LMFDB - Embedded newform 175.2.x.a.103.5

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			103.5
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.5

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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	−0.529192	−	0.848502i	$-0.677505\pi$
$2$	−1.61811	−	0.0848016i	−1.14418	−	0.0599638i	−0.614985	+	0.788539i	$0.710838\pi$
$3$	1.71909	+	2.12290i	0.992519	+	1.22566i	0.974167	+	0.225827i	$0.0725084\pi$
$3$	1.71909	+	2.12290i	0.992519	+	1.22566i	0.0183512	+	0.999832i	$0.494158\pi$
$4$	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	−0.746722	−	0.665137i	$-0.768373\pi$
$11$	−3.84181	+	0.816603i	−1.15835	+	0.246215i	−0.411629	+	0.911352i	$0.635040\pi$
$12$	0.930561	+	1.43294i	0.268630	+	0.413653i
$13$	−0.0865535	−	0.0441012i	−0.0240056	−	0.0122315i	0.441946	−	0.897041i	$-0.354288\pi$
$13$	−0.0865535	−	0.0441012i	−0.0240056	−	0.0122315i	−0.465952	+	0.884810i	$0.654288\pi$
$14$	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	−0.998647	−	0.0520016i	$-0.983440\pi$
$17$	−1.20108	−	3.12891i	−0.291304	−	0.758872i	0.707343	−	0.706870i	$-0.249893\pi$
$18$	1.87124	−	6.98356i	0.441055	−	1.64604i
$19$	0.637130	+	6.06189i	0.146168	+	1.39069i	0.784116	+	0.620614i	$0.213117\pi$
$19$	0.637130	+	6.06189i	0.146168	+	1.39069i	−0.637948	+	0.770079i	$0.720217\pi$
$20$	−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	0.807509	+	0.589856i	$0.200815\pi$
$23$	−0.274480	+	5.23739i	−0.0572331	+	1.09207i	−0.864742	+	0.502217i	$0.832518\pi$
$24$	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	−0.509301	−	0.860589i	$-0.670096\pi$
$29$	2.51245	−	3.45809i	0.466550	−	0.642152i	0.975851	+	0.218437i	$0.0700959\pi$
$30$	4.09097	+	9.01223i	0.746905	+	1.64540i
$31$	−0.287036	+	0.644694i	−0.0515533	+	0.115791i	−0.937486	−	0.348024i	$-0.886853\pi$
$31$	−0.287036	+	0.644694i	−0.0515533	+	0.115791i	0.885932	+	0.463814i	$0.153520\pi$
$32$	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	0.111033	−	0.993817i	$-0.464584\pi$
$37$	6.47261	−	4.20336i	1.06409	−	0.691029i	0.953058	+	0.302788i	$0.0979174\pi$
$38$	−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	−0.299267	−	0.954169i	$-0.596742\pi$
$41$	0.124652	−	0.0405019i	0.0194674	−	0.00632534i	0.318735	+	0.947844i	$0.396742\pi$
$42$	9.86378	−	6.31226i	1.52202	−	0.974003i
$43$	8.25770	+	8.25770i	1.25929	+	1.25929i	0.951434	+	0.307854i	$0.0996108\pi$
$43$	8.25770	+	8.25770i	1.25929	+	1.25929i	0.307854	+	0.951434i	$0.400389\pi$
$44$	−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	0.535755	−	0.844374i	$-0.320027\pi$
$47$	2.52906	+	0.970816i	0.368902	+	0.141608i	−0.166853	+	0.985982i	$0.553361\pi$
$48$	−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	0.256691	−	0.966493i	$-0.417368\pi$
$53$	9.13970	−	7.40118i	1.25543	−	1.01663i	0.998742	−	0.0501369i	$-0.0159658\pi$
$54$	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	−0.924735	−	0.380611i	$-0.875714\pi$
$59$	−3.45304	+	3.83499i	−0.449548	+	0.499273i	0.475188	+	0.879885i	$0.342380\pi$
$60$	−1.39494	−	3.55674i	−0.180086	−	0.459173i
$61$	5.30099	−	4.77304i	0.678723	−	0.611125i	−0.255926	−	0.966696i	$-0.582380\pi$
