LMFDB - Embedded newform 175.2.x.a.47.6

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			47.6
Character	$\chi$	$=$	175.47
Dual form			175.2.x.a.108.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0729528 + 1.39202i) q^{2} +(2.18898 - 1.77260i) q^{3} +(0.0566371 + 0.00595280i) q^{4} +(-0.287895 + 2.21746i) q^{5} +(2.30781 + 3.17642i) q^{6} +(-2.62738 - 0.311259i) q^{7} +(-0.448537 + 2.83195i) q^{8} +(1.02578 - 4.82592i) q^{9} +O(q^{10})$	\(q+(-0.0729528 + 1.39202i) q^{2} +(2.18898 - 1.77260i) q^{3} +(0.0566371 + 0.00595280i) q^{4} +(-0.287895 + 2.21746i) q^{5} +(2.30781 + 3.17642i) q^{6} +(-2.62738 - 0.311259i) q^{7} +(-0.448537 + 2.83195i) q^{8} +(1.02578 - 4.82592i) q^{9} +(-3.06575 - 0.562526i) q^{10} +(1.26199 - 0.268244i) q^{11} +(0.134529 - 0.0873643i) q^{12} +(1.23533 - 2.42447i) q^{13} +(0.624954 - 3.63466i) q^{14} +(3.30047 + 5.36429i) q^{15} +(-3.79801 - 0.807292i) q^{16} +(1.66528 - 0.639239i) q^{17} +(6.64296 + 1.77998i) q^{18} +(-0.525199 - 4.99693i) q^{19} +(-0.0295056 + 0.123876i) q^{20} +(-6.30301 + 3.97595i) q^{21} +(0.281336 + 1.77628i) q^{22} +(-7.99926 - 0.419223i) q^{23} +(4.03808 + 6.99415i) q^{24} +(-4.83423 - 1.27679i) q^{25} +(3.28479 + 1.89648i) q^{26} +(-2.47276 - 4.85307i) q^{27} +(-0.146954 - 0.0332690i) q^{28} +(0.927279 - 1.27629i) q^{29} +(-7.70799 + 4.20299i) q^{30} +(-3.58774 + 8.05820i) q^{31} +(-0.0833536 + 0.311080i) q^{32} +(2.28697 - 2.82418i) q^{33} +(0.768350 + 2.36474i) q^{34} +(1.44661 - 5.73649i) q^{35} +(0.0868249 - 0.267220i) q^{36} +(-1.62445 - 2.50144i) q^{37} +(6.99416 - 0.366549i) q^{38} +(-1.59350 - 7.49685i) q^{39} +(-6.15060 - 1.80991i) q^{40} +(11.6529 - 3.78627i) q^{41} +(-5.07479 - 9.06399i) q^{42} +(-4.19548 + 4.19548i) q^{43} +(0.0730720 - 0.00768018i) q^{44} +(10.4060 + 3.66398i) q^{45} +(1.16714 - 11.1046i) q^{46} +(-2.18114 + 5.68207i) 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} +(0.0843977 - 0.129961i) q^{52} +(-2.51335 - 3.10373i) q^{53} +(6.93598 - 3.08810i) q^{54} +(0.231499 + 2.87563i) q^{55} +(2.05995 - 7.30099i) q^{56} +(-10.0072 - 10.0072i) q^{57} +(1.70898 + 1.38390i) q^{58} +(-2.98267 + 3.31260i) q^{59} +(0.154996 + 0.323464i) q^{60} +(6.76054 - 6.08722i) q^{61} +(-10.9555 - 5.58209i) q^{62} +(-4.19722 + 12.3602i) q^{63} +(-7.81259 - 2.53846i) q^{64} +(5.02051 + 3.43728i) q^{65} +(3.76448 + 3.38955i) q^{66} +(1.57927 + 4.11413i) q^{67} +(0.0981216 - 0.0262916i) q^{68} +(-18.2533 + 13.2618i) q^{69} +(7.87979 + 2.43221i) q^{70} +(6.77041 + 4.91899i) q^{71} +(13.2067 + 5.06956i) q^{72} +(-3.04851 - 1.97972i) q^{73} +(3.60057 - 2.07879i) q^{74} +(-12.8453 + 5.77430i) q^{75} -0.286138i q^{76} +(-3.39921 + 0.311973i) q^{77} +(10.5520 - 1.67128i) q^{78} +(-1.50732 - 3.38549i) q^{79} +(2.88356 - 8.18951i) q^{80} +(-0.493795 - 0.219852i) q^{81} +(4.42046 + 16.4974i) q^{82} +(0.0807312 + 0.0127866i) q^{83} +(-0.380652 + 0.187666i) q^{84} +(0.938062 + 3.87671i) q^{85} +(-5.53413 - 6.14628i) q^{86} +(-0.232558 - 4.43746i) q^{87} +(0.193605 + 3.69420i) q^{88} +(10.7285 + 11.9152i) q^{89} +(-5.85949 + 14.2180i) q^{90} +(-4.00031 + 5.98549i) q^{91} +(-0.450559 - 0.0713615i) q^{92} +(6.43047 + 23.9989i) q^{93} +(-7.75046 - 3.45072i) q^{94} +(11.2317 + 0.273985i) q^{95} +(0.368961 + 0.828699i) q^{96} +(5.33114 - 0.844370i) q^{97} +(-2.77331 + 9.35512i) 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.0729528	+	1.39202i	−0.0515855	+	0.984309i	0.843140	+	0.537693i	$0.180704\pi$
$2$	−0.0729528	+	1.39202i	−0.0515855	+	0.984309i	−0.894726	+	0.446616i	$0.852629\pi$
$3$	2.18898	−	1.77260i	1.26381	−	1.02341i	0.265568	−	0.964092i	$-0.414441\pi$
$3$	2.18898	−	1.77260i	1.26381	−	1.02341i	0.998239	−	0.0593186i	$-0.0188928\pi$
$4$	0.0566371	+	0.00595280i	0.0283185	+	0.00297640i
$5$	−0.287895	+	2.21746i	−0.128750	+	0.991677i
$5$	−0.287895	+	2.21746i	−0.128750	+	0.991677i
$6$	2.30781	+	3.17642i	0.942158	+	1.29677i
$7$	−2.62738	−	0.311259i	−0.993056	−	0.117645i
$7$	−2.62738	−	0.311259i	−0.993056	−	0.117645i
$8$	−0.448537	+	2.83195i	−0.158582	+	1.00125i
$9$	1.02578	−	4.82592i	0.341927	−	1.60864i
$10$	−3.06575	−	0.562526i	−0.969475	−	0.177886i
$11$	1.26199	−	0.268244i	0.380503	−	0.0808785i	−0.0136894	−	0.999906i	$-0.504358\pi$
$11$	1.26199	−	0.268244i	0.380503	−	0.0808785i	0.394193	+	0.919028i	$0.371024\pi$
$12$	0.134529	−	0.0873643i	0.0388352	−	0.0252199i
$13$	1.23533	−	2.42447i	0.342618	−	0.672426i	−0.653829	−	0.756642i	$-0.726839\pi$
$13$	1.23533	−	2.42447i	0.342618	−	0.672426i	0.996448	+	0.0842159i	$0.0268386\pi$
$14$	0.624954	−	3.63466i	0.167026	−	0.971405i
$15$	3.30047	+	5.36429i	0.852177	+	1.38505i
$16$	−3.79801	−	0.807292i	−0.949502	−	0.201823i
$17$	1.66528	−	0.639239i	0.403889	−	0.155038i	−0.147939	−	0.988996i	$-0.547264\pi$
$17$	1.66528	−	0.639239i	0.403889	−	0.155038i	0.551828	+	0.833958i	$0.313931\pi$
$18$	6.64296	+	1.77998i	1.56576	+	0.419544i
$19$	−0.525199	−	4.99693i	−0.120489	−	1.14638i	−0.872974	−	0.487766i	$-0.837812\pi$
$19$	−0.525199	−	4.99693i	−0.120489	−	1.14638i	0.752485	−	0.658609i	$-0.228855\pi$
$20$	−0.0295056	+	0.123876i	−0.00659765	+	0.0276996i
$21$	−6.30301	+	3.97595i	−1.37543	+	0.867624i
$22$	0.281336	+	1.77628i	0.0599810	+	0.378705i
$23$	−7.99926	−	0.419223i	−1.66796	−	0.0874141i	−0.805193	−	0.593013i	$-0.797938\pi$
$23$	−7.99926	−	0.419223i	−1.66796	−	0.0874141i	−0.862768	+	0.505599i	$0.831271\pi$
$24$	4.03808	+	6.99415i	0.824269	+	1.42768i
$25$	−4.83423	−	1.27679i	−0.966847	−	0.255358i
$26$	3.28479	+	1.89648i	0.644201	+	0.371930i
$27$	−2.47276	−	4.85307i	−0.475883	−	0.933973i
$28$	−0.146954	−	0.0332690i	−0.0277717	−	0.00628726i
$29$	0.927279	−	1.27629i	0.172191	−	0.237001i	−0.714196	−	0.699946i	$-0.753207\pi$
$29$	0.927279	−	1.27629i	0.172191	−	0.237001i	0.886387	+	0.462945i	$0.153207\pi$
$30$	−7.70799	+	4.20299i	−1.40728	+	0.767357i
$31$	−3.58774	+	8.05820i	−0.644378	+	1.44730i	0.235395	+	0.971900i	$0.424362\pi$
$31$	−3.58774	+	8.05820i	−0.644378	+	1.44730i	−0.879772	+	0.475396i	$0.842305\pi$
$32$	−0.0833536	+	0.311080i	−0.0147350	+	0.0549917i
$33$	2.28697	−	2.82418i	0.398111	−	0.491626i
$34$	0.768350	+	2.36474i	0.131771	+	0.405549i
$35$	1.44661	−	5.73649i	0.244522	−	0.969644i
$36$	0.0868249	−	0.267220i	0.0144708	−	0.0445366i
$37$	−1.62445	−	2.50144i	−0.267059	−	0.411234i	0.679545	−	0.733634i	$-0.262177\pi$
$37$	−1.62445	−	2.50144i	−0.267059	−	0.411234i	−0.946604	+	0.322399i	$0.895511\pi$
$38$	6.99416	−	0.366549i	1.13460	−	0.0594620i
$39$	−1.59350	−	7.49685i	−0.255165	−	1.20046i
$40$	−6.15060	−	1.80991i	−0.972495	−	0.286173i
$41$	11.6529	−	3.78627i	1.81988	−	0.591316i	0.820065	−	0.572271i	$-0.193937\pi$
$41$	11.6529	−	3.78627i	1.81988	−	0.591316i	0.999819	−	0.0190454i	$-0.00606269\pi$
$42$	−5.07479	−	9.06399i	−0.783058	−	1.39860i
$43$	−4.19548	+	4.19548i	−0.639805	+	0.639805i	−0.950507	−	0.310702i	$-0.899436\pi$
$43$	−4.19548	+	4.19548i	−0.639805	+	0.639805i	0.310702	+	0.950507i	$0.399436\pi$
$44$	0.0730720	−	0.00768018i	0.0110160	−	0.00115783i
$45$	10.4060	+	3.66398i	1.55123	+	0.546194i
$46$	1.16714	−	11.1046i	0.172085	−	1.63728i
$47$	−2.18114	+	5.68207i	−0.318152	+	0.828815i	0.677487	+	0.735534i	$0.263069\pi$
$47$	−2.18114	+	5.68207i	−0.318152	+	0.828815i	−0.995640	+	0.0932810i	$0.970265\pi$
