0.102582i
$369$	1.86552			0.0971153
$370$	−1.81632	−	12.6328i	−0.0944261	−	0.656748i
$371$	−3.42674	+	7.50352i	−0.177908	+	0.389563i
$372$	−13.9916	+	4.10829i	−0.725429	+	0.213005i
$373$	−22.6010	+	26.0829i	−1.17023	+	1.35052i	−0.245736	+	0.969337i	$0.579030\pi$
$373$	−22.6010	+	26.0829i	−1.17023	+	1.35052i	−0.924498	+	0.381186i	$0.875516\pi$
$374$	3.94342	+	1.15789i	0.203910	+	0.0598733i
$375$	18.3369	−	11.7844i	0.946916	−	0.608546i
$376$	−1.59916	−	3.50168i	−0.0824705	−	0.180585i
$377$	−6.89858	−	7.96138i	−0.355295	−	0.410032i
$378$	4.20514	+	2.70248i	0.216289	+	0.139001i
$379$	−4.09445	+	28.4775i	−0.210318	+	1.46279i	0.561779	+	0.827288i	$0.310117\pi$
$379$	−4.09445	+	28.4775i	−0.210318	+	1.46279i	−0.772097	+	0.635505i	$0.780792\pi$
$380$	−1.39908	+	9.73081i	−0.0717713	+	0.499180i
$381$	6.51844	+	4.18915i	0.333950	+	0.214616i
$382$	−1.93261	−	2.23035i	−0.0988809	−	0.114115i
$383$	−7.62616	−	16.6990i	−0.389679	−	0.853278i	−0.998213	−	0.0597502i	$-0.980970\pi$
$383$	−7.62616	−	16.6990i	−0.389679	−	0.853278i	0.608535	−	0.793527i	$-0.291758\pi$
$384$	−1.50724	+	0.968642i	−0.0769159	+	0.0494308i
$385$	−1.77492	−	0.521165i	−0.0904585	−	0.0265610i
$386$	10.4531	−	12.0635i	0.532050	−	0.614018i
$387$	1.16246	−	0.341328i	0.0590911	−	0.0173507i
$388$	6.12515	−	13.4122i	0.310957	−	0.680902i
$389$	2.36709	+	16.4634i	0.120016	+	0.834730i	0.957534	+	0.288320i	$0.0930967\pi$
$389$	2.36709	+	16.4634i	0.120016	+	0.834730i	−0.837518	+	0.546410i	$0.815994\pi$
$390$	−19.3078			−0.977688
$391$	−17.3379	−	8.03530i	−0.876817	−	0.406362i
$392$	−1.00000			−0.0505076
$393$	−1.57195	−	10.9331i	−0.0792942	−	0.551503i
$394$	3.19861	−	7.00398i	0.161144	−	0.352855i
$395$	20.3246	−	5.96785i	1.02264	−	0.300275i
$396$	0.141867	−	0.163723i	0.00712909	−	0.00822741i
$397$	28.7765	+	8.44953i	1.44425	+	0.424070i	0.907636	−	0.419759i	$-0.137885\pi$
$397$	28.7765	+	8.44953i	1.44425	+	0.424070i	0.536613	+	0.843828i	$0.319703\pi$
$398$	5.91951	−	3.80424i	0.296718	−	0.190689i
$399$	−4.07980	−	8.93352i	−0.204246	−	0.447235i
$400$	1.16796	+	1.34790i	0.0583981	+	0.0673950i
$401$	−9.13828	−	5.87281i	−0.456344	−	0.293274i	0.292203	−	0.956356i	$-0.405612\pi$
$401$	−9.13828	−	5.87281i	−0.456344	−	0.293274i	−0.748547	+	0.663082i	$0.769248\pi$
$402$	−2.38747	+	16.6052i	−0.119076	+	0.828195i
$403$	6.95998	−	48.4077i	0.346701	−	2.41136i
$404$	16.7179	+	10.7440i	0.831748	+	0.534532i
$405$	−11.2584	−	12.9928i	−0.559433	−	0.645620i
$406$	0.728290	+	1.59473i	0.0361444	+	0.0791453i
$407$	−6.17487	+	3.96835i	−0.306077	+	0.196704i
$408$	−6.84983	−	2.01129i	−0.339117	−	0.0995738i
$409$	−5.55323	+	6.40877i	−0.274590	+	0.316893i	−0.876248	−	0.481860i	$-0.839961\pi$
$409$	−5.55323	+	6.40877i	−0.274590	+	0.316893i	0.601659	+	0.798753i	$0.294507\pi$
$410$	−15.2844	+	4.48790i	−0.754842	+	0.221642i
$411$	−7.01845	+	15.3683i	−0.346195	+	0.758061i
$412$	−1.49238	−	10.3797i	−0.0735243	−	0.511373i
$413$	−0.0935748			−0.00460451
$414$	−0.764921	+	0.655364i	−0.0375938	+	0.0322094i
$415$	−2.25836			−0.110859
$416$	−0.855142	−	5.94765i	−0.0419268	−	0.291607i
$417$	10.5119	−	23.0178i	0.514770	−	1.12719i
$418$	5.42491	−	1.59290i	0.265341	−	0.0779111i
$419$	15.9382	−	18.3936i	0.778631	−	0.898588i	−0.218379	−	0.975864i	$-0.570077\pi$
$419$	15.9382	−	18.3936i	0.778631	−	0.898588i	0.997010	+	0.0772760i	$0.0246223\pi$
$420$	3.08309	+	0.905277i	0.150439	+	0.0441730i
$421$	−9.23537	+	5.93521i	−0.450104	+	0.289264i	−0.745988	−	0.665960i	$-0.768022\pi$
$421$	−9.23537	+	5.93521i	−0.450104	+	0.289264i	0.295884	+	0.955224i	$0.404386\pi$
$422$	2.26484	+	4.95931i	0.110251	+	0.241416i
$423$	−0.529473	−	0.611045i	−0.0257439	−	0.0297100i
$424$	6.93946	+	4.45972i	0.337010	+	0.216583i
$425$	−1.01138	+	7.03429i	−0.0490590	+	0.341213i
$426$	2.69375	−	18.7354i	0.130512	−	0.907734i
$427$	4.67471	+	3.00425i	0.226225	+	0.145386i
$428$	5.31665	+	6.13574i	0.256990	+	0.296582i
$429$	4.61289	+	10.1008i	0.222712	+	0.487672i
$430$	−8.70297	+	5.59306i	−0.419695	+	0.269721i
$431$	−14.7417	−	4.32857i	−0.710085	−	0.208500i	−0.0933074	−	0.995637i	$-0.529744\pi$
$431$	−14.7417	−	4.32857i	−0.710085	−	0.208500i	−0.616777	+	0.787138i	$0.711562\pi$
$432$	3.27343	−	3.77774i	0.157493	−	0.181757i
$433$	3.06650	−	0.900404i	0.147366	−	0.0432707i	−0.207217	−	0.978295i	$-0.566441\pi$
$433$	3.06650	−	0.900404i	0.147366	−	0.0432707i	0.354584	+	0.935024i	$0.384623\pi$
$434$	−3.38105	+	7.40347i	−0.162296	+	0.355378i
$435$	−0.801710	−	5.57601i	−0.0384390	−	0.267349i
$436$	7.57085			0.362578
$437$	−26.0414	+	3.59586i	−1.24573	+	0.172013i
$438$	−12.0462			−0.575588
$439$	−2.37017	−	16.4849i	−0.113122	−	0.786780i	−0.964851	−	0.262798i	$-0.915355\pi$
$439$	−2.37017	−	16.4849i	−0.113122	−	0.786780i	0.851729	−	0.523983i	$-0.175554\pi$
$440$	−0.768458	+	1.68269i	−0.0366348	+	0.0802190i
$441$	−0.201524	+	0.0591728i	−0.00959638	+	0.00281775i
$442$	15.6791	−	18.0946i	0.745778	−	0.860673i
$443$	−23.1263	−	6.79050i	−1.09877	−	0.322627i	−0.318404	−	0.947955i	$-0.603147\pi$
$443$	−23.1263	−	6.79050i	−1.09877	−	0.322627i	−0.780362	+	0.625329i	$0.784965\pi$
$444$	10.7259	−	6.89313i	0.509030	−	0.327134i
$445$	−3.29184	−	7.20813i	−0.156048	−	0.341698i
$446$	3.86134	+	4.45622i	0.182840	+	0.211008i
$447$	−3.23012	−	2.07587i	−0.152779	−	0.0981853i
$448$	−0.142315	+	0.989821i	−0.00672374	+	0.0467647i
$449$	−3.12956	+	21.7666i	−0.147693	+	1.02723i	0.772290	+	0.635270i	$0.219111\pi$
$449$	−3.12956	+	21.7666i	−0.147693	+	1.02723i	−0.919983	+	0.391958i	$0.871798\pi$
$450$	0.315131	+	0.202523i	0.0148554	+	0.00954701i
$451$	5.99947	+	6.92376i	0.282504	+	0.326027i
$452$	−1.03278	−	2.26148i	−0.0485780	−	0.106371i
$453$	31.8651	−	20.4784i	1.49715	−	0.962161i
$454$	−16.4059	−	4.81720i	−0.769966	−	0.226082i
$455$	−7.05711	+	8.14434i	−0.330843	+	0.381813i
$456$	−9.42321	+	2.76690i	−0.441282	+	0.129572i
