LMFDB - Embedded newform 175.2.t.a.114.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(4,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([3, 20]))

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

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

chi := DirichletCharacter("175.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.t (of order $30$, degree $8$, 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:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			114.4
Character	$\chi$	$=$	175.114
Dual form			175.2.t.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93770 + 0.203661i) q^{2} +(-0.500958 - 2.35682i) q^{3} +(1.75692 - 0.373445i) q^{4} +(-0.306385 - 2.21498i) q^{5} +(1.45070 + 4.46479i) q^{6} +(-2.52107 - 0.802620i) q^{7} +(0.377701 - 0.122722i) q^{8} +(-2.56301 + 1.14113i) q^{9} +O(q^{10})$	\(q+(-1.93770 + 0.203661i) q^{2} +(-0.500958 - 2.35682i) q^{3} +(1.75692 - 0.373445i) q^{4} +(-0.306385 - 2.21498i) q^{5} +(1.45070 + 4.46479i) q^{6} +(-2.52107 - 0.802620i) q^{7} +(0.377701 - 0.122722i) q^{8} +(-2.56301 + 1.14113i) q^{9} +(1.04479 + 4.22957i) q^{10} +(2.26739 + 1.00951i) q^{11} +(-1.76029 - 3.95367i) q^{12} +(-2.29720 + 3.16183i) q^{13} +(5.04855 + 1.04180i) q^{14} +(-5.06682 + 1.83170i) q^{15} +(-3.98864 + 1.77586i) q^{16} +(-2.30076 - 2.07161i) q^{17} +(4.73395 - 2.73315i) q^{18} +(-5.00961 - 1.06483i) q^{19} +(-1.36546 - 3.77712i) q^{20} +(-0.628681 + 6.34379i) q^{21} +(-4.59912 - 1.49435i) q^{22} +(4.53438 - 0.476582i) q^{23} +(-0.478447 - 0.828694i) q^{24} +(-4.81226 + 1.35727i) q^{25} +(3.80736 - 6.59454i) q^{26} +(-0.275367 - 0.379010i) q^{27} +(-4.72905 - 0.468658i) q^{28} +(-0.797815 + 2.45542i) q^{29} +(9.44495 - 4.58121i) q^{30} +(4.22141 - 4.68835i) q^{31} +(6.67927 - 3.85628i) q^{32} +(1.24336 - 5.84955i) q^{33} +(4.88009 + 3.54559i) q^{34} +(-1.00537 + 5.83003i) q^{35} +(-4.07686 + 2.96201i) q^{36} +(3.31862 + 7.45374i) q^{37} +(9.92401 + 1.04306i) q^{38} +(8.60267 + 3.83016i) q^{39} +(-0.387549 - 0.798998i) q^{40} +(-4.21399 - 3.06164i) q^{41} +(-0.0737844 - 12.4204i) q^{42} -5.80714i q^{43} +(4.36062 + 0.926877i) q^{44} +(3.31284 + 5.32739i) q^{45} +(-8.68922 + 1.84695i) q^{46} +(-1.61989 + 1.45856i) q^{47} +(6.18352 + 8.51089i) q^{48} +(5.71160 + 4.04692i) q^{49} +(9.04830 - 3.61005i) q^{50} +(-3.72984 + 6.46027i) q^{51} +(-2.85523 + 6.41296i) q^{52} +(-1.59789 - 7.51748i) q^{53} +(0.610768 + 0.678327i) q^{54} +(1.54134 - 5.33152i) q^{55} +(-1.05071 + 0.00624181i) q^{56} +12.3402i q^{57} +(1.04586 - 4.92036i) q^{58} +(1.15540 - 10.9929i) q^{59} +(-8.21796 + 5.11033i) q^{60} +(-0.904700 - 8.60765i) q^{61} +(-7.22500 + 9.94436i) q^{62} +(7.37743 - 0.819737i) q^{63} +(-5.09255 + 3.69995i) q^{64} +(7.70721 + 4.11952i) q^{65} +(-1.21794 + 11.5879i) q^{66} +(-6.37162 - 5.73703i) q^{67} +(-4.81588 - 2.78045i) q^{68} +(-3.39475 - 10.4480i) q^{69} +(0.760757 - 11.5016i) q^{70} +(4.36571 - 13.4363i) q^{71} +(-0.828010 + 0.745543i) q^{72} +(-5.00373 + 11.2386i) q^{73} +(-7.94853 - 13.7673i) q^{74} +(5.60958 + 10.6617i) q^{75} -9.19914 q^{76} +(-4.90600 - 4.36489i) q^{77} +(-17.4495 - 5.66968i) q^{78} +(-4.18464 - 4.64751i) q^{79} +(5.15555 + 8.29066i) q^{80} +(-6.38718 + 7.09369i) q^{81} +(8.78899 + 5.07433i) q^{82} +(-4.78601 + 1.55507i) q^{83} +(1.26451 + 11.3803i) q^{84} +(-3.88366 + 5.73084i) q^{85} +(1.18269 + 11.2525i) q^{86} +(6.18666 + 0.650245i) q^{87} +(0.980283 + 0.103032i) q^{88} +(1.45225 + 13.8172i) q^{89} +(-7.50428 - 9.64821i) q^{90} +(8.32916 - 6.12742i) q^{91} +(7.78856 - 2.53066i) q^{92} +(-13.1644 - 7.60044i) q^{93} +(2.84182 - 3.15616i) q^{94} +(-0.823699 + 11.4224i) q^{95} +(-12.4346 - 13.8100i) q^{96} +(4.30851 + 1.39992i) q^{97} +(-11.8916 - 6.67851i) q^{98} -6.96332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) $ 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.93770	+	0.203661i	−1.37016	+	0.144010i	−0.760854	−	0.648923i	$-0.775220\pi$
$2$	−1.93770	+	0.203661i	−1.37016	+	0.144010i	−0.609309	+	0.792933i	$0.708553\pi$
$3$	−0.500958	−	2.35682i	−0.289228	−	1.36071i	−0.847386	−	0.530977i	$-0.821825\pi$
$3$	−0.500958	−	2.35682i	−0.289228	−	1.36071i	0.558158	−	0.829735i	$-0.311508\pi$
$4$	1.75692	−	0.373445i	0.878460	−	0.186722i
$5$	−0.306385	−	2.21498i	−0.137019	−	0.990568i
$5$	−0.306385	−	2.21498i	−0.137019	−	0.990568i
$6$	1.45070	+	4.46479i	0.592246	+	1.82274i
$7$	−2.52107	−	0.802620i	−0.952875	−	0.303362i
$7$	−2.52107	−	0.802620i	−0.952875	−	0.303362i
$8$	0.377701	−	0.122722i	0.133537	−	0.0433889i
$9$	−2.56301	+	1.14113i	−0.854338	+	0.380376i
$10$	1.04479	+	4.22957i	0.330390	+	1.33751i
$11$	2.26739	+	1.00951i	0.683644	+	0.304378i	0.719013	−	0.694997i	$-0.244594\pi$
$11$	2.26739	+	1.00951i	0.683644	+	0.304378i	−0.0353694	+	0.999374i	$0.511261\pi$
$12$	−1.76029	−	3.95367i	−0.508151	−	1.14132i
$13$	−2.29720	+	3.16183i	−0.637130	+	0.876934i	−0.998458	−	0.0555046i	$-0.982323\pi$
$13$	−2.29720	+	3.16183i	−0.637130	+	0.876934i	0.361329	+	0.932439i	$0.382323\pi$
$14$	5.04855	+	1.04180i	1.34928	+	0.278432i
$15$	−5.06682	+	1.83170i	−1.30825	+	0.472944i
$16$	−3.98864	+	1.77586i	−0.997161	+	0.443965i
$17$	−2.30076	−	2.07161i	−0.558016	−	0.502440i	0.341173	−	0.940001i	$-0.389176\pi$
$17$	−2.30076	−	2.07161i	−0.558016	−	0.502440i	−0.899189	+	0.437561i	$0.855842\pi$
$18$	4.73395	−	2.73315i	1.11580	−	0.644210i
$19$	−5.00961	−	1.06483i	−1.14928	−	0.244288i	−0.406392	−	0.913699i	$-0.633213\pi$
$19$	−5.00961	−	1.06483i	−1.14928	−	0.244288i	−0.742892	+	0.669411i	$0.766547\pi$
$20$	−1.36546	−	3.77712i	−0.305327	−	0.844590i
$21$	−0.628681	+	6.34379i	−0.137190	+	1.38433i
$22$	−4.59912	−	1.49435i	−0.980537	−	0.318596i
$23$	4.53438	−	0.476582i	0.945483	−	0.0993743i	0.380778	−	0.924667i	$-0.375656\pi$
$23$	4.53438	−	0.476582i	0.945483	−	0.0993743i	0.564706	+	0.825292i	$0.308990\pi$
$24$	−0.478447	−	0.828694i	−0.0976625	−	0.169156i
$25$	−4.81226	+	1.35727i	−0.962451	+	0.271454i
$26$	3.80736	−	6.59454i	0.746684	−	1.29330i
$27$	−0.275367	−	0.379010i	−0.0529943	−	0.0729405i
$28$	−4.72905	−	0.468658i	−0.893707	−	0.0885680i
$29$	−0.797815	+	2.45542i	−0.148151	+	0.455960i	−0.997403	−	0.0720270i	$-0.977053\pi$
$29$	−0.797815	+	2.45542i	−0.148151	+	0.455960i	0.849252	+	0.527987i	$0.177053\pi$
$30$	9.44495	−	4.58121i	1.72440	−	0.836411i
$31$	4.22141	−	4.68835i	0.758187	−	0.842053i	−0.233280	−	0.972410i	$-0.574946\pi$
$31$	4.22141	−	4.68835i	0.758187	−	0.842053i	0.991467	+	0.130357i	$0.0416124\pi$
$32$	6.67927	−	3.85628i	1.18074	−	0.681700i
$33$	1.24336	−	5.84955i	0.216441	−	1.01828i
$34$	4.88009	+	3.54559i	0.836929	+	0.608064i
$35$	−1.00537	+	5.83003i	−0.169938	+	0.985455i
$36$	−4.07686	+	2.96201i	−0.679476	+	0.493669i
$37$	3.31862	+	7.45374i	0.545578	+	1.22539i	0.950411	+	0.310997i	$0.100663\pi$
$37$	3.31862	+	7.45374i	0.545578	+	1.22539i	−0.404833	+	0.914391i	$0.632670\pi$
$38$	9.92401	+	1.04306i	1.60989	+	0.169206i
$39$	8.60267	+	3.83016i	1.37753	+	0.613316i
$40$	−0.387549	−	0.798998i	−0.0612769	−	0.126333i
$41$	−4.21399	−	3.06164i	−0.658114	−	0.478148i	0.207911	−	0.978148i	$-0.433333\pi$
$41$	−4.21399	−	3.06164i	−0.658114	−	0.478148i	−0.866026	+	0.500000i	$0.833333\pi$
$42$	−0.0737844	−	12.4204i	−0.0113852	−	1.91651i
$43$		−	5.80714i		−	0.885580i	−0.896625	−	0.442790i	$-0.853989\pi$
$43$		−	5.80714i		−	0.885580i	0.896625	−	0.442790i	$-0.146011\pi$
$44$	4.36062	+	0.926877i	0.657387	+	0.139732i
