LMFDB - Embedded newform 175.2.x.a.33.6

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			33.6
Character	$\chi$	$=$	175.33
Dual form			175.2.x.a.122.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16905 + 0.759191i) q^{2} +(2.62961 - 1.00941i) q^{3} +(-0.0231633 + 0.0520255i) q^{4} +(1.77643 - 1.35805i) q^{5} +(-2.30781 + 3.17642i) q^{6} +(-0.311259 + 2.62738i) q^{7} +(-0.448537 - 2.83195i) q^{8} +(3.66648 - 3.30131i) q^{9} +O(q^{10})$	\(q+(-1.16905 + 0.759191i) q^{2} +(2.62961 - 1.00941i) q^{3} +(-0.0231633 + 0.0520255i) q^{4} +(1.77643 - 1.35805i) q^{5} +(-2.30781 + 3.17642i) q^{6} +(-0.311259 + 2.62738i) q^{7} +(-0.448537 - 2.83195i) q^{8} +(3.66648 - 3.30131i) q^{9} +(-1.04571 + 2.93628i) q^{10} +(-0.863299 + 0.958791i) q^{11} +(-0.00839509 + 0.160188i) q^{12} +(-1.23533 - 2.42447i) q^{13} +(-1.63080 - 3.30784i) q^{14} +(3.30047 - 5.36429i) q^{15} +(2.59814 + 2.88553i) q^{16} +(1.38624 - 1.12255i) q^{17} +(-1.77998 + 6.64296i) q^{18} +(-4.59007 + 2.04363i) q^{19} +(0.0295056 + 0.123876i) q^{20} +(1.83362 + 7.22316i) q^{21} +(0.281336 - 1.77628i) q^{22} +(4.36269 + 6.71795i) q^{23} +(-4.03808 - 6.99415i) q^{24} +(1.31138 - 4.82496i) q^{25} +(3.28479 + 1.89648i) q^{26} +(2.47276 - 4.85307i) q^{27} +(-0.129481 - 0.0770521i) q^{28} +(0.927279 + 1.27629i) q^{29} +(0.214101 + 8.77681i) q^{30} +(-8.77248 - 0.922025i) q^{31} +(0.311080 + 0.0833536i) q^{32} +(-1.30232 + 3.39266i) q^{33} +(-0.768350 + 2.36474i) q^{34} +(3.01519 + 5.09005i) q^{35} +(0.0868249 + 0.267220i) q^{36} +(2.97854 + 0.156099i) q^{37} +(3.81452 - 5.87385i) q^{38} +(-5.69571 - 5.12844i) q^{39} +(-4.64273 - 4.42162i) q^{40} +(-11.6529 - 3.78627i) q^{41} +(-7.62734 - 7.05217i) q^{42} +(-4.19548 - 4.19548i) q^{43} +(-0.0298848 - 0.0671223i) q^{44} +(2.02987 - 10.8438i) q^{45} +(-10.2004 - 4.54152i) q^{46} +(3.83025 - 4.72996i) q^{47} +(9.74476 + 4.96520i) q^{48} +(-6.80624 - 1.63559i) q^{49} +(2.12999 + 6.63622i) q^{50} +(2.51214 - 4.35115i) q^{51} +(0.154748 - 0.00811002i) q^{52} +(-1.43123 - 3.72849i) q^{53} +(0.793619 + 7.55078i) q^{54} +(-0.231499 + 2.87563i) q^{55} +(7.58022 - 0.297007i) q^{56} +(-10.0072 + 10.0072i) q^{57} +(-2.05298 - 0.788066i) q^{58} +(-4.36013 + 0.926774i) q^{59} +(0.202630 + 0.295963i) q^{60} +(-1.89142 + 8.89841i) q^{61} +(10.9555 - 5.58209i) q^{62} +(7.53257 + 10.6608i) q^{63} +(-7.81259 + 2.53846i) q^{64} +(-5.48702 - 2.62925i) q^{65} +(-1.05320 - 4.95491i) q^{66} +(2.77331 + 3.42475i) q^{67} +(0.0262916 + 0.0981216i) q^{68} +(18.2533 + 13.2618i) q^{69} +(-7.38923 - 3.66143i) q^{70} +(6.77041 - 4.91899i) q^{71} +(-10.9937 - 8.90252i) q^{72} +(0.190237 + 3.62995i) q^{73} +(-3.60057 + 2.07879i) q^{74} +(-1.42195 - 14.0115i) q^{75} -0.286138i q^{76} +(-2.25040 - 2.56665i) q^{77} +(10.5520 + 1.67128i) q^{78} +(3.68558 - 0.387370i) q^{79} +(8.53410 + 1.59752i) q^{80} +(0.0565003 - 0.537564i) q^{81} +(16.4974 - 4.42046i) q^{82} +(-0.0807312 + 0.0127866i) q^{83} +(-0.418261 - 0.0719169i) q^{84} +(0.938062 - 3.87671i) q^{85} +(8.08990 + 1.71956i) q^{86} +(3.72668 + 2.42013i) q^{87} +(3.10247 + 2.01477i) q^{88} +(15.6831 + 3.33355i) q^{89} +(5.85949 + 14.2180i) q^{90} +(6.75450 - 2.49104i) q^{91} +(-0.450559 + 0.0713615i) q^{92} +(-23.9989 + 6.43047i) q^{93} +(-0.886812 + 8.43745i) q^{94} +(-5.37857 + 9.86392i) q^{95} +(0.902155 - 0.0948203i) q^{96} +(-5.33114 - 0.844370i) q^{97} +(9.19856 - 3.25514i) q^{98} +6.36541i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−1.16905	+	0.759191i	−0.826644	+	0.536829i	−0.887226	−	0.461334i	$-0.847371\pi$
$2$	−1.16905	+	0.759191i	−0.826644	+	0.536829i	0.0605824	+	0.998163i	$0.480704\pi$
$3$	2.62961	−	1.00941i	1.51820	−	0.582784i	0.550491	−	0.834841i	$-0.314441\pi$
$3$	2.62961	−	1.00941i	1.51820	−	0.582784i	0.967712	+	0.252057i	$0.0811072\pi$
$4$	−0.0231633	+	0.0520255i	−0.0115816	+	0.0260128i
$5$	1.77643	−	1.35805i	0.794442	−	0.607340i
$5$	1.77643	−	1.35805i	0.794442	−	0.607340i
$6$	−2.30781	+	3.17642i	−0.942158	+	1.29677i
$7$	−0.311259	+	2.62738i	−0.117645	+	0.993056i
$7$	−0.311259	+	2.62738i	−0.117645	+	0.993056i
$8$	−0.448537	−	2.83195i	−0.158582	−	1.00125i
$9$	3.66648	−	3.30131i	1.22216	−	1.10044i
$10$	−1.04571	+	2.93628i	−0.330683	+	0.928533i
$11$	−0.863299	+	0.958791i	−0.260294	+	0.289086i	−0.859100	−	0.511808i	$-0.828976\pi$
$11$	−0.863299	+	0.958791i	−0.260294	+	0.289086i	0.598805	+	0.800895i	$0.295642\pi$
$12$	−0.00839509	+	0.160188i	−0.00242345	+	0.0462423i
$13$	−1.23533	−	2.42447i	−0.342618	−	0.672426i	0.653829	−	0.756642i	$-0.273161\pi$
$13$	−1.23533	−	2.42447i	−0.342618	−	0.672426i	−0.996448	+	0.0842159i	$0.973161\pi$
$14$	−1.63080	−	3.30784i	−0.435851	−	0.884059i
$15$	3.30047	−	5.36429i	0.852177	−	1.38505i
$16$	2.59814	+	2.88553i	0.649535	+	0.721382i
$17$	1.38624	−	1.12255i	0.336211	−	0.272259i	−0.446315	−	0.894876i	$-0.647264\pi$
$17$	1.38624	−	1.12255i	0.336211	−	0.272259i	0.782527	+	0.622617i	$0.213931\pi$
$18$	−1.77998	+	6.64296i	−0.419544	+	1.56576i
$19$	−4.59007	+	2.04363i	−1.05303	+	0.468841i	−0.858905	−	0.512135i	$-0.828855\pi$
$19$	−4.59007	+	2.04363i	−1.05303	+	0.468841i	−0.194129	+	0.980976i	$0.562188\pi$
$20$	0.0295056	+	0.123876i	0.00659765	+	0.0276996i
$21$	1.83362	+	7.22316i	0.400128	+	1.57622i
$22$	0.281336	−	1.77628i	0.0599810	−	0.378705i
$23$	4.36269	+	6.71795i	0.909683	+	1.40079i	0.916161	+	0.400811i	$0.131271\pi$
$23$	4.36269	+	6.71795i	0.909683	+	1.40079i	−0.00647763	+	0.999979i	$0.502062\pi$
$24$	−4.03808	−	6.99415i	−0.824269	−	1.42768i
$25$	1.31138	−	4.82496i	0.262277	−	0.964993i
$26$	3.28479	+	1.89648i	0.644201	+	0.371930i
$27$	2.47276	−	4.85307i	0.475883	−	0.933973i
$28$	−0.129481	−	0.0770521i	−0.0244696	−	0.0145615i
$29$	0.927279	+	1.27629i	0.172191	+	0.237001i	0.886387	−	0.462945i	$-0.153207\pi$
$29$	0.927279	+	1.27629i	0.172191	+	0.237001i	−0.714196	+	0.699946i	$0.753207\pi$
$30$	0.214101	+	8.77681i	0.0390893	+	1.60242i
$31$	−8.77248	−	0.922025i	−1.57558	−	0.165600i	−0.723993	−	0.689808i	$-0.757695\pi$
$31$	−8.77248	−	0.922025i	−1.57558	−	0.165600i	−0.851591	+	0.524207i	$0.824362\pi$
$32$	0.311080	+	0.0833536i	0.0549917	+	0.0147350i
$33$	−1.30232	+	3.39266i	−0.226705	+	0.590587i
$34$	−0.768350	+	2.36474i	−0.131771	+	0.405549i
$35$	3.01519	+	5.09005i	0.509660	+	0.860376i
$36$	0.0868249	+	0.267220i	0.0144708	+	0.0445366i
$37$	2.97854	+	0.156099i	0.489669	+	0.0256625i	0.295573	−	0.955320i	$-0.404489\pi$
$37$	2.97854	+	0.156099i	0.489669	+	0.0256625i	0.194096	+	0.980983i	$0.437823\pi$
$38$	3.81452	−	5.87385i	0.618797	−	0.952864i
$39$	−5.69571	−	5.12844i	−0.912043	−	0.821207i
$40$	−4.64273	−	4.42162i	−0.734080	−	0.699119i
$41$	−11.6529	−	3.78627i	−1.81988	−	0.591316i	−0.999819	−	0.0190454i	$-0.993937\pi$
$41$	−11.6529	−	3.78627i	−1.81988	−	0.591316i	−0.820065	−	0.572271i	$-0.806063\pi$
$42$	−7.62734	−	7.05217i	−1.17692	−	1.08817i
$43$	−4.19548	−	4.19548i	−0.639805	−	0.639805i	0.310702	−	0.950507i	$-0.399436\pi$
$43$	−4.19548	−	4.19548i	−0.639805	−	0.639805i	−0.950507	+	0.310702i	$0.899436\pi$
$44$	−0.0298848	−	0.0671223i	−0.00450530	−	0.0101191i
$45$	2.02987	−	10.8438i	0.302596	−	1.61650i
$46$	−10.2004	−	4.54152i	−1.50397	−	0.669610i
$47$	3.83025	−	4.72996i	0.558699	−	0.689936i	−0.417036	−	0.908890i	$-0.636931\pi$
$47$	3.83025	−	4.72996i	0.558699	−	0.689936i	0.975735	+	0.218954i	$0.0702645\pi$
$48$	9.74476	+	4.96520i	1.40654	+	0.716666i
$49$	−6.80624	−	1.63559i	−0.972319	−	0.233656i
$50$	2.12999	+	6.63622i	0.301226	+	0.938503i
