LMFDB - Embedded newform 175.2.x.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61811 + 0.0848016i) q^{2} +(1.71909 - 2.12290i) q^{3} +(0.622046 - 0.0653797i) q^{4} +(-2.19051 + 0.449052i) q^{5} +(-2.60166 + 3.58087i) q^{6} +(-0.156130 - 2.64114i) q^{7} +(2.19977 - 0.348409i) q^{8} +(-0.927701 - 4.36449i) q^{9} +O(q^{10})$	\(q+(-1.61811 + 0.0848016i) q^{2} +(1.71909 - 2.12290i) q^{3} +(0.622046 - 0.0653797i) q^{4} +(-2.19051 + 0.449052i) q^{5} +(-2.60166 + 3.58087i) q^{6} +(-0.156130 - 2.64114i) q^{7} +(2.19977 - 0.348409i) q^{8} +(-0.927701 - 4.36449i) q^{9} +(3.50641 - 0.912375i) q^{10} +(-3.84181 - 0.816603i) q^{11} +(0.930561 - 1.43294i) q^{12} +(-0.0865535 + 0.0441012i) q^{13} +(0.476608 + 4.26042i) q^{14} +(-2.81240 + 5.42221i) q^{15} +(-4.75353 + 1.01039i) q^{16} +(-1.20108 + 3.12891i) q^{17} +(1.87124 + 6.98356i) q^{18} +(0.637130 - 6.06189i) q^{19} +(-1.33324 + 0.422546i) q^{20} +(-5.87529 - 4.20892i) q^{21} +(6.28573 + 0.995562i) q^{22} +(-0.274480 - 5.23739i) q^{23} +(3.04197 - 5.26884i) q^{24} +(4.59670 - 1.96731i) q^{25} +(0.136313 - 0.0787005i) q^{26} +(-3.55840 - 1.81310i) q^{27} +(-0.269797 - 1.63270i) q^{28} +(2.51245 + 3.45809i) q^{29} +(4.09097 - 9.01223i) q^{30} +(-0.287036 - 0.644694i) q^{31} +(3.30346 - 0.885159i) q^{32} +(-8.33800 + 6.75198i) q^{33} +(1.67814 - 5.16477i) q^{34} +(1.52801 + 5.71535i) q^{35} +(-0.862422 - 2.65426i) q^{36} +(6.47261 + 4.20336i) q^{37} +(-0.516889 + 9.86284i) q^{38} +(-0.0551709 + 0.259559i) q^{39} +(-4.66217 + 1.75101i) q^{40} +(0.124652 + 0.0405019i) q^{41} +(9.86378 + 6.31226i) q^{42} +(8.25770 - 8.25770i) q^{43} +(-2.44318 - 0.256788i) q^{44} +(3.99203 + 9.14389i) q^{45} +(0.888279 + 8.45141i) q^{46} +(2.52906 - 0.970816i) q^{47} +(-6.02679 + 11.8282i) q^{48} +(-6.95125 + 0.824720i) q^{49} +(-7.27115 + 3.57313i) q^{50} +(4.57761 + 7.92865i) q^{51} +(-0.0509570 + 0.0330918i) q^{52} +(9.13970 + 7.40118i) q^{53} +(5.91164 + 2.63203i) q^{54} +(8.78225 + 0.0636062i) q^{55} +(-1.26365 - 5.75550i) q^{56} +(-11.7735 - 11.7735i) q^{57} +(-4.35867 - 5.38252i) q^{58} +(-3.45304 - 3.83499i) q^{59} +(-1.39494 + 3.55674i) q^{60} +(5.30099 + 4.77304i) q^{61} +(0.519128 + 1.01885i) q^{62} +(-11.3824 + 3.13162i) q^{63} +(3.97346 - 1.29105i) q^{64} +(0.169793 - 0.135471i) q^{65} +(12.9192 - 11.6325i) q^{66} +(-0.521089 - 0.200027i) q^{67} +(-0.542557 + 2.02485i) q^{68} +(-11.5903 - 8.42087i) q^{69} +(-2.95716 - 9.11848i) q^{70} +(0.818370 - 0.594581i) q^{71} +(-3.56136 - 9.27765i) q^{72} +(-1.16213 - 1.78952i) q^{73} +(-10.8299 - 6.25262i) q^{74} +(3.72576 - 13.1403i) q^{75} -3.81243i q^{76} +(-1.55694 + 10.2743i) q^{77} +(0.0672616 - 0.424673i) q^{78} +(-6.28497 + 14.1163i) q^{79} +(9.95896 - 4.34787i) q^{80} +(2.26247 - 1.00731i) q^{81} +(-0.205136 - 0.0549659i) q^{82} +(-1.69214 - 10.6837i) q^{83} +(-3.92988 - 2.23402i) q^{84} +(1.22593 - 7.39326i) q^{85} +(-12.6616 + 14.0621i) q^{86} +(11.6603 + 0.611092i) q^{87} +(-8.73562 - 0.457814i) q^{88} +(-0.671570 + 0.745854i) q^{89} +(-7.23495 - 14.4573i) q^{90} +(0.129991 + 0.221714i) q^{91} +(-0.513159 - 3.23996i) q^{92} +(-1.86207 - 0.498939i) q^{93} +(-4.00998 + 1.78536i) q^{94} +(1.32646 + 13.5648i) q^{95} +(3.79985 - 8.53459i) q^{96} +(1.77133 - 11.1837i) q^{97} +(11.1779 - 1.92397i) q^{98} +17.5251i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.61811	+	0.0848016i	−1.14418	+	0.0599638i	−0.614985	−	0.788539i	$-0.710838\pi$
$2$	−1.61811	+	0.0848016i	−1.14418	+	0.0599638i	−0.529192	+	0.848502i	$0.677505\pi$
$3$	1.71909	−	2.12290i	0.992519	−	1.22566i	0.0183512	−	0.999832i	$-0.494158\pi$
$3$	1.71909	−	2.12290i	0.992519	−	1.22566i	0.974167	−	0.225827i	$-0.0725084\pi$
$4$	0.622046	−	0.0653797i	0.311023	−	0.0326899i
$5$	−2.19051	+	0.449052i	−0.979628	+	0.200822i
$5$	−2.19051	+	0.449052i	−0.979628	+	0.200822i
$6$	−2.60166	+	3.58087i	−1.06212	+	1.46189i
$7$	−0.156130	−	2.64114i	−0.0590114	−	0.998257i
$7$	−0.156130	−	2.64114i	−0.0590114	−	0.998257i
$8$	2.19977	−	0.348409i	0.777736	−	0.123181i
$9$	−0.927701	−	4.36449i	−0.309234	−	1.45483i
$10$	3.50641	−	0.912375i	1.10883	−	0.288518i
$11$	−3.84181	−	0.816603i	−1.15835	−	0.246215i	−0.411629	−	0.911352i	$-0.635040\pi$
$11$	−3.84181	−	0.816603i	−1.15835	−	0.246215i	−0.746722	+	0.665137i	$0.768373\pi$
$12$	0.930561	−	1.43294i	0.268630	−	0.413653i
$13$	−0.0865535	+	0.0441012i	−0.0240056	+	0.0122315i	−0.465952	−	0.884810i	$-0.654288\pi$
$13$	−0.0865535	+	0.0441012i	−0.0240056	+	0.0122315i	0.441946	+	0.897041i	$0.354288\pi$
$14$	0.476608	+	4.26042i	0.127379	+	1.13864i
$15$	−2.81240	+	5.42221i	−0.726160	+	1.40001i
$16$	−4.75353	+	1.01039i	−1.18838	+	0.252599i
$17$	−1.20108	+	3.12891i	−0.291304	+	0.758872i	0.707343	+	0.706870i	$0.249893\pi$
$17$	−1.20108	+	3.12891i	−0.291304	+	0.758872i	−0.998647	+	0.0520016i	$0.983440\pi$
$18$	1.87124	+	6.98356i	0.441055	+	1.64604i
$19$	0.637130	−	6.06189i	0.146168	−	1.39069i	−0.637948	−	0.770079i	$-0.720217\pi$
$19$	0.637130	−	6.06189i	0.146168	−	1.39069i	0.784116	−	0.620614i	$-0.213117\pi$
$20$	−1.33324	+	0.422546i	−0.298122	+	0.0944842i
$21$	−5.87529	−	4.20892i	−1.28209	−	0.918461i
$22$	6.28573	+	0.995562i	1.34012	+	0.212254i
$23$	−0.274480	−	5.23739i	−0.0572331	−	1.09207i	−0.864742	−	0.502217i	$-0.832518\pi$
$23$	−0.274480	−	5.23739i	−0.0572331	−	1.09207i	0.807509	−	0.589856i	$-0.200815\pi$
$24$	3.04197	−	5.26884i	0.620939	−	1.07550i
$25$	4.59670	−	1.96731i	0.919341	−	0.393462i
$26$	0.136313	−	0.0787005i	0.0267332	−	0.0154344i
$27$	−3.55840	−	1.81310i	−0.684814	−	0.348930i
$28$	−0.269797	−	1.63270i	−0.0509868	−	0.308552i
$29$	2.51245	+	3.45809i	0.466550	+	0.642152i	0.975851	−	0.218437i	$-0.0700959\pi$
$29$	2.51245	+	3.45809i	0.466550	+	0.642152i	−0.509301	+	0.860589i	$0.670096\pi$
$30$	4.09097	−	9.01223i	0.746905	−	1.64540i
$31$	−0.287036	−	0.644694i	−0.0515533	−	0.115791i	0.885932	−	0.463814i	$-0.153520\pi$
$31$	−0.287036	−	0.644694i	−0.0515533	−	0.115791i	−0.937486	+	0.348024i	$0.886853\pi$
$32$	3.30346	−	0.885159i	0.583975	−	0.156475i
$33$	−8.33800	+	6.75198i	−1.45146	+	1.17537i
$34$	1.67814	−	5.16477i	0.287798	−	0.885751i
$35$	1.52801	+	5.71535i	0.258281	+	0.966070i
$36$	−0.862422	−	2.65426i	−0.143737	−	0.442377i
$37$	6.47261	+	4.20336i	1.06409	+	0.691029i	0.953058	−	0.302788i	$-0.0979174\pi$
$37$	6.47261	+	4.20336i	1.06409	+	0.691029i	0.111033	+	0.993817i	$0.464584\pi$
$38$	−0.516889	+	9.86284i	−0.0838505	+	1.59996i
$39$	−0.0551709	+	0.259559i	−0.00883442	+	0.0415627i
$40$	−4.66217	+	1.75101i	−0.737154	+	0.276858i
$41$	0.124652	+	0.0405019i	0.0194674	+	0.00632534i	0.318735	−	0.947844i	$-0.396742\pi$
$41$	0.124652	+	0.0405019i	0.0194674	+	0.00632534i	−0.299267	+	0.954169i	$0.596742\pi$
$42$	9.86378	+	6.31226i	1.52202	+	0.974003i
$43$	8.25770	−	8.25770i	1.25929	−	1.25929i	0.307854	−	0.951434i	$-0.400389\pi$
$43$	8.25770	−	8.25770i	1.25929	−	1.25929i	0.951434	−	0.307854i	$-0.0996108\pi$
$44$	−2.44318	−	0.256788i	−0.368323	−	0.0387123i
$45$	3.99203	+	9.14389i	0.595096	+	1.36309i
$46$	0.888279	+	8.45141i	0.130970	+	1.24609i
$47$	2.52906	−	0.970816i	0.368902	−	0.141608i	−0.166853	−	0.985982i	$-0.553361\pi$
$47$	2.52906	−	0.970816i	0.368902	−	0.141608i	0.535755	+	0.844374i	$0.320027\pi$
$48$	−6.02679	+	11.8282i	−0.869893	+	1.70726i
$49$	−6.95125	+	0.824720i	−0.993035	+	0.117817i
$50$	−7.27115	+	3.57313i	−1.02830	+	0.505317i
$51$	4.57761	+	7.92865i	0.640993	+	1.11023i
$52$	−0.0509570	+	0.0330918i	−0.00706646	+	0.00458901i
