LMFDB - Embedded newform 650.2.e.h.601.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(451,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.451"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$1.58114 + 2.73861i$ of defining polynomial
Character	$\chi$	$=$	650.601
Dual form			650.2.e.h.451.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.58114 - 2.73861i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.58114 - 2.73861i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.50000 + 6.06218i) q^{9} +(2.08114 + 3.60464i) q^{11} +3.16228 q^{12} +(-0.0811388 + 3.60464i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.581139 - 1.00656i) q^{17} -7.00000 q^{18} +(4.08114 - 7.06874i) q^{19} +3.16228 q^{21} +(-2.08114 + 3.60464i) q^{22} +(3.00000 + 5.19615i) q^{23} +(1.58114 + 2.73861i) q^{24} +(-3.16228 + 1.73205i) q^{26} +12.6491 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.16228 + 2.01312i) q^{29} +0.837722 q^{31} +(0.500000 - 0.866025i) q^{32} +(6.58114 - 11.3989i) q^{33} +1.16228 q^{34} +(-3.50000 - 6.06218i) q^{36} +(3.08114 + 5.33669i) q^{37} +8.16228 q^{38} +(10.0000 - 5.47723i) q^{39} +(-1.16228 - 2.01312i) q^{41} +(1.58114 + 2.73861i) q^{42} +(1.00000 - 1.73205i) q^{43} -4.16228 q^{44} +(-3.00000 + 5.19615i) q^{46} +3.00000 q^{47} +(-1.58114 + 2.73861i) q^{48} +(3.00000 + 5.19615i) q^{49} -3.67544 q^{51} +(-3.08114 - 1.87259i) q^{52} -4.16228 q^{53} +(6.32456 + 10.9545i) q^{54} +(0.500000 - 0.866025i) q^{56} -25.8114 q^{57} +(-1.16228 + 2.01312i) q^{58} +(-1.16228 + 2.01312i) q^{59} +(-5.74342 + 9.94789i) q^{61} +(0.418861 + 0.725489i) q^{62} +(-3.50000 - 6.06218i) q^{63} +1.00000 q^{64} +13.1623 q^{66} +(5.16228 + 8.94133i) q^{67} +(0.581139 + 1.00656i) q^{68} +(9.48683 - 16.4317i) q^{69} +(-4.16228 + 7.20928i) q^{71} +(3.50000 - 6.06218i) q^{72} -9.16228 q^{73} +(-3.08114 + 5.33669i) q^{74} +(4.08114 + 7.06874i) q^{76} -4.16228 q^{77} +(9.74342 + 5.92164i) q^{78} +5.48683 q^{79} +(-9.50000 - 16.4545i) q^{81} +(1.16228 - 2.01312i) q^{82} +9.48683 q^{83} +(-1.58114 + 2.73861i) q^{84} +2.00000 q^{86} +(3.67544 - 6.36606i) q^{87} +(-2.08114 - 3.60464i) q^{88} +(-2.66228 - 4.61120i) q^{89} +(-3.08114 - 1.87259i) q^{91} -6.00000 q^{92} +(-1.32456 - 2.29420i) q^{93} +(1.50000 + 2.59808i) q^{94} -3.16228 q^{96} +(5.74342 - 9.94789i) q^{97} +(-3.00000 + 5.19615i) q^{98} -29.1359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{7} - 4 q^{8} - 14 q^{9} + 2 q^{11} + 6 q^{13} - 4 q^{14} - 2 q^{16} - 4 q^{17} - 28 q^{18} + 10 q^{19} - 2 q^{22} + 12 q^{23} - 2 q^{28} - 8 q^{29} + 16 q^{31} + 2 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^7 - 4 * q^8 - 14 * q^9 + 2 * q^11 + 6 * q^13 - 4 * q^14 - 2 * q^16 - 4 * q^17 - 28 * q^18 + 10 * q^19 - 2 * q^22 + 12 * q^23 - 2 * q^28 - 8 * q^29 + 16 * q^31 + 2 * q^32 + 20 * q^33 - 8 * q^34 - 14 * q^36 + 6 * q^37 + 20 * q^38 + 40 * q^39 + 8 * q^41 + 4 * q^43 - 4 * q^44 - 12 * q^46 + 12 * q^47 + 12 * q^49 - 40 * q^51 - 6 * q^52 - 4 * q^53 + 2 * q^56 - 40 * q^57 + 8 * q^58 + 8 * q^59 - 4 * q^61 + 8 * q^62 - 14 * q^63 + 4 * q^64 + 40 * q^66 + 8 * q^67 - 4 * q^68 - 4 * q^71 + 14 * q^72 - 24 * q^73 - 6 * q^74 + 10 * q^76 - 4 * q^77 + 20 * q^78 - 16 * q^79 - 38 * q^81 - 8 * q^82 + 8 * q^86 + 40 * q^87 - 2 * q^88 + 2 * q^89 - 6 * q^91 - 24 * q^92 + 20 * q^93 + 6 * q^94 + 4 * q^97 - 12 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.58114	−	2.73861i	−0.912871	−	1.58114i	−0.809989	−	0.586445i	$-0.800527\pi$
$3$	−1.58114	−	2.73861i	−0.912871	−	1.58114i	−0.102882	−	0.994694i	$-0.532806\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.58114	−	2.73861i	0.645497	−	1.11803i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000			−0.353553
$9$	−3.50000	+	6.06218i	−1.16667	+	2.02073i
$10$		0			0
$11$	2.08114	+	3.60464i	0.627487	+	1.08684i	0.988054	+	0.154106i	$0.0492498\pi$
$11$	2.08114	+	3.60464i	0.627487	+	1.08684i	−0.360567	+	0.932733i	$0.617417\pi$
$12$	3.16228			0.912871
$13$	−0.0811388	+	3.60464i	−0.0225039	+	0.999747i
$13$	−0.0811388	+	3.60464i	−0.0225039	+	0.999747i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.581139	−	1.00656i	0.140947	−	0.244127i	−0.786907	−	0.617072i	$-0.788319\pi$
$17$	0.581139	−	1.00656i	0.140947	−	0.244127i	0.927853	+	0.372945i	$0.121652\pi$
$18$	−7.00000			−1.64992
$19$	4.08114	−	7.06874i	0.936277	−	1.62168i	0.163937	−	0.986471i	$-0.447580\pi$
$19$	4.08114	−	7.06874i	0.936277	−	1.62168i	0.772340	−	0.635209i	$-0.219086\pi$
$20$		0			0
$21$	3.16228			0.690066
$22$	−2.08114	+	3.60464i	−0.443700	+	0.768511i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	1.58114	+	2.73861i	0.322749	+	0.559017i
$25$		0			0
$26$	−3.16228	+	1.73205i	−0.620174	+	0.339683i
$27$	12.6491			2.43432
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	1.16228	+	2.01312i	0.215830	+	0.373828i	0.953529	−	0.301302i	$-0.0974211\pi$
$29$	1.16228	+	2.01312i	0.215830	+	0.373828i	−0.737699	+	0.675129i	$0.764088\pi$
$30$		0			0
$31$	0.837722			0.150459			0.0752297	−	0.997166i	$-0.476031\pi$
$31$	0.837722			0.150459			0.0752297	+	0.997166i	$0.476031\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	6.58114	−	11.3989i	1.14563	−	1.98429i
$34$	1.16228			0.199329
$35$		0			0
$36$	−3.50000	−	6.06218i	−0.583333	−	1.01036i
$37$	3.08114	+	5.33669i	0.506536	+	0.877346i	0.999971	+	0.00756376i	$0.00240764\pi$
$37$	3.08114	+	5.33669i	0.506536	+	0.877346i	−0.493435	+	0.869783i	$0.664259\pi$
$38$	8.16228			1.32410
$39$	10.0000	−	5.47723i	1.60128	−	0.877058i
$40$		0			0
$41$	−1.16228	−	2.01312i	−0.181517	−	0.314397i	0.760880	−	0.648892i	$-0.224767\pi$
$41$	−1.16228	−	2.01312i	−0.181517	−	0.314397i	−0.942397	+	0.334495i	$0.891434\pi$
$42$	1.58114	+	2.73861i	0.243975	+	0.422577i
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$	−4.16228			−0.627487
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.58114	+	2.73861i	−0.228218	+	0.395285i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$		0			0
$51$	−3.67544			−0.514665
$52$	−3.08114	−	1.87259i	−0.427277	−	0.259681i
$53$	−4.16228			−0.571733			−0.285866	−	0.958269i	$-0.592281\pi$
$53$	−4.16228			−0.571733			−0.285866	+	0.958269i	$0.592281\pi$
$54$	6.32456	+	10.9545i	0.860663	+	1.49071i
$55$		0			0
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−25.8114			−3.41880
$58$	−1.16228	+	2.01312i	−0.152615	+	0.264336i
$59$	−1.16228	+	2.01312i	−0.151316	+	0.262086i	−0.931711	−	0.363200i	$-0.881684\pi$
$59$	−1.16228	+	2.01312i	−0.151316	+	0.262086i	0.780396	+	0.625286i	$0.215018\pi$
$60$		0			0
$61$	−5.74342	+	9.94789i	−0.735369	+	1.27370i	0.219192	+	0.975682i	$0.429658\pi$
$61$	−5.74342	+	9.94789i	−0.735369	+	1.27370i	−0.954561	+	0.298015i	$0.903675\pi$
$62$	0.418861	+	0.725489i	0.0531954	+	0.0921372i
$63$	−3.50000	−	6.06218i	−0.440959	−	0.763763i
$64$	1.00000			0.125000
$65$		0			0
$66$	13.1623			1.62016
$67$	5.16228	+	8.94133i	0.630673	+	1.09236i	0.987414	+	0.158154i	$0.0505542\pi$
$67$	5.16228	+	8.94133i	0.630673	+	1.09236i	−0.356742	+	0.934203i	$0.616112\pi$
$68$	0.581139	+	1.00656i	0.0704734	+	0.122064i
$69$	9.48683	−	16.4317i	1.14208	−	1.97814i
$70$		0			0
$71$	−4.16228	+	7.20928i	−0.493971	+	0.855584i	−0.999976	−	0.00694720i	$-0.997789\pi$
$71$	−4.16228	+	7.20928i	−0.493971	+	0.855584i	0.506004	+	0.862531i	$0.331122\pi$
$72$	3.50000	−	6.06218i	0.412479	−	0.714435i
$73$	−9.16228			−1.07236			−0.536182	−	0.844103i	$-0.680134\pi$
$73$	−9.16228			−1.07236			−0.536182	+	0.844103i	$0.680134\pi$
$74$	−3.08114	+	5.33669i	−0.358175	+	0.620377i
$75$		0			0
$76$	4.08114	+	7.06874i	0.468139	+	0.810840i
$77$	−4.16228			−0.474336
$78$	9.74342	+	5.92164i	1.10322	+	0.670494i
$79$	5.48683			0.617317			0.308658	−	0.951173i	$-0.400120\pi$