$45$	3.31284	+	5.32739i	0.493849	+	0.794161i
$46$	−8.68922	+	1.84695i	−1.28116	+	0.272318i
$47$	−1.61989	+	1.45856i	−0.236286	+	0.212753i	−0.778764	−	0.627317i	$-0.784153\pi$
$47$	−1.61989	+	1.45856i	−0.236286	+	0.212753i	0.542478	+	0.840070i	$0.317486\pi$
$48$	6.18352	+	8.51089i	0.892515	+	1.22844i
$49$	5.71160	+	4.04692i	0.815943	+	0.578132i
$50$	9.04830	−	3.61005i	1.27962	−	0.510539i
$51$	−3.72984	+	6.46027i	−0.522282	+	0.904618i
$52$	−2.85523	+	6.41296i	−0.395950	+	0.889317i
$53$	−1.59789	−	7.51748i	−0.219487	−	1.03260i	−0.940529	−	0.339713i	$-0.889670\pi$
$53$	−1.59789	−	7.51748i	−0.219487	−	1.03260i	0.721042	−	0.692891i	$-0.243663\pi$
$54$	0.610768	+	0.678327i	0.0831150	+	0.0923086i
$55$	1.54134	−	5.33152i	0.207835	−	0.718901i
$56$	−1.05071	+	0.00624181i	−0.140407	+	0.000834097i
$57$			12.3402i			1.63450i
$58$	1.04586	−	4.92036i	0.137328	−	0.646075i
$59$	1.15540	−	10.9929i	0.150420	−	1.43115i	−0.615460	−	0.788168i	$-0.711030\pi$
$59$	1.15540	−	10.9929i	0.150420	−	1.43115i	0.765880	−	0.642983i	$-0.222304\pi$
$60$	−8.21796	+	5.11033i	−1.06093	+	0.659741i
$61$	−0.904700	−	8.60765i	−0.115835	−	1.10210i	−0.885818	−	0.464032i	$-0.846402\pi$
$61$	−0.904700	−	8.60765i	−0.115835	−	1.10210i	0.769983	−	0.638064i	$-0.220264\pi$
$62$	−7.22500	+	9.94436i	−0.917576	+	1.26294i
$63$	7.37743	−	0.819737i	0.929469	−	0.103277i
$64$	−5.09255	+	3.69995i	−0.636568	+	0.462494i
$65$	7.70721	+	4.11952i	0.955962	+	0.510964i
$66$	−1.21794	+	11.5879i	−0.149918	+	1.42637i
$67$	−6.37162	−	5.73703i	−0.778417	−	0.700890i	0.180813	−	0.983518i	$-0.442127\pi$
$67$	−6.37162	−	5.73703i	−0.778417	−	0.700890i	−0.959230	+	0.282628i	$0.908794\pi$
$68$	−4.81588	−	2.78045i	−0.584011	−	0.337179i
$69$	−3.39475	−	10.4480i	−0.408680	−	1.25779i
$70$	0.760757	−	11.5016i	0.0909279	−	1.37471i
$71$	4.36571	−	13.4363i	0.518114	−	1.59459i	−0.259428	−	0.965762i	$-0.583534\pi$
$71$	4.36571	−	13.4363i	0.518114	−	1.59459i	0.777543	−	0.628830i	$-0.216466\pi$
$72$	−0.828010	+	0.745543i	−0.0975819	+	0.0878631i
$73$	−5.00373	+	11.2386i	−0.585642	+	1.31537i	0.341224	+	0.939982i	$0.389159\pi$
$73$	−5.00373	+	11.2386i	−0.585642	+	1.31537i	−0.926866	+	0.375392i	$0.877508\pi$
$74$	−7.94853	−	13.7673i	−0.923998	−	1.60041i
$75$	5.60958	+	10.6617i	0.647739	+	1.23111i
$76$	−9.19914			−1.05521
$77$	−4.90600	−	4.36489i	−0.559091	−	0.497426i
$78$	−17.4495	−	5.66968i	−1.97576	−	0.641965i
$79$	−4.18464	−	4.64751i	−0.470809	−	0.522886i	0.460233	−	0.887798i	$-0.347766\pi$
$79$	−4.18464	−	4.64751i	−0.470809	−	0.522886i	−0.931042	+	0.364912i	$0.881099\pi$
$80$	5.15555	+	8.29066i	0.576408	+	0.926924i
$81$	−6.38718	+	7.09369i	−0.709687	+	0.788187i
$82$	8.78899	+	5.07433i	0.970582	+	0.560366i
$83$	−4.78601	+	1.55507i	−0.525332	+	0.170691i	−0.559664	−	0.828720i	$-0.689070\pi$
$83$	−4.78601	+	1.55507i	−0.525332	+	0.170691i	0.0343315	+	0.999410i	$0.489070\pi$
$84$	1.26451	+	11.3803i	0.137970	+	1.24169i
$85$	−3.88366	+	5.73084i	−0.421242	+	0.621597i
$86$	1.18269	+	11.2525i	0.127532	+	1.21339i
$87$	6.18666	+	0.650245i	0.663280	+	0.0697135i
$88$	0.980283	+	0.103032i	0.104499	+	0.0109832i
$89$	1.45225	+	13.8172i	0.153938	+	1.46463i	0.749867	+	0.661588i	$0.230117\pi$
$89$	1.45225	+	13.8172i	0.153938	+	1.46463i	−0.595929	+	0.803037i	$0.703216\pi$
$90$	−7.50428	−	9.64821i	−0.791020	−	1.01701i
$91$	8.32916	−	6.12742i	0.873134	−	0.642328i
$92$	7.78856	−	2.53066i	0.812014	−	0.263839i
$93$	−13.1644	−	7.60044i	−1.36508	−	0.788129i
$94$	2.84182	−	3.15616i	0.293111	−	0.325533i
$95$	−0.823699	+	11.4224i	−0.0845097	+	1.17192i
$96$	−12.4346	−	13.8100i	−1.26910	−	1.40948i
$97$	4.30851	+	1.39992i	0.437463	+	0.142140i	0.519465	−	0.854492i	$-0.326131\pi$
$97$	4.30851	+	1.39992i	0.437463	+	0.142140i	−0.0820021	+	0.996632i	$0.526131\pi$
$98$	−11.8916	−	6.67851i	−1.20123	−	0.674631i
$99$	−6.96332			−0.699840
$100$	−7.94788	+	4.18173i	−0.794788	+	0.418173i
$101$	−5.70073	−	9.87396i	−0.567244	−	0.982495i	−0.996837	−	0.0794728i	$-0.974676\pi$
$101$	−5.70073	−	9.87396i	−0.567244	−	0.982495i	0.429593	−	0.903023i	$-0.358657\pi$
$102$	5.91161	−	13.2777i	0.585337	−	1.31469i
$103$	1.13579	−	1.02267i	0.111913	−	0.100767i	−0.611274	−	0.791419i	$-0.709343\pi$
$103$	1.13579	−	1.02267i	0.111913	−	0.100767i	0.723188	+	0.690652i	$0.242676\pi$
$104$	−0.479628	+	1.47614i	−0.0470314	+	0.144748i
$105$	14.2440	−	0.551125i	1.39007	−	0.0537843i
$106$	4.62725	+	14.2412i	0.449438	+	1.38323i
$107$	−7.85780	−	4.53670i	−0.759642	−	0.438580i	0.0695249	−	0.997580i	$-0.477852\pi$
$107$	−7.85780	−	4.53670i	−0.759642	−	0.438580i	−0.829167	+	0.559000i	$0.811185\pi$
$108$	−0.625336	−	0.563055i	−0.0601730	−	0.0541800i
$109$	−0.397371	+	3.78073i	−0.0380612	+	0.362129i	0.958870	+	0.283846i	$0.0916104\pi$
$109$	−0.397371	+	3.78073i	−0.0380612	+	0.362129i	−0.996931	+	0.0782828i	$0.975056\pi$
$110$	−1.90084	+	10.6448i	−0.181238	+	1.01494i
$111$	15.9046	−	11.5554i	1.50960	−	1.09679i
$112$	11.4810	−	1.27570i	1.08485	−	0.120542i
$113$	7.52234	−	10.3536i	0.707643	−	0.973986i	−0.292202	−	0.956357i	$-0.594388\pi$
$113$	7.52234	−	10.3536i	0.707643	−	0.973986i	0.999845	−	0.0176298i	$-0.00561202\pi$
$114$	−2.51321	−	23.9116i	−0.235384	−	2.23953i
$115$	−2.44488	−	9.89753i	−0.227987	−	0.922950i
$116$	−0.484732	+	4.61192i	−0.0450062	+	0.428206i
$117$	2.27971	−	10.7252i	0.210760	−	0.991546i
$118$			21.5362i			1.98257i
$119$	4.13766	+	7.06932i	0.379299	+	0.648043i
$120$	−1.68895	+	1.31365i	−0.154179	+	0.119919i
$121$	−3.23849	−	3.59670i	−0.294408	−	0.326973i
$122$	3.50608	+	16.4948i	0.317426	+	1.49337i
$123$	−5.10471	+	11.4654i	−0.460276	+	1.03380i
$124$	5.66584	−	9.81351i	0.508807	−	0.881280i
$125$	4.48072	+	10.2432i	0.400768	+	0.916179i
$126$	−14.1283	+	3.09090i	−1.25865	+	0.275359i
$127$	5.72589	+	7.88102i	0.508091	+	0.699327i	0.983596	−	0.180386i	$-0.0577346\pi$
$127$	5.72589	+	7.88102i	0.508091	+	0.699327i	−0.475505	+	0.879713i	$0.657735\pi$
$128$	−2.34879	+	2.11486i	−0.207605	+	0.186929i
$129$	−13.6864	+	2.90913i	−1.20502	+	0.256135i
$130$	−15.7733	−	6.41275i	−1.38341	−	0.562436i
$131$	17.4629	+	3.71185i	1.52574	+	0.324306i	0.892999	−	0.450059i	$-0.148597\pi$
$131$	17.4629	+	3.71185i	1.52574	+	0.324306i	0.632740	+	0.774365i	$0.281930\pi$
$132$		−	10.7415i		−	0.934929i
$133$	11.7749	+	6.70532i	1.02102	+	0.581425i
$134$	13.5147	+	9.81901i	1.16749	+	0.848233i
$135$	−0.755130	+	0.726054i	−0.0649913	+	0.0624888i
$136$	−1.12323	−	0.500095i	−0.0963163	−	0.0428828i
$137$	−3.22091	−	0.338532i	−0.275181	−	0.0289227i	−0.0340673	−	0.999420i	$-0.510846\pi$
$137$	−3.22091	−	0.338532i	−0.275181	−	0.0289227i	−0.241114	+	0.970497i	$0.577513\pi$
$138$	8.70586	+	19.5537i	0.741092	+	1.66452i
$139$	6.18949	−	4.49693i	0.524986	−	0.381424i	−0.293493	−	0.955961i	$-0.594818\pi$
$139$	6.18949	−	4.49693i	0.524986	−	0.381424i	0.818479	+	0.574537i	$0.194818\pi$
$140$	0.410842	+	10.6183i	0.0347225	+	0.897413i
$141$	4.24906	+	3.08712i	0.357836	+	0.259983i
$142$	−5.72301	+	26.9246i	−0.480264	+	2.25946i
$143$	−8.40055	+	4.85006i	−0.702489	+	0.405582i
$144$	8.19646	−	9.10310i	0.683039	−	0.758591i
$145$	5.68314	+	1.01484i	0.471959	+	0.0842778i
$146$	7.40689	−	22.7961i	0.612999	−	1.88662i
$147$	6.67661	−	15.4886i	0.550677	−	1.27748i
$148$	8.61411	+	11.8563i	0.708075	+	0.974582i
$149$	1.84866	−	3.20197i	0.151448	−	0.262315i	−0.780312	−	0.625390i	$-0.784940\pi$
$149$	1.84866	−	3.20197i	0.151448	−	0.262315i	0.931760	+	0.363075i	$0.118273\pi$
