LMFDB - Embedded newform 175.2.x.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0374168 + 0.00196093i) q^{2} +(0.0687711 - 0.0849253i) q^{3} +(-1.98765 + 0.208910i) q^{4} +(-0.633655 + 2.14441i) q^{5} +(-0.00240666 + 0.00331248i) q^{6} +(-2.20341 + 1.46457i) q^{7} +(0.147975 - 0.0234370i) q^{8} +(0.621252 + 2.92276i) q^{9} +O(q^{10})$	\(q+(-0.0374168 + 0.00196093i) q^{2} +(0.0687711 - 0.0849253i) q^{3} +(-1.98765 + 0.208910i) q^{4} +(-0.633655 + 2.14441i) q^{5} +(-0.00240666 + 0.00331248i) q^{6} +(-2.20341 + 1.46457i) q^{7} +(0.147975 - 0.0234370i) q^{8} +(0.621252 + 2.92276i) q^{9} +(0.0195043 - 0.0814793i) q^{10} +(-1.34592 - 0.286085i) q^{11} +(-0.118951 + 0.183169i) q^{12} +(1.43400 - 0.730661i) q^{13} +(0.0795726 - 0.0591203i) q^{14} +(0.138537 + 0.201287i) q^{15} +(3.90435 - 0.829896i) q^{16} +(-1.56486 + 4.07660i) q^{17} +(-0.0289766 - 0.108142i) q^{18} +(-0.00716074 + 0.0681299i) q^{19} +(0.811494 - 4.39470i) q^{20} +(-0.0271520 + 0.287846i) q^{21} +(0.0509210 + 0.00806510i) q^{22} +(-0.295550 - 5.63942i) q^{23} +(0.00818604 - 0.0141786i) q^{24} +(-4.19696 - 2.71763i) q^{25} +(-0.0522229 + 0.0301509i) q^{26} +(0.583044 + 0.297076i) q^{27} +(4.07364 - 3.37137i) q^{28} +(3.88840 + 5.35192i) q^{29} +(-0.00557832 - 0.00725983i) q^{30} +(1.42674 + 3.20452i) q^{31} +(-0.433891 + 0.116261i) q^{32} +(-0.116856 + 0.0946285i) q^{33} +(0.0505580 - 0.155602i) q^{34} +(-1.74444 - 5.65305i) q^{35} +(-1.84543 - 5.67963i) q^{36} +(-6.49205 - 4.21599i) q^{37} +(0.000134334 - 0.00256324i) q^{38} +(0.0365664 - 0.172031i) q^{39} +(-0.0435068 + 0.332170i) q^{40} +(9.12263 + 2.96412i) q^{41} +(0.000451493 - 0.0108235i) q^{42} +(-3.38639 + 3.38639i) q^{43} +(2.73499 + 0.287459i) q^{44} +(-6.66125 - 0.519805i) q^{45} +(0.0221170 + 0.210429i) q^{46} +(6.65520 - 2.55469i) q^{47} +(0.198028 - 0.388651i) q^{48} +(2.71005 - 6.45412i) q^{49} +(0.162366 + 0.0934549i) q^{50} +(0.238589 + 0.413248i) q^{51} +(-2.69765 + 1.75187i) q^{52} +(2.30489 + 1.86647i) q^{53} +(-0.0223982 - 0.00997230i) q^{54} +(1.46633 - 2.70493i) q^{55} +(-0.291725 + 0.268362i) q^{56} +(0.00529350 + 0.00529350i) q^{57} +(-0.155986 - 0.192627i) q^{58} +(6.88713 + 7.64893i) q^{59} +(-0.317414 - 0.371145i) q^{60} +(5.62046 + 5.06069i) q^{61} +(-0.0596680 - 0.117105i) q^{62} +(-5.64947 - 5.53018i) q^{63} +(-7.57643 + 2.46173i) q^{64} +(0.658171 + 3.53807i) q^{65} +(0.00418683 - 0.00376984i) q^{66} +(-8.28713 - 3.18113i) q^{67} +(2.25874 - 8.42975i) q^{68} +(-0.499255 - 0.362730i) q^{69} +(0.0763564 + 0.208098i) q^{70} +(5.52909 - 4.01712i) q^{71} +(0.160431 + 0.417936i) q^{72} +(-0.233558 - 0.359648i) q^{73} +(0.251179 + 0.145018i) q^{74} +(-0.519425 + 0.169534i) q^{75} -0.136914i q^{76} +(3.38461 - 1.34084i) q^{77} +(-0.00103085 + 0.00650856i) q^{78} +(-3.70296 + 8.31698i) q^{79} +(-0.694378 + 8.89839i) q^{80} +(-8.12386 + 3.61697i) q^{81} +(-0.347152 - 0.0930190i) q^{82} +(0.663758 + 4.19080i) q^{83} +(-0.00616537 - 0.577808i) q^{84} +(-7.75030 - 5.93885i) q^{85} +(0.120067 - 0.133348i) q^{86} +(0.721923 + 0.0378344i) q^{87} +(-0.205868 - 0.0107891i) q^{88} +(-5.38706 + 5.98294i) q^{89} +(0.250262 + 0.00638718i) q^{90} +(-2.08959 + 3.71015i) q^{91} +(1.76558 + 11.1474i) q^{92} +(0.370263 + 0.0992118i) q^{93} +(-0.244007 + 0.108639i) q^{94} +(-0.141561 - 0.0585264i) q^{95} +(-0.0199657 + 0.0448436i) q^{96} +(-2.59509 + 16.3848i) q^{97} +(-0.0887454 + 0.246806i) q^{98} -4.11154i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.0374168	+	0.00196093i	−0.0264576	+	0.00138659i	−0.0655602	−	0.997849i	$-0.520883\pi$
$2$	−0.0374168	+	0.00196093i	−0.0264576	+	0.00138659i	0.0391025	+	0.999235i	$0.487550\pi$
$3$	0.0687711	−	0.0849253i	0.0397050	−	0.0490316i	−0.756907	−	0.653523i	$-0.773290\pi$
$3$	0.0687711	−	0.0849253i	0.0397050	−	0.0490316i	0.796612	+	0.604491i	$0.206624\pi$
$4$	−1.98765	+	0.208910i	−0.993824	+	0.104455i
$5$	−0.633655	+	2.14441i	−0.283379	+	0.959008i
$5$	−0.633655	+	2.14441i	−0.283379	+	0.959008i
$6$	−0.00240666	+	0.00331248i	−0.000982515	+	0.00135232i
$7$	−2.20341	+	1.46457i	−0.832812	+	0.553556i
$7$	−2.20341	+	1.46457i	−0.832812	+	0.553556i
$8$	0.147975	−	0.0234370i	0.0523172	−	0.00828623i
$9$	0.621252	+	2.92276i	0.207084	+	0.974254i
$10$	0.0195043	−	0.0814793i	0.00616780	−	0.0257660i
$11$	−1.34592	−	0.286085i	−0.405811	−	0.0862578i	0.000483800	−	1.00000i	$-0.499846\pi$
$11$	−1.34592	−	0.286085i	−0.405811	−	0.0862578i	−0.406295	+	0.913742i	$0.633179\pi$
$12$	−0.118951	+	0.183169i	−0.0343382	+	0.0528762i
$13$	1.43400	−	0.730661i	0.397721	−	0.202649i	−0.243679	−	0.969856i	$-0.578354\pi$
$13$	1.43400	−	0.730661i	0.397721	−	0.202649i	0.641399	+	0.767207i	$0.278354\pi$
$14$	0.0795726	−	0.0591203i	0.0212667	−	0.0158006i
$15$	0.138537	+	0.201287i	0.0357701	+	0.0519720i
$16$	3.90435	−	0.829896i	0.976088	−	0.207474i
$17$	−1.56486	+	4.07660i	−0.379534	+	0.988720i	0.602180	+	0.798360i	$0.294299\pi$
$17$	−1.56486	+	4.07660i	−0.379534	+	0.988720i	−0.981714	+	0.190360i	$0.939035\pi$
$18$	−0.0289766	−	0.108142i	−0.00682984	−	0.0254893i
$19$	−0.00716074	+	0.0681299i	−0.00164279	+	0.0156301i	−0.995313	−	0.0967102i	$-0.969168\pi$
$19$	−0.00716074	+	0.0681299i	−0.00164279	+	0.0156301i	0.993670	+	0.112340i	$0.0358347\pi$
$20$	0.811494	−	4.39470i	0.181456	−	0.982685i
$21$	−0.0271520	+	0.287846i	−0.00592504	+	0.0628131i
$22$	0.0509210	+	0.00806510i	0.0108564	+	0.00171949i
$23$	−0.295550	−	5.63942i	−0.0616263	−	1.17590i	−0.838015	−	0.545647i	$-0.816284\pi$
$23$	−0.295550	−	5.63942i	−0.0616263	−	1.17590i	0.776389	−	0.630254i	$-0.217049\pi$
$24$	0.00818604	−	0.0141786i	0.00167097	−	0.00289420i
$25$	−4.19696	−	2.71763i	−0.839393	−	0.543526i
$26$	−0.0522229	+	0.0301509i	−0.0102418	+	0.00591308i
$27$	0.583044	+	0.297076i	0.112207	+	0.0571722i
$28$	4.07364	−	3.37137i	0.769846	−	0.637129i
$29$	3.88840	+	5.35192i	0.722058	+	0.993827i	0.999453	+	0.0330712i	$0.0105288\pi$
$29$	3.88840	+	5.35192i	0.722058	+	0.993827i	−0.277395	+	0.960756i	$0.589471\pi$
$30$	−0.00557832	−	0.00725983i	−0.00101846	−	0.00132546i
$31$	1.42674	+	3.20452i	0.256251	+	0.575549i	0.995161	−	0.0982550i	$-0.0313261\pi$
$31$	1.42674	+	3.20452i	0.256251	+	0.575549i	−0.738911	+	0.673804i	$0.764659\pi$
$32$	−0.433891	+	0.116261i	−0.0767017	+	0.0205522i
$33$	−0.116856	+	0.0946285i	−0.0203421	+	0.0164727i
$34$	0.0505580	−	0.155602i	0.00867063	−	0.0266855i
$35$	−1.74444	−	5.65305i	−0.294864	−	0.955539i
$36$	−1.84543	−	5.67963i	−0.307571	−	0.946606i
$37$	−6.49205	−	4.21599i	−1.06729	−	0.693104i	−0.113485	−	0.993540i	$-0.536201\pi$
$37$	−6.49205	−	4.21599i	−1.06729	−	0.693104i	−0.953802	+	0.300436i	$0.902868\pi$
$38$	0.000134334	−	0.00256324i	2.17918e−5	−	0.000415813i
$39$	0.0365664	−	0.172031i	0.00585531	−	0.0275471i
$40$	−0.0435068	+	0.332170i	−0.00687904	+	0.0525207i
$41$	9.12263	+	2.96412i	1.42472	+	0.462918i	0.917097	−	0.398664i	$-0.130526\pi$
$41$	9.12263	+	2.96412i	1.42472	+	0.462918i	0.507618	+	0.861582i	$0.330526\pi$
$42$	0.000451493	−	0.0108235i	6.96669e−5	−	0.00167010i
$43$	−3.38639	+	3.38639i	−0.516420	+	0.516420i	−0.916486	−	0.400067i	$-0.868987\pi$
$43$	−3.38639	+	3.38639i	−0.516420	+	0.516420i	0.400067	+	0.916486i	$0.368987\pi$
$44$	2.73499	+	0.287459i	0.412315	+	0.0433360i
$45$	−6.66125	−	0.519805i	−0.993001	−	0.0774880i
$46$	0.0221170	+	0.210429i	0.00326098	+	0.0310261i
$47$	6.65520	−	2.55469i	0.970761	−	0.372640i	0.179256	−	0.983803i	$-0.442631\pi$
$47$	6.65520	−	2.55469i	0.970761	−	0.372640i	0.791505	+	0.611162i	$0.209298\pi$
$48$	0.198028	−	0.388651i	0.0285828	−	0.0560970i
$49$	2.71005	−	6.45412i	0.387151	−	0.922016i
$50$	0.162366	+	0.0934549i	0.0229620	+	0.0132165i
$51$	0.238589	+	0.413248i	0.0334091	+	0.0578663i