$79$	5.48683			0.617317			0.308658	+	0.951173i	$0.400120\pi$
$80$		0			0
$81$	−9.50000	−	16.4545i	−1.05556	−	1.82828i
$82$	1.16228	−	2.01312i	0.128352	−	0.222312i
$83$	9.48683			1.04132			0.520658	−	0.853766i	$-0.325687\pi$
$83$	9.48683			1.04132			0.520658	+	0.853766i	$0.325687\pi$
$84$	−1.58114	+	2.73861i	−0.172516	+	0.298807i
$85$		0			0
$86$	2.00000			0.215666
$87$	3.67544	−	6.36606i	0.394049	−	0.682513i
$88$	−2.08114	−	3.60464i	−0.221850	−	0.384256i
$89$	−2.66228	−	4.61120i	−0.282201	−	0.488786i	0.689726	−	0.724071i	$-0.257731\pi$
$89$	−2.66228	−	4.61120i	−0.282201	−	0.488786i	−0.971927	+	0.235285i	$0.924398\pi$
$90$		0			0
$91$	−3.08114	−	1.87259i	−0.322991	−	0.196300i
$92$	−6.00000			−0.625543
$93$	−1.32456	−	2.29420i	−0.137350	−	0.237897i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	−3.16228			−0.322749
$97$	5.74342	−	9.94789i	0.583156	−	1.01006i	−0.411947	−	0.911208i	$-0.635151\pi$
$97$	5.74342	−	9.94789i	0.583156	−	1.01006i	0.995103	−	0.0988473i	$-0.0315155\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−29.1359			−2.92827
$100$		0			0
$101$	2.41886	+	4.18959i	0.240686	+	0.416880i	0.960910	−	0.276862i	$-0.0892944\pi$
$101$	2.41886	+	4.18959i	0.240686	+	0.416880i	−0.720224	+	0.693741i	$0.755961\pi$
$102$	−1.83772	−	3.18303i	−0.181962	−	0.315167i
$103$	−13.3246			−1.31291			−0.656454	−	0.754366i	$-0.727944\pi$
$103$	−13.3246			−1.31291			−0.656454	+	0.754366i	$0.727944\pi$
$104$	0.0811388	−	3.60464i	0.00795632	−	0.353464i
$105$		0			0
$106$	−2.08114	−	3.60464i	−0.202138	−	0.350113i
$107$	7.74342	+	13.4120i	0.748584	+	1.29659i	0.948501	+	0.316773i	$0.102599\pi$
$107$	7.74342	+	13.4120i	0.748584	+	1.29659i	−0.199917	+	0.979813i	$0.564067\pi$
$108$	−6.32456	+	10.9545i	−0.608581	+	1.05409i
$109$	−14.6491			−1.40313			−0.701565	−	0.712605i	$-0.747515\pi$
$109$	−14.6491			−1.40313			−0.701565	+	0.712605i	$0.747515\pi$
$110$		0			0
$111$	9.74342	−	16.8761i	0.924804	−	1.60181i
$112$	1.00000			0.0944911
$113$	8.32456	−	14.4186i	0.783108	−	1.35638i	−0.147014	−	0.989134i	$-0.546966\pi$
$113$	8.32456	−	14.4186i	0.783108	−	1.35638i	0.930123	−	0.367249i	$-0.119700\pi$
$114$	−12.9057	−	22.3533i	−1.20873	−	2.09358i
$115$		0			0
$116$	−2.32456			−0.215830
$117$	−21.5680	−	13.1081i	−1.99396	−	1.21185i
$118$	−2.32456			−0.213993
$119$	0.581139	+	1.00656i	0.0532729	+	0.0922714i
$120$		0			0
$121$	−3.16228	+	5.47723i	−0.287480	+	0.497930i
$122$	−11.4868			−1.03997
$123$	−3.67544	+	6.36606i	−0.331404	+	0.574008i
$124$	−0.418861	+	0.725489i	−0.0376148	+	0.0651508i
$125$		0			0
$126$	3.50000	−	6.06218i	0.311805	−	0.540062i
$127$	−4.66228	−	8.07530i	−0.413710	−	0.716567i	0.581582	−	0.813488i	$-0.302434\pi$
$127$	−4.66228	−	8.07530i	−0.413710	−	0.716567i	−0.995292	+	0.0969207i	$0.969101\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.32456			−0.556846
$130$		0			0
$131$	20.8114			1.81830			0.909150	−	0.416469i	$-0.136733\pi$
$131$	20.8114			1.81830			0.909150	+	0.416469i	$0.136733\pi$
$132$	6.58114	+	11.3989i	0.572815	+	0.992144i
$133$	4.08114	+	7.06874i	0.353880	+	0.612937i
$134$	−5.16228	+	8.94133i	−0.445953	+	0.772413i
$135$		0			0
$136$	−0.581139	+	1.00656i	−0.0498322	+	0.0863120i
$137$	−1.74342	+	3.01969i	−0.148950	+	0.257989i	−0.930840	−	0.365428i	$-0.880923\pi$
$137$	−1.74342	+	3.01969i	−0.148950	+	0.257989i	0.781890	+	0.623417i	$0.214256\pi$
$138$	18.9737			1.61515
$139$	2.91886	−	5.05562i	0.247575	−	0.428812i	−0.715278	−	0.698840i	$-0.753700\pi$
$139$	2.91886	−	5.05562i	0.247575	−	0.428812i	0.962852	+	0.270029i	$0.0870331\pi$
$140$		0			0
$141$	−4.74342	−	8.21584i	−0.399468	−	0.691898i
$142$	−8.32456			−0.698581
$143$	−13.1623	+	7.20928i	−1.10068	+	0.602870i
$144$	7.00000			0.583333
$145$		0			0
$146$	−4.58114	−	7.93477i	−0.379138	−	0.656686i
$147$	9.48683	−	16.4317i	0.782461	−	1.35526i
$148$	−6.16228			−0.506536
$149$	−1.83772	+	3.18303i	−0.150552	+	0.260764i	−0.931431	−	0.363919i	$-0.881438\pi$
$149$	−1.83772	+	3.18303i	−0.150552	+	0.260764i	0.780878	+	0.624683i	$0.214772\pi$
$150$		0			0
$151$	−11.1623			−0.908373			−0.454187	−	0.890907i	$-0.650070\pi$
$151$	−11.1623			−0.908373			−0.454187	+	0.890907i	$0.650070\pi$
$152$	−4.08114	+	7.06874i	−0.331024	+	0.573351i
$153$	4.06797	+	7.04593i	0.328876	+	0.569630i
$154$	−2.08114	−	3.60464i	−0.167703	−	0.290470i
$155$		0			0
$156$	−0.256584	+	11.3989i	−0.0205431	+	0.912640i
$157$	5.83772			0.465901			0.232950	−	0.972489i	$-0.425162\pi$
$157$	5.83772			0.465901			0.232950	+	0.972489i	$0.425162\pi$
$158$	2.74342	+	4.75174i	0.218254	+	0.378028i
$159$	6.58114	+	11.3989i	0.521918	+	0.903989i
$160$		0			0
$161$	−6.00000			−0.472866
$162$	9.50000	−	16.4545i	0.746390	−	1.29279i
$163$	−0.743416	+	1.28764i	−0.0582289	+	0.100855i	−0.893670	−	0.448724i	$-0.851879\pi$
$163$	−0.743416	+	1.28764i	−0.0582289	+	0.100855i	0.835442	+	0.549579i	$0.185212\pi$
$164$	2.32456			0.181517
$165$		0			0
$166$	4.74342	+	8.21584i	0.368161	+	0.637673i
$167$	0.337722	+	0.584952i	0.0261337	+	0.0452650i	0.878796	−	0.477197i	$-0.158347\pi$
$167$	0.337722	+	0.584952i	0.0261337	+	0.0452650i	−0.852663	+	0.522462i	$0.825014\pi$
$168$	−3.16228			−0.243975
$169$	−12.9868	−	0.584952i	−0.998987	−	0.0449963i
$170$		0			0
$171$	28.5680	+	49.4812i	2.18465	+	3.78392i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	−2.08114	+	3.60464i	−0.158226	+	0.274056i	−0.934229	−	0.356674i	$-0.883911\pi$
$173$	−2.08114	+	3.60464i	−0.158226	+	0.274056i	0.776003	+	0.630729i	$0.217244\pi$
$174$	7.35089			0.557269
$175$		0			0
$176$	2.08114	−	3.60464i	0.156872	−	0.271710i
$177$	7.35089			0.552527
$178$	2.66228	−	4.61120i	0.199546	−	0.345624i
$179$	−4.83772	−	8.37918i	−0.361588	−	0.626289i	0.626634	−	0.779314i	$-0.284432\pi$
$179$	−4.83772	−	8.37918i	−0.361588	−	0.626289i	−0.988222	+	0.153024i	$0.951099\pi$
$180$		0			0
$181$	−21.8114			−1.62123			−0.810614	−	0.585581i	$-0.800866\pi$
$181$	−21.8114			−1.62123			−0.810614	+	0.585581i	$0.800866\pi$
$182$	0.0811388	−	3.60464i	0.00601441	−	0.267194i
$183$	36.3246			2.68519
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	1.32456	−	2.29420i	0.0971211	−	0.168219i
$187$	4.83772			0.353769
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	−6.32456	+	10.9545i	−0.460044	+	0.796819i
$190$		0			0
$191$	4.74342	−	8.21584i	0.343222	−	0.594477i	−0.641807	−	0.766866i	$-0.721815\pi$
$191$	4.74342	−	8.21584i	0.343222	−	0.594477i	0.985029	+	0.172389i	$0.0551485\pi$
$192$	−1.58114	−	2.73861i	−0.114109	−	0.197642i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	11.4868			0.824707
$195$		0			0
$196$	−6.00000			−0.428571
$197$	0.243416	+	0.421610i	0.0173427	+	0.0300384i	0.874567	−	0.484906i	$-0.161146\pi$
$197$	0.243416	+	0.421610i	0.0173427	+	0.0300384i	−0.857224	+	0.514944i	$0.827813\pi$
$198$	−14.5680	−	25.2325i	−1.03530	−	1.79319i
$199$	13.3246	−	23.0788i	0.944553	−	1.63601i	0.187908	−	0.982187i	$-0.439829\pi$
$199$	13.3246	−	23.0788i	0.944553	−	1.63601i	0.756644	−	0.653827i	$-0.226837\pi$
$200$		0			0
$201$	16.3246	−	28.2750i	1.15145	−	1.99436i
$202$	−2.41886	+	4.18959i	−0.170190	+	0.294779i
$203$	−2.32456			−0.163152
$204$	1.83772	−	3.18303i	0.128666	−	0.222857i
$205$		0			0
$206$	−6.66228	−	11.5394i	−0.464183	−	0.803988i
$207$	−42.0000			−2.91920
$208$	3.16228	−	1.73205i	0.219265	−	0.120096i
$209$	33.9737			2.35001
$210$		0			0
$211$	−9.08114	−	15.7290i	−0.625171	−	1.08283i	−0.988508	−	0.151171i	$-0.951696\pi$
$211$	−9.08114	−	15.7290i	−0.625171	−	1.08283i	0.363336	−	0.931658i	$-0.381638\pi$
$212$	2.08114	−	3.60464i	0.142933	−	0.247568i
$213$	26.3246			1.80373
$214$	−7.74342	+	13.4120i	−0.529329	+	0.916825i
$215$		0			0
$216$	−12.6491			−0.860663
$217$	−0.418861	+	0.725489i	−0.0284341	+	0.0492494i