$48$	−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
$52$	0.0843977	−	0.129961i	0.0117039	−	0.0180224i
$53$	−2.51335	−	3.10373i	−0.345235	−	0.426330i	0.574722	−	0.818349i	$-0.305110\pi$
$53$	−2.51335	−	3.10373i	−0.345235	−	0.426330i	−0.919957	+	0.392019i	$0.871777\pi$
$54$	6.93598	−	3.08810i	0.943867	−	0.420237i
$55$	0.231499	+	2.87563i	0.0312153	+	0.387750i
$56$	2.05995	−	7.30099i	0.275272	−	0.975636i
$57$	−10.0072	−	10.0072i	−1.32549	−	1.32549i
$58$	1.70898	+	1.38390i	0.224400	+	0.181715i
$59$	−2.98267	+	3.31260i	−0.388311	+	0.431263i	−0.905329	−	0.424712i	$-0.860375\pi$
$59$	−2.98267	+	3.31260i	−0.388311	+	0.431263i	0.517018	+	0.855975i	$0.327042\pi$
$60$	0.154996	+	0.323464i	0.0200099	+	0.0417591i
$61$	6.76054	−	6.08722i	0.865598	−	0.779388i	−0.111144	−	0.993804i	$-0.535451\pi$
$61$	6.76054	−	6.08722i	0.865598	−	0.779388i	0.976742	+	0.214416i	$0.0687848\pi$
$62$	−10.9555	−	5.58209i	−1.39135	−	0.708926i
$63$	−4.19722	+	12.3602i	−0.528801	+	1.55724i
$64$	−7.81259	−	2.53846i	−0.976573	−	0.317308i
$65$	5.02051	+	3.43728i	0.622717	+	0.426342i
$66$	3.76448	+	3.38955i	0.463375	+	0.417225i
$67$	1.57927	+	4.11413i	0.192938	+	0.502621i	0.995588	−	0.0938290i	$-0.0299107\pi$
$67$	1.57927	+	4.11413i	0.192938	+	0.502621i	−0.802650	+	0.596450i	$0.796577\pi$
$68$	0.0981216	−	0.0262916i	0.0118990	−	0.00318832i
$69$	−18.2533	+	13.2618i	−2.19744	+	1.59653i
$70$	7.87979	+	2.43221i	0.941815	+	0.290705i
$71$	6.77041	+	4.91899i	0.803500	+	0.583777i	0.911939	−	0.410326i	$-0.134585\pi$
$71$	6.77041	+	4.91899i	0.803500	+	0.583777i	−0.108439	+	0.994103i	$0.534585\pi$
$72$	13.2067	+	5.06956i	1.55642	+	0.597454i
$73$	−3.04851	−	1.97972i	−0.356801	−	0.231709i	0.353774	−	0.935331i	$-0.384898\pi$
$73$	−3.04851	−	1.97972i	−0.356801	−	0.231709i	−0.710575	+	0.703622i	$0.751565\pi$
$74$	3.60057	−	2.07879i	0.418558	−	0.241655i
$75$	−12.8453	+	5.77430i	−1.48324	+	0.666758i
$76$		−	0.286138i		−	0.0328223i
$77$	−3.39921	+	0.311973i	−0.387376	+	0.0355526i
$78$	10.5520	−	1.67128i	1.19478	−	0.189235i
$79$	−1.50732	−	3.38549i	−0.169586	−	0.380897i	0.808680	−	0.588249i	$-0.200182\pi$
$79$	−1.50732	−	3.38549i	−0.169586	−	0.380897i	−0.978267	+	0.207351i	$0.933516\pi$
$80$	2.88356	−	8.18951i	0.322392	−	0.915615i
$81$	−0.493795	−	0.219852i	−0.0548661	−	0.0244279i
$82$	4.42046	+	16.4974i	0.488158	+	1.82183i
$83$	0.0807312	+	0.0127866i	0.00886140	+	0.00140351i	0.160864	−	0.986977i	$-0.448572\pi$
$83$	0.0807312	+	0.0127866i	0.00886140	+	0.00140351i	−0.152002	+	0.988380i	$0.548572\pi$
$84$	−0.380652	+	0.187666i	−0.0415325	+	0.0204760i
$85$	0.938062	+	3.87671i	0.101747	+	0.420488i
$86$	−5.53413	−	6.14628i	−0.596761	−	0.662770i
$87$	−0.232558	−	4.43746i	−0.0249328	−	0.475746i
$88$	0.193605	+	3.69420i	0.0206383	+	0.393803i
$89$	10.7285	+	11.9152i	1.13722	+	1.26301i	0.960357	+	0.278772i	$0.0899274\pi$
$89$	10.7285	+	11.9152i	1.13722	+	1.26301i	0.176860	+	0.984236i	$0.443406\pi$
$90$	−5.85949	+	14.2180i	−0.617645	+	1.49871i
$91$	−4.00031	+	5.98549i	−0.419346	+	0.627449i
$92$	−0.450559	−	0.0713615i	−0.0469740	−	0.00743995i
$93$	6.43047	+	23.9989i	0.666809	+	2.48857i
$94$	−7.75046	−	3.45072i	−0.799398	−	0.355915i
$95$	11.2317	+	0.273985i	1.15235	+	0.0281103i
$96$	0.368961	+	0.828699i	0.0376569	+	0.0845788i
$97$	5.33114	−	0.844370i	0.541296	−	0.0857328i	0.120201	−	0.992750i	$-0.461646\pi$
$97$	5.33114	−	0.844370i	0.541296	−	0.0857328i	0.421095	+	0.907017i	$0.361646\pi$
$98$	−2.77331	+	9.35512i	−0.280147	+	0.945010i
$99$		−	6.36541i		−	0.639747i
$100$	−0.266196	−	0.101091i	−0.0266196	−	0.0101091i
$101$	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	$0.255364\pi$
$102$	5.87363	+	3.81438i	0.581576	+	0.377680i
$103$	0.722703	+	0.277420i	0.0712101	+	0.0273350i	0.393712	−	0.919234i	$-0.371191\pi$
$103$	0.722703	+	0.277420i	0.0712101	+	0.0273350i	−0.322502	+	0.946569i	$0.604524\pi$
$104$	6.31188	+	4.58585i	0.618931	+	0.449679i
$105$	−7.00190	−	15.1213i	−0.683315	−	1.47569i
$106$	4.50382	−	3.27222i	0.437450	−	0.317826i
$107$	2.38325	−	0.638591i	0.230398	−	0.0617349i	−0.141773	−	0.989899i	$-0.545280\pi$
$107$	2.38325	−	0.638591i	0.230398	−	0.0617349i	0.372171	+	0.928164i	$0.378614\pi$
$108$	−0.111161	−	0.289583i	−0.0106964	−	0.0278652i
$109$	−5.77179	−	5.19695i	−0.552837	−	0.497777i	0.344701	−	0.938712i	$-0.387980\pi$
$109$	−5.77179	−	5.19695i	−0.552837	−	0.497777i	−0.897539	+	0.440935i	$0.854647\pi$
$110$	−4.01983	+	0.112467i	−0.383276	+	0.0107233i
$111$	−7.98995	−	2.59609i	−0.758372	−	0.246410i
$112$	9.72753	+	3.30322i	0.919165	+	0.312125i
$113$	−0.329784	−	0.168033i	−0.0310234	−	0.0158072i	0.438410	−	0.898775i	$-0.355542\pi$
$113$	−0.329784	−	0.168033i	−0.0310234	−	0.0158072i	−0.469433	+	0.882968i	$0.655542\pi$
$114$	14.6603	−	13.2002i	1.37307	−	1.23631i
$115$	3.23256	−	17.6173i	0.301437	−	1.64282i
$116$	0.0601158	−	0.0667654i	0.00558161	−	0.00619901i
$117$	−10.4331	−	8.44856i	−0.964541	−	0.781070i
$118$	−4.39362	−	4.39362i	−0.404465	−	0.404465i
$119$	−4.57428	+	1.16119i	−0.419323	+	0.106446i
$120$	−16.6718	+	6.94068i	−1.52192	+	0.633594i
$121$	−8.52834	+	3.79706i	−0.775304	+	0.345188i
$122$	7.98035	+	9.85491i	0.722507	+	0.892222i
$123$	18.7965	−	28.9441i	1.69482	−	2.60980i
$124$	−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	0.662773	−	0.748821i	$-0.269380\pi$
$127$	18.6864	−	9.52119i	1.65815	−	0.844869i	0.995377	−	0.0960485i	$-0.0306204\pi$
$128$	3.87272	−	10.0888i	0.342304	−	0.891731i
$129$	−1.74691	+	16.6207i	−0.153807	+	1.46337i
$130$	−5.15103	+	6.73790i	−0.451775	+	0.590953i
$131$	−7.88372	+	0.828612i	−0.688804	+	0.0723962i	−0.442463	−	0.896787i	$-0.645895\pi$
$131$	−7.88372	+	0.828612i	−0.688804	+	0.0723962i	−0.246341	+	0.969183i	$0.579228\pi$
$132$	0.146339	−	0.146339i	0.0127372	−	0.0127372i
$133$	−0.175443	+	13.2923i	−0.0152128	+	1.15259i
$134$	−5.84218	+	1.89824i	−0.504687	+	0.163983i
$135$	11.4734	−	4.08607i	0.987470	−	0.351673i
$136$	1.06336	+	5.00270i	0.0911821	+	0.428978i
$137$	−8.88855	+	0.465829i	−0.759400	+	0.0397985i	−0.428106	−	0.903729i	$-0.640819\pi$
$137$	−8.88855	+	0.465829i	−0.759400	+	0.0397985i	−0.331295	+	0.943527i	$0.607486\pi$
$138$	−17.1291	−	26.3765i	−1.45813	−	2.24532i
$139$	0.759246	−	2.33672i	0.0643984	−	0.198198i	−0.913680	−	0.406434i	$-0.866772\pi$
$139$	0.759246	−	2.33672i	0.0643984	−	0.198198i	0.978079	+	0.208236i	$0.0667722\pi$
$140$	0.116080	−	0.316287i	0.00981055	−	0.0267311i
$141$	5.29756	+	16.3042i	0.446135	+	1.37306i
$142$	−7.34127	+	9.06571i	−0.616066	+	0.760778i
$143$	0.908619	−	3.39101i	0.0759826	−	0.283571i
$144$	−7.79185	+	17.5008i	−0.649321	+	1.45840i
$145$	2.56316	+	2.42364i	0.212859	+	0.201272i
$146$	2.97822	−	4.09917i	0.246479	−	0.339249i
$147$	17.7979	−	8.48446i	1.46795	−	0.699787i
$148$	−0.0771138	−	0.151344i	−0.00633871	−	0.0124404i
$149$	−0.625395	−	0.361072i	−0.0512344	−	0.0295802i	0.474164	−	0.880437i	$-0.342750\pi$
$149$	−0.625395	−	0.361072i	−0.0512344	−	0.0295802i	−0.525398	+	0.850856i	$0.676084\pi$
$150$	−7.10086	−	18.3022i	−0.579782	−	1.49437i
$151$	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	$0.596549\pi$
$152$	14.3866	+	0.753972i	1.16691	+	0.0611552i
$153$	−1.37671	−	8.69221i	−0.111300	−	0.702723i
$154$	−0.186292	−	4.75454i	−0.0150118	−	0.383132i
$155$	−16.8358	−	10.2756i	−1.35229	−	0.825354i