$52$	−2.69765	+	1.75187i	−0.374097	+	0.242941i
$53$	2.30489	+	1.86647i	0.316601	+	0.256379i	0.774427	−	0.632663i	$-0.218038\pi$
$53$	2.30489	+	1.86647i	0.316601	+	0.256379i	−0.457826	+	0.889042i	$0.651372\pi$
$54$	−0.0223982	−	0.00997230i	−0.00304800	−	0.00135706i
$55$	1.46633	−	2.70493i	0.197720	−	0.364732i
$56$	−0.291725	+	0.268362i	−0.0389835	+	0.0358614i
$57$	0.00529350	+	0.00529350i	0.000701141	+	0.000701141i
$58$	−0.155986	−	0.192627i	−0.0204820	−	0.0252931i
$59$	6.88713	+	7.64893i	0.896627	+	0.995806i	0.999999	+	0.00116291i	$0.000370164\pi$
$59$	6.88713	+	7.64893i	0.896627	+	0.995806i	−0.103372	+	0.994643i	$0.532963\pi$
$60$	−0.317414	−	0.371145i	−0.0409780	−	0.0479146i
$61$	5.62046	+	5.06069i	0.719626	+	0.647954i	0.945283	−	0.326253i	$-0.105786\pi$
$61$	5.62046	+	5.06069i	0.719626	+	0.647954i	−0.225656	+	0.974207i	$0.572453\pi$
$62$	−0.0596680	−	0.117105i	−0.00757784	−	0.0148723i
$63$	−5.64947	−	5.53018i	−0.711767	−	0.696737i
$64$	−7.57643	+	2.46173i	−0.947053	+	0.307716i
$65$	0.658171	+	3.53807i	0.0816361	+	0.438844i
$66$	0.00418683	−	0.00376984i	0.000515363	−	0.000464035i
$67$	−8.28713	−	3.18113i	−1.01243	−	0.388637i	−0.205106	−	0.978740i	$-0.565754\pi$
$67$	−8.28713	−	3.18113i	−1.01243	−	0.388637i	−0.807328	+	0.590103i	$0.799087\pi$
$68$	2.25874	−	8.42975i	0.273913	−	1.02226i
$69$	−0.499255	−	0.362730i	−0.0601032	−	0.0436675i
$70$	0.0763564	+	0.208098i	0.00912633	+	0.0248725i
$71$	5.52909	−	4.01712i	0.656182	−	0.476744i	−0.209189	−	0.977875i	$-0.567082\pi$
$71$	5.52909	−	4.01712i	0.656182	−	0.476744i	0.865372	+	0.501131i	$0.167082\pi$
$72$	0.160431	+	0.417936i	0.0189069	+	0.0492543i
$73$	−0.233558	−	0.359648i	−0.0273359	−	0.0420936i	0.824738	−	0.565514i	$-0.191322\pi$
$73$	−0.233558	−	0.359648i	−0.0273359	−	0.0420936i	−0.852074	+	0.523421i	$0.824656\pi$
$74$	0.251179	+	0.145018i	0.0291989	+	0.0168580i
$75$	−0.519425	+	0.169534i	−0.0599781	+	0.0195761i
$76$		−	0.136914i		−	0.0157051i
$77$	3.38461	−	1.34084i	0.385713	−	0.152803i
$78$	−0.00103085	+	0.00650856i	−0.000116721	+	0.000736949i
$79$	−3.70296	+	8.31698i	−0.416616	+	0.935734i	0.576336	+	0.817213i	$0.304482\pi$
$79$	−3.70296	+	8.31698i	−0.416616	+	0.935734i	−0.992952	+	0.118521i	$0.962185\pi$
$80$	−0.694378	+	8.89839i	−0.0776338	+	0.994870i
$81$	−8.12386	+	3.61697i	−0.902651	+	0.401886i
$82$	−0.347152	−	0.0930190i	−0.0383365	−	0.0102722i
$83$	0.663758	+	4.19080i	0.0728569	+	0.460000i	0.996964	+	0.0778662i	$0.0248107\pi$
$83$	0.663758	+	4.19080i	0.0728569	+	0.460000i	−0.924107	+	0.382134i	$0.875189\pi$
$84$	−0.00616537	−	0.577808i	−0.000672697	−	0.0630440i
$85$	−7.75030	−	5.93885i	−0.840638	−	0.644159i
$86$	0.120067	−	0.133348i	0.0129472	−	0.0143793i
$87$	0.721923	+	0.0378344i	0.0773983	+	0.00405627i
$88$	−0.205868	−	0.0107891i	−0.0219456	−	0.00115012i
$89$	−5.38706	+	5.98294i	−0.571027	+	0.634190i	−0.957611	−	0.288064i	$-0.906988\pi$
$89$	−5.38706	+	5.98294i	−0.571027	+	0.634190i	0.386584	+	0.922254i	$0.373655\pi$
$90$	0.250262	+	0.00638718i	0.0263799	+	0.000673268i
$91$	−2.08959	+	3.71015i	−0.219049	+	0.388929i
$92$	1.76558	+	11.1474i	0.184075	+	1.16220i
$93$	0.370263	+	0.0992118i	0.0383945	+	0.0102878i
$94$	−0.244007	+	0.108639i	−0.0251674	+	0.0112052i
$95$	−0.141561	−	0.0585264i	−0.0145238	−	0.00600468i
$96$	−0.0199657	+	0.0448436i	−0.00203774	+	0.00457684i
$97$	−2.59509	+	16.3848i	−0.263492	+	1.66362i	0.400814	+	0.916159i	$0.368727\pi$
$97$	−2.59509	+	16.3848i	−0.263492	+	1.66362i	−0.664306	+	0.747461i	$0.731273\pi$
$98$	−0.0887454	+	0.246806i	−0.00896464	+	0.0249312i
$99$		−	4.11154i		−	0.413225i
$100$	8.90982	+	4.52490i	0.890982	+	0.452490i
$101$	−3.41526	−	1.97180i	−0.339831	−	0.196202i	0.320366	−	0.947294i	$-0.396194\pi$
$101$	−3.41526	−	1.97180i	−0.339831	−	0.196202i	−0.660197	+	0.751092i	$0.729527\pi$
$102$	−0.00973757	−	0.0149945i	−0.000964164	−	0.00148468i
$103$	2.75221	+	7.16976i	0.271184	+	0.706457i	0.999769	+	0.0215022i	$0.00684488\pi$
$103$	2.75221	+	7.16976i	0.271184	+	0.706457i	−0.728585	+	0.684955i	$0.759822\pi$
$104$	0.195072	−	0.141728i	0.0191284	−	0.0138976i
$105$	−0.600053	−	0.240620i	−0.0585592	−	0.0234821i
$106$	−0.0899016	−	0.0653174i	−0.00873202	−	0.00634418i
$107$	2.79297	−	10.4235i	0.270006	−	1.00768i	−0.689108	−	0.724659i	$-0.741997\pi$
$107$	2.79297	−	10.4235i	0.270006	−	1.00768i	0.959114	−	0.283019i	$-0.0913359\pi$
$108$	−1.22095	−	0.468678i	−0.117486	−	0.0450986i
$109$	2.14125	−	1.92799i	0.205094	−	0.184668i	−0.560182	−	0.828369i	$-0.689269\pi$
$109$	2.14125	−	1.92799i	0.205094	−	0.184668i	0.765277	+	0.643702i	$0.222602\pi$
$110$	−0.0495612	+	0.104085i	−0.00472548	+	0.00992411i
$111$	−0.804510	+	0.261401i	−0.0763607	+	0.0248111i
$112$	−7.38746	+	7.54681i	−0.698049	+	0.713107i
$113$	4.61149	+	9.05056i	0.433812	+	0.851405i	0.999639	+	0.0268803i	$0.00855729\pi$
$113$	4.61149	+	9.05056i	0.433812	+	0.851405i	−0.565826	+	0.824524i	$0.691443\pi$
$114$	−0.000208446	0	0.000187685i	−1.95227e−5	0	1.75783e-5i
$115$	12.2805	+	2.93967i	1.14516	+	0.274126i
$116$	−8.84684	−	9.82541i	−0.821408	−	0.912266i
$117$	3.02642	+	3.73732i	0.279793	+	0.345516i
$118$	−0.272693	−	0.272693i	−0.0251034	−	0.0251034i
$119$	−2.52244	−	11.2743i	−0.231232	−	1.03351i
$120$	0.0252176	+	0.0265386i	0.00230204	+	0.00242263i
$121$	−8.31934	−	3.70401i	−0.756303	−	0.336728i
$122$	−0.220223	−	0.178333i	−0.0199381	−	0.0161455i
$123$	0.879102	−	0.570896i	0.0792660	−	0.0514759i
$124$	−3.50532	−	6.07139i	−0.314787	−	0.545227i
$125$	8.48713	−	7.27796i	0.759112	−	0.650960i
$126$	0.222229	+	0.195843i	0.0197978	+	0.0174471i
$127$	9.60727	−	18.8553i	0.852507	−	1.67314i	0.119588	−	0.992824i	$-0.461843\pi$
$127$	9.60727	−	18.8553i	0.852507	−	1.67314i	0.732919	−	0.680316i	$-0.238157\pi$
$128$	1.11738	−	0.428922i	0.0987634	−	0.0379117i
$129$	0.0547042	+	0.520476i	0.00481644	+	0.0458253i
$130$	−0.0315645	−	0.131093i	−0.00276839	−	0.0114976i
$131$	−1.73179	−	0.182019i	−0.151307	−	0.0159030i	0.0285719	−	0.999592i	$-0.490904\pi$
$131$	−1.73179	−	0.182019i	−0.151307	−	0.0159030i	−0.179879	+	0.983689i	$0.557571\pi$
$132$	0.212501	−	0.212501i	0.0184958	−	0.0184958i
$133$	−0.0840031	−	0.160606i	−0.00728400	−	0.0139263i
$134$	0.316315	+	0.102777i	0.0273255	+	0.00887859i
$135$	−1.00650	+	1.06204i	−0.0866257	+	0.0914058i
$136$	−0.136017	+	0.639911i	−0.0116634	+	0.0548719i
$137$	−0.333352	+	6.36074i	−0.0284802	+	0.543435i	0.946713	+	0.322079i	$0.104382\pi$
$137$	−0.333352	+	6.36074i	−0.0284802	+	0.543435i	−0.975193	+	0.221356i	$0.928952\pi$
$138$	0.0193918	+	0.0125932i	0.00165074	+	0.00107200i
$139$	−6.65731	−	20.4891i	−0.564665	−	1.73786i	−0.668944	−	0.743313i	$-0.733253\pi$
$139$	−6.65731	−	20.4891i	−0.564665	−	1.73786i	0.104278	−	0.994548i	$-0.466747\pi$
$140$	4.64830	+	10.8718i	0.392853	+	0.918838i
$141$	0.240728	−	0.740884i	0.0202729	−	0.0623937i
$142$	−0.199003	+	0.161150i	−0.0167000	+	0.0135234i
$143$	−2.13909	+	0.573166i	−0.178879	+	0.0479306i
$144$	4.85118	+	10.8959i	0.404265	+	0.907993i
$145$	−13.9406	+	4.94704i	−1.15770	+	0.410829i
$146$	0.00944423	+	0.0129989i	0.000781610	+	0.00107579i
$147$	−0.361744	−	0.674009i	−0.0298361	−	0.0555913i
$148$	13.7847	+	7.02364i	1.13309	+	0.577340i
$149$	16.9996	−	9.81475i	1.39266	−	0.804055i	0.399055	−	0.916927i	$-0.369338\pi$
$149$	16.9996	−	9.81475i	1.39266	−	0.804055i	0.993610	+	0.112871i	$0.0360048\pi$
$150$	0.0191028	−	0.00736196i	0.00155973	−	0.000601102i
$151$	4.56259	−	7.90264i	0.371299	−	0.643108i	−0.618467	−	0.785811i	$-0.712246\pi$
$151$	4.56259	−	7.90264i	0.371299	−	0.643108i	0.989766	+	0.142703i	$0.0455793\pi$
$152$	0.000537147		0.0102494i	4.35684e−5		0.000831334i
$153$	−12.8871	−	2.04111i	−1.04186	−	0.165014i
$154$	−0.124012	+	0.0568068i	−0.00999317	+	0.00457762i