$457$	−7.04466	+	15.4257i	−0.329536	+	0.721582i	−0.999789	−	0.0205503i	$-0.993458\pi$
$457$	−7.04466	+	15.4257i	−0.329536	+	0.721582i	0.670253	+	0.742132i	$0.266185\pi$
$458$	−2.97832	−	20.7147i	−0.139168	−	0.967933i
$459$	19.9176			0.929675
$460$	4.69044	−	7.20962i	0.218693	−	0.336150i
$461$	17.6990			0.824323			0.412162	−	0.911111i	$-0.364774\pi$
$461$	17.6990			0.824323			0.412162	+	0.911111i	$0.364774\pi$
$462$	−0.262998	−	1.82919i	−0.0122358	−	0.0851018i
$463$	−5.28535	+	11.5733i	−0.245631	+	0.537857i	−0.991785	−	0.127917i	$-0.959171\pi$
$463$	−5.28535	+	11.5733i	−0.245631	+	0.537857i	0.746154	+	0.665773i	$0.231898\pi$
$464$	1.68215	−	0.493923i	0.0780918	−	0.0229298i
$465$	17.1263	−	19.7648i	0.794213	−	0.916570i
$466$	15.9550	+	4.68481i	0.739102	+	0.217020i
$467$	4.75872	−	3.05824i	0.220207	−	0.141519i	−0.425887	−	0.904777i	$-0.640038\pi$
$467$	4.75872	−	3.05824i	0.220207	−	0.141519i	0.646094	+	0.763258i	$0.276401\pi$
$468$	−0.524270	−	1.14799i	−0.0242344	−	0.0530659i
$469$	6.13173	+	7.07639i	0.283137	+	0.326757i
$470$	5.80801	+	3.73258i	0.267903	+	0.172171i
$471$	5.10251	−	35.4888i	0.235111	−	1.63524i
$472$	−0.0133171	+	0.0926223i	−0.000612968	+	0.00426329i
$473$	5.00525	+	3.21668i	0.230142	+	0.147903i
$474$	13.8578	+	15.9928i	0.636510	+	0.734572i
$475$	4.06129	+	8.89299i	0.186345	+	0.408038i
$476$	−3.35205	+	2.15423i	−0.153641	+	0.0987390i
$477$	1.66236	+	0.488113i	0.0761143	+	0.0223492i
$478$	13.1126	−	15.1328i	0.599758	−	0.692158i
$479$	23.7644	−	6.97786i	1.08582	−	0.318827i	0.310618	−	0.950535i	$-0.399464\pi$
$479$	23.7644	−	6.97786i	1.08582	−	0.318827i	0.775206	+	0.631708i	$0.217646\pi$
$480$	1.33483	−	2.92288i	0.0609265	−	0.133410i
$481$	6.08543	+	42.3251i	0.277472	+	1.92986i
$482$	11.1215			0.506572
$483$	−0.0479909	+	8.59235i	−0.00218366	+	0.390965i
$484$	−9.93611			−0.451641
$485$	3.76335	+	26.1747i	0.170885	+	1.18853i
$486$	0.905102	−	1.98190i	0.0410563	−	0.0899007i
$487$	9.97111	−	2.92778i	0.451834	−	0.132671i	−0.0478946	−	0.998852i	$-0.515251\pi$
$487$	9.97111	−	2.92778i	0.451834	−	0.132671i	0.499729	+	0.866182i	$0.333433\pi$
$488$	3.63895	−	4.19957i	0.164728	−	0.190106i
$489$	−28.6370	−	8.40858i	−1.29501	−	0.380249i
$490$	1.50875	−	0.969614i	0.0681583	−	0.0438027i
$491$	−0.524049	−	1.14751i	−0.0236500	−	0.0517863i	0.897438	−	0.441140i	$-0.145426\pi$
$491$	−0.524049	−	1.14751i	−0.0236500	−	0.0517863i	−0.921088	+	0.389354i	$0.872698\pi$
$492$	−10.4212	−	12.0268i	−0.469826	−	0.542208i
$493$	5.87669	+	3.77672i	0.264673	+	0.170095i
$494$	4.68749	−	32.6022i	0.210900	−	1.46684i
$495$	−0.0552934	+	0.384574i	−0.00248525	+	0.0172853i
$496$	6.84694	+	4.40026i	0.307437	+	0.197578i
$497$	−6.91833	−	7.98417i	−0.310329	−	0.358139i
$498$	−0.937218	−	2.05222i	−0.0419977	−	0.0919622i
$499$	29.3740	−	18.8775i	1.31496	−	0.845075i	0.320205	−	0.947348i	$-0.396248\pi$
$499$	29.3740	−	18.8775i	1.31496	−	0.845075i	0.994756	+	0.102274i	$0.0326117\pi$
$500$	−11.6731	−	3.42754i	−0.522038	−	0.153284i
$501$	10.5106	−	12.1298i	0.469577	−	0.541921i
$502$	−13.0772	+	3.83981i	−0.583664	+	0.171379i
$503$	16.1073	−	35.2701i	0.718189	−	1.57261i	−0.0982358	−	0.995163i	$-0.531320\pi$
$503$	16.1073	−	35.2701i	0.718189	−	1.57261i	0.816425	−	0.577452i	$-0.195953\pi$
$504$	0.0298906	+	0.207894i	0.00133143	+	0.00926033i
$505$	−35.6406			−1.58599
$506$	−4.89230	−	0.731319i	−0.217489	−	0.0325111i
$507$	41.3976			1.83853
$508$	−0.615478	−	4.28074i	−0.0273074	−	0.189927i
$509$	−17.9864	+	39.3848i	−0.797235	+	1.74570i	−0.142567	+	0.989785i	$0.545536\pi$
$509$	−17.9864	+	39.3848i	−0.797235	+	1.74570i	−0.654668	+	0.755917i	$0.727192\pi$
$510$	12.2848	−	3.60716i	0.543982	−	0.159728i
$511$	−4.40295	+	5.08127i	−0.194775	+	0.224782i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	23.0506	−	14.8138i	1.01771	−	0.654043i
$514$	4.33779	+	9.49843i	0.191332	+	0.418958i
$515$	12.3160	+	14.2134i	0.542706	+	0.626316i
$516$	−8.69425	−	5.58746i	−0.382743	−	0.245974i
$517$	0.565078	−	3.93021i	0.0248521	−	0.172850i
$518$	1.01275	−	7.04385i	0.0444978	−	0.309489i
$519$	−27.2794	−	17.5314i	−1.19743	−	0.769544i
$520$	7.05711	+	8.14434i	0.309475	+	0.357153i
$521$	16.5410	+	36.2197i	0.724673	+	1.58681i	0.807238	+	0.590227i	$0.200962\pi$
$521$	16.5410	+	36.2197i	0.724673	+	1.58681i	−0.0825646	+	0.996586i	$0.526311\pi$
$522$	0.309766	−	0.199075i	0.0135581	−	0.00871326i
$523$	−24.4963	−	7.19276i	−1.07115	−	0.314517i	−0.301816	−	0.953366i	$-0.597593\pi$
$523$	−24.4963	−	7.19276i	−1.07115	−	0.314517i	−0.769332	+	0.638849i	$0.779411\pi$
$524$	−4.03721	+	4.65919i	−0.176367	+	0.203538i
$525$	3.06603	−	0.900268i	0.133813	−	0.0392909i
$526$	10.6276	−	23.2713i	0.463387	−	1.01468i
$527$	4.61534	+	32.1004i	0.201047	+	1.39831i
$528$	−1.84800			−0.0804240
$529$	21.9946	+	6.72595i	0.956286	+	0.292433i
$530$	−14.7941			−0.642615
$531$	0.00279701	+	0.0194536i	0.000121380	+	0.000844215i
$532$	−2.27711	+	4.98618i	−0.0987253	+	0.216178i
$533$	51.2090	−	15.0363i	2.21811	−	0.651295i
$534$	5.18407	−	5.98273i	0.224337	−	0.258898i
$535$	−13.9708	−	4.10219i	−0.604009	−	0.177353i
$536$	7.87700	−	5.06224i	0.340235	−	0.218655i
$537$	4.97294	+	10.8892i	0.214598	+	0.469904i
$538$	−17.0342	−	19.6586i	−0.734398	−	0.847541i
$539$	−0.867711	−	0.557644i	−0.0373750	−	0.0240194i
$540$	−1.27583	+	8.87362i	−0.0549031	+	0.381860i
$541$	−2.83397	+	19.7107i	−0.121842	+	0.847429i	0.833625	+	0.552331i	$0.186261\pi$
$541$	−2.83397	+	19.7107i	−0.121842	+	0.847429i	−0.955467	+	0.295098i	$0.904648\pi$
$542$	5.34628	+	3.43585i	0.229643	+	0.147582i
$543$	−4.25345	−	4.90874i	−0.182533	−	0.210654i
$544$	1.65526	+	3.62451i	0.0709686	+	0.155400i
$545$	−11.4225	+	7.34080i	−0.489287	+	0.314445i
$546$	−10.3296	−	3.03305i	−0.442067	−	0.129803i
$547$	−12.2456	+	14.1322i	−0.523583	+	0.604247i	−0.954524	−	0.298133i	$-0.903636\pi$