$218$	−7.32456	−	12.6865i	−0.496081	−	0.859238i
$219$	14.4868	+	25.0919i	0.978929	+	1.69556i
$220$		0			0
$221$	3.58114	+	2.17647i	0.240893	+	0.146405i
$222$	19.4868			1.30787
$223$	−4.66228	−	8.07530i	−0.312209	−	0.540762i	0.666631	−	0.745388i	$-0.267736\pi$
$223$	−4.66228	−	8.07530i	−0.312209	−	0.540762i	−0.978840	+	0.204626i	$0.934402\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	16.6491			1.10748
$227$	−1.16228	+	2.01312i	−0.0771431	+	0.133616i	−0.902016	−	0.431702i	$-0.857913\pi$
$227$	−1.16228	+	2.01312i	−0.0771431	+	0.133616i	0.824873	+	0.565318i	$0.191246\pi$
$228$	12.9057	−	22.3533i	0.854700	−	1.48038i
$229$	9.16228			0.605460			0.302730	−	0.953076i	$-0.402102\pi$
$229$	9.16228			0.605460			0.302730	+	0.953076i	$0.402102\pi$
$230$		0			0
$231$	6.58114	+	11.3989i	0.433007	+	0.749990i
$232$	−1.16228	−	2.01312i	−0.0763073	−	0.132168i
$233$	9.48683			0.621503			0.310752	−	0.950491i	$-0.399419\pi$
$233$	9.48683			0.621503			0.310752	+	0.950491i	$0.399419\pi$
$234$	0.567972	−	25.2325i	0.0371295	−	1.64950i
$235$		0			0
$236$	−1.16228	−	2.01312i	−0.0756578	−	0.131043i
$237$	−8.67544	−	15.0263i	−0.563531	−	0.976064i
$238$	−0.581139	+	1.00656i	−0.0376696	+	0.0652457i
$239$	4.83772			0.312926			0.156463	−	0.987684i	$-0.449991\pi$
$239$	4.83772			0.312926			0.156463	+	0.987684i	$0.449991\pi$
$240$		0			0
$241$	−5.98683	+	10.3695i	−0.385646	+	0.667958i	−0.991859	−	0.127344i	$-0.959355\pi$
$241$	−5.98683	+	10.3695i	−0.385646	+	0.667958i	0.606213	+	0.795303i	$0.292688\pi$
$242$	−6.32456			−0.406558
$243$	−11.0680	+	19.1703i	−0.710011	+	1.22977i
$244$	−5.74342	−	9.94789i	−0.367685	−	0.636848i
$245$		0			0
$246$	−7.35089			−0.468676
$247$	25.1491	+	15.2846i	1.60020	+	0.972534i
$248$	−0.837722			−0.0531954
$249$	−15.0000	−	25.9808i	−0.950586	−	1.64646i
$250$		0			0
$251$	3.24342	−	5.61776i	0.204723	−	0.354590i	−0.745322	−	0.666705i	$-0.767704\pi$
$251$	3.24342	−	5.61776i	0.204723	−	0.354590i	0.950044	+	0.312115i	$0.101037\pi$
$252$	7.00000			0.440959
$253$	−12.4868	+	21.6278i	−0.785040	+	1.35973i
$254$	4.66228	−	8.07530i	0.292537	−	0.506689i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$	−3.16228	−	5.47723i	−0.196875	−	0.340997i
$259$	−6.16228			−0.382905
$260$		0			0
$261$	−16.2719			−1.00720
$262$	10.4057	+	18.0232i	0.642866	+	1.11348i
$263$	6.82456	+	11.8205i	0.420820	+	0.728882i	0.996020	−	0.0891312i	$-0.0284090\pi$
$263$	6.82456	+	11.8205i	0.420820	+	0.728882i	−0.575200	+	0.818013i	$0.695076\pi$
$264$	−6.58114	+	11.3989i	−0.405041	+	0.701552i
$265$		0			0
$266$	−4.08114	+	7.06874i	−0.250231	+	0.433412i
$267$	−8.41886	+	14.5819i	−0.515226	+	0.892397i
$268$	−10.3246			−0.630673
$269$	−10.7434	+	18.6081i	−0.655038	+	1.13456i	0.326847	+	0.945077i	$0.394014\pi$
$269$	−10.7434	+	18.6081i	−0.655038	+	1.13456i	−0.981884	+	0.189481i	$0.939319\pi$
$270$		0			0
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	0.945944	−	0.324329i	$-0.105139\pi$
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	−0.753850	+	0.657047i	$0.771805\pi$
$272$	−1.16228			−0.0704734
$273$	−0.256584	+	11.3989i	−0.0155291	+	0.689891i
$274$	−3.48683			−0.210647
$275$		0			0
$276$	9.48683	+	16.4317i	0.571040	+	0.989071i
$277$	10.2434	−	17.7421i	0.615467	−	1.06602i	−0.374835	−	0.927092i	$-0.622301\pi$
$277$	10.2434	−	17.7421i	0.615467	−	1.06602i	0.990302	−	0.138929i	$-0.0443660\pi$
$278$	5.83772			0.350123
$279$	−2.93203	+	5.07842i	−0.175536	+	0.304037i
$280$		0			0
$281$	18.9737			1.13187			0.565937	−	0.824448i	$-0.308515\pi$
$281$	18.9737			1.13187			0.565937	+	0.824448i	$0.308515\pi$
$282$	4.74342	−	8.21584i	0.282466	−	0.489246i
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	−0.982173	−	0.187980i	$-0.939806\pi$
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	0.328291	−	0.944577i	$-0.393527\pi$
$284$	−4.16228	−	7.20928i	−0.246986	−	0.427792i
$285$		0			0
$286$	−12.8246	−	7.79423i	−0.758332	−	0.460882i
$287$	2.32456			0.137214
$288$	3.50000	+	6.06218i	0.206239	+	0.357217i
$289$	7.82456	+	13.5525i	0.460268	+	0.797207i
$290$		0			0
$291$	−36.3246			−2.12938
$292$	4.58114	−	7.93477i	0.268091	−	0.464347i
$293$	−14.0811	+	24.3892i	−0.822629	+	1.42484i	0.0810891	+	0.996707i	$0.474160\pi$
$293$	−14.0811	+	24.3892i	−0.822629	+	1.42484i	−0.903718	+	0.428128i	$0.859173\pi$
$294$	18.9737			1.10657
$295$		0			0
$296$	−3.08114	−	5.33669i	−0.179088	−	0.310189i
$297$	26.3246	+	45.5955i	1.52751	+	2.64572i
$298$	−3.67544			−0.212913
$299$	−18.9737	+	10.3923i	−1.09728	+	0.601003i
$300$		0			0
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$	−5.58114	−	9.66682i	−0.321158	−	0.556263i
$303$	7.64911	−	13.2486i	0.439430	−	0.761115i
$304$	−8.16228			−0.468139
$305$		0			0
$306$	−4.06797	+	7.04593i	−0.232550	+	0.402789i
$307$	−28.3246			−1.61657			−0.808284	−	0.588793i	$-0.799603\pi$
$307$	−28.3246			−1.61657			−0.808284	+	0.588793i	$0.799603\pi$
$308$	2.08114	−	3.60464i	0.118584	−	0.205393i
$309$	21.0680	+	36.4908i	1.19852	+	2.07589i
$310$		0			0
$311$	15.4868			0.878178			0.439089	−	0.898444i	$-0.355301\pi$
$311$	15.4868			0.878178			0.439089	+	0.898444i	$0.355301\pi$
$312$	−10.0000	+	5.47723i	−0.566139	+	0.310087i
$313$	−4.32456			−0.244438			−0.122219	−	0.992503i	$-0.539001\pi$
$313$	−4.32456			−0.244438			−0.122219	+	0.992503i	$0.539001\pi$
$314$	2.91886	+	5.05562i	0.164721	+	0.285305i
$315$		0			0
$316$	−2.74342	+	4.75174i	−0.154329	+	0.267306i
$317$	6.48683			0.364337			0.182168	−	0.983267i	$-0.441688\pi$
$317$	6.48683			0.364337			0.182168	+	0.983267i	$0.441688\pi$
$318$	−6.58114	+	11.3989i	−0.369052	+	0.639217i
$319$	−4.83772	+	8.37918i	−0.270860	+	0.469144i
$320$		0			0
$321$	24.4868	−	42.4124i	1.36672	−	2.36723i
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$	−4.74342	−	8.21584i	−0.263931	−	0.457141i
$324$	19.0000			1.05556
$325$		0			0
$326$	−1.48683			−0.0823481
$327$	23.1623	+	40.1182i	1.28088	+	2.21854i
$328$	1.16228	+	2.01312i	0.0641760	+	0.111156i
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		0			0
$331$	−0.324555	+	0.562146i	−0.0178392	+	0.0308984i	−0.874807	−	0.484471i	$-0.839012\pi$
$331$	−0.324555	+	0.562146i	−0.0178392	+	0.0308984i	0.856968	+	0.515370i	$0.172345\pi$
$332$	−4.74342	+	8.21584i	−0.260329	+	0.450903i
$333$	−43.1359			−2.36384
$334$	−0.337722	+	0.584952i	−0.0184793	+	0.0320072i
$335$		0			0
$336$	−1.58114	−	2.73861i	−0.0862582	−	0.149404i
$337$	1.48683			0.0809930			0.0404965	−	0.999180i	$-0.487106\pi$
$337$	1.48683			0.0809930			0.0404965	+	0.999180i	$0.487106\pi$
$338$	−5.98683	−	11.5394i	−0.325641	−	0.627661i
$339$	−52.6491			−2.85951
$340$		0			0
$341$	1.74342	+	3.01969i	0.0944113	+	0.163525i
$342$	−28.5680	+	49.4812i	−1.54478	+	2.67564i
$343$	−13.0000			−0.701934
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	−4.16228			−0.223765
$347$	10.7434	−	18.6081i	0.576737	−	0.998937i	−0.419114	−	0.907934i	$-0.637659\pi$
$347$	10.7434	−	18.6081i	0.576737	−	0.998937i	0.995851	−	0.0910037i	$-0.0290075\pi$
$348$	3.67544	+	6.36606i	0.197025	+	0.341256i
$349$	0.743416	+	1.28764i	0.0397942	+	0.0689255i	0.885237	−	0.465141i	$-0.153996\pi$
$349$	0.743416	+	1.28764i	0.0397942	+	0.0689255i	−0.845442	+	0.534067i	$0.820663\pi$
$350$		0			0
$351$	−1.02633	+	45.5955i	−0.0547817	+	2.43371i
$352$	4.16228			0.221850
$353$	−0.581139	−	1.00656i	−0.0309309	−	0.0535739i	0.850146	−	0.526548i	$-0.176514\pi$
$353$	−0.581139	−	1.00656i	−0.0309309	−	0.0535739i	−0.881076	+	0.472974i	$0.843181\pi$
$354$	3.67544	+	6.36606i	0.195348	+	0.338352i
$355$		0			0
$356$	5.32456			0.282201
$357$	1.83772	−	3.18303i	0.0972626	−	0.168464i
$358$	4.83772	−	8.37918i	0.255682	−	0.442853i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	−23.8114	−	41.2425i	−1.25323	−	2.17066i