$155$	−7.77586	+	1.02896i	−0.624572	+	0.0826480i
$156$	−0.0367420	+	0.349577i	−0.00294171	+	0.0279885i
$157$	−4.77834	−	17.8330i	−0.381353	−	1.42323i	−0.843836	−	0.536601i	$-0.819708\pi$
$157$	−4.77834	−	17.8330i	−0.381353	−	1.42323i	0.462483	−	0.886628i	$-0.346959\pi$
$158$	0.122244	−	0.318456i	0.00972519	−	0.0253350i
$159$	0.317020	−	0.0673847i	0.0251413	−	0.00534396i
$160$	0.0256268	−	1.00411i	0.00202598	−	0.0793816i
$161$	8.91056	+	11.9931i	0.702250	+	0.945190i
$162$	0.296876	−	0.151266i	0.0233248	−	0.0118846i
$163$	1.88268	−	2.89908i	0.147463	−	0.227073i	−0.757218	−	0.653162i	$-0.773442\pi$
$163$	1.88268	−	2.89908i	0.147463	−	0.227073i	0.904682	+	0.426088i	$0.140109\pi$
$164$	−18.7518	−	3.98582i	−1.46427	−	0.311240i
$165$	−0.128875	−	0.310549i	−0.0100329	−	0.0241762i
$166$	−0.0330535	−	0.155505i	−0.00256545	−	0.0120695i
$167$	13.0850	−	2.07246i	1.01255	−	0.160372i	0.371954	−	0.928251i	$-0.378688\pi$
$167$	13.0850	−	2.07246i	1.01255	−	0.160372i	0.640595	+	0.767879i	$0.278688\pi$
$168$	0.00272842	+	0.0432304i	0.000210502	+	0.00333530i
$169$	−6.11871	+	8.42168i	−0.470670	+	0.647822i
$170$	0.301637	+	0.207015i	0.0231345	+	0.0158773i
$171$	−0.203576	+	0.0213967i	−0.0155679	+	0.00163625i
$172$	6.02350	−	7.43840i	0.459287	−	0.567173i
$173$	−10.1350	+	0.531152i	−0.770549	+	0.0403828i	−0.433559	−	0.901125i	$-0.642742\pi$
$173$	−10.1350	+	0.531152i	−0.770549	+	0.0403828i	−0.336990	+	0.941508i	$0.609409\pi$
$174$	−0.0270862			−0.00205340
$175$	13.2278	−	0.158700i	0.999928	−	0.0119966i
$176$	−5.49238			−0.414003
$177$	1.12322	−	0.0588656i	0.0844266	−	0.00442461i
$178$	0.189834	−	0.234426i	0.0142287	−	0.0175710i
$179$	8.97496	−	0.943306i	0.670820	−	0.0705060i	0.237006	−	0.971508i	$-0.423834\pi$
$179$	8.97496	−	0.943306i	0.670820	−	0.0705060i	0.433814	+	0.901002i	$0.357167\pi$
$180$	13.3488	−	0.358414i	0.994962	−	0.0267146i
$181$	9.31589	−	12.8222i	0.692445	−	0.953069i	−0.307554	−	0.951531i	$-0.599510\pi$
$181$	9.31589	−	12.8222i	0.692445	−	0.953069i	0.999999	−	0.00153805i	$-0.000489576\pi$
$182$	0.0709105	−	0.142919i	0.00525623	−	0.0105939i
$183$	0.816306	−	0.129290i	0.0603430	−	0.00955740i
$184$	−0.175905	−	0.827568i	−0.0129679	−	0.0610091i
$185$	13.1545	−	11.2501i	0.967139	−	0.827125i
$186$	−0.0140486	−	0.00298612i	−0.00103009	−	0.000218953i
$187$	3.27243	−	5.03910i	0.239304	−	0.368495i
$188$	−12.6945	+	6.46817i	−0.925841	+	0.471740i
$189$	−1.71978	+	0.199330i	−0.125095	+	0.0144991i
$190$	0.00541151	+	0.00191228i	0.000392592	+	0.000138731i
$191$	−21.8970	+	4.65434i	−1.58441	+	0.336776i	−0.914158	−	0.405358i	$-0.867147\pi$
$191$	−21.8970	+	4.65434i	−1.58441	+	0.336776i	−0.670251	+	0.742135i	$0.733813\pi$
$192$	−0.311976	+	0.812726i	−0.0225150	+	0.0586535i
$193$	3.15224	+	11.7643i	0.226903	+	0.846814i	0.981633	+	0.190779i	$0.0611013\pi$
$193$	3.15224	+	11.7643i	0.226903	+	0.846814i	−0.754730	+	0.656036i	$0.772232\pi$
$194$	0.0649705	−	0.618153i	0.00466461	−	0.0443808i
$195$	0.345735	+	0.187422i	0.0247586	+	0.0134216i
$196$	−4.03830	+	13.3947i	−0.288450	+	0.956762i
$197$	13.1804	+	2.08757i	0.939067	+	0.148734i	0.607161	−	0.794579i	$-0.292308\pi$
$197$	13.1804	+	2.08757i	0.939067	+	0.148734i	0.331906	+	0.943313i	$0.392308\pi$
$198$	0.00806244	+	0.153841i	0.000572973	+	0.0109330i
$199$	9.16969	−	15.8824i	0.650022	−	1.12587i	−0.333095	−	0.942893i	$-0.608093\pi$
$199$	9.16969	−	15.8824i	0.650022	−	1.12587i	0.983117	−	0.182978i	$-0.0585738\pi$
$200$	−0.684740	−	0.303778i	−0.0484184	−	0.0214803i
$201$	−0.840074	+	0.485017i	−0.0592542	+	0.0342104i
$202$	0.131654	+	0.0670813i	0.00926318	+	0.00471982i
$203$	−16.4060	−	6.09765i	−1.15148	−	0.427971i
$204$	−0.560562	−	0.771548i	−0.0392472	−	0.0540192i
$205$	−12.1369	+	17.6844i	−0.847677	+	1.23513i
$206$	−0.117038	−	0.262872i	−0.00815444	−	0.0183152i
$207$	16.2991	−	4.36732i	1.13286	−	0.303550i
$208$	4.99248	−	4.04283i	0.346166	−	0.280320i
$209$	0.0291287	−	0.0896490i	0.00201488	−	0.00620115i
$210$	0.0229239	+	0.00782655i	0.00158190	+	0.000540083i
$211$	−2.94624	−	9.06760i	−0.202828	−	0.624239i	−0.999796	−	0.0202178i	$-0.993564\pi$
$211$	−2.94624	−	9.06760i	−0.202828	−	0.624239i	0.796968	−	0.604022i	$-0.206436\pi$
$212$	−4.97124	−	3.22836i	−0.341426	−	0.221725i
$213$	0.0390869	−	0.745822i	0.00267819	−	0.0511029i
$214$	−0.0840641	+	0.395490i	−0.00574650	+	0.0270352i
$215$	−5.11599	−	9.40760i	−0.348908	−	0.641593i
$216$	0.0932387	+	0.0302951i	0.00634409	+	0.00206132i
$217$	−7.83695	−	4.97131i	−0.532007	−	0.337474i
$218$	−0.0763379	+	0.0763379i	−0.00517026	+	0.00517026i
$219$	−0.0466053	−	0.00489841i	−0.00314929	−	0.000331004i
$220$	−2.34946	+	5.68277i	−0.158401	+	0.383132i
$221$	0.734597	+	6.98923i	0.0494144	+	0.470146i
$222$	0.0295896	−	0.0113584i	0.00198592	−	0.000762324i
$223$	−11.4092	+	22.3918i	−0.764015	+	1.49946i	0.0994426	+	0.995043i	$0.468294\pi$
$223$	−11.4092	+	22.3918i	−0.764015	+	1.49946i	−0.863458	+	0.504421i	$0.831706\pi$
$224$	0.785768	−	0.891634i	0.0525013	−	0.0595748i
$225$	5.33561	−	13.9551i	0.355707	−	0.930337i
$226$	−0.190294	−	0.329600i	−0.0126582	−	0.0219246i
$227$	10.3775	−	6.73926i	0.688782	−	0.447300i	−0.152210	−	0.988348i	$-0.548639\pi$
$227$	10.3775	−	6.73926i	0.688782	−	0.447300i	0.840992	+	0.541048i	$0.181972\pi$
$228$	−0.0116275	−	0.00941575i	−0.000770048	−	0.000623573i
$229$	13.4922	+	6.00710i	0.891587	+	0.396960i	0.800815	−	0.598912i	$-0.204400\pi$
$229$	13.4922	+	6.00710i	0.891587	+	0.396960i	0.0907719	+	0.995872i	$0.471067\pi$
$230$	−0.465261	−	0.0859117i	−0.0306784	−	0.00566485i
$231$	0.118893	−	0.379650i	0.00782256	−	0.0249791i
$232$	0.700820	+	0.700820i	0.0460111	+	0.0460111i
$233$	−0.763731	−	0.943130i	−0.0500337	−	0.0617865i	0.751515	−	0.659716i	$-0.229324\pi$
$233$	−0.763731	−	0.943130i	−0.0500337	−	0.0617865i	−0.801549	+	0.597930i	$0.795990\pi$
$234$	−0.120568	−	0.133904i	−0.00788175	−	0.00875357i
$235$	1.26120	+	15.8903i	0.0822716	+	1.03657i
$236$	−15.2871	−	13.7646i	−0.995107	−	0.895998i
$237$	0.451665	+	0.886443i	0.0293388	+	0.0575807i
$238$	0.116490	+	0.416900i	0.00755090	+	0.0270236i
$239$	−24.4748	+	7.95235i	−1.58314	+	0.514395i	−0.962864	−	0.269986i	$-0.912981\pi$
$239$	−24.4748	+	7.95235i	−1.58314	+	0.514395i	−0.620280	+	0.784380i	$0.712981\pi$
$240$	0.707945	+	0.670923i	0.0456977	+	0.0433079i
$241$	−10.1804	+	9.16652i	−0.655780	+	0.590467i	−0.928367	−	0.371664i	$-0.878787\pi$
$241$	−10.1804	+	9.16652i	−0.655780	+	0.590467i	0.272587	+	0.962131i	$0.412121\pi$
$242$	0.318546	+	0.122278i	0.0204769	+	0.00786035i
$243$	−0.759601	+	2.83487i	−0.0487284	+	0.181857i
$244$	−12.2287	−	8.88469i	−0.782864	−	0.568784i
$245$	12.1230	+	9.90114i	0.774511	+	0.632561i
$246$	−0.0317737	+	0.0230849i	−0.00202582	+	0.00147184i
$247$	0.0395113	+	0.102931i	0.00251405	+	0.00654931i
$248$	0.286227	+	0.440751i	0.0181754	+	0.0279877i
$249$	0.401552	+	0.231836i	0.0254473	+	0.0146920i
$250$	−0.303289	+	0.288960i	−0.0191817	+	0.0182754i
$251$			24.5816i			1.55158i	0.630992	+	0.775789i	$0.282648\pi$
$251$			24.5816i			1.55158i	−0.630992	+	0.775789i	$0.717352\pi$
$252$	12.3845	+	9.81182i	0.780148	+	0.618087i
$253$	−1.21556	+	7.67477i	−0.0764219	+	0.482509i
$254$	−0.322499	+	0.724344i	−0.0202354	+	0.0454494i
$255$	−1.03736	+	0.249775i	−0.0649617	+	0.0156415i
$256$	14.5142	−	6.46215i	0.907140	−	0.403885i
$257$	−19.7898	−	5.30267i	−1.23446	−	0.330772i	−0.418143	−	0.908381i	$-0.637319\pi$
$257$	−19.7898	−	5.30267i	−1.23446	−	0.330772i	−0.816313	+	0.577610i	$0.803986\pi$
$258$	−0.00306747	−	0.0193672i	−0.000190972	−	0.00120575i
$259$	20.4793	−	0.218520i	1.27252	−	0.0135782i
$260$	−2.04735	−	6.89494i	−0.126971	−	0.427606i
$261$	−13.2267	+	14.6898i	−0.818713	+	0.909273i