$547$	−12.2456	+	14.1322i	−0.523583	+	0.604247i	0.430941	+	0.902380i	$0.358182\pi$
$548$	9.04787	−	2.65669i	0.386506	−	0.113488i
$549$	0.484835	−	1.06164i	0.0206923	−	0.0453097i
$550$	0.261805	+	1.82090i	0.0111634	+	0.0776432i
$551$	9.61003			0.409401
$552$	8.49806	+	1.27032i	0.361701	+	0.0540684i
$553$	11.8111			0.502260
$554$	−2.09246	−	14.5534i	−0.0889001	−	0.618314i
$555$	−9.49904	+	20.8000i	−0.403212	+	0.882911i
$556$	−13.5515	+	3.97907i	−0.574710	+	0.168750i
$557$	−0.0550711	+	0.0635555i	−0.00233344	+	0.00269293i	−0.756915	−	0.653513i	$-0.773294\pi$
$557$	−0.0550711	+	0.0635555i	−0.00233344	+	0.00269293i	0.754582	+	0.656206i	$0.227840\pi$
$558$	1.64020	+	0.481606i	0.0694351	+	0.0203880i
$559$	29.1585	−	18.7391i	1.23327	−	0.792578i
$560$	−0.745027	−	1.63138i	−0.0314831	−	0.0689385i
$561$	−4.82209	−	5.56499i	−0.203589	−	0.234954i
$562$	4.38217	+	2.81625i	0.184851	+	0.118796i
$563$	−0.0628918	+	0.437422i	−0.00265057	+	0.0184351i	−0.991104	−	0.133091i	$-0.957510\pi$
$563$	−0.0628918	+	0.437422i	−0.00265057	+	0.0184351i	0.988453	+	0.151526i	$0.0484188\pi$
$564$	−0.981556	+	6.82687i	−0.0413310	+	0.287463i
$565$	3.75097	+	2.41060i	0.157804	+	0.101415i
$566$	11.7059	+	13.5093i	0.492034	+	0.567837i
$567$	−3.98216	−	8.71972i	−0.167235	−	0.366194i
$568$	−8.88749	+	5.71164i	−0.372911	+	0.239655i
$569$	2.63818	+	0.774639i	0.110598	+	0.0324746i	0.336563	−	0.941661i	$-0.390735\pi$
$569$	2.63818	+	0.774639i	0.110598	+	0.0324746i	−0.225965	+	0.974135i	$0.572554\pi$
$570$	11.5344	−	13.3114i	0.483124	−	0.557555i
$571$	−42.1115	+	12.3650i	−1.76231	+	0.517461i	−0.992653	−	0.120995i	$-0.961391\pi$
$571$	−42.1115	+	12.3650i	−1.76231	+	0.517461i	−0.769658	+	0.638456i	$0.779573\pi$
$572$	2.57465	−	5.63770i	0.107652	−	0.235724i
$573$	0.752489	+	5.23368i	0.0314357	+	0.218640i
$574$	−8.88211			−0.370732
$575$	0.0477732	−	8.55337i	0.00199228	−	0.356700i
$576$	0.210032			0.00875132
$577$	−1.94093	−	13.4995i	−0.0808019	−	0.561990i	−0.989500	−	0.144535i	$-0.953831\pi$
$577$	−1.94093	−	13.4995i	−0.0808019	−	0.561990i	0.908698	−	0.417455i	$-0.137078\pi$
$578$	0.466536	−	1.02157i	0.0194053	−	0.0424917i
$579$	−27.4406	+	8.05729i	−1.14039	+	0.334849i
$580$	−2.05902	+	2.37624i	−0.0854963	+	0.0986680i
$581$	−1.20822	−	0.354765i	−0.0501253	−	0.0147181i
$582$	−22.2237	+	14.2823i	−0.921201	+	0.592020i
$583$	3.53451	+	7.73950i	0.146385	+	0.320537i
$584$	4.40295	+	5.08127i	0.182195	+	0.210264i
$585$	1.90410	+	1.22369i	0.0787248	+	0.0505934i
$586$	−1.00795	+	7.01043i	−0.0416379	+	0.289598i
$587$	−0.374984	+	2.60807i	−0.0154772	+	0.107646i	−0.996096	−	0.0882810i	$-0.971863\pi$
$587$	−0.374984	+	2.60807i	−0.0154772	+	0.107646i	0.980618	+	0.195928i	$0.0627717\pi$
$588$	1.50724	+	0.968642i	0.0621574	+	0.0399461i
$589$	29.2160	+	33.7171i	1.20383	+	1.38929i
$590$	−0.0697158	−	0.152656i	−0.00287015	−	0.00628476i
$591$	−11.6054	+	7.45835i	−0.477383	+	0.306795i
$592$	−6.82802	−	2.00489i	−0.280630	−	0.0824004i
$593$	24.8736	−	28.7057i	1.02144	−	1.17880i	0.0376805	−	0.999290i	$-0.488003\pi$
$593$	24.8736	−	28.7057i	1.02144	−	1.17880i	0.983756	−	0.179511i	$-0.0574515\pi$
$594$	4.94702	−	1.45258i	0.202979	−	0.0596000i
$595$	2.96863	−	6.50038i	0.121702	−	0.266490i
$596$	0.304991	+	2.12126i	0.0124929	+	0.0868902i
$597$	−12.6071			−0.515972
$598$	−15.7149	+	24.1552i	−0.642631	+	0.987779i
$599$	−14.9719			−0.611734			−0.305867	−	0.952074i	$-0.598946\pi$
$599$	−14.9719			−0.611734			−0.305867	+	0.952074i	$0.598946\pi$
$600$	−0.454763	−	3.16294i	−0.0185656	−	0.129127i
$601$	4.09246	−	8.96123i	0.166935	−	0.365536i	−0.807614	−	0.589711i	$-0.799242\pi$
$601$	4.09246	−	8.96123i	0.166935	−	0.365536i	0.974549	+	0.224175i	$0.0719688\pi$
$602$	−5.53468	+	1.62513i	−0.225577	+	0.0662353i
$603$	1.28786	−	1.48627i	0.0524456	−	0.0605254i
$604$	−20.2850	−	5.95622i	−0.825385	−	0.242355i
$605$	14.9911	−	9.63419i	0.609474	−	0.391685i
$606$	−14.7908	−	32.3874i	−0.600836	−	1.31565i
$607$	−14.1047	−	16.2777i	−0.572492	−	0.660691i	0.393482	−	0.919333i	$-0.371271\pi$
$607$	−14.1047	−	16.2777i	−0.572492	−	0.660691i	−0.965973	+	0.258642i	$0.916725\pi$
$608$	4.61136	+	2.96354i	0.187015	+	0.120188i
$609$	0.447020	−	3.10909i	0.0181142	−	0.125987i
$610$	−1.41830	+	9.86448i	−0.0574252	+	0.399401i
$611$	−19.4592	−	12.5057i	−0.787236	−	0.505926i
$612$	0.548046	+	0.632479i	0.0221535	+	0.0255664i
$613$	8.00468	+	17.5278i	0.323306	+	0.707941i	0.999588	−	0.0287016i	$-0.00913726\pi$
$613$	8.00468	+	17.5278i	0.323306	+	0.707941i	−0.676282	+	0.736643i	$0.736410\pi$
$614$	20.5452	−	13.2036i	0.829137	−	0.532854i
$615$	27.3843	+	8.04077i	1.10424	+	0.324235i
$616$	−0.675456	+	0.779518i	−0.0272149	+	0.0314077i
$617$	−15.3586	+	4.50969i	−0.618314	+	0.181553i	−0.575864	−	0.817545i	$-0.695334\pi$
$617$	−15.3586	+	4.50969i	−0.618314	+	0.181553i	−0.0424494	+	0.999099i	$0.513516\pi$
$618$	−7.80488	+	17.0903i	−0.313958	+	0.687473i
$619$	1.52128	+	10.5808i	0.0611455	+	0.425276i	0.997284	+	0.0736461i	$0.0234635\pi$
$619$	1.52128	+	10.5808i	0.0611455	+	0.425276i	−0.936139	+	0.351630i	$0.885627\pi$
$620$	−14.5969			−0.586224
$621$	−23.7474	+	3.27909i	−0.952951	+	0.131586i
$622$	−7.34449			−0.294487
$623$	−0.628807	−	4.37345i	−0.0251926	−	0.175218i
$624$	−4.47224	+	9.79284i	−0.179033	+	0.392027i
$625$	12.3788	−	3.63474i	0.495152	−	0.145390i
$626$	5.73009	−	6.61288i	0.229021	−	0.264304i
$627$	−9.71957	−	2.85392i	−0.388162	−	0.113975i
$628$	−16.8347	+	10.8190i	−0.671779	+	0.431726i
$629$	−11.7793	−	25.7930i	−0.469671	−	1.02844i
$630$	−0.246674	−	0.284677i	−0.00982773	−	0.0113418i
$631$	−40.1808	−	25.8227i	−1.59957	−	1.02798i	−0.967432	−	0.253131i	$-0.918540\pi$
$631$	−40.1808	−	25.8227i	−1.59957	−	1.02798i	−0.632142	−	0.774853i	$-0.717824\pi$
$632$	1.68090	−	11.6909i	0.0668625	−	0.465039i
$633$	1.39015	−	9.66868i	0.0552534	−	0.384296i
$634$	15.9320	+	10.2389i	0.632740	+	0.406637i
