LMFDB - Embedded newform 961.2.g.o.448.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-2,-4,-8,-24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			448.1
Root			$-0.147826 + 1.40647i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.o.547.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.746033 + 2.29605i) q^{2} +(-1.61542 + 1.79411i) q^{3} +(-3.09726 - 2.25029i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.91421 - 5.04757i) q^{6} +(-0.252354 + 2.40099i) q^{7} +(3.57117 - 2.59461i) q^{8} +(-0.295651 - 2.81293i) q^{9} +(-1.61542 - 1.79411i) q^{10} +(-4.78939 + 2.13237i) q^{11} +(9.04067 - 1.92165i) q^{12} +(-1.78847 - 0.380151i) q^{13} +(-5.32453 - 2.37063i) q^{14} +(-0.746033 - 2.29605i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-0.156740 - 0.0697850i) q^{17} +(6.67921 + 1.41971i) q^{18} +(-1.55113 + 0.329704i) q^{19} +(3.49744 - 1.55716i) q^{20} +(-3.89998 - 4.33137i) q^{21} +(-1.32300 - 12.5875i) q^{22} +(3.23607 - 2.35114i) q^{23} +(-1.11394 + 10.5985i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.20711 - 3.82282i) q^{26} +(-0.335106 - 0.243469i) q^{27} +(6.18453 - 6.86862i) q^{28} +(-0.362036 + 1.11423i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(3.91118 - 12.0374i) q^{33} +(0.277163 - 0.307821i) q^{34} +(-1.95314 - 1.41904i) q^{35} +(-5.41421 + 9.37769i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(0.400180 - 3.80745i) q^{38} +(3.57117 - 2.59461i) q^{39} +(0.461411 + 4.39003i) q^{40} +(6.34689 + 7.04894i) q^{41} +(12.8546 - 5.72322i) q^{42} +(-8.70502 + 1.85031i) q^{43} +(19.6325 + 4.17301i) q^{44} +(2.58390 + 1.15042i) q^{45} +(2.98413 + 9.18421i) q^{46} +(-0.511996 - 1.57576i) q^{47} +(-6.61648 - 2.94585i) q^{48} +(1.14597 + 0.243584i) q^{49} +(-9.44583 + 2.00777i) q^{50} +(0.378403 - 0.168476i) q^{51} +(4.68391 + 5.20201i) q^{52} +(-0.0179342 - 0.170633i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.548005 - 5.21392i) q^{55} +(5.32843 + 9.22911i) q^{56} +(1.91421 - 3.31552i) q^{57} +(-2.28825 - 1.66251i) q^{58} +(-6.73886 + 7.48426i) q^{59} +(-2.85613 + 8.79027i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(-3.03715 + 9.34739i) q^{64} +(1.22346 - 1.35879i) q^{65} +(24.7206 + 17.9606i) q^{66} +(2.62132 - 4.54026i) q^{67} +(0.328427 + 0.568852i) q^{68} +(-1.00942 + 9.60395i) q^{69} +(4.71530 - 3.42586i) q^{70} +(1.47083 + 13.9940i) q^{71} +(-8.35428 - 9.27837i) q^{72} +(3.49744 - 1.55716i) q^{73} +(2.36146 - 0.501943i) q^{74} +(-9.44583 - 2.00777i) q^{75} +(5.54620 + 2.46933i) q^{76} +(-3.91118 - 12.0374i) q^{77} +(3.29315 + 10.1353i) q^{78} +(-13.9248 - 6.19974i) q^{79} +(-2.93444 - 0.623735i) q^{80} +(9.27801 - 1.97210i) q^{81} +(-20.9197 + 9.31406i) q^{82} +(2.72408 + 3.02539i) q^{83} +(2.33242 + 22.1915i) q^{84} +(0.138805 - 0.100848i) q^{85} +(2.24582 - 21.3676i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-11.5711 + 20.0417i) q^{88} +(10.1008 + 7.33866i) q^{89} +(-4.56911 + 5.07451i) q^{90} +(1.36407 - 4.19817i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(0.490035 - 1.50817i) q^{95} +(-2.56172 + 2.84508i) q^{96} +(-8.76038 - 6.36479i) q^{97} +(-1.41421 + 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	−0.746033	+	2.29605i	−0.527525	+	1.62356i	0.231743	+	0.972777i	$0.425557\pi$
$2$	−0.746033	+	2.29605i	−0.527525	+	1.62356i	−0.759268	+	0.650778i	$0.774443\pi$
$3$	−1.61542	+	1.79411i	−0.932666	+	1.03583i	0.0666102	+	0.997779i	$0.478782\pi$
$3$	−1.61542	+	1.79411i	−0.932666	+	1.03583i	−0.999276	+	0.0380510i	$0.987885\pi$
$4$	−3.09726	−	2.25029i	−1.54863	−	1.12515i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−2.91421	−	5.04757i	−1.18972	−	2.06066i
$7$	−0.252354	+	2.40099i	−0.0953809	+	0.907488i	0.837290	+	0.546759i	$0.184139\pi$
$7$	−0.252354	+	2.40099i	−0.0953809	+	0.907488i	−0.932671	+	0.360729i	$0.882528\pi$
$8$	3.57117	−	2.59461i	1.26260	−	0.917333i
$9$	−0.295651	−	2.81293i	−0.0985504	−	0.937644i
$10$	−1.61542	−	1.79411i	−0.510842	−	0.567347i
$11$	−4.78939	+	2.13237i	−1.44406	+	0.642935i	−0.971213	−	0.238212i	$-0.923439\pi$
$11$	−4.78939	+	2.13237i	−1.44406	+	0.642935i	−0.472842	+	0.881147i	$0.656772\pi$
$12$	9.04067	−	1.92165i	2.60982	−	0.554733i
$13$	−1.78847	−	0.380151i	−0.496033	−	0.105435i	−0.0468992	−	0.998900i	$-0.514934\pi$
$13$	−1.78847	−	0.380151i	−0.496033	−	0.105435i	−0.449134	+	0.893465i	$0.648267\pi$
$14$	−5.32453	−	2.37063i	−1.42304	−	0.633579i
$15$	−0.746033	−	2.29605i	−0.192625	−	0.592838i
$16$	0.927051	+	2.85317i	0.231763	+	0.713292i
$17$	−0.156740	−	0.0697850i	−0.0380149	−	0.0169253i	0.387641	−	0.921810i	$-0.373290\pi$
$17$	−0.156740	−	0.0697850i	−0.0380149	−	0.0169253i	−0.425656	+	0.904885i	$0.639957\pi$
$18$	6.67921	+	1.41971i	1.57430	+	0.334629i
$19$	−1.55113	+	0.329704i	−0.355854	+	0.0756392i	−0.382370	−	0.924009i	$-0.624892\pi$
$19$	−1.55113	+	0.329704i	−0.355854	+	0.0756392i	0.0265158	+	0.999648i	$0.491559\pi$
$20$	3.49744	−	1.55716i	0.782052	−	0.348192i
$21$	−3.89998	−	4.33137i	−0.851045	−	0.945181i
$22$	−1.32300	−	12.5875i	−0.282065	−	2.68367i
$23$	3.23607	−	2.35114i	0.674767	−	0.490247i	−0.196851	−	0.980433i	$-0.563071\pi$
$23$	3.23607	−	2.35114i	0.674767	−	0.490247i	0.871617	+	0.490187i	$0.163071\pi$
$24$	−1.11394	+	10.5985i	−0.227383	+	2.16340i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.20711	−	3.82282i	0.432849	−	0.749717i
$27$	−0.335106	−	0.243469i	−0.0644911	−	0.0468556i
$28$	6.18453	−	6.86862i	1.16877	−	1.29805i
$29$	−0.362036	+	1.11423i	−0.0672284	+	0.206908i	−0.979027	−	0.203729i	$-0.934694\pi$
$29$	−0.362036	+	1.11423i	−0.0672284	+	0.206908i	0.911799	+	0.410637i	$0.134694\pi$
$30$	5.82843			1.06412
$31$		0			0
$31$		0			0
$32$	1.58579			0.280330
$33$	3.91118	−	12.0374i	0.680850	−	2.09544i
$34$	0.277163	−	0.307821i	0.0475331	−	0.0527908i
$35$	−1.95314	−	1.41904i	−0.330141	−	0.239861i
$36$	−5.41421	+	9.37769i	−0.902369	+	1.56295i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	0.400180	−	3.80745i	0.0649177	−	0.617651i
$39$	3.57117	−	2.59461i	0.571845	−	0.415470i
$40$	0.461411	+	4.39003i	0.0729555	+	0.694125i
$41$	6.34689	+	7.04894i	0.991218	+	1.10086i	0.994900	+	0.100866i	$0.0321613\pi$
$41$	6.34689	+	7.04894i	0.991218	+	1.10086i	−0.00368202	+	0.999993i	$0.501172\pi$
$42$	12.8546	−	5.72322i	1.98350	−	0.883112i
$43$	−8.70502	+	1.85031i	−1.32750	+	0.282169i	−0.816468	−	0.577390i	$-0.804071\pi$
$43$	−8.70502	+	1.85031i	−1.32750	+	0.282169i	−0.511035	+	0.859560i	$0.670738\pi$
$44$	19.6325	+	4.17301i	2.95971	+	0.629105i
$45$	2.58390	+	1.15042i	0.385185	+	0.171495i
$46$	2.98413	+	9.18421i	0.439986	+	1.35414i
$47$	−0.511996	−	1.57576i	−0.0746823	−	0.229849i	0.906746	−	0.421677i	$-0.138558\pi$
$47$	−0.511996	−	1.57576i	−0.0746823	−	0.229849i	−0.981428	+	0.191828i	$0.938558\pi$
$48$	−6.61648	−	2.94585i	−0.955007	−	0.425196i
$49$	1.14597	+	0.243584i	0.163710	+	0.0347977i
$50$	−9.44583	+	2.00777i	−1.33584	+	0.283942i
$51$	0.378403	−	0.168476i	0.0529870	−	0.0235913i
$52$	4.68391	+	5.20201i	0.649542	+	0.721390i
$53$	−0.0179342	−	0.170633i	−0.00246346	−	0.0234382i	0.993221	−	0.116240i	$-0.0370843\pi$
$53$	−0.0179342	−	0.170633i	−0.00246346	−	0.0234382i	−0.995685	+	0.0928021i	$0.970418\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	0.548005	−	5.21392i	0.0738930	−	0.703045i
$56$	5.32843	+	9.22911i	0.712041	+	1.23329i
$57$	1.91421	−	3.31552i	0.253544	−	0.439151i
$58$	−2.28825	−	1.66251i	−0.300461	−	0.218298i
$59$	−6.73886	+	7.48426i	−0.877325	+	0.974368i	−0.999836	−	0.0180992i	$-0.994239\pi$
$59$	−6.73886	+	7.48426i	−0.877325	+	0.974368i	0.122511	+	0.992467i	$0.460905\pi$
$60$	−2.85613	+	8.79027i	−0.368725	+	1.13482i
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$		0			0
$63$	6.82843			0.860301
$64$	−3.03715	+	9.34739i	−0.379644	+	1.16842i
$65$	1.22346	−	1.35879i	0.151751	−	0.168537i
$66$	24.7206	+	17.9606i	3.04290	+	2.21079i
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	−0.660293	−	0.751008i	$-0.729568\pi$
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	0.980539	+	0.196327i	$0.0629013\pi$
$68$	0.328427	+	0.568852i	0.0398276	+	0.0689835i
$69$	−1.00942	+	9.60395i	−0.121519	+	1.15618i
$70$	4.71530	−	3.42586i	0.563586	−	0.409469i
$71$	1.47083	+	13.9940i	0.174555	+	1.66078i	0.634567	+	0.772868i	$0.281178\pi$
$71$	1.47083	+	13.9940i	0.174555	+	1.66078i	−0.460012	+	0.887913i	$0.652155\pi$
$72$	−8.35428	−	9.27837i	−0.984562	−	1.09347i
$73$	3.49744	−	1.55716i	0.409345	−	0.182252i	−0.191725	−	0.981449i	$-0.561408\pi$
$73$	3.49744	−	1.55716i	0.409345	−	0.182252i	0.601070	+	0.799197i	$0.294741\pi$
$74$	2.36146	−	0.501943i	0.274514	−	0.0583497i
$75$	−9.44583	−	2.00777i	−1.09071	−	0.231838i
$76$	5.54620	+	2.46933i	0.636192	+	0.283251i
$77$	−3.91118	−	12.0374i	−0.445721	−	1.37179i
$78$	3.29315	+	10.1353i	0.372876	+	1.14759i
$79$	−13.9248	−	6.19974i	−1.56667	−	0.697525i	−0.574051	−	0.818820i	$-0.694629\pi$
$79$	−13.9248	−	6.19974i	−1.56667	−	0.697525i	−0.992617	+	0.121294i	$0.961296\pi$
$80$	−2.93444	−	0.623735i	−0.328081	−	0.0697357i
$81$	9.27801	−	1.97210i	1.03089	−	0.219122i
$82$	−20.9197	+	9.31406i	−2.31020	+	1.02857i
$83$	2.72408	+	3.02539i	0.299006	+	0.332080i	0.873861	−	0.486175i	$-0.161608\pi$