$150$	−13.0411	−	19.5167i	−1.06480	−	1.59354i
$151$	1.10361	+	1.91151i	0.0898105	+	0.155556i	0.907431	−	0.420201i	$-0.138041\pi$
$151$	1.10361	+	1.91151i	0.0898105	+	0.155556i	−0.817620	+	0.575758i	$0.804707\pi$
$152$	−2.02281	+	0.212606i	−0.164072	+	0.0172446i
$153$	8.26085	+	2.68411i	0.667850	+	0.216998i
$154$	10.3953	+	7.45870i	0.837679	+	0.601039i
$155$	−11.6780	−	7.91389i	−0.937997	−	0.635659i
$156$	16.5446	+	3.51665i	1.32462	+	0.281558i
$157$	20.8287	−	12.0255i	1.66231	−	0.959738i	0.690709	−	0.723133i	$-0.257299\pi$
$157$	20.8287	−	12.0255i	1.66231	−	0.959738i	0.971606	−	0.236605i	$-0.0760347\pi$
$158$	9.05510	+	8.15325i	0.720385	+	0.648638i
$159$	−16.9169	+	7.53188i	−1.34160	+	0.597317i
$160$	−10.5880	−	13.6129i	−0.837055	−	1.07620i
$161$	−11.8140	−	2.43788i	−0.931074	−	0.192132i
$162$	10.9318	−	15.0463i	0.858880	−	1.18215i
$163$	0.394267	+	0.885537i	0.0308813	+	0.0693606i	0.928328	−	0.371763i	$-0.121247\pi$
$163$	0.394267	+	0.885537i	0.0308813	+	0.0693606i	−0.897446	+	0.441124i	$0.854580\pi$
$164$	−8.54699	−	3.80536i	−0.667408	−	0.297149i
$165$	−13.3376	−	0.961805i	−1.03833	−	0.0748764i
$166$	8.95715	−	3.98798i	0.695210	−	0.309527i
$167$	1.74340	−	0.566466i	0.134908	−	0.0438344i	−0.240785	−	0.970579i	$-0.577405\pi$
$167$	1.74340	−	0.566466i	0.134908	−	0.0438344i	0.375693	+	0.926744i	$0.377405\pi$
$168$	0.541072	+	2.47321i	0.0417446	+	0.190812i
$169$	−0.702803	−	2.16301i	−0.0540618	−	0.166385i
$170$	6.35823	−	11.8956i	0.487654	−	0.912352i
$171$	14.0548	−	2.98744i	1.07480	−	0.228455i
$172$	−2.16865	−	10.2027i	−0.165358	−	0.777947i
$173$	7.79368	−	0.819149i	0.592543	−	0.0622788i	0.196489	−	0.980506i	$-0.437046\pi$
$173$	7.79368	−	0.819149i	0.592543	−	0.0622788i	0.396054	+	0.918227i	$0.370379\pi$
$174$	−12.1203			−0.918841
$175$	13.2214	+	0.440639i	0.999445	+	0.0333092i
$176$	−10.8365			−0.816836
$177$	−26.4871	+	2.78390i	−1.99089	+	0.209251i
$178$	−5.62806	−	26.4780i	−0.421841	−	1.98461i
$179$	−10.4544	+	2.22214i	−0.781396	+	0.166091i	−0.581304	−	0.813686i	$-0.697457\pi$
$179$	−10.4544	+	2.22214i	−0.781396	+	0.166091i	−0.200092	+	0.979777i	$0.564124\pi$
$180$	7.80988	+	8.12264i	0.582114	+	0.605426i
$181$	−1.89456	−	5.83087i	−0.140822	−	0.433405i	0.855628	−	0.517591i	$-0.173171\pi$
$181$	−1.89456	−	5.83087i	−0.140822	−	0.433405i	−0.996450	+	0.0841859i	$0.973171\pi$
$182$	−14.8915	+	13.5694i	−1.10383	+	1.00583i
$183$	−19.8335	+	6.44429i	−1.46613	+	0.476375i
$184$	1.65415	−	0.736475i	0.121946	−	0.0542937i
$185$	15.4931	−	9.63438i	1.13908	−	0.708334i
$186$	27.0565	+	12.0463i	1.98388	+	0.883280i
$187$	−3.12541	−	7.01978i	−0.228553	−	0.513337i
$188$	−2.30133	+	3.16751i	−0.167842	+	0.231014i
$189$	0.390018	+	1.17653i	0.0283697	+	0.0855796i
$190$	−0.730218	−	22.3010i	−0.0529755	−	1.61789i
$191$	19.5821	−	8.71852i	1.41691	−	0.630850i	0.451665	−	0.892188i	$-0.350830\pi$
$191$	19.5821	−	8.71852i	1.41691	−	0.630850i	0.965247	+	0.261338i	$0.0841637\pi$
$192$	11.2713	+	10.1487i	0.813434	+	0.732420i
$193$	−1.64900	+	0.952048i	−0.118697	+	0.0685299i	−0.558173	−	0.829724i	$-0.688498\pi$
$193$	−1.64900	+	0.952048i	−0.118697	+	0.0685299i	0.439476	+	0.898254i	$0.355164\pi$
$194$	−8.63371	−	1.83515i	−0.619865	−	0.131756i
$195$	5.84799	−	20.2282i	0.418783	−	1.44857i
$196$	11.5461	+	4.97715i	0.824723	+	0.355511i
$197$	3.23369	+	1.05069i	0.230391	+	0.0748586i	0.421937	−	0.906625i	$-0.361350\pi$
$197$	3.23369	+	1.05069i	0.230391	+	0.0748586i	−0.191546	+	0.981484i	$0.561350\pi$
$198$	13.4929	−	1.41816i	0.958895	−	0.100784i
$199$	4.13160	+	7.15614i	0.292881	+	0.507286i	0.974490	−	0.224432i	$-0.0720525\pi$
$199$	4.13160	+	7.15614i	0.292881	+	0.507286i	−0.681608	+	0.731717i	$0.738719\pi$
$200$	−1.65102	+	1.10321i	−0.116745	+	0.0780089i
$201$	−10.3292	+	17.8908i	−0.728569	+	1.26192i
$202$	13.0573	+	17.9718i	0.918706	+	1.26449i
$203$	3.98212	−	5.54995i	0.279490	−	0.389530i
$204$	−4.14047	+	12.7431i	−0.289891	+	0.892192i
$205$	−5.49037	+	10.2719i	−0.383464	+	0.717423i
$206$	−1.99255	+	2.21296i	−0.138828	+	0.154184i
$207$	−11.0778	+	6.39579i	−0.769962	+	0.444538i
$208$	3.54777	−	16.6909i	0.245993	−	1.15731i
$209$	−10.2838	−	7.47162i	−0.711345	−	0.516823i
$210$	−27.4884	+	3.96886i	−1.89688	+	0.273877i
$211$	−18.1583	+	13.1928i	−1.25007	+	0.908228i	−0.998226	−	0.0595406i	$-0.981036\pi$
$211$	−18.1583	+	13.1928i	−1.25007	+	0.908228i	−0.251842	+	0.967768i	$0.581036\pi$
$212$	−5.61472	−	12.6109i	−0.385621	−	0.866118i
$213$	−33.8539	−	3.55819i	−2.31963	−	0.243803i
$214$	16.1500	+	7.19046i	1.10399	+	0.491530i
$215$	−12.8627	+	1.77922i	−0.877228	+	0.121342i
$216$	−0.150519	−	0.109359i	−0.0102415	−	0.00744091i
$217$	−14.4054	+	8.43148i	−0.977905	+	0.572366i
$218$		−	7.40687i		−	0.501656i
$219$	28.9940	+	6.16285i	1.95923	+	0.416447i
$220$	0.716988	−	9.94265i	0.0483393	−	0.670333i
$221$	11.8354	−	2.51569i	0.796135	−	0.169224i
$222$	−28.4651	+	25.6301i	−1.91045	+	1.72018i
$223$	5.23518	+	7.20560i	0.350573	+	0.482523i	0.947492	−	0.319779i	$-0.103609\pi$
$223$	5.23518	+	7.20560i	0.350573	+	0.482523i	−0.596919	+	0.802302i	$0.703609\pi$
$224$	−19.9340	+	4.36104i	−1.33190	+	0.291384i
$225$	10.7851	−	8.97010i	0.719004	−	0.598006i
$226$	−12.4674	+	21.5942i	−0.829322	+	1.43643i
$227$	−5.11260	+	11.4831i	−0.339335	+	0.762159i	0.660600	+	0.750738i	$0.270302\pi$
$227$	−5.11260	+	11.4831i	−0.339335	+	0.762159i	−0.999935	+	0.0114208i	$0.996365\pi$
$228$	4.60838	+	21.6807i	0.305198	+	1.43584i
$229$	−11.0658	−	12.2899i	−0.731251	−	0.812137i	0.256767	−	0.966473i	$-0.417343\pi$
$229$	−11.0658	−	12.2899i	−0.731251	−	0.812137i	−0.988018	+	0.154337i	$0.950676\pi$
$230$	6.75320	+	18.6806i	0.445293	+	1.23176i
$231$	−7.82957	+	13.7492i	−0.515148	+	0.904631i
$232$			1.02532i			0.0673158i
$233$	1.21215	−	5.70270i	0.0794104	−	0.373597i	−0.920440	−	0.390884i	$-0.872170\pi$
$233$	1.21215	−	5.70270i	0.0794104	−	0.373597i	0.999851	+	0.0172869i	$0.00550286\pi$
$234$	−2.23310	+	21.2466i	−0.145983	+	1.38893i
$235$	3.72699	+	3.14115i	0.243122	+	0.204906i
$236$	−2.07529	−	19.7451i	−0.135090	−	1.28530i
$237$	−8.85703	+	12.1907i	−0.575326	+	0.791868i
$238$	−9.45730	−	12.8556i	−0.613025	−	0.833302i
$239$	−3.29768	+	2.39590i	−0.213309	+	0.154978i	−0.689310	−	0.724467i	$-0.742086\pi$
$239$	−3.29768	+	2.39590i	−0.213309	+	0.154978i	0.476001	+	0.879445i	$0.342086\pi$
$240$	16.9569	−	16.3040i	1.09456	−	1.05242i
$241$	−2.37867	+	22.6315i	−0.153224	+	1.45783i	0.599968	+	0.800024i	$0.295180\pi$
$241$	−2.37867	+	22.6315i	−0.153224	+	1.45783i	−0.753191	+	0.657801i	$0.771487\pi$
$242$	7.00773	+	6.30979i	0.450474	+	0.405609i
$243$	18.7011	+	10.7971i	1.19968	+	0.692634i
$244$	−4.80397	−	14.7851i	−0.307542	−	0.946518i
$245$	7.21390	−	13.8910i	0.460879	−	0.887463i
$246$	7.55637	−	23.2561i	0.481776	−	1.48276i
$247$	14.8749	−	13.3934i	0.946468	−	0.852203i
$248$	1.01906	−	2.28885i	0.0647106	−	0.145342i
$249$	6.06260	+	10.5007i	0.384202	+	0.665457i
$250$	−10.7684	−	18.9357i	−0.681057	−	1.19760i
$251$	2.64599			0.167014			0.0835068	−	0.996507i	$-0.473388\pi$
$251$	2.64599			0.167014			0.0835068	+	0.996507i	$0.473388\pi$
$252$	12.6554	−	4.19527i	0.797217	−	0.264277i
$253$	10.7623	+	3.49689i	0.676621	+	0.219848i
$254$	−12.7001	−	14.1049i	−0.796877	−	0.885022i
$255$	15.4521	+	6.28218i	0.967649	+	0.393406i
$256$	12.5445	−	13.9321i	0.784033	−	0.870757i
$257$	1.72089	+	0.993558i	0.107346	+	0.0619765i	0.552712	−	0.833372i	$-0.313593\pi$