$51$	2.51214	−	4.35115i	0.351769	−	0.609283i
$52$	0.154748	−	0.00811002i	0.0214597	−	0.00112466i
$53$	−1.43123	−	3.72849i	−0.196595	−	0.512148i	0.799477	−	0.600697i	$-0.205110\pi$
$53$	−1.43123	−	3.72849i	−0.196595	−	0.512148i	−0.996072	+	0.0885493i	$0.971777\pi$
$54$	0.793619	+	7.55078i	0.107998	+	1.02753i
$55$	−0.231499	+	2.87563i	−0.0312153	+	0.387750i
$56$	7.58022	−	0.297007i	1.01295	−	0.0396892i
$57$	−10.0072	+	10.0072i	−1.32549	+	1.32549i
$58$	−2.05298	−	0.788066i	−0.269570	−	0.103478i
$59$	−4.36013	+	0.926774i	−0.567640	+	0.120656i	−0.482787	−	0.875738i	$-0.660375\pi$
$59$	−4.36013	+	0.926774i	−0.567640	+	0.120656i	−0.0848533	+	0.996393i	$0.527042\pi$
$60$	0.202630	+	0.295963i	0.0261595	+	0.0382087i
$61$	−1.89142	+	8.89841i	−0.242171	+	1.13932i	0.674061	+	0.738676i	$0.264549\pi$
$61$	−1.89142	+	8.89841i	−0.242171	+	1.13932i	−0.916232	+	0.400649i	$0.868785\pi$
$62$	10.9555	−	5.58209i	1.39135	−	0.708926i
$63$	7.53257	+	10.6608i	0.949015	+	1.34313i
$64$	−7.81259	+	2.53846i	−0.976573	+	0.317308i
$65$	−5.48702	−	2.62925i	−0.680582	−	0.326118i
$66$	−1.05320	−	4.95491i	−0.129640	−	0.609907i
$67$	2.77331	+	3.42475i	0.338814	+	0.418400i	0.917866	−	0.396890i	$-0.129911\pi$
$67$	2.77331	+	3.42475i	0.338814	+	0.418400i	−0.579052	+	0.815290i	$0.696577\pi$
$68$	0.0262916	+	0.0981216i	0.00318832	+	0.0118990i
$69$	18.2533	+	13.2618i	2.19744	+	1.59653i
$70$	−7.38923	−	3.66143i	−0.883182	−	0.437624i
$71$	6.77041	−	4.91899i	0.803500	−	0.583777i	−0.108439	−	0.994103i	$-0.534585\pi$
$71$	6.77041	−	4.91899i	0.803500	−	0.583777i	0.911939	+	0.410326i	$0.134585\pi$
$72$	−10.9937	−	8.90252i	−1.29562	−	1.04917i
$73$	0.190237	+	3.62995i	0.0222656	+	0.424853i	0.986907	+	0.161288i	$0.0515649\pi$
$73$	0.190237	+	3.62995i	0.0222656	+	0.424853i	−0.964642	+	0.263565i	$0.915102\pi$
$74$	−3.60057	+	2.07879i	−0.418558	+	0.241655i
$75$	−1.42195	−	14.0115i	−0.164192	−	1.61791i
$76$		−	0.286138i		−	0.0328223i
$77$	−2.25040	−	2.56665i	−0.256457	−	0.292496i
$78$	10.5520	+	1.67128i	1.19478	+	0.189235i
$79$	3.68558	−	0.387370i	0.414660	−	0.0435825i	0.105098	−	0.994462i	$-0.466484\pi$
$79$	3.68558	−	0.387370i	0.414660	−	0.0435825i	0.309562	+	0.950879i	$0.399818\pi$
$80$	8.53410	+	1.59752i	0.954142	+	0.178608i
$81$	0.0565003	−	0.537564i	0.00627781	−	0.0597294i
$82$	16.4974	−	4.42046i	1.82183	−	0.488158i
$83$	−0.0807312	+	0.0127866i	−0.00886140	+	0.00140351i	−0.160864	−	0.986977i	$-0.551428\pi$
$83$	−0.0807312	+	0.0127866i	−0.00886140	+	0.00140351i	0.152002	+	0.988380i	$0.451428\pi$
$84$	−0.418261	−	0.0719169i	−0.0456360	−	0.00784678i
$85$	0.938062	−	3.87671i	0.101747	−	0.420488i
$86$	8.08990	+	1.71956i	0.872356	+	0.185425i
$87$	3.72668	+	2.42013i	0.399542	+	0.259465i
$88$	3.10247	+	2.01477i	0.330724	+	0.214775i
$89$	15.6831	+	3.33355i	1.66241	+	0.353355i	0.940804	−	0.338952i	$-0.110073\pi$
$89$	15.6831	+	3.33355i	1.66241	+	0.353355i	0.721602	+	0.692308i	$0.243406\pi$
$90$	5.85949	+	14.2180i	0.617645	+	1.49871i
$91$	6.75450	−	2.49104i	0.708064	−	0.261132i
$92$	−0.450559	+	0.0713615i	−0.0469740	+	0.00743995i
$93$	−23.9989	+	6.43047i	−2.48857	+	0.666809i
$94$	−0.886812	+	8.43745i	−0.0914677	+	0.870257i
$95$	−5.37857	+	9.86392i	−0.551829	+	1.01202i
$96$	0.902155	−	0.0948203i	0.0920758	−	0.00967756i
$97$	−5.33114	−	0.844370i	−0.541296	−	0.0857328i	−0.120201	−	0.992750i	$-0.538354\pi$
$97$	−5.33114	−	0.844370i	−0.541296	−	0.0857328i	−0.421095	+	0.907017i	$0.638354\pi$
$98$	9.19856	−	3.25514i	0.929195	−	0.328819i
$99$			6.36541i			0.639747i
$100$	0.220645	+	0.179987i	0.0220645	+	0.0179987i
$101$	4.22128	−	2.43716i	0.420033	−	0.242506i	−0.275058	−	0.961428i	$-0.588697\pi$
$101$	4.22128	−	2.43716i	0.420033	−	0.242506i	0.695091	+	0.718921i	$0.255364\pi$
$102$	0.366535	+	6.99390i	0.0362924	+	0.692500i
$103$	0.601604	+	0.487170i	0.0592778	+	0.0480022i	0.658501	−	0.752579i	$-0.271191\pi$
$103$	0.601604	+	0.487170i	0.0592778	+	0.0480022i	−0.599224	+	0.800582i	$0.704524\pi$
$104$	−6.31188	+	4.58585i	−0.618931	+	0.449679i
$105$	13.0667	+	10.3413i	1.27518	+	1.00920i
$106$	4.50382	+	3.27222i	0.437450	+	0.317826i
$107$	−0.638591	−	2.38325i	−0.0617349	−	0.230398i	0.928164	−	0.372171i	$-0.121386\pi$
$107$	−0.638591	−	2.38325i	−0.0617349	−	0.230398i	−0.989899	+	0.141773i	$0.954720\pi$
$108$	0.195206	+	0.241060i	0.0187837	+	0.0231960i
$109$	−1.61479	−	7.59699i	−0.154669	−	0.727660i	−0.985299	−	0.170836i	$-0.945353\pi$
$109$	−1.61479	−	7.59699i	−0.154669	−	0.727660i	0.830631	−	0.556824i	$-0.187980\pi$
$110$	−1.91252	−	3.53751i	−0.182351	−	0.337288i
$111$	7.98995	−	2.59609i	0.758372	−	0.246410i
$112$	−8.39006	+	5.92815i	−0.792787	+	0.560158i
$113$	−0.329784	+	0.168033i	−0.0310234	+	0.0158072i	−0.469433	−	0.882968i	$-0.655542\pi$
$113$	−0.329784	+	0.168033i	−0.0310234	+	0.0158072i	0.438410	+	0.898775i	$0.355542\pi$
$114$	4.10156	−	19.2963i	0.384146	−	1.80727i
$115$	16.8733	+	6.00919i	1.57345	+	0.560360i
$116$	−0.0878784	+	0.0186791i	−0.00815931	+	0.00173431i
$117$	−12.5332	−	4.81105i	−1.15870	−	0.444782i
$118$	4.39362	−	4.39362i	0.404465	−	0.404465i
$119$	2.51789	+	3.99157i	0.230815	+	0.365907i
$120$	−16.6718	−	6.94068i	−1.52192	−	0.633594i
$121$	0.975819	+	9.28429i	0.0887108	+	0.844027i
$122$	−4.54443	−	11.8386i	−0.411433	−	1.07182i
$123$	−34.4645	+	1.80621i	−3.10756	+	0.162860i
$124$	0.251168	−	0.435036i	0.0225556	−	0.0390674i
$125$	−4.22298	−	10.3521i	−0.377714	−	0.925922i
$126$	−16.8995	−	6.74435i	−1.50553	−	0.600834i
$127$	18.6864	+	9.52119i	1.65815	+	0.844869i	0.995377	+	0.0960485i	$0.0306204\pi$
$127$	18.6864	+	9.52119i	1.65815	+	0.844869i	0.662773	+	0.748821i	$0.269380\pi$
$128$	6.80078	−	8.39827i	0.601110	−	0.742309i
$129$	−15.2674	−	6.79749i	−1.34422	−	0.598486i
$130$	8.41071	−	1.09197i	0.737668	−	0.0957723i
$131$	−3.22426	−	7.24181i	−0.281705	−	0.632720i	0.716167	−	0.697929i	$-0.245895\pi$
$131$	−3.22426	−	7.24181i	−0.281705	−	0.632720i	−0.997872	+	0.0652097i	$0.979228\pi$
$132$	−0.146339	−	0.146339i	−0.0127372	−	0.0127372i
$133$	−3.94069	−	12.6960i	−0.341701	−	1.10088i
$134$	−5.84218	−	1.89824i	−0.504687	−	0.163983i
$135$	−2.19804	−	11.9793i	−0.189177	−	1.03101i
$136$	−3.80079	−	3.42224i	−0.325915	−	0.293455i
$137$	4.84770	−	7.46480i	0.414167	−	0.637761i	−0.568599	−	0.822615i	$-0.692514\pi$
$137$	4.84770	−	7.46480i	0.414167	−	0.637761i	0.982766	+	0.184854i	$0.0591812\pi$
$138$	−31.4073	−	1.64599i	−2.67357	−	0.140116i
$139$	−0.759246	−	2.33672i	−0.0643984	−	0.198198i	0.913680	−	0.406434i	$-0.133228\pi$
$139$	−0.759246	−	2.33672i	−0.0643984	−	0.198198i	−0.978079	+	0.208236i	$0.933228\pi$
$140$	−0.334654	+	0.0389647i	−0.0282835	+	0.00329312i
$141$	5.29756	−	16.3042i	0.446135	−	1.37306i
$142$	−4.18050	+	10.8906i	−0.350820	+	0.913917i
$143$	3.39101	+	0.908619i	0.283571	+	0.0759826i
$144$	19.0520	+	2.00245i	1.58767	+	0.166871i
$145$	3.38051	+	1.00794i	0.280736	+	0.0837050i
$146$	−2.97822	−	4.09917i	−0.246479	−	0.339249i
$147$	−19.5487	+	2.56934i	−1.61235	+	0.211915i
$148$	−0.0771138	+	0.151344i	−0.00633871	+	0.0124404i
$149$	0.625395	+	0.361072i	0.0512344	+	0.0295802i	0.525398	−	0.850856i	$-0.323916\pi$
$149$	0.625395	+	0.361072i	0.0512344	+	0.0295802i	−0.474164	+	0.880437i	$0.657250\pi$
$150$	12.2997	+	15.3006i	1.00427	+	1.24929i
$151$	8.32092	+	14.4123i	0.677147	+	1.17285i	0.975836	+	0.218503i	$0.0701173\pi$
$151$	8.32092	+	14.4123i	0.677147	+	1.17285i	−0.298689	+	0.954350i	$0.596549\pi$
$152$	7.84628	+	12.0822i	0.636417	+	0.979996i
$153$	1.37671	−	8.69221i	0.111300	−	0.702723i
