LMFDB - Embedded newform 322.2.i.d.71.4

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			71.4
Character	$\chi$	$=$	322.71
Dual form			322.2.i.d.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(0.341180 + 2.37296i) q^{3} +(0.415415 + 0.909632i) q^{4} +(1.96603 + 0.577277i) q^{5} +(-0.995899 + 2.18071i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-2.63604 + 0.774012i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(0.341180 + 2.37296i) q^{3} +(0.415415 + 0.909632i) q^{4} +(1.96603 + 0.577277i) q^{5} +(-0.995899 + 2.18071i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-2.63604 + 0.774012i) q^{9} +(1.34183 + 1.54855i) q^{10} +(0.712290 - 0.457761i) q^{11} +(-2.01679 + 1.29611i) q^{12} +(-3.16858 - 3.65674i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-0.699086 + 4.86225i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.83679 - 4.02201i) q^{17} +(-2.63604 - 0.774012i) q^{18} +(-1.18888 - 2.60328i) q^{19} +(0.291607 + 2.02817i) q^{20} +(2.01679 + 1.29611i) q^{21} +0.846701 q^{22} +(-4.09369 + 2.49834i) q^{23} -2.39736 q^{24} +(-0.674258 - 0.433319i) q^{25} +(-0.688598 - 4.78931i) q^{26} +(0.251636 + 0.551006i) q^{27} +(0.959493 + 0.281733i) q^{28} +(-1.55805 + 3.41164i) q^{29} +(-3.21684 + 3.71243i) q^{30} +(0.210342 - 1.46296i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(1.32927 + 1.53406i) q^{33} +(3.71967 - 2.39049i) q^{34} +(1.72375 - 1.10779i) q^{35} +(-1.79912 - 2.07629i) q^{36} +(-0.504064 + 0.148007i) q^{37} +(0.407292 - 2.83278i) q^{38} +(7.59622 - 8.76651i) q^{39} +(-0.851196 + 1.86386i) q^{40} +(-4.19540 - 1.23188i) q^{41} +(0.995899 + 2.18071i) q^{42} +(1.11619 + 7.76324i) q^{43} +(0.712290 + 0.457761i) q^{44} -5.62935 q^{45} +(-4.79454 - 0.111477i) q^{46} +6.67750 q^{47} +(-2.01679 - 1.29611i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.332952 - 0.729063i) q^{50} +(10.1707 + 2.98640i) q^{51} +(2.01001 - 4.40131i) q^{52} +(7.74248 - 8.93530i) q^{53} +(-0.0862066 + 0.599580i) q^{54} +(1.66464 - 0.488781i) q^{55} +(0.654861 + 0.755750i) q^{56} +(5.77185 - 3.70934i) q^{57} +(-3.15518 + 2.02771i) q^{58} +(-5.02182 - 5.79548i) q^{59} +(-4.71327 + 1.38394i) q^{60} +(-0.355188 + 2.47039i) q^{61} +(0.967889 - 1.11700i) q^{62} +(-1.14128 + 2.49906i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-4.11856 - 9.01839i) q^{65} +(0.288877 + 2.00919i) q^{66} +(9.35908 + 6.01471i) q^{67} +4.42158 q^{68} +(-7.32514 - 8.86176i) q^{69} +2.04903 q^{70} +(8.70851 + 5.59662i) q^{71} +(-0.390986 - 2.71936i) q^{72} +(-4.45054 - 9.74532i) q^{73} +(-0.504064 - 0.148007i) q^{74} +(0.798205 - 1.74783i) q^{75} +(1.87415 - 2.16288i) q^{76} +(0.120498 - 0.838083i) q^{77} +(11.1299 - 3.26803i) q^{78} +(4.16610 + 4.80794i) q^{79} +(-1.72375 + 1.10779i) q^{80} +(-8.15526 + 5.24107i) q^{81} +(-2.86339 - 3.30453i) q^{82} +(-9.69302 + 2.84613i) q^{83} +(-0.341180 + 2.37296i) q^{84} +(5.93300 - 6.84704i) q^{85} +(-3.25813 + 7.13431i) q^{86} +(-8.62726 - 2.53319i) q^{87} +(0.351732 + 0.770186i) q^{88} +(1.59642 + 11.1034i) q^{89} +(-4.73571 - 3.04345i) q^{90} -4.83856 q^{91} +(-3.97315 - 2.68590i) q^{92} +3.54331 q^{93} +(5.61747 + 3.61013i) q^{94} +(-0.834551 - 5.80443i) q^{95} +(-0.995899 - 2.18071i) q^{96} +(-9.05049 - 2.65746i) q^{97} +(0.415415 - 0.909632i) q^{98} +(-1.52331 + 1.75800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	0.341180	+	2.37296i	0.196980	+	1.37003i	0.812985	+	0.582285i	$0.197841\pi$
$3$	0.341180	+	2.37296i	0.196980	+	1.37003i	−0.616005	+	0.787742i	$0.711250\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	1.96603	+	0.577277i	0.879234	+	0.258166i	0.690038	−	0.723773i	$-0.257594\pi$
$5$	1.96603	+	0.577277i	0.879234	+	0.258166i	0.189196	+	0.981939i	$0.439412\pi$
$6$	−0.995899	+	2.18071i	−0.406574	+	0.890273i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	−2.63604	+	0.774012i	−0.878681	+	0.258004i
$10$	1.34183	+	1.54855i	0.424323	+	0.489695i
$11$	0.712290	−	0.457761i	0.214764	−	0.138020i	−0.428837	−	0.903382i	$-0.641076\pi$
$11$	0.712290	−	0.457761i	0.214764	−	0.138020i	0.643600	+	0.765362i	$0.277440\pi$
$12$	−2.01679	+	1.29611i	−0.582196	+	0.374155i
$13$	−3.16858	−	3.65674i	−0.878806	−	1.01420i	−0.999768	−	0.0215391i	$-0.993143\pi$
$13$	−3.16858	−	3.65674i	−0.878806	−	1.01420i	0.120962	−	0.992657i	$-0.461402\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	−0.699086	+	4.86225i	−0.180503	+	1.25543i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.83679	−	4.02201i	0.445487	−	0.975481i	−0.545071	−	0.838390i	$-0.683497\pi$
$17$	1.83679	−	4.02201i	0.445487	−	0.975481i	0.990558	−	0.137091i	$-0.0437754\pi$
$18$	−2.63604	−	0.774012i	−0.621321	−	0.182436i
$19$	−1.18888	−	2.60328i	−0.272747	−	0.597234i	0.722846	−	0.691009i	$-0.242834\pi$
$19$	−1.18888	−	2.60328i	−0.272747	−	0.597234i	−0.995593	+	0.0937756i	$0.970106\pi$
$20$	0.291607	+	2.02817i	0.0652053	+	0.453513i
$21$	2.01679	+	1.29611i	0.440099	+	0.282834i
$22$	0.846701			0.180517
$23$	−4.09369	+	2.49834i	−0.853593	+	0.520940i
$23$	−4.09369	+	2.49834i	−0.853593	+	0.520940i
$24$	−2.39736			−0.489359
$25$	−0.674258	−	0.433319i	−0.134852	−	0.0866639i
$26$	−0.688598	−	4.78931i	−0.135045	−	0.939260i
$27$	0.251636	+	0.551006i	0.0484274	+	0.106041i
$28$	0.959493	+	0.281733i	0.181327	+	0.0532424i
$29$	−1.55805	+	3.41164i	−0.289322	+	0.633526i	−0.997357	−	0.0726504i	$-0.976854\pi$
$29$	−1.55805	+	3.41164i	−0.289322	+	0.633526i	0.708036	+	0.706177i	$0.249582\pi$
$30$	−3.21684	+	3.71243i	−0.587312	+	0.677794i
$31$	0.210342	−	1.46296i	0.0377786	−	0.262756i	−0.962175	−	0.272434i	$-0.912171\pi$
$31$	0.210342	−	1.46296i	0.0377786	−	0.262756i	0.999953	+	0.00967773i	$0.00308057\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	1.32927	+	1.53406i	0.231396	+	0.267045i
$34$	3.71967	−	2.39049i	0.637918	−	0.409965i
$35$	1.72375	−	1.10779i	0.291367	−	0.187250i
$36$	−1.79912	−	2.07629i	−0.299853	−	0.346049i
$37$	−0.504064	+	0.148007i	−0.0828676	+	0.0243321i	−0.322904	−	0.946432i	$-0.604659\pi$
$37$	−0.504064	+	0.148007i	−0.0828676	+	0.0243321i	0.240036	+	0.970764i	$0.422841\pi$
$38$	0.407292	−	2.83278i	0.0660714	−	0.459537i
$39$	7.59622	−	8.76651i	1.21637	−	1.40376i
$40$	−0.851196	+	1.86386i	−0.134586	+	0.294702i
$41$	−4.19540	−	1.23188i	−0.655211	−	0.192387i	−0.0628038	−	0.998026i	$-0.520004\pi$
$41$	−4.19540	−	1.23188i	−0.655211	−	0.192387i	−0.592407	+	0.805639i	$0.701822\pi$
$42$	0.995899	+	2.18071i	0.153671	+	0.336491i
$43$	1.11619	+	7.76324i	0.170217	+	1.18388i	0.878425	+	0.477880i	$0.158595\pi$
$43$	1.11619	+	7.76324i	0.170217	+	1.18388i	−0.708208	+	0.706003i	$0.750496\pi$
$44$	0.712290	+	0.457761i	0.107382	+	0.0690101i
$45$	−5.62935			−0.839173
$46$	−4.79454	−	0.111477i	−0.706916	−	0.0164364i
$47$	6.67750			0.974013			0.487007	−	0.873398i	$-0.338089\pi$
$47$	6.67750			0.974013			0.487007	+	0.873398i	$0.338089\pi$
$48$	−2.01679	−	1.29611i	−0.291098	−	0.187077i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.332952	−	0.729063i	−0.0470865	−	0.103105i
$51$	10.1707	+	2.98640i	1.42419	+	0.418179i
$52$	2.01001	−	4.40131i	0.278738	−	0.610351i
$53$	7.74248	−	8.93530i	1.06351	−	1.22736i	0.0906712	−	0.995881i	$-0.471099\pi$
$53$	7.74248	−	8.93530i	1.06351	−	1.22736i	0.972840	−	0.231477i	$-0.0743558\pi$
$54$	−0.0862066	+	0.599580i	−0.0117312	+	0.0815925i
$55$	1.66464	−	0.488781i	0.224460	−	0.0659073i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	5.77185	−	3.70934i	0.764501	−	0.491315i
$58$	−3.15518	+	2.02771i	−0.414296	+	0.266252i
$59$	−5.02182	−	5.79548i	−0.653785	−	0.754508i	0.327964	−	0.944690i	$-0.393637\pi$
$59$	−5.02182	−	5.79548i	−0.653785	−	0.754508i	−0.981749	+	0.190182i	$0.939092\pi$
$60$	−4.71327	+	1.38394i	−0.608480	+	0.178666i
$61$	−0.355188	+	2.47039i	−0.0454772	+	0.316301i	0.954367	+	0.298637i	$0.0965320\pi$
$61$	−0.355188	+	2.47039i	−0.0454772	+	0.316301i	−0.999844	+	0.0176640i	$0.994377\pi$
$62$	0.967889	−	1.11700i	0.122922	−	0.141860i
$63$	−1.14128	+	2.49906i	−0.143788	+	0.314852i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−4.11856	−	9.01839i	−0.510845	−	1.11859i
$66$	0.288877	+	2.00919i	0.0355583	+	0.247314i
$67$	9.35908	+	6.01471i	1.14339	+	0.734814i	0.968313	−	0.249740i	$-0.0803451\pi$
$67$	9.35908	+	6.01471i	1.14339	+	0.734814i	0.175080	+	0.984554i	$0.443981\pi$
$68$	4.42158			0.536196
$69$	−7.32514	−	8.86176i	−0.881843	−	1.06683i
$70$	2.04903			0.244905
$71$	8.70851	+	5.59662i	1.03351	+	0.664196i	0.943373	−	0.331733i	$-0.107633\pi$
$71$	8.70851	+	5.59662i	1.03351	+	0.664196i	0.0901364	+	0.995929i	$0.471270\pi$
$72$	−0.390986	−	2.71936i	−0.0460781	−	0.320480i
$73$	−4.45054	−	9.74532i	−0.520896	−	1.14060i	−0.969099	−	0.246672i	$-0.920663\pi$
$73$	−4.45054	−	9.74532i	−0.520896	−	1.14060i	0.448203	−	0.893932i	$-0.352064\pi$
$74$	−0.504064	−	0.148007i	−0.0585963	−	0.0172054i
$75$	0.798205	−	1.74783i	0.0921688	−	0.201822i
$76$	1.87415	−	2.16288i	0.214980	−	0.248100i
$77$	0.120498	−	0.838083i	0.0137320	−	0.0955084i
$78$	11.1299	−	3.26803i	1.26021	−	0.370031i
$79$	4.16610	+	4.80794i	0.468723	+	0.540935i	0.940056	−	0.341020i	$-0.110772\pi$
$79$	4.16610	+	4.80794i	0.468723	+	0.540935i	−0.471333	+	0.881955i	$0.656227\pi$