$83$	2.72408	+	3.02539i	0.299006	+	0.332080i	−0.574855	+	0.818255i	$0.694942\pi$
$84$	2.33242	+	22.1915i	0.254488	+	2.42129i
$85$	0.138805	−	0.100848i	0.0150556	−	0.0109385i
$86$	2.24582	−	21.3676i	0.242173	−	2.30413i
$87$	−1.41421	−	2.44949i	−0.151620	−	0.262613i
$88$	−11.5711	+	20.0417i	−1.23348	+	2.13645i
$89$	10.1008	+	7.33866i	1.07068	+	0.777897i	0.976035	−	0.217614i	$-0.0698274\pi$
$89$	10.1008	+	7.33866i	1.07068	+	0.777897i	0.0946482	+	0.995511i	$0.469827\pi$
$90$	−4.56911	+	5.07451i	−0.481626	+	0.534900i
$91$	1.36407	−	4.19817i	0.142993	−	0.440087i
$92$	−15.3137			−1.59656
$93$		0			0
$94$	4.00000			0.412568
$95$	0.490035	−	1.50817i	0.0502765	−	0.154735i
$96$	−2.56172	+	2.84508i	−0.261454	+	0.290374i
$97$	−8.76038	−	6.36479i	−0.889482	−	0.646246i	0.0462609	−	0.998929i	$-0.485269\pi$
$97$	−8.76038	−	6.36479i	−0.889482	−	0.646246i	−0.935743	+	0.352683i	$0.885269\pi$
$98$	−1.41421	+	2.44949i	−0.142857	+	0.247436i
$99$	7.41421	+	12.8418i	0.745157	+	1.29065i
$100$	1.60072	−	15.2298i	0.160072	−	1.52298i
$101$	−6.86474	+	4.98752i	−0.683067	+	0.496277i	−0.874374	−	0.485253i	$-0.838727\pi$
$101$	−6.86474	+	4.98752i	−0.683067	+	0.496277i	0.191307	+	0.981530i	$0.438727\pi$
$102$	0.104528	+	0.994522i	0.0103499	+	0.0984723i
$103$	−8.07712	−	8.97055i	−0.795862	−	0.883895i	0.199519	−	0.979894i	$-0.436062\pi$
$103$	−8.07712	−	8.97055i	−0.795862	−	0.883895i	−0.995381	+	0.0959992i	$0.969395\pi$
$104$	−7.37329	+	3.28280i	−0.723010	+	0.321905i
$105$	5.70106	−	1.21180i	0.556367	−	0.118259i
$106$	0.405162	+	0.0861198i	0.0393528	+	0.00836470i
$107$	8.75705	+	3.89889i	0.846576	+	0.376920i	0.783729	−	0.621103i	$-0.213315\pi$
$107$	8.75705	+	3.89889i	0.846576	+	0.376920i	0.0628473	+	0.998023i	$0.479982\pi$
$108$	0.490035	+	1.50817i	0.0471536	+	0.145124i
$109$	−1.59810	−	4.91846i	−0.153071	−	0.471103i	0.844890	−	0.534941i	$-0.179666\pi$
$109$	−1.59810	−	4.91846i	−0.153071	−	0.471103i	−0.997960	+	0.0638377i	$0.979666\pi$
$110$	11.5626	+	5.14801i	1.10245	+	0.490843i
$111$	2.36146	+	0.501943i	0.224140	+	0.0476423i
$112$	−7.08437	+	1.50583i	−0.669410	+	0.142288i
$113$	4.88121	−	2.17325i	0.459185	−	0.204442i	−0.164089	−	0.986445i	$-0.552469\pi$
$113$	4.88121	−	2.17325i	0.459185	−	0.204442i	0.623275	+	0.782003i	$0.285802\pi$
$114$	6.18453	+	6.86862i	0.579235	+	0.643305i
$115$	0.418114	+	3.97809i	0.0389893	+	0.370959i
$116$	3.62867	−	2.63638i	0.336913	−	0.244782i
$117$	−0.540577	+	5.14324i	−0.0499763	+	0.475493i
$118$	−12.1569	−	21.0563i	−1.11913	−	1.93839i
$119$	0.207107	−	0.358719i	0.0189854	−	0.0328838i
$120$	−8.62158	−	6.26394i	−0.787039	−	0.571817i
$121$	11.0308	−	12.2510i	1.00280	−	1.11372i
$122$	−2.11010	+	6.49422i	−0.191039	+	0.587959i
$123$	−22.8995			−2.06478
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−5.09423	+	15.6784i	−0.453830	+	1.39675i
$127$	−7.29319	+	8.09990i	−0.647166	+	0.718750i	−0.974055	−	0.226312i	$-0.927333\pi$
$127$	−7.29319	+	8.09990i	−0.647166	+	0.718750i	0.326889	+	0.945063i	$0.394000\pi$
$128$	−16.6304	−	12.0827i	−1.46994	−	1.06797i
$129$	10.7426	−	18.6068i	0.945837	−	1.63824i
$130$	2.20711	+	3.82282i	0.193576	+	0.335284i
$131$	0.497279	−	4.73130i	0.0434475	−	0.413375i	−0.951084	−	0.308934i	$-0.900028\pi$
$131$	0.497279	−	4.73130i	0.0434475	−	0.413375i	0.994531	−	0.104442i	$-0.0333055\pi$
$132$	−39.2016	+	28.4816i	−3.41206	+	2.47901i
$133$	−0.400180	−	3.80745i	−0.0347000	−	0.330148i
$134$	8.46909	+	9.40588i	0.731618	+	0.812544i
$135$	0.378403	−	0.168476i	0.0325677	−	0.0145001i
$136$	−0.740809	+	0.157464i	−0.0635239	+	0.0135024i
$137$	7.32171	+	1.55628i	0.625536	+	0.132962i	0.509764	−	0.860314i	$-0.329733\pi$
$137$	7.32171	+	1.55628i	0.625536	+	0.132962i	0.115772	+	0.993276i	$0.463066\pi$
$138$	−21.2981	−	9.48254i	−1.81302	−	0.807207i
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$	2.85613	+	8.79027i	0.241387	+	0.742914i
$141$	3.65418	+	1.62695i	0.307738	+	0.137014i
$142$	−33.2282	−	7.06288i	−2.78845	−	0.592703i
$143$	9.37631	−	1.99300i	0.784087	−	0.166663i
$144$	7.75169	−	3.45127i	0.645974	−	0.287606i
$145$	−0.783935	−	0.870648i	−0.0651023	−	0.0723034i
$146$	0.966119	+	9.19201i	0.0799566	+	0.760736i
$147$	−2.28825	+	1.66251i	−0.188731	+	0.137121i
$148$	−0.400180	+	3.80745i	−0.0328946	+	0.312971i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	11.6569	−	20.1903i	0.951778	−	1.64853i
$151$	14.0071	+	10.1767i	1.13988	+	0.828172i	0.987103	−	0.160089i	$-0.0511781\pi$
$151$	14.0071	+	10.1767i	1.13988	+	0.828172i	0.152778	+	0.988261i	$0.451178\pi$
$152$	−4.68391	+	5.20201i	−0.379916	+	0.421939i
$153$	−0.149960	+	0.461530i	−0.0121236	+	0.0373125i
$154$	30.5563			2.46230
$155$		0			0
$156$	−16.8995			−1.35304
$157$	4.58224	−	14.1027i	0.365702	−	1.12552i	−0.583838	−	0.811870i	$-0.698450\pi$
$157$	4.58224	−	14.1027i	0.365702	−	1.12552i	0.949540	−	0.313646i	$-0.101550\pi$
$158$	24.6233	−	27.3470i	1.95893	−	2.17561i
$159$	0.335106	+	0.243469i	0.0265756	+	0.0193083i
$160$	−0.792893	+	1.37333i	−0.0626837	+	0.108571i
$161$	4.82843	+	8.36308i	0.380533	+	0.659103i
$162$	−2.39365	+	22.7740i	−0.188063	+	1.78930i
$163$	10.4934	−	7.62391i	0.821907	−	0.597150i	−0.0953511	−	0.995444i	$-0.530397\pi$
$163$	10.4934	−	7.62391i	0.821907	−	0.597150i	0.917258	+	0.398293i	$0.130397\pi$
$164$	−3.79582	−	36.1148i	−0.296403	−	2.82009i
$165$	8.46909	+	9.40588i	0.659318	+	0.732246i
$166$	−8.97871	+	3.99758i	−0.696883	+	0.310272i
$167$	8.36937	−	1.77897i	0.647641	−	0.137660i	0.127633	−	0.991821i	$-0.459262\pi$
$167$	8.36937	−	1.77897i	0.647641	−	0.137660i	0.520009	+	0.854161i	$0.325929\pi$
$168$	−25.1657	−	5.34914i	−1.94158	−	0.412695i
$169$	−8.82198	−	3.92780i	−0.678613	−	0.302138i
$170$	0.127999	+	0.393941i	0.00981708	+	0.0302139i
$171$	1.38603	+	4.26576i	0.105992	+	0.326211i
$172$	31.1255	+	13.8580i	2.37329	+	1.05666i
$173$	14.0009	+	2.97599i	1.06447	+	0.226260i	0.706674	−	0.707539i	$-0.250195\pi$
$173$	14.0009	+	2.97599i	1.06447	+	0.226260i	0.357796	+	0.933800i	$0.383528\pi$
$174$	6.67921	−	1.41971i	0.506350	−	0.107628i
$175$	−8.82198	+	3.92780i	−0.666879	+	0.296914i
$176$	−10.5240	−	11.6881i	−0.793279	−	0.881025i
$177$	−2.54147	−	24.1805i	−0.191029	−	1.81752i
$178$	−24.3855	+	17.7171i	−1.82777	+	1.32795i
$179$	0.706336	−	6.72034i	0.0527941	−	0.502302i	−0.935890	−	0.352291i	$-0.885403\pi$
$179$	0.706336	−	6.72034i	0.0527941	−	0.502302i	0.988684	−	0.150010i	$-0.0479307\pi$
$180$	−5.41421	−	9.37769i	−0.403552	−	0.698972i
$181$	5.15685	−	8.93193i	0.383306	−	0.663905i	−0.608227	−	0.793763i	$-0.708119\pi$
$181$	5.15685	−	8.93193i	0.383306	−	0.663905i	0.991533	+	0.129858i	$0.0414522\pi$
$182$	8.62158	+	6.26394i	0.639074	+	0.464314i
$183$	−4.56911	+	5.07451i	−0.337758	+	0.375119i
$184$	5.45627	−	16.7927i	0.402241	−	1.23797i
$185$	1.00000			0.0735215
$186$		0			0
$187$	0.899495			0.0657776
$188$	−1.96014	+	6.03269i	−0.142958	+	0.439979i
$189$	0.669131	−	0.743145i	0.0486721	−	0.0540558i
$190$	3.09726	+	2.25029i	0.224699	+	0.163253i
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	−0.845431	−	0.534084i	$-0.820657\pi$
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	0.885246	+	0.465123i	$0.153990\pi$
$192$	−11.8640	−	20.5490i	−0.856208	−	1.48300i
$193$	2.20995	−	21.0263i	0.159076	−	1.51351i	−0.565751	−	0.824576i	$-0.691414\pi$
$193$	2.20995	−	21.0263i	0.159076	−	1.51351i	0.724827	−	0.688931i	$-0.241920\pi$
$194$	21.1494	−	15.3660i	1.51844	−	1.10321i
$195$	0.461411	+	4.39003i	0.0330423	+	0.314377i
$196$	−3.00124	−	3.33321i	−0.214374	−	0.238087i
$197$	3.18396	−	1.41759i	0.226848	−	0.100999i	−0.290166	−	0.956976i	$-0.593710\pi$
$197$	3.18396	−	1.41759i	0.226848	−	0.100999i	0.517013	+	0.855977i	$0.327044\pi$
$198$	−35.0167	+	7.44303i	−2.48853	+	0.528953i
$199$	−15.2452	−	3.24047i	−1.08070	−	0.229711i	−0.367044	−	0.930204i	$-0.619630\pi$
$199$	−15.2452	−	3.24047i	−1.08070	−	0.229711i	−0.713659	+	0.700493i	$0.752964\pi$
$200$	16.1303	+	7.18169i	1.14059	+	0.507822i
$201$	3.91118	+	12.0374i	0.275874	+	0.849052i
$202$	−6.33030	−	19.4827i	−0.445398	−	1.37080i
$203$	−2.58390	−	1.15042i	−0.181354	−	0.0807440i
$204$	−1.55113	−	0.329704i	−0.108601	−	0.0230839i
$205$	−9.27801	+	1.97210i	−0.648004	+	0.137738i
$206$	26.6227	−	11.8532i	1.85489	−	0.825850i
$207$	−7.57035	−	8.40772i	−0.526176	−	0.584377i
$208$	−0.573368	−	5.45523i	−0.0397559	−	0.378252i
$209$	6.72593	−	4.88668i	0.465242	−	0.338018i
$210$	−1.47083	+	13.9940i	−0.101497	+	0.965677i
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	0.705425	−	0.708785i	$-0.250756\pi$
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	−0.966538	+	0.256523i	$0.917423\pi$
$212$	−0.328427	+	0.568852i	−0.0225565	+	0.0390689i
$213$	−27.4828	−	19.9674i	−1.88309	−	1.36814i
$214$	−15.4851	+	17.1980i	−1.05854	+	1.17563i
$215$	2.75010	−	8.46392i	0.187555	−	0.577235i
$216$	−1.82843			−0.124409
$217$		0			0
$218$	12.4853			0.845610
$219$	−2.85613	+	8.79027i	−0.193000	+	0.593992i
$220$	−13.4302	+	14.9157i	−0.905462	+	1.00562i
$221$	0.253796	+	0.184393i	0.0170721	+	0.0124036i
$222$	−2.91421	+	5.04757i	−0.195589	+	0.338770i
$223$	−0.863961	−	1.49642i	−0.0578551	−	0.100208i	0.835647	−	0.549266i	$-0.185093\pi$
$223$	−0.863961	−	1.49642i	−0.0578551	−	0.100208i	−0.893502	+	0.449059i	$0.851759\pi$
$224$	−0.400180	+	3.80745i	−0.0267381	+	0.254396i