$262$	0.0651550	+	0.00341463i	0.00402529	+	0.000210956i
$263$	12.7212	+	0.666689i	0.784422	+	0.0411098i	0.440341	−	0.897830i	$-0.354857\pi$
$263$	12.7212	+	0.666689i	0.784422	+	0.0411098i	0.344080	+	0.938940i	$0.388191\pi$
$264$	−0.0150741	+	0.0167414i	−0.000927744	+	0.00103036i
$265$	−5.46297	+	3.75993i	−0.335588	+	0.230971i
$266$	0.00345806	+	0.00584462i	0.000212027	+	0.000358357i
$267$	0.137628	+	0.868951i	0.00842272	+	0.0531790i
$268$	17.1365	+	4.59170i	1.04678	+	0.280483i
$269$	18.1556	−	8.08338i	1.10696	−	0.492852i	0.229895	−	0.973215i	$-0.426162\pi$
$269$	18.1556	−	8.08338i	1.10696	−	0.492852i	0.877070	+	0.480363i	$0.159495\pi$
$270$	0.0355774	−	0.0417118i	0.00216517	−	0.00253850i
$271$	3.28374	−	7.37540i	0.199473	−	0.448024i	−0.785918	−	0.618331i	$-0.787809\pi$
$271$	3.28374	−	7.37540i	0.199473	−	0.448024i	0.985391	+	0.170307i	$0.0544760\pi$
$272$	−2.72661	+	17.2151i	−0.165325	+	1.04382i
$273$	0.171382	+	0.432610i	0.0103725	+	0.0261828i
$274$		−	0.238652i		−	0.0144175i
$275$	4.87131	+	4.85840i	0.293751	+	0.292973i
$276$	1.06812	+	0.616679i	0.0642933	+	0.0371197i
$277$	2.20513	+	3.39560i	0.132493	+	0.204022i	0.898690	−	0.438584i	$-0.144520\pi$
$277$	2.20513	+	3.39560i	0.132493	+	0.204022i	−0.766197	+	0.642606i	$0.777853\pi$
$278$	0.289272	+	0.753580i	0.0173494	+	0.0451968i
$279$	−8.47968	+	6.16085i	−0.507665	+	0.368840i
$280$	−0.390624	−	0.795627i	−0.0233442	−	0.0475478i
$281$	1.03849	+	0.754506i	0.0619510	+	0.0450100i	0.618330	−	0.785919i	$-0.287810\pi$
$281$	1.03849	+	0.754506i	0.0619510	+	0.0450100i	−0.556379	+	0.830929i	$0.687810\pi$
$282$	−0.00755443	+	0.0281935i	−0.000449860	+	0.00167890i
$283$	−0.292342	−	0.112220i	−0.0173779	−	0.00667076i	0.349663	−	0.936875i	$-0.386296\pi$
$283$	−0.292342	−	0.112220i	−0.0173779	−	0.00667076i	−0.367041	+	0.930205i	$0.619629\pi$
$284$	−10.1507	+	9.13970i	−0.602331	+	0.542342i
$285$	−0.0147057	+	0.00799716i	−0.000871089	+	0.000473711i
$286$	0.0789137	−	0.0256406i	0.00466627	−	0.00151616i
$287$	−24.4421	+	6.82957i	−1.44277	+	0.403137i
$288$	−0.609358	−	1.19593i	−0.0359067	−	0.0704709i
$289$	−1.53639	−	1.38337i	−0.0903759	−	0.0813748i
$290$	0.511911	−	0.212439i	0.0300605	−	0.0124748i
$291$	1.21301	+	1.34719i	0.0711081	+	0.0789735i
$292$	0.539365	+	0.666061i	0.0315640	+	0.0389783i
$293$	−13.9434	−	13.9434i	−0.814584	−	0.814584i	0.170733	−	0.985317i	$-0.445386\pi$
$293$	−13.9434	−	13.9434i	−0.814584	−	0.814584i	−0.985317	+	0.170733i	$0.945386\pi$
$294$	0.0148570	+	0.0245099i	0.000866476	+	0.00142944i
$295$	−20.7665	+	9.92202i	−1.20907	+	0.577682i
$296$	−1.05947	−	0.471708i	−0.0615806	−	0.0274175i
$297$	−0.699743	−	0.566641i	−0.0406032	−	0.0328798i
$298$	−0.616825	+	0.400571i	−0.0357317	+	0.0232045i
$299$	−4.54432	−	7.87099i	−0.262805	−	0.455191i
$300$	0.997017	−	0.445487i	0.0575628	−	0.0257202i
$301$	2.50200	−	12.4212i	0.144213	−	0.715948i
$302$	−0.155221	+	0.304638i	−0.00893196	+	0.0175300i
$303$	−0.402327	+	0.154439i	−0.0231131	+	0.00887228i
$304$	0.0285827	+	0.271946i	0.00163933	+	0.0155972i
$305$	−14.4136	+	8.84583i	−0.825321	+	0.506511i
$306$	0.486196	+	0.0511012i	0.0277940	+	0.00292126i
$307$	−14.7442	+	14.7442i	−0.841499	+	0.841499i	−0.989054	−	0.147555i	$-0.952860\pi$
$307$	−14.7442	+	14.7442i	−0.841499	+	0.841499i	0.147555	+	0.989054i	$0.452860\pi$
$308$	−6.44730	+	3.37219i	−0.367369	+	0.192149i
$309$	0.798166	+	0.259340i	0.0454061	+	0.0147533i
$310$	0.288930	−	0.0537482i	0.0164101	−	0.00305270i
$311$	1.78340	−	8.39025i	0.101128	−	0.475768i	−0.898217	−	0.439553i	$-0.855137\pi$
$311$	1.78340	−	8.39025i	0.101128	−	0.475768i	0.999344	−	0.0362144i	$-0.0115299\pi$
$312$	0.00137903	−	0.0263134i	7.80720e−5	−	0.00148970i
$313$	20.3951	+	13.2447i	1.15280	+	0.748636i	0.972022	−	0.234888i	$-0.0754724\pi$
$313$	20.3951	+	13.2447i	1.15280	+	0.748636i	0.180776	+	0.983524i	$0.442139\pi$
$314$	0.213759	+	0.657884i	0.0120631	+	0.0371265i
$315$	15.4388	−	8.61054i	0.869877	−	0.485149i
$316$	5.62268	−	17.3048i	0.316300	−	0.973472i
$317$	−3.55609	+	2.87966i	−0.199730	+	0.161738i	−0.723968	−	0.689834i	$-0.757684\pi$
$317$	−3.55609	+	2.87966i	−0.199730	+	0.161738i	0.524238	+	0.851572i	$0.324350\pi$
$318$	−0.0117297	+	0.00314297i	−0.000657771	+	0.000176249i
$319$	−3.70238	−	8.31568i	−0.207293	−	0.465589i
$320$	−0.478111	−	17.8068i	−0.0267272	−	0.995432i
$321$	−0.693143	−	0.954029i	−0.0386875	−	0.0532487i
$322$	−0.356922	−	0.431271i	−0.0198905	−	0.0240338i
$323$	−0.266533	−	0.135805i	−0.0148303	−	0.00755640i
$324$	15.3917	−	8.88642i	0.855097	−	0.493690i
$325$	−8.00412	−	0.830529i	−0.443989	−	0.0460695i
$326$	−0.0647591	+	0.112166i	−0.00358667	+	0.00621230i
$327$	−0.0164789	−	0.314436i	−0.000911285	−	0.0173884i
$328$	1.41939	+	0.224810i	0.0783729	+	0.0124130i
$329$	−10.9226	+	15.3761i	−0.602184	+	0.847710i
$330$	0.00543106	+	0.0113670i	0.000298970	+	0.000625735i
$331$	−0.248393	+	2.36330i	−0.0136529	+	0.129899i	−0.999225	−	0.0393560i	$-0.987469\pi$
$331$	−0.248393	+	2.36330i	−0.0136529	+	0.129899i	0.985572	+	0.169255i	$0.0541360\pi$
$332$	−2.19482	−	8.19117i	−0.120456	−	0.449549i
$333$	8.28913	−	21.5939i	0.454241	−	1.18334i
$334$	−0.485535	+	0.103204i	−0.0265673	+	0.00564705i
$335$	12.0728	−	15.7552i	0.659609	−	0.860801i
$336$	0.132871	+	1.14638i	0.00724872	+	0.0625404i
$337$	19.0320	−	9.69727i	1.03674	−	0.528244i	0.149117	−	0.988820i	$-0.452357\pi$
$337$	19.0320	−	9.69727i	1.03674	−	0.528244i	0.887621	+	0.460575i	$0.152357\pi$
$338$	0.212428	−	0.327110i	0.0115546	−	0.0177925i
$339$	1.08576	+	0.230785i	0.0589703	+	0.0125345i
$340$	16.6456	+	10.1852i	0.902732	+	0.552371i
$341$	−1.00352	−	4.72120i	−0.0543438	−	0.255667i
$342$	0.00757520	−	0.00119979i	0.000409620	−	6.48774e-5i
$343$	3.48115	+	18.1902i	0.187964	+	0.982176i
$344$	−0.421735	+	0.580469i	−0.0227384	+	0.0312968i
$345$	1.09420	−	0.840760i	0.0589095	−	0.0452650i
$346$	0.378177	−	0.0397480i	0.0203309	−	0.00213686i
$347$	16.5160	−	20.3955i	0.886624	−	1.09489i	−0.108286	−	0.994120i	$-0.534536\pi$
$347$	16.5160	−	20.3955i	0.886624	−	1.09489i	0.994910	−	0.100770i	$-0.0321305\pi$
$348$	−1.44283	+	0.0756157i	−0.0773439	+	0.00405342i
$349$	−16.7152			−0.894745			−0.447373	−	0.894348i	$-0.647640\pi$
$349$	−16.7152			−0.894745			−0.447373	+	0.894348i	$0.647640\pi$
$350$	−0.494630	+	0.0318768i	−0.0264391	+	0.00170389i
$351$	1.05315			0.0562129
$352$	0.617243	−	0.0323484i	0.0328992	−	0.00172417i
$353$	18.1261	−	22.3839i	0.964758	−	1.19138i	−0.0167319	−	0.999860i	$-0.505326\pi$
$353$	18.1261	−	22.3839i	0.964758	−	1.19138i	0.981489	−	0.191516i	$-0.0613405\pi$
$354$	−0.0419119	+	0.00440512i	−0.00222759	+	0.000234130i
$355$	5.11080	+	14.4021i	0.271253	+	0.764384i
$356$	9.45769	−	13.0174i	0.501256	−	0.689920i
$357$	−1.13094	−	0.561125i	−0.0598558	−	0.0296979i
$358$	−0.333964	+	0.0528947i	−0.0176505	+	0.00279557i
$359$	0.933188	+	4.39030i	0.0492518	+	0.231711i	0.995888	−	0.0905925i	$-0.0288761\pi$
$359$	0.933188	+	4.39030i	0.0492518	+	0.231711i	−0.946636	+	0.322304i	$0.895543\pi$
$360$	−0.997883	+	0.0792013i	−0.0525931	+	0.00417428i
$361$	18.5802	+	3.94935i	0.977906	+	0.207860i
$362$	−0.323427	+	0.498034i	−0.0169989	+	0.0261761i
$363$	−0.886694	+	0.451793i	−0.0465394	+	0.0237130i
$364$	3.37829	−	7.81100i	0.177070	−	0.409408i
$365$	0.919227	−	0.272951i	0.0481145	−	0.0142869i
$366$	−0.0302900	+	0.00643833i	−0.00158328	+	0.000336537i
$367$	−11.7573	+	30.6289i	−0.613728	+	1.59882i	0.175339	+	0.984508i	$0.443898\pi$
$367$	−11.7573	+	30.6289i	−0.613728	+	1.59882i	−0.789067	+	0.614307i	$0.789436\pi$
$368$	−5.83406	−	21.7730i	−0.304121	−	1.13500i
$369$	−2.99597	+	28.5047i	−0.155964	+	1.48390i
$370$	−0.470139	+	0.446738i	−0.0244413	+	0.0232248i
$371$	−7.81221	−	0.736911i	−0.405590	−	0.0382585i