$61$	5.30099	−	4.77304i	0.678723	−	0.611125i	0.934649	+	0.355572i	$0.115714\pi$
$62$	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	−0.389990	−	0.920819i	$-0.627522\pi$
$67$	−0.521089	+	0.200027i	−0.0636611	+	0.0244372i	0.326329	+	0.945256i	$0.394188\pi$
$68$	−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	0.635287	−	0.772276i	$-0.280882\pi$
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	−0.538164	+	0.842840i	$0.680882\pi$
$72$	−3.56136	+	9.27765i	−0.419710	+	1.09338i
$73$	−1.16213	+	1.78952i	−0.136017	+	0.209448i	−0.900115	−	0.435652i	$-0.856518\pi$
$73$	−1.16213	+	1.78952i	−0.136017	+	0.209448i	0.764098	+	0.645100i	$0.223184\pi$
$74$	−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	−0.805184	−	0.593025i	$-0.797933\pi$
$79$	−6.28497	−	14.1163i	−0.707114	−	1.58820i	0.0980696	−	0.995180i	$-0.468733\pi$
$80$	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	0.701944	+	0.712232i	$0.252316\pi$
$83$	−1.69214	+	10.6837i	−0.185736	+	1.17269i	−0.887680	+	0.460461i	$0.847684\pi$
$84$	−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	0.706500	−	0.707713i	$-0.250273\pi$
$89$	−0.671570	−	0.745854i	−0.0711863	−	0.0790604i	−0.777686	+	0.628653i	$0.783607\pi$
$90$	−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	0.898113	+	0.439764i	$0.144938\pi$
$97$	1.77133	+	11.1837i	0.179851	+	1.13554i	−0.718262	+	0.695773i	$0.755062\pi$
$98$	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	−0.911538	−	0.411216i	$-0.865104\pi$
$101$	−10.1623	+	5.86718i	−1.01118	+	0.583807i	−0.0996449	+	0.995023i	$0.531771\pi$
$102$	−8.07944	+	12.4412i	−0.799983	+	1.23187i
$103$	−3.60931	+	9.40258i	−0.355636	+	0.926464i	0.632730	+	0.774372i	$0.281934\pi$
$103$	−3.60931	+	9.40258i	−0.355636	+	0.926464i	−0.988366	+	0.152092i	$0.951399\pi$
$104$	−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	0.950316	−	0.311287i	$-0.100760\pi$
$107$	−0.292999	−	1.09349i	−0.0283253	−	0.105711i	−0.978641	+	0.205576i	$0.934093\pi$
$108$	−2.33203	+	0.895182i	−0.224400	+	0.0861389i
$109$	−2.17553	−	1.95886i	−0.208378	−	0.187624i	0.558333	−	0.829617i	$-0.311441\pi$
$109$	−2.17553	−	1.95886i	−0.208378	−	0.187624i	−0.766711	+	0.641993i	$0.778108\pi$
$110$	−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	−0.968991	−	0.247097i	$-0.920523\pi$
$113$	−2.12100	+	4.16270i	−0.199527	+	0.391594i	0.769464	+	0.638690i	$0.220523\pi$
$114$	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	−0.937971	−	0.346713i	$-0.887298\pi$
$127$	−7.51832	−	14.7555i	−0.667143	−	1.30934i	0.270829	−	0.962628i	$-0.412702\pi$
$128$	−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	−0.122001	−	0.992530i	$-0.538931\pi$
$131$	−0.400325	+	0.0420758i	−0.0349765	+	0.00367618i	0.0870240	+	0.996206i	$0.472264\pi$
$132$	−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	0.868120	+	0.496354i	$0.165328\pi$
$137$	0.662940	+	12.6497i	0.0566388	+	1.08073i	−0.811481	+	0.584378i	$0.801338\pi$
$138$	19.4685	−	12.6430i	1.65727	−	1.07625i
$139$	4.44619	−	13.6840i	0.377121	−	1.16066i	−0.564915	−	0.825149i	$-0.691091\pi$
$139$	4.44619	−	13.6840i	0.377121	−	1.16066i	0.942036	−	0.335511i	$-0.108909\pi$
