LMFDB - Embedded newform 273.2.by.c.223.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.4
Character	$\chi$	$=$	273.223
Dual form			273.2.by.c.202.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11595 - 0.299019i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.11595 - 0.299019i) q^{6} +(0.347225 - 2.62287i) q^{7} +(2.17732 + 2.17732i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.11595 - 0.299019i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.11595 - 0.299019i) q^{6} +(0.347225 - 2.62287i) q^{7} +(2.17732 + 2.17732i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.448776 + 0.777302i) q^{10} +(-0.824353 + 3.07653i) q^{11} +0.665238 q^{12} +(-2.63686 + 2.45905i) q^{13} +(-1.17177 + 2.82317i) q^{14} +(0.750414 + 0.201073i) q^{15} +(-1.11349 - 1.92862i) q^{16} +(-1.74975 + 3.03065i) q^{17} +(-0.816934 + 0.816934i) q^{18} +(-6.06267 + 1.62449i) q^{19} +(0.133761 + 0.499204i) q^{20} +(1.01073 + 2.44508i) q^{21} +(1.83988 - 3.18676i) q^{22} +(-4.89067 + 2.82363i) q^{23} +(-2.97428 - 0.796956i) q^{24} -4.39645i q^{25} +(3.67792 - 1.95572i) q^{26} +1.00000i q^{27} +(-1.07246 + 1.39557i) q^{28} +(4.54654 + 7.87483i) q^{29} +(-0.777302 - 0.448776i) q^{30} +(0.888029 + 0.888029i) q^{31} +(-0.928002 - 3.46335i) q^{32} +(-0.824353 - 3.07653i) q^{33} +(2.85886 - 2.85886i) q^{34} +(-1.63160 + 1.25010i) q^{35} +(-0.576113 + 0.332619i) q^{36} +(0.151142 - 0.564068i) q^{37} +7.25141 q^{38} +(1.05406 - 3.44804i) q^{39} -2.39219i q^{40} +(-0.704976 + 2.63101i) q^{41} +(-0.396799 - 3.03082i) q^{42} +(6.60921 + 3.81583i) q^{43} +(1.49823 - 1.49823i) q^{44} +(-0.750414 + 0.201073i) q^{45} +(6.30208 - 1.68864i) q^{46} +(-0.267009 + 0.267009i) q^{47} +(1.92862 + 1.11349i) q^{48} +(-6.75887 - 1.82145i) q^{49} +(-1.31462 + 4.90623i) q^{50} -3.49950i q^{51} +(2.33706 - 0.539622i) q^{52} -11.6025 q^{53} +(0.299019 - 1.11595i) q^{54} +(2.14292 - 1.23721i) q^{55} +(6.46685 - 4.95481i) q^{56} +(4.43818 - 4.43818i) q^{57} +(-2.71900 - 10.1474i) q^{58} +(-0.635122 - 2.37031i) q^{59} +(-0.365443 - 0.365443i) q^{60} +(6.70242 + 3.86964i) q^{61} +(-0.725461 - 1.25654i) q^{62} +(-2.09786 - 1.61214i) q^{63} +8.59639i q^{64} +(2.79940 + 0.0976783i) q^{65} +3.67976i q^{66} +(-6.90457 - 1.85007i) q^{67} +(2.01610 - 1.16400i) q^{68} +(2.82363 - 4.89067i) q^{69} +(2.19459 - 0.907181i) q^{70} +(-2.51079 - 9.37039i) q^{71} +(2.97428 - 0.796956i) q^{72} +(7.71628 - 7.71628i) q^{73} +(-0.337334 + 0.584279i) q^{74} +(2.19822 + 3.80744i) q^{75} +(4.03312 + 1.08067i) q^{76} +(7.78309 + 3.23042i) q^{77} +(-2.20731 + 3.53266i) q^{78} -10.8188 q^{79} +(-0.447786 + 1.67116i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.57344 - 2.72528i) q^{82} +(-10.3355 - 10.3355i) q^{83} +(0.230987 - 1.74483i) q^{84} +(2.62607 - 0.703654i) q^{85} +(-6.23456 - 6.23456i) q^{86} +(-7.87483 - 4.54654i) q^{87} +(-8.49348 + 4.90371i) q^{88} +(7.02589 + 1.88258i) q^{89} +0.897552 q^{90} +(5.53419 + 7.76999i) q^{91} +3.75677 q^{92} +(-1.21307 - 0.325041i) q^{93} +(0.377810 - 0.218129i) q^{94} +(4.22288 + 2.43808i) q^{95} +(2.53535 + 2.53535i) q^{96} +(0.704543 - 0.188782i) q^{97} +(6.99793 + 4.05368i) q^{98} +(2.25217 + 2.25217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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 $

$2$	−1.11595	−	0.299019i	−0.789098	−	0.211438i	−0.158306	−	0.987390i	$-0.550603\pi$
$2$	−1.11595	−	0.299019i	−0.789098	−	0.211438i	−0.630792	+	0.775952i	$0.717270\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.576113	−	0.332619i	−0.288056	−	0.166309i
$5$	−0.549341	−	0.549341i	−0.245673	−	0.245673i	0.573519	−	0.819192i	$-0.305578\pi$
$5$	−0.549341	−	0.549341i	−0.245673	−	0.245673i	−0.819192	+	0.573519i	$0.805578\pi$
$6$	1.11595	−	0.299019i	0.455586	−	0.122074i
$7$	0.347225	−	2.62287i	0.131239	−	0.991351i
$7$	0.347225	−	2.62287i	0.131239	−	0.991351i
$8$	2.17732	+	2.17732i	0.769800	+	0.769800i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.448776	+	0.777302i	0.141915	+	0.245805i
$11$	−0.824353	+	3.07653i	−0.248552	+	0.927608i	0.723013	+	0.690834i	$0.242757\pi$
$11$	−0.824353	+	3.07653i	−0.248552	+	0.927608i	−0.971565	+	0.236774i	$0.923910\pi$
$12$	0.665238			0.192038
$13$	−2.63686	+	2.45905i	−0.731335	+	0.682019i
$13$	−2.63686	+	2.45905i	−0.731335	+	0.682019i
$14$	−1.17177	+	2.82317i	−0.313170	+	0.754524i
$15$	0.750414	+	0.201073i	0.193756	+	0.0519168i
$16$	−1.11349	−	1.92862i	−0.278373	−	0.482156i
$17$	−1.74975	+	3.03065i	−0.424376	+	0.735041i	−0.996362	−	0.0852225i	$-0.972840\pi$
$17$	−1.74975	+	3.03065i	−0.424376	+	0.735041i	0.571986	+	0.820263i	$0.306173\pi$
$18$	−0.816934	+	0.816934i	−0.192553	+	0.192553i
$19$	−6.06267	+	1.62449i	−1.39087	+	0.372683i	−0.875058	−	0.484017i	$-0.839177\pi$
$19$	−6.06267	+	1.62449i	−1.39087	+	0.372683i	−0.515814	+	0.856701i	$0.672510\pi$
$20$	0.133761	+	0.499204i	0.0299099	+	0.111625i
$21$	1.01073	+	2.44508i	0.220559	+	0.533561i
$22$	1.83988	−	3.18676i	0.392263	−	0.679420i
$23$	−4.89067	+	2.82363i	−1.01978	+	0.588768i	−0.914039	−	0.405626i	$-0.867053\pi$
$23$	−4.89067	+	2.82363i	−1.01978	+	0.588768i	−0.105737	+	0.994394i	$0.533720\pi$
$24$	−2.97428	−	0.796956i	−0.607122	−	0.162678i
$25$		−	4.39645i		−	0.879290i
$26$	3.67792	−	1.95572i	0.721299	−	0.383548i
$27$			1.00000i			0.192450i
$28$	−1.07246	+	1.39557i	−0.202675	+	0.263739i
$29$	4.54654	+	7.87483i	0.844271	+	1.46232i	0.886253	+	0.463202i	$0.153299\pi$
$29$	4.54654	+	7.87483i	0.844271	+	1.46232i	−0.0419819	+	0.999118i	$0.513367\pi$
$30$	−0.777302	−	0.448776i	−0.141915	−	0.0819349i
$31$	0.888029	+	0.888029i	0.159495	+	0.159495i	0.782343	−	0.622848i	$-0.214025\pi$
$31$	0.888029	+	0.888029i	0.159495	+	0.159495i	−0.622848	+	0.782343i	$0.714025\pi$
$32$	−0.928002	−	3.46335i	−0.164049	−	0.612239i
$33$	−0.824353	−	3.07653i	−0.143501	−	0.535555i
$34$	2.85886	−	2.85886i	0.490290	−	0.490290i
$35$	−1.63160	+	1.25010i	−0.275790	+	0.211306i
$36$	−0.576113	+	0.332619i	−0.0960188	+	0.0554365i
$37$	0.151142	−	0.564068i	0.0248475	−	0.0927322i	−0.952389	−	0.304887i	$-0.901381\pi$
$37$	0.151142	−	0.564068i	0.0248475	−	0.0927322i	0.977236	+	0.212155i	$0.0680480\pi$
$38$	7.25141			1.17633
$39$	1.05406	−	3.44804i	0.168785	−	0.552128i
$40$		−	2.39219i		−	0.378238i
$41$	−0.704976	+	2.63101i	−0.110099	+	0.410894i	−0.998874	−	0.0474499i	$-0.984891\pi$
$41$	−0.704976	+	2.63101i	−0.110099	+	0.410894i	0.888775	+	0.458344i	$0.151557\pi$
$42$	−0.396799	−	3.03082i	−0.0612275	−	0.467666i
$43$	6.60921	+	3.81583i	1.00790	+	0.581909i	0.910575	−	0.413344i	$-0.135639\pi$
$43$	6.60921	+	3.81583i	1.00790	+	0.581909i	0.0973205	+	0.995253i	$0.468973\pi$
$44$	1.49823	−	1.49823i	0.225867	−	0.225867i
$45$	−0.750414	+	0.201073i	−0.111865	+	0.0299742i
$46$	6.30208	−	1.68864i	0.929191	−	0.248976i
$47$	−0.267009	+	0.267009i	−0.0389472	+	0.0389472i	−0.726312	−	0.687365i	$-0.758767\pi$
$47$	−0.267009	+	0.267009i	−0.0389472	+	0.0389472i	0.687365	+	0.726312i	$0.258767\pi$
$48$	1.92862	+	1.11349i	0.278373	+	0.160719i
$49$	−6.75887	−	1.82145i	−0.965553	−	0.260207i
$50$	−1.31462	+	4.90623i	−0.185915	+	0.693845i
$51$		−	3.49950i		−	0.490027i
$52$	2.33706	−	0.539622i	0.324092	−	0.0748321i
$53$	−11.6025			−1.59372			−0.796862	−	0.604161i	$-0.793508\pi$
$53$	−11.6025			−1.59372			−0.796862	+	0.604161i	$0.793508\pi$
$54$	0.299019	−	1.11595i	0.0406913	−	0.151862i
$55$	2.14292	−	1.23721i	0.288951	−	0.166826i
$56$	6.46685	−	4.95481i	0.864169	−	0.662114i
$57$	4.43818	−	4.43818i	0.587852	−	0.587852i
$58$	−2.71900	−	10.1474i	−0.357022	−	1.33242i
$59$	−0.635122	−	2.37031i	−0.0826858	−	0.308588i	0.912180	−	0.409790i	$-0.134398\pi$
$59$	−0.635122	−	2.37031i	−0.0826858	−	0.308588i	−0.994866	+	0.101202i	$0.967731\pi$
$60$	−0.365443	−	0.365443i	−0.0471784	−	0.0471784i
$61$	6.70242	+	3.86964i	0.858157	+	0.495457i	0.863395	−	0.504529i	$-0.168334\pi$
$61$	6.70242	+	3.86964i	0.858157	+	0.495457i	−0.00523788	+	0.999986i	$0.501667\pi$
$62$	−0.725461	−	1.25654i	−0.0921337	−	0.159580i
$63$	−2.09786	−	1.61214i	−0.264305	−	0.203110i
$64$			8.59639i			1.07455i
$65$	2.79940	+	0.0976783i	0.347223	+	0.0121155i
$66$			3.67976i			0.452947i
$67$	−6.90457	−	1.85007i	−0.843528	−	0.226023i	−0.188921	−	0.981992i	$-0.560499\pi$
$67$	−6.90457	−	1.85007i	−0.843528	−	0.226023i	−0.654607	+	0.755970i	$0.727166\pi$
$68$	2.01610	−	1.16400i	0.244488	−	0.141155i
$69$	2.82363	−	4.89067i	0.339925	−	0.588768i
$70$	2.19459	−	0.907181i	0.262303	−	0.108429i
$71$	−2.51079	−	9.37039i	−0.297976	−	1.11206i	−0.938825	−	0.344394i	$-0.888084\pi$
$71$	−2.51079	−	9.37039i	−0.297976	−	1.11206i	0.640849	−	0.767667i	$-0.278582\pi$
$72$	2.97428	−	0.796956i	0.350522	−	0.0939221i
$73$	7.71628	−	7.71628i	0.903122	−	0.903122i	−0.0925826	−	0.995705i	$-0.529512\pi$
$73$	7.71628	−	7.71628i	0.903122	−	0.903122i	0.995705	+	0.0925826i	$0.0295122\pi$
$74$	−0.337334	+	0.584279i	−0.0392142	+	0.0679210i
$75$	2.19822	+	3.80744i	0.253829	+	0.439645i
$76$	4.03312	+	1.08067i	0.462630	+	0.123961i
$77$	7.78309	+	3.23042i	0.886965	+	0.368140i
$78$	−2.20731	+	3.53266i	−0.249929	+	0.399995i
