LMFDB - Embedded newform 833.2.e.h.18.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(18,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("833.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.e (of order $3$, degree $2$, not 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 10x^{7} + 44x^{6} - 49x^{5} + 99x^{4} - 20x^{3} + 31x^{2} - 3x + 9 $ x^10 - 2x^9 + 9x^8 - 10x^7 + 44x^6 - 49x^5 + 99x^4 - 20x^3 + 31x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.4
Root			$-0.272099 - 0.471289i$ of defining polynomial
Character	$\chi$	$=$	833.18
Dual form			833.2.e.h.324.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.704339 + 1.21995i) q^{2} +(1.27991 - 2.21687i) q^{3} +(0.00781334 - 0.0135331i) q^{4} +(0.883300 + 1.52992i) q^{5} +3.60597 q^{6} +2.83937 q^{8} +(-1.77635 - 3.07673i) q^{9} +(-1.24428 + 2.15516i) q^{10} +(2.70385 - 4.68320i) q^{11} +(-0.0200008 - 0.0346424i) q^{12} -5.90575 q^{13} +4.52218 q^{15} +(1.98425 + 3.43682i) q^{16} +(0.500000 - 0.866025i) q^{17} +(2.50231 - 4.33412i) q^{18} +(1.54420 + 2.67463i) q^{19} +0.0276061 q^{20} +7.61770 q^{22} +(3.01563 + 5.22322i) q^{23} +(3.63414 - 6.29452i) q^{24} +(0.939563 - 1.62737i) q^{25} +(-4.15965 - 7.20473i) q^{26} -1.41482 q^{27} -8.99415 q^{29} +(3.18515 + 5.51684i) q^{30} +(-1.13233 + 1.96125i) q^{31} +(0.0441979 - 0.0765530i) q^{32} +(-6.92138 - 11.9882i) q^{33} +1.40868 q^{34} -0.0555169 q^{36} +(0.839369 + 1.45383i) q^{37} +(-2.17528 + 3.76769i) q^{38} +(-7.55884 + 13.0923i) q^{39} +(2.50801 + 4.34401i) q^{40} -4.25753 q^{41} +4.06177 q^{43} +(-0.0422522 - 0.0731829i) q^{44} +(3.13810 - 5.43535i) q^{45} +(-4.24805 + 7.35783i) q^{46} +(-2.15115 - 3.72590i) q^{47} +10.1587 q^{48} +2.64708 q^{50} +(-1.27991 - 2.21687i) q^{51} +(-0.0461436 + 0.0799231i) q^{52} +(0.276351 - 0.478654i) q^{53} +(-0.996513 - 1.72601i) q^{54} +9.55324 q^{55} +7.90575 q^{57} +(-6.33493 - 10.9724i) q^{58} +(-1.08840 + 1.88516i) q^{59} +(0.0353334 - 0.0611992i) q^{60} +(1.87123 + 3.24107i) q^{61} -3.19017 q^{62} +8.06153 q^{64} +(-5.21655 - 9.03533i) q^{65} +(9.74999 - 16.8875i) q^{66} +(-4.29198 + 7.43392i) q^{67} +(-0.00781334 - 0.0135331i) q^{68} +15.4390 q^{69} +5.26519 q^{71} +(-5.04372 - 8.73597i) q^{72} +(-0.719107 + 1.24553i) q^{73} +(-1.18240 + 2.04798i) q^{74} +(-2.40512 - 4.16578i) q^{75} +0.0482614 q^{76} -21.2960 q^{78} +(2.96850 + 5.14160i) q^{79} +(-3.50538 + 6.07149i) q^{80} +(3.51821 - 6.09371i) q^{81} +(-2.99874 - 5.19398i) q^{82} -9.02540 q^{83} +1.76660 q^{85} +(2.86086 + 4.95516i) q^{86} +(-11.5117 + 19.9389i) q^{87} +(7.67722 - 13.2973i) q^{88} +(7.04978 + 12.2106i) q^{89} +8.84115 q^{90} +0.0942485 q^{92} +(2.89856 + 5.02045i) q^{93} +(3.03027 - 5.24859i) q^{94} +(-2.72798 + 4.72500i) q^{95} +(-0.113139 - 0.195962i) q^{96} +0.119116 q^{97} -19.2119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 2 q^{6} + 12 q^{8} - 11 q^{9} + 4 q^{10} + 2 q^{11} - 22 q^{12} - 4 q^{13} + 16 q^{15} - 4 q^{16} + 5 q^{17} + 18 q^{18} + 6 q^{19} + 38 q^{20} + 12 q^{22} + 10 q^{23}+ \cdots - 124 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 2 * q^6 + 12 * q^8 - 11 * q^9 + 4 * q^10 + 2 * q^11 - 22 * q^12 - 4 * q^13 + 16 * q^15 - 4 * q^16 + 5 * q^17 + 18 * q^18 + 6 * q^19 + 38 * q^20 + 12 * q^22 + 10 * q^23 + 2 * q^24 - 21 * q^25 - 26 * q^26 + 52 * q^27 - 16 * q^29 + 51 * q^30 - 9 * q^32 + 6 * q^33 - 4 * q^34 + 78 * q^36 - 8 * q^37 + 14 * q^38 - 14 * q^39 + 5 * q^40 - 36 * q^41 + 16 * q^43 + 14 * q^44 - 8 * q^46 - 10 * q^47 + 54 * q^48 + 54 * q^50 + 2 * q^51 + 4 * q^52 - 4 * q^53 + 5 * q^54 + 48 * q^55 + 24 * q^57 - 12 * q^58 + 8 * q^59 + 7 * q^60 + 22 * q^61 - 32 * q^62 - 32 * q^64 + 30 * q^65 + 68 * q^66 - 16 * q^67 + 10 * q^68 + 64 * q^69 - 4 * q^71 - 9 * q^72 + 10 * q^73 + 40 * q^74 - 14 * q^75 - 48 * q^76 + 60 * q^78 - 18 * q^79 - 4 * q^80 - 25 * q^81 - 31 * q^82 + 24 * q^83 - 23 * q^86 - 26 * q^87 + 46 * q^88 + 20 * q^89 - 194 * q^90 + 56 * q^92 + 28 * q^93 - 42 * q^94 + 22 * q^95 - 18 * q^96 - 24 * q^97 - 124 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.704339	+	1.21995i	0.498043	+	0.862635i	0.999997	−	0.00225847i	$-0.000718893\pi$
$2$	0.704339	+	1.21995i	0.498043	+	0.862635i	−0.501955	+	0.864894i	$0.667386\pi$
$3$	1.27991	−	2.21687i	0.738958	−	1.27991i	−0.214007	−	0.976832i	$-0.568652\pi$
$3$	1.27991	−	2.21687i	0.738958	−	1.27991i	0.952965	−	0.303080i	$-0.0980150\pi$
$4$	0.00781334	−	0.0135331i	0.00390667	−	0.00676655i
$5$	0.883300	+	1.52992i	0.395024	+	0.684201i	0.993104	−	0.117235i	$-0.0374031\pi$
$5$	0.883300	+	1.52992i	0.395024	+	0.684201i	−0.598081	+	0.801436i	$0.704070\pi$
$6$	3.60597			1.47213
$7$		0			0
$7$		0			0
$8$	2.83937			1.00387
$9$	−1.77635	−	3.07673i	−0.592117	−	1.02558i
$10$	−1.24428	+	2.15516i	−0.393477	+	0.681523i
$11$	2.70385	−	4.68320i	0.815241	−	1.41204i	−0.0939137	−	0.995580i	$-0.529938\pi$
$11$	2.70385	−	4.68320i	0.815241	−	1.41204i	0.909155	−	0.416459i	$-0.136729\pi$
$12$	−0.0200008	−	0.0346424i	−0.00577373	−	0.0100004i
$13$	−5.90575			−1.63796			−0.818980	−	0.573822i	$-0.805460\pi$
$13$	−5.90575			−1.63796			−0.818980	+	0.573822i	$0.805460\pi$
$14$		0			0
$15$	4.52218			1.16762
$16$	1.98425	+	3.43682i	0.496063	+	0.859206i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	2.50231	−	4.33412i	0.589799	−	1.02156i
$19$	1.54420	+	2.67463i	0.354263	+	0.613602i	0.986992	−	0.160772i	$-0.0513983\pi$
$19$	1.54420	+	2.67463i	0.354263	+	0.613602i	−0.632728	+	0.774374i	$0.718065\pi$
$20$	0.0276061			0.00617291
$21$		0			0
$22$	7.61770			1.62410
$23$	3.01563	+	5.22322i	0.628802	+	1.08912i	0.987793	+	0.155775i	$0.0497876\pi$
$23$	3.01563	+	5.22322i	0.628802	+	1.08912i	−0.358991	+	0.933341i	$0.616879\pi$
$24$	3.63414	−	6.29452i	0.741816	−	1.28486i
$25$	0.939563	−	1.62737i	0.187913	−	0.325474i
$26$	−4.15965	−	7.20473i	−0.815775	−	1.41296i
$27$	−1.41482			−0.272282
$28$		0			0
$29$	−8.99415			−1.67017			−0.835086	−	0.550120i	$-0.814582\pi$
$29$	−8.99415			−1.67017			−0.835086	+	0.550120i	$0.814582\pi$
$30$	3.18515	+	5.51684i	0.581526	+	1.00723i
$31$	−1.13233	+	1.96125i	−0.203372	+	0.352250i	−0.949613	−	0.313426i	$-0.898523\pi$
$31$	−1.13233	+	1.96125i	−0.203372	+	0.352250i	0.746241	+	0.665676i	$0.231857\pi$
$32$	0.0441979	−	0.0765530i	0.00781316	−	0.0135328i
$33$	−6.92138	−	11.9882i	−1.20486	−	2.08687i
$34$	1.40868			0.241586
$35$		0			0
$36$	−0.0555169			−0.00925282
$37$	0.839369	+	1.45383i	0.137991	+	0.239008i	0.926736	−	0.375713i	$-0.122602\pi$
$37$	0.839369	+	1.45383i	0.137991	+	0.239008i	−0.788745	+	0.614721i	$0.789269\pi$
$38$	−2.17528	+	3.76769i	−0.352877	+	0.611200i
$39$	−7.55884	+	13.0923i	−1.21038	+	2.09645i
$40$	2.50801	+	4.34401i	0.396552	+	0.686848i
$41$	−4.25753			−0.664915			−0.332457	−	0.943118i	$-0.607878\pi$
$41$	−4.25753			−0.664915			−0.332457	+	0.943118i	$0.607878\pi$
$42$		0			0
$43$	4.06177			0.619414			0.309707	−	0.950832i	$-0.399769\pi$
$43$	4.06177			0.619414			0.309707	+	0.950832i	$0.399769\pi$
$44$	−0.0422522	−	0.0731829i	−0.00636975	−	0.0110327i
$45$	3.13810	−	5.43535i	0.467800	−	0.810254i
$46$	−4.24805	+	7.35783i	−0.626340	+	1.08485i
$47$	−2.15115	−	3.72590i	−0.313777	−	0.543478i	0.665400	−	0.746487i	$-0.268261\pi$
$47$	−2.15115	−	3.72590i	−0.313777	−	0.543478i	−0.979177	+	0.203010i	$0.934928\pi$
$48$	10.1587			1.46628
$49$		0			0
$50$	2.64708			0.374354
$51$	−1.27991	−	2.21687i	−0.179224	−	0.310424i
$52$	−0.0461436	+	0.0799231i	−0.00639897	+	0.0110833i
$53$	0.276351	−	0.478654i	0.0379597	−	0.0657482i	−0.846421	−	0.532514i	$-0.821247\pi$
$53$	0.276351	−	0.478654i	0.0379597	−	0.0657482i	0.884381	+	0.466766i	$0.154581\pi$
$54$	−0.996513	−	1.72601i	−0.135608	−	0.234880i
$55$	9.55324			1.28816
$56$		0			0
$57$	7.90575			1.04714
$58$	−6.33493	−	10.9724i	−0.831817	−	1.44075i
$59$	−1.08840	+	1.88516i	−0.141697	+	0.245427i	−0.928136	−	0.372242i	$-0.878589\pi$
$59$	−1.08840	+	1.88516i	−0.141697	+	0.245427i	0.786439	+	0.617668i	$0.211923\pi$
$60$	0.0353334	−	0.0611992i	0.00456152	−	0.00790078i
$61$	1.87123	+	3.24107i	0.239587	+	0.414977i	0.960596	−	0.277949i	$-0.0896546\pi$