$140$	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	0.828404	−	0.560131i	$-0.189249\pi$
$149$	9.24670	+	5.33859i	0.757519	+	0.437354i	−0.0708851	+	0.997484i	$0.522582\pi$
$150$	−4.91436	−	21.5785i	−0.401256	−	1.76188i
$151$	−10.4396	−	18.0820i	−0.849565	−	1.47149i	−0.881597	−	0.472003i	$-0.843531\pi$
$151$	−10.4396	−	18.0820i	−0.849565	−	1.47149i	0.0320315	−	0.999487i	$-0.489802\pi$
$152$	−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	−0.725483	−	0.688241i	$-0.758383\pi$
$157$	3.09395	−	11.5468i	0.246924	−	0.921533i	0.972407	−	0.233293i	$-0.0749500\pi$
$158$	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	0.999607	+	0.0280333i	$0.00892443\pi$
$163$	7.89827	+	12.1623i	0.618640	+	0.952622i	−0.380967	+	0.924589i	$0.624409\pi$
$164$	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	0.220032	−	0.975493i	$-0.429384\pi$
$167$	1.65219	+	0.261681i	0.127850	+	0.0202495i	−0.0921813	+	0.995742i	$0.529384\pi$
$168$	−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	0.0416561	−	0.999132i	$-0.486737\pi$
$173$	−0.280864	−	0.0147195i	−0.0213537	−	0.00111910i	−0.0630098	+	0.998013i	$0.520070\pi$
$174$	−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	0.578506	−	0.815678i	$-0.303636\pi$
$179$	13.0417	+	1.37074i	0.974782	+	0.102454i	0.396275	+	0.918132i	$0.370303\pi$
$180$	3.08105	−	5.42693i	0.229648	−	0.404499i
$181$	13.5383	+	18.6338i	1.00629	+	1.38504i	0.921384	+	0.388653i	$0.127060\pi$
$181$	13.5383	+	18.6338i	1.00629	+	1.38504i	0.0849076	+	0.996389i	$0.472940\pi$
$182$	−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	0.0624813	−	0.998046i	$-0.480099\pi$
$191$	−3.95786	−	0.841270i	−0.286381	−	0.0608722i	−0.348862	+	0.937174i	$0.613432\pi$
$192$	4.08996	+	10.6547i	0.295167	+	0.768937i
$193$	0.795745	−	2.96976i	0.0572790	−	0.213768i	−0.931355	−	0.364114i	$-0.881372\pi$
$193$	0.795745	−	2.96976i	0.0572790	−	0.213768i	0.988634	+	0.150346i	$0.0480386\pi$
$194$	−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	0.303973	−	0.952681i	$-0.401687\pi$
$197$	12.4561	−	1.97286i	0.887464	−	0.140560i	0.583490	+	0.812120i	$0.301687\pi$
$198$	−1.48616	+	28.3576i	−0.105617	+	2.01529i
$199$	−2.17496	−	3.76715i	−0.154179	−	0.267046i	0.778581	−	0.627545i	$-0.215940\pi$
$199$	−2.17496	−	3.76715i	−0.154179	−	0.267046i	−0.932760	+	0.360498i	$0.882607\pi$
$200$	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	−0.854780	−	0.518991i	$-0.826308\pi$
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	0.996587	+	0.0825543i	$0.0263078\pi$
$212$	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	−0.997486	−	0.0708583i	$-0.977426\pi$
$223$	−6.99626	−	13.7309i	−0.468504	−	0.919491i	0.528982	−	0.848633i	$-0.322574\pi$
$224$	−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	0.120382	−	0.992728i	$-0.461588\pi$
$227$	−11.1124	−	7.21647i	−0.737556	−	0.478974i	−0.857938	+	0.513753i	$0.828255\pi$
$228$	−8.09342	+	6.55393i	−0.536000	+	0.434044i
$229$	−3.78909	+	1.68701i	−0.250390	+	0.111481i	−0.528094	−	0.849186i	$-0.677093\pi$
$229$	−3.78909	+	1.68701i	−0.250390	+	0.111481i	0.277704	+	0.960667i	$0.410426\pi$