$635$	5.07927	+	5.86178i	0.201564	+	0.232618i
$636$	−6.13954	−	13.4437i	−0.243449	−	0.533078i
$637$	−5.05493	+	3.24861i	−0.200284	+	0.128714i
$638$	1.73505	+	0.509457i	0.0686913	+	0.0201696i
$639$	−1.45307	+	1.67693i	−0.0574825	+	0.0663383i
$640$	−1.72081	+	0.505274i	−0.0680208	+	0.0199727i
$641$	−12.7151	+	27.8422i	−0.502217	+	1.09970i	0.473525	+	0.880780i	$0.342981\pi$
$641$	−12.7151	+	27.8422i	−0.502217	+	1.09970i	−0.975742	+	0.218922i	$0.929746\pi$
$642$	−2.07011	−	14.3979i	−0.0817008	−	0.568241i
$643$	36.0311			1.42093			0.710465	−	0.703733i	$-0.248485\pi$
$643$	36.0311			1.42093			0.710465	+	0.703733i	$0.248485\pi$
$644$	3.64193	−	3.12031i	0.143512	−	0.122957i
$645$	18.5351			0.729819
$646$	3.10839	+	21.6193i	0.122298	+	0.850602i
$647$	−11.6295	+	25.4651i	−0.457203	+	1.00113i	0.530913	+	0.847426i	$0.321849\pi$
$647$	−11.6295	+	25.4651i	−0.457203	+	1.00113i	−0.988116	+	0.153709i	$0.950878\pi$
$648$	−9.19768	+	2.70068i	−0.361319	+	0.106093i
$649$	−0.0632057	+	0.0729432i	−0.00248104	+	0.00286327i
$650$	10.2828	+	3.01929i	0.403323	+	0.118426i
$651$	12.2674	−	7.88376i	0.480796	−	0.308989i
$652$	6.92011	+	15.1529i	0.271013	+	0.593435i
$653$	30.9824	+	35.7556i	1.21243	+	1.39922i	0.892050	+	0.451937i	$0.149267\pi$
$653$	30.9824	+	35.7556i	1.21243	+	1.39922i	0.320385	+	0.947287i	$0.396188\pi$
$654$	−11.4111	−	7.33345i	−0.446208	−	0.286761i
$655$	1.57352	−	10.9441i	0.0614826	−	0.427621i
$656$	−1.26406	+	8.79170i	−0.0493531	+	0.343258i
$657$	1.18797	+	0.763463i	0.0463472	+	0.0297855i
$658$	2.52092	+	2.90930i	0.0982757	+	0.113416i
$659$	15.9697	+	34.9687i	0.622090	+	1.36219i	0.913989	+	0.405738i	$0.132986\pi$
$659$	15.9697	+	34.9687i	0.622090	+	1.36219i	−0.291899	+	0.956449i	$0.594287\pi$
$660$	2.78817	−	1.79185i	0.108529	−	0.0697477i
$661$	18.1768	+	5.33720i	0.706997	+	0.207593i	0.615414	−	0.788204i	$-0.288989\pi$
$661$	18.1768	+	5.33720i	0.706997	+	0.207593i	0.0915834	+	0.995797i	$0.470807\pi$
$662$	−5.53954	+	6.39297i	−0.215300	+	0.248470i
$663$	−41.1593	+	12.0855i	−1.59850	+	0.469360i
$664$	−0.523101	+	1.14543i	−0.0203003	+	0.0444514i
$665$	−1.39908	−	9.73081i	−0.0542540	−	0.377345i
$666$	−1.49464			−0.0579163
$667$	−7.62845	−	3.53542i	−0.295375	−	0.136892i
$668$	−8.95824			−0.346605
$669$	−1.50347	−	10.4568i	−0.0581274	−	0.404285i
$670$	−6.97599	+	15.2753i	−0.269506	+	0.590136i
$671$	5.49943	−	1.61478i	0.212303	−	0.0623378i
$672$	1.17329	−	1.35404i	0.0452605	−	0.0522334i
$673$	−23.9591	−	7.03502i	−0.923555	−	0.271180i	−0.214819	−	0.976654i	$-0.568916\pi$
$673$	−23.9591	−	7.03502i	−0.923555	−	0.271180i	−0.708736	+	0.705474i	$0.750734\pi$
$674$	−14.8473	+	9.54176i	−0.571895	+	0.367535i
$675$	3.70353	+	8.10960i	0.142549	+	0.312139i
$676$	−15.1310	−	17.4622i	−0.581963	−	0.671622i
$677$	−25.5011	−	16.3886i	−0.980087	−	0.629864i	−0.0506005	−	0.998719i	$-0.516114\pi$
$677$	−25.5011	−	16.3886i	−0.980087	−	0.629864i	−0.929487	+	0.368855i	$0.879750\pi$
$678$	−0.633915	+	4.40898i	−0.0243454	+	0.169326i
$679$	−2.09838	+	14.5946i	−0.0805285	+	0.560088i
$680$	−6.01174	−	3.86351i	−0.230540	−	0.148159i
$681$	20.0614	+	23.1521i	0.768755	+	0.887190i
$682$	3.48739	+	7.63631i	0.133539	+	0.292410i
$683$	−7.43933	+	4.78096i	−0.284658	+	0.182939i	−0.675176	−	0.737657i	$-0.735932\pi$
$683$	−7.43933	+	4.78096i	−0.284658	+	0.182939i	0.390518	+	0.920595i	$0.372296\pi$
$684$	1.10466	+	0.324358i	0.0422377	+	0.0124021i
$685$	−11.0750	+	12.7812i	−0.423154	+	0.488345i
$686$	0.959493	−	0.281733i	0.0366336	−	0.0107566i
$687$	−15.5761	+	34.1068i	−0.594264	+	1.30126i
$688$	0.820920	+	5.70963i	0.0312973	+	0.217677i
$689$	49.5664			1.88833
$690$	−14.0532	+	6.32324i	−0.534994	+	0.240722i
$691$	−16.1488			−0.614331			−0.307165	−	0.951656i	$-0.599380\pi$
$691$	−16.1488			−0.614331			−0.307165	+	0.951656i	$0.599380\pi$
$692$	2.57575	+	17.9147i	0.0979154	+	0.681017i
$693$	−0.0899943	+	0.197060i	−0.00341860	+	0.00748569i
$694$	4.26436	−	1.25213i	0.161873	−	0.0475302i
$695$	16.5876	−	19.1431i	0.629203	−	0.726139i
$696$	−3.01383	−	0.884940i	−0.114239	−	0.0335436i
$697$	−29.7733	+	19.1341i	−1.12774	+	0.724756i
$698$	−2.17853	−	4.77032i	−0.0824586	−	0.180559i
$699$	−19.5101	−	22.5158i	−0.737939	−	0.851627i
$700$	−1.50040	−	0.964248i	−0.0567098	−	0.0364451i
$701$	−1.18506	+	8.24226i	−0.0447590	+	0.311306i	0.955127	+	0.296197i	$0.0957185\pi$
$701$	−1.18506	+	8.24226i	−0.0447590	+	0.311306i	−0.999886	+	0.0151087i	$0.995191\pi$
$702$	4.27457	−	29.7303i	0.161333	−	1.12210i
$703$	−32.8157	−	21.0894i	−1.23767	−	0.795402i
$704$	0.675456	+	0.779518i	0.0254572	+	0.0293792i
$705$	−5.13851	−	11.2518i	−0.193527	−	0.423766i
$706$	−3.78482	+	2.43235i	−0.142443	+	0.0915428i
$707$	−19.0676	−	5.59877i	−0.717113	−	0.210563i
$708$	0.109790	−	0.126704i	0.00412616	−	0.00476184i
$709$	29.7694	−	8.74110i	1.11802	−	0.328279i	0.330028	−	0.943971i	$-0.392942\pi$
$709$	29.7694	−	8.74110i	1.11802	−	0.328279i	0.787987	+	0.615692i	$0.211124\pi$
$710$	7.87090	−	17.2349i	0.295389	−	0.646813i
$711$	−0.353042	−	2.45546i	−0.0132401	−	0.0920869i
$712$	−4.41842			−0.165587
$713$	−10.7876	−	37.5129i	−0.403997	−	1.40487i
$714$	7.13901			0.267171
$715$	1.58189	+	11.0023i	0.0591594	+	0.411462i
$716$	2.77561	−	6.07774i	0.103729	−	0.227136i
$717$	−34.4221	+	10.1072i	−1.28552	+	0.377462i
$718$	18.5767	−	21.4387i	0.693278	−	0.800086i
$719$	42.0410	+	12.3444i	1.56787	+	0.460367i	0.946379	−	0.323058i	$-0.104711\pi$
$719$	42.0410	+	12.3444i	1.56787	+	0.460367i	0.621486	+	0.783425i	$0.286529\pi$
$720$	−0.316885	+	0.203650i	−0.0118096	+	0.00758957i
$721$	4.35624	+	9.53883i	0.162235	+	0.355245i
$722$	7.23440	+	8.34895i	0.269237	+	0.310716i
$723$	−16.7628	−	10.7728i	−0.623415	−	0.400644i
$724$	−0.515926	+	3.58835i	−0.0191743	+	0.133360i
$725$	−0.444992	+	3.09499i	−0.0165266	+	0.114945i
$726$	14.9761	+	9.62454i	0.555814	+	0.357200i