$362$	−10.9057	−	18.8892i	−0.573191	−	0.992795i
$363$	20.0000			1.04973
$364$	3.16228	−	1.73205i	0.165748	−	0.0907841i
$365$		0			0
$366$	18.1623	+	31.4580i	0.949357	+	1.64434i
$367$	−10.3246	−	17.8827i	−0.538937	−	0.933467i	−0.998962	−	0.0455606i	$-0.985493\pi$
$367$	−10.3246	−	17.8827i	−0.538937	−	0.933467i	0.460024	−	0.887906i	$-0.347841\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$	16.2719			0.847081
$370$		0			0
$371$	2.08114	−	3.60464i	0.108047	−	0.187143i
$372$	2.64911			0.137350
$373$	−2.67544	+	4.63401i	−0.138529	+	0.239940i	−0.926940	−	0.375209i	$-0.877571\pi$
$373$	−2.67544	+	4.63401i	−0.138529	+	0.239940i	0.788411	+	0.615149i	$0.210904\pi$
$374$	2.41886	+	4.18959i	0.125076	+	0.216639i
$375$		0			0
$376$	−3.00000			−0.154713
$377$	−7.35089	+	4.02625i	−0.378590	+	0.207362i
$378$	−12.6491			−0.650600
$379$	3.59431	+	6.22552i	0.184627	+	0.319784i	0.943451	−	0.331513i	$-0.107559\pi$
$379$	3.59431	+	6.22552i	0.184627	+	0.319784i	−0.758824	+	0.651296i	$0.774226\pi$
$380$		0			0
$381$	−14.7434	+	25.5363i	−0.755328	+	1.30827i
$382$	9.48683			0.485389
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	−0.173005	−	0.984921i	$-0.555348\pi$
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	0.939469	−	0.342634i	$-0.111319\pi$
$384$	1.58114	−	2.73861i	0.0806872	−	0.139754i
$385$		0			0
$386$	2.00000	−	3.46410i	0.101797	−	0.176318i
$387$	7.00000	+	12.1244i	0.355830	+	0.616316i
$388$	5.74342	+	9.94789i	0.291578	+	0.505028i
$389$	19.1623			0.971566			0.485783	−	0.874079i	$-0.338535\pi$
$389$	19.1623			0.971566			0.485783	+	0.874079i	$0.338535\pi$
$390$		0			0
$391$	6.97367			0.352673
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$	−32.9057	−	56.9943i	−1.65987	−	2.87498i
$394$	−0.243416	+	0.421610i	−0.0122631	+	0.0212404i
$395$		0			0
$396$	14.5680	−	25.2325i	0.732068	−	1.26798i
$397$	9.75658	−	16.8989i	0.489669	−	0.848131i	−0.510260	−	0.860020i	$-0.670451\pi$
$397$	9.75658	−	16.8989i	0.489669	−	0.848131i	0.999929	+	0.0118885i	$0.00378433\pi$
$398$	26.6491			1.33580
$399$	12.9057	−	22.3533i	0.646093	−	1.11907i
$400$		0			0
$401$	7.98683	+	13.8336i	0.398843	+	0.690817i	0.993583	−	0.113101i	$-0.0360784\pi$
$401$	7.98683	+	13.8336i	0.398843	+	0.690817i	−0.594740	+	0.803918i	$0.702745\pi$
$402$	32.6491			1.62839
$403$	−0.0679718	+	3.01969i	−0.00338592	+	0.150421i
$404$	−4.83772			−0.240686
$405$		0			0
$406$	−1.16228	−	2.01312i	−0.0576829	−	0.0999097i
$407$	−12.8246	+	22.2128i	−0.635690	+	1.10105i
$408$	3.67544			0.181962
$409$	−1.82456	+	3.16022i	−0.0902185	+	0.156263i	−0.907603	−	0.419830i	$-0.862090\pi$
$409$	−1.82456	+	3.16022i	−0.0902185	+	0.156263i	0.817385	+	0.576092i	$0.195423\pi$
$410$		0			0
$411$	11.0263			0.543889
$412$	6.66228	−	11.5394i	0.328227	−	0.568506i
$413$	−1.16228	−	2.01312i	−0.0571919	−	0.0990594i
$414$	−21.0000	−	36.3731i	−1.03209	−	1.78764i
$415$		0			0
$416$	3.08114	+	1.87259i	0.151065	+	0.0918112i
$417$	−18.4605			−0.904015
$418$	16.9868	+	29.4221i	0.830853	+	1.43908i
$419$	5.32456	+	9.22240i	0.260122	+	0.450544i	0.966274	−	0.257516i	$-0.0829040\pi$
$419$	5.32456	+	9.22240i	0.260122	+	0.450544i	−0.706152	+	0.708060i	$0.749571\pi$
$420$		0			0
$421$	3.16228			0.154120			0.0770600	−	0.997026i	$-0.475447\pi$
$421$	3.16228			0.154120			0.0770600	+	0.997026i	$0.475447\pi$
$422$	9.08114	−	15.7290i	0.442063	−	0.765675i
$423$	−10.5000	+	18.1865i	−0.510527	+	0.884260i
$424$	4.16228			0.202138
$425$		0			0
$426$	13.1623	+	22.7977i	0.637714	+	1.10455i
$427$	−5.74342	−	9.94789i	−0.277943	−	0.481412i
$428$	−15.4868			−0.748584
$429$	40.5548	+	24.6475i	1.95800	+	1.18999i
$430$		0			0
$431$	1.74342	+	3.01969i	0.0839774	+	0.145453i	0.904955	−	0.425507i	$-0.139904\pi$
$431$	1.74342	+	3.01969i	0.0839774	+	0.145453i	−0.820978	+	0.570960i	$0.806571\pi$
$432$	−6.32456	−	10.9545i	−0.304290	−	0.527046i
$433$	−3.16228	+	5.47723i	−0.151969	+	0.263219i	−0.931951	−	0.362583i	$-0.881895\pi$
$433$	−3.16228	+	5.47723i	−0.151969	+	0.263219i	0.779982	+	0.625802i	$0.215228\pi$
$434$	−0.837722			−0.0402120
$435$		0			0
$436$	7.32456	−	12.6865i	0.350783	−	0.607573i
$437$	48.9737			2.34273
$438$	−14.4868	+	25.0919i	−0.692208	+	1.19894i
$439$	13.9057	+	24.0854i	0.663683	+	1.14953i	0.979641	+	0.200759i	$0.0643408\pi$
$439$	13.9057	+	24.0854i	0.663683	+	1.14953i	−0.315958	+	0.948773i	$0.602326\pi$
$440$		0			0
$441$	−42.0000			−2.00000
$442$	−0.0943058	+	4.18959i	−0.00448567	+	0.199278i
$443$	−1.35089			−0.0641827			−0.0320913	−	0.999485i	$-0.510217\pi$
$443$	−1.35089			−0.0641827			−0.0320913	+	0.999485i	$0.510217\pi$
$444$	9.74342	+	16.8761i	0.462402	+	0.800904i
$445$		0			0
$446$	4.66228	−	8.07530i	0.220765	−	0.382377i
$447$	11.6228			0.549738
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	19.9868	−	34.6182i	0.943237	−	1.63373i	0.183994	−	0.982927i	$-0.441097\pi$
$449$	19.9868	−	34.6182i	0.943237	−	1.63373i	0.759243	−	0.650807i	$-0.225569\pi$
$450$		0			0
$451$	4.83772	−	8.37918i	0.227799	−	0.394560i
$452$	8.32456	+	14.4186i	0.391554	+	0.678192i
$453$	17.6491	+	30.5692i	0.829228	+	1.43626i
$454$	−2.32456			−0.109097
$455$		0			0
$456$	25.8114			1.20873
$457$	−16.2302	−	28.1116i	−0.759219	−	1.31501i	−0.943249	−	0.332085i	$-0.892248\pi$
$457$	−16.2302	−	28.1116i	−0.759219	−	1.31501i	0.184030	−	0.982921i	$-0.441086\pi$
$458$	4.58114	+	7.93477i	0.214063	+	0.370767i
$459$	7.35089	−	12.7321i	0.343110	−	0.594284i
$460$		0			0
$461$	−1.25658	+	2.17647i	−0.0585249	+	0.101368i	−0.893803	−	0.448459i	$-0.851973\pi$
$461$	−1.25658	+	2.17647i	−0.0585249	+	0.101368i	0.835279	+	0.549827i	$0.185306\pi$
$462$	−6.58114	+	11.3989i	−0.306182	+	0.530323i
$463$	0.324555			0.0150834			0.00754168	−	0.999972i	$-0.497599\pi$
$463$	0.324555			0.0150834			0.00754168	+	0.999972i	$0.497599\pi$
$464$	1.16228	−	2.01312i	0.0539574	−	0.0934569i
$465$		0			0
$466$	4.74342	+	8.21584i	0.219735	+	0.380591i
$467$	−7.35089			−0.340159			−0.170079	−	0.985430i	$-0.554402\pi$
$467$	−7.35089			−0.340159			−0.170079	+	0.985430i	$0.554402\pi$
$468$	22.1359	−	12.1244i	1.02323	−	0.560449i
$469$	−10.3246			−0.476744
$470$		0			0
$471$	−9.23025	−	15.9873i	−0.425307	−	0.736654i
$472$	1.16228	−	2.01312i	0.0534982	−	0.0926615i
$473$	8.32456			0.382763
$474$	8.67544	−	15.0263i	0.398476	−	0.690181i
$475$		0			0
$476$	−1.16228			−0.0532729
$477$	14.5680	−	25.2325i	0.667022	−	1.15532i
$478$	2.41886	+	4.18959i	0.110636	+	0.191627i
$479$	−16.0680	−	27.8305i	−0.734164	−	1.27161i	−0.955089	−	0.296319i	$-0.904241\pi$
$479$	−16.0680	−	27.8305i	−0.734164	−	1.27161i	0.220925	−	0.975291i	$-0.429093\pi$
$480$		0			0
$481$	−19.4868	+	10.6734i	−0.888523	+	0.486664i
$482$	−11.9737			−0.545386
$483$	9.48683	+	16.4317i	0.431666	+	0.747667i
$484$	−3.16228	−	5.47723i	−0.143740	−	0.248965i
$485$		0			0
$486$	−22.1359			−1.00411
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	−0.877132	−	0.480250i	$-0.840546\pi$
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	0.854475	+	0.519493i	$0.173879\pi$
$488$	5.74342	−	9.94789i	0.259992	−	0.450320i
$489$	4.70178			0.212622
$490$		0			0
$491$	−18.2434	−	31.5985i	−0.823314	−	1.42602i	−0.903201	−	0.429218i	$-0.858789\pi$
$491$	−18.2434	−	31.5985i	−0.823314	−	1.42602i	0.0798873	−	0.996804i	$-0.474544\pi$
$492$	−3.67544	−	6.36606i	−0.165702	−	0.287004i
$493$	2.70178			0.121682
$494$	−0.662278	+	29.4221i	−0.0297973	+	1.32376i
$495$		0			0
$496$	−0.418861	−	0.725489i	−0.0188074	−	0.0325754i
$497$	−4.16228	−	7.20928i	−0.186704	−	0.323380i
$498$	15.0000	−	25.9808i	0.672166	−	1.16423i
$499$	−22.0000			−0.984855			−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000			−0.984855			−0.492428	+	0.870353i	$0.663890\pi$
$500$		0			0