$257$	1.72089	+	0.993558i	0.107346	+	0.0619765i	−0.445366	+	0.895349i	$0.646926\pi$
$258$	25.9277	−	8.42441i	1.61419	−	0.524481i
$259$	−2.38396	−	21.4550i	−0.148132	−	1.33315i
$260$	15.0794	+	4.35945i	0.935182	+	0.270362i
$261$	−0.757138	−	7.20369i	−0.0468657	−	0.445897i
$262$	−34.5938	−	3.63596i	−2.13721	−	0.224630i
$263$	29.2703	+	3.07643i	1.80488	+	0.189701i	0.946369	−	0.323089i	$-0.104721\pi$
$263$	29.2703	+	3.07643i	1.80488	+	0.189701i	0.858514	+	0.512789i	$0.171388\pi$
$264$	−0.248253	−	2.36197i	−0.0152789	−	0.145369i
$265$	−16.1615	+	5.84253i	−0.992792	+	0.358904i
$266$	−24.1820	−	10.5948i	−1.48269	−	0.649610i
$267$	31.8373	−	10.3446i	1.94841	−	0.633077i
$268$	−13.3369	−	7.70005i	−0.814679	−	0.470355i
$269$	−16.0029	+	17.7731i	−0.975716	+	1.08364i	0.0207615	+	0.999784i	$0.493391\pi$
$269$	−16.0029	+	17.7731i	−0.975716	+	1.08364i	−0.996478	+	0.0838581i	$0.973276\pi$
$270$	1.31535	−	1.56067i	0.0800496	−	0.0949792i
$271$	8.07573	+	8.96901i	0.490566	+	0.544829i	0.936698	−	0.350139i	$-0.113865\pi$
$271$	8.07573	+	8.96901i	0.490566	+	0.544829i	−0.446132	+	0.894967i	$0.647199\pi$
$272$	12.8558	+	4.17710i	0.779497	+	0.253274i
$273$	−18.6138	−	16.5608i	−1.12656	−	1.00230i
$274$	6.31012			0.381208
$275$	−12.2814	−	1.78055i	−0.740598	−	0.107371i
$276$	−9.86605	−	17.0885i	−0.593866	−	1.02861i
$277$	7.59132	−	17.0504i	0.456118	−	1.02446i	−0.528371	−	0.849013i	$-0.677197\pi$
$277$	7.59132	−	17.0504i	0.456118	−	1.02446i	0.984489	−	0.175444i	$-0.0561362\pi$
$278$	−11.0775	+	9.97426i	−0.664387	+	0.598217i
$279$	−5.46952	+	16.8335i	−0.327452	+	1.00779i
$280$	0.335747	+	2.32539i	0.0200647	+	0.138968i
$281$	2.07291	+	6.37978i	0.123660	+	0.380585i	0.993655	−	0.112475i	$-0.0358780\pi$
$281$	2.07291	+	6.37978i	0.123660	+	0.380585i	−0.869995	+	0.493061i	$0.835878\pi$
$282$	−8.86214	−	5.11656i	−0.527733	−	0.304687i
$283$	6.62608	+	5.96615i	0.393880	+	0.354651i	0.842146	−	0.539249i	$-0.181292\pi$
$283$	6.62608	+	5.96615i	0.393880	+	0.354651i	−0.448267	+	0.893900i	$0.647958\pi$
$284$	2.65249	−	25.2368i	0.157397	−	1.49753i
$285$	27.3333	−	3.78085i	1.61908	−	0.223958i
$286$	15.2900	−	11.1088i	0.904116	−	0.656879i
$287$	8.16643	+	11.1008i	0.482049	+	0.655262i
$288$	−12.7186	+	17.5056i	−0.749448	+	1.03153i
$289$	−0.775072	−	7.37431i	−0.0455924	−	0.433783i
$290$	−11.2189	−	0.809024i	−0.658798	−	0.0475075i
$291$	1.14098	−	10.8557i	0.0668853	−	0.636371i
$292$	−4.59417	+	21.6139i	−0.268853	+	1.26486i
$293$		−	21.1628i		−	1.23634i	−0.786043	−	0.618171i	$-0.787874\pi$
$293$		−	21.1628i		−	1.23634i	0.786043	−	0.618171i	$-0.212126\pi$
$294$	−9.78287	+	31.3720i	−0.570548	+	1.82965i
$295$	−24.7030	+	0.808866i	−1.43826	+	0.0470940i
$296$	2.16819	+	2.40801i	0.126023	+	0.139963i
$297$	−0.241751	−	1.13735i	−0.0140278	−	0.0659956i
$298$	−2.93003	+	6.58096i	−0.169732	+	0.381225i
$299$	−8.90952	+	15.4317i	−0.515251	+	0.892441i
$300$	13.8371	+	16.6369i	0.798887	+	0.960530i
$301$	−4.66093	+	14.6402i	−0.268651	+	0.843848i
$302$	−2.52777	−	3.47917i	−0.145457	−	0.200204i
$303$	−20.4153	+	18.3820i	−1.17283	+	1.05602i
$304$	21.8725	−	4.64915i	1.25448	−	0.266647i
$305$	−18.7886	+	4.64114i	−1.07583	+	0.265751i
$306$	−16.5537	−	3.51860i	−0.946313	−	0.201145i
$307$		−	20.4087i		−	1.16479i	−0.812907	−	0.582393i	$-0.802116\pi$
$307$		−	20.4087i		−	1.16479i	0.812907	−	0.582393i	$-0.197884\pi$
$308$	−10.2495	−	5.83664i	−0.584019	−	0.332573i
$309$	−2.97925	−	2.16455i	−0.169483	−	0.123137i
$310$	24.2402	+	12.9564i	1.37675	+	0.735876i
$311$	−2.62585	−	1.16910i	−0.148898	−	0.0662937i	0.330935	−	0.943654i	$-0.392636\pi$
$311$	−2.62585	−	1.16910i	−0.148898	−	0.0662937i	−0.479833	+	0.877360i	$0.659303\pi$
$312$	3.71928	+	0.390912i	0.210563	+	0.0221310i
$313$	−1.66346	−	3.73620i	−0.0940244	−	0.211182i	0.860410	−	0.509602i	$-0.170207\pi$
$313$	−1.66346	−	3.73620i	−0.0940244	−	0.211182i	−0.954435	+	0.298419i	$0.903541\pi$
$314$	−37.9108	+	27.5438i	−2.13943	+	1.55439i
$315$	−4.07603	−	16.0897i	−0.229658	−	0.906551i
$316$	−9.08766	−	6.60257i	−0.511221	−	0.371424i
$317$	−0.712202	+	3.35065i	−0.0400012	+	0.188191i	−0.993612	−	0.112852i	$-0.964001\pi$
$317$	−0.712202	+	3.35065i	−0.0400012	+	0.188191i	0.953611	+	0.301043i	$0.0973348\pi$
$318$	31.2459	−	18.0398i	1.75218	−	1.01162i
$319$	−4.28772	+	4.76200i	−0.240066	+	0.266621i
$320$	9.75559	+	10.1463i	0.545354	+	0.567194i
$321$	−6.75577	+	20.7921i	−0.377071	+	1.16050i
$322$	23.3885	+	2.31785i	1.30339	+	0.129169i
$323$	9.32001	+	12.8279i	0.518579	+	0.713763i
$324$	−8.57267	+	14.8483i	−0.476259	+	0.824905i
$325$	6.76328	−	18.3335i	0.375159	−	1.01696i
$326$	−0.944320	−	1.63561i	−0.0523011	−	0.0905881i
$327$	9.10958	−	0.957455i	0.503761	−	0.0529474i
$328$	−1.96736	−	0.639233i	−0.108629	−	0.0352957i
$329$	5.25454	−	2.37697i	0.289692	−	0.131047i
$330$	26.0401	−	0.852650i	1.43346	−	0.0469368i
$331$	−26.3412	−	5.59900i	−1.44784	−	0.307749i	−0.584101	−	0.811681i	$-0.698553\pi$
$331$	−26.3412	−	5.59900i	−1.44784	−	0.307749i	−0.863743	+	0.503932i	$0.831886\pi$
$332$	−7.82789	+	4.51944i	−0.429612	+	0.248036i
$333$	−17.0113	−	15.3171i	−0.932215	−	0.839370i
$334$	−3.26283	+	1.45270i	−0.178534	+	0.0794885i
$335$	−10.7552	+	15.8707i	−0.587621	+	0.867111i
$336$	−8.75809	−	26.4196i	−0.477793	−	1.44131i
$337$	15.3283	−	21.0976i	0.834986	−	1.14926i	−0.151988	−	0.988382i	$-0.548568\pi$
$337$	15.3283	−	21.0976i	0.834986	−	1.14926i	0.986974	−	0.160877i	$-0.0514323\pi$
$338$	1.80234	+	4.04813i	0.0980345	+	0.220189i
$339$	−28.1700	−	12.5421i	−1.52998	−	0.681193i
$340$	−4.68312	+	11.5190i	−0.253978	+	0.624703i
$341$	14.3045	−	6.36877i	0.774632	−	0.344888i
$342$	−26.6256	+	8.65119i	−1.43975	+	0.467803i
$343$	−11.1512	−	14.7868i	−0.602109	−	0.798414i
$344$	−0.712666	−	2.19336i	−0.0384244	−	0.118258i
$345$	−22.1019	+	10.7204i	−1.18993	+	0.577167i
$346$	−14.9350	+	3.17454i	−0.802911	+	0.170664i
$347$	−5.06067	−	23.8086i	−0.271671	−	1.27811i	−0.876362	−	0.481652i	$-0.840037\pi$
$347$	−5.06067	−	23.8086i	−0.271671	−	1.27811i	0.604691	−	0.796460i	$-0.293297\pi$
$348$	11.1123	−	1.16795i	0.595682	−	0.0626087i
$349$	28.5904			1.53041			0.765206	−	0.643786i	$-0.222637\pi$
$349$	28.5904			1.53041			0.765206	+	0.643786i	$0.222637\pi$
$350$	−25.7089	+	1.83886i	−1.37420	+	0.0982910i
$351$	1.83094			0.0977282
$352$	19.0374	−	2.00092i	1.01470	−	0.106649i
$353$	−0.362725	−	1.70649i	−0.0193059	−	0.0908270i	0.967440	−	0.253101i	$-0.0814505\pi$
$353$	−0.362725	−	1.70649i	−0.0193059	−	0.0908270i	−0.986746	+	0.162274i	$0.948117\pi$
$354$	50.7571	−	10.7888i	2.69771	−	0.573416i
$355$	−31.0986	−	5.55329i	−1.65054	−	0.294738i
$356$	7.71147	+	23.7335i	0.408707	+	1.25787i
$357$	14.5883	−	13.2932i	0.772096	−	0.703548i
$358$	19.8049	−	6.43500i	1.04672	−	0.340100i
$359$	9.94263	−	4.42674i	0.524752	−	0.233635i	−0.127224	−	0.991874i	$-0.540607\pi$
$359$	9.94263	−	4.42674i	0.524752	−	0.233635i	0.651976	+	0.758239i	$0.273940\pi$
$360$	1.90505	+	1.60560i	0.100405	+	0.0846226i
$361$	6.60502	+	2.94074i	0.347633	+	0.154776i
$362$	4.85862	+	10.9126i	0.255363	+	0.573556i
$363$	−6.85444	+	9.43433i	−0.359765	+	0.495174i
$364$	12.3454	−	13.8759i	0.647076	−	0.727293i
$365$	26.4262	+	7.63983i	1.38321	+	0.399887i
$366$	37.1189	−	16.5264i	1.94024	−	0.863849i
$367$	9.26076	+	8.33843i	0.483408	+	0.435262i	0.874454	−	0.485109i	$-0.161220\pi$
$367$	9.26076	+	8.33843i	0.483408	+	0.435262i	−0.391046	+	0.920371i	$0.627887\pi$