$727$	9.44938	+	10.9052i	0.350458	+	0.404450i	0.903420	−	0.428756i	$-0.141048\pi$
$727$	9.44938	+	10.9052i	0.350458	+	0.404450i	−0.552962	+	0.833206i	$0.686503\pi$
$728$	2.49615	+	5.46580i	0.0925134	+	0.202576i
$729$	20.9088	−	13.4372i	0.774399	−	0.497676i
$730$	−11.5698	−	3.39720i	−0.428218	−	0.125736i
$731$	−15.0516	+	17.3705i	−0.556704	+	0.642471i
$732$	−9.55265	+	2.80491i	−0.353076	+	0.103672i
$733$	−2.34385	+	5.13232i	−0.0865722	+	0.189567i	−0.947966	−	0.318370i	$-0.896864\pi$
$733$	−2.34385	+	5.13232i	−0.0865722	+	0.189567i	0.861394	+	0.507937i	$0.169592\pi$
$734$	−1.84831	−	12.8553i	−0.0682225	−	0.474498i
$735$	−3.21325			−0.118523
$736$	−2.57025	−	4.04893i	−0.0947406	−	0.149245i
$737$	9.65789			0.355753
$738$	0.265492	+	1.84654i	0.00977289	+	0.0679719i
$739$	21.0043	−	45.9930i	0.772656	−	1.69188i	0.0519402	−	0.998650i	$-0.483459\pi$
$739$	21.0043	−	45.9930i	0.772656	−	1.69188i	0.720716	−	0.693231i	$-0.243813\pi$
$740$	12.2457	−	3.59567i	0.450162	−	0.132180i
$741$	−38.6451	+	44.5988i	−1.41966	+	1.63838i
$742$	−7.91482	−	2.32400i	−0.290562	−	0.0853167i
$743$	19.8614	−	12.7642i	0.728645	−	0.468272i	−0.122989	−	0.992408i	$-0.539248\pi$
$743$	19.8614	−	12.7642i	0.728645	−	0.468272i	0.851634	+	0.524136i	$0.175612\pi$
$744$	−6.05768	−	13.2645i	−0.222086	−	0.486299i
$745$	−2.51696	−	2.90472i	−0.0922142	−	0.106421i
$746$	−29.0339	−	18.6589i	−1.06301	−	0.683153i
$747$	−0.0376390	+	0.261785i	−0.00137714	+	0.00957822i
$748$	−0.584900	+	4.06807i	−0.0213861	+	0.148743i
$749$	−6.82992	−	4.38932i	−0.249560	−	0.160382i
$750$	14.2741	+	16.4732i	0.521217	+	0.601516i
$751$	20.9656	+	45.9082i	0.765044	+	1.67521i	0.737270	+	0.675598i	$0.236115\pi$
$751$	20.9656	+	45.9082i	0.765044	+	1.67521i	0.0277737	+	0.999614i	$0.491158\pi$
$752$	3.23845	−	2.08123i	0.118094	−	0.0758945i
$753$	23.4299	+	6.87963i	0.853831	+	0.250707i
$754$	6.89858	−	7.96138i	0.251231	−	0.289936i
$755$	36.3802	−	10.6822i	1.32401	−	0.388765i
$756$	−2.07652	+	4.54694i	−0.0755223	+	0.165371i
$757$	−5.97701	−	41.5710i	−0.217238	−	1.51092i	−0.748168	−	0.663509i	$-0.769066\pi$
$757$	−5.97701	−	41.5710i	−0.217238	−	1.51092i	0.530930	−	0.847416i	$-0.321843\pi$
$758$	−28.7704			−1.04499
$759$	6.66547	+	5.84116i	0.241941	+	0.212021i
$760$	−9.83088			−0.356603
$761$	−6.33824	−	44.0834i	−0.229761	−	1.59802i	−0.699112	−	0.715012i	$-0.746421\pi$
$761$	−6.33824	−	44.0834i	−0.229761	−	1.59802i	0.469351	−	0.883012i	$-0.344488\pi$
$762$	−3.21884	+	7.04827i	−0.116606	+	0.255332i
$763$	−7.26418	+	2.13296i	−0.262981	+	0.0772182i
$764$	1.93261	−	2.23035i	0.0699194	−	0.0806913i
$765$	−1.44012	−	0.422859i	−0.0520678	−	0.0152885i
$766$	15.4437	−	9.92505i	0.558003	−	0.358607i
$767$	0.233577	+	0.511461i	0.00843396	+	0.0184678i
$768$	−1.17329	−	1.35404i	−0.0423373	−	0.0488598i
$769$	−16.2571	−	10.4478i	−0.586246	−	0.376758i	0.213637	−	0.976913i	$-0.431469\pi$
$769$	−16.2571	−	10.4478i	−0.586246	−	0.376758i	−0.799883	+	0.600156i	$0.795105\pi$
$770$	0.263262	−	1.83103i	0.00948731	−	0.0659857i
$771$	2.66251	−	18.5181i	0.0958879	−	0.666915i
$772$	13.4284	+	8.62990i	0.483298	+	0.310597i
$773$	−22.4201	−	25.8741i	−0.806393	−	0.930627i	0.192320	−	0.981332i	$-0.438399\pi$
$773$	−22.4201	−	25.8741i	−0.806393	−	0.930627i	−0.998714	+	0.0507048i	$0.983853\pi$
$774$	0.503289	+	1.10205i	0.0180904	+	0.0396124i
$775$	−12.2117	+	7.84799i	−0.438658	+	0.281908i
$776$	14.1474	+	4.15405i	0.507862	+	0.149122i
$777$	−8.34943	+	9.63575i	−0.299534	+	0.345681i
$778$	−15.9590	+	4.68598i	−0.572158	+	0.168001i
$779$	−20.2256	+	44.2878i	−0.724656	+	1.58678i
$780$	−2.74779	−	19.1113i	−0.0983865	−	0.684293i
$781$	−10.8968			−0.389919
$782$	5.48607	−	18.3050i	0.196181	−	0.654585i
$783$	8.76347			0.313181
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	14.9091	−	32.6464i	0.532129	−	1.16520i
$786$	10.5981	−	3.11189i	0.378023	−	0.110998i
$787$	1.60764	−	1.85532i	0.0573063	−	0.0661350i	−0.726373	−	0.687301i	$-0.758795\pi$
$787$	1.60764	−	1.85532i	0.0573063	−	0.0661350i	0.783679	+	0.621166i	$0.213341\pi$
$788$	7.38790	+	2.16928i	0.263183	+	0.0772775i
$789$	−38.5599	+	24.7809i	−1.37277	+	0.882225i
$790$	8.79960	+	19.2684i	0.313076	+	0.685540i
$791$	1.62808	+	1.87890i	0.0578878	+	0.0668061i
$792$	0.182247	+	0.117123i	0.00647586	+	0.00416178i
$793$	4.75188	−	33.0501i	0.168744	−	1.17364i
$794$	−4.26821	+	29.6860i	−0.151473	+	1.05352i
$795$	22.2982	+	14.3302i	0.790837	+	0.508240i
$796$	4.60795	+	5.31786i	0.163324	+	0.188486i
$797$	7.13288	+	15.6188i	0.252659	+	0.553247i	0.992880	−	0.119117i	$-0.0380063\pi$
$797$	7.13288	+	15.6188i	0.252659	+	0.553247i	−0.740221	+	0.672364i	$0.765279\pi$
$798$	8.26197	−	5.30965i	0.292471	−	0.187960i
$799$	14.7175	+	4.32146i	0.520669	+	0.152882i
$800$	−1.16796	+	1.34790i	−0.0412937	+	0.0476555i
$801$	−0.890417	+	0.261450i	−0.0314613	+	0.00923788i
$802$	4.51253	−	9.88105i	0.159343	−	0.348912i
$803$	0.986945	+	6.86435i	0.0348285	+	0.242238i
$804$	−16.7760			−0.591644
$805$	−2.46926	+	8.23903i	−0.0870301	+	0.290388i
$806$	48.9055			1.72262
$807$	6.63252	+	46.1302i	0.233476	+	1.62386i
$808$	−8.25539	+	18.0768i	−0.290424	+	0.635939i
$809$	−47.1961	+	13.8580i	−1.65933	+	0.487222i	−0.971180	−	0.238349i	$-0.923394\pi$
$809$	−47.1961	+	13.8580i	−1.65933	+	0.487222i	−0.688147	+	0.725571i	$0.741576\pi$
$810$	11.2584	−	12.9928i	0.395579	−	0.456522i
$811$	8.37662	+	2.45960i	0.294143	+	0.0863681i	0.425475	−	0.904970i	$-0.360107\pi$
$811$	8.37662	+	2.45960i	0.294143	+	0.0863681i	−0.131332	+	0.991338i	$0.541925\pi$
$812$	−1.47485	+	0.947832i	−0.0517573	+	0.0332624i
$813$	−4.73001	−	10.3573i	−0.165889	−	0.363245i
$814$	−4.80673	−	5.54727i	−0.168476	−	0.194432i
$815$	−25.1332	−	16.1521i	−0.880378	−	0.565784i
$816$	1.01599	−	7.06635i	0.0355667	−	0.247372i
$817$	−4.49990	+	31.2975i	−0.157432	+	1.09496i
$818$	−7.13384	−	4.58464i	−0.249429	−	0.160298i