$501$	1.06797	−	1.84978i	0.0477135	−	0.0826421i
$502$	6.48683			0.289522
$503$	18.1491	−	31.4352i	0.809229	−	1.40163i	−0.104170	−	0.994560i	$-0.533219\pi$
$503$	18.1491	−	31.4352i	0.809229	−	1.40163i	0.913399	−	0.407066i	$-0.133448\pi$
$504$	3.50000	+	6.06218i	0.155902	+	0.270031i
$505$		0			0
$506$	−24.9737			−1.11021
$507$	18.9320	+	36.4908i	0.840801	+	1.62061i
$508$	9.32456			0.413710
$509$	−18.4868	−	32.0201i	−0.819414	−	1.41927i	−0.906114	−	0.423033i	$-0.860965\pi$
$509$	−18.4868	−	32.0201i	−0.819414	−	1.41927i	0.0866998	−	0.996234i	$-0.472368\pi$
$510$		0			0
$511$	4.58114	−	7.93477i	0.202658	−	0.351013i
$512$	−1.00000			−0.0441942
$513$	51.6228	−	89.4133i	2.27920	−	3.94769i
$514$		0			0
$515$		0			0
$516$	3.16228	−	5.47723i	0.139212	−	0.241121i
$517$	6.24342	+	10.8139i	0.274585	+	0.475595i
$518$	−3.08114	−	5.33669i	−0.135377	−	0.234481i
$519$	13.1623			0.577760
$520$		0			0
$521$	35.3246			1.54760			0.773798	−	0.633432i	$-0.218354\pi$
$521$	35.3246			1.54760			0.773798	+	0.633432i	$0.218354\pi$
$522$	−8.13594	−	14.0919i	−0.356101	−	0.616784i
$523$	5.64911	+	9.78455i	0.247018	+	0.427848i	0.962697	−	0.270581i	$-0.0872159\pi$
$523$	5.64911	+	9.78455i	0.247018	+	0.427848i	−0.715679	+	0.698430i	$0.753883\pi$
$524$	−10.4057	+	18.0232i	−0.454575	+	0.787347i
$525$		0			0
$526$	−6.82456	+	11.8205i	−0.297565	+	0.515397i
$527$	0.486833	−	0.843219i	0.0212068	−	0.0367312i
$528$	−13.1623			−0.572815
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−8.13594	−	14.0919i	−0.353070	−	0.611535i
$532$	−8.16228			−0.353880
$533$	7.35089	−	4.02625i	0.318402	−	0.174396i
$534$	−16.8377			−0.728640
$535$		0			0
$536$	−5.16228	−	8.94133i	−0.222976	−	0.386207i
$537$	−15.2982	+	26.4973i	−0.660167	+	1.14344i
$538$	−21.4868			−0.926363
$539$	−12.4868	+	21.6278i	−0.537846	+	0.931577i
$540$		0			0
$541$	33.1623			1.42576			0.712879	−	0.701287i	$-0.247391\pi$
$541$	33.1623			1.42576			0.712879	+	0.701287i	$0.247391\pi$
$542$	−3.16228	+	5.47723i	−0.135831	+	0.235267i
$543$	34.4868	+	59.7329i	1.47997	+	2.56339i
$544$	−0.581139	−	1.00656i	−0.0249161	−	0.0431560i
$545$		0			0
$546$	−10.0000	+	5.47723i	−0.427960	+	0.234404i
$547$	−18.6491			−0.797378			−0.398689	−	0.917086i	$-0.630535\pi$
$547$	−18.6491			−0.797378			−0.398689	+	0.917086i	$0.630535\pi$
$548$	−1.74342	−	3.01969i	−0.0744751	−	0.128995i
$549$	−40.2039	−	69.6352i	−1.71586	−	2.97196i
$550$		0			0
$551$	18.9737			0.808305
$552$	−9.48683	+	16.4317i	−0.403786	+	0.699379i
$553$	−2.74342	+	4.75174i	−0.116662	+	0.202064i
$554$	20.4868			0.870402
$555$		0			0
$556$	2.91886	+	5.05562i	0.123787	+	0.214406i
$557$	11.0811	+	19.1931i	0.469523	+	0.813238i	0.999393	−	0.0348414i	$-0.0110926\pi$
$557$	11.0811	+	19.1931i	0.469523	+	0.813238i	−0.529870	+	0.848079i	$0.677759\pi$
$558$	−5.86406			−0.248245
$559$	6.16228	+	3.74517i	0.260637	+	0.158404i
$560$		0			0
$561$	−7.64911	−	13.2486i	−0.322946	−	0.559358i
$562$	9.48683	+	16.4317i	0.400178	+	0.693128i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$	9.48683			0.399468
$565$		0			0
$566$	11.0000	−	19.0526i	0.462364	−	0.800839i
$567$	19.0000			0.797925
$568$	4.16228	−	7.20928i	0.174645	−	0.302495i
$569$	−1.98683	−	3.44130i	−0.0832924	−	0.144267i	0.821370	−	0.570396i	$-0.193210\pi$
$569$	−1.98683	−	3.44130i	−0.0832924	−	0.144267i	−0.904662	+	0.426129i	$0.859877\pi$
$570$		0			0
$571$	19.1359			0.800814			0.400407	−	0.916337i	$-0.368869\pi$
$571$	19.1359			0.800814			0.400407	+	0.916337i	$0.368869\pi$
$572$	0.337722	−	15.0035i	0.0141209	−	0.627328i
$573$	−30.0000			−1.25327
$574$	1.16228	+	2.01312i	0.0485125	+	0.0840262i
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	−0.837722			−0.0348748			−0.0174374	−	0.999848i	$-0.505551\pi$
$577$	−0.837722			−0.0348748			−0.0174374	+	0.999848i	$0.505551\pi$
$578$	−7.82456	+	13.5525i	−0.325459	+	0.563711i
$579$	−6.32456	+	10.9545i	−0.262840	+	0.455251i
$580$		0			0
$581$	−4.74342	+	8.21584i	−0.196790	+	0.340850i
$582$	−18.1623	−	31.4580i	−0.752851	−	1.30398i
$583$	−8.66228	−	15.0035i	−0.358755	−	0.621382i
$584$	9.16228			0.379138
$585$		0			0
$586$	−28.1623			−1.16337
$587$	−12.4868	−	21.6278i	−0.515387	−	0.892676i	−0.999841	−	0.0178592i	$-0.994315\pi$
$587$	−12.4868	−	21.6278i	−0.515387	−	0.892676i	0.484454	−	0.874817i	$-0.339018\pi$
$588$	9.48683	+	16.4317i	0.391230	+	0.677631i
$589$	3.41886	−	5.92164i	0.140872	−	0.243997i
$590$		0			0
$591$	0.769751	−	1.33325i	0.0316633	−	0.0548425i
$592$	3.08114	−	5.33669i	0.126634	−	0.219337i
$593$	28.6491			1.17648			0.588239	−	0.808687i	$-0.299821\pi$
$593$	28.6491			1.17648			0.588239	+	0.808687i	$0.299821\pi$
$594$	−26.3246	+	45.5955i	−1.08011	+	1.87080i
$595$		0			0
$596$	−1.83772	−	3.18303i	−0.0752760	−	0.130382i
$597$	−84.2719			−3.44902
$598$	−18.4868	−	11.2355i	−0.755983	−	0.459455i
$599$	−31.9473			−1.30533			−0.652666	−	0.757646i	$-0.726350\pi$
$599$	−31.9473			−1.30533			−0.652666	+	0.757646i	$0.726350\pi$
$600$		0			0
$601$	8.14911	+	14.1147i	0.332409	+	0.575750i	0.982984	−	0.183693i	$-0.0588052\pi$
$601$	8.14911	+	14.1147i	0.332409	+	0.575750i	−0.650575	+	0.759442i	$0.725472\pi$
$602$	−1.00000	+	1.73205i	−0.0407570	+	0.0705931i
$603$	−72.2719			−2.94314
$604$	5.58114	−	9.66682i	0.227093	−	0.393337i
$605$		0			0
$606$	15.2982			0.621448
$607$	2.50000	−	4.33013i	0.101472	−	0.175754i	−0.810819	−	0.585296i	$-0.800978\pi$
$607$	2.50000	−	4.33013i	0.101472	−	0.175754i	0.912291	+	0.409542i	$0.134311\pi$
$608$	−4.08114	−	7.06874i	−0.165512	−	0.286675i
$609$	3.67544	+	6.36606i	0.148937	+	0.257966i
$610$		0			0
$611$	−0.243416	+	10.8139i	−0.00984758	+	0.437484i
$612$	−8.13594			−0.328876
$613$	0.756584	+	1.31044i	0.0305581	+	0.0529282i	0.880900	−	0.473302i	$-0.156938\pi$
$613$	0.756584	+	1.31044i	0.0305581	+	0.0529282i	−0.850342	+	0.526231i	$0.823605\pi$
$614$	−14.1623	−	24.5298i	−0.571543	−	0.989942i
$615$		0			0
$616$	4.16228			0.167703
$617$	21.9737	−	38.0595i	0.884626	−	1.53222i	0.0384853	−	0.999259i	$-0.487747\pi$
$617$	21.9737	−	38.0595i	0.884626	−	1.53222i	0.846141	−	0.532959i	$-0.178920\pi$
$618$	−21.0680	+	36.4908i	−0.847478	+	1.46788i
$619$	27.4605			1.10373			0.551865	−	0.833933i	$-0.313916\pi$
$619$	27.4605			1.10373			0.551865	+	0.833933i	$0.313916\pi$
$620$		0			0
$621$	37.9473	+	65.7267i	1.52277	+	2.63752i
$622$	7.74342	+	13.4120i	0.310483	+	0.537772i
$623$	5.32456			0.213324
$624$	−9.74342	−	5.92164i	−0.390049	−	0.237055i
$625$		0			0
$626$	−2.16228	−	3.74517i	−0.0864220	−	0.149687i
$627$	−53.7171	−	93.0407i	−2.14525	−	3.71569i
$628$	−2.91886	+	5.05562i	−0.116475	+	0.201741i
$629$	7.16228			0.285579
$630$		0			0
$631$	0.837722	−	1.45098i	0.0333492	−	0.0577625i	−0.848869	−	0.528603i	$-0.822716\pi$
$631$	0.837722	−	1.45098i	0.0333492	−	0.0577625i	0.882218	+	0.470841i	$0.156049\pi$
$632$	−5.48683			−0.218254
$633$	−28.7171	+	49.7394i	−1.14140	+	1.97697i
$634$	3.24342	+	5.61776i	0.128813	+	0.223110i
$635$		0			0
$636$	−13.1623			−0.521918
$637$	−18.9737	+	10.3923i	−0.751764	+	0.411758i
$638$	−9.67544			−0.383055
$639$	−29.1359	−	50.4649i	−1.15260	−	1.99636i
$640$		0			0
$641$	−13.9868	+	24.2259i	−0.552447	+	0.956866i	0.445651	+	0.895207i	$0.352972\pi$
$641$	−13.9868	+	24.2259i	−0.552447	+	0.956866i	−0.998097	+	0.0616587i	$0.980361\pi$
$642$	48.9737			1.93284
$643$	−22.2302	+	38.5039i	−0.876675	+	1.51845i	−0.0217083	+	0.999764i	$0.506911\pi$
$643$	−22.2302	+	38.5039i	−0.876675	+	1.51845i	−0.854967	+	0.518682i	$0.826423\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$		0			0
$646$	4.74342	−	8.21584i	0.186627	−	0.323248i
$647$	10.9868	+	19.0298i	0.431937	+	0.748137i	0.997040	−	0.0768835i	$-0.0244970\pi$
$647$	10.9868	+	19.0298i	0.431937	+	0.748137i	−0.565103	+	0.825020i	$0.691164\pi$