$80$	−1.72375	+	1.10779i	−0.192721	+	0.123854i
$81$	−8.15526	+	5.24107i	−0.906140	+	0.582341i
$82$	−2.86339	−	3.30453i	−0.316208	−	0.364924i
$83$	−9.69302	+	2.84613i	−1.06395	+	0.312403i	−0.766440	−	0.642316i	$-0.777973\pi$
$83$	−9.69302	+	2.84613i	−1.06395	+	0.312403i	−0.297507	+	0.954720i	$0.596155\pi$
$84$	−0.341180	+	2.37296i	−0.0372258	+	0.258911i
$85$	5.93300	−	6.84704i	0.643524	−	0.742666i
$86$	−3.25813	+	7.13431i	−0.351333	+	0.769313i
$87$	−8.62726	−	2.53319i	−0.924939	−	0.271587i
$88$	0.351732	+	0.770186i	0.0374948	+	0.0821021i
$89$	1.59642	+	11.1034i	0.169221	+	1.17696i	0.880500	+	0.474046i	$0.157207\pi$
$89$	1.59642	+	11.1034i	0.169221	+	1.17696i	−0.711280	+	0.702909i	$0.751884\pi$
$90$	−4.73571	−	3.04345i	−0.499187	−	0.320808i
$91$	−4.83856			−0.507218
$92$	−3.97315	−	2.68590i	−0.414230	−	0.280025i
$93$	3.54331			0.367424
$94$	5.61747	+	3.61013i	0.579398	+	0.372356i
$95$	−0.834551	−	5.80443i	−0.0856231	−	0.595522i
$96$	−0.995899	−	2.18071i	−0.101643	−	0.222568i
$97$	−9.05049	−	2.65746i	−0.918938	−	0.269825i	−0.212140	−	0.977239i	$-0.568043\pi$
$97$	−9.05049	−	2.65746i	−0.918938	−	0.269825i	−0.706799	+	0.707415i	$0.749861\pi$
$98$	0.415415	−	0.909632i	0.0419633	−	0.0918867i
$99$	−1.52331	+	1.75800i	−0.153099	+	0.176685i
$100$	0.114064	−	0.793334i	0.0114064	−	0.0793334i
$101$	14.8588	−	4.36294i	1.47851	−	0.434128i	0.559652	−	0.828728i	$-0.310935\pi$
$101$	14.8588	−	4.36294i	1.47851	−	0.434128i	0.918853	+	0.394599i	$0.129117\pi$
$102$	6.94160	+	8.01103i	0.687321	+	0.793211i
$103$	−10.5895	+	6.80546i	−1.04341	+	0.670561i	−0.945829	−	0.324666i	$-0.894748\pi$
$103$	−10.5895	+	6.80546i	−1.04341	+	0.670561i	−0.0975851	+	0.995227i	$0.531112\pi$
$104$	4.07045	−	2.61592i	0.399141	−	0.256512i
$105$	3.21684	+	3.71243i	0.313931	+	0.362296i
$106$	11.3442	−	3.33095i	1.10184	−	0.323531i
$107$	−0.401733	+	2.79411i	−0.0388370	+	0.270117i	−0.999982	−	0.00592521i	$-0.998114\pi$
$107$	−0.401733	+	2.79411i	−0.0388370	+	0.270117i	0.961145	+	0.276042i	$0.0890230\pi$
$108$	−0.396679	+	0.457792i	−0.0381705	+	0.0440511i
$109$	−3.62364	+	7.93466i	−0.347081	+	0.760002i	0.652915	+	0.757431i	$0.273546\pi$
$109$	−3.62364	+	7.93466i	−0.347081	+	0.760002i	−0.999997	+	0.00257125i	$0.999182\pi$
$110$	1.66464	+	0.488781i	0.158717	+	0.0466035i
$111$	−0.523190	−	1.14563i	−0.0496590	−	0.108738i
$112$	0.142315	+	0.989821i	0.0134475	+	0.0935293i
$113$	−12.3724	−	7.95124i	−1.16389	−	0.747990i	−0.191537	−	0.981485i	$-0.561347\pi$
$113$	−12.3724	−	7.95124i	−1.16389	−	0.747990i	−0.972358	+	0.233496i	$0.924983\pi$
$114$	6.86101			0.642593
$115$	−9.49054	+	2.54861i	−0.884997	+	0.237659i
$116$	−3.75058			−0.348232
$117$	11.1829	+	7.18679i	1.03386	+	0.664419i
$118$	−1.09134	−	7.59047i	−0.100466	−	0.698759i
$119$	−1.83679	−	4.02201i	−0.168378	−	0.368697i
$120$	−4.71327	−	1.38394i	−0.430261	−	0.126336i
$121$	−4.27175	+	9.35383i	−0.388341	+	0.850349i
$122$	−1.63440	+	1.88619i	−0.147971	+	0.170768i
$123$	1.49181	−	10.3758i	0.134512	−	0.935554i
$124$	1.41814	−	0.416403i	0.127352	−	0.0373941i
$125$	−7.78460	−	8.98390i	−0.696276	−	0.803545i
$126$	−2.31120	+	1.48532i	−0.205898	+	0.132323i
$127$	0.216235	−	0.138966i	0.0191877	−	0.0123312i	−0.531012	−	0.847364i	$-0.678188\pi$
$127$	0.216235	−	0.138966i	0.0191877	−	0.0123312i	0.550200	+	0.835033i	$0.314552\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−18.0410	+	5.29732i	−1.58842	+	0.466403i
$130$	1.41096	−	9.81341i	0.123749	−	0.860693i
$131$	1.01110	−	1.16687i	0.0883401	−	0.101950i	−0.709858	−	0.704344i	$-0.751241\pi$
$131$	1.01110	−	1.16687i	0.0883401	−	0.101950i	0.798199	+	0.602394i	$0.205787\pi$
$132$	−0.843229	+	1.84641i	−0.0733936	+	0.160710i
$133$	−2.74598	−	0.806292i	−0.238107	−	0.0699144i
$134$	4.62156	+	10.1198i	0.399242	+	0.874217i
$135$	0.176640	+	1.22856i	0.0152027	+	0.105737i
$136$	3.71967	+	2.39049i	0.318959	+	0.204983i
$137$	−12.3571			−1.05574			−0.527868	−	0.849326i	$-0.677008\pi$
$137$	−12.3571			−1.05574			−0.527868	+	0.849326i	$0.677008\pi$
$138$	−1.37127	−	11.4153i	−0.116730	−	0.971731i
$139$	11.9697			1.01526			0.507628	−	0.861576i	$-0.330522\pi$
$139$	11.9697			1.01526			0.507628	+	0.861576i	$0.330522\pi$
$140$	1.72375	+	1.10779i	0.145683	+	0.0936251i
$141$	2.27823	+	15.8454i	0.191861	+	1.33442i
$142$	4.30030	+	9.41635i	0.360873	+	0.790202i
$143$	−3.93086	−	1.15420i	−0.328715	−	0.0965195i
$144$	1.14128	−	2.49906i	0.0951068	−	0.208255i
$145$	−5.03262	+	5.80796i	−0.417936	+	0.482324i
$146$	1.52469	−	10.6044i	0.126184	−	0.877629i
$147$	2.30025	−	0.675414i	0.189721	−	0.0557072i
$148$	−0.344027	−	0.397029i	−0.0282789	−	0.0326356i
$149$	16.5780	−	10.6540i	1.35812	−	0.872810i	0.359931	−	0.932979i	$-0.382800\pi$
$149$	16.5780	−	10.6540i	1.35812	−	0.872810i	0.998188	+	0.0601690i	$0.0191640\pi$
$150$	1.61644	−	1.03882i	0.131982	−	0.0848195i
$151$	−2.79794	−	3.22899i	−0.227693	−	0.262772i	0.630395	−	0.776275i	$-0.282893\pi$
$151$	−2.79794	−	3.22899i	−0.227693	−	0.262772i	−0.858088	+	0.513503i	$0.828348\pi$
$152$	2.74598	−	0.806292i	0.222728	−	0.0653989i
$153$	−1.72877	+	12.0239i	−0.139763	+	0.972074i
$154$	0.554471	−	0.639894i	0.0446806	−	0.0515641i
$155$	1.25807	−	2.75480i	0.101051	−	0.221271i
$156$	11.1299	+	3.26803i	0.891104	+	0.261652i
$157$	8.06469	+	17.6592i	0.643633	+	1.40936i	0.897018	+	0.441993i	$0.145729\pi$
$157$	8.06469	+	17.6592i	0.643633	+	1.40936i	−0.253386	+	0.967365i	$0.581544\pi$
$158$	0.905380	+	6.29706i	0.0720282	+	0.500967i
$159$	23.8447	+	15.3240i	1.89100	+	1.21527i
$160$	−2.04903			−0.161990
$161$	−0.792676	+	4.72987i	−0.0624716	+	0.372766i
$162$	−9.69417			−0.761646
$163$	2.79199	+	1.79430i	0.218685	+	0.140540i	0.645397	−	0.763847i	$-0.276692\pi$
$163$	2.79199	+	1.79430i	0.218685	+	0.140540i	−0.426712	+	0.904388i	$0.640328\pi$
$164$	−0.622274	−	4.32801i	−0.0485914	−	0.337961i
$165$	1.72780	+	3.78335i	0.134509	+	0.294533i
$166$	−9.69302	−	2.84613i	−0.752324	−	0.220902i
$167$	5.51951	−	12.0860i	0.427112	−	0.935245i	−0.566674	−	0.823942i	$-0.691770\pi$
$167$	5.51951	−	12.0860i	0.427112	−	0.935245i	0.993786	−	0.111303i	$-0.0355026\pi$
$168$	−1.56994	+	1.81180i	−0.121123	+	0.139784i
$169$	−1.48173	+	10.3056i	−0.113979	+	0.792742i
$170$	8.69295	−	2.55248i	0.666719	−	0.195766i
$171$	5.14890	+	5.94215i	0.393746	+	0.454408i
$172$	−6.59801	+	4.24029i	−0.503094	+	0.323319i
$173$	3.12074	−	2.00558i	0.237265	−	0.152481i	−0.416606	−	0.909087i	$-0.636780\pi$
$173$	3.12074	−	2.00558i	0.237265	−	0.152481i	0.653871	+	0.756606i	$0.273144\pi$
$174$	−5.88816	−	6.79530i	−0.446380	−	0.515151i
$175$	−0.769026	+	0.225806i	−0.0581329	+	0.0170694i
$176$	−0.120498	+	0.838083i	−0.00908289	+	0.0631729i
$177$	12.0391	−	13.8939i	0.904914	−	1.04433i
$178$	−4.65994	+	10.2038i	−0.349277	+	0.764810i
$179$	−16.5766	−	4.86734i	−1.23900	−	0.363802i	−0.404358	−	0.914601i	$-0.632505\pi$
$179$	−16.5766	−	4.86734i	−1.23900	−	0.363802i	−0.834638	+	0.550799i	$0.814323\pi$
$180$	−2.33851	−	5.12063i	−0.174303	−	0.381669i
$181$	0.608488	+	4.23213i	0.0452286	+	0.314572i	0.999859	+	0.0167792i	$0.00534122\pi$
$181$	0.608488	+	4.23213i	0.0452286	+	0.314572i	−0.954631	+	0.297792i	$0.903750\pi$
$182$	−4.07045	−	2.61592i	−0.301722	−	0.193905i
$183$	−5.98331			−0.442299
$184$	−1.89032	−	4.40757i	−0.139356	−	0.324931i
$185$	−1.07644			−0.0791417
$186$	2.98082	+	1.91566i	0.218565	+	0.140463i
$187$	−0.532792	−	3.70565i	−0.0389616	−	0.270984i
$188$	2.77393	+	6.07407i	0.202310	+	0.442997i
$189$	0.581209	+	0.170658i	0.0422767	+	0.0124136i
$190$	2.43604	−	5.33419i	0.176729	−	0.386983i
$191$	−5.30167	+	6.11845i	−0.383615	+	0.442716i	−0.914413	−	0.404783i	$-0.867347\pi$
$191$	−5.30167	+	6.11845i	−0.383615	+	0.442716i	0.530798	+	0.847499i	$0.321892\pi$
$192$	0.341180	−	2.37296i	0.0246225	−	0.171253i
$193$	−21.2103	+	6.22789i	−1.52675	+	0.448294i	−0.934053	−	0.357134i	$-0.883754\pi$
$193$	−21.2103	+	6.22789i	−1.52675	+	0.448294i	−0.592695	+	0.805427i	$0.701936\pi$
$194$	−6.17703	−	7.12867i	−0.443485	−	0.511808i
$195$	19.9951	−	12.8501i	1.43188	−	0.920212i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	−4.64192	−	5.35706i	−0.330723	−	0.381675i	0.565896	−	0.824476i	$-0.308530\pi$
$197$	−4.64192	−	5.35706i	−0.330723	−	0.381675i	−0.896620	+	0.442801i	$0.853985\pi$
$198$	−2.23194	+	0.655357i	−0.158617	+	0.0465742i
$199$	−0.0334717	+	0.232800i	−0.00237274	+	0.0165028i	−0.990973	−	0.134059i	$-0.957199\pi$
$199$	−0.0334717	+	0.232800i	−0.00237274	+	0.0165028i	0.988601	+	0.150561i	$0.0481081\pi$
$200$	0.524866	−	0.605728i	0.0371136	−	0.0428314i
$201$	−11.0795	+	24.2608i	−0.781490	+	1.71122i
$202$	14.8588	+	4.36294i	1.04546	+	0.306975i
$203$	1.55805	+	3.41164i	0.109353	+	0.239450i
$204$	1.50855	+	10.4922i	0.105620	+	0.734603i
$205$	−7.53713	−	4.84382i	−0.526416	−	0.338307i
$206$	−12.5878			−0.877031
$207$	8.85739	−	9.75430i	0.615631	−	0.677970i
$208$	4.83856			0.335493
$209$	−2.03851	−	1.31007i	−0.141007	−	0.0906194i
$210$	0.699086	+	4.86225i	0.0482415	+	0.335527i
$211$	7.23242	+	15.8368i	0.497901	+	1.09025i	0.977146	+	0.212569i	$0.0681831\pi$
$211$	7.23242	+	15.8368i	0.497901	+	1.09025i	−0.479245	+	0.877681i	$0.659090\pi$