$154$	4.57940	+	1.29206i	0.369019	+	0.104117i
$155$	−16.8358	+	10.2756i	−1.35229	+	0.825354i
$156$	0.398741	−	0.177531i	0.0319248	−	0.0142138i
$157$	0.888573	−	3.31620i	0.0709158	−	0.264661i	−0.921360	−	0.388709i	$-0.872921\pi$
$157$	0.888573	−	3.31620i	0.0709158	−	0.264661i	0.992276	+	0.124048i	$0.0395877\pi$
$158$	−4.01454	+	3.25091i	−0.319380	+	0.258629i
$159$	−7.52716	−	8.35976i	−0.596943	−	0.662972i
$160$	0.665809	−	0.274391i	0.0526368	−	0.0216925i
$161$	−19.0085	+	9.37141i	−1.49808	+	0.738571i
$162$	0.342062	+	0.671335i	0.0268749	+	0.0527450i
$163$	0.166306	−	3.17331i	0.0130261	−	0.248553i	−0.984353	−	0.176206i	$-0.943618\pi$
$163$	0.166306	−	3.17331i	0.0130261	−	0.248553i	0.997379	−	0.0723474i	$-0.0230490\pi$
$164$	0.466903	−	0.518548i	0.0364590	−	0.0404918i
$165$	2.29394	+	7.79544i	0.178583	+	0.606874i
$166$	0.0846715	−	0.0762386i	0.00657178	−	0.00591726i
$167$	1.83269	+	11.5711i	0.141818	+	0.895401i	0.951302	+	0.308260i	$0.0997467\pi$
$167$	1.83269	+	11.5711i	0.141818	+	0.895401i	−0.809485	+	0.587141i	$0.800253\pi$
$168$	19.6332	−	8.43256i	1.51473	−	0.650586i
$169$	3.28920	−	4.52720i	0.253016	−	0.348246i
$170$	1.84652	+	5.24424i	0.141622	+	0.402215i
$171$	−10.0827	+	22.6462i	−0.771046	+	1.73180i
$172$	0.315453	−	0.121091i	0.0240531	−	0.00923311i
$173$	19.0292	−	12.3577i	1.44676	−	0.939537i	0.447791	−	0.894138i	$-0.352211\pi$
$173$	19.0292	−	12.3577i	1.44676	−	0.939537i	0.998969	−	0.0453988i	$-0.0144558\pi$
$174$	−6.19402			−0.469567
$175$	12.2688	+	4.94732i	0.927436	+	0.373982i
$176$	−5.00959			−0.377612
$177$	−10.5299	+	6.83821i	−0.791477	+	0.513991i
$178$	−20.8652	+	8.00938i	−1.56391	+	0.600328i
$179$	3.14774	−	7.06995i	0.235273	−	0.528433i	−0.756866	−	0.653570i	$-0.773270\pi$
$179$	3.14774	−	7.06995i	0.235273	−	0.528433i	0.992139	+	0.125137i	$0.0399371\pi$
$180$	0.517137	+	0.356783i	0.0385451	+	0.0265931i
$181$	2.15081	−	2.96033i	0.159868	−	0.220040i	−0.721567	−	0.692345i	$-0.756578\pi$
$181$	2.15081	−	2.96033i	0.159868	−	0.220040i	0.881435	+	0.472305i	$0.156578\pi$
$182$	−6.00518	+	8.04010i	−0.445134	+	0.595972i
$183$	4.00848	+	25.3085i	0.296315	+	1.87086i
$184$	17.0681	−	15.3682i	1.25828	−	1.13296i
$185$	5.50315	−	3.76772i	0.404599	−	0.277008i
$186$	23.1739	−	25.7373i	1.69920	−	1.88715i
$187$	−0.120444	+	2.29821i	−0.00880773	+	0.168062i
$188$	0.157358	+	0.308832i	0.0114765	+	0.0225239i
$189$	11.9812	+	8.00744i	0.871502	+	0.582456i
$190$	−1.20078	−	15.6148i	−0.0871136	−	1.13282i
$191$	14.1270	+	15.6896i	1.02219	+	1.13526i	0.990743	+	0.135753i	$0.0433454\pi$
$191$	14.1270	+	15.6896i	1.02219	+	1.13526i	0.0314486	+	0.999505i	$0.489988\pi$
$192$	−17.9817	+	14.5613i	−1.29771	+	1.05087i
$193$	5.23417	−	19.5342i	0.376764	−	1.40610i	−0.473987	−	0.880532i	$-0.657186\pi$
$193$	5.23417	−	19.5342i	0.376764	−	1.40610i	0.850751	−	0.525569i	$-0.176148\pi$
$194$	6.87342	−	3.06024i	0.493483	−	0.219713i
$195$	−17.0827	−	1.37522i	−1.22332	−	0.0984818i
$196$	0.242747	−	0.316212i	0.0173391	−	0.0225866i
$197$	−1.00475	+	6.34375i	−0.0715856	+	0.451974i	0.925695	+	0.378272i	$0.123481\pi$
$197$	−1.00475	+	6.34375i	−0.0715856	+	0.451974i	−0.997280	+	0.0737022i	$0.976519\pi$
$198$	−4.83256	−	7.44148i	−0.343435	−	0.528843i
$199$	6.15950	+	10.6686i	0.436636	+	0.756275i	0.997428	−	0.0716817i	$-0.0228366\pi$
$199$	6.15950	+	10.6686i	0.436636	+	0.756275i	−0.560792	+	0.827957i	$0.689503\pi$
$200$	−14.2523	−	1.54960i	−1.00779	−	0.109573i
$201$	10.7497	+	6.20633i	0.758224	+	0.437761i
$202$	−3.08463	+	6.05392i	−0.217033	+	0.425952i
$203$	−3.64192	+	2.03906i	−0.255613	+	0.143114i
$204$	0.168182	+	0.231482i	0.0117751	+	0.0162070i
$205$	−25.8425	+	9.09928i	−1.80492	+	0.635521i
$206$	−1.07316	−	0.112794i	−0.0747707	−	0.00785871i
$207$	38.1738	+	10.2286i	2.65326	+	0.710939i
$208$	3.78631	−	9.86367i	0.262533	−	0.683923i
$209$	2.00319	−	6.16518i	0.138563	−	0.426455i
$210$	−23.1266	−	2.16933i	−1.59589	−	0.149698i
$211$	0.536205	+	1.65027i	0.0369139	+	0.113609i	0.967816	−	0.251661i	$-0.0809767\pi$
$211$	0.536205	+	1.65027i	0.0369139	+	0.113609i	−0.930902	+	0.365270i	$0.880977\pi$
$212$	0.227129	+	0.0119033i	0.0155993	+	0.000817523i
$213$	12.8382	−	19.7691i	0.879660	−	1.35456i
$214$	2.55589	+	2.30133i	0.174717	+	0.157316i
$215$	−13.1506	−	1.75528i	−0.896867	−	0.119709i
$216$	−14.8528	−	4.82596i	−1.01060	−	0.328365i
$217$	5.15302	−	22.7616i	0.349810	−	1.54516i
$218$	7.65534	+	7.65534i	0.518485	+	0.518485i
$219$	4.16436	+	9.35330i	0.281401	+	0.632037i
$220$	−0.144244	−	0.0786528i	−0.00972491	−	0.00530277i
$221$	−4.43404	−	1.97416i	−0.298266	−	0.132797i
$222$	−7.36973	+	9.10086i	−0.494624	+	0.610810i
$223$	−18.0830	−	9.21376i	−1.21093	−	0.616999i	−0.272395	−	0.962186i	$-0.587816\pi$
$223$	−18.0830	−	9.21376i	−1.21093	−	0.616999i	−0.938534	+	0.345187i	$0.887816\pi$
$224$	−0.315828	+	0.791380i	−0.0211021	+	0.0528763i
$225$	−11.1205	−	22.0199i	−0.741370	−	1.46799i
$226$	0.257965	−	0.446808i	0.0171596	−	0.0297212i
$227$	0.785840	−	0.0411841i	0.0521580	−	0.00273349i	−0.0262391	−	0.999656i	$-0.508353\pi$
$227$	0.785840	−	0.0411841i	0.0521580	−	0.00273349i	0.0783971	+	0.996922i	$0.475020\pi$
$228$	−0.288831	−	0.752430i	−0.0191283	−	0.0498309i
$229$	0.946620	+	9.00649i	0.0625544	+	0.595165i	0.980234	+	0.197843i	$0.0633937\pi$
$229$	0.946620	+	9.00649i	0.0625544	+	0.595165i	−0.917679	+	0.397322i	$0.869940\pi$
$230$	−24.2879	+	5.78503i	−1.60150	+	0.381453i
$231$	−8.50846	−	4.47769i	−0.559815	−	0.294610i
$232$	3.19847	−	3.19847i	0.209990	−	0.209990i
$233$	−7.85073	−	3.01361i	−0.514319	−	0.197428i	0.0873449	−	0.996178i	$-0.472162\pi$
$233$	−7.85073	−	3.01361i	−0.514319	−	0.197428i	−0.601663	+	0.798750i	$0.705495\pi$
$234$	18.3045	−	3.89074i	1.19660	−	0.254346i
$235$	0.380616	−	13.6041i	0.0248287	−	0.887434i
$236$	0.0527789	−	0.248305i	0.00343561	−	0.0161633i
$237$	9.30060	−	4.73889i	0.604139	−	0.307824i
$238$	−5.97390	−	2.75479i	−0.387231	−	0.178567i
$239$	−15.6184	+	5.07472i	−1.01027	+	0.328256i	−0.766962	−	0.641693i	$-0.778232\pi$
$239$	−15.6184	+	5.07472i	−1.01027	+	0.328256i	−0.243308	+	0.969949i	$0.578232\pi$
$240$	24.0539	−	4.41358i	1.55267	−	0.284895i
$241$	3.51030	+	16.5147i	0.226118	+	1.06380i	0.933945	+	0.357417i	$0.116343\pi$
$241$	3.51030	+	16.5147i	0.226118	+	1.06380i	−0.707826	+	0.706386i	$0.750324\pi$
$242$	−8.18933	−	10.1130i	−0.526430	−	0.650087i
$243$	3.83510	+	14.3128i	0.246022	+	0.918165i
$244$	−0.419133	−	0.304518i	−0.0268322	−	0.0194948i
$245$	−14.3120	+	6.33772i	−0.914360	+	0.404902i
$246$	38.9195	−	28.2767i	2.48142	−	1.80286i
$247$	10.6250	+	8.60392i	0.676050	+	0.547454i
$248$	1.32365	+	25.2568i	0.0840520	+	1.60381i
$249$	−0.199384	+	0.115115i	−0.0126355	+	0.00729509i
$250$	12.7961	+	8.89612i	0.809297	+	0.562640i
$251$		−	22.9915i		−	1.45121i	−0.688113	−	0.725604i	$-0.741560\pi$
$251$		−	22.9915i		−	1.45121i	0.688113	−	0.725604i	$-0.258440\pi$
$252$	−0.729112	+	0.144948i	−0.0459298	+	0.00913083i
$253$	−10.2074	−	1.61670i	−0.641735	−	0.101641i
$254$	−29.0737	+	3.05577i	−1.82425	+	0.191736i
$255$	−1.44646	−	11.1411i	−0.0905810	−	0.697683i
$256$	0.142750	−	1.35818i	0.00892188	−	0.0848861i
$257$	−14.6401	+	3.92282i	−0.913227	+	0.244698i	−0.684688	−	0.728836i	$-0.740062\pi$
$257$	−14.6401	+	3.92282i	−0.913227	+	0.244698i	−0.228539	+	0.973535i	$0.573395\pi$
$258$	23.0090	−	3.64427i	1.43248	−	0.226882i
$259$	−1.33723	+	7.77716i	−0.0830912	+	0.483249i
$260$	0.263885	−	0.224563i	0.0163655	−	0.0139268i
$261$	7.61328	+	1.61825i	0.471250	+	0.100167i
$262$	9.26724	+	6.01821i	0.572532	+	0.371806i