$648$	9.50000	+	16.4545i	0.373195	+	0.646393i
$649$	−9.67544			−0.379794
$650$		0			0
$651$	2.64911			0.103827
$652$	−0.743416	−	1.28764i	−0.0291144	−	0.0504277i
$653$	18.2434	+	31.5985i	0.713920	+	1.23655i	0.963375	+	0.268159i	$0.0864154\pi$
$653$	18.2434	+	31.5985i	0.713920	+	1.23655i	−0.249455	+	0.968387i	$0.580251\pi$
$654$	−23.1623	+	40.1182i	−0.905717	+	1.56875i
$655$		0			0
$656$	−1.16228	+	2.01312i	−0.0453793	+	0.0785993i
$657$	32.0680	−	55.5434i	1.25109	−	2.16695i
$658$	−3.00000			−0.116952
$659$	13.6491	−	23.6410i	0.531694	−	0.920921i	−0.467622	−	0.883929i	$-0.654889\pi$
$659$	13.6491	−	23.6410i	0.531694	−	0.920921i	0.999316	−	0.0369921i	$-0.0117776\pi$
$660$		0			0
$661$	8.58114	+	14.8630i	0.333768	+	0.578102i	0.983247	−	0.182276i	$-0.0583466\pi$
$661$	8.58114	+	14.8630i	0.333768	+	0.578102i	−0.649480	+	0.760379i	$0.725013\pi$
$662$	−0.649111			−0.0252284
$663$	0.298221	−	13.2486i	0.0115820	−	0.514535i
$664$	−9.48683			−0.368161
$665$		0			0
$666$	−21.5680	−	37.3568i	−0.835742	−	1.44755i
$667$	−6.97367	+	12.0787i	−0.270021	+	0.467691i
$668$	−0.675445			−0.0261337
$669$	−14.7434	+	25.5363i	−0.570013	+	0.987292i
$670$		0			0
$671$	−47.8114			−1.84574
$672$	1.58114	−	2.73861i	0.0609938	−	0.105644i
$673$	−11.4868	−	19.8958i	−0.442785	−	0.766926i	0.555110	−	0.831777i	$-0.312676\pi$
$673$	−11.4868	−	19.8958i	−0.442785	−	0.766926i	−0.997895	+	0.0648510i	$0.979343\pi$
$674$	0.743416	+	1.28764i	0.0286353	+	0.0495979i
$675$		0			0
$676$	7.00000	−	10.9545i	0.269231	−	0.421325i
$677$	−24.9737			−0.959816			−0.479908	−	0.877319i	$-0.659330\pi$
$677$	−24.9737			−0.959816			−0.479908	+	0.877319i	$0.659330\pi$
$678$	−26.3246	−	45.5955i	−1.01099	−	1.75108i
$679$	5.74342	+	9.94789i	0.220412	+	0.381765i
$680$		0			0
$681$	7.35089			0.281687
$682$	−1.74342	+	3.01969i	−0.0667589	+	0.115630i
$683$	16.1623	−	27.9939i	0.618432	−	1.07116i	−0.371340	−	0.928497i	$-0.621101\pi$
$683$	16.1623	−	27.9939i	0.618432	−	1.07116i	0.989772	−	0.142659i	$-0.0455653\pi$
$684$	−57.1359			−2.18465
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	−14.4868	−	25.0919i	−0.552707	−	0.957317i
$688$	−2.00000			−0.0762493
$689$	0.337722	−	15.0035i	0.0128662	−	0.571588i
$690$		0			0
$691$	−3.56797	−	6.17991i	−0.135732	−	0.235095i	0.790145	−	0.612920i	$-0.210005\pi$
$691$	−3.56797	−	6.17991i	−0.135732	−	0.235095i	−0.925877	+	0.377825i	$0.876672\pi$
$692$	−2.08114	−	3.60464i	−0.0791130	−	0.137028i
$693$	14.5680	−	25.2325i	0.553391	−	0.958502i
$694$	21.4868			0.815629
$695$		0			0
$696$	−3.67544	+	6.36606i	−0.139317	+	0.241305i
$697$	−2.70178			−0.102337
$698$	−0.743416	+	1.28764i	−0.0281387	+	0.0487377i
$699$	−15.0000	−	25.9808i	−0.567352	−	0.982683i
$700$		0			0
$701$	−16.8377			−0.635952			−0.317976	−	0.948099i	$-0.603003\pi$
$701$	−16.8377			−0.635952			−0.317976	+	0.948099i	$0.603003\pi$
$702$	−40.0000	+	21.9089i	−1.50970	+	0.826898i
$703$	50.2982			1.89703
$704$	2.08114	+	3.60464i	0.0784359	+	0.135855i
$705$		0			0
$706$	0.581139	−	1.00656i	0.0218714	−	0.0378825i
$707$	−4.83772			−0.181941
$708$	−3.67544	+	6.36606i	−0.138132	+	0.239251i
$709$	−11.2566	+	19.4970i	−0.422750	+	0.732224i	−0.996207	−	0.0870111i	$-0.972268\pi$
$709$	−11.2566	+	19.4970i	−0.422750	+	0.732224i	0.573457	+	0.819235i	$0.305602\pi$
$710$		0			0
$711$	−19.2039	+	33.2622i	−0.720203	+	1.24743i
$712$	2.66228	+	4.61120i	0.0997731	+	0.172812i
$713$	2.51317	+	4.35293i	0.0941188	+	0.163019i
$714$	3.67544			0.137550
$715$		0			0
$716$	9.67544			0.361588
$717$	−7.64911	−	13.2486i	−0.285661	−	0.494780i
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	−0.955947	−	0.293538i	$-0.905167\pi$
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	0.732185	+	0.681106i	$0.238501\pi$
$720$		0			0
$721$	6.66228	−	11.5394i	0.248116	−	0.429750i
$722$	23.8114	−	41.2425i	0.886168	−	1.53489i
$723$	37.8641			1.40818
$724$	10.9057	−	18.8892i	0.405307	−	0.702012i
$725$		0			0
$726$	10.0000	+	17.3205i	0.371135	+	0.642824i
$727$	33.3246			1.23594			0.617970	−	0.786202i	$-0.287955\pi$
$727$	33.3246			1.23594			0.617970	+	0.786202i	$0.287955\pi$
$728$	3.08114	+	1.87259i	0.114195	+	0.0694027i
$729$	13.0000			0.481481
$730$		0			0
$731$	−1.16228	−	2.01312i	−0.0429884	−	0.0744581i
$732$	−18.1623	+	31.4580i	−0.671297	+	1.16272i
$733$	10.4868			0.387340			0.193670	−	0.981067i	$-0.437961\pi$
$733$	10.4868			0.387340			0.193670	+	0.981067i	$0.437961\pi$
$734$	10.3246	−	17.8827i	0.381086	−	0.660061i
$735$		0			0
$736$	6.00000			0.221163
$737$	−21.4868	+	37.2163i	−0.791478	+	1.37088i
$738$	8.13594	+	14.0919i	0.299488	+	0.518729i
$739$	6.59431	+	11.4217i	0.242575	+	0.420153i	0.961447	−	0.274990i	$-0.0886745\pi$
$739$	6.59431	+	11.4217i	0.242575	+	0.420153i	−0.718872	+	0.695143i	$0.755341\pi$
$740$		0			0
$741$	2.09431	−	93.0407i	0.0769362	−	3.41794i
$742$	4.16228			0.152802
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	0.652369	−	0.757902i	$-0.273775\pi$
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	−0.982547	+	0.186017i	$0.940442\pi$
$744$	1.32456	+	2.29420i	0.0485606	+	0.0841093i
$745$		0			0
$746$	−5.35089			−0.195910
$747$	−33.2039	+	57.5109i	−1.21487	+	2.10421i
$748$	−2.41886	+	4.18959i	−0.0884423	+	0.153187i
$749$	−15.4868			−0.565877
$750$		0			0
$751$	−1.48683	−	2.57527i	−0.0542553	−	0.0939729i	0.837622	−	0.546250i	$-0.183945\pi$
$751$	−1.48683	−	2.57527i	−0.0542553	−	0.0939729i	−0.891877	+	0.452277i	$0.850612\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	−20.5132			−0.747541
$754$	−7.16228	−	4.35293i	−0.260835	−	0.158524i
$755$		0			0
$756$	−6.32456	−	10.9545i	−0.230022	−	0.398410i
$757$	13.9189	+	24.1082i	0.505890	+	0.876227i	0.999977	+	0.00681414i	$0.00216903\pi$
$757$	13.9189	+	24.1082i	0.505890	+	0.876227i	−0.494087	+	0.869412i	$0.664498\pi$
$758$	−3.59431	+	6.22552i	−0.130551	+	0.226121i
$759$	78.9737			2.86656
$760$		0			0
$761$	−21.1491	+	36.6313i	−0.766655	+	1.32788i	0.172713	+	0.984972i	$0.444747\pi$
$761$	−21.1491	+	36.6313i	−0.766655	+	1.32788i	−0.939367	+	0.342913i	$0.888587\pi$
$762$	−29.4868			−1.06820
$763$	7.32456	−	12.6865i	0.265167	−	0.459282i
$764$	4.74342	+	8.21584i	0.171611	+	0.297239i
$765$		0			0
$766$	30.0000			1.08394
$767$	−7.16228	−	4.35293i	−0.258615	−	0.157175i
$768$	3.16228			0.114109
$769$	3.16228	+	5.47723i	0.114035	+	0.197514i	0.917393	−	0.397981i	$-0.130289\pi$
$769$	3.16228	+	5.47723i	0.114035	+	0.197514i	−0.803359	+	0.595495i	$0.796956\pi$
$770$		0			0
$771$		0			0
$772$	4.00000			0.143963
$773$	−10.8925	+	18.8664i	−0.391777	+	0.678578i	−0.992684	−	0.120741i	$-0.961473\pi$
$773$	−10.8925	+	18.8664i	−0.391777	+	0.678578i	0.600907	+	0.799319i	$0.294806\pi$
$774$	−7.00000	+	12.1244i	−0.251610	+	0.435801i
$775$		0			0
$776$	−5.74342	+	9.94789i	−0.206177	+	0.357108i
$777$	9.74342	+	16.8761i	0.349543	+	0.605426i
$778$	9.58114	+	16.5950i	0.343500	+	0.594960i
$779$	−18.9737			−0.679802
$780$		0			0
$781$	−34.6491			−1.23984
$782$	3.48683	+	6.03937i	0.124689	+	0.215967i
$783$	14.7018	+	25.4642i	0.525399	+	0.910017i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$		0			0
$786$	32.9057	−	56.9943i	1.17371	−	2.03292i
$787$	−0.932028	+	1.61432i	−0.0332232	+	0.0575443i	−0.882159	−	0.470952i	$-0.843911\pi$
$787$	−0.932028	+	1.61432i	−0.0332232	+	0.0575443i	0.848936	+	0.528496i	$0.177244\pi$
$788$	−0.486833			−0.0173427
$789$	21.5811	−	37.3796i	0.768309	−	1.33075i
$790$		0			0
$791$	8.32456	+	14.4186i	0.295987	+	0.512665i
$792$	29.1359			1.03530
$793$	−35.3925	−	21.5101i	−1.25683	−	0.763846i
$794$	19.5132			0.692496
$795$		0			0
$796$	13.3246	+	23.0788i	0.472276	+	0.818007i
$797$	−13.1623	+	22.7977i	−0.466232	+	0.807537i	−0.999256	−	0.0385627i	$-0.987722\pi$