$225$	9.15298	−	6.65003i	0.610199	−	0.443335i
$226$	1.34836	+	12.8288i	0.0896919	+	0.853361i
$227$	−10.4289	−	11.5825i	−0.692192	−	0.768757i	0.289921	−	0.957051i	$-0.406371\pi$
$227$	−10.4289	−	11.5825i	−0.692192	−	0.768757i	−0.982113	+	0.188293i	$0.939704\pi$
$228$	−13.3897	+	5.96148i	−0.886755	+	0.394809i
$229$	−11.2343	+	2.38792i	−0.742383	+	0.157798i	−0.563551	−	0.826081i	$-0.690565\pi$
$229$	−11.2343	+	2.38792i	−0.742383	+	0.157798i	−0.178832	+	0.983880i	$0.557232\pi$
$230$	−9.44583	−	2.00777i	−0.622840	−	0.132389i
$231$	27.9146	+	12.4284i	1.83665	+	0.817728i
$232$	1.59810	+	4.91846i	0.104921	+	0.322913i
$233$	−4.58224	−	14.1027i	−0.300192	−	0.923897i	−0.981428	−	0.191832i	$-0.938557\pi$
$233$	−4.58224	−	14.1027i	−0.300192	−	0.923897i	0.681235	−	0.732064i	$-0.261443\pi$
$234$	−11.4059	−	5.07822i	−0.745625	−	0.331974i
$235$	1.62065	+	0.344479i	0.105719	+	0.0224714i
$236$	37.7138	−	8.01632i	2.45496	−	0.521818i
$237$	33.6176	−	14.9675i	2.18369	−	0.972243i
$238$	0.669131	+	0.743145i	0.0433733	+	0.0481709i
$239$	1.33351	+	12.6875i	0.0862574	+	0.820684i	0.949050	+	0.315126i	$0.102047\pi$
$239$	1.33351	+	12.6875i	0.0862574	+	0.820684i	−0.862792	+	0.505558i	$0.831287\pi$
$240$	5.85942	−	4.25712i	0.378224	−	0.274796i
$241$	−2.57734	+	24.5218i	−0.166021	+	1.57959i	0.521390	+	0.853318i	$0.325414\pi$
$241$	−2.57734	+	24.5218i	−0.166021	+	1.57959i	−0.687411	+	0.726268i	$0.741253\pi$
$242$	19.8995	+	34.4669i	1.27919	+	2.21562i
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$	−8.76038	−	6.36479i	−0.560826	−	0.407464i
$245$	−0.783935	+	0.870648i	−0.0500838	+	0.0556237i
$246$	17.0838	−	52.5785i	1.08922	−	3.35228i
$247$	2.89949			0.184490
$248$		0			0
$249$	−9.82843			−0.622851
$250$	6.71430	−	20.6645i	0.424649	−	1.30694i
$251$	2.39936	−	2.66476i	0.151446	−	0.168198i	−0.662648	−	0.748931i	$-0.730567\pi$
$251$	2.39936	−	2.66476i	0.151446	−	0.168198i	0.814094	+	0.580733i	$0.197234\pi$
$252$	−21.1494	−	15.3660i	−1.33229	−	0.967965i
$253$	−10.4853	+	18.1610i	−0.659204	+	1.14177i
$254$	−13.1569	−	22.7883i	−0.825534	−	1.42987i
$255$	−0.0432971	+	0.411944i	−0.00271137	+	0.0257970i
$256$	24.2467	−	17.6163i	1.51542	−	1.10102i
$257$	0.0327915	+	0.311990i	0.00204548	+	0.0194614i	0.995497	−	0.0947928i	$-0.0302188\pi$
$257$	0.0327915	+	0.311990i	0.00204548	+	0.0194614i	−0.993452	+	0.114254i	$0.963552\pi$
$258$	34.7078	+	38.5470i	2.16082	+	2.39983i
$259$	2.20549	−	0.981949i	0.137043	−	0.0610153i
$260$	−6.84703	+	1.45538i	−0.424635	+	0.0902589i
$261$	3.24130	+	0.688959i	0.200631	+	0.0426455i
$262$	10.4923	+	4.67148i	0.648218	+	0.288605i
$263$	−0.212076	−	0.652702i	−0.0130772	−	0.0402473i	0.944305	−	0.329071i	$-0.106736\pi$
$263$	−0.212076	−	0.652702i	−0.0130772	−	0.0402473i	−0.957382	+	0.288824i	$0.906736\pi$
$264$	−17.2648	−	53.1356i	−1.06257	−	3.27027i
$265$	0.156740	+	0.0697850i	0.00962844	+	0.00428686i
$266$	9.04067	+	1.92165i	0.554319	+	0.117824i
$267$	−29.4835	+	6.26690i	−1.80436	+	0.383528i
$268$	−18.3358	+	8.16364i	−1.12004	+	0.498674i
$269$	−21.2974	−	23.6531i	−1.29852	−	1.44216i	−0.829012	−	0.559231i	$-0.811097\pi$
$269$	−21.2974	−	23.6531i	−1.29852	−	1.44216i	−0.469512	−	0.882926i	$-0.655570\pi$
$270$	0.104528	+	0.994522i	0.00636140	+	0.0605247i
$271$	18.8612	−	13.7035i	1.14574	−	0.832426i	0.157827	−	0.987467i	$-0.449551\pi$
$271$	18.8612	−	13.7035i	1.14574	−	0.832426i	0.987908	+	0.155041i	$0.0495510\pi$
$272$	0.0538027	−	0.511899i	0.00326227	−	0.0310384i
$273$	5.32843	+	9.22911i	0.322491	+	0.558571i
$274$	−9.03553	+	15.6500i	−0.545857	+	0.945451i
$275$	−16.9655	−	12.3262i	−1.02306	−	0.743297i
$276$	24.7381	−	27.4745i	1.48906	−	1.65377i
$277$	−4.37016	+	13.4500i	−0.262577	+	0.808130i	0.729664	+	0.683806i	$0.239676\pi$
$277$	−4.37016	+	13.4500i	−0.262577	+	0.808130i	−0.992242	+	0.124325i	$0.960324\pi$
$278$		0			0
$279$		0			0
$280$	−10.6569			−0.636869
$281$	0.618034	−	1.90211i	0.0368688	−	0.113471i	−0.930928	−	0.365202i	$-0.881000\pi$
$281$	0.618034	−	1.90211i	0.0368688	−	0.113471i	0.967797	+	0.251731i	$0.0809999\pi$
$282$	−6.46170	+	7.17644i	−0.384788	+	0.427351i
$283$	1.89564	+	1.37727i	0.112684	+	0.0818700i	0.642700	−	0.766118i	$-0.277814\pi$
$283$	1.89564	+	1.37727i	0.112684	+	0.0818700i	−0.530016	+	0.847988i	$0.677814\pi$
$284$	26.9350	−	46.6528i	1.59830	−	2.76834i
$285$	1.91421	+	3.31552i	0.113388	+	0.196394i
$286$	−2.41901	+	23.0154i	−0.143039	+	1.36093i
$287$	−18.5261	+	13.4600i	−1.09356	+	0.794518i
$288$	−0.468840	−	4.46071i	−0.0276266	−	0.262850i
$289$	−11.3555	−	12.6116i	−0.667972	−	0.741858i
$290$	2.58390	−	1.15042i	0.151732	−	0.0675553i
$291$	25.5709	−	5.43526i	1.49899	−	0.318620i
$292$	−14.3366	−	3.04733i	−0.838984	−	0.178332i
$293$	−22.6550	−	10.0867i	−1.32352	−	0.589269i	−0.381358	−	0.924428i	$-0.624543\pi$
$293$	−22.6550	−	10.0867i	−1.32352	−	0.589269i	−0.942162	+	0.335159i	$0.891210\pi$
$294$	−2.11010	−	6.49422i	−0.123064	−	0.378751i
$295$	−3.11213	−	9.57815i	−0.181195	−	0.557662i
$296$	−4.03258	−	1.79542i	−0.234389	−	0.104357i
$297$	2.12412	+	0.451495i	0.123254	+	0.0261984i
$298$	2.36146	−	0.501943i	0.136796	−	0.0290768i
$299$	−6.68141	+	2.97475i	−0.386396	+	0.172034i
$300$	24.7381	+	27.4745i	1.42826	+	1.58624i
$301$	−2.24582	−	21.3676i	−0.129447	−	1.23161i
$302$	−33.8161	+	24.5688i	−1.94590	+	1.41378i
$303$	2.14129	−	20.3731i	0.123014	−	1.17040i
$304$	−2.37868	−	4.11999i	−0.136427	−	0.236298i
$305$	−1.41421	+	2.44949i	−0.0809776	+	0.140257i
$306$	−0.947822	−	0.688633i	−0.0541834	−	0.0393665i
$307$	−1.84503	+	2.04912i	−0.105302	+	0.116949i	−0.793492	−	0.608581i	$-0.791739\pi$
$307$	−1.84503	+	2.04912i	−0.105302	+	0.116949i	0.688190	+	0.725531i	$0.258406\pi$
$308$	−14.9737	+	46.0842i	−0.853205	+	2.62589i
$309$	29.1421			1.65784
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$	6.02128	−	18.5316i	0.340888	−	1.04915i
$313$	2.56172	−	2.84508i	0.144797	−	0.160813i	−0.666384	−	0.745609i	$-0.732159\pi$
$313$	2.56172	−	2.84508i	0.144797	−	0.160813i	0.811181	+	0.584796i	$0.198825\pi$
$314$	28.9620	+	21.0421i	1.63442	+	1.18748i
$315$	−3.41421	+	5.91359i	−0.192369	+	0.333193i
$316$	29.1777	+	50.5372i	1.64137	+	2.84294i
$317$	0.226991	−	2.15968i	0.0127491	−	0.121300i	−0.986296	−	0.164984i	$-0.947243\pi$
$317$	0.226991	−	2.15968i	0.0127491	−	0.121300i	0.999045	+	0.0436841i	$0.0139095\pi$
$318$	−0.809017	+	0.587785i	−0.0453674	+	0.0329614i
$319$	−0.642028	−	6.10849i	−0.0359467	−	0.342010i
$320$	−6.57650	−	7.30394i	−0.367638	−	0.408303i
$321$	−21.1414	+	9.41275i	−1.18000	+	0.525369i
$322$	−22.8042	+	4.84719i	−1.27083	+	0.270123i
$323$	0.266132	+	0.0565682i	0.0148080	+	0.00314754i
$324$	−33.1742	−	14.7701i	−1.84301	−	0.820562i
$325$	−2.26006	−	6.95575i	−0.125366	−	0.385836i
$326$	9.67647	+	29.7811i	0.535930	+	1.64942i
$327$	11.4059	+	5.07822i	0.630746	+	0.280826i
$328$	40.9551	+	8.70527i	2.26137	+	0.480668i
$329$	3.91259	−	0.831647i	0.215708	−	0.0458502i
$330$	−27.9146	+	12.4284i	−1.53665	+	0.684160i
$331$	0.506772	+	0.562828i	0.0278547	+	0.0309358i	0.756911	−	0.653518i	$-0.226708\pi$
$331$	0.506772	+	0.562828i	0.0278547	+	0.0309358i	−0.729056	+	0.684454i	$0.760041\pi$
$332$	−1.62916	−	15.5004i	−0.0894117	−	0.850695i
$333$	−2.28825	+	1.66251i	−0.125395	+	0.0911049i
$334$	−2.15923	+	20.5437i	−0.118148	+	1.12410i
$335$	2.62132	+	4.54026i	0.143218	+	0.248061i
$336$	8.74264	−	15.1427i	0.476950	−	0.826102i
$337$	10.7710	+	7.82560i	0.586735	+	0.426288i	0.841146	−	0.540808i	$-0.181882\pi$
$337$	10.7710	+	7.82560i	0.586735	+	0.426288i	−0.254411	+	0.967096i	$0.581882\pi$
$338$	15.5999	−	17.3255i	0.848524	−	0.942381i
$339$	−3.98616	+	12.2681i	−0.216499	+	0.666314i
$340$	−0.656854			−0.0356229
$341$		0			0
$342$	−10.8284			−0.585534
$343$	−6.09626	+	18.7624i	−0.329167	+	1.01307i
$344$	−26.2863	+	29.1939i	−1.41726	+	1.57403i
$345$	−7.81256	−	5.67616i	−0.420614	−	0.305594i
$346$	−17.2782	+	29.9267i	−0.928880	+	1.60887i
$347$	−11.2782	−	19.5344i	−0.605444	−	1.04866i	−0.991981	−	0.126386i	$-0.959662\pi$
$347$	−11.2782	−	19.5344i	−0.605444	−	1.04866i	0.386537	−	0.922274i	$-0.373671\pi$
$348$	−1.13188	+	10.7691i	−0.0606751	+	0.577285i
$349$	−28.4068	+	20.6387i	−1.52058	+	1.10477i	−0.559380	+	0.828911i	$0.688961\pi$
$349$	−28.4068	+	20.6387i	−1.52058	+	1.10477i	−0.961199	+	0.275854i	$0.911039\pi$
$350$	−2.43695	−	23.1860i	−0.130260	−	1.23934i
$351$	0.506772	+	0.562828i	0.0270495	+	0.0300415i
$352$	−7.59495	+	3.38149i	−0.404812	+	0.180234i
$353$	−2.93444	+	0.623735i	−0.156185	+	0.0331981i	−0.285340	−	0.958426i	$-0.592107\pi$
$353$	−2.93444	+	0.623735i	−0.156185	+	0.0331981i	0.129156	+	0.991624i	$0.458773\pi$
$354$	57.4158	+	12.2041i	3.05161	+	0.648641i
$355$	−12.8546	−	5.72322i	−0.682249	−	0.303757i
$356$	−14.7707	−	45.4595i	−0.782846	−	2.40935i
$357$	0.309017	+	0.951057i	0.0163549	+	0.0503352i
$358$	14.9033	+	6.63538i	0.787665	+	0.350691i
$359$	−26.3117	−	5.59272i	−1.38868	−	0.295172i	−0.547895	−	0.836547i	$-0.684571\pi$
$359$	−26.3117	−	5.59272i	−1.38868	−	0.295172i	−0.840782	+	0.541374i	$0.817904\pi$
$360$	12.2124	−	2.59584i	0.643653	−	0.136813i
$361$	−15.0601	+	6.70517i	−0.792634	+	0.352904i
$362$	16.6610	+	18.5039i	0.875683	+	0.972545i
$363$	4.16013	+	39.5810i	0.218350	+	2.07746i