$156$	−0.0456242	−	0.434085i	−0.00365286	−	0.0347546i
$157$	3.31620	+	0.888573i	0.264661	+	0.0709158i	0.388709	−	0.921360i	$-0.372921\pi$
$157$	3.31620	+	0.888573i	0.264661	+	0.0709158i	−0.124048	+	0.992276i	$0.539588\pi$
$158$	4.82264	−	1.85124i	0.383669	−	0.147277i
$159$	−11.0033	−	2.33883i	−0.872622	−	0.185482i
$160$	−0.665809	−	0.274391i	−0.0526368	−	0.0216925i
$161$	20.8866	+	3.59130i	1.64609	+	0.283034i
$162$	0.342062	−	0.671335i	0.0268749	−	0.0527450i
$163$	2.66502	−	1.73068i	0.208740	−	0.135557i	−0.436035	−	0.899930i	$-0.643618\pi$
$163$	2.66502	−	1.73068i	0.208740	−	0.135557i	0.644775	+	0.764372i	$0.276951\pi$
$164$	0.682527	−	0.145076i	0.0532964	−	0.0113285i
$165$	5.60408	+	5.88433i	0.436277	+	0.458094i
$166$	−0.0236888	+	0.111447i	−0.00183861	+	0.00864996i
$167$	−1.83269	+	11.5711i	−0.141818	+	0.895401i	0.809485	+	0.587141i	$0.199747\pi$
$167$	−1.83269	+	11.5711i	−0.141818	+	0.895401i	−0.951302	+	0.308260i	$0.900253\pi$
$168$	−8.43256	−	19.6332i	−0.650586	−	1.51473i
$169$	3.28920	+	4.52720i	0.253016	+	0.348246i
$170$	−5.46491	+	1.02299i	−0.419139	+	0.0784595i
$171$	−24.6535	−	2.59119i	−1.88530	−	0.198153i
$172$	−0.262595	+	0.212645i	−0.0200226	+	0.0162140i
$173$	−1.18749	+	22.6586i	−0.0902829	+	1.72270i	0.460168	+	0.887832i	$0.347789\pi$
$173$	−1.18749	+	22.6586i	−0.0902829	+	1.72270i	−0.550451	+	0.834868i	$0.685544\pi$
$174$	6.19402			0.469567
$175$	12.3039	+	4.85931i	0.930091	+	0.367329i
$176$	−5.00959			−0.377612
$177$	−0.657104	+	12.5383i	−0.0493909	+	0.942435i
$178$	−17.3689	+	14.0651i	−1.30185	+	1.05422i
$179$	−7.69663	−	0.808948i	−0.575273	−	0.0604636i	−0.187575	−	0.982250i	$-0.560063\pi$
$179$	−7.69663	−	0.808948i	−0.575273	−	0.0604636i	−0.387698	+	0.921787i	$0.626730\pi$
$180$	0.567552	+	0.269462i	0.0423028	+	0.0200845i
$181$	−2.15081	−	2.96033i	−0.159868	−	0.220040i	0.721567	−	0.692345i	$-0.243422\pi$
$181$	−2.15081	−	2.96033i	−0.159868	−	0.220040i	−0.881435	+	0.472305i	$0.843422\pi$
$182$	−8.04010	−	6.00518i	−0.595972	−	0.445134i
$183$	4.00848	−	25.3085i	0.296315	−	1.87086i
$184$	4.77518	−	22.4655i	0.352031	−	1.65618i
$185$	6.01451	−	2.88201i	0.442196	−	0.211889i
$186$	−33.8761	+	7.20058i	−2.48392	+	0.527972i
$187$	1.93008	−	1.25341i	0.141142	−	0.0916585i
$188$	−0.157358	+	0.308832i	−0.0114765	+	0.0225239i
$189$	4.98632	+	13.5205i	0.362701	+	0.983473i
$190$	−1.20078	+	15.6148i	−0.0871136	+	1.13282i
$191$	−20.6511	−	4.38952i	−1.49426	−	0.317614i	−0.612937	−	0.790132i	$-0.710012\pi$
$191$	−20.6511	−	4.38952i	−1.49426	−	0.317614i	−0.881321	+	0.472517i	$0.843345\pi$
$192$	−21.6013	+	8.29195i	−1.55894	+	0.598420i
$193$	−19.5342	−	5.23417i	−1.40610	−	0.376764i	−0.525569	−	0.850751i	$-0.676148\pi$
$193$	−19.5342	−	5.23417i	−1.40610	−	0.376764i	−0.880532	+	0.473987i	$0.842814\pi$
$194$	0.786461	+	7.48268i	0.0564646	+	0.537225i
$195$	17.0827	−	1.37522i	1.22332	−	0.0984818i
$196$	0.375749	+	0.133151i	0.0268392	+	0.00951079i
$197$	−1.00475	−	6.34375i	−0.0715856	−	0.451974i	−0.997280	−	0.0737022i	$-0.976519\pi$
$197$	−1.00475	−	6.34375i	−0.0715856	−	0.451974i	0.925695	−	0.378272i	$-0.123481\pi$
$198$	8.86079	+	0.464374i	0.629709	+	0.0330017i
$199$	−6.15950	−	10.6686i	−0.436636	−	0.756275i	0.560792	−	0.827957i	$-0.310497\pi$
$199$	−6.15950	−	10.6686i	−0.436636	−	0.756275i	−0.997428	+	0.0716817i	$0.977163\pi$
$200$	5.78413	−	13.1176i	0.409000	−	0.927556i
$201$	10.7497	+	6.20633i	0.758224	+	0.437761i
$202$	3.08463	+	6.05392i	0.217033	+	0.425952i
$203$	−2.83357	+	3.06467i	−0.198878	+	0.215098i
$204$	0.168182	−	0.231482i	0.0117751	−	0.0162070i
$205$	5.04107	+	26.9299i	0.352084	+	1.88087i
$206$	−0.438898	+	0.985781i	−0.0305795	+	0.0686826i
$207$	−10.2286	+	38.1738i	−0.710939	+	2.65326i
$208$	−6.64904	+	8.21088i	−0.461028	+	0.569322i
$209$	−2.00319	−	6.16518i	−0.138563	−	0.426455i
$210$	21.5600	−	8.64366i	1.48778	−	0.596469i
$211$	0.536205	−	1.65027i	0.0369139	−	0.113609i	−0.930902	−	0.365270i	$-0.880977\pi$
$211$	0.536205	−	1.65027i	0.0369139	−	0.113609i	0.967816	+	0.251661i	$0.0809767\pi$
$212$	−0.123873	−	0.190748i	−0.00850763	−	0.0131006i
$213$	23.5397	−	1.23366i	1.61291	−	0.0845291i
$214$	0.715068	+	3.36413i	0.0488810	+	0.229967i
$215$	−8.09544	−	10.5112i	−0.552105	−	0.716855i
$216$	14.8528	−	4.82596i	1.01060	−	0.328365i
$217$	11.9345	−	20.0552i	0.810170	−	1.36144i
$218$	7.65534	−	7.65534i	0.518485	−	0.518485i
$219$	−10.1824	+	1.07021i	−0.688061	+	0.0723181i
$220$	−0.00400659	+	0.164245i	−0.000270124	+	0.0110734i
$221$	0.507346	−	4.82708i	0.0341278	−	0.324704i
$222$	4.19671	−	10.9328i	0.281665	−	0.733762i
$223$	18.0830	−	9.21376i	1.21093	−	0.616999i	0.272395	−	0.962186i	$-0.412184\pi$
$223$	18.0830	−	9.21376i	1.21093	−	0.616999i	0.938534	+	0.345187i	$0.112184\pi$
$224$	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
$227$	0.428586	−	0.659965i	0.0284463	−	0.0438034i	−0.824161	−	0.566355i	$-0.808353\pi$
$227$	0.428586	−	0.659965i	0.0284463	−	0.0438034i	0.852608	+	0.522552i	$0.175020\pi$
$228$	−0.507208	−	0.626350i	−0.0335907	−	0.0414810i
$229$	8.27315	−	3.68345i	0.546705	−	0.243409i	−0.114749	−	0.993395i	$-0.536606\pi$
$229$	8.27315	−	3.68345i	0.546705	−	0.243409i	0.661454	+	0.749986i	$0.269940\pi$
$230$	24.2879	+	5.78503i	1.60150	+	0.381453i
$231$	−6.88779	+	6.70834i	−0.453184	+	0.441376i
$232$	3.19847	+	3.19847i	0.209990	+	0.209990i
$233$	6.53523	+	5.29213i	0.428137	+	0.346699i	0.819043	−	0.573732i	$-0.194505\pi$
$233$	6.53523	+	5.29213i	0.428137	+	0.346699i	−0.390906	+	0.920431i	$0.627838\pi$
$234$	12.5217	−	13.9068i	0.818571	−	0.909115i
$235$	−11.9718	−	6.47243i	−0.780955	−	0.422215i
$236$	−0.188649	+	0.169860i	−0.0122800	+	0.0110570i
$237$	−9.30060	−	4.73889i	−0.604139	−	0.307824i
$238$	−1.28270	−	6.45221i	−0.0831451	−	0.418235i
$239$	−15.6184	−	5.07472i	−1.01027	−	0.328256i	−0.243308	−	0.969949i	$-0.578232\pi$
$239$	−15.6184	−	5.07472i	−1.01027	−	0.328256i	−0.766962	+	0.641693i	$0.778232\pi$
$240$	−8.20466	−	23.0381i	−0.529609	−	1.48710i
$241$	−12.5470	−	11.2973i	−0.808222	−	0.727726i	0.157440	−	0.987529i	$-0.449676\pi$
$241$	−12.5470	−	11.2973i	−0.808222	−	0.727726i	−0.965662	+	0.259802i	$0.916343\pi$
$242$	−4.66343	−	12.1487i	−0.299777	−	0.780945i
$243$	14.3128	−	3.83510i	0.918165	−	0.246022i
$244$	0.419133	−	0.304518i	0.0268322	−	0.0194948i
$245$	−5.58633	+	14.6217i	−0.356897	+	0.934144i
$246$	38.9195	+	28.2767i	2.48142	+	1.80286i
$247$	−12.7637	−	4.89952i	−0.812134	−	0.311749i
$248$	−21.2112	−	13.7747i	−1.34691	−	0.874695i
$249$	0.199384	−	0.115115i	0.0126355	−	0.00729509i
$250$	14.1023	+	6.63370i	0.891909	+	0.419552i
$251$		−	22.9915i		−	1.45121i	−0.688113	−	0.725604i	$-0.741560\pi$
$251$		−	22.9915i		−	1.45121i	0.688113	−	0.725604i	$-0.258440\pi$
$252$	−0.311296	+	0.675062i	−0.0196098	+	0.0425249i
$253$	−10.2074	+	1.61670i	−0.641735	+	0.101641i
$254$	11.8905	+	26.7065i	0.746076	+	1.67571i
$255$	8.92525	+	6.82323i	0.558921	+	0.427287i
$256$	−1.24759	−	0.555463i	−0.0779744	−	0.0347165i
$257$	−3.92282	−	14.6401i	−0.244698	−	0.913227i	−0.973535	−	0.228539i	$-0.926605\pi$
$257$	−3.92282	−	14.6401i	−0.244698	−	0.913227i	0.728836	−	0.684688i	$-0.240062\pi$
$258$	−23.0090	−	3.64427i	−1.43248	−	0.226882i
$259$	3.48946	+	7.07786i	0.216825	+	0.439797i
$260$	0.263885	+	0.224563i	0.0163655	+	0.0139268i