$263$	19.8491	+	12.8901i	1.22395	+	0.794840i	0.984383	−	0.176041i	$-0.0563292\pi$
$263$	19.8491	+	12.8901i	1.22395	+	0.794840i	0.239563	+	0.970881i	$0.422996\pi$
$264$	10.1920	+	2.16638i	0.627274	+	0.133331i
$265$	−7.60597	−	4.67970i	−0.467231	−	0.287472i
$266$	14.2455	+	11.8505i	0.873449	+	0.726599i
$267$	44.6053	−	7.06478i	2.72980	−	0.432358i
$268$	−0.242413	+	0.0649545i	−0.0148078	+	0.00396773i
$269$	1.73155	−	16.4746i	0.105574	−	1.00447i	−0.805602	−	0.592457i	$-0.798158\pi$
$269$	1.73155	−	16.4746i	0.105574	−	1.00447i	0.911177	−	0.412016i	$-0.135175\pi$
$270$	11.6642	+	12.3356i	0.709859	+	0.750723i
$271$	−15.1303	+	1.59026i	−0.919101	+	0.0966014i	−0.552250	−	0.833678i	$-0.686231\pi$
$271$	−15.1303	+	1.59026i	−0.919101	+	0.0966014i	−0.366851	+	0.930280i	$0.619564\pi$
$272$	6.84078	+	1.08347i	0.414783	+	0.0656952i
$273$	15.2472	−	13.3685i	0.922802	−	0.809099i
$274$			12.4071i			0.749538i
$275$	3.49401	+	5.42273i	0.210697	+	0.327003i
$276$	−1.11276	+	0.642452i	−0.0669802	+	0.0386711i
$277$	0.835970	+	15.9513i	0.0502286	+	0.958418i	0.901253	+	0.433293i	$0.142648\pi$
$277$	0.835970	+	15.9513i	0.0502286	+	0.958418i	−0.851025	+	0.525126i	$0.824018\pi$
$278$	2.66161	+	2.15533i	0.159633	+	0.129268i
$279$	−35.2080	+	25.5801i	−2.10785	+	1.53144i
$280$	13.0623	−	10.8219i	0.780625	−	0.646735i
$281$	−21.8808	−	15.8974i	−1.30530	−	0.948357i	−0.305309	−	0.952253i	$-0.598760\pi$
$281$	−21.8808	−	15.8974i	−1.30530	−	0.948357i	−0.999992	+	0.00389666i	$0.998760\pi$
$282$	6.18489	+	23.0823i	0.368305	+	1.37453i
$283$	−0.172080	−	0.212502i	−0.0102291	−	0.0126319i	0.772006	−	0.635616i	$-0.219254\pi$
$283$	−0.172080	−	0.212502i	−0.0102291	−	0.0126319i	−0.782235	+	0.622984i	$0.785920\pi$
$284$	0.0990884	+	0.466174i	0.00587981	+	0.0276623i
$285$	−4.18676	+	31.3674i	−0.248002	+	1.85804i
$286$	−4.65408	+	1.51220i	−0.275202	+	0.0894185i
$287$	13.5750	−	29.4382i	0.801309	−	1.73768i
$288$	1.41574	−	0.721357i	0.0834235	−	0.0425064i
$289$	−2.87297	+	13.5163i	−0.168998	+	0.795075i
$290$	−4.71721	+	1.38812i	−0.277004	+	0.0815131i
$291$	−14.8711	+	3.16095i	−0.871761	+	0.185298i
$292$	−0.193256	−	0.0741842i	−0.0113095	−	0.00434130i
$293$	4.77266	−	4.77266i	0.278822	−	0.278822i	−0.553817	−	0.832639i	$-0.686829\pi$
$293$	4.77266	−	4.77266i	0.278822	−	0.278822i	0.832639	+	0.553817i	$0.186829\pi$
$294$	20.9028	−	17.8449i	1.21908	−	1.04073i
$295$	−6.48684	+	7.56763i	−0.377679	+	0.440605i
$296$	−0.893921	−	8.50509i	−0.0519581	−	0.494348i
$297$	2.51834	+	6.56051i	0.146129	+	0.380679i
$298$	−1.00524	+	0.0526825i	−0.0582321	+	0.00305181i
$299$	10.8981	−	18.8761i	0.630253	−	1.09163i
$300$	0.761891	+	0.250574i	0.0439878	+	0.0144669i
$301$	12.3290	−	9.71724i	0.710632	−	0.560092i
$302$	−20.6692	−	10.5315i	−1.18938	−	0.606020i
$303$	8.64021	−	10.6698i	0.496367	−	0.612962i
$304$	−17.8226	−	7.93513i	−1.02220	−	0.455111i
$305$	8.72455	+	18.3760i	0.499566	+	1.05221i
$306$	4.98960	+	11.2068i	0.285236	+	0.640651i
$307$	−15.6825	−	15.6825i	−0.895046	−	0.895046i	0.0999465	−	0.994993i	$-0.468133\pi$
$307$	−15.6825	−	15.6825i	−0.895046	−	0.895046i	−0.994993	+	0.0999465i	$0.968133\pi$
$308$	0.185658	−	0.0576262i	0.0105788	−	0.00328356i
$309$	2.07374	+	0.673798i	0.117971	+	0.0383310i
$310$	11.8808	−	24.7943i	0.674785	−	1.40822i
$311$	−11.9547	−	10.7640i	−0.677888	−	0.610373i	0.256537	−	0.966534i	$-0.417419\pi$
$311$	−11.9547	−	10.7640i	−0.677888	−	0.610373i	−0.934424	+	0.356162i	$0.884085\pi$
$312$	−11.9687	+	18.4303i	−0.677597	+	1.04341i
$313$	−18.0120	−	0.943970i	−1.01810	−	0.0533563i	−0.464024	−	0.885823i	$-0.653595\pi$
$313$	−18.0120	−	0.943970i	−1.01810	−	0.0533563i	−0.554076	+	0.832466i	$0.686928\pi$
$314$	1.47884	+	4.55140i	0.0834558	+	0.256850i
$315$	27.8590	+	8.70848i	1.56968	+	0.490667i
$316$	−0.0652169	+	0.200717i	−0.00366874	+	0.0112912i
$317$	2.58550	−	6.73546i	0.145216	−	0.378301i	−0.841610	−	0.540086i	$-0.818392\pi$
$317$	2.58550	−	6.73546i	0.145216	−	0.378301i	0.986826	+	0.161785i	$0.0517250\pi$
$318$	15.1463	+	4.05844i	0.849362	+	0.227586i
$319$	−2.02421	−	0.212753i	−0.113334	−	0.0119119i
$320$	−10.4311	+	15.1193i	−0.583117	+	0.845194i
$321$	−4.08492	−	5.62241i	−0.227998	−	0.313812i
$322$	15.1072	−	25.3868i	0.841894	−	1.41475i
$323$	−4.06884	+	7.98554i	−0.226396	+	0.444328i
$324$	0.0266583	+	0.0153912i	0.00148102	+	0.000855067i
$325$	−13.3180	+	2.78100i	−0.738747	+	0.154262i
$326$	2.21473	+	3.83602i	0.122662	+	0.212458i
$327$	−11.9147	−	18.3471i	−0.658887	−	1.01460i
$328$	−5.49575	+	34.6988i	−0.303452	+	1.91592i
$329$	11.2352	+	11.5357i	0.619417	+	0.635986i
$330$	−8.59996	−	7.37173i	−0.473412	−	0.405801i
$331$	−20.4919	+	9.12360i	−1.12634	+	0.501479i	−0.883427	−	0.468570i	$-0.844770\pi$
$331$	−20.4919	+	9.12360i	−1.12634	+	0.501479i	−0.242913	+	0.970048i	$0.578103\pi$
$332$	0.00120477	−	0.00449626i	6.61204e−5	−	0.000246765i
$333$	11.4361	−	9.26075i	0.626693	−	0.507486i
$334$	−10.9272	−	12.1359i	−0.597910	−	0.664046i
$335$	9.57757	+	2.31752i	0.523279	+	0.126620i
$336$	−16.0786	+	24.0577i	−0.877160	+	1.31246i
$337$	4.68604	+	9.19687i	0.255265	+	0.500985i	0.982703	−	0.185188i	$-0.0592893\pi$
$337$	4.68604	+	9.19687i	0.255265	+	0.500985i	−0.727438	+	0.686173i	$0.759289\pi$
$338$	−0.408239	+	7.78966i	−0.0222053	+	0.423702i
$339$	−0.697586	+	0.774748i	−0.0378877	+	0.0420785i
$340$	0.179959	+	0.138600i	0.00975967	+	0.00751666i
$341$	8.45730	−	7.61499i	0.457989	−	0.412375i
$342$	−5.40554	−	34.1293i	−0.292298	−	1.84550i
$343$	6.41581	−	17.3735i	0.346421	−	0.938079i
$344$	−9.99956	+	13.7632i	−0.539140	+	0.742063i
$345$	50.4359	−	1.23033i	2.71538	−	0.0662389i
$346$	−12.8642	+	28.8935i	−0.691585	+	1.55333i
$347$	−3.50537	+	1.34559i	−0.188178	+	0.0722349i	−0.450632	−	0.892710i	$-0.648801\pi$
$347$	−3.50537	+	1.34559i	−0.188178	+	0.0722349i	0.262454	+	0.964944i	$0.415468\pi$
$348$	−0.212231	+	0.137824i	−0.0113768	+	0.00738815i
$349$	30.7324			1.64507			0.822534	−	0.568716i	$-0.192560\pi$
$349$	30.7324			1.64507			0.822534	+	0.568716i	$0.192560\pi$
$350$	−18.0988	+	3.53071i	−0.967424	+	0.188724i
$351$	−14.8208			−0.791074
$352$	−0.348474	+	0.226301i	−0.0185737	+	0.0120619i
$353$	−25.3065	+	9.71426i	−1.34693	+	0.517038i	−0.921649	−	0.388024i	$-0.873158\pi$
$353$	−25.3065	+	9.71426i	−1.34693	+	0.517038i	−0.425280	+	0.905062i	$0.639825\pi$
$354$	7.11851	−	15.9884i	0.378345	−	0.849776i
$355$	5.34689	−	17.9328i	0.283783	−	0.951774i
$356$	−0.536701	+	0.738706i	−0.0284451	+	0.0391513i
$357$	10.6502	+	7.95467i	0.563668	+	0.421006i
$358$	1.68757	+	10.6549i	0.0891906	+	0.563127i
$359$	14.4191	−	12.9831i	0.761013	−	0.685219i	−0.194258	−	0.980950i	$-0.562230\pi$
$359$	14.4191	−	12.9831i	0.761013	−	0.685219i	0.955271	+	0.295731i	$0.0955632\pi$
$360$	−31.6196	−	0.884655i	−1.66650	−	0.0466254i
$361$	4.17884	−	4.64107i	0.219939	−	0.244267i
$362$	−0.266947	+	5.09365i	−0.0140304	+	0.267717i
$363$	11.9377	+	23.4290i	0.626566	+	1.22970i
$364$	−0.0268587	+	0.409107i	−0.00140778	+	0.0214430i
$365$	5.26760	+	6.18998i	0.275719	+	0.323998i
$366$	−23.9001	−	26.5438i	−1.24928	−	1.38746i
$367$	19.5907	−	15.8642i	1.02263	−	0.828107i	0.0373896	−	0.999301i	$-0.488096\pi$
$367$	19.5907	−	15.8642i	1.02263	−	0.828107i	0.985237	+	0.171194i	$0.0547624\pi$
$368$	−8.04995	+	30.0428i	−0.419633	+	1.56609i
$369$	−55.2249	+	24.5877i	−2.87489	+	1.27999i
$370$	−3.57305	+	8.58259i	−0.185754	+	0.446188i
$371$	10.2416	−	2.59987i	0.531720	−	0.134978i
$372$	0.221343	−	1.39750i	0.0114761	−	0.0724572i