$368$	−17.2397	+	9.95333i	−0.898680	+	0.518853i
$369$	14.2942	+	3.03833i	0.744128	+	0.158169i
$370$	−28.0589	+	21.8239i	−1.45871	+	1.13457i
$371$	−2.00528	+	20.2346i	−0.104109	+	1.05053i
$372$	−25.9670	−	8.43721i	−1.34633	−	0.437449i
$373$	12.9487	−	1.36096i	0.670459	−	0.0704680i	0.236818	−	0.971554i	$-0.423895\pi$
$373$	12.9487	−	1.36096i	0.670459	−	0.0704680i	0.433641	+	0.901086i	$0.357229\pi$
$374$	7.48577	+	12.9657i	0.387080	+	0.670442i
$375$	21.8967	−	15.6917i	1.13074	−	0.810315i
$376$	−0.432837	+	0.749696i	−0.0223219	+	0.0386626i
$377$	−5.93088	−	8.16316i	−0.305456	−	0.420424i
$378$	−0.995352	−	2.20033i	−0.0511954	−	0.113173i
$379$	2.26229	−	6.96260i	0.116206	−	0.357645i	−0.875991	−	0.482328i	$-0.839791\pi$
$379$	2.26229	−	6.96260i	0.116206	−	0.357645i	0.992197	+	0.124683i	$0.0397914\pi$
$380$	2.81847	+	20.3759i	0.144585	+	1.04526i
$381$	15.7057	−	17.4430i	0.804628	−	0.893630i
$382$	−36.1687	+	20.8820i	−1.85055	+	1.06842i
$383$	1.43254	−	6.73956i	0.0731993	−	0.344375i	−0.926273	−	0.376853i	$-0.877006\pi$
$383$	1.43254	−	6.73956i	0.0731993	−	0.344375i	0.999472	+	0.0324772i	$0.0103396\pi$
$384$	6.16098	+	4.47622i	0.314401	+	0.228426i
$385$	−8.16502	+	12.2040i	−0.416128	+	0.621974i
$386$	3.00137	−	2.18062i	0.152766	−	0.110991i
$387$	6.62668	+	14.8838i	0.336853	+	0.756585i
$388$	8.09249	+	0.850555i	0.410834	+	0.0431804i
$389$	9.15883	+	4.07778i	0.464371	+	0.206751i	0.625566	−	0.780171i	$-0.284868\pi$
$389$	9.15883	+	4.07778i	0.464371	+	0.206751i	−0.161195	+	0.986923i	$0.551535\pi$
$390$	−7.21197	+	40.3873i	−0.365192	+	2.04509i
$391$	−11.4198	−	8.29697i	−0.577524	−	0.419596i
$392$	2.65392	+	0.827584i	0.134043	+	0.0417993i
$393$		−	43.0164i		−	2.16989i
$394$	−6.47992	−	1.37735i	−0.326454	−	0.0693898i
$395$	−9.01203	+	10.6928i	−0.453445	+	0.538014i
$396$	−12.2340	+	2.60042i	−0.614782	+	0.130676i
$397$	−8.25028	+	7.42859i	−0.414070	+	0.372830i	−0.849674	−	0.527308i	$-0.823201\pi$
$397$	−8.25028	+	7.42859i	−0.414070	+	0.372830i	0.435604	+	0.900138i	$0.356535\pi$
$398$	−9.46324	−	13.0250i	−0.474349	−	0.652886i
$399$	9.90449	−	31.1105i	0.495845	−	1.55747i
$400$	16.7841	−	13.9596i	0.839203	−	0.697978i
$401$	3.57303	−	6.18867i	0.178429	−	0.309048i	−0.762914	−	0.646500i	$-0.776232\pi$
$401$	3.57303	−	6.18867i	0.178429	−	0.309048i	0.941343	+	0.337453i	$0.109565\pi$
$402$	16.3714	−	36.7707i	0.816529	−	1.83395i
$403$	5.12633	+	24.1175i	0.255361	+	1.20138i
$404$	−13.7031	−	15.2188i	−0.681755	−	0.757165i
$405$	17.6693	+	11.9741i	0.877994	+	0.594997i
$406$	−6.58586	+	11.5652i	−0.326851	+	0.573969i
$407$			20.2507i			1.00379i
$408$	−0.615942	+	2.89778i	−0.0304937	+	0.143462i
$409$	0.409804	−	3.89903i	0.0202635	−	0.192795i	−0.979707	−	0.200434i	$-0.935765\pi$
$409$	0.409804	−	3.89903i	0.0202635	−	0.192795i	0.999971	+	0.00763899i	$0.00243159\pi$
$410$	8.54671	−	21.0221i	0.422092	−	1.03821i
$411$	0.815683	+	7.76071i	0.0402347	+	0.382808i
$412$	1.61359	−	2.22091i	0.0794957	−	0.109416i
$413$	−11.7359	+	26.7865i	−0.577488	+	1.31808i
$414$	20.1630	−	14.6493i	0.990956	−	0.719972i
$415$	4.91080	+	10.1245i	0.241062	+	0.496990i
$416$	−3.15075	+	29.9774i	−0.154478	+	1.46976i
$417$	−13.6991	−	12.3347i	−0.670849	−	0.604035i
$418$	21.4486	+	12.3834i	1.04909	+	0.605690i
$419$	−7.25128	−	22.3171i	−0.354248	−	1.09026i	−0.956444	−	0.291915i	$-0.905707\pi$
$419$	−7.25128	−	22.3171i	−0.354248	−	1.09026i	0.602196	−	0.798348i	$-0.294293\pi$
$420$	24.8197	−	6.28762i	1.21108	−	0.306805i
$421$	−10.2298	+	31.4841i	−0.498571	+	1.53444i	0.312746	+	0.949837i	$0.398751\pi$
$421$	−10.2298	+	31.4841i	−0.498571	+	1.53444i	−0.811317	+	0.584606i	$0.801249\pi$
$422$	32.4985	−	29.2618i	1.58200	−	1.42444i
$423$	2.48741	−	5.58681i	0.120942	−	0.271640i
$424$	−1.52609	−	2.64326i	−0.0741133	−	0.128368i
$425$	13.8836	+	6.84638i	0.673452	+	0.332098i
$426$	66.3235			3.21339
$427$	−4.62786	+	22.4266i	−0.223958	+	1.08530i
$428$	−15.4997	−	5.03617i	−0.749208	−	0.243432i
$429$	15.6390	+	17.3689i	0.755060	+	0.838579i
$430$	24.5617	−	6.06722i	1.18447	−	0.292587i
$431$	−13.8289	+	15.3585i	−0.666113	+	0.739793i	−0.977603	−	0.210456i	$-0.932505\pi$
$431$	−13.8289	+	15.3585i	−0.666113	+	0.739793i	0.311490	+	0.950249i	$0.399172\pi$
$432$	1.77141	+	1.02272i	0.0852269	+	0.0492058i
$433$	−25.2950	+	8.21886i	−1.21560	+	0.394973i	−0.845479	−	0.534009i	$-0.820685\pi$
$433$	−25.2950	+	8.21886i	−1.21560	+	0.394973i	−0.370124	+	0.928982i	$0.620685\pi$
$434$	26.1963	−	19.2715i	1.25746	−	0.925063i
$435$	−0.455220	−	13.9026i	−0.0218261	−	0.666576i
$436$	0.713746	+	6.79084i	0.0341822	+	0.325222i
$437$	−23.2230	−	2.44083i	−1.11091	−	0.116761i
$438$	−57.4368	−	6.03685i	−2.74444	−	0.288452i
$439$	−1.23134	−	11.7154i	−0.0587687	−	0.559147i	−0.983802	−	0.179260i	$-0.942630\pi$
$439$	−1.23134	−	11.7154i	−0.0587687	−	0.559147i	0.925033	−	0.379887i	$-0.124037\pi$
$440$	−0.0721301	−	2.20287i	−0.00343867	−	0.105018i
$441$	−19.2570	−	3.85466i	−0.916998	−	0.183555i
$442$	−22.4211	+	7.28507i	−1.06646	+	0.346515i
$443$	−0.871479	−	0.503149i	−0.0414052	−	0.0239053i	0.479154	−	0.877731i	$-0.340943\pi$
$443$	−0.871479	−	0.503149i	−0.0414052	−	0.0239053i	−0.520560	+	0.853825i	$0.674277\pi$
$444$	23.6279	−	26.2414i	1.12133	−	1.24536i
$445$	30.1600	−	7.45010i	1.42972	−	0.353168i
$446$	−11.6117	−	12.8961i	−0.549831	−	0.610649i
$447$	−8.47257	−	2.75290i	−0.400739	−	0.130208i
$448$	15.8083	−	5.24046i	0.746873	−	0.247589i
$449$	29.0408			1.37052			0.685261	−	0.728298i	$-0.259688\pi$
$449$	29.0408			1.37052			0.685261	+	0.728298i	$0.259688\pi$
$450$	−19.0714	+	19.5779i	−0.899034	+	0.922910i
$451$	−6.46400	−	11.1960i	−0.304378	−	0.527198i
$452$	9.34965	−	20.9996i	0.439770	−	0.987740i
$453$	3.95222	−	3.55860i	0.185692	−	0.167198i
$454$	7.56804	−	23.2920i	0.355186	−	1.09315i
$455$	−16.1240	−	16.5716i	−0.755906	−	0.776887i
$456$	1.51442	+	4.66090i	0.0709191	+	0.218267i
$457$	11.1386	+	6.43087i	0.521041	+	0.300823i	0.737361	−	0.675499i	$-0.236072\pi$
$457$	11.1386	+	6.43087i	0.521041	+	0.300823i	−0.216319	+	0.976323i	$0.569405\pi$
$458$	23.9453	+	21.5604i	1.11889	+	1.00745i
$459$	−0.151609	+	1.44246i	−0.00707650	+	0.0673284i
$460$	−7.99164	−	16.4761i	−0.372612	−	0.768204i
$461$	−9.56290	+	6.94785i	−0.445389	+	0.323594i	−0.787772	−	0.615966i	$-0.788766\pi$
$461$	−9.56290	+	6.94785i	−0.445389	+	0.323594i	0.342384	+	0.939560i	$0.388766\pi$
$462$	12.3712	−	28.2364i	0.575561	−	1.31368i
$463$	−20.4731	+	28.1788i	−0.951465	+	1.30958i	−0.000592125		1.00000i	$0.500188\pi$
$463$	−20.4731	+	28.1788i	−0.951465	+	1.30958i	−0.950873	+	0.309580i	$0.899812\pi$
$464$	−1.17828	−	11.2106i	−0.0547004	−	0.520439i
$465$	−12.8015	+	31.4874i	−0.593654	+	1.46019i
$466$	−1.18736	+	11.2970i	−0.0550036	+	0.523324i
$467$	4.91443	−	23.1206i	0.227412	−	1.06989i	−0.705199	−	0.709010i	$-0.749142\pi$
$467$	4.91443	−	23.1206i	0.227412	−	1.06989i	0.932611	−	0.360882i	$-0.117524\pi$
$468$		−	19.6947i		−	0.910387i
$469$	11.4586	+	19.5774i	0.529111	+	0.904002i
$470$	−7.86152	−	5.32757i	−0.362625	−	0.245743i
$471$	−38.7762	−	43.0654i	−1.78671	−	1.98435i
$472$	−0.912678	−	4.29381i	−0.0420094	−	0.197639i
$473$	5.86235	−	13.1670i	0.269551	−	0.605421i
$474$	14.6795	−	25.4257i	0.674253	−	1.16784i
$475$	25.5528	−	1.67518i	1.17244	−	0.0768626i
$476$	9.90953	+	10.8750i	0.454203	+	0.498456i
$477$	12.6738	+	17.4440i	0.580294	+	0.798706i
$478$	5.90197	−	5.31416i	0.269950	−	0.243064i