$212$	11.3442	+	3.33095i	0.779121	+	0.228771i
$213$	−10.3094	+	22.5744i	−0.706386	+	1.54677i
$214$	−1.84857	+	2.13337i	−0.126366	+	0.145834i
$215$	−2.28709	+	15.9071i	−0.155978	+	1.08485i
$216$	−0.581209	+	0.170658i	−0.0395463	+	0.0116118i
$217$	−0.967889	−	1.11700i	−0.0657046	−	0.0758271i
$218$	−7.33819	+	4.71597i	−0.497005	+	0.319406i
$219$	21.6068	−	13.8858i	1.46005	−	0.938319i
$220$	1.13613	+	1.31116i	0.0765976	+	0.0883983i
$221$	−20.5275	+	6.02741i	−1.38083	+	0.405447i
$222$	0.179237	−	1.24662i	0.0120296	−	0.0836676i
$223$	−19.2864	+	22.2576i	−1.29151	+	1.49048i	−0.520163	+	0.854067i	$0.674129\pi$
$223$	−19.2864	+	22.2576i	−1.29151	+	1.49048i	−0.771347	+	0.636415i	$0.780417\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	2.11277	+	0.620364i	0.140851	+	0.0413576i
$226$	−6.10953	−	13.3780i	−0.406400	−	0.889892i
$227$	−3.12727	−	21.7507i	−0.207564	−	1.44364i	−0.781072	−	0.624441i	$-0.785327\pi$
$227$	−3.12727	−	21.7507i	−0.207564	−	1.44364i	0.573507	−	0.819200i	$-0.305582\pi$
$228$	5.77185	+	3.70934i	0.382250	+	0.245657i
$229$	−9.01469			−0.595708			−0.297854	−	0.954611i	$-0.596271\pi$
$229$	−9.01469			−0.595708			−0.297854	+	0.954611i	$0.596271\pi$
$230$	−9.36183	−	2.98694i	−0.617301	−	0.196953i
$231$	2.02985			0.133554
$232$	−3.15518	−	2.02771i	−0.207148	−	0.133126i
$233$	−0.703431	−	4.89247i	−0.0460833	−	0.320516i	−0.999804	−	0.0198210i	$-0.993690\pi$
$233$	−0.703431	−	4.89247i	−0.0460833	−	0.320516i	0.953720	−	0.300695i	$-0.0972187\pi$
$234$	5.52215	+	12.0918i	0.360994	+	0.790468i
$235$	13.1281	+	3.85477i	0.856385	+	0.251457i
$236$	3.18562	−	6.97553i	0.207366	−	0.454069i
$237$	−9.98764	+	11.5263i	−0.648767	+	0.748717i
$238$	0.629257	−	4.37658i	0.0407887	−	0.283691i
$239$	20.7936	−	6.10556i	1.34503	−	0.394936i	0.471567	−	0.881830i	$-0.343688\pi$
$239$	20.7936	−	6.10556i	1.34503	−	0.394936i	0.873461	+	0.486894i	$0.161870\pi$
$240$	−3.21684	−	3.71243i	−0.207646	−	0.239636i
$241$	21.0569	−	13.5325i	1.35640	−	0.871703i	0.358313	−	0.933601i	$-0.383352\pi$
$241$	21.0569	−	13.5325i	1.35640	−	0.871703i	0.998082	+	0.0618986i	$0.0197156\pi$
$242$	−8.65069	+	5.55946i	−0.556088	+	0.357376i
$243$	−14.0292	−	16.1906i	−0.899973	−	1.03862i
$244$	−2.39470	+	0.703146i	−0.153305	+	0.0450143i
$245$	0.291607	−	2.02817i	0.0186301	−	0.129575i
$246$	6.86457	−	7.92214i	0.437669	−	0.505097i
$247$	−5.75246	+	12.5961i	−0.366020	+	0.801472i
$248$	1.41814	+	0.416403i	0.0900518	+	0.0264416i
$249$	−10.0608	−	22.0301i	−0.637577	−	1.39610i
$250$	−1.69175	−	11.7664i	−0.106996	−	0.744173i
$251$	9.52616	+	6.12209i	0.601286	+	0.386423i	0.805580	−	0.592487i	$-0.201854\pi$
$251$	9.52616	+	6.12209i	0.601286	+	0.386423i	−0.204295	+	0.978909i	$0.565490\pi$
$252$	−2.74733			−0.173065
$253$	−1.77225	+	3.65348i	−0.111420	+	0.229692i
$254$	0.257039			0.0161281
$255$	18.2720	+	11.7427i	1.14423	+	0.735355i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−3.62946	−	7.94740i	−0.226399	−	0.495745i	0.762009	−	0.647567i	$-0.224213\pi$
$257$	−3.62946	−	7.94740i	−0.226399	−	0.495745i	−0.988408	+	0.151822i	$0.951486\pi$
$258$	−18.0410	−	5.29732i	−1.12318	−	0.329797i
$259$	−0.218236	+	0.477870i	−0.0135605	+	0.0296934i
$260$	6.49250	−	7.49275i	0.402648	−	0.464681i
$261$	1.46642	−	10.1992i	0.0907691	−	0.631313i
$262$	1.48145	−	0.434992i	0.0915242	−	0.0268739i
$263$	−2.36520	−	2.72958i	−0.145844	−	0.168313i	0.678127	−	0.734945i	$-0.262792\pi$
$263$	−2.36520	−	2.72958i	−0.145844	−	0.168313i	−0.823971	+	0.566631i	$0.808246\pi$
$264$	−1.70762	+	1.09742i	−0.105096	+	0.0675414i
$265$	20.3801	−	13.0975i	1.25194	−	0.804571i
$266$	−1.87415	−	2.16288i	−0.114911	−	0.132615i
$267$	−25.8032	+	7.57649i	−1.57913	+	0.463674i
$268$	−1.58327	+	11.0119i	−0.0967139	+	0.672660i
$269$	9.98432	−	11.5225i	0.608755	−	0.702541i	−0.364776	−	0.931095i	$-0.618854\pi$
$269$	9.98432	−	11.5225i	0.608755	−	0.702541i	0.973531	+	0.228555i	$0.0733999\pi$
$270$	−0.515609	+	1.12903i	−0.0313789	+	0.0687103i
$271$	−23.7761	−	6.98130i	−1.44430	−	0.424083i	−0.536644	−	0.843809i	$-0.680308\pi$
$271$	−23.7761	−	6.98130i	−1.44430	−	0.424083i	−0.907651	+	0.419725i	$0.862127\pi$
$272$	1.83679	+	4.02201i	0.111372	+	0.243870i
$273$	−1.65082	−	11.4817i	−0.0999120	−	0.694903i
$274$	−10.3954	−	6.68074i	−0.628011	−	0.403598i
$275$	−0.678624			−0.0409226
$276$	5.01797	−	10.3445i	0.302046	−	0.622665i
$277$	23.6549			1.42129			0.710644	−	0.703552i	$-0.248404\pi$
$277$	23.6549			1.42129			0.710644	+	0.703552i	$0.248404\pi$
$278$	10.0696	+	6.47131i	0.603932	+	0.388123i
$279$	0.577879	+	4.01924i	0.0345967	+	0.240626i
$280$	0.851196	+	1.86386i	0.0508687	+	0.111387i
$281$	24.2967	+	7.13414i	1.44942	+	0.425587i	0.909349	−	0.416034i	$-0.136580\pi$
$281$	24.2967	+	7.13414i	1.44942	+	0.425587i	0.540068	+	0.841621i	$0.318399\pi$
$282$	−6.65011	+	14.5617i	−0.396008	+	0.867138i
$283$	14.0259	−	16.1867i	0.833751	−	0.962199i	−0.165963	−	0.986132i	$-0.553073\pi$
$283$	14.0259	−	16.1867i	0.833751	−	0.962199i	0.999714	+	0.0239325i	$0.00761869\pi$
$284$	−1.47322	+	10.2465i	−0.0874194	+	0.608015i
$285$	13.4889	−	3.96071i	0.799015	−	0.234612i
$286$	−2.68284	−	3.09616i	−0.158640	−	0.183080i
$287$	−3.67840	+	2.36396i	−0.217129	+	0.139540i
$288$	2.31120	−	1.48532i	0.136189	−	0.0875232i
$289$	−1.67015	−	1.92746i	−0.0982442	−	0.113380i
$290$	−7.37373	+	2.16512i	−0.433000	+	0.127140i
$291$	3.21820	−	22.3831i	0.188654	−	1.31212i
$292$	7.01584	−	8.09671i	0.410571	−	0.473824i
$293$	4.94653	−	10.8314i	0.288980	−	0.632777i	−0.708346	−	0.705865i	$-0.750558\pi$
$293$	4.94653	−	10.8314i	0.288980	−	0.632777i	0.997325	+	0.0730885i	$0.0232856\pi$
$294$	2.30025	+	0.675414i	0.134153	+	0.0393909i
$295$	−6.52742	−	14.2931i	−0.380041	−	0.832174i
$296$	−0.0747643	−	0.519997i	−0.00434558	−	0.0302242i
$297$	0.431467	+	0.277287i	0.0250362	+	0.0160898i
$298$	19.7063			1.14155
$299$	22.1070	+	7.05335i	1.27848	+	0.407906i
$300$	1.92146			0.110936
$301$	6.59801	+	4.24029i	0.380303	+	0.244406i
$302$	−0.608050	−	4.22908i	−0.0349893	−	0.243356i
$303$	15.4226	+	33.7707i	0.886004	+	1.94008i
$304$	2.74598	+	0.806292i	0.157493	+	0.0462440i
$305$	−2.12441	+	4.65181i	−0.121643	+	0.266362i
$306$	−7.95494	+	9.18050i	−0.454754	+	0.524814i
$307$	4.35574	−	30.2948i	0.248595	−	1.72902i	−0.357751	−	0.933817i	$-0.616456\pi$
$307$	4.35574	−	30.2948i	0.248595	−	1.72902i	0.606346	−	0.795201i	$-0.292635\pi$
$308$	0.812404	−	0.238543i	0.0462910	−	0.0135923i
$309$	−19.7620	−	22.8065i	−1.12422	−	1.29742i
$310$	2.54772	−	1.63732i	0.144700	−	0.0929934i
$311$	12.5162	−	8.04365i	0.709727	−	0.456114i	−0.135323	−	0.990802i	$-0.543207\pi$
$311$	12.5162	−	8.04365i	0.709727	−	0.456114i	0.845050	+	0.534688i	$0.179571\pi$
$312$	7.59622	+	8.76651i	0.430051	+	0.496306i
$313$	−7.11746	+	2.08988i	−0.402303	+	0.118127i	−0.476623	−	0.879108i	$-0.658139\pi$
$313$	−7.11746	+	2.08988i	−0.402303	+	0.118127i	0.0743204	+	0.997234i	$0.476321\pi$
$314$	−2.76284	+	19.2160i	−0.155916	+	1.08442i
$315$	−3.68644	+	4.25438i	−0.207707	+	0.239707i
$316$	−2.64279	+	5.78691i	−0.148669	+	0.325539i
$317$	−30.2205	−	8.87355i	−1.69735	−	0.498388i	−0.717241	−	0.696825i	$-0.754595\pi$
$317$	−30.2205	−	8.87355i	−1.69735	−	0.498388i	−0.980114	+	0.198437i	$0.936413\pi$
$318$	11.7746	+	25.7828i	0.660287	+	1.44583i
$319$	0.451937	+	3.14329i	0.0253036	+	0.175991i
$320$	−1.72375	−	1.10779i	−0.0963606	−	0.0619272i
$321$	−6.76738			−0.377718
$322$	−3.22400	+	3.55047i	−0.179667	+	0.197860i
$323$	−12.6542			−0.704096
$324$	−8.15526	−	5.24107i	−0.453070	−	0.291170i
$325$	0.551906	+	3.83859i	0.0306143	+	0.212927i
$326$	1.37870	+	3.01892i	0.0763589	+	0.167203i
$327$	−20.0649	−	5.89159i	−1.10959	−	0.325806i
$328$	1.81641	−	3.97738i	0.100294	−	0.219614i
$329$	4.37283	−	5.04652i	0.241082	−	0.278224i
$330$	−0.591917	+	4.11687i	−0.0325840	+	0.226626i
$331$	−28.5695	+	8.38876i	−1.57032	+	0.461088i	−0.947095	−	0.320953i	$-0.895997\pi$
$331$	−28.5695	+	8.38876i	−1.57032	+	0.461088i	−0.623227	+	0.782041i	$0.714179\pi$
$332$	−6.61555	−	7.63476i	−0.363076	−	0.419012i
$333$	1.21417	−	0.780303i	0.0665364	−	0.0427603i
$334$	11.1775	−	7.18335i	0.611606	−	0.393055i
$335$	14.9280	+	17.2279i	0.815605	+	0.941259i
$336$	−2.30025	+	0.675414i	−0.125489	+	0.0368469i
$337$	0.358631	−	2.49433i	0.0195359	−	0.135875i	−0.977719	−	0.209917i	$-0.932681\pi$
$337$	0.358631	−	2.49433i	0.0195359	−	0.135875i	0.997255	+	0.0740418i	$0.0235898\pi$
$338$	−6.81816	+	7.86858i	−0.370859	+	0.427994i
$339$	14.6467	−	32.0719i	0.795502	−	1.74191i
$340$	8.69295	+	2.55248i	0.471441	+	0.138428i
$341$	−0.519863	−	1.13834i	−0.0281522	−	0.0616446i
$342$	1.11896	+	7.78256i	0.0605066	+	0.420833i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	−7.84307			−0.422870
$345$	−9.28572	−	21.6511i	−0.499926	−	1.16566i
$346$	3.70963			0.199431
$347$	−29.7066	−	19.0913i	−1.59473	−	1.02487i	−0.969708	−	0.244268i	$-0.921452\pi$
$347$	−29.7066	−	19.0913i	−1.59473	−	1.02487i	−0.625026	−	0.780604i	$-0.714911\pi$
$348$	−1.27962	−	8.89995i	−0.0685948	−	0.477088i
$349$	11.1673	+	24.4530i	0.597772	+	1.30894i	0.930630	+	0.365962i	$0.119260\pi$
$349$	11.1673	+	24.4530i	0.597772	+	1.30894i	−0.332858	+	0.942977i	$0.608013\pi$