$373$	−13.3724	−	20.5917i	−0.692395	−	1.06620i	−0.993635	−	0.112647i	$-0.964067\pi$
$373$	−13.3724	−	20.5917i	−0.692395	−	1.06620i	0.301240	−	0.953548i	$-0.402600\pi$
$374$	−1.60397	−	2.77816i	−0.0829394	−	0.143655i
$375$	−21.5543	−	22.9593i	−1.11306	−	1.18561i
$376$	−15.1130	−	8.72551i	−0.779394	−	0.449984i
$377$	1.94883	−	3.82479i	0.100370	−	0.196987i
$378$	−20.0858	−	0.265109i	−1.03310	−	0.0136357i
$379$	15.0440	+	20.7063i	0.772758	+	1.06361i	0.996044	+	0.0888570i	$0.0283214\pi$
$379$	15.0440	+	20.7063i	0.772758	+	1.06361i	−0.223287	+	0.974753i	$0.571679\pi$
$380$	−0.388591	−	0.508303i	−0.0199343	−	0.0260754i
$381$	58.7486	+	6.17473i	3.00978	+	0.316341i
$382$	−28.4265	−	7.61687i	−1.45443	−	0.389713i
$383$	−0.743500	+	1.93688i	−0.0379911	+	0.0989701i	−0.951264	−	0.308379i	$-0.900213\pi$
$383$	−0.743500	+	1.93688i	−0.0379911	+	0.0989701i	0.913272	+	0.407349i	$0.133547\pi$
$384$	9.40607	−	28.9489i	0.480002	−	1.47729i
$385$	−7.48331	−	1.50330i	−0.381385	−	0.0766153i
$386$	8.71116	+	26.8102i	0.443386	+	1.36460i
$387$	−29.2332	−	1.53205i	−1.48601	−	0.0778784i
$388$	0.167416	−	0.257797i	0.00849924	−	0.0130877i
$389$	−10.2406	−	9.22064i	−0.519217	−	0.467505i	0.367365	−	0.930077i	$-0.380260\pi$
$389$	−10.2406	−	9.22064i	−0.519217	−	0.467505i	−0.886582	+	0.462572i	$0.846927\pi$
$390$	21.0146	−	11.3613i	1.06412	−	0.575303i
$391$	13.5890	+	4.41532i	0.687223	+	0.223292i
$392$	−1.57906	+	20.0085i	−0.0797545	+	1.01058i
$393$	−15.7885	−	15.7885i	−0.796424	−	0.796424i
$394$	−3.64151	−	8.17897i	−0.183457	−	0.412051i
$395$	6.02109	−	5.69335i	0.302954	−	0.286463i
$396$	−0.331164	−	0.147444i	−0.0166416	−	0.00740932i
$397$	−17.5765	+	21.7052i	−0.882140	+	1.08935i	0.113262	+	0.993565i	$0.463870\pi$
$397$	−17.5765	+	21.7052i	−0.882140	+	1.08935i	−0.995402	+	0.0957871i	$0.969463\pi$
$398$	−15.3003	−	7.79587i	−0.766932	−	0.390772i
$399$	−23.1779	−	29.4076i	−1.16035	−	1.47222i
$400$	17.3297	−	8.75189i	0.866486	−	0.437595i
$401$	−7.51425	+	13.0151i	−0.375244	+	0.649941i	−0.990364	−	0.138492i	$-0.955774\pi$
$401$	−7.51425	+	13.0151i	−0.375244	+	0.649941i	0.615120	+	0.788434i	$0.289108\pi$
$402$	−17.2787	+	0.905540i	−0.861784	+	0.0451642i
$403$	8.60147	+	22.4076i	0.428470	+	1.11620i
$404$	0.0290158	+	0.276067i	0.00144359	+	0.0137348i
$405$	−0.629672	−	1.03167i	−0.0312887	−	0.0512643i
$406$	2.70956	−	5.14867i	0.134473	−	0.255524i
$407$	−2.72104	+	2.72104i	−0.134877	+	0.134877i
$408$	−13.4490	−	5.16259i	−0.665826	−	0.255586i
$409$	29.3407	−	6.23656i	1.45081	−	0.308378i	0.585929	−	0.810363i	$-0.300730\pi$
$409$	29.3407	−	6.23656i	1.45081	−	0.308378i	0.864877	+	0.501985i	$0.167397\pi$
$410$	23.3032	−	30.2569i	1.15086	−	1.49428i
$411$	5.21248	−	24.5228i	0.257113	−	1.20962i
$412$	−0.0392804	+	0.0200144i	−0.00193521	+	0.000986036i
$413$	−1.07786	−	11.7442i	−0.0530379	−	0.577893i
$414$	−52.3925	+	17.0234i	−2.57495	+	0.836653i
$415$	−0.126048	+	0.132352i	−0.00618747	+	0.00649689i
$416$	−0.182197	−	0.857172i	−0.00893297	−	0.0420263i
$417$	−4.35523	−	5.37826i	−0.213276	−	0.263374i
$418$	2.33872	+	8.72822i	0.114390	+	0.426911i
$419$	29.1668	+	21.1909i	1.42489	+	1.03524i	0.990939	+	0.134309i	$0.0428816\pi$
$419$	29.1668	+	21.1909i	1.42489	+	1.03524i	0.433953	+	0.900936i	$0.357118\pi$
$420$	−0.840677	+	0.440265i	−0.0410208	+	0.0214828i
$421$	−4.26114	+	3.09590i	−0.207675	+	0.150885i	−0.686761	−	0.726883i	$-0.740968\pi$
$421$	−4.26114	+	3.09590i	−0.207675	+	0.150885i	0.479086	+	0.877768i	$0.340968\pi$
$422$	−1.87972	−	1.52217i	−0.0915034	−	0.0740980i
$423$	−1.57156	−	29.9871i	−0.0764118	−	1.45802i
$424$	−9.91694	+	5.72555i	−0.481609	+	0.278057i
$425$	−3.59838	−	8.16063i	−0.174547	−	0.395849i
$426$			32.8578i			1.59196i
$427$	−22.7908	−	7.73917i	−1.10292	−	0.374525i
$428$	0.138782	+	0.0219809i	0.00670827	+	0.00106249i
$429$	9.83420	−	1.03362i	0.474800	−	0.0499034i
$430$	16.7064	−	7.93184i	0.805653	−	0.382507i
$431$	−1.36568	+	12.9936i	−0.0657826	+	0.625880i	0.911112	+	0.412159i	$0.135225\pi$
$431$	−1.36568	+	12.9936i	−0.0657826	+	0.625880i	−0.976895	+	0.213721i	$0.931442\pi$
$432$	20.4282	−	5.47373i	0.982854	−	0.263355i
$433$	18.2189	−	2.88559i	0.875544	−	0.138673i	0.297543	−	0.954708i	$-0.403833\pi$
$433$	18.2189	−	2.88559i	0.875544	−	0.138673i	0.578001	+	0.816036i	$0.303833\pi$
$434$	11.2563	+	30.5216i	0.540319	+	1.46509i
$435$	9.90684	−	0.761836i	0.474996	−	0.0365273i
$436$	0.432641	+	0.0919608i	0.0207198	+	0.00440412i
$437$	−33.7541	−	21.9201i	−1.61468	−	1.04858i
$438$	−11.9693	−	7.77294i	−0.571914	−	0.371406i
$439$	−23.3224	−	4.95733i	−1.11312	−	0.236601i	−0.385584	−	0.922673i	$-0.626000\pi$
$439$	−23.3224	−	4.95733i	−1.11312	−	0.236601i	−0.727534	+	0.686072i	$0.759333\pi$
$440$	8.24747	−	0.634231i	0.393183	−	0.0302358i
$441$	−30.3545	+	16.4727i	−1.44545	+	0.784412i
$442$	6.68239	−	1.05839i	0.317849	−	0.0503423i
$443$	−1.51225	+	0.405207i	−0.0718493	+	0.0192520i	−0.294565	−	0.955632i	$-0.595175\pi$
$443$	−1.51225	+	0.405207i	−0.0718493	+	0.0192520i	0.222715	+	0.974884i	$0.428508\pi$
$444$	−0.0500102	+	0.475815i	−0.00237338	+	0.0225812i
$445$	32.3870	−	15.3767i	1.53529	−	0.728925i
$446$	28.1350	−	2.95711i	1.33223	−	0.140023i
$447$	2.00901	+	0.318196i	0.0950230	+	0.0150502i
$448$	−4.23777	−	21.3167i	−0.200216	−	1.00712i
$449$		−	11.3780i		−	0.536963i	−0.963285	−	0.268482i	$-0.913478\pi$
$449$		−	11.3780i		−	0.536963i	0.963285	−	0.268482i	$-0.0865219\pi$
$450$	29.7178	+	17.2998i	1.40091	+	0.815520i
$451$	13.6902	−	7.90405i	0.644647	−	0.372187i
$452$	−0.00110315	−	0.0210494i	−5.18878e−5	−	0.000990079i
$453$	36.4286	+	29.4993i	1.71157	+	1.38600i
$454$	−0.887420	+	0.644748i	−0.0416487	+	0.0302595i
$455$	8.61591	−	13.5981i	0.403920	−	0.637489i
$456$	32.8285	+	23.8513i	1.53734	+	1.11694i
$457$	0.966035	+	3.60529i	0.0451892	+	0.168648i	0.984833	−	0.173507i	$-0.0555098\pi$
$457$	0.966035	+	3.60529i	0.0451892	+	0.168648i	−0.939643	+	0.342155i	$0.888843\pi$
$458$	−7.94429	−	9.81038i	−0.371212	−	0.458409i
$459$	−2.01999	−	9.50329i	−0.0942849	−	0.443576i
$460$	−0.703472	+	0.738652i	−0.0327996	+	0.0344398i
$461$	−12.7265	+	4.13508i	−0.592730	+	0.192590i	−0.589995	−	0.807407i	$-0.700870\pi$
$461$	−12.7265	+	4.13508i	−0.592730	+	0.192590i	−0.00273459	+	0.999996i	$0.500870\pi$
$462$	13.3462	−	1.22489i	0.620923	−	0.0569871i
$463$	−9.37027	+	4.77439i	−0.435473	+	0.221885i	−0.657963	−	0.753050i	$-0.728582\pi$
$463$	−9.37027	+	4.77439i	−0.435473	+	0.221885i	0.222490	+	0.974935i	$0.428582\pi$
$464$	−1.27357	+	5.99167i	−0.0591239	+	0.278156i
$465$	−33.8993	+	44.0150i	−1.57204	+	2.04115i
$466$	11.4658	−	2.43713i	0.531144	−	0.112898i
$467$	−5.92483	−	2.27433i	−0.274168	−	0.105243i	0.217399	−	0.976083i	$-0.430243\pi$
$467$	−5.92483	−	2.27433i	−0.274168	−	0.105243i	−0.491568	+	0.870839i	$0.663576\pi$
$468$	0.540608	−	0.540608i	0.0249896	−	0.0249896i
$469$	−9.86133	+	6.22055i	−0.455354	+	0.287238i
$470$	9.88315	+	16.1929i	0.455876	+	0.746921i
$471$	−1.01081	−	9.61723i	−0.0465757	−	0.443138i
$472$	4.58026	+	11.9320i	0.210823	+	0.549214i
$473$	7.64454	−	0.400634i	0.351496	−	0.0184211i
$474$	−7.27515	+	12.6009i	−0.334159	+	0.578780i
$475$	3.84110	+	24.8269i	0.176242	+	1.13914i
$476$	−0.265986	+	0.0385368i	−0.0121914	+	0.00176633i
$477$	−17.5565	−	8.94549i	−0.803857	−	0.409586i
$478$	14.4060	−	17.7899i	0.658916	−	0.813693i
$479$	3.90254	+	1.73752i	0.178312	+	0.0793895i	0.493951	−	0.869490i	$-0.335552\pi$
$479$	3.90254	+	1.73752i	0.178312	+	0.0793895i	−0.315639	+	0.948879i	$0.602219\pi$