$261$	−5.20809	−	5.78417i	−0.322372	−	0.358031i
$262$	−0.578308	−	11.0348i	−0.0357280	−	0.681730i
$263$	1.23865	+	23.6349i	0.0763785	+	1.45739i	0.721026	+	0.692908i	$0.243671\pi$
$263$	1.23865	+	23.6349i	0.0763785	+	1.45739i	−0.644648	+	0.764480i	$0.722996\pi$
$264$	6.97213	+	7.74334i	0.429105	+	0.476570i
$265$	7.60597	−	4.67970i	0.467231	−	0.287472i
$266$	−18.4904	−	1.21393i	−1.13372	−	0.0744310i
$267$	44.6053	+	7.06478i	2.72980	+	0.432358i
$268$	0.0649545	+	0.242413i	0.00396773	+	0.0148078i
$269$	15.1332	+	6.73772i	0.922686	+	0.410806i	0.812404	−	0.583094i	$-0.198158\pi$
$269$	15.1332	+	6.73772i	0.922686	+	0.410806i	0.110281	+	0.993900i	$0.464825\pi$
$270$	4.85089	+	16.2693i	0.295216	+	0.990117i
$271$	−6.18795	−	13.8984i	−0.375891	−	0.844265i	−0.998112	−	0.0614235i	$-0.980436\pi$
$271$	−6.18795	−	13.8984i	−0.375891	−	0.844265i	0.622221	−	0.782842i	$-0.286231\pi$
$272$	−6.84078	+	1.08347i	−0.414783	+	0.0656952i
$273$	1.85328	+	20.1930i	0.112166	+	1.22214i
$274$		−	12.4071i		−	0.749538i
$275$	−6.44323	−	0.314539i	−0.388541	−	0.0189674i
$276$	−1.11276	+	0.642452i	−0.0669802	+	0.0386711i
$277$	13.3962	+	8.69960i	0.804900	+	0.522708i	0.880284	−	0.474446i	$-0.157352\pi$
$277$	13.3962	+	8.69960i	0.804900	+	0.522708i	−0.0753843	+	0.997155i	$0.524018\pi$
$278$	3.19738	+	1.22736i	0.191766	+	0.0736121i
$279$	35.2080	+	25.5801i	2.10785	+	1.53144i
$280$	15.5966	+	6.66976i	0.932075	+	0.398594i
$281$	−21.8808	+	15.8974i	−1.30530	+	0.948357i	−0.999992	−	0.00389666i	$-0.998760\pi$
$281$	−21.8808	+	15.8974i	−1.30530	+	0.948357i	−0.305309	+	0.952253i	$0.598760\pi$
$282$	−23.0823	+	6.18489i	−1.37453	+	0.368305i
$283$	0.0979916	+	0.255277i	0.00582500	+	0.0151746i	0.936462	−	0.350769i	$-0.114080\pi$
$283$	0.0979916	+	0.255277i	0.00582500	+	0.0151746i	−0.930637	+	0.365943i	$0.880746\pi$
$284$	0.354174	+	0.318900i	0.0210164	+	0.0189232i
$285$	25.0716	−	19.3095i	1.48511	−	1.14380i
$286$	4.65408	+	1.51220i	0.275202	+	0.0894185i
$287$	−31.7952	+	6.32088i	−1.87681	+	0.373110i
$288$	1.41574	+	0.721357i	0.0834235	+	0.0425064i
$289$	−10.2689	+	9.24620i	−0.604056	+	0.543894i
$290$	−3.56075	+	3.39117i	−0.209094	+	0.199136i
$291$	10.1730	−	11.2983i	0.596353	−	0.662318i
$292$	−0.160874	−	0.130273i	−0.00941441	−	0.00762364i
$293$	−4.77266	−	4.77266i	−0.278822	−	0.278822i	0.553817	−	0.832639i	$-0.313171\pi$
$293$	−4.77266	−	4.77266i	−0.278822	−	0.278822i	−0.832639	+	0.553817i	$0.813171\pi$
$294$	10.5122	+	25.3941i	0.613081	+	1.48102i
$295$	−6.48684	−	7.56763i	−0.377679	−	0.440605i
$296$	7.81258	−	3.47839i	0.454097	−	0.202177i
$297$	−4.42240	−	5.46120i	−0.256613	−	0.316891i
$298$	0.548245	−	0.844223i	0.0317590	−	0.0489046i
$299$	−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
$303$	4.92019	−	12.8175i	0.282657	−	0.736347i
$304$	−2.03927	+	19.4024i	−0.116960	+	1.11280i
$305$	11.5518	+	16.7437i	0.661455	+	0.958741i
$306$	12.2002	−	1.28229i	0.697438	−	0.0733037i
$307$	15.6825	−	15.6825i	0.895046	−	0.895046i	−0.0999465	−	0.994993i	$-0.531867\pi$
$307$	15.6825	−	15.6825i	0.895046	−	0.895046i	0.994993	+	0.0999465i	$0.0318672\pi$
$308$	−0.194378	−	0.00256557i	−0.0110757	−	0.000146187i
$309$	2.07374	−	0.673798i	0.117971	−	0.0383310i
$310$	15.5321	−	22.6862i	0.882162	−	1.28849i
$311$	3.34459	+	15.7351i	0.189655	+	0.892254i	0.965312	+	0.261100i	$0.0840852\pi$
$311$	3.34459	+	15.7351i	0.189655	+	0.892254i	−0.775657	+	0.631154i	$0.782581\pi$
$312$	21.9454	−	1.15011i	1.24242	−	0.0651122i
$313$	−9.82351	−	15.1269i	−0.555258	−	0.855022i	0.443899	−	0.896077i	$-0.353595\pi$
$313$	−9.82351	−	15.1269i	−0.555258	−	0.855022i	−0.999157	+	0.0410549i	$0.986928\pi$
$314$	−1.47884	+	4.55140i	−0.0834558	+	0.256850i
$315$	−26.1999	−	12.8656i	−1.47620	−	0.724895i
$316$	−0.0652169	−	0.200717i	−0.00366874	−	0.0112912i
$317$	4.54033	−	5.60684i	0.255010	−	0.314912i	−0.633523	−	0.773724i	$-0.718392\pi$
$317$	4.54033	−	5.60684i	0.255010	−	0.314912i	0.888533	+	0.458812i	$0.151725\pi$
$318$	4.05844	−	15.1463i	0.227586	−	0.849362i
$319$	0.827857	−	1.85940i	0.0463511	−	0.104106i
$320$	7.87814	−	16.5933i	0.440401	−	0.927592i
$321$	4.08492	−	5.62241i	0.227998	−	0.313812i
$322$	−6.52291	+	28.8126i	−0.363507	+	1.60567i
$323$	−4.06884	−	7.98554i	−0.226396	−	0.444328i
$324$	−0.0266583	−	0.0153912i	−0.00148102	−	0.000855067i
$325$	−9.06739	+	10.1432i	−0.502969	+	0.562643i
$326$	2.21473	+	3.83602i	0.122662	+	0.212458i
$327$	−21.8464	−	1.14492i	−1.20811	−	0.0633144i
$328$	5.49575	+	34.6988i	0.303452	+	1.91592i
$329$	7.49928	−	14.2501i	0.413449	−	0.785631i
$330$	−8.59996	+	7.37173i	−0.473412	+	0.405801i
$331$	2.34470	+	22.3083i	0.128876	+	1.22618i	0.847506	+	0.530785i	$0.178103\pi$
$331$	2.34470	+	22.3083i	0.128876	+	1.22618i	−0.718630	+	0.695393i	$0.755230\pi$
$332$	0.00449626	+	0.00120477i	0.000246765	+	6.61204e-5i
$333$	−13.7381	+	5.27356i	−0.752843	+	0.288989i
$334$	−15.9736	−	3.39529i	−0.874036	−	0.185782i
$335$	−9.57757	+	2.31752i	−0.523279	+	0.126620i
$336$	27.1486	−	10.0123i	1.48108	−	0.546217i
$337$	4.68604	−	9.19687i	0.255265	−	0.500985i	−0.727438	−	0.686173i	$-0.759289\pi$
$337$	4.68604	−	9.19687i	0.255265	−	0.500985i	0.982703	+	0.185188i	$0.0592893\pi$
$338$	−6.54192	+	4.24837i	−0.355834	+	0.231081i
$339$	−1.01974	+	0.216753i	−0.0553849	+	0.0117724i
$340$	0.0300518	+	0.225150i	0.00162979	+	0.0122105i
$341$	−2.36612	+	11.1317i	−0.128133	+	0.602817i
$342$	5.40554	−	34.1293i	0.292298	−	1.84550i
$343$	−17.3735	−	6.41581i	−0.938079	−	0.346421i
$344$	−9.99956	−	13.7632i	−0.539140	−	0.742063i
$345$	−24.1525	−	44.2940i	−1.30033	−	2.38471i
$346$	−31.4546	−	3.30602i	−1.69101	−	0.177732i
$347$	2.91800	−	2.36295i	0.156646	−	0.126850i	−0.547793	−	0.836614i	$-0.684532\pi$
$347$	2.91800	−	2.36295i	0.156646	−	0.126850i	0.704439	+	0.709764i	$0.251199\pi$
$348$	0.0132439	−	0.252709i	0.000709949	−	0.0135466i
$349$	−30.7324			−1.64507			−0.822534	−	0.568716i	$-0.807440\pi$
$349$	−30.7324			−1.64507			−0.822534	+	0.568716i	$0.807440\pi$
$350$	−7.66187	+	16.7729i	−0.409544	+	0.896548i
$351$	−14.8208			−0.791074
$352$	−0.0217460	+	0.414938i	−0.00115906	+	0.0221163i
$353$	−21.0661	+	17.0590i	−1.12123	+	0.907957i	−0.996447	−	0.0842271i	$-0.973158\pi$
$353$	−21.0661	+	17.0590i	−1.12123	+	0.907957i	−0.124786	+	0.992184i	$0.539825\pi$
$354$	−17.4056	−	1.82941i	−0.925100	−	0.0972319i
$355$	−12.8568	+	13.5969i	−0.682369	+	0.721651i
$356$	0.536701	+	0.738706i	0.0284451	+	0.0391513i
$357$	−7.95467	+	10.6502i	−0.421006	+	0.563668i
$358$	1.68757	−	10.6549i	0.0891906	−	0.563127i
$359$	4.03408	−	18.9789i	0.212911	−	1.00167i	−0.733746	−	0.679424i	$-0.762230\pi$
$359$	4.03408	−	18.9789i	0.212911	−	1.00167i	0.946657	−	0.322243i	$-0.104437\pi$
$360$	−15.0437	+	27.8257i	−0.792871	+	1.46654i
$361$	−6.10870	+	1.29845i	−0.321511	+	0.0683392i
$362$	4.27776	−	2.77801i	0.224834	−	0.146009i
$363$	−11.9377	+	23.4290i	−0.626566	+	1.22970i
$364$	−0.262196	+	0.315187i	−0.0137428	+	0.0165203i
$365$	5.26760	−	6.18998i	0.275719	−	0.323998i
$366$	34.9376	+	7.42622i	1.82622	+	0.388175i
$367$	23.5342	−	9.03393i	1.22848	−	0.471567i	0.344361	−	0.938837i	$-0.388096\pi$
$367$	23.5342	−	9.03393i	1.22848	−	0.471567i	0.884115	+	0.467270i	$0.154762\pi$
$368$	30.0428	+	8.04995i	1.56609	+	0.419633i
$369$	−6.31887	−	60.1200i	−0.328947	−	3.12972i