$350$	−0.769026	−	0.225806i	−0.0411062	−	0.0120699i
$351$	1.21755	−	2.66607i	0.0649883	−	0.142304i
$352$	−0.554471	+	0.639894i	−0.0295534	+	0.0341065i
$353$	−1.68773	+	11.7384i	−0.0898290	+	0.624775i	0.894320	+	0.447429i	$0.147660\pi$
$353$	−1.68773	+	11.7384i	−0.0898290	+	0.624775i	−0.984149	+	0.177346i	$0.943249\pi$
$354$	17.6395	−	5.17943i	0.937529	−	0.275283i
$355$	13.8904	+	16.0303i	0.737223	+	0.850801i
$356$	−9.43680	+	6.06467i	−0.500150	+	0.321427i
$357$	8.91739	−	5.73086i	0.471958	−	0.303309i
$358$	−11.3137	−	13.0567i	−0.597946	−	0.690067i
$359$	12.2600	−	3.59986i	0.647058	−	0.189993i	0.0582955	−	0.998299i	$-0.481433\pi$
$359$	12.2600	−	3.59986i	0.647058	−	0.189993i	0.588763	+	0.808306i	$0.299615\pi$
$360$	0.801139	−	5.57205i	0.0422238	−	0.293673i
$361$	7.07871	−	8.16927i	0.372564	−	0.429962i
$362$	−1.77617	+	3.88927i	−0.0933533	+	0.204415i
$363$	−23.6537	−	6.94535i	−1.24150	−	0.364536i
$364$	−2.01001	−	4.40131i	−0.105353	−	0.230691i
$365$	−3.12412	−	21.7288i	−0.163524	−	1.13734i
$366$	−5.03348	−	3.23482i	−0.263104	−	0.169087i
$367$	7.64902			0.399276			0.199638	−	0.979870i	$-0.436023\pi$
$367$	7.64902			0.399276			0.199638	+	0.979870i	$0.436023\pi$
$368$	0.792676	−	4.72987i	0.0413211	−	0.246561i
$369$	12.0127			0.625358
$370$	−0.905562	−	0.581969i	−0.0470779	−	0.0302552i
$371$	−1.68260	−	11.7028i	−0.0873563	−	0.607577i
$372$	1.47195	+	3.22311i	0.0763168	+	0.167111i
$373$	8.33763	+	2.44815i	0.431706	+	0.126760i	0.490364	−	0.871518i	$-0.336864\pi$
$373$	8.33763	+	2.44815i	0.431706	+	0.126760i	−0.0586578	+	0.998278i	$0.518682\pi$
$374$	1.55521	−	3.40544i	0.0804182	−	0.176091i
$375$	18.6625	−	21.5376i	0.963726	−	1.11220i
$376$	−0.950307	+	6.60953i	−0.0490084	+	0.340861i
$377$	17.4123	−	5.11270i	0.896778	−	0.263318i
$378$	0.396679	+	0.457792i	0.0204030	+	0.0235463i
$379$	−4.68399	+	3.01022i	−0.240600	+	0.154625i	−0.655385	−	0.755295i	$-0.727493\pi$
$379$	−4.68399	+	3.01022i	−0.240600	+	0.154625i	0.414784	+	0.909920i	$0.363857\pi$
$380$	4.93321	−	3.17038i	0.253068	−	0.162637i
$381$	0.403535	+	0.465704i	0.0206737	+	0.0238587i
$382$	−7.76793	+	2.28087i	−0.397442	+	0.116699i
$383$	−2.38181	+	16.5659i	−0.121705	+	0.846476i	0.833919	+	0.551887i	$0.186092\pi$
$383$	−2.38181	+	16.5659i	−0.121705	+	0.846476i	−0.955624	+	0.294589i	$0.904817\pi$
$384$	1.56994	−	1.81180i	0.0801155	−	0.0924582i
$385$	0.720709	−	1.57813i	0.0367307	−	0.0804291i
$386$	−21.2103	−	6.22789i	−1.07957	−	0.316991i
$387$	−8.95115	−	19.6003i	−0.455013	−	0.996339i
$388$	−1.34240	−	9.33657i	−0.0681498	−	0.473992i
$389$	16.9150	+	10.8706i	0.857626	+	0.551163i	0.893945	−	0.448177i	$-0.147927\pi$
$389$	16.9150	+	10.8706i	0.857626	+	0.551163i	−0.0363184	+	0.999340i	$0.511563\pi$
$390$	23.7682			1.20355
$391$	2.52911	+	21.0538i	0.127902	+	1.06474i
$392$	1.00000			0.0505076
$393$	3.11390	+	2.00118i	0.157075	+	0.100946i
$394$	−1.00879	−	7.01626i	−0.0508219	−	0.353474i
$395$	5.41515	+	11.8575i	0.272466	+	0.596617i
$396$	−2.23194	−	0.655357i	−0.112159	−	0.0329329i
$397$	11.5362	−	25.2608i	0.578985	−	1.26780i	−0.362888	−	0.931833i	$-0.618209\pi$
$397$	11.5362	−	25.2608i	0.578985	−	1.26780i	0.941873	−	0.335968i	$-0.109064\pi$
$398$	−0.154020	+	0.177748i	−0.00772030	+	0.00890970i
$399$	0.976424	−	6.79118i	0.0488823	−	0.339984i
$400$	0.769026	−	0.225806i	0.0384513	−	0.0112903i
$401$	1.74102	+	2.00924i	0.0869423	+	0.100337i	0.797554	−	0.603248i	$-0.206127\pi$
$401$	1.74102	+	2.00924i	0.0869423	+	0.100337i	−0.710611	+	0.703585i	$0.751582\pi$
$402$	−22.4371	+	14.4194i	−1.11906	+	0.719176i
$403$	−6.01616	+	3.86635i	−0.299686	+	0.192597i
$404$	10.1412	+	11.7036i	0.504545	+	0.582276i
$405$	−19.0590	+	5.59623i	−0.947049	+	0.278079i
$406$	−0.533762	+	3.71240i	−0.0264902	+	0.184243i
$407$	−0.291288	+	0.336165i	−0.0144386	+	0.0166631i
$408$	−4.40345	+	9.64221i	−0.218003	+	0.477360i
$409$	−7.49279	−	2.20008i	−0.370495	−	0.108787i	0.0911846	−	0.995834i	$-0.470935\pi$
$409$	−7.49279	−	2.20008i	−0.370495	−	0.108787i	−0.461679	+	0.887047i	$0.652753\pi$
$410$	−3.72187	−	8.14976i	−0.183810	−	0.402488i
$411$	−4.21598	−	29.3228i	−0.207959	−	1.44639i
$412$	−10.5895	−	6.80546i	−0.521707	−	0.335281i
$413$	−7.66852			−0.377343
$414$	12.7249	−	3.41717i	0.625394	−	0.167945i
$415$	−20.6997			−1.01611
$416$	4.07045	+	2.61592i	0.199570	+	0.128256i
$417$	4.08382	+	28.4036i	0.199985	+	1.39093i
$418$	−1.00662	−	2.20420i	−0.0492356	−	0.107811i
$419$	−4.19963	−	1.23312i	−0.205165	−	0.0602420i	0.177535	−	0.984114i	$-0.443188\pi$
$419$	−4.19963	−	1.23312i	−0.205165	−	0.0602420i	−0.382700	+	0.923872i	$0.625006\pi$
$420$	−2.04062	+	4.46834i	−0.0995722	+	0.218033i
$421$	10.1277	−	11.6880i	0.493594	−	0.569638i	−0.453228	−	0.891395i	$-0.649728\pi$
$421$	10.1277	−	11.6880i	0.493594	−	0.569638i	0.946822	+	0.321756i	$0.104273\pi$
$422$	−2.47772	+	17.2329i	−0.120613	+	0.838885i
$423$	−17.6022	+	5.16846i	−0.855847	+	0.251299i
$424$	7.74248	+	8.93530i	0.376008	+	0.433936i
$425$	−2.98129	+	1.91596i	−0.144614	+	0.0929376i
$426$	−20.8774	+	13.4171i	−1.01151	+	0.650061i
$427$	1.63440	+	1.88619i	0.0790940	+	0.0912794i
$428$	−2.70850	+	0.795288i	−0.130920	+	0.0384417i
$429$	1.39775	−	9.72155i	0.0674839	−	0.469361i
$430$	−10.5240	+	12.1454i	−0.507515	+	0.585703i
$431$	−14.8865	+	32.5970i	−0.717059	+	1.57014i	0.100922	+	0.994894i	$0.467821\pi$
$431$	−14.8865	+	32.5970i	−0.717059	+	1.57014i	−0.817981	+	0.575246i	$0.804907\pi$
$432$	−0.581209	−	0.170658i	−0.0279634	−	0.00821080i
$433$	13.7987	+	30.2150i	0.663125	+	1.45204i	0.879581	+	0.475748i	$0.157823\pi$
$433$	13.7987	+	30.2150i	0.663125	+	1.45204i	−0.216457	+	0.976292i	$0.569450\pi$
$434$	−0.210342	−	1.46296i	−0.0100968	−	0.0702245i
$435$	−15.4991	−	9.96064i	−0.743123	−	0.477576i
$436$	−8.72293			−0.417753
$437$	11.3708	+	7.68680i	0.543938	+	0.367709i
$438$	25.6841			1.22723
$439$	−4.25309	−	2.73330i	−0.202989	−	0.130453i	0.435197	−	0.900335i	$-0.356679\pi$
$439$	−4.25309	−	2.73330i	−0.202989	−	0.130453i	−0.638186	+	0.769882i	$0.720315\pi$
$440$	0.246904	+	1.71725i	0.0117707	+	0.0818669i
$441$	1.14128	+	2.49906i	0.0543467	+	0.119003i
$442$	−20.5275	−	6.02741i	−0.976392	−	0.286695i
$443$	−0.846468	+	1.85351i	−0.0402169	+	0.0880627i	−0.928674	−	0.370897i	$-0.879050\pi$
$443$	−0.846468	+	1.85351i	−0.0402169	+	0.0880627i	0.888457	+	0.458959i	$0.151778\pi$
$444$	0.824757	−	0.951820i	0.0391412	−	0.0451714i
$445$	−3.27111	+	22.7511i	−0.155066	+	1.07851i
$446$	−28.2581	+	8.29733i	−1.33806	+	0.392890i
$447$	30.9376	+	35.7038i	1.46330	+	1.68873i
$448$	−0.841254	+	0.540641i	−0.0397455	+	0.0255429i
$449$	24.4459	−	15.7104i	1.15367	−	0.741420i	0.183306	−	0.983056i	$-0.441320\pi$
$449$	24.4459	−	15.7104i	1.15367	−	0.741420i	0.970367	+	0.241636i	$0.0776839\pi$
$450$	1.44198	+	1.66413i	0.0679755	+	0.0784479i
$451$	−3.55225	+	1.04303i	−0.167269	+	0.0491146i
$452$	2.09303	−	14.5574i	0.0984480	−	0.684721i
$453$	6.70766	−	7.74105i	0.315153	−	0.363706i
$454$	9.12846	−	19.9885i	0.428420	−	0.938109i
$455$	−9.51273	−	2.79319i	−0.445964	−	0.130947i
$456$	2.85017	+	6.24100i	0.133471	+	0.292262i
$457$	0.0153365	+	0.106668i	0.000717411	+	0.00498970i	0.990177	−	0.139820i	$-0.0446522\pi$
$457$	0.0153365	+	0.106668i	0.000717411	+	0.00498970i	−0.989460	+	0.144809i	$0.953743\pi$
$458$	−7.58364	−	4.87371i	−0.354360	−	0.227734i
$459$	2.67836			0.125015
$460$	−6.26081	−	7.57416i	−0.291912	−	0.353147i
$461$	−21.9711			−1.02330			−0.511648	−	0.859195i	$-0.670965\pi$
$461$	−21.9711			−1.02330			−0.511648	+	0.859195i	$0.670965\pi$
$462$	1.70762	+	1.09742i	0.0794454	+	0.0510565i
$463$	2.09407	+	14.5646i	0.0973196	+	0.676873i	0.978825	+	0.204699i	$0.0656214\pi$
$463$	2.09407	+	14.5646i	0.0973196	+	0.676873i	−0.881505	+	0.472174i	$0.843469\pi$
$464$	−1.55805	−	3.41164i	−0.0723304	−	0.158382i
$465$	6.96625	+	2.04547i	0.323052	+	0.0948566i
$466$	2.05330	−	4.49611i	0.0951175	−	0.208278i
$467$	10.8380	−	12.5077i	0.501523	−	0.578788i	−0.447385	−	0.894341i	$-0.647645\pi$
$467$	10.8380	−	12.5077i	0.501523	−	0.578788i	0.948908	+	0.315553i	$0.102190\pi$
$468$	−1.89181	+	13.1578i	−0.0874487	+	0.608219i
$469$	10.6745	−	3.13432i	0.492903	−	0.144729i
$470$	8.96005	+	10.3404i	0.413296	+	0.476969i
$471$	−39.1530	+	25.1621i	−1.80408	+	1.15941i
$472$	6.45117	−	4.14592i	0.296939	−	0.190831i
$473$	4.34876	+	5.01874i	0.199956	+	0.230762i
$474$	−14.6337	+	4.29686i	−0.672150	+	0.197361i
$475$	−0.326441	+	2.27045i	−0.0149781	+	0.104175i
$476$	2.89552	−	3.34161i	0.132716	−	0.153162i
$477$	−13.4935	+	29.5466i	−0.617824	+	1.35285i
$478$	20.7936	+	6.10556i	0.951079	+	0.279262i
$479$	4.54086	+	9.94309i	0.207477	+	0.454311i	0.984551	−	0.175098i	$-0.0560242\pi$
$479$	4.54086	+	9.94309i	0.207477	+	0.454311i	−0.777074	+	0.629409i	$0.783297\pi$
$480$	−0.699086	−	4.86225i	−0.0319088	−	0.221930i
$481$	2.13839	+	1.37426i	0.0975021	+	0.0626608i
$482$	25.0304			1.14010
$483$	−11.4942	−	0.267250i	−0.523005	−	0.0121603i
$484$	−10.2831			−0.467414
$485$	−16.2594	−	10.4493i	−0.738302	−	0.474478i
$486$	−3.04884	−	21.2051i	−0.138298	−	0.961884i
$487$	9.87364	+	21.6203i	0.447417	+	0.979707i	0.990177	+	0.139819i	$0.0446522\pi$
$487$	9.87364	+	21.6203i	0.447417	+	0.979707i	−0.542760	+	0.839888i	$0.682621\pi$