$53$	9.13970	+	7.40118i	1.25543	+	1.01663i	0.998742	+	0.0501369i	$0.0159658\pi$
$53$	9.13970	+	7.40118i	1.25543	+	1.01663i	0.256691	+	0.966493i	$0.417368\pi$
$54$	5.91164	+	2.63203i	0.804472	+	0.358174i
$55$	8.78225	+	0.0636062i	1.18420	+	0.00857666i
$56$	−1.26365	−	5.75550i	−0.168862	−	0.769111i
$57$	−11.7735	−	11.7735i	−1.55944	−	1.55944i
$58$	−4.35867	−	5.38252i	−0.572322	−	0.706759i
$59$	−3.45304	−	3.83499i	−0.449548	−	0.499273i	0.475188	−	0.879885i	$-0.342380\pi$
$59$	−3.45304	−	3.83499i	−0.449548	−	0.499273i	−0.924735	+	0.380611i	$0.875714\pi$
$60$	−1.39494	+	3.55674i	−0.180086	+	0.459173i
$61$	5.30099	+	4.77304i	0.678723	+	0.611125i	0.934649	−	0.355572i	$-0.115714\pi$
$61$	5.30099	+	4.77304i	0.678723	+	0.611125i	−0.255926	+	0.966696i	$0.582380\pi$
$62$	0.519128	+	1.01885i	0.0659293	+	0.129394i
$63$	−11.3824	+	3.13162i	−1.43405	+	0.394546i
$64$	3.97346	−	1.29105i	0.496682	−	0.161382i
$65$	0.169793	−	0.135471i	0.0210602	−	0.0168032i
$66$	12.9192	−	11.6325i	1.59025	−	1.43187i
$67$	−0.521089	−	0.200027i	−0.0636611	−	0.0244372i	0.326329	−	0.945256i	$-0.394188\pi$
$67$	−0.521089	−	0.200027i	−0.0636611	−	0.0244372i	−0.389990	+	0.920819i	$0.627522\pi$
$68$	−0.542557	+	2.02485i	−0.0657947	+	0.245549i
$69$	−11.5903	−	8.42087i	−1.39531	−	1.01375i
$70$	−2.95716	−	9.11848i	−0.353449	−	1.08987i
$71$	0.818370	−	0.594581i	0.0971227	−	0.0705637i	−0.538164	−	0.842840i	$-0.680882\pi$
$71$	0.818370	−	0.594581i	0.0971227	−	0.0705637i	0.635287	+	0.772276i	$0.280882\pi$
$72$	−3.56136	−	9.27765i	−0.419710	−	1.09338i
$73$	−1.16213	−	1.78952i	−0.136017	−	0.209448i	0.764098	−	0.645100i	$-0.223184\pi$
$73$	−1.16213	−	1.78952i	−0.136017	−	0.209448i	−0.900115	+	0.435652i	$0.856518\pi$
$74$	−10.8299	−	6.25262i	−1.25894	−	0.726852i
$75$	3.72576	−	13.1403i	0.430213	−	1.51732i
$76$		−	3.81243i		−	0.437316i
$77$	−1.55694	+	10.2743i	−0.177430	+	1.17086i
$78$	0.0672616	−	0.424673i	0.00761588	−	0.0480848i
$79$	−6.28497	+	14.1163i	−0.707114	+	1.58820i	0.0980696	+	0.995180i	$0.468733\pi$
$79$	−6.28497	+	14.1163i	−0.707114	+	1.58820i	−0.805184	+	0.593025i	$0.797933\pi$
$80$	9.95896	−	4.34787i	1.11345	−	0.486106i
$81$	2.26247	−	1.00731i	0.251385	−	0.111924i
$82$	−0.205136	−	0.0549659i	−0.0226534	−	0.00606997i
$83$	−1.69214	−	10.6837i	−0.185736	−	1.17269i	−0.887680	−	0.460461i	$-0.847684\pi$
$83$	−1.69214	−	10.6837i	−0.185736	−	1.17269i	0.701944	−	0.712232i	$-0.252316\pi$
$84$	−3.92988	−	2.23402i	−0.428785	−	0.243751i
$85$	1.22593	−	7.39326i	0.132971	−	0.801912i
$86$	−12.6616	+	14.0621i	−1.36534	+	1.51636i
$87$	11.6603	+	0.611092i	1.25012	+	0.0655159i
$88$	−8.73562	−	0.457814i	−0.931220	−	0.0488032i
$89$	−0.671570	+	0.745854i	−0.0711863	+	0.0790604i	−0.777686	−	0.628653i	$-0.783607\pi$
$89$	−0.671570	+	0.745854i	−0.0711863	+	0.0790604i	0.706500	+	0.707713i	$0.250273\pi$
$90$	−7.23495	−	14.4573i	−0.762631	−	1.52393i
$91$	0.129991	+	0.221714i	0.0136268	+	0.0232420i
$92$	−0.513159	−	3.23996i	−0.0535005	−	0.337789i
$93$	−1.86207	−	0.498939i	−0.193087	−	0.0517376i
$94$	−4.00998	+	1.78536i	−0.413597	+	0.184145i
$95$	1.32646	+	13.5648i	0.136092	+	1.39172i
$96$	3.79985	−	8.53459i	0.387820	−	0.871058i
$97$	1.77133	−	11.1837i	0.179851	−	1.13554i	−0.718262	−	0.695773i	$-0.755062\pi$
$97$	1.77133	−	11.1837i	0.179851	−	1.13554i	0.898113	−	0.439764i	$-0.144938\pi$
$98$	11.1779	−	1.92397i	1.12914	−	0.194350i
$99$			17.5251i			1.76134i
$100$	2.73074	−	1.52429i	0.273074	−	0.152429i
$101$	−10.1623	−	5.86718i	−1.01118	−	0.583807i	−0.0996449	−	0.995023i	$-0.531771\pi$
$101$	−10.1623	−	5.86718i	−1.01118	−	0.583807i	−0.911538	+	0.411216i	$0.865104\pi$
$102$	−8.07944	−	12.4412i	−0.799983	−	1.23187i
$103$	−3.60931	−	9.40258i	−0.355636	−	0.926464i	−0.988366	−	0.152092i	$-0.951399\pi$
$103$	−3.60931	−	9.40258i	−0.355636	−	0.926464i	0.632730	−	0.774372i	$-0.281934\pi$
$104$	−0.175032	+	0.127168i	−0.0171633	+	0.0124699i
$105$	14.7599	+	6.58139i	1.44042	+	0.642278i
$106$	−15.4167	−	11.2009i	−1.49740	−	1.08792i
$107$	−0.292999	+	1.09349i	−0.0283253	+	0.105711i	−0.978641	−	0.205576i	$-0.934093\pi$
$107$	−0.292999	+	1.09349i	−0.0283253	+	0.105711i	0.950316	+	0.311287i	$0.100760\pi$
$108$	−2.33203	−	0.895182i	−0.224400	−	0.0861389i
$109$	−2.17553	+	1.95886i	−0.208378	+	0.187624i	−0.766711	−	0.641993i	$-0.778108\pi$
$109$	−2.17553	+	1.95886i	−0.208378	+	0.187624i	0.558333	+	0.829617i	$0.311441\pi$
$110$	−14.2160	+	0.641826i	−1.35545	+	0.0611958i
$111$	20.0504	−	6.51476i	1.90310	−	0.618353i
$112$	3.41076	+	12.3970i	0.322287	+	1.17141i
$113$	−2.12100	−	4.16270i	−0.199527	−	0.391594i	0.769464	−	0.638690i	$-0.220523\pi$
$113$	−2.12100	−	4.16270i	−0.199527	−	0.391594i	−0.968991	+	0.247097i	$0.920523\pi$
$114$	20.0493	+	18.0524i	1.87779	+	1.69077i
$115$	2.95311	+	11.3493i	0.275379	+	1.05833i
$116$	1.78895	+	1.98683i	0.166100	+	0.184473i
$117$	0.272775	+	0.336849i	0.0252181	+	0.0311417i
$118$	5.91261	+	5.91261i	0.544300	+	0.544300i
$119$	8.45141	+	2.68369i	0.774739	+	0.246014i
$120$	−4.29749	+	12.9075i	−0.392305	+	1.17829i
$121$	4.04370	+	1.80037i	0.367609	+	0.163670i
$122$	−8.98236	−	7.27377i	−0.813224	−	0.658536i
$123$	0.300270	−	0.194998i	0.0270745	−	0.0175824i
$124$	−0.220700	−	0.382263i	−0.0198194	−	0.0343283i
$125$	−9.18572	+	6.37358i	−0.821596	+	0.570070i
$126$	18.1524	−	6.03254i	1.61714	−	0.537422i
$127$	−7.51832	+	14.7555i	−0.667143	+	1.30934i	0.270829	+	0.962628i	$0.412702\pi$
$127$	−7.51832	+	14.7555i	−0.667143	+	1.30934i	−0.937971	+	0.346713i	$0.887298\pi$
$128$	−12.7057	+	4.87725i	−1.12303	+	0.431092i
$129$	−3.33454	−	31.7260i	−0.293590	−	2.79332i
$130$	−0.263256	+	0.233606i	−0.0230890	+	0.0204886i
$131$	−0.400325	−	0.0420758i	−0.0349765	−	0.00367618i	0.0870240	−	0.996206i	$-0.472264\pi$
$131$	−0.400325	−	0.0420758i	−0.0349765	−	0.00367618i	−0.122001	+	0.992530i	$0.538931\pi$
$132$	−4.74518	+	4.74518i	−0.413015	+	0.413015i
$133$	−16.1098	−	0.736311i	−1.39690	−	0.0638462i
$134$	0.860142	+	0.279477i	0.0743049	+	0.0241431i
$135$	8.60890	+	2.37370i	0.740936	+	0.204296i
$136$	−1.55195	+	7.30134i	−0.133078	+	0.626085i
$137$	0.662940	−	12.6497i	0.0566388	−	1.08073i	−0.811481	−	0.584378i	$-0.801338\pi$
$137$	0.662940	−	12.6497i	0.0566388	−	1.08073i	0.868120	−	0.496354i	$-0.165328\pi$
$138$	19.4685	+	12.6430i	1.65727	+	1.07625i
$139$	4.44619	+	13.6840i	0.377121	+	1.16066i	0.942036	+	0.335511i	$0.108909\pi$
$139$	4.44619	+	13.6840i	0.377121	+	1.16066i	−0.564915	+	0.825149i	$0.691091\pi$
$140$	1.32416	+	3.45531i	0.111912	+	0.292027i
$141$	2.28674	−	7.03788i	0.192579	−	0.592696i
$142$	−1.27379	+	1.03150i	−0.106894	+	0.0865612i
$143$	0.368536	−	0.0987488i	0.0308185	−	0.00825779i
$144$	8.81972	+	19.8094i	0.734976	+	1.65078i
$145$	−7.05642	−	6.44678i	−0.586004	−	0.535376i
$146$	2.03221	+	2.79710i	0.168187	+	0.231489i
$147$	−10.1990	+	16.1746i	−0.841202	+	1.33406i
$148$	4.30108	+	2.19151i	0.353547	+	0.180141i
$149$	9.24670	−	5.33859i	0.757519	−	0.437354i	−0.0708851	−	0.997484i	$-0.522582\pi$
$149$	9.24670	−	5.33859i	0.757519	−	0.437354i	0.828404	+	0.560131i	$0.189249\pi$
$150$	−4.91436	+	21.5785i	−0.401256	+	1.76188i
$151$	−10.4396	+	18.0820i	−0.849565	+	1.47149i	0.0320315	+	0.999487i	$0.489802\pi$
$151$	−10.4396	+	18.0820i	−0.849565	+	1.47149i	−0.881597	+	0.472003i	$0.843531\pi$
$152$	−0.710479	−	13.5567i	−0.0576274	−	1.09960i
$153$	14.7703	+	2.33939i	1.19411	+	0.189128i
$154$	1.64803	−	16.7569i	0.132802	−	1.35031i
$155$	0.918259	+	1.28332i	0.0737563	+	0.103079i