$364$	−13.6720	+	9.93327i	−0.716606	+	0.520645i
$365$	−0.400180	+	3.80745i	−0.0209464	+	0.199291i
$366$	−8.24264	−	14.2767i	−0.430850	−	0.746254i
$367$	−9.10660	+	15.7731i	−0.475361	+	0.823349i	−0.999602	−	0.0282210i	$-0.991016\pi$
$367$	−9.10660	+	15.7731i	−0.475361	+	0.823349i	0.524241	+	0.851570i	$0.324349\pi$
$368$	9.70820	+	7.05342i	0.506075	+	0.367685i
$369$	17.9517	−	19.9374i	0.934529	−	1.03790i
$370$	−0.746033	+	2.29605i	−0.0387844	+	0.119366i
$371$	0.414214			0.0215049
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−0.671053	+	2.06529i	−0.0346993	+	0.106794i
$375$	14.5388	−	16.1470i	0.750781	−	0.833827i
$376$	−5.91691	−	4.29889i	−0.305142	−	0.221698i
$377$	1.07107	−	1.85514i	0.0551628	−	0.0955448i
$378$	1.20711	+	2.09077i	0.0620869	+	0.107538i
$379$	3.07155	−	29.2238i	0.157775	−	1.50113i	−0.573592	−	0.819141i	$-0.694450\pi$
$379$	3.07155	−	29.2238i	0.157775	−	1.50113i	0.731366	−	0.681985i	$-0.238883\pi$
$380$	−4.91160	+	3.56848i	−0.251960	+	0.183059i
$381$	−2.75053	−	26.1696i	−0.140914	−	1.34071i
$382$	1.77778	+	1.97443i	0.0909593	+	0.101020i
$383$	22.7468	−	10.1275i	1.16231	−	0.517493i	0.267331	−	0.963605i	$-0.413858\pi$
$383$	22.7468	−	10.1275i	1.16231	−	0.517493i	0.894977	+	0.446112i	$0.147192\pi$
$384$	48.5429	−	10.3181i	2.47720	−	0.526544i
$385$	12.3803	+	2.63151i	0.630957	+	0.134114i
$386$	46.6288	+	20.7605i	2.37335	+	1.05668i
$387$	7.77844	+	23.9396i	0.395401	+	1.21692i
$388$	12.8106	+	39.4269i	0.650358	+	2.00160i
$389$	15.6601	+	6.97233i	0.794000	+	0.353511i	0.763322	−	0.646018i	$-0.223567\pi$
$389$	15.6601	+	6.97233i	0.794000	+	0.353511i	0.0306774	+	0.999529i	$0.490234\pi$
$390$	−10.4240	−	2.21568i	−0.527839	−	0.112196i
$391$	−0.671294	+	0.142688i	−0.0339488	+	0.00721604i
$392$	4.72447	−	2.10347i	0.238622	−	0.106241i
$393$	7.68515	+	8.53523i	0.387665	+	0.430545i
$394$	0.879525	+	8.36812i	0.0443098	+	0.421580i
$395$	12.3316	−	8.95940i	0.620468	−	0.450796i
$396$	5.93403	−	56.4586i	0.298196	−	2.83715i
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	0.995368	−	0.0961392i	$-0.0306494\pi$
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	−0.580943	+	0.813944i	$0.697316\pi$
$398$	18.8137	−	32.5863i	0.943046	−	1.63340i
$399$	7.47745	+	5.43269i	0.374341	+	0.271975i
$400$	−8.02957	+	8.91774i	−0.401478	+	0.445887i
$401$	−6.54238	+	20.1354i	−0.326711	+	1.00551i	0.643952	+	0.765066i	$0.277294\pi$
$401$	−6.54238	+	20.1354i	−0.326711	+	1.00551i	−0.970663	+	0.240446i	$0.922706\pi$
$402$	−30.5563			−1.52401
$403$		0			0
$404$	32.4853			1.61620
$405$	−2.93111	+	9.02104i	−0.145648	+	0.448259i
$406$	4.56911	−	5.07451i	0.226761	−	0.251844i
$407$	4.24139	+	3.08155i	0.210238	+	0.152747i
$408$	0.914214	−	1.58346i	0.0452603	−	0.0783932i
$409$	−4.67157	−	8.09140i	−0.230994	−	0.400094i	0.727107	−	0.686525i	$-0.240865\pi$
$409$	−4.67157	−	8.09140i	−0.230994	−	0.400094i	−0.958101	+	0.286431i	$0.907531\pi$
$410$	2.39365	−	22.7740i	0.118214	−	1.12473i
$411$	−14.6198	+	10.6219i	−0.721142	+	0.523940i
$412$	4.83060	+	45.9600i	0.237986	+	2.26429i
$413$	−16.2690	−	18.0686i	−0.800547	−	0.889098i
$414$	24.9523	−	11.1095i	1.22634	−	0.546001i
$415$	−3.98211	+	0.846423i	−0.195474	+	0.0415493i
$416$	−2.83613	−	0.602839i	−0.139053	−	0.0295566i
$417$		0			0
$418$	6.20230	+	19.0887i	0.303364	+	0.933660i
$419$	8.65248	+	26.6296i	0.422701	+	1.30094i	0.905178	+	0.425032i	$0.139737\pi$
$419$	8.65248	+	26.6296i	0.422701	+	1.30094i	−0.482477	+	0.875908i	$0.660263\pi$
$420$	−20.3846	−	9.07580i	−0.994666	−	0.442854i
$421$	2.79541	+	0.594183i	0.136240	+	0.0289587i	0.275527	−	0.961293i	$-0.411148\pi$
$421$	2.79541	+	0.594183i	0.136240	+	0.0289587i	−0.139287	+	0.990252i	$0.544481\pi$
$422$	17.9135	−	3.80763i	0.872016	−	0.185353i
$423$	−4.28114	+	1.90609i	−0.208156	+	0.0926771i
$424$	−0.506772	−	0.562828i	−0.0246110	−	0.0273333i
$425$	−0.0717370	−	0.682532i	−0.00347976	−	0.0331077i
$426$	66.3493	−	48.2056i	3.21463	−	2.33557i
$427$	−0.713765	+	6.79102i	−0.0345415	+	0.328641i
$428$	−18.3492	−	31.7818i	−0.886944	−	1.53623i
$429$	−11.5711	+	20.0417i	−0.558656	+	0.967621i
$430$	17.3820	+	12.6287i	0.838232	+	0.609012i
$431$	−16.8906	+	18.7589i	−0.813593	+	0.903586i	−0.996836	−	0.0794813i	$-0.974674\pi$
$431$	−16.8906	+	18.7589i	−0.813593	+	0.903586i	0.183244	+	0.983068i	$0.441340\pi$
$432$	0.383997	−	1.18182i	0.0184751	−	0.0568604i
$433$	−35.1127			−1.68741			−0.843704	−	0.536808i	$-0.819630\pi$
$433$	−35.1127			−1.68741			−0.843704	+	0.536808i	$0.819630\pi$
$434$		0			0
$435$	2.82843			0.135613
$436$	−6.11822	+	18.8300i	−0.293010	+	0.901791i
$437$	−4.24439	+	4.71388i	−0.203037	+	0.225495i
$438$	−18.0522	−	13.1157i	−0.862566	−	0.626691i
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	−0.685286	−	0.728274i	$-0.740323\pi$
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	0.973347	+	0.229339i	$0.0736563\pi$
$440$	−11.5711	−	20.0417i	−0.551629	−	0.955449i
$441$	0.346377	−	3.29556i	0.0164941	−	0.156931i
$442$	−0.612717	+	0.445165i	−0.0291440	+	0.0211743i
$443$	1.38423	+	13.1701i	0.0657669	+	0.625730i	0.976912	+	0.213644i	$0.0685332\pi$
$443$	1.38423	+	13.1701i	0.0657669	+	0.625730i	−0.911145	+	0.412086i	$0.864800\pi$
$444$	−6.18453	−	6.86862i	−0.293505	−	0.325970i
$445$	−11.4059	+	5.07822i	−0.540690	+	0.240731i
$446$	4.08041	−	0.867319i	0.193213	−	0.0410687i
$447$	2.36146	+	0.501943i	0.111693	+	0.0237411i
$448$	−21.6765	−	9.65102i	−1.02412	−	0.455968i
$449$	1.42995	+	4.40094i	0.0674835	+	0.207693i	0.979112	−	0.203323i	$-0.0651741\pi$
$449$	1.42995	+	4.40094i	0.0674835	+	0.207693i	−0.911628	+	0.411016i	$0.865174\pi$
$450$	8.44040	+	25.9769i	0.397884	+	1.22456i
$451$	−45.4287	−	20.2262i	−2.13915	−	0.952413i
$452$	−20.0088	−	4.25301i	−0.941136	−	0.200045i
$453$	−40.8856	+	8.69050i	−1.92097	+	0.408315i
$454$	34.3744	−	15.3044i	1.61327	−	0.718273i
$455$	2.95369	+	3.28040i	0.138471	+	0.153788i
$456$	−1.76648	−	16.8069i	−0.0827229	−	0.787056i
$457$	−25.1707	+	18.2876i	−1.17744	+	0.855457i	−0.991880	−	0.127177i	$-0.959409\pi$
$457$	−25.1707	+	18.2876i	−1.17744	+	0.855457i	−0.185556	+	0.982634i	$0.559409\pi$
$458$	2.89836	−	27.5760i	0.135431	−	1.28854i
$459$	0.0355339	+	0.0615465i	0.00165858	+	0.00287275i
$460$	7.65685	−	13.2621i	0.357003	−	0.618347i
$461$	−21.1494	−	15.3660i	−0.985027	−	0.715664i	−0.0262008	−	0.999657i	$-0.508341\pi$
$461$	−21.1494	−	15.3660i	−0.985027	−	0.715664i	−0.958826	+	0.283993i	$0.908341\pi$
$462$	−49.3615	+	54.8215i	−2.29650	+	2.55053i
$463$	7.71633	−	23.7484i	0.358608	−	1.10368i	−0.595279	−	0.803519i	$-0.702959\pi$
$463$	7.71633	−	23.7484i	0.358608	−	1.10368i	0.953888	−	0.300164i	$-0.0970413\pi$
$464$	−3.51472			−0.163167
$465$		0			0
$466$	35.7990			1.65836
$467$	−2.47214	+	7.60845i	−0.114397	+	0.352077i	−0.991821	−	0.127639i	$-0.959260\pi$
$467$	−2.47214	+	7.60845i	−0.114397	+	0.352077i	0.877424	+	0.479716i	$0.159260\pi$
$468$	13.2481	−	14.7135i	0.612394	−	0.680133i
$469$	10.2396	+	7.43951i	0.472821	+	0.343525i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	17.8995	+	31.0028i	0.824765	+	1.42854i
$472$	−4.64690	+	44.2123i	−0.213891	+	2.03504i
$473$	37.7462	−	27.4242i	1.73557	−	1.26097i
$474$	9.28637	+	88.3539i	0.426537	+	4.05823i
$475$	−4.24439	−	4.71388i	−0.194746	−	0.216287i
$476$	−1.44869	+	0.644997i	−0.0664005	+	0.0295634i
$477$	−0.474677	+	0.100896i	−0.0217340	+	0.00461970i
$478$	−30.1260	−	6.40347i	−1.37793	−	0.292888i
$479$	8.88690	+	3.95670i	0.406053	+	0.180786i	0.599591	−	0.800306i	$-0.295330\pi$
$479$	8.88690	+	3.95670i	0.406053	+	0.180786i	−0.193539	+	0.981093i	$0.561996\pi$
$480$	−1.18305	−	3.64105i	−0.0539986	−	0.166190i
$481$	0.565015	+	1.73894i	0.0257625	+	0.0792887i
$482$	−54.3805	−	24.2118i	−2.47697	−	1.10282i
$483$	−22.8042	−	4.84719i	−1.03763	−	0.220555i
$484$	−61.7335	+	13.1219i	−2.80607	+	0.596449i
$485$	9.89226	−	4.40432i	0.449184	−	0.199990i
$486$	−34.9850	−	38.8548i	−1.58695	−	1.76249i
$487$	1.81720	+	17.2895i	0.0823454	+	0.783464i	0.955295	+	0.295654i	$0.0955375\pi$
$487$	1.81720	+	17.2895i	0.0823454	+	0.783464i	−0.872950	+	0.487810i	$0.837796\pi$
$488$	10.1008	−	7.33866i	0.457242	−	0.332206i
$489$	−3.27317	+	31.1422i	−0.148018	+	1.40830i
$490$	−1.41421	−	2.44949i	−0.0638877	−	0.110657i
$491$	−2.20711	+	3.82282i	−0.0996053	+	0.172522i	−0.911521	−	0.411253i	$-0.865091\pi$
$491$	−2.20711	+	3.82282i	−0.0996053	+	0.172522i	0.811916	+	0.583774i	$0.198425\pi$
$492$	70.9257	+	51.5306i	3.19758	+	2.32318i
$493$	0.134502	−	0.149380i	0.00605767	−	0.00672772i
$494$	−2.16312	+	6.65740i	−0.0973233	+	0.299530i
$495$	−14.8284			−0.666488
$496$		0			0
$497$	−33.9706			−1.52379
$498$	7.33233	−	22.5666i	0.328570	−	1.01123i
$499$	26.9079	−	29.8842i	1.20456	−	1.33780i	0.278498	−	0.960437i	$-0.410163\pi$
$499$	26.9079	−	29.8842i	1.20456	−	1.33780i	0.926065	−	0.377365i	$-0.123170\pi$
$500$	27.8754	+	20.2526i	1.24662	+	0.905725i
$501$	−10.3284	+	17.8894i	−0.461440	+	0.799238i
$502$	4.32843	+	7.49706i	0.193187	+	0.334610i
$503$	−2.44437	+	23.2567i	−0.108989	+	1.03696i	0.794181	+	0.607681i	$0.207900\pi$
$503$	−2.44437	+	23.2567i	−0.108989	+	1.03696i	−0.903170	+	0.429282i	$0.858766\pi$
$504$	24.3855	−	17.7171i	1.08622	−	0.789182i
$505$	−0.886953	−	8.43880i	−0.0394689	−	0.375522i