$479$	9.90164	−	2.10466i	0.452418	−	0.0961643i	0.0239333	−	0.999714i	$-0.492381\pi$
$479$	9.90164	−	2.10466i	0.452418	−	0.0961643i	0.428484	+	0.903549i	$0.359048\pi$
$480$	−26.7791	+	31.7735i	−1.22229	+	1.45026i
$481$	−31.1910	−	6.62985i	−1.42219	−	0.302295i
$482$		−	44.3376i		−	2.01952i
$483$	0.172661	+	29.0648i	0.00785636	+	1.32249i
$484$	−7.03293	−	5.10972i	−0.319678	−	0.232260i
$485$	1.78073	−	9.97216i	0.0808588	−	0.452813i
$486$	−38.4361	−	17.1129i	−1.74350	−	0.776256i
$487$	−11.8899	−	1.24968i	−0.538783	−	0.0566284i	−0.168771	−	0.985655i	$-0.553980\pi$
$487$	−11.8899	−	1.24968i	−0.538783	−	0.0566284i	−0.370012	+	0.929027i	$0.620646\pi$
$488$	−1.39806	−	3.14009i	−0.0632870	−	0.142145i
$489$	1.88954	−	1.37283i	0.0854480	−	0.0620816i
$490$	−11.1494	+	28.3858i	−0.503676	+	1.28234i
$491$	0.443578	+	0.322278i	0.0200184	+	0.0145442i	0.597749	−	0.801683i	$-0.296062\pi$
$491$	0.443578	+	0.322278i	0.0200184	+	0.0145442i	−0.577731	+	0.816227i	$0.696062\pi$
$492$	−4.68688	+	22.0501i	−0.211301	+	0.994093i
$493$	6.92226	−	3.99657i	0.311763	−	0.179996i
$494$	−26.0954	+	28.9819i	−1.17409	+	1.30396i
$495$	2.13345	+	15.4236i	0.0958917	+	0.693240i
$496$	−8.51185	+	26.1968i	−0.382193	+	1.17627i
$497$	−21.7905	+	30.3698i	−0.977437	+	1.36227i
$498$	−13.8861	−	19.1126i	−0.622252	−	0.856456i
$499$	−20.0243	+	34.6832i	−0.896412	+	1.55263i	−0.0643647	+	0.997926i	$0.520502\pi$
$499$	−20.0243	+	34.6832i	−0.896412	+	1.55263i	−0.832047	+	0.554705i	$0.812831\pi$
$500$	11.6975	+	16.3232i	0.523130	+	0.729994i
$501$	−2.20843	−	3.82511i	−0.0986654	−	0.170893i
$502$	−5.12715	+	0.538885i	−0.228836	+	0.0240516i
$503$	−11.8433	−	3.84812i	−0.528066	−	0.171579i	0.0328365	−	0.999461i	$-0.489546\pi$
$503$	−11.8433	−	3.84812i	−0.528066	−	0.171579i	−0.560903	+	0.827882i	$0.689546\pi$
$504$	2.68586	−	1.21499i	0.119638	−	0.0541200i
$505$	−20.1240	+	15.6522i	−0.895505	+	0.696515i
$506$	−21.5664	−	4.58407i	−0.958741	−	0.203787i
$507$	−4.74574	+	2.73996i	−0.210766	+	0.121686i
$508$	13.0031	+	11.7080i	0.576917	+	0.519459i
$509$	11.7881	−	5.24840i	0.522498	−	0.232631i	−0.128501	−	0.991709i	$-0.541017\pi$
$509$	11.7881	−	5.24840i	0.522498	−	0.232631i	0.651000	+	0.759078i	$0.274350\pi$
$510$	−31.2210	−	9.02601i	−1.38249	−	0.399679i
$511$	21.6351	−	24.3171i	0.957079	−	1.07573i
$512$	−17.7546	+	24.4372i	−0.784652	+	1.07998i
$513$	0.975901	+	2.19191i	0.0430871	+	0.0967752i
$514$	−3.53693	−	1.57474i	−0.156007	−	0.0694589i
$515$	−2.61319	−	2.20243i	−0.115151	−	0.0970506i
$516$	−22.9595	+	10.2222i	−1.01073	+	0.450008i
$517$	−5.14536	+	1.67183i	−0.226292	+	0.0735269i
$518$	8.98894	+	41.0879i	0.394951	+	1.80530i
$519$	−5.83490	−	17.9580i	−0.256124	−	0.788267i
$520$	3.41658	+	0.610098i	0.149827	+	0.0267546i
$521$	38.3716	−	8.15613i	1.68109	−	0.357327i	0.734212	−	0.678921i	$-0.237552\pi$
$521$	38.3716	−	8.15613i	1.68109	−	0.357327i	0.946878	+	0.321594i	$0.104219\pi$
$522$	2.93422	+	13.8044i	0.128427	+	0.604202i
$523$	7.66514	−	0.805639i	0.335173	−	0.0352281i	0.0645529	−	0.997914i	$-0.479438\pi$
$523$	7.66514	−	0.805639i	0.335173	−	0.0352281i	0.270620	+	0.962686i	$0.412771\pi$
$524$	32.0670			1.40085
$525$	−5.58487	−	31.3813i	−0.243744	−	1.36959i
$526$	−57.3437			−2.50030
$527$	−19.4249	+	2.04164i	−0.846161	+	0.0889351i
$528$	5.42866	+	25.5398i	0.236252	+	1.11148i
$529$	−2.16393	+	0.459958i	−0.0940841	+	0.0199982i
$530$	30.1262	−	14.6125i	1.30860	−	0.634728i
$531$	9.58297	+	29.4934i	0.415866	+	1.27990i
$532$	23.1917	+	7.38341i	1.00549	+	0.320112i
$533$	19.3608	−	6.29070i	0.838608	−	0.272480i
$534$	−59.5844	+	26.5287i	−2.57847	+	1.14801i
$535$	−7.64119	+	18.7948i	−0.330358	+	0.812572i
$536$	−3.11062	−	1.38494i	−0.134359	−	0.0598203i
$537$	10.4744	+	23.5259i	0.452003	+	1.01522i
$538$	27.3893	−	37.6981i	1.18083	−	1.62528i
$539$	8.86503	+	14.9419i	0.381844	+	0.643591i
$540$	−1.05556	+	1.55762i	−0.0454241	+	0.0670292i
$541$	17.4699	−	7.77812i	0.751091	−	0.334407i	0.00476580	−	0.999989i	$-0.498483\pi$
$541$	17.4699	−	7.77812i	0.751091	−	0.334407i	0.746325	+	0.665581i	$0.231816\pi$
$542$	−17.4750	−	15.7346i	−0.750616	−	0.675858i
$543$	−12.7932	+	7.38617i	−0.549009	+	0.316971i
$544$	−23.3561	−	4.96449i	−1.00138	−	0.212851i
$545$	8.49599	−	0.278190i	0.363928	−	0.0119163i
$546$	39.4408	+	28.2990i	1.68791	+	1.21108i
$547$	−17.8957	−	5.81466i	−0.765164	−	0.248617i	−0.0996705	−	0.995020i	$-0.531779\pi$
$547$	−17.8957	−	5.81466i	−0.765164	−	0.248617i	−0.665494	+	0.746404i	$0.731779\pi$
$548$	−5.78531	+	0.608060i	−0.247136	+	0.0259751i
$549$	12.1412	+	21.0291i	0.518173	+	0.897501i
$550$	24.1604	+	0.948924i	1.03020	+	0.0404623i
$551$	6.61134	−	11.4512i	0.281653	−	0.487837i
$552$	−2.56440	−	3.52959i	−0.109148	−	0.150229i
$553$	6.81959	+	15.0754i	0.289998	+	0.641071i
$554$	−11.2372	+	34.5846i	−0.477424	+	1.46936i
$555$	−30.4679	−	31.6881i	−1.29329	−	1.34508i
$556$	9.19508	−	10.2122i	0.389958	−	0.433092i
$557$	2.99630	−	1.72991i	0.126957	−	0.0732988i	−0.435176	−	0.900345i	$-0.643314\pi$
$557$	2.99630	−	1.72991i	0.126957	−	0.0732988i	0.562134	+	0.827046i	$0.309981\pi$
$558$	7.17000	−	33.7322i	0.303530	−	1.42800i
$559$	18.3612	+	13.3402i	0.776596	+	0.564230i
$560$	−6.34325	−	25.0393i	−0.268051	−	1.05810i
$561$	−14.9787	+	10.8826i	−0.632400	+	0.459466i
$562$	−5.31600	−	11.9399i	−0.224242	−	0.503656i
$563$	−31.8022	−	3.34255i	−1.34030	−	0.140872i	−0.592918	−	0.805263i	$-0.702024\pi$
$563$	−31.8022	−	3.34255i	−1.34030	−	0.140872i	−0.747385	+	0.664391i	$0.768691\pi$
$564$	8.61813	+	3.83704i	0.362889	+	0.161568i
$565$	−25.2378	−	13.4896i	−1.06176	−	0.567513i
$566$	−14.0545	−	10.2112i	−0.590753	−	0.429207i
$567$	21.7961	−	12.7572i	0.915349	−	0.535752i
$568$		−	5.61066i		−	0.235418i
$569$	0.855097	+	0.181756i	0.0358475	+	0.00761963i	0.225801	−	0.974174i	$-0.427500\pi$
$569$	0.855097	+	0.181756i	0.0358475	+	0.00761963i	−0.189953	+	0.981793i	$0.560834\pi$
$570$	−52.1938	+	12.8929i	−2.18616	+	0.540023i
$571$	7.16292	−	1.52253i	0.299759	−	0.0637158i	−0.0555769	−	0.998454i	$-0.517700\pi$
$571$	7.16292	−	1.52253i	0.299759	−	0.0637158i	0.355336	+	0.934739i	$0.384366\pi$
$572$	−12.9479	+	11.6583i	−0.541377	+	0.487458i
$573$	−30.3578	−	41.7839i	−1.26822	−	1.74555i
$574$	−18.0849	−	19.8470i	−0.754850	−	0.828396i
$575$	−21.1737	+	8.44781i	−0.883006	+	0.352298i
$576$	8.83015	−	15.2943i	0.367923	−	0.637261i
$577$	−9.30611	+	20.9019i	−0.387418	+	0.870156i	0.609580	+	0.792725i	$0.291338\pi$
$577$	−9.30611	+	20.9019i	−0.387418	+	0.870156i	−0.996998	+	0.0774306i	$0.975328\pi$
$578$	3.00372	+	14.1314i	0.124938	+	0.587788i
$579$	3.06988	+	3.40945i	0.127580	+	0.141692i
$580$	10.3638	−	0.339349i	0.430334	−	0.0140907i
$581$	13.3140	−	0.0790927i	0.552357	−	0.00328132i
$582$			21.2675i			0.881564i
$583$	3.96591	−	18.6581i	0.164251	−	0.772741i
$584$	−0.510689	+	4.85888i	−0.0211325	+	0.201062i
$585$	−24.4546	−	1.76348i	−1.01107	−	0.0729109i
$586$	4.31003	+	41.0072i	0.178046	+	1.69399i
$587$	15.5422	−	21.3920i	0.641496	−	0.882943i	−0.357199	−	0.934028i	$-0.616268\pi$
$587$	15.5422	−	21.3920i	0.641496	−	0.882943i	0.998694	+	0.0510854i	$0.0162681\pi$
$588$	5.94614	−	29.7055i	0.245214	−	1.22503i
$589$	−26.1399	+	18.9918i	−1.07708	+	0.782542i
$590$	47.7023	−	6.59837i	1.96387	−	0.271651i
$591$	0.856346	−	8.14759i	0.0352254	−	0.335147i
$592$	−26.4736	−	23.8369i	−1.08806	−	0.979691i
$593$	7.97900	+	4.60668i	0.327658	+	0.189174i	0.654801	−	0.755801i	$-0.272752\pi$