$61$	1.87123	+	3.24107i	0.239587	+	0.414977i	−0.721009	+	0.692926i	$0.756321\pi$
$62$	−3.19017			−0.405152
$63$		0			0
$64$	8.06153			1.00769
$65$	−5.21655	−	9.03533i	−0.647033	−	1.12069i
$66$	9.74999	−	16.8875i	1.20014	−	2.07871i
$67$	−4.29198	+	7.43392i	−0.524349	+	0.908198i	0.475250	+	0.879851i	$0.342358\pi$
$67$	−4.29198	+	7.43392i	−0.524349	+	0.908198i	−0.999598	+	0.0283473i	$0.990976\pi$
$68$	−0.00781334	−	0.0135331i	−0.000947507	−	0.00164113i
$69$	15.4390			1.85863
$70$		0			0
$71$	5.26519			0.624863			0.312431	−	0.949940i	$-0.398857\pi$
$71$	5.26519			0.624863			0.312431	+	0.949940i	$0.398857\pi$
$72$	−5.04372	−	8.73597i	−0.594408	−	1.02954i
$73$	−0.719107	+	1.24553i	−0.0841651	+	0.145778i	−0.905035	−	0.425337i	$-0.860156\pi$
$73$	−0.719107	+	1.24553i	−0.0841651	+	0.145778i	0.820870	+	0.571115i	$0.193489\pi$
$74$	−1.18240	+	2.04798i	−0.137451	+	0.238072i
$75$	−2.40512	−	4.16578i	−0.277719	−	0.481023i
$76$	0.0482614			0.00553596
$77$		0			0
$78$	−21.2960			−2.41129
$79$	2.96850	+	5.14160i	0.333983	+	0.578475i	0.983289	−	0.182052i	$-0.0582740\pi$
$79$	2.96850	+	5.14160i	0.333983	+	0.578475i	−0.649306	+	0.760527i	$0.724941\pi$
$80$	−3.50538	+	6.07149i	−0.391913	+	0.678813i
$81$	3.51821	−	6.09371i	0.390912	−	0.677079i
$82$	−2.99874	−	5.19398i	−0.331156	−	0.573579i
$83$	−9.02540			−0.990666			−0.495333	−	0.868703i	$-0.664954\pi$
$83$	−9.02540			−0.990666			−0.495333	+	0.868703i	$0.664954\pi$
$84$		0			0
$85$	1.76660			0.191615
$86$	2.86086	+	4.95516i	0.308495	+	0.534329i
$87$	−11.5117	+	19.9389i	−1.23419	+	2.13767i
$88$	7.67722	−	13.2973i	0.818395	−	1.41750i
$89$	7.04978	+	12.2106i	0.747275	+	1.29432i	0.949124	+	0.314901i	$0.101971\pi$
$89$	7.04978	+	12.2106i	0.747275	+	1.29432i	−0.201850	+	0.979417i	$0.564695\pi$
$90$	8.84115			0.931939
$91$		0			0
$92$	0.0942485			0.00982608
$93$	2.89856	+	5.02045i	0.300566	+	0.520596i
$94$	3.03027	−	5.24859i	0.312549	−	0.541350i
$95$	−2.72798	+	4.72500i	−0.279885	+	0.484775i
$96$	−0.113139	−	0.195962i	−0.0115472	−	0.0200003i
$97$	0.119116			0.0120944			0.00604718	−	0.999982i	$-0.498075\pi$
$97$	0.119116			0.0120944			0.00604718	+	0.999982i	$0.498075\pi$
$98$		0			0
$99$	−19.2119			−1.93087
$100$	−0.0146822	−	0.0254304i	−0.00146822	−	0.00254304i
$101$	4.87062	−	8.43616i	0.484645	−	0.839430i	−0.515199	−	0.857070i	$-0.672282\pi$
$101$	4.87062	−	8.43616i	0.484645	−	0.839430i	0.999844	+	0.0176406i	$0.00561546\pi$
$102$	1.80298	−	3.12286i	0.178522	−	0.309209i
$103$	−7.42430	−	12.8593i	−0.731538	−	1.26706i	−0.956226	−	0.292631i	$-0.905469\pi$
$103$	−7.42430	−	12.8593i	−0.731538	−	1.26706i	0.224687	−	0.974431i	$-0.427864\pi$
$104$	−16.7686			−1.64430
$105$		0			0
$106$	0.778579			0.0756223
$107$	1.43069	+	2.47803i	0.138310	+	0.239560i	0.926857	−	0.375414i	$-0.122500\pi$
$107$	1.43069	+	2.47803i	0.138310	+	0.239560i	−0.788547	+	0.614975i	$0.789166\pi$
$108$	−0.0110545	+	0.0191469i	−0.00106372	+	0.00184241i
$109$	−8.40770	+	14.5626i	−0.805311	+	1.39484i	0.110769	+	0.993846i	$0.464669\pi$
$109$	−8.40770	+	14.5626i	−0.805311	+	1.39484i	−0.916081	+	0.400994i	$0.868665\pi$
$110$	6.72872	+	11.6545i	0.641558	+	1.11121i
$111$	4.29727			0.407879
$112$		0			0
$113$	−12.5273			−1.17847			−0.589237	−	0.807960i	$-0.700571\pi$
$113$	−12.5273			−1.17847			−0.589237	+	0.807960i	$0.700571\pi$
$114$	5.56833	+	9.64463i	0.521522	+	0.903302i
$115$	−5.32740	+	9.22734i	−0.496783	+	0.860453i
$116$	−0.0702743	+	0.121719i	−0.00652481	+	0.0113013i
$117$	10.4907	+	18.1704i	0.969864	+	1.67985i
$118$	−3.06640			−0.282285
$119$		0			0
$120$	12.8402			1.17214
$121$	−9.12159	−	15.7991i	−0.829236	−	1.43628i
$122$	−2.63597	+	4.56563i	−0.238649	+	0.413353i
$123$	−5.44927	+	9.43841i	−0.491344	+	0.851032i
$124$	0.0176945	+	0.0306478i	0.00158901	+	0.00275225i
$125$	12.1527			1.08697
$126$		0			0
$127$	0.0546476			0.00484919			0.00242460	−	0.999997i	$-0.499228\pi$
$127$	0.0546476			0.00484919			0.00242460	+	0.999997i	$0.499228\pi$
$128$	5.58965	+	9.68156i	0.494060	+	0.855737i
$129$	5.19871	−	9.00443i	0.457721	−	0.792796i
$130$	7.34844	−	12.7279i	0.644501	−	1.11631i
$131$	2.81736	+	4.87980i	0.246154	+	0.426350i	0.962455	−	0.271440i	$-0.0874999\pi$
$131$	2.81736	+	4.87980i	0.246154	+	0.426350i	−0.716302	+	0.697791i	$0.754167\pi$
$132$	−0.216316			−0.0188279
$133$		0			0
$134$	−12.0920			−1.04459
$135$	−1.24971	−	2.16456i	−0.107558	−	0.186296i
$136$	1.41968	−	2.45897i	0.121737	−	0.210855i
$137$	−9.58584	+	16.6032i	−0.818973	+	1.41850i	0.0874660	+	0.996168i	$0.472123\pi$
$137$	−9.58584	+	16.6032i	−0.818973	+	1.41850i	−0.906439	+	0.422336i	$0.861210\pi$
$138$	10.8743	+	18.8348i	0.925678	+	1.60332i
$139$	−21.6094			−1.83288			−0.916441	−	0.400170i	$-0.868951\pi$
$139$	−21.6094			−1.83288			−0.916441	+	0.400170i	$0.868951\pi$
$140$		0			0
$141$	−11.0131			−0.927472
$142$	3.70848	+	6.42327i	0.311208	+	0.539029i
$143$	−15.9683	+	27.6578i	−1.33533	+	2.31286i
$144$	7.04945	−	12.2100i	0.587454	−	1.01750i
$145$	−7.94453	−	13.7603i	−0.659757	−	1.14273i
$146$	−2.02598			−0.167671
$147$		0			0
$148$	0.0262331			0.00215635
$149$	2.20866	+	3.82551i	0.180940	+	0.313398i	0.942201	−	0.335048i	$-0.108753\pi$
$149$	2.20866	+	3.82551i	0.180940	+	0.313398i	−0.761261	+	0.648446i	$0.775419\pi$
$150$	3.38803	−	5.86825i	0.276632	−	0.479140i
$151$	6.49646	−	11.2522i	0.528675	−	0.915691i	−0.470766	−	0.882258i	$-0.656023\pi$
$151$	6.49646	−	11.2522i	0.528675	−	0.915691i	0.999441	−	0.0334333i	$-0.0106441\pi$
$152$	4.38455	+	7.59426i	0.355634	+	0.615976i
$153$	−3.55270			−0.287219
$154$		0			0
$155$	−4.00074			−0.321347
$156$	0.118120	+	0.204589i	0.00945714	+	0.0163802i
$157$	−6.91775	+	11.9819i	−0.552096	+	0.956259i	0.446027	+	0.895020i	$0.352839\pi$
$157$	−6.91775	+	11.9819i	−0.552096	+	0.956259i	−0.998123	+	0.0612392i	$0.980495\pi$
$158$	−4.18166	+	7.24285i	−0.332675	+	0.576211i
$159$	−0.707410	−	1.22527i	−0.0561013	−	0.0971702i
$160$	0.156160			0.0123455
$161$		0			0
$162$	9.91204			0.778764
$163$	−8.27218	−	14.3278i	−0.647927	−	1.12224i	−0.983617	−	0.180270i	$-0.942303\pi$
$163$	−8.27218	−	14.3278i	−0.647927	−	1.12224i	0.335690	−	0.941972i	$-0.391030\pi$
$164$	−0.0332655	+	0.0576176i	−0.00259760	+	0.00449918i
$165$	12.2273	−	21.1783i	0.951894	−	1.64873i
$166$	−6.35694	−	11.0105i	−0.493394	−	0.854584i
$167$	6.68337			0.517174			0.258587	−	0.965988i	$-0.416743\pi$
$167$	6.68337			0.517174			0.258587	+	0.965988i	$0.416743\pi$
$168$		0			0
$169$	21.8779			1.68292
$170$	1.24428	+	2.15516i	0.0954323	+	0.165294i
$171$	5.48607	−	9.50216i	0.419531	−	0.726648i
$172$	0.0317360	−	0.0549683i	0.00241985	−	0.00419130i
$173$	9.31019	+	16.1257i	0.707840	+	1.22602i	0.965657	+	0.259821i	$0.0836637\pi$
$173$	9.31019	+	16.1257i	0.707840	+	1.22602i	−0.257816	+	0.966194i	$0.583003\pi$
$174$	−32.4326			−2.45871
$175$		0			0
$176$	21.4605			1.61764
$177$	2.78610	+	4.82567i	0.209416	+	0.362720i
$178$	−9.93086	+	17.2008i	−0.744350	+	1.28925i
$179$	4.35019	−	7.53474i	0.325148	−	0.563173i	−0.656394	−	0.754418i	$-0.727919\pi$
$179$	4.35019	−	7.53474i	0.325148	−	0.563173i	0.981542	+	0.191245i	$0.0612525\pi$
$180$	−0.0490381	−	0.0849365i	−0.00365508	−	0.00633079i
$181$	−2.99611			−0.222699			−0.111349	−	0.993781i	$-0.535517\pi$
$181$	−2.99611			−0.222699			−0.111349	+	0.993781i	$0.535517\pi$
$182$		0			0
$183$	9.58006			0.708179
$184$	8.56248	+	14.8306i	0.631234	+	1.09333i
$185$	−1.48283	+	2.56833i	−0.109020	+	0.188828i
$186$	−4.08313	+	7.07220i	−0.299390	+	0.518559i
$187$	−2.70385	−	4.68320i	−0.197725	−	0.342470i
$188$	−0.0672306			−0.00490329
$189$		0			0
$190$	−7.68569			−0.557578
$191$	−0.884280	−	1.53162i	−0.0639843	−	0.110824i	0.832259	−	0.554387i	$-0.187047\pi$
$191$	−0.884280	−	1.53162i	−0.0639843	−	0.110824i	−0.896243	+	0.443563i	$0.853714\pi$
$192$	10.3180	−	17.8714i	0.744641	−	1.28976i
$193$	3.77023	−	6.53023i	0.271387	−	0.470056i	−0.697830	−	0.716263i	$-0.745851\pi$
$193$	3.77023	−	6.53023i	0.271387	−	0.470056i	0.969217	+	0.246207i	$0.0791843\pi$
$194$	0.0838977	+	0.145315i	0.00602350	+	0.0104330i
$195$	−26.7069			−1.91252
$196$		0			0
$197$	−26.0165			−1.85360			−0.926800	−	0.375555i	$-0.877452\pi$