$372$	−0.756679	−	0.119846i	−0.0392320	−	0.00621374i
$373$	−1.97463	−	37.6781i	−0.102242	−	1.95090i	−0.265033	−	0.964239i	$-0.585383\pi$
$373$	−1.97463	−	37.6781i	−0.102242	−	1.95090i	0.162791	−	0.986661i	$-0.447950\pi$
$374$	−0.112562	+	0.194964i	−0.00582046	+	0.0100813i
$375$	−0.0344132	−	1.22128i	−0.00177709	−	0.0630669i
$376$	0.924931	−	0.534009i	0.0476997	−	0.0275394i
$377$	9.48641	+	4.83357i	0.488575	+	0.248941i
$378$	0.0639575	−	0.0108306i	0.00328962	−	0.000557067i
$379$	−2.24596	−	3.09129i	−0.115367	−	0.158789i	0.747428	−	0.664343i	$-0.231288\pi$
$379$	−2.24596	−	3.09129i	−0.115367	−	0.158789i	−0.862795	+	0.505553i	$0.831288\pi$
$380$	0.293600	+	0.0867564i	0.0150614	+	0.00445051i
$381$	−0.940591	−	2.11260i	−0.0481879	−	0.108232i
$382$	0.810186	−	0.217089i	0.0414527	−	0.0111072i
$383$	−12.5030	+	10.1248i	−0.638876	+	0.517351i	−0.893137	−	0.449784i	$-0.851501\pi$
$383$	−12.5030	+	10.1248i	−0.638876	+	0.517351i	0.254262	+	0.967135i	$0.418168\pi$
$384$	0.0404172	−	0.124391i	0.00206253	−	0.00634782i
$385$	0.730626	+	8.10762i	0.0372361	+	0.413202i
$386$	−0.141016	−	0.434001i	−0.00717751	−	0.0220901i
$387$	−12.0014	−	7.79381i	−0.610066	−	0.396182i
$388$	1.73518	−	33.1093i	0.0880906	−	1.68087i
$389$	−3.20212	+	15.0648i	−0.162354	+	0.763815i	0.819334	+	0.573317i	$0.194344\pi$
$389$	−3.20212	+	15.0648i	−0.162354	+	0.763815i	−0.981688	+	0.190498i	$0.938990\pi$
$390$	−0.0133038	−	0.00633475i	−0.000673664	−	0.000320773i
$391$	23.4521	+	7.62006i	1.18603	+	0.385363i
$392$	0.249756	−	1.01857i	0.0126146	−	0.0514453i
$393$	−0.134555	+	0.134555i	−0.00678742	+	0.00678742i
$394$	−0.497262	−	0.0522644i	−0.0250517	−	0.00263304i
$395$	−15.4886	−	13.2108i	−0.779316	−	0.664705i
$396$	0.858943	+	8.17229i	0.0431635	+	0.410673i
$397$	−10.9348	+	4.19748i	−0.548802	+	0.210665i	−0.616939	−	0.787011i	$-0.711628\pi$
$397$	−10.9348	+	4.19748i	−0.548802	+	0.210665i	0.0681376	+	0.997676i	$0.478294\pi$
$398$	−0.311956	+	0.612248i	−0.0156369	+	0.0306892i
$399$	−0.0194165	−	0.00391105i	−0.000972040	−	0.000195797i
$400$	−18.6418	−	7.12754i	−0.932089	−	0.356377i
$401$	6.37349	+	11.0392i	0.318277	+	0.551271i	0.980129	−	0.198363i	$-0.0635626\pi$
$401$	6.37349	+	11.0392i	0.318277	+	0.551271i	−0.661852	+	0.749635i	$0.730229\pi$
$402$	0.0304818	−	0.0197951i	0.00152029	−	0.000987289i
$403$	4.38737	+	3.55282i	0.218550	+	0.176979i
$404$	7.20026	+	3.20576i	0.358226	+	0.159493i
$405$	−2.60854	−	19.7128i	−0.129619	−	0.979535i
$406$	0.625817	+	0.195983i	0.0310588	+	0.00972649i
$407$	7.53167	+	7.53167i	0.373331	+	0.373331i
$408$	0.0449906	+	0.0555587i	0.00222736	+	0.00275057i
$409$	6.77254	+	7.52166i	0.334880	+	0.371922i	0.886942	−	0.461881i	$-0.152825\pi$
$409$	6.77254	+	7.52166i	0.334880	+	0.371922i	−0.552061	+	0.833803i	$0.686159\pi$
$410$	0.419445	−	0.685492i	0.0207149	−	0.0338541i
$411$	0.517262	+	0.465745i	0.0255147	+	0.0229735i
$412$	−6.96826	−	13.6760i	−0.343302	−	0.673768i
$413$	−26.3776	−	6.76705i	−1.29796	−	0.332985i
$414$	−0.601294	+	0.195372i	−0.0295520	+	0.00960203i
$415$	−9.40738	−	1.23216i	−0.461790	−	0.0604841i
$416$	−0.537253	+	0.483745i	−0.0263410	+	0.0237175i
$417$	−2.19787	−	0.843684i	−0.107630	−	0.0413154i
$418$	−0.000914107		0.00341149i	−4.47104e−5		0.000166862i
$419$	−2.20460	−	1.60174i	−0.107702	−	0.0782499i	0.532631	−	0.846348i	$-0.321203\pi$
$419$	−2.20460	−	1.60174i	−0.107702	−	0.0782499i	−0.640333	+	0.768098i	$0.721203\pi$
$420$	1.24296	+	0.352910i	0.0606504	+	0.0172202i
$421$	27.0480	−	19.6515i	1.31824	−	0.957756i	0.318286	−	0.947995i	$-0.396893\pi$
$421$	27.0480	−	19.6515i	1.31824	−	0.957756i	0.999952	−	0.00976112i	$-0.00310711\pi$
$422$	0.128020	+	0.333503i	0.00623190	+	0.0162347i
$423$	11.6013	+	17.8645i	0.564075	+	0.868600i
$424$	0.384812	+	0.222171i	0.0186881	+	0.0107896i
$425$	17.6463	−	12.8566i	0.855973	−	0.623638i
$426$			0.0279829i			0.00135577i
$427$	−19.7959	−	2.91921i	−0.957993	−	0.141270i
$428$	−3.37386	+	21.3017i	−0.163082	+	1.02966i
$429$	−0.0984310	+	0.221080i	−0.00475230	+	0.0106738i
$430$	0.209872	+	0.341970i	0.0101209	+	0.0164912i
$431$	−28.4527	+	12.6680i	−1.37052	+	0.610194i	−0.954240	−	0.299043i	$-0.903332\pi$
$431$	−28.4527	+	12.6680i	−1.37052	+	0.610194i	−0.416278	+	0.909237i	$0.636666\pi$
$432$	2.52295	+	0.676023i	0.121386	+	0.0325252i
$433$	−0.835932	−	5.27787i	−0.0401723	−	0.253638i	0.959427	−	0.281959i	$-0.0909841\pi$
$433$	−0.835932	−	5.27787i	−0.0401723	−	0.253638i	−0.999599	+	0.0283205i	$0.990984\pi$
$434$	0.302982	+	0.170642i	0.0145436	+	0.00819110i
$435$	−0.538582	+	1.52412i	−0.0258231	+	0.0730761i
$436$	−3.85327	+	4.27949i	−0.184538	+	0.204950i
$437$	0.386330	+	0.0202467i	0.0184807	+	0.000968530i
$438$	0.00175342		9.18930e-5i	8.37818e−5		4.39082e-6i
$439$	17.8883	−	19.8670i	0.853763	−	0.948200i	−0.145389	−	0.989375i	$-0.546443\pi$
$439$	17.8883	−	19.8670i	0.853763	−	0.948200i	0.999152	+	0.0411749i	$0.0131101\pi$
$440$	0.153586	−	0.434629i	0.00732191	−	0.0207201i
$441$	20.5475	+	3.91121i	0.978451	+	0.186248i
$442$	−0.0411916	−	0.260074i	−0.00195929	−	0.0123704i
$443$	28.5150	+	7.64058i	1.35479	+	0.363015i	0.861901	−	0.507077i	$-0.169274\pi$
$443$	28.5150	+	7.64058i	1.35479	+	0.363015i	0.492889	+	0.870092i	$0.335941\pi$
$444$	1.54447	−	0.687643i	0.0732974	−	0.0326341i
$445$	−9.41632	−	15.3432i	−0.446376	−	0.727336i
$446$	0.382986	−	0.860200i	0.0181349	−	0.0407317i
$447$	0.335564	−	2.11867i	0.0158717	−	0.100210i
$448$	13.0886	−	16.5204i	0.618379	−	0.780517i
$449$			16.6858i			0.787450i	0.919228	+	0.393725i	$0.128814\pi$
$449$			16.6858i			0.787450i	−0.919228	+	0.393725i	$0.871186\pi$
$450$	−0.172276	+	0.532616i	−0.00812118	+	0.0251077i
$451$	−11.4304	−	6.59932i	−0.538235	−	0.310750i
$452$	−11.0568	−	17.0259i	−0.520067	−	0.800832i
$453$	−0.357359	−	0.930953i	−0.0167902	−	0.0437400i
$454$	−0.375079	+	0.272511i	−0.0176033	+	0.0127896i
$455$	−6.63198	−	6.83189i	−0.310912	−	0.320284i
$456$	0.000907371	0	0.000659243i	4.24915e−5	0	3.08719e-5i
$457$	−2.74552	+	10.2464i	−0.128430	+	0.479308i	−0.999939	−	0.0110724i	$-0.996475\pi$
$457$	−2.74552	+	10.2464i	−0.128430	+	0.479308i	0.871509	+	0.490380i	$0.163142\pi$
$458$	−0.516612	−	0.198309i	−0.0241397	−	0.00926637i
$459$	−2.12344	+	1.91195i	−0.0991136	+	0.0892423i
$460$	−25.0234	−	3.27751i	−1.16672	−	0.152814i
$461$	19.5350	−	6.34729i	0.909833	−	0.295623i	0.183544	−	0.983012i	$-0.441243\pi$
$461$	19.5350	−	6.34729i	0.909833	−	0.295623i	0.726290	+	0.687389i	$0.241243\pi$
$462$	−0.00370411	+	0.0144384i	−0.000172331	+	0.000671736i
$463$	−1.32037	−	2.59137i	−0.0613628	−	0.120431i	0.858288	−	0.513168i	$-0.171528\pi$
$463$	−1.32037	−	2.59137i	−0.0613628	−	0.120431i	−0.919651	+	0.392737i	$0.871528\pi$
$464$	19.6232	+	17.6688i	0.910985	+	0.820255i
$465$	−0.447370	+	0.731129i	−0.0207463	+	0.0339053i
$466$	0.0304258	+	0.0337912i	0.00140945	+	0.00156535i
$467$	4.61554	+	5.69972i	0.213582	+	0.263752i	0.872666	−	0.488318i	$-0.162389\pi$
$467$	4.61554	+	5.69972i	0.213582	+	0.263752i	−0.659084	+	0.752069i	$0.729056\pi$
$468$	−6.79623	−	6.79623i	−0.314156	−	0.314156i
$469$	22.9190	−	5.12776i	1.05830	−	0.236778i
$470$	−0.0783497	−	0.592089i	−0.00361400	−	0.0273110i
$471$	−1.84309	−	0.820595i	−0.0849249	−	0.0378110i
$472$	1.19839	+	0.970439i	0.0551605	+	0.0446681i
$473$	5.52661	−	3.58902i	0.254114	−	0.165023i
$474$	−0.0186381	−	0.0322821i	−0.000856077	−	0.00148277i
$475$	0.215205	−	0.266478i	0.00987429	−	0.0122269i
$476$	7.36903	+	21.8823i	0.337759	+	1.00297i
$477$	−4.02332	+	7.89620i	−0.184215	+	0.361542i
$478$	0.900174	−	0.345545i	0.0411730	−	0.0158048i
$479$	0.617027	+	5.87062i	0.0281927	+	0.268235i	0.999533	+	0.0305441i	$0.00972400\pi$
$479$	0.617027	+	5.87062i	0.0281927	+	0.268235i	−0.971341	+	0.237691i	$0.923609\pi$