$370$	3.57305	+	8.58259i	0.185754	+	0.446188i
$371$	5.63746	+	8.93698i	0.292683	+	0.463985i
$372$	0.221343	+	1.39750i	0.0114761	+	0.0724572i
$373$	24.5191	+	1.28499i	1.26955	+	0.0665343i	0.675177	−	0.737655i	$-0.264067\pi$
$373$	24.5191	+	1.28499i	1.26955	+	0.0665343i	0.594373	+	0.804190i	$0.297400\pi$
$374$	1.60397	+	2.77816i	0.0829394	+	0.143655i
$375$	−9.10617	−	30.1462i	−0.470241	−	1.55674i
$376$	−15.1130	−	8.72551i	−0.779394	−	0.449984i
$377$	−1.94883	−	3.82479i	−0.100370	−	0.196987i
$378$	−19.1846	+	5.95471i	−0.986751	+	0.306277i
$379$	15.0440	−	20.7063i	0.772758	−	1.06361i	−0.223287	−	0.974753i	$-0.571679\pi$
$379$	15.0440	−	20.7063i	0.772758	−	1.06361i	0.996044	−	0.0888570i	$-0.0283214\pi$
$380$	0.634499	+	0.0823777i	0.0325491	+	0.00422589i
$381$	24.0268	−	53.9652i	1.23093	−	2.76472i
$382$	7.61687	−	28.4265i	0.389713	−	1.45443i
$383$	1.30564	−	1.61233i	0.0667151	−	0.0823863i	−0.742696	−	0.669629i	$-0.766453\pi$
$383$	1.30564	−	1.61233i	0.0667151	−	0.0823863i	0.809411	+	0.587243i	$0.199787\pi$
$384$	−9.40607	−	28.9489i	−0.480002	−	1.47729i
$385$	0.286828	−	7.62742i	0.0146181	−	0.388729i
$386$	8.71116	−	26.8102i	0.443386	−	1.36460i
$387$	15.9434	+	24.5507i	0.810449	+	1.24798i
$388$	0.306967	−	0.0160874i	0.0155839	−	0.000816716i
$389$	−2.86503	−	13.4789i	−0.145263	−	0.683408i	−0.989153	−	0.146891i	$-0.953073\pi$
$389$	−2.86503	−	13.4789i	−0.145263	−	0.683408i	0.843890	−	0.536516i	$-0.180260\pi$
$390$	0.668111	+	23.8798i	0.0338311	+	1.20920i
$391$	−13.5890	+	4.41532i	−0.687223	+	0.223292i
$392$	−7.68475	+	18.5413i	−0.388139	+	0.936477i
$393$	−15.7885	+	15.7885i	−0.796424	+	0.796424i
$394$	8.90395	−	0.935843i	0.448575	−	0.0471471i
$395$	7.94113	−	2.36775i	0.399561	−	0.119134i
$396$	0.0378920	−	0.360518i	0.00190414	−	0.0181167i
$397$	10.0090	−	26.0743i	0.502337	−	1.30863i	−0.414747	−	0.909937i	$-0.636130\pi$
$397$	10.0090	−	26.0743i	0.502337	−	1.30863i	0.917084	−	0.398695i	$-0.130537\pi$
$398$	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	$0.289108\pi$
$402$	−9.42358	+	14.5110i	−0.470006	+	0.723745i
$403$	15.1048	+	18.6529i	0.752424	+	0.929166i
$404$	0.253589	−	0.112905i	0.0126165	−	0.00561723i
$405$	0.629672	−	1.03167i	0.0312887	−	0.0512643i
$406$	−4.05938	−	4.16797i	−0.201464	−	0.206853i
$407$	−2.72104	−	2.72104i	−0.134877	−	0.134877i
$408$	11.1954	+	9.06589i	0.554257	+	0.448829i
$409$	20.0714	−	22.2915i	0.992466	−	1.10225i	−0.00229310	−	0.999997i	$-0.500730\pi$
$409$	20.0714	−	22.2915i	0.992466	−	1.10225i	0.994759	−	0.102248i	$-0.0326034\pi$
$410$	−37.8549	+	5.05267i	−1.86952	+	0.249534i
$411$	−18.6311	+	16.7755i	−0.919005	+	0.827476i
$412$	0.0392804	+	0.0200144i	0.00193521	+	0.000986036i
$413$	8.86769	−	7.77506i	0.436350	−	0.382586i
$414$	−52.3925	−	17.0234i	−2.57495	−	0.836653i
$415$	−0.0515958	+	0.175337i	−0.00253274	+	0.00860695i
$416$	0.651234	+	0.586373i	0.0319294	+	0.0287493i
$417$	−2.48009	−	6.46087i	−0.121451	−	0.316390i
$418$	8.72822	−	2.33872i	0.426911	−	0.114390i
$419$	−29.1668	+	21.1909i	−1.42489	+	1.03524i	−0.433953	+	0.900936i	$0.642882\pi$
$419$	−29.1668	+	21.1909i	−1.42489	+	1.03524i	−0.990939	+	0.134309i	$0.957118\pi$
$420$	−0.306553	−	0.898108i	−0.0149582	−	0.0438232i
$421$	−4.26114	−	3.09590i	−0.207675	−	0.150885i	0.479086	−	0.877768i	$-0.340968\pi$
$421$	−4.26114	−	3.09590i	−0.207675	−	0.150885i	−0.686761	+	0.726883i	$0.740968\pi$
$422$	2.25810	+	0.866802i	0.109922	+	0.0421953i
$423$	25.1838	+	16.3546i	1.22448	+	0.795187i
$424$	9.91694	−	5.72555i	0.481609	−	0.278057i
$425$	−8.86650	+	0.964027i	−0.430089	+	0.0467622i
$426$			32.8578i			1.59196i
$427$	−19.6572	+	13.8891i	−0.951279	+	0.672143i
$428$	0.138782	−	0.0219809i	0.00670827	−	0.00106249i
$429$	−4.02196	−	9.03347i	−0.194182	−	0.436140i
$430$	15.2224	−	10.5022i	0.734087	−	0.506462i
$431$	11.9356	+	5.31409i	0.574919	+	0.255971i	0.673535	−	0.739155i	$-0.264775\pi$
$431$	11.9356	+	5.31409i	0.574919	+	0.255971i	−0.0986160	+	0.995126i	$0.531442\pi$
$432$	5.47373	+	20.4282i	0.263355	+	0.982854i
$433$	−18.2189	−	2.88559i	−0.875544	−	0.138673i	−0.297543	−	0.954708i	$-0.596167\pi$
$433$	−18.2189	−	2.88559i	−0.875544	−	0.138673i	−0.578001	+	0.816036i	$0.696167\pi$
$434$	27.0467	+	18.0762i	1.29828	+	0.867688i
$435$	9.90684	+	0.761836i	0.474996	+	0.0365273i
$436$	−0.295961	−	0.328698i	−0.0141740	−	0.0157418i
$437$	2.10637	+	40.1919i	0.100761	+	1.92264i
$438$	−0.746925	−	14.2522i	−0.0356894	−	0.680995i
$439$	−15.9544	−	17.7191i	−0.761461	−	0.845688i	0.230389	−	0.973099i	$-0.426000\pi$
$439$	−15.9544	−	17.7191i	−0.761461	−	0.845688i	−0.991850	+	0.127410i	$0.959333\pi$
$440$	−8.24747	−	0.634231i	−0.393183	−	0.0302358i
$441$	14.8749	−	31.1686i	0.708330	−	1.48422i
$442$	6.68239	+	1.05839i	0.317849	+	0.0503423i
$443$	0.405207	+	1.51225i	0.0192520	+	0.0718493i	0.974884	−	0.222715i	$-0.0714920\pi$
$443$	0.405207	+	1.51225i	0.0192520	+	0.0718493i	−0.955632	+	0.294565i	$0.904825\pi$
$444$	−0.437073	−	0.194598i	−0.0207426	−	0.00923519i
$445$	−29.5101	+	20.3596i	−1.39891	+	0.965140i
$446$	11.5066	+	25.8442i	0.544851	+	1.22376i
$447$	−2.00901	+	0.318196i	−0.0950230	+	0.0150502i
$448$	19.7365	+	9.10124i	0.932462	+	0.429993i
$449$			11.3780i			0.536963i	0.963285	+	0.268482i	$0.0865219\pi$
$449$			11.3780i			0.536963i	−0.963285	+	0.268482i	$0.913478\pi$
$450$	−29.8410	−	17.0865i	−1.40672	−	0.805464i
$451$	13.6902	−	7.90405i	0.644647	−	0.372187i
$452$	−0.0176777	−	0.0114800i	−0.000831489	−	0.000539976i
$453$	43.7615	+	16.7985i	2.05609	+	0.789260i
$454$	0.887420	+	0.644748i	0.0416487	+	0.0302595i
$455$	−12.1209	−	10.5937i	−0.568236	−	0.496641i
$456$	32.8285	−	23.8513i	1.53734	−	1.11694i
$457$	−3.60529	+	0.966035i	−0.168648	+	0.0451892i	−0.342155	−	0.939643i	$-0.611157\pi$
$457$	−3.60529	+	0.966035i	−0.168648	+	0.0451892i	0.173507	+	0.984833i	$0.444490\pi$
$458$	4.52389	+	11.7851i	0.211388	+	0.550684i
$459$	−7.22010	−	6.50101i	−0.337005	−	0.303441i
$460$	0.287955	−	0.978551i	0.0134260	−	0.0456252i
$461$	12.7265	+	4.13508i	0.592730	+	0.192590i	0.589995	−	0.807407i	$-0.299130\pi$
$461$	12.7265	+	4.13508i	0.592730	+	0.192590i	0.00273459	+	0.999996i	$0.499130\pi$
$462$	−8.83568	−	10.0774i	−0.411073	−	0.468841i
$463$	−9.37027	−	4.77439i	−0.435473	−	0.221885i	0.222490	−	0.974935i	$-0.428582\pi$
$463$	−9.37027	−	4.77439i	−0.435473	−	0.221885i	−0.657963	+	0.753050i	$0.728582\pi$
$464$	−4.55215	+	4.09877i	−0.211328	+	0.190281i
$465$	−55.0677	+	7.35015i	−2.55370	+	0.340855i
$466$	−7.84353	+	8.71112i	−0.363344	+	0.403535i
$467$	−4.93204	−	3.99389i	−0.228228	−	0.184815i	0.508385	−	0.861130i	$-0.330243\pi$
$467$	−4.93204	−	3.99389i	−0.228228	−	0.184815i	−0.736613	+	0.676315i	$0.763576\pi$
$468$	−0.540608	−	0.540608i	−0.0249896	−	0.0249896i
$469$	−2.86877	−	11.3009i	−0.132468	−	0.521829i
$470$	9.88315	−	16.1929i	0.455876	−	0.746921i
$471$	8.83417	−	3.93322i	0.407057	−	0.181233i
$472$	−8.04326	−	9.93260i	−0.370221	−	0.457185i
$473$	−4.16923	+	6.42005i	−0.191701	+	0.295194i
$474$	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
$478$	8.20354	−	21.3709i	0.375221	−	0.977484i
$479$	0.446532	−	4.24847i	0.0204026	−	0.194117i	−0.979573	−	0.201088i	$-0.935552\pi$
$479$	0.446532	−	4.24847i	0.0204026	−	0.194117i	0.999976	+	0.00697082i	$0.00221890\pi$
$480$	−1.94383	+	0.579576i	−0.0887232	+	0.0264539i