$156$	−0.0173490	+	0.165065i	−0.00138903	+	0.0132157i
$157$	3.09395	+	11.5468i	0.246924	+	0.921533i	0.972407	+	0.233293i	$0.0749500\pi$
$157$	3.09395	+	11.5468i	0.246924	+	0.921533i	−0.725483	+	0.688241i	$0.758383\pi$
$158$	8.97269	−	23.3747i	0.713829	−	1.85959i
$159$	31.4240	−	6.67937i	2.49208	−	0.529709i
$160$	−6.83879	+	3.42238i	−0.540654	+	0.270563i
$161$	−13.7898	+	1.54265i	−1.08679	+	0.121578i
$162$	−3.57550	+	1.82181i	−0.280918	+	0.143135i
$163$	7.89827	−	12.1623i	0.618640	−	0.952622i	−0.380967	−	0.924589i	$-0.624409\pi$
$163$	7.89827	−	12.1623i	0.618640	−	0.952622i	0.999607	−	0.0280333i	$-0.00892443\pi$
$164$	0.0801874	+	0.0170444i	0.00626159	+	0.00133094i
$165$	15.2325	−	18.5345i	1.18585	−	1.44291i
$166$	3.64407	+	17.1440i	0.282834	+	1.33063i
$167$	1.65219	−	0.261681i	0.127850	−	0.0202495i	−0.0921813	−	0.995742i	$-0.529384\pi$
$167$	1.65219	−	0.261681i	0.127850	−	0.0202495i	0.220032	+	0.975493i	$0.429384\pi$
$168$	−14.3907	−	7.21164i	−1.11027	−	0.556390i
$169$	−7.63566	+	10.5096i	−0.587359	+	0.808430i
$170$	−1.35673	+	12.0671i	−0.104056	+	0.925502i
$171$	−27.0481	+	2.84287i	−2.06842	+	0.217400i
$172$	4.59679	−	5.67656i	0.350502	−	0.432834i
$173$	−0.280864	+	0.0147195i	−0.0213537	+	0.00111910i	−0.0630098	−	0.998013i	$-0.520070\pi$
$173$	−0.280864	+	0.0147195i	−0.0213537	+	0.00111910i	0.0416561	+	0.999132i	$0.486737\pi$
$174$	−18.9195			−1.43429
$175$	−5.91362	−	11.8334i	−0.447028	−	0.894520i
$176$	19.0873			1.43876
$177$	−14.0774	+	0.737766i	−1.05812	+	0.0554539i
$178$	1.02343	−	1.26383i	0.0767090	−	0.0947277i
$179$	13.0417	−	1.37074i	0.974782	−	0.102454i	0.396275	−	0.918132i	$-0.370303\pi$
$179$	13.0417	−	1.37074i	0.974782	−	0.102454i	0.578506	+	0.815678i	$0.303636\pi$
$180$	3.08105	+	5.42693i	0.229648	+	0.404499i
$181$	13.5383	−	18.6338i	1.00629	−	1.38504i	0.0849076	−	0.996389i	$-0.472940\pi$
$181$	13.5383	−	18.6338i	1.00629	−	1.38504i	0.921384	−	0.388653i	$-0.127060\pi$
$182$	−0.229142	−	0.347735i	−0.0169851	−	0.0257758i
$183$	19.2456	−	3.04820i	1.42268	−	0.225330i
$184$	−2.42855	−	11.4254i	−0.179035	−	0.842294i
$185$	−16.0659	−	6.30099i	−1.18119	−	0.463258i
$186$	3.05534	+	0.649432i	0.224028	+	0.0476187i
$187$	7.16938	−	11.0399i	0.524277	−	0.807316i
$188$	1.50972	−	0.769242i	0.110108	−	0.0561027i
$189$	−4.23307	+	9.68131i	−0.307910	+	0.704212i
$190$	−3.29667	−	21.8368i	−0.239166	−	1.58421i
$191$	−3.95786	+	0.841270i	−0.286381	+	0.0608722i	−0.348862	−	0.937174i	$-0.613432\pi$
$191$	−3.95786	+	0.841270i	−0.286381	+	0.0608722i	0.0624813	+	0.998046i	$0.480099\pi$
$192$	4.08996	−	10.6547i	0.295167	−	0.768937i
$193$	0.795745	+	2.96976i	0.0572790	+	0.213768i	0.988634	−	0.150346i	$-0.0480386\pi$
$193$	0.795745	+	2.96976i	0.0572790	+	0.213768i	−0.931355	+	0.364114i	$0.881372\pi$
$194$	−1.91781	+	18.2467i	−0.137691	+	1.31004i
$195$	0.00429733	−	0.593342i	0.000307738	−	0.0424901i
$196$	−4.27008	+	0.967485i	−0.305006	+	0.0691061i
$197$	12.4561	+	1.97286i	0.887464	+	0.140560i	0.583490	−	0.812120i	$-0.301687\pi$
$197$	12.4561	+	1.97286i	0.887464	+	0.140560i	0.303973	+	0.952681i	$0.401687\pi$
$198$	−1.48616	−	28.3576i	−0.105617	−	2.01529i
$199$	−2.17496	+	3.76715i	−0.154179	+	0.267046i	−0.932760	−	0.360498i	$-0.882607\pi$
$199$	−2.17496	+	3.76715i	−0.154179	+	0.267046i	0.778581	+	0.627545i	$0.215940\pi$
$200$	9.42626	−	5.92916i	0.666537	−	0.419255i
$201$	−1.32044	+	0.762355i	−0.0931365	+	0.0537724i
$202$	16.9412	+	8.63198i	1.19198	+	0.607344i
$203$	8.74104	−	7.17565i	0.613501	−	0.503632i
$204$	3.36586	+	4.63270i	0.235657	+	0.324354i
$205$	−0.291240	−	0.0327448i	−0.0203411	−	0.00228700i
$206$	6.63762	+	14.9083i	0.462465	+	1.03871i
$207$	−22.6039	+	6.05670i	−1.57108	+	0.420970i
$208$	0.366875	−	0.297090i	0.0254382	−	0.0205995i
$209$	−7.39789	+	22.7684i	−0.511723	+	1.57492i
$210$	−24.4413	−	9.39775i	−1.68661	−	0.648506i
$211$	2.05986	+	6.33961i	0.141807	+	0.436437i	0.996587	−	0.0825543i	$-0.0263078\pi$
$211$	2.05986	+	6.33961i	0.141807	+	0.436437i	−0.854780	+	0.518991i	$0.826308\pi$
$212$	6.16920	+	4.00633i	0.423703	+	0.275156i
$213$	0.144617	−	2.75946i	0.00990900	−	0.189075i
$214$	0.381375	−	1.79423i	0.0260703	−	0.122651i
$215$	−14.3805	+	21.7967i	−0.980740	+	1.48653i
$216$	−8.45936	−	2.74861i	−0.575586	−	0.187019i
$217$	−1.65791	+	0.858760i	−0.112547	+	0.0582964i
$218$	3.35413	−	3.35413i	0.227171	−	0.227171i
$219$	−5.79680	−	0.609268i	−0.391711	−	0.0411705i
$220$	5.46712	−	0.534615i	0.368593	−	0.0360437i
$221$	−0.0340314	−	0.323787i	−0.00228920	−	0.0217803i
$222$	−31.8912	+	12.2419i	−2.14040	+	0.821622i
$223$	−6.99626	+	13.7309i	−0.468504	+	0.919491i	0.528982	+	0.848633i	$0.322574\pi$
$223$	−6.99626	+	13.7309i	−0.468504	+	0.919491i	−0.997486	+	0.0708583i	$0.977426\pi$
$224$	−2.85360	−	8.58670i	−0.190664	−	0.573723i
$225$	−12.8507	−	18.2372i	−0.856711	−	1.21581i
$226$	3.78502	+	6.55584i	0.251776	+	0.436088i
$227$	−11.1124	+	7.21647i	−0.737556	+	0.478974i	−0.857938	−	0.513753i	$-0.828255\pi$
$227$	−11.1124	+	7.21647i	−0.737556	+	0.478974i	0.120382	+	0.992728i	$0.461588\pi$
$228$	−8.09342	−	6.55393i	−0.536000	−	0.434044i
$229$	−3.78909	−	1.68701i	−0.250390	−	0.111481i	0.277704	−	0.960667i	$-0.410426\pi$
$229$	−3.78909	−	1.68701i	−0.250390	−	0.111481i	−0.528094	+	0.849186i	$0.677093\pi$
$230$	−5.74091	−	18.1140i	−0.378544	−	1.19440i
$231$	19.1347	+	20.9677i	1.25897	+	1.37957i
$232$	6.73164	+	6.73164i	0.441954	+	0.441954i
$233$	16.2166	+	20.0258i	1.06238	+	1.31194i	0.947920	+	0.318508i	$0.103182\pi$
$233$	16.2166	+	20.0258i	1.06238	+	1.31194i	0.114464	+	0.993427i	$0.463485\pi$
$234$	−0.469946	−	0.521927i	−0.0307213	−	0.0341195i
$235$	−5.10400	+	3.26227i	−0.332948	+	0.212807i
$236$	−2.39868	−	2.15978i	−0.156141	−	0.140590i
$237$	19.1630	+	37.6096i	1.24477	+	2.44300i
$238$	−13.9029	−	3.62582i	−0.901191	−	0.235027i
$239$	−0.618920	+	0.201099i	−0.0400346	+	0.0130080i	−0.328966	−	0.944342i	$-0.606700\pi$
$239$	−0.618920	+	0.201099i	−0.0400346	+	0.0130080i	0.288931	+	0.957350i	$0.406700\pi$
$240$	7.89028	−	28.6163i	0.509315	−	1.84717i
$241$	−0.853202	+	0.768226i	−0.0549596	+	0.0494858i	−0.696153	−	0.717894i	$-0.745106\pi$
$241$	−0.853202	+	0.768226i	−0.0549596	+	0.0494858i	0.641193	+	0.767379i	$0.278440\pi$
$242$	−6.69582	−	2.57029i	−0.430424	−	0.165224i
$243$	4.85188	−	18.1075i	0.311248	−	1.16159i
$244$	3.60952	+	2.62247i	0.231076	+	0.167887i
$245$	14.8565	−	4.92803i	0.949145	−	0.314840i
$246$	−0.469334	+	0.340991i	−0.0299237	+	0.0217408i
$247$	0.212191	+	0.552776i	0.0135014	+	0.0351723i
$248$	−0.856031	−	1.31817i	−0.0543580	−	0.0837040i
$249$	−25.5895	−	14.7741i	−1.62167	−	0.936270i
$250$	14.3230	−	11.0921i	0.905868	−	0.701527i
$251$		−	13.8492i		−	0.874153i	−0.899424	−	0.437076i	$-0.856014\pi$
$251$		−	13.8492i		−	0.874153i	0.899424	−	0.437076i	$-0.143986\pi$
$252$	−6.87563	+	2.69219i	−0.433124	+	0.169592i
$253$	−3.22237	+	20.3452i	−0.202589	+	1.27909i
$254$	10.9142	−	24.5136i	0.684816	−	1.53812i
$255$	−13.5877	−	15.3122i	−0.850894	−	0.958889i
$256$	12.5121	−	5.57076i	0.782008	−	0.348172i
$257$	−0.352213	−	0.0943752i	−0.0219704	−	0.00588696i	0.247817	−	0.968807i	$-0.420287\pi$
$257$	−0.352213	−	0.0943752i	−0.0219704	−	0.00588696i	−0.269788	+	0.962920i	$0.586953\pi$
$258$	8.08608	+	51.0535i	0.503417	+	3.17845i
$259$	10.0911	−	17.7513i	0.627031	−	1.10302i
$260$	0.0967620	−	0.0953705i	0.00600092	−	0.00591462i
$261$	12.7620	−	14.1736i	0.789948	−	0.877327i
$262$	0.651338	+	0.0341352i	0.0402398	+	0.00210888i