$506$	−33.8764	−	37.6235i	−1.50599	−	1.67257i
$507$	21.2981	−	9.48254i	0.945883	−	0.421134i
$508$	40.8161	−	8.67572i	1.81092	−	0.384923i
$509$	−6.65042	−	1.41359i	−0.294774	−	0.0626563i	0.0581506	−	0.998308i	$-0.481480\pi$
$509$	−6.65042	−	1.41359i	−0.294774	−	0.0626563i	−0.352925	+	0.935652i	$0.614813\pi$
$510$	−0.913545	−	0.406737i	−0.0404525	−	0.0180106i
$511$	2.85613	+	8.79027i	0.126348	+	0.388859i
$512$	9.65451	+	29.7135i	0.426673	+	1.31316i
$513$	0.600066	+	0.267167i	0.0264936	+	0.0117957i
$514$	−0.740809	−	0.157464i	−0.0326757	−	0.00694543i
$515$	11.8073	−	2.50972i	0.520291	−	0.110591i
$516$	−75.1435	+	33.4561i	−3.30801	+	1.47282i
$517$	5.81226	+	6.45517i	0.255623	+	0.283898i
$518$	0.609237	+	5.79650i	0.0267683	+	0.254684i
$519$	−27.9567	+	20.3117i	−1.22716	+	0.891585i
$520$	0.843656	−	8.02685i	0.0369968	−	0.352001i
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	−0.978698	−	0.205304i	$-0.934182\pi$
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	0.311551	−	0.950229i	$-0.399152\pi$
$522$	−4.00000	+	6.92820i	−0.175075	+	0.303239i
$523$	6.47214	+	4.70228i	0.283007	+	0.205616i	0.720228	−	0.693738i	$-0.244037\pi$
$523$	6.47214	+	4.70228i	0.283007	+	0.205616i	−0.437221	+	0.899354i	$0.644037\pi$
$524$	−12.1870	+	13.5350i	−0.532392	+	0.591281i
$525$	7.20433	−	22.1727i	0.314423	−	0.967694i
$526$	1.65685			0.0722423
$527$		0			0
$528$	37.9706			1.65246
$529$	−2.16312	+	6.65740i	−0.0940487	+	0.289452i
$530$	−0.277163	+	0.307821i	−0.0120392	+	0.0133709i
$531$	23.0451	+	16.7432i	1.00007	+	0.726594i
$532$	−7.32843	+	12.6932i	−0.317728	+	0.550320i
$533$	−8.67157	−	15.0196i	−0.375608	−	0.650571i
$534$	7.60649	−	72.3709i	0.329165	−	3.13180i
$535$	−7.75506	+	5.63438i	−0.335281	+	0.243596i
$536$	−2.41901	−	23.0154i	−0.104485	−	0.994112i
$537$	10.9160	+	12.1234i	0.471060	+	0.523165i
$538$	70.1974	−	31.2539i	3.02642	−	1.34745i
$539$	−6.00792	+	1.27702i	−0.258779	+	0.0550052i
$540$	−1.55113	−	0.329704i	−0.0667501	−	0.0141882i
$541$	23.0983	+	10.2840i	0.993075	+	0.442145i	0.837949	−	0.545749i	$-0.183755\pi$
$541$	23.0983	+	10.2840i	0.993075	+	0.442145i	0.155126	+	0.987895i	$0.450422\pi$
$542$	17.3928	+	53.5295i	0.747085	+	2.29929i
$543$	7.69437	+	23.6808i	0.330197	+	1.01624i
$544$	−0.248556	−	0.110664i	−0.0106567	−	0.00474468i
$545$	5.05856	+	1.07523i	0.216685	+	0.0460578i
$546$	−25.1657	+	5.34914i	−1.07699	+	0.228922i
$547$	5.23272	−	2.32976i	0.223735	−	0.0996132i	−0.291808	−	0.956477i	$-0.594257\pi$
$547$	5.23272	−	2.32976i	0.223735	−	0.0996132i	0.515543	+	0.856864i	$0.327590\pi$
$548$	−19.1752	−	21.2962i	−0.819123	−	0.909728i
$549$	−0.836228	−	7.95618i	−0.0356893	−	0.339561i
$550$	40.9584	−	29.7580i	1.74647	−	1.26889i
$551$	0.194200	−	1.84769i	0.00827319	−	0.0787141i
$552$	21.3137	+	36.9164i	0.907172	+	1.57127i
$553$	18.3995	−	31.8689i	0.782426	−	1.35520i
$554$	−27.6216	−	20.0682i	−1.17353	−	0.852618i
$555$	−1.61542	+	1.79411i	−0.0685709	+	0.0761557i
$556$		0			0
$557$	44.4853			1.88490			0.942451	−	0.334344i	$-0.108515\pi$
$557$	44.4853			1.88490			0.942451	+	0.334344i	$0.108515\pi$
$558$		0			0
$559$	16.2721			0.688236
$560$	2.23810	−	6.88816i	0.0945769	−	0.291078i
$561$	−1.45307	+	1.61379i	−0.0613485	+	0.0681344i
$562$	3.90628	+	2.83808i	0.164776	+	0.119717i
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	−0.911787	−	0.410663i	$-0.865297\pi$
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	0.811538	+	0.584300i	$0.198631\pi$
$564$	−7.65685	−	13.2621i	−0.322412	−	0.558433i
$565$	−0.558511	+	5.31388i	−0.0234967	+	0.223556i
$566$	−4.57649	+	3.32502i	−0.192364	+	0.139761i
$567$	2.39365	+	22.7740i	0.100524	+	0.956420i
$568$	41.5615	+	46.1587i	1.74388	+	1.93678i
$569$	13.8330	−	6.15886i	0.579911	−	0.258193i	−0.0957502	−	0.995405i	$-0.530525\pi$
$569$	13.8330	−	6.15886i	0.579911	−	0.258193i	0.675661	+	0.737212i	$0.263858\pi$
$570$	−9.04067	+	1.92165i	−0.378672	+	0.0804892i
$571$	40.0057	+	8.50348i	1.67419	+	0.355860i	0.944650	−	0.328080i	$-0.106402\pi$
$571$	40.0057	+	8.50348i	1.67419	+	0.355860i	0.729538	+	0.683940i	$0.239735\pi$
$572$	−33.5257	−	14.9266i	−1.40178	−	0.624113i
$573$	0.821013	+	2.52682i	0.0342983	+	0.105559i
$574$	−17.0838	−	52.5785i	−0.713063	−	2.19458i
$575$	14.6167	+	6.50779i	0.609560	+	0.271393i
$576$	27.1915	+	5.77973i	1.13298	+	0.240822i
$577$	33.2282	−	7.06288i	1.38331	−	0.294031i	0.544639	−	0.838671i	$-0.316667\pi$
$577$	33.2282	−	7.06288i	1.38331	−	0.294031i	0.838670	+	0.544639i	$0.183333\pi$
$578$	37.4285	−	16.6642i	1.55682	−	0.693141i
$579$	34.1535	+	37.9313i	1.41937	+	1.57637i
$580$	0.468840	+	4.46071i	0.0194675	+	0.185221i
$581$	−7.95136	+	5.77700i	−0.329878	+	0.239671i
$582$	−6.59707	+	62.7670i	−0.273457	+	2.60177i
$583$	0.449747	+	0.778985i	0.0186266	+	0.0322623i
$584$	8.44975	−	14.6354i	0.349653	−	0.605617i
$585$	−4.18389	−	3.03977i	−0.172983	−	0.125679i
$586$	40.0609	−	44.4921i	1.65490	−	1.83795i
$587$	−6.28638	+	19.3475i	−0.259467	+	0.798556i	0.733450	+	0.679743i	$0.237909\pi$
$587$	−6.28638	+	19.3475i	−0.259467	+	0.798556i	−0.992917	+	0.118813i	$0.962091\pi$
$588$	10.8284			0.446557
$589$		0			0
$590$	24.3137			1.00098
$591$	−2.60013	+	8.00239i	−0.106955	+	0.329174i
$592$	2.00739	−	2.22943i	0.0825033	−	0.0916292i
$593$	−17.2432	−	12.5279i	−0.708091	−	0.514459i	0.174466	−	0.984663i	$-0.444180\pi$
$593$	−17.2432	−	12.5279i	−0.708091	−	0.514459i	−0.882557	+	0.470205i	$0.844180\pi$
$594$	−2.62132	+	4.54026i	−0.107554	+	0.186289i
$595$	0.207107	+	0.358719i	0.00849055	+	0.0147061i
$596$	−0.400180	+	3.80745i	−0.0163920	+	0.155959i
$597$	30.4412	−	22.1168i	1.24588	−	0.905182i
$598$	−1.84564	−	17.5601i	−0.0754740	−	0.718087i
$599$	23.3523	+	25.9354i	0.954150	+	1.05969i	0.998159	+	0.0606597i	$0.0193204\pi$
$599$	23.3523	+	25.9354i	0.954150	+	1.05969i	−0.0440086	+	0.999031i	$0.514013\pi$
$600$	−38.9421	+	17.3381i	−1.58980	+	0.707826i
$601$	22.9721	−	4.88286i	0.937050	−	0.199176i	0.286016	−	0.958225i	$-0.407669\pi$
$601$	22.9721	−	4.88286i	0.937050	−	0.199176i	0.651034	+	0.759049i	$0.274336\pi$
$602$	50.7366	+	10.7844i	2.06787	+	0.439539i
$603$	−13.5464	−	6.03126i	−0.551654	−	0.245612i
$604$	−20.4830	−	63.0401i	−0.833440	−	2.56506i
$605$	5.09423	+	15.6784i	0.207110	+	0.637419i
$606$	45.1802	+	20.1155i	1.83532	+	0.817136i
$607$	4.31775	+	0.917767i	0.175252	+	0.0372510i	0.294702	−	0.955589i	$-0.404780\pi$
$607$	4.31775	+	0.917767i	0.175252	+	0.0372510i	−0.119450	+	0.992840i	$0.538113\pi$
$608$	−2.45977	+	0.522839i	−0.0997567	+	0.0212039i
$609$	6.23808	−	2.77737i	0.252780	−	0.112545i
$610$	−4.56911	−	5.07451i	−0.184998	−	0.205461i
$611$	0.316662	+	3.01284i	0.0128108	+	0.121887i
$612$	1.50304	−	1.09203i	0.0607569	−	0.0441425i
$613$	1.07808	−	10.2572i	0.0435431	−	0.414285i	−0.950939	−	0.309378i	$-0.899879\pi$
$613$	1.07808	−	10.2572i	0.0435431	−	0.414285i	0.994482	−	0.104906i	$-0.0334543\pi$
$614$	−3.32843	−	5.76500i	−0.134324	−	0.232657i
$615$	11.4497	−	19.8315i	0.461698	−	0.799685i
$616$	−45.1998	−	32.8396i	−1.82115	−	1.32315i
$617$	15.5802	−	17.3036i	0.627236	−	0.696616i	−0.342847	−	0.939391i	$-0.611391\pi$
$617$	15.5802	−	17.3036i	0.627236	−	0.696616i	0.970083	+	0.242775i	$0.0780578\pi$
$618$	−21.7410	+	66.9119i	−0.874551	+	2.69159i
$619$	−31.6569			−1.27240			−0.636198	−	0.771526i	$-0.719494\pi$
$619$	−31.6569			−1.27240			−0.636198	+	0.771526i	$0.719494\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$	8.44040	−	25.9769i	0.338429	−	1.04158i
$623$	−20.1690	+	22.4000i	−0.808055	+	0.897436i
$624$	10.7135	+	7.78383i	0.428884	+	0.311603i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	4.62132	+	8.00436i	0.184705	+	0.319919i
$627$	−2.09800	+	19.9611i	−0.0837860	+	0.797170i
$628$	−45.9275	+	33.3683i	−1.83271	+	1.33154i
$629$	0.0179342	+	0.170633i	0.000715085	+	0.00680358i
$630$	−11.0308	−	12.2510i	−0.439478	−	0.488090i
$631$	−29.2446	+	13.0205i	−1.16421	+	0.518339i	−0.895578	−	0.444904i	$-0.853238\pi$
$631$	−29.2446	+	13.0205i	−1.16421	+	0.518339i	−0.268631	+	0.963243i	$0.586571\pi$
$632$	−65.8139	+	13.9892i	−2.61794	+	0.556460i
$633$	17.9135	+	3.80763i	0.711998	+	0.151340i
$634$	4.78939	+	2.13237i	0.190211	+	0.0846874i
$635$	−3.36813	−	10.3660i	−0.133660	−	0.411364i
$636$	−0.490035	−	1.50817i	−0.0194312	−	0.0598029i
$637$	−1.95694	−	0.871285i	−0.0775367	−	0.0345216i
$638$	14.5044	+	3.08300i	0.574234	+	0.122057i
$639$	38.9293	−	8.27468i	1.54002	−	0.327341i
$640$	18.7792	−	8.36102i	0.742311	−	0.330498i
$641$	13.3629	+	14.8410i	0.527803	+	0.586185i	0.946808	−	0.321799i	$-0.104288\pi$
$641$	13.3629	+	14.8410i	0.527803	+	0.586185i	−0.419005	+	0.907984i	$0.637621\pi$
$642$	−5.84001	−	55.5640i	−0.230487	−	2.19294i
$643$	−10.2634	+	7.45682i	−0.404750	+	0.294068i	−0.771473	−	0.636262i	$-0.780480\pi$
$643$	−10.2634	+	7.45682i	−0.404750	+	0.294068i	0.366723	+	0.930330i	$0.380480\pi$
$644$	3.86448	−	36.7680i	0.152282	−	1.44886i
$645$	10.7426	+	18.6068i	0.422991	+	0.732642i
$646$	−0.328427	+	0.568852i	−0.0129218	+	0.0223812i
$647$	18.3536	+	13.3347i	0.721554	+	0.524240i	0.886880	−	0.461999i	$-0.152868\pi$
$647$	18.3536	+	13.3347i	0.721554	+	0.524240i	−0.165326	+	0.986239i	$0.552868\pi$
$648$	28.0165	−	31.1155i	1.10059	−	1.22233i
$649$	16.3158	−	50.2148i	0.640451	−	1.97110i
$650$	17.6569			0.692559