$197$	−26.0165			−1.85360			−0.926800	+	0.375555i	$0.877452\pi$
$198$	−13.5317	−	23.4376i	−0.961657	−	1.66564i
$199$	−4.25329	+	7.36691i	−0.301508	+	0.522226i	−0.976478	−	0.215619i	$-0.930823\pi$
$199$	−4.25329	+	7.36691i	−0.301508	+	0.522226i	0.674970	+	0.737845i	$0.264157\pi$
$200$	2.66777	−	4.62071i	0.188640	−	0.326733i
$201$	10.9867	+	19.0295i	0.774943	+	1.34224i
$202$	13.7223			0.965496
$203$		0			0
$204$	−0.0400016			−0.00280067
$205$	−3.76068	−	6.51368i	−0.262657	−	0.454935i
$206$	10.4585	−	18.1146i	0.728675	−	1.26210i
$207$	10.7136	−	18.5565i	0.744648	−	1.28977i
$208$	−11.7185	−	20.2970i	−0.812531	−	1.40735i
$209$	16.7011			1.15524
$210$		0			0
$211$	−14.9389			−1.02844			−0.514219	−	0.857659i	$-0.671918\pi$
$211$	−14.9389			−1.02844			−0.514219	+	0.857659i	$0.671918\pi$
$212$	−0.00431845	−	0.00747977i	−0.000296592	−	0.000513713i
$213$	6.73898	−	11.6723i	0.461747	−	0.799770i
$214$	−2.01538	+	3.49074i	−0.137769	+	0.238622i
$215$	3.58776	+	6.21418i	0.244683	+	0.423804i
$216$	−4.01720			−0.273336
$217$		0			0
$218$	−23.6875			−1.60432
$219$	1.84079	+	3.18834i	0.124389	+	0.215448i
$220$	0.0746427	−	0.129285i	0.00503241	−	0.00871639i
$221$	−2.95288	+	5.11453i	−0.198632	+	0.344041i
$222$	3.02674	+	5.24246i	0.203141	+	0.351851i
$223$	1.84521			0.123564			0.0617821	−	0.998090i	$-0.480322\pi$
$223$	1.84521			0.123564			0.0617821	+	0.998090i	$0.480322\pi$
$224$		0			0
$225$	−6.67597			−0.445065
$226$	−8.82350	−	15.2827i	−0.586930	−	1.01659i
$227$	2.27537	−	3.94106i	0.151022	−	0.261577i	−0.780582	−	0.625054i	$-0.785077\pi$
$227$	2.27537	−	3.94106i	0.151022	−	0.261577i	0.931603	+	0.363477i	$0.118410\pi$
$228$	0.0617703	−	0.106989i	0.00409084	−	0.00708554i
$229$	5.58547	+	9.67432i	0.369098	+	0.639297i	0.989425	−	0.145047i	$-0.0463333\pi$
$229$	5.58547	+	9.67432i	0.369098	+	0.639297i	−0.620327	+	0.784344i	$0.713000\pi$
$230$	−15.0092			−0.989677
$231$		0			0
$232$	−25.5377			−1.67663
$233$	−3.16579	−	5.48331i	−0.207398	−	0.359224i	0.743496	−	0.668740i	$-0.233166\pi$
$233$	−3.16579	−	5.48331i	−0.207398	−	0.359224i	−0.950894	+	0.309516i	$0.899833\pi$
$234$	−14.7780	+	25.5962i	−0.966068	+	1.67328i
$235$	3.80021	−	6.58217i	0.247899	−	0.429373i
$236$	0.0170080	+	0.0294587i	0.00110713	+	0.00191760i
$237$	15.1977			0.987196
$238$		0			0
$239$	4.12428			0.266777			0.133389	−	0.991064i	$-0.457414\pi$
$239$	4.12428			0.266777			0.133389	+	0.991064i	$0.457414\pi$
$240$	8.97315	+	15.5420i	0.579214	+	1.00323i
$241$	13.5049	−	23.3912i	0.869927	−	1.50676i	0.00785612	−	0.999969i	$-0.497499\pi$
$241$	13.5049	−	23.3912i	0.869927	−	1.50676i	0.862071	−	0.506788i	$-0.169167\pi$
$242$	12.8494	−	22.2558i	0.825990	−	1.43066i
$243$	−11.1282	−	19.2746i	−0.713876	−	1.23647i
$244$	0.0584824			0.00374395
$245$		0			0
$246$	−15.3525			−0.978841
$247$	−9.11965	−	15.7957i	−0.580269	−	1.00506i
$248$	−3.21509	+	5.56871i	−0.204159	+	0.353613i
$249$	−11.5517	+	20.0082i	−0.732061	+	1.26797i
$250$	8.55959	+	14.8256i	0.541356	+	0.937656i
$251$	16.1431			1.01894			0.509471	−	0.860488i	$-0.329841\pi$
$251$	16.1431			1.01894			0.509471	+	0.860488i	$0.329841\pi$
$252$		0			0
$253$	32.6152			2.05050
$254$	0.0384905	+	0.0666674i	0.00241511	+	0.00418309i
$255$	2.26109	−	3.91633i	0.141595	−	0.245250i
$256$	0.187509	−	0.324775i	0.0117193	−	0.0202984i
$257$	−4.19242	−	7.26148i	−0.261516	−	0.452959i	0.705129	−	0.709079i	$-0.250889\pi$
$257$	−4.19242	−	7.26148i	−0.261516	−	0.452959i	−0.966645	+	0.256120i	$0.917556\pi$
$258$	14.6466			0.911858
$259$		0			0
$260$	−0.163035			−0.0101110
$261$	15.9768	+	27.6726i	0.988937	+	1.71289i
$262$	−3.96875	+	6.87407i	−0.245190	+	0.424682i
$263$	−11.9058	+	20.6214i	−0.734140	+	1.27157i	0.220960	+	0.975283i	$0.429081\pi$
$263$	−11.9058	+	20.6214i	−0.734140	+	1.27157i	−0.955100	+	0.296285i	$0.904252\pi$
$264$	−19.6523	−	34.0389i	−1.20952	−	2.09495i
$265$	0.976403			0.0599800
$266$		0			0
$267$	36.0924			2.20882
$268$	0.0670694	+	0.116168i	0.00409691	+	0.00709606i
$269$	−0.555197	+	0.961629i	−0.0338509	+	0.0586316i	−0.882455	−	0.470398i	$-0.844110\pi$
$269$	−0.555197	+	0.961629i	−0.0338509	+	0.0586316i	0.848604	+	0.529029i	$0.177444\pi$
$270$	1.76044	−	3.04917i	0.107137	−	0.185567i
$271$	−4.22952	−	7.32575i	−0.256925	−	0.445008i	0.708491	−	0.705719i	$-0.249376\pi$
$271$	−4.22952	−	7.32575i	−0.256925	−	0.445008i	−0.965417	+	0.260712i	$0.916043\pi$
$272$	3.96850			0.240626
$273$		0			0
$274$	−27.0067			−1.63154
$275$	−5.08087	−	8.80033i	−0.306388	−	0.530680i
$276$	0.120630	−	0.208937i	0.00726106	−	0.0125765i
$277$	11.7015	−	20.2676i	0.703074	−	1.21776i	−0.264308	−	0.964438i	$-0.585143\pi$
$277$	11.7015	−	20.2676i	0.703074	−	1.21776i	0.967382	−	0.253322i	$-0.0815232\pi$
$278$	−15.2203	−	26.3624i	−0.912854	−	1.58111i
$279$	8.04564			0.481680
$280$		0			0
$281$	−17.1406			−1.02252			−0.511261	−	0.859425i	$-0.670821\pi$
$281$	−17.1406			−1.02252			−0.511261	+	0.859425i	$0.670821\pi$
$282$	−7.75697	−	13.4355i	−0.461921	−	0.800070i
$283$	3.27484	−	5.67218i	0.194669	−	0.337176i	−0.752123	−	0.659023i	$-0.770970\pi$
$283$	3.27484	−	5.67218i	0.194669	−	0.337176i	0.946792	+	0.321846i	$0.104303\pi$
$284$	0.0411387	−	0.0712543i	0.00244113	−	0.00422817i
$285$	6.98315	+	12.0952i	0.413646	+	0.716456i
$286$	−44.9883			−2.66021
$287$		0			0
$288$	−0.314044			−0.0185052
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	11.1913	−	19.3839i	0.657175	−	1.13826i
$291$	0.152457	−	0.264064i	0.00893721	−	0.0154797i
$292$	0.0112373	+	0.0194635i	0.000657611	+	0.00113902i
$293$	1.27837			0.0746829			0.0373415	−	0.999303i	$-0.488111\pi$
$293$	1.27837			0.0746829			0.0373415	+	0.999303i	$0.488111\pi$
$294$		0			0
$295$	−3.84552			−0.223895
$296$	2.38328	+	4.12796i	0.138525	+	0.239933i
$297$	−3.82546	+	6.62589i	−0.221976	+	0.384473i
$298$	−3.11129	+	5.38891i	−0.180232	+	0.312171i
$299$	−17.8095	−	30.8470i	−1.02995	−	1.78393i
$300$	−0.0751680			−0.00433982
$301$		0			0
$302$	18.3028			1.05321
$303$	−12.4679	−	21.5951i	−0.716264	−	1.24061i
$304$	−6.12815	+	10.6143i	−0.351474	+	0.608770i
$305$	−3.30572	+	5.72568i	−0.189285	+	0.327851i
$306$	−2.50231	−	4.33412i	−0.143047	−	0.247765i
$307$	17.0396			0.972504			0.486252	−	0.873819i	$-0.338364\pi$
$307$	17.0396			0.972504			0.486252	+	0.873819i	$0.338364\pi$
$308$		0			0
$309$	−38.0098			−2.16230
$310$	−2.81787	−	4.88070i	−0.160045	−	0.277205i
$311$	10.7481	−	18.6162i	0.609467	−	1.05563i	−0.381861	−	0.924220i	$-0.624717\pi$
$311$	10.7481	−	18.6162i	0.609467	−	1.05563i	0.991328	−	0.131408i	$-0.0419499\pi$
$312$	−21.4623	+	37.1739i	−1.21507	+	2.10456i
$313$	−7.80855	−	13.5248i	−0.441366	−	0.764468i	0.556426	−	0.830897i	$-0.312172\pi$
$313$	−7.80855	−	13.5248i	−0.441366	−	0.764468i	−0.997791	+	0.0664299i	$0.978839\pi$
$314$	−19.4898			−1.09987
$315$		0			0
$316$	0.0927757			0.00521904
$317$	−0.815974	−	1.41331i	−0.0458297	−	0.0793793i	0.842201	−	0.539164i	$-0.181260\pi$
$317$	−0.815974	−	1.41331i	−0.0458297	−	0.0793793i	−0.888030	+	0.459785i	$0.847926\pi$
$318$	0.996513	−	1.72601i	0.0558817	−	0.0967899i
$319$	−24.3188	+	42.1214i	−1.36159	+	2.35835i
$320$	7.12074	+	12.3335i	0.398062	+	0.689463i
$321$	7.32464			0.408821
$322$		0			0
$323$	3.08840			0.171843
$324$	−0.0549779	−	0.0952245i	−0.00305433	−	0.00529025i
$325$	−5.54883	+	9.61085i	−0.307793	+	0.533114i
$326$	11.6528	−	20.1833i	0.645391	−	1.11785i
$327$	21.5222	+	37.2776i	1.19018	+	2.06146i
$328$	−12.0887			−0.667487
$329$		0			0
$330$	34.4487			1.89634
$331$	14.4228	+	24.9810i	0.792748	+	1.37308i	0.924259	+	0.381765i	$0.124684\pi$
$331$	14.4228	+	24.9810i	0.792748	+	1.37308i	−0.131512	+	0.991315i	$0.541983\pi$
$332$	−0.0705185	+	0.122142i	−0.00387021	+	0.00670339i
$333$	2.98203	−	5.16502i	0.163414	−	0.283041i
$334$	4.70735	+	8.15338i	0.257575	+	0.446133i
$335$	−15.1644			−0.828520
$336$		0			0
$337$	3.80896			0.207487			0.103744	−	0.994604i	$-0.466918\pi$
$337$	3.80896			0.207487			0.103744	+	0.994604i	$0.466918\pi$
$338$	15.4095	+	26.6900i	0.838164	+	1.45174i
$339$	−16.0339	+	27.7715i	−0.870842	+	1.50834i
$340$	0.0138030	−	0.0239076i	0.000748575	−	0.00129657i
$341$	6.12328	+	10.6058i	0.331594	+	0.574338i