$593$	7.97900	+	4.60668i	0.327658	+	0.189174i	−0.327143	+	0.944975i	$0.606086\pi$
$594$	0.700074	+	2.15461i	0.0287244	+	0.0884045i
$595$	14.3907	−	11.3308i	0.589960	−	0.464516i
$596$	2.05218	−	6.31597i	0.0840607	−	0.258712i
$597$	14.7960	−	13.3224i	0.605560	−	0.545248i
$598$	14.1212	−	31.7167i	0.577457	−	1.29699i
$599$	−6.03999	−	10.4616i	−0.246787	−	0.427448i	0.715845	−	0.698259i	$-0.246042\pi$
$599$	−6.03999	−	10.4616i	−0.246787	−	0.427448i	−0.962633	+	0.270811i	$0.912708\pi$
$600$	3.42717	+	3.33851i	0.139914	+	0.136294i
$601$	−18.7934			−0.766597			−0.383299	−	0.923624i	$-0.625212\pi$
$601$	−18.7934			−0.766597			−0.383299	+	0.923624i	$0.625212\pi$
$602$	6.04985	−	29.3176i	0.246574	−	1.19490i
$603$	22.8772	+	7.43326i	0.931632	+	0.302706i
$604$	2.65280	+	2.94623i	0.107941	+	0.119880i
$605$	−6.97440	+	8.27515i	−0.283549	+	0.336433i
$606$	35.8151	−	39.7767i	1.45489	−	1.61582i
$607$	−3.61582	−	2.08760i	−0.146762	−	0.0847329i	0.424821	−	0.905277i	$-0.360337\pi$
$607$	−3.61582	−	2.08760i	−0.146762	−	0.0847329i	−0.571583	+	0.820544i	$0.693670\pi$
$608$	−37.5668	+	12.2062i	−1.52354	+	0.495027i
$609$	−15.0751	−	6.60485i	−0.610875	−	0.267642i
$610$	35.4614	−	12.8196i	1.43579	−	0.519052i
$611$	−0.890489	−	8.47244i	−0.0360253	−	0.342758i
$612$	15.5160	+	1.63080i	0.627197	+	0.0659211i
$613$	22.1605	+	2.32916i	0.895054	+	0.0940740i	0.540874	−	0.841103i	$-0.318093\pi$
$613$	22.1605	+	2.32916i	0.895054	+	0.0940740i	0.354180	+	0.935177i	$0.384760\pi$
$614$	4.15645	+	39.5460i	0.167741	+	1.59595i
$615$	26.9595	+	7.79401i	1.08711	+	0.314285i
$616$	−2.38867	−	1.04655i	−0.0962422	−	0.0421665i
$617$	25.9217	−	8.42248i	1.04357	−	0.339076i	0.263428	−	0.964679i	$-0.415147\pi$
$617$	25.9217	−	8.42248i	1.04357	−	0.339076i	0.780142	+	0.625603i	$0.215147\pi$
$618$	6.21373	+	3.58750i	0.249953	+	0.144310i
$619$	−12.7084	+	14.1141i	−0.510792	+	0.567292i	−0.942280	−	0.334827i	$-0.891322\pi$
$619$	−12.7084	+	14.1141i	−0.510792	+	0.567292i	0.431488	+	0.902119i	$0.357989\pi$
$620$	−23.4726	−	9.54299i	−0.942684	−	0.383256i
$621$	−1.42925	−	1.58734i	−0.0573537	−	0.0636977i
$622$	5.32621	+	1.73059i	0.213562	+	0.0693904i
$623$	7.42877	−	35.9999i	0.297627	−	1.44230i
$624$	−41.1148			−1.64591
$625$	21.3156	−	13.0631i	0.852625	−	0.522523i
$626$	3.98421	+	6.90086i	0.159241	+	0.275814i
$627$	−12.4575	+	27.9800i	−0.497505	+	1.11742i
$628$	32.1036	−	28.9062i	1.28107	−	1.15348i
$629$	7.80592	−	24.0242i	0.311242	−	0.957906i
$630$	11.1750	+	30.3469i	0.445222	+	1.20905i
$631$	−10.1285	−	31.1724i	−0.403210	−	1.24095i	−0.922380	−	0.386283i	$-0.873759\pi$
$631$	−10.1285	−	31.1724i	−0.403210	−	1.24095i	0.519170	−	0.854671i	$-0.326241\pi$
$632$	−2.15089	−	1.24182i	−0.0855580	−	0.0493969i
$633$	40.1895	+	36.1868i	1.59739	+	1.43830i
$634$	0.697640	−	6.63760i	0.0277068	−	0.263613i
$635$	15.7020	−	15.0974i	0.623113	−	0.599120i
$636$	−26.9088	+	19.5504i	−1.06700	+	0.775224i
$637$	−25.9164	+	8.76251i	−1.02685	+	0.347183i
$638$	7.33850	−	10.1006i	0.290534	−	0.399886i
$639$	4.14312	+	39.4192i	0.163899	+	1.55940i
$640$	5.40399	+	4.55455i	0.213612	+	0.180034i
$641$	−4.10837	+	39.0885i	−0.162271	+	1.54390i	0.545892	+	0.837855i	$0.316191\pi$
$641$	−4.10837	+	39.0885i	−0.162271	+	1.54390i	−0.708163	+	0.706049i	$0.750476\pi$
$642$	8.85614	−	41.6649i	0.349524	−	1.64438i
$643$			28.8706i			1.13854i	0.822149	+	0.569272i	$0.192775\pi$
$643$			28.8706i			1.13854i	−0.822149	+	0.569272i	$0.807225\pi$
$644$	−21.6667	+	0.128712i	−0.853786	+	0.00507198i
$645$	10.6370	+	29.4237i	0.418830	+	1.15856i
$646$	−20.6719	−	22.9585i	−0.813327	−	0.903291i
$647$	−1.08427	−	5.10109i	−0.0426271	−	0.200545i	0.951681	−	0.307089i	$-0.0993548\pi$
$647$	−1.08427	−	5.10109i	−0.0426271	−	0.200545i	−0.994308	+	0.106544i	$0.966021\pi$
$648$	−1.54189	+	3.46314i	−0.0605711	+	0.136045i
$649$	13.7171	−	23.7588i	0.538444	−	0.932613i
$650$	−9.37142	+	36.9022i	−0.367577	+	1.44742i
$651$	27.0880	+	29.7272i	1.06166	+	1.16510i
$652$	1.02339	+	1.40858i	0.0400792	+	0.0551643i
$653$	17.1943	−	15.4818i	0.672864	−	0.605849i	−0.260202	−	0.965554i	$-0.583789\pi$
$653$	17.1943	−	15.4818i	0.672864	−	0.605849i	0.933066	+	0.359705i	$0.117123\pi$
$654$	−17.4567	+	3.71053i	−0.682609	+	0.145093i
$655$	2.87131	−	39.8171i	0.112191	−	1.55578i
$656$	22.2451	+	4.72835i	0.868527	+	0.184611i
$657$		−	34.5145i		−	1.34654i
$658$	−9.69763	+	5.67601i	−0.378053	+	0.221274i
$659$	2.56376	+	1.86268i	0.0998698	+	0.0725596i	0.636599	−	0.771195i	$-0.280340\pi$
$659$	2.56376	+	1.86268i	0.0998698	+	0.0725596i	−0.536730	+	0.843754i	$0.680340\pi$
$660$	−23.7922	+	3.29103i	−0.926111	+	0.128103i
$661$	7.09726	+	3.15991i	0.276052	+	0.122906i	0.540093	−	0.841605i	$-0.318389\pi$
$661$	7.09726	+	3.15991i	0.276052	+	0.122906i	−0.264042	+	0.964511i	$0.585056\pi$
$662$	52.1817	+	5.48452i	2.02810	+	0.213162i
$663$	−11.8581	−	26.6337i	−0.460529	−	1.03437i
$664$	−1.61684	+	1.17470i	−0.0627454	+	0.0455872i
$665$	11.2445	−	28.1357i	0.436042	−	1.09105i
$666$	36.0824	+	26.2154i	1.39816	+	1.01583i
$667$	−2.44738	+	11.5140i	−0.0947631	+	0.445825i
$668$	2.85147	−	1.64630i	0.110327	−	0.0636972i
$669$	14.3597	−	15.9481i	0.555179	−	0.616588i
$670$	17.6082	−	32.9432i	0.680264	−	1.27271i
$671$	6.63817	−	20.4302i	0.256264	−	0.788699i
$672$	20.2643	+	44.7963i	0.781712	+	1.72805i
$673$	−1.93901	−	2.66881i	−0.0747432	−	0.102875i	0.770009	−	0.638034i	$-0.220252\pi$
$673$	−1.93901	−	2.66881i	−0.0747432	−	0.102875i	−0.844752	+	0.535158i	$0.820252\pi$
$674$	−25.4049	+	44.0027i	−0.978562	+	1.69492i
$675$	1.83955	+	1.45015i	0.0708045	+	0.0558161i
$676$	−2.04253	−	3.53777i	−0.0785589	−	0.136068i
$677$	−16.2618	+	1.70919i	−0.624993	+	0.0656894i	−0.411730	−	0.911306i	$-0.635075\pi$
$677$	−16.2618	+	1.70919i	−0.624993	+	0.0656894i	−0.213262	+	0.976995i	$0.568409\pi$
$678$	57.1394	+	18.5657i	2.19443	+	0.713012i
$679$	−9.73845	−	6.98739i	−0.373727	−	0.268151i
$680$	−0.763558	+	2.64115i	−0.0292811	+	0.101284i
$681$	29.6248	+	6.29694i	1.13522	+	0.241299i
$682$	−26.4208	+	15.2541i	−1.01170	+	0.584108i
$683$	−29.0960	−	26.1981i	−1.11333	−	1.00244i	−0.999960	−	0.00889049i	$-0.997170\pi$
$683$	−29.0960	−	26.1981i	−1.11333	−	1.00244i	−0.113366	−	0.993553i	$-0.536163\pi$
$684$	23.5775	−	10.4974i	0.901509	−	0.401378i
$685$	0.236998	+	7.23797i	0.00905522	+	0.276549i
$686$	24.6192	+	26.3814i	0.939967	+	1.00725i
$687$	−23.4215	+	32.2369i	−0.893585	+	1.22991i
$688$	10.3127	+	23.1626i	0.393166	+	0.883066i
$689$	27.4397	+	12.2169i	1.04537	+	0.465428i
$690$	40.6437	−	25.2742i	1.54728	−	0.962174i
$691$	32.7326	−	14.5735i	1.24521	−	0.554402i	0.324956	−	0.945729i	$-0.394650\pi$
$691$	32.7326	−	14.5735i	1.24521	−	0.554402i	0.920252	+	0.391327i	$0.127984\pi$
$692$	13.3870	−	4.34969i	0.508896	−	0.165350i
$693$	17.5550	+	5.58890i	0.666861	+	0.212305i
$694$	14.6550	+	45.1033i	0.556295	+	1.71210i
$695$	−11.8570	−	12.3318i	−0.449760	−	0.467772i
$696$	2.41651	−	0.513644i	0.0915974	−	0.0194696i
$697$	3.35283	+	15.7738i	0.126998	+	0.597477i
$698$	−55.3998	+	5.82275i	−2.09691	+	0.220394i
$699$	−14.0475			−0.531325
$700$	23.3935	−	4.16330i	0.884192	−	0.157358i
$701$	4.06365			0.153482			0.0767409	−	0.997051i	$-0.475549\pi$
$701$	4.06365			0.153482			0.0767409	+	0.997051i	$0.475549\pi$
$702$	−3.54781	+	0.372890i	−0.133904	+	0.0140738i
$703$	−8.68806	−	40.8741i	−0.327677	−	1.54160i
$704$	−15.2819	+	3.24827i	−0.575959	+	0.122424i