$481$	−8.07140	+	0.848338i	−0.368024	+	0.0386809i
$482$	16.6415	−	16.6415i	0.758000	−	0.758000i
$483$	52.0862	−	29.1623i	2.37001	−	1.32693i
$484$	−0.505624	+	0.164287i	−0.0229829	+	0.00746759i
$485$	0.337546	+	12.0647i	0.0153272	+	0.547829i
$486$	4.29439	+	20.2035i	0.194797	+	0.916450i
$487$	−17.0588	+	0.894014i	−0.773009	+	0.0405117i	−0.434761	−	0.900546i	$-0.643167\pi$
$487$	−17.0588	+	0.894014i	−0.773009	+	0.0405117i	−0.338247	+	0.941057i	$0.609834\pi$
$488$	14.2063	+	21.8759i	0.643091	+	0.990273i
$489$	2.76586	−	8.51243i	0.125076	−	0.384945i
$490$	−19.9462	−	8.84299i	−0.901075	−	0.399486i
$491$	2.07485	+	6.38573i	0.0936366	+	0.288184i	0.986896	−	0.161358i	$-0.0515873\pi$
$491$	2.07485	+	6.38573i	0.0936366	+	0.288184i	−0.893259	+	0.449542i	$0.851587\pi$
$492$	1.23688	−	1.52741i	0.0557627	−	0.0688612i
$493$	0.728320	−	2.71813i	0.0328019	−	0.122418i
$494$	7.75140	−	17.4099i	0.348752	−	0.783309i
$495$	14.1150	+	1.83257i	0.634423	+	0.0823678i
$496$	20.1316	−	27.7088i	0.903935	−	1.24416i
$497$	−16.2574	−	15.0314i	−0.729242	−	0.674250i
$498$	0.145697	+	0.285946i	0.00652882	+	0.0128135i
$499$	16.7831	+	9.68973i	0.751315	+	0.433772i	0.826169	−	0.563422i	$-0.190516\pi$
$499$	16.7831	+	9.68973i	0.751315	+	0.433772i	−0.0748537	+	0.997195i	$0.523849\pi$
$500$	0.300801	−	0.561175i	0.0134522	−	0.0250965i
$501$	16.4993	+	28.5776i	0.737133	+	1.27675i
$502$	32.0046	+	1.67729i	1.42844	+	0.0748612i
$503$	−3.99874	−	25.2471i	−0.178295	−	1.12571i	−0.900764	−	0.434308i	$-0.856993\pi$
$503$	−3.99874	−	25.2471i	−0.178295	−	1.12571i	0.722469	−	0.691403i	$-0.243007\pi$
$504$	−33.1210	−	17.4303i	−1.47532	−	0.776409i
$505$	4.18901	+	10.0622i	0.186408	+	0.447760i
$506$	−1.50582	−	14.3269i	−0.0669418	−	0.636908i
$507$	15.2249	+	4.07950i	0.676162	+	0.181177i
$508$	1.11502	−	0.428016i	0.0494710	−	0.0189901i
$509$	−9.39640	−	1.99727i	−0.416488	−	0.0885273i	−0.00509877	−	0.999987i	$-0.501623\pi$
$509$	−9.39640	−	1.99727i	−0.416488	−	0.0885273i	−0.411389	+	0.911460i	$0.634956\pi$
$510$	−10.1492	+	11.9264i	−0.449415	+	0.528109i
$511$	7.39337	+	6.15036i	0.327064	+	0.272076i
$512$	10.6764	−	20.9536i	0.471834	−	0.926026i
$513$	−22.9518	+	14.9050i	−1.01335	+	0.658074i
$514$	20.6656	−	4.39261i	0.911521	−	0.193750i
$515$	−0.823229	+	1.52270i	−0.0362758	+	0.0670980i
$516$	−0.197880	+	0.930950i	−0.00871116	+	0.0409828i
$517$	−1.22839	+	7.75578i	−0.0540247	+	0.341099i
$518$	−10.1071	+	4.34106i	−0.444081	+	0.190735i
$519$	37.5652	+	51.7041i	1.64893	+	2.26956i
$520$	−11.9861	+	12.6761i	−0.525624	+	0.555883i
$521$	9.34459	+	0.982156i	0.409394	+	0.0430290i	0.306987	−	0.951714i	$-0.400679\pi$
$521$	9.34459	+	0.982156i	0.409394	+	0.0430290i	0.102407	+	0.994743i	$0.467346\pi$
$522$	8.43164	−	6.82781i	0.369043	−	0.298845i
$523$	−0.284342	+	5.42556i	−0.0124334	+	0.237243i	0.985343	+	0.170587i	$0.0545664\pi$
$523$	−0.284342	+	5.42556i	−0.0124334	+	0.237243i	−0.997776	+	0.0666562i	$0.978767\pi$
$524$	−0.451443			−0.0197214
$525$	35.5467	−	11.1731i	1.55138	−	0.487632i
$526$	−32.9906			−1.43846
$527$	−0.823460	+	15.7126i	−0.0358705	+	0.684449i
$528$	−10.9659	+	8.87999i	−0.477229	+	0.386452i
$529$	40.9384	+	4.30280i	1.77993	+	0.187078i
$530$	5.95938	+	10.9291i	0.258859	+	0.474729i
$531$	12.9267	+	17.7921i	0.560973	+	0.772113i
$532$	−0.0890630	+	0.751793i	−0.00386137	+	0.0325944i
$533$	5.21551	−	32.9295i	0.225909	−	1.42633i
$534$	−13.0884	+	61.5762i	−0.566392	+	2.66466i
$535$	0.729921	+	5.46861i	0.0315572	+	0.236428i
$536$	−12.3594	+	2.62707i	−0.533844	+	0.113472i
$537$	−18.2817	+	11.8723i	−0.788913	+	0.512326i
$538$	−10.4831	+	20.5742i	−0.451957	+	0.887016i
$539$	9.02812	+	0.238363i	0.388868	+	0.0102670i
$540$	0.674141	−	0.163124i	0.0290104	−	0.00701976i
$541$	−12.3954	−	2.63473i	−0.532922	−	0.113276i	−0.0664124	−	0.997792i	$-0.521155\pi$
$541$	−12.3954	−	2.63473i	−0.532922	−	0.113276i	−0.466509	+	0.884516i	$0.654489\pi$
$542$	19.7983	−	7.59985i	0.850409	−	0.326441i
$543$	−9.95556	−	2.66758i	−0.427234	−	0.114477i
$544$	0.0600478	+	0.571316i	0.00257453	+	0.0244950i
$545$	13.1857	−	11.3025i	0.564812	−	0.484147i
$546$	−28.2444	+	1.10667i	−1.20875	+	0.0473610i
$547$	4.53361	+	28.6241i	0.193843	+	1.22388i	0.872202	+	0.489146i	$0.162691\pi$
$547$	4.53361	+	28.6241i	0.193843	+	1.22388i	−0.678359	+	0.734731i	$0.737309\pi$
$548$	−0.506195	−	0.0265285i	−0.0216236	−	0.00113324i
$549$	−22.4416	−	38.8700i	−0.957784	−	1.65893i
$550$	0.907897	−	8.94618i	0.0387129	−	0.381466i
$551$	−6.86454	−	3.96324i	−0.292439	−	0.168840i
$552$	−29.3695	−	57.6409i	−1.25005	−	2.45336i
$553$	2.90653	+	9.36413i	0.123598	+	0.398203i
$554$	−13.0873	+	18.0132i	−0.556028	+	0.765306i
$555$	8.05699	−	16.9700i	0.342000	−	0.720335i
$556$	0.0569115	−	0.127825i	0.00241358	−	0.00542100i
$557$	3.15789	−	11.7854i	0.133804	−	0.499364i	−0.866196	−	0.499705i	$-0.833442\pi$
$557$	3.15789	−	11.7854i	0.133804	−	0.499364i	1.00000		0.000340697i	$0.000108447\pi$
$558$	−38.1766	+	47.1442i	−1.61615	+	1.99577i
$559$	4.98901	+	15.3546i	0.211013	+	0.649430i
$560$	−10.1253	+	20.6194i	−0.427871	+	0.871329i
$561$	2.00312	−	6.16496i	0.0845716	−	0.260285i
$562$	−20.5332	−	31.6184i	−0.866142	−	1.33374i
$563$	−5.04157	+	0.264218i	−0.212477	+	0.0111354i	−0.158277	−	0.987395i	$-0.550594\pi$
$563$	−5.04157	+	0.264218i	−0.212477	+	0.0111354i	−0.0541995	+	0.998530i	$0.517261\pi$
$564$	0.202983	+	0.954959i	0.00854711	+	0.0402110i
$565$	0.467549	−	0.682905i	0.0196699	−	0.0287300i
$566$	−0.362500	+	0.117783i	−0.0152370	+	0.00495081i
$567$	1.22895	+	0.731331i	0.0516112	+	0.0307130i
$568$	−16.9671	+	16.9671i	−0.711924	+	0.711924i
$569$	8.68031	−	0.912337i	0.363897	−	0.0382472i	0.0791845	−	0.996860i	$-0.474768\pi$
$569$	8.68031	−	0.912337i	0.363897	−	0.0382472i	0.284713	+	0.958613i	$0.408102\pi$
$570$	25.0503	+	36.3089i	1.04924	+	1.52081i
$571$	2.74150	−	26.0836i	0.114728	−	1.09156i	−0.774018	−	0.633164i	$-0.781756\pi$
$571$	2.74150	−	26.0836i	0.114728	−	1.09156i	0.888746	−	0.458401i	$-0.151577\pi$
$572$	0.0716476	−	0.186648i	0.00299573	−	0.00780416i
$573$	−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
$577$	2.41399	−	3.71722i	0.100496	−	0.154750i	−0.784846	−	0.619691i	$-0.787258\pi$
$577$	2.41399	−	3.71722i	0.100496	−	0.154750i	0.885342	+	0.464941i	$0.153925\pi$
$578$	−12.1218	−	14.9691i	−0.504199	−	0.622635i
$579$	−52.0380	+	23.1688i	−2.16262	+	0.962862i
$580$	0.130742	+	0.152526i	0.00542878	+	0.00633328i
$581$	−0.208132	−	0.0587235i	−0.00863475	−	0.00243626i
$582$	14.9853	+	14.9853i	0.621162	+	0.621162i
$583$	−4.00437	−	3.24268i	−0.165844	−	0.134298i
$584$	6.97384	−	7.74524i	0.288580	−	0.320500i
$585$	21.7380	−	20.7027i	0.898754	−	0.855950i
$586$	6.99184	−	6.29548i	0.288830	−	0.260064i
$587$	22.6393	+	11.5353i	0.934426	+	0.476114i	0.853783	−	0.520629i	$-0.174303\pi$
$587$	22.6393	+	11.5353i	0.934426	+	0.476114i	0.0806428	+	0.996743i	$0.474303\pi$
$588$	1.05853	−	0.374587i	0.0436530	−	0.0154477i
$589$	42.1506	+	13.6956i	1.73678	+	0.564315i
$590$	11.0076	−	8.47775i	0.453174	−	0.349024i
$591$	−13.4443	−	12.1053i	−0.553025	−	0.497946i
$592$	4.15030	+	10.8119i	0.170576	+	0.444367i
$593$	36.7909	−	9.85810i	1.51082	−	0.404824i	0.594114	−	0.804381i	$-0.297503\pi$
$593$	36.7909	−	9.85810i	1.51082	−	0.404824i	0.916708	+	0.399557i	$0.130836\pi$