$263$	29.7070	+	1.55688i	1.83181	+	0.0960011i	0.936762	−	0.349967i	$-0.113807\pi$
$263$	29.7070	+	1.55688i	1.83181	+	0.0960011i	0.895049	+	0.445968i	$0.147141\pi$
$264$	−15.9892	+	17.7578i	−0.984069	+	1.09292i
$265$	−23.3441	−	12.1082i	−1.43402	−	0.743800i
$266$	26.1298	−	0.174703i	1.60212	−	0.0107117i
$267$	0.428885	+	2.70787i	0.0262473	+	0.165719i
$268$	−0.337219	−	0.0903576i	−0.0205989	−	0.00551947i
$269$	18.9335	−	8.42973i	1.15439	−	0.513970i	0.261930	−	0.965087i	$-0.415641\pi$
$269$	18.9335	−	8.42973i	1.15439	−	0.513970i	0.892465	+	0.451117i	$0.148974\pi$
$270$	−14.1314	−	3.11087i	−0.860012	−	0.189321i
$271$	−2.28034	+	5.12174i	−0.138521	+	0.311123i	−0.969464	−	0.245235i	$-0.921135\pi$
$271$	−2.28034	+	5.12174i	−0.138521	+	0.311123i	0.830943	+	0.556358i	$0.187802\pi$
$272$	2.54792	−	16.0869i	0.154490	−	0.975413i
$273$	0.694145	+	0.105189i	0.0420116	+	0.00636635i
$274$			20.5248i			1.23995i
$275$	−19.2662	+	3.80435i	−1.16180	+	0.229411i
$276$	−7.76028	−	4.48040i	−0.467114	−	0.269688i
$277$	−3.21957	−	4.95771i	−0.193445	−	0.297880i	0.728617	−	0.684922i	$-0.240164\pi$
$277$	−3.21957	−	4.95771i	−0.193445	−	0.297880i	−0.922062	+	0.387042i	$0.873497\pi$
$278$	−8.35486	−	21.7651i	−0.501091	−	1.30539i
$279$	−2.54748	+	1.85085i	−0.152514	+	0.110808i
$280$	5.35255	+	12.0401i	0.319876	+	0.719532i
$281$	−6.92124	−	5.02858i	−0.412887	−	0.299980i	0.361883	−	0.932224i	$-0.382134\pi$
$281$	−6.92124	−	5.02858i	−0.412887	−	0.299980i	−0.774769	+	0.632244i	$0.782134\pi$
$282$	−3.10338	+	11.5820i	−0.184804	+	0.689697i
$283$	14.0882	+	5.40796i	0.837458	+	0.321470i	0.739028	−	0.673674i	$-0.235285\pi$
$283$	14.0882	+	5.40796i	0.837458	+	0.321470i	0.0984291	+	0.995144i	$0.468618\pi$
$284$	0.470191	−	0.423361i	0.0279007	−	0.0251219i
$285$	31.0770	+	20.5031i	1.84084	+	1.21450i
$286$	−0.587957	+	0.191039i	−0.0347666	+	0.0112964i
$287$	0.0875094	−	0.335547i	0.00516552	−	0.0198067i
$288$	−6.92789	−	13.5968i	−0.408230	−	0.801196i
$289$	4.28598	+	3.85911i	0.252116	+	0.227007i
$290$	11.9648	+	9.83320i	0.702595	+	0.577426i
$291$	−20.6969	−	22.9863i	−1.21327	−	1.34748i
$292$	−0.839898	−	1.03719i	−0.0491513	−	0.0606968i
$293$	−7.80680	−	7.80680i	−0.456078	−	0.456078i	0.441288	−	0.897366i	$-0.354522\pi$
$293$	−7.80680	−	7.80680i	−0.456078	−	0.456078i	−0.897366	+	0.441288i	$0.854522\pi$
$294$	15.1315	−	27.0372i	0.882489	−	1.57684i
$295$	9.28604	+	6.85000i	0.540654	+	0.398823i
$296$	15.7027	+	6.99131i	0.912703	+	0.406362i
$297$	12.1901	+	9.87137i	0.707343	+	0.572795i
$298$	−14.5095	+	9.42256i	−0.840511	+	0.545834i
$299$	0.254733	+	0.441210i	0.0147316	+	0.0255158i
$300$	1.45848	−	8.41749i	0.0842055	−	0.485984i
$301$	−23.0990	−	20.5205i	−1.33141	−	1.18278i
$302$	15.3591	−	30.1439i	0.883817	−	1.73459i
$303$	−29.9253	+	11.4873i	−1.71917	+	0.659926i
$304$	3.09628	+	29.4592i	0.177584	+	1.68960i
$305$	−13.7552	−	8.07498i	−0.787623	−	0.462372i
$306$	−24.0984	−	2.53284i	−1.37761	−	0.144793i
$307$	−8.14095	+	8.14095i	−0.464628	+	0.464628i	−0.900169	−	0.435541i	$-0.856557\pi$
$307$	−8.14095	+	8.14095i	−0.464628	+	0.464628i	0.435541	+	0.900169i	$0.356557\pi$
$308$	−0.296762	+	6.49286i	−0.0169096	+	0.369965i
$309$	−26.1655	−	8.50169i	−1.48850	−	0.483644i
$310$	−1.59467	−	1.99868i	−0.0905712	−	0.113517i
$311$	5.97488	−	28.1096i	0.338804	−	1.59395i	−0.397700	−	0.917516i	$-0.630192\pi$
$311$	5.97488	−	28.1096i	0.338804	−	1.59395i	0.736504	−	0.676433i	$-0.236475\pi$
$312$	−0.0309306	+	0.590191i	−0.00175110	+	0.0334130i
$313$	−7.98245	−	5.18386i	−0.451195	−	0.293009i	0.298967	−	0.954263i	$-0.403358\pi$
$313$	−7.98245	−	5.18386i	−0.451195	−	0.293009i	−0.750162	+	0.661254i	$0.770025\pi$
$314$	−5.98554	−	18.4216i	−0.337783	−	1.03959i
$315$	23.5270	−	11.9711i	1.32560	−	0.674497i
$316$	−2.98662	+	9.19189i	−0.168011	+	0.517084i
$317$	−6.06620	+	4.91231i	−0.340712	+	0.275903i	−0.784370	−	0.620293i	$-0.787014\pi$
$317$	−6.06620	+	4.91231i	−0.340712	+	0.275903i	0.443658	+	0.896196i	$0.353680\pi$
$318$	−50.2810	+	13.4728i	−2.81962	+	0.755515i
$319$	−6.82848	−	15.3370i	−0.382322	−	0.858708i
$320$	−8.12416	+	4.61236i	−0.454154	+	0.257839i
$321$	1.81768	+	2.50182i	0.101453	+	0.139638i
$322$	22.1827	−	3.66558i	1.23619	−	0.204275i
$323$	18.2019	+	9.27431i	1.01278	+	0.516036i
$324$	1.34150	−	0.774516i	0.0745278	−	0.0430287i
$325$	−0.311100	+	0.372998i	−0.0172567	+	0.0206902i
$326$	−11.7489	+	20.3497i	−0.650711	+	1.12706i
$327$	0.418523	+	7.98590i	0.0231444	+	0.441621i
$328$	0.288317	+	0.0456650i	0.0159197	+	0.00252143i
$329$	−2.95892	−	6.52804i	−0.163131	−	0.359902i
$330$	−23.0762	+	31.2826i	−1.27030	+	1.72205i
$331$	−0.108165	+	1.02912i	−0.00594527	+	0.0565654i	−0.997092	−	0.0762035i	$-0.975720\pi$
$331$	−0.108165	+	1.02912i	−0.00594527	+	0.0565654i	0.991147	+	0.132769i	$0.0423868\pi$
$332$	−1.75109	−	6.53515i	−0.0961035	−	0.358663i
$333$	12.3409	−	32.1491i	0.676277	−	1.76176i
$334$	−2.65124	+	0.563538i	−0.145069	+	0.0308354i
$335$	1.23127	+	0.204167i	0.0672717	+	0.0111548i
$336$	32.1810	+	14.0709i	1.75562	+	0.767629i
$337$	−1.66773	+	0.849753i	−0.0908472	+	0.0462890i	−0.498824	−	0.866703i	$-0.666235\pi$
$337$	−1.66773	+	0.849753i	−0.0908472	+	0.0462890i	0.407977	+	0.912992i	$0.366235\pi$
$338$	11.4641	−	17.6532i	0.623566	−	0.960207i
$339$	−12.4832	−	2.65339i	−0.677994	−	0.144112i
$340$	0.279216	−	4.67910i	0.0151426	−	0.253760i
$341$	0.576281	+	2.71119i	0.0312074	+	0.146819i
$342$	43.5258	−	6.89381i	2.35361	−	0.372774i
$343$	3.26350	+	18.2305i	0.176212	+	0.984352i
$344$	15.2880	−	21.0421i	0.824272	−	1.13451i
$345$	29.1702	+	13.2414i	1.57047	+	0.712892i
$346$	0.453221	−	0.0476355i	0.0243653	−	0.00256090i
$347$	1.25122	−	1.54512i	0.0671688	−	0.0829465i	−0.742454	−	0.669897i	$-0.766338\pi$
$347$	1.25122	−	1.54512i	0.0671688	−	0.0829465i	0.809623	+	0.586950i	$0.199672\pi$
$348$	7.29322	−	0.382221i	0.390958	−	0.0204892i
$349$	−4.37015			−0.233929			−0.116964	−	0.993136i	$-0.537316\pi$
$349$	−4.37015			−0.233929			−0.116964	+	0.993136i	$0.537316\pi$
$350$	10.5724	+	18.6462i	0.565118	+	0.996684i
$351$	0.387952			0.0207073
$352$	−13.4141	+	0.703003i	−0.714974	+	0.0374702i
$353$	−11.7526	+	14.5133i	−0.625529	+	0.772464i	−0.987139	−	0.159865i	$-0.948894\pi$
$353$	−11.7526	+	14.5133i	−0.625529	+	0.772464i	0.361610	+	0.932330i	$0.382227\pi$
$354$	22.7162	−	2.38757i	1.20735	−	0.126898i
$355$	−1.52565	+	1.66993i	−0.0809733	+	0.0886306i
$356$	−0.368984	+	0.507863i	−0.0195561	+	0.0269167i
$357$	20.2260	−	13.3280i	1.07047	−	0.705393i
$358$	−20.9867	+	3.32396i	−1.10918	+	0.175677i
$359$	−3.47497	−	16.3485i	−0.183402	−	0.862838i	−0.969568	−	0.244823i	$-0.921270\pi$
$359$	−3.47497	−	16.3485i	−0.183402	−	0.862838i	0.786166	−	0.618016i	$-0.212063\pi$
$360$	11.9673	+	18.7236i	0.630735	+	0.986820i
$361$	−17.7558	−	3.77411i	−0.934515	−	0.198637i
$362$	−20.3262	+	31.2997i	−1.06832	+	1.64507i
$363$	10.7735	−	5.48937i	0.565462	−	0.288117i
$364$	0.0953561	+	0.129418i	0.00499802	+	0.00678334i
$365$	3.34925	+	3.39812i	0.175308	+	0.177866i
$366$	−30.8830	+	6.56439i	−1.61428	+	0.343126i
$367$	3.46192	−	9.01861i	0.180711	−	0.470768i	−0.813064	−	0.582174i	$-0.802202\pi$
$367$	3.46192	−	9.01861i	0.180711	−	0.470768i	0.993775	+	0.111406i	$0.0355356\pi$
$368$	6.59659	+	24.6188i	0.343871	+	1.28334i
$369$	0.0611304	−	0.581617i	0.00318232	−	0.0302778i
$370$	26.5307	+	8.83328i	1.37927	+	0.459221i
$371$	18.1206	−	25.2948i	0.940774	−	1.31324i
$372$	−1.19091	−	0.188622i	−0.0617459	−	0.00977959i