$230$	−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	0.114464	−	0.993427i	$-0.463485\pi$
$233$	16.2166	−	20.0258i	1.06238	−	1.31194i	0.947920	−	0.318508i	$-0.103182\pi$
$234$	−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	0.288931	−	0.957350i	$-0.406700\pi$
$239$	−0.618920	−	0.201099i	−0.0400346	−	0.0130080i	−0.328966	+	0.944342i	$0.606700\pi$
$240$	7.89028	+	28.6163i	0.509315	+	1.84717i
$241$	−0.853202	−	0.768226i	−0.0549596	−	0.0494858i	0.641193	−	0.767379i	$-0.278440\pi$
$241$	−0.853202	−	0.768226i	−0.0549596	−	0.0494858i	−0.696153	+	0.717894i	$0.745106\pi$
$242$	−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	$0.143986\pi$
$251$			13.8492i			0.874153i	−0.899424	+	0.437076i	$0.856014\pi$
$252$	−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	−0.269788	−	0.962920i	$-0.586953\pi$
$257$	−0.352213	+	0.0943752i	−0.0219704	+	0.00588696i	0.247817	+	0.968807i	$0.420287\pi$
$258$	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	0.895049	−	0.445968i	$-0.147141\pi$
$263$	29.7070	−	1.55688i	1.83181	−	0.0960011i	0.936762	+	0.349967i	$0.113807\pi$
$264$	−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	0.892465	−	0.451117i	$-0.148974\pi$
$269$	18.9335	+	8.42973i	1.15439	+	0.513970i	0.261930	+	0.965087i	$0.415641\pi$
$270$	−14.1314	+	3.11087i	−0.860012	+	0.189321i
$271$	−2.28034	−	5.12174i	−0.138521	−	0.311123i	0.830943	−	0.556358i	$-0.187802\pi$
$271$	−2.28034	−	5.12174i	−0.138521	−	0.311123i	−0.969464	+	0.245235i	$0.921135\pi$
$272$	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	−0.922062	−	0.387042i	$-0.873497\pi$
$277$	−3.21957	+	4.95771i	−0.193445	+	0.297880i	0.728617	+	0.684922i	$0.240164\pi$
$278$	−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	−0.774769	−	0.632244i	$-0.782134\pi$
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	0.361883	+	0.932224i	$0.382134\pi$
$282$	−3.10338	−	11.5820i	−0.184804	−	0.689697i
$283$	14.0882	−	5.40796i	0.837458	−	0.321470i	0.0984291	−	0.995144i	$-0.468618\pi$
$283$	14.0882	−	5.40796i	0.837458	−	0.321470i	0.739028	+	0.673674i	$0.235285\pi$
$284$	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	−0.897366	−	0.441288i	$-0.854522\pi$
$293$	−7.80680	+	7.80680i	−0.456078	+	0.456078i	0.441288	+	0.897366i	$0.354522\pi$
$294$	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	0.435541	−	0.900169i	$-0.356557\pi$
$307$	−8.14095	−	8.14095i	−0.464628	−	0.464628i	−0.900169	+	0.435541i	$0.856557\pi$
$308$	−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	0.736504	+	0.676433i	$0.236475\pi$
$311$	5.97488	+	28.1096i	0.338804	+	1.59395i	−0.397700	+	0.917516i	$0.630192\pi$
$312$	−0.0309306	−	0.590191i	−0.00175110	−	0.0334130i
$313$	−7.98245	+	5.18386i	−0.451195	+	0.293009i	−0.750162	−	0.661254i	$-0.770025\pi$
$313$	−7.98245	+	5.18386i	−0.451195	+	0.293009i	0.298967	+	0.954263i	$0.403358\pi$
$314$	−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	0.443658	−	0.896196i	$-0.353680\pi$
$317$	−6.06620	−	4.91231i	−0.340712	−	0.275903i	−0.784370	+	0.620293i	$0.787014\pi$
$318$	−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	0.991147	−	0.132769i	$-0.0423868\pi$