$342$	15.4562			0.835777
$343$		0			0
$344$	11.5329			0.621810
$345$	13.6372	+	23.6204i	0.734203	+	1.27168i
$346$	−13.1151	+	22.7159i	−0.705070	+	1.22122i
$347$	−2.52218	+	4.36855i	−0.135398	+	0.234516i	−0.925749	−	0.378138i	$-0.876565\pi$
$347$	−2.52218	+	4.36855i	−0.135398	+	0.234516i	0.790351	+	0.612654i	$0.209898\pi$
$348$	0.179890	+	0.311579i	0.00964311	+	0.0167024i
$349$	24.7187			1.32316			0.661581	−	0.749874i	$-0.269886\pi$
$349$	24.7187			1.32316			0.661581	+	0.749874i	$0.269886\pi$
$350$		0			0
$351$	8.35558			0.445988
$352$	−0.239009	−	0.413976i	−0.0127392	−	0.0220650i
$353$	12.4028	−	21.4823i	0.660136	−	1.14339i	−0.320444	−	0.947268i	$-0.603832\pi$
$353$	12.4028	−	21.4823i	0.660136	−	1.14339i	0.980580	−	0.196121i	$-0.0628346\pi$
$354$	−3.92472	+	6.79782i	−0.208597	+	0.361300i
$355$	4.65074	+	8.05532i	0.246836	+	0.427532i
$356$	0.220329			0.0116774
$357$		0			0
$358$	12.2560			0.647751
$359$	−1.97710	−	3.42444i	−0.104347	−	0.180735i	0.809124	−	0.587638i	$-0.199942\pi$
$359$	−1.97710	−	3.42444i	−0.104347	−	0.180735i	−0.913471	+	0.406903i	$0.866609\pi$
$360$	8.91023	−	15.4330i	0.469610	−	0.813389i
$361$	4.73091	−	8.19417i	0.248995	−	0.431272i
$362$	−2.11028	−	3.65511i	−0.110914	−	0.192108i
$363$	−46.6994			−2.45108
$364$		0			0
$365$	−2.54075			−0.132989
$366$	6.74761	+	11.6872i	0.352703	+	0.610900i
$367$	7.09142	−	12.2827i	0.370169	−	0.641151i	−0.619422	−	0.785058i	$-0.712633\pi$
$367$	7.09142	−	12.2827i	0.370169	−	0.641151i	0.989591	+	0.143907i	$0.0459665\pi$
$368$	−11.9675	+	20.7284i	−0.623850	+	1.08054i
$369$	7.56287	+	13.0993i	0.393707	+	0.681921i
$370$	−4.17765			−0.217186
$371$		0			0
$372$	0.0905897			0.00469686
$373$	3.27628	+	5.67468i	0.169639	+	0.293824i	0.938293	−	0.345841i	$-0.112406\pi$
$373$	3.27628	+	5.67468i	0.169639	+	0.293824i	−0.768654	+	0.639665i	$0.779073\pi$
$374$	3.80885	−	6.59712i	0.196951	−	0.341129i
$375$	15.5543	−	26.9409i	0.803223	−	1.39122i
$376$	−6.10790	−	10.5792i	−0.314991	−	0.545580i
$377$	53.1172			2.73567
$378$		0			0
$379$	29.6732			1.52421			0.762106	−	0.647453i	$-0.224166\pi$
$379$	29.6732			1.52421			0.762106	+	0.647453i	$0.224166\pi$
$380$	0.0426293	+	0.0738360i	0.00218683	+	0.00378771i
$381$	0.0699442	−	0.121147i	0.00358335	−	0.00620654i
$382$	1.24567	−	2.15756i	0.0637338	−	0.110390i
$383$	17.5505	+	30.3984i	0.896788	+	1.55328i	0.831575	+	0.555412i	$0.187439\pi$
$383$	17.5505	+	30.3984i	0.896788	+	1.55328i	0.0652131	+	0.997871i	$0.479227\pi$
$384$	28.6171			1.46036
$385$		0			0
$386$	10.6221			0.540650
$387$	−7.21513	−	12.4970i	−0.366766	−	0.635257i
$388$	0.000930690	−	0.00161200i	4.72486e−5	−	8.18370e-5i
$389$	10.8369	−	18.7701i	0.549453	−	0.951681i	−0.448859	−	0.893603i	$-0.648169\pi$
$389$	10.8369	−	18.7701i	0.549453	−	0.951681i	0.998312	−	0.0580782i	$-0.0184973\pi$
$390$	−18.8107	−	32.5811i	−0.952517	−	1.64981i
$391$	6.03125			0.305014
$392$		0			0
$393$	14.4239			0.727588
$394$	−18.3244	−	31.7389i	−0.923172	−	1.59898i
$395$	−5.24416	+	9.08314i	−0.263862	+	0.457023i
$396$	−0.150109	+	0.259997i	−0.00754328	+	0.0130653i
$397$	−2.52636	−	4.37578i	−0.126794	−	0.219614i	0.795639	−	0.605772i	$-0.207135\pi$
$397$	−2.52636	−	4.37578i	−0.126794	−	0.219614i	−0.922433	+	0.386157i	$0.873802\pi$
$398$	−11.9830			−0.600655
$399$		0			0
$400$	7.45732			0.372866
$401$	−6.25419	−	10.8326i	−0.312319	−	0.540953i	0.666545	−	0.745465i	$-0.267773\pi$
$401$	−6.25419	−	10.8326i	−0.312319	−	0.540953i	−0.978864	+	0.204512i	$0.934439\pi$
$402$	−15.4767	+	26.8065i	−0.771909	+	1.33699i
$403$	6.68724	−	11.5826i	0.333115	−	0.576972i
$404$	−0.0761116	−	0.131829i	−0.00378670	−	0.00655875i
$405$	12.4305			0.617678
$406$		0			0
$407$	9.07810			0.449985
$408$	−3.63414	−	6.29452i	−0.179917	−	0.311625i
$409$	17.5840	−	30.4563i	0.869471	−	1.50597i	0.00693207	−	0.999976i	$-0.497793\pi$
$409$	17.5840	−	30.4563i	0.869471	−	1.50597i	0.862539	−	0.505991i	$-0.168873\pi$
$410$	5.29758	−	9.17568i	0.261629	−	0.453155i
$411$	24.5381	+	42.5012i	1.21037	+	2.09643i
$412$	−0.232034			−0.0114315
$413$		0			0
$414$	30.1841			1.48347
$415$	−7.97213	−	13.8081i	−0.391337	−	0.677815i
$416$	−0.261022	+	0.452103i	−0.0127976	+	0.0221662i
$417$	−27.6581	+	47.9052i	−1.35442	+	2.34593i
$418$	11.7632	+	20.3745i	0.575359	+	0.996551i
$419$	7.43256			0.363105			0.181552	−	0.983381i	$-0.441888\pi$
$419$	7.43256			0.363105			0.181552	+	0.983381i	$0.441888\pi$
$420$		0			0
$421$	17.3069			0.843488			0.421744	−	0.906715i	$-0.361418\pi$
$421$	17.3069			0.843488			0.421744	+	0.906715i	$0.361418\pi$
$422$	−10.5221	−	18.2248i	−0.512207	−	0.887168i
$423$	−7.64238	+	13.2370i	−0.371585	+	0.643605i
$424$	0.784662	−	1.35907i	0.0381066	−	0.0660025i
$425$	−0.939563	−	1.62737i	−0.0455755	−	0.0789391i
$426$	18.9861			0.919879
$427$		0			0
$428$	0.0447139			0.00216133
$429$	40.8759	+	70.7992i	1.97351	+	3.41822i
$430$	−5.05400	+	8.75378i	−0.243725	+	0.422145i
$431$	−1.82099	+	3.15404i	−0.0877139	+	0.151925i	−0.906544	−	0.422110i	$-0.861289\pi$
$431$	−1.82099	+	3.15404i	−0.0877139	+	0.151925i	0.818831	+	0.574035i	$0.194623\pi$
$432$	−2.80736	−	4.86249i	−0.135069	−	0.233947i
$433$	7.23197			0.347546			0.173773	−	0.984786i	$-0.444404\pi$
$433$	7.23197			0.347546			0.173773	+	0.984786i	$0.444404\pi$
$434$		0			0
$435$	−40.6732			−1.95013
$436$	0.131384	+	0.227564i	0.00629217	+	0.0108984i
$437$	−9.31345	+	16.1314i	−0.445523	+	0.771668i
$438$	−2.59308	+	4.49134i	−0.123902	+	0.214605i
$439$	−16.8957	−	29.2641i	−0.806386	−	1.39670i	−0.915352	−	0.402655i	$-0.868087\pi$
$439$	−16.8957	−	29.2641i	−0.806386	−	1.39670i	0.108966	−	0.994045i	$-0.465246\pi$
$440$	27.1252			1.29314
$441$		0			0
$442$	−8.31930			−0.395709
$443$	6.11380	+	10.5894i	0.290475	+	0.503118i	0.973922	−	0.226882i	$-0.0728533\pi$
$443$	6.11380	+	10.5894i	0.290475	+	0.503118i	−0.683447	+	0.730000i	$0.739520\pi$
$444$	0.0335761	−	0.0581554i	0.00159345	−	0.00275993i
$445$	−12.4541	+	21.5712i	−0.590382	+	1.02257i
$446$	1.29965	+	2.25106i	0.0615402	+	0.106591i
$447$	11.3076			0.534829
$448$		0			0
$449$	−31.8397			−1.50261			−0.751305	−	0.659955i	$-0.770575\pi$
$449$	−31.8397			−1.50261			−0.751305	+	0.659955i	$0.770575\pi$
$450$	−4.70215	−	8.14436i	−0.221661	−	0.383929i
$451$	−11.5117	+	19.9389i	−0.542066	+	0.938885i
$452$	−0.0978804	+	0.169534i	−0.00460391	+	0.00797420i
$453$	−16.6298	−	28.8037i	−0.781336	−	1.35331i
$454$	6.41053			0.300861
$455$		0			0
$456$	22.4473			1.05119
$457$	2.18849	+	3.79057i	0.102373	+	0.177316i	0.912662	−	0.408715i	$-0.134023\pi$
$457$	2.18849	+	3.79057i	0.102373	+	0.177316i	−0.810289	+	0.586031i	$0.800690\pi$
$458$	−7.86813	+	13.6280i	−0.367653	+	0.636794i
$459$	−0.707410	+	1.22527i	−0.0330191	+	0.0571907i
$460$	0.0832496	+	0.144193i	0.00388153	+	0.00672302i
$461$	−14.1763			−0.660256			−0.330128	−	0.943936i	$-0.607092\pi$
$461$	−14.1763			−0.660256			−0.330128	+	0.943936i	$0.607092\pi$
$462$		0			0
$463$	0.854854			0.0397284			0.0198642	−	0.999803i	$-0.493677\pi$
$463$	0.854854			0.0397284			0.0198642	+	0.999803i	$0.493677\pi$
$464$	−17.8466	−	30.9113i	−0.828510	−	1.43502i
$465$	−5.12059	+	8.86912i	−0.237462	+	0.411296i
$466$	4.45958	−	7.72422i	0.206586	−	0.357818i
$467$	8.70262	+	15.0734i	0.402709	+	0.697513i	0.994052	−	0.108907i	$-0.0347352\pi$
$467$	8.70262	+	15.0734i	0.402709	+	0.697513i	−0.591342	+	0.806421i	$0.701402\pi$
$468$	0.327869			0.0151558
$469$		0			0
$470$	10.7066			0.493857
$471$	17.7082	+	30.6715i	0.815952	+	1.41327i
$472$	−3.09036	+	5.35266i	−0.142245	+	0.246376i
$473$	10.9824	−	19.0221i	0.504972	−	0.874637i
$474$	10.7043	+	18.5404i	0.491666	+	0.851590i
$475$	5.80349			0.266282
$476$		0			0
$477$	−1.96359			−0.0899064
$478$	2.90489	+	5.03142i	0.132867	+	0.230132i
$479$	3.61468	−	6.26082i	0.165159	−	0.286064i	−0.771553	−	0.636165i	$-0.780520\pi$
$479$	3.61468	−	6.26082i	0.165159	−	0.286064i	0.936712	+	0.350101i	$0.113853\pi$
$480$	0.199871	−	0.346187i	0.00912283	−	0.0158012i
$481$	−4.95710	−	8.58595i	−0.226024	−	0.391486i
$482$	38.0481			1.73304
$483$		0			0
$484$	−0.285080			−0.0129582
$485$	0.105215	+	0.182237i	0.00477755	+	0.00827497i