$819$	0.826460	+	0.953786i	0.0288789	+	0.0333280i
$820$	−6.61741	−	14.4901i	−0.231090	−	0.506017i
$821$	8.79857	−	5.65450i	0.307072	−	0.197343i	−0.378024	−	0.925796i	$-0.623396\pi$
$821$	8.79857	−	5.65450i	0.307072	−	0.197343i	0.685096	+	0.728452i	$0.259760\pi$
$822$	−16.2107	−	4.75988i	−0.565412	−	0.166020i
$823$	−26.8216	+	30.9538i	−0.934943	+	1.07898i	0.0617800	+	0.998090i	$0.480322\pi$
$823$	−26.8216	+	30.9538i	−0.934943	+	1.07898i	−0.996723	+	0.0808918i	$0.974223\pi$
$824$	10.0617	−	2.95438i	0.350516	−	0.102921i
$825$	1.36919	−	2.99812i	0.0476692	−	0.104381i
$826$	−0.0133171	−	0.0926223i	−0.000463361	−	0.00322274i
$827$	−30.5452			−1.06216			−0.531080	−	0.847322i	$-0.678214\pi$
$827$	−30.5452			−1.06216			−0.531080	+	0.847322i	$0.678214\pi$
$828$	−0.757553	−	0.663867i	−0.0263268	−	0.0230710i
$829$	−34.0792			−1.18362			−0.591810	−	0.806077i	$-0.701586\pi$
$829$	−34.0792			−1.18362			−0.591810	+	0.806077i	$0.701586\pi$
$830$	−0.321398	−	2.23538i	−0.0111559	−	0.0775910i
$831$	−10.9432	+	23.9622i	−0.379615	+	0.831241i
$832$	5.76541	−	1.69288i	0.199880	−	0.0586899i
$833$	2.60935	−	3.01135i	0.0904086	−	0.104337i
$834$	24.2795	+	7.12912i	0.840732	+	0.246861i
$835$	13.5157	−	8.68603i	0.467731	−	0.300592i
$836$	2.34873	+	5.14300i	0.0812324	+	0.177874i
$837$	26.6424	+	30.7469i	0.920895	+	1.06277i
$838$	20.4747	+	13.1583i	0.707285	+	0.454545i
$839$	−6.38333	+	44.3970i	−0.220377	+	1.53276i	0.516239	+	0.856444i	$0.327331\pi$
$839$	−6.38333	+	44.3970i	−0.220377	+	1.53276i	−0.736616	+	0.676311i	$0.763578\pi$
$840$	−0.457293	+	3.18054i	−0.0157781	+	0.109739i
$841$	−21.8107	−	14.0169i	−0.752093	−	0.483341i
$842$	−7.18913	−	8.29669i	−0.247754	−	0.285923i
$843$	−3.87703	−	8.48952i	−0.133532	−	0.292395i
$844$	−4.58651	+	2.94757i	−0.157874	+	0.101460i
$845$	39.7605	+	11.6747i	1.36780	+	0.401623i
$846$	0.529473	−	0.611045i	0.0182037	−	0.0210081i
$847$	9.53363	−	2.79933i	0.327579	−	0.0961860i
$848$	−3.42674	+	7.50352i	−0.117675	+	0.257672i
$849$	−4.55784	−	31.7005i	−0.156425	−	1.08796i
$850$	−7.10662			−0.243755
$851$	18.2906	+	28.8133i	0.626994	+	0.987708i
$852$	18.9281			0.648466
$853$	−5.44089	−	37.8423i	−0.186293	−	1.29569i	−0.841505	−	0.540249i	$-0.818330\pi$
$853$	−5.44089	−	37.8423i	−0.186293	−	1.29569i	0.655212	−	0.755445i	$-0.272579\pi$
$854$	−2.30839	+	5.05467i	−0.0789916	+	0.172967i
$855$	−1.98116	+	0.581720i	−0.0677541	+	0.0198944i
$856$	−5.31665	+	6.13574i	−0.181719	+	0.209715i
$857$	25.3878	+	7.45453i	0.867230	+	0.254642i	0.684937	−	0.728602i	$-0.259830\pi$
$857$	25.3878	+	7.45453i	0.867230	+	0.254642i	0.182293	+	0.983244i	$0.441648\pi$
$858$	−9.34153	+	6.00344i	−0.318915	+	0.204954i
$859$	−10.1006	−	22.1172i	−0.344628	−	0.754629i	0.655372	−	0.755306i	$-0.272512\pi$
$859$	−10.1006	−	22.1172i	−0.344628	−	0.754629i	−1.00000		0.000676892i	$0.999785\pi$
$860$	−6.77469	−	7.81841i	−0.231015	−	0.266606i
$861$	13.3874	+	8.60359i	0.456243	+	0.293209i
$862$	2.18654	−	15.2077i	0.0744738	−	0.517977i
$863$	3.69093	−	25.6710i	0.125641	−	0.873849i	−0.825348	−	0.564624i	$-0.809021\pi$
$863$	3.69093	−	25.6710i	0.125641	−	0.873849i	0.950989	−	0.309225i	$-0.100070\pi$
$864$	4.20514	+	2.70248i	0.143062	+	0.0919403i
$865$	−21.2565	−	24.5314i	−0.722744	−	0.834091i
$866$	1.32765	+	2.90714i	0.0451153	+	0.0987887i
$867$	−1.69272	+	1.08784i	−0.0574877	+	0.0369451i
$868$	−7.80929	−	2.29301i	−0.265065	−	0.0778300i
$869$	7.97789	−	9.20698i	0.270631	−	0.312325i
$870$	5.40516	−	1.58710i	0.183252	−	0.0538077i
$871$	23.3725	−	51.1785i	0.791945	−	1.73412i
$872$	1.07744	+	7.49379i	0.0364869	+	0.253772i
$873$	3.09684			0.104812
$874$	−7.26534	−	25.2646i	−0.245754	−	0.854589i
$875$	12.1659			0.411284
$876$	−1.71435	−	11.9236i	−0.0579225	−	0.402860i
$877$	21.0458	−	46.0839i	0.710667	−	1.55614i	−0.115872	−	0.993264i	$-0.536966\pi$
$877$	21.0458	−	46.0839i	0.710667	−	1.55614i	0.826539	−	0.562880i	$-0.190307\pi$
$878$	15.9798	−	4.69209i	0.539291	−	0.158350i
$879$	8.30982	−	9.59004i	0.280283	−	0.323464i
$880$	−1.77492	−	0.521165i	−0.0598327	−	0.0175685i
$881$	2.49419	−	1.60292i	0.0840315	−	0.0540038i	−0.497950	−	0.867206i	$-0.665914\pi$
$881$	2.49419	−	1.60292i	0.0840315	−	0.0540038i	0.581982	+	0.813202i	$0.302277\pi$
$882$	−0.0872503	−	0.191051i	−0.00293787	−	0.00643304i
$883$	−10.1646	−	11.7306i	−0.342066	−	0.394766i	0.558486	−	0.829514i	$-0.311383\pi$
$883$	−10.1646	−	11.7306i	−0.342066	−	0.394766i	−0.900552	+	0.434749i	$0.856837\pi$
$884$	20.1418	+	12.9444i	0.677442	+	0.435366i
$885$	−0.0427911	+	0.297619i	−0.00143841	+	0.0100043i
$886$	3.43017	−	23.8573i	0.115239	−	0.801503i
$887$	−19.7974	−	12.7230i	−0.664732	−	0.427197i	0.164291	−	0.986412i	$-0.447466\pi$
$887$	−19.7974	−	12.7230i	−0.664732	−	0.427197i	−0.829023	+	0.559215i	$0.811103\pi$
$888$	8.34943	+	9.63575i	0.280188	+	0.323355i
$889$	1.79657	+	3.93394i	0.0602550	+	0.131940i
$890$	6.66628	−	4.28416i	0.223454	−	0.143605i
$891$	−9.48695	−	2.78562i	−0.317825	−	0.0933218i
$892$	−3.86134	+	4.45622i	−0.129287	+	0.149205i
$893$	20.2467	−	5.94497i	0.677530	−	0.198941i
$894$	1.59505	−	3.49267i	0.0533464	−	0.116812i
$895$	1.70536	+	11.8610i	0.0570039	+	0.396471i
$896$	−1.00000			−0.0334077
$897$	47.0839	−	21.1855i	1.57208	−	0.707362i
$898$	−21.9904			−0.733829
$899$	2.03068	+	14.1237i	0.0677271	+	0.471052i
$900$	−0.155613	+	0.340746i	−0.00518711	+	0.0113582i
$901$	−31.5373	+	9.26018i	−1.05066	+	0.308501i
$902$	−5.99947	+	6.92376i	−0.199761	+	0.230536i
$903$	9.91624	+	2.91167i	0.329992	+	0.0968944i
$904$	2.09148	−	1.34411i	0.0695615	−	0.0447045i
$905$	−2.70091	−	5.91416i	−0.0897812	−	0.196593i
$906$	24.8049	+	28.6263i	0.824087	+	0.951047i
$907$	49.9055	+	32.0723i	1.65708	+	1.06494i	0.922171	+	0.386783i	$0.126414\pi$
$907$	49.9055	+	32.0723i	1.65708	+	1.06494i	0.734914	+	0.678161i	$0.237223\pi$
$908$	2.43337	−	16.9245i	0.0807542	−	0.561658i