$373$	−0.257388	−	4.91126i	−0.0133271	−	0.254295i	−0.997166	−	0.0752376i	$-0.976028\pi$
$373$	−0.257388	−	4.91126i	−0.0133271	−	0.254295i	0.983839	−	0.179058i	$-0.0573049\pi$
$374$	−10.6647	+	18.4717i	−0.551456	+	0.955150i
$375$	−2.26063	+	30.4572i	−0.116738	+	1.57280i
$376$	5.22511	−	3.01672i	0.269465	−	0.155575i
$377$	−0.369967	−	0.188508i	−0.0190543	−	0.00970865i
$378$	6.02858	−	16.0244i	0.310077	−	0.824206i
$379$	7.39900	+	10.1839i	0.380061	+	0.523109i	0.955601	−	0.294665i	$-0.0952079\pi$
$379$	7.39900	+	10.1839i	0.380061	+	0.523109i	−0.575540	+	0.817774i	$0.695208\pi$
$380$	1.71198	+	8.35119i	0.0878227	+	0.428407i
$381$	18.3999	+	41.3268i	0.942654	+	2.11723i
$382$	6.33292	−	1.69690i	0.324020	−	0.0868210i
$383$	−13.9353	+	11.2845i	−0.712058	+	0.576613i	−0.915425	−	0.402489i	$-0.868145\pi$
$383$	−13.9353	+	11.2845i	−0.712058	+	0.576613i	0.203366	+	0.979103i	$0.434812\pi$
$384$	−11.4883	+	35.3574i	−0.586260	+	1.80432i
$385$	−1.20318	−	23.2051i	−0.0613195	−	1.18264i
$386$	−1.53944	−	4.73792i	−0.0783556	−	0.241154i
$387$	−43.7013	−	28.3800i	−2.22146	−	1.44264i
$388$	0.370660	−	7.07262i	0.0188174	−	0.359058i
$389$	−2.47971	+	11.6661i	−0.125726	+	0.591495i	0.869503	+	0.493928i	$0.164439\pi$
$389$	−2.47971	+	11.6661i	−0.125726	+	0.591495i	−0.995229	+	0.0975672i	$0.968894\pi$
$390$	0.0433628	+	0.960457i	0.00219576	+	0.0486346i
$391$	16.7170	+	5.43168i	0.845415	+	0.274692i
$392$	−15.0038	+	4.23607i	−0.757806	+	0.213954i
$393$	−0.777518	+	0.777518i	−0.0392206	+	0.0392206i
$394$	−20.3227	−	2.13600i	−1.02384	−	0.107610i
$395$	7.42838	−	33.7442i	0.373762	−	1.69785i
$396$	1.14579	+	10.9014i	0.0575780	+	0.547818i
$397$	35.0286	−	13.4462i	1.75803	−	0.674846i	0.758297	−	0.651909i	$-0.226032\pi$
$397$	35.0286	−	13.4462i	1.75803	−	0.674846i	0.999737	−	0.0229366i	$-0.00730159\pi$
$398$	3.19987	−	6.28010i	0.160395	−	0.314793i
$399$	−29.2573	+	32.9337i	−1.46470	+	1.64875i
$400$	−19.8628	+	13.9962i	−0.993141	+	0.699808i
$401$	0.106730	+	0.184861i	0.00532982	+	0.00923152i	0.868678	−	0.495377i	$-0.164970\pi$
$401$	0.106730	+	0.184861i	0.00532982	+	0.00923152i	−0.863348	+	0.504609i	$0.831637\pi$
$402$	2.07197	−	1.34555i	0.103340	−	0.0671099i
$403$	0.0532758	+	0.0431419i	0.00265386	+	0.00214905i
$404$	−6.70499	−	2.98525i	−0.333586	−	0.148522i
$405$	−4.50363	+	3.22250i	−0.223787	+	0.160127i
$406$	−13.5355	+	12.3522i	−0.671754	+	0.613032i
$407$	−21.4341	−	21.4341i	−1.06245	−	1.06245i
$408$	12.8321	+	15.8463i	0.635283	+	0.784509i
$409$	21.3736	+	23.7377i	1.05685	+	1.17376i	0.984320	+	0.176390i	$0.0564419\pi$
$409$	21.3736	+	23.7377i	1.05685	+	1.17376i	0.0725340	+	0.997366i	$0.476891\pi$
$410$	0.474035	+	0.0282871i	0.0234109	+	0.00139700i
$411$	−25.7143	−	23.1533i	−1.26839	−	1.14207i
$412$	−2.85990	−	5.61287i	−0.140897	−	0.276526i
$413$	−9.58962	+	9.71872i	−0.471875	+	0.478227i
$414$	36.0620	−	11.7173i	1.77235	−	0.575872i
$415$	8.50421	+	22.6430i	0.417455	+	1.11150i
$416$	−0.246889	+	0.222300i	−0.0121047	+	0.0108992i
$417$	36.6932	+	14.0852i	1.79687	+	0.689755i
$418$	10.0398	−	37.4691i	0.491063	−	1.83267i
$419$	8.57555	+	6.23050i	0.418943	+	0.304380i	0.777212	−	0.629238i	$-0.216633\pi$
$419$	8.57555	+	6.23050i	0.418943	+	0.304380i	−0.358269	+	0.933618i	$0.616633\pi$
$420$	9.61164	+	3.12893i	0.469000	+	0.152676i
$421$	7.12732	−	5.17830i	0.347364	−	0.252375i	−0.400398	−	0.916341i	$-0.631128\pi$
$421$	7.12732	−	5.17830i	0.347364	−	0.252375i	0.747762	+	0.663966i	$0.231128\pi$
$422$	−3.87070	−	10.0835i	−0.188423	−	0.490858i
$423$	−6.58333	−	10.1374i	−0.320093	−	0.492899i
$424$	22.6839	+	13.0965i	1.10163	+	0.636024i
$425$	0.634540	+	16.7456i	0.0307797	+	0.812279i
$426$			4.47737i			0.216929i
$427$	11.7786	−	14.7459i	0.570007	−	0.713603i
$428$	−0.110767	+	0.699356i	−0.00535413	+	0.0338047i
$429$	0.423913	−	0.952124i	0.0204667	−	0.0459690i
$430$	21.4208	−	36.4890i	1.03300	−	1.75966i
$431$	5.59847	−	2.49260i	0.269669	−	0.120064i	−0.267448	−	0.963572i	$-0.586180\pi$
$431$	5.59847	−	2.49260i	0.269669	−	0.120064i	0.537116	+	0.843508i	$0.319514\pi$
$432$	18.7469	+	5.02322i	0.901961	+	0.241680i
$433$	−5.58866	−	35.2854i	−0.268574	−	1.69571i	−0.640913	−	0.767613i	$-0.721444\pi$
$433$	−5.58866	−	35.2854i	−0.268574	−	1.69571i	0.372339	−	0.928097i	$-0.378556\pi$
$434$	2.60986	−	1.53016i	0.125277	−	0.0734501i
$435$	−25.8165	+	3.89749i	−1.23781	+	0.186870i
$436$	−1.22521	+	1.36074i	−0.0586770	+	0.0651674i
$437$	−31.9234	−	1.67303i	−1.52710	−	0.0800321i
$438$	9.43153	+	0.494285i	0.450656	+	0.0236179i
$439$	−17.4485	+	19.3785i	−0.832769	+	0.924884i	−0.998116	−	0.0613516i	$-0.980459\pi$
$439$	−17.4485	+	19.3785i	−0.832769	+	0.924884i	0.165347	+	0.986235i	$0.447126\pi$
$440$	19.3411	−	2.91990i	0.922049	−	0.139201i
$441$	10.0482	+	29.5736i	0.478484	+	1.40826i
$442$	0.0825241	+	0.521037i	0.00392527	+	0.0247832i
$443$	32.7161	+	8.76626i	1.55439	+	0.416498i	0.930882	−	0.365319i	$-0.119040\pi$
$443$	32.7161	+	8.76626i	1.55439	+	0.416498i	0.623508	+	0.781817i	$0.285707\pi$
$444$	12.0463	−	5.36337i	0.571693	−	0.254534i
$445$	1.13616	−	1.93537i	0.0538590	−	0.0917456i
$446$	10.1563	−	22.8115i	0.480915	−	1.08015i
$447$	4.56264	−	28.8074i	0.215805	−	1.36254i
$448$	−4.03023	−	10.2929i	−0.190410	−	0.486293i
$449$			17.8247i			0.841199i	0.907246	+	0.420600i	$0.138180\pi$
$449$			17.8247i			0.841199i	−0.907246	+	0.420600i	$0.861820\pi$
$450$	22.3403	+	28.4201i	1.05313	+	1.33973i
$451$	−0.445816	−	0.257392i	−0.0209927	−	0.0121201i
$452$	−1.59152	−	2.45072i	−0.0748586	−	0.115272i
$453$	20.4396	+	53.2469i	0.960335	+	2.50176i
$454$	17.3691	−	12.6194i	0.815173	−	0.592258i
$455$	−0.384309	−	0.427296i	−0.0180167	−	0.0200319i
$456$	−30.0010	−	21.7970i	−1.40493	−	1.02074i
$457$	−2.20826	+	8.24133i	−0.103298	+	0.385513i	−0.998147	−	0.0608568i	$-0.980617\pi$
$457$	−2.20826	+	8.24133i	−0.103298	+	0.385513i	0.894849	+	0.446370i	$0.147283\pi$
$458$	6.27422	+	2.40845i	0.293175	+	0.112539i
$459$	9.94691	−	8.95624i	0.464282	−	0.418042i
$460$	2.57899	+	6.86674i	0.120246	+	0.320163i
$461$	−25.2246	+	8.19596i	−1.17483	+	0.381724i	−0.830442	−	0.557105i	$-0.811912\pi$
$461$	−25.2246	+	8.19596i	−1.17483	+	0.381724i	−0.344384	+	0.938829i	$0.611912\pi$
$462$	−32.7402	−	32.3053i	−1.52321	−	1.50298i
$463$	−10.3899	−	20.3912i	−0.482857	−	0.947661i	−0.996000	−	0.0893575i	$-0.971519\pi$
$463$	−10.3899	−	20.3912i	−0.482857	−	0.947661i	0.513142	−	0.858304i	$-0.328481\pi$
$464$	−15.4371	−	13.8996i	−0.716647	−	0.645272i
$465$	4.30293	+	0.256769i	0.199544	+	0.0119074i
$466$	−27.9385	−	31.0288i	−1.29422	−	1.43738i
$467$	−5.61149	−	6.92961i	−0.259669	−	0.320664i	0.630593	−	0.776114i	$-0.282812\pi$
$467$	−5.61149	−	6.92961i	−0.259669	−	0.320664i	−0.890262	+	0.455450i	$0.849479\pi$
$468$	0.191702	+	0.191702i	0.00886142	+	0.00886142i
$469$	−0.446943	+	1.40750i	−0.0206379	+	0.0649922i
$470$	7.98219	−	5.71154i	0.368191	−	0.263453i
$471$	29.8315	+	13.2818i	1.37456	+	0.611994i
$472$	−8.93204	−	7.23302i	−0.411130	−	0.332927i
$473$	−38.4678	+	24.9813i	−1.76875	+	1.14864i
$474$	−34.1972	−	59.2314i	−1.57073	−	2.72059i
$475$	−8.99691	−	29.1182i	−0.412807	−	1.33603i
$476$	5.43263	+	1.11683i	0.249004	+	0.0511899i
$477$	23.8235	−	46.7562i	1.09080	−	2.14082i
$478$	0.984427	−	0.377886i	0.0450266	−	0.0172841i
$479$	−0.250187	−	2.38037i	−0.0114314	−	0.108762i	0.987318	−	0.158753i	$-0.0507474\pi$
$479$	−0.250187	−	2.38037i	−0.0114314	−	0.108762i	−0.998750	+	0.0499911i	$0.984081\pi$
$480$	−4.49114	+	20.4015i	−0.204992	+	0.931196i