$79$	−10.8188			−1.21721			−0.608607	−	0.793472i	$-0.708271\pi$
$79$	−10.8188			−1.21721			−0.608607	+	0.793472i	$0.708271\pi$
$80$	−0.447786	+	1.67116i	−0.0500640	+	0.186841i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.57344	−	2.72528i	0.173757	−	0.300956i
$83$	−10.3355	−	10.3355i	−1.13447	−	1.13447i	−0.989426	−	0.145040i	$-0.953669\pi$
$83$	−10.3355	−	10.3355i	−1.13447	−	1.13447i	−0.145040	−	0.989426i	$-0.546331\pi$
$84$	0.230987	−	1.74483i	0.0252028	−	0.190377i
$85$	2.62607	−	0.703654i	0.284837	−	0.0763220i
$86$	−6.23456	−	6.23456i	−0.672290	−	0.672290i
$87$	−7.87483	−	4.54654i	−0.844271	−	0.487440i
$88$	−8.49348	+	4.90371i	−0.905408	+	0.522737i
$89$	7.02589	+	1.88258i	0.744743	+	0.199553i	0.611185	−	0.791488i	$-0.290693\pi$
$89$	7.02589	+	1.88258i	0.744743	+	0.199553i	0.133558	+	0.991041i	$0.457360\pi$
$90$	0.897552			0.0946102
$91$	5.53419	+	7.76999i	0.580141	+	0.814516i
$92$	3.75677			0.391670
$93$	−1.21307	−	0.325041i	−0.125790	−	0.0337052i
$94$	0.377810	−	0.218129i	0.0389681	−	0.0224983i
$95$	4.22288	+	2.43808i	0.433258	+	0.250142i
$96$	2.53535	+	2.53535i	0.258763	+	0.258763i
$97$	0.704543	−	0.188782i	0.0715355	−	0.0191679i	−0.222874	−	0.974847i	$-0.571544\pi$
$97$	0.704543	−	0.188782i	0.0715355	−	0.0191679i	0.294409	+	0.955679i	$0.404877\pi$
$98$	6.99793	+	4.05368i	0.706898	+	0.409484i
$99$	2.25217	+	2.25217i	0.226352	+	0.226352i
$100$	−1.46234	+	2.53285i	−0.146234	+	0.253285i
$101$	5.71320	+	9.89554i	0.568484	+	0.984643i	0.996716	+	0.0809746i	$0.0258033\pi$
$101$	5.71320	+	9.89554i	0.568484	+	0.984643i	−0.428232	+	0.903669i	$0.640863\pi$
$102$	−1.04641	+	3.90527i	−0.103610	+	0.386679i
$103$	−19.3170			−1.90336			−0.951679	−	0.307094i	$-0.900643\pi$
$103$	−19.3170			−1.90336			−0.951679	+	0.307094i	$0.900643\pi$
$104$	−11.0955	−	0.387150i	−1.08800	−	0.0379631i
$105$	0.787950	−	1.89842i	0.0768961	−	0.185267i
$106$	12.9478	+	3.46936i	1.25760	+	0.336974i
$107$	−4.59094	−	7.95175i	−0.443823	−	0.768724i	0.554146	−	0.832419i	$-0.313045\pi$
$107$	−4.59094	−	7.95175i	−0.443823	−	0.768724i	−0.997969	+	0.0636951i	$0.979711\pi$
$108$	0.332619	−	0.576113i	0.0320063	−	0.0554365i
$109$	1.79167	−	1.79167i	0.171610	−	0.171610i	−0.616076	−	0.787687i	$-0.711279\pi$
$109$	1.79167	−	1.79167i	0.171610	−	0.171610i	0.787687	+	0.616076i	$0.211279\pi$
$110$	−2.76134	+	0.739899i	−0.263284	+	0.0705466i
$111$	0.151142	+	0.564068i	0.0143457	+	0.0535390i
$112$	−5.44516	+	2.25088i	−0.514519	+	0.212688i
$113$	1.25451	−	2.17288i	0.118015	−	0.204407i	−0.800966	−	0.598710i	$-0.795680\pi$
$113$	1.25451	−	2.17288i	0.118015	−	0.204407i	0.918981	+	0.394302i	$0.129014\pi$
$114$	−6.27990	+	3.62570i	−0.588167	+	0.339578i
$115$	4.23779	+	1.13551i	0.395176	+	0.105887i
$116$		−	6.04906i		−	0.561641i
$117$	0.811171	+	3.51312i	0.0749928	+	0.324788i
$118$			2.83506i			0.260989i
$119$	7.34144	+	5.64167i	0.672989	+	0.517171i
$120$	1.19609	+	2.07170i	0.109188	+	0.189119i
$121$	0.740817	+	0.427711i	0.0673470	+	0.0388828i
$122$	−6.32249	−	6.32249i	−0.572411	−	0.572411i
$123$	−0.704976	−	2.63101i	−0.0635655	−	0.237230i
$124$	−0.216230	−	0.806980i	−0.0194180	−	0.0724689i
$125$	−5.16186	+	5.16186i	−0.461691	+	0.461691i
$126$	1.85905	+	2.42637i	0.165617	+	0.216158i
$127$	−14.6248	+	8.44360i	−1.29774	+	0.749249i	−0.980013	−	0.198934i	$-0.936252\pi$
$127$	−14.6248	+	8.44360i	−1.29774	+	0.749249i	−0.317724	+	0.948183i	$0.602919\pi$
$128$	0.714478	−	2.66647i	0.0631515	−	0.235685i
$129$	−7.63166			−0.671930
$130$	−3.09479	−	0.946077i	−0.271431	−	0.0829764i
$131$			9.18546i			0.802537i	0.915960	+	0.401269i	$0.131431\pi$
$131$			9.18546i			0.802537i	−0.915960	+	0.401269i	$0.868569\pi$
$132$	−0.548391	+	2.04662i	−0.0477313	+	0.178136i
$133$	2.15571	+	16.4657i	0.186923	+	1.42775i
$134$	7.15197	+	4.12919i	0.617836	+	0.356708i
$135$	0.549341	−	0.549341i	0.0472798	−	0.0472798i
$136$	−10.4085	+	2.78894i	−0.892519	+	0.239150i
$137$	6.08217	−	1.62971i	0.519635	−	0.139236i	0.0105372	−	0.999944i	$-0.496646\pi$
$137$	6.08217	−	1.62971i	0.519635	−	0.139236i	0.509098	+	0.860709i	$0.329979\pi$
$138$	−4.61344	+	4.61344i	−0.392722	+	0.392722i
$139$	16.6243	+	9.59802i	1.41005	+	0.814093i	0.995393	−	0.0958840i	$-0.0305678\pi$
$139$	16.6243	+	9.59802i	1.41005	+	0.814093i	0.414658	+	0.909977i	$0.363901\pi$
$140$	1.35579	−	0.177502i	0.114585	−	0.0150017i
$141$	0.0977320	−	0.364741i	0.00823052	−	0.0307167i
$142$			11.2077i			0.940528i
$143$	−5.39164	−	10.1395i	−0.450872	−	0.847909i
$144$	−2.22698			−0.185582
$145$	1.82837	−	6.82358i	0.151838	−	0.566667i
$146$	−10.9183	+	6.30369i	−0.903606	+	0.521697i
$147$	6.76408	−	1.80201i	0.557892	−	0.148627i
$148$	−0.274694	+	0.274694i	−0.0225797	+	0.0225797i
$149$	−2.99088	−	11.1621i	−0.245022	−	0.914435i	−0.973372	−	0.229230i	$-0.926379\pi$
$149$	−2.99088	−	11.1621i	−0.245022	−	0.914435i	0.728350	−	0.685205i	$-0.240287\pi$
$150$	−1.31462	−	4.90623i	−0.107338	−	0.400592i
$151$	8.90574	+	8.90574i	0.724738	+	0.724738i	0.969567	−	0.244828i	$-0.0787315\pi$
$151$	8.90574	+	8.90574i	0.724738	+	0.724738i	−0.244828	+	0.969567i	$0.578732\pi$
$152$	−16.7374	−	9.66336i	−1.35759	−	0.783802i
$153$	1.74975	+	3.03065i	0.141459	+	0.245014i
$154$	−7.71960	−	5.93228i	−0.622063	−	0.478037i
$155$		−	0.975662i		−	0.0783671i
$156$	−1.75414	+	1.63586i	−0.140444	+	0.130973i
$157$			5.49387i			0.438459i	0.975673	+	0.219229i	$0.0703543\pi$
$157$			5.49387i			0.438459i	−0.975673	+	0.219229i	$0.929646\pi$
$158$	12.0733	+	3.23503i	0.960501	+	0.257365i
$159$	10.0480	−	5.80124i	0.796862	−	0.460068i
$160$	−1.39277	+	2.41235i	−0.110108	+	0.190713i
$161$	5.70785	+	13.8080i	0.449841	+	1.08822i
$162$	0.299019	+	1.11595i	0.0234931	+	0.0876775i
$163$	10.2964	−	2.75892i	0.806480	−	0.216096i	0.168053	−	0.985778i	$-0.446252\pi$
$163$	10.2964	−	2.75892i	0.806480	−	0.216096i	0.638427	+	0.769682i	$0.279585\pi$
$164$	1.28127	−	1.28127i	0.100050	−	0.100050i
$165$	−1.23721	+	2.14292i	−0.0963169	+	0.166826i
$166$	8.44340	+	14.6244i	0.655335	+	1.13507i
$167$	−12.5089	−	3.35175i	−0.967967	−	0.259366i	−0.259998	−	0.965609i	$-0.583722\pi$
$167$	−12.5089	−	3.35175i	−0.967967	−	0.259366i	−0.707969	+	0.706243i	$0.750389\pi$
$168$	−3.12305	+	7.52442i	−0.240949	+	0.580521i
$169$	0.906105	−	12.9684i	0.0697004	−	0.997568i
$170$	−3.14098			−0.240902
$171$	−1.62449	+	6.06267i	−0.124228	+	0.463624i
$172$	−2.53843	−	4.39670i	−0.193554	−	0.335245i
$173$	−0.498608	+	0.863615i	−0.0379085	+	0.0656594i	−0.884357	−	0.466811i	$-0.845403\pi$
$173$	−0.498608	+	0.863615i	−0.0379085	+	0.0656594i	0.846449	+	0.532470i	$0.178736\pi$
$174$	7.42844	+	7.42844i	0.563149	+	0.563149i
$175$	−11.5313	−	1.52656i	−0.871684	−	0.115397i
$176$	6.85138	−	1.83582i	0.516442	−	0.138380i
$177$	1.73518	+	1.73518i	0.130424	+	0.130424i
$178$	−7.27763	−	4.20174i	−0.545482	−	0.314934i
$179$	−4.88304	+	2.81922i	−0.364975	+	0.210719i	−0.671261	−	0.741221i	$-0.734247\pi$
$179$	−4.88304	+	2.81922i	−0.364975	+	0.210719i	0.306286	+	0.951940i	$0.400914\pi$
$180$	0.499204	+	0.133761i	0.0372085	+	0.00996998i
$181$	21.5094			1.59878			0.799390	−	0.600813i	$-0.205156\pi$
$181$	21.5094			1.59878			0.799390	+	0.600813i	$0.205156\pi$
$182$	−3.85252	−	10.3258i	−0.285568	−	0.765397i
$183$	−7.73929			−0.572104
$184$	−16.7965	−	4.50062i	−1.23826	−	0.331790i
$185$	−0.392894	+	0.226838i	−0.0288862	+	0.0166774i
$186$	1.25654	+	0.725461i	0.0921337	+	0.0531934i
$187$	−7.88147	−	7.88147i	−0.576350	−	0.576350i
$188$	0.242639	−	0.0650150i	0.0176963	−	0.00474171i
$189$	2.62287	+	0.347225i	0.190786	+	0.0252569i
$190$	−3.98350	−	3.98350i	−0.288993	−	0.288993i
$191$	−4.39198	+	7.60714i	−0.317793	+	0.550433i	−0.980027	−	0.198863i	$-0.936275\pi$
$191$	−4.39198	+	7.60714i	−0.317793	+	0.550433i	0.662234	+	0.749297i	$0.269608\pi$
$192$	−4.29820	−	7.44469i	−0.310196	−	0.537274i
$193$	0.249296	−	0.930384i	0.0179447	−	0.0669705i	−0.956373	−	0.292149i	$-0.905630\pi$
$193$	0.249296	−	0.930384i	0.0179447	−	0.0669705i	0.974318	+	0.225178i	$0.0722964\pi$
$194$	−0.842685			−0.0605013
$195$	−2.47319	+	1.31511i	−0.177109	+	0.0941768i
$196$	3.28802	+	3.29749i	0.234859	+	0.235535i
$197$	−16.6329	−	4.45678i	−1.18505	−	0.317532i	−0.388120	−	0.921609i	$-0.626876\pi$
$197$	−16.6329	−	4.45678i	−1.18505	−	0.317532i	−0.796926	+	0.604076i	$0.793542\pi$
$198$	−1.83988	−	3.18676i	−0.130754	−	0.226473i
$199$	1.12555	−	1.94951i	0.0797883	−	0.138197i	−0.823370	−	0.567505i	$-0.807909\pi$
$199$	1.12555	−	1.94951i	0.0797883	−	0.138197i	0.903159	+	0.429307i	$0.141242\pi$
$200$	9.57249	−	9.57249i	0.676877	−	0.676877i
$201$	6.90457	−	1.85007i	0.487011	−	0.130494i
$202$	−3.41670	−	12.7513i	−0.240398	−	0.897179i
$203$	22.2333	−	9.19063i	1.56047	−	0.645056i
$204$	−1.16400	+	2.01610i	−0.0814961	+	0.141155i
$205$	1.83259	−	1.05805i	0.127994	−	0.0738973i
$206$	21.5568	+	5.77613i	1.50194	+	0.402442i
$207$			5.64726i			0.392512i
$208$	7.67872	+	2.34738i	0.532423	+	0.162762i
$209$		−	19.9911i		−	1.38282i
$210$	−1.44698	+	1.88294i	−0.0998510	+	0.129935i
$211$	−10.3549	−	17.9352i	−0.712859	−	1.23471i	−0.963780	−	0.266700i	$-0.914067\pi$
$211$	−10.3549	−	17.9352i	−0.712859	−	1.23471i	0.250921	−	0.968008i	$-0.419267\pi$