$594$	7.92475	−	5.75767i	0.325156	−	0.236240i
$595$	−1.25798	−	10.4776i	−0.0515723	−	0.429538i
$596$	−0.0332712	−	0.0241729i	−0.00136284	−	0.000990161i
$597$	−32.3941	−	12.4349i	−1.32580	−	0.508928i
$598$	−25.4809	−	16.5475i	−1.04199	−	0.676676i
$599$	18.8301	−	10.8716i	0.769377	−	0.444200i	−0.0632751	−	0.997996i	$-0.520155\pi$
$599$	18.8301	−	10.8716i	0.769377	−	0.444200i	0.832652	+	0.553796i	$0.186821\pi$
$600$	−10.5909	−	38.9671i	−0.432373	−	1.59083i
$601$			0.106137i			0.00432940i	0.999998	+	0.00216470i	$0.000689047\pi$
$601$			0.106137i			0.00432940i	−0.999998	+	0.00216470i	$0.999311\pi$
$602$	12.6272	+	17.8711i	0.514646	+	0.728374i
$603$	21.4744	−	3.40122i	0.874507	−	0.138508i
$604$	0.385479	+	0.865801i	0.0156849	+	0.0352289i
$605$	−5.96456	−	20.0044i	−0.242494	−	0.813294i
$606$	17.4833	+	7.78409i	0.710213	+	0.316207i
$607$	−0.359253	−	1.34075i	−0.0145816	−	0.0544194i	0.958252	−	0.285926i	$-0.0923012\pi$
$607$	−0.359253	−	1.34075i	−0.0145816	−	0.0544194i	−0.972833	+	0.231507i	$0.925634\pi$
$608$	1.59822	+	0.253134i	0.0648165	+	0.0102659i
$609$	−0.770182	+	11.7313i	−0.0312094	+	0.475376i
$610$	−24.1503	+	14.8589i	−0.977819	+	0.601619i
$611$	11.0816	+	12.3073i	0.448312	+	0.497901i
$612$	−0.0262299	−	0.500496i	−0.00106028	−	0.0202314i
$613$	0.869711	+	16.5951i	0.0351273	+	0.670269i	0.958279	+	0.285834i	$0.0922705\pi$
$613$	0.869711	+	16.5951i	0.0351273	+	0.670269i	−0.923152	+	0.384435i	$0.874396\pi$
$614$	20.6863	+	22.9745i	0.834831	+	0.927174i
$615$	58.7708	+	50.0133i	2.36987	+	2.01673i
$616$	0.641179	−	9.76632i	0.0258338	−	0.393496i
$617$	−34.8080	−	5.51305i	−1.40132	−	0.221947i	−0.590402	−	0.807109i	$-0.701031\pi$
$617$	−34.8080	−	5.51305i	−1.40132	−	0.221947i	−0.810916	+	0.585162i	$0.801031\pi$
$618$	0.786657	+	2.93584i	0.0316440	+	0.118097i
$619$	−13.7308	−	6.11335i	−0.551888	−	0.245716i	0.111794	−	0.993731i	$-0.464340\pi$
$619$	−13.7308	−	6.11335i	−0.551888	−	0.245716i	−0.663682	+	0.748015i	$0.731007\pi$
$620$	−0.892363	−	0.682199i	−0.0358382	−	0.0273978i
$621$	17.7457	+	39.8576i	0.712112	+	1.59943i
$622$	−22.1476	+	3.50783i	−0.888037	+	0.140651i
$623$	−24.4791	−	34.6451i	−0.980734	−	1.38803i
$624$			29.7595i			1.19133i
$625$	21.7396	+	12.3446i	0.869585	+	0.493784i
$626$	21.7736	−	12.5710i	0.870249	−	0.502439i
$627$	−15.3133	−	9.94460i	−0.611556	−	0.397149i
$628$	0.182530	+	0.0700668i	0.00728375	+	0.00279597i
$629$	−4.30418	−	3.12717i	−0.171619	−	0.124689i
$630$	19.8206	−	35.5323i	0.789671	−	1.41564i
$631$	−15.3013	+	11.1170i	−0.609134	+	0.442562i	−0.849109	−	0.528217i	$-0.822861\pi$
$631$	−15.3013	+	11.1170i	−0.609134	+	0.442562i	0.239975	+	0.970779i	$0.422861\pi$
$632$	10.2636	−	2.75013i	0.408265	−	0.109394i
$633$	−1.75153	−	4.56288i	−0.0696169	−	0.181358i
$634$	7.47362	+	6.72928i	0.296815	+	0.267254i
$635$	15.7331	+	44.1774i	0.624350	+	1.75313i
$636$	−0.609275	−	0.197965i	−0.0241593	−	0.00784983i
$637$	12.3734	−	14.4810i	0.490251	−	0.573758i
$638$	2.52793	+	1.28804i	0.100082	+	0.0509942i
$639$	30.6836	−	27.6276i	1.21382	−	1.09293i
$640$	21.2565	+	11.4921i	0.840238	+	0.454265i
$641$	−0.00964018	+	0.0107065i	−0.000380764	+	0.000422881i	−0.743335	−	0.668919i	$-0.766757\pi$
$641$	−0.00964018	+	0.0107065i	−0.000380764	+	0.000422881i	0.742954	+	0.669342i	$0.233424\pi$
$642$	7.52852	+	6.09648i	0.297127	+	0.240609i
$643$	−13.5176	−	13.5176i	−0.533083	−	0.533083i	0.388405	−	0.921489i	$-0.373026\pi$
$643$	−13.5176	−	13.5176i	−0.533083	−	0.533083i	−0.921489	+	0.388405i	$0.873026\pi$
$644$	1.16158	+	0.327734i	0.0457726	+	0.0129145i
$645$	−36.3528	−	8.65871i	−1.43139	−	0.340937i
$646$	11.4129	−	5.08135i	0.449034	−	0.199923i
$647$	−7.58979	−	9.37261i	−0.298385	−	0.368475i	0.605799	−	0.795618i	$-0.292854\pi$
$647$	−7.58979	−	9.37261i	−0.298385	−	0.368475i	−0.904184	+	0.427143i	$0.859520\pi$
$648$	0.844094	−	1.29979i	0.0331591	−	0.0510606i
$649$	−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
$653$	12.2814	−	31.9942i	0.480609	−	1.25203i	−0.452284	−	0.891874i	$-0.649391\pi$
$653$	12.2814	−	31.9942i	0.480609	−	1.25203i	0.932893	−	0.360154i	$-0.117276\pi$
$654$	3.18752	−	30.3272i	0.124642	−	1.18589i
$655$	0.432270	−	17.7204i	0.0168902	−	0.692392i
$656$	−47.3146	+	4.97296i	−1.84732	+	0.194162i
$657$	−12.6811	+	12.6811i	−0.494736	+	0.494736i
$658$	19.2893	+	11.4788i	0.751976	+	0.447489i
$659$	−33.4008	+	10.8526i	−1.30111	+	0.422756i	−0.875967	−	0.482371i	$-0.839776\pi$
$659$	−33.4008	+	10.8526i	−1.30111	+	0.422756i	−0.425142	+	0.905127i	$0.639776\pi$
$660$	0.282371	+	0.366631i	0.0109913	+	0.0142711i
$661$	8.15884	+	38.3843i	0.317342	+	1.49298i	0.790753	+	0.612136i	$0.209689\pi$
$661$	8.15884	+	38.3843i	0.317342	+	1.49298i	−0.473410	+	0.880842i	$0.656977\pi$
$662$	−31.2248	+	1.63642i	−1.21359	+	0.0636013i
$663$	−7.44590	−	11.4657i	−0.289175	−	0.445290i
$664$	−0.0724219	+	0.222892i	−0.00281051	+	0.00864987i
$665$	−29.4246	−	4.21582i	−1.14104	−	0.163483i
$666$	−6.33868	−	19.5085i	−0.245619	−	0.755937i
$667$	−7.95259	+	9.82063i	−0.307926	+	0.380257i
$668$	−0.172679	+	0.644445i	−0.00668114	+	0.0249343i
$669$	23.2510	−	52.2227i	0.898937	−	2.01905i
$670$	−2.52733	−	13.5013i	−0.0976393	−	0.521600i
$671$	6.89886	−	9.49546i	0.266327	−	0.366568i
$672$	−0.711460	−	2.29215i	−0.0274451	−	0.0884216i
$673$	4.21677	+	8.27589i	0.162545	+	0.319012i	0.957885	−	0.287151i	$-0.0927081\pi$
$673$	4.21677	+	8.27589i	0.162545	+	0.319012i	−0.795341	+	0.606163i	$0.792708\pi$
$674$	12.4604	+	7.19401i	0.479956	+	0.277103i
$675$	5.75756	+	26.6181i	0.221609	+	1.02453i
$676$	0.159341	+	0.275987i	0.00612851	+	0.0106149i
$677$	7.95521	+	0.416915i	0.305744	+	0.0160233i	0.204591	−	0.978848i	$-0.434414\pi$
$677$	7.95521	+	0.416915i	0.305744	+	0.0160233i	0.101153	+	0.994871i	$0.467747\pi$
$678$	−0.227333	−	1.43532i	−0.00873065	−	0.0551232i
$679$	−14.2698	+	0.559115i	−0.547623	+	0.0214569i
$680$	−11.3994	+	0.917696i	−0.437147	+	0.0351920i
$681$	−0.231688	−	2.20436i	−0.00887829	−	0.0844713i
$682$	−15.3230	−	4.10579i	−0.586749	−	0.157219i
$683$	−41.6585	+	15.9912i	−1.59402	+	0.611887i	−0.983628	−	0.180213i	$-0.942321\pi$
$683$	−41.6585	+	15.9912i	−1.59402	+	0.611887i	−0.610392	+	0.792100i	$0.708988\pi$
$684$	−1.38088	−	0.293515i	−0.0527992	−	0.0112228i
$685$	1.52601	−	19.8441i	0.0583059	−	0.758204i
$686$	10.1984	−	23.7162i	0.389377	−	0.905489i
$687$	11.5805	−	22.7280i	0.441823	−	0.867126i
$688$	19.3214	−	12.5475i	0.736623	−	0.478369i
$689$	−10.6297	+	2.25941i	−0.404960	+	0.0860768i
$690$	63.4202	−	30.3894i	2.41437	−	1.15691i
$691$	0.280036	−	1.31747i	0.0106531	−	0.0501188i	−0.972500	−	0.232903i	$-0.925178\pi$
$691$	0.280036	−	1.31747i	0.0106531	−	0.0501188i	0.983153	+	0.182784i	$0.0585109\pi$
$692$	−0.202138	+	1.27625i	−0.00768412	+	0.0485156i
$693$	−1.98129	+	16.7243i	−0.0752629	+	0.635305i
$694$	3.07640	+	4.23431i	0.116779	+	0.160732i
$695$	4.96299	+	2.35633i	0.188257	+	0.0893805i
$696$	12.6710	+	1.33177i	0.480292	+	0.0504808i
$697$	16.9850	−	13.7542i	0.643354	−	0.520978i
$698$	2.24202	−	42.7802i	0.0848616	−	1.61926i
$699$	23.6863			0.895898
$700$	0.667933	+	0.348460i	0.0252455	+	0.0131705i
$701$	20.4883			0.773831			0.386915	−	0.922115i	$-0.373541\pi$
$701$	20.4883			0.773831			0.386915	+	0.922115i	$0.373541\pi$
$702$	1.08122	−	20.6309i	0.0408079	−	0.778662i