$480$	−0.0835117	−	0.0712299i	−0.00381177	−	0.00325119i
$481$	−12.3901	−	1.30225i	−0.564939	−	0.0593774i
$482$	0.362945	−	0.362945i	0.0165317	−	0.0165317i
$483$	1.63131	+	0.0680487i	0.0742271	+	0.00309632i
$484$	17.3097	+	5.62427i	0.786805	+	0.255649i
$485$	−33.4912	−	15.9472i	−1.52076	−	0.724126i
$486$	0.0228628	−	0.107561i	0.00103708	−	0.00487907i
$487$	−0.910186	+	17.3674i	−0.0412444	+	0.786991i	0.897213	+	0.441597i	$0.145588\pi$
$487$	−0.910186	+	17.3674i	−0.0412444	+	0.786991i	−0.938458	+	0.345394i	$0.887745\pi$
$488$	0.950297	+	0.617130i	0.0430179	+	0.0279362i
$489$	−0.116731	−	0.359261i	−0.00527875	−	0.0162463i
$490$	−0.473019	−	0.346696i	−0.0213688	−	0.0156621i
$491$	−1.67096	+	5.14268i	−0.0754092	+	0.232086i	−0.981655	−	0.190665i	$-0.938936\pi$
$491$	−1.67096	+	5.14268i	−0.0754092	+	0.232086i	0.906246	+	0.422751i	$0.138936\pi$
$492$	−1.62808	+	1.31839i	−0.0733995	+	0.0594377i
$493$	−27.9024	+	7.47643i	−1.25666	+	0.336721i
$494$	−0.00168022	−	0.00377385i	−7.55969e−5	−	0.000169793i
$495$	8.81682	+	2.60530i	0.396286	+	0.117099i
$496$	8.22993	+	11.3275i	0.369535	+	0.508621i
$497$	−6.29951	+	16.9491i	−0.282572	+	0.760272i
$498$	−0.0154794	−	0.00788715i	−0.000693648	−	0.000353432i
$499$	−2.08554	+	1.20409i	−0.0933616	+	0.0539023i	−0.545954	−	0.837815i	$-0.683833\pi$
$499$	−2.08554	+	1.20409i	−0.0933616	+	0.0539023i	0.452592	+	0.891718i	$0.350499\pi$
$500$	−15.3490	+	16.2391i	−0.686427	+	0.726233i
$501$	0.723867	−	1.25377i	0.0323400	−	0.0560145i
$502$	−0.0482028	−	0.919765i	−0.00215140	−	0.0410511i
$503$	24.0156	+	3.80370i	1.07080	+	0.169599i	0.666859	−	0.745184i	$-0.267638\pi$
$503$	24.0156	+	3.80370i	1.07080	+	0.169599i	0.403946	+	0.914783i	$0.367638\pi$
$504$	−0.965593	−	0.685924i	−0.0430109	−	0.0305535i
$505$	6.39244	−	6.07426i	0.284460	−	0.270301i
$506$	0.0304328	−	0.289549i	0.00135290	−	0.0128720i
$507$	0.294423	+	1.09880i	0.0130758	+	0.0487995i
$508$	−15.1568	+	39.4848i	−0.672474	+	1.75185i
$509$	−17.7343	+	3.76954i	−0.786058	+	0.167082i	−0.583419	−	0.812172i	$-0.698285\pi$
$509$	−17.7343	+	3.76954i	−0.786058	+	0.167082i	−0.202639	+	0.979253i	$0.564952\pi$
$510$	0.0383247	−	0.0113800i	0.00169705	−	0.000503913i
$511$	1.04136	+	0.450390i	0.0460668	+	0.0199241i
$512$	−2.66325	+	1.35700i	−0.117700	+	0.0599713i
$513$	−0.0244148	+	0.0375954i	−0.00107794	+	0.00165988i
$514$	0.750870	+	0.159602i	0.0331194	+	0.00703976i
$515$	−17.1188	+	1.35871i	−0.754346	+	0.0598719i
$516$	−0.217465	−	1.02309i	−0.00957338	−	0.0450392i
$517$	−9.68824	+	1.53447i	−0.426088	+	0.0674858i
$518$	−0.765840	+	0.0483347i	−0.0336491	+	0.00212371i
$519$	−0.651886	+	0.897245i	−0.0286146	+	0.0393847i
$520$	0.180315	+	0.508122i	0.00790733	+	0.0222826i
$521$	15.4005	−	1.61866i	0.674708	−	0.0709147i	0.239023	−	0.971014i	$-0.423173\pi$
$521$	15.4005	−	1.61866i	0.674708	−	0.0709147i	0.435685	+	0.900099i	$0.356506\pi$
$522$	0.466095	−	0.575580i	0.0204004	−	0.0251924i
$523$	−19.7096	+	1.03294i	−0.861843	+	0.0451673i	−0.478134	−	0.878287i	$-0.658687\pi$
$523$	−19.7096	+	1.03294i	−0.861843	+	0.0451673i	−0.383709	+	0.923454i	$0.625353\pi$
$524$	3.48022			0.152034
$525$	0.896213	−	1.13429i	0.0391140	−	0.0495044i
$526$	−0.477293			−0.0208110
$527$	−15.2962	+	0.801639i	−0.666312	+	0.0349199i
$528$	−0.377717	+	0.466442i	−0.0164380	+	0.0202993i
$529$	−8.84171	+	0.929301i	−0.384422	+	0.0404044i
$530$	0.197034	−	0.151397i	0.00855860	−	0.00657627i
$531$	−18.0774	+	24.8813i	−0.784490	+	1.07976i
$532$	0.200521	+	0.301679i	0.00869368	+	0.0130794i
$533$	15.2476	−	2.41499i	0.660448	−	0.104605i
$534$	−0.00685356	−	0.0322435i	−0.000296582	−	0.00139531i
$535$	20.5824	+	12.5942i	0.889857	+	0.544493i
$536$	−1.30085	−	0.276503i	−0.0561880	−	0.0119431i
$537$	0.537107	−	0.827073i	0.0231779	−	0.0356908i
$538$	−0.663472	+	0.338056i	−0.0286043	+	0.0145746i
$539$	−5.49395	+	7.91143i	−0.236641	+	0.340770i
$540$	1.77870	−	2.32123i	0.0765429	−	0.0998898i
$541$	26.7198	−	5.67947i	1.14877	−	0.244179i	0.406098	−	0.913830i	$-0.366889\pi$
$541$	26.7198	−	5.67947i	1.14877	−	0.244179i	0.742677	+	0.669650i	$0.233556\pi$
$542$	−0.108404	+	0.282403i	−0.00465636	+	0.0121302i
$543$	−0.448267	−	1.67295i	−0.0192370	−	0.0717933i
$544$	0.205030	−	1.95073i	0.00879058	−	0.0836368i
$545$	2.77758	+	5.81339i	0.118978	+	0.249018i
$546$	−0.00726086	−	0.0158508i	−0.000310736	−	0.000678352i
$547$	10.0134	+	1.58597i	0.428143	+	0.0678111i	0.366787	−	0.930305i	$-0.380458\pi$
$547$	10.0134	+	1.58597i	0.428143	+	0.0678111i	0.0613554	+	0.998116i	$0.480458\pi$
$548$	−0.666236	−	12.7125i	−0.0284602	−	0.543053i
$549$	−11.2995	+	19.5712i	−0.482249	+	0.835280i
$550$	−0.191796	−	0.172233i	−0.00817820	−	0.00734406i
$551$	−0.392470	+	0.226593i	−0.0167198	+	0.00965317i
$552$	−0.0823786	−	0.0419740i	−0.00350627	−	0.00178653i
$553$	−4.02168	−	23.7490i	−0.171019	−	1.00991i
$554$	−0.0891673	−	0.122728i	−0.00378836	−	0.00521423i
$555$	−0.0507687	−	1.89083i	−0.00215501	−	0.0802614i
$556$	17.5128	+	39.3343i	0.742706	+	1.66815i
$557$	−0.335189	+	0.0898136i	−0.0142024	+	0.00380552i	−0.265913	−	0.963997i	$-0.585673\pi$
$557$	−0.335189	+	0.0898136i	−0.0142024	+	0.00380552i	0.251711	+	0.967802i	$0.419007\pi$
$558$	0.305201	−	0.247147i	0.0129202	−	0.0104626i
$559$	−2.38179	+	7.33039i	−0.100739	+	0.310042i
$560$	−11.5023	−	20.6238i	−0.486062	−	0.871514i
$561$	−0.202898	−	0.624456i	−0.00856637	−	0.0263646i
$562$	−0.0403364	−	0.0261948i	−0.00170149	−	0.00110496i
$563$	−0.792034	+	15.1129i	−0.0333803	+	0.636933i	0.929798	+	0.368070i	$0.119981\pi$
$563$	−0.792034	+	15.1129i	−0.0333803	+	0.636933i	−0.963178	+	0.268863i	$0.913352\pi$
$564$	−0.323704	+	1.52291i	−0.0136304	+	0.0641259i
$565$	−22.3302	+	4.15398i	−0.939437	+	0.174759i
$566$	0.0111585	+	0.00362563i	0.000469029	+	0.000152397i
$567$	12.6029	−	19.8677i	0.529271	−	0.834363i
$568$	0.724020	−	0.724020i	0.0303792	−	0.0303792i
$569$	−8.99190	−	0.945086i	−0.376960	−	0.0396201i	−0.0858458	−	0.996308i	$-0.527359\pi$
$569$	−8.99190	−	0.945086i	−0.376960	−	0.0396201i	−0.291114	+	0.956688i	$0.594026\pi$
$570$	0.000534557	0	0.000328065i	2.23901e−5	0	1.37411e-5i
$571$	−1.93251	−	18.3867i	−0.0808732	−	0.769457i	−0.957529	−	0.288338i	$-0.906897\pi$
$571$	−1.93251	−	18.3867i	−0.0808732	−	0.769457i	0.876655	−	0.481119i	$-0.159769\pi$
$572$	4.13201	−	1.58613i	0.172768	−	0.0663194i
$573$	−1.11061	+	2.17969i	−0.0463963	+	0.0910579i
$574$	0.901151	−	0.303469i	0.0376133	−	0.0126666i
$575$	−14.0854	+	24.4716i	−0.587403	+	1.02054i
$576$	−11.9019	−	20.6147i	−0.495914	−	0.858947i
$577$	−22.1789	+	14.4031i	−0.923318	+	0.599610i	−0.916355	−	0.400366i	$-0.868883\pi$
$577$	−22.1789	+	14.4031i	−0.923318	+	0.599610i	−0.00696286	+	0.999976i	$0.502216\pi$
$578$	0.0601994	+	0.0487485i	0.00250397	+	0.00202767i
$579$	1.21587	+	0.541341i	0.0505299	+	0.0224974i
$580$	26.6755	−	12.7453i	1.10764	−	0.529220i
$581$	−7.60026	−	8.26194i	−0.315312	−	0.342763i
$582$	−0.0480288	−	0.0480288i	−0.00199086	−	0.00199086i
$583$	−2.56824	−	3.17151i	−0.106366	−	0.131351i
$584$	−0.0429899	−	0.0477451i	−0.00177893	−	0.00197571i
$585$	−9.93205	+	4.12171i	−0.410640	+	0.170412i
$586$	0.549060	+	0.494376i	0.0226815	+	0.0204225i
$587$	8.79450	+	17.2602i	0.362988	+	0.712404i	0.998202	−	0.0599321i	$-0.0190884\pi$
$587$	8.79450	+	17.2602i	0.362988	+	0.712404i	−0.635215	+	0.772336i	$0.719088\pi$
$588$	0.859827	+	1.26412i	0.0354587	+	0.0521314i
$589$	−0.228540	+	0.0742572i	−0.00941683	+	0.00305971i
$590$	0.757558	−	0.411971i	0.0311882	−	0.0169606i
$591$	1.08372	−	0.975787i	0.0445783	−	0.0401385i
$592$	−28.8461	−	11.0730i	−1.18557	−	0.455097i
$593$	10.6910	−	39.8994i	0.439027	−	1.63847i	−0.292215	−	0.956353i	$-0.594392\pi$
$593$	10.6910	−	39.8994i	0.439027	−	1.63847i	0.731242	−	0.682118i	$-0.238941\pi$