$212$	6.68434	+	3.85920i	0.459082	+	0.265051i
$213$	6.85960	+	6.85960i	0.470012	+	0.470012i
$214$	2.74555	+	10.2465i	0.187682	+	0.700440i
$215$	−1.53452	−	5.72691i	−0.104653	−	0.390572i
$216$	−2.17732	+	2.17732i	−0.148148	+	0.148148i
$217$	2.63753	−	2.02084i	0.179047	−	0.137183i
$218$	−2.53516	+	1.46367i	−0.171702	+	0.0991325i
$219$	−2.82435	+	10.5406i	−0.190852	+	0.712270i
$220$	−1.64608			−0.110979
$221$	−2.83869	−	12.2941i	−0.190951	−	0.826993i
$222$		−	0.674667i		−	0.0452807i
$223$	5.92307	−	22.1052i	0.396638	−	1.48027i	−0.422333	−	0.906441i	$-0.638789\pi$
$223$	5.92307	−	22.1052i	0.396638	−	1.48027i	0.818972	−	0.573834i	$-0.194545\pi$
$224$	−9.40613	+	1.23146i	−0.628474	+	0.0822806i
$225$	−3.80744	−	2.19822i	−0.253829	−	0.146548i
$226$	−2.04971	+	2.04971i	−0.136345	+	0.136345i
$227$	15.1087	−	4.04837i	1.00280	−	0.268699i	0.280182	−	0.959947i	$-0.409605\pi$
$227$	15.1087	−	4.04837i	1.00280	−	0.268699i	0.722618	+	0.691248i	$0.242939\pi$
$228$	−4.03312	+	1.08067i	−0.267100	+	0.0715692i
$229$	−3.61172	+	3.61172i	−0.238669	+	0.238669i	−0.816299	−	0.577630i	$-0.803978\pi$
$229$	−3.61172	+	3.61172i	−0.238669	+	0.238669i	0.577630	+	0.816299i	$0.303978\pi$
$230$	−4.38963	−	2.53435i	−0.289444	−	0.167110i
$231$	−8.35556	+	1.09392i	−0.549755	+	0.0719747i
$232$	−7.24678	+	27.0453i	−0.475774	+	1.77561i
$233$		−	3.18656i		−	0.208758i	−0.994538	−	0.104379i	$-0.966714\pi$
$233$		−	3.18656i		−	0.208758i	0.994538	−	0.104379i	$-0.0332855\pi$
$234$	0.145259	−	4.16303i	0.00949587	−	0.272146i
$235$	0.293358			0.0191366
$236$	−0.422507	+	1.57682i	−0.0275029	+	0.102642i
$237$	9.36939	−	5.40942i	0.608607	−	0.351379i
$238$	−6.50574	−	8.49107i	−0.421704	−	0.550394i
$239$	−1.61918	+	1.61918i	−0.104736	+	0.104736i	−0.757533	−	0.652797i	$-0.773596\pi$
$239$	−1.61918	+	1.61918i	−0.104736	+	0.104736i	0.652797	+	0.757533i	$0.273596\pi$
$240$	−0.447786	−	1.67116i	−0.0289045	−	0.107873i
$241$	1.64242	+	6.12960i	0.105798	+	0.394842i	0.998434	−	0.0559344i	$-0.0178138\pi$
$241$	1.64242	+	6.12960i	0.105798	+	0.394842i	−0.892637	+	0.450777i	$0.851147\pi$
$242$	−0.698823	−	0.698823i	−0.0449221	−	0.0449221i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.57423	−	4.45870i	−0.164798	−	0.285439i
$245$	2.71233	+	4.71353i	0.173284	+	0.301136i
$246$			3.14688i			0.200638i
$247$	11.9917	−	19.1920i	0.763016	−	1.22116i
$248$			3.86705i			0.245558i
$249$	14.1185	+	3.78305i	0.894725	+	0.239741i
$250$	7.30388	−	4.21690i	0.461938	−	0.266700i
$251$	−10.7306	+	18.5859i	−0.677308	+	1.17313i	0.298481	+	0.954416i	$0.403520\pi$
$251$	−10.7306	+	18.5859i	−0.677308	+	1.17313i	−0.975789	+	0.218716i	$0.929813\pi$
$252$	0.672374	+	1.62656i	0.0423556	+	0.102464i
$253$	−4.65534	−	17.3740i	−0.292679	−	1.09229i
$254$	18.8453	−	5.04959i	1.18246	−	0.316839i
$255$	−1.92242	+	1.92242i	−0.120386	+	0.120386i
$256$	7.00174	−	12.1274i	0.437609	−	0.757961i
$257$	14.1914	+	24.5801i	0.885232	+	1.53327i	0.845447	+	0.534059i	$0.179334\pi$
$257$	14.1914	+	24.5801i	0.885232	+	1.53327i	0.0397853	+	0.999208i	$0.487333\pi$
$258$	8.51657	+	2.28201i	0.530219	+	0.142072i
$259$	−1.42700	−	0.592283i	−0.0886692	−	0.0368027i
$260$	−1.58028	−	0.987406i	−0.0980048	−	0.0612364i
$261$	9.09308			0.562847
$262$	2.74662	−	10.2505i	0.169687	−	0.633280i
$263$	6.33755	+	10.9770i	0.390790	+	0.676868i	0.992554	−	0.121806i	$-0.0388686\pi$
$263$	6.33755	+	10.9770i	0.390790	+	0.676868i	−0.601764	+	0.798674i	$0.705535\pi$
$264$	4.90371	−	8.49348i	0.301803	−	0.522737i
$265$	6.37373	+	6.37373i	0.391535	+	0.391535i
$266$	2.51787	−	19.0195i	0.154381	−	1.16616i
$267$	−7.02589	+	1.88258i	−0.429977	+	0.115212i
$268$	3.36244	+	3.36244i	0.205394	+	0.205394i
$269$	−5.62758	−	3.24908i	−0.343120	−	0.198100i	0.318531	−	0.947912i	$-0.396810\pi$
$269$	−5.62758	−	3.24908i	−0.343120	−	0.198100i	−0.661651	+	0.749812i	$0.730144\pi$
$270$	−0.777302	+	0.448776i	−0.0473051	+	0.0273116i
$271$	6.14616	+	1.64686i	0.373353	+	0.100040i	0.440616	−	0.897696i	$-0.354760\pi$
$271$	6.14616	+	1.64686i	0.373353	+	0.100040i	−0.0672633	+	0.997735i	$0.521427\pi$
$272$	7.79332			0.472539
$273$	−8.67774	−	3.96192i	−0.525201	−	0.239786i
$274$	−7.27473			−0.439482
$275$	13.5258	+	3.62423i	0.815636	+	0.218549i
$276$	−3.25346	+	1.87839i	−0.195835	+	0.113066i
$277$	15.6622	+	9.04260i	0.941053	+	0.543317i	0.890290	−	0.455394i	$-0.150501\pi$
$277$	15.6622	+	9.04260i	0.941053	+	0.543317i	0.0507626	+	0.998711i	$0.483835\pi$
$278$	−15.6819	−	15.6819i	−0.940538	−	0.940538i
$279$	1.21307	−	0.325041i	0.0726246	−	0.0194597i
$280$	−6.27439	−	0.830628i	−0.374967	−	0.0496395i
$281$	−6.43538	−	6.43538i	−0.383903	−	0.383903i	0.488603	−	0.872506i	$-0.337507\pi$
$281$	−6.43538	−	6.43538i	−0.383903	−	0.383903i	−0.872506	+	0.488603i	$0.837507\pi$
$282$	−0.218129	+	0.377810i	−0.0129894	+	0.0224983i
$283$	−7.33715	−	12.7083i	−0.436148	−	0.755431i	0.561240	−	0.827653i	$-0.310324\pi$
$283$	−7.33715	−	12.7083i	−0.436148	−	0.755431i	−0.997389	+	0.0722219i	$0.976991\pi$
$284$	−1.67027	+	6.23354i	−0.0991124	+	0.369892i
$285$	−4.87616			−0.288839
$286$	2.98491	+	12.9274i	0.176502	+	0.764414i
$287$	6.65599	+	2.76261i	0.392891	+	0.163072i
$288$	−3.46335	−	0.928002i	−0.204080	−	0.0546830i
$289$	2.37677	+	4.11668i	0.139810	+	0.242158i
$290$	−4.08075	+	7.06807i	−0.239630	+	0.415051i
$291$	−0.515761	+	0.515761i	−0.0302344	+	0.0302344i
$292$	−7.01203	+	1.87887i	−0.410348	+	0.109952i
$293$	−1.69762	−	6.33562i	−0.0991763	−	0.370131i	0.898443	−	0.439090i	$-0.144699\pi$
$293$	−1.69762	−	6.33562i	−0.0991763	−	0.370131i	−0.997620	+	0.0689587i	$0.978032\pi$
$294$	−8.08723	−	0.0116252i	−0.471657	−	0.000677996i
$295$	−0.953209	+	1.65101i	−0.0554980	+	0.0961253i
$296$	1.55724	−	0.899074i	0.0905129	−	0.0522576i
$297$	−3.07653	−	0.824353i	−0.178518	−	0.0478338i
$298$			13.3507i			0.773385i
$299$	5.95258	−	19.4720i	0.344246	−	1.12609i
$300$		−	2.92468i		−	0.168857i
$301$	12.3033	−	16.0101i	0.709150	−	0.922809i
$302$	−7.27540	−	12.6014i	−0.418652	−	0.725127i
$303$	−9.89554	−	5.71320i	−0.568484	−	0.328214i
$304$	9.88377	+	9.88377i	0.566873	+	0.566873i
$305$	−1.55616	−	5.80767i	−0.0891055	−	0.332546i
$306$	−1.04641	−	3.90527i	−0.0598195	−	0.223249i
$307$	−23.5768	+	23.5768i	−1.34560	+	1.34560i	−0.455225	+	0.890377i	$0.650441\pi$
$307$	−23.5768	+	23.5768i	−1.34560	+	1.34560i	−0.890377	+	0.455225i	$0.849559\pi$
$308$	−3.40944	−	4.44988i	−0.194271	−	0.253556i
$309$	16.7290	−	9.65849i	0.951679	−	0.549452i
$310$	−0.291741	+	1.08879i	−0.0165698	+	0.0618393i
$311$	2.90579			0.164772			0.0823861	−	0.996600i	$-0.473746\pi$
$311$	2.90579			0.164772			0.0823861	+	0.996600i	$0.473746\pi$
$312$	9.80253	−	5.21245i	0.554959	−	0.295097i
$313$			0.960626i			0.0542978i	0.999631	+	0.0271489i	$0.00864282\pi$
$313$			0.960626i			0.0542978i	−0.999631	+	0.0271489i	$0.991357\pi$
$314$	1.64277	−	6.13090i	0.0927069	−	0.345987i
$315$	0.266825	+	2.03806i	0.0150339	+	0.114831i
$316$	6.23287	+	3.59855i	0.350626	+	0.202434i
$317$	−23.7216	+	23.7216i	−1.33234	+	1.33234i	−0.429064	+	0.903274i	$0.641156\pi$
$317$	−23.7216	+	23.7216i	−1.33234	+	1.33234i	−0.903274	+	0.429064i	$0.858844\pi$
$318$	−12.9478	+	3.46936i	−0.726078	+	0.194552i
$319$	−27.9751	+	7.49590i	−1.56630	+	0.419690i
$320$	4.72235	−	4.72235i	0.263988	−	0.263988i
$321$	7.95175	+	4.59094i	0.443823	+	0.256241i
$322$	−2.24083	−	17.1158i	−0.124877	−	0.953829i
$323$	5.68489	−	21.2163i	0.316316	−	1.18051i
$324$			0.665238i			0.0369576i
$325$	10.8111	+	11.5928i	0.599692	+	0.643055i
$326$	−12.3153			−0.682082
$327$	−0.655795	+	2.44746i	−0.0362656	+	0.135345i
$328$	−7.26351	+	4.19359i	−0.401060	+	0.231552i
$329$	0.607617	+	0.793041i	0.0334990	+	0.0437218i
$330$	2.02144	−	2.02144i	0.111277	−	0.111277i
$331$	3.27417	+	12.2194i	0.179965	+	0.671637i	0.995653	+	0.0931447i	$0.0296919\pi$
$331$	3.27417	+	12.2194i	0.179965	+	0.671637i	−0.815688	+	0.578492i	$0.803641\pi$
$332$	2.51662	+	9.39217i	0.138118	+	0.515462i
$333$	−0.412926	−	0.412926i	−0.0226282	−	0.0226282i
$334$	12.9571	+	7.48078i	0.708981	+	0.409330i
$335$	2.77665	+	4.80929i	0.151704	+	0.262760i
$336$	3.59021	−	4.67189i	0.195862	−	0.254873i
$337$		−	12.8172i		−	0.698196i	−0.937086	−	0.349098i	$-0.886488\pi$
$337$		−	12.8172i		−	0.698196i	0.937086	−	0.349098i	$-0.113512\pi$
$338$	−4.88896	+	14.2012i	−0.265924	+	0.772441i
$339$			2.50903i			0.136272i
$340$	−1.74696	−	0.468097i	−0.0947423	−	0.0253861i
$341$	−3.46410	+	2.00000i	−0.187591	+	0.108306i
$342$	3.62570	−	6.27990i	0.196056	−	0.339578i
$343$	−7.12427	+	17.0952i	−0.384675	+	0.923052i
$344$	6.08209	+	22.6987i	0.327925	+	1.22383i
$345$	−4.23779	+	1.13551i	−0.228155	+	0.0611339i
$346$	0.814660	−	0.814660i	0.0437964	−	0.0437964i
$347$	−9.29372	+	16.0972i	−0.498913	+	0.864143i	−0.999999	−	0.00125445i	$-0.999601\pi$
$347$	−9.29372	+	16.0972i	−0.498913	+	0.864143i	0.501086	+	0.865397i	$0.332934\pi$
$348$	3.02453	+	5.23864i	0.162132	+	0.280820i
$349$	4.62637	+	1.23963i	0.247644	+	0.0663560i	0.380506	−	0.924779i	$-0.375750\pi$
$349$	4.62637	+	1.23963i	0.247644	+	0.0663560i	−0.132862	+	0.991135i	$0.542417\pi$