$486$	15.6761	−	27.1518i	0.711082	−	1.23163i
$487$	4.04074	−	6.99876i	0.183103	−	0.317144i	−0.759832	−	0.650119i	$-0.774719\pi$
$487$	4.04074	−	6.99876i	0.183103	−	0.317144i	0.942936	+	0.332975i	$0.108052\pi$
$488$	5.31312	+	9.20260i	0.240514	+	0.416582i
$489$	−42.3506			−1.91516
$490$		0			0
$491$	−20.5372			−0.926829			−0.463415	−	0.886142i	$-0.653376\pi$
$491$	−20.5372			−0.926829			−0.463415	+	0.886142i	$0.653376\pi$
$492$	0.0851539	+	0.147491i	0.00383904	+	0.00664941i
$493$	−4.49707	+	7.78916i	−0.202538	+	0.350806i
$494$	12.8466	−	22.2510i	0.577998	−	1.00112i
$495$	−16.9699	−	29.3927i	−0.762740	−	1.32110i
$496$	−8.98728			−0.403541
$497$		0			0
$498$	−32.5453			−1.45839
$499$	−12.9646	−	22.4554i	−0.580376	−	1.00524i	−0.995435	−	0.0954465i	$-0.969572\pi$
$499$	−12.9646	−	22.4554i	−0.580376	−	1.00524i	0.415058	−	0.909795i	$-0.363761\pi$
$500$	0.0949529	−	0.164463i	0.00424642	−	0.00735502i
$501$	8.55412	−	14.8162i	0.382170	−	0.661938i
$502$	11.3702	+	19.6938i	0.507477	+	0.878976i
$503$	−29.5089			−1.31574			−0.657869	−	0.753133i	$-0.728542\pi$
$503$	−29.5089			−1.31574			−0.657869	+	0.753133i	$0.728542\pi$
$504$		0			0
$505$	17.2089			0.765785
$506$	22.9721	+	39.7889i	1.02124	+	1.76883i
$507$	28.0018	−	48.5005i	1.24360	−	2.15398i
$508$	0.000426981	0	0.000739552i	1.89442e−5	0	3.28123e-5i
$509$	−5.29631	−	9.17347i	−0.234755	−	0.406607i	0.724447	−	0.689331i	$-0.242095\pi$
$509$	−5.29631	−	9.17347i	−0.234755	−	0.406607i	−0.959201	+	0.282724i	$0.908762\pi$
$510$	6.37030			0.282082
$511$		0			0
$512$	22.8869			1.01147
$513$	−2.18476	−	3.78412i	−0.0964596	−	0.167073i
$514$	5.90577	−	10.2291i	0.260492	−	0.451186i
$515$	13.1158	−	22.7172i	0.577950	−	1.00104i
$516$	−0.0812386	−	0.140709i	−0.00357633	−	0.00619438i
$517$	−23.2655			−1.02322
$518$		0			0
$519$	47.6649			2.09226
$520$	−14.8117	−	25.6546i	−0.649536	−	1.12503i
$521$	3.81020	−	6.59946i	0.166928	−	0.289128i	−0.770410	−	0.637548i	$-0.779949\pi$
$521$	3.81020	−	6.59946i	0.166928	−	0.289128i	0.937338	+	0.348421i	$0.113282\pi$
$522$	−22.5061	+	38.9817i	−0.985066	+	1.70618i
$523$	−8.00977	−	13.8733i	−0.350243	−	0.606639i	0.636049	−	0.771649i	$-0.280568\pi$
$523$	−8.00977	−	13.8733i	−0.350243	−	0.606639i	−0.986292	+	0.165010i	$0.947234\pi$
$524$	0.0880518			0.00384656
$525$		0			0
$526$	−33.5427			−1.46253
$527$	1.13233	+	1.96125i	0.0493249	+	0.0854333i
$528$	27.4675	−	47.5751i	1.19537	−	2.07044i
$529$	−6.68801	+	11.5840i	−0.290783	+	0.503651i
$530$	0.687719	+	1.19116i	0.0298726	+	0.0517408i
$531$	7.73349			0.335605
$532$		0			0
$533$	25.1439			1.08910
$534$	25.4213	+	44.0309i	1.10009	+	1.90540i
$535$	−2.52746	+	4.37769i	−0.109272	+	0.189264i
$536$	−12.1865	+	21.1076i	−0.526377	+	0.911712i
$537$	−11.1357	−	19.2876i	−0.480542	−	0.832322i
$538$	−1.56419			−0.0674369
$539$		0			0
$540$	−0.0390576			−0.00168077
$541$	6.77564	+	11.7357i	0.291307	+	0.504559i	0.974119	−	0.226035i	$-0.0725764\pi$
$541$	6.77564	+	11.7357i	0.291307	+	0.504559i	−0.682812	+	0.730594i	$0.739243\pi$
$542$	5.95804	−	10.3196i	0.255920	−	0.443266i
$543$	−3.83476	+	6.64199i	−0.164565	+	0.285035i
$544$	−0.0441979	−	0.0765530i	−0.00189497	−	0.00328218i
$545$	−29.7061			−1.27247
$546$		0			0
$547$	−10.6651			−0.456008			−0.228004	−	0.973660i	$-0.573220\pi$
$547$	−10.6651			−0.456008			−0.228004	+	0.973660i	$0.573220\pi$
$548$	0.149795	+	0.259452i	0.00639892	+	0.0110832i
$549$	6.64794	−	11.5146i	0.283727	−	0.491430i
$550$	7.15731	−	12.3968i	0.305189	−	0.528603i
$551$	−13.8887	−	24.0560i	−0.591680	−	1.02482i
$552$	43.8369			1.86582
$553$		0			0
$554$	32.9673			1.40064
$555$	3.79578	+	6.57448i	0.161122	+	0.279071i
$556$	−0.168841	+	0.292442i	−0.00716046	+	0.0124023i
$557$	−7.01425	+	12.1490i	−0.297203	+	0.514771i	−0.975495	−	0.220022i	$-0.929387\pi$
$557$	−7.01425	+	12.1490i	−0.297203	+	0.514771i	0.678292	+	0.734793i	$0.262721\pi$
$558$	5.66686	+	9.81528i	0.239897	+	0.415514i
$559$	−23.9878			−1.01458
$560$		0			0
$561$	−13.8428			−0.584442
$562$	−12.0728	−	20.9107i	−0.509260	−	0.882064i
$563$	−7.76099	+	13.4424i	−0.327087	+	0.566531i	−0.981932	−	0.189232i	$-0.939400\pi$
$563$	−7.76099	+	13.4424i	−0.327087	+	0.566531i	0.654846	+	0.755763i	$0.272734\pi$
$564$	−0.0860492	+	0.149042i	−0.00362333	+	0.00627578i
$565$	−11.0654	−	19.1658i	−0.465525	−	0.806313i
$566$	9.22638			0.387814
$567$		0			0
$568$	14.9498			0.627280
$569$	−15.7484	−	27.2770i	−0.660207	−	1.14351i	−0.980561	−	0.196214i	$-0.937135\pi$
$569$	−15.7484	−	27.2770i	−0.660207	−	1.14351i	0.320355	−	0.947298i	$-0.396198\pi$
$570$	−9.83701	+	17.0382i	−0.412027	+	0.713651i
$571$	11.6600	−	20.1956i	0.487954	−	0.845161i	−0.511950	−	0.859015i	$-0.671077\pi$
$571$	11.6600	−	20.1956i	0.487954	−	0.845161i	0.999904	+	0.0138542i	$0.00441006\pi$
$572$	0.249531	+	0.432200i	0.0104334	+	0.0180712i
$573$	−4.52721			−0.189127
$574$		0			0
$575$	11.3335			0.472639
$576$	−14.3201	−	24.8031i	−0.596671	−	1.03346i
$577$	14.3827	−	24.9116i	0.598761	−	1.03709i	−0.394243	−	0.919006i	$-0.628993\pi$
$577$	14.3827	−	24.9116i	0.598761	−	1.03709i	0.993004	−	0.118079i	$-0.0376736\pi$
$578$	0.704339	−	1.21995i	0.0292966	−	0.0507433i
$579$	−9.65113	−	16.7162i	−0.401087	−	0.694704i
$580$	−0.248293			−0.0103098
$581$		0			0
$582$	0.429527			0.0178045
$583$	−1.49442	−	2.58842i	−0.0618926	−	0.107201i
$584$	−2.04181	+	3.53652i	−0.0844907	+	0.146342i
$585$	−18.5328	+	32.0998i	−0.766239	+	1.32716i
$586$	0.900403	+	1.55954i	0.0371953	+	0.0644241i
$587$	6.73037			0.277792			0.138896	−	0.990307i	$-0.455645\pi$
$587$	6.73037			0.277792			0.138896	+	0.990307i	$0.455645\pi$
$588$		0			0
$589$	−6.99415			−0.288189
$590$	−2.70855	−	4.69134i	−0.111509	−	0.193140i
$591$	−33.2989	+	57.6753i	−1.36973	+	2.37245i
$592$	−3.33104	+	5.76952i	−0.136905	+	0.237126i
$593$	−9.22118	−	15.9715i	−0.378668	−	0.655873i	0.612200	−	0.790703i	$-0.290285\pi$
$593$	−9.22118	−	15.9715i	−0.378668	−	0.655873i	−0.990869	+	0.134830i	$0.956951\pi$
$594$	−10.7777			−0.442214
$595$		0			0
$596$	0.0690280			0.00282750
$597$	10.8877	+	18.8580i	0.445603	+	0.771806i
$598$	25.0879	−	43.4535i	1.02592	−	1.77695i
$599$	−15.7729	+	27.3194i	−0.644462	+	1.11624i	0.339964	+	0.940439i	$0.389585\pi$
$599$	−15.7729	+	27.3194i	−0.644462	+	1.11624i	−0.984426	+	0.175802i	$0.943748\pi$
$600$	−6.82901	−	11.8282i	−0.278793	−	0.482884i
$601$	−42.7597			−1.74420			−0.872102	−	0.489324i	$-0.837244\pi$
$601$	−42.7597			−1.74420			−0.872102	+	0.489324i	$0.837244\pi$
$602$		0			0
$603$	30.4962			1.24190
$604$	−0.101518	−	0.175835i	−0.00413071	−	0.00715461i
$605$	16.1142	−	27.9106i	0.655136	−	1.13473i
$606$	17.5633	−	30.4205i	0.713461	−	1.23575i
$607$	−4.06733	−	7.04481i	−0.165088	−	0.285940i	0.771599	−	0.636110i	$-0.219457\pi$
$607$	−4.06733	−	7.04481i	−0.165088	−	0.285940i	−0.936686	+	0.350169i	$0.886124\pi$
$608$	0.273001			0.0110717
$609$		0			0
$610$	−9.31339			−0.377088
$611$	12.7041	+	22.0042i	0.513954	+	0.890195i
$612$	−0.0277585	+	0.0480791i	−0.00112207	+	0.00194348i
$613$	18.0859	−	31.3257i	0.730482	−	1.26523i	−0.226195	−	0.974082i	$-0.572629\pi$
$613$	18.0859	−	31.3257i	0.730482	−	1.26523i	0.956677	−	0.291150i	$-0.0940380\pi$
$614$	12.0017	+	20.7875i	0.484349	+	0.838916i
$615$	−19.2533			−0.776370
$616$		0			0
$617$	−38.7539			−1.56017			−0.780086	−	0.625672i	$-0.784825\pi$
$617$	−38.7539			−1.56017			−0.780086	+	0.625672i	$0.784825\pi$
$618$	−26.7718	−	46.3701i	−1.07692	−	1.86528i
$619$	12.8857	−	22.3186i	0.517918	−	0.897061i	−0.481865	−	0.876245i	$-0.660041\pi$
$619$	12.8857	−	22.3186i	0.517918	−	0.897061i	0.999783	−	0.0208152i	$-0.00662616\pi$
$620$	−0.0312591	+	0.0541424i	−0.00125540	+	0.00217441i
$621$	−4.26657	−	7.38991i	−0.171212	−	0.296547i
$622$	30.2811			1.21416
$623$		0			0
$624$	−59.9946			−2.40171
$625$	6.03663	+	10.4557i	0.241465	+	0.418230i
$626$	10.9997	−	19.0521i	0.439638	−	0.761475i
$627$	21.3760	−	37.0242i	0.853673	−	1.47861i
$628$	0.108101	+	0.187237i	0.00431372	+	0.00747157i
$629$	1.67874			0.0669356
$630$		0			0
$631$	−34.2365			−1.36293			−0.681467	−	0.731849i	$-0.738658\pi$
$631$	−34.2365			−1.36293			−0.681467	+	0.731849i	$0.738658\pi$