$331$	−0.108165	−	1.02912i	−0.00594527	−	0.0565654i	−0.997092	+	0.0762035i	$0.975720\pi$
$332$	−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	0.407977	−	0.912992i	$-0.366235\pi$
$337$	−1.66773	−	0.849753i	−0.0908472	−	0.0462890i	−0.498824	+	0.866703i	$0.666235\pi$
$338$	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	0.809623	−	0.586950i	$-0.199672\pi$
$347$	1.25122	+	1.54512i	0.0671688	+	0.0829465i	−0.742454	+	0.669897i	$0.766338\pi$
$348$	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	0.361610	−	0.932330i	$-0.382227\pi$
$353$	−11.7526	−	14.5133i	−0.625529	−	0.772464i	−0.987139	+	0.159865i	$0.948894\pi$
$354$	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	0.786166	+	0.618016i	$0.212063\pi$
$359$	−3.47497	+	16.3485i	−0.183402	+	0.862838i	−0.969568	+	0.244823i	$0.921270\pi$
$360$	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	0.993775	−	0.111406i	$-0.0355356\pi$
$367$	3.46192	+	9.01861i	0.180711	+	0.470768i	−0.813064	+	0.582174i	$0.802202\pi$
$368$	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	0.983839	+	0.179058i	$0.0573049\pi$
$373$	−0.257388	+	4.91126i	−0.0133271	+	0.254295i	−0.997166	+	0.0752376i	$0.976028\pi$
$374$	−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	−0.575540	−	0.817774i	$-0.695208\pi$
$379$	7.39900	−	10.1839i	0.380061	−	0.523109i	0.955601	+	0.294665i	$0.0952079\pi$
$380$	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	0.203366	−	0.979103i	$-0.434812\pi$
$383$	−13.9353	−	11.2845i	−0.712058	−	0.576613i	−0.915425	+	0.402489i	$0.868145\pi$
$384$	−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	−0.995229	−	0.0975672i	$-0.968894\pi$
$389$	−2.47971	−	11.6661i	−0.125726	−	0.591495i	0.869503	−	0.493928i	$-0.164439\pi$
$390$	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	0.999737	+	0.0229366i	$0.00730159\pi$
$397$	35.0286	+	13.4462i	1.75803	+	0.674846i	0.758297	+	0.651909i	$0.226032\pi$
$398$	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	−0.863348	−	0.504609i	$-0.831637\pi$
$401$	0.106730	−	0.184861i	0.00532982	−	0.00923152i	0.868678	+	0.495377i	$0.164970\pi$
$402$	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	0.0725340	−	0.997366i	$-0.476891\pi$
$409$	21.3736	−	23.7377i	1.05685	−	1.17376i	0.984320	−	0.176390i	$-0.0564419\pi$
$410$	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	−0.358269	−	0.933618i	$-0.616633\pi$
$419$	8.57555	−	6.23050i	0.418943	−	0.304380i	0.777212	+	0.629238i	$0.216633\pi$
$420$	9.61164	−	3.12893i	0.469000	−	0.152676i
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	0.747762	−	0.663966i	$-0.231128\pi$
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	−0.400398	+	0.916341i	$0.631128\pi$
$422$	−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	0.537116	−	0.843508i	$-0.319514\pi$
$431$	5.59847	+	2.49260i	0.269669	+	0.120064i	−0.267448	+	0.963572i	$0.586180\pi$
$432$	18.7469	−	5.02322i	0.901961	−	0.241680i
$433$	−5.58866	+	35.2854i	−0.268574	+	1.69571i	0.372339	+	0.928097i	$0.378556\pi$
$433$	−5.58866	+	35.2854i	−0.268574	+	1.69571i	−0.640913	+	0.767613i	$0.721444\pi$
$434$	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	0.165347	−	0.986235i	$-0.447126\pi$