$350$	12.4119	+	5.15164i	0.663445	+	0.275367i
$351$	−2.45905	−	2.63686i	−0.131255	−	0.140745i
$352$	11.4201			0.608693
$353$	−3.19876	+	11.9379i	−0.170253	+	0.635392i	0.827059	+	0.562116i	$0.190012\pi$
$353$	−3.19876	+	11.9379i	−0.170253	+	0.635392i	−0.997312	+	0.0732769i	$0.976654\pi$
$354$	−1.41753	−	2.45524i	−0.0753410	−	0.130494i
$355$	−3.76826	+	6.52683i	−0.199999	+	0.346408i
$356$	−3.42152	−	3.42152i	−0.181340	−	0.181340i
$357$	−9.17871	−	1.21511i	−0.485789	−	0.0643106i
$358$	6.29224	−	1.68600i	0.332555	−	0.0891079i
$359$	4.20137	+	4.20137i	0.221740	+	0.221740i	0.809231	−	0.587491i	$-0.199884\pi$
$359$	4.20137	+	4.20137i	0.221740	+	0.221740i	−0.587491	+	0.809231i	$0.699884\pi$
$360$	−2.07170	−	1.19609i	−0.109188	−	0.0630397i
$361$	17.6626	−	10.1975i	0.929608	−	0.536710i
$362$	−24.0035	−	6.43171i	−1.26159	−	0.338043i
$363$	−0.855422			−0.0448980
$364$	−0.603871	−	6.31716i	−0.0316514	−	0.331109i
$365$	−8.47775			−0.443746
$366$	8.63668	+	2.31419i	0.451446	+	0.120965i
$367$	5.05707	−	2.91970i	0.263977	−	0.152407i	−0.362170	−	0.932112i	$-0.617964\pi$
$367$	5.05707	−	2.91970i	0.263977	−	0.152407i	0.626147	+	0.779705i	$0.284631\pi$
$368$	10.8914	+	6.28818i	0.567756	+	0.327794i
$369$	1.92603	+	1.92603i	0.100265	+	0.100265i
$370$	0.506280	−	0.135657i	0.0263202	−	0.00705249i
$371$	−4.02867	+	30.4318i	−0.209158	+	1.57994i
$372$	0.590750	+	0.590750i	0.0306290	+	0.0306290i
$373$	−5.17801	+	8.96858i	−0.268107	+	0.464375i	−0.968373	−	0.249507i	$-0.919731\pi$
$373$	−5.17801	+	8.96858i	−0.268107	+	0.464375i	0.700266	+	0.713882i	$0.253065\pi$
$374$	6.43864	+	11.1521i	0.332934	+	0.576659i
$375$	1.88937	−	7.05123i	0.0975667	−	0.364124i
$376$	−1.16273			−0.0599632
$377$	−31.3532	−	9.58469i	−1.61477	−	0.493636i
$378$	−2.82317	−	1.17177i	−0.145208	−	0.0602695i
$379$	6.76845	+	1.81360i	0.347672	+	0.0931584i	0.428429	−	0.903575i	$-0.359067\pi$
$379$	6.76845	+	1.81360i	0.347672	+	0.0931584i	−0.0807572	+	0.996734i	$0.525734\pi$
$380$	−1.62190	−	2.80922i	−0.0832018	−	0.144110i
$381$	8.44360	−	14.6248i	0.432579	−	0.749249i
$382$	7.17592	−	7.17592i	0.367152	−	0.367152i
$383$	−7.14098	+	1.91342i	−0.364887	+	0.0977711i	−0.436604	−	0.899654i	$-0.643819\pi$
$383$	−7.14098	+	1.91342i	−0.364887	+	0.0977711i	0.0717170	+	0.997425i	$0.477152\pi$
$384$	0.714478	+	2.66647i	0.0364605	+	0.136073i
$385$	−2.50097	−	6.05017i	−0.127461	−	0.308345i
$386$	−0.556404	+	0.963720i	−0.0283202	+	0.0490521i
$387$	6.60921	−	3.81583i	0.335965	−	0.193970i
$388$	−0.468688	−	0.125585i	−0.0237940	−	0.00637559i
$389$		−	10.2280i		−	0.518581i	−0.965799	−	0.259290i	$-0.916511\pi$
$389$		−	10.2280i		−	0.518581i	0.965799	−	0.259290i	$-0.0834886\pi$
$390$	3.15320	−	0.728068i	0.159669	−	0.0368672i
$391$		−	19.7626i		−	0.999436i
$392$	−10.7504	−	18.6821i	−0.542975	−	0.943590i
$393$	−4.59273	−	7.95484i	−0.231673	−	0.401269i
$394$	17.2289	+	9.94711i	0.867979	+	0.501128i
$395$	5.94323	+	5.94323i	0.299037	+	0.299037i
$396$	−0.548391	−	2.04662i	−0.0275577	−	0.102847i
$397$	−7.30250	−	27.2533i	−0.366502	−	1.36780i	−0.865373	−	0.501128i	$-0.832919\pi$
$397$	−7.30250	−	27.2533i	−0.366502	−	1.36780i	0.498872	−	0.866676i	$-0.333748\pi$
$398$	−1.83900	+	1.83900i	−0.0921810	+	0.0921810i
$399$	−10.0997	−	13.1818i	−0.505618	−	0.659916i
$400$	−8.47910	+	4.89541i	−0.423955	+	0.244770i
$401$	−1.82731	+	6.81960i	−0.0912514	+	0.340555i	−0.996424	−	0.0844884i	$-0.973074\pi$
$401$	−1.82731	+	6.81960i	−0.0912514	+	0.340555i	0.905173	+	0.425043i	$0.139741\pi$
$402$	−8.25838			−0.411891
$403$	−4.52532	−	0.157900i	−0.225422	−	0.00786558i
$404$		−	7.60126i		−	0.378177i
$405$	−0.201073	+	0.750414i	−0.00999139	+	0.0372884i
$406$	−27.5595	+	3.60813i	−1.36776	+	0.179068i
$407$	1.61078	+	0.929982i	0.0798432	+	0.0460975i
$408$	7.61953	−	7.61953i	0.377223	−	0.377223i
$409$	−30.3999	+	8.14562i	−1.50318	+	0.402775i	−0.914163	−	0.405348i	$-0.867150\pi$
$409$	−30.3999	+	8.14562i	−1.50318	+	0.402775i	−0.589014	+	0.808123i	$0.700484\pi$
$410$	−2.36146	+	0.632752i	−0.116624	+	0.0312494i
$411$	−4.45246	+	4.45246i	−0.219624	+	0.219624i
$412$	11.1288	+	6.42519i	0.548274	+	0.316546i
$413$	−6.43753	+	0.842810i	−0.316770	+	0.0414720i
$414$	1.68864	−	6.30208i	0.0829919	−	0.309730i
$415$			11.3554i			0.557415i
$416$	10.9636	+	6.85037i	0.537534	+	0.335867i
$417$	−19.1960			−0.940034
$418$	−5.97772	+	22.3092i	−0.292380	+	1.09118i
$419$	−20.4187	+	11.7887i	−0.997519	+	0.575918i	−0.907513	−	0.420023i	$-0.862022\pi$
$419$	−20.4187	+	11.7887i	−0.997519	+	0.575918i	−0.0900058	+	0.995941i	$0.528689\pi$
$420$	−1.08540	+	0.831617i	−0.0529620	+	0.0405787i
$421$	4.63273	−	4.63273i	0.225785	−	0.225785i	−0.585144	−	0.810929i	$-0.698962\pi$
$421$	4.63273	−	4.63273i	0.225785	−	0.225785i	0.810929	+	0.585144i	$0.198962\pi$
$422$	6.19260	+	23.1111i	0.301451	+	1.12503i
$423$	0.0977320	+	0.364741i	0.00475189	+	0.0177343i
$424$	−25.2624	−	25.2624i	−1.22685	−	1.22685i
$425$	13.3241	+	7.69267i	0.646314	+	0.373149i
$426$	−5.60384	−	9.70614i	−0.271507	−	0.470264i
$427$	12.4768	−	16.2359i	0.603795	−	0.785711i
$428$			6.10813i			0.295248i
$429$	9.73905	+	6.08526i	0.470206	+	0.293799i
$430$			6.84981i			0.330327i
$431$	27.8082	+	7.45118i	1.33947	+	0.358911i	0.856239	−	0.516580i	$-0.172795\pi$
$431$	27.8082	+	7.45118i	1.33947	+	0.358911i	0.483234	+	0.875491i	$0.339462\pi$
$432$	1.92862	−	1.11349i	0.0927910	−	0.0535729i
$433$	1.92063	−	3.32663i	0.0922998	−	0.159868i	−0.816179	−	0.577800i	$-0.803912\pi$
$433$	1.92063	−	3.32663i	0.0922998	−	0.159868i	0.908478	+	0.417932i	$0.137245\pi$
$434$	−3.54763	+	1.46649i	−0.170291	+	0.0703937i
$435$	1.82837	+	6.82358i	0.0876637	+	0.327165i
$436$	−1.62814	+	0.436260i	−0.0779739	+	0.0208930i
$437$	25.0636	−	25.0636i	1.19895	−	1.19895i
$438$	6.30369	−	10.9183i	0.301202	−	0.521697i
$439$	−7.29107	−	12.6285i	−0.347984	−	0.602726i	0.637907	−	0.770113i	$-0.279800\pi$
$439$	−7.29107	−	12.6285i	−0.347984	−	0.602726i	−0.985891	+	0.167388i	$0.946467\pi$
$440$	7.35963	+	1.97201i	0.350857	+	0.0940118i
$441$	−4.95686	+	4.94263i	−0.236041	+	0.235363i
$442$	−0.508333	+	14.5685i	−0.0241789	+	0.692953i
$443$	32.2060			1.53015			0.765076	−	0.643940i	$-0.222701\pi$
$443$	32.2060			1.53015			0.765076	+	0.643940i	$0.222701\pi$
$444$	0.100545	−	0.375239i	0.00477166	−	0.0178081i
$445$	−2.82543	−	4.89379i	−0.133938	−	0.231988i
$446$	−13.2197	+	22.8973i	−0.625973	+	1.08422i
$447$	8.17122	+	8.17122i	0.386486	+	0.386486i
$448$	22.5472	+	2.98488i	1.06525	+	0.141022i
$449$	−19.3546	+	5.18606i	−0.913402	+	0.244745i	−0.684763	−	0.728766i	$-0.740094\pi$
$449$	−19.3546	+	5.18606i	−0.913402	+	0.244745i	−0.228639	+	0.973511i	$0.573428\pi$
$450$	3.59161	+	3.59161i	0.169310	+	0.169310i
$451$	−7.51321	−	4.33776i	−0.353783	−	0.204257i
$452$	−1.44548	+	0.834549i	−0.0679897	+	0.0392539i
$453$	−12.1655	−	3.25973i	−0.571583	−	0.153155i
$454$	−18.0711			−0.848120
$455$	1.22822	−	7.30854i	0.0575798	−	0.342630i
$456$	19.3267			0.905057
$457$	14.5061	+	3.88690i	0.678567	+	0.181822i	0.581611	−	0.813467i	$-0.302423\pi$
$457$	14.5061	+	3.88690i	0.678567	+	0.181822i	0.0969563	+	0.995289i	$0.469089\pi$
$458$	5.11049	−	2.95054i	0.238797	−	0.137870i
$459$	−3.03065	−	1.74975i	−0.141459	−	0.0816712i
$460$	−2.06375	−	2.06375i	−0.0962228	−	0.0962228i
$461$	29.9515	−	8.02549i	1.39498	−	0.373784i	0.518441	−	0.855113i	$-0.326512\pi$
$461$	29.9515	−	8.02549i	1.39498	−	0.373784i	0.876540	+	0.481329i	$0.159846\pi$
$462$	9.65151	+	1.27770i	0.449029	+	0.0594441i
$463$	3.61564	+	3.61564i	0.168033	+	0.168033i	0.786114	−	0.618081i	$-0.212090\pi$
$463$	3.61564	+	3.61564i	0.168033	+	0.168033i	−0.618081	+	0.786114i	$0.712090\pi$
$464$	10.1251	−	17.5371i	0.470044	−	0.814141i
$465$	0.487831	+	0.844949i	0.0226226	+	0.0391835i
$466$	−0.952840	+	3.55605i	−0.0441395	+	0.164731i
$467$	17.6775			0.818017			0.409009	−	0.912530i	$-0.365875\pi$
$467$	17.6775			0.818017			0.409009	+	0.912530i	$0.365875\pi$
$468$	0.701203	−	2.29376i	0.0324131	−	0.106029i
$469$	−7.24994	+	17.4674i	−0.334771	+	0.806569i
$470$	−0.327374	−	0.0877195i	−0.0151006	−	0.00404620i
$471$	−2.74694	−	4.75783i	−0.126572	−	0.219229i
$472$	3.77806	−	6.54379i	0.173899	−	0.301202i
$473$	−17.1878	+	17.1878i	−0.790297	+	0.790297i
$474$	−12.0733	+	3.23503i	−0.554545	+	0.148590i
$475$	7.14198	+	26.6542i	0.327696	+	1.22298i
$476$	−2.35297	−	5.69214i	−0.107848	−	0.260899i
$477$	−5.80124	+	10.0480i	−0.265621	+	0.460068i
$478$	2.29110	−	1.32276i	0.104792	−	0.0605018i
$479$	−19.1281	−	5.12537i	−0.873987	−	0.234184i	−0.206176	−	0.978515i	$-0.566102\pi$
$479$	−19.1281	−	5.12537i	−0.873987	−	0.234184i	−0.667811	+	0.744331i	$0.732769\pi$
$480$		−	2.78554i		−	0.127142i
$481$	0.988534	+	1.85904i	0.0450733	+	0.0847647i
$482$		−	7.33146i		−	0.333939i
$483$	−11.8472	−	9.10417i	−0.539064	−	0.414254i
$484$	−0.284529	−	0.492819i	−0.0129332	−	0.0224009i
$485$	−0.490740	−	0.283329i	−0.0222834	−	0.0128653i
$486$	−0.816934	−	0.816934i	−0.0370569	−	0.0370569i
$487$	10.1291	+	37.8022i	0.458992	+	1.71298i	0.676080	+	0.736828i	$0.263677\pi$
$487$	10.1291	+	37.8022i	0.458992	+	1.71298i	−0.217089	+	0.976152i	$0.569656\pi$