$632$	8.42867	+	14.5989i	0.335275	+	0.580713i
$633$	−19.1205	+	33.1177i	−0.759973	+	1.31631i
$634$	1.14945	−	1.99090i	0.0456503	−	0.0790686i
$635$	0.0482703	+	0.0836065i	0.00191555	+	0.00331782i
$636$	−0.0221089			−0.000876676
$637$		0			0
$638$	−68.5147			−2.71252
$639$	−9.35282	−	16.1996i	−0.369992	−	0.640845i
$640$	−9.87467	+	17.1034i	−0.390331	+	0.676073i
$641$	5.90924	−	10.2351i	0.233401	−	0.404262i	−0.725406	−	0.688322i	$-0.758348\pi$
$641$	5.90924	−	10.2351i	0.233401	−	0.404262i	0.958807	+	0.284059i	$0.0916812\pi$
$642$	5.15903	+	8.93569i	0.203611	+	0.352664i
$643$	35.9141			1.41631			0.708156	−	0.706056i	$-0.249527\pi$
$643$	35.9141			1.41631			0.708156	+	0.706056i	$0.249527\pi$
$644$		0			0
$645$	18.3681			0.723242
$646$	2.17528	+	3.76769i	0.0855851	+	0.148238i
$647$	−0.0802926	+	0.139071i	−0.00315663	+	0.00546744i	−0.867599	−	0.497264i	$-0.834338\pi$
$647$	−0.0802926	+	0.139071i	−0.00315663	+	0.00546744i	0.864443	+	0.502731i	$0.167671\pi$
$648$	9.98949	−	17.3023i	0.392424	−	0.679699i
$649$	5.88572	+	10.1944i	0.231035	+	0.400164i
$650$	−15.6330			−0.613177
$651$		0			0
$652$	−0.258533			−0.0101249
$653$	11.3335	+	19.6303i	0.443516	+	0.768192i	0.997948	−	0.0640371i	$-0.0203976\pi$
$653$	11.3335	+	19.6303i	0.443516	+	0.768192i	−0.554432	+	0.832229i	$0.687064\pi$
$654$	−30.3179	+	52.5121i	−1.18552	+	2.05339i
$655$	−4.97714	+	8.62066i	−0.194473	+	0.336837i
$656$	−8.44801	−	14.6324i	−0.329839	−	0.571299i
$657$	5.10955			0.199342
$658$		0			0
$659$	11.8789			0.462737			0.231369	−	0.972866i	$-0.425680\pi$
$659$	11.8789			0.462737			0.231369	+	0.972866i	$0.425680\pi$
$660$	−0.191072	−	0.330947i	−0.00743747	−	0.0128821i
$661$	13.5716	−	23.5066i	0.527872	−	0.914302i	−0.471600	−	0.881813i	$-0.656323\pi$
$661$	13.5716	−	23.5066i	0.527872	−	0.914302i	0.999472	−	0.0324892i	$-0.0103434\pi$
$662$	−20.3171	+	35.1902i	−0.789645	+	1.36770i
$663$	7.55884	+	13.0923i	0.293561	+	0.508463i
$664$	−25.6264			−0.994499
$665$		0			0
$666$	8.40143			0.325549
$667$	−27.1230	−	46.9784i	−1.05021	−	1.81901i
$668$	0.0522194	−	0.0904467i	0.00202043	−	0.00349949i
$669$	2.36170	−	4.09059i	0.0913087	−	0.158151i
$670$	−10.6809	−	18.4998i	−0.412639	−	0.714711i
$671$	20.2381			0.781285
$672$		0			0
$673$	20.7262			0.798935			0.399468	−	0.916747i	$-0.369195\pi$
$673$	20.7262			0.798935			0.399468	+	0.916747i	$0.369195\pi$
$674$	2.68280	+	4.64675i	0.103338	+	0.178986i
$675$	−1.32931	+	2.30244i	−0.0511653	+	0.0886208i
$676$	0.170939	−	0.296076i	0.00657459	−	0.0113875i
$677$	−6.74321	−	11.6796i	−0.259162	−	0.448882i	0.706855	−	0.707358i	$-0.250113\pi$
$677$	−6.74321	−	11.6796i	−0.259162	−	0.448882i	−0.966018	+	0.258476i	$0.916780\pi$
$678$	−45.1732			−1.73487
$679$		0			0
$680$	5.01603			0.192356
$681$	−5.82455	−	10.0884i	−0.223197	−	0.386589i
$682$	−8.62573	+	14.9402i	−0.330296	+	0.572090i
$683$	−10.6760	+	18.4913i	−0.408505	+	0.707552i	−0.994722	−	0.102602i	$-0.967283\pi$
$683$	−10.6760	+	18.4913i	−0.408505	+	0.707552i	0.586217	+	0.810154i	$0.300616\pi$
$684$	−0.0857291	−	0.148487i	−0.00327794	−	0.00567755i
$685$	−33.8687			−1.29406
$686$		0			0
$687$	28.5956			1.09099
$688$	8.05957	+	13.9596i	0.307268	+	0.532204i
$689$	−1.63206	+	2.82681i	−0.0621765	+	0.107693i
$690$	−19.2105	+	33.2735i	−0.731329	+	1.26670i
$691$	4.33509	+	7.50860i	0.164915	+	0.285641i	0.936625	−	0.350334i	$-0.113932\pi$
$691$	4.33509	+	7.50860i	0.164915	+	0.285641i	−0.771710	+	0.635974i	$0.780598\pi$
$692$	0.290975			0.0110612
$693$		0			0
$694$	−7.10589			−0.269736
$695$	−19.0875	−	33.0606i	−0.724032	−	1.25406i
$696$	−32.6860	+	56.6138i	−1.23896	+	2.14594i
$697$	−2.12877	+	3.68713i	−0.0806327	+	0.139660i
$698$	17.4103	+	30.1556i	0.658991	+	1.14141i
$699$	−16.2077			−0.613033
$700$		0			0
$701$	48.2784			1.82345			0.911725	−	0.410801i	$-0.134751\pi$
$701$	48.2784			1.82345			0.911725	+	0.410801i	$0.134751\pi$
$702$	5.88516	+	10.1934i	0.222121	+	0.384725i
$703$	−2.59230	+	4.49000i	−0.0977705	+	0.169344i
$704$	21.7971	−	37.7538i	0.821511	−	1.42290i
$705$	−9.72788	−	16.8492i	−0.366373	−	0.634577i
$706$	34.9432			1.31510
$707$		0			0
$708$	0.0870751			0.00327248
$709$	−10.0895	−	17.4756i	−0.378920	−	0.656309i	0.611985	−	0.790869i	$-0.290371\pi$
$709$	−10.0895	−	17.4756i	−0.378920	−	0.656309i	−0.990905	+	0.134560i	$0.957038\pi$
$710$	−6.55139	+	11.3473i	−0.245869	+	0.425858i
$711$	10.5462	−	18.2666i	0.395514	−	0.685050i
$712$	20.0169	+	34.6703i	0.750165	+	1.29932i
$713$	−13.6587			−0.511522
$714$		0			0
$715$	−56.4190			−2.10995
$716$	−0.0679790	−	0.117743i	−0.00254049	−	0.00440026i
$717$	5.27871	−	9.14300i	0.197137	−	0.341452i
$718$	2.78510	−	4.82393i	0.103939	−	0.180028i
$719$	−9.71227	−	16.8222i	−0.362207	−	0.627360i	0.626117	−	0.779729i	$-0.284643\pi$
$719$	−9.71227	−	16.8222i	−0.362207	−	0.627360i	−0.988324	+	0.152369i	$0.951310\pi$
$720$	24.9071			0.928234
$721$		0			0
$722$	13.3286			0.496041
$723$	−34.5702	−	59.8773i	−1.28568	−	2.22686i
$724$	−0.0234096	+	0.0405466i	−0.000870011	+	0.00150690i
$725$	−8.45057	+	14.6368i	−0.313846	+	0.543598i
$726$	−32.8922	−	56.9709i	−1.22074	−	2.11439i
$727$	5.10313			0.189265			0.0946323	−	0.995512i	$-0.469832\pi$
$727$	5.10313			0.189265			0.0946323	+	0.995512i	$0.469832\pi$
$728$		0			0
$729$	−35.8634			−1.32827
$730$	−1.78955	−	3.09959i	−0.0662341	−	0.114721i
$731$	2.03089	−	3.51760i	0.0751150	−	0.130103i
$732$	0.0748523	−	0.129648i	0.00276662	−	0.00479193i
$733$	25.3132	+	43.8438i	0.934965	+	1.61941i	0.774697	+	0.632332i	$0.217902\pi$
$733$	25.3132	+	43.8438i	0.934965	+	1.61941i	0.160267	+	0.987074i	$0.448764\pi$
$734$	19.9790			0.737440
$735$		0			0
$736$	0.533138			0.0196517
$737$	23.2097	+	40.2004i	0.854941	+	1.48080i
$738$	−10.6536	+	18.4527i	−0.392166	+	0.679252i
$739$	20.6427	−	35.7543i	0.759355	−	1.31524i	−0.183824	−	0.982959i	$-0.558848\pi$
$739$	20.6427	−	35.7543i	0.759355	−	1.31524i	0.943180	−	0.332283i	$-0.107819\pi$
$740$	0.0231717	+	0.0401345i	0.000851808	+	0.00147537i
$741$	−46.6894			−1.71518
$742$		0			0
$743$	−0.115352			−0.00423186			−0.00211593	−	0.999998i	$-0.500674\pi$
$743$	−0.115352			−0.00423186			−0.00211593	+	0.999998i	$0.500674\pi$
$744$	8.23008	+	14.2549i	0.301729	+	0.522610i
$745$	−3.90181	+	6.75814i	−0.142951	+	0.247599i
$746$	−4.61522	+	7.99380i	−0.168975	+	0.292674i
$747$	16.0323	+	27.7687i	0.586590	+	1.01600i
$748$	−0.0845043			−0.00308978
$749$		0			0
$750$	43.8221			1.60016
$751$	26.1711	+	45.3297i	0.954997	+	1.65410i	0.734375	+	0.678744i	$0.237475\pi$
$751$	26.1711	+	45.3297i	0.954997	+	1.65410i	0.220621	+	0.975360i	$0.429191\pi$
$752$	8.53683	−	14.7862i	0.311306	−	0.539198i
$753$	20.6617	−	35.7872i	0.752956	−	1.30416i
$754$	37.4125	+	64.8004i	1.36248	+	2.35989i
$755$	22.9533			0.835356
$756$		0			0
$757$	−19.1277			−0.695207			−0.347604	−	0.937642i	$-0.613005\pi$
$757$	−19.1277			−0.695207			−0.347604	+	0.937642i	$0.613005\pi$
$758$	20.9000	+	36.1999i	0.759123	+	1.31484i
$759$	41.7446	−	72.3037i	1.51523	−	2.62446i
$760$	−7.74574	+	13.4160i	−0.280967	+	0.486650i
$761$	1.02273	+	1.77143i	0.0370741	+	0.0642142i	0.883967	−	0.467549i	$-0.154863\pi$
$761$	1.02273	+	1.77143i	0.0370741	+	0.0642142i	−0.846893	+	0.531763i	$0.821530\pi$
$762$	0.197058			0.00713865
$763$		0			0
$764$	−0.0276367			−0.000999862
$765$	−3.13810	−	5.43535i	−0.113458	−	0.196515i
$766$	−24.7230	+	42.8215i	−0.893278	+	1.54720i
$767$	6.42780	−	11.1333i	0.232094	−	0.401999i
$768$	−0.479989	−	0.831366i	−0.0173201	−	0.0299993i
$769$	45.2661			1.63234			0.816168	−	0.577814i	$-0.196094\pi$
$769$	45.2661			1.63234			0.816168	+	0.577814i	$0.196094\pi$
$770$		0			0
$771$	−21.4637			−0.772997
$772$	−0.0589162	−	0.102046i	−0.00212044	−	0.00367271i
$773$	−1.36828	+	2.36992i	−0.0492135	+	0.0852402i	−0.889583	−	0.456774i	$-0.849005\pi$
$773$	−1.36828	+	2.36992i	−0.0492135	+	0.0852402i	0.840369	+	0.542014i	$0.182338\pi$
$774$	10.1638	−	17.6042i	0.365330	−	0.632770i
$775$	2.12778	+	3.68543i	0.0764323	+	0.132385i
$776$	0.338213			0.0121411
$777$		0			0
$778$	30.5314			1.09461
$779$	−6.57447	−	11.3873i	−0.235555	−	0.407993i
$780$	−0.208670	+	0.361427i	−0.00747159	+	0.0129412i