$439$	−17.4485	−	19.3785i	−0.832769	−	0.924884i	−0.998116	+	0.0613516i	$0.980459\pi$
$440$	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	0.623508	−	0.781817i	$-0.285707\pi$
$443$	32.7161	−	8.76626i	1.55439	−	0.416498i	0.930882	+	0.365319i	$0.119040\pi$
$444$	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	$-0.861820\pi$
$449$		−	17.8247i		−	0.841199i	0.907246	−	0.420600i	$-0.138180\pi$
$450$	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	0.894849	−	0.446370i	$-0.147283\pi$
$457$	−2.20826	−	8.24133i	−0.103298	−	0.385513i	−0.998147	+	0.0608568i	$0.980617\pi$
$458$	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	−0.344384	−	0.938829i	$-0.611912\pi$
$461$	−25.2246	−	8.19596i	−1.17483	−	0.381724i	−0.830442	+	0.557105i	$0.811912\pi$
$462$	−32.7402	+	32.3053i	−1.52321	+	1.50298i
$463$	−10.3899	+	20.3912i	−0.482857	+	0.947661i	0.513142	+	0.858304i	$0.328481\pi$
$463$	−10.3899	+	20.3912i	−0.482857	+	0.947661i	−0.996000	+	0.0893575i	$0.971519\pi$
$464$	−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	−0.890262	−	0.455450i	$-0.849479\pi$
$467$	−5.61149	+	6.92961i	−0.259669	+	0.320664i	0.630593	+	0.776114i	$0.282812\pi$
$468$	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	−0.998750	−	0.0499911i	$-0.984081\pi$
$479$	−0.250187	+	2.38037i	−0.0114314	+	0.108762i	0.987318	+	0.158753i	$0.0507474\pi$
$480$	−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	−0.998338	−	0.0576252i	$-0.981647\pi$
$487$	−0.253617	−	4.83930i	−0.0114925	−	0.219290i	0.986846	−	0.161664i	$-0.0516862\pi$
$488$	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	−0.912073	−	0.410029i	$-0.865519\pi$
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	0.496874	−	0.867823i	$-0.334481\pi$
$492$	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	0.999957	+	0.00931623i	$0.00296549\pi$
$499$	33.6862	+	19.4488i	1.50800	+	0.870646i	0.508046	+	0.861330i	$0.330368\pi$
$500$	−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	−0.919120	−	0.393979i	$-0.871098\pi$
$503$	−37.4880	+	5.93752i	−1.67151	+	0.264741i	−0.752389	+	0.658719i	$0.771098\pi$
$504$	−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	−0.0226937	−	0.999742i	$-0.507224\pi$
$509$	−10.1538	−	2.15825i	−0.450057	−	0.0956626i	−0.427364	+	0.904080i	$0.640558\pi$
$510$	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	−0.161099	−	0.986938i	$-0.551504\pi$
$521$	−11.9577	−	1.25680i	−0.523874	−	0.0550614i	−0.362775	+	0.931877i	$0.618171\pi$
$522$	−19.4484	−	24.0168i	−0.851233	−	1.05119i
$523$	−23.9442	−	1.25486i	−1.04701	−	0.0548713i	−0.478935	−	0.877850i	$-0.658977\pi$
$523$	−23.9442	−	1.25486i	−1.04701	−	0.0548713i	−0.568071	+	0.822979i	$0.692310\pi$
$524$	−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	0.592008	−	0.805932i	$-0.298336\pi$
$541$	18.7246	+	3.98003i	0.805031	+	0.171115i	0.213024	+	0.977047i	$0.431669\pi$
$542$	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	−0.414226	−	0.910174i	$-0.635948\pi$
$547$	−12.3236	+	1.95187i	−0.526919	+	0.0834558i	−0.112693	+	0.993630i	$0.535948\pi$
$548$	−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	0.692713	−	0.721213i	$-0.256415\pi$