$488$	6.16787	+	23.0188i	0.279206	+	1.04201i
$489$	−7.53752	+	7.53752i	−0.340859	+	0.340859i
$490$	−1.61740	−	6.07111i	−0.0730666	−	0.274265i
$491$	16.0715	−	9.27889i	0.725297	−	0.418750i	−0.0914021	−	0.995814i	$-0.529135\pi$
$491$	16.0715	−	9.27889i	0.725297	−	0.418750i	0.816699	+	0.577064i	$0.195802\pi$
$492$	−0.468976	+	1.75024i	−0.0211431	+	0.0789071i
$493$	−31.8212			−1.43315
$494$	−19.1210	+	17.8316i	−0.860293	+	0.802282i
$495$		−	2.47443i		−	0.111217i
$496$	0.723862	−	2.70149i	0.0325023	−	0.121300i
$497$	−25.4491	+	3.33183i	−1.14155	+	0.149453i
$498$	−14.6244	−	8.44340i	−0.655335	−	0.378358i
$499$	3.54363	−	3.54363i	0.158635	−	0.158635i	−0.623327	−	0.781962i	$-0.714219\pi$
$499$	3.54363	−	3.54363i	0.158635	−	0.158635i	0.781962	+	0.623327i	$0.214219\pi$
$500$	4.69074	−	1.25688i	0.209776	−	0.0562094i
$501$	12.5089	−	3.35175i	0.558856	−	0.149745i
$502$	17.5323	−	17.5323i	0.782507	−	0.782507i
$503$	2.98438	+	1.72303i	0.133067	+	0.0768262i	0.565056	−	0.825053i	$-0.308855\pi$
$503$	2.98438	+	1.72303i	0.133067	+	0.0768262i	−0.431989	+	0.901879i	$0.642188\pi$
$504$	−1.05756	−	8.07786i	−0.0471077	−	0.359817i
$505$	2.29754	−	8.57453i	0.102239	−	0.381561i
$506$			20.7805i			0.923808i
$507$	5.69948	+	11.6840i	0.253123	+	0.518905i
$508$	11.2340			0.498428
$509$	−7.93556	+	29.6159i	−0.351737	+	1.31270i	0.532803	+	0.846239i	$0.321138\pi$
$509$	−7.93556	+	29.6159i	−0.351737	+	1.31270i	−0.884541	+	0.466463i	$0.845528\pi$
$510$	2.72017	−	1.57049i	0.120451	−	0.0695424i
$511$	−17.5595	−	22.9181i	−0.776786	−	1.01384i
$512$	−15.3439	+	15.3439i	−0.678111	+	0.678111i
$513$	−1.62449	−	6.06267i	−0.0717229	−	0.267674i
$514$	−8.48696	−	31.6738i	−0.374344	−	1.39707i
$515$	10.6116	+	10.6116i	0.467604	+	0.467604i
$516$	4.39670	+	2.53843i	0.193554	+	0.111748i
$517$	−0.601351	−	1.04157i	−0.0264474	−	0.0458082i
$518$	1.41536	+	1.08766i	0.0621872	+	0.0477889i
$519$		−	0.997217i		−	0.0437729i
$520$	5.88252	+	6.30787i	0.257966	+	0.276619i
$521$			13.0906i			0.573510i	0.958004	+	0.286755i	$0.0925766\pi$
$521$			13.0906i			0.573510i	−0.958004	+	0.286755i	$0.907423\pi$
$522$	−10.1474	−	2.71900i	−0.444141	−	0.119007i
$523$	29.9435	−	17.2879i	1.30934	−	0.755946i	0.327351	−	0.944903i	$-0.393844\pi$
$523$	29.9435	−	17.2879i	1.30934	−	0.755946i	0.981985	+	0.188957i	$0.0605106\pi$
$524$	3.05526	−	5.29186i	0.133469	−	0.231176i
$525$	10.7497	−	4.44361i	0.469154	−	0.193935i
$526$	−3.79009	−	14.1448i	−0.165256	−	0.616743i
$527$	−4.24513	+	1.13748i	−0.184921	+	0.0495494i
$528$	−5.01556	+	5.01556i	−0.218274	+	0.218274i
$529$	4.44578	−	7.70032i	0.193295	−	0.334797i
$530$	−5.20691	−	9.01864i	−0.226174	−	0.391745i
$531$	−2.37031	−	0.635122i	−0.102863	−	0.0275619i
$532$	4.23486	−	10.2031i	0.183604	−	0.442360i
$533$	−4.61086	−	8.67118i	−0.199719	−	0.375590i
$534$	8.40349			0.363654
$535$	−1.84623	+	6.89022i	−0.0798194	+	0.297890i
$536$	−11.0053	−	19.0617i	−0.475355	−	0.823340i
$537$	2.81922	−	4.88304i	0.121658	−	0.210719i
$538$	5.30857	+	5.30857i	0.228869	+	0.228869i
$539$	11.1754	−	19.2923i	0.481360	−	0.830979i
$540$	−0.499204	+	0.133761i	−0.0214823	+	0.00575617i
$541$	23.6775	+	23.6775i	1.01797	+	1.01797i	0.999835	+	0.0181382i	$0.00577388\pi$
$541$	23.6775	+	23.6775i	1.01797	+	1.01797i	0.0181382	+	0.999835i	$0.494226\pi$
$542$	−6.36638	−	3.67563i	−0.273460	−	0.157882i
$543$	−18.6277	+	10.7547i	−0.799390	+	0.461528i
$544$	12.1200	+	3.24754i	0.519640	+	0.139237i
$545$	−1.96847			−0.0843201
$546$	8.49926	+	7.01612i	0.363735	+	0.300262i
$547$	−9.25725			−0.395811			−0.197906	−	0.980221i	$-0.563414\pi$
$547$	−9.25725			−0.395811			−0.197906	+	0.980221i	$0.563414\pi$
$548$	−4.04609	−	1.08415i	−0.172840	−	0.0463124i
$549$	6.70242	−	3.86964i	0.286052	−	0.165152i
$550$	−14.0104	−	8.08893i	−0.597407	−	0.344913i
$551$	−40.3567	−	40.3567i	−1.71926	−	1.71926i
$552$	16.7965	−	4.50062i	0.714908	−	0.191559i
$553$	−3.75657	+	28.3764i	−0.159746	+	1.20669i
$554$	−14.7744	−	14.7744i	−0.627705	−	0.627705i
$555$	0.226838	−	0.392894i	0.00962872	−	0.0166774i
$556$	−6.38496	−	11.0591i	−0.270783	−	0.469009i
$557$	2.46966	−	9.21689i	0.104643	−	0.390532i	−0.893662	−	0.448742i	$-0.851872\pi$
$557$	2.46966	−	9.21689i	0.104643	−	0.390532i	0.998304	+	0.0582092i	$0.0185390\pi$
$558$	−1.45092			−0.0614224
$559$	−26.8109	+	6.19058i	−1.13398	+	0.261834i
$560$	4.22775	+	1.75475i	0.178655	+	0.0741518i
$561$	10.7663	+	2.88482i	0.454553	+	0.121797i
$562$	5.25728	+	9.10588i	0.221765	+	0.384108i
$563$	1.08829	−	1.88498i	0.0458661	−	0.0794424i	−0.842181	−	0.539195i	$-0.818729\pi$
$563$	1.08829	−	1.88498i	0.0458661	−	0.0794424i	0.888047	+	0.459753i	$0.152062\pi$
$564$	−0.177624	+	0.177624i	−0.00747933	+	0.00747933i
$565$	−1.88281	+	0.504497i	−0.0792104	+	0.0212244i
$566$	4.38789	+	16.3758i	0.184437	+	0.688327i
$567$	−2.44508	+	1.01073i	−0.102684	+	0.0424466i
$568$	14.9356	−	25.8692i	0.626683	−	1.08545i
$569$	20.3648	−	11.7576i	0.853738	−	0.492906i	−0.00817222	−	0.999967i	$-0.502601\pi$
$569$	20.3648	−	11.7576i	0.853738	−	0.492906i	0.861910	+	0.507061i	$0.169268\pi$
$570$	5.44156	+	1.45806i	0.227922	+	0.0610715i
$571$		−	13.2414i		−	0.554134i	−0.960851	−	0.277067i	$-0.910638\pi$
$571$		−	13.2414i		−	0.554134i	0.960851	−	0.277067i	$-0.0893624\pi$
$572$	−0.266400	+	7.63486i	−0.0111388	+	0.319230i
$573$		−	8.78397i		−	0.366955i
$574$	−6.60170	−	5.07321i	−0.275550	−	0.211752i
$575$	12.4139	+	21.5016i	0.517697	+	0.896678i
$576$	7.44469	+	4.29820i	0.310196	+	0.179091i
$577$	−1.10520	−	1.10520i	−0.0460102	−	0.0460102i	0.683727	−	0.729738i	$-0.260358\pi$
$577$	−1.10520	−	1.10520i	−0.0460102	−	0.0460102i	−0.729738	+	0.683727i	$0.760358\pi$
$578$	−1.42140	−	5.30472i	−0.0591223	−	0.220647i
$579$	0.249296	+	0.930384i	0.0103604	+	0.0386654i
$580$	−3.32300	+	3.32300i	−0.137980	+	0.137980i
$581$	−30.6973	+	23.5198i	−1.27354	+	0.975768i
$582$	0.729787	−	0.421343i	0.0302506	−	0.0174652i
$583$	9.56454	−	35.6954i	0.396123	−	1.47835i
$584$	33.6017			1.39045
$585$	1.48429	−	2.37551i	0.0613679	−	0.0982153i
$586$			7.57788i			0.313039i
$587$	6.57121	−	24.5241i	0.271223	−	1.01222i	−0.687108	−	0.726556i	$-0.741120\pi$
$587$	6.57121	−	24.5241i	0.271223	−	1.01222i	0.958331	−	0.285662i	$-0.0922133\pi$
$588$	−4.49625	−	1.21170i	−0.185422	−	0.0499696i
$589$	−6.82642	−	3.94124i	−0.281278	−	0.162396i
$590$	1.55742	−	1.55742i	0.0641179	−	0.0641179i
$591$	16.6329	−	4.45678i	0.684187	−	0.183327i
$592$	−1.25617	+	0.336590i	−0.0516283	+	0.0138338i
$593$	13.5799	−	13.5799i	0.557660	−	0.557660i	−0.370981	−	0.928641i	$-0.620978\pi$
$593$	13.5799	−	13.5799i	0.557660	−	0.557660i	0.928641	+	0.370981i	$0.120978\pi$
$594$	3.18676	+	1.83988i	0.130754	+	0.0754911i
$595$	−0.933753	−	7.13216i	−0.0382801	−	0.292390i
$596$	−1.98964	+	7.42545i	−0.0814989	+	0.304158i
$597$			2.25111i			0.0921316i
$598$	−12.4653	+	19.9499i	−0.509743	+	0.815810i
$599$	−6.33246			−0.258737			−0.129369	−	0.991597i	$-0.541295\pi$
$599$	−6.33246			−0.258737			−0.129369	+	0.991597i	$0.541295\pi$
$600$	−3.50377	+	13.0763i	−0.143041	+	0.533836i
$601$	20.1592	−	11.6389i	0.822309	−	0.474760i	−0.0289030	−	0.999582i	$-0.509201\pi$
$601$	20.1592	−	11.6389i	0.822309	−	0.474760i	0.851212	+	0.524822i	$0.175868\pi$
$602$	−18.5172	+	14.1876i	−0.754706	+	0.578245i
$603$	−5.05450	+	5.05450i	−0.205835	+	0.205835i
$604$	−2.16849	−	8.09292i	−0.0882347	−	0.329296i
$605$	−0.172002	−	0.641921i	−0.00699288	−	0.0260978i
$606$	9.33461	+	9.33461i	0.379192	+	0.379192i
$607$	9.09221	+	5.24939i	0.369041	+	0.213066i	0.673040	−	0.739607i	$-0.264988\pi$
$607$	9.09221	+	5.24939i	0.369041	+	0.213066i	−0.303998	+	0.952673i	$0.598322\pi$
$608$	11.2523	+	19.4896i	0.456343	+	0.790409i
$609$	−14.6593	+	19.0760i	−0.594025	+	0.772998i
$610$			6.94641i			0.281252i
$611$	0.0474768	−	1.36066i	0.00192071	−	0.0550462i
$612$		−	2.32800i		−	0.0941036i
$613$	−8.40441	−	2.25196i	−0.339451	−	0.0909556i	0.0850667	−	0.996375i	$-0.472890\pi$
$613$	−8.40441	−	2.25196i	−0.339451	−	0.0909556i	−0.424518	+	0.905420i	$0.639556\pi$
$614$	33.3606	−	19.2607i	1.34632	−	0.777300i
$615$	−1.05805	+	1.83259i	−0.0426646	+	0.0738973i
$616$	9.91264	+	23.9800i	0.399392	+	0.966180i
$617$	7.98973	+	29.8181i	0.321654	+	1.20043i	0.917633	+	0.397430i	$0.130098\pi$
$617$	7.98973	+	29.8181i	0.321654	+	1.20043i	−0.595978	+	0.803000i	$0.703236\pi$
$618$	−21.5568	+	5.77613i	−0.867143	+	0.232350i
$619$	2.31233	−	2.31233i	0.0929403	−	0.0929403i	−0.659108	−	0.752048i	$-0.729066\pi$
$619$	2.31233	−	2.31233i	0.0929403	−	0.0929403i	0.752048	+	0.659108i	$0.229066\pi$
$620$	−0.324524	+	0.562091i	−0.0130332	+	0.0225741i
$621$	−2.82363	−	4.89067i	−0.113308	−	0.196256i
$622$	−3.24272	−	0.868885i	−0.130021	−	0.0348391i
$623$	7.37733	−	17.7743i	0.295566	−	0.712112i
$624$	−7.82366	+	1.80647i	−0.313197	+	0.0723165i
$625$	−16.3110			−0.652440
$626$	0.287245	−	1.07201i	0.0114806	−	0.0428462i
$627$	9.99557	+	17.3128i	0.399184	+	0.691408i
$628$	1.82737	−	3.16509i	0.0729198	−	0.126301i
$629$	1.44503	+	1.44503i	0.0576173	+	0.0576173i
$630$	0.311652	−	2.35416i	0.0124165	−	0.0937919i