$488$	−2.39470	−	0.703146i	−0.108403	−	0.0318299i
$489$	−3.30523	+	7.23744i	−0.149468	+	0.327288i
$490$	1.34183	−	1.54855i	0.0606176	−	0.0699564i
$491$	−3.72795	+	25.9285i	−0.168240	+	1.17014i	0.714280	+	0.699860i	$0.246754\pi$
$491$	−3.72795	+	25.9285i	−0.168240	+	1.17014i	−0.882520	+	0.470275i	$0.844155\pi$
$492$	10.0579	−	2.95326i	0.453444	−	0.133143i
$493$	10.8599	+	12.5330i	0.489104	+	0.564456i
$494$	−11.6493	+	7.48652i	−0.524125	+	0.336834i
$495$	−4.00973	+	2.57690i	−0.180224	+	0.115823i
$496$	0.967889	+	1.11700i	0.0434595	+	0.0501549i
$497$	9.93250	−	2.91645i	0.445534	−	0.130820i
$498$	3.44668	−	23.9722i	0.154449	−	1.07422i
$499$	−7.86675	+	9.07871i	−0.352164	+	0.406419i	−0.903999	−	0.427534i	$-0.859382\pi$
$499$	−7.86675	+	9.07871i	−0.352164	+	0.406419i	0.551835	+	0.833953i	$0.313928\pi$
$500$	4.93821	−	10.8132i	0.220843	−	0.483580i
$501$	30.5628	+	8.97404i	1.36544	+	0.400931i
$502$	4.70406	+	10.3005i	0.209953	+	0.459732i
$503$	2.05241	+	14.2749i	0.0915127	+	0.636485i	0.983023	+	0.183484i	$0.0587374\pi$
$503$	2.05241	+	14.2749i	0.0915127	+	0.636485i	−0.891510	+	0.453001i	$0.850353\pi$
$504$	−2.31120	−	1.48532i	−0.102949	−	0.0661613i
$505$	31.7314			1.41203
$506$	−3.46613	+	2.11535i	−0.154088	+	0.0940387i
$507$	−24.9604			−1.10853
$508$	0.216235	+	0.138966i	0.00959387	+	0.00616561i
$509$	5.47513	+	38.0803i	0.242681	+	1.68788i	0.638555	+	0.769576i	$0.279533\pi$
$509$	5.47513	+	38.0803i	0.242681	+	1.68788i	−0.395874	+	0.918305i	$0.629558\pi$
$510$	9.02278	+	19.7571i	0.399535	+	0.874861i
$511$	−10.2795	−	3.01834i	−0.454739	−	0.133523i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	1.13526	−	1.31016i	0.0501229	−	0.0578449i
$514$	1.24340	−	8.64801i	0.0548439	−	0.381447i
$515$	−24.7479	+	7.26663i	−1.09052	+	0.320206i
$516$	−12.3131	−	14.2101i	−0.542055	−	0.625565i
$517$	4.75632	−	3.05670i	0.209183	−	0.134434i
$518$	−0.441948	+	0.284022i	−0.0194181	+	0.0124792i
$519$	5.82388	+	6.72111i	0.255640	+	0.295024i
$520$	9.51273	−	2.79319i	0.417161	−	0.122489i
$521$	−1.77312	+	12.3323i	−0.0776817	+	0.540288i	0.913403	+	0.407056i	$0.133445\pi$
$521$	−1.77312	+	12.3323i	−0.0776817	+	0.540288i	−0.991085	+	0.133232i	$0.957464\pi$
$522$	6.74772	−	7.78729i	0.295340	−	0.340840i
$523$	−12.6639	+	27.7302i	−0.553756	+	1.21256i	0.401250	+	0.915969i	$0.368576\pi$
$523$	−12.6639	+	27.7302i	−0.553756	+	1.21256i	−0.955006	+	0.296587i	$0.904151\pi$
$524$	1.48145	+	0.434992i	0.0647173	+	0.0190027i
$525$	−0.798205	−	1.74783i	−0.0348365	−	0.0762814i
$526$	−0.514006	−	3.57499i	−0.0224117	−	0.155877i
$527$	−5.49770	−	3.53316i	−0.239484	−	0.153907i
$528$	−2.02985			−0.0883377
$529$	10.5166	−	20.4549i	0.457243	−	0.889342i
$530$	24.2258			1.05230
$531$	17.7235	+	11.3902i	0.769134	+	0.494292i
$532$	−0.407292	−	2.83278i	−0.0176583	−	0.122816i
$533$	8.78880	+	19.2448i	0.380685	+	0.833584i
$534$	−25.8032	−	7.57649i	−1.11661	−	0.327867i
$535$	−2.40280	+	5.26139i	−0.103882	+	0.227470i
$536$	−7.28543	+	8.40783i	−0.314683	+	0.363163i
$537$	5.89438	−	40.9963i	0.254361	−	1.76912i
$538$	14.6289	−	4.29543i	0.630696	−	0.185189i
$539$	−0.554471	−	0.639894i	−0.0238828	−	0.0275622i
$540$	−1.04415	+	0.671038i	−0.0449333	+	0.0288769i
$541$	19.6717	−	12.6423i	0.845754	−	0.543533i	−0.0444939	−	0.999010i	$-0.514168\pi$
$541$	19.6717	−	12.6423i	0.845754	−	0.543533i	0.890248	+	0.455477i	$0.150531\pi$
$542$	−16.2274	−	18.7274i	−0.697025	−	0.804410i
$543$	−9.83505	+	2.88783i	−0.422062	+	0.123929i
$544$	−0.629257	+	4.37658i	−0.0269792	+	0.187644i
$545$	−11.7047	+	13.5079i	−0.501372	+	0.578615i
$546$	4.81871	−	10.5515i	0.206222	−	0.451563i
$547$	−11.4753	−	3.36946i	−0.490649	−	0.144068i	0.0270434	−	0.999634i	$-0.491391\pi$
$547$	−11.4753	−	3.36946i	−0.490649	−	0.144068i	−0.517693	+	0.855567i	$0.673209\pi$
$548$	−5.13331	−	11.2404i	−0.219284	−	0.480166i
$549$	−0.975819	−	6.78697i	−0.0416469	−	0.289661i
$550$	−0.570895	−	0.366892i	−0.0243431	−	0.0156443i
$551$	10.7338			0.457275
$552$	9.81404	−	5.98942i	0.417713	−	0.254927i
$553$	6.36181			0.270532
$554$	19.8998	+	12.7888i	0.845461	+	0.543345i
$555$	−0.367261	−	2.55435i	−0.0155894	−	0.108426i
$556$	4.97239	+	10.8880i	0.210876	+	0.461755i
$557$	10.1197	+	2.97140i	0.428784	+	0.125902i	0.489002	−	0.872283i	$-0.337361\pi$
$557$	10.1197	+	2.97140i	0.428784	+	0.125902i	−0.0602173	+	0.998185i	$0.519179\pi$
$558$	−1.68682	+	3.69362i	−0.0714089	+	0.156364i
$559$	24.8514	−	28.6801i	1.05110	−	1.21304i
$560$	−0.291607	+	2.02817i	−0.0123226	+	0.0857058i
$561$	8.61158	−	2.52859i	0.363581	−	0.106757i
$562$	16.5826	+	19.1374i	0.699496	+	0.807262i
$563$	−15.3892	+	9.89003i	−0.648577	+	0.416815i	−0.823146	−	0.567830i	$-0.807783\pi$
$563$	−15.3892	+	9.89003i	−0.648577	+	0.416815i	0.174569	+	0.984645i	$0.444147\pi$
$564$	−13.4671	+	8.65477i	−0.567067	+	0.364432i
$565$	−19.7343	−	22.7746i	−0.830229	−	0.958136i
$566$	20.5505	−	6.03417i	0.863802	−	0.253635i
$567$	−1.37962	+	9.59550i	−0.0579388	+	0.402973i
$568$	−6.77900	+	7.82339i	−0.284441	+	0.328262i
$569$	−1.51236	+	3.31160i	−0.0634013	+	0.138829i	−0.938680	−	0.344789i	$-0.887950\pi$
$569$	−1.51236	+	3.31160i	−0.0634013	+	0.138829i	0.875279	+	0.483618i	$0.160678\pi$
$570$	13.4889	+	3.96071i	0.564989	+	0.165896i
$571$	15.4982	+	33.9362i	0.648577	+	1.42019i	0.892794	+	0.450466i	$0.148742\pi$
$571$	15.4982	+	33.9362i	0.648577	+	1.42019i	−0.244216	+	0.969721i	$0.578531\pi$
$572$	−0.583037	−	4.05511i	−0.0243780	−	0.169553i
$573$	−16.3276	−	10.4931i	−0.682097	−	0.438357i
$574$	−4.37252			−0.182505
$575$	3.84278	+	0.0893478i	0.160255	+	0.00372606i
$576$	2.74733			0.114472
$577$	−23.0141	−	14.7903i	−0.958089	−	0.615726i	−0.0346204	−	0.999401i	$-0.511022\pi$
$577$	−23.0141	−	14.7903i	−0.958089	−	0.615726i	−0.923469	+	0.383674i	$0.874659\pi$
$578$	−0.362958	−	2.52443i	−0.0150971	−	0.105002i
$579$	−22.0150	−	48.2062i	−0.914913	−	2.00338i
$580$	−7.37373	−	2.16512i	−0.306177	−	0.0899018i
$581$	−4.19662	+	9.18931i	−0.174105	+	0.381237i
$582$	14.8085	−	17.0900i	0.613834	−	0.708402i
$583$	1.42466	−	9.90873i	0.0590034	−	0.410378i
$584$	10.2795	−	3.01834i	0.425369	−	0.124900i
$585$	17.8370	+	20.5850i	0.737471	+	0.851086i
$586$	10.0172	−	6.43765i	0.413806	−	0.265937i
$587$	23.6883	−	15.2236i	0.977722	−	0.628344i	0.0488738	−	0.998805i	$-0.484437\pi$
$587$	23.6883	−	15.2236i	0.977722	−	0.628344i	0.928848	+	0.370461i	$0.120800\pi$
$588$	1.56994	+	1.81180i	0.0647431	+	0.0747175i
$589$	−4.05858	+	1.19171i	−0.167231	+	0.0491034i
$590$	2.23619	−	15.5531i	0.0920626	−	0.640310i
$591$	11.1284	−	12.8428i	0.457759	−	0.528282i
$592$	0.218236	−	0.477870i	0.00896944	−	0.0196403i
$593$	32.6300	+	9.58103i	1.33995	+	0.393446i	0.871653	−	0.490123i	$-0.163048\pi$
$593$	32.6300	+	9.58103i	1.33995	+	0.393446i	0.468301	+	0.883569i	$0.344866\pi$
$594$	0.213060	+	0.466537i	0.00874198	+	0.0191423i
$595$	−1.28936	−	8.96772i	−0.0528588	−	0.367641i
$596$	16.5780	+	10.6540i	0.679059	+	0.436405i
$597$	−0.563845			−0.0230766
$598$	14.7842	+	17.8856i	0.604572	+	0.731396i
$599$	26.1591			1.06883			0.534417	−	0.845221i	$-0.320531\pi$
$599$	26.1591			1.06883			0.534417	+	0.845221i	$0.320531\pi$
$600$	1.61644	+	1.03882i	0.0659908	+	0.0424097i
$601$	−1.69407	−	11.7825i	−0.0691027	−	0.480620i	−0.994758	−	0.102253i	$-0.967395\pi$
$601$	−1.69407	−	11.7825i	−0.0691027	−	0.480620i	0.925656	−	0.378367i	$-0.123514\pi$
$602$	3.25813	+	7.13431i	0.132791	+	0.290773i
$603$	−29.3264	−	8.61100i	−1.19426	−	0.350667i
$604$	1.77489	−	3.88646i	0.0722192	−	0.158138i
$605$	−13.7981	+	15.9239i	−0.560974	+	0.647398i
$606$	−5.28354	+	36.7478i	−0.214629	+	1.49278i
$607$	−44.8360	+	13.1650i	−1.81984	+	0.534352i	−0.999306	−	0.0372511i	$-0.988140\pi$
$607$	−44.8360	+	13.1650i	−1.81984	+	0.534352i	−0.820530	+	0.571603i	$0.806322\pi$
$608$	1.87415	+	2.16288i	0.0760068	+	0.0877165i
$609$	−7.56411	+	4.86116i	−0.306513	+	0.196984i
$610$	−4.30212	+	2.76481i	−0.174188	+	0.111944i
$611$	−21.1582	−	24.4179i	−0.855969	−	0.987841i
$612$	−11.6555	+	3.42236i	−0.471145	+	0.138341i
$613$	2.69593	−	18.7506i	0.108888	−	0.757331i	−0.860083	−	0.510155i	$-0.829588\pi$
$613$	2.69593	−	18.7506i	0.108888	−	0.757331i	0.968970	−	0.247177i	$-0.0795028\pi$
$614$	20.0429	−	23.1308i	0.808866	−	0.933481i
$615$	8.92266	−	19.5379i	0.359796	−	0.787844i
$616$	0.812404	+	0.238543i	0.0327327	+	0.00961118i
$617$	−4.59525	−	10.0622i	−0.184998	−	0.405089i	0.794297	−	0.607530i	$-0.207840\pi$
$617$	−4.59525	−	10.0622i	−0.184998	−	0.405089i	−0.979294	+	0.202442i	$0.935112\pi$
$618$	−4.29469	−	29.8702i	−0.172758	−	1.20156i
$619$	−20.4241	−	13.1258i	−0.820915	−	0.527570i	0.0614638	−	0.998109i	$-0.480423\pi$
$619$	−20.4241	−	13.1258i	−0.820915	−	0.527570i	−0.882379	+	0.470539i	$0.844059\pi$
$620$	3.02847			0.121626
$621$	−2.40672	−	1.62697i	−0.0965784	−	0.0652882i
$622$	14.8780			0.596553
$623$	9.43680	+	6.06467i	0.378078	+	0.242976i
$624$	1.65082	+	11.4817i	0.0660856	+	0.459635i
$625$	−8.45376	−	18.5111i	−0.338150	−	0.740446i
$626$	−7.11746	−	2.08988i	−0.284471	−	0.0835282i
$627$	2.41324	−	5.28426i	0.0963755	−	0.211033i
$628$	−12.7132	+	14.6718i	−0.507312	+	0.585469i