$481$	−0.745601	−	0.0783658i	−0.0339965	−	0.00357317i
$482$	1.31543	−	1.31543i	0.0599161	−	0.0599161i
$483$	−20.4311	+	31.9265i	−0.929648	+	1.45270i
$484$	2.63308	+	0.855538i	0.119685	+	0.0388881i
$485$	1.14196	+	25.2936i	0.0518535	+	1.14852i
$486$	−6.31534	+	29.7113i	−0.286470	+	1.34773i
$487$	−0.253617	+	4.83930i	−0.0114925	+	0.219290i	0.986846	+	0.161664i	$0.0516862\pi$
$487$	−0.253617	+	4.83930i	−0.0114925	+	0.219290i	−0.998338	+	0.0576252i	$0.981647\pi$
$488$	13.3239	+	8.65266i	0.603146	+	0.391688i
$489$	−12.2414	−	37.6753i	−0.553577	−	1.70374i
$490$	−23.6215	+	9.23395i	−1.06711	+	0.417147i
$491$	−9.20020	+	28.3153i	−0.415199	+	1.27785i	0.496874	+	0.867823i	$0.334481\pi$
$491$	−9.20020	+	28.3153i	−0.415199	+	1.27785i	−0.912073	+	0.410029i	$0.865519\pi$
$492$	0.174033	−	0.140929i	0.00784602	−	0.00635358i
$493$	−13.8377	+	3.70780i	−0.623218	+	0.166991i
$494$	−0.390225	−	0.876459i	−0.0175570	−	0.0394337i
$495$	−7.86969	−	38.3890i	−0.353716	−	1.72546i
$496$	2.01583	+	2.77456i	0.0905136	+	0.124581i
$497$	−1.69814	−	2.06860i	−0.0761721	−	0.0927893i
$498$	42.6595	+	21.7361i	1.91162	+	0.974018i
$499$	33.6862	−	19.4488i	1.50800	−	0.870646i	0.508046	−	0.861330i	$-0.330368\pi$
$499$	33.6862	−	19.4488i	1.50800	−	0.870646i	0.999957	−	0.00931623i	$-0.00296549\pi$
$500$	−5.29724	+	4.56522i	−0.236900	+	0.204163i
$501$	2.28474	−	3.95729i	0.102075	−	0.176799i
$502$	1.17443	+	22.4095i	0.0524175	+	1.00019i
$503$	−37.4880	−	5.93752i	−1.67151	−	0.264741i	−0.752389	−	0.658719i	$-0.771098\pi$
$503$	−37.4880	−	5.93752i	−1.67151	−	0.264741i	−0.919120	+	0.393979i	$0.871098\pi$
$504$	−23.9475	+	10.8546i	−1.06671	+	0.483501i
$505$	24.8952	+	8.28877i	1.10782	+	0.368845i
$506$	3.48884	−	33.1941i	0.155098	−	1.47566i
$507$	9.18442	+	34.2767i	0.407894	+	1.52228i
$508$	−3.71203	+	9.67017i	−0.164695	+	0.429044i
$509$	−10.1538	+	2.15825i	−0.450057	+	0.0956626i	−0.427364	−	0.904080i	$-0.640558\pi$
$509$	−10.1538	+	2.15825i	−0.450057	+	0.0956626i	−0.0226937	+	0.999742i	$0.507224\pi$
$510$	23.2849	+	23.6246i	1.03107	+	1.04612i
$511$	−4.54494	+	3.34875i	−0.201056	+	0.148140i
$512$	4.47894	−	2.28214i	0.197943	−	0.100857i
$513$	−13.2579	+	20.4155i	−0.585353	+	0.901364i
$514$	0.577923	+	0.122841i	0.0254911	+	0.00541830i
$515$	12.1285	+	18.9757i	0.534446	+	0.836170i
$516$	−4.14848	−	19.5171i	−0.182627	−	0.859191i
$517$	−10.5090	+	1.66446i	−0.462184	+	0.0732027i
$518$	−14.8232	+	29.5794i	−0.651293	+	1.29964i
$519$	−0.451584	+	0.621552i	−0.0198223	+	0.0272831i
$520$	0.326306	−	0.357163i	0.0143095	−	0.0156626i
$521$	−11.9577	+	1.25680i	−0.523874	+	0.0550614i	−0.362775	−	0.931877i	$-0.618171\pi$
$521$	−11.9577	+	1.25680i	−0.523874	+	0.0550614i	−0.161099	+	0.986938i	$0.551504\pi$
$522$	−19.4484	+	24.0168i	−0.851233	+	1.05119i
$523$	−23.9442	+	1.25486i	−1.04701	+	0.0548713i	−0.568071	−	0.822979i	$-0.692310\pi$
$523$	−23.9442	+	1.25486i	−1.04701	+	0.0548713i	−0.478935	+	0.877850i	$0.658977\pi$
$524$	−0.251771			−0.0109987
$525$	−35.2872	−	7.78865i	−1.54006	−	0.339925i
$526$	−48.2012			−2.10167
$527$	2.36194	−	0.123784i	0.102888	−	0.00539212i
$528$	32.8128	−	40.5204i	1.42799	−	1.76343i
$529$	−4.48096	+	0.470968i	−0.194824	+	0.0204769i
$530$	38.8002	+	17.6128i	1.68537	+	0.765050i
$531$	−13.5344	+	18.6285i	−0.587342	+	0.808407i
$532$	−10.0692	+	0.595233i	−0.436554	+	0.0258066i
$533$	−0.0125753	+	0.00199173i	−0.000544695	+	8.62712e-5i
$534$	−0.923615	−	4.34527i	−0.0399687	−	0.188038i
$535$	0.150786	−	2.52687i	0.00651905	−	0.109246i
$536$	−1.21597	−	0.258462i	−0.0525217	−	0.0111638i
$537$	19.5099	−	30.0427i	0.841916	−	1.29644i
$538$	−29.9216	+	15.2458i	−1.29001	+	0.657294i
$539$	27.3789	+	2.50799i	1.17929	+	0.108027i
$540$	5.51033	+	0.913707i	0.237127	+	0.0393197i
$541$	18.7246	−	3.98003i	0.805031	−	0.171115i	0.213024	−	0.977047i	$-0.431669\pi$
$541$	18.7246	−	3.98003i	0.805031	−	0.171115i	0.592008	+	0.805932i	$0.298336\pi$
$542$	3.25552	−	8.48091i	0.139836	−	0.364286i
$543$	−16.2843	−	60.7737i	−0.698825	−	2.60805i
$544$	−1.19812	+	11.3994i	−0.0513690	+	0.488744i
$545$	3.88590	−	5.26783i	0.166454	−	0.225649i
$546$	−1.13212	−	0.111343i	−0.0484504	−	0.00476506i
$547$	−12.3236	−	1.95187i	−0.526919	−	0.0834558i	−0.112693	−	0.993630i	$-0.535948\pi$
$547$	−12.3236	−	1.95187i	−0.526919	−	0.0834558i	−0.414226	+	0.910174i	$0.635948\pi$
$548$	−0.414651	−	7.91201i	−0.0177130	−	0.337984i
$549$	15.9141	−	27.5641i	0.679199	−	1.17641i
$550$	30.8522	−	7.78967i	1.31554	−	0.332153i
$551$	22.5633	−	13.0269i	0.961230	−	0.554967i
$552$	−28.4300	−	14.4858i	−1.21006	−	0.616556i
$553$	38.2643	+	14.3955i	1.62716	+	0.612160i
$554$	5.63005	+	7.74910i	0.239198	+	0.329228i
$555$	−40.9951	+	23.2743i	−1.74015	+	0.987940i
$556$	3.66039	+	8.22138i	0.155235	+	0.348664i
$557$	21.9963	−	5.89390i	0.932014	−	0.249732i	0.239301	−	0.970946i	$-0.423082\pi$
$557$	21.9963	−	5.89390i	0.932014	−	0.249732i	0.692713	+	0.721213i	$0.256415\pi$
$558$	3.96515	−	3.21091i	0.167858	−	0.135929i
$559$	−0.350558	+	1.07891i	−0.0148270	+	0.0456329i
$560$	−13.0382	−	25.6242i	−0.550965	−	1.08282i
$561$	−11.1118	−	34.1985i	−0.469139	−	1.44386i
$562$	11.6258	+	7.54986i	0.490403	+	0.318472i
$563$	1.52735	−	29.1436i	0.0643701	−	1.22826i	−0.755284	−	0.655397i	$-0.772501\pi$
$563$	1.52735	−	29.1436i	0.0643701	−	1.22826i	0.819654	−	0.572858i	$-0.194165\pi$
$564$	0.962327	−	4.52739i	0.0405213	−	0.190638i
$565$	6.51535	+	8.16601i	0.274103	+	0.343547i
$566$	−23.2549	−	7.55597i	−0.977476	−	0.317601i
$567$	−3.01370	−	5.81822i	−0.126563	−	0.244342i
$568$	1.59307	−	1.59307i	0.0668436	−	0.0668436i
$569$	−1.57943	−	0.166005i	−0.0662130	−	0.00695927i	0.0713640	−	0.997450i	$-0.477265\pi$
$569$	−1.57943	−	0.166005i	−0.0662130	−	0.00695927i	−0.137577	+	0.990491i	$0.543931\pi$
$570$	−52.0247	−	30.5410i	−2.17907	−	1.27922i
$571$	−0.375690	−	3.57445i	−0.0157221	−	0.149586i	0.983844	−	0.179025i	$-0.0572945\pi$
$571$	−0.375690	−	3.57445i	−0.0157221	−	0.149586i	−0.999567	+	0.0294394i	$0.990628\pi$
$572$	0.222790	−	0.0855211i	0.00931532	−	0.00357582i
$573$	−5.01800	+	9.84838i	−0.209630	+	0.411422i
$574$	−0.113145	+	0.550374i	−0.00472258	+	0.0229722i
$575$	−11.5653	−	23.5348i	−0.482305	−	0.981468i
$576$	−9.32098	−	16.1444i	−0.388374	−	0.672683i
$577$	18.7335	−	12.1657i	0.779887	−	0.506465i	−0.0922444	−	0.995736i	$-0.529404\pi$
$577$	18.7335	−	12.1657i	0.779887	−	0.506465i	0.872131	+	0.489272i	$0.162737\pi$
$578$	−7.26245	−	5.88101i	−0.302078	−	0.244618i
$579$	7.67247	+	3.41601i	0.318857	+	0.141964i
$580$	−4.81091	−	3.54885i	−0.199762	−	0.147358i
$581$	−27.9531	+	6.13722i	−1.15969	+	0.254615i
$582$	35.4392	+	35.4392i	1.46900	+	1.46900i
$583$	−29.0692	−	35.8975i	−1.20392	−	1.48672i
$584$	−3.17991	−	3.53164i	−0.131585	−	0.146140i
$585$	−0.748781	−	0.615383i	−0.0309583	−	0.0254429i
$586$	13.2943	+	11.9702i	0.549182	+	0.494486i
$587$	19.7026	+	38.6684i	0.813211	+	1.59602i	0.802933	+	0.596070i	$0.203272\pi$
$587$	19.7026	+	38.6684i	0.813211	+	1.59602i	0.0102788	+	0.999947i	$0.496728\pi$
$588$	−5.28678	+	10.7282i	−0.218023	+	0.442422i
$589$	−4.09095	+	1.32923i	−0.168565	+	0.0547699i
$590$	−15.6067	−	10.2966i	−0.642519	−	0.423904i
$591$	25.6015	−	23.0517i	1.05310	−	0.948218i
$592$	−35.0148	−	13.4409i	−1.43910	−	0.552419i
$593$	−3.34701	+	12.4912i	−0.137445	+	0.512953i	0.862531	+	0.506005i	$0.168878\pi$
$593$	−3.34701	+	12.4912i	−0.137445	+	0.512953i	−0.999976	+	0.00694789i	$0.997788\pi$
$594$	−20.5621	−	14.9392i	−0.843673	−	0.612964i