$651$		0			0
$652$	−49.6569			−1.94471
$653$	6.84230	−	21.0584i	0.267760	−	0.824080i	−0.723285	−	0.690550i	$-0.757369\pi$
$653$	6.84230	−	21.0584i	0.267760	−	0.824080i	0.991045	−	0.133530i	$-0.0426313\pi$
$654$	−20.1690	+	22.4000i	−0.788671	+	0.875908i
$655$	3.84878	+	2.79631i	0.150384	+	0.109261i
$656$	−14.2279	+	24.6435i	−0.555507	+	0.962166i
$657$	−5.41421	−	9.37769i	−0.211229	−	0.365859i
$658$	−1.00942	+	9.60395i	−0.0393511	+	0.374401i
$659$	−7.81256	+	5.67616i	−0.304334	+	0.221112i	−0.729462	−	0.684022i	$-0.760229\pi$
$659$	−7.81256	+	5.67616i	−0.304334	+	0.221112i	0.425127	+	0.905134i	$0.360229\pi$
$660$	−5.06501	−	48.1904i	−0.197155	−	1.87581i
$661$	22.1764	+	24.6294i	0.862563	+	0.957973i	0.999468	−	0.0326112i	$-0.0103823\pi$
$661$	22.1764	+	24.6294i	0.862563	+	0.957973i	−0.136905	+	0.990584i	$0.543716\pi$
$662$	−1.67035	+	0.743688i	−0.0649200	+	0.0289043i
$663$	−0.740809	+	0.157464i	−0.0287706	+	0.00611539i
$664$	17.5779	+	3.73629i	0.682153	+	0.144996i
$665$	3.49744	+	1.55716i	0.135625	+	0.0603841i
$666$	−2.11010	−	6.49422i	−0.0817647	−	0.251646i
$667$	1.44814	+	4.45693i	0.0560723	+	0.172573i
$668$	−29.9253	−	13.3236i	−1.15785	−	0.515506i
$669$	4.08041	+	0.867319i	0.157758	+	0.0335325i
$670$	−12.3803	+	2.63151i	−0.478292	+	0.101664i
$671$	−13.5464	+	6.03126i	−0.522955	+	0.232834i
$672$	−6.18453	−	6.86862i	−0.238574	−	0.264963i
$673$	−2.15923	−	20.5437i	−0.0832322	−	0.791901i	−0.953919	−	0.300064i	$-0.902992\pi$
$673$	−2.15923	−	20.5437i	−0.0832322	−	0.791901i	0.870687	−	0.491838i	$-0.163675\pi$
$674$	−26.0035	+	18.8927i	−1.00162	+	0.727719i
$675$	0.173188	−	1.64778i	0.00666603	−	0.0634230i
$676$	18.4853	+	32.0174i	0.710972	+	1.23144i
$677$	−20.2990	+	35.1589i	−0.780154	+	1.35127i	0.151698	+	0.988427i	$0.451526\pi$
$677$	−20.2990	+	35.1589i	−0.780154	+	1.35127i	−0.931852	+	0.362839i	$0.881808\pi$
$678$	−25.1945	−	18.3049i	−0.967590	−	0.702995i
$679$	17.4925	−	19.4274i	0.671301	−	0.745555i
$680$	0.234037	−	0.720292i	0.00897491	−	0.0276219i
$681$	37.6274			1.44189
$682$		0			0
$683$	−46.6274			−1.78415			−0.892074	−	0.451889i	$-0.850750\pi$
$683$	−46.6274			−1.78415			−0.892074	+	0.451889i	$0.850750\pi$
$684$	5.30631	−	16.3311i	0.202892	−	0.624437i
$685$	−5.00863	+	5.56265i	−0.191370	+	0.212538i
$686$	−38.5314	−	27.9947i	−1.47114	−	1.06884i
$687$	13.8640	−	24.0131i	0.528943	−	0.916156i
$688$	−13.3492	−	23.1216i	−0.508935	−	0.881501i
$689$	−0.0327915	+	0.311990i	−0.00124926	+	0.0118859i
$690$	18.8612	−	13.7035i	0.718033	−	0.521682i
$691$	−1.47083	−	13.9940i	−0.0559529	−	0.532356i	−0.986216	−	0.165463i	$-0.947088\pi$
$691$	−1.47083	−	13.9940i	−0.0559529	−	0.532356i	0.930263	−	0.366893i	$-0.119579\pi$
$692$	−36.6677	−	40.7236i	−1.39390	−	1.54808i
$693$	−32.7040	+	14.5608i	−1.24232	+	0.553118i
$694$	53.2659	−	11.3220i	2.02194	−	0.429777i
$695$		0			0
$696$	−11.4059	−	5.07822i	−0.432338	−	0.192489i
$697$	−0.502900	−	1.54777i	−0.0190487	−	0.0586258i
$698$	−26.1952	−	80.6206i	−0.991504	−	3.05154i
$699$	32.7040	+	14.5608i	1.23698	+	0.550739i
$700$	36.1627	+	7.68661i	1.36682	+	0.290527i
$701$	−3.40912	+	0.724631i	−0.128761	+	0.0273689i	−0.271841	−	0.962342i	$-0.587633\pi$
$701$	−3.40912	+	0.724631i	−0.128761	+	0.0273689i	0.143081	+	0.989711i	$0.454299\pi$
$702$	−1.67035	+	0.743688i	−0.0630433	+	0.0280687i
$703$	1.06110	+	1.17847i	0.0400201	+	0.0444468i
$704$	−5.38603	−	51.2446i	−0.202994	−	1.93136i
$705$	−3.23607	+	2.35114i	−0.121877	+	0.0885491i
$706$	0.757062	−	7.20296i	0.0284924	−	0.271087i
$707$	−10.2426	−	17.7408i	−0.385214	−	0.667210i
$708$	−46.5416	+	80.6125i	−1.74914	+	3.02960i
$709$	4.29888	+	3.12332i	0.161448	+	0.117299i	0.665576	−	0.746330i	$-0.268186\pi$
$709$	4.29888	+	3.12332i	0.161448	+	0.117299i	−0.504128	+	0.863629i	$0.668186\pi$
$710$	22.7307	−	25.2450i	0.853070	−	0.947430i
$711$	−13.3226	+	41.0026i	−0.499635	+	1.53772i
$712$	55.1127			2.06544
$713$		0			0
$714$	−2.41421			−0.0903497
$715$	−2.96217	+	9.11662i	−0.110779	+	0.340942i
$716$	−17.3104	+	19.2252i	−0.646922	+	0.718479i
$717$	−24.9169	−	18.1032i	−0.930539	−	0.676076i
$718$	32.4706	−	56.2407i	1.21179	−	2.09888i
$719$	−3.03553	−	5.25770i	−0.113206	−	0.196079i	0.803855	−	0.594825i	$-0.202779\pi$
$719$	−3.03553	−	5.25770i	−0.113206	−	0.196079i	−0.917061	+	0.398746i	$0.869445\pi$
$720$	−0.886953	+	8.43880i	−0.0330548	+	0.314495i
$721$	23.5765	−	17.1293i	0.878034	−	0.637929i
$722$	−4.16013	−	39.5810i	−0.154824	−	1.47305i
$723$	−39.8313	−	44.2371i	−1.48134	−	1.64520i
$724$	−36.0716	+	16.0601i	−1.34059	+	0.596869i
$725$	−4.58388	+	0.974335i	−0.170241	+	0.0361859i
$726$	−93.9836	−	19.9768i	−3.48806	−	0.741410i
$727$	−42.7910	−	19.0518i	−1.58703	−	0.706592i	−0.591980	−	0.805953i	$-0.701654\pi$
$727$	−42.7910	−	19.0518i	−1.58703	−	0.706592i	−0.995052	+	0.0993605i	$0.968320\pi$
$728$	−6.02128	−	18.5316i	−0.223164	−	0.686827i
$729$	−7.36339	−	22.6622i	−0.272718	−	0.839340i
$730$	−8.44357	−	3.75932i	−0.312511	−	0.139139i
$731$	1.49355	+	0.317463i	0.0552408	+	0.0117418i
$732$	25.5709	−	5.43526i	0.945126	−	0.200893i
$733$	−27.0660	+	12.0506i	−0.999705	+	0.445097i	−0.840303	−	0.542116i	$-0.817623\pi$
$733$	−27.0660	+	12.0506i	−0.999705	+	0.445097i	−0.159402	+	0.987214i	$0.550957\pi$
$734$	−29.4220	−	32.6765i	−1.08599	−	1.20611i
$735$	−0.295651	−	2.81293i	−0.0109053	−	0.103757i
$736$	5.13171	−	3.72841i	0.189157	−	0.137431i
$737$	−2.87299	+	27.3347i	−0.105828	+	1.00689i
$738$	32.3848	+	56.0921i	1.19210	+	2.06478i
$739$	3.93503	−	6.81567i	0.144752	−	0.250718i	−0.784528	−	0.620093i	$-0.787095\pi$
$739$	3.93503	−	6.81567i	0.144752	−	0.250718i	0.929281	+	0.369375i	$0.120428\pi$
$740$	−3.09726	−	2.25029i	−0.113858	−	0.0827224i
$741$	−4.68391	+	5.20201i	−0.172068	+	0.191101i
$742$	−0.309017	+	0.951057i	−0.0113444	+	0.0349144i
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−7.46033	+	22.9605i	−0.273142	+	0.840645i
$747$	7.70485	−	8.55710i	0.281906	−	0.313088i
$748$	−2.78597	−	2.02413i	−0.101865	−	0.0740094i
$749$	−11.5711	+	20.0417i	−0.422798	+	0.732307i
$750$	26.2279	+	45.4281i	0.957708	+	1.65880i
$751$	0.129891	−	1.23583i	0.00473980	−	0.0450962i	−0.991896	−	0.127050i	$-0.959449\pi$
$751$	0.129891	−	1.23583i	0.00473980	−	0.0450962i	0.996636	+	0.0819535i	$0.0261159\pi$
$752$	4.02127	−	2.92162i	0.146641	−	0.106541i
$753$	0.904888	+	8.60943i	0.0329759	+	0.313745i
$754$	3.46046	+	3.84323i	0.126022	+	0.139962i
$755$	−15.8169	+	7.04212i	−0.575634	+	0.256289i
$756$	−3.74477	+	0.795975i	−0.136196	+	0.0289493i
$757$	−33.8995	−	7.20557i	−1.23210	−	0.261891i	−0.454555	−	0.890719i	$-0.650202\pi$
$757$	−33.8995	−	7.20557i	−1.23210	−	0.261891i	−0.777544	+	0.628828i	$0.783535\pi$
$758$	64.8079	+	28.8544i	2.35393	+	1.04804i
$759$	−15.6447	−	48.1495i	−0.567868	−	1.74772i
$760$	−2.16312	−	6.65740i	−0.0784646	−	0.241489i
$761$	−18.6873	−	8.32014i	−0.677416	−	0.301605i	0.0390399	−	0.999238i	$-0.487570\pi$
$761$	−18.6873	−	8.32014i	−0.677416	−	0.301605i	−0.716456	+	0.697633i	$0.754237\pi$
$762$	62.1387	+	13.2080i	2.25105	+	0.478475i
$763$	12.2124	−	2.59584i	0.442120	−	0.0939756i
$764$	−3.84895	+	1.71366i	−0.139250	+	0.0619982i
$765$	−0.324717	−	0.360634i	−0.0117402	−	0.0130388i
$766$	6.28349	+	59.7834i	0.227032	+	2.16006i
$767$	14.8974	−	10.8236i	0.537914	−	0.390818i
$768$	−7.56319	+	71.9590i	−0.272913	+	2.59660i
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	0.999443	−	0.0333680i	$-0.0106233\pi$
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	−0.528619	+	0.848859i	$0.677290\pi$
$770$	−15.2782	+	26.4626i	−0.550587	+	0.953645i
$771$	−0.612717	−	0.445165i	−0.0220664	−	0.0160322i
$772$	−54.1602	+	60.1510i	−1.94927	+	2.16488i
$773$	5.56231	−	17.1190i	0.200062	−	0.615728i	−0.799818	−	0.600243i	$-0.795071\pi$
$773$	5.56231	−	17.1190i	0.200062	−	0.615728i	0.999880	−	0.0154855i	$-0.00492938\pi$
$774$	−60.7696			−2.18432
$775$		0			0
$776$	−47.7990			−1.71588
$777$	−1.80108	+	5.54316i	−0.0646135	+	0.198860i
$778$	−27.6918	+	30.7549i	−0.992800	+	1.10262i
$779$	−12.1689	−	8.84125i	−0.435997	−	0.316771i
$780$	8.44975	−	14.6354i	0.302549	−	0.524031i
$781$	−36.8848	−	63.8863i	−1.31984	−	2.28603i
$782$	0.173188	−	1.64778i	0.00619321	−	0.0589244i
$783$	0.392601	−	0.285241i	0.0140304	−	0.0101937i
$784$	0.367388	+	3.49546i	0.0131210	+	0.124838i
$785$	9.92215	+	11.0197i	0.354137	+	0.393309i
$786$	−25.3307	+	11.2780i	−0.903517	+	0.402272i
$787$	−38.7207	+	8.23035i	−1.38025	+	0.293380i	−0.837463	−	0.546493i	$-0.815962\pi$
$787$	−38.7207	+	8.23035i	−1.38025	+	0.293380i	−0.542782	+	0.839874i	$0.682629\pi$
$788$	−13.0516	−	2.77420i	−0.464943	−	0.0988266i
$789$	1.51361	+	0.673903i	0.0538860	+	0.0239916i
$790$	11.3715	+	34.9979i	0.404580	+	1.24517i
$791$	3.98616	+	12.2681i	0.141732	+	0.436205i
$792$	59.7969	+	26.6233i	2.12479	+	0.946017i
$793$	−5.05856	−	1.07523i	−0.179635	−	0.0381826i
$794$	−38.9988	+	8.28945i	−1.38402	+	0.294182i
$795$	−0.378403	+	0.168476i	−0.0134206	+	0.00597522i
$796$	39.9264	+	44.3427i	1.41515	+	1.57169i
$797$	2.34727	+	22.3328i	0.0831447	+	0.791069i	0.954056	+	0.299629i	$0.0968628\pi$
$797$	2.34727	+	22.3328i	0.0831447	+	0.791069i	−0.870911	+	0.491441i	$0.836471\pi$
$798$	−18.0522	+	13.1157i	−0.639040	+	0.464290i