$629$	−0.330576	+	2.29921i	−0.0131809	+	0.0916755i
$630$	−5.40132	+	1.58597i	−0.215194	+	0.0631866i
$631$	−19.9481	−	23.0213i	−0.794120	−	0.916463i	0.203924	−	0.978987i	$-0.434631\pi$
$631$	−19.9481	−	23.0213i	−0.794120	−	0.916463i	−0.998043	+	0.0625237i	$0.980085\pi$
$632$	−5.35190	+	3.43946i	−0.212887	+	0.136814i
$633$	−35.1125	+	22.5654i	−1.39560	+	0.896895i
$634$	−20.6257	−	23.8034i	−0.819152	−	0.945352i
$635$	0.505345	−	0.148383i	0.0200540	−	0.00588839i
$636$	−4.03380	+	28.0557i	−0.159951	+	1.11248i
$637$	−3.16858	+	3.65674i	−0.125544	+	0.144885i
$638$	−1.31920	+	2.88864i	−0.0522276	+	0.114362i
$639$	−27.2878	−	8.01243i	−1.07949	−	0.316967i
$640$	−0.851196	−	1.86386i	−0.0336465	−	0.0736755i
$641$	−0.363901	−	2.53099i	−0.0143732	−	0.0999680i	0.981372	−	0.192117i	$-0.0615354\pi$
$641$	−0.363901	−	2.53099i	−0.0143732	−	0.0999680i	−0.995745	+	0.0921493i	$0.970626\pi$
$642$	−5.69308	−	3.65872i	−0.224688	−	0.144398i
$643$	27.5611			1.08690			0.543452	−	0.839440i	$-0.317117\pi$
$643$	27.5611			1.08690			0.543452	+	0.839440i	$0.317117\pi$
$644$	−4.63173	+	1.24382i	−0.182516	+	0.0490132i
$645$	−38.5271			−1.51700
$646$	−10.6454	−	6.84135i	−0.418836	−	0.269169i
$647$	0.825315	+	5.74019i	0.0324465	+	0.225670i	0.999592	−	0.0285521i	$-0.00908964\pi$
$647$	0.825315	+	5.74019i	0.0324465	+	0.225670i	−0.967146	+	0.254222i	$0.918181\pi$
$648$	−4.02711	−	8.81813i	−0.158200	−	0.346409i
$649$	−6.22994	−	1.82927i	−0.244546	−	0.0718053i
$650$	−1.61101	+	3.52761i	−0.0631889	+	0.138364i
$651$	2.32038	−	2.67786i	0.0909427	−	0.104953i
$652$	−0.472320	+	3.28506i	−0.0184975	+	0.128653i
$653$	9.81690	−	2.88250i	0.384165	−	0.112801i	−0.0839469	−	0.996470i	$-0.526753\pi$
$653$	9.81690	−	2.88250i	0.384165	−	0.112801i	0.468112	+	0.883669i	$0.344934\pi$
$654$	−13.6944	−	15.8042i	−0.535495	−	0.617994i
$655$	2.66145	−	1.71041i	0.103992	−	0.0668313i
$656$	3.67840	−	2.36396i	0.143617	−	0.0922972i
$657$	19.2748	+	22.2443i	0.751982	+	0.867833i
$658$	6.40701	−	1.88127i	0.249771	−	0.0733395i
$659$	−4.38260	+	30.4817i	−0.170722	+	1.18740i	0.706642	+	0.707571i	$0.250209\pi$
$659$	−4.38260	+	30.4817i	−0.170722	+	1.18740i	−0.877364	+	0.479826i	$0.840700\pi$
$660$	−2.72370	+	3.14332i	−0.106020	+	0.122354i
$661$	10.6879	−	23.4032i	0.415711	−	0.910279i	−0.579722	−	0.814814i	$-0.696839\pi$
$661$	10.6879	−	23.4032i	0.415711	−	0.910279i	0.995433	−	0.0954651i	$-0.0304338\pi$
$662$	−28.5695	−	8.38876i	−1.11039	−	0.326039i
$663$	−21.3063	−	46.6544i	−0.827469	−	1.81191i
$664$	−1.43770	−	9.99940i	−0.0557935	−	0.388052i
$665$	−4.93321	−	3.17038i	−0.191302	−	0.122942i
$666$	1.44329			0.0559265
$667$	−2.14530	−	17.8587i	−0.0830662	−	0.691493i
$668$	13.2867			0.514079
$669$	−59.3965	−	38.1718i	−2.29640	−	1.47581i
$670$	3.24417	+	22.5637i	0.125333	+	0.871712i
$671$	0.877851	+	1.92223i	0.0338891	+	0.0742067i
$672$	−2.30025	−	0.675414i	−0.0887340	−	0.0260547i
$673$	2.97302	−	6.51001i	0.114601	−	0.250942i	−0.843636	−	0.536915i	$-0.819589\pi$
$673$	2.97302	−	6.51001i	0.114601	−	0.250942i	0.958238	+	0.285973i	$0.0923168\pi$
$674$	1.65024	−	1.90447i	0.0635647	−	0.0733576i
$675$	0.0690940	−	0.480559i	0.00265943	−	0.0184967i
$676$	−9.98988	+	2.93329i	−0.384226	+	0.112819i
$677$	33.4584	+	38.6131i	1.28591	+	1.48402i	0.786404	+	0.617712i	$0.211940\pi$
$677$	33.4584	+	38.6131i	1.28591	+	1.48402i	0.499508	+	0.866310i	$0.333514\pi$
$678$	29.6610	−	19.0620i	1.13912	−	0.732071i
$679$	−7.93519	+	5.09964i	−0.304525	+	0.195706i
$680$	5.93300	+	6.84704i	0.227520	+	0.262572i
$681$	50.5464	−	14.8418i	1.93694	−	0.568738i
$682$	0.178097	−	1.23869i	0.00681969	−	0.0474320i
$683$	19.4824	−	22.4839i	0.745473	−	0.860322i	−0.248648	−	0.968594i	$-0.579986\pi$
$683$	19.4824	−	22.4839i	0.745473	−	0.860322i	0.994121	+	0.108272i	$0.0345317\pi$
$684$	−3.26624	+	7.15207i	−0.124888	+	0.273466i
$685$	−24.2943	−	7.13346i	−0.928239	−	0.272555i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	−3.07563	−	21.3915i	−0.117343	−	0.816136i
$688$	−6.59801	−	4.24029i	−0.251547	−	0.161659i
$689$	−57.2067			−2.17940
$690$	3.89382	−	23.2343i	0.148235	−	0.884515i
$691$	−38.0862			−1.44887			−0.724433	−	0.689345i	$-0.757899\pi$
$691$	−38.0862			−1.44887			−0.724433	+	0.689345i	$0.757899\pi$
$692$	3.12074	+	2.00558i	0.118633	+	0.0762406i
$693$	0.331048	+	2.30249i	0.0125755	+	0.0874643i
$694$	−14.6693	−	32.1212i	−0.556837	−	1.21930i
$695$	23.5327	+	6.90984i	0.892648	+	0.262105i
$696$	3.73519	−	8.17893i	0.141582	−	0.310022i
$697$	−12.6607	+	14.6112i	−0.479559	+	0.553440i
$698$	−3.82575	+	26.6087i	−0.144807	+	1.00715i
$699$	11.3696	−	3.33842i	0.430038	−	0.126271i
$700$	−0.524866	−	0.605728i	−0.0198381	−	0.0228943i
$701$	43.4869	−	27.9474i	1.64248	−	1.05556i	0.704012	−	0.710188i	$-0.251390\pi$
$701$	43.4869	−	27.9474i	1.64248	−	1.05556i	0.938467	−	0.345370i	$-0.112246\pi$
$702$	2.46566	−	1.58458i	0.0930603	−	0.0598062i
$703$	0.984574	+	1.13626i	0.0371339	+	0.0428548i
$704$	−0.812404	+	0.238543i	−0.0306186	+	0.00899044i
$705$	−4.66815	+	32.4677i	−0.175813	+	1.22280i
$706$	−7.76610	+	8.96255i	−0.292281	+	0.337310i
$707$	6.43315	−	14.0866i	0.241944	−	0.529783i
$708$	17.6395	+	5.17943i	0.662933	+	0.194655i
$709$	10.6042	+	23.2199i	0.398248	+	0.872041i	0.997445	+	0.0714395i	$0.0227593\pi$
$709$	10.6042	+	23.2199i	0.398248	+	0.872041i	−0.599197	+	0.800602i	$0.704513\pi$
$710$	3.01866	+	20.9953i	0.113288	+	0.787938i
$711$	−14.7034	−	9.44931i	−0.551421	−	0.354377i
$712$	−11.2175			−0.420395
$713$	2.79391	+	6.51442i	0.104633	+	0.243967i
$714$	10.6001			0.396699
$715$	−7.06188	−	4.53839i	−0.264099	−	0.169726i
$716$	−2.45870	−	17.1006i	−0.0918858	−	0.639080i
$717$	21.5826	+	47.2593i	0.806017	+	1.76493i
$718$	12.2600	+	3.59986i	0.457539	+	0.134346i
$719$	3.02078	−	6.61458i	0.112656	−	0.246682i	−0.844903	−	0.534920i	$-0.820342\pi$
$719$	3.02078	−	6.61458i	0.112656	−	0.246682i	0.957559	+	0.288237i	$0.0930692\pi$
$720$	3.68644	−	4.25438i	0.137385	−	0.158551i
$721$	−1.79142	+	12.4596i	−0.0667161	+	0.464021i
$722$	10.3716	−	3.04539i	0.385992	−	0.113338i
$723$	39.2962	+	45.3502i	1.46144	+	1.68659i
$724$	−3.59690	+	2.31159i	−0.133678	+	0.0859095i
$725$	2.52886	−	1.62520i	0.0939194	−	0.0603583i
$726$	−16.1438	−	18.6309i	−0.599153	−	0.691459i
$727$	−14.0831	+	4.13517i	−0.522313	+	0.153365i	−0.532253	−	0.846586i	$-0.678654\pi$
$727$	−14.0831	+	4.13517i	−0.522313	+	0.153365i	0.00993930	+	0.999951i	$0.496836\pi$
$728$	0.688598	−	4.78931i	0.0255212	−	0.177504i
$729$	14.5880	−	16.8355i	0.540297	−	0.623535i
$730$	9.11927	−	19.9684i	0.337519	−	0.739065i
$731$	33.2741	+	9.77015i	1.23069	+	0.361362i
$732$	−2.48556	−	5.44261i	−0.0918688	−	0.201165i
$733$	−2.33442	−	16.2363i	−0.0862238	−	0.599700i	−0.986423	−	0.164222i	$-0.947489\pi$
$733$	−2.33442	−	16.2363i	−0.0862238	−	0.599700i	0.900200	−	0.435478i	$-0.143421\pi$
$734$	6.43477	+	4.13537i	0.237512	+	0.152639i
$735$	4.91225			0.181191
$736$	3.22400	−	3.55047i	0.118838	−	0.130872i
$737$	9.41968			0.346978
$738$	10.1058	+	6.49458i	0.371998	+	0.239069i
$739$	−4.67618	−	32.5236i	−0.172016	−	1.19640i	−0.874617	−	0.484814i	$-0.838887\pi$
$739$	−4.67618	−	32.5236i	−0.172016	−	1.19640i	0.702601	−	0.711584i	$-0.252022\pi$
$740$	−0.447171	−	0.979168i	−0.0164383	−	0.0359949i
$741$	−31.8527	−	9.35279i	−1.17014	−	0.343583i
$742$	4.91149	−	10.7547i	0.180307	−	0.394816i
$743$	−2.85745	+	3.29767i	−0.104829	+	0.120980i	−0.805740	−	0.592270i	$-0.798232\pi$
$743$	−2.85745	+	3.29767i	−0.104829	+	0.120980i	0.700910	+	0.713250i	$0.252777\pi$
$744$	−0.504266	+	3.50725i	−0.0184873	+	0.128582i
$745$	38.7430	−	11.3760i	1.41943	−	0.416783i
$746$	5.69049	+	6.56717i	0.208344	+	0.240441i
$747$	23.3483	−	15.0050i	0.854268	−	0.549005i
$748$	3.14945	−	2.02403i	0.115155	−	0.0740058i
$749$	1.84857	+	2.13337i	0.0675453	+	0.0779515i
$750$	27.3440	−	8.02892i	0.998462	−	0.293175i
$751$	7.47383	−	51.9816i	0.272724	−	1.89684i	−0.146921	−	0.989148i	$-0.546936\pi$
$751$	7.47383	−	51.9816i	0.272724	−	1.89684i	0.419645	−	0.907688i	$-0.362155\pi$
$752$	−4.37283	+	5.04652i	−0.159461	+	0.184028i
$753$	−11.2773	+	24.6939i	−0.410968	+	0.899895i
$754$	17.4123	+	5.11270i	0.634118	+	0.186194i
$755$	−3.63679	−	7.96347i	−0.132356	−	0.289820i
$756$	0.0862066	+	0.599580i	0.00313530	+	0.0218065i
$757$	−26.3365	−	16.9254i	−0.957215	−	0.615165i	−0.0339889	−	0.999422i	$-0.510821\pi$
$757$	−26.3365	−	16.9254i	−0.957215	−	0.615165i	−0.923226	+	0.384258i	$0.874457\pi$
$758$	−5.56787			−0.202234
$759$	−9.27420	−	2.95898i	−0.336632	−	0.107404i
$760$	5.86412			0.212714
$761$	−31.6265	−	20.3251i	−1.14646	−	0.736784i	−0.177527	−	0.984116i	$-0.556810\pi$
$761$	−31.6265	−	20.3251i	−1.14646	−	0.736784i	−0.968931	+	0.247332i	$0.920446\pi$
$762$	0.0876964	+	0.609942i	0.00317691	+	0.0220959i
$763$	3.62364	+	7.93466i	0.131184	+	0.287254i
$764$	−7.76793	−	2.28087i	−0.281034	−	0.0825190i
$765$	−10.3399	+	22.6413i	−0.373841	+	0.818598i
$766$	−10.9599	+	12.6484i	−0.395997	+	0.457005i
$767$	−5.28053	+	36.7269i	−0.190669	+	1.32613i
$768$	2.30025	−	0.675414i	0.0830031	−	0.0243719i
$769$	15.0375	+	17.3542i	0.542266	+	0.625808i	0.959064	−	0.283191i	$-0.0913930\pi$
$769$	15.0375	+	17.3542i	0.542266	+	0.625808i	−0.416797	+	0.908999i	$0.636848\pi$