$909$	−0.594005	+	4.13140i	−0.0197019	+	0.137030i
$910$	−9.06578	−	5.82622i	−0.300528	−	0.193137i
$911$	−35.7910	−	41.3050i	−1.18581	−	1.36850i	−0.913782	−	0.406205i	$-0.866852\pi$
$911$	−35.7910	−	41.3050i	−1.18581	−	1.36850i	−0.272026	−	0.962290i	$-0.587694\pi$
$912$	−4.07980	−	8.93352i	−0.135096	−	0.295818i
$913$	−1.09264	+	0.702200i	−0.0361612	+	0.0232394i
$914$	−16.2712	−	4.77766i	−0.538204	−	0.158031i
$915$	11.6929	−	13.4943i	0.386554	−	0.446107i
$916$	20.0800	−	5.89601i	0.663461	−	0.194810i
$917$	2.56103	−	5.60788i	0.0845727	−	0.185188i
$918$	2.83457	+	19.7149i	0.0935548	+	0.650688i
$919$	28.7820			0.949432			0.474716	−	0.880139i	$-0.342551\pi$
$919$	28.7820			0.949432			0.474716	+	0.880139i	$0.342551\pi$
$920$	7.80375	+	3.61667i	0.257282	+	0.119238i
$921$	−43.7561			−1.44181
$922$	2.51883	+	17.5188i	0.0829531	+	0.576952i
$923$	−26.3707	+	57.7439i	−0.868004	+	1.90066i
$924$	1.77315	−	0.520643i	0.0583322	−	0.0171279i
$925$	8.31155	−	9.59204i	0.273282	−	0.315384i
$926$	−12.2077	−	3.58450i	−0.401169	−	0.117794i
$927$	1.85285	−	1.19076i	0.0608557	−	0.0391096i
$928$	0.728290	+	1.59473i	0.0239073	+	0.0523497i
$929$	22.9997	+	26.5430i	0.754594	+	0.870848i	0.995005	−	0.0998231i	$-0.0318277\pi$
$929$	22.9997	+	26.5430i	0.754594	+	0.870848i	−0.240411	+	0.970671i	$0.577282\pi$
$930$	22.0009	+	14.1391i	0.721439	+	0.463641i
$931$	0.780104	−	5.42574i	0.0255669	−	0.177822i
$932$	−2.36649	+	16.4593i	−0.0775171	+	0.539143i
$933$	11.0699	+	7.11419i	0.362412	+	0.232908i
$934$	3.70435	+	4.27505i	0.121210	+	0.139884i
$935$	−3.06199	−	6.70482i	−0.100138	−	0.219271i
$936$	1.06170	−	0.682310i	0.0347026	−	0.0223020i
$937$	−1.43622	−	0.421712i	−0.0469193	−	0.0137767i	0.258189	−	0.966095i	$-0.416874\pi$
$937$	−1.43622	−	0.421712i	−0.0469193	−	0.0137767i	−0.305108	+	0.952318i	$0.598693\pi$
$938$	−6.13173	+	7.07639i	−0.200208	+	0.231052i
$939$	−15.0421	+	4.41676i	−0.490881	+	0.144136i
$940$	−2.86802	+	6.28009i	−0.0935445	+	0.204834i
$941$	−3.86347	−	26.8710i	−0.125945	−	0.875969i	−0.950619	−	0.310360i	$-0.899550\pi$
$941$	−3.86347	−	26.8710i	−0.125945	−	0.875969i	0.824674	−	0.565609i	$-0.191359\pi$
$942$	35.8537			1.16818
$943$	32.3480	−	27.7149i	1.05340	−	0.902522i
$944$	−0.0935748			−0.00304560
$945$	−1.27583	−	8.87362i	−0.0415029	−	0.288659i
$946$	−2.47162	+	5.41209i	−0.0803592	+	0.175962i
$947$	−39.0342	+	11.4615i	−1.26844	+	0.372448i	−0.845630	−	0.533769i	$-0.820775\pi$
$947$	−39.0342	+	11.4615i	−1.26844	+	0.372448i	−0.422812	+	0.906217i	$0.638957\pi$
$948$	−13.8578	+	15.9928i	−0.450081	+	0.519421i
$949$	38.7636	+	11.3820i	1.25832	+	0.369476i
$950$	−8.22449	+	5.28556i	−0.266838	+	0.171486i
$951$	−14.0955	−	30.8648i	−0.457077	−	1.00086i
$952$	−2.60935	−	3.01135i	−0.0845695	−	0.0975984i
$953$	22.8031	+	14.6546i	0.738664	+	0.474710i	0.855084	−	0.518490i	$-0.173506\pi$
$953$	22.8031	+	14.6546i	0.738664	+	0.474710i	−0.116420	+	0.993200i	$0.537142\pi$
$954$	−0.246566	+	1.71491i	−0.00798288	+	0.0555222i
$955$	−0.753243	+	5.23892i	−0.0243744	+	0.169528i
$956$	16.8449	+	10.8255i	0.544802	+	0.350123i
$957$	−2.12165	−	2.44852i	−0.0685833	−	0.0791493i
$958$	10.2889	+	22.5295i	0.332418	+	0.727894i
$959$	−7.93289	+	5.09816i	−0.256166	+	0.164628i
$960$	3.08309	+	0.905277i	0.0995063	+	0.0292177i
$961$	−23.0792	+	26.6348i	−0.744491	+	0.859189i
$962$	−41.0283	+	12.0470i	−1.32280	+	0.388410i
$963$	−0.708363	+	1.55110i	−0.0228267	+	0.0499834i
$964$	1.58276	+	11.0083i	0.0509772	+	0.354555i
$965$	−28.6277			−0.921559
$966$	−8.51172	+	1.17532i	−0.273860	+	0.0378152i
$967$	−10.7593			−0.345996			−0.172998	−	0.984922i	$-0.555345\pi$
$967$	−10.7593			−0.345996			−0.172998	+	0.984922i	$0.555345\pi$
$968$	−1.41406	−	9.83498i	−0.0454495	−	0.316108i
$969$	16.2563	−	35.5964i	0.522229	−	1.14352i
$970$	−25.3727	+	7.45009i	−0.814667	+	0.239208i
$971$	34.3020	−	39.5866i	1.10080	−	1.27040i	0.140913	−	0.990022i	$-0.454996\pi$
$971$	34.3020	−	39.5866i	1.10080	−	1.27040i	0.959891	−	0.280374i	$-0.0904585\pi$
$972$	2.09053	+	0.613836i	0.0670539	+	0.0196888i
$973$	11.8815	−	7.63577i	0.380903	−	0.244792i
$974$	4.31702	+	9.45295i	0.138326	+	0.302892i
$975$	−12.5739	−	14.5111i	−0.402689	−	0.464727i
$976$	4.67471	+	3.00425i	0.149634	+	0.0961637i
$977$	3.71709	−	25.8529i	0.118920	−	0.827108i	−0.839828	−	0.542852i	$-0.817344\pi$
$977$	3.71709	−	25.8529i	0.118920	−	0.827108i	0.958748	−	0.284256i	$-0.0917466\pi$
$978$	4.24752	−	29.5422i	0.135821	−	0.944655i
$979$	−3.83391	−	2.46391i	−0.122532	−	0.0787467i
$980$	1.17446	+	1.35540i	0.0375168	+	0.0432967i
$981$	0.660559	+	1.44642i	0.0210900	+	0.0461807i
$982$	1.06125	−	0.682023i	0.0338658	−	0.0217642i
$983$	−11.8756	−	3.48699i	−0.378773	−	0.111218i	0.0868035	−	0.996225i	$-0.472335\pi$
$983$	−11.8756	−	3.48699i	−0.378773	−	0.111218i	−0.465576	+	0.885008i	$0.654153\pi$
$984$	10.4212	−	12.0268i	0.332217	−	0.383399i
$985$	−13.2498	+	3.89051i	−0.422175	+	0.123962i
$986$	−2.90194	+	6.35436i	−0.0924165	+	0.202364i
$987$	−0.981556	−	6.82687i	−0.0312433	−	0.217302i
$988$	32.9375			1.04788
$989$	15.0860	−	23.1885i	0.479708	−	0.737352i
$990$	−0.388528			−0.0123482
$991$	2.08728	+	14.5173i	0.0663045	+	0.461158i	0.995742	+	0.0921794i	$0.0293833\pi$
$991$	2.08728	+	14.5173i	0.0663045	+	0.461158i	−0.929438	+	0.368979i	$0.879708\pi$
$992$	−3.38105	+	7.40347i	−0.107349	+	0.235061i
$993$	14.5419	−	4.26989i	0.461474	−	0.135501i
$994$	6.91833	−	7.98417i	0.219436	−	0.253243i
$995$	−12.1085	−	3.55538i	−0.383865	−	0.112713i
$996$	1.89795	−	1.21974i	0.0601389	−	0.0386489i
$997$	5.81398	+	12.7308i	0.184131	+	0.403190i	0.979077	−	0.203490i	$-0.0652284\pi$
$997$	5.81398	+	12.7308i	0.184131	+	0.403190i	−0.794946	+	0.606680i	$0.792501\pi$
$998$	22.8657	+	26.3885i	0.723803	+	0.835313i
$999$	−29.9250	−	19.2316i	−0.946784	−	0.608461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.e.141.4	✓	40