$705$	5.53607	−	10.3574i	0.208500	−	0.390083i
$706$	1.05040	+	3.23279i	0.0395322	+	0.121668i
$707$	6.44692	+	29.4685i	0.242461	+	1.10828i
$708$	−45.4960	+	14.7825i	−1.70984	+	0.555562i
$709$	27.1377	−	12.0825i	1.01918	−	0.453767i	0.172011	−	0.985095i	$-0.444974\pi$
$709$	27.1377	−	12.0825i	1.01918	−	0.453767i	0.847166	+	0.531328i	$0.178307\pi$
$710$	61.3909	+	4.42705i	2.30396	+	0.166144i
$711$	16.0287	+	7.13643i	0.601123	+	0.267637i
$712$	2.24420	+	5.04056i	0.0841050	+	0.188903i
$713$	16.9071	−	23.2706i	0.633175	−	0.871491i
$714$	−25.5605	+	28.7293i	−0.956579	+	1.07517i
$715$	13.3166	+	17.1210i	0.498011	+	0.640291i
$716$	−17.5376	+	7.80825i	−0.655412	+	0.291808i
$717$	7.29872	+	6.57179i	0.272576	+	0.245428i
$718$	−18.3643	+	10.6026i	−0.685350	+	0.395687i
$719$	−12.2332	−	2.60025i	−0.456222	−	0.0969730i	−0.0259321	−	0.999664i	$-0.508255\pi$
$719$	−12.2332	−	2.60025i	−0.456222	−	0.0969730i	−0.430290	+	0.902691i	$0.641589\pi$
$720$	−22.6744	−	15.3659i	−0.845026	−	0.572655i
$721$	−3.68424	+	1.66662i	−0.137208	+	0.0620683i
$722$	−13.3975	−	4.35310i	−0.498603	−	0.162006i
$723$	54.5301	−	5.73135i	2.02800	−	0.213151i
$724$	−5.50610	−	9.53685i	−0.204633	−	0.354434i
$725$	0.506620	−	12.8990i	0.0188154	−	0.479056i
$726$	11.3605	−	19.6769i	0.421626	−	0.730278i
$727$	21.7358	+	29.9167i	0.806135	+	1.10955i	0.991908	+	0.126957i	$0.0405211\pi$
$727$	21.7358	+	29.9167i	0.806135	+	1.10955i	−0.185773	+	0.982593i	$0.559479\pi$
$728$	2.39396	−	3.33650i	0.0887260	−	0.123659i
$729$	7.22919	−	22.2491i	0.267748	−	0.824043i
$730$	−52.7621	−	9.42174i	−1.95281	−	0.348714i
$731$	−12.0301	+	13.3608i	−0.444951	+	0.494168i
$732$	−32.4392	+	18.7288i	−1.19899	+	0.692236i
$733$	−6.77300	+	31.8644i	−0.250166	+	1.17694i	0.656246	+	0.754547i	$0.272143\pi$
$733$	−6.77300	+	31.8644i	−0.250166	+	1.17694i	−0.906413	+	0.422393i	$0.861190\pi$
$734$	−19.6428	−	14.2713i	−0.725030	−	0.526765i
$735$	−36.3524	−	10.0431i	−1.34088	−	0.370445i
$736$	28.4485	−	20.6690i	1.04863	−	0.761871i
$737$	−8.65537	−	19.4403i	−0.318825	−	0.716092i
$738$	−28.3167	−	2.97621i	−1.04235	−	0.109556i
$739$	−22.7306	−	10.1203i	−0.836157	−	0.372281i	−0.0564346	−	0.998406i	$-0.517973\pi$
$739$	−22.7306	−	10.1203i	−0.836157	−	0.372281i	−0.779723	+	0.626125i	$0.784640\pi$
$740$	23.6222	−	22.7126i	0.868370	−	0.834933i
$741$	−39.0176	−	28.3480i	−1.43335	−	1.04139i
$742$	−0.235348	−	39.6170i	−0.00863988	−	1.45439i
$743$			37.2111i			1.36514i	0.730819	+	0.682572i	$0.239138\pi$
$743$			37.2111i			1.36514i	−0.730819	+	0.682572i	$0.760862\pi$
$744$	−5.90493	−	1.25513i	−0.216485	−	0.0460153i
$745$	−7.65869	−	3.11370i	−0.280593	−	0.114077i
$746$	−24.8136	+	5.27429i	−0.908489	+	0.193105i
$747$	10.4921	−	9.44710i	0.383885	−	0.345651i
$748$	−8.11259	−	11.1660i	−0.296626	−	0.408270i
$749$	16.1688	+	17.7442i	0.590796	+	0.648358i
$750$	−39.2336	+	34.8653i	−1.43261	+	1.27310i
$751$	−2.82557	+	4.89402i	−0.103106	+	0.178585i	−0.912963	−	0.408042i	$-0.866212\pi$
$751$	−2.82557	+	4.89402i	−0.103106	+	0.178585i	0.809857	+	0.586628i	$0.199545\pi$
$752$	3.87098	−	8.69437i	0.141160	−	0.317051i
$753$	−1.32553	−	6.23613i	−0.0483050	−	0.227257i
$754$	13.1548	+	14.6099i	0.479070	+	0.532061i
$755$	3.89582	−	3.03013i	0.141783	−	0.110278i
$756$	1.12460	+	1.92141i	0.0409012	+	0.0698810i
$757$		−	38.6504i		−	1.40477i	−0.711796	−	0.702386i	$-0.752118\pi$
$757$		−	38.6504i		−	1.40477i	0.711796	−	0.702386i	$-0.247882\pi$
$758$	−2.96563	+	13.9522i	−0.107716	+	0.506766i
$759$	2.85008	−	27.1167i	0.103451	−	0.984272i
$760$	1.09068	+	4.41535i	0.0395630	+	0.160161i
$761$	0.140549	+	1.33724i	0.00509490	+	0.0484748i	0.996774	−	0.0802600i	$-0.0255751\pi$
$761$	0.140549	+	1.33724i	0.00509490	+	0.0484748i	−0.991679	+	0.128735i	$0.958908\pi$
$762$	−26.8806	+	36.9979i	−0.973780	+	1.34029i
$763$	4.03629	−	9.21256i	0.146124	−	0.333517i
$764$	31.1483	−	22.6306i	1.12691	−	0.818745i
$765$	3.41425	−	19.1200i	0.123443	−	0.691284i
$766$	−1.40325	+	13.3510i	−0.0507014	+	0.482392i
$767$	32.1034	+	28.9061i

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.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93770 + 0.203661i) q^{2} +(-0.500958 - 2.35682i) q^{3} +(1.75692 - 0.373445i) q^{4} +(-0.306385 - 2.21498i) q^{5} +(1.45070 + 4.46479i) q^{6} +(-2.52107 - 0.802620i) q^{7} +(0.377701 - 0.122722i) q^{8} +(-2.56301 + 1.14113i) q^{9} +O(q^{10})\)	\(q+(-1.93770 + 0.203661i) q^{2} +(-0.500958 - 2.35682i) q^{3} +(1.75692 - 0.373445i) q^{4} +(-0.306385 - 2.21498i) q^{5} +(1.45070 + 4.46479i) q^{6} +(-2.52107 - 0.802620i) q^{7} +(0.377701 - 0.122722i) q^{8} +(-2.56301 + 1.14113i) q^{9} +(1.04479 + 4.22957i) q^{10} +(2.26739 + 1.00951i) q^{11} +(-1.76029 - 3.95367i) q^{12} +(-2.29720 + 3.16183i) q^{13} +(5.04855 + 1.04180i) q^{14} +(-5.06682 + 1.83170i) q^{15} +(-3.98864 + 1.77586i) q^{16} +(-2.30076 - 2.07161i) q^{17} +(4.73395 - 2.73315i) q^{18} +(-5.00961 - 1.06483i) q^{19} +(-1.36546 - 3.77712i) q^{20} +(-0.628681 + 6.34379i) q^{21} +(-4.59912 - 1.49435i) q^{22} +(4.53438 - 0.476582i) q^{23} +(-0.478447 - 0.828694i) q^{24} +(-4.81226 + 1.35727i) q^{25} +(3.80736 - 6.59454i) q^{26} +(-0.275367 - 0.379010i) q^{27} +(-4.72905 - 0.468658i) q^{28} +(-0.797815 + 2.45542i) q^{29} +(9.44495 - 4.58121i) q^{30} +(4.22141 - 4.68835i) q^{31} +(6.67927 - 3.85628i) q^{32} +(1.24336 - 5.84955i) q^{33} +(4.88009 + 3.54559i) q^{34} +(-1.00537 + 5.83003i) q^{35} +(-4.07686 + 2.96201i) q^{36} +(3.31862 + 7.45374i) q^{37} +(9.92401 + 1.04306i) q^{38} +(8.60267 + 3.83016i) q^{39} +(-0.387549 - 0.798998i) q^{40} +(-4.21399 - 3.06164i) q^{41} +(-0.0737844 - 12.4204i) q^{42} -5.80714i q^{43} +(4.36062 + 0.926877i) q^{44} +(3.31284 + 5.32739i) q^{45} +(-8.68922 + 1.84695i) q^{46} +(-1.61989 + 1.45856i) q^{47} +(6.18352 + 8.51089i) q^{48} +(5.71160 + 4.04692i) q^{49} +(9.04830 - 3.61005i) q^{50} +(-3.72984 + 6.46027i) q^{51} +(-2.85523 + 6.41296i) q^{52} +(-1.59789 - 7.51748i) q^{53} +(0.610768 + 0.678327i) q^{54} +(1.54134 - 5.33152i) q^{55} +(-1.05071 + 0.00624181i) q^{56} +12.3402i q^{57} +(1.04586 - 4.92036i) q^{58} +(1.15540 - 10.9929i) q^{59} +(-8.21796 + 5.11033i) q^{60} +(-0.904700 - 8.60765i) q^{61} +(-7.22500 + 9.94436i) q^{62} +(7.37743 - 0.819737i) q^{63} +(-5.09255 + 3.69995i) q^{64} +(7.70721 + 4.11952i) q^{65} +(-1.21794 + 11.5879i) q^{66} +(-6.37162 - 5.73703i) q^{67} +(-4.81588 - 2.78045i) q^{68} +(-3.39475 - 10.4480i) q^{69} +(0.760757 - 11.5016i) q^{70} +(4.36571 - 13.4363i) q^{71} +(-0.828010 + 0.745543i) q^{72} +(-5.00373 + 11.2386i) q^{73} +(-7.94853 - 13.7673i) q^{74} +(5.60958 + 10.6617i) q^{75} -9.19914 q^{76} +(-4.90600 - 4.36489i) q^{77} +(-17.4495 - 5.66968i) q^{78} +(-4.18464 - 4.64751i) q^{79} +(5.15555 + 8.29066i) q^{80} +(-6.38718 + 7.09369i) q^{81} +(8.78899 + 5.07433i) q^{82} +(-4.78601 + 1.55507i) q^{83} +(1.26451 + 11.3803i) q^{84} +(-3.88366 + 5.73084i) q^{85} +(1.18269 + 11.2525i) q^{86} +(6.18666 + 0.650245i) q^{87} +(0.980283 + 0.103032i) q^{88} +(1.45225 + 13.8172i) q^{89} +(-7.50428 - 9.64821i) q^{90} +(8.32916 - 6.12742i) q^{91} +(7.78856 - 2.53066i) q^{92} +(-13.1644 - 7.60044i) q^{93} +(2.84182 - 3.15616i) q^{94} +(-0.823699 + 11.4224i) q^{95} +(-12.4346 - 13.8100i) q^{96} +(4.30851 + 1.39992i) q^{97} +(-11.8916 - 6.67851i) q^{98} -6.96332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Introduction

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