$770$	1.45950	−	0.937965i	0.0525968	−	0.0338019i
$771$	17.6205	−	11.3240i	0.634588	−	0.407825i
$772$	−14.4762	−	16.7064i	−0.521008	−	0.601275i
$773$	−12.3573	+	3.62843i	−0.444461	+	0.130506i	−0.496302	−	0.868150i	$-0.665309\pi$
$773$	−12.3573	+	3.62843i	−0.444461	+	0.130506i	0.0518410	+	0.998655i	$0.483491\pi$
$774$	3.06653	−	21.3282i	0.110224	−	0.766625i
$775$	−0.775755	+	0.895270i	−0.0278660	+	0.0321590i
$776$	3.91843	−	8.58018i	0.140664	−	0.308010i
$777$	−1.20842	−	0.354825i	−0.0433519	−	0.0127293i
$778$	8.35272	+	18.2899i	0.299460	+	0.655725i
$779$	1.78089	+	12.3864i	0.0638070	+	0.443787i
$780$	19.9951	+	12.8501i	0.715939	+	0.460106i
$781$	8.76490			0.313633
$782$	−9.25492	+	19.0789i	−0.330955	+	0.682261i
$783$	−2.27190			−0.0811909
$784$	0.841254	+	0.540641i	0.0300448	+	0.0193086i
$785$	5.66113	+	39.3740i	0.202054	+	1.40532i
$786$	1.53766	+	3.36700i	0.0548464	+	0.120097i
$787$	−16.9510	−	4.97726i	−0.604238	−	0.177420i	−0.0347169	−	0.999397i	$-0.511053\pi$
$787$	−16.9510	−	4.97726i	−0.604238	−	0.177420i	−0.569521	+	0.821977i	$0.692871\pi$
$788$	2.94463	−	6.44785i	0.104898	−	0.229695i
$789$	5.67023	−	6.54379i	0.201865	−	0.232965i
$790$	−1.85515	+	12.9028i	−0.0660032	+	0.459062i
$791$	−14.1113	+	4.14346i	−0.501741	+	0.147324i
$792$	−1.52331	−	1.75800i	−0.0541286	−	0.0624678i
$793$	10.1590	−	6.52880i	0.360757	−	0.231844i
$794$	23.3619	−	15.0138i	0.829082	−	0.532818i
$795$	38.0330	+	43.8924i	1.34889	+	1.55670i
$796$	−0.225667	+	0.0662619i	−0.00799857	+	0.00234859i
$797$	−3.73214	+	25.9576i	−0.132199	+	0.919466i	0.810480	+	0.585766i	$0.199206\pi$
$797$	−3.73214	+	25.9576i	−0.132199	+	0.919466i	−0.942679	+	0.333700i	$0.891703\pi$
$798$	4.49301	−	5.18521i	0.159051	−	0.183554i
$799$	12.2652	−	26.8570i	0.433911	−	0.950132i
$800$	0.769026	+	0.225806i	0.0271892	+	0.00798347i
$801$	−12.8024	−	28.0333i	−0.452350	−	0.990508i
$802$	0.378359	+	2.63155i	0.0133603	+	0.0929232i
$803$	−7.63111	−	4.90422i	−0.269296	−	0.173066i
$804$	−26.6710			−0.940613
$805$	−4.28887	+	8.84145i	−0.151163	+	0.311620i
$806$	−7.15142			−0.251898
$807$	30.7489	+	19.7611i	1.08241	+	0.695624i
$808$	2.20390	+	15.3285i	0.0775329	+	0.539253i
$809$	−11.7142	−	25.6505i	−0.411849	−	0.901823i	−0.995930	−	0.0901279i	$-0.971272\pi$
$809$	−11.7142	−	25.6505i	−0.411849	−	0.901823i	0.584081	−	0.811695i	$-0.301455\pi$
$810$	−19.0590	−	5.59623i	−0.669665	−	0.196631i
$811$	16.1325	−	35.3253i	0.566490	−	1.24044i	−0.382155	−	0.924098i	$-0.624818\pi$
$811$	16.1325	−	35.3253i	0.566490	−	1.24044i	0.948645	−	0.316342i	$-0.102455\pi$
$812$	−2.45610	+	2.83450i	−0.0861924	+	0.0994713i
$813$	8.45439	−	58.8016i	0.296508	−	2.06226i
$814$	−0.426792	+	0.125317i	−0.0149590	+	0.00439237i
$815$	4.45331	+	5.13939i	0.155993	+	0.180025i
$816$	−8.91739	+	5.73086i	−0.312171	+	0.200620i
$817$	18.8829	−	12.1353i	0.660629	−	0.424560i
$818$	−5.11388	−	5.90173i	−0.178803	−	0.206349i
$819$	12.7546	−	3.74510i	0.445683	−	0.130864i
$820$	1.27506	−	8.86821i	0.0445269	−	0.309691i
$821$	−18.0697	+	20.8536i	−0.630639	+	0.727796i	−0.977691	−	0.210050i	$-0.932637\pi$
$821$	−18.0697	+	20.8536i	−0.630639	+	0.727796i	0.347052	+	0.937846i	$0.387183\pi$
$822$	12.3064	−	26.9472i	0.429235	−	0.939893i
$823$	13.6562	+	4.00983i	0.476026	+	0.139774i	0.510940	−	0.859616i	$-0.329297\pi$
$823$	13.6562	+	4.00983i	0.476026	+	0.139774i	−0.0349138	+	0.999390i	$0.511116\pi$
$824$	−5.22914	−	11.4502i	−0.182166	−	0.398888i
$825$	−0.231533	−	1.61035i	−0.00806094	−	0.0560651i
$826$	−6.45117	−	4.14592i	−0.224465	−	0.144255i
$827$	24.4713			0.850952			0.425476	−	0.904970i	$-0.360107\pi$
$827$	24.4713			0.850952			0.425476	+	0.904970i	$0.360107\pi$
$828$	12.5523	+	4.00488i	0.436223	+	0.139179i
$829$	−0.351641			−0.0122130			−0.00610649	−	0.999981i	$-0.501944\pi$
$829$	−0.351641			−0.0122130			−0.00610649	+	0.999981i	$0.501944\pi$
$830$	−17.4137	−	11.1911i	−0.604439	−	0.388449i
$831$	8.07058	+	56.1321i	0.279965	+	1.94720i
$832$	2.01001	+	4.40131i	0.0696845	+	0.152588i
$833$	−4.24248	−	1.24570i	−0.146993	−	0.0431611i
$834$	−11.9206	+	26.1025i	−0.412777	+	0.903856i
$835$	17.8285	−	20.5752i	0.616980	−	0.712033i
$836$	0.344854	−	2.39851i	0.0119270	−	0.0829543i
$837$	0.859031	−	0.252234i	0.0296925	−	0.00871849i
$838$	−2.86628	−	3.30786i	−0.0990139	−	0.114268i
$839$	5.80925	−	3.73338i	0.200558	−	0.128891i	−0.436507	−	0.899701i	$-0.643785\pi$
$839$	5.80925	−	3.73338i	0.200558	−	0.128891i	0.637065	+	0.770810i	$0.280148\pi$
$840$	−4.13245	+	2.65576i	−0.142583	+	0.0916325i
$841$	9.77916	+	11.2857i	0.337212	+	0.389164i
$842$	14.8390	−	4.35712i	0.511385	−	0.150156i
$843$	−8.63948	+	60.0889i	−0.297560	+	2.06957i
$844$	−11.4012	+	13.1577i	−0.392446	+	0.452906i
$845$	−8.86233	+	19.4058i	−0.304874	+	0.667580i
$846$	−17.6022	−	5.16846i	−0.605175	−	0.177695i
$847$	4.27175	+	9.35383i	0.146779	+	0.321402i
$848$	1.68260	+	11.7028i	0.0577808	+	0.401874i
$849$	43.1957	+	27.7602i	1.48247	+	0.952727i
$850$	−3.54386			−0.121554
$851$	1.69371	−	1.86522i	0.0580596	−	0.0639388i
$852$	−24.8170			−0.850217
$853$	17.9368	+	11.5273i	0.614146	+	0.394688i	0.810410	−	0.585864i	$-0.199245\pi$
$853$	17.9368	+	11.5273i	0.614146	+	0.394688i	−0.196264	+	0.980551i	$0.562881\pi$
$854$	0.355188	+	2.47039i	0.0121543	+	0.0845350i
$855$	6.69261	+	14.6548i	0.228882	+	0.501183i
$856$	−2.70850	−	0.795288i	−0.0925747	−	0.0271824i
$857$	−4.84244	+	10.6035i	−0.165415	+	0.362208i	−0.974129	−	0.225995i	$-0.927437\pi$
$857$	−4.84244	+	10.6035i	−0.165415	+	0.362208i	0.808714	+	0.588202i	$0.200164\pi$
$858$	6.43173	−	7.42261i	0.219576	−	0.253404i
$859$	−3.90733	+	27.1761i	−0.133317	+	0.927237i	0.807873	+	0.589357i	$0.200619\pi$
$859$	−3.90733	+	27.1761i	−0.133317	+	0.927237i	−0.941189	+	0.337880i	$0.890290\pi$
$860$	−15.4197	+	4.52763i	−0.525807	+	0.154391i
$861$	−6.86457	−	7.92214i	−0.233944	−	0.269986i
$862$	−30.1466	+	19.3740i	−1.02680	+	0.659882i
$863$	−37.9708	+	24.4024i	−1.29254	+	0.830666i	−0.992379	−	0.123222i	$-0.960677\pi$
$863$	−37.9708	+	24.4024i	−1.29254	+	0.830666i	−0.300163	+	0.953888i	$0.597041\pi$
$864$	−0.396679	−	0.457792i	−0.0134953	−	0.0155744i
$865$	7.29322	−	2.14148i	0.247977	−	0.0728126i
$866$	−4.72723	+	32.8786i	−0.160638	+	1.11726i
$867$	4.00395	−	4.62080i	0.135981	−	0.156931i
$868$	0.613986	−	1.34444i	0.0208401	−	0.0456334i
$869$	5.16836	+	1.51757i	0.175325	+	0.0514799i
$870$	−7.65351	−	16.7588i	−0.259478	−	0.568178i
$871$	−7.66076	−	53.2818i	−0.259575	−	1.80538i
$872$	−7.33819	−	4.71597i	−0.248503	−	0.159703i
$873$	25.9144			0.877069
$874$	5.40992	+	12.6141i	0.182993	+	0.426677i
$875$	−11.8874			−0.401868
$876$	21.6068	+	13.8858i	0.730026	+	0.469159i
$877$	3.21500	+	22.3608i	0.108563	+	0.755072i	0.969275	+	0.245980i	$0.0791097\pi$
$877$	3.21500	+	22.3608i	0.108563	+	0.755072i	−0.860712	+	0.509092i	$0.829981\pi$
$878$	−2.10020	−	4.59879i	−0.0708782	−	0.155202i
$879$	27.3901	+	8.04246i	0.923845	+	0.271265i
$880$	−0.720709	+	1.57813i	−0.0242951	+	0.0531988i
$881$	−31.5449	+	36.4047i	−1.06277	+	1.22651i	−0.0897101	+	0.995968i	$0.528594\pi$
$881$	−31.5449	+	36.4047i	−1.06277	+	1.22651i	−0.973063	+	0.230538i	$0.925951\pi$
$882$	−0.390986	+	2.71936i	−0.0131652	+	0.0915657i
$883$	−18.7429	+	5.50341i	−0.630748	+	0.185204i	−0.581453	−	0.813580i	$-0.697516\pi$
$883$	−18.7429	+	5.50341i	−0.630748	+	0.185204i	−0.0492952	+	0.998784i	$0.515697\pi$
$884$	−14.0101	−	16.1686i	−0.471212	−	0.543808i
$885$	31.6898	−	20.3658i	1.06524	−	0.684588i
$886$	−1.71417	+	1.10163i	−0.0575888	+	0.0370101i
$887$	19.8185	+	22.8717i	0.665439	+	0.767958i	0.983656	−	0.180060i	$-0.0576292\pi$
$887$	19.8185	+	22.8717i	0.665439	+	0.767958i	−0.318216	+	0.948018i	$0.603084\pi$
$888$	1.20842	−	0.354825i	0.0405520	−	0.0119071i
$889$	0.0365804	−	0.254423i	0.00122687	−	0.00853306i
$890$	−15.0520	+	17.3709i	−0.504544	+	0.582275i
$891$	−3.40975	+	7.46632i	−0.114231	+	0.250131i
$892$	−28.2581	−	8.29733i	−0.946151	−	0.277815i
$893$	−7.93874	−	17.3834i	−0.265660	−	0.581714i
$894$	6.72337	+	46.7621i	0.224863	+	1.56396i
$895$	−29.7803	−	19.1386i	−0.995446	−	0.639734i
$896$	−1.00000			−0.0334077
$897$	−9.19484	+	54.8653i	−0.307007	+	1.83190i
$898$	29.0589			0.969707
$899$	4.66338	+	2.99698i	0.155533	+	0.0999547i
$900$	0.313372	+	2.17955i	0.0104457	+	0.0726516i
$901$	−21.7166	−	47.5526i	−0.723484	−	1.58421i
$902$	−3.55225	−	1.04303i	−0.118277	−	0.0347292i
$903$	−7.81091	+	17.1035i	−0.259931	+	0.569169i
$904$	9.63108	−	11.1149i	0.320325	−	0.369675i
$905$	−1.24681	+	8.67174i	−0.0414453	+	0.288258i
$906$	9.82797	−	2.88575i	0.326512	−	0.0958727i
$907$	2.24203	+	2.58744i	0.0744454	+	0.0859146i	0.791750	−	0.610845i	$-0.209170\pi$
$907$	2.24203	+	2.58744i	0.0744454	+	0.0859146i	−0.717305	+	0.696759i	$0.754625\pi$
$908$	18.4860	−	11.8802i	0.613479	−	0.394259i
$909$	−35.7914	+	23.0018i	−1.18713	+	0.762920i
$910$	−6.49250	−	7.49275i	−0.215224	−	0.248382i
$911$	1.60622	−	0.471628i	0.0532163	−	0.0156257i	−0.255016	−	0.966937i	$-0.582081\pi$
$911$	1.60622	−	0.471628i	0.0532163	−	0.0156257i	0.308232	+	0.951311i	$0.400263\pi$
$912$	−0.976424	+	6.79118i	−0.0323326	+	0.224878i
$913$	−5.60140	+	6.46436i	−0.185379	+	0.213939i