$480$	1.47384	−	1.39362i	0.0672714	−	0.0636096i
$481$	−3.30102	−	7.41420i	−0.150513	−	0.338059i
$482$	−16.6415	−	16.6415i	−0.758000	−	0.758000i
$483$	−40.5253	+	43.8305i	−1.84397	+	1.99436i
$484$	−0.505624	−	0.164287i	−0.0229829	−	0.00746759i
$485$	−10.6171	+	5.74001i	−0.482097	+	0.260641i
$486$	−15.3496	−	13.8208i	−0.696270	−	0.626924i
$487$	9.30365	−	14.3264i	0.421588	−	0.649189i	−0.562515	−	0.826787i	$-0.690166\pi$
$487$	9.30365	−	14.3264i	0.421588	−	0.649189i	0.984103	+	0.177598i	$0.0568327\pi$
$488$	26.0482	+	1.36513i	1.17915	+	0.0617965i
$489$	−2.76586	−	8.51243i	−0.125076	−	0.384945i
$490$	11.9199	−	18.2747i	0.538487	−	0.825565i
$491$	2.07485	−	6.38573i	0.0936366	−	0.288184i	−0.893259	−	0.449542i	$-0.851587\pi$
$491$	2.07485	−	6.38573i	0.0936366	−	0.288184i	0.986896	+	0.161358i	$0.0515873\pi$
$492$	0.704342	−	1.83487i	0.0317542	−	0.0827225i
$493$	2.71813	+	0.728320i	0.122418	+	0.0328019i
$494$	−18.9531	−	1.99205i	−0.852742	−	0.0896268i
$495$	8.64456	+	11.3077i	0.388544	+	0.508242i
$496$	−20.1316	−	27.7088i	−0.903935	−	1.24416i
$497$	10.8167	+	19.3195i	0.485195	+	0.866598i
$498$	0.145697	−	0.285946i	0.00652882	−	0.0128135i
$499$	−16.7831	−	9.68973i	−0.751315	−	0.433772i	0.0748537	−	0.997195i	$-0.476151\pi$
$499$	−16.7831	−	9.68973i	−0.751315	−	0.433772i	−0.826169	+	0.563422i	$0.809484\pi$
$500$	0.636393	+	0.0200864i	0.0284603	+	0.000898290i
$501$	16.4993	+	28.5776i	0.737133	+	1.27675i
$502$	17.4549	+	26.8782i	0.779050	+	1.19963i
$503$	3.99874	−	25.2471i	0.178295	−	1.12571i	−0.722469	−	0.691403i	$-0.756993\pi$
$503$	3.99874	−	25.2471i	0.178295	−	1.12571i	0.900764	−	0.434308i	$-0.143007\pi$
$504$	26.8122	−	26.1136i	1.19431	−	1.16319i
$505$	4.18901	−	10.0622i	0.186408	−	0.447760i
$506$	13.1604	−	5.85937i	0.585050	−	0.260481i
$507$	4.07950	−	15.2249i	0.181177	−	0.676162i
$508$	−0.928183	+	0.751628i	−0.0411815	+	0.0333481i
$509$	−6.42788	−	7.13889i	−0.284911	−	0.316426i	0.583653	−	0.812003i	$-0.301623\pi$
$509$	−6.42788	−	7.13889i	−0.284911	−	0.316426i	−0.868564	+	0.495578i	$0.834956\pi$
$510$	10.1492	+	11.9264i	0.449415	+	0.528109i
$511$	−9.59645	−	0.630027i	−0.424522	−	0.0278707i
$512$	10.6764	+	20.9536i	0.471834	+	0.926026i
$513$	−1.43227	+	27.3293i	−0.0632362	+	1.20662i
$514$	14.1369	−	15.7006i	0.623553	−	0.692525i
$515$	1.73031	+	0.0484107i	0.0762465	+	0.00213323i
$516$	0.707286	−	0.636844i	0.0311366	−	0.0280355i
$517$	1.22839	+	7.75578i	0.0540247	+	0.341099i
$518$	−4.34106	−	10.1071i	−0.190735	−	0.444081i
$519$	37.5652	−	51.7041i	1.64893	−	2.26956i
$520$	−4.98477	+	16.7183i	−0.218596	+	0.733146i
$521$	3.82172	−	8.58373i	0.167433	−	0.376060i	−0.810269	−	0.586058i	$-0.800679\pi$
$521$	3.82172	−	8.58373i	0.167433	−	0.376060i	0.977702	+	0.209998i	$0.0673457\pi$
$522$	−10.1289	+	3.88811i	−0.443329	+	0.170178i
$523$	4.55650	−	2.95903i	0.199242	−	0.129389i	−0.441162	−	0.897427i	$-0.645434\pi$
$523$	4.55650	−	2.95903i	0.199242	−	0.129389i	0.640404	+	0.768038i	$0.278767\pi$
$524$	0.451443			0.0197214
$525$	37.2560	+	0.625204i	1.62599	+	0.0272861i
$526$	−32.9906			−1.43846
$527$	−13.1957	+	8.56941i	−0.574815	+	0.373289i
$528$	−13.1732	+	5.05673i	−0.573292	+	0.220066i
$529$	−16.7429	+	37.6051i	−0.727951	+	1.63500i
$530$	12.4446	−	0.303572i	0.540557	−	0.0131863i
$531$	−12.9267	+	17.7921i	−0.560973	+	0.772113i
$532$	0.751793	+	0.0890630i	0.0325944	+	0.00386137i
$533$	5.21551	+	32.9295i	0.225909	+	1.42633i
$534$	−46.7824	+	42.1230i	−2.02447	+	1.82284i
$535$	−4.37099	−	3.36643i	−0.188974	−	0.145544i
$536$	8.45479	−	9.39000i	0.365191	−	0.405586i
$537$	1.14084	−	21.7685i	0.0492309	−	0.939382i
$538$	10.4831	+	20.5742i	0.451957	+	0.887016i
$539$	7.44401	−	5.11375i	0.320636	−	0.220265i
$540$	0.674141	+	0.163124i	0.0290104	+	0.00701976i
$541$	8.47947	+	9.41740i	0.364561	+	0.404886i	0.897320	−	0.441381i	$-0.145511\pi$
$541$	8.47947	+	9.41740i	0.364561	+	0.404886i	−0.532759	+	0.846267i	$0.678845\pi$
$542$	16.4808	−	13.3459i	0.707911	−	0.573255i
$543$	2.66758	−	9.95556i	0.114477	−	0.427234i
$544$	0.524798	−	0.233655i	0.0225005	−	0.0100179i
$545$	−13.1857	−	11.3025i	−0.564812	−	0.484147i
$546$	−7.67549	+	27.2040i	−0.328481	+	1.16422i
$547$	4.53361	−	28.6241i	0.193843	−	1.22388i	−0.678359	−	0.734731i	$-0.737309\pi$
$547$	4.53361	−	28.6241i	0.193843	−	1.22388i	0.872202	−	0.489146i	$-0.162691\pi$
$548$	0.276072	+	0.425113i	0.0117932	+	0.0181599i
$549$	22.4416	+	38.8700i	0.957784	+	1.65893i
$550$	−8.20157	−	3.68683i	−0.349716	−	0.157207i
$551$	−6.86454	−	3.96324i	−0.292439	−	0.168840i
$552$	29.3695	−	57.6409i	1.25005	−	2.45336i
$553$	−0.129401	+	9.80398i	−0.00550270	+	0.416908i
$554$	−13.0873	−	18.0132i	−0.556028	−	0.765306i
$555$	10.6679	−	15.4625i	0.452828	−	0.656348i
$556$	0.139156	+	0.0146259i	0.00590152	+	0.000620274i
$557$	−11.7854	−	3.15789i	−0.499364	−	0.133804i	0.000340697	−	1.00000i	$-0.499892\pi$
$557$	−11.7854	−	3.15789i	−0.499364	−	0.133804i	−0.499705	+	0.866196i	$0.666558\pi$
$558$	21.7398	−	56.6340i	0.920318	−	2.39751i
$559$	−4.98901	+	15.3546i	−0.211013	+	0.649430i
$560$	−6.85359	+	21.9251i	−0.289617	+	0.926504i
$561$	2.00312	+	6.16496i	0.0845716	+	0.260285i
$562$	37.6489	+	1.97310i	1.58812	+	0.0832301i
$563$	−2.74960	+	4.23402i	−0.115882	+	0.178443i	−0.891852	−	0.452327i	$-0.850594\pi$
$563$	−2.74960	+	4.23402i	−0.115882	+	0.178443i	0.775970	+	0.630770i	$0.217261\pi$
$564$	0.725527	+	0.653267i	0.0305502	+	0.0275075i
$565$	−0.357639	+	0.746362i	−0.0150460	+	0.0313997i
$566$	0.362500	+	0.117783i	0.0152370	+	0.00495081i
$567$	1.39480	+	0.315769i	0.0585761	+	0.0132611i
$568$	−16.9671	−	16.9671i	−0.711924	−	0.711924i
$569$	−3.55005	−	7.97354i	−0.148826	−	0.334268i	0.823714	−	0.567006i	$-0.191898\pi$
$569$	−3.55005	−	7.97354i	−0.148826	−	0.334268i	−0.972540	+	0.232738i	$0.925232\pi$
$570$	−18.9193	−	39.8486i	−0.792442	−	1.66908i
$571$	−23.9598	−	10.6676i	−1.00269	−	0.446425i	−0.161327	−	0.986901i	$-0.551577\pi$
$571$	−23.9598	−	10.6676i	−1.00269	−	0.446425i	−0.841359	+	0.540476i	$0.818244\pi$
$572$	−0.125818	+	0.155373i	−0.00526073	+	0.00649646i
$573$	52.9856	+	26.9975i	2.21350	+	1.12784i
$574$	6.47927	+	44.7208i	0.270439	+	1.86661i
$575$	38.1350	−	12.2400i	1.59034	−	0.510443i
$576$	−20.2644	+	35.0990i	−0.844351	+	1.46246i
$577$	4.42620	−	0.231967i	0.184265	−	0.00965693i	0.0400198	−	0.999199i	$-0.487258\pi$
$577$	4.42620	−	0.231967i	0.184265	−	0.00965693i	0.144245	+	0.989542i	$0.453925\pi$
$578$	−6.90277	−	17.9823i	−0.287118	−	0.747967i
$579$	−5.95422	−	56.6506i	−0.247449	−	2.35432i
$580$	−0.130742	+	0.152526i	−0.00542878	+	0.00633328i
$581$	−0.00846686	−	0.216091i	−0.000351265	−	0.00896498i
$582$	14.9853	−	14.9853i	0.621162	−	0.621162i
$583$	4.81043	+	1.84655i	0.199228	+	0.0764763i
$584$	10.1945	−	2.16691i	0.421851	−	0.0896672i
$585$	−28.7980	+	8.47430i	−1.19065	+	0.350369i
$586$	−1.95613	+	9.20285i	−0.0808068	+	0.380166i
$587$	−22.6393	+	11.5353i	−0.934426	+	0.476114i	−0.853783	−	0.520629i	$-0.825697\pi$
$587$	−22.6393	+	11.5353i	−0.934426	+	0.476114i	−0.0806428	+	0.996743i	$0.525697\pi$
$588$	0.319140	−	1.07655i	0.0131611	−	0.0443960i
$589$	42.1506	−	13.6956i	1.73678	−	0.564315i
$590$	1.83817	−	13.7717i	0.0756764	−	0.566972i
$591$	3.76135	+	17.6958i	0.154721	+	0.727907i
$592$	7.28823	+	9.00022i	0.299545	+	0.369907i
$593$	9.85810	+	36.7909i	0.404824	+	1.51082i	0.804381	+	0.594114i	$0.202497\pi$
$593$	9.85810	+	36.7909i	0.404824	+	1.51082i	−0.399557	+	0.916708i	$0.630836\pi$
$594$	−7.92475	−	5.75767i	−0.325156	−	0.236240i