$799$	−0.0297144	+	0.282714i	−0.00105122	+	0.0100017i
$800$	3.17157	+	5.49333i	0.112132	+	0.194218i
$801$	17.6569	−	30.5826i	0.623874	−	1.08058i
$802$	−41.3510	−	30.0433i	−1.46016	−	1.06087i
$803$	−13.4302	+	14.9157i	−0.473940	+	0.526364i
$804$	14.9737	−	46.0842i	0.528081	−	1.62527i
$805$	−9.65685			−0.340359
$806$		0			0
$807$	76.8406			2.70492
$808$	−11.5745	+	35.6226i	−0.407189	+	1.25320i
$809$	−30.7603	+	34.1628i	−1.08147	+	1.20110i	−0.103011	+	0.994680i	$0.532848\pi$
$809$	−30.7603	+	34.1628i	−1.08147	+	1.20110i	−0.978464	+	0.206419i	$0.933819\pi$
$810$	−18.5261	−	13.4600i	−0.650940	−	0.472936i
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	−0.950423	−	0.310961i	$-0.899349\pi$
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	0.744511	+	0.667610i	$0.232683\pi$
$812$	5.41421	+	9.37769i	0.190002	+	0.329093i
$813$	−5.88331	+	55.9759i	−0.206337	+	1.96316i
$814$	−10.2396	+	7.43951i	−0.358898	+	0.260755i
$815$	1.35579	+	12.8995i	0.0474914	+	0.451850i
$816$	0.831489	+	0.923462i	0.0291079	+	0.0323276i
$817$	12.8926	−	5.74015i	0.451055	−	0.200822i
$818$	22.0634	−	4.68973i	0.771430	−	0.163973i
$819$	−12.2124	−	2.59584i	−0.426737	−	0.0907058i
$820$	33.1742	+	14.7701i	1.15849	+	0.515795i
$821$	−2.62210	−	8.06998i	−0.0915118	−	0.281644i	0.894817	−	0.446433i	$-0.147306\pi$
$821$	−2.62210	−	8.06998i	−0.0915118	−	0.281644i	−0.986329	+	0.164789i	$0.947306\pi$
$822$	−13.4816	−	41.4921i	−0.470225	−	1.44720i
$823$	−5.67604	−	2.52714i	−0.197854	−	0.0880905i	0.305418	−	0.952219i	$-0.401204\pi$
$823$	−5.67604	−	2.52714i	−0.197854	−	0.0880905i	−0.503272	+	0.864128i	$0.667871\pi$
$824$	−52.1199	−	11.0784i	−1.81568	−	0.385935i
$825$	49.5211	−	10.5260i	1.72410	−	0.366469i
$826$	53.6237	−	23.8748i	1.86581	−	0.830711i
$827$	11.4425	+	12.7082i	0.397894	+	0.441906i	0.908485	−	0.417918i	$-0.137240\pi$
$827$	11.4425	+	12.7082i	0.397894	+	0.441906i	−0.510591	+	0.859824i	$0.670573\pi$
$828$	4.52752	+	43.0764i	0.157342	+	1.49701i
$829$	37.5598	−	27.2888i	1.30450	−	0.947778i	0.304515	−	0.952507i	$-0.401506\pi$
$829$	37.5598	−	27.2888i	1.30450	−	0.947778i	0.999989	+	0.00472973i	$0.00150553\pi$
$830$	1.02735	−	9.77459i	0.0356599	−	0.339281i
$831$	−17.0711	−	29.5680i	−0.592189	−	1.02570i
$832$	8.98528	−	15.5630i	0.311509	−	0.539549i
$833$	−0.162621	−	0.118151i	−0.00563447	−	0.00409368i
$834$		0			0
$835$	−2.64406	+	8.13757i	−0.0915014	+	0.281612i
$836$	−31.8284			−1.10081
$837$		0			0
$838$	−67.5980			−2.33513
$839$	9.46439	−	29.1284i	0.326747	−	1.00562i	−0.643899	−	0.765111i	$-0.722684\pi$
$839$	9.46439	−	29.1284i	0.326747	−	1.00562i	0.970646	−	0.240513i	$-0.0773158\pi$
$840$	17.2153	−	19.1196i	0.593986	−	0.659688i
$841$	22.3510	+	16.2390i	0.770726	+	0.559965i
$842$	−3.44975	+	5.97514i	−0.118886	+	0.205917i
$843$	2.41421	+	4.18154i	0.0831499	+	0.144020i
$844$	−3.03568	+	28.8825i	−0.104492	+	0.994178i
$845$	7.81256	−	5.67616i	0.268760	−	0.195266i
$846$	−1.18260	−	11.2517i	−0.0406588	−	0.386842i
$847$	26.6307	+	29.5764i	0.915042	+	1.01626i
$848$	0.470219	−	0.209355i	0.0161474	−	0.00718928i
$849$	−5.53324	+	1.17613i	−0.189900	+	0.0403645i
$850$	1.62065	+	0.344479i	0.0555878	+	0.0118155i
$851$	−3.65418	−	1.62695i	−0.125264	−	0.0557710i
$852$	40.1888	+	123.689i	1.37685	+	4.23750i
$853$	−10.0385	−	30.8953i	−0.343712	−	1.05784i	−0.962270	−	0.272097i	$-0.912283\pi$
$853$	−10.0385	−	30.8953i	−0.343712	−	1.05784i	0.618558	−	0.785739i	$-0.287717\pi$
$854$	−15.0601	−	6.70517i	−0.515344	−	0.229446i
$855$	−4.38727	−	0.932542i	−0.150041	−	0.0318923i
$856$	41.3891	−	8.79751i	1.41465	−	0.300693i
$857$	−2.29731	+	1.02283i	−0.0784746	+	0.0349391i	−0.445599	−	0.895233i	$-0.647009\pi$
$857$	−2.29731	+	1.02283i	−0.0784746	+	0.0349391i	0.367124	+	0.930172i	$0.380342\pi$
$858$	−37.3844	−	41.5195i	−1.27628	−	1.41745i
$859$	1.31865	+	12.5461i	0.0449918	+	0.428068i	0.993713	+	0.111955i	$0.0357112\pi$
$859$	1.31865	+	12.5461i	0.0449918	+	0.428068i	−0.948722	+	0.316113i	$0.897622\pi$
$860$	−27.5641	+	20.0265i	−0.939927	+	0.682897i
$861$	5.77878	−	54.9814i	0.196940	−	1.87376i
$862$	−30.4706	−	52.7766i	−1.03783	−	1.79758i
$863$	19.6924	−	34.1082i	0.670337	−	1.16106i	−0.307472	−	0.951557i	$-0.599483\pi$
$863$	19.6924	−	34.1082i	0.670337	−	1.16106i	0.977809	−	0.209500i	$-0.0671836\pi$
$864$	−0.531406	−	0.386089i	−0.0180788	−	0.0131350i
$865$	−9.57774	+	10.6372i	−0.325653	+	0.361674i
$866$	26.1952	−	80.6206i	0.890150	−	2.73960i
$867$	40.9706			1.39143
$868$		0			0
$869$	79.9117			2.71082
$870$	−2.11010	+	6.49422i	−0.0715391	+	0.220175i
$871$	−6.41414	+	7.12363i	−0.217335	+	0.241375i
$872$	−18.4686	−	13.4182i	−0.625425	−	0.454398i
$873$	−15.3137	+	26.5241i	−0.518291	+	0.897705i
$874$	−7.65685	−	13.2621i	−0.258997	−	0.448596i
$875$	2.27119	−	21.6089i	0.0767801	−	0.730514i
$876$	28.6269	−	20.7986i	0.967213	−	0.702721i
$877$	−5.03530	−	47.9077i	−0.170030	−	1.61773i	−0.663645	−	0.748047i	$-0.730992\pi$
$877$	−5.03530	−	47.9077i	−0.170030	−	1.61773i	0.493615	−	0.869680i	$-0.335675\pi$
$878$	19.4999	+	21.6568i	0.658090	+	0.730883i
$879$	54.6940	−	24.3513i	1.84478	−	0.821351i
$880$	15.3842	−	3.27002i	0.518602	−	0.110232i
$881$	−33.5639	−	7.13422i	−1.13080	−	0.240358i	−0.395738	−	0.918363i	$-0.629511\pi$
$881$	−33.5639	−	7.13422i	−1.13080	−	0.240358i	−0.735057	+	0.678005i	$0.762845\pi$
$882$	7.30836	+	3.25389i	0.246085	+	0.109564i
$883$	8.12229	+	24.9978i	0.273337	+	0.841244i	0.989655	+	0.143470i	$0.0458260\pi$
$883$	8.12229	+	24.9978i	0.273337	+	0.841244i	−0.716318	+	0.697774i	$0.754174\pi$
$884$	−0.371133	−	1.14223i	−0.0124825	−	0.0384173i
$885$	22.2117	+	9.88928i	0.746637	+	0.332424i
$886$	−31.2719	−	6.64705i	−1.05060	−	0.223312i
$887$	−52.1606	+	11.0871i	−1.75138	+	0.372268i	−0.968327	−	0.249685i	$-0.919673\pi$
$887$	−52.1606	+	11.0871i	−1.75138	+	0.372268i	−0.783055	+	0.621953i	$0.786339\pi$
$888$	9.73552	−	4.33453i	0.326703	−	0.145457i
$889$	−17.6073	−	19.5549i	−0.590530	−	0.655850i
$890$	−3.15071	−	29.9770i	−0.105612	−	1.00483i
$891$	−40.2307	+	29.2293i	−1.34778	+	0.979220i
$892$	−0.691479	+	6.57898i	−0.0231524	+	0.220281i
$893$	1.31371	+	2.27541i	0.0439616	+	0.0761437i
$894$	−2.91421	+	5.04757i	−0.0974659	+	0.168816i
$895$	5.46682	+	3.97188i	0.182736	+	0.132765i
$896$	33.2072	−	36.8804i	1.10938	−	1.23209i
$897$	5.45627	−	16.7927i	0.182179	−	0.560691i
$898$	−11.1716			−0.372800
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−0.00909661	+	0.0279965i	−0.000303052	+	0.000932698i
$902$	80.3317	−	89.2174i	2.67475	−	2.97061i
$903$	41.9638	+	30.4885i	1.39647	+	1.01459i
$904$	11.7929	−	20.4259i	0.392226	−	0.679355i
$905$	5.15685	+	8.93193i	0.171420	+	0.296908i
$906$	10.5481	−	100.359i	0.350439	−	3.33420i
$907$	−44.7497	+	32.5126i	−1.48589	+	1.07956i	−0.510292	+	0.860001i	$0.670463\pi$
$907$	−44.7497	+	32.5126i	−1.48589	+	1.07956i	−0.975599	+	0.219561i	$0.929537\pi$
$908$	6.23711	+	59.3422i	0.206986	+	1.96934i
$909$	16.0591	+	17.8355i	0.532648	+	0.591565i
$910$	−9.73552	+	4.33453i	−0.322729	+	0.143688i
$911$	−47.9700	+	10.1963i	−1.58932	+	0.337819i	−0.915888	−	0.401434i	$-0.868512\pi$
$911$	−47.9700	+	10.1963i	−1.58932	+	0.337819i	−0.673427	+	0.739253i	$0.735179\pi$
$912$	11.2343	+	2.38792i	0.372005	+	0.0790721i
$913$	−19.4979	−	8.68104i	−0.645287	−	0.287300i
$914$	−23.2111	−	71.4364i	−0.767755	−	2.36291i
$915$	−2.11010	−	6.49422i	−0.0697578	−	0.214692i
$916$	40.1691	+	17.8844i	1.32722	+	0.590919i
$917$	11.2343	+	2.38792i	0.370989	+	0.0788562i
$918$	−0.167824	+	0.0356720i	−0.00553900	+	0.00117735i
$919$	−13.7950	+	6.14193i	−0.455055	+	0.202604i	−0.621447	−	0.783456i	$-0.713455\pi$
$919$	−13.7950	+	6.14193i	−0.455055	+	0.202604i	0.166392	+	0.986060i	$0.446788\pi$
$920$	11.8147	+	13.1216i	0.389520	+	0.432606i
$921$	−0.695831	−	6.62039i	−0.0229284	−	0.218149i
$922$	51.0592	−	37.0967i	1.68155	−	1.22172i
$923$	2.68930	−	25.5870i	0.0885194	−	0.842206i
$924$	−58.4914	−	101.310i	−1.92423	−	3.33286i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	48.7710	+	35.4342i	1.60271	+	1.16444i
$927$	−22.8455	+	25.3726i	−0.750346	+	0.833344i
$928$	−0.574112	+	1.76693i	−0.0188461	+	0.0580025i
$929$	24.4853			0.803336			0.401668	−	0.915785i	$-0.368431\pi$
$929$	24.4853			0.803336			0.401668	+	0.915785i	$0.368431\pi$
$930$		0			0
$931$	−1.85786			−0.0608890
$932$	−17.5428	+	53.9911i	−0.574632	+	1.76854i
$933$	18.2764	−	20.2980i	0.598344	−	0.664528i
$934$	−15.6251	−	11.3523i	−0.511269	−	0.371459i
$935$	−0.449747	+	0.778985i	−0.0147083	+	0.0254755i
$936$	11.4142	+	19.7700i	0.373085	+	0.646203i
$937$	−4.00487	+	38.1038i	−0.130834	+	1.24480i	0.710272	+	0.703927i	$0.248572\pi$
$937$	−4.00487	+	38.1038i	−0.130834	+	1.24480i	−0.841106	+	0.540871i	$0.818095\pi$
$938$	−24.7206	+	17.9606i	−0.807156	+	0.586433i
$939$	0.966119	+	9.19201i	0.0315281	+	0.299970i
$940$	−4.24439	−	4.71388i	−0.138437	−	0.153750i
$941$	−31.9741	+	14.2358i	−1.04233	+	0.464073i	−0.855219	−	0.518266i	$-0.826578\pi$
$941$	−31.9741	+	14.2358i	−1.04233	+	0.464073i	−0.187106	+	0.982340i	$0.559911\pi$
$942$	−84.5378	+	17.9691i	−2.75439	+	0.585464i
$943$	37.1120	+	7.88840i	1.20853	+	0.256882i
$944$	−27.6011	−	12.2888i	−0.898340	−	0.399967i
$945$	0.309017	+	0.951057i	0.0100523	+	0.0309379i
$946$	34.8076	+	107.127i	1.13169	+	3.48299i