$594$	0.0272933	+	0.0198297i	0.00111986	+	0.000813623i
$595$	25.7750	+	1.73486i	1.05667	+	0.0711222i
$596$	−31.7389	+	23.0597i	−1.30008	+	0.944560i
$597$	−0.718205	−	1.87099i	−0.0293942	−	0.0765744i
$598$	0.185468	+	0.285596i	0.00758436	+	0.0116789i
$599$	−2.44181	−	1.40978i	−0.0997698	−	0.0576021i	0.449285	−	0.893389i	$-0.351679\pi$
$599$	−2.44181	−	1.40978i	−0.0997698	−	0.0576021i	−0.549055	+	0.835786i	$0.685012\pi$
$600$	−0.0728887	+	0.0372606i	−0.00297567	+	0.00152116i
$601$		−	33.6982i		−	1.37458i	−0.726384	−	0.687289i	$-0.758801\pi$
$601$		−	33.6982i		−	1.37458i	0.726384	−	0.687289i	$-0.241199\pi$
$602$	−0.0692596	+	0.469668i	−0.00282281	+	0.0191422i
$603$	4.14929	−	26.1976i	0.168972	−	1.06685i
$604$	−7.41788	+	16.6608i	−0.301829	+	0.677920i
$605$	13.2145	−	15.4930i	0.537245	−	0.629879i
$606$	0.0147509	−	0.00656754i	0.000599215	−	0.000266788i
$607$	32.6488	+	8.74821i	1.32517	+	0.355079i	0.850913	−	0.525306i	$-0.176049\pi$
$607$	32.6488	+	8.74821i	1.32517	+	0.355079i	0.474259	+	0.880385i	$0.342716\pi$
$608$	−0.00481385	−	0.0303934i	−0.000195227	−	0.00123262i
$609$	−1.64611	+	0.973944i	−0.0667036	+	0.0394662i
$610$	0.521964	−	0.359246i	0.0211337	−	0.0145455i
$611$	7.67696	−	8.52613i	0.310577	−	0.344930i
$612$	26.0414	+	1.36477i	1.05266	+	0.0551676i
$613$	5.90313	+	0.309370i	0.238425	+	0.0124953i	0.171174	−	0.985241i	$-0.445244\pi$
$613$	5.90313	+	0.309370i	0.238425	+	0.0124953i	0.0672508	+	0.997736i	$0.478577\pi$
$614$	0.522769	−	0.580594i	0.0210973	−	0.0234309i
$615$	0.667185	+	2.24690i	0.0269035	+	0.0906039i
$616$	0.469414	−	0.277736i	0.0189132	−	0.0111903i
$617$	−0.740149	−	4.67312i	−0.0297973	−	0.188133i	0.968300	−	0.249790i	$-0.0803615\pi$
$617$	−0.740149	−	4.67312i	−0.0297973	−	0.188133i	−0.998097	+	0.0616571i	$0.980361\pi$
$618$	−0.0303733	−	0.00813851i	−0.00122180	−	0.000327379i
$619$	−0.987941	+	0.439860i	−0.0397087	+	0.0176795i	−0.426495	−	0.904490i	$-0.640252\pi$
$619$	−0.987941	+	0.439860i	−0.0397087	+	0.0176795i	0.386786	+	0.922169i	$0.373585\pi$
$620$	15.2407	−	3.66967i	0.612081	−	0.147377i
$621$	1.50302	−	3.37583i	0.0603140	−	0.135467i
$622$	−0.0502765	+	0.317433i	−0.00201590	+	0.0127279i
$623$	3.10747	−	21.0726i	0.124498	−	0.844257i
$624$		−	0.702018i		−	0.0281032i
$625$	10.2290	+	22.8116i	0.409160	+	0.912463i
$626$	−0.789090	−	0.455581i	−0.0315384	−	0.0182087i
$627$	−0.00561025	−	0.00863903i	−0.000224052	−	0.000345010i
$628$	13.2232	+	34.4475i	0.527661	+	1.37460i
$629$	27.3460	−	19.8680i	1.09036	−	0.792191i
$630$	−0.560784	+	0.352453i	−0.0223422	+	0.0140421i
$631$	−17.6839	−	12.8481i	−0.703983	−	0.511474i	0.177244	−	0.984167i	$-0.443282\pi$
$631$	−17.6839	−	12.8481i	−0.703983	−	0.511474i	−0.881227	+	0.472693i	$0.843282\pi$
$632$	−0.353022	+	1.31749i	−0.0140424	+	0.0524071i
$633$	−0.972685	−	0.373379i	−0.0386608	−	0.0148405i
$634$	0.127410	−	0.114721i	0.00506012	−	0.00455615i
$635$	34.3458	+	32.5497i	1.36297	+	1.29169i
$636$	−0.616047	+	0.200166i	−0.0244279	+	0.00793709i
$637$	−0.829543	−	11.2353i	−0.0328677	−	0.445161i
$638$	0.154838	+	0.303886i	0.00613008	+	0.0120310i
$639$	15.1760	+	13.6646i	0.600355	+	0.540562i
$640$	0.211750	+	2.66791i	0.00837015	+	0.105458i
$641$	−14.7391	−	16.3694i	−0.582159	−	0.646553i	0.378066	−	0.925779i	$-0.376589\pi$
$641$	−14.7391	−	16.3694i	−0.582159	−	0.646553i	−0.960226	+	0.279225i	$0.909922\pi$
$642$	0.0278059	+	0.0343375i	0.00109741	+	0.00135519i
$643$	7.57933	+	7.57933i	0.298899	+	0.298899i	0.840583	−	0.541683i	$-0.182213\pi$
$643$	7.57933	+	7.57933i	0.298899	+	0.298899i	−0.541683	+	0.840583i	$0.682213\pi$
$644$	−20.2165	−	21.9766i	−0.796643	−	0.865999i
$645$	−1.15078	−	0.212494i	−0.0453117	−	0.00836694i
$646$	0.0102391	+	0.00455874i	0.000402852	+	0.000179361i
$647$	−26.9950	−	21.8601i	−1.06128	−	0.859410i	−0.0708609	−	0.997486i	$-0.522575\pi$
$647$	−26.9950	−	21.8601i	−1.06128	−	0.859410i	−0.990422	+	0.138077i	$0.955908\pi$
$648$	−1.11736	+	0.725621i	−0.0438940	+	0.0285051i
$649$	−7.08130	−	12.2652i	−0.277965	−	0.481450i
$650$	0.301117	+	0.0153802i	0.0118108	+	0.000603262i
$651$	−0.961146	+	0.323673i	−0.0376703	+	0.0126857i
$652$	−3.13647	+	6.15566i	−0.122834	+	0.241074i
$653$	−15.4967	+	5.94863i	−0.606433	+	0.232788i	−0.642156	−	0.766574i	$-0.721960\pi$
$653$	−15.4967	+	5.94863i	−0.606433	+	0.232788i	0.0357231	+	0.999362i	$0.488627\pi$
$654$	0.00123317	+	0.0117329i	4.82209e−5	+	0.000458791i
$655$	1.48768	−	3.59833i	0.0581285	−	0.140598i
$656$	38.0779	+	4.00215i	1.48669	+	0.156258i
$657$	0.906067	−	0.906067i	0.0353490	−	0.0353490i
$658$	0.378538	−	0.596741i	0.0147569	−	0.0232634i
$659$	−23.7349	−	7.71192i	−0.924579	−	0.300414i	−0.192235	−	0.981349i	$-0.561574\pi$
$659$	−23.7349	−	7.71192i	−0.924579	−	0.300414i	−0.732344	+	0.680935i	$0.761574\pi$
$660$	0.321036	+	0.590340i	0.0124963	+	0.0229789i
$661$	−0.637712	+	3.00020i	−0.0248041	+	0.116694i	−0.988808	−	0.149194i	$-0.952332\pi$
$661$	−0.637712	+	3.00020i	−0.0248041	+	0.116694i	0.964004	+	0.265889i	$0.0856653\pi$
$662$	0.00465979	−	0.0889140i	0.000181108	−	0.00345574i
$663$	0.644081	+	0.418271i	0.0250140	+	0.0162443i
$664$	0.196439	+	0.604578i	0.00762333	+	0.0234622i
$665$	0.397633	−	0.0783683i	0.0154195	−	0.00303899i
$666$	−0.267808	+	0.824229i	−0.0103774	+	0.0319382i
$667$	29.0325	−	23.5101i	1.12414	−	0.910314i
$668$	−25.5754	+	6.85292i	−0.989543	+	0.265147i
$669$	1.11701	+	2.50884i	0.0431859	+	0.0969972i
$670$	−0.420831	+	0.613184i	−0.0162581	+	0.0236894i
$671$	−6.11692	−	8.41922i	−0.236141	−	0.325020i
$672$	−0.0216841	−	0.128050i	−0.000836484	−	0.00493965i
$673$	8.48294	+	4.32228i	0.326993	+	0.166611i	0.609779	−	0.792572i	$-0.291258\pi$
$673$	8.48294	+	4.32228i	0.326993	+	0.166611i	−0.282785	+	0.959183i	$0.591258\pi$
$674$	−0.693099	+	0.400161i	−0.0266972	+	0.0154136i
$675$	−1.63967	−	2.83131i	−0.0631110	−	0.108977i
$676$	10.4025	−	18.0176i	0.400095	−	0.692985i
$677$	−0.545808	−	10.4146i	−0.0209771	−	0.400267i	−0.988858	−	0.148859i	$-0.952440\pi$
$677$	−0.545808	−	10.4146i	−0.0209771	−	0.400267i	0.967881	−	0.251408i	$-0.0808935\pi$
$678$	−0.0410781	−	0.00650613i	−0.00157760	−	0.000249867i
$679$	−18.2786	−	39.9031i	−0.701469	−	1.53134i
$680$	−1.28604	−	0.697159i	−0.0493174	−	0.0267348i
$681$	0.141342	−	1.34478i	0.00541625	−	0.0515322i
$682$	0.0468065	+	0.174684i	0.00179231	+	0.00668901i
$683$	3.42318	−	8.91768i	0.130984	−	0.341226i	−0.852366	−	0.522946i	$-0.824833\pi$
$683$	3.42318	−	8.91768i	0.130984	−	0.341226i	0.983350	+	0.181720i	$0.0581664\pi$
$684$	0.400168	−	0.0850583i	0.0153008	−	0.00325228i
$685$	−13.4288	−	4.74536i	−0.513087	−	0.181311i
$686$	−0.165923	−	0.673790i	−0.00633497	−	0.0257254i
$687$	1.43803	−	0.732711i	0.0548641	−	0.0279546i
$688$	−10.4113	+	16.0320i	−0.396927	+	0.611215i
$689$	4.66898	+	0.992421i	0.177874	+	0.0378082i
$690$	−0.0392926	+	0.0336041i	−0.00149584	+	0.00127929i
$691$	4.86605	+	22.8929i	0.185113	+	0.870889i	0.968434	+	0.249271i	$0.0801910\pi$
$691$	4.86605	+	22.8929i	0.185113	+	0.870889i	−0.783321	+	0.621618i	$0.786476\pi$
$692$	20.0338	−	3.17305i	0.761572	−	0.120621i
$693$	6.02165	+	9.05942i	0.228744	+	0.344139i
$694$	−0.577980	+	0.795521i	−0.0219398	+	0.0301976i
$695$	48.1554	−	1.29297i	1.82664	−	0.0490450i
$696$	0.107713	−	0.0113211i	0.00408287	−	0.000429127i
$697$	−26.3592	+	32.5508i	−0.998424	+	1.23295i
$698$	0.625429	−	0.0327774i	0.0236728	−	0.00124064i
$699$	−0.132618			−0.00501608
$700$	−26.2591	+	3.07886i	−0.992499	+	0.116370i
$701$	24.9909			0.943892			0.471946	−	0.881628i	$-0.343552\pi$
$701$	24.9909			0.943892			0.471946	+	0.881628i	$0.343552\pi$
$702$	−0.0394054	+	0.00206515i	−0.00148726	+	7.79440e-5i
$703$	0.333723	−	0.412113i	0.0125866	−	0.0155431i