$595$	9.89361	+	3.67130i	0.405598	+	0.150509i
$596$	−0.0332712	+	0.0241729i	−0.00136284	+	0.000990161i
$597$	26.9660	+	21.8367i	1.10365	+	0.893715i
$598$	1.59009	+	30.3408i	0.0650238	+	1.24073i
$599$	−18.8301	+	10.8716i	−0.769377	+	0.444200i	−0.832652	−	0.553796i	$-0.813179\pi$
$599$	−18.8301	+	10.8716i	−0.769377	+	0.444200i	0.0632751	+	0.997996i	$0.479845\pi$
$600$	−39.0420	+	10.3115i	−1.59388	+	0.420967i
$601$			0.106137i			0.00432940i	0.999998	+	0.00216470i	$0.000689047\pi$
$601$			0.106137i			0.00432940i	−0.999998	+	0.00216470i	$0.999311\pi$
$602$	−7.03599	+	20.7200i	−0.286766	+	0.844484i
$603$	21.4744	+	3.40122i	0.874507	+	0.138508i
$604$	−0.942545	+	0.0990655i	−0.0383516	+	0.00403092i
$605$	14.3420	+	15.1677i	0.583087	+	0.616653i
$606$	−2.00046	+	19.0331i	−0.0812630	+	0.773166i
$607$	−1.34075	+	0.359253i	−0.0544194	+	0.0145816i	−0.285926	−	0.958252i	$-0.592301\pi$
$607$	−1.34075	+	0.359253i	−0.0544194	+	0.0145816i	0.231507	+	0.972833i	$0.425634\pi$
$608$	−1.59822	+	0.253134i	−0.0648165	+	0.0102659i
$609$	−7.51856	+	9.03810i	−0.304668	+	0.366242i
$610$	−24.1503	−	14.8589i	−0.977819	−	0.601619i
$611$	−16.1992	−	3.44326i	−0.655351	−	0.139299i
$612$	0.420328	+	0.272964i	0.0169907	+	0.0110339i
$613$	13.9369	+	9.05073i	0.562906	+	0.365556i	0.794507	−	0.607255i	$-0.207730\pi$
$613$	13.9369	+	9.05073i	0.562906	+	0.365556i	−0.231601	+	0.972811i	$0.574396\pi$
$614$	30.2396	+	6.42763i	1.22037	+	0.259398i
$615$	−58.7708	+	50.0133i	−2.36987	+	2.01673i
$616$	−6.25923	+	7.52425i	−0.252191	+	0.303161i
$617$	−34.8080	+	5.51305i	−1.40132	+	0.221947i	−0.810916	−	0.585162i	$-0.801031\pi$
$617$	−34.8080	+	5.51305i	−1.40132	+	0.221947i	−0.590402	+	0.807109i	$0.701031\pi$
$618$	−2.93584	+	0.786657i	−0.118097	+	0.0316440i
$619$	−1.57109	+	14.9479i	−0.0631474	+	0.600807i	0.916493	+	0.400050i	$0.131007\pi$
$619$	−1.57109	+	14.9479i	−0.0631474	+	0.600807i	−0.979641	+	0.200758i	$0.935660\pi$
$620$	−0.144620	−	1.11391i	−0.00580808	−	0.0447356i
$621$	43.3906	−	4.56053i	1.74120	−	0.183008i
$622$	22.1476	+	3.50783i	0.888037	+	0.140651i
$623$	−13.6400	+	40.1679i	−0.546475	+	1.60929i
$624$		−	29.7595i		−	1.19133i
$625$	−21.5605	−	12.6548i	−0.862422	−	0.506191i
$626$	21.7736	−	12.5710i	0.870249	−	0.502439i
$627$	−0.955605	−	18.2340i	−0.0381632	−	0.728197i
$628$	0.151945	+	0.123042i	0.00606325	+	0.00490993i
$629$	4.30418	−	3.12717i	0.171619	−	0.124689i
$630$	−39.1800	+	10.9696i	−1.56097	+	0.437040i
$631$	−15.3013	−	11.1170i	−0.609134	−	0.442562i	0.239975	−	0.970779i	$-0.422861\pi$
$631$	−15.3013	−	11.1170i	−0.609134	−	0.442562i	−0.849109	+	0.528217i	$0.822861\pi$
$632$	−2.75013	−	10.2636i	−0.109394	−	0.408265i
$633$	3.07581	+	3.79831i	0.122252	+	0.150969i
$634$	2.09092	+	9.83699i	0.0830409	+	0.390677i
$635$	46.1253	−	8.46341i	1.83043	−	0.335860i
$636$	0.609275	−	0.197965i	0.0241593	−	0.00784983i
$637$	4.44250	+	18.5220i	0.176018	+	0.733868i
$638$	2.52793	−	1.28804i	0.100082	−	0.0509942i
$639$	8.58444	−	40.3866i	0.339595	−	1.59767i
$640$	0.675802	−	24.1547i	0.0267134	−	0.954800i
$641$	0.0140922	−	0.00299539i	0.000556608	−	0.000118311i	−0.207633	−	0.978207i	$-0.566576\pi$
$641$	0.0140922	−	0.00299539i	0.000556608	−	0.000118311i	0.208190	+	0.978088i	$0.433243\pi$
$642$	9.04396	+	3.47165i	0.356937	+	0.137015i
$643$	13.5176	−	13.5176i	0.533083	−	0.533083i	−0.388405	−	0.921489i	$-0.626974\pi$
$643$	13.5176	−	13.5176i	0.533083	−	0.533083i	0.921489	+	0.388405i	$0.126974\pi$
$644$	−0.0472533	−	1.20600i	−0.00186204	−	0.0475231i
$645$	−36.3528	+	8.65871i	−1.43139	+	0.340937i
$646$	−1.30587	−	12.4245i	−0.0513788	−	0.488837i
$647$	4.32202	+	11.2593i	0.169916	+	0.442647i	0.991925	−	0.126828i	$-0.0404797\pi$
$647$	4.32202	+	11.2593i	0.169916	+	0.442647i	−0.822008	+	0.569475i	$0.807146\pi$
$648$	−1.54770	+	0.0811114i	−0.0607993	+	0.00318636i
$649$	2.87551	−	4.98053i	0.112874	−	0.195503i
$650$	13.4581	−	13.3620i	0.527868	−	0.524101i
$651$	−9.42544	−	65.0556i	−0.369412	−	2.54973i
$652$	0.161241	+	0.0821564i	0.00631469	+	0.00321749i
$653$	21.5671	−	26.6331i	0.843984	−	1.04223i	−0.154544	−	0.987986i	$-0.549391\pi$
$653$	21.5671	−	26.6331i	0.843984	−	1.04223i	0.998528	−	0.0542474i	$-0.0172760\pi$
$654$	27.8579	+	12.4031i	1.08933	+	0.485001i
$655$	−15.5624	−	8.48582i	−0.608074	−	0.331569i
$656$	−19.3506	−	43.4621i	−0.755513	−	1.69691i
$657$	12.6811	+	12.6811i	0.494736	+	0.494736i
$658$	−21.8924	−	4.95622i	−0.853453	−	0.193214i
$659$	−33.4008	−	10.8526i	−1.30111	−	0.422756i	−0.425142	−	0.905127i	$-0.639776\pi$
$659$	−33.4008	−	10.8526i	−1.30111	−	0.422756i	−0.875967	+	0.482371i	$0.839776\pi$
$660$	−0.458697	−	0.0612245i	−0.0178548	−	0.00238316i
$661$	−29.1624	−	26.2579i	−1.13429	−	1.02132i	−0.999537	−	0.0304355i	$-0.990311\pi$
$661$	−29.1624	−	26.2579i	−1.13429	−	1.02132i	−0.134749	−	0.990880i	$-0.543023\pi$
$662$	17.0296	−	26.2233i	0.661873	−	1.01920i
$663$	−13.6525	−	0.715499i	−0.530220	−	0.0277877i
$664$	0.0724219	+	0.222892i	0.00281051	+	0.00864987i
$665$	−24.2421	−	17.2018i	−0.940069	−	0.667056i
$666$	−6.33868	+	19.5085i	−0.245619	+	0.755937i
$667$	−4.52862	+	11.7975i	−0.175349	+	0.456800i
$668$	−0.644445	−	0.172679i	−0.0249343	−	0.00668114i
$669$	−56.8517	−	5.97535i	−2.19801	−	0.231020i
$670$	−12.9561	+	4.56190i	−0.500538	+	0.176242i
$671$	−6.89886	−	9.49546i	−0.266327	−	0.366568i
$672$	−0.0316748	+	2.39982i	−0.00122188	+	0.0925749i
$673$	4.21677	−	8.27589i	0.162545	−	0.319012i	−0.795341	−	0.606163i	$-0.792708\pi$
$673$	4.21677	−	8.27589i	0.162545	−	0.319012i	0.957885	+	0.287151i	$0.0927081\pi$
$674$	−12.4604	−	7.19401i	−0.479956	−	0.277103i
$675$	−20.1731	−	18.2952i	−0.776464	−	0.704183i
$676$	0.159341	+	0.275987i	0.00612851	+	0.0106149i
$677$	4.33866	+	6.68096i	0.166748	+	0.256770i	0.912160	−	0.409835i	$-0.134414\pi$
$677$	4.33866	+	6.68096i	0.166748	+	0.256770i	−0.745411	+	0.666605i	$0.767747\pi$
$678$	0.227333	−	1.43532i	0.00873065	−	0.0551232i
$679$	3.87785	−	13.7441i	0.148818	−	0.527451i
$680$	−11.3994	−	0.917696i	−0.437147	−	0.0351920i
$681$	2.02488	−	0.901533i	0.0775934	−	0.0345468i
$682$	−4.10579	+	15.3230i	−0.157219	+	0.586749i
$683$	34.6781	−	28.0817i	1.32692	−	1.07452i	0.335745	−	0.941953i	$-0.391012\pi$
$683$	34.6781	−	28.0817i	1.32692	−	1.07452i	0.991174	−	0.132565i	$-0.0423213\pi$
$684$	−0.944631	−	1.04912i	−0.0361189	−	0.0401141i
$685$	−1.52601	−	19.8441i	−0.0583059	−	0.758204i
$686$	5.68936	+	25.1813i	0.217221	+	0.961426i
$687$	11.5805	+	22.7280i	0.441823	+	0.867126i
$688$	1.20573	−	23.0066i	0.0459679	−	0.877119i
$689$	−7.27156	+	8.07589i	−0.277025	+	0.307667i
$690$	−58.0281	+	39.7288i	−2.20909	+	1.51245i
$691$	−1.00094	+	0.901253i	−0.0380776	+	0.0342853i	−0.687950	−	0.725758i	$-0.741489\pi$
$691$	−1.00094	+	0.901253i	−0.0380776	+	0.0342853i	0.649872	+	0.760044i	$0.274822\pi$
$692$	0.202138	+	1.27625i	0.00768412	+	0.0485156i
$693$	−16.7243	−	1.98129i	−0.635305	−	0.0752629i
$694$	3.07640	−	4.23431i	0.116779	−	0.160732i
$695$	−4.52213	−	3.11992i	−0.171534	−	0.118345i
$696$	5.18214	−	11.6393i	0.196429	−	0.441186i
$697$	−20.4040	+	7.83236i	−0.772857	+	0.296672i
$698$	−35.9277	+	23.3318i	−1.35989	+	0.883120i
$699$	−23.6863			−0.895898
$700$	−0.541573	+	0.523696i	−0.0204695	+	0.0197939i
$701$	20.4883			0.773831			0.386915	−	0.922115i	$-0.373541\pi$
$701$	20.4883			0.773831			0.386915	+	0.922115i	$0.373541\pi$
$702$	17.3262	−	11.2518i	0.653937	−	0.424672i
$703$	−13.9907	+	5.37053i	−0.527670	+	0.202553i
$704$	4.31074	−	9.68209i	0.162467	−	0.364907i
$705$	−12.7313	−	36.1576i	−0.479487	−	1.36178i