$595$	−19.7180	−	2.08355i	−0.808361	−	0.0854171i
$596$	5.40284	−	3.92539i	0.221309	−	0.160790i
$597$	4.25833	+	11.0933i	0.174282	+	0.454019i
$598$	−0.449601	−	0.692325i	−0.0183855	−	0.0283113i
$599$	−19.9444	−	11.5149i	−0.814905	−	0.470485i	0.0337516	−	0.999430i	$-0.489255\pi$
$599$	−19.9444	−	11.5149i	−0.814905	−	0.470485i	−0.848656	+	0.528945i	$0.822588\pi$
$600$	3.61759	−	30.2038i	0.147687	−	1.23307i
$601$			14.0409i			0.572740i	0.958119	+	0.286370i	$0.0924486\pi$
$601$			14.0409i			0.572740i	−0.958119	+	0.286370i	$0.907551\pi$
$602$	39.1169	+	31.2456i	1.59429	+	1.27347i
$603$	−0.389602	+	2.45985i	−0.0158658	+	0.100173i
$604$	−5.31174	+	11.9304i	−0.216132	+	0.485440i
$605$	−9.66624	−	2.12791i	−0.392988	−	0.0865117i
$606$	47.4483	−	21.1254i	1.92746	−	0.858159i
$607$	38.2415	+	10.2468i	1.55218	+	0.415904i	0.930176	−	0.367113i	$-0.119654\pi$
$607$	38.2415	+	10.2468i	1.55218	+	0.415904i	0.622000	+	0.783017i	$0.286320\pi$
$608$	−3.26100	−	20.5892i	−0.132251	−	0.835001i
$609$	−0.206542	−	30.8920i	−0.00836952	−	1.25181i
$610$	22.9423	+	11.8997i	0.928906	+	0.481807i
$611$	−0.176085	+	0.195562i	−0.00712364	+	0.00791160i
$612$	9.34078	+	0.489529i	0.377579	+	0.0197881i
$613$	−3.87544	−	0.203103i	−0.156527	−	0.00820325i	−0.0260887	−	0.999660i	$-0.508305\pi$
$613$	−3.87544	−	0.203103i	−0.156527	−	0.00820325i	−0.130439	+	0.991456i	$0.541639\pi$
$614$	12.4826	−	13.8633i	0.503756	−	0.559478i
$615$	−0.570182	+	0.561982i	−0.0229920	+	0.0226613i
$616$	0.154736	+	23.1435i	0.00623450	+	0.932477i
$617$	−4.36290	−	27.5463i	−0.175644	−	1.10897i	−0.905180	−	0.425029i	$-0.860264\pi$
$617$	−4.36290	−	27.5463i	−0.175644	−	1.10897i	0.729536	−	0.683943i	$-0.239736\pi$
$618$	43.0597	+	11.5378i	1.73211	+	0.464118i
$619$	−24.6623	+	10.9803i	−0.991260	+	0.441337i	−0.837302	−	0.546740i	$-0.815869\pi$
$619$	−24.6623	+	10.9803i	−0.991260	+	0.441337i	−0.153958	+	0.988077i	$0.549202\pi$
$620$	0.655102	+	0.738248i	0.0263095	+	0.0296487i
$621$	−8.51918	+	19.1344i	−0.341863	+	0.767837i
$622$	−7.28427	+	45.9911i	−0.292073	+	1.84408i
$623$	2.07476	+	1.65726i	0.0831234	+	0.0663968i
$624$		−	1.28957i		−	0.0516239i
$625$	17.2594	−	18.0863i	0.690376	−	0.723451i
$626$	13.3561	+	7.71114i	0.533816	+	0.308199i
$627$	35.6174	+	54.8460i	1.42242	+	2.19034i
$628$	2.67950	+	6.98035i	0.106924	+	0.278546i
$629$	−20.9260	+	15.2037i	−0.834376	+	0.606209i
$630$	−37.0542	+	21.3657i	−1.47627	+	0.851232i
$631$	8.70119	+	6.32178i	0.346389	+	0.251666i	0.747353	−	0.664428i	$-0.231325\pi$
$631$	8.70119	+	6.32178i	0.346389	+	0.251666i	−0.400964	+	0.916094i	$0.631325\pi$
$632$	−8.90724	+	33.2423i	−0.354311	+	1.32231i
$633$	16.9995	+	6.52549i	0.675668	+	0.259365i
$634$	9.39921	−	8.46309i	0.373290	−	0.336112i
$635$	9.84298	−	35.6983i	0.390607	−	1.41664i
$636$	19.1105	−	6.20937i	0.757780	−	0.246217i
$637$	0.565284	−	0.377941i	0.0223974	−	0.0149746i
$638$	12.3498	+	24.2379i	0.488935	+	0.959589i
$639$	−3.35424	−	3.02018i	−0.132692	−	0.119476i
$640$	25.6418	−	16.3892i	1.01358	−	0.647840i
$641$	20.1580	+	22.3877i	0.796191	+	0.884260i	0.995411	−	0.0956947i	$-0.0305073\pi$
$641$	20.1580	+	22.3877i	0.796191	+	0.884260i	−0.199219	+	0.979955i	$0.563841\pi$
$642$	−3.15336	−	3.89407i	−0.124453	−	0.153687i
$643$	20.4056	+	20.4056i	0.804720	+	0.804720i	0.983829	−	0.179110i	$-0.0573217\pi$
$643$	20.4056	+	20.4056i	0.804720	+	0.804720i	−0.179110	+	0.983829i	$0.557322\pi$
$644$	−8.47706	+	1.86118i	−0.334043	+	0.0733407i
$645$	21.5510	+	67.9990i	0.848570	+	2.67746i
$646$	−30.2391	−	13.4633i	−1.18974	−	0.529707i
$647$	−14.8771	−	12.0473i	−0.584880	−	0.473627i	0.290624	−	0.956837i	$-0.406137\pi$
$647$	−14.8771	−	12.0473i	−0.584880	−	0.473627i	−0.875504	+	0.483211i	$0.839471\pi$
$648$	4.62594	−	3.00412i	0.181724	−	0.118013i
$649$	10.1343	+	17.5531i	0.397805	+	0.689019i
$650$	0.471764	−	0.629933i	0.0185041	−	0.0247080i
$651$	−1.02704	+	4.99588i	−0.0402531	+	0.195804i
$652$	4.11792	−	8.08188i	0.161270	−	0.316511i
$653$	−11.2686	+	4.32563i	−0.440976	+	0.169275i	−0.568718	−	0.822533i	$-0.692560\pi$
$653$	−11.2686	+	4.32563i	−0.440976	+	0.169275i	0.127742	+	0.991807i	$0.459227\pi$
$654$	−1.35443	−	12.8866i	−0.0529625	−	0.503905i
$655$	0.895811	−	0.0875989i	0.0350022	−	0.00342277i
$656$	−0.633461	−	0.0665794i	−0.0247325	−	0.00259949i
$657$	−6.73225	+	6.73225i	−0.262650	+	0.262650i
$658$	5.34145	+	10.3122i	0.208232	+	0.402010i
$659$	15.5052	+	5.03793i	0.603995	+	0.196250i	0.595022	−	0.803710i	$-0.297144\pi$
$659$	15.5052	+	5.03793i	0.603995	+	0.196250i	0.00897383	+	0.999960i	$0.497144\pi$
$660$	8.26356	−	12.5252i	0.321658	−	0.487544i
$661$	−2.91594	+	13.7184i	−0.113417	+	0.533585i	0.884352	+	0.466821i	$0.154601\pi$
$661$	−2.91594	+	13.7184i	−0.113417	+	0.533585i	−0.997769	+	0.0667642i	$0.978732\pi$
$662$	0.0877515	−	1.67440i	0.00341056	−	0.0650774i
$663$	−0.745871	−	0.484374i	−0.0289672	−	0.0188115i
$664$	−7.44463	−	22.9122i	−0.288908	−	0.889166i
$665$	35.6193	−	5.62123i	1.38126	−	0.217982i
$666$	−17.2426	+	53.0674i	−0.668138	+	2.05632i
$667$	17.4218	−	14.1079i	0.674574	−	0.546259i
$668$	1.01063	−	0.270798i	0.0391025	−	0.0104775i
$669$	17.1222	+	38.4571i	0.661983	+	1.48684i
$670$	−2.00965	−	0.225950i	−0.0776396	−	0.00872921i
$671$	−16.4678	−	22.6659i	−0.635731	−	0.875008i
$672$	−23.1343	−	8.70342i	−0.892426	−	0.335742i
$673$	−0.252552	−	0.128682i	−0.00973515	−	0.00496031i	0.449116	−	0.893473i	$-0.351739\pi$
$673$	−0.252552	−	0.128682i	−0.00973515	−	0.00496031i	−0.458851	+	0.888513i	$0.651739\pi$
$674$	2.62652	−	1.51642i	0.101170	−	0.0584103i
$675$	−19.9238	−	1.33379i	−0.766869	−	0.0513377i
$676$	−4.06262	+	7.03667i	−0.156255	+	0.270641i
$677$	1.75299	+	33.4491i	0.0673729	+	1.28555i	0.797951	+	0.602723i	$0.205917\pi$
$677$	1.75299	+	33.4491i	0.0673729	+	1.28555i	−0.730578	+	0.682829i	$0.760749\pi$
$678$	20.4242	+	3.23488i	0.784387	+	0.124235i
$679$	−29.8144	−	2.93222i	−1.14417	−	0.112528i
$680$	0.120883	−	16.6906i	0.00463566	−	0.640055i
$681$	−3.78337	+	35.9963i	−0.144979	+	1.37938i
$682$	−1.16240	−	4.33814i	−0.0445106	−	0.166116i
$683$	−8.10815	+	21.1225i	−0.310250	+	0.808228i	0.686460	+	0.727168i	$0.259164\pi$
$683$	−8.10815	+	21.1225i	−0.310250	+	0.808228i	−0.996709	+	0.0810601i	$0.974169\pi$
$684$	−16.6393	+	3.53680i	−0.636221	+	0.135233i
$685$	4.22817	+	28.0069i	0.161550	+	1.07009i
$686$	−6.82667	−	29.2221i	−0.260644	−	1.11571i
$687$	−10.0951	+	5.14374i	−0.385154	+	0.196246i
$688$	−30.9097	+	47.5968i	−1.17842	+	1.81461i
$689$	−1.11747	−	0.237526i	−0.0425724	−	0.00904903i
$690$	−48.3235	−	18.9523i	−1.83964	−	0.721503i
$691$	−5.91700	−	27.8373i	−0.225093	−	1.05898i	−0.934990	−	0.354674i	$-0.884592\pi$
$691$	−5.91700	−	27.8373i	−0.225093	−	1.05898i	0.709897	−	0.704306i	$-0.248742\pi$
$692$	−0.173748	+	0.0275190i	−0.00660492	+	0.00104612i
$693$	46.2863	−	2.73619i	1.75827	−	0.103939i
$694$	−1.89358	+	2.60628i	−0.0718792	+	0.0989332i
$695$	−15.8843	−	27.9784i	−0.602525	−	1.06128i
$696$	25.8629	−	2.71830i	0.980332	−	0.103037i
$697$	−0.276443	+	0.341379i	−0.0104710	+	0.0129307i
$698$	7.07139	−	0.370596i	0.267656	−	0.0140273i
$699$	70.3907			2.66242
$700$	−4.45221	−	6.97429i	−0.168278	−	0.263603i
$701$	29.7376			1.12317			0.561587	−	0.827418i	$-0.310191\pi$
$701$	29.7376			1.12317			0.561587	+	0.827418i	$0.310191\pi$
$702$	−0.627749	+	0.0328989i	−0.0236928	+	0.00124169i
$703$	29.6042	−	36.5582i	1.11654	−	1.37882i
$704$	−16.3196	+	1.71525i	−0.615067	+	0.0646461i