$631$	5.07213	−	1.35907i	0.201918	−	0.0541039i	−0.156442	−	0.987687i	$-0.550003\pi$
$631$	5.07213	−	1.35907i	0.201918	−	0.0541039i	0.358361	+	0.933583i	$0.383336\pi$
$632$	−23.5561	−	23.5561i	−0.937011	−	0.937011i
$633$	17.9352	+	10.3549i	0.712859	+	0.411569i
$634$	33.5654	−	19.3790i	1.33305	−	0.769638i
$635$	12.6724	+	3.39556i	0.502889	+	0.134749i
$636$	−7.71841			−0.306055
$637$	22.3013	−	11.8175i	0.883608	−	0.468227i
$638$	33.4603			1.32471
$639$	−9.37039	−	2.51079i	−0.370687	−	0.0993253i
$640$	−1.85729	+	1.07231i	−0.0734160	+	0.0423867i
$641$	−28.4420	−	16.4210i	−1.12339	−	0.648589i	−0.181126	−	0.983460i	$-0.557974\pi$
$641$	−28.4420	−	16.4210i	−1.12339	−	0.648589i	−0.942264	+	0.334871i	$0.891307\pi$
$642$	−7.50099	−	7.50099i	−0.296041	−	0.296041i
$643$	35.7163	−	9.57017i	1.40852	−	0.377411i	0.527120	−	0.849791i	$-0.323272\pi$
$643$	35.7163	−	9.57017i	1.40852	−	0.377411i	0.881395	+	0.472380i	$0.156605\pi$
$644$	1.30444	−	9.85351i	0.0514023	−	0.388283i
$645$	4.19239	+	4.19239i	0.165075	+	0.165075i
$646$	−12.6881	+	21.9765i	−0.499208	+	0.864653i
$647$	−24.0363	−	41.6322i	−0.944966	−	1.63673i	−0.755819	−	0.654780i	$-0.772761\pi$
$647$	−24.0363	−	41.6322i	−0.944966	−	1.63673i	−0.189147	−	0.981949i	$-0.560572\pi$
$648$	0.796956	−	2.97428i	0.0313074	−	0.116841i
$649$	7.81588			0.306800
$650$	−8.59821	−	16.1698i	−0.337249	−	0.634231i
$651$	−1.27375	+	3.06886i	−0.0499221	+	0.120278i
$652$	−6.84958	−	1.83534i	−0.268250	−	0.0718775i
$653$	17.6801	+	30.6228i	0.691876	+	1.19836i	0.971223	+	0.238174i	$0.0765488\pi$
$653$	17.6801	+	30.6228i	0.691876	+	1.19836i	−0.279347	+	0.960190i	$0.590118\pi$
$654$	1.46367	−	2.53516i	0.0572341	−	0.0991325i
$655$	5.04595	−	5.04595i	0.197162	−	0.197162i
$656$	5.85921	−	1.56997i	0.228764	−	0.0612970i
$657$	−2.82435	−	10.5406i	−0.110189	−	0.411229i
$658$	−0.440938	−	1.06669i	−0.0171895	−	0.0415837i
$659$	14.6210	−	25.3243i	0.569554	−	0.986496i	−0.427056	−	0.904225i	$-0.640449\pi$
$659$	14.6210	−	25.3243i	0.569554	−	0.986496i	0.996610	−	0.0822711i	$-0.0262173\pi$
$660$	1.42555	−	0.823040i	0.0554894	−	0.0320368i
$661$	−21.1225	−	5.65976i	−0.821570	−	0.220139i	−0.176537	−	0.984294i	$-0.556490\pi$
$661$	−21.1225	−	5.65976i	−0.821570	−	0.220139i	−0.645033	+	0.764155i	$0.723156\pi$
$662$		−	14.6153i		−	0.568038i
$663$	8.60545	+	9.22769i	0.334208	+	0.358374i
$664$		−	45.0073i		−	1.74662i
$665$	7.86105	−	10.2295i	0.304838	−	0.396682i
$666$	0.337334	+	0.584279i	0.0130714	+	0.0226403i
$667$	−44.4713	−	25.6755i	−1.72193	−	0.994159i
$668$	6.09168	+	6.09168i	0.235694	+	0.235694i
$669$	5.92307	+	22.1052i	0.228999	+	0.854637i
$670$	−1.66054	−	6.19721i	−0.0641521	−	0.239419i
$671$	−17.4302	+	17.4302i	−0.672886	+	0.672886i
$672$	7.53022	−	5.76954i	0.290484	−	0.222565i
$673$	−6.52213	+	3.76555i	−0.251409	+	0.145151i	−0.620409	−	0.784278i	$-0.713034\pi$
$673$	−6.52213	+	3.76555i	−0.251409	+	0.145151i	0.369000	+	0.929429i	$0.379700\pi$
$674$	−3.83258	+	14.3034i	−0.147625	+	0.550945i
$675$	4.39645			0.169219
$676$	−4.83555	+	7.16986i	−0.185983	+	0.275764i
$677$			30.7509i			1.18185i	0.806726	+	0.590926i	$0.201237\pi$
$677$			30.7509i			1.18185i	−0.806726	+	0.590926i	$0.798763\pi$
$678$	0.750245	−	2.79995i	0.0288130	−	0.107532i
$679$	−0.250514	−	1.91347i	−0.00961386	−	0.0734323i
$680$	7.24989	+	4.18573i	0.278021	+	0.160515i
$681$	−11.0603	+	11.0603i	−0.423833	+	0.423833i
$682$	4.46380	−	1.19607i	0.170928	−	0.0458000i
$683$	14.8258	−	3.97256i	0.567293	−	0.152006i	0.0362380	−	0.999343i	$-0.488463\pi$
$683$	14.8258	−	3.97256i	0.567293	−	0.152006i	0.531055	+	0.847338i	$0.321796\pi$
$684$	2.95245	−	2.95245i	0.112890	−	0.112890i
$685$	−4.23646	−	2.44592i	−0.161867	−	0.0934538i
$686$	13.0621	−	16.9471i	0.498714	−	0.647044i
$687$	1.32198	−	4.93371i	0.0504368	−	0.188233i
$688$		−	16.9956i		−	0.647951i
$689$	30.5942	−	28.5311i	1.16555	−	1.08695i
$690$	5.06871			0.192962
$691$	−12.7049	+	47.4152i	−0.483316	+	1.80376i	0.104212	+	0.994555i	$0.466768\pi$
$691$	−12.7049	+	47.4152i	−0.483316	+	1.80376i	−0.587528	+	0.809204i	$0.699899\pi$
$692$	0.574509	−	0.331693i	0.0218396	−	0.0126091i
$693$	6.68917	−	5.12514i	0.254100	−	0.194688i
$694$	15.1847	−	15.1847i	0.576404	−	0.576404i
$695$	−3.85980	−	14.4050i	−0.146411	−	0.546412i
$696$	−7.24678	−	27.0453i	−0.274688	−	1.02515i
$697$	−6.74013	−	6.74013i	−0.255301	−	0.255301i
$698$	−4.79214	−	2.76674i	−0.181385	−	0.104723i
$699$	1.59328	+	2.75964i	0.0602633	+	0.104379i
$700$	6.13557	+	4.71500i	0.231903	+	0.178210i
$701$		−	40.9218i		−	1.54559i	−0.634653	−	0.772797i	$-0.718857\pi$
$701$		−	40.9218i		−	1.54559i	0.634653	−	0.772797i	$-0.281143\pi$
$702$	1.95572	+	3.67792i	0.0738138	+	0.138814i
$703$			3.66529i			0.138239i
$704$	−26.4470	−	7.08646i	−0.996760	−	0.267081i
$705$	−0.254056	+	0.146679i	−0.00956829	+	0.00552425i
$706$	7.13933	−	12.3657i	0.268692	−	0.465389i
$707$	27.9385	−	11.5490i	1.05073	−	0.434344i
$708$	−0.422507	−	1.57682i	−0.0158788	−	0.0592604i
$709$	−20.0521	+	5.37294i	−0.753071	+	0.201785i	−0.614880	−	0.788621i	$-0.710796\pi$
$709$	−20.0521	+	5.37294i	−0.753071	+	0.201785i	−0.138191	+	0.990406i	$0.544129\pi$
$710$	6.15685	−	6.15685i	0.231062	−	0.231062i
$711$	−5.40942	+	9.36939i	−0.202869	+	0.351379i
$712$	11.1986	+	19.3966i	0.419687	+	0.726919i
$713$	−6.85053	−	1.83559i	−0.256554	−	0.0687435i
$714$	9.87967	+	4.10061i	0.369737	+	0.153462i
$715$	−2.60820	+	8.53191i	−0.0975413	+	0.319075i
$716$	3.75090			0.140178
$717$	0.592662	−	2.21184i	0.0221333	−	0.0826028i
$718$	−3.43224	−	5.94482i	−0.128090	−	0.221859i
$719$	−6.50138	+	11.2607i	−0.242461	+	0.419954i	−0.961415	−	0.275103i	$-0.911288\pi$
$719$	−6.50138	+	11.2607i	−0.242461	+	0.419954i	0.718954	+	0.695058i	$0.244621\pi$
$720$	1.22337	+	1.22337i	0.0455925	+	0.0455925i
$721$	−6.70734	+	50.6659i	−0.249794	+	1.88690i
$722$	−22.7598	+	6.09847i	−0.847033	+	0.226962i
$723$	−4.48718	−	4.48718i	−0.166880	−	0.166880i
$724$	−12.3918	−	7.15442i	−0.460539	−	0.265892i
$725$	34.6213	−	19.9886i	1.28580	−	0.742359i
$726$	0.954610	+	0.255787i	0.0354289	+	0.00949315i
$727$	−9.09604			−0.337353			−0.168677	−	0.985671i	$-0.553949\pi$
$727$	−9.09604			−0.337353			−0.168677	+	0.985671i	$0.553949\pi$
$728$	−4.86806	+	28.9675i	−0.180422	+	1.07361i
$729$	−1.00000			−0.0370370
$730$	9.46076	+	2.53500i	0.350159	+	0.0938247i
$731$	−23.1289	+	13.3535i	−0.855453	+	0.493896i
$732$	4.45870	+	2.57423i	0.164798	+	0.0951463i
$733$	−24.5299	−	24.5299i	−0.906033	−	0.906033i	0.0899161	−	0.995949i	$-0.471340\pi$
$733$	−24.5299	−	24.5299i	−0.906033	−	0.906033i	−0.995949	+	0.0899161i	$0.971340\pi$
$734$	−6.51649	+	1.74609i	−0.240528	+	0.0644493i
$735$	−4.70571	−	2.72587i	−0.173573	−	0.100545i
$736$	14.3178	+	14.3178i	0.527760	+	0.527760i
$737$	11.3836	−	19.7170i	0.419321	−	0.726285i
$738$	−1.57344	−	2.72528i	−0.0579191	−	0.100319i
$739$	−12.5301	+	46.7628i	−0.460926	+	1.72020i	0.209130	+	0.977888i	$0.432937\pi$
$739$	−12.5301	+	46.7628i	−0.460926	+	1.72020i	−0.670056	+	0.742311i	$0.733730\pi$
$740$	0.301802			0.0110945
$741$	−0.789153	+	22.6166i	−0.0289903	+	0.830843i
$742$	13.5955	−	32.7558i	0.499106	−	1.20250i
$743$	−11.2679	−	3.01923i	−0.413379	−	0.110765i	0.0461346	−	0.998935i	$-0.485310\pi$
$743$	−11.2679	−	3.01923i	−0.413379	−	0.110765i	−0.459514	+	0.888171i	$0.651976\pi$
$744$	−1.93353	−	3.34897i	−0.0708865	−	0.122779i
$745$	−4.48879	+	7.77482i	−0.164457	+	0.284847i
$746$	8.46019	−	8.46019i	0.309749	−	0.309749i
$747$	−14.1185	+	3.78305i	−0.516570	+	0.138414i
$748$	1.91909	+	7.16214i	0.0701689	+	0.261874i
$749$	−22.4505	+	9.28039i	−0.820322	+	0.339098i
$750$	−4.21690	+	7.30388i	−0.153979	+	0.266700i
$751$	−12.9544	+	7.47922i	−0.472712	+	0.272921i	−0.717374	−	0.696688i	$-0.754656\pi$
$751$	−12.9544	+	7.47922i	−0.472712	+	0.272921i	0.244662	+	0.969608i	$0.421323\pi$
$752$	0.812272	+	0.217648i	0.0296205	+	0.00793679i
$753$		−	21.4611i		−	0.782088i
$754$	32.1227	+	20.0713i	1.16984	+	0.730952i
$755$		−	9.78458i		−	0.356097i
$756$	−1.39557	−	1.07246i	−0.0507565	−	0.0390048i
$757$	13.2377	+	22.9284i	0.481134	+	0.833348i	0.999766	−	0.0216496i	$-0.00689182\pi$
$757$	13.2377	+	22.9284i	0.481134	+	0.833348i	−0.518632	+	0.854998i	$0.673558\pi$
$758$	−7.01097	−	4.04778i	−0.254650	−	0.147022i
$759$	12.7186	+	12.7186i	0.461657	+	0.461657i
$760$	3.88608	+	14.5031i	0.140963	+	0.526081i
$761$	−10.6129	−	39.6079i	−0.384718	−	1.43579i	−0.838611	−	0.544731i	$-0.816632\pi$
$761$	−10.6129	−	39.6079i	−0.384718	−	1.43579i	0.453893	−	0.891056i	$-0.350035\pi$
$762$	−13.7957	+	13.7957i	−0.499767	+	0.499767i
$763$	−4.07719	−	5.32141i	−0.147604	−	0.192648i
$764$	5.06055	−	2.92171i	0.183084	−	0.105704i
$765$	0.703654	−	2.62607i	0.0254407	−	0.0949458i
$766$	8.54114			0.308604
$767$	7.50344	+	4.68838i	0.270934	+	0.169288i
$768$			14.0035i			0.505307i
$769$	0.837092	−	3.12407i	0.0301863	−	0.112657i	−0.949189	−	0.314707i	$-0.898094\pi$
$769$	0.837092	−	3.12407i	0.0301863	−	0.112657i	0.979375	+	0.202050i	$0.0647604\pi$
$770$	0.981851	+	7.49955i	0.0353834	+	0.270265i
$771$	−24.5801	−	14.1914i	−0.885232	−	0.511089i
$772$	−0.453085	+	0.453085i	−0.0163069	+	0.0163069i