$781$	14.2363	−	24.6579i	0.509414	−	0.882331i
$782$	4.24805	+	7.35783i	0.151910	+	0.263116i
$783$	12.7251			0.454758
$784$		0			0
$785$	−24.4418			−0.872364
$786$	10.1593	+	17.5964i	0.362370	+	0.627643i
$787$	−11.4780	+	19.8804i	−0.409145	+	0.708660i	−0.994794	−	0.101905i	$-0.967506\pi$
$787$	−11.4780	+	19.8804i	−0.409145	+	0.708660i	0.585649	+	0.810565i	$0.300840\pi$
$788$	−0.203276	+	0.352084i	−0.00724140	+	0.0125425i
$789$	30.4766	+	52.7871i	1.08500	+	1.87927i
$790$	−14.7747			−0.525658
$791$		0			0
$792$	−54.5498			−1.93834
$793$	−11.0510	−	19.1410i	−0.392434	−	0.679716i
$794$	3.55883	−	6.16407i	0.126298	−	0.218755i
$795$	1.24971	−	2.16456i	0.0443227	−	0.0767691i
$796$	0.0664647	+	0.115120i	0.00235578	+	0.00408033i
$797$	23.9778			0.849337			0.424669	−	0.905349i	$-0.360391\pi$
$797$	23.9778			0.849337			0.424669	+	0.905349i	$0.360391\pi$
$798$		0			0
$799$	−4.30229			−0.152204
$800$	−0.0830534	−	0.143853i	−0.00293638	−	0.00508596i
$801$	25.0458	−	43.3805i	0.884948	−	1.53278i
$802$	8.81014	−	15.2596i	0.311097	−	0.538835i
$803$	3.88871	+	6.73545i	0.137230	+	0.237689i
$804$	0.343372			0.0121098
$805$		0			0
$806$	18.8403			0.663623
$807$	1.42121	+	2.46160i	0.0500288	+	0.0866525i
$808$	13.8295	−	23.9534i	0.486520	−	0.842677i
$809$	−0.273936	+	0.474470i	−0.00963106	+	0.0166815i	−0.870801	−	0.491636i	$-0.836399\pi$
$809$	−0.273936	+	0.474470i	−0.00963106	+	0.0166815i	0.861170	+	0.508318i	$0.169732\pi$
$810$	8.75530	+	15.1646i	0.307630	+	0.532831i
$811$	−37.1882			−1.30585			−0.652927	−	0.757421i	$-0.726459\pi$
$811$	−37.1882			−1.30585			−0.652927	+	0.757421i	$0.726459\pi$
$812$		0			0
$813$	−21.6537			−0.759428
$814$	6.39406	+	11.0748i	0.224112	+	0.388173i
$815$	14.6136	−	25.3115i	0.511893	−	0.886625i
$816$	5.07934	−	8.79767i	0.177812	−	0.307980i
$817$	6.27218	+	10.8637i	0.219436	+	0.380074i
$818$	49.5403			1.73213
$819$		0			0
$820$	−0.117534			−0.00410446
$821$	3.63972	+	6.30417i	0.127027	+	0.220017i	0.922523	−	0.385941i	$-0.126123\pi$
$821$	3.63972	+	6.30417i	0.127027	+	0.220017i	−0.795496	+	0.605958i	$0.792790\pi$
$822$	−34.5662	+	59.8705i	−1.20564	+	2.08822i
$823$	−7.32180	+	12.6817i	−0.255222	+	0.442057i	−0.964956	−	0.262413i	$-0.915482\pi$
$823$	−7.32180	+	12.6817i	−0.255222	+	0.442057i	0.709734	+	0.704470i	$0.248815\pi$
$824$	−21.0803	−	36.5122i	−0.734368	−	1.27196i
$825$	−26.0123			−0.905631
$826$		0			0
$827$	−12.0435			−0.418795			−0.209397	−	0.977831i	$-0.567150\pi$
$827$	−12.0435			−0.418795			−0.209397	+	0.977831i	$0.567150\pi$
$828$	−0.167418	−	0.289977i	−0.00581819	−	0.0100774i
$829$	−13.1369	+	22.7538i	−0.456264	+	0.790273i	−0.998760	−	0.0497855i	$-0.984146\pi$
$829$	−13.1369	+	22.7538i	−0.456264	+	0.790273i	0.542495	+	0.840059i	$0.317480\pi$
$830$	11.2302	−	19.4512i	0.389805	−	0.675162i
$831$	−29.9538	−	51.8814i	−1.03908	−	1.79975i
$832$	−47.6094			−1.65056
$833$		0			0
$834$	−77.9227			−2.69824
$835$	5.90341	+	10.2250i	0.204296	+	0.353851i
$836$	0.130491	−	0.226018i	0.00451314	−	0.00781699i
$837$	1.60204	−	2.77481i	0.0553746	−	0.0959115i
$838$	5.23504	+	9.06736i	0.180842	+	0.313227i
$839$	−45.9248			−1.58550			−0.792750	−	0.609547i	$-0.791352\pi$
$839$	−45.9248			−1.58550			−0.792750	+	0.609547i	$0.791352\pi$
$840$		0			0
$841$	51.8947			1.78947
$842$	12.1899	+	21.1136i	0.420093	+	0.727622i
$843$	−21.9385	+	37.9985i	−0.755601	+	1.30874i
$844$	−0.116723	+	0.202170i	−0.00401777	+	0.00695898i
$845$	19.3247	+	33.4714i	0.664791	+	1.15145i
$846$	−21.5313			−0.740262
$847$		0			0
$848$	2.19340			0.0753216
$849$	−8.38301	−	14.5198i	−0.287704	−	0.498318i
$850$	1.32354	−	2.29244i	0.0453971	−	0.0786301i
$851$	−5.06245	+	8.76841i	−0.173538	+	0.300577i
$852$	−0.105308	−	0.182399i	−0.00360779	−	0.00624887i
$853$	10.4825			0.358915			0.179457	−	0.983766i	$-0.442566\pi$
$853$	10.4825			0.358915			0.179457	+	0.983766i	$0.442566\pi$
$854$		0			0
$855$	19.3834			0.662898
$856$	4.06226	+	7.03604i	0.138845	+	0.240487i
$857$	−20.9609	+	36.3053i	−0.716009	+	1.24016i	0.246560	+	0.969128i	$0.420700\pi$
$857$	−20.9609	+	36.3053i	−0.716009	+	1.24016i	−0.962569	+	0.271037i	$0.912634\pi$
$858$	−57.5810	+	99.7333i	−1.96578	+	3.40484i
$859$	5.25655	+	9.10461i	0.179351	+	0.310645i	0.941658	−	0.336570i	$-0.109267\pi$
$859$	5.25655	+	9.10461i	0.179351	+	0.310645i	−0.762307	+	0.647215i	$0.775933\pi$
$860$	0.112130			0.00382359
$861$		0			0
$862$	−5.13037			−0.174741
$863$	9.40967	+	16.2980i	0.320309	+	0.554791i	0.980552	−	0.196261i	$-0.0628800\pi$
$863$	9.40967	+	16.2980i	0.320309	+	0.554791i	−0.660243	+	0.751052i	$0.729547\pi$
$864$	−0.0625321	+	0.108309i	−0.00212738	+	0.00368474i
$865$	−16.4474	+	28.4877i	−0.559227	+	0.968610i
$866$	5.09376	+	8.82265i	0.173093	+	0.299806i
$867$	−2.55982			−0.0869362
$868$		0			0
$869$	32.1055			1.08911
$870$	−28.6477	−	49.6193i	−0.971249	−	1.68225i
$871$	25.3474	−	43.9029i	0.858862	−	1.48759i
$872$	−23.8726	+	41.3485i	−0.808427	+	1.40024i
$873$	−0.211591	−	0.366486i	−0.00716127	−	0.0124037i
$874$	−26.2393			−0.887558
$875$		0			0
$876$	0.0575308			0.00194379
$877$	26.2417	+	45.4520i	0.886119	+	1.53480i	0.844425	+	0.535673i	$0.179942\pi$
$877$	26.2417	+	45.4520i	0.886119	+	1.53480i	0.0416942	+	0.999130i	$0.486724\pi$
$878$	23.8005	−	41.2237i	0.803229	−	1.39123i
$879$	1.63620	−	2.83397i	0.0551875	−	0.0955876i
$880$	18.9560	+	32.8328i	0.639007	+	1.10679i
$881$	1.43758			0.0484335			0.0242167	−	0.999707i	$-0.492291\pi$
$881$	1.43758			0.0484335			0.0242167	+	0.999707i	$0.492291\pi$
$882$		0			0
$883$	−3.17781			−0.106942			−0.0534710	−	0.998569i	$-0.517028\pi$
$883$	−3.17781			−0.106942			−0.0534710	+	0.998569i	$0.517028\pi$
$884$	0.0461436	+	0.0799231i	0.00155198	+	0.00268811i
$885$	−4.92193	+	8.52503i	−0.165449	+	0.286566i
$886$	−8.61237	+	14.9171i	−0.289338	+	0.501149i
$887$	−1.88718	−	3.26868i	−0.0633652	−	0.109752i	0.832602	−	0.553871i	$-0.186850\pi$
$887$	−1.88718	−	3.26868i	−0.0633652	−	0.109752i	−0.895968	+	0.444119i	$0.853517\pi$
$888$	12.2015			0.409457
$889$		0			0
$890$	−35.0877			−1.17614
$891$	−19.0254	−	32.9530i	−0.637375	−	1.10397i
$892$	0.0144172	−	0.0249714i	0.000482724	−	0.000836103i
$893$	6.64359	−	11.5070i	0.222319	−	0.385068i
$894$	7.96435	+	13.7947i	0.266368	+	0.461362i
$895$	15.3701			0.513765
$896$		0			0
$897$	−91.1786			−3.04437
$898$	−22.4260	−	38.8429i	−0.748364	−	1.29620i
$899$	10.1843	−	17.6398i	0.339666	−	0.588319i
$900$	−0.0521617	+	0.0903466i	−0.00173872	+	0.00301155i
$901$	−0.276351	−	0.478654i	−0.00920659	−	0.0159463i
$902$	−32.4326			−1.07989
$903$		0			0
$904$	−35.5698			−1.18303
$905$	−2.64646	−	4.58381i	−0.0879714	−	0.152371i
$906$	23.4260	−	40.5751i	0.778278	−	1.34802i
$907$	24.3460	−	42.1685i	0.808395	−	1.40018i	−0.105580	−	0.994411i	$-0.533670\pi$
$907$	24.3460	−	42.1685i	0.808395	−	1.40018i	0.913975	−	0.405770i	$-0.132997\pi$
$908$	−0.0355565	−	0.0615856i	−0.00117998	−	0.00204379i
$909$	−34.6077			−1.14787
$910$		0			0
$911$	52.2254			1.73030			0.865152	−	0.501510i	$-0.167222\pi$
$911$	52.2254			1.73030			0.865152	+	0.501510i	$0.167222\pi$
$912$	15.6870	+	27.1707i	0.519448	+	0.899711i
$913$	−24.4033	+	42.2678i	−0.807632	+	1.39886i
$914$	−3.08288	+	5.33970i	−0.101972	+	0.176621i
$915$	8.46207	+	14.6567i	0.279747	+	0.484537i
$916$	0.174565			0.00576778
$917$		0			0
$918$	−1.99303			−0.0657796
$919$	−28.4848	−	49.3370i	−0.939625	−	1.62748i	−0.766171	−	0.642637i	$-0.777840\pi$
$919$	−28.4848	−	49.3370i	−0.939625	−	1.62748i	−0.173455	−	0.984842i	$-0.555493\pi$
$920$	−15.1265	+	26.1998i	−0.498705	+	0.863782i
$921$	21.8093	−	37.7747i	0.718639	−	1.24472i
$922$	−9.98492	−	17.2944i	−0.328836	−	0.569560i
$923$	−31.0949			−1.02350
$924$		0			0
$925$	3.15456			0.103721
$926$	0.602107	+	1.04288i	0.0197865	+	0.0342712i
$927$	−26.3763	+	45.6852i	−0.866313	+	1.50050i
$928$	−0.397522	+	0.688529i	−0.0130493	+	0.0226021i
$929$	−5.56936	−	9.64642i	−0.182725	−	0.316489i	0.760083	−	0.649826i	$-0.225158\pi$
$929$	−5.56936	−	9.64642i	−0.182725	−	0.316489i	−0.942808	+	0.333338i	$0.891825\pi$
$930$	−14.4265			−0.473064
$931$		0			0
$932$	−0.0989417			−0.00324094