23.8	even	11	inner	322.2.i.e.169.4	yes	40
23.10	odd	22		7406.2.a.bs.1.15		20
23.13	even	11		7406.2.a.bt.1.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.141.4	✓	40	1.1	even	1	trivial
322.2.i.e.169.4	yes	40	23.8	even	11	inner
7406.2.a.bs.1.15		20	23.10	odd	22
7406.2.a.bt.1.15		20	23.13	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.744281 - 1.62975i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.17446 - 1.35540i) q^{5} +(1.71908 + 0.504768i) q^{6} +(0.841254 - 0.540641i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.137541 - 0.158731i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.744281 - 1.62975i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(1.17446 - 1.35540i) q^{5} +(1.71908 + 0.504768i) q^{6} +(0.841254 - 0.540641i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.137541 - 0.158731i) q^{9} +(1.50875 + 0.969614i) q^{10} +(0.146791 - 1.02095i) q^{11} +(-0.254979 + 1.77342i) q^{12} +(-5.05493 - 3.24861i) q^{13} +(0.654861 + 0.755750i) q^{14} +(-1.33483 - 2.92288i) q^{15} +(0.841254 - 0.540641i) q^{16} +(3.82318 + 1.12259i) q^{17} +(0.137541 - 0.158731i) q^{18} +(5.25950 - 1.54433i) q^{19} +(-0.745027 + 1.63138i) q^{20} +(-0.254979 - 1.77342i) q^{21} +1.03145 q^{22} +(-4.74313 - 0.709021i) q^{23} -1.79166 q^{24} +(0.253822 + 1.76537i) q^{25} +(2.49615 - 5.46580i) q^{26} +(4.79618 - 1.40829i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(1.68215 + 0.493923i) q^{29} +(2.70316 - 1.73721i) q^{30} +(3.38105 + 7.40347i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.55464 - 0.999106i) q^{33} +(-0.567066 + 3.94403i) q^{34} +(0.255235 - 1.77520i) q^{35} +(0.176690 + 0.113552i) q^{36} +(-4.66017 - 5.37813i) q^{37} +(2.27711 + 4.98618i) q^{38} +(-9.05670 + 5.82038i) q^{39} +(-1.72081 - 0.505274i) q^{40} +(-5.81654 + 6.71265i) q^{41} +(1.71908 - 0.504768i) q^{42} +(-2.39625 + 5.24707i) q^{43} +(0.146791 + 1.02095i) q^{44} -0.376682 q^{45} +(0.0267858 - 4.79576i) q^{46} +3.84955 q^{47} +(-0.254979 - 1.77342i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-1.71128 + 0.502478i) q^{50} +(4.67506 - 5.39530i) q^{51} +(5.76541 + 1.69288i) q^{52} +(-6.93946 + 4.45972i) q^{53} +(2.07652 + 4.54694i) q^{54} +(-1.21140 - 1.39803i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(1.39768 - 9.72106i) q^{57} +(-0.249501 + 1.73532i) q^{58} +(-0.0787201 - 0.0505904i) q^{59} +(2.10423 + 2.42841i) q^{60} +(2.30839 + 5.05467i) q^{61} +(-6.84694 + 4.40026i) q^{62} +(-0.201524 - 0.0591728i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-10.3400 + 3.03609i) q^{65} +(0.767688 - 1.68100i) q^{66} +(1.33255 + 9.26810i) q^{67} -3.98459 q^{68} +(-4.68575 + 7.20240i) q^{69} +1.79345 q^{70} +(-1.50350 - 10.4570i) q^{71} +(-0.0872503 + 0.191051i) q^{72} +(-6.45114 + 1.89422i) q^{73} +(4.66017 - 5.37813i) q^{74} +(3.06603 + 0.900268i) q^{75} +(-4.61136 + 2.96354i) q^{76} +(-0.428480 - 0.938240i) q^{77} +(-7.05004 - 8.13618i) q^{78} +(9.93614 + 6.38557i) q^{79} +(0.255235 - 1.77520i) q^{80} +(1.36423 - 9.48841i) q^{81} +(-7.47211 - 4.80203i) q^{82} +(-0.824618 - 0.951659i) q^{83} +(0.744281 + 1.62975i) q^{84} +(6.01174 - 3.86351i) q^{85} +(-5.53468 - 1.62513i) q^{86} +(2.05696 - 2.37386i) q^{87} +(-0.989669 + 0.290593i) q^{88} +(1.83548 - 4.01914i) q^{89} +(-0.0536074 - 0.372848i) q^{90} -6.00881 q^{91} +(4.75075 - 0.655994i) q^{92} +14.5822 q^{93} +(0.547848 + 3.81037i) q^{94} +(4.08389 - 8.94248i) q^{95} +(1.71908 - 0.504768i) q^{96} +(-9.65569 + 11.1433i) q^{97} +(0.959493 + 0.281733i) q^{98} +(-0.182247 + 0.117123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8	\( 40 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 9 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 2 q^{10} + 2 q^{12} + 4 q^{13} + 4 q^{14} - 11 q^{15} - 4 q^{16} - 21 q^{17} + 4 q^{19} + 2 q^{20} + 2 q^{21} - 11 q^{23} - 2 q^{24} + 5 q^{25} - 15 q^{26} + 95 q^{27} - 4 q^{28} + 22 q^{30} - 12 q^{31} + 4 q^{32} - 8 q^{33} + 10 q^{34} - 9 q^{35} + 41 q^{37} + 7 q^{38} - 38 q^{39} - 13 q^{40} + 25 q^{41} - 2 q^{42} - 59 q^{43} - 6 q^{45} + 11 q^{46} - 60 q^{47} + 2 q^{48} - 4 q^{49} + 61 q^{50} - 87 q^{51} + 4 q^{52} + 47 q^{53} - 29 q^{54} - 30 q^{55} + 4 q^{56} + 20 q^{57} - 96 q^{59} - 11 q^{60} + 84 q^{61} - 65 q^{62} - 4 q^{64} + 52 q^{65} - 3 q^{66} + 11 q^{67} - 10 q^{68} - 42 q^{69} - 2 q^{70} - 13 q^{71} + 11 q^{72} - 48 q^{73} - 41 q^{74} + 23 q^{75} + 26 q^{76} - 83 q^{78} + 80 q^{79} - 9 q^{80} + 2 q^{81} + 30 q^{82} - 20 q^{83} + 2 q^{84} - 71 q^{85} - 40 q^{86} + 99 q^{87} - 30 q^{89} + 116 q^{90} + 26 q^{91} - 22 q^{92} + 20 q^{93} - 17 q^{94} - 4 q^{95} - 2 q^{96} - 56 q^{97} + 4 q^{98} + 138 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 9 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 2 * q^10 + 2 * q^12 + 4 * q^13 + 4 * q^14 - 11 * q^15 - 4 * q^16 - 21 * q^17 + 4 * q^19 + 2 * q^20 + 2 * q^21 - 11 * q^23 - 2 * q^24 + 5 * q^25 - 15 * q^26 + 95 * q^27 - 4 * q^28 + 22 * q^30 - 12 * q^31 + 4 * q^32 - 8 * q^33 + 10 * q^34 - 9 * q^35 + 41 * q^37 + 7 * q^38 - 38 * q^39 - 13 * q^40 + 25 * q^41 - 2 * q^42 - 59 * q^43 - 6 * q^45 + 11 * q^46 - 60 * q^47 + 2 * q^48 - 4 * q^49 + 61 * q^50 - 87 * q^51 + 4 * q^52 + 47 * q^53 - 29 * q^54 - 30 * q^55 + 4 * q^56 + 20 * q^57 - 96 * q^59 - 11 * q^60 + 84 * q^61 - 65 * q^62 - 4 * q^64 + 52 * q^65 - 3 * q^66 + 11 * q^67 - 10 * q^68 - 42 * q^69 - 2 * q^70 - 13 * q^71 + 11 * q^72 - 48 * q^73 - 41 * q^74 + 23 * q^75 + 26 * q^76 - 83 * q^78 + 80 * q^79 - 9 * q^80 + 2 * q^81 + 30 * q^82 - 20 * q^83 + 2 * q^84 - 71 * q^85 - 40 * q^86 + 99 * q^87 - 30 * q^89 + 116 * q^90 + 26 * q^91 - 22 * q^92 + 20 * q^93 - 17 * q^94 - 4 * q^95 - 2 * q^96 - 56 * q^97 + 4 * q^98 + 138 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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