$773$	−20.3857	+	5.46232i	−0.733221	+	0.196466i	−0.606063	−	0.795417i	$-0.707252\pi$
$773$	−20.3857	+	5.46232i	−0.733221	+	0.196466i	−0.127158	+	0.991882i	$0.540585\pi$
$774$	−8.51657	+	2.28201i	−0.306122	+	0.0820251i
$775$	3.90417	−	3.90417i	0.140242	−	0.140242i
$776$	1.94506	+	1.12298i	0.0698234	+	0.0403126i
$777$	1.53196	−	0.200566i	0.0549586	−	0.00719525i
$778$	−3.05836	+	11.4140i	−0.109648	+	0.409211i
$779$		−	17.0962i		−	0.612533i
$780$	1.86227	+	0.0649793i	0.0666798	+	0.00232663i
$781$	30.8980			1.10562
$782$	−5.90937	+	22.0541i	−0.211319	+	0.788652i
$783$	−7.87483	+	4.54654i	−0.281424	+	0.162480i
$784$	4.01305	+	15.0635i	0.143323	+	0.537982i
$785$	3.01801	−	3.01801i	0.107718	−	0.107718i
$786$	2.74662	+	10.2505i	0.0979688	+	0.365625i
$787$	12.5317	+	46.7690i	0.446707	+	1.66713i	0.711389	+	0.702798i	$0.248066\pi$
$787$	12.5317	+	46.7690i	0.446707	+	1.66713i	−0.264682	+	0.964336i	$0.585267\pi$
$788$	8.10003	+	8.10003i	0.288552	+	0.288552i
$789$	−10.9770	−	6.33755i	−0.390790	−	0.225623i
$790$	−4.85523	−	8.40951i	−0.172741	−	0.299197i
$791$	−5.26358	−	4.04490i	−0.187151	−	0.143820i
$792$			9.80742i			0.348492i
$793$	−27.1890	+	6.27789i	−0.965511	+	0.222934i
$794$			32.5970i			1.15682i
$795$	−8.70667	−	2.33295i	−0.308794	−	0.0827411i
$796$	−1.29689	+	0.748760i	−0.0459671	+	0.0265391i
$797$	−22.9487	+	39.7483i	−0.812884	+	1.40796i	0.0979535	+	0.995191i	$0.468770\pi$
$797$	−22.9487	+	39.7483i	−0.812884	+	1.40796i	−0.910837	+	0.412765i	$0.864563\pi$
$798$	7.32920	+	17.7303i	0.259451	+	0.627646i
$799$	−0.342013	−	1.27641i	−0.0120995	−	0.0451561i
$800$	−15.2264	+	4.07991i	−0.538336	+	0.144247i
$801$	5.14331	−	5.14331i	0.181730	−	0.181730i
$802$	4.07838	−	7.06395i	0.144012	−	0.249437i
$803$	17.3784	+	30.1003i	0.613271	+	1.06222i
$804$	−4.59318	−	1.23074i	−0.161989	−	0.0434048i
$805$	4.44976	−	10.7209i	0.156834	−	0.377861i
$806$	5.00283	+	1.52937i	0.176217	+	0.0538696i
$807$	6.49817			0.228746
$808$	−9.10633	+	33.9853i	−0.320359	+	1.19560i
$809$	22.7833	+	39.4619i	0.801019	+	1.38740i	0.918946	+	0.394383i	$0.129042\pi$
$809$	22.7833	+	39.4619i	0.801019	+	1.38740i	−0.117928	+	0.993022i	$0.537625\pi$
$810$	0.448776	−	0.777302i	0.0157684	−	0.0273116i
$811$	15.7365	+	15.7365i	0.552584	+	0.552584i	0.927186	−	0.374602i	$-0.122221\pi$
$811$	15.7365	+	15.7365i	0.552584	+	0.552584i	−0.374602	+	0.927186i	$0.622221\pi$
$812$	−15.8659	−	2.10038i	−0.556783	−	0.0737090i
$813$	−6.14616	+	1.64686i	−0.215555	+	0.0577579i
$814$	−1.51947	−	1.51947i	−0.0532573	−	0.0532573i
$815$	−7.17186	−	4.14067i	−0.251219	−	0.145041i
$816$	−6.74921	+	3.89666i	−0.236270	+	0.136410i
$817$	−46.2683	−	12.3975i	−1.61872	−	0.433735i
$818$	36.3605			1.27132
$819$	9.49610	−	0.907752i	0.331821	−	0.0317194i
$820$	−1.40771			−0.0491592
$821$	−51.3616	−	13.7623i	−1.79253	−	0.480307i	−0.799759	−	0.600322i	$-0.795039\pi$
$821$	−51.3616	−	13.7623i	−1.79253	−	0.480307i	−0.992772	+	0.120014i	$0.961706\pi$
$822$	6.30010	−	3.63736i	0.219741	−	0.126868i
$823$	0.0980900	+	0.0566323i	0.00341920	+	0.00197408i	0.501709	−	0.865037i	$-0.332705\pi$
$823$	0.0980900	+	0.0566323i	0.00341920	+	0.00197408i	−0.498289	+	0.867011i	$0.666038\pi$
$824$	−42.0593	−	42.0593i	−1.46521	−	1.46521i
$825$	−13.5258	+	3.62423i	−0.470908	+	0.126179i
$826$	7.43600	+	0.984405i	0.258731	+	0.0342518i
$827$	5.18917	+	5.18917i	0.180445	+	0.180445i	0.791550	−	0.611105i	$-0.209275\pi$
$827$	5.18917	+	5.18917i	0.180445	+	0.180445i	−0.611105	+	0.791550i	$0.709275\pi$
$828$	1.87839	−	3.25346i	0.0652784	−	0.113066i
$829$	2.19576	+	3.80317i	0.0762620	+	0.132090i	0.901634	−	0.432499i	$-0.142368\pi$
$829$	2.19576	+	3.80317i	0.0762620	+	0.132090i	−0.825372	+	0.564589i	$0.809035\pi$
$830$	3.39548	−	12.6721i	0.117859	−	0.439855i
$831$	−18.0852			−0.627369
$832$	−21.1390	−	22.6675i	−0.732863	−	0.785855i
$833$	17.3465	−	17.2967i	0.601021	−	0.599295i
$834$	21.4219	+	5.73997i	0.741779	+	0.198759i
$835$	5.03040	+	8.71291i	0.174084	+	0.301523i
$836$	−6.64943	+	11.5171i	−0.229975	+	0.398329i
$837$	−0.888029	+	0.888029i	−0.0306948	+	0.0306948i
$838$	26.3114	−	7.05011i	0.908911	−	0.243542i
$839$	−0.0267890	−	0.0999778i	−0.000924858	−	0.00345162i	0.965462	−	0.260544i	$-0.0839021\pi$
$839$	−0.0267890	−	0.0999778i	−0.000924858	−	0.00345162i	−0.966387	+	0.257093i	$0.917235\pi$
$840$	5.84910	−	2.41785i	0.201813	−	0.0834238i
$841$	−26.8420	+	46.4917i	−0.925587	+	1.60316i
$842$	−6.55517	+	3.78463i	−0.225906	+	0.130427i
$843$	8.79089	+	2.35551i	0.302774	+	0.0811282i
$844$			13.7769i			0.474220i
$845$	−7.62183	+	6.62631i	−0.262199	+	0.227952i
$846$		−	0.436257i		−	0.0149988i
$847$	1.37906	−	1.79455i	0.0473850	−	0.0616616i
$848$	12.9193	+	22.3768i	0.443650	+	0.768424i
$849$	12.7083	+	7.33715i	0.436148	+	0.251810i
$850$	−12.5688	−	12.5688i	−0.431107	−	0.431107i
$851$	0.853536	+	3.18544i	0.0292588	+	0.109195i
$852$	−1.67027	−	6.23354i	−0.0572225	−	0.213557i
$853$	−30.7045	+	30.7045i	−1.05130	+	1.05130i	−0.0526924	+	0.998611i	$0.516780\pi$
$853$	−30.7045	+	30.7045i	−1.05130	+	1.05130i	−0.998611	+	0.0526924i	$0.983220\pi$
$854$	−18.7784	+	14.3877i	−0.642583	+	0.492338i
$855$	4.22288	−	2.43808i	0.144419	−	0.0833805i
$856$	7.31756	−	27.3095i	0.250109	−	0.933419i
$857$	−46.5367			−1.58966			−0.794831	−	0.606831i	$-0.792441\pi$
$857$	−46.5367			−1.58966			−0.794831	+	0.606831i	$0.792441\pi$
$858$	−9.04872	−	9.70302i	−0.308918	−	0.331255i
$859$			34.8981i			1.19071i	0.803464	+	0.595354i	$0.202988\pi$
$859$			34.8981i			1.19071i	−0.803464	+	0.595354i	$0.797012\pi$
$860$	−1.02082	+	3.80975i	−0.0348097	+	0.129912i
$861$	−7.14557	+	0.935507i	−0.243520	+	0.0318820i
$862$	−28.8046	−	16.6303i	−0.981088	−	0.566431i
$863$	33.6057	−	33.6057i	1.14395	−	1.14395i	0.156232	−	0.987720i	$-0.450065\pi$
$863$	33.6057	−	33.6057i	1.14395	−	1.14395i	0.987720	−	0.156232i	$-0.0499348\pi$
$864$	3.46335	−	0.928002i	0.117826	−	0.0315713i
$865$	0.748326	−	0.200513i	0.0254438	−	0.00681766i
$866$	−3.13806	+	3.13806i	−0.106636	+	0.106636i
$867$	−4.11668	−	2.37677i	−0.139810	−	0.0807193i
$868$	−2.19168	+	0.286938i	−0.0743905	+	0.00973931i
$869$	8.91854	−	33.2844i	0.302541	−	1.12910i
$870$		−	8.16150i		−	0.276701i
$871$	22.7559	−	12.1003i	0.771053	−	0.410004i
$872$	7.80207			0.264212
$873$	0.188782	−	0.704543i	0.00638929	−	0.0238452i
$874$	−35.4643	+	20.4753i	−1.19960	+	0.692587i
$875$	11.7465	+	15.3312i	0.397106	+	0.518289i
$876$	5.13316	−	5.13316i	0.173433	−	0.173433i
$877$	0.133090	+	0.496699i	0.00449413	+	0.0167723i	0.968136	−	0.250423i	$-0.0805697\pi$
$877$	0.133090	+	0.496699i	0.00449413	+	0.0167723i	−0.963642	+	0.267195i	$0.913903\pi$
$878$	4.36033	+	16.2730i	0.147154	+	0.549186i
$879$	4.63800	+	4.63800i	0.156436	+	0.156436i
$880$	−4.77224	−	2.75525i	−0.160872	−	0.0928796i
$881$	−18.3777	−	31.8310i	−0.619159	−	1.07242i	−0.989639	−	0.143575i	$-0.954140\pi$
$881$	−18.3777	−	31.8310i	−0.619159	−	1.07242i	0.370480	−	0.928840i	$-0.379193\pi$
$882$	7.00956	−	4.03355i	0.236024	−	0.135817i
$883$			25.7950i			0.868071i	0.900896	+	0.434036i	$0.142911\pi$
$883$			25.7950i			0.868071i	−0.900896	+	0.434036i	$0.857089\pi$
$884$	−2.45386	+	8.02701i	−0.0825321	+	0.269978i
$885$		−	1.90642i		−	0.0640835i
$886$	−35.9403	−	9.63019i	−1.20744	−	0.323532i
$887$	32.5539	−	18.7950i	1.09305	−	0.631074i	0.158665	−	0.987332i	$-0.449281\pi$
$887$	32.5539	−	18.7950i	1.09305	−	0.631074i	0.934388	+	0.356258i	$0.115948\pi$
$888$	−0.899074	+	1.55724i	−0.0301710	+	0.0522576i
$889$	17.0684	+	41.2906i	0.572455	+	1.38484i
$890$	1.68971	+	6.30610i	0.0566393	+	0.211381i
$891$	3.07653	−	0.824353i	0.103068	−	0.0276169i
$892$	−10.7650	+	10.7650i	−0.360438	+	0.360438i
$893$	1.18503	−	2.05254i	0.0396557	−	0.0686856i
$894$	−6.67535	−	11.5620i	−0.223257	−	0.386693i
$895$	4.23117	+	1.13374i	0.141432	+	0.0378967i
$896$	−6.74571	−	2.79985i	−0.225358	−	0.0935363i
$897$	4.58090	+	19.8395i	0.152952	+	0.662422i
$898$	23.1496			0.772512
$899$	−2.95562	+	11.0305i	−0.0985756	+	0.367889i
$900$	1.46234	+	2.53285i	0.0487447	+	0.0844283i
$901$	20.3014	−	35.1631i	0.676338	−	1.17145i
$902$	7.08732	+	7.08732i	0.235982	+	0.235982i
$903$	−2.64990	+	20.0168i	−0.0881833	+	0.666119i
$904$	7.46254	−	1.99958i	0.248200	−	0.0665051i
$905$	−11.8160	−	11.8160i	−0.392777	−	0.392777i
$906$	12.6014	+	7.27540i	0.418652	+	0.241709i
$907$	−25.7384	+	14.8601i	−0.854631	+	0.493421i	−0.862211	−	0.506550i	$-0.830921\pi$
$907$	−25.7384	+	14.8601i	−0.854631	+	0.493421i	0.00757996	+	0.999971i	$0.497587\pi$
$908$	−10.0509	−	2.69312i	−0.333550	−	0.0893745i
$909$	11.4264			0.378989
$910$	−3.55602	+	7.78872i	−0.117881	+	0.258194i
$911$	−35.4837			−1.17563			−0.587814	−	0.808996i	$-0.700011\pi$
$911$	−35.4837			−1.17563			−0.587814	+	0.808996i	$0.700011\pi$
$912$	−13.5015	−	3.61771i	−0.447079	−	0.119794i
$913$	40.3175	−	23.2773i	1.33431	−	0.770366i
$914$	−15.0259	−	8.67519i	−0.497012	−	0.286950i
$915$	4.25151	+	4.25151i	0.140551	+	0.140551i
$916$	3.28209	−	0.879433i	0.108443	−	0.0290573i
$917$	24.0922	+	3.18942i	0.795596	+	0.105324i
$918$	2.85886	+	2.85886i	0.0943563	+	0.0943563i