$914$	−0.0447670	+	0.0980261i	−0.00148076	+	0.00324242i
$915$	−11.7633	−	3.45403i	−0.388884	−	0.114187i
$916$	−3.74484	−	8.20005i	−0.123733	−	0.270937i
$917$	−0.219733	−	1.52827i	−0.00725621	−	0.0504681i
$918$	2.25318	+	1.44803i	0.0743659	+	0.0477921i
$919$	−6.89729			−0.227520			−0.113760	−	0.993508i	$-0.536290\pi$
$919$	−6.89729			−0.227520			−0.113760	+	0.993508i	$0.536290\pi$
$920$	−1.17203	−	9.75664i	−0.0386405	−	0.321667i
$921$	73.3744			2.41777
$922$	−18.4833	−	11.8785i	−0.608714	−	0.391197i
$923$	−7.12825	−	49.5780i	−0.234629	−	1.63188i
$924$	0.843229	+	1.84641i	0.0277402	+	0.0607425i
$925$	0.404003	+	0.118626i	0.0132836	+	0.00390040i
$926$	−6.11255	+	13.3846i	−0.200871	+	0.439846i
$927$	22.6468	−	26.1359i	0.743820	−	0.858414i
$928$	0.533762	−	3.71240i	0.0175216	−	0.121865i
$929$	4.52308	−	1.32810i	0.148397	−	0.0435734i	−0.206690	−	0.978406i	$-0.566269\pi$
$929$	4.52308	−	1.32810i	0.148397	−	0.0435734i	0.355088	+	0.934833i	$0.384451\pi$
$930$	4.75451	+	5.48700i	0.155907	+	0.179926i
$931$	−2.40759	+	1.54726i	−0.0789055	+	0.0507095i
$932$	4.15813	−	2.67227i	0.136204	−	0.0875330i
$933$	23.3575	+	26.9560i	0.764690	+	0.882499i
$934$	15.8797	−	4.66269i	0.519599	−	0.152568i
$935$	1.09171	−	7.59298i	0.0357026	−	0.248317i
$936$	−8.70513	+	10.0463i	−0.284536	+	0.328372i
$937$	−12.0745	+	26.4395i	−0.394457	+	0.863741i	0.603345	+	0.797480i	$0.293834\pi$
$937$	−12.0745	+	26.4395i	−0.394457	+	0.863741i	−0.997802	+	0.0662608i	$0.978893\pi$
$938$	10.6745	+	3.13432i	0.348535	+	0.102339i
$939$	−7.38752	−	16.1764i	−0.241083	−	0.527897i
$940$	1.94720	+	13.5431i	0.0635108	+	0.441727i
$941$	−23.0601	−	14.8198i	−0.751738	−	0.483113i	0.107808	−	0.994172i	$-0.465617\pi$
$941$	−23.0601	−	14.8198i	−0.751738	−	0.483113i	−0.859546	+	0.511059i	$0.829253\pi$
$942$	−46.5413			−1.51640
$943$	20.2523	−	5.43860i	0.659506	−	0.177105i
$944$	7.66852			0.249589
$945$	1.04415	+	0.671038i	0.0339664	+	0.0218289i
$946$	0.945076	+	6.57315i	0.0307271	+	0.213711i
$947$	−20.8688	−	45.6963i	−0.678144	−	1.48493i	−0.864597	−	0.502465i	$-0.832426\pi$
$947$	−20.8688	−	45.6963i	−0.678144	−	1.48493i	0.186453	−	0.982464i	$-0.440301\pi$
$948$	−14.6337	−	4.29686i	−0.475282	−	0.139555i
$949$	−21.5342	+	47.1533i	−0.699029	+	1.53066i
$950$	−1.50212	+	1.73354i	−0.0487351	+	0.0562433i
$951$	10.7459	−	74.7395i	0.348460	−	2.42359i
$952$	4.24248	−	1.24570i	0.137499	−	0.0403735i
$953$	−32.5173	−	37.5269i	−1.05334	−	1.21562i	−0.975809	−	0.218626i	$-0.929842\pi$
$953$	−32.5173	−	37.5269i	−1.05334	−	1.21562i	−0.0775288	−	0.996990i	$-0.524703\pi$
$954$	−27.3255	+	17.5611i	−0.884697	+	0.568560i
$955$	−13.9553	+	8.96850i	−0.451582	+	0.290214i
$956$	14.1918	+	16.3782i	0.458996	+	0.529709i
$957$	−7.30471	+	2.14486i	−0.236128	+	0.0693333i
$958$	−1.55563	+	10.8196i	−0.0502601	+	0.349566i
$959$	−8.09216	+	9.33885i	−0.261310	+	0.301567i
$960$	2.04062	−	4.46834i	0.0658608	−	0.144215i
$961$	27.6483	+	8.11826i	0.891880	+	0.261879i
$962$	1.05595	+	2.31220i	0.0340451	+	0.0745483i
$963$	−1.10369	−	7.67635i	−0.0355660	−	0.247367i
$964$	21.0569	+	13.5325i	0.678198	+	0.435851i
$965$	−45.2951			−1.45810
$966$	−9.52507	−	6.43907i	−0.306464	−	0.207174i
$967$	−28.3248			−0.910865			−0.455432	−	0.890270i	$-0.650515\pi$
$967$	−28.3248			−0.910865			−0.455432	+	0.890270i	$0.650515\pi$
$968$	−8.65069	−	5.55946i	−0.278044	−	0.178688i
$969$	−4.31734	−	30.0278i	−0.138693	−	0.964631i
$970$	−8.02897	−	17.5810i	−0.257795	−	0.564492i
$971$	43.7378	+	12.8426i	1.40361	+	0.412137i	0.893923	−	0.448221i	$-0.147942\pi$
$971$	43.7378	+	12.8426i	1.40361	+	0.412137i	0.509689	+	0.860359i	$0.329761\pi$
$972$	8.89951	−	19.4872i	0.285452	−	0.625052i
$973$	7.83849	−	9.04610i	0.251290	−	0.290005i
$974$	−3.38256	+	23.5262i	−0.108384	+	0.753828i
$975$	−8.92052	+	2.61930i	−0.285685	+	0.0838847i
$976$	−1.63440	−	1.88619i	−0.0523158	−	0.0603756i
$977$	2.79014	−	1.79311i	0.0892645	−	0.0573668i	−0.495247	−	0.868752i	$-0.664922\pi$
$977$	2.79014	−	1.79311i	0.0892645	−	0.0573668i	0.584512	+	0.811385i	$0.301286\pi$
$978$	−6.69339	+	4.30158i	−0.214031	+	0.137549i
$979$	6.21981	+	7.17804i	0.198786	+	0.229411i
$980$	1.96603	−	0.577277i	0.0628024	−	0.0184404i
$981$	3.41054	−	23.7208i	0.108890	−	0.757347i
$982$	−17.1541	+	19.7969i	−0.547411	+	0.631746i
$983$	4.50231	−	9.85869i	0.143602	−	0.314444i	−0.824141	−	0.566385i	$-0.808342\pi$
$983$	4.50231	−	9.85869i	0.143602	−	0.314444i	0.967743	+	0.251941i	$0.0810689\pi$
$984$	10.0579	+	2.95326i	0.320633	+	0.0941464i
$985$	−6.03363	−	13.2118i	−0.192247	−	0.420963i
$986$	2.36007	+	16.4147i	0.0751601	+	0.522750i
$987$	13.4671	+	8.65477i	0.428662	+	0.275484i
$988$	−13.8475			−0.440547
$989$	−23.9645	−	28.9917i	−0.762028	−	0.921882i
$990$	−4.76637			−0.151485
$991$	−26.6275	−	17.1124i	−0.845849	−	0.543594i	0.0444285	−	0.999013i	$-0.485853\pi$
$991$	−26.6275	−	17.1124i	−0.845849	−	0.543594i	−0.890278	+	0.455418i	$0.849490\pi$
$992$	0.210342	+	1.46296i	0.00667838	+	0.0464491i
$993$	−29.6535	−	64.9321i	−0.941026	−	2.06056i
$994$	9.93250	+	2.91645i	0.315040	+	0.0925040i
$995$	−0.200197	+	0.438369i	−0.00634666	+	0.0138972i
$996$	15.8599	−	18.3032i	0.502539	−	0.579961i
$997$	−0.351200	+	2.44265i	−0.0111226	+	0.0773595i	−0.994627	−	0.103526i	$-0.966987\pi$
$997$	−0.351200	+	2.44265i	−0.0111226	+	0.0773595i	0.983504	+	0.180886i	$0.0578965\pi$
$998$	−11.5263	+	3.38441i	−0.364857	+	0.107132i
$999$	−0.208393	−	0.240498i	−0.00659327	−	0.00760903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.71.4	✓	40
23.9	even	11		7406.2.a.bu.1.3		20
23.12	even	11	inner	322.2.i.d.127.4	yes	40
23.14	odd	22		7406.2.a.bv.1.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.71.4	✓	40	1.1	even	1	trivial
322.2.i.d.127.4	yes	40	23.12	even	11	inner
7406.2.a.bu.1.3		20	23.9	even	11
7406.2.a.bv.1.3		20	23.14	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.341180 + 2.37296i) q^{3} +(0.415415 + 0.909632i) q^{4} +(1.96603 + 0.577277i) q^{5} +(-0.995899 + 2.18071i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-2.63604 + 0.774012i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.341180 + 2.37296i) q^{3} +(0.415415 + 0.909632i) q^{4} +(1.96603 + 0.577277i) q^{5} +(-0.995899 + 2.18071i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-2.63604 + 0.774012i) q^{9} +(1.34183 + 1.54855i) q^{10} +(0.712290 - 0.457761i) q^{11} +(-2.01679 + 1.29611i) q^{12} +(-3.16858 - 3.65674i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-0.699086 + 4.86225i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.83679 - 4.02201i) q^{17} +(-2.63604 - 0.774012i) q^{18} +(-1.18888 - 2.60328i) q^{19} +(0.291607 + 2.02817i) q^{20} +(2.01679 + 1.29611i) q^{21} +0.846701 q^{22} +(-4.09369 + 2.49834i) q^{23} -2.39736 q^{24} +(-0.674258 - 0.433319i) q^{25} +(-0.688598 - 4.78931i) q^{26} +(0.251636 + 0.551006i) q^{27} +(0.959493 + 0.281733i) q^{28} +(-1.55805 + 3.41164i) q^{29} +(-3.21684 + 3.71243i) q^{30} +(0.210342 - 1.46296i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(1.32927 + 1.53406i) q^{33} +(3.71967 - 2.39049i) q^{34} +(1.72375 - 1.10779i) q^{35} +(-1.79912 - 2.07629i) q^{36} +(-0.504064 + 0.148007i) q^{37} +(0.407292 - 2.83278i) q^{38} +(7.59622 - 8.76651i) q^{39} +(-0.851196 + 1.86386i) q^{40} +(-4.19540 - 1.23188i) q^{41} +(0.995899 + 2.18071i) q^{42} +(1.11619 + 7.76324i) q^{43} +(0.712290 + 0.457761i) q^{44} -5.62935 q^{45} +(-4.79454 - 0.111477i) q^{46} +6.67750 q^{47} +(-2.01679 - 1.29611i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.332952 - 0.729063i) q^{50} +(10.1707 + 2.98640i) q^{51} +(2.01001 - 4.40131i) q^{52} +(7.74248 - 8.93530i) q^{53} +(-0.0862066 + 0.599580i) q^{54} +(1.66464 - 0.488781i) q^{55} +(0.654861 + 0.755750i) q^{56} +(5.77185 - 3.70934i) q^{57} +(-3.15518 + 2.02771i) q^{58} +(-5.02182 - 5.79548i) q^{59} +(-4.71327 + 1.38394i) q^{60} +(-0.355188 + 2.47039i) q^{61} +(0.967889 - 1.11700i) q^{62} +(-1.14128 + 2.49906i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-4.11856 - 9.01839i) q^{65} +(0.288877 + 2.00919i) q^{66} +(9.35908 + 6.01471i) q^{67} +4.42158 q^{68} +(-7.32514 - 8.86176i) q^{69} +2.04903 q^{70} +(8.70851 + 5.59662i) q^{71} +(-0.390986 - 2.71936i) q^{72} +(-4.45054 - 9.74532i) q^{73} +(-0.504064 - 0.148007i) q^{74} +(0.798205 - 1.74783i) q^{75} +(1.87415 - 2.16288i) q^{76} +(0.120498 - 0.838083i) q^{77} +(11.1299 - 3.26803i) q^{78} +(4.16610 + 4.80794i) q^{79} +(-1.72375 + 1.10779i) q^{80} +(-8.15526 + 5.24107i) q^{81} +(-2.86339 - 3.30453i) q^{82} +(-9.69302 + 2.84613i) q^{83} +(-0.341180 + 2.37296i) q^{84} +(5.93300 - 6.84704i) q^{85} +(-3.25813 + 7.13431i) q^{86} +(-8.62726 - 2.53319i) q^{87} +(0.351732 + 0.770186i) q^{88} +(1.59642 + 11.1034i) q^{89} +(-4.73571 - 3.04345i) q^{90} -4.83856 q^{91} +(-3.97315 - 2.68590i) q^{92} +3.54331 q^{93} +(5.61747 + 3.61013i) q^{94} +(-0.834551 - 5.80443i) q^{95} +(-0.995899 - 2.18071i) q^{96} +(-9.05049 - 2.65746i) q^{97} +(0.415415 - 0.909632i) q^{98} +(-1.52331 + 1.75800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

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Database

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