$797$	−13.1623	+	22.7977i	−0.466232	+	0.807537i	0.533024	+	0.846100i	$0.321055\pi$
$798$	25.8114			0.913713
$799$	1.74342	−	3.01969i	0.0616776	−	0.106829i
$800$		0			0
$801$	37.2719			1.31694
$802$	−7.98683	+	13.8336i	−0.282025	+	0.488481i
$803$	−19.0680	−	33.0267i	−0.672894	−	1.16549i
$804$	16.3246	+	28.2750i	0.575723	+	0.997181i
$805$		0			0
$806$	−2.64911	+	1.45098i	−0.0933109	+	0.0511085i
$807$	67.9473			2.39186
$808$	−2.41886	−	4.18959i	−0.0850952	−	0.147389i
$809$	1.16228	+	2.01312i	0.0408635	+	0.0707777i	0.885734	−	0.464194i	$-0.153656\pi$
$809$	1.16228	+	2.01312i	0.0408635	+	0.0707777i	−0.844870	+	0.534971i	$0.820322\pi$
$810$		0			0
$811$	0.162278			0.00569834			0.00284917	−	0.999996i	$-0.499093\pi$
$811$	0.162278			0.00569834			0.00284917	+	0.999996i	$0.499093\pi$
$812$	1.16228	−	2.01312i	0.0407879	−	0.0706468i
$813$	10.0000	−	17.3205i	0.350715	−	0.607457i
$814$	−25.6491			−0.899001
$815$		0			0
$816$	1.83772	+	3.18303i	0.0643331	+	0.111428i
$817$	−8.16228	−	14.1375i	−0.285562	−	0.494608i
$818$	−3.64911			−0.127588
$819$	22.1359	−	12.1244i	0.773492	−	0.423659i
$820$		0			0
$821$	−0.581139	−	1.00656i	−0.0202819	−	0.0351293i	0.855706	−	0.517462i	$-0.173123\pi$
$821$	−0.581139	−	1.00656i	−0.0202819	−	0.0351293i	−0.875988	+	0.482333i	$0.839790\pi$
$822$	5.51317	+	9.54909i	0.192294	+	0.333063i
$823$	23.5000	−	40.7032i	0.819159	−	1.41882i	−0.0871445	−	0.996196i	$-0.527774\pi$
$823$	23.5000	−	40.7032i	0.819159	−	1.41882i	0.906303	−	0.422628i	$-0.138892\pi$
$824$	13.3246			0.464183
$825$		0			0
$826$	1.16228	−	2.01312i	0.0404408	−	0.0700455i
$827$	32.5132			1.13059			0.565297	−	0.824888i	$-0.308762\pi$
$827$	32.5132			1.13059			0.565297	+	0.824888i	$0.308762\pi$
$828$	21.0000	−	36.3731i	0.729800	−	1.26405i
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	−0.997848	−	0.0655624i	$-0.979116\pi$
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	0.442145	−	0.896943i	$-0.354217\pi$
$830$		0			0
$831$	−64.7851			−2.24737
$832$	−0.0811388	+	3.60464i	−0.00281298	+	0.124968i
$833$	6.97367			0.241623
$834$	−9.23025	−	15.9873i	−0.319617	−	0.553594i
$835$		0			0
$836$	−16.9868	+	29.4221i	−0.587502	+	1.01758i
$837$	10.5964			0.366267
$838$	−5.32456	+	9.22240i	−0.183934	+	0.318583i
$839$	8.41886	−	14.5819i	0.290651	−	0.503423i	−0.683313	−	0.730126i	$-0.739461\pi$
$839$	8.41886	−	14.5819i	0.290651	−	0.503423i	0.973964	+	0.226703i	$0.0727947\pi$
$840$		0			0
$841$	11.7982	−	20.4351i	0.406835	−	0.704659i
$842$	1.58114	+	2.73861i	0.0544896	+	0.0943788i
$843$	−30.0000	−	51.9615i	−1.03325	−	1.78965i
$844$	18.1623			0.625171
$845$		0			0
$846$	−21.0000			−0.721995
$847$	−3.16228	−	5.47723i	−0.108657	−	0.188200i
$848$	2.08114	+	3.60464i	0.0714666	+	0.123784i
$849$	−34.7851	+	60.2495i	−1.19382	+	2.06776i
$850$		0			0
$851$	−18.4868	+	32.0201i	−0.633720	+	1.09764i
$852$	−13.1623	+	22.7977i	−0.450932	+	0.781037i
$853$	32.2719			1.10497			0.552484	−	0.833523i	$-0.313680\pi$
$853$	32.2719			1.10497			0.552484	+	0.833523i	$0.313680\pi$
$854$	5.74342	−	9.94789i	0.196536	−	0.340410i
$855$		0			0
$856$	−7.74342	−	13.4120i	−0.264665	−	0.458412i
$857$	14.1359			0.482875			0.241437	−	0.970416i	$-0.422381\pi$
$857$	14.1359			0.482875			0.241437	+	0.970416i	$0.422381\pi$
$858$	−1.06797	+	47.4452i	−0.0364600	+	1.61975i
$859$	2.86406			0.0977203			0.0488602	−	0.998806i	$-0.484441\pi$
$859$	2.86406			0.0977203			0.0488602	+	0.998806i	$0.484441\pi$
$860$		0			0
$861$	−3.67544	−	6.36606i	−0.125259	−	0.216955i
$862$	−1.74342	+	3.01969i	−0.0593810	+	0.102851i
$863$	18.0000			0.612727			0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000			0.612727			0.306364	+	0.951915i	$0.400888\pi$
$864$	6.32456	−	10.9545i	0.215166	−	0.372678i
$865$		0			0
$866$	−6.32456			−0.214917
$867$	24.7434	−	42.8569i	0.840330	−	1.45550i
$868$	−0.418861	−	0.725489i	−0.0142171	−	0.0246247i
$869$	11.4189	+	19.7780i	0.387358	+	0.670924i
$870$		0			0
$871$	−32.6491	+	17.8827i	−1.10627	+	0.605931i
$872$	14.6491			0.496081
$873$	40.2039	+	69.6352i	1.36070	+	2.35680i
$874$	24.4868	+	42.4124i	0.828279	+	1.43462i
$875$		0			0
$876$	−28.9737			−0.978929
$877$	−18.1623	+	31.4580i	−0.613297	+	1.06226i	0.377384	+	0.926057i	$0.376824\pi$
$877$	−18.1623	+	31.4580i	−0.613297	+	1.06226i	−0.990681	+	0.136204i	$0.956510\pi$
$878$	−13.9057	+	24.0854i	−0.469294	+	0.812842i
$879$	89.0569			3.00382
$880$		0			0
$881$	10.0132	+	17.3433i	0.337352	+	0.584311i	0.983934	−	0.178534i	$-0.0571354\pi$
$881$	10.0132	+	17.3433i	0.337352	+	0.584311i	−0.646582	+	0.762845i	$0.723802\pi$
$882$	−21.0000	−	36.3731i	−0.707107	−	1.22474i
$883$	−16.5132			−0.555712			−0.277856	−	0.960623i	$-0.589624\pi$
$883$	−16.5132			−0.555712			−0.277856	+	0.960623i	$0.589624\pi$
$884$	−3.67544	+	2.01312i	−0.123619	+	0.0677087i
$885$		0			0
$886$	−0.675445	−	1.16990i	−0.0226920	−	0.0393037i
$887$	−13.3114	−	23.0560i	−0.446953	−	0.774145i	0.551233	−	0.834351i	$-0.314157\pi$
$887$	−13.3114	−	23.0560i	−0.446953	−	0.774145i	−0.998186	+	0.0602064i	$0.980824\pi$
$888$	−9.74342	+	16.8761i	−0.326968	+	0.566325i
$889$	9.32456			0.312736
$890$		0			0
$891$	39.5416	−	68.4881i	1.32469	−	2.29444i
$892$	9.32456			0.312209
$893$	12.2434	−	21.2062i	0.409710	−	0.709639i
$894$	5.81139	+	10.0656i	0.194362	+	0.336645i
$895$		0			0
$896$	−1.00000			−0.0334077
$897$	58.4605	+	35.5298i	1.95194	+	1.18631i
$898$	39.9737			1.33394
$899$	0.973666	+	1.68644i	0.0324736	+	0.0562459i
$900$		0			0
$901$	−2.41886	+	4.18959i	−0.0805839	+	0.139575i
$902$	9.67544			0.322157
$903$	3.16228	−	5.47723i	0.105234	−	0.182271i
$904$	−8.32456	+	14.4186i	−0.276871	+	0.479554i
$905$		0			0
$906$	−17.6491	+	30.5692i	−0.586352	+	1.01559i
$907$	14.0680	+	24.3664i	0.467119	+	0.809074i	0.999294	−	0.0375599i	$-0.0119585\pi$
$907$	14.0680	+	24.3664i	0.467119	+	0.809074i	−0.532175	+	0.846634i	$0.678625\pi$
$908$	−1.16228	−	2.01312i	−0.0385715	−	0.0668079i
$909$	−33.8641			−1.12320
$910$		0			0
$911$	33.2982			1.10322			0.551610	−	0.834102i	$-0.314014\pi$
$911$	33.2982			1.10322			0.551610	+	0.834102i	$0.314014\pi$
$912$	12.9057	+	22.3533i	0.427350	+	0.740192i
$913$	19.7434	+	34.1966i	0.653412	+	1.13174i
$914$	16.2302	−	28.1116i	0.536849	−	0.929850i
$915$		0			0
$916$	−4.58114	+	7.93477i	−0.151365	+	0.262172i
$917$	−10.4057	+	18.0232i	−0.343626	+	0.595178i
$918$	14.7018			0.485231
$919$	12.1623	−	21.0657i	0.401197	−	0.694893i	−0.592674	−	0.805442i	$-0.701928\pi$
$919$	12.1623	−	21.0657i	0.401197	−	0.694893i	0.993871	+	0.110550i	$0.0352611\pi$
$920$		0			0
$921$	44.7851	+	77.5700i	1.47572	+	2.55602i
$922$	−2.51317			−0.0827667
$923$	−25.6491	−	15.5885i	−0.844251	−	0.513100i
$924$	−13.1623			−0.433007
$925$		0			0
$926$	0.162278	+	0.281073i	0.00533277	+	0.00923664i
$927$	46.6359	−	80.7758i	1.53173	−	2.65303i
$928$	2.32456			0.0763073
$929$	−27.0000	+	46.7654i	−0.885841	+	1.53432i	−0.0410949	+	0.999155i	$0.513085\pi$
$929$	−27.0000	+	46.7654i	−0.885841	+	1.53432i	−0.844746	+	0.535167i	$0.820249\pi$
$930$		0			0
$931$	48.9737			1.60505
$932$	−4.74342	+	8.21584i	−0.155376	+	0.269119i
$933$	−24.4868	−	42.4124i	−0.801663	−	1.38852i
$934$	−3.67544	−	6.36606i	−0.120264	−	0.208304i
$935$		0			0
$936$	21.5680	+	13.1081i	0.704971	+	0.428452i
$937$	−40.3246			−1.31735			−0.658673	−	0.752429i	$-0.728882\pi$
$937$	−40.3246			−1.31735			−0.658673	+	0.752429i	$0.728882\pi$
$938$	−5.16228	−	8.94133i	−0.168554	−	0.291945i
$939$	6.83772	+	11.8433i	0.223141	+	0.386491i
$940$		0			0
$941$	9.67544			0.315410			0.157705	−	0.987486i	$-0.449590\pi$
$941$	9.67544			0.315410			0.157705	+	0.987486i	$0.449590\pi$
$942$	9.23025	−	15.9873i	0.300738	−	0.520893i
$943$	6.97367	−	12.0787i	0.227094	−	0.393338i
$944$	2.32456			0.0756578