$705$	−1.84878	+	16.4434i	−0.0696289	+	0.619296i
$706$	17.7863	−	24.4807i	0.669396	−	0.921345i
$707$	−13.9094	+	27.7560i	−0.523118	+	1.04387i
$708$	−8.70856	+	1.37930i	−0.327288	+	0.0518373i
$709$	−1.79995	−	8.46811i	−0.0675986	−	0.318026i	0.931337	−	0.364159i	$-0.118644\pi$
$709$	−1.79995	−	8.46811i	−0.0675986	−	0.318026i	−0.998935	+	0.0461328i	$0.985310\pi$
$710$	2.32706	−	2.83151i	0.0873331	−	0.106265i
$711$	67.4409	+	14.3350i	2.52923	+	0.537605i
$712$	−1.21744	+	1.87469i	−0.0456254	+	0.0702569i
$713$	−3.29773	+	1.68028i	−0.123501	+	0.0629269i
$714$	−31.5976	+	23.2814i	−1.18251	+	0.871283i
$715$	−0.762939	+	0.381802i	−0.0285323	+	0.0142786i
$716$	8.02292	−	1.70532i	0.299830	−	0.0637309i
$717$	−0.637066	+	1.65961i	−0.0237917	+	0.0619794i
$718$	7.00926	+	26.1589i	0.261583	+	0.976242i
$719$	−2.82649	+	26.8922i	−0.105410	+	1.00291i	0.806141	+	0.591724i	$0.201552\pi$
$719$	−2.82649	+	26.8922i	−0.105410	+	1.00291i	−0.911551	+	0.411187i	$0.865114\pi$
$720$	−28.2152	−	39.4323i	−1.05152	−	1.46955i
$721$	−24.2700	+	11.0007i	−0.903863	+	0.409689i
$722$	29.0509	+	4.60121i	1.08116	+	0.171239i
$723$	0.164137	+	3.13192i	0.00610431	+	0.116477i
$724$	7.20316	−	12.4762i	0.267703	−	0.463676i
$725$	18.3521	+	10.9531i	0.681581	+	0.406786i
$726$	−16.9672	+	9.79602i	−0.629712	+	0.363565i
$727$	−15.5218	−	7.90873i	−0.575670	−	0.293318i	0.141814	−	0.989893i	$-0.454706\pi$
$727$	−15.5218	−	7.90873i	−0.575670	−	0.293318i	−0.717484	+	0.696575i	$0.754706\pi$
$728$	0.363198	+	0.442430i	0.0134610	+	0.0163976i
$729$	−25.7325	−	35.4177i	−0.953055	−	1.31177i
$730$	−5.70763	−	5.21452i	−0.211249	−	0.192998i
$731$	15.9195	+	35.7557i	0.588803	+	1.32247i
$732$	11.7724	−	3.15439i	0.435119	−	0.116590i
$733$	35.6797	−	28.8928i	1.31786	−	1.06718i	0.325275	−	0.945619i	$-0.394543\pi$
$733$	35.6797	−	28.8928i	1.31786	−	1.06718i	0.992584	−	0.121562i	$-0.0387902\pi$
$734$	−4.83698	+	14.8867i	−0.178536	+	0.549477i
$735$	15.0779	−	40.0106i	0.556157	−	1.47581i
$736$	−5.54266	−	17.0586i	−0.204305	−	0.628787i
$737$	1.83858	+	1.19399i	0.0677251	+	0.0439812i
$738$	−0.0495937	+	0.946304i	−0.00182557	+	0.0348339i
$739$	−5.11747	+	24.0758i	−0.188249	+	0.885642i	0.778046	+	0.628207i	$0.216211\pi$
$739$	−5.11747	+	24.0758i	−0.188249	+	0.885642i	−0.966296	+	0.257435i	$0.917123\pi$
$740$	−10.4057	−	2.86913i	−0.382520	−	0.105471i
$741$	1.53827	+	0.499813i	0.0565096	+	0.0183611i
$742$	−27.1761	+	42.4664i	−0.997665	+	1.55899i
$743$	−10.2323	+	10.2323i	−0.375388	+	0.375388i	−0.869435	−	0.494047i	$-0.835517\pi$
$743$	−10.2323	+	10.2323i	−0.375388	+	0.375388i	0.494047	+	0.869435i	$0.335517\pi$
$744$	−4.26995	−	0.448790i	−0.156544	−	0.0164534i
$745$	−17.8577	+	15.8465i	−0.654257	+	0.580571i
$746$	0.832965	+	7.92513i	0.0304970	+	0.290160i
$747$	−45.0593	+	17.2966i	−1.64863	+	0.632851i
$748$	3.73790	−	7.33605i	0.136671	−	0.268233i
$749$	2.93380	+	0.603126i	0.107199	+	0.0220377i
$750$	1.07513	−	49.4748i	0.0392581	−	1.80656i
$751$	5.60583	+	9.70959i	0.204560	+	0.354308i	0.949992	−	0.312273i	$-0.101090\pi$
$751$	5.60583	+	9.70959i	0.204560	+	0.354308i	−0.745433	+	0.666581i	$0.767757\pi$
$752$	−11.0411	+	7.17016i	−0.402627	+	0.261469i
$753$	−29.4005	−	23.8080i	−1.07141	−	0.867613i
$754$	0.614634	+	0.273653i	0.0223836	+	0.00996584i
$755$	14.7484	−	44.2968i	0.536750	−	1.61212i
$756$	−2.00020	+	6.29898i	−0.0727467	+	0.229092i
$757$	−34.2009	−	34.2009i	−1.24305	−	1.24305i	−0.958728	−	0.284326i	$-0.908230\pi$
$757$	−34.2009	−	34.2009i	−1.24305	−	1.24305i	−0.284326	−	0.958728i	$-0.591770\pi$
$758$	−12.8360	−	15.8511i	−0.466225	−	0.575740i
$759$	37.6514	+	41.8161i	1.36666	+	1.51783i
$760$	7.64399	+	29.3772i	0.277277	+	1.06562i
$761$	12.7666	+	11.4951i	0.462789	+	0.416697i	0.867261	−	0.497853i	$-0.165878\pi$
$761$	12.7666	+	11.4951i	0.462789	+	0.416697i	−0.404472	+	0.914550i	$0.632545\pi$
$762$	−33.2776	−	65.3109i	−1.20552	−	2.36597i
$763$	5.51328	+	5.44005i	0.199594	+	0.196943i
$764$	−2.40697	+	0.782073i	−0.0870812	+	0.0282944i
$765$	−33.4051	+	1.50818i	−1.20776	+	0.0545282i
$766$	21.5918	−	19.4414i	0.780145	−	0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.61811 + 0.0848016i) q^{2} +(1.71909 - 2.12290i) q^{3} +(0.622046 - 0.0653797i) q^{4} +(-2.19051 + 0.449052i) q^{5} +(-2.60166 + 3.58087i) q^{6} +(-0.156130 - 2.64114i) q^{7} +(2.19977 - 0.348409i) q^{8} +(-0.927701 - 4.36449i) q^{9} +O(q^{10})\)	\(q+(-1.61811 + 0.0848016i) q^{2} +(1.71909 - 2.12290i) q^{3} +(0.622046 - 0.0653797i) q^{4} +(-2.19051 + 0.449052i) q^{5} +(-2.60166 + 3.58087i) q^{6} +(-0.156130 - 2.64114i) q^{7} +(2.19977 - 0.348409i) q^{8} +(-0.927701 - 4.36449i) q^{9} +(3.50641 - 0.912375i) q^{10} +(-3.84181 - 0.816603i) q^{11} +(0.930561 - 1.43294i) q^{12} +(-0.0865535 + 0.0441012i) q^{13} +(0.476608 + 4.26042i) q^{14} +(-2.81240 + 5.42221i) q^{15} +(-4.75353 + 1.01039i) q^{16} +(-1.20108 + 3.12891i) q^{17} +(1.87124 + 6.98356i) q^{18} +(0.637130 - 6.06189i) q^{19} +(-1.33324 + 0.422546i) q^{20} +(-5.87529 - 4.20892i) q^{21} +(6.28573 + 0.995562i) q^{22} +(-0.274480 - 5.23739i) q^{23} +(3.04197 - 5.26884i) q^{24} +(4.59670 - 1.96731i) q^{25} +(0.136313 - 0.0787005i) q^{26} +(-3.55840 - 1.81310i) q^{27} +(-0.269797 - 1.63270i) q^{28} +(2.51245 + 3.45809i) q^{29} +(4.09097 - 9.01223i) q^{30} +(-0.287036 - 0.644694i) q^{31} +(3.30346 - 0.885159i) q^{32} +(-8.33800 + 6.75198i) q^{33} +(1.67814 - 5.16477i) q^{34} +(1.52801 + 5.71535i) q^{35} +(-0.862422 - 2.65426i) q^{36} +(6.47261 + 4.20336i) q^{37} +(-0.516889 + 9.86284i) q^{38} +(-0.0551709 + 0.259559i) q^{39} +(-4.66217 + 1.75101i) q^{40} +(0.124652 + 0.0405019i) q^{41} +(9.86378 + 6.31226i) q^{42} +(8.25770 - 8.25770i) q^{43} +(-2.44318 - 0.256788i) q^{44} +(3.99203 + 9.14389i) q^{45} +(0.888279 + 8.45141i) q^{46} +(2.52906 - 0.970816i) q^{47} +(-6.02679 + 11.8282i) q^{48} +(-6.95125 + 0.824720i) q^{49} +(-7.27115 + 3.57313i) q^{50} +(4.57761 + 7.92865i) q^{51} +(-0.0509570 + 0.0330918i) q^{52} +(9.13970 + 7.40118i) q^{53} +(5.91164 + 2.63203i) q^{54} +(8.78225 + 0.0636062i) q^{55} +(-1.26365 - 5.75550i) q^{56} +(-11.7735 - 11.7735i) q^{57} +(-4.35867 - 5.38252i) q^{58} +(-3.45304 - 3.83499i) q^{59} +(-1.39494 + 3.55674i) q^{60} +(5.30099 + 4.77304i) q^{61} +(0.519128 + 1.01885i) q^{62} +(-11.3824 + 3.13162i) q^{63} +(3.97346 - 1.29105i) q^{64} +(0.169793 - 0.135471i) q^{65} +(12.9192 - 11.6325i) q^{66} +(-0.521089 - 0.200027i) q^{67} +(-0.542557 + 2.02485i) q^{68} +(-11.5903 - 8.42087i) q^{69} +(-2.95716 - 9.11848i) q^{70} +(0.818370 - 0.594581i) q^{71} +(-3.56136 - 9.27765i) q^{72} +(-1.16213 - 1.78952i) q^{73} +(-10.8299 - 6.25262i) q^{74} +(3.72576 - 13.1403i) q^{75} -3.81243i q^{76} +(-1.55694 + 10.2743i) q^{77} +(0.0672616 - 0.424673i) q^{78} +(-6.28497 + 14.1163i) q^{79} +(9.95896 - 4.34787i) q^{80} +(2.26247 - 1.00731i) q^{81} +(-0.205136 - 0.0549659i) q^{82} +(-1.69214 - 10.6837i) q^{83} +(-3.92988 - 2.23402i) q^{84} +(1.22593 - 7.39326i) q^{85} +(-12.6616 + 14.0621i) q^{86} +(11.6603 + 0.611092i) q^{87} +(-8.73562 - 0.457814i) q^{88} +(-0.671570 + 0.745854i) q^{89} +(-7.23495 - 14.4573i) q^{90} +(0.129991 + 0.221714i) q^{91} +(-0.513159 - 3.23996i) q^{92} +(-1.86207 - 0.498939i) q^{93} +(-4.00998 + 1.78536i) q^{94} +(1.32646 + 13.5648i) q^{95} +(3.79985 - 8.53459i) q^{96} +(1.77133 - 11.1837i) q^{97} +(11.1779 - 1.92397i) q^{98} +17.5251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

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