$557$	21.9963	+	5.89390i	0.932014	+	0.249732i	0.239301	+	0.970946i	$0.423082\pi$
$558$	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	0.819654	+	0.572858i	$0.194165\pi$
$563$	1.52735	+	29.1436i	0.0643701	+	1.22826i	−0.755284	+	0.655397i	$0.772501\pi$
$564$	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	−0.137577	−	0.990491i	$-0.543931\pi$
$569$	−1.57943	+	0.166005i	−0.0662130	+	0.00695927i	0.0713640	+	0.997450i	$0.477265\pi$
$570$	−52.0247	+	30.5410i	−2.17907	+	1.27922i
$571$	−0.375690	+	3.57445i	−0.0157221	+	0.149586i	−0.999567	−	0.0294394i	$-0.990628\pi$
$571$	−0.375690	+	3.57445i	−0.0157221	+	0.149586i	0.983844	+	0.179025i	$0.0572945\pi$
$572$	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	0.872131	−	0.489272i	$-0.162737\pi$
$577$	18.7335	+	12.1657i	0.779887	+	0.506465i	−0.0922444	+	0.995736i	$0.529404\pi$
$578$	−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	0.0102788	−	0.999947i	$-0.496728\pi$
$587$	19.7026	−	38.6684i	0.813211	−	1.59602i	0.802933	−	0.596070i	$-0.203272\pi$
$588$	−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	−0.999976	−	0.00694789i	$-0.997788\pi$
$593$	−3.34701	−	12.4912i	−0.137445	−	0.512953i	0.862531	−	0.506005i	$-0.168878\pi$
$594$	−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	−0.848656	−	0.528945i	$-0.822588\pi$
$599$	−19.9444	+	11.5149i	−0.814905	+	0.470485i	0.0337516	+	0.999430i	$0.489255\pi$
$600$	3.61759	+	30.2038i	0.147687	+	1.23307i
$601$		−	14.0409i		−	0.572740i	−0.958119	−	0.286370i	$-0.907551\pi$
$601$		−	14.0409i		−	0.572740i	0.958119	−	0.286370i	$-0.0924486\pi$
$602$	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	0.622000	−	0.783017i	$-0.286320\pi$
$607$	38.2415	−	10.2468i	1.55218	−	0.415904i	0.930176	+	0.367113i	$0.119654\pi$
$608$	−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	−0.130439	−	0.991456i	$-0.541639\pi$
$613$	−3.87544	+	0.203103i	−0.156527	+	0.00820325i	−0.0260887	+	0.999660i	$0.508305\pi$
$614$	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	0.729536	+	0.683943i	$0.239736\pi$
$617$	−4.36290	+	27.5463i	−0.175644	+	1.10897i	−0.905180	+	0.425029i	$0.860264\pi$
$618$	43.0597	−	11.5378i	1.73211	−	0.464118i
$619$	−24.6623	−	10.9803i	−0.991260	−	0.441337i	−0.153958	−	0.988077i	$-0.549202\pi$
$619$	−24.6623	−	10.9803i	−0.991260	−	0.441337i	−0.837302	+	0.546740i	$0.815869\pi$
$620$	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	−0.400964	−	0.916094i	$-0.631325\pi$
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	0.747353	+	0.664428i	$0.231325\pi$
$632$	−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	−0.199219	−	0.979955i	$-0.563841\pi$
$641$	20.1580	−	22.3877i	0.796191	−	0.884260i	0.995411	+	0.0956947i	$0.0305073\pi$
$642$	−3.15336	+	3.89407i	−0.124453	+	0.153687i
$643$	20.4056	−	20.4056i	0.804720	−	0.804720i	−0.179110	−	0.983829i	$-0.557322\pi$
$643$	20.4056	−	20.4056i	0.804720	−	0.804720i	0.983829	+	0.179110i	$0.0573217\pi$
$644$	−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	−0.875504	−	0.483211i	$-0.839471\pi$
$647$	−14.8771	+	12.0473i	−0.584880	+	0.473627i	0.290624	+	0.956837i	$0.406137\pi$