$706$	22.2096	−	30.5689i	0.835871	−	1.15048i
$707$	5.08942	+	11.8495i	0.191408	+	0.445646i
$708$	−0.111854	−	0.706220i	−0.00420374	−	0.0265414i
$709$	−25.6540	+	23.0990i	−0.963458	+	0.867501i	−0.991235	−	0.132113i	$-0.957824\pi$
$709$	−25.6540	+	23.0990i	−0.963458	+	0.867501i	0.0277767	+	0.999614i	$0.491157\pi$
$710$	7.36363	+	25.0237i	0.276352	+	0.939122i
$711$	12.2343	−	13.5875i	0.458821	−	0.509572i
$712$	2.40599	−	45.9090i	0.0901682	−	1.72051i
$713$	−32.0775	−	62.9556i	−1.20131	−	2.35770i
$714$	−18.4897	−	1.21389i	−0.691960	−	0.0454286i
$715$	7.25784	−	2.99108i	0.271428	−	0.111860i
$716$	0.294906	+	0.327526i	0.0110211	+	0.0122402i
$717$	−35.9477	+	29.1099i	−1.34249	+	1.08713i
$718$	−7.00010	+	26.1247i	−0.261241	+	0.974966i
$719$	−5.69365	+	2.53498i	−0.212337	+	0.0945386i	−0.510149	−	0.860086i	$-0.670410\pi$
$719$	−5.69365	+	2.53498i	−0.212337	+	0.0945386i	0.297812	+	0.954625i	$0.403743\pi$
$720$	36.5640	−	22.3165i	1.36266	−	0.831686i
$721$	−1.46723	+	1.42901i	−0.0546426	+	0.0532190i
$722$	−1.36182	+	8.59818i	−0.0506816	+	0.319991i
$723$	25.9008	+	39.8837i	0.963261	+	1.48329i
$724$	0.104193	+	0.180468i	0.00387231	+	0.00670704i
$725$	7.37407	−	2.80038i	0.273866	−	0.104003i
$726$	−31.7429	−	18.3267i	−1.17809	−	0.680169i
$727$	−10.2720	+	20.1599i	−0.380967	+	0.747690i	−0.999268	−	0.0382513i	$-0.987821\pi$
$727$	−10.2720	+	20.1599i	−0.380967	+	0.747690i	0.618301	+	0.785941i	$0.287821\pi$
$728$	−10.0841	−	18.0111i	−0.373743	−	0.667535i
$729$	25.4854	+	35.0777i	0.943904	+	1.29917i
$730$	−10.8575	−	3.23729i	−0.401853	−	0.119817i
$731$	−10.5256	−	1.10628i	−0.389302	−	0.0409173i
$732$	−1.40954	−	0.377685i	−0.0520980	−	0.0139596i
$733$	−2.08743	+	5.43794i	−0.0771010	+	0.200855i	−0.966714	−	0.255861i	$-0.917641\pi$
$733$	−2.08743	+	5.43794i	−0.0771010	+	0.200855i	0.889613	+	0.456716i	$0.150974\pi$
$734$	−10.8586	+	33.4192i	−0.400797	+	1.23353i
$735$	−31.2375	+	31.1124i	−1.15221	+	1.14760i
$736$	0.797179	+	2.45346i	0.0293844	+	0.0904359i
$737$	−5.67781	−	0.297562i	−0.209145	−	0.0109608i
$738$	45.8940	−	70.6705i	1.68938	−	2.60142i
$739$	37.4594	+	33.7286i	1.37797	+	1.24073i	0.939752	+	0.341856i	$0.111056\pi$
$739$	37.4594	+	33.7286i	1.37797	+	1.24073i	0.438214	+	0.898871i	$0.355611\pi$
$740$	0.0685466	+	0.373577i	0.00251982	+	0.0137330i
$741$	36.6243	+	11.9000i	1.34543	+	0.437156i
$742$	−9.99921	+	10.8147i	−0.367083	+	0.397022i
$743$	1.41788	+	1.41788i	0.0520170	+	0.0520170i	0.732637	−	0.680620i	$-0.238289\pi$
$743$	1.41788	+	1.41788i	0.0520170	+	0.0520170i	−0.680620	+	0.732637i	$0.738289\pi$
$744$	28.9751	+	65.0792i	1.06228	+	2.38592i
$745$	1.60132	−	0.207902i	0.0586680	−	0.00761692i
$746$	31.2660	+	13.9205i	1.14473	+	0.509666i
$747$	−0.253787	+	0.313401i	−0.00928558	+	0.0114667i
$748$	−0.116776	−	0.0595001i	−0.00426974	−	0.00217554i
$749$	6.46047	−	0.936011i	0.236061	−	0.0342011i
$750$	42.6286	+	10.4767i	1.55657	+	0.382557i
$751$	−19.4772	+	33.7356i	−0.710735	+	1.23103i	0.253847	+	0.967244i	$0.418304\pi$
$751$	−19.4772	+	33.7356i	−0.710735	+	1.23103i	−0.964582	+	0.263784i	$0.915029\pi$
$752$	23.5999	−	1.23682i	0.860601	−	0.0451022i
$753$	−23.2078	−	60.4585i	−0.845740	−	2.20323i
$754$	0.625466	+	5.95091i	0.0227781	+	0.216719i
$755$	34.3541	+	14.3021i	1.25027	+	0.520506i
$756$	−0.694114	+	0.437849i	−0.0252447	+	0.0159244i
$757$	9.13491	−	9.13491i	0.332014	−	0.332014i	−0.521337	−	0.853351i	$-0.674567\pi$
$757$	9.13491	−	9.13491i	0.332014	−	0.332014i	0.853351	+	0.521337i	$0.174567\pi$
$758$	−33.3072	−	12.7854i	−1.20977	−	0.464388i
$759$	−28.4734	+	6.05220i	−1.03352	+	0.219681i
$760$	30.3466	+	10.8075i	1.10079	+	0.392029i
$761$	−3.54451	+	16.6756i	−0.128488	+	0.604491i	0.866036	+	0.499982i	$0.166660\pi$
$761$	−3.54451	+	16.6756i	−0.128488	+	0.604491i	−0.994524	+	0.104508i	$0.966673\pi$
$762$	−73.3679	+	37.3828i	−2.65784	+	1.35424i
$763$	20.4628	−	1.87804i	0.740803	−	0.0679895i
$764$	−1.14349	+	0.371541i	−0.0413699	+	0.0134419i
$765$	−9.35885	−	17.3107i	−0.338370	−	0.625870i
$766$	−0.601274	−	2.82877i	−0.0217249	−	0.102208i

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)

\(f(q)\)	\(=\)	\(q+(-1.16905 + 0.759191i) q^{2} +(2.62961 - 1.00941i) q^{3} +(-0.0231633 + 0.0520255i) q^{4} +(1.77643 - 1.35805i) q^{5} +(-2.30781 + 3.17642i) q^{6} +(-0.311259 + 2.62738i) q^{7} +(-0.448537 - 2.83195i) q^{8} +(3.66648 - 3.30131i) q^{9} +O(q^{10})\)	\(q+(-1.16905 + 0.759191i) q^{2} +(2.62961 - 1.00941i) q^{3} +(-0.0231633 + 0.0520255i) q^{4} +(1.77643 - 1.35805i) q^{5} +(-2.30781 + 3.17642i) q^{6} +(-0.311259 + 2.62738i) q^{7} +(-0.448537 - 2.83195i) q^{8} +(3.66648 - 3.30131i) q^{9} +(-1.04571 + 2.93628i) q^{10} +(-0.863299 + 0.958791i) q^{11} +(-0.00839509 + 0.160188i) q^{12} +(-1.23533 - 2.42447i) q^{13} +(-1.63080 - 3.30784i) q^{14} +(3.30047 - 5.36429i) q^{15} +(2.59814 + 2.88553i) q^{16} +(1.38624 - 1.12255i) q^{17} +(-1.77998 + 6.64296i) q^{18} +(-4.59007 + 2.04363i) q^{19} +(0.0295056 + 0.123876i) q^{20} +(1.83362 + 7.22316i) q^{21} +(0.281336 - 1.77628i) q^{22} +(4.36269 + 6.71795i) q^{23} +(-4.03808 - 6.99415i) q^{24} +(1.31138 - 4.82496i) q^{25} +(3.28479 + 1.89648i) q^{26} +(2.47276 - 4.85307i) q^{27} +(-0.129481 - 0.0770521i) q^{28} +(0.927279 + 1.27629i) q^{29} +(0.214101 + 8.77681i) q^{30} +(-8.77248 - 0.922025i) q^{31} +(0.311080 + 0.0833536i) q^{32} +(-1.30232 + 3.39266i) q^{33} +(-0.768350 + 2.36474i) q^{34} +(3.01519 + 5.09005i) q^{35} +(0.0868249 + 0.267220i) q^{36} +(2.97854 + 0.156099i) q^{37} +(3.81452 - 5.87385i) q^{38} +(-5.69571 - 5.12844i) q^{39} +(-4.64273 - 4.42162i) q^{40} +(-11.6529 - 3.78627i) q^{41} +(-7.62734 - 7.05217i) q^{42} +(-4.19548 - 4.19548i) q^{43} +(-0.0298848 - 0.0671223i) q^{44} +(2.02987 - 10.8438i) q^{45} +(-10.2004 - 4.54152i) q^{46} +(3.83025 - 4.72996i) q^{47} +(9.74476 + 4.96520i) q^{48} +(-6.80624 - 1.63559i) q^{49} +(2.12999 + 6.63622i) q^{50} +(2.51214 - 4.35115i) q^{51} +(0.154748 - 0.00811002i) q^{52} +(-1.43123 - 3.72849i) q^{53} +(0.793619 + 7.55078i) q^{54} +(-0.231499 + 2.87563i) q^{55} +(7.58022 - 0.297007i) q^{56} +(-10.0072 + 10.0072i) q^{57} +(-2.05298 - 0.788066i) q^{58} +(-4.36013 + 0.926774i) q^{59} +(0.202630 + 0.295963i) q^{60} +(-1.89142 + 8.89841i) q^{61} +(10.9555 - 5.58209i) q^{62} +(7.53257 + 10.6608i) q^{63} +(-7.81259 + 2.53846i) q^{64} +(-5.48702 - 2.62925i) q^{65} +(-1.05320 - 4.95491i) q^{66} +(2.77331 + 3.42475i) q^{67} +(0.0262916 + 0.0981216i) q^{68} +(18.2533 + 13.2618i) q^{69} +(-7.38923 - 3.66143i) q^{70} +(6.77041 - 4.91899i) q^{71} +(-10.9937 - 8.90252i) q^{72} +(0.190237 + 3.62995i) q^{73} +(-3.60057 + 2.07879i) q^{74} +(-1.42195 - 14.0115i) q^{75} -0.286138i q^{76} +(-2.25040 - 2.56665i) q^{77} +(10.5520 + 1.67128i) q^{78} +(3.68558 - 0.387370i) q^{79} +(8.53410 + 1.59752i) q^{80} +(0.0565003 - 0.537564i) q^{81} +(16.4974 - 4.42046i) q^{82} +(-0.0807312 + 0.0127866i) q^{83} +(-0.418261 - 0.0719169i) q^{84} +(0.938062 - 3.87671i) q^{85} +(8.08990 + 1.71956i) q^{86} +(3.72668 + 2.42013i) q^{87} +(3.10247 + 2.01477i) q^{88} +(15.6831 + 3.33355i) q^{89} +(5.85949 + 14.2180i) q^{90} +(6.75450 - 2.49104i) q^{91} +(-0.450559 + 0.0713615i) q^{92} +(-23.9989 + 6.43047i) q^{93} +(-0.886812 + 8.43745i) q^{94} +(-5.37857 + 9.86392i) q^{95} +(0.902155 - 0.0948203i) q^{96} +(-5.33114 - 0.844370i) q^{97} +(9.19856 - 3.25514i) q^{98} +6.36541i 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

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