$947$	35.5365	+	15.8218i	1.15478	+	0.514141i	0.892587	−	0.450875i	$-0.148888\pi$
$947$	35.5365	+	15.8218i	1.15478	+	0.514141i	0.262192	+	0.965016i	$0.415555\pi$
$948$	−137.804	−	29.2911i	−4.47565	−	0.951330i
$949$	−6.84703	+	1.45538i	−0.222264	+	0.0472437i
$950$	13.9898	−	6.22865i	0.453888	−	0.202084i
$951$	3.50801	+	3.89604i	0.113755	+	0.126338i
$952$	−0.191123	−	1.81841i	−0.00619432	−	0.0589350i
$953$	−16.5729	+	12.0409i	−0.536850	+	0.390045i	−0.822914	−	0.568166i	$-0.807653\pi$
$953$	−16.5729	+	12.0409i	−0.536850	+	0.390045i	0.286064	+	0.958211i	$0.407653\pi$
$954$	0.122463	−	1.16515i	0.00396488	−	0.0377233i
$955$	0.550253	+	0.953065i	0.0178058	+	0.0308405i
$956$	24.4203	−	42.2972i	0.789809	−	1.36799i
$957$	11.9964	+	8.71593i	0.387790	+	0.281746i
$958$	−15.7147	+	17.4530i	−0.507720	+	0.563880i
$959$	−5.58427	+	17.1866i	−0.180325	+	0.554984i
$960$	23.7279			0.765815
$961$		0			0
$962$	−4.41421			−0.142320
$963$	8.37828	−	25.7857i	0.269986	−	0.830933i
$964$	63.1639	−	70.1506i	2.03437	−	2.25940i
$965$	17.1043	+	12.4270i	0.550608	+	0.400040i
$966$	28.1421	−	48.7436i	0.905458	−	1.56830i
$967$	23.2782	+	40.3190i	0.748576	+	1.29657i	0.948505	+	0.316761i	$0.102595\pi$
$967$	23.2782	+	40.3190i	0.748576	+	1.29657i	−0.199930	+	0.979810i	$0.564071\pi$
$968$	7.60649	−	72.3709i	0.244482	−	2.32609i
$969$	−0.531406	+	0.386089i	−0.0170712	+	0.0124030i
$970$	2.73260	+	25.9989i	0.0877384	+	0.834775i
$971$	39.2770	+	43.6215i	1.26046	+	1.39988i	0.879925	+	0.475112i	$0.157592\pi$
$971$	39.2770	+	43.6215i	1.26046	+	1.39988i	0.380532	+	0.924768i	$0.375741\pi$
$972$	75.7436	−	33.7232i	2.42948	−	1.08167i
$973$		0			0
$974$	−41.0534	−	8.72617i	−1.31544	−	0.279605i
$975$	16.1303	+	7.18169i	0.516584	+	0.229998i
$976$	2.62210	+	8.06998i	0.0839313	+	0.258314i
$977$	5.09423	+	15.6784i	0.162979	+	0.501598i	0.998882	−	0.0472800i	$-0.0150553\pi$
$977$	5.09423	+	15.6784i	0.162979	+	0.501598i	−0.835903	+	0.548878i	$0.815055\pi$
$978$	−69.0622	−	30.7485i	−2.20837	−	0.983228i
$979$	−64.0255	−	13.6090i	−2.04626	−	0.434947i
$980$	4.38727	−	0.932542i	0.140146	−	0.0297890i
$981$	−13.3628	+	5.94951i	−0.426642	+	0.189953i
$982$	−7.13083	−	7.91959i	−0.227554	−	0.252724i
$983$	−5.10523	−	48.5731i	−0.162832	−	1.54924i	−0.705145	−	0.709064i	$-0.749118\pi$
$983$	−5.10523	−	48.5731i	−0.162832	−	1.54924i	0.542313	−	0.840177i	$-0.317549\pi$
$984$	−81.7781	+	59.4153i	−2.60699	+	1.89409i
$985$	−0.364311	+	3.46619i	−0.0116079	+	0.110442i
$986$	0.242641	+	0.420266i	0.00772725	+	0.0133840i
$987$	−4.82843	+	8.36308i	−0.153691	+	0.266200i
$988$	−8.98050	−	6.52471i	−0.285708	−	0.207579i
$989$	−23.8197	+	26.4545i	−0.757422	+	0.841203i
$990$	11.0625	−	34.0469i	0.351589	−	1.08208i
$991$	−19.9411			−0.633451			−0.316725	−	0.948517i	$-0.602583\pi$
$991$	−19.9411			−0.633451			−0.316725	+	0.948517i	$0.602583\pi$
$992$		0			0
$993$	−1.82843			−0.0580234
$994$	25.3432	−	77.9982i	0.803836	−	2.47395i
$995$	10.4289	−	11.5825i	0.330619	−	0.367190i
$996$	30.4412	+	22.1168i	0.964567	+	0.700799i
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	−0.215559	−	0.976491i	$-0.569157\pi$
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	0.953445	−	0.301566i	$-0.0975093\pi$
$998$	48.5416	+	84.0766i	1.53656	+	2.66140i
$999$	−0.0432971	+	0.411944i	−0.00136986	+	0.0130333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.o.448.1		16
31.2	even	5		31.2.c.a.25.1	yes	4
31.3	odd	30		961.2.d.i.374.2		8
31.4	even	5	inner	961.2.g.o.844.1		16
31.5	even	3	inner	961.2.g.o.846.1		16
31.6	odd	6		961.2.d.i.628.1		8
31.7	even	15		961.2.d.l.531.1		8
31.8	even	5	inner	961.2.g.o.338.2		16
31.9	even	15	inner	961.2.g.o.235.2		16
31.10	even	15		31.2.c.a.5.1	✓	4
31.11	odd	30		961.2.g.r.547.1		16
31.12	odd	30		961.2.a.c.1.1		2
31.13	odd	30		961.2.g.r.816.2		16
31.14	even	15		961.2.d.l.388.2		8
31.15	odd	10		961.2.g.r.732.2		16
31.16	even	5	inner	961.2.g.o.732.2		16
31.17	odd	30		961.2.d.i.388.2		8
31.18	even	15	inner	961.2.g.o.816.2		16
31.19	even	15		961.2.a.a.1.1		2
31.20	even	15	inner	961.2.g.o.547.1		16
31.21	odd	30		961.2.c.a.439.1		4
31.22	odd	30		961.2.g.r.235.2		16
31.23	odd	10		961.2.g.r.338.2		16
31.24	odd	30		961.2.d.i.531.1		8
31.25	even	3		961.2.d.l.628.1		8
31.26	odd	6		961.2.g.r.846.1		16
31.27	odd	10		961.2.g.r.844.1		16
31.28	even	15		961.2.d.l.374.2		8
31.29	odd	10		961.2.c.a.521.1		4
31.30	odd	2		961.2.g.r.448.1		16
93.2	odd	10		279.2.h.c.118.2		4
93.41	odd	30		279.2.h.c.253.2		4
93.50	odd	30		8649.2.a.l.1.2		2
93.74	even	30		8649.2.a.k.1.2		2
124.95	odd	10		496.2.i.h.273.1		4
124.103	odd	30		496.2.i.h.129.1		4
155.2	odd	20		775.2.o.d.149.1		8
155.33	odd	20		775.2.o.d.149.4		8
155.64	even	10		775.2.e.e.676.2		4
155.72	odd	60		775.2.o.d.749.1		8
155.103	odd	60		775.2.o.d.749.4		8
155.134	even	30		775.2.e.e.501.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	31.10	even	15
31.2.c.a.25.1	yes	4	31.2	even	5
279.2.h.c.118.2		4	93.2	odd	10
279.2.h.c.253.2		4	93.41	odd	30
496.2.i.h.129.1		4	124.103	odd	30
496.2.i.h.273.1		4	124.95	odd	10
775.2.e.e.501.2		4	155.134	even	30
775.2.e.e.676.2		4	155.64	even	10
775.2.o.d.149.1		8	155.2	odd	20
775.2.o.d.149.4		8	155.33	odd	20
775.2.o.d.749.1		8	155.72	odd	60
775.2.o.d.749.4		8	155.103	odd	60
961.2.a.a.1.1		2	31.19	even	15
961.2.a.c.1.1		2	31.12	odd	30
961.2.c.a.439.1		4	31.21	odd	30
961.2.c.a.521.1		4	31.29	odd	10
961.2.d.i.374.2		8	31.3	odd	30
961.2.d.i.388.2		8	31.17	odd	30
961.2.d.i.531.1		8	31.24	odd	30
961.2.d.i.628.1		8	31.6	odd	6
961.2.d.l.374.2		8	31.28	even	15
961.2.d.l.388.2		8	31.14	even	15
961.2.d.l.531.1		8	31.7	even	15
961.2.d.l.628.1		8	31.25	even	3
961.2.g.o.235.2		16	31.9	even	15	inner
961.2.g.o.338.2		16	31.8	even	5	inner
961.2.g.o.448.1		16	1.1	even	1	trivial
961.2.g.o.547.1		16	31.20	even	15	inner
961.2.g.o.732.2		16	31.16	even	5	inner
961.2.g.o.816.2		16	31.18	even	15	inner
961.2.g.o.844.1		16	31.4	even	5	inner
961.2.g.o.846.1		16	31.5	even	3	inner
961.2.g.r.235.2		16	31.22	odd	30
961.2.g.r.338.2		16	31.23	odd	10
961.2.g.r.448.1		16	31.30	odd	2
961.2.g.r.547.1		16	31.11	odd	30
961.2.g.r.732.2		16	31.15	odd	10
961.2.g.r.816.2		16	31.13	odd	30
961.2.g.r.844.1		16	31.27	odd	10
961.2.g.r.846.1		16	31.26	odd	6
8649.2.a.k.1.2		2	93.74	even	30
8649.2.a.l.1.2		2	93.50	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.746033 + 2.29605i) q^{2} +(-1.61542 + 1.79411i) q^{3} +(-3.09726 - 2.25029i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.91421 - 5.04757i) q^{6} +(-0.252354 + 2.40099i) q^{7} +(3.57117 - 2.59461i) q^{8} +(-0.295651 - 2.81293i) q^{9} +(-1.61542 - 1.79411i) q^{10} +(-4.78939 + 2.13237i) q^{11} +(9.04067 - 1.92165i) q^{12} +(-1.78847 - 0.380151i) q^{13} +(-5.32453 - 2.37063i) q^{14} +(-0.746033 - 2.29605i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-0.156740 - 0.0697850i) q^{17} +(6.67921 + 1.41971i) q^{18} +(-1.55113 + 0.329704i) q^{19} +(3.49744 - 1.55716i) q^{20} +(-3.89998 - 4.33137i) q^{21} +(-1.32300 - 12.5875i) q^{22} +(3.23607 - 2.35114i) q^{23} +(-1.11394 + 10.5985i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.20711 - 3.82282i) q^{26} +(-0.335106 - 0.243469i) q^{27} +(6.18453 - 6.86862i) q^{28} +(-0.362036 + 1.11423i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(3.91118 - 12.0374i) q^{33} +(0.277163 - 0.307821i) q^{34} +(-1.95314 - 1.41904i) q^{35} +(-5.41421 + 9.37769i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(0.400180 - 3.80745i) q^{38} +(3.57117 - 2.59461i) q^{39} +(0.461411 + 4.39003i) q^{40} +(6.34689 + 7.04894i) q^{41} +(12.8546 - 5.72322i) q^{42} +(-8.70502 + 1.85031i) q^{43} +(19.6325 + 4.17301i) q^{44} +(2.58390 + 1.15042i) q^{45} +(2.98413 + 9.18421i) q^{46} +(-0.511996 - 1.57576i) q^{47} +(-6.61648 - 2.94585i) q^{48} +(1.14597 + 0.243584i) q^{49} +(-9.44583 + 2.00777i) q^{50} +(0.378403 - 0.168476i) q^{51} +(4.68391 + 5.20201i) q^{52} +(-0.0179342 - 0.170633i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.548005 - 5.21392i) q^{55} +(5.32843 + 9.22911i) q^{56} +(1.91421 - 3.31552i) q^{57} +(-2.28825 - 1.66251i) q^{58} +(-6.73886 + 7.48426i) q^{59} +(-2.85613 + 8.79027i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(-3.03715 + 9.34739i) q^{64} +(1.22346 - 1.35879i) q^{65} +(24.7206 + 17.9606i) q^{66} +(2.62132 - 4.54026i) q^{67} +(0.328427 + 0.568852i) q^{68} +(-1.00942 + 9.60395i) q^{69} +(4.71530 - 3.42586i) q^{70} +(1.47083 + 13.9940i) q^{71} +(-8.35428 - 9.27837i) q^{72} +(3.49744 - 1.55716i) q^{73} +(2.36146 - 0.501943i) q^{74} +(-9.44583 - 2.00777i) q^{75} +(5.54620 + 2.46933i) q^{76} +(-3.91118 - 12.0374i) q^{77} +(3.29315 + 10.1353i) q^{78} +(-13.9248 - 6.19974i) q^{79} +(-2.93444 - 0.623735i) q^{80} +(9.27801 - 1.97210i) q^{81} +(-20.9197 + 9.31406i) q^{82} +(2.72408 + 3.02539i) q^{83} +(2.33242 + 22.1915i) q^{84} +(0.138805 - 0.100848i) q^{85} +(2.24582 - 21.3676i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-11.5711 + 20.0417i) q^{88} +(10.1008 + 7.33866i) q^{89} +(-4.56911 + 5.07451i) q^{90} +(1.36407 - 4.19817i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(0.490035 - 1.50817i) q^{95} +(-2.56172 + 2.84508i) q^{96} +(-8.76038 - 6.36479i) q^{97} +(-1.41421 + 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more