$704$	10.9015	−	1.14580i	0.410867	−	0.0431839i
$705$	1.43622	+	0.985683i	0.0540911	+	0.0371230i
$706$	−0.634328	+	0.873078i	−0.0238733	+	0.0328587i
$707$	10.4131	−	0.657204i	0.391624	−	0.0247167i
$708$	−2.22027	+	0.351657i	−0.0834430	+	0.0132161i
$709$	−10.0976	−	47.5054i	−0.379223	−	1.78410i	−0.590881	−	0.806759i	$-0.701220\pi$
$709$	−10.0976	−	47.5054i	−0.379223	−	1.78410i	0.211658	−	0.977344i	$-0.432114\pi$
$710$	−0.219471	−	0.528858i	−0.00823661	−	0.0198477i
$711$	−26.6090	−	5.65593i	−0.997917	−	0.212114i
$712$	−0.656930	+	1.01158i	−0.0246195	+	0.0379107i
$713$	17.6500	−	8.99310i	0.660996	−	0.336794i
$714$	0.0434165	+	0.0187778i	0.00162482	+	0.000702741i
$715$	0.126340	−	4.95026i	0.00472487	−	0.185129i
$716$	−17.6420	+	3.74992i	−0.659312	+	0.140141i
$717$	−1.00781	+	2.62542i	−0.0376372	+	0.0980482i
$718$	−0.0435259	−	0.162441i	−0.00162437	−	0.00606224i
$719$	−0.622106	+	5.91894i	−0.0232006	+	0.220739i	0.976778	+	0.214252i	$0.0687315\pi$
$719$	−0.622106	+	5.91894i	−0.0232006	+	0.220739i	−0.999979	+	0.00648680i	$0.997935\pi$
$720$	−26.4393	+	3.49864i	−0.985333	+	0.130387i
$721$	−16.5649	−	11.7671i	−0.616909	−	0.438231i
$722$	−0.702956	−	0.111337i	−0.0261613	−	0.00414354i
$723$	0.0783480	+	1.49497i	0.00291379	+	0.0555985i
$724$	−15.8380	+	27.4323i	−0.588615	+	1.01951i
$725$	−1.77493	−	33.0290i	−0.0659193	−	1.22667i
$726$	0.0322913	−	0.0186434i	0.00119844	−	0.000691921i
$727$	9.26956	+	4.72308i	0.343789	+	0.175169i	0.617356	−	0.786684i	$-0.288204\pi$
$727$	9.26956	+	4.72308i	0.343789	+	0.175169i	−0.273567	+	0.961853i	$0.588204\pi$
$728$	−0.222253	+	0.597984i	−0.00823726	+	0.0221628i
$729$	−15.4924	−	21.3235i	−0.573793	−	0.789759i
$730$	−0.0338592	+	0.0120155i	−0.00125319	+	0.000444713i
$731$	−8.50572	−	19.1042i	−0.314595	−	0.706593i
$732$	−1.59552	+	0.427518i	−0.0589720	+	0.0158015i
$733$	29.7961	−	24.1284i	1.10054	−	0.891202i	0.105880	−	0.994379i	$-0.466234\pi$
$733$	29.7961	−	24.1284i	1.10054	−	0.891202i	0.994663	+	0.103177i	$0.0329007\pi$
$734$	0.379860	−	1.16909i	0.0140209	−	0.0431519i
$735$	1.67457	−	0.348637i	0.0617675	−	0.0128597i
$736$	0.783879	+	2.41253i	0.0288942	+	0.0889271i
$737$	10.2438	+	6.65238i	0.377334	+	0.245043i
$738$	0.0562037	−	1.07243i	0.00206889	−	0.0394767i
$739$	6.02962	−	28.3671i	0.221803	−	1.04350i	−0.716473	−	0.697615i	$-0.754245\pi$
$739$	6.02962	−	28.3671i	0.221803	−	1.04350i	0.938276	−	0.345887i	$-0.112422\pi$
$740$	−23.7963	+	25.1094i	−0.874768	+	0.923039i
$741$	0.0114586	+	0.00372314i	0.000420944	+	0.000136773i
$742$	0.293752	+	0.0122536i	0.0107840	+	0.000449845i
$743$	−26.0302	+	26.0302i	−0.954956	+	0.954956i	−0.999028	−	0.0440723i	$-0.985967\pi$
$743$	−26.0302	+	26.0302i	−0.954956	+	0.954956i	0.0440723	+	0.999028i	$0.485967\pi$
$744$	0.0571151	+	0.00600303i	0.00209394	+	0.000220082i
$745$	10.2749	+	42.6733i	0.376443	+	1.56343i
$746$	0.147768	+	1.40592i	0.00541018	+	0.0514744i
$747$	−11.8364	+	4.54355i	−0.433069	+	0.166240i
$748$	−5.45172	+	10.6996i	−0.199335	+	0.391216i
$749$	9.11191	+	27.0578i	0.332942	+	0.988669i
$750$	0.00368248	+	0.0456290i	0.000134465	+	0.00166614i
$751$	3.63171	+	6.29030i	0.132523	+	0.229536i	0.924648	−	0.380822i	$-0.124359\pi$
$751$	3.63171	+	6.29030i	0.132523	+	0.229536i	−0.792126	+	0.610358i	$0.791026\pi$
$752$	23.8641	−	15.4975i	0.870235	−	0.565137i
$753$	2.08760	+	1.69051i	0.0760764	+	0.0616055i
$754$	−0.364429	−	0.162254i	−0.0132717	−	0.00590895i
$755$	14.0554	+	14.7916i	0.511527	+	0.538322i
$756$	3.37667	−	0.755476i	0.122808	−	0.0274764i
$757$	−19.0809	−	19.0809i	−0.693507	−	0.693507i	0.269495	−	0.963002i	$-0.413143\pi$
$757$	−19.0809	−	19.0809i	−0.693507	−	0.693507i	−0.963002	+	0.269495i	$0.913143\pi$
$758$	0.0900982	+	0.111262i	0.00327252	+	0.00404122i
$759$	0.568187	+	0.631035i	0.0206239	+	0.0229051i
$760$	−0.0223192	−	0.00534270i	−0.000809602	−	0.000193800i
$761$	4.12455	+	3.71376i	0.149515	+	0.134624i	0.740494	−	0.672063i	$-0.234592\pi$
$761$	4.12455	+	3.71376i	0.149515	+	0.134624i	−0.590979	+	0.806687i	$0.701258\pi$
$762$	0.0393365	+	0.0772023i	0.00142501	+	0.00279674i
$763$	−1.89438	+	7.38417i	−0.0685810	+	0.267325i
$764$	42.5511	−	13.8257i	1.53944	−	0.500196i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0374168 + 0.00196093i) q^{2} +(0.0687711 - 0.0849253i) q^{3} +(-1.98765 + 0.208910i) q^{4} +(-0.633655 + 2.14441i) q^{5} +(-0.00240666 + 0.00331248i) q^{6} +(-2.20341 + 1.46457i) q^{7} +(0.147975 - 0.0234370i) q^{8} +(0.621252 + 2.92276i) q^{9} +O(q^{10})\)	\(q+(-0.0374168 + 0.00196093i) q^{2} +(0.0687711 - 0.0849253i) q^{3} +(-1.98765 + 0.208910i) q^{4} +(-0.633655 + 2.14441i) q^{5} +(-0.00240666 + 0.00331248i) q^{6} +(-2.20341 + 1.46457i) q^{7} +(0.147975 - 0.0234370i) q^{8} +(0.621252 + 2.92276i) q^{9} +(0.0195043 - 0.0814793i) q^{10} +(-1.34592 - 0.286085i) q^{11} +(-0.118951 + 0.183169i) q^{12} +(1.43400 - 0.730661i) q^{13} +(0.0795726 - 0.0591203i) q^{14} +(0.138537 + 0.201287i) q^{15} +(3.90435 - 0.829896i) q^{16} +(-1.56486 + 4.07660i) q^{17} +(-0.0289766 - 0.108142i) q^{18} +(-0.00716074 + 0.0681299i) q^{19} +(0.811494 - 4.39470i) q^{20} +(-0.0271520 + 0.287846i) q^{21} +(0.0509210 + 0.00806510i) q^{22} +(-0.295550 - 5.63942i) q^{23} +(0.00818604 - 0.0141786i) q^{24} +(-4.19696 - 2.71763i) q^{25} +(-0.0522229 + 0.0301509i) q^{26} +(0.583044 + 0.297076i) q^{27} +(4.07364 - 3.37137i) q^{28} +(3.88840 + 5.35192i) q^{29} +(-0.00557832 - 0.00725983i) q^{30} +(1.42674 + 3.20452i) q^{31} +(-0.433891 + 0.116261i) q^{32} +(-0.116856 + 0.0946285i) q^{33} +(0.0505580 - 0.155602i) q^{34} +(-1.74444 - 5.65305i) q^{35} +(-1.84543 - 5.67963i) q^{36} +(-6.49205 - 4.21599i) q^{37} +(0.000134334 - 0.00256324i) q^{38} +(0.0365664 - 0.172031i) q^{39} +(-0.0435068 + 0.332170i) q^{40} +(9.12263 + 2.96412i) q^{41} +(0.000451493 - 0.0108235i) q^{42} +(-3.38639 + 3.38639i) q^{43} +(2.73499 + 0.287459i) q^{44} +(-6.66125 - 0.519805i) q^{45} +(0.0221170 + 0.210429i) q^{46} +(6.65520 - 2.55469i) q^{47} +(0.198028 - 0.388651i) q^{48} +(2.71005 - 6.45412i) q^{49} +(0.162366 + 0.0934549i) q^{50} +(0.238589 + 0.413248i) q^{51} +(-2.69765 + 1.75187i) q^{52} +(2.30489 + 1.86647i) q^{53} +(-0.0223982 - 0.00997230i) q^{54} +(1.46633 - 2.70493i) q^{55} +(-0.291725 + 0.268362i) q^{56} +(0.00529350 + 0.00529350i) q^{57} +(-0.155986 - 0.192627i) q^{58} +(6.88713 + 7.64893i) q^{59} +(-0.317414 - 0.371145i) q^{60} +(5.62046 + 5.06069i) q^{61} +(-0.0596680 - 0.117105i) q^{62} +(-5.64947 - 5.53018i) q^{63} +(-7.57643 + 2.46173i) q^{64} +(0.658171 + 3.53807i) q^{65} +(0.00418683 - 0.00376984i) q^{66} +(-8.28713 - 3.18113i) q^{67} +(2.25874 - 8.42975i) q^{68} +(-0.499255 - 0.362730i) q^{69} +(0.0763564 + 0.208098i) q^{70} +(5.52909 - 4.01712i) q^{71} +(0.160431 + 0.417936i) q^{72} +(-0.233558 - 0.359648i) q^{73} +(0.251179 + 0.145018i) q^{74} +(-0.519425 + 0.169534i) q^{75} -0.136914i q^{76} +(3.38461 - 1.34084i) q^{77} +(-0.00103085 + 0.00650856i) q^{78} +(-3.70296 + 8.31698i) q^{79} +(-0.694378 + 8.89839i) q^{80} +(-8.12386 + 3.61697i) q^{81} +(-0.347152 - 0.0930190i) q^{82} +(0.663758 + 4.19080i) q^{83} +(-0.00616537 - 0.577808i) q^{84} +(-7.75030 - 5.93885i) q^{85} +(0.120067 - 0.133348i) q^{86} +(0.721923 + 0.0378344i) q^{87} +(-0.205868 - 0.0107891i) q^{88} +(-5.38706 + 5.98294i) q^{89} +(0.250262 + 0.00638718i) q^{90} +(-2.08959 + 3.71015i) q^{91} +(1.76558 + 11.1474i) q^{92} +(0.370263 + 0.0992118i) q^{93} +(-0.244007 + 0.108639i) q^{94} +(-0.141561 - 0.0585264i) q^{95} +(-0.0199657 + 0.0448436i) q^{96} +(-2.59509 + 16.3848i) q^{97} +(-0.0887454 + 0.246806i) q^{98} -4.11154i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

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