$945$		0			0
$946$	4.16228	+	7.20928i	0.135327	+	0.234394i
$947$	14.9057	+	25.8174i	0.484370	+	0.838953i	0.999839	−	0.0179549i	$-0.00571554\pi$
$947$	14.9057	+	25.8174i	0.484370	+	0.838953i	−0.515469	+	0.856908i	$0.672382\pi$
$948$	17.3509			0.563531
$949$	0.743416	−	33.0267i	0.0241323	−	1.07209i
$950$		0			0
$951$	−10.2566	−	17.7649i	−0.332593	−	0.576067i
$952$	−0.581139	−	1.00656i	−0.0188348	−	0.0326229i
$953$	−10.7434	+	18.6081i	−0.348013	+	0.602777i	−0.985896	−	0.167356i	$-0.946477\pi$
$953$	−10.7434	+	18.6081i	−0.348013	+	0.602777i	0.637883	+	0.770133i	$0.279810\pi$
$954$	29.1359			0.943311
$955$		0			0
$956$	−2.41886	+	4.18959i	−0.0782316	+	0.135501i
$957$	30.5964			0.989043
$958$	16.0680	−	27.8305i	0.519133	−	0.899164i
$959$	−1.74342	−	3.01969i	−0.0562979	−	0.0975107i
$960$		0			0
$961$	−30.2982			−0.977362
$962$	−18.9868	−	11.5394i	−0.612160	−	0.372045i
$963$	−108.408			−3.49339
$964$	−5.98683	−	10.3695i	−0.192823	−	0.333979i
$965$		0			0
$966$	−9.48683	+	16.4317i	−0.305234	+	0.528681i
$967$	−46.6228			−1.49929			−0.749644	−	0.661842i	$-0.769775\pi$
$967$	−46.6228			−1.49929			−0.749644	+	0.661842i	$0.769775\pi$
$968$	3.16228	−	5.47723i	0.101639	−	0.176045i
$969$	−15.0000	+	25.9808i	−0.481869	+	0.834622i
$970$		0			0
$971$	4.89253	−	8.47411i	0.157009	−	0.271947i	−0.776780	−	0.629772i	$-0.783148\pi$
$971$	4.89253	−	8.47411i	0.157009	−	0.271947i	0.933789	+	0.357825i	$0.116482\pi$
$972$	−11.0680	−	19.1703i	−0.355005	−	0.614887i
$973$	2.91886	+	5.05562i	0.0935744	+	0.162076i
$974$	−1.00000			−0.0320421
$975$		0			0
$976$	11.4868			0.367685
$977$	−9.48683	−	16.4317i	−0.303511	−	0.525696i	0.673418	−	0.739262i	$-0.264825\pi$
$977$	−9.48683	−	16.4317i	−0.303511	−	0.525696i	−0.976929	+	0.213566i	$0.931492\pi$
$978$	2.35089	+	4.07186i	0.0751732	+	0.130204i
$979$	11.0811	−	19.1931i	0.354155	−	0.613414i
$980$		0			0
$981$	51.2719	−	88.8055i	1.63699	−	2.83534i
$982$	18.2434	−	31.5985i	0.582171	−	1.00835i
$983$	−55.6491			−1.77493			−0.887465	−	0.460874i	$-0.847536\pi$
$983$	−55.6491			−1.77493			−0.887465	+	0.460874i	$0.847536\pi$
$984$	3.67544	−	6.36606i	0.117169	−	0.202942i
$985$		0			0
$986$	1.35089	+	2.33981i	0.0430211	+	0.0745147i
$987$	9.48683			0.301969
$988$	−25.8114	+	14.1375i	−0.821170	+	0.449773i
$989$	12.0000			0.381578
$990$		0			0
$991$	−5.64911	−	9.78455i	−0.179450	−	0.310816i	0.762242	−	0.647292i	$-0.224098\pi$
$991$	−5.64911	−	9.78455i	−0.179450	−	0.310816i	−0.941692	+	0.336475i	$0.890765\pi$
$992$	0.418861	−	0.725489i	0.0132989	−	0.0230343i
$993$	2.05267			0.0651395
$994$	4.16228	−	7.20928i	0.132019	−	0.228664i
$995$		0			0
$996$	30.0000			0.950586
$997$	9.08114	−	15.7290i	0.287603	−	0.498142i	−0.685634	−	0.727946i	$-0.740475\pi$
$997$	9.08114	−	15.7290i	0.287603	−	0.498142i	0.973237	+	0.229804i	$0.0738085\pi$
$998$	−11.0000	−	19.0526i	−0.348199	−	0.603098i
$999$	38.9737	+	67.5044i	1.23307	+	2.13574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.e.h.601.1		4
5.2	odd	4		650.2.o.g.549.1		8
5.3	odd	4		650.2.o.g.549.4		8
5.4	even	2		130.2.e.c.81.2	yes	4
13.3	even	3		8450.2.a.bc.1.2		2
13.9	even	3	inner	650.2.e.h.451.1		4
13.10	even	6		8450.2.a.bj.1.2		2
15.14	odd	2		1170.2.i.q.991.1		4
20.19	odd	2		1040.2.q.m.81.1		4
65.4	even	6		1690.2.e.m.191.2		4
65.9	even	6		130.2.e.c.61.2	✓	4
65.19	odd	12		1690.2.l.k.1161.4		8
65.22	odd	12		650.2.o.g.399.4		8
65.24	odd	12		1690.2.d.g.1351.3		4
65.29	even	6		1690.2.a.n.1.1		2
65.34	odd	4		1690.2.l.k.361.4		8
65.44	odd	4		1690.2.l.k.361.2		8
65.48	odd	12		650.2.o.g.399.1		8
65.49	even	6		1690.2.a.k.1.1		2
65.54	odd	12		1690.2.d.g.1351.1		4
65.59	odd	12		1690.2.l.k.1161.2		8
65.64	even	2		1690.2.e.m.991.2		4
195.74	odd	6		1170.2.i.q.451.1		4
260.139	odd	6		1040.2.q.m.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.c.61.2	✓	4	65.9	even	6
130.2.e.c.81.2	yes	4	5.4	even	2
650.2.e.h.451.1		4	13.9	even	3	inner
650.2.e.h.601.1		4	1.1	even	1	trivial
650.2.o.g.399.1		8	65.48	odd	12
650.2.o.g.399.4		8	65.22	odd	12
650.2.o.g.549.1		8	5.2	odd	4
650.2.o.g.549.4		8	5.3	odd	4
1040.2.q.m.81.1		4	20.19	odd	2
1040.2.q.m.321.1		4	260.139	odd	6
1170.2.i.q.451.1		4	195.74	odd	6
1170.2.i.q.991.1		4	15.14	odd	2
1690.2.a.k.1.1		2	65.49	even	6
1690.2.a.n.1.1		2	65.29	even	6
1690.2.d.g.1351.1		4	65.54	odd	12
1690.2.d.g.1351.3		4	65.24	odd	12
1690.2.e.m.191.2		4	65.4	even	6
1690.2.e.m.991.2		4	65.64	even	2
1690.2.l.k.361.2		8	65.44	odd	4
1690.2.l.k.361.4		8	65.34	odd	4
1690.2.l.k.1161.2		8	65.59	odd	12
1690.2.l.k.1161.4		8	65.19	odd	12
8450.2.a.bc.1.2		2	13.3	even	3
8450.2.a.bj.1.2		2	13.10	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.58114 - 2.73861i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.58114 - 2.73861i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.50000 + 6.06218i) q^{9} +(2.08114 + 3.60464i) q^{11} +3.16228 q^{12} +(-0.0811388 + 3.60464i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.581139 - 1.00656i) q^{17} -7.00000 q^{18} +(4.08114 - 7.06874i) q^{19} +3.16228 q^{21} +(-2.08114 + 3.60464i) q^{22} +(3.00000 + 5.19615i) q^{23} +(1.58114 + 2.73861i) q^{24} +(-3.16228 + 1.73205i) q^{26} +12.6491 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.16228 + 2.01312i) q^{29} +0.837722 q^{31} +(0.500000 - 0.866025i) q^{32} +(6.58114 - 11.3989i) q^{33} +1.16228 q^{34} +(-3.50000 - 6.06218i) q^{36} +(3.08114 + 5.33669i) q^{37} +8.16228 q^{38} +(10.0000 - 5.47723i) q^{39} +(-1.16228 - 2.01312i) q^{41} +(1.58114 + 2.73861i) q^{42} +(1.00000 - 1.73205i) q^{43} -4.16228 q^{44} +(-3.00000 + 5.19615i) q^{46} +3.00000 q^{47} +(-1.58114 + 2.73861i) q^{48} +(3.00000 + 5.19615i) q^{49} -3.67544 q^{51} +(-3.08114 - 1.87259i) q^{52} -4.16228 q^{53} +(6.32456 + 10.9545i) q^{54} +(0.500000 - 0.866025i) q^{56} -25.8114 q^{57} +(-1.16228 + 2.01312i) q^{58} +(-1.16228 + 2.01312i) q^{59} +(-5.74342 + 9.94789i) q^{61} +(0.418861 + 0.725489i) q^{62} +(-3.50000 - 6.06218i) q^{63} +1.00000 q^{64} +13.1623 q^{66} +(5.16228 + 8.94133i) q^{67} +(0.581139 + 1.00656i) q^{68} +(9.48683 - 16.4317i) q^{69} +(-4.16228 + 7.20928i) q^{71} +(3.50000 - 6.06218i) q^{72} -9.16228 q^{73} +(-3.08114 + 5.33669i) q^{74} +(4.08114 + 7.06874i) q^{76} -4.16228 q^{77} +(9.74342 + 5.92164i) q^{78} +5.48683 q^{79} +(-9.50000 - 16.4545i) q^{81} +(1.16228 - 2.01312i) q^{82} +9.48683 q^{83} +(-1.58114 + 2.73861i) q^{84} +2.00000 q^{86} +(3.67544 - 6.36606i) q^{87} +(-2.08114 - 3.60464i) q^{88} +(-2.66228 - 4.61120i) q^{89} +(-3.08114 - 1.87259i) q^{91} -6.00000 q^{92} +(-1.32456 - 2.29420i) q^{93} +(1.50000 + 2.59808i) q^{94} -3.16228 q^{96} +(5.74342 - 9.94789i) q^{97} +(-3.00000 + 5.19615i) q^{98} -29.1359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{7} - 4 q^{8} - 14 q^{9} + 2 q^{11} + 6 q^{13} - 4 q^{14} - 2 q^{16} - 4 q^{17} - 28 q^{18} + 10 q^{19} - 2 q^{22} + 12 q^{23} - 2 q^{28} - 8 q^{29} + 16 q^{31} + 2 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^7 - 4 * q^8 - 14 * q^9 + 2 * q^11 + 6 * q^13 - 4 * q^14 - 2 * q^16 - 4 * q^17 - 28 * q^18 + 10 * q^19 - 2 * q^22 + 12 * q^23 - 2 * q^28 - 8 * q^29 + 16 * q^31 + 2 * q^32 + 20 * q^33 - 8 * q^34 - 14 * q^36 + 6 * q^37 + 20 * q^38 + 40 * q^39 + 8 * q^41 + 4 * q^43 - 4 * q^44 - 12 * q^46 + 12 * q^47 + 12 * q^49 - 40 * q^51 - 6 * q^52 - 4 * q^53 + 2 * q^56 - 40 * q^57 + 8 * q^58 + 8 * q^59 - 4 * q^61 + 8 * q^62 - 14 * q^63 + 4 * q^64 + 40 * q^66 + 8 * q^67 - 4 * q^68 - 4 * q^71 + 14 * q^72 - 24 * q^73 - 6 * q^74 + 10 * q^76 - 4 * q^77 + 20 * q^78 - 16 * q^79 - 38 * q^81 - 8 * q^82 + 8 * q^86 + 40 * q^87 - 2 * q^88 + 2 * q^89 - 6 * q^91 - 24 * q^92 + 20 * q^93 + 6 * q^94 + 4 * q^97 - 12 * q^98 - 28 * q^99

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