$648$	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	0.127742	−	0.991807i	$-0.459227\pi$
$653$	−11.2686	−	4.32563i	−0.440976	−	0.169275i	−0.568718	+	0.822533i	$0.692560\pi$
$654$	−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	0.00897383	−	0.999960i	$-0.497144\pi$
$659$	15.5052	−	5.03793i	0.603995	−	0.196250i	0.595022	+	0.803710i	$0.297144\pi$
$660$	8.26356	+	12.5252i	0.321658	+	0.487544i
$661$	−2.91594	−	13.7184i	−0.113417	−	0.533585i	−0.997769	−	0.0667642i	$-0.978732\pi$
$661$	−2.91594	−	13.7184i	−0.113417	−	0.533585i	0.884352	−	0.466821i	$-0.154601\pi$
$662$	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	−0.458851	−	0.888513i	$-0.651739\pi$
$673$	−0.252552	+	0.128682i	−0.00973515	+	0.00496031i	0.449116	+	0.893473i	$0.351739\pi$
$674$	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	−0.730578	−	0.682829i	$-0.760749\pi$
$677$	1.75299	−	33.4491i	0.0673729	−	1.28555i	0.797951	−	0.602723i	$-0.205917\pi$
$678$	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	−0.996709	−	0.0810601i	$-0.974169\pi$
$683$	−8.10815	−	21.1225i	−0.310250	−	0.808228i	0.686460	−	0.727168i	$-0.259164\pi$
$684$	−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	0.709897	+	0.704306i	$0.248742\pi$
$691$	−5.91700	+	27.8373i	−0.225093	+	1.05898i	−0.934990	+	0.354674i	$0.884592\pi$
$692$	−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	−0.998935	−	0.0461328i	$-0.985310\pi$
$709$	−1.79995	+	8.46811i	−0.0675986	+	0.318026i	0.931337	+	0.364159i	$0.118644\pi$
$710$	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	−0.911551	−	0.411187i	$-0.865114\pi$
$719$	−2.82649	−	26.8922i	−0.105410	−	1.00291i	0.806141	−	0.591724i	$-0.201552\pi$
$720$	−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	−0.717484	−	0.696575i	$-0.754706\pi$
$727$	−15.5218	+	7.90873i	−0.575670	+	0.293318i	0.141814	+	0.989893i	$0.454706\pi$
$728$	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	0.992584	+	0.121562i	$0.0387902\pi$
$733$	35.6797	+	28.8928i	1.31786	+	1.06718i	0.325275	+	0.945619i	$0.394543\pi$
$734$	−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	−0.966296	−	0.257435i	$-0.917123\pi$
$739$	−5.11747	−	24.0758i	−0.188249	−	0.885642i	0.778046	−	0.628207i	$-0.216211\pi$
$740$	−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	0.494047	−	0.869435i	$-0.335517\pi$
$743$	−10.2323	−	10.2323i	−0.375388	−	0.375388i	−0.869435	+	0.494047i	$0.835517\pi$
$744$	−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	−0.745433	−	0.666581i	$-0.767757\pi$
$751$	5.60583	−	9.70959i	0.204560	−	0.354308i	0.949992	+	0.312273i	$0.101090\pi$
$752$	−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	−0.284326	+	0.958728i	$0.591770\pi$
$757$	−34.2009	+	34.2009i	−1.24305	+	1.24305i	−0.958728	+	0.284326i	$0.908230\pi$
$758$	−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	−0.404472	−	0.914550i	$-0.632545\pi$
$761$	12.7666	−	11.4951i	0.462789	−	0.416697i	0.867261	+	0.497853i	$0.165878\pi$
$762$	−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

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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