$703$	−11.6464	+	9.43105i	−0.439251	+	0.355699i
$704$	−10.5403	−	1.10783i	−0.397253	−	0.0417529i
$705$	−37.6791	+	7.05322i	−1.41908	+	0.265640i
$706$	−22.2096	−	30.5689i	−0.835871	−	1.15048i
$707$	−11.8495	+	5.08942i	−0.445646	+	0.191408i
$708$	−0.111854	+	0.706220i	−0.00420374	+	0.0265414i
$709$	−7.17730	+	33.7666i	−0.269549	+	1.26813i	0.610030	+	0.792378i	$0.291157\pi$
$709$	−7.17730	+	33.7666i	−0.269549	+	1.26813i	−0.879580	+	0.475752i	$0.842176\pi$
$710$	−17.9893	−	18.8889i	−0.675127	−	0.708889i
$711$	−17.8843	+	3.80142i	−0.670713	+	0.142564i
$712$	−38.5554	+	25.0381i	−1.44492	+	0.938344i
$713$	32.0775	−	62.9556i	1.20131	−	2.35770i
$714$	−14.2450	−	11.8500i	−0.533105	−	0.443477i
$715$	7.25784	+	2.99108i	0.271428	+	0.111860i
$716$	−0.431099	−	0.0916329i	−0.0161109	−	0.00342448i
$717$	−43.1838	+	16.5767i	−1.61273	+	0.619068i
$718$	26.1247	+	7.00010i	0.974966	+	0.261241i
$719$	−0.651471	−	6.19833i	−0.0242958	−	0.231159i	−0.999931	−	0.0117592i	$-0.996257\pi$
$719$	−0.651471	−	6.19833i	−0.0242958	−	0.231159i	0.975635	−	0.219400i	$-0.0704098\pi$
$720$	−36.5640	−	22.3165i	−1.36266	−	0.831686i
$721$	−1.81247	−	0.953835i	−0.0674998	−	0.0355227i
$722$	−1.36182	−	8.59818i	−0.0506816	−	0.319991i
$723$	−47.4907	−	2.48888i	−1.76620	−	0.0925626i
$724$	−0.104193	−	0.180468i	−0.00387231	−	0.00670704i
$725$	−6.11223	+	4.98594i	−0.227003	+	0.185173i
$726$	−31.7429	−	18.3267i	−1.17809	−	0.680169i
$727$	10.2720	+	20.1599i	0.380967	+	0.747690i	0.999268	−	0.0382513i	$-0.0121787\pi$
$727$	10.2720	+	20.1599i	0.380967	+	0.747690i	−0.618301	+	0.785941i	$0.712179\pi$
$728$	−15.1563	−	14.0134i	−0.561730	−	0.519371i
$729$	25.4854	−	35.0777i	0.943904	−	1.29917i
$730$	8.23231	+	7.78420i	0.304691	+	0.288106i
$731$	−4.30471	+	9.66855i	−0.159216	+	0.357604i
$732$	0.377685	−	1.40954i	0.0139596	−	0.0520980i
$733$	3.66568	−	4.52674i	0.135395	−	0.167199i	−0.704939	−	0.709268i	$-0.749026\pi$
$733$	3.66568	−	4.52674i	0.135395	−	0.167199i	0.840334	+	0.542069i	$0.182359\pi$
$734$	10.8586	+	33.4192i	0.400797	+	1.23353i
$735$	13.6900	+	41.9088i	0.504963	+	1.54583i
$736$	0.797179	−	2.45346i	0.0293844	−	0.0904359i
$737$	3.09660	+	4.76835i	0.114065	+	0.175644i
$738$	84.1495	−	4.41009i	3.09758	−	0.162338i
$739$	10.4801	+	49.3051i	0.385518	+	1.81372i	0.559338	+	0.828940i	$0.311056\pi$
$739$	10.4801	+	49.3051i	0.385518	+	1.81372i	−0.173820	+	0.984777i	$0.555611\pi$
$740$	0.357800	−	0.127425i	0.0131530	−	0.00468425i
$741$	−36.6243	+	11.9000i	−1.34543	+	0.437156i
$742$	−12.8518	+	7.19550i	−0.471803	+	0.264155i
$743$	1.41788	−	1.41788i	0.0520170	−	0.0520170i	−0.680620	−	0.732637i	$-0.738289\pi$
$743$	1.41788	−	1.41788i	0.0520170	−	0.0520170i	0.732637	+	0.680620i	$0.238289\pi$
$744$	−70.8479	+	7.44641i	−2.59741	+	0.272999i
$745$	0.980710	−	1.28284i	0.0359304	−	0.0469995i
$746$	−3.57747	+	34.0374i	−0.130981	+	1.24620i
$747$	0.144520	−	0.376486i	0.00528769	−	0.0137749i
$748$	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	$0.915029\pi$
$752$	12.8711	−	19.8197i	0.469360	−	0.722752i
$753$	−40.7546	−	50.3278i	−1.48518	−	1.83405i
$754$	5.46637	−	2.43379i	0.199074	−	0.0886333i
$755$	−34.3541	+	14.3021i	−1.25027	+	0.520506i
$756$	0.201926	+	0.795445i	0.00734397	+	0.0289300i
$757$	9.13491	+	9.13491i	0.332014	+	0.332014i	0.853351	−	0.521337i	$-0.174567\pi$
$757$	9.13491	+	9.13491i	0.332014	+	0.332014i	−0.521337	+	0.853351i	$0.674567\pi$
$758$	27.7261	+	22.4522i	1.00706	+	0.815499i
$759$	−19.4781	+	21.6326i	−0.707008	+	0.785212i
$760$	−5.81374	+	31.6847i	−0.210886	+	1.14932i
$761$	12.6693	−	11.4074i	0.459260	−	0.413520i	−0.406755	−	0.913537i	$-0.633340\pi$
$761$	12.6693	−	11.4074i	0.459260	−	0.413520i	0.866015	+	0.500018i	$0.166673\pi$
$762$	73.3679	+	37.3828i	2.65784	+	1.35424i
$763$	13.5471	+	15.4509i	0.490438	+	0.559359i
$764$	−1.14349	−	0.371541i	−0.0413699	−	0.0134419i
$765$	19.6709	−	0.550355i	0.711204	−	0.0198981i
$766$	2.14915	+	1.93511i	0.0776520	+	0.0699

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)

\(f(q)\)	\(=\)	\(q+(-0.0729528 + 1.39202i) q^{2} +(2.18898 - 1.77260i) q^{3} +(0.0566371 + 0.00595280i) q^{4} +(-0.287895 + 2.21746i) q^{5} +(2.30781 + 3.17642i) q^{6} +(-2.62738 - 0.311259i) q^{7} +(-0.448537 + 2.83195i) q^{8} +(1.02578 - 4.82592i) q^{9} +O(q^{10})\)	\(q+(-0.0729528 + 1.39202i) q^{2} +(2.18898 - 1.77260i) q^{3} +(0.0566371 + 0.00595280i) q^{4} +(-0.287895 + 2.21746i) q^{5} +(2.30781 + 3.17642i) q^{6} +(-2.62738 - 0.311259i) q^{7} +(-0.448537 + 2.83195i) q^{8} +(1.02578 - 4.82592i) q^{9} +(-3.06575 - 0.562526i) q^{10} +(1.26199 - 0.268244i) q^{11} +(0.134529 - 0.0873643i) q^{12} +(1.23533 - 2.42447i) q^{13} +(0.624954 - 3.63466i) q^{14} +(3.30047 + 5.36429i) q^{15} +(-3.79801 - 0.807292i) q^{16} +(1.66528 - 0.639239i) q^{17} +(6.64296 + 1.77998i) q^{18} +(-0.525199 - 4.99693i) q^{19} +(-0.0295056 + 0.123876i) q^{20} +(-6.30301 + 3.97595i) q^{21} +(0.281336 + 1.77628i) q^{22} +(-7.99926 - 0.419223i) q^{23} +(4.03808 + 6.99415i) q^{24} +(-4.83423 - 1.27679i) q^{25} +(3.28479 + 1.89648i) q^{26} +(-2.47276 - 4.85307i) q^{27} +(-0.146954 - 0.0332690i) q^{28} +(0.927279 - 1.27629i) q^{29} +(-7.70799 + 4.20299i) q^{30} +(-3.58774 + 8.05820i) q^{31} +(-0.0833536 + 0.311080i) q^{32} +(2.28697 - 2.82418i) q^{33} +(0.768350 + 2.36474i) q^{34} +(1.44661 - 5.73649i) q^{35} +(0.0868249 - 0.267220i) q^{36} +(-1.62445 - 2.50144i) q^{37} +(6.99416 - 0.366549i) q^{38} +(-1.59350 - 7.49685i) q^{39} +(-6.15060 - 1.80991i) q^{40} +(11.6529 - 3.78627i) q^{41} +(-5.07479 - 9.06399i) q^{42} +(-4.19548 + 4.19548i) q^{43} +(0.0730720 - 0.00768018i) q^{44} +(10.4060 + 3.66398i) q^{45} +(1.16714 - 11.1046i) q^{46} +(-2.18114 + 5.68207i) 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} +(0.0843977 - 0.129961i) q^{52} +(-2.51335 - 3.10373i) q^{53} +(6.93598 - 3.08810i) q^{54} +(0.231499 + 2.87563i) q^{55} +(2.05995 - 7.30099i) q^{56} +(-10.0072 - 10.0072i) q^{57} +(1.70898 + 1.38390i) q^{58} +(-2.98267 + 3.31260i) q^{59} +(0.154996 + 0.323464i) q^{60} +(6.76054 - 6.08722i) q^{61} +(-10.9555 - 5.58209i) q^{62} +(-4.19722 + 12.3602i) q^{63} +(-7.81259 - 2.53846i) q^{64} +(5.02051 + 3.43728i) q^{65} +(3.76448 + 3.38955i) q^{66} +(1.57927 + 4.11413i) q^{67} +(0.0981216 - 0.0262916i) q^{68} +(-18.2533 + 13.2618i) q^{69} +(7.87979 + 2.43221i) q^{70} +(6.77041 + 4.91899i) q^{71} +(13.2067 + 5.06956i) q^{72} +(-3.04851 - 1.97972i) q^{73} +(3.60057 - 2.07879i) q^{74} +(-12.8453 + 5.77430i) q^{75} -0.286138i q^{76} +(-3.39921 + 0.311973i) q^{77} +(10.5520 - 1.67128i) q^{78} +(-1.50732 - 3.38549i) q^{79} +(2.88356 - 8.18951i) q^{80} +(-0.493795 - 0.219852i) q^{81} +(4.42046 + 16.4974i) q^{82} +(0.0807312 + 0.0127866i) q^{83} +(-0.380652 + 0.187666i) q^{84} +(0.938062 + 3.87671i) q^{85} +(-5.53413 - 6.14628i) q^{86} +(-0.232558 - 4.43746i) q^{87} +(0.193605 + 3.69420i) q^{88} +(10.7285 + 11.9152i) q^{89} +(-5.85949 + 14.2180i) q^{90} +(-4.00031 + 5.98549i) q^{91} +(-0.450559 - 0.0713615i) q^{92} +(6.43047 + 23.9989i) q^{93} +(-7.75046 - 3.45072i) q^{94} +(11.2317 + 0.273985i) q^{95} +(0.368961 + 0.828699i) q^{96} +(5.33114 - 0.844370i) q^{97} +(-2.77331 + 9.35512i) 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

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