$919$	0.276560	−	0.479016i	0.00912288	−	0.0158013i	−0.861428	−	0.507880i	$-0.830429\pi$
$919$	0.276560	−	0.479016i	0.00912288	−	0.0158013i	0.870551	+	0.492079i	$0.163763\pi$
$920$	6.75466	+	11.6994i	0.222694	+	0.385718i
$921$	8.62972	−	32.2066i	0.284359	−	1.06124i
$922$	−35.8242			−1.17981
$923$	29.6629	+	18.5343i	0.976367	+	0.610063i
$924$	5.17760	+	2.14899i	0.170331	+	0.0706967i
$925$	−2.47990	−	0.664486i	−0.0815384	−	0.0218482i
$926$	−2.95374	−	5.11603i	−0.0970659	−	0.168123i
$927$	−9.65849	+	16.7290i	−0.317226	+	0.549452i
$928$	23.0541	−	23.0541i	0.756788	−	0.756788i
$929$	0.202032	−	0.0541344i	0.00662846	−	0.00177609i	−0.255503	−	0.966808i	$-0.582241\pi$
$929$	0.202032	−	0.0541344i	0.00662846	−	0.00177609i	0.262132	+	0.965032i	$0.415574\pi$
$930$	−0.291741	−	1.08879i	−0.00956657	−	0.0357029i
$931$	43.9357	+	0.0631567i	1.43994	+	0.00206988i
$932$	−1.05991	+	1.83582i	−0.0347185	+	0.0601341i
$933$	−2.51649	+	1.45290i	−0.0823861	+	0.0475656i
$934$	−19.7273	−	5.28590i	−0.645496	−	0.172960i
$935$			8.65924i			0.283187i
$936$	−5.88301	+	9.41538i	−0.192292	+	0.307751i
$937$			7.20471i			0.235368i	0.993051	+	0.117684i	$0.0375470\pi$
$937$			7.20471i			0.235368i	−0.993051	+	0.117684i	$0.962453\pi$
$938$	13.3137	−	17.3249i	0.434707	−	0.565678i
$939$	−0.480313	−	0.831926i	−0.0156744	−	0.0271489i
$940$	−0.169007	−	0.0975764i	−0.00551241	−	0.00318259i
$941$	−27.6042	−	27.6042i	−0.899870	−	0.899870i	0.0955544	−	0.995424i	$-0.469538\pi$
$941$	−27.6042	−	27.6042i	−0.899870	−	0.899870i	−0.995424	+	0.0955544i	$0.969538\pi$
$942$	1.64277	+	6.13090i	0.0535244	+	0.199756i
$943$	−3.98118	−	14.8580i	−0.129645	−	0.483842i
$944$	−3.86423	+	3.86423i	−0.125770	+	0.125770i
$945$	−1.25010	−	1.63160i	−0.0406659	−	0.0530758i
$946$	24.3203	−	14.0413i	0.790721	−	0.456523i
$947$	10.3004	−	38.4417i	0.334719	−	1.24919i	−0.569455	−	0.822022i	$-0.692846\pi$
$947$	10.3004	−	38.4417i	0.334719	−	1.24919i	0.904174	−	0.427164i	$-0.140487\pi$
$948$	−7.19710			−0.233751
$949$	−1.37203	+	39.3215i	−0.0445380	+	1.27643i
$950$		−	31.8804i		−	1.03434i
$951$	8.68271	−	32.4043i	0.281556	−	1.05078i
$952$	3.70094	+	28.2684i	0.119948	+	0.916185i
$953$	32.2352	+	18.6110i	1.04420	+	0.602870i	0.921020	−	0.389514i	$-0.127357\pi$
$953$	32.2352	+	18.6110i	1.04420	+	0.602870i	0.123181	+	0.992384i	$0.460690\pi$
$954$	9.47846	−	9.47846i	0.306877	−	0.306877i
$955$	6.59162	−	1.76622i	0.213300	−	0.0571535i
$956$	1.47140	−	0.394261i	0.0475885	−	0.0127513i
$957$	20.4792	−	20.4792i	0.661998	−	0.661998i
$958$	19.8135	+	11.4393i	0.640145	+	0.369588i
$959$	−2.16264	−	16.5186i	−0.0698352	−	0.533414i
$960$	−1.72850	+	6.45086i	−0.0557872	+	0.208200i
$961$		−	29.4228i		−	0.949123i
$962$	−0.547271	−	2.37019i	−0.0176447	−	0.0764179i
$963$	−9.18189			−0.295882
$964$	1.09260	−	4.07764i	0.0351903	−	0.131332i
$965$	−0.648047	+	0.374150i	−0.0208614	+	0.0120443i
$966$	10.4985	+	13.7023i	0.337785	+	0.440866i
$967$	3.64583	−	3.64583i	0.117242	−	0.117242i	−0.646052	−	0.763294i	$-0.723581\pi$
$967$	3.64583	−	3.64583i	0.117242	−	0.117242i	0.763294	+	0.646052i	$0.223581\pi$
$968$	0.681733	+	2.54426i	0.0219117	+	0.0817757i
$969$	5.68489	+	21.2163i	0.182625	+	0.681566i
$970$	0.462922	+	0.462922i	0.0148635	+	0.0148635i
$971$	25.7260	+	14.8529i	0.825587	+	0.476653i	0.852339	−	0.522989i	$-0.175183\pi$
$971$	25.7260	+	14.8529i	0.825587	+	0.476653i	−0.0267525	+	0.999642i	$0.508517\pi$
$972$	−0.332619	−	0.576113i	−0.0106688	−	0.0184788i
$973$	30.9467	−	40.2705i	0.992105	−	1.29101i
$974$		−	45.2142i		−	1.44876i
$975$	−15.1591	−	4.63414i	−0.485480	−	0.148411i
$976$		−	17.2353i		−	0.551687i
$977$	44.1801	+	11.8380i	1.41345	+	0.378732i	0.883154	−	0.469083i	$-0.155415\pi$
$977$	44.1801	+	11.8380i	1.41345	+	0.378732i	0.530293	+	0.847815i	$0.322082\pi$
$978$	10.6654	−	6.15766i	0.341041	−	0.196900i
$979$	−11.5836	+	20.0634i	−0.370214	+	0.641230i
$980$	0.00520036	−	3.61769i	0.000166119	−	0.115563i
$981$	−0.655795	−	2.44746i	−0.0209379	−	0.0781414i
$982$	−20.7096	+	5.54912i	−0.660870	+	0.177080i
$983$	36.4493	−	36.4493i	1.16255	−	1.16255i	0.178637	−	0.983915i	$-0.442831\pi$
$983$	36.4493	−	36.4493i	1.16255	−	1.16255i	0.983915	−	0.178637i	$-0.0571687\pi$
$984$	4.19359	−	7.26351i	0.133687	−	0.231552i
$985$	6.68886	+	11.5854i	0.213125	+	0.369143i
$986$	35.5109	+	9.51512i	1.13090	+	0.303023i
$987$	−0.922732	−	0.382985i	−0.0293709	−	0.0121906i
$988$	−13.2922	+	7.06807i	−0.422882	+	0.224865i
$989$	−43.0980			−1.37044
$990$	−0.739899	+	2.76134i	−0.0235155	+	0.0877612i
$991$	−1.36323	−	2.36118i	−0.0433043	−	0.0750052i	0.843561	−	0.537034i	$-0.180455\pi$
$991$	−1.36323	−	2.36118i	−0.0433043	−	0.0750052i	−0.886865	+	0.462028i	$0.847122\pi$
$992$	2.25146	−	3.89965i	0.0714840	−	0.123814i
$993$	−8.94519	−	8.94519i	−0.283867	−	0.283867i
$994$	29.3963	+	3.89159i	0.932393	+	0.123434i
$995$	−1.68926	+	0.452636i	−0.0535532	+	0.0143495i
$996$	−6.87555	−	6.87555i	−0.217860	−	0.217860i
$997$	9.41930	+	5.43824i	0.298312	+	0.172231i	0.641684	−	0.766969i	$-0.278236\pi$
$997$	9.41930	+	5.43824i	0.298312	+	0.172231i	−0.343372	+	0.939199i	$0.611569\pi$
$998$	−5.01414	+	2.89492i	−0.158720	+	0.0916370i
$999$	0.564068	+	0.151142i	0.0178463	+	0.00478191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.c.223.4	yes	32
3.2	odd	2		819.2.fm.f.496.5		32
7.6	odd	2		273.2.by.d.223.4	yes	32
13.7	odd	12		273.2.by.d.202.4	yes	32
21.20	even	2		819.2.fm.e.496.5		32
39.20	even	12		819.2.fm.e.748.5		32
91.20	even	12	inner	273.2.by.c.202.4	✓	32
273.20	odd	12		819.2.fm.f.748.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.4	✓	32	91.20	even	12	inner
273.2.by.c.223.4	yes	32	1.1	even	1	trivial
273.2.by.d.202.4	yes	32	13.7	odd	12
273.2.by.d.223.4	yes	32	7.6	odd	2
819.2.fm.e.496.5		32	21.20	even	2
819.2.fm.e.748.5		32	39.20	even	12
819.2.fm.f.496.5		32	3.2	odd	2
819.2.fm.f.748.5		32	273.20	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11595 - 0.299019i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.11595 - 0.299019i) q^{6} +(0.347225 - 2.62287i) q^{7} +(2.17732 + 2.17732i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.11595 - 0.299019i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.576113 - 0.332619i) q^{4} +(-0.549341 - 0.549341i) q^{5} +(1.11595 - 0.299019i) q^{6} +(0.347225 - 2.62287i) q^{7} +(2.17732 + 2.17732i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.448776 + 0.777302i) q^{10} +(-0.824353 + 3.07653i) q^{11} +0.665238 q^{12} +(-2.63686 + 2.45905i) q^{13} +(-1.17177 + 2.82317i) q^{14} +(0.750414 + 0.201073i) q^{15} +(-1.11349 - 1.92862i) q^{16} +(-1.74975 + 3.03065i) q^{17} +(-0.816934 + 0.816934i) q^{18} +(-6.06267 + 1.62449i) q^{19} +(0.133761 + 0.499204i) q^{20} +(1.01073 + 2.44508i) q^{21} +(1.83988 - 3.18676i) q^{22} +(-4.89067 + 2.82363i) q^{23} +(-2.97428 - 0.796956i) q^{24} -4.39645i q^{25} +(3.67792 - 1.95572i) q^{26} +1.00000i q^{27} +(-1.07246 + 1.39557i) q^{28} +(4.54654 + 7.87483i) q^{29} +(-0.777302 - 0.448776i) q^{30} +(0.888029 + 0.888029i) q^{31} +(-0.928002 - 3.46335i) q^{32} +(-0.824353 - 3.07653i) q^{33} +(2.85886 - 2.85886i) q^{34} +(-1.63160 + 1.25010i) q^{35} +(-0.576113 + 0.332619i) q^{36} +(0.151142 - 0.564068i) q^{37} +7.25141 q^{38} +(1.05406 - 3.44804i) q^{39} -2.39219i q^{40} +(-0.704976 + 2.63101i) q^{41} +(-0.396799 - 3.03082i) q^{42} +(6.60921 + 3.81583i) q^{43} +(1.49823 - 1.49823i) q^{44} +(-0.750414 + 0.201073i) q^{45} +(6.30208 - 1.68864i) q^{46} +(-0.267009 + 0.267009i) q^{47} +(1.92862 + 1.11349i) q^{48} +(-6.75887 - 1.82145i) q^{49} +(-1.31462 + 4.90623i) q^{50} -3.49950i q^{51} +(2.33706 - 0.539622i) q^{52} -11.6025 q^{53} +(0.299019 - 1.11595i) q^{54} +(2.14292 - 1.23721i) q^{55} +(6.46685 - 4.95481i) q^{56} +(4.43818 - 4.43818i) q^{57} +(-2.71900 - 10.1474i) q^{58} +(-0.635122 - 2.37031i) q^{59} +(-0.365443 - 0.365443i) q^{60} +(6.70242 + 3.86964i) q^{61} +(-0.725461 - 1.25654i) q^{62} +(-2.09786 - 1.61214i) q^{63} +8.59639i q^{64} +(2.79940 + 0.0976783i) q^{65} +3.67976i q^{66} +(-6.90457 - 1.85007i) q^{67} +(2.01610 - 1.16400i) q^{68} +(2.82363 - 4.89067i) q^{69} +(2.19459 - 0.907181i) q^{70} +(-2.51079 - 9.37039i) q^{71} +(2.97428 - 0.796956i) q^{72} +(7.71628 - 7.71628i) q^{73} +(-0.337334 + 0.584279i) q^{74} +(2.19822 + 3.80744i) q^{75} +(4.03312 + 1.08067i) q^{76} +(7.78309 + 3.23042i) q^{77} +(-2.20731 + 3.53266i) q^{78} -10.8188 q^{79} +(-0.447786 + 1.67116i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.57344 - 2.72528i) q^{82} +(-10.3355 - 10.3355i) q^{83} +(0.230987 - 1.74483i) q^{84} +(2.62607 - 0.703654i) q^{85} +(-6.23456 - 6.23456i) q^{86} +(-7.87483 - 4.54654i) q^{87} +(-8.49348 + 4.90371i) q^{88} +(7.02589 + 1.88258i) q^{89} +0.897552 q^{90} +(5.53419 + 7.76999i) q^{91} +3.75677 q^{92} +(-1.21307 - 0.325041i) q^{93} +(0.377810 - 0.218129i) q^{94} +(4.22288 + 2.43808i) q^{95} +(2.53535 + 2.53535i) q^{96} +(0.704543 - 0.188782i) q^{97} +(6.99793 + 4.05368i) q^{98} +(2.25217 + 2.25217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Introduction

L-functions

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