$933$	−27.5132	−	47.6542i	−0.900741	−	1.56013i
$934$	−12.2592	+	21.2335i	−0.401133	+	0.694783i
$935$	4.77662	−	8.27334i	0.156212	−	0.270567i
$936$	29.7869	+	51.5925i	0.973616	+	1.68635i
$937$	−18.6644			−0.609740			−0.304870	−	0.952394i	$-0.598613\pi$
$937$	−18.6644			−0.609740			−0.304870	+	0.952394i	$0.598613\pi$
$938$		0			0
$939$	−39.9771			−1.30460
$940$	−0.0593847	−	0.102857i	−0.00193692	−	0.00335484i
$941$	−21.6492	+	37.4975i	−0.705743	+	1.22238i	0.260679	+	0.965426i	$0.416054\pi$
$941$	−21.6492	+	37.4975i	−0.705743	+	1.22238i	−0.966423	+	0.256958i	$0.917280\pi$
$942$	−24.9452	+	43.2063i	−0.812758	+	1.40774i
$943$	−12.8391	−	22.2380i	−0.418099	−	0.724169i
$944$	−8.63860			−0.281163
$945$		0			0
$946$	30.9414			1.00599
$947$	−9.36396	−	16.2189i	−0.304288	−	0.527042i	0.672815	−	0.739811i	$-0.265085\pi$
$947$	−9.36396	−	16.2189i	−0.304288	−	0.527042i	−0.977103	+	0.212769i	$0.931752\pi$
$948$	0.118745	−	0.205672i	0.00385665	−	0.00667991i
$949$	4.24687	−	7.35579i	0.137859	−	0.238779i
$950$	4.08762	+	7.07997i	0.132620	+	0.229704i
$951$	−4.17750			−0.135465
$952$		0			0
$953$	−22.3380			−0.723598			−0.361799	−	0.932256i	$-0.617837\pi$
$953$	−22.3380			−0.723598			−0.361799	+	0.932256i	$0.617837\pi$
$954$	−1.38303	−	2.39548i	−0.0447772	−	0.0775564i
$955$	1.56217	−	2.70576i	0.0505506	−	0.0875562i
$956$	0.0322244	−	0.0558143i	0.00104221	−	0.00180516i
$957$	62.2519	+	107.823i	2.01232	+	3.48544i
$958$	10.1839			0.329025
$959$		0			0
$960$	36.4557			1.17660
$961$	12.9357	+	22.4052i	0.417280	+	0.722750i
$962$	6.98296	−	12.0948i	0.225140	−	0.389953i
$963$	5.08282	−	8.80370i	0.163792	−	0.283695i
$964$	−0.211037	−	0.365526i	−0.00679703	−	0.0117728i
$965$	13.3210			0.428817
$966$		0			0
$967$	−40.0648			−1.28840			−0.644199	−	0.764858i	$-0.722809\pi$
$967$	−40.0648			−1.28840			−0.644199	+	0.764858i	$0.722809\pi$
$968$	−25.8996	−	44.8594i	−0.832444	−	1.44183i
$969$	3.95288	−	6.84658i	0.126985	−	0.219944i
$970$	−0.148214	+	0.256714i	−0.00475885	+	0.00824258i
$971$	−3.85524	−	6.67747i	−0.123721	−	0.214290i	0.797512	−	0.603304i	$-0.206149\pi$
$971$	−3.85524	−	6.67747i	−0.123721	−	0.214290i	−0.921232	+	0.389013i	$0.872816\pi$
$972$	−0.347794			−0.0111555
$973$		0			0
$974$	11.3842			0.364773
$975$	14.2040	+	24.6021i	0.454893	+	0.787897i
$976$	−7.42600	+	12.8622i	−0.237700	+	0.411709i
$977$	−7.15670	+	12.3958i	−0.228963	+	0.396576i	−0.957501	−	0.288430i	$-0.906867\pi$
$977$	−7.15670	+	12.3958i	−0.228963	+	0.396576i	0.728538	+	0.685005i	$0.240200\pi$
$978$	−29.8292	−	51.6657i	−0.953833	−	1.65209i
$979$	76.2461			2.43684
$980$		0			0
$981$	59.7401			1.90735
$982$	−14.4651	−	25.0543i	−0.461601	−	0.799516i
$983$	−10.2813	+	17.8077i	−0.327922	+	0.567977i	−0.982099	−	0.188364i	$-0.939681\pi$
$983$	−10.2813	+	17.8077i	−0.327922	+	0.567977i	0.654178	+	0.756341i	$0.273015\pi$
$984$	−15.4725	+	26.7991i	−0.493245	+	0.854325i
$985$	−22.9804	−	39.8032i	−0.732216	−	1.26824i
$986$	−12.6699			−0.403490
$987$		0			0
$988$	−0.285020			−0.00906768
$989$	12.2488	+	21.2155i	0.389489	+	0.674614i
$990$	23.9051	−	41.4049i	0.759755	−	1.31593i
$991$	−8.74528	+	15.1473i	−0.277803	+	0.481169i	−0.970838	−	0.239735i	$-0.922940\pi$
$991$	−8.74528	+	15.1473i	−0.277803	+	0.481169i	0.693036	+	0.720903i	$0.256273\pi$
$992$	0.100093	+	0.173366i	0.00317795	+	0.00550438i
$993$	73.8396			2.34323
$994$		0			0
$995$	−15.0277			−0.476410
$996$	0.180515	+	0.312661i	0.00571984	+	0.00990705i
$997$	−25.8753	+	44.8174i	−0.819479	+	1.41938i	0.0865870	+	0.996244i	$0.472404\pi$
$997$	−25.8753	+	44.8174i	−0.819479	+	1.41938i	−0.906066	+	0.423136i	$0.860929\pi$
$998$	18.2630	−	31.6324i	0.578105	−	1.00131i
$999$	−1.18756	−	2.05691i	−0.0375726	−	0.0650776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.e.h.18.4		10
7.2	even	3	inner	833.2.e.h.324.4		10
7.3	odd	6		119.2.a.b.1.2	✓	5
7.4	even	3		833.2.a.g.1.2		5
7.5	odd	6		833.2.e.i.324.4		10
7.6	odd	2		833.2.e.i.18.4		10
21.11	odd	6		7497.2.a.br.1.4		5
21.17	even	6		1071.2.a.m.1.4		5
28.3	even	6		1904.2.a.t.1.1		5
35.24	odd	6		2975.2.a.m.1.4		5
56.3	even	6		7616.2.a.bq.1.5		5
56.45	odd	6		7616.2.a.bt.1.1		5
119.101	odd	6		2023.2.a.j.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.2	✓	5	7.3	odd	6
833.2.a.g.1.2		5	7.4	even	3
833.2.e.h.18.4		10	1.1	even	1	trivial
833.2.e.h.324.4		10	7.2	even	3	inner
833.2.e.i.18.4		10	7.6	odd	2
833.2.e.i.324.4		10	7.5	odd	6
1071.2.a.m.1.4		5	21.17	even	6
1904.2.a.t.1.1		5	28.3	even	6
2023.2.a.j.1.2		5	119.101	odd	6
2975.2.a.m.1.4		5	35.24	odd	6
7497.2.a.br.1.4		5	21.11	odd	6
7616.2.a.bq.1.5		5	56.3	even	6
7616.2.a.bt.1.1		5	56.45	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.704339 + 1.21995i) q^{2} +(1.27991 - 2.21687i) q^{3} +(0.00781334 - 0.0135331i) q^{4} +(0.883300 + 1.52992i) q^{5} +3.60597 q^{6} +2.83937 q^{8} +(-1.77635 - 3.07673i) q^{9} +(-1.24428 + 2.15516i) q^{10} +(2.70385 - 4.68320i) q^{11} +(-0.0200008 - 0.0346424i) q^{12} -5.90575 q^{13} +4.52218 q^{15} +(1.98425 + 3.43682i) q^{16} +(0.500000 - 0.866025i) q^{17} +(2.50231 - 4.33412i) q^{18} +(1.54420 + 2.67463i) q^{19} +0.0276061 q^{20} +7.61770 q^{22} +(3.01563 + 5.22322i) q^{23} +(3.63414 - 6.29452i) q^{24} +(0.939563 - 1.62737i) q^{25} +(-4.15965 - 7.20473i) q^{26} -1.41482 q^{27} -8.99415 q^{29} +(3.18515 + 5.51684i) q^{30} +(-1.13233 + 1.96125i) q^{31} +(0.0441979 - 0.0765530i) q^{32} +(-6.92138 - 11.9882i) q^{33} +1.40868 q^{34} -0.0555169 q^{36} +(0.839369 + 1.45383i) q^{37} +(-2.17528 + 3.76769i) q^{38} +(-7.55884 + 13.0923i) q^{39} +(2.50801 + 4.34401i) q^{40} -4.25753 q^{41} +4.06177 q^{43} +(-0.0422522 - 0.0731829i) q^{44} +(3.13810 - 5.43535i) q^{45} +(-4.24805 + 7.35783i) q^{46} +(-2.15115 - 3.72590i) q^{47} +10.1587 q^{48} +2.64708 q^{50} +(-1.27991 - 2.21687i) q^{51} +(-0.0461436 + 0.0799231i) q^{52} +(0.276351 - 0.478654i) q^{53} +(-0.996513 - 1.72601i) q^{54} +9.55324 q^{55} +7.90575 q^{57} +(-6.33493 - 10.9724i) q^{58} +(-1.08840 + 1.88516i) q^{59} +(0.0353334 - 0.0611992i) q^{60} +(1.87123 + 3.24107i) q^{61} -3.19017 q^{62} +8.06153 q^{64} +(-5.21655 - 9.03533i) q^{65} +(9.74999 - 16.8875i) q^{66} +(-4.29198 + 7.43392i) q^{67} +(-0.00781334 - 0.0135331i) q^{68} +15.4390 q^{69} +5.26519 q^{71} +(-5.04372 - 8.73597i) q^{72} +(-0.719107 + 1.24553i) q^{73} +(-1.18240 + 2.04798i) q^{74} +(-2.40512 - 4.16578i) q^{75} +0.0482614 q^{76} -21.2960 q^{78} +(2.96850 + 5.14160i) q^{79} +(-3.50538 + 6.07149i) q^{80} +(3.51821 - 6.09371i) q^{81} +(-2.99874 - 5.19398i) q^{82} -9.02540 q^{83} +1.76660 q^{85} +(2.86086 + 4.95516i) q^{86} +(-11.5117 + 19.9389i) q^{87} +(7.67722 - 13.2973i) q^{88} +(7.04978 + 12.2106i) q^{89} +8.84115 q^{90} +0.0942485 q^{92} +(2.89856 + 5.02045i) q^{93} +(3.03027 - 5.24859i) q^{94} +(-2.72798 + 4.72500i) q^{95} +(-0.113139 - 0.195962i) q^{96} +0.119116 q^{97} -19.2119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 2 q^{3} - 10 q^{4} + 2 q^{6} + 12 q^{8} - 11 q^{9} + 4 q^{10} + 2 q^{11} - 22 q^{12} - 4 q^{13} + 16 q^{15} - 4 q^{16} + 5 q^{17} + 18 q^{18} + 6 q^{19} + 38 q^{20} + 12 q^{22} + 10 q^{23}+ \cdots - 124 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 2 * q^6 + 12 * q^8 - 11 * q^9 + 4 * q^10 + 2 * q^11 - 22 * q^12 - 4 * q^13 + 16 * q^15 - 4 * q^16 + 5 * q^17 + 18 * q^18 + 6 * q^19 + 38 * q^20 + 12 * q^22 + 10 * q^23 + 2 * q^24 - 21 * q^25 - 26 * q^26 + 52 * q^27 - 16 * q^29 + 51 * q^30 - 9 * q^32 + 6 * q^33 - 4 * q^34 + 78 * q^36 - 8 * q^37 + 14 * q^38 - 14 * q^39 + 5 * q^40 - 36 * q^41 + 16 * q^43 + 14 * q^44 - 8 * q^46 - 10 * q^47 + 54 * q^48 + 54 * q^50 + 2 * q^51 + 4 * q^52 - 4 * q^53 + 5 * q^54 + 48 * q^55 + 24 * q^57 - 12 * q^58 + 8 * q^59 + 7 * q^60 + 22 * q^61 - 32 * q^62 - 32 * q^64 + 30 * q^65 + 68 * q^66 - 16 * q^67 + 10 * q^68 + 64 * q^69 - 4 * q^71 - 9 * q^72 + 10 * q^73 + 40 * q^74 - 14 * q^75 - 48 * q^76 + 60 * q^78 - 18 * q^79 - 4 * q^80 - 25 * q^81 - 31 * q^82 + 24 * q^83 - 23 * q^86 - 26 * q^87 + 46 * q^88 + 20 * q^89 - 194 * q^90 + 56 * q^92 + 28 * q^93 - 42 * q^94 + 22 * q^95 - 18 * q^96 - 24 * q^97 - 124 * q^99

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